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Thermodynamic studies on alternate binary working fluid combinations and configurations for a combined power and cooling...

University of Florida Institutional Repository

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THERMODYNAMIC STUDIES ON A LTERNATE BINARY WORKING FLUID COMBINATIONS AND CONFIGURATIO NS FOR A COMBINED POWER AND COOLING CYCLE By SANJAY VIJAYARAGHAVAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2003

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ACKNOWLEDGMENTS The work presented in this dissertation was completed with the encouragement and support of many wonderful people. Working with Dr. Yogi Goswami has been a tremendous experience. He expects his students to be self-starters, who work independently on their projects. I appreciate his patience and mentorship in areas within and beyond the realm of research and graduate school. Dr. Sherif Sherif was a terrific source of discussion, advice, encouragement and hard to find AES proceedings. Dr. James Klausner, Dr. David Hahn, and Dr. Ulrich Kurzweg agreed to be on my committee and took the time to read and critique my work, for which I am grateful. Dr. Hahn was also on my masters committee and supervised me during my assignment as a TA for two terms. Dr. Bill Lear has to be thanked for advice on jet pumps and Dr. Skip Ingley for his interest in the cycle. Dr. Leon Lasdon from the University of Texas sent me the FORTRAN version of the GRG code and answered my questions very promptly. Although my particular project did not require much of his marvelous skills, the senior engineering technician at the Solar Park, Chuck Garretson, was very supportive. Watching him and working with him have taught me many things. He is a wonderful resource for any student at the lab. Barbara Graham over the years and now recently Vitrell McNair at the solar office have cheerfully helped me in many ways in the course of my stay here. Mrs. Becky Hoover will have to be thanked for her help and constant reminders to finish up. ii

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My fellow students at the solar lab have been stimulating company. Some of them particularly have to be acknowledged. Gunnar Tamm, Chris Martin and Nitin Goel took interest in my work and provided constructive feedback. Gunnar has also been at the lab almost as long as I have, and he has been fun to work with. Former students such as Viktoria and Andrew Martin, and Adrienne Cooper have stayed in touch and encouraged me. I would like to particularly thank my family for putting up with my being so far away from home, and for their love, support and eternal optimism. This section is not complete without mentioning friends, old and new, too many to name individually, who have been great pals and confidants over the years. iii

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS...................................................................................................ii LIST OF TABLES...........................................................................................................viii LIST OF FIGURES............................................................................................................ix NOMENCLATURE.........................................................................................................xiii ABSTRACT.....................................................................................................................xvi CHAPTER 1 BACKGROUND.........................................................................................................1 Introduction..................................................................................................................1 Background..................................................................................................................2 Rankine Cycle.......................................................................................................3 Power Cycles for Low Temperature Heat Sources...............................................5 Organic Rankine cycles (ORC).....................................................................5 Supercritical cycles........................................................................................6 Maloney and Robertson cycle.......................................................................8 Kalina cycle...................................................................................................9 Other ammonia based cycles.......................................................................13 Use of Mixtures as Working Fluids in Thermodynamic Cycles........................14 The Combined Power and Cooling Cycle..........................................................16 Introduction.................................................................................................16 A summary of past research on the cycle....................................................18 Specific motivation for work in this dissertation.........................................21 2 EFFICIENCY DEFINITIONS FOR THE COMBINED CYCLE.............................24 Conventional Efficiency Definitions.........................................................................24 First Law Efficiency...........................................................................................25 Exergy Efficiency...............................................................................................25 Second Law Efficiency.......................................................................................26 The Choice of Efficiency Definition..................................................................28 Efficiency Expressions for the Combined Cycle.......................................................28 First Law Efficiency...........................................................................................28 Exergy Efficiency...............................................................................................30 iv

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Second Law Efficiency.......................................................................................30 Lorenz cycle................................................................................................30 Cascaded cycle analogy...............................................................................32 Validity of Expressions.......................................................................................35 Case 1: Comparing this Cycle to Other Combined Cooling and Power Generation Options................................................................................36 Case 2: Comparing a Combined Cycle to a Power Cycle...........................36 Some Examples of Application to the Combined Cycle............................................37 Conclusions................................................................................................................41 3 CYCLE SIMULATION AND OPTIMIZATION.....................................................42 Optimization Method Background.............................................................................42 Search Termination.............................................................................................46 Sensitivity Analysis............................................................................................46 Application Notes...............................................................................................47 Cycle Modeling..........................................................................................................48 State Point Calculation........................................................................................49 State point 1.................................................................................................49 Point 2..........................................................................................................51 Points 5 and 11............................................................................................52 Points 6 and 7..............................................................................................53 Point 8..........................................................................................................53 Point 9..........................................................................................................54 Point 10........................................................................................................54 Points 12 and 3............................................................................................55 Point 13........................................................................................................56 Point 14........................................................................................................56 Point 15........................................................................................................57 Point 4..........................................................................................................57 Variable Limits...................................................................................................57 Constraint Equations...........................................................................................59 Model Limitations...............................................................................................61 4 OPTIMIZATION OF BASIC CYCLE CONFIGURATION USING AMMONIA-WATER MIXTURE AS THE WORKING FLUID..................................................62 Simulated Conditions.................................................................................................63 Optimization results...................................................................................................65 Resource Utilization Efficiency..........................................................................65 Exergy Efficiency...............................................................................................67 First Law Efficiency...........................................................................................69 Exergy Analysis.........................................................................................................70 Optimization Considering Losses..............................................................................74 Discussion..................................................................................................................79 Conclusions................................................................................................................84 v

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5 RESULTS AND DISCUSSION: ORGANIC WORKING FLUIDS........................86 Working Fluid Selection............................................................................................86 Preliminary Simulation..............................................................................................89 Simulation of Higher Boiling Components...............................................................94 Discussion..................................................................................................................99 Factors Affecting Cycle Performance......................................................................100 Rectification......................................................................................................100 Boiler Conditions..............................................................................................101 Basic Solution Concentration...........................................................................104 Pressure and Temperature Ratio.......................................................................104 Volatility Ratio.................................................................................................108 Liquid Formation During Expansion................................................................109 Conclusions..............................................................................................................113 6 RESULTS AND DISCUSSION: IMPROVED CONFIGURATIONS...................115 Motivation................................................................................................................115 Reflux Mixed with Boiler Inlet................................................................................115 Addition of a Preheater............................................................................................118 Jet Pump Assisted Cycle..........................................................................................120 Jet Pump Background.......................................................................................122 Jet Pump Analysis.............................................................................................123 Primary nozzle...........................................................................................126 Secondary nozzle.......................................................................................128 Mixing section...........................................................................................128 Diffuser......................................................................................................130 Simplified Model Used in Simulation..............................................................131 Results...............................................................................................................132 Conclusions.......................................................................................................135 Distillation (Thermal Compression) Methods.........................................................135 Using Heat Source............................................................................................136 Using Absorber Heat Recovery........................................................................142 Conclusions..............................................................................................................149 7 CONCLUSIONS......................................................................................................150 Summary of Results.................................................................................................150 Future Work.............................................................................................................153 APPENDIX A WORKING FLUID PROPERTY CALCULATION...............................................157 Property Prediction Methods...................................................................................157 Methods Used for Properties in this Study..............................................................159 Ammonia Water Properties Prediction.............................................................159 vi

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Organic Fluid Mixture Properties.....................................................................160 B OPTIMIZED STATE POINTS................................................................................164 Conditions................................................................................................................164 Basic Cycle Configuration................................................................................165 Fluid: AmmoniaWater.............................................................................165 Fluid: Propane-n-Undecane.......................................................................168 Fluid: Isobutane-n-Undecane.....................................................................169 Configuration with Preheater............................................................................170 Configuration with Jet Pump............................................................................170 Configuration with Kalina Thermal Compression............................................171 Using heat source for distillation...............................................................171 Using absorber heat recovery for distillation............................................173 C SIMULATION SOURCE CODE............................................................................176 Basic Cycle Configuration.......................................................................................176 Header file.........................................................................................................176 Cycle Simulation...............................................................................................177 Interface to Supertrapp.............................................................................................186 LIST OF REFERENCES................................................................................................202 BIOGRAPHICAL SKETCH...........................................................................................208 vii

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LIST OF TABLES Table page 1.1 Efficiency definitions used in various papers published on the cycle.....................22 2.1 Some examples of efficiencies applied to the Rankine cycle and the vapor compression refrigeration cycle...............................................................................26 2.2 Cycle parameters that yield optimum exergy and second law efficiencies.............38 2.3 Efficiency and cycle parameters optimized for effective exergy efficiency...........39 2.4 Efficiency and cycle parameters optimized for effective first law efficiency.........40 3.1 Independent cycle parameters and their limits........................................................58 3.2 Constraints used in the optimization.......................................................................60 5.1 List of working fluids Considered Initially ............................................................. 88 5.2 Higher boiling components considered...................................................................95 5.3 Calculated R/cp values for certain gases in the temperature range of the cycle being studied..........................................................................................................106 5.4 Volatility ratio of selected pairs.............................................................................109 5.5 I values of certain pure components at 300 K and corresponding saturation pressure..................................................................................................................110 viii

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LIST OF FIGURES Figure page 1.1 A schematic diagram of a simple Rankine cycle.......................................................4 1.2 Diagram showing a supercritical Rankine cycle on the T-s diagram for isobutane..7 1.3 Arrangement of a simple Kalina cycle .....................................................................9 1.4 Schematic diagram of Kalina System 12.................................................................12 1.5 Illustration of the difference in temperature profiles for a pure fluid being boiled and a multi-component mixture being boiled..........................................................15 1.6 The basic configuration of the combined power and cooling cycle........................17 1.7 Effect of turbine inlet pressure on the thermal efficiency (%) of the cycle ........... 20 1.8 Effect of turbine inlet pressure on the cooling capacity (kJ/kg) of the cycle ......... 20 2.1 A cyclic heat engine working between a hot and cold reservoir.............................27 2.2 The T-S diagram for a Lorenz cycle........................................................................31 2.3 Thermodynamic representation of (a) combined power/cooling cycle and (b) cascaded cycle.........................................................................................................33 3.1 The basic cycle configuration with the variables shown.........................................50 4.1 Block diagram showing the basic scheme of the combined power and cooling cycle. Same as Fig. 1.6...........................................................................................64 4.2 Optimized resource utilization efficiencies for the basic cycle configuration........66 4.3 Optimized exergy efficiencies for the basic cycle configuration............................68 4.4 Optimized First Law Efficiencies for the Cycle Configuration in Fig. 4.1.............70 4.5 Exergy destruction in the cycle represented as a percentage of exergy of the heat source, for optimized RUE corresponding to 280 K turbine exit temperature........71 ix

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4.6 Exergy destruction in the cycle represented as a percentage of exergy of the heat source, for optimized RUE corresponding to pure work output..............................71 4.7 Exergy destruction in the cycle for optimized exergy efficiency corresponding to 280 K turbine exit temperature................................................................................73 4.8 Exergy destruction in the cycle for optimized exergy efficiency corresponding to pure work output......................................................................................................73 4.9 Optimized RUE for the basic cycle configuration using a non isentropic turbine and pump.................................................................................................................75 4.10 Effect of recovery heat exchanger effectiveness on RUE at optimum RUE conditions, with cooling output...............................................................................75 4.11 Optimized exergy efficiencies for the basic cycle configuration using a non isentropic turbine and pump....................................................................................77 4.12 Effect of recovery heat exchanger effectiveness on effective efficiency................77 4.13 Exergy destruction in the optimized RUE case.......................................................78 4.14 Exergy destruction in the optimized exergy efficiency case...................................78 4.15 Working fluid temperatures and vapor fractions in boiler: at maximum RUE and with cooling.............................................................................................................80 4.16 Working fluid temperatures and vapor fractions in boiler: at maximum RUE with pure work output......................................................................................................80 4.17 Cycle pressure ratios and the influence of solution heat exchanger effectiveness..82 4.18 Cooling to work output ratios at optimum conditions.............................................82 4.19 First law efficiency at optimized exergy efficiency conditions...............................83 4.20 First law efficiency at optimum RUE conditions....................................................84 5.1 Basic configuration simulated. In this configuration, the condensate from the rectifier is redirected to the absorber.......................................................................90 5.2 Optimized second law efficiencies of the combined power and cooling cycle using organic working fluid pairs......................................................................................92 5.3 Alternate configuration, where the condensate from the rectifier is mixed with the strong solution inlet stream to the boiler.................................................................93 5.4 Comparison of the second law efficiency performance of the two configurations in Fig. 5.1 and 5.3, using a propane-hexane mixture as the working fluid..................94 x

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5.5 Optimized exergy efficiency using higher boiling non volatile mixtures...............95 5.6 Optimized resource utilization efficiency using higher boiling non volatile mixtures...................................................................................................................96 5.7 Pressure ratios at optimum exergy efficiency..........................................................98 5.8 Pressure ratios at optimum RUE.............................................................................98 5.9 Maximum (limiting) pressure ratio using some working fluid mixtures at various basic solution concentrations in the absorber and using a 360 K heat source.......100 5.10 Phase diagram of a part of the cycle using isobutane-n-decane at 400 K, optimized for exergy efficiency.............................................................................102 5.11 Close up of a portion of Fig. 5.10..........................................................................102 5.12 Effect of low pressure (propane-hexane mixture as working fluid)......................105 5.13 Calculated isentropic temperature ratio as a function of pressure ratio using perfect gas assumptions.........................................................................................107 5.14 T-s diagram for concentrated propane-n-undecane mixtures................................111 5.15 T-s diagram for concentrated isobutane-n-undecane mixtures..............................112 5.16 T-s diagram for concentrated propane-n-hexane mixtures....................................112 5.17 T-s diagram for concentrated ammonia-water mixtures........................................113 6.1 Modification of the basic cycle configuration which has the liquid condensate from the rectifier mixed with the strong solution at the boiler inlet......................116 6.2 Optimum exergy efficiencies obtained with the modified configuration shown in Fig. 6.1...............................................................................................................117 6.3 Major exergy destruction categories for the modified cycle, at optimum exergy efficiency conditions..............................................................................................118 6.4 Modified cycle configuration with part of the basic solution being preheated by the heat source fluid...............................................................................................119 6.5 Optimized RUE for the modified configuration in Fig. 6.4 compared to the base configuration in Fig. 4.1........................................................................................121 6.6 Major exergy losses in different parts of the modified cycle, optimized for RUE121 6.7 Schematic drawing of a jet pump showing the different sections and the flow through it................................................................................................................124 xi

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6.8 Cycle configuration incorporating the jet pump....................................................132 6.9 Improvement in resource utilization efficiency with the addition of a jet pump...134 6.10 Influence of the choice of turbine exit temperatures on the improvement achievable with a jet pump using an isentropic turbine and pump........................134 6.11 Cycle configuration using the heat source to produce vapor in the distiller.........137 6.12 Maximum RUE of the cycle configuration modified with heat source fluid powered thermal compression modification..........................................................139 6.13 First law efficiency at maximum RUE conditions for configuration with heat source powered thermal compression modification..............................................139 6.14 Exergy destruction in the cycle with heat source powered thermal compression modification, when operated to provide power and cooling.................................140 6.15 Exergy destruction in the cycle with heat source powered thermal compression modification, when operated to provide only power output..................................140 6.16 Some parameters for optimized RUE conditions in the cooling domain..............141 6.17 Some parameters for optimized RUE in the work domain....................................142 6.18 Cycle configuration using heat of condensation to produce vapor in the distiller144 6.19 Maximum RUE of the cycle configuration modified with a condensing mixture providing heat of distillation..................................................................................145 6.20 First law efficiency at maximum RUE conditions for configuration using heat of condensation to produce vapor in the distiller..................................................145 6.21 Exergy destruction in cooling domain in modified cycle with a condensing mixture providing heat of distillation....................................................................146 6.22 Exergy destruction in work domain with a condensing mixture providing heat of distillation..........................................................................................................147 6.23 Some parameters for optimized RUE (strict definition) in the cooling domain for the modified cycle with a condensing mixture providing heat of distillation.......148 6.24 Some parameters for optimized RUE in the work domain for the modified cycle with a condensing mixture providing heat of distillation......................................148 xii

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NOMENCLATURE COP Coefficient of Performance pc Specific heat E Exergy f refrigeration weight factor h specific enthalpy i Exergy Index lmf Liquid mass fraction m mass NTU Number of Transfer Units Obj Objective function p Pressure Q Heat Interaction T Temperature S Entropy s specific entropy R Universal gas constant r Ratio of cooling to work output v Specific volume vmf Vapor mass fraction xiii

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W Work Interaction x Mass fraction of ammonia (volatile component) in a binary mixture y Mole fraction of volatile component in a binary mixture Greek Symbols 21 Volatility of component 2 w.r.t component 1 Efficiency Subscripts 0 Reference state b Boiling basic Referring to basic solution stream, from absorber Carnot Carnot Cycle c Cooling cf Chilled Fluid crit Critical eff Effective exergy Exergy exit At Exit of a Device fg Liquid to gas (representing phase change from liquid to gas) H E Heat engine h Heat Source high High xiv

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hr Heat rejection Fluid hs Heat Source Fluid in Input Lorenz Lorenz Cycle low Low m Melting max maximum net Net out Output p Pump R Resource Utilization Efficiency r Reduced rev Reversible ref Refrigeration sys System useful Useful I First Law II Second Law xv

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xvi Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THERMODYNAMIC STUDIES ON A LTERNATE BINARY WORKING FLUID COMBINATIONS AND CONFIGURATIO NS FOR A COMBINED POWER AND COOLING CYCLE By Sanjay Vijayaraghavan August 2003 Chair: D. Y. Goswami Major Department: Mechanic al and Aerospace Engineering A combined power and cooling cycle was i nvestigated. The cycle is a combination of the Rankine cycle and an absorption refriger ation cycle. A binary mixture of ammonia and water is partially boiled to produce a vapor rich in ammoni a. This vapor is further enriched in a rectifie r/condenser and after s uperheating, expanded thr ough a turbine. The vapor exiting the turbine in this cycle is co ld enough to extract refrigeration output. By suitable selection of operational parameters fo r the cycle, the useful output can have a large range of refrigeration to work ratios. This combined cycle is being proposed for applications with lower temperature heat sources, with the primary objective of producing power. Some examples of ener gy sources include solar, geothermal, or industrial waste heat. Evaluating the efficiency of this cycle is made difficult by the fact that there are two different outputs, namely power and refrig eration. An efficiency expression has to suitably weight the cooling component in orde r to be able to compare this cycle with

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xvii other cycles. Several expr essions are proposed for the first law and second law efficiencies for the combined cycle based on ex isting definitions in th e literature. Some of the developed equations have been r ecommended for use over others, depending on the comparison being made. This study extended the applic ation of the cycle to wo rking fluids other than ammonia-water mixtures, specifi cally to organic fluid mixtur es. It was found that very low temperatures (well below ambient) are not achievable using or ganic fluid mixtures, while with an ammonia-water mixture; temp eratures that were substantially below ambient were obtained under similar conditi ons. Thermodynamic efficiencies obtained with hydrocarbon mixtures are lower than thos e seen with an ammonia-water mixture as the working fluid. Based on the exergy analysis, the cycle conf iguration has been modified to improve its second law efficiency. A significant improvement in the resource utilization efficiency of more than 25% was achieved with the best among the improved schemes. Increased efficiencies can also be obtain ed for the cases where only work output is desired.

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CHAPTER 1 BACKGROUND Introduction The goal of this study is to investigate the use of organic fluid binary mixtures as possible alternate working fluids for a new thermodynamic power cycle (henceforth referred to as the cycle) proposed by Goswami [1]. The power cycle under study is unique in that the working fluid exiting the turbine could be cold enough to extract refrigeration. This cycle is a combination of the Rankine and absorption refrigeration cycles. The performance of the cycle has been studied extensively and optimized in earlier studies [2-8]. A mixture of ammonia and water has been considered so far for the working fluid. An experimental setup was built and a preliminary verification of ammonia boiling and condensation behavior performed [8]. The cycle has been found to be more suited to low temperature heat sources, based on earlier simulation results. The use of a volatile component such as ammonia allows vapor to be formed at high enough pressures that are useful for power generation. It is, therefore, anticipated that this cycle will be used in low temperature applications such as those involving solar, geothermal, and waste heat sources. Traditionally, the trend in thermal energy conversion in general, is to use higher temperatures in thermal energy conversion plants. Heat associated with high temperatures has a larger availability, and therefore systems operating at higher temperatures normally achieve greater first law efficiencies of conversion. Some of the 1

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2 best efficiencies (around 58% first law efficiency) achieved today are with combined cycle power plants. Attempts are being made to break the 60% efficiency barrier in some combined cycle plants being designed currently [9]. In combined cycle plants being built today, a gas turbine power cycle is the first stage, and the exhaust from the turbine is used to run a steam power plant. In the case of solar power generation, to operate at high temperatures, considerable concentration of the solar radiation is required. Solar energy being a dilute resource, the collection system is a large part of the cost of a solar power plant. The optics required for achieving high concentration increases the cost of the collection system. Some of the biggest disadvantages of solar energy as an energy source for electricity generation are a) the dilute nature of the resource, b) the intermittent nature of the energy and c) the high cost of producing power. It is hoped that by using cheaper, low concentration collection systems and a cycle that utilizes a large percentage of the exergy in that temperature range, the cost of solar power production can be brought down. The combined power and cooling cycle is being developed to efficiently utilize the exergy of low temperature heat sources. Since the cycle can operate at low temperatures, it could be applied to other low temperature heat sources such as geothermal and waste heat. Background Thermal power cycles can be classified on the basis of the working fluid used, as vapor power cycles and gas power cycles. In a vapor power cycle, the gas that spins the turbine is obtained from vaporizing a liquid. An example of such a cycle is the classic Rankine cycle. In a gas power cycle, such as the Brayton cycle, the working fluid is in a gaseous state throughout the cycle.

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3 Rankine Cycle The most commonly used vapor power cycle is the Rankine cycle. Even though a description of the Rankine cycle can be found in any engineering thermodynamics textbook [10], it is briefly covered here. The simple Rankine cycle, shown in Fig. 1.1 consists of four steps. The working fluid is pumped to a high pressure and circulated through the boiler. The fluid is boiled at a constant pressure in the boiler after which the high-pressure vapor produced is expanded through a turbine, thus extracting work from it. The vapor exiting the turbine is condensed in a condenser by rejecting heat to a cooling fluid. There are several modifications to the Rankine cycle that are used to achieve better efficiencies. These include superheating, reheating and regeneration. Water (Steam) is the working fluid of choice for most vapor power cycles. Water works over a broad range of temperatures and pressures, has a large heat capacity, and is stable, safe and very environmentally friendly. The energy sources used to generate steam include gas, coal, oil, and nuclear sources. A small percentage of steam power plants use geothermal and solar energy sources. The first commercially successful steam engine was the one patented by Thomas Savery in 1698. The better-known Newcomens engine eventually displaced this engine in the early 18th century [11]. The steam power plant has come a long way in the 100 odd years since central steam generating plants started being built. The first central station steam turbine in the United States operated (in 1900) with steam conditions of 1MPa and 483 K. In contrast, a typical central steam power station today operates at high pressure turbine inlet pressures and temperatures of 16.4 MPa and 800 K respectively [11].

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4 Fig. 1.1 A schematic diagram of a simple Rankine cycle While steam is the working fluid of choice today, there are certain situations in which it does not work efficiently, particularly with low temperature resources. For example, consider the case of a binary1 geothermal power plant. In such a plant, a fluid such as isobutane is boiled using a relatively low temperature geothermal fluid, and used to spin a turbine working on a Rankine cycle. If steam were to be used in such applications (or if the plant is designed as a flash type plant), very low pressures and large vacuums at turbine exit would result. 1 It needs to be pointed out that in a binary geothermal power plant, a high pressure fluid is heated by a hot geofluid, boiled and expanded through a turbine. This is not the same as a plant using a binary fluid mixture for a working fluid.

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5 Power Cycles for Low Temperature Heat Sources The cycle being studied here appears to work well with low temperature heat sources, based on past studies. Low temperature heat sources are usually those deriving their energy from geothermal, solar or some waste heat sources. Solar energy can be used at various temperatures, depending on the collection method used. Low temperature heat sources have low availability and are not usually the energy sources of choice. Such sources would be considered useful only if some economic advantage is found in their utilization. For instance, a geothermal power plant could prove to be economically feasible to supply an area in the vicinity of a geothermal steam field. Several power cycles that are suitable for use with low temperature heat sources have been proposed in the literature and have been used in practice. The Rankine cycle has been adapted for use with low temperature heat sources by using low boiling working fluids such as organic fluids. Organic Rankine cycles (ORC) have been extensively used in binary geothermal power plants and low temperature solar power conversion. Several ammonia-water mixture based cycles have also been proposed for low temperature applications. Organic Rankine cycles (ORC) Since the first Rankine cycle-based thermal power plant was built, there have been several improvements in the configuration, components, and materials used, but the working fluid of choice has almost always been water. While water has several properties that make it a very good choice as a working fluid, in low temperature applications, better choices are available. Organic working fluids are a popular choice for such applications. Despite the fact that these fluids have lower heats of vaporization than water, which requires larger flow rates, smaller turbine sizes are obtained due to the

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6 higher density at the turbine exit conditions. A variety of fluids, both pure components and binary and ternary mixtures, have been considered for use in ORCs. These include saturated hydrocarbons such as propane, isobutane, pentane, hexane and heptane; aromatics such as benzene and toluene; refrigerants such as R11, R113, R114; and some other synthetic compounds such as Dowtherm A. Organic Rankine cycles have been proposed and used in a variety of applications Binary geothermal power plants: A flash type geothermal power plant is unsuitable for low temperature, liquid dominated, geothermal resources (nominally below 180 C). Instead, the geofluid is used to boil an organic working fluid that is subsequently expanded in a turbine. Isobutane is an example of a common working fluid in such applications. Solar thermal power: ORC plants can also be applied to the conversion of low and medium temperature (say up to 300 C) solar heat. The Coolidge plant [12] that was a 200 kW plant built near the town of Coolidge, AZ, is a good example. For higher temperature heat sources, toluene seems to be a common choice of working fluid. Bottoming cycle applications: ORCs have been proposed for the bottoming cycle in some applications Mixtures of organic fluids have also been studied for use in ORCs. The advantages of the use of mixtures will be discussed later in this chapter. Binary mixtures have been found to have a better performance compared to pure fluid ORCs [13-16]. Organic fluid turbines have been found to be very reliable and to have a relatively high efficiency even at small sizes. Due to their reliability, some people have even suggested their use in space applications, with the ORC as the bottoming stage of a Brayton or Rankine cycle power plant. Supercritical cycles The use of mixtures is one way to obtain good thermal matching with sensible heat sources. Other methods that have been proposed include multi-pressure boiling and supercritical operation. Multi pressure boiling has not been very popular in the industry

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7 because of the costs involved. The other option is to use supercritical cycles. The cycle high pressure and temperature exceed that at the working fluid critical point in a supercritical cycle. The boiling process does not pass through a distinct two-phase region, and a better thermal match is obtained in the boiler. Figure 1.2 shows the boiling process in a supercritical cycle on a T-s diagram. Notice the better thermal match in a boiling heat exchanger. Supercritical cycles have to operate at a higher pressure, since the boiler pressure has to exceed the critical pressure of the working fluid. This is a disadvantage. Equipment costs go up at higher pressures, although there is an improvement in performance. Fig. 1.2 Diagram showing a supercritical Rankine cycle on the T-s diagram for isobutane

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8 Supercritical cycles have been studied in the United States for geothermal applications as a part of the DOE Heat Cycle Research Program [17] and have been found to improve geofluid effectiveness (power output per unit mass of geothermal fluid consumed, usually expressed as kWh/lb). Boretz [18] studied the use of supercritical operation in space applications. He suggested the use of a supercritical cycle in order to avoid the two-phase boiling encountered at subcritical conditions. Several power cycles utilizing ammonia-water mixtures as the working fluid have been proposed in the literature. A common characteristic of most of these cycles is that all or part of the heat rejection occurs in an absorber condenser. These range from the simple Maloney and Robertson cycle to the relatively sophisticated Kalina cycle. Some of these cycles are discussed below. Maloney and Robertson cycle Although ammonia based cycles have been proposed earlier in the literature, in this chapter the oldest cycle considered is one by Maloney and Robertson [19]. Maloney and Robertson studied the ammonia-water binary mixture as a candidate for a simple absorption based power cycle. They studied the cycle within the range of properties available to them at that time and concluded that in all cases a steam Rankine cycle was more efficient. The range of temperatures, pressures, and compositions for which property data were available at the time of the study was limited. This is a serious shortcoming of Maloney and Robertsons results. Further, the cycle did not have a super heater included in the loop, which could have changed somewhat the efficiencies obtained.

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9 Kalina cycle Another ammonia-water mixture based cycle of more recent origin that shows considerable promise is the Kalina cycle [20,21]. The first Kalina cycle was first developed in the late 1970s and early 1980s. This cycle, developed by Alexander Kalina, is essentially a Rankine cycle that utilizes a binary mixture of ammonia and water as the working fluid. This results in better thermal matching in the boiler, as will be discussed later. Another feature of the Kalina cycle is the extensive internal heat recovery and exchange arrangement that minimizes irreversibilities in the heat transfer processes in the cycle. Many of the Kalina cycle configurations proposed also have an arrangement that uses the heat in the vapor leaving the turbine in a distiller to concentrate the liquid stream that is boiled and expanded in the turbine. Fig. 1.3 Arrangement of a simple Kalina cycle [20]

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10 The basic version of the Kalina cycle is shown in Fig. 1.3. The composition of the working fluid passing through the boiler (or the working solution) is different from the basic solution in the absorber. This is accomplished through the distillation method that has also been called a thermal compression arrangement in some papers. The hot vapor leaving the turbine is used to distil a fraction of the pressurized basic solution (state 2) to produce vapor (state 6) rich in ammonia. The remaining liquid is combined with the cooled turbine exhaust vapor in an absorber (state 13). The turbine exhaust is normally at too high a concentration to be fully condensed at the corresponding pressure. Combining with the weak liquid enables condensation. The vapor from the distiller is combined with the rest of the basic solution and condensed (state 8) to form the working fluid. The working fluid is vaporized, and superheated (state 10) in the boiler and expanded in the turbine. The advantages of a Kalina cycle plant are the following The use of a mixture results in a better thermal match in the boiler due to variable temperature boiling Better internal heat recovery is also possible due to use of mixtures The distillation arrangement along with absorption condensation allows a lower turbine exit pressure despite using a high concentration vapor. Higher work output is therefore obtained Several studies have shown that the Kalina cycle performs substantially better than a steam Rankine cycle system [20-22]. El-Sayed and Tribus [23] showed that the Kalina cycle has 10-20% higher second law efficiency than a simple Rankine cycle operating between the same thermal boundary conditions. A second law analysis of various Kalina systems shows that using a binary fluid and the resulting reduced irreversibility generation in the boiler is one source of the improved efficiency of the cycle [24-25].

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11 Marston [26] verified some of the results of El-Sayed, Tribus, and Kalina and through a parametric analysis concluded that composition at turbine inlet and temperature at the separator of a simple Kalina cycle are the key parameters in optimizing cycle performance. Several Kalina cycle variations have been proposed, each optimized for different applications. A common feature of each of these systems as the developers of this cycle prefer to call the versions, is the improved and sometimes counterintuitive application of internal heat recovery in the cycle to minimize exergy losses. For instance, in a bottoming cycle for utility applications, (Kalina System 6) [22], the vapor is actually cooled between the IP and LP turbines and used to evaporate part of the working fluid stream. The Kalina Cycle System 12 [27] is a variation of the Kalina cycle that was proposed for geothermal applications. This version does not have the trademark distillation arrangement. Instead, a more complicated network of recovery heat exchangers is used to improve efficiency. Figure 1. 4 shows the Kalina 12 system. Bliem [28] studied the application of the Kalina cycle to hydrothermal (liquid dominated geothermal) energy conversion. The supercritical, recuperated Rankine cycle technology studied as part of the heat cycle research program proved to have a slightly higher second law efficiency compared to the Kalina System 12. The Heber binary geothermal plant summer design conditions were used as a reference. Both these technologies were superior to the supercritical isobutane based Rankine cycle being used at Heber.

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12 Fig. 1.4 Schematic diagram of Kalina System 12 The Kalina type distillation-condensation subsystem was also evaluated in supercritical organic cycles, but the improvement was found to be minimal. Bliem and Mines [29] also showed that the Kalina System 12 and the supercritical cycle approach a realistic upper limit of conversion, for the relatively high temperature resources (460 K and 500 K) studied. Ibrahim and Klein [30] compared the thermodynamic performance of the Maloney and Robertson cycle and the Kalina cycle based on a second law analysis. The second law efficiency was defined as the ratio of the first law efficiency of the cycle to that of a maximum power cycle operating between the same thermodynamic conditions. The

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13 maximum power cycle used is essentially the Lorenz cycle. These concepts are explained in greater detail in chapter 2. Based on the results from that study, the Kalina cycle outperforms the Maloney and Robertson cycle at large heat exchanger sizes (large NTU). The Kalina cycle has been criticized for the fact that obtaining the output predicted by calculations for the cycle requires 100% vaporization of the working fluid in a single pass countercurrent boiler. The heat exchanger surfaces would dry out at high vapor fractions, resulting in lower overall heat transfer coefficients and a larger heat exchange area. The first Kalina geothermal plant (of 2 MWe capacity) [31] built in Husavik, Iceland, does not use the system 12 configuration. Instead, about 70 % of the flow is vaporized and the remaining liquid throttled back through a series of recovery heat exchangers. Over the last twenty years, the Kalina cycle has caught a lot of attention from the engineering community, but that has translated to very few plants actually being built. The first bottoming cycle demonstration of the plant was at the Energy Technology and Engineering Center, a DOE facility near Canoga Park, California [32]. A 3 MW demonstration plant was constructed that started operation in 1992. Tests were conducted till the end of 1996. Other ammonia based cycles Rogdakis and Antonopoulos [33] proposed an ammonia-water absorption power cycle. This cycle is somewhat similar to the Kalina cycle, with the major difference being that the distillation-absorption condensation process is replaced with a simple absorption condensation process. The authors calculated a substantially higher (greater than 20%) first law efficiency as compared to a steam Rankine cycle, while keeping similar superheating and condensation temperatures. The improvement is particularly

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14 good at low heat source temperatures. An application of this cycle for recovering waste heat from gas turbine exhaust is discussed by Kouremenos et al. [34]. Use of Mixtures as Working Fluids in Thermodynamic Cycles In a conventional Rankine cycle in which a pure fluid is used, boiling occurs at the saturation temperature corresponding to its pressure. This results in a mismatch between the temperature profile of the heat source fluid (fuel combustion products, geothermal fluids etc.) and the working fluid in the boiler. Consequently, there is significant exergy destruction during heat transfer in the boiler. One of the methods around this limitation, practiced in industry, is to boil at different pressures, resulting in a moderate increase in efficiency. The other option is to use a mixture in the working fluid. The use of mixtures as working fluids in Rankine cycles is not a new idea. As a mixture vaporizes, the changing composition of the liquid results in boiling occurring over a range of temperatures. This gives what is called a temperature glide between the temperatures at which the mixture starts boiling to those at which the fluid is completely vaporized. Figure 1.5 qualitatively shows an example of the difference in boiling behavior just described. With a multi-component mixture, the fluid boils throughout in the boiler, achieving a good temperature match with the heat source fluid. While the pure fluid boils at one temperature and is then subsequently superheated, the mixture boils at varying temperatures and achieves a better thermal match in the boiler [35]. The condensation of mixtures is also a variable temperature process. This results in a better thermal match with the heat rejection fluid. The advantages of better thermal matching in the condenser are debatable. In a power plant, there is normally very little cost associated with the heat rejection fluid itself. The size of the condenser is the

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15 Fig. 1.5 Illustration of the difference in temperature profiles for a pure fluid being boiled and a multi-component mixture being boiled. limitation. Also, for complete condensation of a fluid, the bubble point at the cycle low pressure has to be a little above the heat rejection fluid temperature. The use of mixtures has another advantage, particularly in geothermal power plants. Any degradation in the quality of the heat resource with time can be countered to a certain extent by changing the composition of the working fluid. Several cycles have been developed in the literature to take advantage of mixtures. Binary mixtures have been recommended as working fluids in binary geothermal power plants. It is found that a geothermal resource is utilized more efficiently by the use of these mixtures.

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16 The Combined Power and Cooling Cycle Introduction A unique feature of the combined power and cooling cycle proposed by Prof. Goswami is the simultaneous production of power and refrigeration (cooling) in the same loop. Other combined power and cooling cycles utilize the waste heat rejected from the power cycle to run a coupled heat fired cooling cycle, such as an absorption refrigeration cycle. The cycle can be viewed as a combination of the Rankine cycle and an absorption refrigeration cycle. A binary mixture of ammonia and water has been used as the working fluid in all studies performed so far. Using that as an example, consider the schematic (basic configuration) of the cycle shown in Fig. 1.6. A mixture of ammonia and water (borrowing from absorption refrigeration literature, this mixture is called the strong solution, or basic solution) is pumped to a high pressure. This stream is preheated and pumped to the boiler, where it is partially boiled. Being the component with a lower boiling point, the vapor generated is rich in ammonia. A rectifier is used to increase the concentration of ammonia in the vapor by condensing some of the water out. The rectified vapor is superheated and expanded to low temperatures in an expander such as a turbine. This is possible since ammonia is a volatile component that does not condense at the temperatures and pressures at the turbine exit. The cold ammonia is used to produce refrigeration. The remaining hot liquid in the boiler, called the weak solution, is used to preheat the working fluid in the recovery or solution heat exchanger. This high pressure liquid is then throttled back to the absorber. The vapor is absorbed into the weak solution and

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17 condensed in the absorber. The absorber takes the place of a regular condenser in the cycle. Fig. 1.6 The basic configuration of the combined power and cooling cycle

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18 A portion of the strong solution stream is used to recover heat from the condensing vapor in the rectifier. The word rectification is used in the absorption cooling literature, by some authors, to refer to a particular configuration that employs a rectification column to purify the ammonia vapor. We use the word rectification to refer to a process used to purify vapor leaving the boiler in all the papers and reports associated with the study of this cycle. Some of the key features of the cycle are listed below. Output consists of both power and cooling Uses a mixture as the working fluid, which makes it suitable for sensible heat sources Absorption condensation is used to condense the vapor Works best using low temperature heat sources A summary of past research on the cycle The combined power and cooling cycle has been the subject of a sustained research effort at the University of Florida for the past eight years. A summary of the work done to date and the status of the development of the cycle is discussed below. The results of a parametric analysis of the cycle using low temperature sensible heat sources are reported in Goswami and Xu [2] and Xu et al.[36]. The analysis established that theoretically, both power and cooling could be obtained from the proposed configuration. Ideal turbine and pump were assumed, heat losses and pressure drops were neglected. The following range of parameters were studied 1. Boiler Temperature : 400 K 2. Condenser Temperature : 350 K 400 K 3. Turbine Inlet Temperature : 410 K 500 K 4. Turbine Inlet Pressure : 18 bar 32 bar 5. Ammonia Concentration : 0.20 0.55 6. Absorber Temperature : 280 K 7. Recovery HX. Exit Temp. : 350 K

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19 The parametric study results indicate the general behavior of the cycle. Figure 1.7 shows the effect of turbine inlet pressure on the thermal efficiency2 of the cycle. For a set absorber pressure (as in a parametric analysis), the pressure ratio increases with a higher pressure, but the vapor generation rate drops until the pressure becomes too large to generate any vapor at all. A similar effect is seen with the cooling capacity. A larger pressure ratio results in a larger temperature drop in the turbine, but the drop in vapor generation rate limits cooling at higher pressures (see Fig. 1.8). The boiler temperature strongly influences the output, as the vapor generated goes up. The heat input also goes up with increased vapor generation; therefore the thermal efficiency reaches a limit after initially increasing. The cooling capacity of the cycle is strongly influenced by the superheater and condenser temperatures. A higher superheater temperature raises the turbine exit temperature, until no refrigeration is produced at all. The parametric study also clearly shows that there is an optimum value of parameters for the best operation of the cycle. Based on these results, Lu and Goswami [3] performed a mathematical optimization of the efficiency of the cycle using an optimization program that uses the Generalized Reduced Gradient (GRG) algorithm. The optimization program has since then been used extensively to maximize the thermodynamic output of the cycle in several studies [5,6]. Lu and Goswami [4] also used the program to determine the lowest temperatures that could be achieved using the cycle. They concluded that temperatures as low as 205 K are achievable, however, the vapor generation drops substantially at very low temperatures since lower absorber pressures and purer ammonia vapor generation is required. Hasan and Goswami [5] 2 See Table 1.1 for the definition of efficiency

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20 14 16 18 20 22 24 1618 20 22 24 26 28 30 32 34 turbine inlet pressure (bar) x=0.47 x=0.5 x=0.53 thermal efficiency (%) Fig. 1.7 Effect of turbine inlet pressure on the thermal efficiency (%) of the cycle [2] 0 5 101520253016 18 20 2224 2628 3032 34 turbine inlet pressure (bar) x=0.47 x=0.5 x=0.53 cooling capacity (kJ/kg) Fig. 1.8 Effect of turbine inlet pressure on the cooling capacity (kJ/kg) of the cycle [2]

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21 performed an exergy analysis of results optimized for second law efficiency and looked at various aspects of the optimized results such as the refrigeration to work output ratio, pressure ratio etc. An experimental system was built to verify the actual performance of the combined power and cooling cycle. The initial system was a simplified version of the cycle without an actual turbine present. A throttling valve and a heat exchanger performed the functions of expanding and cooling the vapor, thus simulating the turbine in the loop. The experimental system also lacked a rectification arrangement that would have been useful to purify the vapor. Operating this limited version of the cycle [8] verified the boiling and absorption processes. The results indicated that both power and cooling can be obtained simultaneously and that efficiencies close to the predicted values should be achievable. Specific motivation for work in this dissertation Efficiency definition. While a significant amount of work has been done on the theoretical analysis of the cycle, there are some shortcomings that need to be addressed. The first question deals with the right efficiency definitions for the cycle. Since the output consists of both power and cooling, the questions that arises is how the two components would be added so as to arrive at a meaningful efficiency definition. Table 1.1 summarizes the efficiency definitions used in different papers written on the cycle. Initial papers simply added the work and cooling output to generate an efficiency, which really is an energy efficiency. Later papers divided the cooling output by a Carnot COP (evaluated at the average of the inlet and exit temperatures of the refrigeration heat

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22 exchanger). Such a definition gives a very small weight to the cooling output. The subject of efficiency definitions is discussed further in chapter 2. Table 1.1 Efficiency Definitions used in Various Papers Published on the Cycle Reference First Law Definition Second Law Definition Goswami and Xu [2] Xu et al. [36] () hcnetQQW+ N.A. Lu and Goswami [3] () hcnetQQW+ () inhscnetEQW,+ Hasan and Goswami [5] Tamm et al. [7] () hcnetQQW+ ()[] inhscarnotcnetECOPQW,+ Cycle simulation. The cycle simulation program written by Lu and Hasan had some shortcomings that were discovered when early simulations were being performed to compare results. These are listed below: A pinch point check was not implemented in the recovery heat exchanger. Sometimes the strong solution starts boiling there resulting in the pinch point condition being violated The fraction of the strong solution stream entering the rectifier was calculated by setting the temperature after the rectifier and using an energy balance. This temperature need not be set; it can actually be optimized. The liquid condensate in the rectifier was assumed to return to the boiler and boil as a separate stream. Yet this was not considered when calculating pinch point in the boiler. The result was that the pinch point was improperly calculated. In addition, the design of such a heat exchanger with three streams is also complicated. Working fluid. All the work performed so far has been based on using an ammonia-water mixture as the working fluid. It is logical to assume that other mixtures could also be used in this new thermodynamic cycle to provide simultaneous power and cooling output. Organic fluids have been used in Rankine cycles designed for low

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23 temperature heat sources. Therefore, these fluids seem like natural choice for use in this cycle. Based on these motivations, the work presented in the subsequent chapters follows an outline as follows. First, there is a discussion of the various efficiency definitions that can be used for this cycle. That is followed by a description of the simulation and optimization methods. The basic cycle configuration is optimized using the proposed efficiency definitions, the results of which are discussed in chapter 4. Chapter 5 contains results of simulations performed using organic fluid mixtures and an analysis of the results. Some modified and improved configurations of the cycle are proposed and discussed in chapter 6. The final chapter suggests some directions for the development of the cycle in the light of this study.

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CHAPTER 2 EFFICIENCY DEFINITIONS FOR THE COMBINED CYCLE The combined power and cooling cycle is a combination of the Rankine cycle and an absorption refrigeration cycle. Evaluating the efficiency of this cycle is made difficult by the fact that there are two different simultaneous outputs, namely power and refrigeration. An efficiency expression has to appropriately weigh the cooling component in order to allow comparison of this cycle with other cycles. This chapter develops several expressions for the first law, second law and exergy efficiencies for the combined cycle based on existing definitions in the literature. Some of the developed equations have been recommended for use over others, depending on the comparison being made. Finally, some of these definitions are applied to the cycle and the performance of the cycle optimized for maximum efficiency. A Generalized Reduced Gradient (GRG) method was used to perform the optimization. This method is described in detail in the following chapter. Conventional Efficiency Definitions Performance of a thermodynamic cycle is conventionally evaluated using an efficiency or a coefficient of performance (COP). These measures of performance are generally of the form measure of performance = useful output / input (2.1) 24

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25 First Law Efficiency The first law measure of efficiency is simply a ratio of useful output energy to input energy. This quantity is normally referred to simply as efficiency, in the case of power cycles, and as a coefficient of performance for refrigeration cycles. Table 2.1 gives two typical first law efficiency definitions. For the case of an absorption refrigeration cycle, the input is in the form of heat and pump work. Therefore, its COP is expressed in terms of refrigeration output, heat input, and pump work as [37] ( ) phcWQQCOP+= (2.2) Exergy Efficiency The first law fails to account for the quality of heat. Therefore, a first law efficiency does not reflect all the losses due to irreversibilities in a cycle. Exergy efficiency measures the fraction of the exergy going into the cycle that comes out as useful output [38]. The remaining exergy is lost due to irreversibilitites in devices. inoutexergyEE= (2.3) Two examples are given in table 2.1. For the absorption refrigeration cycle, the corresponding exergy efficiency expression is given as () inincexergyWEE+= (2.4) Here Ec is the change in exergy of the cooled medium. A resource utilization efficiency [39] is a special case of the exergy efficiency that is more suitable for use in some cases. Consider for instance a binary geothermal power cycle, where the geofluid is reinjected into the ground after transferring heat to the cycle working fluid. In this case, the unextracted availability of the geofluid that is lost on

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26 Table 2.1 Some examples of efficiencies applied to the Rankine cycle and the vapor compression refrigeration cycle Cycle Type Rankine Vapor Compression First Law hnetIQW= (2.5) incWQCOP= (2.8) Exergy innetexergyEW= (2.6) incexergyWE= (2.9) Second Law revII = (2.7) revIICOPCOP= (2.10) reinjection has to be accounted for. Therefore, a modified definition of the form hsoutREE= (2.11) is used, where the Ehs is the exergy of the heat source. Another measure of exergy efficiency found in the literature is what is called the exergy index defined as the ratio of useful exergy to exergy loss in the process [40], usefulinusefulexergyEEEi= (2.12) Second Law Efficiency Second law efficiency is defined as the ratio of the efficiency of the cycle to the efficiency of a reversible cycle operating between the same thermodynamic conditions. revII = (2.13) The reversible cycle efficiency is the first law efficiency or COP depending on the cycle being considered. The second law efficiency of a refrigeration cycle (defined in terms of a COP ratio) is also called the thermal efficiency of refrigeration [37]. For constant temperature heat addition and rejection conditions, the reversible cycle is the Carnot cycle. On the other hand for sensible heat addition and rejection, the Lorenz cycle is the applicable reversible cycle [41].

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27 The exergy efficiency and second law efficiency are often similar or even identical. For example, in a cycle operating between a hot and a cold reservoir (see Fig. 2.1), the exergy efficiency is ( ) hhnetTTQW01 exergy= (2.14) while the second law efficiency is ( ) hchnetTTQW1 II= (2.15) Where T is the ambient or the ground state temperature. For the special case where the cold reservoir temperature T is the same as the ground state temperature T, the exergy efficiency is identical to the second law efficiency. 0 r 0 Fig. 2.1 A cyclic heat engine working between a hot and cold reservoir

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28 The Choice of Efficiency Definition The first law, exergy and second law efficiency definitions can be applied under different situations. The first law efficiency has been the most commonly used measure of efficiency. The first law does not account for the quality of heat input or output. Consider two power plants with identical first law efficiencies. Even if one of these power plants uses a higher temperature heat source (that has a much higher availability), the first law efficiency will not distinguish between the performance of the two plants. Using an exergy or second law efficiency though will show that one of these plants has higher losses than the other. The first law efficiency, though, is still a very useful measure of plant performance. For example, a power plant with a 40% first law efficiency rejects less heat than one of the same capacity with a 30% efficiency; and so would probably have a smaller condensor. An exergy efficiency or second law efficiency is an excellent choice when comparing energy conversion options for the same resource. Ultimately, the choice of conversion method is based on economic considerations. Efficiency Expressions for the Combined Cycle The performance evaluation functions discussed above will be applied to the combined power and cooling cycle. When evaluating the performance of a cycle, there are normally two goals. One is to pick parameters that result in the best cycle performance. The other goal is to compare this cycle with other energy conversion options. For instance, to compare the novel cycle with a power cycle that uses waste heat to run an absorption refrigeration system. First Law Efficiency Following the pattern of first law efficiency definitions given in the previous section, a simple definition for the first law efficiency would be

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29 () hcnetQQW+ I= (2.16) Equation (2.16) overestimates the efficiency of the cycle, by not attributing a quality to the refrigeration output. Using this definition, in some cases, the first law efficiency of the novel cycle approaches Carnot values or even exceeds them. Such a situation appears to violate the fact that the Carnot3 efficiency specifies the upper limit of first law conversion efficiencies. The confusion arises due to the addition of work and refrigeration in the output. Refrigeration output cannot be considered in an efficiency expression without accounting for its quality. To avoid this confusion, it may be better to use the definition of the first law efficiency given as () hcnetIQEW+= (2.17) The term Ec represents the exergy associated with the refrigeration output. In other words, this refers to the exergy transfer in the refrigeration heat exchanger. Depending on the way the cycle is modeled, this could refer to the change in the exergy of the working fluid in the refrigeration heat exchanger. Alternately, to account for irreversibilities of heat transfer in the refrigeration heat exchanger, the exergy change of the chilled fluid would be considered. ( ) [ ] outcfincfooutcfincfcssThhmE,,,,= (2.18) Rosen and Le [42] studied efficiency expressions for processes integrating combined heat and power and district cooling. They recommended the use of an exergy efficiency in which the cooling was weighted using a Carnot COP. However, the Carnot 3 The Carnot cycle is not the reversible cycle corresponding to the combined cycle. This is discussed later in this chapter.

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30 COP is based on the minimum reversible work needed to produce the cooling output. This results in refrigeration output being weighted very poorly in relation to work. Exergy Efficiency Following the definition of exergy efficiency described previously Eq.(2.3), the appropriate equation for exergy efficiency to be used for the combined cycle is given below. Since a sensible heat source provides the heat for this cycle, the denominator is the change in the exergy of the heat source, which is equivalent to the exergy input into the cycle. () ( ) outhsinhscnetexergyEEEW,,+= (2.19) Second Law Efficiency The second law efficiency of the combined cycle needs a suitable reversible cycle to be defined. Once that is accomplished, the definition of a second law efficiency is a simple process. Lorenz cycle The Lorenz cycle is the appropriate reversible cycle for use with variable temperature heat input and rejection. A T-S diagram of the cycle is shown in Fig. 2.2. 12341QQ Lorenz= (2.20) If the heat input and rejection were written in terms of the heat source and heat rejection fluids, the efficiency would be given as: ( ) ( ) 1,,,,outhsinhshsinhrouthrhrLorenzhhmhhm= (2.21) Knowing that processes 4-1 and 2-3 are isentropic, it is easily shown that in terms of specific entropies of the heat source and heat rejection fluids that

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31 ( ) () outhsinhsinhrouthrhrhsssssm,,,, m= (2.22) The efficiency expression for the Lorenz cycle then reduces to ( ) ( ) ()( ) outhsinhsouthsinhsinhrouthrinhrouthrLorenzsshhsshh,,,,,,,,1= (2.23) This can also be written as ( ) () hsshrsTT1 Lorenz= (2.24) Here, the temperatures in the expression above are entropic average temperatures, of the form Fig. 2.2 The T-S diagram for a Lorenz cycle () ( ) 1212sshhs T= (2.25)

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32 For constant specific heat fluids, the entropic average temperature can be reduced to () ( ) 1212lnTTTTs T= (2.26) The Lorenz efficiency can therefore be written in terms of temperatures as ( ) ( ) () ( ) outhsinhsouthsinhsinhrouthrinhrouthrLorenzTTTTTTTT,,,,,,,,lnln1= (2.27) It is easily seen that if the heat transfer processes were isothermal, like in the Carnot cycle, the entropic average temperatures would reduce to the temperature of the heat reservoir, yielding the Carnot efficiency. Similarly the COP of a Lorenz refrigerator can be shown to be () () () cfshrscfsLorenzTTT= COP (2.28) Cascaded cycle analogy An analogy to the combined cycle is a cascaded power and refrigeration cycle, where part of the work output is directed into a refrigeration machine to obtain cooling. If the heat engine and refrigeration machine were to be treated together as a black box, the input to the entire system is heat, while output consists of work and refrigeration. This looks exactly like the new combined power/refrigeration cycle. Figure 2.3 shows the analogy, with a dotted line around the components in the cascaded cycle representing a black box. One way to look at an ideal combined cycle would be as two Lorenz cycle engines cascaded together (Fig 2.3b). Assume that the combined cycle and the cascaded arrangement both have the same thermal boundary conditions. This assumption implies

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33 Fig. 2.3 Thermodynamic representation of (a) combined power/cooling cycle and (b) cascaded cycle that the heat source fluid, chilled fluid and heat rejection fluid have identical inlet and exit temperatures in both cases. The first law efficiency of the cascaded system, using a weight factor f for refrigeration is hccoutsysQfQWW+, I= (2.29) The weight factor, f is a function of the thermal boundary conditions. Therefore, the first law efficiency of the combined cycle can also be written as hcnetQfQ+ IW= (2.30) The work and heat quantities in the cascaded cycle can also be related using the efficiencies of the cascaded devices

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34 W HEhoutQ = (2.31) COPQcc= W (2.32) By specifying identical refrigeration to work ratios (r) in the combined cycle and the corresponding reversible cascaded cycle as netcWQr= (2.33) and using Eq.(2.29) and Eqs.(2.31 2.33), one can arrive at the efficiency of the cascaded system as () ++COPrCOPfrHEsys1/11 =I, (2.34) assuming the cascaded cycle to be reversible, the efficiency expression reduces to () ++=LorenzLorenzLorenzrevICOPrCOPfr111, (2.35) Here Lorenz is the first law efficiency of the Lorenz heat engine and COPLorenz is the COP of the Lorenz refrigerator. A second law efficiency would then be written as revIIII, = (2.36) If the new cycle and its equivalent reversible cascaded cycle have identical heat input (Qh), the second law efficiency can also be written as revcrevnetcnetrevIIfQWfQW,,,++= II= (2.37) This reduces further to ()() revnetnetrevnetnetWWfrfrW,,11=++ IIW= (2.38)

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35 Evidently, the refrigeration weight factor (f) does not affect the value of the second law efficiency. This is true as long as f is a factor defined such that it is identical for both the combined cycle and the analogous cascaded version. This follows if f is a function of the thermal boundary conditions. Assuming a value of unity for f simplifies the second law efficiency expression even further. The corresponding reversible cycle efficiency would be, ++LorenzLorenzrevCOPrr11, =I (2.39) The resulting second law efficiency equation is a good choice for second law analysis. The expression does not have the drawback of trying to weight the refrigeration with respect to the work output. Being a second law efficiency, the expression also reflects the irreversibility present in the cycle, just like the exergy efficiency. Validity of Expressions Expressions for the first law, exergy and second law efficiencies have been recommended for the combined power and cooling cycle in Eqs. (2.17), (2.19) and (2.37) respectively. These definitions give thermodynamically consistent evaluations of cycle performance, but they are not entirely suitable for comparing the cycle to other energy conversion options. Substituting for refrigeration with the equivalent exergy is equivalent to replacing it with the minimum work required to produce that cooling. This would be valid if in the equivalent cascaded arrangement, the refrigeration machine were reversible. Therefore, when comparing the combined cycle with other options, such a substitution is debatable. This is where the difficulty arises in arriving at a reasonable definition of efficiency. Two cases are discussed here to illustrate the point.

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36 Case 1: Comparing this Cycle to Other Combined Cooling and Power Generation Options Consider the situation where the novel cycle is being designed to meet a certain power and refrigeration load. The goal then, would be to compare the thermodynamic performance of the novel cycle with other options designed to meet the same load. If the performance of both cycles were evaluated using Eqs.(2.17), (2.19) and (2.35), such a comparison would be perfectly valid. Case 2: Comparing a Combined Cycle to a Power Cycle In some instances, a combined cycle would have to be compared to a power cycle. For example, this cycle could be configured so as to operate as a power cycle. In this situation, the refrigeration would have to be weighted differently, so as to get a valid comparison. One way of doing this would be to use a practically achievable value of refrigeration COP to weight the cooling output. Another option is to divide the exergy of cooling by a reasonable second law efficiency of refrigeration (also called thermal efficiency of refrigeration). Such efficiencies are named effective efficiencies in this study. ( ) hpracticalcneteffQCOPQW+, I= (2.40) ( ) hrefIIcneteffQEW,, I = (2.41) + ( ) ( ) outhsinhspracticalcneteffEECOPQW,,,+= exergy (2.42) ( ) ( ) outhsinhsrefIIcneteffEEEW,,,,+= exergy (2.43)

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37 Some Examples of Application to the Combined Cycle An optimization program was used to optimize the performance of the Goswami cycle. A description of the methodology adopted is given in the following chapter. Optimization results using different efficiency definitions as objective functions are given in this section. The cycle simulations were performed using simple energy and mass balances. Approach temperature limits of 5 K were imposed on all heat exchangers. Boiler pinch points were assumed to be at least 5 K. It was assumed that there were no pressure losses in the devices and that the turbine and pump operated isentropically. The vapor at the turbine exit is constrained to be at least 90% dry. A turbine exit temperature of 270 K or lower was required to generate refrigeration. The optimization was also constrained so that refrigeration was always generated. The heat source fluid was assumed to be hot water at 400 K at the saturation pressure of water at that temperature. The absorber temperature was 5 K above the ambient which was assumed to be 298 K. Saturation conditions were assumed in the absorber to fix the concentration of ammonia in the binary mixture. The schematic of the cycle in Fig.1.6 differs slightly from previously published versions in that the liquid reflux from the rectifier is sent back to the absorber. The optimization results of the cycle evaluated using the exergy efficiency and second law efficiency Eqs.(2.19) and (2.36) are both identical. That is not surprising, since exergy efficiency and second law efficiency are very similar. The cycle parameters are presented in Table 2.2. It was assumed that the chilled fluid was liquid water for these simulations.

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38 Table 2.2 Cycle parameters that yield optimum exergy and second law efficiencies. Parameters Optimized Case exergy (%) 61.35 II (%) 61.35 exitboilerT, (K) 395 exitrectifierT, (K) 365.15 exitrsuperheateT, (K) 365.15 exitturbineT, 269.96 highp (bars) 10.84 lowp (bars) 1.00 basicx Ammonia mass fraction in absorber 0.288 hsm Mass flow rate of heat source (kg/s) 10.93 basicm Mass flow rate of basic solution (kg/s) 3 netW Net work output (kW) 79.15 cQ Cooling output (kW) 25.99 Tables 2.3 and 2.4 give results optimized for effective efficiencies. Different second law efficiencies of refrigeration were assumed. The exergy of cooling was calculated on the working fluid side. It is seen that assuming different second law efficiencies of refrigeration has a significant effect on the equivalent exergy efficiency.

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39 Table 2.3 Efficiency and cycle parameters optimized for effective exergy efficiency Parameters Case I Case II Case III Case IV refII, (%) 30 50 70 100 effexergy, (%) 72.52 65.20 62.74 62.10 (%),effI 17.70 15.89 15.11 15.08 exitboilerT, (K) 395 395 395 395 exitrectifierT, (K) 342.85 343.88 368.75 370.67 exitrsuperheateT, (K) 342.85 343.88 368.75 370.67 exitturbineT, 253.68 252.10 270 270 highp (bars) 16.7 15.3 17.4 18.0 lowp (bars) 1.8 1.64 2.0 1.96 basicx Ammonia mass fraction in absorber 0.374 0.360 0.390 0.388 hsm Mass flow rate of heat source 10.82 10.79 10.92 10.95 basicm Mass flow rate of basic solution 3 3 3 3 netW Net Work Output 69.2 72.2 97.4 87.63 cQ Cooling Output 59.1 58.1 34.2 30.55

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40 Table 2.4 Efficiency and cycle parameters optimized for effective first law efficiency Parameters Case I Case II Case III Case IV refII, (%) 30 50 70 100 effI, (%) 17.73 15.92 15.21 15.08 exitboilerT, (K) 395 395 395 395 exitrectifierT, (K) 343.69 344.92 348.99 370.67 exitrsuperheateT, (K) 343.69 344.92 348.99 370.67 exitturbineT, 253.08 251.49 249.72 270 highp (bars) 16.79 15.46 13.37 18.0 lowp (bars) 1.74 1.59 1.31 1.96 basicx Ammonia mass fraction in absorber 0.369 0.355 0.327 0.388 basicm Mass flow rate of basic solution 3 3 3 3 netW Net work output 64.5 66.83 68.26 87.63 cQ Cooling output 55.1 53.80 48.18 30.55

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41 To get a feel for second law efficiencies, a typical 10 EER vapor compression air conditioning system operates at a COP of around 3 at the standard rated conditions. The corresponding Carnot COP, assuming 280 K cold temperature and an ambient temperature of 308 K (selected based on standard rating conditions) is around 10. This implies a second law efficiency of 30%. Refrigeration cycles are inherently irreversible since they include a throttling process. The last case in tables 2.3 and 2.4 is the case where a second law efficiency of refrigeration is not considered. It is interesting to note that the optimization results in table 2.3, case IV are different from those in table 2.2. The reason for the difference is that irreversibilites in the refrigeration heat exchanger are considered in the optimization in table 2.2. The exergy of cooling Ec, is calculated on the working fluid side in both tables 2.3 and 2.4. Conclusions In defining efficiencies of a combined power and cooling cycle, it is necessary to weight the refrigeration output to obtain meaningful values. Definitions of first law, exergy and second law efficiencies have been developed in this chapter. From the basis of a strict thermodynamic analysis, the definitions given in Eqs. (2.17) and (2.19) are the correct efficiency definitions of the cycle. However, these definitions do not realistically weight the cooling content. When comparing the combined power and cooling cycle to one producing work alone, effective efficiencies defined in Eqs. (2.41) and (2.43) are recommended. It has also been shown in this paper that the weight assigned to refrigeration output has an impact on the optimum parameters for the cycle.

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CHAPTER 3 CYCLE SIMULATION AND OPTIMIZATION The combined cycle has been studied by a simple simulation model coupled to an optimization algorithm. The simulation model is simplistic, and is based on simple mass and energy balances. Ammonia water properties are calculated using a Gibbs free energy based method [43] while organic fluid properties were estimated using a NIST program that is based on a corresponding states method (see Appendix A). The optimization is performed by a search method. Search methods require an initial point to be specified. From there the algorithm searches for a better point in the feasible domain of parameters. This process goes on until certain criteria that indicate that the current point is optimum are satisfied. Optimization Method Background The optimization of the working of the cycle is a non linear programming (NLP) problem. A NLP is one in which either the objective function or one of the constraints are non-linear functions. The cycle optimization method chosen for the analysis of this cycle is a search method. Search methods are used to refer to a general class of optimization methods that search within a domain to arrive at the optimum solution. It is necessary to specify an initial starting point in search schemes. The optimization algorithm picks a new point in the neighborhood of the initial point such that the objective function (the function being optimized) value improves without violating any constraints. A simple method of determining the direction of change is to calculate the 42

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43 gradient of the objective function at the current point [44]. Such methods are also classified as steepest ascent (or descent) methods, since the algorithm looks for the direction of maximum change. By repeating these steps until a termination condition is satisfied, the algorithm is able to arrive at an optimized value of the objective. When implementing steepest ascent type methods for constrained optimization problems, the constraints pose some limits on the search algorithm. If a constraint function is at its bound, the direction of search might have to be modified such that the bounds are not violated. The Generalized Reduced Gradient (GRG) method was used to optimize the cycle. GRG is one of the most popular NLP methods in use today. A description of the GRG method can be found in several sources [44-46]. There are several variations of the GRG algorithm. A commercially available program called the GRG2 was used for ammonia water optimization, and a more recent version called the LSGRG2 was used for alternate fluid work. LSGRG2 is able to handle more variables and constraints than the GRG2 code, and is based on a sparse matrix representation of the problem Jacobian (matrix of first partial derivatives). The method used in the software has been discussed by Himmelblau et al. [46] and Lasdon et al. [47]. A brief description of the concept of the algorithm, heavily adapted [46, 47] is presented below: Consider the optimization problem defined as: Minimize objective function: ()Xgm1+ Subject to equality and inequality type constraints as given below (3.1) ()0=Xgi neqi,...,1= neqi= (3.2) ())(0inubXgi+ m,...,1+

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44 The variables are constrained by an upper and lower bound. ), (3.3) ()(iubXilbi ni,...,1= Here X is the variable vector consisting of n variables. As in many optimization algorithms, the inequality constraints are set to equality form by adding slack variables, mnnXX++,...,1 The optimization program then becomes Minimize: ()Xgm1+ Subject to: (3.4) ()0=+iniXXg mi,...,1= ), (3.5) ()(iubXilbi mni+=,...,1 0, (3.6) )()(==iubilb neqnni++=,...,1 (3.7) 0 )(=ilb mnneqni+++=,...,1 The last two equations specify the bounds for the slack variables. Eq. (3.6) specifies that the slack variables are zero for the equality constraints, while the variables are positive for the inequality constraints. The variables are called the natural variables. nXX,...,1 Consider any feasible point (satisfies all constraints), which could be a starting point, or any other point after each successful search iteration. Assume that nb of the constraints are binding, or in other words, hold as equality constraints at a bound. In the GRG algorithm used in the GRG2 and LSGRG2 software, using the nb binding constraint equations, nb of the natural variables (called basic variables) are solved for in terms of

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45 the remaining n-nb natural variables and the nb slack variables associated with the binding constraints. These n variables are called the nonbasic variables. The binding constraints can be written as (3.8) ()0,=xyg Here y and x are vectors of the nb basic and n nonbasic variables respectively and g is a vector of the binding constraint functions. The binding constraints Eq. (3.8) can be solved for y in terms of x, reducing the objective to a function of x only. ()()xFxxygm=+,1 () This equation is reasonably valid in the neighborhood of the current point to a simpler reduced problem. Minimize ()xF Subject to the variable limits for the components of the vector x. (3.9) uxl The gradient of the reduced objective is called the reduced gradient. ()xF ()xF Now the search direction can be determined from the reduced gradient. A basic descent algorithm can now be used to determine an improved point from here. The choice of basic variables is determined by the fact that the nb by nb basis matrix consisting of ( ) jiyg should be nonsingular terms should be nonsingular at the current point. A more detailed description of the theory and the implementation of the GRG algorithm and the optimization program can be found elsewhere [46-48]. This algorithm is a robust method that appears to work well for the purposes of optimizing this cycle, the way it has been implemented in our study.

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46 Search Termination The search will terminate if an improved feasible point cannot be found in a particular iteration. A well known test for optimality is by checking if the Kuhn-Tucker conditions are satisfied. The Kuhn-Tucker conditions are explained in detail in [45,46]. It can be mathematically explained in terms of the gradients of the objective functions and inequality constraints as: () (3.10) ()011=+==+XguXgjjmjjm 0ju ,()() [ ] 0=jubXgj uj (3.11) ()gj, (3.12) (jubX ) mj,...,1= Here, uj is a Lagrange Multiplier for the inequality constraints. Unfortunately, the Kuhn-Tucker conditions are valid only for strictly convex problems, a definition that most optimization problems do not satisfy. A disadvantage of using a search method, such as the GRG algorithm that has been used in this study, is that the program can terminate at a local optimum. There is no way to conclusively determine if the point of termination is a local or global optimum [46]. The procedure is to run the optimization program starting from several initial points. Sensitivity Analysis The sensitivity of the results to the active constraints can be determined using the corresponding Lagrange multipliers. () jubVuj= (3.13) Where, V is the value of the objective at the optimum.

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47 Application Notes There are some factors in the optimization of the cycle studied using GRG2 and LSGRG2 that are interesting to mention. In a search scheme, it is possible that the termination point could be a local optimum, or not an optimum at all. It is necessary to determine the nature of the optimum returned by the program. Prior to the optimization, during setup, close attention should be paid to: Scaling of the variables Limits set for different convergence criteria Method used to numerically calculate the gradient The relative scaling of the variables affects the accuracy of the differentiation and the actual value of the components in the gradient, which determines the search direction. Experimenting with the numerical calculation of the gradient is useful during scaling. Too small a convergence criterion, particularly for the Newton-Raphson method used during the one-dimensional search can cause premature termination of the optimization program. The accuracy of the numerical gradient affects the search process. This was clearly seen when setting up the program with the SUPERTRAPP program. A forward differencing scheme was not accurate enough for the search to proceed forward. Once the program was setup, the following methods were used in the process in order to obtain a global optimum: For each case, several runs were performed, from multiple starting points. Optimized results using different objective functions were useful as starting points for other cases. Examining the constraints indicated if the point was truly an optimum. For instance, at maximum second law efficiencies, the pinch point in the boiler was expected to be at its lower bound. The results were perturbed and optimized, particularly with respect to what would be expected to very sensitive variables, to see if a better point could be obtained.

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48 For example, in RUE optimization, the heat source flow rate is a very sensitive variable. Perturbing the optimum results w.r.t the heat source flow rate was very useful to get better points. Another method is to change the scaling of variables that appear to be insensitive to check if better points can be obtained. For each configuration, comparing the results for different heat source and turbine exit temperatures was used to identify non-optimum and local optimum points. At the end of this exhaustive process, it is assumed with reasonable confidence that the resulting point is indeed a global optimum. The optimization process using GRG is to a certain extent art not science. Unfortunately, this is a problem with almost all NLP methods currently in use. Cycle Modeling Several cycle configurations have been studied in this dissertation. The model used for the basic cycle configuration shown in Fig. 3.1 is first discussed. The modeling of additional features in modified configurations is discussed, if necessary, when the alternate configuration is introduced. Consider the basic cycle configuration shown in Fig. 3.1 Eight independent variables are sufficient to determine the operation of the cycle. Two more variables are required to determine heat source conditions. Pressure drops and heat losses are neglected. Cycle high pressure Cycle low pressure Absorber temperature Temperature at boiler exit Temperature at rectifier / condenser exit Superheater exit temperature

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49 Effectiveness of the heat recovery heat exchanger, R1 Ratio of the mass flow rates of the strong solution in the heat recovery heat exchanger and the rectifier, R2 Heat source temperature Mass flow rate of heat source The absorber temperature is set a little above the ambient temperature. The following general assumptions were used in the simulation Pressure losses in piping and equipment are neglected. An isentropic efficiency is assumed for the pump and turbine All processes are assumed to end in equilibrium thermodynamic states. Using the variables and assumptions listed above, the properties at all state points in the cycle can be determined. For a binary mixture, two intensive properties and the composition of the mixture are sufficient to establish all the other properties. Some combinations include pressure, temperature and composition (p,T,x); pressure, specific enthalpy and composition (p,h,x); or pressure, specific entropy and composition (p,s,x). Property calculation methods are discussed in Appendix B. State Point Calculation The calculation of state points for each state in Fig. 3.1 is described below. State point 1 The mixture in the absorber is assumed to be at saturation conditions. The low pressure of the cycle and the temperature of the absorber allow the calculation of ammonia concentration of the basic solution. Absorber temperature is assumed to be 5 K above ambient temperature. A reference flow rate is assumed and all other flow rates in the

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50 Fig. 3.1 The basic cycle configuration with the variables shown

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51 system are scaled to this value. The choice of reference flow rate is to an extent decided by the optimization program. The value is determined after a few trials so that other parameters (particularly heat source mass flow rate) are reasonably large. This is important so that error in gradient calculation is limited. Relative magnitudes of the optimized variables are important to ensure reasonable values in gradient calculations. In equation form: (3.14a) absorberTT=1 pp= (3.14b) low1 satconx= (3.14c) ),(111Tp 3=m (3.14d) 1 Satcon is a function in the ammonia-water properties program to calculate saturated liquid concentration given the pressure and temperature. Knowing three properties, the remaining properties of the binary mixture can be determined. This is implicit in the rest of this section. Point 2 The pump pressurizes the strong solution to the high pressure in the cycle. Knowing the isentropic efficiency of the pump, the pressure and enthalpy at state 2 is easily computed. The composition of the solution remains the same as in state 1. pp= (3.15a) high2 ss= (3.15b) 1isen xx= (3.15c) 12

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52 Calculate enthalpy at pump exit, hisen, for isentropic compression. Then, knowing the pump efficiency, the actual enthalpy can be calculated using Eq. (3.15d) below. 112hhhhisenp= (3.15d) Points 5 and 11 Since the boiler exit temperature and pressure are known, vapor-liquid equilibrium correlations yield the vapor and liquid compositions leaving the boiler. A mass balance is used to determine the vapor and liquid mass fractions. TTT== (3.16a) boiler115 pp== (3.16b) highp115 Use VLE data to get equilibrium compositions of vapor and liquid. The vapor and liquid mass fractions in the boiler can be computed from a mass balance as shown below. 115114xxxxvmfboiler= (3.16c) 11545xxxboiler xlmf= (3.16d) Therefore, the mass flow rates would be vmfm= (3.16e) 45mboiler mlmfm= (3.16f) 411boiler

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53 Points 6 and 7 The rectifier exit temperature and pressure are known, as well as the boiler vapor mass fraction and composition. This allows the calculation of vapor and liquid compositions and mass fractions leaving the rectifier. TTT== (3.17a) rectifier76 pp== (3.17b) highp76 VLE data is used to get equilibrium compositions of vapor and liquid. Once again, a mass balance gives the vapor and liquid mass fraction leaving the rectifier as 6765xxxxrectifier= vmf (3.17c) 6756xxxxrectifier lmf= (3.17d) Therefore, the mass flow rates would be vmfm= (3.17e) 57mrectifier mlmfm= (3.17f) 56rectifier Point 8 The superheater exit temperature is specified for each simulation, and the pressures and composition of the vapor are known. TT= (3.18a) erheatersup8 pp= (3.18b) high8 xx= (3.18c) 78

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54 Point 9 The turbine isentropic efficiency is assumed, the turbine exit pressure is the system low pressure and the composition of the vapor is known. Therefore state points at the turbine exit can be calculated. pp= (3.19a) low9 ss= (3.19b) 8isen xx= (3.19c) 89 Calculate an enthalpy corresponding to isentropic expansion and use in equation below to calculate enthalpy at turbine exit. isenhhhh898 t= (3.19d) Point 10 If the vapor is cold enough, it is assumed that the vapor leaves the refrigeration heat exchanger at 5 K below ambient. If the vapor leaving the turbine is not cold enough to yield refrigeration, state 10 is identical to state 9. The pressure and composition are already known. If min9TT 5=TT (3.20a) 010 pp= (3.20b) 910 xx= (3.20c) 910 Else, point 10 is identical to state point 9.

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55 Points 12 and 3 The maximum heat recovered from the weak solution is decided by the approach temperature limits. A fraction of this heat (variable R1) is recovered. xx= (3.21a) 1112 pp= (3.21b) 1112 A 5 K approach temperature difference is assumed in the recovery heat exchanger, i.e., Other properties at the state point are calculated using this temperature to obtain maximum possible heat transfer. This assumption eliminates the use of a constraint at that point. 5212+=bTT Q (3.21c) (121111max,,hhmhotHRHXb= )) On the other side of the heat exchanger, pp= (3.21d) high3 xx= (3.21e) 23 mRm= (3.21f) 223 Set the maximum temperature at the heat exchanger outlet 5=bTT (3.21g) 113 Now a cold side maximum heat transfer can be calculated (3.21h) (333max,,hhmQcoldHRHXb=

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56 The smaller of the values from Eq. (3.21c) and Eq. (3.21h) represents the maximum heat transfer possible. Now, using the ratio of the actual heat transfer to the maximum possible heat transfer, R1, enthalpy h12 is calculated as 11max,11112mQRHRHX hh= (3.21i) ( ) 3max,123mQRHRHX hh+= (3.21j) This allows the calculation of other state points. Note that R1 is a pseudo heat exchanger effectiveness. The advantage of this assumption is that approach temperature constraints can be eliminated for the heat exchanger. Point 13 The liquid reflux stream from the rectifier, and that from the boiler mix to form the fluid at state 13. The mixing is modeled as a constant total enthalpy process. pp= (3.9a) high13 1312126613mhmh+ mh= (3.9b) 1312126613mxm+ xmx= (3.9c) Point 14 The weak solution at high pressure is throttled to a low pressure. The throttling is modeled as a constant enthalpy process. hh= (3.10a) 1314 pp= (3.10b) low14

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57 xx= (3.10c) 1314 Point 15 The heat lost by the condensing fluid in the rectifier is recovered by the part of the strong solution stream flowing through the rectifier. A simple energy balance allows the determination of the state of the fluid at point 15. pp= (3.12a) high15 xx= (3.12b) 215 (m= (3.12c) )22151mR mQ= (3.12d) 776655hmhmhrectifier 15215mrectifier Qhh+= (3.12e) Point 4 The two strong solution streams mix to form the fluid at state 4. This is also modeled as a constant total enthalpy process, as in state13. The composition of the two streams are the same, and hence no mass balance is needed. hhh+= (3.13a) 1534 xx= (3.13b) 24 pp= (3.13c) high4 Variable Limits In any constrained optimization problem, limits of variable values have to be specified. The purpose of specifying limits is to ensure that the values at optimum

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58 conditions are achievable, meaningful, and desirable in practice. An upper and lower bound is specified for the variables in the GRG optimization program. If the variable is to be held fixed, the upper bound is set to be equal to the lower bound, both of which are set equal to the value of the parameter. Unbounded variables are specified by setting a very large limit. Table 3.1 shows the upper and lower bounds of the variables used in the cycle optimization. Some of the bounds are arbitrarily specified when a clear value was Table 3.1 Independent cycle parameters and their limits Variable Lower Limit Upper Limit Name and Units absorberT 55 0+T 0+T Absorber Temperature (K) boilerT 55 0+T heatsourceT Boiler Exit Temperature (K) rectifierT 55 0+T heatsourceT Rectifier Exit Temperature (K) rsuperheateT 55 0+T heatsourceT Superheater Exit Temperature (K) highP 2 100 Cycle High Pressure (bars) lowP 1 100 Cycle Low Pressure (bars) heatsourceT heatsourceT heatsourceT Heat Source Temperature (K) heatsourcem 0 18 Mass Flow Rate of Heat Source Fluid (kg/s) 1R 0 1 Pseudo Heat Exchanger Effectiveness 2R 0.01 0.99 Flow Split Ratio

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59 not available. For instance, although the rectifier exit temperature can reach its upper limit, the value always has to be below the boiler exit temperature. The actual domain in which these variables may vary is further restricted by additional constraints that are specified. The lower limit for the low pressure is set at 1 bar, to avoid vacuum pressures anywhere in the system. At vacuum pressures, non-condensable gases enter the system. Additional equipment is required to remove these gases. The highest pressures in the optimization are set arbitrarily at around 100 bars. Constraint Equations To ensure that cycle parameters stay within limits that are practical and physically achievable, it is necessary to specify limits in the form of constraint equations. Constraints are implemented in GRG2 by defining constraint functions and setting an upper and lower bound for the function. Table 3.2 summarizes the constraint equations used for simulation of the basic cycle. If the constraint is unbounded in one direction, a value of the order of 1030 is specified. In GRG2, the objective function is also specified among the constraint functions. The program treats the objective function as unbounded. A brief discussion of the constraints specified in Table 3.2 follows. The rectifier/condenser exit temperature should be below the boiler temperature and superheater temperature. A minimum approach temperature of 5K is assumed for all devices. A pinch point temperature difference of 5K is also assumed in the boiler. For the contingency that boiling could begin in the rectifier or recovery heat exchanger, a pinch point calculation is implemented in those two devices also. To ensure that the reflux flow from the boiler is in the right direction, a constraint is used to maintain that value positive. Additional constraints are used to keep the vapor mass fraction at the turbine exit (dryness of vapor) greater than 90%. Two additional constraints (that might

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60 Table 3.2 Constraints used in the optimization Constraint Description Lower Limit Upper Limit boilerrectifierTT Measure of condensation in the rectifier -1E+30 0 erheaterrectifierTTsup Measure of Superheating -1E+30 0 26TT Rectifier exit approach T t 5 1E+30 155TT Rectifier inlet approach T t 5 1E+30 7,TTIIhs Boiler exit approach T t 5 1E+30 4,TTIIIhs Boiler inlet approach T t 5 1E+30 boilerpinchT, Pinch Point T t in Boiler 5 1E+30 HRHXpinchT, Pinch T t in HRHX (if applicable) 5 1E+30 rectifierpinchT, Pinch T t in Rectifier (if applicable) 5 1E+30 10011m Boiler reflux mass flow rate 0 1E+30 100turbinevmf Vapor mass fraction at turbine exit 90 100 100boilervmf Vapor mass fraction at boiler exit 1E-05 100 100rectifierlmf Liquid mass fraction 1E-05 100 cQ Cycle Cooling Output 0.1 1E+30 Objective Efficiency Percentage 0 100

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61 be redundant) are used to ensure that some vapor is generated in the boiler and that there is some condensation in the rectifier. These ensure that there is no heat addition to the vapor in the rectifier. A final constraint is used so that there is always some minimum positive cooling achieved in the cycle. This is to make sure that the cycle behavior does not go into a mode where only power is produced. Model Limitations The model used to simulate the cycle is a simple one with the advantage of being computationally fast. The results are expected to give a good idea of the trends that would be seen in real equipment. Such simple models are regularly found in the literature for preliminary analysis of thermodynamic cycles. The efficiencies obtained from such models would be higher than actually achievable efficiencies. While the results of the optimization study will indicate an approximate value for the maximum efficiency of the cycle, the cycle parameters are not necessarily practical. The ultimate predictor of the usefulness of the cycle is in the economics of using it.

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CHAPTER 4 OPTIMIZATION OF BASIC CYCLE CONFIGURATION USING AMMONIA-WATER MIXTURE AS THE WORKING FLUID Initial parametric studies of the combined power and cooling cycle using ammonia-water mixtures as the working fluid suggested that some optimum conditions of operation exist for the cycle performance [2,36]. An optimization scheme was implemented to determine the best conditions of operation (from a thermodynamic efficiency perspective) for various applications [3], such as for utilizing geothermal and solar resources, and for achieving very low temperature cooling. Work done in the past has used a variety of different efficiency definitions. In this chapter, some of the past optimization work has been repeated with the efficiency definitions discussed in chapter 2. Additional results are presented, that use isentropic efficiencies for the turbine and pump. The modeling of the cycle in earlier work was improved upon for the optimization work discussed in this chapter. Two additional variables were added to vary the effectiveness of the Heat Recovery Heat eXchanger (HRHX) and to control the ratio in which the strong solution stream was split between the HRHX and the rectifier. Earlier modeling had the liquid reflux from the rectifier going back into the boiler and boiling as a separate stream. Such a model makes the pinch point calculation in the boiler difficult. The stream was diverted to a point after the recovery heat exchanger. Additional pinch point checks were introduced in the rectifier and HRHX to account for the possibility of the start of boiling of the strong solution before entering the boiling heat exchanger. 62

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63 Simulated Conditions The modeling of the cycle in the optimization study carried out here has been discussed in the previous chapter. One of the questions that remained unanswered in earlier optimization work is the influence of the turbine exit temperature (the low temperature in the cycle) on the optimized efficiencies. Turbine exit temperatures were varied from 255 K to 280 K in 5 K increments. Optimizing for work output maximization, one ends up working with a cycle similar to the Maloney and Robertson cycle. A low pressure limit of 5 bars was used in the work optimization in order that the cycle remained an absorption type cycle. This limit was arbitrarily set so that there is a reasonable amount of absorbent in the basic solution at the absorber temperature. To study the effect of heat source temperatures, four values, 360 K, 400 K, 440 K and 480 K were picked for simulation. This covers a range of low to medium temperature solar heat. The heat source was assumed to be water at the saturation pressure corresponding to the heat source temperature. The ambient temperature was assumed to be 298 K for all simulations. The objective functions corresponding to efficiency definitions developed in chapter 2 are shown in Eqs. (4.1-4.5) () inhscnetRREEWObj,+== (4.1) () ( ) outhsinhscnetexergyexergyEEEWObj,,+== (4.2) () hcnetIIQEWObj+== (4.3) ( ) inhsrefIIcneteffReffREEWObj,,,, +== (4.4) ( ) ( ) outhsinhsrefIIcneteffexergyeffexergyEEEWObj,,,,,+== (4.5)

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64 Fig. 4.1 Block diagram showing the basic scheme of the combined power and cooling cycle. Same as Fig. 1.6

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65 Exergy losses in each component were calculated in the optimized results using the entropy generation in each device. The turbine and pump were the only devices assumed without losses in the model. Results discussed later in this chapter assume a value for isentropic efficiencies for these devices. The exergy loss in each process is calculated using the Guoy-Stodola theorem, from an entropy balance on each device, as in Eq. (4.6). (4.6) ()inoutgenlossSSTSTE==00 Here, T0 is the ground state temperature with respect to which exergy is defined, set at 298 K for all cases. The ground state pressure was set at 1.013 bar (1 atmosphere). Optimization results Resource Utilization Efficiency The resource utilization efficiency is the recommended choice in evaluating an energy conversion device for resources that are discarded after use in the cycle. A good example is the case of a geothermal application, where, the heating fluid is reinjected into the ground after extraction of energy from it in the power plant. The availability of the geofluid at the point of reinjection is wasted exergy that the power plant is incapable of utilizing. This efficiency can also be applied to other applications. In a coal power plant, the resource utilization efficiency would consider either the exergy of the coal and the air used for combustion, or the exergy of the products of combustion (hot gases and any solid residue such as ash). Unutilized exergy leaving the power plant through hot combustion products leaving the smokestack and in hot ash dumped into an ash pit is wasted. Optimizing for resource utilization efficiency is a good choice to

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66 Fig. 4.2 Optimized resource utilization efficiencies for the basic cycle configuration ensure that maximum use is made of the energy source or fuel. The resource utilization efficiency is written as (also see Eqs. (4.3) and (2.11)) ([ )] oinhsooinhshscnetRssThhmEW+=,,)( (4.7) The specific enthalpy ho and specific entropy so are calculated at the ground state. To maximize the efficiency of Eq. (4.7), the sum of the net work output and the exergy of cooling has to be increased, while the mass flow rate of the heat source is decreased. The objective function, therefore, is very sensitive to the flow rate of the heat source. The optimum resource utilization efficiencies (RUE) are shown in Fig. 4.2. Three different cases have been plotted. Maximum efficiency obtained using two different turbine exit temperature limits are shown. There is a slight drop off in RUE with lower

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67 turbine exit temperatures. Optimizing purely for work output gives a better RUE value. An upper limit of 5 bars (0.5 MPa) was used for the work maximization simulations. Without this constraint, the optimum conditions were seen to be at conditions where the cycle operates using nearly pure ammonia as a Rankine cycle. The absorber model used is not valid at those conditions and the results are also not valid. Exergy Efficiency In solar thermal power plants, normally solar energy is collected and stored in a heat storage medium. This medium acts as the heat source for the power plant. The exergy of the heat source is not lost in the unextracted heat leaving in the fluid exiting the cycle because it is recirculated through the collector system to the storage tank. In such a case, the exergy efficiency is a reasonable choice for the objective function. This assumes though that the collection system efficiency is unrelated to the inlet and outlet temperatures of the cycle, which might not be the case. Even for solar resources, ultimately, resource utilization efficiency can be calculated, if the solar radiation were to be treated as the input. The definition of exergy of solar radiation is still being debated but the values of different definitions in the literature give values that are fairly close to each other. Exergy efficiency is defined in terms of the exergy transferred from the heat source fluid to the working fluid in the boiler. This function is relatively less sensitive to mass flow rate of the heat source. Changing the mass flow rate would be compensated by a change in specific exergy change in the heat source fluid, in the denominator of the exergy efficiency equation, Eq. (4.6). A large heat source flow rate results in a small temperature drop of the heat source and a bad thermal match in the boiler.

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68 Fig.4.3 Optimized exergy efficiencies for the basic cycle configuration ([ )] outhsinhsoouthsinhshscnetexergyssThhmEW,,,,)(+= (4.6) For the exergy efficiency case, as seen in Fig. 4.3, efficiency is maximum at 400 K (of the four temperatures considered here), which is still lower than the efficiency in the work output optimized case, with a 5 bar upper limit on pressure. The optimized results are not bound at the 5 bar pressure limit. The reason for the drop in efficiency at higher temperatures is primarily due to the boiler temperature not increasing corresponding to the increase in heat source temperatures. There are limits to the temperatures in the boiler and condenser at which refrigeration can be obtained efficiently, since it becomes difficult to achieve sufficient temperature drop in the turbine across a given pressure ratio. A similar effect can also be seen in first law efficiency optimization (see Fig. 4.4)

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69 where the efficiency curve plateaus at higher heat source temperatures. The effect of lower turbine exit temperatures is to lower optimum efficiencies slightly. First Law Efficiency The first law efficiency is not sensitive to mass flow rate of the heat source. Once the optimum operating conditions of the cycle are determined, as long as the pinch point conditions are not violated, changing the mass flow rate does not affect the first law efficiency at all, since the heat input to the cycle remains the same. An advantage of using a binary mixture is the improved thermal matching in the boiler. Since the first law efficiency does not account for the heat source behavior, the exergy efficiency is a better choice for evaluating binary mixtures. It might be a better choice to use the first law efficiency corresponding to the optimum exergy efficiency. A first law efficiency is a useful measure of the cycles performance. It is a direct measure of the heat transfer requirements in the boiler and condenser. A cycle with a high first law efficiency would have a much smaller boiler heat transfer area requirement per unit work output. Similarly, the condenser load being smaller, would use a much smaller condenser for the same boiler size. Note that this is a simplistic statement. Several other factors such as the heat transfer coefficients and pressures play a role in the size of the equipment. Optimized first law efficiencies in the refrigeration domain are shown in Fig.4.4 Once again, the work optimization results show a higher value of efficiency. The effect of lower temperatures in the cycle is a small drop off in efficiency. It is also seen from the results that the cycle optimized in the refrigeration domain fails to take advantage of higher heat source temperatures. The optimized parameter values for heat source

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70 Fig. 4.4 Optimized First Law Efficiencies for the Cycle Configuration in Fig. 4.1 temperatures of 440 and 480 K are almost identical. Optimizing in the work output domain, one sees an increase in efficiency going from 440 K to 480 K. This implies that while the first law efficiency improves, a corresponding increase in exergy efficiency is not seen. Exergy Analysis An exergy analysis was performed to determine the various pathways of losses in the cycle. For the optimized RUE results, the major exergy losses in different parts of the cycle are plotted in Figs. 4.5 and 4.6. Figure 4.5 shows the losses occurring for the case where cooling is produced and the turbine exit temperature limit was set to 280 K. A large fraction of the exergy of the heat source is lost in the fluid leaving the cycle. Approximately 30 % of the exergy available in the heat source is lost in this fashion. The

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71 Fig. 4.5 Exergy destruction in the cycle represented as a percentage of exergy of the heat source, for optimized RUE corresponding to 280 K turbine exit temperature Fig. 4.6 Exergy destruction in the cycle represented as a percentage of exergy of the heat source, for optimized RUE corresponding to pure work output

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72 losses in the heat addition process (boiler and superheater combined) are also high due to the poor thermal matching in the boiler. At the optimized condition, the mass flow rate of the heat source is very small. At these conditions, the strong solution enters the boiler at a temperature slightly above the bubble point. This removes the pinch point constraint in the boiler and allows a small heat source flowrate at the expense of thermal matching. In the work domain, there is no rectification at optimum conditions. The process of rectification is a source of exergy loss and is unnecessary if refrigeration is not desired. At higher heat source temperatures (440 K and 480 K), there is no heat recovered in the solution heat exchanger under optimum conditions. The hot weak solution is throttled and then cooled in the absorber, with considerable losses. The heat source is used to preheat the working fluid and therefore leaves the cycle at low temperatures. As a result, the exergy losses in heat rejection and throttling go up, while the loss through unrecovered exergy in the heat source drops (Fig. 4.6). Similar plots are shown for exergy destruction in the optimized exergy efficiency cases in Figs. 4.7 and 4.8. In the case with cooling output, the losses in the boiler are small. There is good thermal matching in the boiler, except at the 480 K heat source temperature. The exergy loss during heat rejection, in the absorber, is a major source of irreversibility in the system. That is surprising because the vapor has been expanded to very low temperatures and a large fraction of the heat recovered from the weak solution. Apparently, the mixing and absorption losses are high. Once again the optimum parameters in the work domain do not show any rectification. The internal heat exchange category in Fig. 4.8 is the sum of exergy destruction in the solution heat exchanger and rectifier. It is seen that exergy destruction

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73 Fig. 4.7 Exergy destruction in the cycle for optimized exergy efficiency corresponding to 280 K turbine exit temperature Fig. 4.8 Exergy destruction in the cycle for optimized exergy efficiency corresponding to pure work output

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74 in the boiler and superheater is small. The thermal matching in the boiler is reasonably good in the exergy efficiency optimized cases, but it appears to be poorer than in the cooling domain. In the work domain, the requirement for work output does not limit the boiler exit temperature. However, the superheating seen at optimum conditions is larger and therefore, the thermal match in the boiler is poorer. In addition, the vapor fraction in the boiler is large enough that there is not enough weak solution to preheat the strong solution sufficiently to eliminate the pinch point in the boiler at 440 K and 480 K. This accounts for the odd looking inflections in the curves in Fig. 4.8 and contributes to increased exergy losses in the boiler. Optimization Considering Losses The optimization discussed so far assumes isentropic turbine and pump. Only approach temperature constraints are placed on the solution heat exchanger. The resulting effectiveness is close to 95%. Additional simulations were performed considering the turbine and pump as non ideal devices and using a lower effectiveness for the recovery heat exchanger. Optimization calculations were also performed using effective efficiency definitions developed in chapter 2. An isentropic efficiency of 0.85 was assumed for the turbine, while a value of 0.8 was assumed for the pump. The values assumed are relatively optimistic, actual values would depend on the type of expander used and the size and scale of the equipment. Although the effect is predictable, the basic cycle configuration was also optimized using heat exchangers with lower effectiveness of 70 % and 80%. A turbine exit temperature limit of 270 K was set for all simulations. The optimized RUE is plotted in Fig. 4.9. The effect of including an isentropic efficiency for the turbine and pump is to lower the RUE (see Fig. 4.2). In effective

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75 Fig. 4.9 Optimized RUE for the basic cycle configuration using a non isentropic turbine and pump Fig. 4.10 Effect of recovery heat exchanger effectiveness on RUE at optimum RUE conditions, with cooling output

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76 efficiency definitions, as discussed earlier, the cooling component is given a larger weight. Therefore, better efficiencies are obtained and a larger amount of refrigeration is produced at optimum conditions. The cycle was also optimized so as to obtain maximum work output with an upper limit on low pressure set at 5 bars, as in the previous optimizations. As seen in the earlier results, the efficiency is higher when optimizing for work output. It can be seen that with sufficient weight given to the refrigeration output, the cycle could have a higher effective efficiency in the refrigeration mode. Figure 4.10 represents the effect of solution heat exchanger effectiveness on the RUE. As expected, a lower effectiveness results in a lower efficiency. Figures 4.11 and 4.12 show optimized exergy efficiencies for the cycle with an irreversible turbine and pump. It is seen that effective exergy efficiencies are comparable to the optimum efficiencies obtained for pure work output at lower heat source temperatures. At higher source temperatures, the optimum conditions in the pure work output case are still superior. The best efficiency in the refrigeration domain is seen at the heat source temperature of 400 K. At higher source temperatures, the boiler exit temperature does not get very close to the heat source inlet temperature because it is difficult to drop to cold temperatures through the turbine if the inlet temperature is very high. The effect of lower recovery heat exchanger effectiveness is a drop in efficiency. The exergy destruction in some of the major processes in the cycle (appropriately normalized), when optimized for RUE and exergy efficiency in the cooling domain, is plotted in Figs. 4.13 and 4.14. It is seen that the effect of turbine irreversibility is to lower the RUE by about 5% (absolute) and the exergy efficiency by about 10%. Once again the largest source of losses in the RUE optimization is the

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77 Fig. 4.11 Optimized exergy efficiencies for the basic cycle configuration using a non isentropic turbine and pump Fig. 4.12 Effect of recovery heat exchanger effectiveness on effective efficiency

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78 Fig. 4.13 Exergy destruction in the optimized RUE case Fig. 4.14 Exergy destruction in the optimized exergy efficiency case

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79 unrecovered exergy lost from the heat source. The bad thermal match in the boiler is reflected in the large exergy destruction during heat addition. The losses in the absorber are also quite big. The dominant losses when maximizing exergy efficiency (Fig. 4.14) are in the absorber and the internal heat recovery process. Discussion The basic configuration of the cycle has been optimized in order to gauge its thermodynamic performance. An exergy analysis is performed to determine the potential areas of improvement in the cycle. The results of the exergy analysis are applied to improving the performance of the cycle, which is discussed in a later chapter. It is seen that RUE values obtained with the cycle are quite low. The optimized cycle state points show that the strong solution starts boiling before entering the boiler (in the HRHX and rectifier), thereby eliminating the pinch point in the boiler. Figures 4.15 and 4.16 show the boiler inlet and exit conditions of the working fluid at the heat source temperatures studied. The cycle performance is maximized by reduction of mass flow rate of the heat source until the approach temperature constraint at the boiler entrance (state 4 in Fig. 4.1) is at the bound. High exergy destruction occurs in the boiler, when the parameters are set to yield maximum RUE while providing both power and cooling (see Figs. 4.5 and 4.13). The reason for the observed trend is the low vapor fraction in the cycle (boiler) when operated to produce power and refrigeration (see Fig. 4.15). It is seen that the vapor fraction is between 9 and 15 % when producing work and cooling at high efficiency, while in the work domain it is between 20 and 28 % (Fig. 4.16). In order to expand the vapor to low temperatures, relatively high concentration vapor is required. Other requirements include a high pressure ratio, and lower pressures at the turbine exit such that the temperature drop in the turbine is high. All these factors

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80 Fig. 4.15 Working fluid temperatures and vapor fractions in boiler: at maximum RUE and with cooling Fig. 4.16 Working fluid temperatures and vapor fractions in boiler: at maximum RUE with pure work output

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81 promote low vapor fraction in the boiler. Consequently, there is a large temperature difference at the boiler exit (between heat source state II and vapor at state 5) and the result is poor thermal matching in the boiler. A large temperature glide would be needed for good thermal matching in the boiler, which only occurs at large vapor fractions. From Fig. 4.1, it can be seen that the exergy in the heat source fluid leaving the boiler is not utilized elsewhere. In order to remove as much of the exergy out of the heat source as possible, the temperature of the heat source should be dropped to the maximum extent possible in the boiler. Since the fluid enters the boiler at a condition where it is beginning to boil, the bubble point of the strong solution should be low. This is achieved by having a high basic (strong) solution concentration and lower boiler pressures. However when operating at these conditions, the pressure ratios are lower resulting in a lower temperature drop in the turbine. Figure 4.17 clearly shows that the pressure ratios are lower in the RUE optimized results compared to the exergy efficiency optimized results. Interestingly, it is seen that setting a lower limit for recovery heat exchanger effectiveness results in a substantial reduction in pressure ratio in the optimized exergy efficiency results. With ammonia-water mixtures, lower absorber pressures result in higher pressure ratios. However, the basic (strong) solution concentration then becomes smaller limiting the vapor fractions in the boiler. With the resulting increase in the weak solution flow, the load on the recovery heat exchanger goes up. A reduction in the effectiveness of the recovery unit pushes the optimum towards higher absorber pressures and lower pressure ratios.

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82 Fig.4.17 Cycle pressure ratios and the influence of solution heat exchanger effectiveness Fig.4.18 Cooling to work output ratios at optimum conditions

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83 Figure 4.18 shows the cooling to work output ratio at optimum conditions using the basic cycle configuration. Clearly, assigning a larger weight to the refrigeration output results in a larger cooling output at optimum conditions in the cooling domain. Unlike classic refrigeration cycles, the cold fluid is in the form of dry or slightly wet vapor. The cooling is by sensible heating of the vapor, and not by the vaporization of a two-phase mixture as in a typical evaporator. When weight assigned to cooling is larger, in some cases, the turbine output temperature drops well below the set limit of 270 K in the simulations. The corresponding first law efficiency of the cycle at optimum exergy efficiency and optimum RUE conditions is plotted in Fig. 4.19 and 4.20 respectively. Since the heat source temperature is low, the corresponding first law efficiency is generally low. Fig. 4.19 First law efficiency at optimized exergy efficiency conditions

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84 Fig. 4.20 First law efficiency at optimum RUE conditions The first law efficiency corresponding to the RUE is lower. This is because for high RUE, the goal is to remove as much energy from the heat source as possible. Conclusions The basic cycle configuration has been optimized for maximum resource utilization efficiency and exergy efficiency. It is seen that the RUE values obtained with this configuration are low, primarily because of the difficulty in removing heat from the source fluid while maintaining high efficiencies. The exergy efficiency values appear to be relatively high at 360 K and 400 K. At higher values of 440 K and 480 K, the second law efficiency is lower. When the cycle is operated to give only work output the efficiencies are higher in almost all cases. However, when considering effective efficiencies, the basic

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85 configuration performs comparably in the cooling domain or the pure work output domain, at low heat source temperatures. At higher temperatures (440 K and 480 K), this configuration does not efficiently produce both work and cooling simultaneously.

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CHAPTER 5 RESULTS AND DISCUSSION: ORGANIC WORKING FLUIDS The combined power and cooling cycle has been extensively studied using a binary mixture of ammonia and water as the working fluid. Ammonia, however, is a corrosive fluid and poses some challenges in turbine design, particularly in limiting the leakage at the seals and in material compatibility issues. While a limited number of ammonia based (Kalina) power plants have been built in the past few years, hydrocarbon mixtures would be easier to work with. Hydrocarbons and halocarbons have been used in binary geothermal power plants for the last couple of decades and the industry has significant experience with them. Working Fluid Selection There are several considerations for desirable properties of working fluids used in thermodynamic cycles. There are some obvious general properties that would be ideal to have in a working fluid. The working fluid should be Stable Non Fouling Non Corrosive Non Toxic Non Flammable The working fluid stability at the pressures and temperatures encountered in the cycle, and over long term use is critical. Non corrosive, non fouling, non toxic, non flammable fluids simplify the design and cost of a power plant significantly. A suggested application of this cycle is in small power plants sized for residential, commercial and 86

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87 industrial buildings. For some of these cas es, a non toxic, non fl ammable fluid would help to meet building code requirements. Th e organic working fluids considered in this chapter all have high flammability. The heavie r components are skin and eye irritants. Data available on long term temperature a nd pressure stability appears limited, but indications are that the com pounds are stable and that hazar dous polymerization is not a concern. Several references [16,35, 49-54] were used to shortlist work ing fluids and for background on the properties of working fluids re quired in cycles of the type considered here. The list consists of alkanes, alkenes and dienes. The optimization work discussed in this chapter focuses on mixtures of satu rated hydrocarbons (alkan es). Halocarbons are not considered due to concerns about thei r environmental friendliness. The NIST Database 4, also called the NIST Thermophys ical Properties of Hydrocarbon Mixtures Database or SUPERTRAPP is used to calcula te property data for the working fluids. This database includes a properties subroutin e source code, which was adapted for use in cycle simulations. Properties were available in this database for a majority of the candidate fluid pairs that were identified. A list of the fluids considered for initial study is given in table 5.1. To determine the performan ce of the cycle with a given working fluid pair, the performance of the cycle was optimized using that pair as the working fluid. After studying initial optimization and simulation results, the list of working fluids was extended such that higher efficiencies are obtained. When picking the working fluid components for this cycle, it is important that the low boiling component be volatile. If the low boiling component is not volatile,

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88 Table 5.1 List of Working Fluids Considered Initially No. Fluid Mol. Wt. Tm (K) Tb (K) Tc (K) pc (MPa) 1 water 18.02 273.15 373.15 646.99 22.06 2 ammonia 17.03 195.3 239.85 405.5 11.35 3 methane 16.04 90.7 111.6 190.5 4.60 4 ethane 30.07 90.3 184.5 305.4 4.88 5 ethylene 28.05 104 169.4 282.3 5.04 6 propane 44.10 85.5 231.0 369.8 4.25 7 propylene 42.08 87.9 225.3 364.8 4.601 8 n-butane 58.12 134.9 272.6 425.1 3.78 9 isobutane 58.12 134.8 261.4 407.8 3.63 10 n-pentane 72.15 143.15 309.25 469.7 3.36 11 cyclopentane 70.13 179.3 322.4 511.7 4.51 12 n-hexane 86.18 178.15 342.15 507.7 3.01 vacuum pressures will be needed at the turbine exit in order to attain low temperatures. This is generally not desirable, since then the problem of air leaking into the system arises. The volatile component can be chosen from any of the compounds containing 1 to 4 carbon atoms in table 5.1. Methane, ethane and ethylene would not be good choices, since the vapor pressure at ambient conditions are high. The pressure needed to maintain a binary mixture containing these fluids in a liquid state in the absorber would be very

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89 large. The corresponding cycle high pressures would be large, and pressure ratios and efficiencies low. In addition, the costs of building equipment rated at the high pressures encountered would be much higher compared to other fluids. Note that these fluids also have a low critical temperature and relatively larger critical pressure, compared with the other fluids in the table 5.1. From the remaining fluids listed in the table, propane and isobutane were selected for study as the volatile component. Preliminary Simulation The basic cycle configuration shown again in Fig 5.1 was simulated using different hydrocarbon working fluid pairs selected from table 5.1. Reasonable low temperatures were only obtained using hexane as the higher boiling component. It was seen in preliminary simulations that low temperatures achievable were limited in comparison to those with ammonia-water mixtures. Therefore it was assumed that if a minimum turbine exit temperature of 285 K (12 C) was not achieved, useful refrigeration could not be obtained, for an ambient temperature of 298 K (25 C). The other assumptions used were similar to those described for ammonia-water simulations, including assumptions of isentropic turbine and pump, minimum 5 K approach and pinch temperatures in heat exchangers etc. Heat source temperatures of 360, 400 and 440 K were studied. With a search based method, it is necessary to have many feasible or near feasible initial points for the optimization. The following procedure proved to be very effective in the optimization:

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90 Fig. 5.1 Basic configuration simulated. In this configuration, the condensate from the rectifier is redirected to the absorber. 1. Run the optimization program to minimize turbine exit temperature starting from randomly chosen feasible starting points. A constraint equation was set such that the turbine exit temperature would not go below 285 K. 2. Using the termination points from simulations in the previous step, optimizations are run to maximize the exergy of cooling (), output of the cycle. This second step was used because optimizations used to minimize turbine exit temperature tend cE

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91 to terminate at points where vapor generation is also minimal, due to large rectification requirements. 3. The termination points from steps (1) and (2) can then be used as initial points for different optimizations for exergy and resource utilization efficiency. The termination points from these optimizations yield more initial points for additional optimizations. 4. Some state points in the optimum conditions from step (3) are perturbed to see if further improvement is possible. After step (1), it was concluded that sufficiently low temperatures were not achieved with pentane as the heavy component. 285 K turbine exit temperature could not be achieved using an isobutane-hexane pair for the cycle configuration being simulated. In fact, temperatures below ambient were not obtained in step (1). Optimized exergy and resource utilization efficiency are plotted for the three temperatures studied using ethane and propane as the volatile component and hexane as the second component of the binary mixture, in Fig. 5.2. The optimized exergy and resource utilization efficiencies are defined as in previous chapter, and are repeated in Eqs. (5.1) and (5.2) for convenience. () ( ) outhsinhscnetexergyEEEW,,+= (5.1) () ( ) inhscnetREEW,+= (5.2) It can be seen that the efficiencies with ethane as the volatile component are extremely low. The absorber pressure is large and the corresponding boiler pressure is also very high, while the pressure ratio obtained across the expander is small. The optimization procedure sometimes returned meaningless values since portions of the cycle entered the supercritical region. The properties program is invalid near or above critical conditions.

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92 Fig. 5.2 Optimized second law efficiencies of the combined power and cooling cycle using organic working fluid pairs A rather large amount of rectification was observed in these optimized cases. Figure 5.3 shows a different configuration for the cycle, where the reflux from the rectifier joins with the strong solution stream entering the boiler. Generally, the liquid reflux from the rectifier has a high volatile component concentration. Therefore, the advantage of the configuration in Fig. 5.3 is that the strong solution entering the boiler has a higher concentration of the volatile component. This results in larger vapor generation and consequently, an improvement in efficiency. Figure 5.4 shows the improvement obtained by using the modified configuration of Fig. 5.3. The efficiency numbers seen with organic fluid pairs considered so far are poor when compared to ammonia water mixtures. The data showed that the vapor has a lower concentration of volatile component, and significant rectification is required to obtain

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93 Fig. 5.3 Alternate configuration, where the condensate from the rectifier is mixed with the strong solution inlet stream to the boiler.

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94 Fig. 5.4 Comparison of the second law efficiency performance of the two configurations in Fig. 5.1 and 5.3, using a propane-hexane mixture as the working fluid high concentration vapor. This appears to indicate that the volatility ratio is low. In other words, more of the high boiling component tends to vaporize out initially with the volatile component. Simulation of Higher Boiling Components Higher molecular weight components were then studied with propane and isobutane (see table 5.2). These new binary components work much better in the cycle. Optimized second law efficiency results are shown in Figs. 5.5 and 5.6. The efficiency increases by selecting higher boiling components. Using propane, the second law efficiencies show an increase on moving from n-octane to n-dodecane in table 5.2, as the second component. The improvement seen rapidly diminishes and the efficiency improves very little from n-decane to n-dodecane.

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95 Table 5.2 Higher boiling components considered No. Fluid Mol. Wt. Tm (K) Tb (K) Tc (K) pc (MPa) 1 n-octane 114.23 216.3 398.8 568.9 2.493 2 n-nonane 128.60 219.6 424.0 594.6 2.288 3 n-decane 142.29 243.4 447.3 617.7 2.104 4 n-undecane 156.39 247.5 469.1 638.8 1.966 5 n-dodecane 170.34 263.5 489.5 658.2 1.824 Fig. 5.5 Optimized exergy efficiency using higher boiling non volatile mixtures

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96 Fig. 5.6 Optimized resource utilization efficiency using higher boiling non volatile mixtures The use of isobutane as the volatile component appears to give better RUE than propane. The best efficiency is seen with an isobutane-n-undecane pair. The next higher combination of isobutane-n-dodecane has slightly lower efficiencies. Comparing the results to those using ammonia-water mixtures, it is seen from Figs. 5.5 and 5.6 that the performance of the organic fluid mixtures is relatively poor. A summary of the results of optimization performed using organic working fluids in the combined power and cooling cycle are as follows: The efficiencies are much lower than those obtained with ammonia-water mixtures. Low temperatures that are obtainable are limited, compared to those using NH3-H2O mixtures. The pressure ratios across the turbine are lower.

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97 Substantial condensation occurs during rectification, which is accompanied by a large temperature drop. The concentration of vapor is extremely high at optimum conditions. The mass fraction of the volatile component in the vapor is greater than 0.99, which is higher than the concentrations seen with ammonia-water mixtures. Mixtures with heavier (higher boiling) nonvolatile fraction appear to improve performance, although the improvement is very small beyond a certain point. The optimum exergy efficiency decreases with temperature in the range studied, while with ammonia-water an optimum exists within that range. Among the combinations studied, the best efficiency was observed with a isobutane-n-undecane mixture. The pressure ratios at optimum conditions are plotted in Figs. 5.7 and 5.8. It is seen that isobutane based mixtures have higher pressure ratios. With both isobutane and propane, the combination giving higher efficiency has a greater pressure ratio. The data also shows a trend of higher boiler exit temperatures and better temperature matching in the boiler using heavier molecular weight components. The working fluid boiler exit temperature does not increase much as the source temperature is increased from 400 K to 440 K, when optimizing for exergy efficiency. This result is similar to what is seen with ammonia-water optimization when comparing the source temperatures of 440 K and 480 K. The reason for this trend is the inability to expand the high temperature fluid at the turbine inlet to low turbine exit temperatures while maintaining efficiency. Cycle parameters optimized for resource utilization efficiency do not show a good thermal match in the boiler, which is similar to the results for ammonia-water mixtures. Instead, the mass flow rate of the heat source is minimized to the extent allowed by the approach temperature constraint at the boiler inlet.

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98 Fig. 5.7 Pressure ratios at optimum exergy efficiency Fig. 5.8 Pressure ratios at optimum RUE

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99 Discussion A reason for the poorer performance seen with the organic fluids considered here appears to be lower pressure ratios. The pressure ratios seen with ammonia-water mixtures are much larger in comparison. The maximum pressure achievable at a certain basic solution concentration and heat source temperature is determined by the bubble pressure at the highest possible boiler temperature. In some cases, the turbine exit dryness constraint also limits the pressure ratio, which is not considered in Fig. 5.9. This limiting pressure ratio is plotted for two of the best performing organic fluid mixtures and for ammonia-water combination, in Fig. 5.9. It is clear that the limiting pressure ratio is much larger with ammonia-water mixtures. The limiting pressure ratio curve for the ammonia-water mixtures also shows a large reduction from lower to higher ammonia-mass fraction in the basic solution. At lower basic solution concentrations, a higher pressure ratio is achievable. However, vapor generation and the ammonia concentration in the vapor might be limited at the lower absorber pressures. When the cycle is operated to obtain refrigeration, there are several tradeoffs that come into play during operation. The low pressure has to be small enough that the vapor remains relatively dry at the cold temperature condition at the turbine exit. Therefore, the vapor in the turbine has to be rich in the volatile component to produce refrigeration. A higher concentration of the basic solution (larger absorber pressure) would allow more vapor generation since there is more volatile component present, but the purity required in the vapor is larger since the dryness constraint could be violated at the pressures and temperatures of the turbine exit. Further, for higher mass fractions in the absorber, the

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100 Fig. 5.9 Maximum (limiting) pressure ratio using some working fluid mixtures at various basic solution concentrations in the absorber and using a 360 K heat source limiting pressure ratio is lower which affects the temperature drop that could be achieved. The temperature drop of the vapor on expansion over a certain pressure ratio is a property of the fluid. If the temperature drop is not large, the rectification may be used to lower the turbine inlet temperature such that the desired cold temperature is reached at the turbine exit. Factors Affecting Cycle Performance A general discussion on the effect of mixture properties and some cycle parameters on the behavior of the cycle follows. Rectification A common characteristic in all optimized results is the requirement of rectification where the vapor is partially condensed resulting in a drop in temperature of the vapor

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101 going into the turbine (assuming no superheating). Rectification increases the concentration of the vapor such that the mass fraction of the volatile component is larger. Figures 5.10 and 5.11 show on a phase diagram, some of the state points of the cycle optimized for exergy efficiency, using a mixture of isobutane and n-decane as the working fluid. The heat source fluid inlet temperature is 400 K. Figure 5.10 consists of two sets of bubble and dew point lines, corresponding to the system high and low pressure. Several horizontal lines indicating the temperature at different points in the cycle are drawn on the plot. The point at which the absorber temperature line intersects the low pressure bubble point curve (location 1) determines the strong solution concentration. When this solution is heated to the boiler exit temperature (location 2), the point at which the boiler temperature line intersects the high pressure dew point curve gives the equilibrium vapor concentration. A partial condensation process (rectification) would result in a higher concentration vapor (location 4), which can then be expanded to low temperatures. Figure 5.11 shows a portion of Fig. 5.10 in more detail. If no rectification were to be done, the vapor exiting the boiler would expand through the turbine to the low pressure at condition 5'. Rectification allows the expansion to condition 5, which is at a much lower temperature. Rectification reduces the temperature at the turbine inlet which produces lower temperatures at the turbine exit when expanded over the allowable pressure ratio. Boiler Conditions Vapor produced in the boiler should be of high concentration so that rectification required is small. Rectification is an additional process that involves irreversibility and lowers the amount of vapor available to spin the turbine. Minimizing the need for

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102 Fig. 5.10 Phase diagram of a part of the cycle using isobutane-n-decane at 400 K, optimized for exergy efficiency Fig. 5.11 Close up of a portion of Fig. 5.10

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103 rectification will improve the efficiency of the cycle. For a given concentration of the basic solution (also called strong solution) and boiler pressure, a higher vapor fraction in the boiler results in vapor with a lower concentration of the volatile component, requiring more rectification. The influence of the vapor fraction on the exergy efficiency can be explained from the efficiency definition in Eq. (5.1). Since the contribution of the cooling component is small, consider the approximate expression given below. () ( ) outhsinhsnetexergyEEW,,n (5.3) This can also be written, on the basis of Fig. 5.1 as () ( ) outhsinhshsexergymhhm,,988 n (5.4) Here is the specific exergy of the heat source fluid. In the optimized case, the goal is to maximize the numerator while minimizing the denominator. The work output requires large vapor flow rate and enthalpy drop across the turbine. Specific enthalpy drop across the turbine for a given working fluid is a strong function of the pressure ratio in the cycle. The low pressure is governed by the absorber temperature and strong solution concentration. The high pressure is limited by the heat source inlet temperature and the basic solution concentration and the resulting ability to produce vapor. The vapor mass flow rate is a function of the heat source temperature, strong solution concentration (mass fraction), system high pressure and rectifier exit temperature. In the denominator, a large heat source flow rate generally results in a smaller specific exergy drop for the fluid. Naturally a tradeoff exists, where at optimum conditions, a small heat source flow rate is desirable, along with a moderate temperature drop in the heat source fluid.

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104 The effect of vapor fraction in the boiler can be qualitatively analyzed by considering the cycle shown in Fig. 5.1. A part of the strong solution is boiled to produce vapor and hot weak solution. A portion of the heat supplied in the boiler is utilized in generating vapor. The remaining heat is used to raise the temperature of the solution. This heat is subsequently recovered in the solution (recovery) heat exchanger, and used to preheat the strong solution. If the vapor fraction in the boiler is very low, the fraction of heat transferred to the vapor is low. Since it is the vapor that expands through a turbine to produce work, the cycle efficiency is smaller under these conditions. A reasonably high vapor fraction is required to get good efficiencies. Basic Solution Concentration Figure 5.12 shows the effect of a lower pressure on the low temperature achievable in a cycle. The T-x diagram shows the optimized case obtained using a propane-n-hexane mixture with the heat source at 400 K. The low pressure was 3.45 bars (0.345 MPa). The bubble and dew point curves for 3 bar (0.3 MPa) are also shown in the figure. The vapor leaving the turbine is at location 5 in figure, under optimized conditions, with a 285 K limit imposed for refrigeration at turbine exit. If the low pressure was 3 bars, it can be seen that: A lower turbine exit temperature would be achieved (5'). Note that propane is a wetting fluid, unlike isobutane. The basic solution concentration would be lower (1'). The vapor fraction produced would be lower Pressure and Temperature Ratio The temperature drop across a turbine is determined by the pressure ratio. The pressure ratio is also a measure of specific work output in the turbine. A qualitative

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105 Fig. 5.12 Effect of low pressure (propane-hexane mixture as working fluid) understanding of achievable temperature drops with pressure ratios can be obtained by considering perfect gas behavior. Assume that the vapor is superheated throughout the expansion process and also that the vapor behaves as a perfect gas with constant specific heat in the expander. These assumptions are not really valid for the results discussed in this dissertation. Superheating at optimum conditions is seen only in few of the ammonia-water mixture optimized results. Since the vapor is in or close to the two-phase region during expansion, perfect gas behavior is not expected. The relatively small temperature range considered here does support the assumption of constant specific heat. For a perfect gas, the change in entropy can be related as () (121212lnlnppRTTcssp= ) (5.5)

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106 For isentropic expansion, it is easily seen that pcRppTT=1212 (5.6) The non-dimensional term, pcR is a predictor of the ability to obtain low temperatures at the turbine exit with reasonable pressure ratios. Table 5.3 gives a list of fluids and the temperature ratio that would be obtained for certain pressure ratios. Table 5.3 Calculated R/cp values for certain gases in the temperature range of the cycle being studied Gas cp (J/mol.K) R/cp water (steam) 37.1 0.2243 ammonia 36.5 0.2275 air 29.4 0.2827 ethane 58.1 0.1431 propane 92.9 0.0895 isobutane 116.2 0.0715 It is seen that for the same pressure ratio, organic working fluids have a much smaller temperature ratio. The optimum pressure ratio is limited by several factors. The system high pressure is limited by the heat source temperature and the basic solution concentration. The low pressure is limited, once again by the heat source temperature and the high pressure, since if the pressure is too low, the basic solution concentration is also lowered. This increases the bubble point in the boiler and limits the vapor fraction.

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107 Fig. 5.13 Calculated isentropic temperature ratio as a function of pressure ratio using perfect gas assumptions Another factor limiting the pressure ratio is the tendency to form wet vapor. Certain fluids tend to go into the two-phase region during expansion. While this is not a constraint for the organic fluids considered here, it is definitely a limiting factor for ammonia. The constraint setting dryness at the turbine exit is never at the bound in any of the organic fluid simulations. That is not the case in simulations with ammonia-water. The temperature drop during expansion in the two-phase region for a binary mixture is difficult to study analytically. For pure components, the Clausius-Clapeyron equation (Eq. 5.5) relates temperature change to pressure change in the two-phase region.

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108 fgfgsatsvdpdT= (5.7) A higher ratio of specific volume change to entropy change would be desirable for the volatile component used in the cycle. Volatility Ratio The shape of the bubble and dew point curve plays a role in the efficiency that can be obtained using a certain working fluid pair in the combined power and cooling cycle. The difference in boiling points of the two fluids is a parameter that would clearly affect the shape of the curve. Another measure of the shape of the diagram is the volatility ratio. The volatility ratio is defined as [55] fgfgfgfgxxxxyyyy1122112221== (5.8) Here 21 is the volatility ratio of component 2 of the (binary) mixture with respect to component 1. This is defined as the ratio of the mole fraction y (or mass fraction x) of the components in the vapor and liquid phases. In general, the volatility ratio is a measure of the shape of the vapor liquid equilibrium (VLE) curves. Pairs with a higher volatility ratio will boil off more of the volatile component than the higher boiling component. Similarly, during condensation, the non volatile fluid will condense out more easily. The volatility ratio as defined in Eq. (5.8) is an inconsistent factor. The volatility ratio changes with temperature between the bubble and dew points. The definition given here would give a single value at a given pressure only if the bubble and dew point curve can be fitted to exponential functions. Most binary pairs do not fit that description. It is therefore not easy to use this definition to compare working fluids. Table 5.4 lists the

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109 volatility ratio of some pairs of working fluids considered. The evaluations in this table were done at the pressure corresponding to the optimum efficiency at 400 K and at the average of the bubble and dew point temperatures corresponding to a concentration of 50% by mass. Among the components listed in Table 5.4, for a given volatile component, the absorbent pair with a higher volatility ratio performs better. However, with isobutane as the volatile component, there was a drop off in efficiency between using n-undecane and n-dodecane. Therefore, there may be a point where the high volatility ratio is not advantageous anymore. Table 5.4 Volatility ratio of selected pairs Volatile Absorbent 21 Pressure bars ammonia water 17.0 20.0 propane hexane 16.9 7.0 propane decane 62.8 15.8 isobutane hexane 6.1 6.6 isobutane decane 71.3 5.3 Liquid Formation During Expansion The slope of the dew point intercept on a T-s projection of the phase diagram would determine the tendency of the working fluid to form liquid during isentropic expansion. In the literature, a factor known as the I factor is used to determine the

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110 tendency of the (pure) working fluid to form liquid during isentropic expansion. The non-dimensional quantity, I is defined as [50, 51]: ....11vapsatvapsatpdhdsTcTdTdsI== (5.7) The factor has a small dependence on the temperature at which it is evaluated. Nevertheless, the I value gives a fair idea of the wetting tendency of the fluid. The tendency of a working fluid to enter the two phase region can be determined from the slope of the line partitioning the vapor and two phase region in the T-s diagram. Table 5.5 I values of certain pure components at 300 K and corresponding saturation pressure Fluid Index I Evaluated at 300 K Water 3.10 Ammonia 4.55 Propane 1.21 iso-butane 0.82 n-hexane 0.74 A value of I greater than 1 means that the fluid becomes wet on isentropic expansion. If I is less than 1, the vapor is always superheated at the turbine exit. It is seen that the hydrocarbon working fluids considered here have small values of I, while ammonia and water have values that are substantially larger than 1. Ammonia has a relatively larger tendency to form liquid in the turbine. Hydrocarbons therefore can be expanded over a larger pressure ratio in the turbine without the two-phase region being a

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111 problem. Ammonia and water are highly wetting fluids compared to the organic working fluids considered here. There is an interesting aspect of binary mixture wetting behavior that was observed using the properties programs. The wetting tendency of the fluid changes with even a small amount of non volatile component present. This is particularly pronounced when the difference in boiling points is very high. Figures 5.14-5.17 show the projection into the T-s plane of the bubble and dew point of three organic fluid pairs and the ammonia-water pair. The change in the slope of the vapor dome is clearly seen. Figure 5.15 shows how a non-wetting isobutane mixture becomes wetting with small amounts of n-undecane. Note that due to the concentrated nature of the vapor, the dryness fraction would remain high even if all of the higher boiling component condenses. Fig. 5.14 T-s diagram for concentrated propane-n-undecane mixtures

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112 Fig. 5.15 T-s diagram for concentrated isobutane-n-undecane mixtures Fig. 5.16 T-s diagram for concentrated propane-n-hexane mixtures

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113 Fig. 5.17 T-s diagram for concentrated ammonia-water mixtures Conclusions It is shown that organic working fluids can be used in a combined power and cooling cycle. Based on the optimization studies, ammonia-water mixtures give better efficiencies when used in the cycle, as compared to a mixture of organic working fluids. The low temperature range that can be achieved using these mixtures is also limited, when compared with the ammonia-water pair. These fluids have a large molar specific heat cp that limits the ability to get low temperatures over reasonable pressure ratios. Therefore, substantial rectification is required in order to get purer vapor and lower temperatures at turbine inlet to get sufficiently low temperatures. In the organic fluid mixtures considered, isobutane

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114 performs better as the volatile component that propane. A higher volatility ratio of the mixture appears to improve the performance in the cycle.

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CHAPTER 6 RESULTS AND DISCUSSION: IMPROVED CONFIGURATIONS Motivation Optimization results of the cycle using the basic configuration given in Fig. 4.1 clearly show that the basic cycle configuration has some limitations. At conditions giving maximum RUE, there is a large unutilized fraction of heat source exergy lost due to the inability of the cycle to remove heat from the source fluid. This leads to low values of resource utilization efficiency. The optimum exergy efficiencies obtained using the cycle are reasonably good. In order to improve the performance of the cycle, modifications to the basic cycle configuration were proposed to utilize the available energy better. Various configurations were modeled and optimized using ammonia-water mixtures as the working fluid. Some of the combinations showed improved efficiencies, particularly with respect to resource effectiveness (RUE). The assumptions used for all the optimization in this chapter are similar to those described in Chapters 3 and 4. Isentropic efficiencies were assumed for the turbine and pumps. A turbine exit temperature upper limit of 270 K was set for all simulations. Reflux Mixed with Boiler Inlet A slight improvement in efficiency can be achieved by modifying the configuration such that the condensate from the rectifier mixes with the strong solution stream entering 115

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116 Fig. 6.1 Modification of the basic cycle configuration which has the liquid condensate from the rectifier mixed with the strong solution at the boiler inlet the boiler. This configuration is shown in Fig. 6.1. The condensate from the rectifier is richer in ammonia content compared to the strong solution stream. Therefore it is possible to increase the concentration of the boiler inlet stream by this mixing process. A higher concentration results in a higher vapor fraction in the boiler. Note that in the configuration shown in Fig. 6.1 pressure drop between the boiler inlet and the rectifier is neglected. In reality, a pressure drop will exist and some sort of pumping arrangement

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117 will be needed to get the liquid from state 5 to mix with streams 13 and 14. There are other alternate designs that can be used in practice to approximate this configuration. The improvement in RUE seen with this modified configuration is small. However, exergy efficiencies improve noticeably (see Fig. 6.2). The improvement seen is larger at the higher heat source temperatures of 440 and 480 K. At these temperatures, the base cycle configuration shows a limited increase in boiler exit temperatures (from the 400 K case) and a larger rectification requirement. This results in lower exergy destruction in the boiler (hear addition) due to better thermal matching, as shown by comparing Figs. 6.3 and 4.14. The boiler vapor fraction is slightly higher in the modified configuration. Fig. 6.2 Optimum exergy efficiencies obtained with the modified configuration shown in Fig. 6.1

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118 Fig. 6.3 Major exergy destruction categories for the modified cycle, at optimum exergy efficiency conditions. Addition of a Preheater Two configurations of the cycle have been discussed thus far. These are the basic cycle configuration in Fig. 4.1 and the one shown in Fig. 6.1, where the condensate from the rectifier is assumed to be mixed with the strong solution feed entering the boiler. The RUE is low in both these configurations. High RUE is important for the use of this cycle in geothermal and waste heat recovery applications. An exergy analysis has shown that the largest losses are due to the unrecovered exergy from the heat source. A slightly different configuration is shown in Fig. 6.4 that has the strong solution stream split into three parts after the system pump. One stream (2-3 in Fig. 6.4) is used to recover heat from the weak solution. The second stream (2-5) is used to recover the heat of condensation from the rectifier. The heat source fluid preheats the third stream (2-4).

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119 Fig. 6.4 Modified cycle configuration with part of the basic solution being preheated by the heat source fluid.

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120 This configuration allows the removal of more heat from the heat source at the expense of recovering heat from the weak solution, with a possible increase in optimum RUE. However, the modified configuration does not lead to an increase in the exergy efficiency. Unrecovered exergy in the heat source fluid has no influence on the exergy efficiency. Instead, it is more important to recover exergy from the weak solution in the recovery heat exchanger. This was also clear from optimization results, since the flow through the preheater was seen to be zero under maximum exergy efficiency conditions. When optimizing the cycle configuration shown in Fig. 6.4 with respect to RUE, an improvement is seen in the values. Figure 6.5 shows optimum efficiencies using a strict definition of RUE, Eq. (4.1) and an effective efficiency assuming the second law efficiency of refrigeration production to be 40 %. An improvement in efficiency is clearly seen in both cases. The resulting optimum conditions are seen to have larger absorber pressures, and higher vapor fractions in the boiler. Similarly, this configuration optimized for work output alone also performs better than the basic cycle configuration (data not shown in plots). As expected, an exergy analysis shows much lower losses through the pathway of unrecovered exergy in the heat source, while the losses associated with throttling and heat rejection increase, since all the heat is not recovered due to the lower flow. From the perspective of system design, this indicates a requirement for larger heat transfer area in the absorber. The size of the recovery heat exchanger would be smaller, but a separate preheater would be required adding to heat transfer area requirements. Jet Pump Assisted Cycle It would be desirable to have a low turbine exit pressure order to have higher pressure ratio and temperature drop through the turbine. However, higher absorber

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121 Fig. 6.5 Optimized RUE for the modified configuration in Fig. 6.4 compared to the base configuration in Fig. 4.1 Fig. 6.6 Major exergy losses in different parts of the modified cycle, optimized for RUE

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122 pressures are desirable so that the basic solution mass fraction is high resulting in higher vapor flow rates. All the cycle configurations studied so far have the absorber pressure set to be the same as the turbine exit pressure. In practice, taking into account pressure drops in the system, the absorber pressure would be a little lower than the turbine exit pressure. One of the ways of boosting the absorber pressure above turbine exit would be to use a jet pump to raise the pressure of vapor leaving the turbine. The high pressure liquid returning from the boiler to the absorber would be the high pressure primary fluid that is used to raise the pressure. The advantages of using a jet pump in the combined power and cooling cycle are the following: The expansion in the turbine can be carried out to a pressure lower than the absorber pressure. Higher absorber pressures allow for lower bubble points of the strong solution and larger vapor fractions in the boiler. Lower rectification would be required to achieve lower temperatures. The vapor will be well mixed and entrained in the liquid in the form of small bubbles. This will simplify the design of the absorber condenser substantially. Jet Pump Background Jet pumps and ejectors are a class of fluid pumping devices that have been studied for a number of years. In a jet pump, a high pressure primary fluid is expanded through a primary nozzle. At the low pressure region after the primary nozzle exit, a secondary nozzle is used to introduce the secondary fluid. A mixing section follows in which momentum and kinetic energy is transferred from the primary fluid to the secondary fluid and the secondary fluid is properly entrained and mixed in the primary fluid flow. A diffuser is then used to raise the pressure of the mixture. The primary and secondary

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123 fluids could be any combination of liquid, gas, or a two-phase mixture. An ejector is a term that generally refers to a device where both the primary and secondary fluids are gases. There are several well known applications of jet pumps and ejectors. In steam jet refrigeration, water is used as the working fluid. High pressure steam is used as the primary fluid in an ejector to compress the water vapor from the evaporator. Jet pumps are also used to create and maintain vacuum in several chemical operations such as distillation and evaporation and to remove accumulated non-condensable gases from steam power plant condensers. Ejectors are also found in jet propulsion systems such as an ejector ramjet type engine. The use of jet pumps, ejectors or similar devices have been suggested also been suggested in power and refrigeration cycles. Different configurations have been investigated [56], which involves using ejectors in ammonia water mixture based absorption refrigeration cycles. Nord et al. [57] discuss a combined power and cooling cycle, primarily for space applications that uses a jet pump. A patent search showed an idea very similar to the one being studied in this section. The patent [58] proposes the use of a device called a hydrokinetic amplifier, which somewhat resembles a jet pump, in absorption refrigeration cycles and power cycles. Unfortunately, there is no other literature or operational data available on this device or its application to ammonia-water based cycles. Jet Pump Analysis It is proposed that the liquid weak solution from the boiler be used as the primary fluid in the jet pump. Simulation results indicated that the subcooled weak solution that has given up heat in the recovery heat exchanger does not provide much of a pressure boost. The hot, saturated weak solution works best for that purpose. The secondary fluid

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124 is the low-pressure vapor exiting the refrigeration heat exchanger. The primary fluid is accelerated through a nozzle in order to achieve a higher velocity. This high speed primary fluid exits the nozzle with a large velocity and low static pressure. At this point, the secondary fluid (ammonia rich vapor) is introduced through a secondary nozzle into a mixing chamber. The secondary fluid is entrained in the primary fluid jet inside the mixing chamber. Mixing chambers are generally classified as two types, even though many mixing chamber geometries do not fit either category. These are the constant pressure type and constant area type mixing chambers. Within the mixing chamber, the secondary fluid is entrained in and accelerated by the primary jet. There is a transfer of momentum and kinetic energy from the primary jet to the secondary fluid. Assuming the mixing chamber is long enough, it is reasonable to say that the two streams are completely mixed at its exit. Fig. 6.7 Schematic drawing of a jet pump showing the different sections and the flow through it The mixed stream subsequently enters the diffuser where the flow is slowed down and kinetic energy is used to compress the mixture. This compressed mixture would then be routed to the absorber-condenser where heat is removed from it and the vapor condenses back into the liquid.

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125 The analysis presented here discusses the operation of a jet pump, as a part of the (ammonia-water based) combined power and cooling cycle. The model presented here is that used by Sherif et al. [59]. This model is then further simplified for use in the simulations. An ideal nozzle would be modeled as an isentropic device. To incorporate losses, an isentropic efficiency is assumed for the nozzle. Since the primary fluid is a saturated binary liquid mixture, several issues become important in the analysis. As the pressure drops within the nozzle, the fluid in the nozzle begins to vaporize accompanied by a drop in the temperature of the fluid. Since, the speed of sound in a two-phase mixture is significantly lower than that in a liquid there is a possibility that sonic conditions could be achieved within the nozzle. In this case, the nozzle would have to be designed as a converging diverging nozzle in order to achieve the desired pressure at the nozzle exit. For analysis purposes, the flow would also have to be assumed to be homogeneous. In other words, the gas is evenly distributed in the liquid phase or vice versa. Choking at the nozzle throat would also limit the achievable mass flow rate in a given nozzle geometry. The nozzle would have to be suitably designed in order to accommodate the design mass flow rate of primary fluid in the cycle. In the mixing section, the primary and secondary streams mix and exchange momentum and kinetic energy. Since the volume of liquid is very small in comparison to the volume of vapor, it is assumed that the liquid would be finely dispersed as droplets within the vapor at the mixing section exit. The mixture then enters the diffuser where the velocity is slowed down accompanied by an increase in pressure, and partial condensation of some vapor back

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126 into liquid. If the flow in the mixing chamber is supersonic in nature, a shock wave can be expected at or close to the diffuser entrance. Since the pressure at the diffuser exit will be much lower than that of the primary fluid entering the nozzle, condensation is not expected to be significantly large. Further, the binary mixture nature of the fluid also implies a lack of a sharp phase transition. Therefore, the phenomenon of condensation shock is not expected within the diffuser. Equations that describe the behavior of the jet pump are discussed below. The flow is assumed to be one dimensional, and homogenous at every point that a two phase mixture is analyzed. Primary nozzle In the ideal case, the nozzle is treated as an isentropic expansion device without any losses. If the occurrence of supersonic conditions were not a concern, the expansion through the nozzle would be treated as an isentropic process. The equations that need to be satisfied are the continuity and energy relationships. Continuity: nonononininiAVAV f f = (6.1) Energy: 222121nononiniVhVh+=+ (6.2) Isentropic Condition: (6.3) noniss= Knowing the exit pressure condition, and assuming an isentropic process, the remaining state properties can be calculated. The resulting enthalpy and density values should satisfy the continuity and energy equation respectively. An iterative process might be required to determine the nozzle design. The speed of sound in a two-phase mixture can

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127 be very low. For example, the speed of sound in a 50-50 volumetric mixture of air and water is 1.5% of the speed of sound in water, and 6.8% of the speed of sound in air. That fact should indicate the possibility for sonic conditions being achieved in the nozzle. Therefore, it would be more likely that the nozzle is a converging diverging nozzle that will have to be analyzed in two sections. From the inlet to the throat and from the throat to the nozzle outlet. The fundamental equations are the same. ntntntnininiAVAV f f = (6.4) 222121ntntniniVhVh+=+ (6.5) (6.6) ntniss= In addition, the condition for choked flow at the nozzle throat applies, which means that the Mach number at the throat is unity. The local speed of sound at the throat is calculated as: sntpa=f (6.7) 1==ntntntaVM (6.8) Obviously, this condition limits the mass flow rate through a given throat cross-sectional area. The throat to nozzle outlet calculations can be performed easily assuming isentropic expansion. It would be reasonable to assume that the flow would not revert to subsonic conditions within the nozzle. From the energy equation, it can be seen that the change in enthalpy of the fluid through the nozzle is converted to a gain in the kinetic energy of the weak solution.

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128 Secondary nozzle The low pressure secondary fluid, which in this case is ammonia rich vapor from the refrigeration heat exchanger is introduced via a secondary nozzle into the mixing section entrance of the jet pump. An isentropic assumption allows for the calculation of the condition of the secondary fluid at the mixing section inlet. The pressure is assumed to be the same as the primary nozzle outlet pressure. sosososisisiAVAV f f = (6.9) 222121sososisiVhVh+=+ (6.10) (6.11) sosiss= Mixing section The mixing section is probably the most critical of all the components of a jet pump. There are two standard configurations that are assumed while modeling jet pumps in the literature. A constant area mixing section that has a uniform cross sectional area and a constant pressure mixing section which is shaped such that the pressure is constant throughout the mixing section length. Obviously, a constant pressure mixing section would be more difficult to design in practice. The primary fluid jet that enters the mixing section would start breaking up after a few diameters past the nozzle at its edges. Viscous interaction at the boundary of the primary jet and the secondary stream would entrain some of the secondary fluid into the flow. The jet would start breaking up at the boundaries. After a sufficient length of flow, one would expect to see a completely mixed flow. One concern is the occurrence of what is called Fabri choking in the mixing section. For the case where there is a very small viscous interaction between the primary

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129 and secondary streams, as the primary flow from the nozzle expands in the mixing section, the available flow area for the secondary flow reduces. It then becomes possible that the secondary flow would get choked, limiting the entrainment ratio achievable with a given jet pump/ejector. The fluid that exits from the nozzle is a mixture of vapor and saturated liquid. It is assumed that the temperature difference between the secondary and primary streams is small enough not to have a significant effect on the liquid vapor equilibrium. For the constant pressure case, it is reasonable to assume that there is no condensation in the mixing section. For the constant area case (or in general, for all mixing sections excluding the constant pressure type), a rise in pressure would result in some condensation accompanied with a temperature rise. To model the mixing section the following equations are used. Define the mass entrainment ratio as: psmm=r (6.12) Equations of mass conservation, momentum and energy have to be solved in conjunction with the equation of state (properties correlations) to determine conditions at the mixing section exit (6.13) ()momomopVApm=r+1 (6.14) ()sopnopmopmomososononoVmVmVmApApAprr+=+1 () +r+=+r++2222112121momososononoVhVhVh (6.15) For the constant pressure case, the exit pressure is known while for the constant area solution, a value of pressure would have to be assumed and iterated until convergence. Notice that the analysis above assumes that the flow is completely mixed

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130 at the mixer exit. The mixing section would have to be long enough for this to be accomplished. It has been experimentally verified for the case of LJG (Liquid Jet Gas compression) pumps that if mixing continues into the diffuser, there is degradation in the performance of the jet pump [60]. Diffuser There is a very high chance that the flow at the diffuser inlet is supersonic, especially since it would be a relatively homogeneous mixture of liquid and gas. As this flow is decelerated to subsonic speeds, there is a good possibility of a shock wave developing. In practice, there are two ways that a supersonic mixture could be dealt with in a diffuser. Case a: The diffuser inlet could be set to supersonic mixer exit conditions. An isentropic process is assumed. This is called the second solution of the diffuser flow problem. Operation in such a mode, while theoretically and experimentally possible, is very difficult. This is due to the stringent requirements on the geometry of the diffuser and the need for specific inlet conditions for the diffuser. Case b: A more common solution, called the first solution assumes shock at the nozzle inlet. The Rankine-Hugoniot equations are used to model shock. The equations then would be as follows. ssssmomoVV f f = (6.16) (6.17) 22ssssssmomomoVpVpff+=+ 222121ssssmomoVhVh+=+ (6.18) (hp, ) f f = (6.19)

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131 Once the conditions after the shock are determined, isentropic assumptions can be used to determine the conditions at the diffuser exit. Simplified Model Used in Simulation For the purposes of integrating a jet pump with the cycle simulation, a more simplified model is used, which does not involve as many parameters as in the model discussed above, and is free of dimensional information about the jet pump. The simplified model assumes the following 1. The effect of choking in the primary nozzle is neglected. The nozzle is modeled with an isentropic efficiency of 0.6. Nozzles are generally efficient devices. The low isentropic efficiency assumed is in order to compensate for assuming an ideal mixing section. 2. The pressure drop in the secondary nozzle is neglected. 3. Mixing section is assumed to be without any losses. In general, the process of mixing usually is where the most losses occur in a jet pump. This section has a high speed jet mixing with and entraining the secondary flow. Although the momentum transfer is relatively efficient, the transfer of kinetic energy between the streams is not. Mixing losses are lumped with the primary nozzle isentropic efficiency. 4. Shock at the diffuser inlet is ignored. The diffuser is modeled using an isentropic efficiency of 0.8. This model is somewhat similar to assuming an expander-compressor tandem operating to expand the primary stream and compress the mixed primary-secondary streams. Jet pumps are normally low efficiency devices. The assumptions above imply a total efficiency of 0.48 for the jet pump, which might be a slightly optimistic assumption. Efficiencies of up to 0.40 have been reported for liquid-air jet pumps [61].

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132 Fig. 6.8 Cycle configuration incorporating the jet pump Results It was observed that the pressure improvement observed with LGJ pumps, where the weak solution, after heat recovery is used to pressurize the gas; was very small. Looking at the volumetric entrainment ratio and comparing with data from the literature

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133 and that for commercially available jet pumps, it was determined that the ratio in our case is too large to give a useful pressure increase. Another alternative is to use the high temperature saturated weak solution leaving the boiler/separator as the primary fluid. The process of expansion through a nozzle will result in a high velocity two-phase mixture leaving the primary nozzle. Simulating this case produces a larger pressure boost. A disadvantage here is that the preheating of the strong solution prior to the boiler is mostly done by the heat source. Therefore, while improved resource utilization efficiencies can be achieved, the exergy efficiency does not improve Maximizing resource utilization efficiency results in a small improvement. The results of simulations using a non isentropic turbine and pump are shown in Fig. 6.9. It is seen that the improvement is larger at heat source temperatures of 400 K and 440 K, while at 480 K, there is actually a decrease in efficiency by using a jet pump. Since the jet pump is an inefficient device, it appears that it is more effective to recover the exergy in the hot weak solution through the recovery heat exchanger than to use it in the jet pump to compress the vapor exiting the turbine. Optimizations performed using higher, and possibly unrealistic efficiency for the jet pump show a dramatic improvement in resource utilization efficiency at all temperatures. Further, since the jet pump allows a lower turbine exit pressure at a given absorber pressure, the extra work is obtained by additional expansion in the turbine. The limits set on low temperature at the turbine exit also influence efficiency, as seen in Fig. 6.10. Higher vapor concentrations and/or lower turbine exit pressures are needed for achieving lower temperatures. A higher low temperature allows larger turbine exit pressures and even higher absorber pressures.

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134 Fig. 6.9 Improvement in resource utilization efficiency with the addition of a jet pump. Fig. 6.10 Influence of the choice of turbine exit temperatures on the improvement achievable with a jet pump using an isentropic turbine and pump.

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135 Conclusions A jet pump used in the cycle as shown in Fig. 6.8 will improve the efficiency of the cycle at certain heat source temperatures. Two important factors affecting the improvement are the efficiency of the jet pump and the efficiency of the turbine being used. Jet pumps are low efficiency devices and contribute substantially to losses in the cycle. The fluids considered here for use in the jet pump are parts of a miscible refrigerant-absorbent pair. The primary fluid is in fact a binary mixture. More work and experimentation are required in order to estimate the performance of a jet pump with this combination better. The addition of a preheater to the basic cycle configuration, discussed in the previous section, gives a larger improvement in efficiency than with using a jet pump. Other configurations that have some separation between the absorber and turbine exit pressures are discussed in the following section. Distillation (Thermal Compression) Methods The use of a jet pump in the cycle showed that separation of absorber and turbine exit pressures results in improvement in RUE of the cycle. Due to the low efficiencies of the jet pump, the RUE does not improve much with that device used in the cycle. There is another method described in the literature, that can be adapted to achieve a similar effect as with the jet pump. In the first Kalina cycle that was proposed [20], a distillation arrangement was described in which hot vapor from the turbine exhaust is used in a distillation column. The vapor generated in the distiller is used to increase the concentration of the strong solution going to the boiler. In this configuration, the turbine exit pressure does not directly limit the strong solution concentration. This method has been called a thermal-compression method in some papers.

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136 Two different configurations are discussed below that incorporate the thermal compression feature in the combined power and cooling cycle. Since the cycle has cold vapor at the turbine exhaust, the vapor cannot be used as a source of heat in the distiller. Two different configurations are discussed below. In the first case, the heat source fluid is used to produce vapor in the distiller. In the second case, the weak solution and vapor streams are mixed and the heat of condensation of the resulting mixture is used to produce vapor in the distiller. Using Heat Source The configuration of the cycle discussed in this section is shown in Fig. 6.11. This configuration has some additional components when compared to the basic cycle configuration. There is an extra absorber, an additional recovery heat exchanger and a distillation column. Some of the ammonia-water mixture in the low pressure absorber is pumped into the high pressure absorber at a slightly higher pressure. The remaining solution is sent to the distiller where the heat source is used to boil off a fraction into vapor that is rich in ammonia. This vapor is routed into the high pressure absorber where is it recombined with the solution pumped there. The resulting solution in the high pressure absorber has a higher mass fraction of ammonia. This high concentration strong solution is partially vaporized in the boiler. The higher mass fraction of ammonia in the strong solution entering the boiler results in a higher vapor fraction. The distiller portion also helps in extracting more energy (and exergy) from the heat source. Consequently, the exergy lost in the heat source leaving the cycle is lower. The pressure difference between the LP and HP absorbers results in a higher pressure ratio in the cycle. The extra expansion possible permits lower temperatures at the turbine exit and more work output in the turbine.

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137 Fig. 6.11 Cycle configuration using the heat source to produce vapor in the distiller

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138 The optimized RUE values obtained using this cycle configuration are plotted in Fig. 6.12. Three cases are plotted. One case uses a definition of effective RUE with a second law efficiency of refrigeration of 100%. The second case uses a second law efficiency of refrigeration of 40%. The third efficiency that is considered is the case where only work output is considered (work domain). Corresponding maximum efficiencies of the basic cycle configuration are also plotted for comparison. The modified configuration greatly improves the optimum RUE of the cycle, with the largest improvement being at lower heat source temperatures. Once again, the optimum RUE in the work domain is substantially higher. The first law efficiency of the modified cycle at optimum RUE conditions is plotted in Fig. 6.13. Comparing with Fig. 4.20 in chapter 4, it is clearly seen that the first law efficiency improves significantly over the basic cycle configuration.. The exergy destruction through major processes in the cycle in the cooling and work domain is shown in Figs. 6.14 and 6.15 respectively. Comparing Figs. 4.13 and 6.14, it is evident that the loss through unrecovered exergy is much lower in the modified configuration. The losses through heat rejection in the absorbers are higher in comparison. This can be explained by the fact that the amount of heat addition is larger, since the heat source provides heat in both the boiler and the distiller. Therefore, there is larger heat rejection in the absorber. The exergy destruction in the boiler itself is lower in the modified configuration, since the higher strong solution concentration and resulting larger vapor fractions result in higher boiler exit temperatures and better thermal matching in the boiler. However, the irreversibility of heat addition, including the distiller, is higher in the modified cycle.

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139 Fig. 6.12 Maximum RUE of the cycle configuration modified with heat source fluid powered thermal compression modification Fig. 6.13 First law efficiency at maximum RUE conditions for configuration with heat source powered thermal compression modification

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140 Fig. 6.14 Exergy destruction in the cycle with heat source powered thermal compression modification, when operated to provide power and cooling Fig. 6.15 Exergy destruction in the cycle with heat source powered thermal compression modification, when operated to provide only power output

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141 Fig. 6.16 Some parameters for optimized RUE conditions in the cooling domain The vapor fractions produced in the modified configuration are plotted in Fig. 6.16, and the values are up to 3 times higher than the basic cycle configuration. Comparing Fig. 6.16 with Fig. 4.17, it is seen that the pressure ratios are also improved in the modified configuration. This is expected since the turbine exit pressure is not the same as the strong solution saturation pressure with the thermal compression scheme implemented. Figure 6.17 shows the pressure ratios and boiler vapor fractions for the optimum conditions in the work domain. The vapor fractions observed are substantially higher in the work domain, since the vapor does not have to be expanded to low temperatures and therefore can have a large concentration of water. In fact, at higher temperatures (440 K and 480 K), almost all of the strong solution is boiled off in the boiler. Since the simulation model has the boiling heat exchanger set up as a single pass

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142 Fig. 6.17 Some parameters for optimized RUE in the work domain counter current type, the higher vapor fractions may not be easily achievable in practice. The modified configuration is not suitable for improving exergy efficiency, since the increased heat addition in the distiller increases the exergy input to the cycle without a proportionate improvement in output. However, it is interesting to note that the pressures of operation for the modified cycle in the work domain are rather low. Lower pressures could translate to lower equipment costs. Using Absorber Heat Recovery The heat supplied to the distiller can come from different sources. Kalina uses the heat of condensation of the hot exhaust vapor coming out of the turbine for boiling in the distiller. This cycle, when operating in the refrigeration mode is designed to produce cold vapor through the turbine. The weak solution is one available source, but by itself

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143 does not match very well with the heating profile of the liquid entering the distiller. Some simulations were performed to confirm this. However, if the weak solution were to be mixed with the vapor, the heat of condensation of the two-phase mixture would match well with the requirements of boiling in the distiller. The challenge then is in mixing the vapor and liquid streams. A jet pump like device (without a diffuser section to slow the stream and raise the pressure) could be used to mix the two streams. Other configurations possible include absorber designs built so as to recover the heat of condensation from it. Such designs have already been developed for GAX (Generator-Absorber Exchange) type of absorption refrigeration cycles. These cycles use heat from the absorber to preheat the working fluid entering the generator (boiler). In the simulations performed for the results presented in this section, the mixing process is modeled as isenthalpic. While this may be difficult to achieve in practice, the results of these simulations give a general idea of what is achievable. A diagram of this configuration is shown in Fig. 6.18. An actual design would probably differ in some ways from the schematic presented here. The optimized RUE values are plotted for the new configuration in Fig. 6.19. As in earlier cases, the work domain gives the best results. In the cooling domain, the modified configuration shows a distinct improvement over the basic cycle configuration. While the configuration studied in the previous section has higher RUE at lower temperatures, at higher heat source temperatures, the present configuration works better. In the work domain, the optimum efficiency of the configuration using the condensing mixture as the heat source is better. However, the first law efficiency is poor and is comparable to the values obtained for the basic cycle configuration (See Fig. 6.20).

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144 Fig. 6.18 Cycle configuration using heat of condensation to produce vapor in the distiller

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145 Fig. 6.19 Maximum RUE of the cycle configuration modified with a condensing mixture providing heat of distillation Fig. 6.20 First law efficiency at maximum RUE conditions for configuration using heat of condensation to produce vapor in the distiller

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146 The exergy destruction plots once again show a much lower fraction of exergy lost in the heat source fluid leaving the boiler. In this configuration, the heat source is used to preheat a portion of the strong solution and that process lowers the temperature of the heat source exiting the cycle. The major losses are through exergy destruction in heat addition (boiler, superheater and preheater), and in the absorbers (heat rejection). In the work mode, the exergy losses due to heat addition are lower than in the refrigeration mode. This is attributable to better thermal matching in the boiler, since higher temperatures are attained at the boiler exit with the higher vapor fractions. Fig. 6.21 Exergy destruction in cooling domain in modified cycle with a condensing mixture providing heat of distillation

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147 Fig. 6.22 Exergy destruction in work domain with a condensing mixture providing heat of distillation The pressure ratios are higher in this configuration (Fig. 6.21) than in the basic cycle configuration or in the modified configuration discussed in earlier in this chapter where a preheater is added to the basic cycle configuration. The boiler vapor fraction is again high compared to the basic cycle configuration. In the work domain, the boiler vapor fraction at optimum conditions approaches unity at 440 K and 480 K. This means that there is no weak solution reflux stream returning from the boiler. Consequently, the cycle configuration becomes similar to the basic Kalina cycle configuration (Fig. 1.3). Once again, the question of once through boiling of all of the strong solution arises. It remains to be seen if that can be accomplished effectively.

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148 Fig. 6.23 Some parameters for optimized RUE (strict definition) in the cooling domain for the modified cycle with a condensing mixture providing heat of distillation Fig. 6.24 Some parameters for optimized RUE in the work domain for the modified cycle with a condensing mixture providing heat of distillation

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149 Conclusions Several configurations of the combined power and cooling cycle have been simulated and optimized. Most of the configurations discussed improve the RUE of the cycle. The exergy efficiency of the basic cycle configuration itself is relatively high. Most of the configurations considered did not show a better exergy efficiency. The simplest method of increasing RUE is to add another heat exchanger where the heat source is used to preheat a portion of the strong solution, before the boiler. A jet pump was added in the cycle configuration in order to use the high pressure weak solution and raise the pressure of the vapor after the refrigeration heat exchanger. Due to the low efficiency of jet pumps, the improvement seen in efficiency is small. Another means of achieving the same effect as using a jet pump is to use the distillation compression method proposed by Kalina. Two configurations implementing that method were simulated. In one case, heat from the heat source was used for the distillation, while in the other case; a condensing mixture of weak solution and vapor was used. Both methods improved RUE. When optimized to provide work output, both cycles tend to have very high vapor fractions in the boiler, especially at higher heat source temperatures. The efficiencies at maximum work RUE conditions are also much higher. The advantage of operating in the work mode is that there is no restriction on the composition of the vapor. Therefore, a large fraction of the binary mixture can be boiled off, taking advantage of the larger temperature glide available.

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CHAPTER 7 CONCLUSIONS The combined power and cooling cycle has been studied. The methodology followed for the study consists of optimizing a simple simulation model of the cycle. Four sensible heat source temperatures were studied that covered the range of low to moderate temperature solar and geothermal sources. Summary of Results The work performed in this study builds on previous theoretical and experimental work on the combined cycle. The following are the contributions of this study: 1. Efficiency definitions were developed for the combined power and cooling cycle. It was shown that it is important to assign a realistic weight to the refrigeration output of the cycle, when defining the efficiency. 2. The basic cycle configuration of the cycle (see Fig. 4.1) was optimized for maximum second law efficiency. These optimizations differed from earlier work since the calculations used the new efficiency definitions, and considered isentropic efficiencies for the turbine and pump. 3. The basic cycle configuration was shown to have reasonable exergy efficiencies and poor resource utilization efficiencies. 4. The cycle was shown to have a better exergy efficiency using lower temperature heat sources, when operated to deliver both power and cooling. 5. Binary mixtures of alkanes were considered as working fluids for the combined cycle. It was shown that power and cooling could be obtained simultaneously using these fluids. 6. The organic fluids considered performed poorly compared to the original choice of ammonia-water mixtures. 7. Among the organic fluid mixtures, it was found that combinations with higher volatility ratios and higher limiting pressure ratios performed better. 8. Alternate configurations of the cycle were investigated in order to improve the RUE. 9. Configurations that decouple the absorber and turbine exit pressure were shown to perform better than the basic cycle configuration. 10. While using a jet pump to decouple the pressures had a small effect on the cycle RUE, other configurations using a Kalina thermal compression scheme performed very well. 150

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151 11. In all cases, the cycle operated in the work domain gave a higher RUE than when operated to yield simultaneous power and cooling output. A set of thermodynamic efficiency definitions was developed for this novel cycle, which has simultaneous power and refrigeration output. It has been recommended that the refrigeration output be assigned a weight that reflects the efficiency of a comparable refrigeration cycle. Efficiency definitions have been developed that are based on a second law efficiency of a comparable refrigeration cycle. The optimum parameters are found to be different when assigning a larger weight to refrigeration. The basic configuration of the cycle (shown in Fig. 4.1) was optimized for exergy and resource utilization efficiency. Since the cycle can either provide work and cooling output, or alternately simply provide work output, both cases were considered. When only providing work output, the cycle is essentially a Maloney Robertson (M-R) cycle. The configuration is different from the original M-R cycle [19] in that a superheater is added in the combined power and cooling cycle. Substantial superheating is seen in the optimized results. It is seen that based on an effective exergy efficiency, the cycle operating in the cooling mode has efficiencies comparable to the M-R cycle. Overall, while the exergy efficiencies seem reasonable, the resource utilization values are very low. The primary reason for the low RUE is the limited ability of the cycle to remove heat from the heat source. Binary mixtures of alkanes were investigated as alternate working fluids in the cycle. These fluids were selected on the basis of their previous application in organic Rankine cycles. The second law efficiencies (exergy and RUE) achievable are lower with these fluid mixtures. Further, the low temperature that can be obtained using these fluids is also limited. The temperature drop with pressure drop is higher using ammonia

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152 in a turbine. The limiting pressure ratios that can be obtained are also much higher using ammonia-water mixtures. Comparing organic working fluid mixtures, while isobutane has a lower temperature drop with pressure drop in the turbine, the limiting pressure ratios (and optimum pressure ratios) are higher. Mixtures containing isobutane give a better efficiency than mixtures with propane. A higher volatility ratio between the two components appears to be advantageous when operating in the cooling mode. Several configurations were studied in order to improve the efficiency of the cycle. A modified cycle, where a heat exchanger was used to preheat part of the working fluid stream using the heat source, while the remaining preheating was done in the recovery heat exchanger improves the RUE of the cycle. A jet pump was proposed in the cycle so that the weak solution at the high pressure could be used to compress the vapor from the refrigeration heat exchanger into the absorber. The most efficient use would have been to use a LJG compressor. Unfortunately, the liquid stream volume is too small in relation to the vapor to be compressed; in other words, the entrainment ratio is too high for a LJG pump to work. Assuming a two-phase jet pump that expands hot, saturated weak solution in the primary nozzle indicated the possibility of some improvement. The very low efficiency of the jet pumps limits the improvement substantially. Another method of raising the concentration of the working solution entering the boiler without increasing the turbine exit pressure is to use a modification of the so-called thermal compression method introduced by Kalina. Kalina uses the heat recovered from the hot vapor exiting the turbine to distil an ammonia water mixture. The distilled vapor is combined with some of the original mixture to make a concentrated solution, which is

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153 boiled and expanded in the turbine. In the cycle studied here, the vapor leaving the turbine is cold, and therefore it is unsuitable for providing the heat of distillation. The weak solution is also badly matched to the requirement of providing heat in the distiller. The cycle on the other hand is limited in the amount of heat that it is able to remove from the heat source. Therefore, using the heat source itself in the distiller is a possible source of heat. This solution improved the RUE of the cycle (while producing cooling) substantially over the base cycle values. An effective efficiency of about 39 % was obtained at 400 K heat source temperature. Another method of recovering heat in the distillation section is to use the heat of condensation from the absorber. Such a model shows a slightly improved resource utilization efficiency of the cycle. The model used for simulation assumes the condensation in a heat exchanger with countercurrent flow, of a mixture of the weak solution and the condensed vapor. Such a design may not be easy to implement in practice. The condensing vapor matches better with the boiling liquid in the distiller. Both models also show much higher RUE with pure work output. Under optimum conditions, the absorber heat recovery model begins to appear very similar to the basic Kalina cycle, with only a negligible weak solution flow from the boiler/separator. Under these conditions, where only work output is desired, these configurations appear to have the advantage of having low pressures of operation. Future Work More work is needed to better understand the performance of a power plant built on the combined power and cooling cycle. While some work is already in progress, some recommendations to extend the results of this work are presented below. The suggestions are listed and a discussion elaborating on some of these topics follows.

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154 1. The simulation study has to be extended using more realistic models incorporating losses such as pressure losses and device efficiencies. 2. Additional inputs required such as cooling fluid pumping work should be considered. 3. Cycle performance should be evaluated for the demands and conditions of some actual applications, which might be currently satisfied by other cycles, such as ORCs. 4. An economic analysis is important to determine the feasibility of actually using this cycle. 5. The search for working fluid pairs is not over. Simply pairing ammonia with a better absorbent than water might give an improved efficiency. 6. The Kalina thermal compression schemes do not show high exergy efficiency. Nevertheless, when considering the efficiency of the collector, it might prove to be advantageous in that application. This should be investigated. 7. The application of jet pumps in the cycle still holds some promise. Some work needs to be done to investigate jet pumps using the fluid combination proposed here. Some commercial products in the market may also hold promise. All the theoretical work done so far on the cycle has been on the basis of simple simulation models. While such models are useful for determining the advantages and disadvantages of different cycle configurations and an approximate idea of different parameters, more realistic models are necessary to determine the sizes of different equipment and the losses expected in the cycle. While the models consider the turbine work output and pump input, additional power consumption such as power required for circulating the cooling fluid in the absorber condenser and the heat source are not considered. Energy is also consumed in removing non-condensable gases from the absorber. This additional power consumed comes under the category of parasitic losses. While parasitic losses are small in power plants converting high temperature heat sources, they tend to become significant in low temperature power plants. Another point of concern is the size (scale) of the power plant. The scale of the project will have an influence on the selection of the expander. While steam turbines in

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155 large power plants are very efficient, at smaller sizes, the effect of losses such as blade tip leakage losses becomes larger. Efficiencies expected at smaller sizes might be smaller. In this study, the cycle is optimized from the point of view of optimum thermodynamic performance. High recovery heat exchanger effectiveness is permitted. Relatively low pinch points and approach temperature limits are assumed. It is important to recognize that the ultimate determining factor in cycle design for most applications is the cost. For instance, it might be more economical to have a smaller recovery heat exchanger. An economic analysis is required to determine these factors. Some case studies where a cycle design is developed for specific applications might be useful. For instance, a solar, geothermal, and waste heat conversion application can be considered. Each of these applications has different requirements. For example, there is a limit in geothermal applications on the temperature of the brine (geofluid) leaving the cycle, to prevent silica precipitation. The cycle designs developed can be compared to standard cycles in use now and to the most promising alternative determined, particularly through an economic analysis. The search for better working fluids can be expanded on the basis of some of the conditions discussed here. Ammonia is a good choice of volatile component. There may be a better choice of absorbent in the place of water such that the pair has an even higher volatility ratio. More complex (ternary) mixtures may also prove to be an option. The optimization program can be setup to handle a more complicated simulation model. A key criteria to keep in mind would be the computational requirements for a given simulation. Since the model involves calculating the gradients for all variables, which requires invoking the function several times for each step, the computational time

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156 requirements can dramatically increase. The model, as it exists now can easily be optimized on a PC. The configurations based on the Kalina thermal compression arrangement would be the best choice for geothermal and waste heat applications. The basic cycle configuration is better suited to utilizing solar resources. The Kalina compression based cycles may have some advantage when considering the effect of heat source exit temperature on collector system efficiency. These have to be computed. The use of a jet pump was shown to have a slight advantage under certain conditions. The main reason for the lack of improvement is the low efficiency of the jet pump itself. If it were possible to build an improved jet pump, the use of that device in the cycle would be advantageous. A company has claimed to have a very efficient jet pump like device (hydrokinetic amplifier) that may work well in such applications. Keeping that in mind, it might be worthwhile to pursue the jet pump method further and to try to improve the efficiency of these devices.

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APPENDIX A WORKING FLUID PROPERTY CALCULATION The simulation of the combined cycle and its accuracy depend substantially on the accuracy of prediction of the working fluid properties. In the work presented here, a properties program written by Xu (see Xu and Goswami [43]) has been utilized for ammonia-water mixture properties. For hydrocarbon mixtures, the program SUPERTRAPP (TRAnsport Properties Prediction) program, available from NIST was used. A brief discussion on the property prediction methods for binary mixtures is given below, using ammonia-water mixtures as an example, along with a summary of the theory behind the programs used in this study. Property Prediction Methods The experimental measurement of properties of working fluids at all possible pressures and temperatures is very difficult. The normal practice is to make accurate measurements in a relatively small number of points within the range of values desired, and to then use theories on thermophysical properties of substances to predict the properties at all other values. Some of the commonly used thermophysical property prediction methods for binary mixtures can be broadly classified as those based on (see Thorin et al. [62]) Equations of State Gibbs excess energy Law of corresponding states 157

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158 Equations of state based methods use equations of state defined for the fluid mixtures to compute properties at all points. Some equations that are commonly used are the Helmholtz equations of state, cubic equations of state, and virial equations of states. Helmholtz equations of state are the most common form of accurate equations of states being developed with a large range of applicability [63]. For ammonia water mixtures, one of the more recent methods used to predict properties is one developed at NIST, using reduced Helmholtz equations of state [64]. Cubic equations of state, such as the Peng Robinson equation or the Redlich Kwong equation are recommended for use when no other equations are available. For instance, Elnick et al. [65] found that a Peng-Robinson equation based method was less accurate than the WATAM proprietary properties code developed by Exergy Inc. Cubic equations have parameters that can be correlated with a limited amount of experimental data [63]. For the prediction of properties of organic mixtures, the Benedict-Webb-Rubin equation, which is a more complicated (and not a cubic) equation of state used to be a popular choice. Virial equations are truncated power series functions in terms of molar volumes or pressures. The coefficients of the power terms can be empirically correlated using PVT data or estimated using molecular thermodynamics [63]. Gibbs energy function is a characteristic function, i.e., a function from which all other thermodynamic properties can be derived by simple algebra or calculus. Gibbs excess energy methods use correlations for the Gibbs energies of the pure components and correlations for the excess free energy of mixtures to account for their mutual interaction. The properties program used in our study uses a Gibbs excess energy based method.

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159 The principle of corresponding states correlates the behavior of substances using reduced properties. To introduce the concept simplistically, using reduced properties that are normalized using critical properties, given as critrppp= critrTT= T and critrvvv= an equation of state could be written as ()rrrTvfp,= (A.1) Principles of statistical mechanics can be used to improve the quality of prediction of the corresponding states methods. Corresponding states methods do not always have the accuracy of empirical correlations, but these are very useful to estimate properties beyond the range of existing data. Methods Used for Properties in this Study Ammonia Water Properties Prediction Xu and Goswami [43] describe in detail the ammonia-water properties program used in this study. A program written by Xu in the C language was modified and used in this study. A small error in the implementation of the calculation of specific volume was corrected and additional functions added for convenience, during the course of this study. The method combines the Gibbs free energy method for mixture property prediction and bubble and dew point correlations for phase equilibrium. Ammonia-water mixtures in the vapor state are assumed to be ideal mixtures, such that the properties of pure water and ammonia are added up by weighting with the composition of the mixture. For the liquid state on the other hand, an excess Gibbs energy term is used to account for the deviation from ideal solution behavior. The entropies in both states (liquid and vapor) are naturally, not additive. Entropy of mixing term is used to account for the additional irreversibility of mixing. Phase equilibrium calculations are performed using

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160 equations developed by El-Sayed and Tribus [66]. These correlations directly yield the bubble and dew point values, therefore avoiding the iterative method of equating fugacity coefficients of each component in the vapor and liquid state in equilibrium. Xu [67] gives a review of ammonia-water mixture property prediction methods as well as a detailed description of the method used in this study. The properties predicted by these correlations were compared to measured values in the literature and the agreement was found to be good [43]. The property correlations used are valid in the 0.2-110 bar (0.02 MPa to 11 MPa) range, and from -43 to 327 C (230 to 600 K) range. Organic Fluid Mixture Properties The SUPERTRAPP program for mixtures, developed at NIST, is one of the five computerized databases distributed by the Standard Reference Data (SRD) Program of NIST. Although the database was developed with an emphasis on accurate density prediction, the calculation of other properties is excellent also [68]. An earlier version of this program was used for the calculations in the DOE heat cycle research program conducted at Idaho National Engineering Laboratory. The properties calculation can be performed using extended corresponding states (EXCST) models or a Peng-Robinson equation of state (PRS) equation based model. Vapor liquid equilibrium calculations are always performed using a PRS model. For simulations, the EXCST model was used for phase calculations and the PRS for phase equilibrium predictions. Mason and Uribe [69] provide an excellent review of the EXCST, along with application to dilute gases and a short description of the historical evolution of the method. Huber and Hanley [70] review the application of the method to dense fluids

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161 with particular reference to the SUPERTRAPP program. Nowarski and Friend [71] describe the application of the extended corresponding states method to the calculation of ammonia-water mixture thermodynamic properties. Simply put, the basic corresponding states principle is extended by knowledge of the intermolecular interactions to come up with the extended corresponding states method. A brief description of the method, adapted from Huber and Hanley [70], is given below. Consider a given fluid. The property of this fluid is related to a reference fluid at a corresponding-state point using two functions, and These are functions of the critical parameters and the acentric factor xF xH The Pitzer acentric factor is a parameter based on the slope of the vapor-pressure curve. In the limiting case of a two-parameter corresponding states model between two pure fluids, these functions reduce to a ratio of critical parameters of the fluid with respect to the reference fluid. 0,,cxcxTTF= (A.2) xccxH,0,f f = (A.3) The subscript 0 refers to the reference fluid, and the subscript x to the fluid under consideration. The concept of extended corresponding states broadens considerably, the range of applicability of the corresponding states. The functions given in Eqs.(A.2) and (A.3) are modified by adding shape factors. (xxrxrxcxcxTTTFf,,,,0,,= ) (A.4)

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162 (xxrxrxxccxTHff ) f ,,,,,0,= (A.5) The shape factors are functions of reduced parameters and the acentric factor. In the SUPERTRAPP program, the shape factors are calculated semi-empirically using information on the pure fluid components. Mixture properties are calculated using mixing rules. The mixture is first characterized as a hypothetical pure fluid and is related to the reference fluid. The mixing rule equations used are (A.6) ===ninjijjixHxxH11 (A.7) ===ninjijijjixxHFxxHF11 Where, (ijjiijkFFF=1 ) (A.8) +=8133/131ijjiijlHHH (A.9) Here is the concentration of the ith component in the mixture of n components. and l are binary interaction parameters that can be non zero when ix ijk ij j i. Additional mixing formulas may be used for transport properties. The properties predicted by the SUPERTRAPP algorithm worked well with the simulation program. The VLE calculation results were slightly noisy, due to which a function written to calculate the saturation concentration at a given temperature and pressure would not converge. Further, it was necessary to use the central differencing

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163 scheme in the gradient calculations in order to prevent the search from terminating at obviously non-optimum points. The numerical error in the central differencing scheme is lower.

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APPENDIX B OPTIMIZED STATE POINTS The optimized state points for some cycle configurations are tabulated here. The numbers are from computer program outputs and may contain significant figures exceeding the accuracy of the properties program. The state points correspond to the numbers in the respective figures referenced. The following assumptions hold for the simulations. Conditions Heat Source Temperature : 400 K Ambient Temperature : 298 K Dead State Temperature : 298 K Reference flow rate : 1 kg/s For ammonia-water fluid based Simulations Upper limit on Turbine exit Temp. : 270 K Turbine isentropic efficiency : 80 % Pump isentropic efficiency : 85 % For Organic fluid simulations Upper limit on Turbine exit Temp. : 285 K Turbine isentropic efficiency : 100 % Pump isentropic efficiency : 100 % 164

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165 Basic Cycle Configuration Fluid: AmmoniaWater Exergy Efficiency Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.001.000.288-55.840.373.000 2303.1010.340.288-54.530.373.000 3381.8410.340.288326.711.482.622 4382.8610.340.288342.591.523.000 5394.9610.340.8311718.965.460.340 6357.1110.340.391147.791.050.081 7357.1110.340.9701472.394.890.259 8359.8210.340.9701479.334.910.259 9270.001.000.9701201.835.090.259 10293.001.000.9701299.815.440.259 11394.9610.340.219379.331.562.660 12308.1010.340.2193.530.492.660 13309.8110.340.2247.810.512.741 14310.011.000.2247.810.512.741 17389.9610.340.288452.651.800.378 HeatSource: Inlet:400.00K Outlet:387.86K Heatsourceflowrate:11.01kg/s Effective Exergy Efficiency Optimized 4.0,=refII Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.001.860.380-90.300.323.000 2303.1816.530.380-88.180.333.000 3381.8216.530.380303.141.462.577 4382.5216.530.380314.271.493.000 5395.0016.530.9051617.375.030.378 6341.8716.530.60188.660.850.085 7341.8716.530.9921380.404.420.293 8341.8716.530.9921380.404.420.293 9255.261.860.9921147.074.580.293 10293.001.860.9921324.735.240.293 11395.0016.530.304345.201.532.622 12308.1816.530.304-39.390.442.622 13310.0216.530.314-35.390.462.707 14310.331.860.314-35.390.462.707 17386.8716.530.380382.071.660.423

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166 HeatSource: Inlet:400.00K Outlet:387.52K Heatsourceflowrate:10.82kg/s RUE Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.002.600.434-101.750.303.000 2303.088.610.434-100.870.303.000 3344.168.610.434110.060.952.691 4344.588.610.434117.630.973.000 5357.688.610.9601491.225.020.400 6324.428.610.542-5.860.600.029 7324.428.610.9931371.884.680.371 8324.428.610.9931371.884.680.371 9270.002.600.9931235.894.770.371 10293.002.600.9931316.185.050.371 11357.688.610.353159.171.072.600 12308.088.610.353-59.190.412.600 13308.378.610.355-58.600.412.629 14308.502.600.355-58.600.412.629 17348.348.610.434183.651.160.309 HeatSource: Inlet:400.00K Outlet:349.58K Heatsourceflowrate:3.09kg/s Effective RUE Optimized 4.0,=refII Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.002.540.430-101.220.303.000 2303.088.750.430-100.310.313.000 3345.578.750.430119.110.982.569 4345.708.750.430121.490.983.000 5357.008.750.9631486.455.000.354 6312.108.750.653-33.680.450.035 7312.108.750.9971335.004.560.319 8312.108.750.9971335.004.560.319 9261.882.540.9971202.284.650.319 10293.002.540.9971327.635.100.319 11357.008.750.359154.361.062.646 12308.688.750.359-58.680.412.646 13309.038.750.363-58.350.422.681 14309.152.540.363-58.350.422.681 17346.508.750.430135.721.020.431

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167 HeatSource: Inlet:400.00K Outlet:350.67K Heatsourceflowrate:10.82kg/s Work Domain Exergy Efficiency Optimized Low Pressure Limit of 5 bars. Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.001.000.288-55.840.373.000 2303.1010.130.288-54.560.373.000 3381.2410.130.288326.831.482.601 4377.9910.130.288276.151.353.000 5395.0010.130.8271724.775.480.359 6395.0010.130.215381.291.560.000 7395.0010.130.8271724.775.480.359 8395.0010.130.8271724.775.480.359 9323.081.000.8271412.695.650.359 10323.081.000.8271412.695.650.359 11395.0010.130.215381.291.562.641 12308.1010.130.2155.660.492.641 13308.1010.130.2155.660.492.641 14308.301.000.2155.660.492.641 17303.1010.130.288-54.560.370.399 HeatSource: Inlet:400.00K Outlet:382.99K Heatsourceflowrate:11.04kg/s RUE Optimized Low Pressure Limit of 5 bars Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.005.000.565-100.200.293.000 2303.1715.510.565-98.550.293.000 3344.4515.510.565102.230.912.970 4344.3715.510.565100.220.903.000 5368.6315.510.9681483.944.740.809 6368.6315.510.416197.451.190.000 7368.6315.510.9681483.944.740.809 8395.0015.510.9681554.054.920.809 9332.985.000.9681397.325.000.809 10332.985.000.9681397.325.000.809 11368.6315.510.416197.451.192.191 12308.1715.510.416-74.720.382.191 13308.1715.510.416-74.720.382.191 14308.385.000.416-74.720.392.191 17303.1715.510.565-98.550.290.030

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168 HeatSource: Inlet:400.00K Outlet:382.99K Heatsourceflowrate:6.50kg/s Fluid: Propane-n-Undecane Exergy Efficiency Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.06.3370.313114-2291.783.48110.000 2303.419.0870.313114-2289.873.48110.000 3375.119.0870.313114-2082.674.0858.539 4375.719.0870.313114-2080.414.09110.000 5395.019.0870.967003-2187.095.9831.752 6333.219.0870.776900-2499.304.4520.254 7333.219.0870.999262-2351.365.6391.498 8333.219.0870.999262-2351.365.6391.498 9285.06.3370.999262-2402.745.6391.498 10293.06.3370.999262-2386.455.6961.498 11395.019.0870.174205-1972.493.9098.248 12308.419.0870.174205-2186.993.2988.248 13309.519.0870.192224-2196.333.3368.502 14309.96.3370.192224-2196.333.3428.502 17379.019.0870.313114-2067.214.1261.461 HeatSource: Inlet:400.00K Outlet:380.70K Heatsourceflowrate:8.59kg/s RUE Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.06.5830.334172-2305.443.51410.000 2303.213.1370.334172-2304.453.51410.000 3342.513.1370.334172-2185.853.8778.383 4342.413.1370.334172-2185.943.87710.000 5357.813.1370.991529-2271.695.9011.697 6314.013.1370.852730-2596.674.4110.096 7314.013.1370.999863-2371.355.6331.601 8314.013.1370.999863-2371.355.6331.601 9285.06.5830.999863-2403.485.6331.601 10293.06.5830.999863-2387.375.6891.601 11357.813.1370.199785-2085.043.6998.303 12308.213.1370.199785-2204.793.3398.303 13308.413.1370.207260-2209.283.3538.399 14308.66.5830.207260-2209.283.3568.399 17342.313.1370.334172-2186.463.8751.617

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169 HeatSource: Inlet:400.00K Outlet:347.44K Heatsourceflowrate:3.12kg/s Fluid: Isobutane-n-Undecane Exergy Efficiency Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.01.6220.230908-2218.663.19110.000 2303.15.7780.230908-2218.063.19110.000 3376.65.7780.230908-2016.163.7808.812 4376.85.7780.230908-2015.493.78210.000 5391.35.7780.954950-2125.495.2941.249 6322.25.7780.741997-2461.203.7710.217 7322.25.7780.999666-2293.934.9361.032 8322.25.7780.999666-2293.934.9361.032 9285.01.6220.999666-2344.344.9361.032 10293.01.6220.999666-2330.664.9831.032 11391.35.7780.127585-1943.423.7138.751 12308.15.7780.127585-2146.733.1308.751 13308.55.7780.142432-2154.333.1488.968 14308.71.6220.142432-2154.333.1508.968 17378.25.7780.230908-2010.483.7951.188 HeatSource: Inlet:400.00K Outlet:381.78K Heatsourceflowrate:6.38kg/s RUE Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.01.8950.283372-2248.963.23910.000 2303.14.3680.283372-2248.603.23910.000 3342.54.3680.283372-2140.563.5718.832 4342.44.3680.283372-2140.843.57010.000 5353.74.3680.989706-2220.985.1621.179 6309.34.3680.819779-2535.063.7340.067 7309.34.3680.999889-2313.094.9111.112 8309.34.3680.999889-2313.094.9111.112 9285.01.8950.999889-2345.644.9111.112 10293.01.8950.999889-2331.954.9581.112 11353.74.3680.189007-2073.843.5188.821 12308.34.3680.189007-2182.023.1918.821 13308.34.3680.193736-2184.663.1968.888 14308.41.8950.193736-2184.663.1978.888 17342.04.3680.283372-2143.013.5641.168

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170 HeatSource: Inlet:400.00K Outlet:347.40K Heatsourceflowrate:2.24kg/s Configuration with Preheater RUE Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.002.870.451-103.920.303.000 2303.099.490.451-102.940.303.000 3361.259.490.451388.231.740.635 4346.569.490.451145.771.051.864 5353.849.490.451270.301.410.501 6350.709.490.451217.881.263.000 7366.259.490.9451525.505.070.592 8324.329.490.569-1.780.600.068 9324.329.490.9941366.114.620.525 10324.329.490.9941366.114.620.525 11270.002.870.9941231.374.710.525 12293.002.870.9941315.175.000.525 13366.259.490.329204.851.182.408 14337.089.490.32975.340.812.408 15337.129.490.33673.230.812.475 16326.902.870.33673.230.812.475 HeatSource: Inlet:400.00K BoilerOutlet:355.69K PreheaterOutlet:327.82K Heatsourceflowrate:3.97kg/s Configuration with Jet Pump RUE Optimized: Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.004.200.524-105.180.293.000 2303.1917.000.524-103.220.293.000 3303.1917.000.524-103.220.292.851 4357.1217.000.524198.781.190.149 5306.5317.000.524-88.180.343.000 6363.5817.000.9781454.524.620.347 7341.3417.000.61690.630.850.014 8341.3417.000.9931376.004.390.333 9341.3417.000.9931376.004.390.333 10270.003.290.9931194.834.510.333 11293.003.290.9931306.834.910.333

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171 12363.5817.000.465171.071.122.653 13363.5817.000.465171.071.122.653 14363.4617.000.466170.661.122.667 15318.313.290.466159.541.142.667 16317.613.290.524286.881.563.000 17323.934.200.524296.891.573.000 HeatSource: Inlet:400.00K Outlet:311.53K Heatsourceflowrate:3.29kg/s Configuration with Kalina Thermal Compression Using heat source for distillation RUE Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.003.680.497-106.260.291.165 2303.1212.380.497-104.940.291.165 3350.5212.380.497193.331.190.843 4346.1612.380.497108.750.950.322 5349.2812.380.497169.961.121.165 6373.2112.380.9471530.724.960.292 7343.5212.380.50678.540.860.025 8343.5212.380.9881409.254.630.267 9343.5212.380.9881409.254.630.267 10270.002.340.9881217.684.760.267 11293.002.340.9881304.275.060.267 12373.2112.380.347231.651.260.873 13308.1212.380.347-56.520.410.873 14309.3412.380.351-52.760.430.898 15309.552.340.351-52.760.430.898 16303.002.340.417-98.840.313.000 17303.023.680.417-98.640.313.000 18317.173.680.417-27.090.542.001 19325.863.680.36614.060.651.835 20308.023.680.366-63.970.401.835 21308.042.340.366-63.970.401.835 22325.863.680.9821413.545.200.166 23303.023.680.417-98.640.310.999 HeatSource: Inlet:400.00K BoilerOutlet:354.27K Distilleroutlet:322.17K Heatsourceflowrate:2.34kg/s

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172 Effective RUE optimized 4.0,=refII Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.003.080.463-105.080.301.283 2303.1111.390.463-103.830.301.283 3352.6711.390.463192.271.180.973 4357.0811.390.463268.131.400.310 5353.7111.390.463210.611.241.283 6373.2711.390.9401541.895.020.280 7321.9111.390.65111.100.590.046 8321.9111.390.9961347.104.480.235 9321.9111.390.9961347.104.480.235 10254.561.890.9961158.294.610.235 11293.001.890.9961333.195.260.235 12373.2711.390.330236.511.271.003 13308.1111.390.330-50.720.421.003 14309.9111.390.344-48.040.441.049 15309.861.890.344-48.040.441.049 16303.001.890.382-90.920.323.000 17303.013.080.382-90.750.323.000 18318.133.080.382-10.860.581.893 19328.353.080.32239.540.701.717 20308.013.080.322-48.540.421.717 21308.041.890.322-48.540.431.717 22328.353.080.9731432.625.340.176 23303.013.080.382-90.750.321.107 HeatSource: Inlet:400.00K BoilerOutlet:358.71K Distilleroutlet:323.13K Heatsourceflowrate:2.28kg/s Work Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.002.670.438-102.400.300.962 2303.099.710.438-101.360.300.962 3357.619.710.438293.361.470.568 4303.099.710.438-101.360.300.393 5348.119.710.438132.011.010.962 6395.009.710.8181736.235.520.363 7395.009.710.208384.811.560.000 8395.009.710.8181736.235.520.363 9395.009.710.8181736.235.520.363 10330.441.280.8181458.695.660.363 11330.441.280.8181458.695.660.363 12395.009.710.208384.811.560.598 13308.099.710.2089.820.490.598 14308.099.710.2089.820.490.598 15308.271.280.2089.820.500.598 16303.001.280.323-71.090.353.000

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173 17303.022.670.323-70.890.353.000 18324.362.670.32331.550.682.216 19333.992.670.26986.550.802.038 20308.022.670.269-24.810.462.038 21308.041.280.269-24.810.462.038 22333.992.670.9471477.445.520.177 23303.022.670.323-70.890.350.784 HeatSource: Inlet:400.00K BoilerOutlet:353.11K Distilleroutlet:329.36K Heatsourceflowrate:3.71kg/s Using absorber heat recovery for distillation RUE Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.003.350.479-105.970.291.438 2303.1010.550.479-104.890.291.438 3370.3810.550.479544.392.160.278 4370.3810.550.479544.392.160.235 5351.5210.550.479248.871.350.925 6357.9710.550.479354.321.641.438 7375.3810.550.9261566.025.120.402 8332.3110.550.53930.080.710.059 9332.3110.550.9921384.074.630.343 10332.3110.550.9921384.074.630.343 11270.002.640.9921226.674.730.343 12293.002.640.9921311.355.030.343 13375.3810.550.306254.011.301.036 14336.0810.550.30679.910.811.036 15336.6010.550.31977.230.811.095 16327.312.640.31977.230.811.095 17324.632.640.479371.421.831.438 18315.382.640.479225.301.371.438 19303.002.640.437-102.170.303.000 20303.013.350.437-102.060.303.000 21310.383.350.437-65.110.421.672 22317.003.350.398-33.130.521.562 23308.013.350.398-72.690.391.562 24308.022.640.398-72.690.391.562 25317.003.350.9881387.375.170.110 26303.013.350.437-102.060.301.328 HeatSource: Inlet:400.00K BoilerOutlet:362.97K Preheateroutlet:331.04K Heatsourceflowrate:2.44kg/s

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174 Effective RUE Optimized 4.0,=refII Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.003.650.496-106.270.291.350 2303.1211.810.496-105.030.291.350 3375.7611.810.496612.282.340.251 4375.7611.810.496612.282.340.253 5358.2111.810.496345.091.610.846 6364.5911.810.496444.841.891.350 7380.7611.810.9181582.605.100.423 8333.8211.810.55940.420.730.072 9333.8211.810.9921381.304.570.351 10333.8211.810.9921381.304.570.351 11270.002.850.9921220.894.670.351 12293.002.850.9921310.004.990.351 13380.7611.810.303279.681.370.927 14337.1211.810.30385.830.820.927 15338.0311.810.32182.550.830.999 16329.082.850.32182.550.830.999 17326.002.850.496401.361.921.350 18315.172.850.496232.151.391.350 19303.002.850.450-103.840.303.000 20303.013.650.450-103.720.303.000 21309.673.650.450-74.130.401.764 22316.973.650.413-36.340.511.650 23309.803.650.413-67.980.411.650 24309.522.850.413-67.980.411.650 25316.973.650.9891384.515.120.114 26303.013.650.450-103.720.301.236 HeatSource: Inlet:400.00K BoilerOutlet:369.59K Preheateroutlet:333.95K Heatsourceflowrate:2.54kg/s Work Optimized Tpxhsflowrate KbarskJ/kgkJ/kg.Kkg/s 1303.002.030.394-93.880.320.554 2303.034.570.394-93.510.320.554 3382.994.570.3941043.623.530.060 4331.714.570.39488.550.880.006 5380.034.570.394963.413.320.488 6380.034.570.394963.413.320.554 7387.994.570.6471934.626.170.289 8387.934.570.117405.231.510.000 9387.934.570.6481933.536.170.289 10387.934.570.6481933.536.170.289 11343.501.000.6481720.766.280.289 12343.501.000.6481720.766.280.289 13387.994.570.117405.691.510.264 14326.714.570.117145.910.780.264 15326.814.570.117146.350.790.265

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175 16326.881.000.117146.350.790.265 17341.551.000.394967.723.660.554 18318.191.000.394426.902.030.554 19303.001.000.288-55.840.373.000 20303.012.030.288-55.690.373.000 21313.162.030.288-12.050.522.534 22326.722.030.26457.550.712.446 23316.162.030.26412.340.572.446 24309.511.000.26412.340.572.446 25326.722.030.9521458.015.600.088 26303.012.030.288-55.690.370.466 HeatSource: Inlet:400.00K BoilerOutlet:385.03K Preheateroutlet:326.60K Heatsourceflowrate:2.10kg/s

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APPENDIX C SIMULATION SOURCE CODE A sample source code used in the simulation of the basic cycle configuration is included here. The programs were written in the C language. The functions used to calculate fluid properties should be clearly identifiable. The code for other cycle configurations can be easily written suing the code below and the description in the text. Basic Cycle Configuration Header File Cycver0.h double x_boiler, y_boiler, x_cond, y_cond; double t_boilermin, t_condmin, t_dewb, t_bubblec; double T_coolMax=270 ; double molarweight_water=18.01528; //[Handbook of Chemistry and Physics, 72nd ed.] double hhs1_massbasis, hhs2_massbasis, hhs3_massbasis,hhsm_massbasis,f_hs; double amv_boiler, aml_boiler, amv_cond, aml_cond, amv_rcond, aml_rcond; double ms = 1.; double x_in, x_sat, r1,r2; double t_ab, t_boiler, t_cond, t_super, p_high, p_low, p_inter; double h[18], s[18], v[18], t[18], p[18], x[18], f[18]; double h_is, s_is, v_is, t_is; double h_boiler[6], s_boiler[6], v_boiler[6]; double irr[11]; double q_absorber, q_boiler, q_cond, q_super, q_cooler, q_hrhx; double wt, eff, eff_withoutcooling, pump; double x_turbine, y_turbine; double amv_turbine, aml_turbine; double molehs, phs; double ths1, hhs1, shs1, vhs1; double ths2, hhs2, shs2, vhs2; double ths3, hhs3, shs3, vhs3; double hhs4, shs4, vhs4; double thsm, hhsm, shsm, vhsm; double tcf1, hcf1, scf1, vcf1; 176

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177 double tcf2, hcf2, scf2, vcf2; double molecf, pcf; double td,hd,sd,vd; double t_pin, h_pin, s_pin, v_pin, q_pin, q_hot, q_cold; double t0=298, p0, h0, s0, v0; double exhs,exhs1,exhs2,effrue, effxgy, effex; double deltat, deltat2, deltat3; double h_hs_b; double etaIS_pump=0.8; double etaIS_turb=0.85; Cycle Simulation cycver0.c #include #include #include "propertyv2.c" #include "cycver0.h" /********************************************************************** 1. This program simulates the basic power cooling cycle. 2. No pressure losses are assumed 3. Isentropic Efficiencies are assumed for the turbine and pump ***********************************************************************/ // BOILER FUNCTION***************************************************** void boiler(double p_boiler_in, double x_in, double t_boiler, double t_cond, double h_boiler[], double s_boiler[], double v_boiler[]) { // ammonia mass fraction in boiler and condenser, x: liquid, y: vapor double h_re, s_re, v_re; // incoming mixture property t_boilermin=bubble(p_boiler_in, x_in); t_dewb=dew(p_boiler_in, x_in); amm_fraction(t_boiler, p_boiler_in, &x_boiler, &y_boiler); amv_boiler = (x_in x_boiler)/(y_boiler x_boiler); aml_boiler = (y_boiler x_in)/(y_boiler x_boiler); //condensor equations

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178 t_condmin = dew(p_boiler_in, y_boiler); t_bubblec = bubble(p_boiler_in, y_boiler); amm_fraction(t_cond, p_boiler_in, &x_cond, &y_cond); amv_cond = (y_boiler x_cond)/(y_cond x_cond); aml_cond = (y_cond y_boiler)/(y_cond x_cond); // Mass balances implemented f[12]=aml_boiler*f[1]; f[5]=amv_boiler*f[1]; f[7]=amv_cond*f[5]; f[6]=aml_cond*f[5]; mix_l(t_boiler, p_boiler_in, x_boiler, &h_re, &s_re, &v_re); h_boiler[2] = h_re; s_boiler[2] = s_re; v_boiler[2] = v_re; mix_v(t_boiler, p_boiler_in, y_boiler, &h_re, &s_re, &v_re); h_boiler[3] = h_re; s_boiler[3] = s_re; v_boiler[3] = v_re; mix_l(t_cond, p_boiler_in, x_cond, &h_re, &s_re, &v_re); h_boiler[4] = h_re; s_boiler[4] = s_re; v_boiler[4] = v_re; mix_v(t_cond, p_boiler_in, y_cond, &h_re, &s_re, &v_re); h_boiler[5] = h_re; s_boiler[5] = s_re; v_boiler[5] = v_re; return; } //************ END OF BOILER FUNCTION void main() { char filename[30]; FILE *fp; double g[17], gub[17], glb[17]; int i=0; gets(filename); fp=fopen(filename,"a"); t_ab=303; scanf("%lf",&t_ab); scanf("%lf",&t_boiler);

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179 scanf("%lf",&t_cond); scanf("%lf",&t_super); scanf("%lf",&p_high); scanf("%lf",&p_low); scanf("%lf",&ths1); scanf("%lf",&molehs); scanf("%lf",&r1); scanf("%lf",&r2); x_in = sat_con(p_low, t_ab); p_inter=p_low; //HEAT SOURCE HEAT SOURCE HEAT SOURCE HEAT SOURCE HEAT SOURCE HEAT SOURCE f_hs=molehs*molarweight_water; //flow rate of the heat source in kg/s phs = h2o_sat_p(ths1); //heat source pressure steam_l(ths1, phs, &hhs1, &shs1, &vhs1); //molar basis hhs1_massbasis=hhs1/molarweight_water; //HEAT SOURCE HEAT SOURCE HEAT SOURCE HEAT SOURCE HEAT SOURCE //point 1 t[1] = t_ab; p[1] = p_low; x[1] = x_in; // DEFINE AS AN UPPER BOUND LIMIT? f[1] = 3.; // REFERENCE FLOWRATE. HOW TO SCALE? mix_l(t[1], p[1], x[1], &h[1], &s[1], &v[1]); //point 2 (AFTER PUMP) p[2] = p_high; x[2] = x[1]; //THE NEXT THREE LINES ACCOUNT FOR THE ISENTROPIC EFFICIENCY OF PUMP. s_is=s[1]; property_s_t(p[2],s_is,x_in,&h_is,&t_is,&v_is); h[2]=(h_is-h[1])/etaIS_pump+h[1]; f[2] = f[1]; property_h_t(p[2], h[2], x[2], &t[2], &s[2], &v[2]); // CALL TO BOILER FUNCTION boiler(p_high,x_in,t_boiler,t_cond,h_boiler,s_boiler,v_boiler); //point 12 Weak solution return from boiler t[12] = t_boiler; p[12] = p_high; x[12] = x_boiler; s[12] = s_boiler[2]; v[12] = v_boiler[2];

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180 h[12] = h_boiler[2]; //point 13 and point 3 t[13] = t[2]; p[13] = p[12]; x[13] = x[12]; f[13] = f[12]; property(t[13], p[13], x[13], &h[13], &s[13], &v[13]); q_hot = f[12]*(h[12] h[13]); t[3] = t[12] ; p[3] = p[2]; x[3] = x[2]; f[3] = f[2]*r2/100; property(t[3], p[3], x[3], &h[3], &s[3], &v[3]); q_cold = f[3]*(h[3] h[2]); if(q_hot <= q_cold){ q_hot = q_hot*r1/100; q_hrhx = q_hot; h[13]=h[12] q_hot/f[12]; property_h_t(p[13], h[13], x[13], &t[13], &s[13], &v[13]); h[3] = h[2] + q_hot/f[3]; property_h_t(p[3], h[3], x[3], &t[3], &s[3], &v[3]); } else { q_cold = q_cold*r1/100; q_hrhx = q_cold; h[13]=h[12] q_cold/f[12]; property_h_t(p[13], h[13], x[13], &t[13], &s[13], &v[13]); h[3] = h[2] + q_cold/f[3]; property_h_t(p[3], h[3], x[3], &t[3], &s[3], &v[3]); } //point 5 (Vapor) t[5] = t_boiler; p[5] = p_high; h[5] = h_boiler[3]; s[5] = s_boiler[3]; v[5] = v_boiler[3]; x[5] = y_boiler; // point 6 Reflux from Rectifier t[6] = t_cond; p[6] = p[5]; h[6] = h_boiler[4]; s[6] = s_boiler[4]; v[6] = v_boiler[4];

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181 x[6] = x_cond; //point 14 Mixing of Reflux from condensor and weaksolution return from boiler p[14] = p[13]; x[14] = (f[13]*x[13]+f[6]*x[6])/(f[13]+f[6]); h[14] = (f[13]*h[13]+f[6]*h[6])/(f[13]+f[6]); property_h_t(p[14], h[14], x[14], &t[14], &s[14], &v[14]); f[14]=f[13]+f[6]; //point 15 p[15] = p_low; x[15] = x[14]; h[15] = h[14]; //isenthalpic expansion property_h_t(p[15], h[15], x[15], &t[15], &s[15], &v[15]); f[15]=f[14]; // point 7 Vapor from Rectifier t[7] = t_cond; p[7] = p[6]; x[7] = y_cond; h[7] = h_boiler[5]; s[7] = s_boiler[5]; v[7] = v_boiler[5]; // point 8 Super Heater t[8] = t_super; p[8] = p[7]; x[8] = x[7]; f[8] = f[7]; mix_v(t[8], p[8], x[8], &h[8], &s[8], &v[8]); //point 9 Turbine p[9] = p_inter; //new variable s_is=s[8]; x[9] = x[8]; f[9]=f[8]; property_s_t(p[9],s_is,x[9],&h_is,&t_is,&v_is); h[9]=h[8]-etaIS_turb*(h[8]-h_is); property_h_t(p[9], h[9], x[9], &t[9], &s[9], &v[9]); amm_fraction(t[9], p[9], &x_turbine, &y_turbine); amv_turbine=(y_cond-x_turbine)/(y_turbine-x_turbine); aml_turbine=(y_turbine-y_cond)/(y_turbine-x_turbine); //point 10 isenthalpic expansion -redundant p[10]=p_low; x[10] = x[9]; h[10] = h[9]; //isenthalpic expansion property_h_t(p[10], h[10], x[10], &t[10], &s[10], &v[10]); f[10]=f[9]; //point 11 cooler p[11] = p_low ; x[11] = x[10];

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182 f[11]=f[10]; if(t[10]=t_boilermin) { h[16] = h[13]+ ms*f[3]*(h_pin-h[2])/f[13]; x[16] = x[12]; p[16] = p[12];

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183 f[16] = f[12]; property_h_t(p[16], h[16], x[16], &t[16], &s[16], &v[16]); deltat=t[16]-t_pin; } else deltat = t[13]-t[2]; if(t[4]t_boilermin) { h[16] = h[5]f[17]*(h[17]-h_pin)/f[5]; x[16] = x[5]; p[16] = p[6]; f[16] = f[5]; property_h_t(p[16], h[16], x[16], &t[16], &s[16], &v[16]); deltat2=t[16]-t_pin; } else deltat2= t[6]-t[2]; t0=298.0; p0=1.013; steam_l(t0, p0, &h0, &s0, &v0); //Heats q_boiler = ms (f[5]*h[5]+f[12]*h[12]-f[4]*h[4]); q_cond = ms (f[6] h[6] + f[7] h[7] f[5] h[5]); q_super = ms f[7] (h[8] h[7]); q_absorber = ms (f[15] h[15] + f[11] h[11]-f[1] h[1]); wt = ms f[8] (h[8] h[9]); pump = ms f[1] (h[2] h[1]); // eff = ((wt-pump+q_cooler) / (q_super + q_boiler)) 100; eff = (wt-pump+(f[10]*(h[10]-h[11]-t0*(s[10]-s[11])))/0.3)* 100. / (q_super + q_boiler) ; exhs=molehs*((hhs1-h0)-t0*(shs1-s0)); exhs1=molehs*((hhs1-hhs3)-t0*(shs1-shs3)); // effrue = (wt-pump+q_cooler)* 100./ exhs ; effrue = (wt-pump+ (f[10]*(h[10]-h[11]-t0*(s[10]-s[11])))/0.3)* 100./ exhs ; // effrue = ((wt-pump)* (t[10]/(298-t[10]))+q_cooler)* 100./ exhs; // effrue = ((wt-pump)* (T_coolMax/(298-T_coolMax))+q_cooler)* 100./ exhs; // effrue = (f[10]*(h[10]-h[11]-t0*(s[10]-s[11])))* 100./ exhs ; // effrue = (wt-pump)* 100./ exhs ;

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184 // effxgy = (wt-pump+q_cooler)* 100./ exhs1 ; effxgy = (wt-pump+ (f[10]*(h[10]-h[11]-t0*(s[10]-s[11])))/0.3)* 100./ exhs1 ; // effxgy = ((wt-pump)* (t[10]/(298-t[10]))+q_cooler)* 100./ exhs1; // effxgy = ((wt-pump)* (T_coolMax/(298-T_coolMax))+q_cooler)* 100./ exhs1; // effxgy = (f[10]*(h[10]-h[11]-t0*(s[10]-s[11])))* 100./ exhs1 ; // effxgy = (wt-pump)* 100./ exhs1 ; // constraint functions g[1] = t_cond t_boiler; g[2] = t_cond t_super; g[3] = t[12] t[3]; g[4] = t[5] t[17]; g[5] = ths1 t[8]; g[6] = ths2 t[5]; g[7] = ths3 t[4]; g[8] = deltat; g[9] = deltat2; g[10]= deltat3; g[11]= f[12] 100.; g[12]= amv_turbine 100.; g[13]= amv_boiler*100; g[14]= q_cooler; g[15]= effrue; g[16]= p_high-p_low; //Irreversibilities // Boiler irr[0]=t0*(f[5]*s[5] + f[12]*s[12] f[4]*s[4]+ molehs*(shs3-shs2)); //Rectifier irr[1]=t0*(f[7]*s[7] + f[6]*s[6] + f[17]*s[17] f[17]*s[2] f[5]*s[5]); //Recup. Hx irr[2]=t0*(f[3]*s[3] + f[13]*s[13] f[3]*s[2] f[12]*s[12]); //Super Heater irr[3]=t0*(f[8]*(s[8]-s[7]) + molehs*(shs2-shs1)); //Throttle Valve irr[4]=t0*f[14]*(s[15]-s[14]); //Mixing 1 irr[5]= t0*(f[14]*s[14] f[6]*s[6] f[13]*s[13]); //Mixing 2 irr[6]= t0*(f[4]*s[4] f[17]*s[17] f[3]*s[3]); //Absorber irr[7]= t0*(f[1]*s[1] f[15]*s[15] f[11]*s[11] + q_absorber/t0); //Exergy Lost from Source Reinjection irr[8] = exhs-exhs1; // Turbine Irreversibility irr[9] = t0*f[9]*(s[9] s[8]); // Pump irreversibility

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185 irr[10] = t0*f[1]*(s[2] s[1]); // Constraint limits glb[1] = -1.0e+30 ; gub[1] = 0.00 ; glb[2] = -1.0e+30 ; gub[2] = 0.00 ; glb[3] = 5. ; gub[3] = 1.0e+30 ; glb[4] = 5. ; gub[4] = 1.0e+30 ; glb[5] = 5. ; gub[5] = 1.0e+30 ; glb[6] = 5. ; gub[6] = 1.0e+30 ; glb[7] = 5. ; gub[7] = 1.0e+30 ; glb[8] = 5. ; gub[8] = 1.0e+30 ; glb[9] = 5. ; gub[9] = 1.0e+30 ; glb[10] = 5. ; gub[10] = 1.0e+30 ; glb[11] = 0.00 ; gub[11] = 300 ; glb[12] = 90. ; gub[12] = 1.0e+30 ; glb[13] = 0.01 ; gub[13] = 100.0 ; glb[14] = 0.1 ; gub[14] = 1.0e+30 ; glb[15] = 0.0 ; gub[15] = 100.0 ; glb[16] = 0.0 ; gub[16] = 1.0e+30 ; fprintf(fp,"PARAMETERS OF CYCLE FOR TRANSFER TO SPREADSHEET\n"); fprintf(fp,"Heat Source Temperature: %f \t Low temperature: %f \t Objective function: %f \n", ths1, t[10], g[15]); fprintf(fp,"t_ambient: %f \t t_ab: %f \n", t0, t_ab); fprintf(fp,"\n\n"); for(i=1;i<=16;i++){ if(g[i]gub[i]) fprintf(fp,"g[%d]: %f \t0\n", i,g[i]); else fprintf(fp,"g[%d]: %f \t1\n", i,g[i]); } for(i=1 ; i<18 ; i++){ fprintf(fp,"%2i %6.2f %5.2f %5.3f %7.2f %8.2f %8.3f %7.3f\n", i,t[i],p[i],x[i],h[i],s[i],v[i],f[i]); } fprintf(fp,"pin %6.2f %5.2f %5.3f %7.2f %8.2f %8.3f %7.3f\n", t_pin,p[3],x[3],h_pin,s_pin,v_pin,f[3]); fprintf(fp,"\n\n"); fprintf(fp, "%f \t %f \t %f \n", ths1, hhs1,shs1); fprintf(fp, "%f \t %f \t %f \n", ths2, hhs2,shs2); fprintf(fp, "%f \t %f \t %f \n", ths3, hhs3,shs3); fprintf(fp, "%f \t %f \t %f \n", t0, h0,s0); fprintf(fp,"\n\n"); fprintf(fp," %f \n",t_boiler); fprintf(fp," %f \n",t_cond); fprintf(fp," %f \n",t_super); fprintf(fp," %f \n",p_high); fprintf(fp," %f \n",p_low); fprintf(fp," %f \n",x_in);

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186 fprintf(fp," %f \n",t_dewb); fprintf(fp," %f \n",t_boilermin); fprintf(fp," %f \n",t[10]); fprintf(fp," %f \n",r1); fprintf(fp," %f \n",r2); fprintf(fp," %f \n",eff); fprintf(fp," %f \n",effrue); fprintf(fp," %f \n",effxgy); fprintf(fp," %f \n",wt-pump); fprintf(fp," %f \n",q_cooler); fprintf(fp," %f \n",molehs); fprintf(fp," %f \n",q_boiler); fprintf(fp," %f \n",-1*q_cond); fprintf(fp," %f \n",q_hrhx); fprintf(fp," %f \n",q_super); fprintf(fp," %f \n",q_absorber); fprintf(fp," %f \n",ths3); fprintf(fp," %f \n",exhs); fprintf(fp," %f \n",exhs1); fprintf(fp," %f \n",amv_turbine); fprintf(fp," %f \n",amv_boiler); fprintf(fp,"\n\n"); for(i=0; i<=10; i++)fprintf(fp," %f \n", irr[i]); fprintf(fp,"\n\n"); fclose(fp); } Interface to Supertrapp The program written to interface the cycle simulation to the SUPERTRAPP source code is given below. This program, written in FORTRAN 77 uses subroutines in SUPERTRAPP and has specific subroutines similar to those in the ammonia-water properties program. Propty.for CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CDRIVERSUBROUTINESTOOBTAINVARIOUSPROPERTIESNEEDEDINCYCLE

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187 CSIMULATION C CINTERNALUNITSOFTHECODEARESPECIFIEDBELOW CPROPERTYUNITS C............................................................. CTEMPERATURE[K] CPRESSURE[BAR] CVOLUME[LITER/MOL] CDENSITY[MOL/L] CENTHALPY[CAL/MOL] CENTROPY[CAL/MOL.K] CCP[CAL/MOL.K] CCV[CAL/MOL.K] CSOUNDSPEED[M/SEC] CJTCOEFFICIENT[K/BAR] CVISCOSITY[MICROPOISE] CTHERMALCONDUCTIVITY[MW/M.K] CCOMPOSITION[MOLFRACTION] C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLEPRECISIONFUNCTIONWTMOL(P,T,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) CHARACTERNAME(20)*50 DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) DIMENSIONXL(20),XV(20) C CSELECTEXTENDEDCORRESPONDINGSTATESMODEL,METHOD=2 METHOD=2 NC=1 FEED(1)=1 CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C CALLFLASH(P,T,FEED,AK,X,PSI,NPH,IER) DO111I=1,NC XL(I)=X(I,1) XV(I)=X(I,2) 111CONTINUE CEVALUATEPROPERTIESIFNOERRORSFROMFLASH IF(IER.EQ.0)THEN CALLPHASEP(P,T,XL,XV,PSI,NPH,METHOD,PROPS,IERPP) IF(IERPP.NE.0)THEN WRITE(2,*)'FAILUREINPHASEP' ELSE CJ=1ISLIQUIDPHASE,J=2ISVAPOR WTMOL=PROPS(1,1)*PROPS(2,1)+PROPS(1,2)*PROPS(2,2) ENDIF ENDIF

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188 C C RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C SUBROUTINEPRPTPX(P,T,XIN1,H,S,V,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) CHARACTERNAME(20)*50 COMMON/PVARS/NC,METHOD DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) DIMENSIONXL(20),XV(20) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C CFIRSTDEMONSTRATET,PFLASH CINTERNALUNITSTX[K],PX[BAR] CALLFLASH(P,T,FEED,AK,X,PSI,NPH,IER) DO111I=1,NC XL(I)=X(I,1) XV(I)=X(I,2) 111CONTINUE CEVALUATEPROPERTIESIFNOERRORSFROMFLASH IF(IER.EQ.0)THEN CALLPHASEP(P,T,XL,XV,PSI,NPH,METHOD,PROPS,IERPP) IF(IERPP.NE.0)THEN WRITE(2,*)'FAILUREINPHASEPVIAPRPTPX' ELSE CJ=1ISLIQUIDPHASE,J=2ISVAPOR H=PROPS(1,1)*PROPS(5,1)+PROPS(1,2)*PROPS(5,2) S=PROPS(1,1)*PROPS(6,1)+PROPS(1,2)*PROPS(6,2) V=PROPS(1,1)/PROPS(4,1)+PROPS(1,2)/PROPS(4,2) ENDIF ENDIF C C CALLUNIT2(FEED(1),H,S,V) RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C SUBROUTINESPTPX(P,T,XIN1,NP,H,S,V,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) CHARACTERNAME(20)*50 COMMON/PVARS/NC,METHOD DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) DIMENSIONXL(20),XV(20)

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189 C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C CFIRSTDEMONSTRATET,PFLASH CINTERNALUNITSTX[K],PX[BAR] NPH=NP CALLFLASHO(P,T,FEED,AK,X,PSI,NPH,IER) DO111I=1,NC XL(I)=X(I,1) XV(I)=X(I,2) 111CONTINUE CEVALUATEPROPERTIESIFNOERRORSFROMFLASH IF(IER.EQ.0)THEN CALLPHASEP(P,T,XL,XV,PSI,NPH,METHOD,PROPS,IERPP) IF(IERPP.NE.0)THEN WRITE(2,*)'FAILUREINPHASEPVIASPTPX' ELSE CJ=1ISLIQUIDPHASE,J=2ISVAPOR H=PROPS(1,1)*PROPS(5,1)+PROPS(1,2)*PROPS(5,2) S=PROPS(1,1)*PROPS(6,1)+PROPS(1,2)*PROPS(6,2) V=PROPS(1,1)/PROPS(4,1)+PROPS(1,2)/PROPS(4,2) ENDIF ENDIF C C CALLUNIT2(FEED(1),H,S,V) RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC SUBROUTINEPRPSPX(P,S,XIN1,H,T,V,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) CHARACTERNAME(20)*50 COMMON/PVARS/NC,METHOD DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) DIMENSIONXL(20),XV(20) C CALLUNIT1(XIN1,H,S,V) CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF

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190 CALLFLPS(P,S,FEED,METHOD,XL,XV,T,PSI,NPH,IER) C CEVALUATEPROPERTIESIFNOERRORSFROMFLASH IF(IER.EQ.0)THEN CALLPHASEP(P,T,XL,XV,PSI,NPH,METHOD,PROPS,IERPP) IF(IERPP.NE.0)THEN WRITE(2,*)'FAILUREINPHASEPVIAPRPSPX' ELSE C CJ=1ISLIQUIDPHASE,J=2ISVAPOR H=PROPS(1,1)*PROPS(5,1)+PROPS(1,2)*PROPS(5,2) V=PROPS(1,1)/PROPS(4,1)+PROPS(1,2)/PROPS(4,2) ENDIF ELSE WRITE(2,*)'CONVERGENCEFAILUREINFLPSVIAPRPSPX' ENDIF C C CALLUNIT2(FEED(1),H,S,V) RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C SUBROUTINEPRPHPX(P,H,XIN1,S,T,V,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) CHARACTERNAME(20)*50 COMMON/PVARS/NC,METHOD DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) DIMENSIONXL(20),XV(20) C CALLUNIT1(XIN1,H,S,V) CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF CALLFLPH(P,H,FEED,METHOD,XL,XV,T,PSI,NPH,IER) C CEVALUATEPROPERTIESIFNOERRORSFROMFLASH IF(IER.EQ.0)THEN CALLPHASEP(P,T,XL,XV,PSI,NPH,METHOD,PROPS,IERPP) IF(IERPP.NE.0)THEN WRITE(2,*)'FAILUREINPHASEPVIAPRPHPX' ELSE C CJ=1ISLIQUIDPHASE,J=2ISVAPOR S=PROPS(1,1)*PROPS(6,1)+PROPS(1,2)*PROPS(6,2) V=PROPS(1,1)/PROPS(4,1)+PROPS(1,2)/PROPS(4,2) ENDIF

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191 ELSE WRITE(2,*)'CONVERGENCEFAILUREINFLPHVIAPRPHPX' ENDIF C C CALLUNIT2(FEED(1),H,S,V) RETURN END C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CPROPERTIESOFMIXTUREINVAPORPHASE C SUBROUTINEVAPTPX(P,T,XIN1,H,S,V,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) CHARACTERNAME(20)*50 COMMON/PVARS/NC,METHOD DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) DIMENSIONXL(20),XV(20) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C CFIRSTDEMONSTRATET,PFLASH CINTERNALUNITSTX[K],PX[BAR] CALLFLASH(P,T,FEED,AK,X,PSI,NPH,IER) DO111I=1,NC XL(I)=X(I,1) XV(I)=X(I,2) 111CONTINUE CEVALUATEPROPERTIESIFNOERRORSFROMFLASH IF(IER.EQ.0)THEN CALLPHASEP(P,T,XL,XV,PSI,NPH,METHOD,PROPS,IERPP) IF(IERPP.NE.0)THEN WRITE(2,*)'FAILUREINPHASEPVIAVAPTPX' ELSE CJ=1ISLIQUIDPHASE,J=2ISVAPOR H=PROPS(5,2) S=PROPS(6,2) V=1/PROPS(4,2) ENDIF ENDIF C C CALLUNIT2(FEED(1),H,S,V) RETURN END C

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192 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CPROPERTIESOFMIXTUREINLIQUIDPHASE C SUBROUTINELIQTPX(P,T,XIN1,H,S,V,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) CHARACTERNAME(20)*50 COMMON/PVARS/NC,METHOD DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) DIMENSIONXL(20),XV(20) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C CFIRSTDEMONSTRATET,PFLASH CINTERNALUNITSTX[K],PX[BAR] CALLFLASH(P,T,FEED,AK,X,PSI,NPH,IER) DO111I=1,NC XL(I)=X(I,1) XV(I)=X(I,2) 111CONTINUE CEVALUATEPROPERTIESIFNOERRORSFROMFLASH IF(IER.EQ.0)THEN CALLPHASEP(P,T,XL,XV,PSI,NPH,METHOD,PROPS,IERPP) IF(IERPP.NE.0)THEN WRITE(2,*)'FAILUREINPHASEPVIALIQTPX' ELSE CJ=1ISLIQUIDPHASE,J=2ISVAPOR H=PROPS(5,1) S=PROPS(6,1) V=1/PROPS(4,1) ENDIF ENDIF C C CALLUNIT2(FEED(1),H,S,V) RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C CBUBBLEANDDEWPOINTDATAROUTINES C SUBROUTINEBUBLT(PX,TX,XIN1,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/PVARS/NC,METHOD PARAMETER(MX=20) CHARACTERNAME(MX)*50

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193 DIMENSIONFEED(MX),X(MX,2),PROPS(20,2),XL(20),XV(20) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVRYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C C CUSEBUBTTOGETSATURATIONVALUESFORPURECOMPONENT CALLBUBT(PX,TX,FEED,AK,X,PSI,NPH,IER) C RETURN END C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C SUBROUTINEDT(PX,TX,XIN1,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/PVARS/NC,METHOD PARAMETER(MX=20) CHARACTERNAME(MX)*50 DIMENSIONFEED(MX),X(MX,2),PROPS(20,2),XL(20),XV(20) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVRYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C C CUSEDEWTTOGETSATURATIONVALUESFORPURECOMPONENT CALLDEWT(PX,TX,FEED,AK,X,PSI,NPH,IER) C RETURN END C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CBUBBLEPOINTPRESSURECALCULATION C SUBROUTINEBUBLP(PX,TX,XIN1,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/PVARS/NC,METHOD

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194 PARAMETER(MX=20) CHARACTERNAME(MX)*50 DIMENSIONFEED(MX),X(MX,2),PROPS(20,2),XL(20),XV(20) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVRYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C C CUSEBUBPTOGETSATURATIONVALUESFORPURECOMPONENT CALLBUBP(PX,TX,FEED,AK,X,PSI,NPH,IER) C RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C SUBROUTINEDP(PX,TX,XIN1,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/PVARS/NC,METHOD PARAMETER(MX=20) CHARACTERNAME(MX)*50 DIMENSIONFEED(MX),X(MX,2),PROPS(20,2),XL(20),XV(20) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVRYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C C CUSEDEWPTOGETSATURATIONVALUESFORPURECOMPONENT CALLDEWP(PX,TX,FEED,AK,X,PSI,NPH,IER) C RETURN END C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C CSUBROUTINEFORVAPORANDLIQUIDCONCENTRATIONS C

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195 SUBROUTINEVAPLIQ(P,T,XIN1,XV,XL,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/PVARS/NC,METHOD CHARACTERNAME(20)*50 DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE' STOP ENDIF C CINTERNALUNITSTX[K],PX[BAR] CALLFLASH(P,T,FEED,AK,X,PSI,NPH,IER) IF(NPH.EQ.0)THEN CALLXD1(X(1,2),XV) XL=0 ELSEIF(NPH.EQ.1)THEN XV=0 CALLXD1(X(1,1),XL) ELSEIF(NPH.EQ.2)THEN CALLXD1(X(1,1),XL) CALLXD1(X(1,2),XV) ENDIF RETURN END C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CSUBROUTINETOCALCULATELIQUIDANDVAPORFLOWFRACTIONS CUNTESTED01/28/03,TESTBEFOREUSING!!!! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC SUBROUTINEVLFLOW(P,T,XIN1,FV,FL,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/PVARS/NC,METHOD COMMON/MW/WTMOL1,WTMOL2 CHARACTERNAME(20)*50 DIMENSIONX(20,2),FEED(20),AK(20),PROPS(20,2) DIMENSIONXL(20),XV(20) C CALLXC1(XIN1,FEED(1)) FEED(2)=1D0-FEED(1) CADDITIONALSETUP,REQUIREDEVERYTIMECOMPONENTS CORFEEDCHANGED CALLSETCOM(NAME,FEED,NC,IER) IF(IER.NE.0)THEN WRITE(*,*)'COMPONENTNAMESPELLEDINCORRECTLY,OR' WRITE(*,*)'ITISNOTPRESENTINTHEDATABASE'

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196 STOP ENDIF C CINTERNALUNITSTX[K],PX[BAR] CALLFLASH(P,T,FEED,AK,X,PSI,NPH,IER) DO111I=1,NC XL(I)=X(I,1) XV(I)=X(I,2) 111CONTINUE CEVALUATEPROPERTIESIFNOERRORSFROMFLASH IF(IER.EQ.0)THEN CALLPHASEP(P,T,XL,XV,PSI,NPH,METHOD,PROPS,IERPP) IF(IERPP.NE.0)THEN WRITE(2,*)'FAILUREINPHASEPVIAVLFLOW' ELSE CJ=1ISLIQUIDPHASE,J=2ISVAPOR FL=PROPS(1,1)*PROPS(2,1) FV=PROPS(1,2)*PROPS(2,2) ENDIF ENDIF RETURN END C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C CSUBROUTINEFORSATURATIONCONCENTRATIONINABSORBER CWILLWORKFORNONAZEOTROPICFLUIDMIXTURES. CDONOTUSEFOROTHERS. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C SUBROUTINESATC(PX,TX,XIN1,NAME) IMPLICITDOUBLEPRECISION(A-H,O-Z) LOGICALIEQ PARAMETER(MX=20) CHARACTERNAME(MX)*50 XIN11=1.0D0 XIN12=0.0D0 CALLBUBLT(PX,TX1,XIN11,NAME) CALLBUBLT(PX,TX2,XIN12,NAME) IF(TX.GT.TX1.AND.TX.GT.TX2)THEN WRITE(*,*)'NOSAT.LIQUIDATTHISTEMPERATUREANDPRESSURE' ENDIF C C221IF(TX.LT.TX1.AND.TX.LT.TX2)THEN CNCOUNT=0 CDX=1.0D-04 CERROR=(TX-TX1)/TX CERROR=DABS(ERROR) CPRINT*,ERROR C225IF(ERROR.GT.1.0D-10)THEN CXIN12=XIN11-DX CCALLBUBLT(PX,TX2,XIN12,NAME) CS=(TX2-TX1)/(XIN12-XIN11)

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197 CPRINT*,S CXNEW=(TX-TX1)/S+XIN11 CCALLBUBLT(PX,TNEW,XNEW,NAME) CXIN12=XNEW+DX C230CALLBUBLT(PX,TX2,XIN12,NAME) CSNEW=(TX2-TNEW)/(XIN12-XNEW) CR=SNEW/S CIF(R.LT.0)THEN CXNEW=(XIN11+XNEW)/2 CGOTO230 CENDIF CERROR=(TX-TNEW)/TX CERROR=DABS(ERROR) CXIN11=XNEW CTX1=TNEW CGOTO225 CENDIF CENDIF CRETURN CEND NCOUNT=0 ERR=1.0 222IF(ERR.GT.1D-12.AND.NCOUNT.LT.1000)THEN S=(XIN11-XIN12)/(TX1-TX2) XIN11=(TX-TX2)*S WRITE(*,*)XIN11,TX1,TX2 CALLBUBLT(PX,TX1,XIN11,NAME) ERR=(TX-TX1)/TX ERR=DABS(ERR) NCOUNT=NCOUNT+1 GOTO222 ELSEIF(ERR.LE.1D-12)THEN XIN1=XIN11 TX=TX1 ENDIF RETURN END C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C CMASSTOMOL SUBROUTINEXC1(XMAS,XMOL) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/MW/WTMOL1,WTMOL2 XMOL=XMAS*WTMOL2/((1.0D0-XMAS)*WTMOL1+XMAS*WTMOL2) RETURN END C CMOLETOMASS SUBROUTINEXD1(XMOL,XMAS) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/MW/WTMOL1,WTMOL2 XMAS=XMOL*WTMOL1/(XMOL*WTMOL1+(1.0D0-XMOL)*WTMOL2) RETURN END

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198 CUNIT1CONVERTSDATAFROMSIUNITSTO CSUPERTRAPPDEFAULTUNITS,NEEDSMASSFRACTION. SUBROUTINEUNIT1(X1,H,S,V) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/MW/WTMOL1,WTMOL2 H=H*WTMOL1*WTMOL2/(4.1868D0*(X1*(WTMOL2-WTMOL1)+WTMOL1)) S=S*WTMOL1*WTMOL2/(4.1868D0*(X1*(WTMOL2-WTMOL1)+WTMOL1)) V=V*WTMOL1*WTMOL2/(X1*(WTMOL2-WTMOL1)+WTMOL1) RETURN END C CUNIT2CONVERTSDATAFROMSUPERTRAPPDEFAULTUNITS CTOSIUNITS,NEEDSMOLFRACTIONINPUT. SUBROUTINEUNIT2(X1,H,S,V) IMPLICITDOUBLEPRECISION(A-H,O-Z) COMMON/MW/WTMOL1,WTMOL2 H=H*4.1868D0/(X1*(WTMOL1-WTMOL2)+WTMOL2) S=S*4.1868D0/(X1*(WTMOL1-WTMOL2)+WTMOL2) V=V/(X1*(WTMOL1-WTMOL2)+WTMOL2) RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CSUBROUTINESFORWATERPROPERTIES CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC SUBROUTINESTEAML(TX,PX,HH2OL,SH2OL,VH2OL) IMPLICITDOUBLEPRECISION(A-H,O-Z) C CCONSTANTS TB=100 PB=10 R=8.3144 H2OLRO=21.821141 C H2OA1=2.748796D-02 H2OA2=-1.016665D-05 H2OA3=-4.452025D-03 H2OA4=8.389246D-04 C H2OB1=12.14557 H2OB2=-1.898065 H2OB3=0.2911966 C H2OTD=5.0705 H2OPD=3.0000 C H2OSLD=5.733498 C TR=TX/TB PR=PX/PB CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

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199 H=-H2OLRO+H2OB1*H2OTD+H2OB2/2*(H2OTD**2+TR**2)+ 1H2OB3/3*(H2OTD**3-TR**3)-H2OB1*TR-H2OB2*(TR**2)+ 2(H2OA4*(TR**2)-H2OA1)*(PR-H2OPD)-H2OA2/2*(PR**2-H2OPD**2) HH2OL=-R*TB*H C S=-H2OSLD-H2OB1*log(TR/H2OTD)+H2OB2*(H2OTD-TR) 3+H2OB3/2*(H2OTD**2-TR**2)+(H2OA3+2*H2OA4*TR)*(PR-H2OPD) SH2OL=-R*S C V=H2OA1+H2OA2*PR+H2OA3*TR+H2OA4*TR**2 VH2OL=R*TB/PB*V C RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC SUBROUTINESTEAMV(TX,PX,HH2OV,SH2OV,VH2OV) IMPLICITDOUBLEPRECISION(A-H,O-Z) CCONSTANTS TB=100.0D0 PB=10.0D0 R=8.3144D0 C H2OGRO=60.965058 H2OD1=4.019170 H2OD2=-5.175550D-02 H2OD3=1.951939D-02 C H2OC1=2.136131D-02 H2OC2=-31.69291 H2OC3=-4.634611D04 H2OC4=0.0 C H2OTD=5.0705 H2OPD=3.0000 C H20SGD=13.453430 C TR=TX/TB PR=PX/PB CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC H=-H2OGRO+H2OD1*H2OTD+H2OD2/2*(H2OTD**2+TR**2) 1+H2OD3/3*(H2OTD**3-TR**3)-H2OD1*TR 2-H2OD2*(TR**2)-H2OC1*(PR-H2OPD) 3+H2OC2*4*(H2OPD/H2OTD**3-PR/TR**3) 4+H2OC3*12*(H2OPD/H2OTD**11-PR/TR**11) 5+H2OC4*4*(H2OPD**3/H2OTD**11-PR**3/TR**11) HH2OV=-R*TB*H C S=-H20SGD-H2OD1*LOG(TR/H2OTD)+H2OD2*(H2OTD-TR) 6+H2OD3/2*(H2OTD**2-TR**2)+LOG(PR/H2OPD) 7+3*H2OC2*(H2OPD/H2OTD**4-PR/TR**4) 8+11*H2OC3*(H2OPD/H2OTD**12-PR/TR**12) 9+11/3*H2OC4*(H2OPD**3/H2OTD**12-PR**3/TR**12) SH2OV=-R*S

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200 C V=TR/PR+H2OC1+H2OC2/TR**3+(H2OC3+H2OC4*PR*PR)/TR**11 VH2OV=R*TB/PB*V C RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C SUBROUTINEH2OSP(TX,PX) IMPLICITDOUBLEPRECISION(A-H,O-Z) DIMENSIONFRRAY(10) DATAFRRAY/0.0,-7.691234564,-2.608023696D01,-1.681706546D02, 16.423285504D01,-1.189646225D02,4.16711732, 22.09750676D01,1.0D09,6.0/ ZT=TX/647.3D0 ZTT=1-ZT PK=0 DO30I=6,1,-1 PK=PK*ZTT+FRRAY(I) 30CONTINUE PK=PK/(ZT*(1+FRRAY(7)*ZTT+FRRAY(8)*ZTT*ZTT)) PK=PK-ZTT/(FRRAY(9)*ZTT*ZTT+FRRAY(10)) PX=EXP(PK)*221.20 RETURN END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C SUBROUTINESTMLPH(PX,HX,TH2OL,SH2OL,VH2OL) IMPLICITDOUBLEPRECISION(A-H,O-Z) TT1=300.0D0 TT2=500.0D0 TT=0 SS=0 HH=0 VV=0 ERR=1 50IF(ERR.GT.1D-20)THEN TTOLD=TT TT=(TT1+TT2)/2 CALLSTEAML(TT,PX,HH,SS,VV) IF(HH.GT.HX)THEN TT2=TT ELSE TT1=TT ENDIF ERR=TT-TTOLD ERR=DABS(ERR) GOTO50 ENDIF TH2OL=TT SH2OL=SS VH2OL=VV RETURN

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201 END C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

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203 11. Babcock and Wilcox Company, 1978, Steam/Its Generation and Use, Babcock and Wilcox Company, NY. 12. Larson, D. L., 1987, Performance of the Coolidge Solar Thermal Electric Power Plant, Journal of Solar Energy Engineering, 109(1), pp. 2-8. 13. Angelino, G., and Paliano, P. C. D., 1998, Multicomponent Working Fluids for Organic Rankine Cycles, Energy, 23(6), pp. 449-463. 14. Demuth, O. J., 1980, Analysis of Binary Thermodynamic Cycles for a Moderately Low-Temperature Geothermal Resource, Proceedings of the 15th Intersociety Energy Conversion Engineering Conference, 1, AIAA, NY, pp. 798-803. 15. Demuth, O. J., 1981, Analysis of Mixed Hydrocarbon Binary Thermodynamic Cycles for a Moderate Temperature Geothermal Resources, Proceedings of the 16th Intersociety Energy Conversion Engineering Conference, 2, IEEE, NY, pp. 1316-1321. 16. Iqbal, K. Z., Fish, L. W., and Starling, K. E., 1976, Advantages of Using Mixtures as Working Fluids in Geothermal Binary Cycles, Proceedings of Oklahoma Academy of Sciences, 56, pp. 110-113. 17. Demuth, O. J., 1984, Heat Cycle Research Program, TransactionsGeothermal Resources Council, 8, pp. 41-46. 18. Boretz, J. E., 1986, Supercritical Organic Rankine Engines (SCORE), Proceedings of the 21st Intersociety Energy Conversion Engineering Conference, ACS, Washington D. C., pp. 2050-2054. 19. Maloney, J. D. Jr., and Robertson, R. C., 1953, Thermodynamic Study of Ammonia-Water Heat Power Cycles, Report No. 53-8-43, Oakridge National Laboratory, 60p. 20. Kalina, A. I., 1983, Combined Cycle and Waste Heat Recovery Power Systems Based on a Novel Thermodynamic Energy Cycle Utilizing Low-Temperature Heat for Power Generation, Paper # 83-JPGC-GT-3, American Society of Mechanical Engineers, NY, pp. 1-5. 21. Kalina, A. I., 1984, Combined-Cycle System with Novel Bottoming Cycle, Journal of Engineering for Gas Turbines and Power, 106, pp. 737-742. 22. Kalina, A. I., and Leibowitz, H. M., 1987, Applying Kalina Technology to a Bottoming Cycle for Utility Combined Cycles, Paper # 87-GT-35, American Society of Mechanical Engineers, NY, 6p. 23. El-Sayed, Y. M., and Tribus, M., 1985, Theoretical Comparison of the Rankine and Kalina Cycles, ASME Special Publications, AES -1, American Society of Mechanical Engineers, NY, pp. 97-102.

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PAGE 225

BIOGRAPHICAL SKETCH Sanjay Vijayaraghavan was born on June 23, 1976, in the village of Kodakara in the southern state of Kerala, India. He was brought up entirely in the coastal city of Chennai (formerly known as Madras), the capital of the state of Tamilnadu. In June 1997, he graduated with a bachelors degree in mechanical engineering from the University of Roorkee (now called the Indian Institute of Technology, Roorkee) located in the new state of Uttaranchal, 15 miles south of the Himalayan foothills. Places and institutions he is associated with tend to change names and shape, so watch out Gainesville and UF. Sanjay enrolled in the Department of Mechanical Engineering at the University of Florida in the fall of 1997 and worked on photocatalytic detoxification of contaminated water for his masters degree. He stayed on for a Ph.D. and spent almost a year working on antenna solar energy conversion. After preparing a roadmap for research on the topic and not being sure of his competence to implement it, has been working on the topic of this dissertation. In the meantime, the merger of two departments resulted in the new Mechanical and Aerospace Engineering Department. 208


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Creator: Vijayaraghavan, Sanjay ( Author, Primary )
Publication Date: 2003
Copyright Date: 2003

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THERMODYNAMIC STUDIES ON ALTERNATE BINARY WORKING FLUID
COMBINATIONS AND CONFIGURATIONS FOR A COMBINED POWER AND
COOLING CYCLE















By

SANJAY VIJAYARAGHAVAN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2003















ACKNOWLEDGMENTS

The work presented in this dissertation was completed with the encouragement and

support of many wonderful people. Working with Dr. Yogi Goswami has been a

tremendous experience. He expects his students to be self-starters, who work

independently on their projects. I appreciate his patience and mentorship in areas within

and beyond the realm of research and graduate school. Dr. Sherif Sherif was a terrific

source of discussion, advice, encouragement and hard to find AES proceedings. Dr.

James Klausner, Dr. David Hahn, and Dr. Ulrich Kurzweg agreed to be on my committee

and took the time to read and critique my work, for which I am grateful. Dr. Hahn was

also on my master's committee and supervised me during my assignment as a TA for two

terms.

Dr. Bill Lear has to be thanked for advice on jet pumps and Dr. Skip Ingley for his

interest in the cycle. Dr. Leon Lasdon from the University of Texas sent me the

FORTRAN version of the GRG code and answered my questions very promptly.

Although my particular project did not require much of his marvelous skills, the senior

engineering technician at the Solar Park, Chuck Garretson, was very supportive.

Watching him and working with him have taught me many things. He is a wonderful

resource for any student at the lab. Barbara Graham over the years and now recently

Vitrell McNair at the solar office have cheerfully helped me in many ways in the course

of my stay here. Mrs. Becky Hoover will have to be thanked for her help and constant

reminders to finish up.









My fellow students at the solar lab have been stimulating company. Some of them

particularly have to be acknowledged. Gunnar Tamm, Chris Martin and Nitin Goel took

interest in my work and provided constructive feedback. Gunnar has also been at the lab

almost as long as I have, and he has been fun to work with. Former students such as

Viktoria and Andrew Martin, and Adrienne Cooper have stayed in touch and encouraged

me.

I would like to particularly thank my family for putting up with my being so far

away from home, and for their love, support and eternal optimism. This section is not

complete without mentioning friends, old and new, too many to name individually, who

have been great pals and confidants over the years.
















TABLE OF CONTENTS
Page

A C K N O W L E D G M E N T S ......... .. ................................................................. ............... ii

LIST OF TABLES ......... .......... ............................. .......... .............. viii

L IST O F FIG U R E S .......... .. .......... .................................. .. ........ ........ ..... ix

N O M EN CL A TU R E ........... ........................................................................ xiii

A B ST R A C T ............................................................................. ........................................ xvi

CHAPTER

1 B A C K G R O U N D ............ ................................................. .. ...... ............... .. 1

In tro d u ctio n .................................................................. 1
Background ................................. .......................... ..... ..... ........ 2
R ankine C y cle ................. ...... ............................. 3
Power Cycles for Low Temperature Heat Sources ......................................... 5
O organic R ankine cycles (O R C) .......................................................... ..... 5
Supercritical cycles...................................... 6
M alone and R obertson cycle ................................................... ....... 8
Kalina cycle ................ .................... .......... ....... 9
Other am m onia based cycles ........................... .. ... ...................... 13
Use of Mixtures as Working Fluids in Thermodynamic Cycles ...................... 14
The Combined Power and Cooling Cycle ................................. .............. 16
Introdu action ............................................................ ....... .. 16
A summary of past research on the cycle ...................................................... 18
Specific motivation for work in this dissertation................... 21

2 EFFICIENCY DEFINITIONS FOR THE COMBINED CYCLE............... 24

C conventional Efficiency D definitions ............................... ........................................ 24
First Law Efficiency ................. ................. ..... ...................... 25
E x ergy E fficien cy ................................................. .............. ...... .............. 2 5
Second Law Efficiency .............. ......... ............................... .............. 26
The Choice of Efficiency Definition ......... ........................... .. ............ 28
Efficiency Expressions for the Combined Cycle ............................................... 28
F first L aw E fficien cy ............................................................. .......................... 2 8
Exergy Efficiency .......... ................ ........................................ ............. 30









Second L aw Efficiency ............................................... .............................. 30
Lorenz cycle ........................................... 30
Cascaded cycle analogy .................................................... 32
V validity of E xpressions......................... ........... ....... .... ..... .......... 35
Case 1: Comparing this Cycle to Other Combined Cooling and Power
G generation O options ............................................................... .. 36
Case 2: Comparing a Combined Cycle to a Power Cycle ......................... 36
Some Examples of Application to the Combined Cycle ......................................... 37
Conclusions ................ .......... .............. .............................. 41

3 CYCLE SIMULATION AND OPTIMIZATION .............................................. 42

O ptim ization M ethod B ackground........................................................ .............. 42
Search T erm nation ........................................ ...................... .. ................ 46
Sensitivity Analysis .............. ...................................... ...... .............. 46
A application N otes ......... ........................ ................ ..... .. .......... 47
Cycle Modeling ............... ......... .................. 48
State P oint C alculation ................................................... ........... ........... 49
State point 1 ...................................... .............. 49
P o in t 2 ................. .............. .............. ...... 5 1
Points 5 and 11 ............. ........................... 52
Points 6 and 7 .. ... ........ ................... .............. 53
P point 8.. ................ ............................ 53
P point 9.. ................ ............................ 54
P point 10 ............................................................................................. 54
Points 12 and 3 .............. ................... .............. 55
Point 13 .................. ......... ............ 56
P point 14 ............................................................................................. 56
P point 15 ............................................................................................. 57
P point 4.............................................. 57
V variable L im its ...................................................... .............. 57
Constraint Equations ........ .......... ......... ................ .............. 59
M odel Limitations................... ... ................... .............. 61

4 OPTIMIZATION OF BASIC CYCLE CONFIGURATION USING AMMONIA-
WATER MIXTURE AS THE WORKING FLUID .................................... 62

Sim ulated C condition s ....................................................................... 63
Optimization results ................................... ......... ................. 65
R source U tilization Efficiency .................................................................... 65
Exergy Efficiency ..........................................67
First Law Efficiency ............. .................. .............. 69
Exergy Analysis ............................................... ........ ...... ......... 70
Optim ization Considering Losses ................................................................... 74
D iscu ssion ........................................................................................................ 79
C conclusions ............................................................................................................ 84



v









5 RESULTS AND DISCUSSION: ORGANIC WORKING FLUIDS ........................ 86

W working F lu id S election ............................................................................................ 86
Prelim inary Simulation ....................... ................................................................ 89
Simulation of Higher Boiling Components .................................................... 94
D discussion ............................................................................................................. 99
Factors Affecting Cycle Performance .............................................. ........... 100
Rectification ............................ .............. 100
B oiler C conditions .............................................................. .. 10 1
Basic Solution Concentration .............................. 104
Pressure and Tem perature Ratio............................................... ................. 104
Volatility Ratio .. ....................... ....... .. ............ .......... 108
Liquid Formation During Expansion....................... ..... .............. 109
Conclusions ..................................... ................................ .......... 113

6 RESULTS AND DISCUSSION: IMPROVED CONFIGURATIONS................. 115

M o tiv atio n ............................................................................. 1 1 5
Reflux Mixed with Boiler Inlet................................. .............. 115
A addition of a Preheater .......................................................... ... .............. 118
Jet Pum p A assisted C ycle ....................................................................... 120
Jet Pum p B background ......................................................... .............. 122
Jet Pum p A nalysis............................................. .................... .. ................ 123
Primary nozzle ...... ........ ...... ................ ..1............... 126
Secondary nozzle ....... ........ ...................... ..1.... .... .... 128
M ixing section ........ ... .. ........... .... ......... ......... ... ......... ..... 128
D iffuser ....................................................... ... .. ... ............ .............. 130
Simplified M odel U sed in Simulation .................................... .............. 131
R esu lts ................................................................................... .............. 13 2
Conclusions................. ............... ..... .............. 135
Distillation (Thermal Compression) Methods ............................................... 135
Using Heat Source ... ..... ............................................................. 136
Using Absorber Heat Recovery ................. ..... ............. .. .............. 142
Conclusions ......................................... 149

7 CONCLUSIONS ............ ............. ............ .............. 150

Summary of Results ......................................... ................... 150
Future W ork ............................................................. ........ 153

APPENDIX

A WORKING FLUID PROPERTY CALCULATION .......................................... 157

P property P reduction M ethods ................................................................................... 157
M ethods Used for Properties in this Study .................................... .............. 159
Ammonia Water Properties Prediction................... ....................... 159









Organic Fluid Mixture Properties ........................................ ............. 160

B OPTIM IZED STATE POINTS..................................................... 164

Conditions ............................................................... .... ...... ........ 164
Basic Cycle Configuration........................... .......... .... 165
Fluid: A m m onia- W ater.................................................... 165
Fluid: Propane-n-Undecane ............... ........ ........... .............. 168
Fluid: Isobutane-n-Undecane....................... ........... 169
Configuration with Preheater............................. .............. 170
Configuration with Jet Pum p .............. .............. ............................ ...... 170
Configuration with Kalina Thermal Compression....................................... 171
U sing heat source for distillation.............. ........................ ....... ....... 171
Using absorber heat recovery for distillation ............ ...... ............ .. 173

C SIMULATION SOURCE CODE .................... .. ................. .............. 176

B asic C ycle C configuration ...................... .. .. .................... .................... .............. 176
H eader file............................................ 176
Cycle Sim ulation .................. ...................... ..... .... ...... .. ......... ..... 177
Interface to Supertrapp .......................................................... ... .............. 186

LIST OF REFEREN CES ................................................... ................................. 202

BIOGRAPHICAL SKETCH .............................................................. ...208
















LIST OF TABLES


Table p

1.1 Efficiency definitions used in various papers published on the cycle................. 22

2.1 Some examples of efficiencies applied to the Rankine cycle and the vapor
com pression refrigeration cycle..................................................... .............. 26

2.2 Cycle parameters that yield optimum exergy and second law efficiencies ............ 38

2.3 Efficiency and cycle parameters optimized for effective exergy efficiency .......... 39

2.4 Efficiency and cycle parameters optimized for effective first law efficiency......... 40

3.1 Independent cycle parameters and their limits ............................................ .. 58

3.2 Constraints used in the optimization .............. ...... ......................... ........... 60

5.1 List of working fluids Considered Initially .............. ..... .... .......... .... 88

5.2 Higher boiling components considered ............. ...................... .......... ........ 95

5.3 Calculated R/cp values for certain gases in the temperature range of the cycle
b ein g stu d ied ................................................... ................ 10 6

5.4 V olatility ratio of selected pairs.................................................... 109

5.5 Ivalues of certain pure components at 300 K and corresponding saturation
p re ssu re ...................... .. .. ......... .. .. ............................................... 1 10
















LIST OF FIGURES


Figure pge

1.1 A schematic diagram of a simple Rankine cycle................................................. 4

1.2 Diagram showing a supercritical Rankine cycle on the T-s diagram for isobutane.. 7

1.3 Arrangem ent of a sim ple K alina cycle ........................................... .............. 9

1.4 Schematic diagram of Kalina System 12................. .......................... .............. 12

1.5 Illustration of the difference in temperature profiles for a pure fluid being boiled
and a multi-component mixture being boiled ....... ...... ........ ......................... 15

1.6 The basic configuration of the combined power and cooling cycle..................... 17

1.7 Effect of turbine inlet pressure on the thermal efficiency (%) of the cycle ........... 20

1.8 Effect of turbine inlet pressure on the cooling capacity (kJ/kg) of the cycle ......... 20

2.1 A cyclic heat engine working between a hot and cold reservoir ............................. 27

2.2 The T-S diagram for a L orenz cycle.............................................. ... ................. 31

2.3 Thermodynamic representation of (a) combined power/cooling cycle and (b)
cascaded cycle ..... ...................................... ............... 33

3.1 The basic cycle configuration with the variables shown...................................... 50

4.1 Block diagram showing the basic scheme of the combined power and cooling
cycle. Same as Fig. 1.6 ...... .... ........................................ .... ............ .. 64

4.2 Optimized resource utilization efficiencies for the basic cycle configuration ........ 66

4.3 Optimized exergy efficiencies for the basic cycle configuration ........................ 68

4.4 Optimized First Law Efficiencies for the Cycle Configuration in Fig. 4.1 ............ 70

4.5 Exergy destruction in the cycle represented as a percentage of exergy of the heat
source, for optimized RUE corresponding to 280 K turbine exit temperature........ 71









4.6 Exergy destruction in the cycle represented as a percentage of exergy of the heat
source, for optimized RUE corresponding to pure work output............................ 71

4.7 Exergy destruction in the cycle for optimized exergy efficiency corresponding to
280 K turbine exit tem perature...................................................... .............. 73

4.8 Exergy destruction in the cycle for optimized exergy efficiency corresponding to
pure w ork output.................... .................................... .. .. .... ...... .............. 73

4.9 Optimized RUE for the basic cycle configuration using a non isentropic turbine
and pump ...... ........... ............................ 75

4.10 Effect of recovery heat exchanger effectiveness on RUE at optimum RUE
conditions, with cooling output ............................................. ............. ........ 75

4.11 Optimized exergy efficiencies for the basic cycle configuration using a non
isentropic turbine and pum p .............. .................................................................. 77

4.12 Effect of recovery heat exchanger effectiveness on effective efficiency .............. 77

4.13 Exergy destruction in the optimized RUE case.............. ............ ......... ..... 78

4.14 Exergy destruction in the optimized exergy efficiency case ................................. 78

4.15 Working fluid temperatures and vapor fractions in boiler: at maximum RUE and
w ith co o lin g ..................................................................................... 8 0

4.16 Working fluid temperatures and vapor fractions in boiler: at maximum RUE with
pure w ork output.................... .............. .................... .. .... ............ .. .............. 80

4.17 Cycle pressure ratios and the influence of solution heat exchanger effectiveness.. 82

4.18 Cooling to work output ratios at optimum conditions ....................................... 82

4.19 First law efficiency at optimized exergy efficiency conditions............................... 83

4.20 First law efficiency at optimum RUE conditions ........................................ 84

5.1 Basic configuration simulated. In this configuration, the condensate from the
rectifier is redirected to the absorber. ............. ...... .......................... .......... 90

5.2 Optimized second law efficiencies of the combined power and cooling cycle using
organic w working fluid pairs..................... ................................. .......................... 92

5.3 Alternate configuration, where the condensate from the rectifier is mixed with the
strong solution inlet stream to the boiler. ............. ............................... ....... ....... 93

5.4 Comparison of the second law efficiency performance of the two configurations in
Fig. 5.1 and 5.3, using a propane-hexane mixture as the working fluid................ 94









5.5 Optimized exergy efficiency using higher boiling non volatile mixtures ............ 95

5.6 Optimized resource utilization efficiency using higher boiling non volatile
mixtures ........ ..................................... ............... 96

5.7 Pressure ratios at optimum exergy efficiency.............................. .................... 98

5.8 Pressure ratios at optim um RU E ........................................ .................. ...... 98

5.9 Maximum (limiting) pressure ratio using some working fluid mixtures at various
basic solution concentrations in the absorber and using a 360 K heat source....... 100

5.10 Phase diagram of a part of the cycle using isobutane-n-decane at 400 K,
optim ized for exergy efficiency.................................... ............................. ...... 102

5.11 Close up of a portion of Fig. 5.10............... .................................... ................. 102

5.12 Effect of low pressure (propane-hexane mixture as working fluid)................. 105

5.13 Calculated isentropic temperature ratio as a function of pressure ratio using
perfect gas assume options .................................. .............. ................................... 107

5.14 T-s diagram for concentrated propane-n-undecane mixtures ............................. 111

5.15 T-s diagram for concentrated isobutane-n-undecane mixtures............................. 112

5.16 T-s diagram for concentrated propane-n-hexane mixtures.............................. 112

5.17 T-s diagram for concentrated ammonia-water mixtures..................................... 113

6.1 Modification of the basic cycle configuration which has the liquid condensate
from the rectifier mixed with the strong solution at the boiler inlet.................... 116

6.2 Optimum exergy efficiencies obtained with the modified configuration shown
in F ig 6 .1 ........................................................ ................. 1 1 7

6.3 Major exergy destruction categories for the modified cycle, at optimum exergy
efficiency conditions........................................ ........................... ...... .... .. 118

6.4 Modified cycle configuration with part of the basic solution being preheated by
the heat source fluid............ ................. ......................... ... .. .......... 119

6.5 Optimized RUE for the modified configuration in Fig. 6.4 compared to the base
con figu ration in F ig 4 .1 ...................................... ............................................ 12 1

6.6 Major exergy losses in different parts of the modified cycle, optimized for RUE 121

6.7 Schematic drawing of a jet pump showing the different sections and the flow
th rou g h it .................. .................................. ...... .......... ..... 12 4









6.8 Cycle configuration incorporating the jet pump..................... .............. 132

6.9 Improvement in resource utilization efficiency with the addition of a jet pump... 134

6.10 Influence of the choice of turbine exit temperatures on the improvement
achievable with ajet pump using an isentropic turbine and pump....................... 134

6.11 Cycle configuration using the heat source to produce vapor in the distiller ......... 137

6.12 Maximum RUE of the cycle configuration modified with heat source fluid
powered thermal compression modification....................... ... ........... ... 139

6.13 First law efficiency at maximum RUE conditions for configuration with heat
source powered thermal compression modification ......................... ................. 139

6.14 Exergy destruction in the cycle with heat source powered thermal compression
modification, when operated to provide power and cooling ............................... 140

6.15 Exergy destruction in the cycle with heat source powered thermal compression
modification, when operated to provide only power output................................ 140

6.16 Some parameters for optimized RUE conditions in the cooling domain ............. 141

6.17 Some parameters for optimized RUE in the work domain........................... .. 142

6.18 Cycle configuration using heat of condensation to produce vapor in the distiller 144

6.19 Maximum RUE of the cycle configuration modified with a condensing mixture
providing heat of distillation......................................................... .............. 145

6.20 First law efficiency at maximum RUE conditions for configuration using heat
of condensation to produce vapor in the distiller ............................................... 145

6.21 Exergy destruction in cooling domain in modified cycle with a condensing
mixture providing heat of distillation ..... ........... .. ................................. 146

6.22 Exergy destruction in work domain with a condensing mixture providing heat
o f d istillatio n .................................................................... .............. 14 7

6.23 Some parameters for optimized RUE (strict definition) in the cooling domain for
the modified cycle with a condensing mixture providing heat of distillation ....... 148

6.24 Some parameters for optimized RUE in the work domain for the modified cycle
with a condensing mixture providing heat of distillation............................. 148















NOMENCLATURE

COP Coefficient of Performance

cp Specific heat

E Exergy

f refrigeration weight factor

h specific enthalpy

i Exergy Index

Imf Liquid mass fraction

m mass

NTU Number of Transfer Units

Obj Objective function

p Pressure

Q Heat Interaction

T Temperature

S Entropy

s specific entropy

R Universal gas constant

r Ratio of cooling to work output

v Specific volume

vmf Vapor mass fraction









W Work Interaction

x Mass fraction of ammonia (volatile component) in a binary mixture

y Mole fraction of volatile component in a binary mixture



Greek Symbols

a21 Volatility of component 2 w.r.t component 1

r7 Efficiency


Subscripts

0 Reference state

b Boiling

basic Referring to basic solution stream, from absorber

Carnot Carnot Cycle

c Cooling

cf Chilled Fluid

crit Critical

eff Effective

exergy Exergy

exit At Exit of a Device

fg Liquid to gas (representing phase change from liquid to gas)

HE Heat engine

h Heat Source

high High









hr Heat rejection Fluid

hs Heat Source Fluid

in Input

Lorenz Lorenz Cycle

low Low

m Melting

max maximum

net Net

out Output

p Pump

R Resource Utilization Efficiency

r Reduced

rev Reversible

ref Refrigeration

sys System

useful Useful

I First Law

II Second Law















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

THERMODYNAMIC STUDIES ON ALTERNATE BINARY WORKING FLUID
COMBINATIONS AND CONFIGURATIONS FOR A COMBINED POWER AND
COOLING CYCLE

By

Sanjay Vijayaraghavan

August 2003

Chair: D. Y. Goswami
Major Department: Mechanical and Aerospace Engineering

A combined power and cooling cycle was investigated. The cycle is a combination

of the Rankine cycle and an absorption refrigeration cycle. A binary mixture of ammonia

and water is partially boiled to produce a vapor rich in ammonia. This vapor is further

enriched in a rectifier/condenser and after superheating, expanded through a turbine. The

vapor exiting the turbine in this cycle is cold enough to extract refrigeration output. By

suitable selection of operational parameters for the cycle, the useful output can have a

large range of refrigeration to work ratios. This combined cycle is being proposed for

applications with lower temperature heat sources, with the primary objective of

producing power. Some examples of energy sources include solar, geothermal, or

industrial waste heat.

Evaluating the efficiency of this cycle is made difficult by the fact that there are

two different outputs, namely power and refrigeration. An efficiency expression has to

suitably weight the cooling component in order to be able to compare this cycle with









other cycles. Several expressions are proposed for the first law and second law

efficiencies for the combined cycle based on existing definitions in the literature. Some

of the developed equations have been recommended for use over others, depending on

the comparison being made.

This study extended the application of the cycle to working fluids other than

ammonia-water mixtures, specifically to organic fluid mixtures. It was found that very

low temperatures (well below ambient) are not achievable using organic fluid mixtures,

while with an ammonia-water mixture; temperatures that were substantially below

ambient were obtained under similar conditions. Thermodynamic efficiencies obtained

with hydrocarbon mixtures are lower than those seen with an ammonia-water mixture as

the working fluid.

Based on the exergy analysis, the cycle configuration has been modified to improve

its second law efficiency. A significant improvement in the resource utilization

efficiency of more than 25% was achieved with the best among the improved schemes.

Increased efficiencies can also be obtained for the cases where only work output is

desired.














CHAPTER 1
BACKGROUND



Introduction

The goal of this study is to investigate the use of organic fluid binary mixtures as

possible alternate working fluids for a new thermodynamic power cycle (henceforth

referred to as the cycle) proposed by Goswami [1]. The power cycle under study is

unique in that the working fluid exiting the turbine could be cold enough to extract

refrigeration. This cycle is a combination of the Rankine and absorption refrigeration

cycles. The performance of the cycle has been studied extensively and optimized in

earlier studies [2-8]. A mixture of ammonia and water has been considered so far for the

working fluid. An experimental setup was built and a preliminary verification of

ammonia boiling and condensation behavior performed [8].

The cycle has been found to be more suited to low temperature heat sources, based

on earlier simulation results. The use of a volatile component such as ammonia allows

vapor to be formed at high enough pressures that are useful for power generation. It is,

therefore, anticipated that this cycle will be used in low temperature applications such as

those involving solar, geothermal, and waste heat sources.

Traditionally, the trend in thermal energy conversion in general, is to use higher

temperatures in thermal energy conversion plants. Heat associated with high

temperatures has a larger availability, and therefore systems operating at higher

temperatures normally achieve greater first law efficiencies of conversion. Some of the









best efficiencies (around 58% first law efficiency) achieved today are with combined

cycle power plants. Attempts are being made to break the 60% efficiency barrier in some

combined cycle plants being designed currently [9]. In combined cycle plants being built

today, a gas turbine power cycle is the first stage, and the exhaust from the turbine is used

to run a steam power plant. In the case of solar power generation, to operate at high

temperatures, considerable concentration of the solar radiation is required. Solar energy

being a dilute resource, the collection system is a large part of the cost of a solar power

plant. The optics required for achieving high concentration increases the cost of the

collection system.

Some of the biggest disadvantages of solar energy as an energy source for

electricity generation are a) the dilute nature of the resource, b) the intermittent nature of

the energy and c) the high cost of producing power. It is hoped that by using cheaper,

low concentration collection systems and a cycle that utilizes a large percentage of the

exergy in that temperature range, the cost of solar power production can be brought

down. The combined power and cooling cycle is being developed to efficiently utilize

the exergy of low temperature heat sources. Since the cycle can operate at low

temperatures, it could be applied to other low temperature heat sources such as

geothermal and waste heat.

Background

Thermal power cycles can be classified on the basis of the working fluid used, as

vapor power cycles and gas power cycles. In a vapor power cycle, the gas that spins the

turbine is obtained from vaporizing a liquid. An example of such a cycle is the classic

Rankine cycle. In a gas power cycle, such as the Brayton cycle, the working fluid is in a

gaseous state throughout the cycle.









Rankine Cycle

The most commonly used vapor power cycle is the Rankine cycle. Even though a

description of the Rankine cycle can be found in any engineering thermodynamics

textbook [10], it is briefly covered here. The simple Rankine cycle, shown in Fig. 1.1

consists of four steps. The working fluid is pumped to a high pressure and circulated

through the boiler. The fluid is boiled at a constant pressure in the boiler after which the

high-pressure vapor produced is expanded through a turbine, thus extracting work from

it. The vapor exiting the turbine is condensed in a condenser by rejecting heat to a

cooling fluid. There are several modifications to the Rankine cycle that are used to

achieve better efficiencies. These include superheating, reheating and regeneration.

Water (Steam) is the working fluid of choice for most vapor power cycles. Water

works over a broad range of temperatures and pressures, has a large heat capacity, and is

stable, safe and very environmentally friendly. The energy sources used to generate

steam include gas, coal, oil, and nuclear sources. A small percentage of steam power

plants use geothermal and solar energy sources. The first commercially successful steam

engine was the one patented by Thomas Savery in 1698. The better-known Newcomen's

engine eventually displaced this engine in the early 18th century [11]. The steam power

plant has come a long way in the 100 odd years since central steam generating plants

started being built. The first central station steam turbine in the United States operated

(in 1900) with steam conditions of IMPa and 483 K. In contrast, a typical central steam

power station today operates at high pressure turbine inlet pressures and temperatures of

16.4 MPa and 800 K respectively [11].







































Fig. 1.1 A schematic diagram of a simple Rankine cycle

While steam is the working fluid of choice today, there are certain situations in

which it does not work efficiently, particularly with low temperature resources. For

example, consider the case of a binary1 geothermal power plant. In such a plant, a fluid

such as isobutane is boiled using a relatively low temperature geothermal fluid, and used

to spin a turbine working on a Rankine cycle. If steam were to be used in such

applications (or if the plant is designed as a flash type plant), very low pressures and

large vacuums at turbine exit would result.


1 It needs to be pointed out that in a binary geothermal power plant, a high pressure fluid is heated by a hot
geofluid, boiled and expanded through a turbine. This is not the same as a plant using a binary fluid
mixture for a working fluid.









Power Cycles for Low Temperature Heat Sources

The cycle being studied here appears to work well with low temperature heat

sources, based on past studies. Low temperature heat sources are usually those deriving

their energy from geothermal, solar or some waste heat sources. Solar energy can be

used at various temperatures, depending on the collection method used. Low temperature

heat sources have low availability and are not usually the energy sources of choice. Such

sources would be considered useful only if some economic advantage is found in their

utilization. For instance, a geothermal power plant could prove to be economically

feasible to supply an area in the vicinity of a geothermal steam field.

Several power cycles that are suitable for use with low temperature heat sources

have been proposed in the literature and have been used in practice. The Rankine cycle

has been adapted for use with low temperature heat sources by using low boiling working

fluids such as organic fluids. Organic Rankine cycles (ORC) have been extensively used

in binary geothermal power plants and low temperature solar power conversion. Several

ammonia-water mixture based cycles have also been proposed for low temperature

applications.

Organic Rankine cycles (ORC)

Since the first Rankine cycle-based thermal power plant was built, there have been

several improvements in the configuration, components, and materials used, but the

working fluid of choice has almost always been water. While water has several

properties that make it a very good choice as a working fluid, in low temperature

applications, better choices are available. Organic working fluids are a popular choice

for such applications. Despite the fact that these fluids have lower heats of vaporization

than water, which requires larger flow rates, smaller turbine sizes are obtained due to the









higher density at the turbine exit conditions. A variety of fluids, both pure components

and binary and ternary mixtures, have been considered for use in ORCs. These include

saturated hydrocarbons such as propane, isobutane, pentane, hexane and heptane;

aromatics such as benzene and toluene; refrigerants such as R11, R113, R114; and some

other synthetic compounds such as Dowtherm A.

Organic Rankine cycles have been proposed and used in a variety of applications

* Binary geothermal power plants: A flash type geothermal power plant is unsuitable
for low temperature, liquid dominated, geothermal resources (nominally below 180
C). Instead, the geofluid is used to boil an organic working fluid that is
subsequently expanded in a turbine. Isobutane is an example of a common
working fluid in such applications.
* Solar thermal power: ORC plants can also be applied to the conversion of low and
medium temperature (say up to 300 C) solar heat. The Coolidge plant [12] that
was a 200 kW plant built near the town of Coolidge, AZ, is a good example. For
higher temperature heat sources, toluene seems to be a common choice of working
fluid.
* Bottoming cycle applications: ORCs have been proposed for the bottoming cycle
in some applications

Mixtures of organic fluids have also been studied for use in ORCs. The advantages

of the use of mixtures will be discussed later in this chapter. Binary mixtures have been

found to have a better performance compared to pure fluid ORCs [13-16]. Organic fluid

turbines have been found to be very reliable and to have a relatively high efficiency even

at small sizes. Due to their reliability, some people have even suggested their use in

space applications, with the ORC as the bottoming stage of a Brayton or Rankine cycle

power plant.

Supercritical cycles

The use of mixtures is one way to obtain good thermal matching with sensible heat

sources. Other methods that have been proposed include multi-pressure boiling and

supercritical operation. Multi pressure boiling has not been very popular in the industry










because of the costs involved. The other option is to use supercritical cycles. The cycle

high pressure and temperature exceed that at the working fluid critical point in a

supercritical cycle. The boiling process does not pass through a distinct two-phase

region, and a better thermal match is obtained in the boiler. Figure 1.2 shows the boiling

process in a supercritical cycle on a T-s diagram. Notice the better thermal match in a

boiling heat exchanger. Supercritical cycles have to operate at a higher pressure, since

the boiler pressure has to exceed the critical pressure of the working fluid. This is a

disadvantage. Equipment costs go up at higher pressures, although there is an

improvement in performance.




420
heat source
400 -

380 -

360 -
q)
2 3 /
S340 -
1)
E
w 320
I--

300 -

280 -

260


Fig. 1.2 Diagram showing a supercritical Rankine cycle on the T-s diagram for isobutane









Supercritical cycles have been studied in the United States for geothermal

applications as a part of the DOE Heat Cycle Research Program [17] and have been

found to improve geofluid effectiveness (power output per unit mass of geothermal fluid

consumed, usually expressed as kWh/lb). Boretz [18] studied the use of supercritical

operation in space applications. He suggested the use of a supercritical cycle in order to

avoid the two-phase boiling encountered at subcritical conditions.

Several power cycles utilizing ammonia-water mixtures as the working fluid have

been proposed in the literature. A common characteristic of most of these cycles is that

all or part of the heat rejection occurs in an absorber condenser. These range from the

simple Maloney and Robertson cycle to the relatively sophisticated Kalina cycle. Some

of these cycles are discussed below.

Maloney and Robertson cycle

Although ammonia based cycles have been proposed earlier in the literature, in this

chapter the oldest cycle considered is one by Maloney and Robertson [19]. Maloney and

Robertson studied the ammonia-water binary mixture as a candidate for a simple

absorption based power cycle. They studied the cycle within the range of properties

available to them at that time and concluded that in all cases a steam Rankine cycle was

more efficient. The range of temperatures, pressures, and compositions for which

property data were available at the time of the study was limited. This is a serious

shortcoming of Maloney and Robertson's results. Further, the cycle did not have a super

heater included in the loop, which could have changed somewhat the efficiencies

obtained.










Kalina cycle

Another ammonia-water mixture based cycle of more recent origin that shows

considerable promise is the Kalina cycle [20,21]. The first Kalina cycle was first

developed in the late 1970's and early 1980's. This cycle, developed by Alexander

Kalina, is essentially a Rankine cycle that utilizes a binary mixture of ammonia and water

as the working fluid. This results in better thermal matching in the boiler, as will be

discussed later. Another feature of the Kalina cycle is the extensive internal heat

recovery and exchange arrangement that minimizes irreversibilities in the heat transfer

processes in the cycle. Many of the Kalina cycle configurations proposed also have an

arrangement that uses the heat in the vapor leaving the turbine in a distiller to concentrate

the liquid stream that is boiled and expanded in the turbine.

10

0 Turbine

Boiler

96 11
9r
5
Distiller

Recovery
t7 Hx.


Fig. 1.3 Arrangement of a simple Kalina cycle [20]









The basic version of the Kalina cycle is shown in Fig. 1.3. The composition of the

working fluid passing through the boiler (or the working solution) is different from the

basic solution in the absorber. This is accomplished through the distillation method that

has also been called a "thermal compression" arrangement in some papers.

The hot vapor leaving the turbine is used to distil a fraction of the pressurized basic

solution (state 2) to produce vapor (state 6) rich in ammonia. The remaining liquid is

combined with the cooled turbine exhaust vapor in an absorber (state 13). The turbine

exhaust is normally at too high a concentration to be fully condensed at the corresponding

pressure. Combining with the weak liquid enables condensation. The vapor from the

distiller is combined with the rest of the basic solution and condensed (state 8) to form

the working fluid. The working fluid is vaporized, and superheated (state 10) in the

boiler and expanded in the turbine.

The advantages of a Kalina cycle plant are the following

* The use of a mixture results in a better thermal match in the boiler due to variable
temperature boiling
* Better internal heat recovery is also possible due to use of mixtures
* The distillation arrangement along with absorption condensation allows a lower
turbine exit pressure despite using a high concentration vapor. Higher work output
is therefore obtained


Several studies have shown that the Kalina cycle performs substantially better than

a steam Rankine cycle system [20-22]. El-Sayed and Tribus [23] showed that the Kalina

cycle has 10-20% higher second law efficiency than a simple Rankine cycle operating

between the same thermal boundary conditions. A second law analysis of various Kalina

systems shows that using a binary fluid and the resulting reduced irreversibility

generation in the boiler is one source of the improved efficiency of the cycle [24-25].









Marston [26] verified some of the results of El-Sayed, Tribus, and Kalina and through a

parametric analysis concluded that composition at turbine inlet and temperature at the

separator of a simple Kalina cycle are the key parameters in optimizing cycle

performance.

Several Kalina cycle variations have been proposed, each optimized for different

applications. A common feature of each of these "systems" as the developers of this

cycle prefer to call the versions, is the improved and sometimes counterintuitive

application of internal heat recovery in the cycle to minimize exergy losses. For instance,

in a bottoming cycle for utility applications, (Kalina System 6) [22], the vapor is actually

cooled between the IP and LP turbines and used to evaporate part of the working fluid

stream.

The Kalina Cycle System 12 [27] is a variation of the Kalina cycle that was

proposed for geothermal applications. This version does not have the trademark

distillation arrangement. Instead, a more complicated network of recovery heat

exchangers is used to improve efficiency. Figure 1. 4 shows the Kalina 12 system.

Bliem [28] studied the application of the Kalina cycle to hydrothermal (liquid

dominated geothermal) energy conversion. The supercritical, recuperated Rankine cycle

technology studied as part of the heat cycle research program proved to have a slightly

higher second law efficiency compared to the Kalina System 12. The Heber binary

geothermal plant summer design conditions were used as a reference. Both these

technologies were superior to the supercritical isobutane based Rankine cycle being used

at Heber.












STurbine HP TurbineLP

---- --------------------------- 7


Superheater Reheater


Geofluid ------------- 8
in 5 I
In

Evaporator 2

3 Recovery
Hx. 1
Evaporator 1

10

Geofluid out
Recovery
Hx. 2









Condenser


Fig. 1.4 Schematic diagram of Kalina System 12

The Kalina type distillation-condensation subsystem was also evaluated in


supercritical organic cycles, but the improvement was found to be minimal. Bliem and


Mines [29] also showed that the Kalina System 12 and the supercritical cycle approach a


realistic upper limit of conversion, for the relatively high temperature resources (460 K


and 500 K) studied.


Ibrahim and Klein [30] compared the thermodynamic performance of the Maloney


and Robertson cycle and the Kalina cycle based on a second law analysis. The second


law efficiency was defined as the ratio of the first law efficiency of the cycle to that of a

"maximum power" cycle operating between the same thermodynamic conditions. The









maximum power cycle used is essentially the Lorenz cycle. These concepts are

explained in greater detail in chapter 2. Based on the results from that study, the Kalina

cycle outperforms the Maloney and Robertson cycle at large heat exchanger sizes (large

NTU).

The Kalina cycle has been criticized for the fact that obtaining the output predicted

by calculations for the cycle requires 100% vaporization of the working fluid in a single

pass countercurrent boiler. The heat exchanger surfaces would dry out at high vapor

fractions, resulting in lower overall heat transfer coefficients and a larger heat exchange

area. The first Kalina geothermal plant (of 2 MWe capacity) [31] built in Husavik,

Iceland, does not use the system 12 configuration. Instead, about 70 % of the flow is

vaporized and the remaining liquid throttled back through a series of recovery heat

exchangers. Over the last twenty years, the Kalina cycle has caught a lot of attention

from the engineering community, but that has translated to very few plants actually being

built. The first bottoming cycle demonstration of the plant was at the Energy Technology

and Engineering Center, a DOE facility near Canoga Park, California [32]. A 3 MW

demonstration plant was constructed that started operation in 1992. Tests were

conducted till the end of 1996.

Other ammonia based cycles

Rogdakis and Antonopoulos [33] proposed an ammonia-water absorption power

cycle. This cycle is somewhat similar to the Kalina cycle, with the major difference

being that the distillation-absorption condensation process is replaced with a simple

absorption condensation process. The authors calculated a substantially higher (greater

than 20%) first law efficiency as compared to a steam Rankine cycle, while keeping

similar superheating and condensation temperatures. The improvement is particularly









good at low heat source temperatures. An application of this cycle for recovering waste

heat from gas turbine exhaust is discussed by Kouremenos et al. [34].

Use of Mixtures as Working Fluids in Thermodynamic Cycles

In a conventional Rankine cycle in which a pure fluid is used, boiling occurs at the

saturation temperature corresponding to its pressure. This results in a mismatch between

the temperature profile of the heat source fluid (fuel combustion products, geothermal

fluids etc.) and the working fluid in the boiler. Consequently, there is significant exergy

destruction during heat transfer in the boiler. One of the methods around this limitation,

practiced in industry, is to boil at different pressures, resulting in a moderate increase in

efficiency. The other option is to use a mixture in the working fluid. The use of mixtures

as working fluids in Rankine cycles is not a new idea. As a mixture vaporizes, the

changing composition of the liquid results in boiling occurring over a range of

temperatures. This gives what is called a "temperature glide" between the temperatures

at which the mixture starts boiling to those at which the fluid is completely vaporized.

Figure 1.5 qualitatively shows an example of the difference in boiling behavior just

described. With a multi-component mixture, the fluid boils throughout in the boiler,

achieving a good temperature match with the heat source fluid. While the pure fluid boils

at one temperature and is then subsequently superheated, the mixture boils at varying

temperatures and achieves a better thermal match in the boiler [35].

The condensation of mixtures is also a variable temperature process. This results in

a better thermal match with the heat rejection fluid. The advantages of better thermal

matching in the condenser are debatable. In a power plant, there is normally very little

cost associated with the heat rejection fluid itself. The size of the condenser is the










Pure Fluid
mixtures




Heat S rce,"



Q pin point
-2
-'Working Fluid

E
I- //







Q (Heat)

Fig. 1.5 Illustration of the difference in temperature profiles for a pure fluid being boiled
and a multi-component mixture being boiled.

limitation. Also, for complete condensation of a fluid, the bubble point at the cycle low

pressure has to be a little above the heat rejection fluid temperature. The use of mixtures

has another advantage, particularly in geothermal power plants. Any degradation in the

quality of the heat resource with time can be countered to a certain extent by changing the

composition of the working fluid.

Several cycles have been developed in the literature to take advantage of mixtures.

Binary mixtures have been recommended as working fluids in binary geothermal power

plants. It is found that a geothermal resource is utilized more efficiently by the use of

these mixtures.









The Combined Power and Cooling Cycle

Introduction

A unique feature of the combined power and cooling cycle proposed by Prof

Goswami is the simultaneous production of power and refrigeration (cooling) in the same

loop. Other combined power and cooling cycles utilize the waste heat rejected from the

power cycle to run a coupled heat fired cooling cycle, such as an absorption refrigeration

cycle.

The cycle can be viewed as a combination of the Rankine cycle and an absorption

refrigeration cycle. A binary mixture of ammonia and water has been used as the

working fluid in all studies performed so far. Using that as an example, consider the

schematic (basic configuration) of the cycle shown in Fig. 1.6. A mixture of ammonia

and water (borrowing from absorption refrigeration literature, this mixture is called the

strong solution, or basic solution) is pumped to a high pressure. This stream is preheated

and pumped to the boiler, where it is partially boiled. Being the component with a lower

boiling point, the vapor generated is rich in ammonia. A "rectifier" is used to increase

the concentration of ammonia in the vapor by condensing some of the water out. The

rectified vapor is superheated and expanded to low temperatures in an expander such as a

turbine. This is possible since ammonia is a volatile component that does not condense at

the temperatures and pressures at the turbine exit. The cold ammonia is used to produce

refrigeration.

The remaining hot liquid in the boiler, called the weak solution, is used to preheat the

working fluid in the recovery or solution heat exchanger. This high pressure liquid is

then throttled back to the absorber. The vapor is absorbed into the weak solution and






17


condensed in the absorber. The absorber takes the place of a regular condenser in the

cycle.


Superheater














9


Fig. 1.6 The basic configuration of the combined power and cooling cycle









A portion of the strong solution stream is used to recover heat from the condensing

vapor in the rectifier. The word rectification is used in the absorption cooling literature,

by some authors, to refer to a particular configuration that employs a rectification column

to purify the ammonia vapor. We use the word rectification to refer to a process used to

purify vapor leaving the boiler in all the papers and reports associated with the study of

this cycle.

Some of the key features of the cycle are listed below.

* Output consists of both power and cooling
* Uses a mixture as the working fluid, which makes it suitable for sensible heat
sources
* Absorption condensation is used to condense the vapor
* Works best using low temperature heat sources


A summary of past research on the cycle

The combined power and cooling cycle has been the subject of a sustained research

effort at the University of Florida for the past eight years. A summary of the work done

to date and the status of the development of the cycle is discussed below. The results of a

parametric analysis of the cycle using low temperature sensible heat sources are reported

in Goswami and Xu [2] and Xu et al.[36]. The analysis established that theoretically,

both power and cooling could be obtained from the proposed configuration. Ideal turbine

and pump were assumed, heat losses and pressure drops were neglected. The following

range of parameters were studied

1. Boiler Temperature 400 K
2. Condenser Temperature 350 K 400 K
3. Turbine Inlet Temperature 410 K 500 K
4. Turbine Inlet Pressure 18 bar 32 bar
5. Ammonia Concentration 0.20 0.55
6. Absorber Temperature 280 K
7. Recovery HX. Exit Temp. 350 K









The parametric study results indicate the general behavior of the cycle. Figure 1.7

shows the effect of turbine inlet pressure on the thermal efficiency2 of the cycle. For a set

absorber pressure (as in a parametric analysis), the pressure ratio increases with a higher

pressure, but the vapor generation rate drops until the pressure becomes too large to

generate any vapor at all. A similar effect is seen with the cooling capacity. A larger

pressure ratio results in a larger temperature drop in the turbine, but the drop in vapor

generation rate limits cooling at higher pressures (see Fig. 1.8).

The boiler temperature strongly influences the output, as the vapor generated goes

up. The heat input also goes up with increased vapor generation; therefore the thermal

efficiency reaches a limit after initially increasing. The cooling capacity of the cycle is

strongly influenced by the superheater and condenser temperatures. A higher superheater

temperature raises the turbine exit temperature, until no refrigeration is produced at all.

The parametric study also clearly shows that there is an optimum value of

parameters for the best operation of the cycle. Based on these results, Lu and Goswami

[3] performed a mathematical optimization of the efficiency of the cycle using an

optimization program that uses the Generalized Reduced Gradient (GRG) algorithm.

The optimization program has since then been used extensively to maximize the

thermodynamic output of the cycle in several studies [5,6]. Lu and Goswami [4] also

used the program to determine the lowest temperatures that could be achieved using the

cycle. They concluded that temperatures as low as 205 K are achievable, however, the

vapor generation drops substantially at very low temperatures since lower absorber

pressures and purer ammonia vapor generation is required. Hasan and Goswami [5]


2 See Table 1.1 for the definition of efficiency





















22




u 20


E

S18





16


- x=0.47
---x=0.5
--x=0.53


16 18 20 22 24 26 28 30 32 34
turbine inlet pressure (bar)

Fig. 1.7 Effect of turbine inlet pressure on the thermal efficiency (%) of the cycle [2]





30


--x=0.47
--x=0.5
25 -A-x=0.53


20




i 15

rC
0

0 10



5


16 18 20 22 24 26 28 30 32 34
turbine inlet pressure (bar)
Fig. 1.8 Effect of turbine inlet pressure on the cooling capacity (kJ/kg) of the cycle [2]












performed an exergy analysis of results optimized for second law efficiency and looked

at various aspects of the optimized results such as the refrigeration to work output ratio,

pressure ratio etc.

An experimental system was built to verify the actual performance of the combined

power and cooling cycle. The initial system was a simplified version of the cycle without

an actual turbine present. A throttling valve and a heat exchanger performed the

functions of expanding and cooling the vapor, thus simulating the turbine in the loop.

The experimental system also lacked a rectification arrangement that would have been

useful to purify the vapor. Operating this limited version of the cycle [8] verified the

boiling and absorption processes. The results indicated that both power and cooling can

be obtained simultaneously and that efficiencies close to the predicted values should be

achievable.

Specific motivation for work in this dissertation

Efficiency definition. While a significant amount of work has been done on the

theoretical analysis of the cycle, there are some shortcomings that need to be addressed.

The first question deals with the right efficiency definitions for the cycle. Since the

output consists of both power and cooling, the questions that arises is how the two

components would be added so as to arrive at a meaningful efficiency definition. Table

1.1 summarizes the efficiency definitions used in different papers written on the cycle.

Initial papers simply added the work and cooling output to generate an efficiency, which

really is an "energy" efficiency. Later papers divided the cooling output by a Carnot

COP (evaluated at the average of the inlet and exit temperatures of the refrigeration heat









exchanger). Such a definition gives a very small weight to the cooling output. The

subject of efficiency definitions is discussed further in chapter 2.


Table 1.1 Efficiency Definitions used in Various Papers Published on the Cycle
Reference First Law Definition Second Law Definition

Goswami and Xu [2] (Wet + Q,)/Qh N.A.

Xu et al. [36]

Lu and Goswami [3] (We + QO)/Qh (,, + Q)/E,,,

Hasan and Goswami [5] (Wt + Q )/Qh [Wne + (QOCOP E a o)]/Eh,,,.

Tamm et al. [7]



Cycle simulation. The cycle simulation program written by Lu and Hasan had

some shortcomings that were discovered when early simulations were being performed to

compare results. These are listed below:

* A pinch point check was not implemented in the recovery heat exchanger.
Sometimes the strong solution starts boiling there resulting in the pinch point
condition being violated
* The fraction of the strong solution stream entering the rectifier was calculated by
setting the temperature after the rectifier and using an energy balance. This
temperature need not be set; it can actually be optimized.
* The liquid condensate in the rectifier was assumed to return to the boiler and boil as
a separate stream. Yet this was not considered when calculating pinch point in the
boiler. The result was that the pinch point was improperly calculated. In addition,
the design of such a heat exchanger with three streams is also complicated.


Working fluid. All the work performed so far has been based on using an

ammonia-water mixture as the working fluid. It is logical to assume that other mixtures

could also be used in this new thermodynamic cycle to provide simultaneous power and

cooling output. Organic fluids have been used in Rankine cycles designed for low









temperature heat sources. Therefore, these fluids seem like natural choice for use in this

cycle.

Based on these motivations, the work presented in the subsequent chapters follows

an outline as follows. First, there is a discussion of the various efficiency definitions that

can be used for this cycle. That is followed by a description of the simulation and

optimization methods. The basic cycle configuration is optimized using the proposed

efficiency definitions, the results of which are discussed in chapter 4. Chapter 5 contains

results of simulations performed using organic fluid mixtures and an analysis of the

results. Some modified and improved configurations of the cycle are proposed and

discussed in chapter 6. The final chapter suggests some directions for the development of

the cycle in the light of this study.














CHAPTER 2
EFFICIENCY DEFINITIONS FOR THE COMBINED CYCLE



The combined power and cooling cycle is a combination of the Rankine cycle and

an absorption refrigeration cycle. Evaluating the efficiency of this cycle is made difficult

by the fact that there are two different simultaneous outputs, namely power and

refrigeration. An efficiency expression has to appropriately weigh the cooling

component in order to allow comparison of this cycle with other cycles. This chapter

develops several expressions for the first law, second law and exergy efficiencies for the

combined cycle based on existing definitions in the literature. Some of the developed

equations have been recommended for use over others, depending on the comparison

being made. Finally, some of these definitions are applied to the cycle and the

performance of the cycle optimized for maximum efficiency. A Generalized Reduced

Gradient (GRG) method was used to perform the optimization. This method is described

in detail in the following chapter.

Conventional Efficiency Definitions

Performance of a thermodynamic cycle is conventionally evaluated using an

efficiency or a coefficient of performance (COP). These measures of performance are

generally of the form

measure ofperformance = useful output / input (2.1)









First Law Efficiency

The first law measure of efficiency is simply a ratio of useful output energy to input

energy. This quantity is normally referred to simply as efficiency, in the case of power

cycles, and as a coefficient of performance for refrigeration cycles. Table 2.1 gives two

typical first law efficiency definitions. For the case of an absorption refrigeration cycle,

the input is in the form of heat and pump work. Therefore, its COP is expressed in terms

of refrigeration output, heat input, and pump work as [37]

COP =Qc/(Qh +w) (2.2)

Exergy Efficiency

The first law fails to account for the quality of heat. Therefore, a first law

efficiency does not reflect all the losses due to irreversibilities in a cycle. Exergy

efficiency measures the fraction of the exergy going into the cycle that comes out as

useful output [38]. The remaining exergy is lost due to irreversibilitites in devices.

*Rexergy = lE,,u /IE,' (2.3)

Two examples are given in table 2.1. For the absorption refrigeration cycle, the

corresponding exergy efficiency expression is given as

rexergy = Ec / (E + W) (2.4)

Here Ec is the change in exergy of the cooled medium.

A resource utilization efficiency [39] is a special case of the exergy efficiency that

is more suitable for use in some cases. Consider for instance a binary geothermal power

cycle, where the geofluid is reinjected into the ground after transferring heat to the cycle

working fluid. In this case, the unextracted availability of the geofluid that is lost on










Table 2.1 Some examples of efficiencies applied to the Rankine cycle and the vapor
compression refrigeration cycle
Cycle Type Rankine Vapor Compression

First Law 1I = Wne/Qh (2.5) COP= Qc/W, (2.8)

Exergy re, = Wn,/E, (2.6) qer = Ec/W, (2.9)

Second Law rH = r/rrev, (2.7) qH = COP/COP_ (2.10)



reinjection has to be accounted for. Therefore, a modified definition of the form

1R = ZEu, /Eh (2.11)

is used, where the Ehs is the exergy of the heat source.

Another measure of exergy efficiency found in the literature is what is called the

exergy index defined as the ratio of useful exergy to exergy loss in the process [40],

IE
er = useful
T 'Ein Euseful (2.12)

Second Law Efficiency

Second law efficiency is defined as the ratio of the efficiency of the cycle to the

efficiency of a reversible cycle operating between the same thermodynamic conditions.

7, = 717/rev (2.13)

The reversible cycle efficiency is the first law efficiency or COP depending on the

cycle being considered. The second law efficiency of a refrigeration cycle (defined in

terms of a COP ratio) is also called the thermal efficiency of refrigeration [37]. For

constant temperature heat addition and rejection conditions, the reversible cycle is the

Carnot cycle. On the other hand for sensible heat addition and rejection, the Lorenz cycle

is the applicable reversible cycle [41].






27


The exergy efficiency and second law efficiency are often similar or even identical.

For example, in a cycle operating between a hot and a cold reservoir (see Fig. 2.1), the

exergy efficiency is

W
Snexr et (2.14)
Qh 1-0 .Th)

while the second law efficiency is

Wet
nr ne (2.15)
Q h (1 h

Where To is the ambient or the ground state temperature. For the special case

where the cold reservoir temperature Tr is the same as the ground state temperature To,

the exergy efficiency is identical to the second law efficiency.


Th


Qh



Cyclic W
nfav/ir-a net


Fig. 2.1 A cyclic heat engine working between a hot and cold reservoir









The Choice of Efficiency Definition

The first law, exergy and second law efficiency definitions can be applied under

different situations. The first law efficiency has been the most commonly used measure

of efficiency. The first law does not account for the quality of heat input or output.

Consider two power plants with identical first law efficiencies. Even if one of these

power plants uses a higher temperature heat source (that has a much higher availability),

the first law efficiency will not distinguish between the performance of the two plants.

Using an exergy or second law efficiency though will show that one of these plants has

higher losses than the other. The first law efficiency, though, is still a very useful

measure of plant performance. For example, a power plant with a 40% first law

efficiency rejects less heat than one of the same capacity with a 30% efficiency; and so

would probably have a smaller condensor. An exergy efficiency or second law efficiency

is an excellent choice when comparing energy conversion options for the same resource.

Ultimately, the choice of conversion method is based on economic considerations.

Efficiency Expressions for the Combined Cycle

The performance evaluation functions discussed above will be applied to the

combined power and cooling cycle. When evaluating the performance of a cycle, there

are normally two goals. One is to pick parameters that result in the best cycle

performance. The other goal is to compare this cycle with other energy conversion

options. For instance, to compare the novel cycle with a power cycle that uses waste heat

to run an absorption refrigeration system.

First Law Efficiency

Following the pattern of first law efficiency definitions given in the previous

section, a simple definition for the first law efficiency would be









i = (Wn,, + Qc)/ (2.16)

Equation (2.16) overestimates the efficiency of the cycle, by not attributing a quality to

the refrigeration output. Using this definition, in some cases, the first law efficiency of

the novel cycle approaches Carnot values or even exceeds them. Such a situation appears

to violate the fact that the Carnot3 efficiency specifies the upper limit of first law

conversion efficiencies. The confusion arises due to the addition of work and

refrigeration in the output. Refrigeration output cannot be considered in an efficiency

expression without accounting for its quality. To avoid this confusion, it may be better to

use the definition of the first law efficiency given as

7 = (We, + Ec)/Qh (2.17)

The term Ec represents the exergy associated with the refrigeration output. In other

words, this refers to the exergy transfer in the refrigeration heat exchanger. Depending

on the way the cycle is modeled, this could refer to the change in the exergy of the

working fluid in the refrigeration heat exchanger. Alternately, to account for

irreversibilities of heat transfer in the refrigeration heat exchanger, the exergy change of

the chilled fluid would be considered.

Ec =m [h cf,,n hf,out -To (s f,, scf,out) (2.18)

Rosen and Le [42] studied efficiency expressions for processes integrating

combined heat and power and district cooling. They recommended the use of an exergy

efficiency in which the cooling was weighted using a Carnot COP. However, the Carnot




3 The Carnot cycle is not the reversible cycle corresponding to the combined cycle. This is discussed later
in this chapter.









COP is based on the minimum reversible work needed to produce the cooling output.

This results in refrigeration output being weighted very poorly in relation to work.

Exergy Efficiency

Following the definition of exergy efficiency described previously Eq.(2.3), the

appropriate equation for exergy efficiency to be used for the combined cycle is given

below. Since a sensible heat source provides the heat for this cycle, the denominator is

the change in the exergy of the heat source, which is equivalent to the exergy input into

the cycle.

rexer, = (-Wne + Ec )/(Eh ,,, Eh o,,t) (2.19)

Second Law Efficiency

The second law efficiency of the combined cycle needs a suitable reversible cycle

to be defined. Once that is accomplished, the definition of a second law efficiency is a

simple process.

Lorenz cycle

The Lorenz cycle is the appropriate "reversible cycle" for use with variable

temperature heat input and rejection. A T-S diagram of the cycle is shown in Fig. 2.2.

S1 34
12Loren Q, (2.20)


If the heat input and rejection were written in terms of the heat source and heat rejection

fluids, the efficiency would be given as:

mhr(hhr,.,,o hh,..,,)
1Lorenz mh (hr, ,n- h~,o, (2.21)


Knowing that processes 4-1 and 2-3 are isentropic, it is easily shown that in terms of

specific entropies of the heat source and heat rejection fluids that










mhs _(Shr out Shr,n )
mhr- (Shin Sh.o.ut )


(2.22)


The efficiency expression for the Lorenz cycle then reduces to


lLorenz


1 -(hhrout hhr, )/ (Shr out Shr, ,ln)
sn s,out hszn hs,out


(2.23)


This can also be written as


7lLoren. 1
TVshs


(2.24)


Here, the temperatures in the expression above are entropic average temperatures, of the

form


Fig. 2.2 The T-S diagram for a Lorenz cycle


(2.25)


T = (h2 hi)
(S2 S)









For constant specific heat fluids, the entropic average temperature can be reduced to

(T -T,)
T = T2 (2.26)
In(T2 Ti )

The Lorenz efficiency can therefore be written in terms of temperatures as

L (T routt Thrn )/ln(Thr,out /Thr, n )
= 1- (T Th )Iln(Th Tht ) (2.27)
(Thsn hsout ln( n hs,out (2.27)

It is easily seen that if the heat transfer processes were isothermal, like in the

Carnot cycle, the entropic average temperatures would reduce to the temperature of the

heat reservoir, yielding the Carnot efficiency. Similarly the COP of a Lorenz refrigerator

can be shown to be


COPLo = (2.28)
)hr ),f

Cascaded cycle analogy

An analogy to the combined cycle is a cascaded power and refrigeration cycle,

where part of the work output is directed into a refrigeration machine to obtain cooling.

If the heat engine and refrigeration machine were to be treated together as a black box,

the input to the entire system is heat, while output consists of work and refrigeration.

This looks exactly like the new combined power/refrigeration cycle. Figure 2.3 shows

the analogy, with a dotted line around the components in the cascaded cycle representing

a black box.

One way to look at an ideal combined cycle would be as two Lorenz cycle engines

cascaded together (Fig 2.3b). Assume that the combined cycle and the cascaded

arrangement both have the same thermal boundary conditions. This assumption implies






























a b

Fig. 2.3 Thermodynamic representation of (a) combined power/cooling cycle and (b)
cascaded cycle

that the heat source fluid, chilled fluid and heat rejection fluid have identical inlet and

exit temperatures in both cases. The first law efficiency of the cascaded system, using a

weight factor for refrigeration is

w, w, + feo
Sws t + fQ (2.29)
Qh

The weight factor,f is a function of the thermal boundary conditions. Therefore, the first

law efficiency of the combined cycle can also be written as

Whet + fQ
rI = Q (2.30)
Qh

The work and heat quantities in the cascaded cycle can also be related using the

efficiencies of the cascaded devices









Wot = QhrHE (2.31)

W, = Q /COP (2.32)

By specifying identical refrigeration to work ratios (r) in the combined cycle and the

corresponding reversible cascaded cycle as

r = Q /Wet (2.33)

and using Eq.(2.29) and Eqs.(2.31 2.33), one can arrive at the efficiency of the cascaded

system as


Ss 7HE r(f -l COPOP) (2.34)
lIys = rHE 1+ +rCOP ]


assuming the cascaded cycle to be reversible, the efficiency expression reduces to


l, rev = 'Lorenz f COPLoren (2.35)
1 + rCc7Lorenz

Here 7Lorenz is the first law efficiency of the Lorenz heat engine and COPLorenz is the COP

of the Lorenz refrigerator. A second law efficiency would then be written as

rhI = r, /1l, rev (2.36)

If the new cycle and its equivalent reversible cascaded cycle have identical heat input

(Qh), the second law efficiency can also be written as

n, W + fQ
Wnet + fQ (2.37)
r1I,rev Wnetrev + fc, rev

This reduces further to

net 1 + f net (2.38)
Wnet.rev (1 + fr) W.netrev









Evidently, the refrigeration weight factor (f) does not affect the value of the second

law efficiency. This is true as long as f is a factor defined such that it is identical for both

the combined cycle and the analogous cascaded version. This follows iffis a function of

the thermal boundary conditions. Assuming a value of unity forfsimplifies the second

law efficiency expression even further. The corresponding reversible cycle efficiency

would be,

l+r
r7,rev -= Lorenz 1+ r/COP 1 (2.39)
1 / 1 + _Lorenz

The resulting second law efficiency equation is a good choice for second law

analysis. The expression does not have the drawback of trying to weight the refrigeration

with respect to the work output. Being a second law efficiency, the expression also

reflects the irreversibility present in the cycle, just like the exergy efficiency.

Validity of Expressions

Expressions for the first law, exergy and second law efficiencies have been

recommended for the combined power and cooling cycle in Eqs. (2.17), (2.19) and (2.37)

respectively. These definitions give thermodynamically consistent evaluations of cycle

performance, but they are not entirely suitable for comparing the cycle to other energy

conversion options. Substituting for refrigeration with the equivalent exergy is

equivalent to replacing it with the minimum work required to produce that cooling. This

would be valid if in the equivalent cascaded arrangement, the refrigeration machine were

reversible. Therefore, when comparing the combined cycle with other options, such a

substitution is debatable. This is where the difficulty arises in arriving at a reasonable

definition of efficiency. Two cases are discussed here to illustrate the point.









Case 1: Comparing this Cycle to Other Combined Cooling and Power Generation
Options

Consider the situation where the novel cycle is being designed to meet a certain

power and refrigeration load. The goal then, would be to compare the thermodynamic

performance of the novel cycle with other options designed to meet the same load. If the

performance of both cycles were evaluated using Eqs.(2.17), (2.19) and (2.35), such a

comparison would be perfectly valid.

Case 2: Comparing a Combined Cycle to a Power Cycle

In some instances, a combined cycle would have to be compared to a power cycle.

For example, this cycle could be configured so as to operate as a power cycle. In this

situation, the refrigeration would have to be weighted differently, so as to get a valid

comparison. One way of doing this would be to use a practically achievable value of

refrigeration COP to weight the cooling output. Another option is to divide the exergy of

cooling by a reasonable second law efficiency of refrigeration (also called thermal

efficiency of refrigeration). Such efficiencies are named "effective" efficiencies in this

study.

(Wnet + Qc COPpractcal)
r1,ef Qh (2.40)


(WUnet + E, GIH,ref )
7i,eff = h (2.41)


Rexergy,eff = (Wnet + Q COpractical )/(Ehs,n Ehs,out (2.42)

lexergy,eff = (net + Ec /I, ref )/ (E,,in Ehsout ) (2.43)









Some Examples of Application to the Combined Cycle

An optimization program was used to optimize the performance of the Goswami

cycle. A description of the methodology adopted is given in the following chapter.

Optimization results using different efficiency definitions as objective functions are given

in this section. The cycle simulations were performed using simple energy and mass

balances. Approach temperature limits of 5 K were imposed on all heat exchangers.

Boiler pinch points were assumed to be at least 5 K. It was assumed that there were no

pressure losses in the devices and that the turbine and pump operated isentropically. The

vapor at the turbine exit is constrained to be at least 90% dry. A turbine exit temperature

of 270 K or lower was required to generate refrigeration. The optimization was also

constrained so that refrigeration was always generated.

The heat source fluid was assumed to be hot water at 400 K at the saturation

pressure of water at that temperature. The absorber temperature was 5 K above the

ambient which was assumed to be 298 K. Saturation conditions were assumed in the

absorber to fix the concentration of ammonia in the binary mixture. The schematic of the

cycle in Fig. 1.6 differs slightly from previously published versions in that the liquid

reflux from the rectifier is sent back to the absorber.

The optimization results of the cycle evaluated using the exergy efficiency and

second law efficiency Eqs.(2.19) and (2.36) are both identical. That is not surprising,

since exergy efficiency and second law efficiency are very similar. The cycle parameters

are presented in Table 2.2. It was assumed that the chilled fluid was liquid water for

these simulations.









Table 2.2 Cycle parameters that yield optimum exergy and second law efficiencies.

Parameters Optimized Case

exery (%) 61.35

( (%) 61.35

Tboder,exit (K) 395

Tectifierexit (K) 365.15

superheater, exit (K) 365.15

Tturbne,exit 269.96

Phgh (bars) 10.84

pow (bars) 1.00

basic, Ammonia mass fraction in absorber 0.288

1h hs, Mass flow rate of heat source (kg/s) 10.93

basic Mass flow rate of basic solution (kg/s) 3

Wnet, Net work output (kW) 79.15

Q,, Cooling output (kW) 25.99



Tables 2.3 and 2.4 give results optimized for effective efficiencies. Different

second law efficiencies of refrigeration were assumed. The exergy of cooling was

calculated on the working fluid side. It is seen that assuming different second law

efficiencies of refrigeration has a significant effect on the equivalent exergy efficiency.










Table 2.3 Efficiency and cycle parameters optimized for effective exergy efficiency


S, o Case Case Case
laorcmro rTlOfo T


(%,ref (%)


1exergy,eff (%)


h,,eff (%)

Tboder, exit (K)
fWer, ^ (K)
Trectifier,ext (K)


Tuperheater, exit (K)


tu rbineexit


Phgh (bars)

Pow (bars)

xbasc Ammonia mass

fraction in absorber

ih,, Mass flow rate of

heat source

basic Mass flow rate of

basic solution

Wet, Net Work Output

Qc, Cooling Output


I LLILLIII~L~IJ ~LLJ~I


0.374 0.360 0.390 0.388




10.82 10.79 10.92 10.95


69.2

59.1


72.2

58.1


97.4

34.2


87.63

30.55


30


72.52


17.70


395


342.85


342.85


253.68


16.7

1.8


II
50


65.20


15.89


395


343.88


343.88


252.10


15.3

1.64


III
70


62.74


15.11


395


368.75


368.75


270


17.4

2.0


IV
100


62.10


15.08


395


370.67


370.67


270


18.0

1.96







40


Table 2.4 Efficiency and cycle parameters optimized for effective first law efficiency


SCase Case Case
l-roirntro r Of T


r1nu,ref (%)


7h,eff (%)


Tbodlerexit (K)


Trecfier,exit (K)


Tsuperheater,exit (K)


turbine,exit


Phgh (bars)


Piow (bars)

xbsic, Ammonia mass

fraction in absorber

basic Mass flow rate

of basic solution

Wet, Net work output

Qc, Cooling output


I LLILLIII~L~IJ ~LLJ~I


0.369 0.355 0.327 0.388


64.5

55.1


66.83

53.80


68.26

48.18


87.63

30.55


II
50


15.92


395


344.92


344.92


251.49


15.46


1.59


III
70


15.21


395


348.99


348.99


249.72


13.37


1.31


IV
100


15.08


395


370.67


370.67


270


18.0


1.96


30


17.73


395


343.69


343.69


253.08


16.79


1.74









To get a feel for second law efficiencies, a typical 10 EER vapor compression air

conditioning system operates at a COP of around 3 at the standard rated conditions. The

corresponding Carnot COP, assuming 280 K cold temperature and an ambient

temperature of 308 K (selected based on standard rating conditions) is around 10. This

implies a second law efficiency of 30%. Refrigeration cycles are inherently irreversible

since they include a throttling process. The last case in tables 2.3 and 2.4 is the case

where a second law efficiency of refrigeration is not considered. It is interesting to note

that the optimization results in table 2.3, case IV are different from those in table 2.2.

The reason for the difference is that irreversibilites in the refrigeration heat exchanger are

considered in the optimization in table 2.2. The exergy of cooling Ec, is calculated on the

working fluid side in both tables 2.3 and 2.4.

Conclusions

In defining efficiencies of a combined power and cooling cycle, it is necessary to

weight the refrigeration output to obtain meaningful values. Definitions of first law,

exergy and second law efficiencies have been developed in this chapter. From the basis

of a strict thermodynamic analysis, the definitions given in Eqs. (2.17) and (2.19) are the

correct efficiency definitions of the cycle. However, these definitions do not realistically

weight the cooling content. When comparing the combined power and cooling cycle to

one producing work alone, effective efficiencies defined in Eqs. (2.41) and (2.43) are

recommended. It has also been shown in this paper that the weight assigned to

refrigeration output has an impact on the optimum parameters for the cycle.














CHAPTER 3
CYCLE SIMULATION AND OPTIMIZATION



The combined cycle has been studied by a simple simulation model coupled to an

optimization algorithm. The simulation model is simplistic, and is based on simple mass

and energy balances. Ammonia water properties are calculated using a Gibbs free energy

based method [43] while organic fluid properties were estimated using a NIST program

that is based on a corresponding states method (see Appendix A). The optimization is

performed by a search method. Search methods require an initial point to be specified.

From there the algorithm searches for a "better" point in the feasible domain of

parameters. This process goes on until certain criteria that indicate that the current point

is optimum are satisfied.

Optimization Method Background

The optimization of the working of the cycle is a non linear programming (NLP)

problem. A NLP is one in which either the objective function or one of the constraints

are non-linear functions. The cycle optimization method chosen for the analysis of this

cycle is a search method. Search methods are used to refer to a general class of

optimization methods that search within a domain to arrive at the optimum solution. It is

necessary to specify an initial starting point in search schemes. The optimization

algorithm picks a new point in the neighborhood of the initial point such that the

objective function (the function being optimized) value improves without violating any

constraints. A simple method of determining the direction of change is to calculate the









gradient of the objective function at the current point [44]. Such methods are also

classified as steepest ascent (or descent) methods, since the algorithm looks for the

direction of maximum change. By repeating these steps until a termination condition is

satisfied, the algorithm is able to arrive at an optimized value of the objective.

When implementing steepest ascent type methods for constrained optimization

problems, the constraints pose some limits on the search algorithm. If a constraint

function is at its bound, the direction of search might have to be modified such that the

bounds are not violated. The Generalized Reduced Gradient (GRG) method was used to

optimize the cycle. GRG is one of the most popular NLP methods in use today. A

description of the GRG method can be found in several sources [44-46].

There are several variations of the GRG algorithm. A commercially available

program called the GRG2 was used for ammonia water optimization, and a more recent

version called the LSGRG2 was used for alternate fluid work. LSGRG2 is able to handle

more variables and constraints than the GRG2 code, and is based on a sparse matrix

representation of the problem Jacobian (matrix of first partial derivatives). The method

used in the software has been discussed by Himmelblau et al. [46] and Lasdon et al. [47].

A brief description of the concept of the algorithm, heavily adapted [46, 47] is presented

below:

Consider the optimization problem defined as:

Minimize objective function: g,, (X)

Subject to equality and inequality type constraints as given below

g,(X)= 0, i=,...,neq (3.1)

0< g, (X) < ub(n +i), i = neq + ,...,m (3.2)









The variables are constrained by an upper and lower bound.

lb(i) < X, < ub(i), i = 1,...,n (3.3)

Here X is the variable vector consisting of n variables.

As in many optimization algorithms, the inequality constraints are set to equality form by

adding slack variables, Xl,...,Xn+m

The optimization program then becomes

Minimize: g, (X)

Subject to:

g, (X)-X,+ =0, i= ,...,m (3.4)

lb(i) < X, < ub(i), i = 1,...,n+m (3.5)

lb(i) = ub(i) = 0, i = n + 1,..., n + neq (3.6)

lb(i) = O, i = n+neq+l,...,n+m (3.7)

The last two equations specify the bounds for the slack variables. Eq. (3.6)

specifies that the slack variables are zero for the equality constraints, while the variables

are positive for the inequality constraints. The variables X,,..., X, are called the natural

variables.

Consider any feasible point (satisfies all constraints), which could be a starting

point, or any other point after each successful search iteration. Assume that nb of the

constraints are binding, or in other words, hold as equality constraints at a bound. In the

GRG algorithm used in the GRG2 and LSGRG2 software, using the nb binding constraint

equations, nb of the natural variables (called basic variables) are solved for in terms of









the remaining n-nb natural variables and the nb slack variables associated with the

binding constraints. These n variables are called the nonbasic variables.

The binding constraints can be written as

g(y,x)=O (3.8)

Here y and x are vectors of the nb basic and n nonbasic variables respectively and g is a

vector of the binding constraint functions. The binding constraints Eq. (3.8) can be

solved fory in terms of x, reducing the objective to a function of x only.

gl (y(x), x) = F(x)

This equation is reasonably valid in the neighborhood of the current point to a simpler

reduced problem.

Minimize F(x)

Subject to the variable limits for the components of the vector x.

l x u (3.9)

The gradient of the reduced objective F(x), VF(x) is called the reduced gradient.

Now the search direction can be determined from the reduced gradient. A basic descent

algorithm can now be used to determine an improved point from here. The choice of

basic variables is determined by the fact that the nb by nb basis matrix consisting of

(g, /ly, )should be nonsingular terms should be nonsingular at the current point.

A more detailed description of the theory and the implementation of the GRG

algorithm and the optimization program can be found elsewhere [46-48]. This algorithm

is a robust method that appears to work well for the purposes of optimizing this cycle, the

way it has been implemented in our study.









Search Termination

The search will terminate if an improved feasible point cannot be found in a

particular iteration. A well known test for optimality is by checking if the Kuhn-Tucker

conditions are satisfied. The Kuhn-Tucker conditions are explained in detail in [45,46].

It can be mathematically explained in terms of the gradients of the objective functions

and inequality constraints as:


Vg +, (X)+ uVg, (X) 0 (3.10)

uJ >0, u,[g (X)-ub(j)]=0 (3.11)

g, (X)< ubj), j= 1,...,m (3.12)

Here, u, is a Lagrange Multiplier for the inequality constraints.

Unfortunately, the Kuhn-Tucker conditions are valid only for strictly convex

problems, a definition that most optimization problems do not satisfy. A disadvantage of

using a search method, such as the GRG algorithm that has been used in this study, is that

the program can terminate at a local optimum. There is no way to conclusively determine

if the point of termination is a local or global optimum [46]. The procedure is to run the

optimization program starting from several initial points.

Sensitivity Analysis

The sensitivity of the results to the active constraints can be determined using the

corresponding Lagrange multipliers.


u= (3.13)
Saub(j)

Where, Vis the value of the objective at the optimum.









Application Notes

There are some factors in the optimization of the cycle studied using GRG2 and

LSGRG2 that are interesting to mention. In a search scheme, it is possible that the

termination point could be a local optimum, or not an optimum at all. It is necessary to

determine the nature of the "optimum" returned by the program. Prior to the

optimization, during setup, close attention should be paid to:

* Scaling of the variables
* Limits set for different convergence criteria
* Method used to numerically calculate the gradient

The relative scaling of the variables affects the accuracy of the differentiation and

the actual value of the components in the gradient, which determines the search direction.

Experimenting with the numerical calculation of the gradient is useful during scaling.

Too small a convergence criterion, particularly for the Newton-Raphson method used

during the one-dimensional search can cause premature termination of the optimization

program. The accuracy of the numerical gradient affects the search process. This was

clearly seen when setting up the program with the SUPERTRAPP program. A forward

differencing scheme was not accurate enough for the search to proceed forward.

Once the program was setup, the following methods were used in the process in

order to obtain a global optimum:

* For each case, several runs were performed, from multiple starting points.

* Optimized results using different objective functions were useful as starting points
for other cases.

* Examining the constraints indicated if the point was truly an optimum. For
instance, at maximum second law efficiencies, the pinch point in the boiler was
expected to be at its lower bound.

* The results were perturbed and optimized, particularly with respect to what would
be expected to very sensitive variables, to see if a better point could be obtained.









For example, in RUE optimization, the heat source flow rate is a very sensitive
variable. Perturbing the optimum results w.r.t the heat source flow rate was very
useful to get better points.

* Another method is to change the scaling of variables that appear to be insensitive to
check if better points can be obtained.

* For each configuration, comparing the results for different heat source and turbine
exit temperatures was used to identify non-optimum and local optimum points.

At the end of this exhaustive process, it is assumed with reasonable confidence that the

resulting point is indeed a global optimum. The optimization process using GRG is to a

certain extent "art" not "science". Unfortunately, this is a problem with almost all NLP

methods currently in use.

Cycle Modeling

Several cycle configurations have been studied in this dissertation. The model used

for the basic cycle configuration shown in Fig. 3.1 is first discussed. The modeling of

additional features in modified configurations is discussed, if necessary, when the

alternate configuration is introduced. Consider the basic cycle configuration shown in

Fig. 3.1

Eight independent variables are sufficient to determine the operation of the cycle.

Two more variables are required to determine heat source conditions. Pressure drops and

heat losses are neglected.

* Cycle high pressure

* Cycle low pressure

* Absorber temperature

* Temperature at boiler exit

* Temperature at rectifier / condenser exit

* Superheater exit temperature









* Effectiveness of the heat recovery heat exchanger, R1

* Ratio of the mass flow rates of the strong solution in the heat recovery heat
exchanger and the rectifier, R2

* Heat source temperature

* Mass flow rate of heat source

The absorber temperature is set a little above the ambient temperature. The

following general assumptions were used in the simulation

* Pressure losses in piping and equipment are neglected.
* An isentropic efficiency is assumed for the pump and turbine
* All processes are assumed to end in equilibrium thermodynamic states.



Using the variables and assumptions listed above, the properties at all state points in the

cycle can be determined. For a binary mixture, two intensive properties and the

composition of the mixture are sufficient to establish all the other properties. Some

combinations include pressure, temperature and composition (p, T,x); pressure, specific

enthalpy and composition (p,h,x); or pressure, specific entropy and composition (p,s,x).

Property calculation methods are discussed in Appendix B.

State Point Calculation

The calculation of state points for each state in Fig. 3.1 is described below.

State point 1

The mixture in the absorber is assumed to be at saturation conditions. The low pressure

of the cycle and the temperature of the absorber allow the calculation of ammonia

concentration of the basic solution. Absorber temperature is assumed to be 5 K above

ambient temperature. A reference flow rate is assumed and all other flow rates in the









































(1-R m,








m = 1 kg/s
reference
flow rate


Fig. 3.1 The basic cycle configuration with the variables shown


Superheater









system are scaled to this value. The choice of reference flow rate is to an extent decided

by the optimization program. The value is determined after a few trials so that other

parameters (particularly heat source mass flow rate) are reasonably large. This is

important so that error in gradient calculation is limited. Relative magnitudes of the

optimized variables are important to ensure reasonable values in gradient calculations. In

equation form:

T, = Tabsorbev (3.14a)


P = Plo (3.14b)


x, = satcon(p, T,) (3.14c)


ih, =3 (3.14d)


Satcon is a function in the ammonia-water properties program to calculate saturated

liquid concentration given the pressure and temperature. Knowing three properties, the

remaining properties of the binary mixture can be determined. This is implicit in the rest

of this section.

Point 2

The pump pressurizes the strong solution to the high pressure in the cycle.

Knowing the isentropic efficiency of the pump, the pressure and enthalpy at state 2 is

easily computed. The composition of the solution remains the same as in state 1.

P2 = Phgh (3.15a)


s.sen = S1 (3.15b)


(3.15c)


X2 = X1









Calculate enthalpy at pump exit, h,,,,en, for isentropic compression. Then, knowing

the pump efficiency, the actual enthalpy can be calculated using Eq. (3.15d) below.

h2 h1
77 2 -hI (3.15d)
h.se,, h,


Points 5 and 11

Since the boiler exit temperature and pressure are known, vapor-liquid equilibrium

correlations yield the vapor and liquid compositions leaving the boiler. A mass balance

is used to determine the vapor and liquid mass fractions.

T5 = T, = Tboler (3.16a)


P5 = P11 = Phigh (3.16b)


Use VLE data to get equilibrium compositions of vapor and liquid. The vapor and liquid

mass fractions in the boiler can be computed from a mass balance as shown below.


vmfboler -4 -1 (3.16c)
X5 11



lmfbod er _5 x- 4 (3.16d)
X5 X I
x5 "11


Therefore, the mass flow rates would be

Ih5 = vmfboler1 4 (3.16e)


1111 =lmfboilerim4


(3.16f)






53


Points 6 and 7

The rectifier exit temperature and pressure are known, as well as the boiler vapor

mass fraction and composition. This allows the calculation of vapor and liquid

compositions and mass fractions leaving the rectifier.

T6 T7 = Tectfer (3.17a)


P6 P7 = Phgh (3.17b)


VLE data is used to get equilibrium compositions of vapor and liquid. Once again, a

mass balance gives the vapor and liquid mass fraction leaving the rectifier as


Vmfrecfer = X5 (3.17c)
x7 -x


Infrecr = X -5 (3.17d)
x7 6


Therefore, the mass flow rates would be

Mi7 = vmfretfier j5 (3.17e)


h6 = mfrechfier1j5 (3.17f)


Point 8

The superheater exit temperature is specified for each simulation, and the pressures

and composition of the vapor are known.

T8 superheater (3.18a)


P = Phgh (3.18b)


(3.18c)


X8 = X7






54


Point 9

The turbine isentropic efficiency is assumed, the turbine exit pressure is the system

low pressure and the composition of the vapor is known. Therefore state points at the

turbine exit can be calculated.

P9 = Plow (3.19a)


8sen = s, (3.19b)


x9 = X, (3.19c)


Calculate an enthalpy corresponding to isentropic expansion and use in equation below to

calculate enthalpy at turbine exit.

hs h9
t = 9 (3.19d)
h8 hsen


Point 10

If the vapor is cold enough, it is assumed that the vapor leaves the refrigeration heat

exchanger at 5 K below ambient. If the vapor leaving the turbine is not cold enough to

yield refrigeration, state 10 is identical to state 9. The pressure and composition are

already known.

If T9 < Tm


T,0 = To -5 (3.20a)


Po = P9 (3.20b)


10 = x9 (3.20c)


Else, point 10 is identical to state point 9.









Points 12 and 3

The maximum heat recovered from the weak solution is decided by the approach

temperature limits. A fraction of this heat (variable R,) is recovered.

x12 = x,1 (3.21a)


PA2 = 11 (3.21b)

A 5 K approach temperature difference is assumed in the recovery heat exchanger, i.e.,

TI = T2 + 5. Other properties at the state point are calculated using this temperature to

obtain maximum possible heat transfer. This assumption eliminates the use of a

constraint at that point.

QHRHX,max,hot = ml(hl, hl ) (3.21c)

On the other side of the heat exchanger,

P3 =Phgh (3.21d)


3 = X (3.21e)


Ih3 = Rh2, (3.21f)


Set the maximum temperature at the heat exchanger outlet

T'= T, -5 (3.21g)

Now a cold side maximum heat transfer can be calculated

QHRHXmaxcold = l3 (h h3) (3.21h)









The smaller of the values from Eq. (3.21c) and Eq. (3.21h) represents the maximum heat

transfer possible. Now, using the ratio of the actual heat transfer to the maximum possible

heat transfer, RI, enthalpy h12 is calculated as


h12 = hll QHR x (3.21i)
/ 11


h3 =h2+(RlQHRHXmx /1 '/3) (3.21j)


This allows the calculation of other state points. Note that R1 is a pseudo heat

exchanger effectiveness. The advantage of this assumption is that approach temperature

constraints can be eliminated for the heat exchanger.

Point 13

The liquid reflux stream from the rectifier, and that from the boiler mix to form the

fluid at state 13. The mixing is modeled as a constant total enthalpy process.

P13 =Phgh (3.9a)


h13 6h6 12h(3.9b)
m13


/m6 X6 +--/12 X12
x"13 = (3.9c)
m13


Point 14

The weak solution at high pressure is throttled to a low pressure. The throttling is

modeled as a constant enthalpy process.

h14 = h13 (3.10a)


(3.10b)


P14 = Plow






57


X14 = 13 (3.10c)


Point 15

The heat lost by the condensing fluid in the rectifier is recovered by the part of the

strong solution stream flowing through the rectifier. A simple energy balance allows the

determination of the state of the fluid at point 15.

P15 =Phgh (3.12a)


15 = X2 (3.12b)


h15 = (1 R2 )2 (3.12c)


Qrectier = lhh5 lh6h6 l7h7 (3.12d)


h15 = h2 +Qrecfer /5 (3.12e)


Point 4

The two strong solution streams mix to form the fluid at state 4. This is also

modeled as a constant total enthalpy process, as in statel3. The composition of the two

streams are the same, and hence no mass balance is needed.

h4 = h3 + h1 (3.13a)


X4 =2 (3.13b)


P4= Phgh (3.13c)

Variable Limits

In any constrained optimization problem, limits of variable values have to be

specified. The purpose of specifying limits is to ensure that the values at optimum









conditions are achievable, meaningful, and desirable in practice. An upper and lower

bound is specified for the variables in the GRG optimization program. If the variable is

to be held fixed, the upper bound is set to be equal to the lower bound, both of which are

set equal to the value of the parameter. Unbounded variables are specified by setting a

very large limit. Table 3.1 shows the upper and lower bounds of the variables used in the

cycle optimization. Some of the bounds are arbitrarily specified when a clear value was


Table 3.1 Independent cycle parameters and their limits
Variable Lower Limit Upper Limit Name and Units


Tabsorber T + 5 To +5 Absorber Temperature (K)


Tboder T + 5 Theatsource 5 Boiler Exit Temperature (K)


Tecfi T + 5 That.ou 5 Rectifier Exit Temperature (K)


Tsuperheater T + 5 Theaturce 5 Superheater Exit Temperature (K)


Ph/gh 2 100 Cycle High Pressure (bars)


ow 1 100 Cycle Low Pressure (bars)
, T, .T, Heat Source Temperature (K)
Theatsource Theatsource Theatsource Heat Source Temperature (K)


hheatsource 0 18 Mass Flow Rate of Heat Source Fluid (kg/s)


R 0 1 Pseudo Heat Exchanger Effectiveness


R2 0.01 0.99 Flow Split Ratio









not available. For instance, although the rectifier exit temperature can reach its upper

limit, the value always has to be below the boiler exit temperature. The actual domain in

which these variables may vary is further restricted by additional constraints that are

specified. The lower limit for the low pressure is set at 1 bar, to avoid vacuum pressures

anywhere in the system. At vacuum pressures, non-condensable gases enter the system.

Additional equipment is required to remove these gases. The highest pressures in the

optimization are set arbitrarily at around 100 bars.

Constraint Equations

To ensure that cycle parameters stay within limits that are practical and physically

achievable, it is necessary to specify limits in the form of constraint equations.

Constraints are implemented in GRG2 by defining constraint functions and setting an

upper and lower bound for the function. Table 3.2 summarizes the constraint equations

used for simulation of the basic cycle. If the constraint is unbounded in one direction, a

value of the order of 1030 is specified. In GRG2, the objective function is also specified

among the constraint functions. The program treats the objective function as unbounded.

A brief discussion of the constraints specified in Table 3.2 follows. The

rectifier/condenser exit temperature should be below the boiler temperature and

superheater temperature. A minimum approach temperature of 5K is assumed for all

devices. A pinch point temperature difference of 5K is also assumed in the boiler. For

the contingency that boiling could begin in the rectifier or recovery heat exchanger, a

pinch point calculation is implemented in those two devices also. To ensure that the

reflux flow from the boiler is in the right direction, a constraint is used to maintain that

value positive. Additional constraints are used to keep the vapor mass fraction at the

turbine exit (dryness of vapor) greater than 90%. Two additional constraints (that might






60


Table 3.2 Constraints used in the optimization
Constraint Description Lower Limit Upper Limit


T -Toler Measure of condensation in the rectifier -1E+30 0
rectifier boiler

Trecqfier -Tu erheater Measure of Superheating -1E+30 0


T6 -T Rectifier exit approach AT 5 1E+30


5 T5 Rectifier inlet approach AT 5 1E+30


Ths,l -T7 Boiler exit approach AT 5 1E+30


Ths, -T4 Boiler inlet approach AT 5 1E+30


Th,, Pinch Point AT in Boiler 5 1E+30
pinch,boiler


Tpnh,HRHX Pinch AT in HRHX (if applicable) 5 1E+30


Tplnch,ectiie Pinch AT in Rectifier (if applicable) 5 1E+30


,hl x100 Boiler reflux mass flow rate 0 1E+30


vmf.rbne x100 Vapor mass fraction at turbine exit 90 100


vmfboler x100 Vapor mass fraction at boiler exit 1E-05 100


Imfrecer x 100 Liquid mass fraction 1E-05 100


QC Cycle Cooling Output 0.1 1E+30

Objective Efficiency Percentage 0 100









be redundant) are used to ensure that some vapor is generated in the boiler and that there

is some condensation in the rectifier. These ensure that there is no heat addition to the

vapor in the rectifier. A final constraint is used so that there is always some minimum

positive cooling achieved in the cycle. This is to make sure that the cycle behavior does

not go into a mode where only power is produced.

Model Limitations

The model used to simulate the cycle is a simple one with the advantage of being

computationally fast. The results are expected to give a good idea of the trends that

would be seen in real equipment. Such simple models are regularly found in the

literature for preliminary analysis of thermodynamic cycles. The efficiencies obtained

from such models would be higher than actually achievable efficiencies.

While the results of the optimization study will indicate an approximate value for

the maximum efficiency of the cycle, the cycle parameters are not necessarily practical.

The ultimate predictor of the usefulness of the cycle is in the economics of using it.














CHAPTER 4
OPTIMIZATION OF BASIC CYCLE CONFIGURATION USING AMMONIA-
WATER MIXTURE AS THE WORKING FLUID



Initial parametric studies of the combined power and cooling cycle using ammonia-

water mixtures as the working fluid suggested that some optimum conditions of operation

exist for the cycle performance [2,36]. An optimization scheme was implemented to

determine the best conditions of operation (from a thermodynamic efficiency perspective)

for various applications [3], such as for utilizing geothermal and solar resources, and for

achieving very low temperature cooling. Work done in the past has used a variety of

different efficiency definitions. In this chapter, some of the past optimization work has

been repeated with the efficiency definitions discussed in chapter 2. Additional results

are presented, that use isentropic efficiencies for the turbine and pump.

The modeling of the cycle in earlier work was improved upon for the optimization

work discussed in this chapter. Two additional variables were added to vary the

effectiveness of the Heat Recovery Heat eXchanger (HRHX) and to control the ratio in

which the strong solution stream was split between the HRHX and the rectifier. Earlier

modeling had the liquid reflux from the rectifier going back into the boiler and boiling as

a separate stream. Such a model makes the pinch point calculation in the boiler difficult.

The stream was diverted to a point after the recovery heat exchanger. Additional pinch

point checks were introduced in the rectifier and HRHX to account for the possibility of

the start of boiling of the strong solution before entering the boiling heat exchanger.









Simulated Conditions

The modeling of the cycle in the optimization study carried out here has been

discussed in the previous chapter. One of the questions that remained unanswered in

earlier optimization work is the influence of the turbine exit temperature (the low

temperature in the cycle) on the optimized efficiencies. Turbine exit temperatures were

varied from 255 K to 280 K in 5 K increments. Optimizing for work output

maximization, one ends up working with a cycle similar to the Maloney and Robertson

cycle. A low pressure limit of 5 bars was used in the work optimization in order that the

cycle remained an absorption type cycle. This limit was arbitrarily set so that there is a

reasonable amount of absorbent in the basic solution at the absorber temperature.

To study the effect of heat source temperatures, four values, 360 K, 400 K, 440 K

and 480 K were picked for simulation. This covers a range of low to medium

temperature solar heat. The heat source was assumed to be water at the saturation

pressure corresponding to the heat source temperature. The ambient temperature was

assumed to be 298 K for all simulations. The objective functions corresponding to

efficiency definitions developed in chapter 2 are shown in Eqs. (4.1-4.5)

ObjR ,,R =(We,+E)/Eim, (4.1)


Obex = exerg = (Wnet + E )/(EhsLn EL ut ) (4.2)


Obj = r = (Wnet + E )/h (4.3)


ObjRk, =R,eff = (Wet +E c/l iref )/E,sn (4.4)


Objexergy eff = exergyeff = (Wnet +E c ref r(E ,n Ehsout )


(4.5)





























i Superheater
11 Heat
:Source
Outlet 8

Heat Source
Inlet

Recovery Tur
Heat Turbine L
Exchanger
12

1 9
13


Refrigeration
2 14 Heat Exchanger


1 Absorber
10

Pump



Fig. 4.1 Block diagram showing the basic scheme of the combined power and cooling
cycle. Same as Fig. 1.6









Exergy losses in each component were calculated in the optimized results using the

entropy generation in each device. The turbine and pump were the only devices assumed

without losses in the model. Results discussed later in this chapter assume a value for

isentropic efficiencies for these devices. The exergy loss in each process is calculated

using the Guoy-Stodola theorem, from an entropy balance on each device, as in Eq. (4.6).

Eos = ToSg,, = To(ISo,, S,,) (4.6)


Here, To is the ground state temperature with respect to which exergy is defined, set at

298 K for all cases. The ground state pressure was set at 1.013 bar (1 atmosphere).

Optimization results

Resource Utilization Efficiency

The resource utilization efficiency is the recommended choice in evaluating an

energy conversion device for resources that are "discarded" after use in the cycle. A

good example is the case of a geothermal application, where, the heating fluid is

reinjected into the ground after extraction of energy from it in the power plant. The

availability of the geofluid at the point of reinjection is wasted exergy that the power

plant is incapable of utilizing. This efficiency can also be applied to other applications.

In a coal power plant, the resource utilization efficiency would consider either the exergy

of the coal and the air used for combustion, or the exergy of the products of combustion

(hot gases and any solid residue such as ash). Unutilized exergy leaving the power plant

through hot combustion products leaving the smokestack and in hot ash dumped into an

ash pit is wasted. Optimizing for resource utilization efficiency is a good choice to












100


80


60

3 work
40
40 280 K
255 K

20 -
20



340 360 380 400 420 440 460 480 500
Heat Source Temperature (K)


Fig. 4.2 Optimized resource utilization efficiencies for the basic cycle configuration




ensure that maximum use is made of the energy source or fuel. The resource utilization

efficiency is written as (also see Eqs. (4.3) and (2.11))


(wet +Ec)
i h... h- To (sh so) (4.7)


The specific enthalpy ho and specific entropy So are calculated at the ground state.

To maximize the efficiency of Eq. (4.7), the sum of the net work output and the exergy of

cooling has to be increased, while the mass flow rate of the heat source is decreased. The

objective function, therefore, is very sensitive to the flow rate of the heat source.

The optimum resource utilization efficiencies (RUE) are shown in Fig. 4.2. Three

different cases have been plotted. Maximum efficiency obtained using two different

turbine exit temperature limits are shown. There is a slight drop off in RUE with lower









turbine exit temperatures. Optimizing purely for work output gives a better RUE value.

An upper limit of 5 bars (0.5 MPa) was used for the work maximization simulations.

Without this constraint, the optimum conditions were seen to be at conditions where the

cycle operates using nearly pure ammonia as a Rankine cycle. The absorber model used

is not valid at those conditions and the results are also not valid.

Exergy Efficiency

In solar thermal power plants, normally solar energy is collected and stored in a

heat storage medium. This medium acts as the heat source for the power plant. The

exergy of the heat source is not lost in the unextracted heat leaving in the fluid exiting the

cycle because it is recirculated through the collector system to the storage tank. In such a

case, the exergy efficiency is a reasonable choice for the objective function. This

assumes though that the collection system efficiency is unrelated to the inlet and outlet

temperatures of the cycle, which might not be the case. Even for solar resources,

ultimately, resource utilization efficiency can be calculated, if the solar radiation were to

be treated as the input. The definition of exergy of solar radiation is still being debated,

but the values of different definitions in the literature give values that are fairly close to

each other.

Exergy efficiency is defined in terms of the exergy transferred from the heat

source fluid to the working fluid in the boiler. This function is relatively less sensitive to

mass flow rate of the heat source. Changing the mass flow rate would be compensated

by a change in specific exergy change in the heat source fluid, in the denominator of the

exergy efficiency equation, Eq. (4.6). A large heat source flow rate results in a small

temperature drop of the heat source and a bad thermal match in the boiler.







68




100



80

work
S60 280 K

C-: 255 K

LU
>, 40

w
20 -
20


0 i-i i -- i i
340 360 380 400 420 440 460 480 500
Heat Source Temperature (K)


Fig.4.3 Optimized exergy efficiencies for the basic cycle configuration




(W,,,et +Ec)
1exergvy [- (, E s (4.6)
m' lh,, hsout o (Shsin hrs,out


For the exergy efficiency case, as seen in Fig. 4.3, efficiency is maximum at 400 K

(of the four temperatures considered here), which is still lower than the efficiency in the

work output optimized case, with a 5 bar upper limit on pressure. The optimized results

are not bound at the 5 bar pressure limit. The reason for the drop in efficiency at higher

temperatures is primarily due to the boiler temperature not increasing corresponding to

the increase in heat source temperatures. There are limits to the temperatures in the

boiler and condenser at which refrigeration can be obtained efficiently, since it becomes

difficult to achieve sufficient temperature drop in the turbine across a given pressure

ratio. A similar effect can also be seen in first law efficiency optimization (see Fig. 4.4)









where the efficiency curve plateaus at higher heat source temperatures. The effect of

lower turbine exit temperatures is to lower optimum efficiencies slightly.

First Law Efficiency

The first law efficiency is not sensitive to mass flow rate of the heat source. Once

the optimum operating conditions of the cycle are determined, as long as the pinch point

conditions are not violated, changing the mass flow rate does not affect the first law

efficiency at all, since the heat input to the cycle remains the same. An advantage of

using a binary mixture is the improved thermal matching in the boiler. Since the first law

efficiency does not account for the heat source behavior, the exergy efficiency is a better

choice for evaluating binary mixtures. It might be a better choice to use the first law

efficiency corresponding to the optimum exergy efficiency.

A first law efficiency is a useful measure of the cycle's performance. It is a direct

measure of the heat transfer requirements in the boiler and condenser. A cycle with a

high first law efficiency would have a much smaller boiler heat transfer area requirement

per unit work output. Similarly, the condenser load being smaller, would use a much

smaller condenser for the same boiler size. Note that this is a simplistic statement.

Several other factors such as the heat transfer coefficients and pressures play a role in the

size of the equipment.

Optimized first law efficiencies in the refrigeration domain are shown in Fig.4.4

Once again, the work optimization results show a higher value of efficiency. The effect

of lower temperatures in the cycle is a small drop off in efficiency. It is also seen from

the results that the cycle optimized in the refrigeration domain fails to take advantage of

higher heat source temperatures. The optimized parameter values for heat source







70




30


25

I work
220
S20 280 K
S- 255 K
4 15-
LL

-J
S10 -






340 360 380 400 420 440 460 480 500
Heat Source Temperature (K)

Fig. 4.4 Optimized First Law Efficiencies for the Cycle Configuration in Fig. 4.1




temperatures of 440 and 480 K are almost identical. Optimizing in the work output

domain, one sees an increase in efficiency going from 440 K to 480 K. This implies that

while the first law efficiency improves, a corresponding increase in exergy efficiency is

not seen.

Exergy Analysis

An exergy analysis was performed to determine the various pathways of losses in

the cycle. For the optimized RUE results, the major exergy losses in different parts of the

cycle are plotted in Figs. 4.5 and 4.6. Figure 4.5 shows the losses occurring for the case

where cooling is produced and the turbine exit temperature limit was set to 280 K. A

large fraction of the exergy of the heat source is lost in the fluid leaving the cycle.

Approximately 30 % of the exergy available in the heat source is lost in this fashion. The






















0
03


40
o
4',
EP

a) r
xo
&s 20-

(0




0-


340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)


Fig. 4.5 Exergy destruction in the cycle represented as a percentage of exergy of the heat
source, for optimized RUE corresponding to 280 K turbine exit temperature


heat addition
-v internal Hx
-I- heat rejection + throttling
-- ---- unrecovered from heat source



4-------------*

0-,











40 360 380 400 420 440 460 480
40 30 30 40 420 440 460 480


Heat Source Temperature (K)

Fig. 4.6 Exergy destruction in the cycle represented as a percentage of exergy of the heat
source, for optimized RUE corresponding to pure work output


heat addition
-v internal Hx
--- heat rejection + throttling
---0- -- unrecovered from heat source






------- ,-



--V


0



2|0 40



(0


3 >
(0
y)





3-









losses in the heat addition process (boiler and superheater combined) are also high due to

the poor thermal matching in the boiler. At the optimized condition, the mass flow rate

of the heat source is very small. At these conditions, the strong solution enters the boiler

at a temperature slightly above the bubble point. This removes the pinch point constraint

in the boiler and allows a small heat source flowrate at the expense of thermal matching.

In the work domain, there is no rectification at optimum conditions. The process of

rectification is a source of exergy loss and is unnecessary if refrigeration is not desired.

At higher heat source temperatures (440 K and 480 K), there is no heat recovered in the

solution heat exchanger under optimum conditions. The hot weak solution is throttled

and then cooled in the absorber, with considerable losses. The heat source is used to

preheat the working fluid and therefore leaves the cycle at low temperatures. As a result,

the exergy losses in heat rejection and throttling go up, while the loss through

unrecovered exergy in the heat source drops (Fig. 4.6).

Similar plots are shown for exergy destruction in the optimized exergy efficiency

cases in Figs. 4.7 and 4.8. In the case with cooling output, the losses in the boiler are

small. There is good thermal matching in the boiler, except at the 480 K heat source

temperature. The exergy loss during heat rejection, in the absorber, is a major source of

irreversibility in the system. That is surprising because the vapor has been expanded to

very low temperatures and a large fraction of the heat recovered from the weak solution.

Apparently, the mixing and absorption losses are high.

Once again the optimum parameters in the work domain do not show any

rectification. The internal heat exchange category in Fig. 4.8 is the sum of exergy

destruction in the solution heat exchanger and rectifier. It is seen that exergy destruction














50 -



40-


00
2. 30-


(b
2 20-


340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)



Fig. 4.7 Exergy destruction in the cycle for optimized exergy efficiency corresponding
to 280 K turbine exit temperature




50

S-* heat addition
internal Hx
S40 -- heat rejection + throttling



3X
=S





2)Gd3 20








0
>, x ---U


(010 .-

10 I I- i i-- r



340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)



Fig. 4.8 Exergy destruction in the cycle for optimized exergy efficiency corresponding
to pure work output


heat addition
-I internal Hx
-E- heat rejection + throttling





a-^


v- -
-U --_









in the boiler and superheater is small. The thermal matching in the boiler is reasonably

good in the exergy efficiency optimized cases, but it appears to be poorer than in the

cooling domain. In the work domain, the requirement for work output does not limit the

boiler exit temperature. However, the superheating seen at optimum conditions is larger

and therefore, the thermal match in the boiler is poorer. In addition, the vapor fraction in

the boiler is large enough that there is not enough weak solution to preheat the strong

solution sufficiently to eliminate the pinch point in the boiler at 440 K and 480 K. This

accounts for the odd looking inflections in the curves in Fig. 4.8 and contributes to

increased exergy losses in the boiler.

Optimization Considering Losses

The optimization discussed so far assumes isentropic turbine and pump. Only

approach temperature constraints are placed on the solution heat exchanger. The

resulting effectiveness is close to 95%. Additional simulations were performed

considering the turbine and pump as non ideal devices and using a lower effectiveness for

the recovery heat exchanger. Optimization calculations were also performed using

effective efficiency definitions developed in chapter 2.

An isentropic efficiency of 0.85 was assumed for the turbine, while a value of 0.8

was assumed for the pump. The values assumed are relatively optimistic, actual values

would depend on the type of expander used and the size and scale of the equipment.

Although the effect is predictable, the basic cycle configuration was also optimized using

heat exchangers with lower effectiveness of 70 % and 80%. A turbine exit temperature

limit of 270 K was set for all simulations.

The optimized RUE is plotted in Fig. 4.9. The effect of including an isentropic

efficiency for the turbine and pump is to lower the RUE (see Fig. 4.2). In effective































10 -




0 --
340


-U
------









S qRi, Eq. (4.1)
-- 'R with irer=0.4, Eq. 14 4
'1R.t with ,llr,=0.3, Eq. :4 4
------ Only work output



360 380 400 420 440 460 480 500


Heat Source Temperature (K)


Fig. 4.9 Optimized RUE for the basic cycle configuration using a non isentropic turbine
and pump




40




30
----- --



UL 20



REq. (4.1), =0.8
10 -- R.ef with nir,=0.4, Eq. 14.4i ,.=0.8
lR, Eq. (4.1 ..=0.7
------ lRef with nr ,,=0.3, Eq. (4.4), e=0.7


0 --
340


360 380 400 420 440 460 480 500

Heat Source Temperature (K)


Fig. 4.10 Effect of recovery heat exchanger effectiveness on RUE at optimum RUE
conditions, with cooling output









efficiency definitions, as discussed earlier, the cooling component is given a larger

weight. Therefore, better efficiencies are obtained and a larger amount of refrigeration is

produced at optimum conditions. The cycle was also optimized so as to obtain maximum

work output with an upper limit on low pressure set at 5 bars, as in the previous

optimizations. As seen in the earlier results, the efficiency is higher when optimizing for

work output. It can be seen that with sufficient weight given to the refrigeration output,

the cycle could have a higher effective efficiency in the refrigeration mode. Figure 4.10

represents the effect of solution heat exchanger effectiveness on the RUE. As expected, a

lower effectiveness results in a lower efficiency.

Figures 4.11 and 4.12 show optimized exergy efficiencies for the cycle with an

irreversible turbine and pump. It is seen that effective exergy efficiencies are comparable

to the optimum efficiencies obtained for pure work output at lower heat source

temperatures. At higher source temperatures, the optimum conditions in the pure work

output case are still superior. The best efficiency in the refrigeration domain is seen at

the heat source temperature of 400 K. At higher source temperatures, the boiler exit

temperature does not get very close to the heat source inlet temperature because it is

difficult to drop to cold temperatures through the turbine if the inlet temperature is very

high. The effect of lower recovery heat exchanger effectiveness is a drop in efficiency.

The exergy destruction in some of the major processes in the cycle (appropriately

normalized), when optimized for RUE and exergy efficiency in the cooling domain, is

plotted in Figs. 4.13 and 4.14. It is seen that the effect of turbine irreversibility is to

lower the RUE by about 5% (absolute) and the exergy efficiency by about 10%. Once

again the largest source of losses in the RUE optimization is the








77











S- 0 ------------







lexergy, Eq. (4.2)
i 1i..,,,,w~ with ,i,,,,,=0.4, Eq. (4.5)
-l- egy.enwith, ll.re,=0.3, Eq. (4.5)
_- -- Only work output


340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)


Fig. 4.11 Optimized exergy efficiencies for the basic cycle configuration using a non
isentropic turbine and pump







.-. ., Eq. (4.2), s=0.8
60 -- -O -- ,1. _.. _n with ,lll~=0.4, Eq. (4.5), E=0.8
--- m- E, Eq. (4.2), e=0.7
------ i with r =0.4, Eq. (4.5), c=0.7







X
C) v- ----





L 20






340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)
Fig. 4.12 Effect of recovery heat exchanger effectiveness on effective efficiency


60




.)
c 40-

w

0)
x
LU 20-





0








78







-- Heat addition
60 Internal Hx.
-- Heat rejection + throttling
2 ------- Turbine
-I
0 ....... A .......- Unrecovered from heat source


2 5 40 -
A.



... .. . . .
20
CU
--------------------------
.-_-- ----- -_---------- -- -- -- --0



340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)


Fig. 4.13 Exergy destruction in the optimized RUE case







50

---- Heat addition
S- -v Internal Hx.
40- -- heat rejection + throttling
(3 ---0--- Turbine

._ o
30 -
._c
Q >D--^

1' 20 "-
,- -- V

0 --






340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)
Fig. 4.14 Exergy destruction in the optimized exergy efficiency case









unrecovered exergy lost from the heat source. The bad thermal match in the boiler is

reflected in the large exergy destruction during heat addition. The losses in the absorber

are also quite big. The dominant losses when maximizing exergy efficiency (Fig. 4.14)

are in the absorber and the internal heat recovery process.

Discussion

The basic configuration of the cycle has been optimized in order to gauge its

thermodynamic performance. An exergy analysis is performed to determine the potential

areas of improvement in the cycle. The results of the exergy analysis are applied to

improving the performance of the cycle, which is discussed in a later chapter.

It is seen that RUE values obtained with the cycle are quite low. The optimized

cycle state points show that the strong solution starts boiling before entering the boiler (in

the HRHX and rectifier), thereby eliminating the "pinch point" in the boiler. Figures

4.15 and 4.16 show the boiler inlet and exit conditions of the working fluid at the heat

source temperatures studied. The cycle performance is maximized by reduction of mass

flow rate of the heat source until the approach temperature constraint at the boiler

entrance (state 4 in Fig. 4.1) is at the bound. High exergy destruction occurs in the boiler,

when the parameters are set to yield maximum RUE while providing both power and

cooling (see Figs. 4.5 and 4.13). The reason for the observed trend is the low vapor

fraction in the cycle (boiler) when operated to produce power and refrigeration (see Fig.

4.15). It is seen that the vapor fraction is between 9 and 15 % when producing work and

cooling at high efficiency, while in the work domain it is between 20 and 28 % (Fig.

4.16). In order to expand the vapor to low temperatures, relatively high concentration

vapor is required. Other requirements include a high pressure ratio, and lower pressures

at the turbine exit such that the temperature drop in the turbine is high. All these factors














-0.18

-0.16

- 0.14

-0.12

-0.10 f
o.o
-0.08

-0.06 m

- 0.04

S0.02

- 0.00


340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)


Fig. 4.15 Working fluid temperatures and vapor fractions in boiler: at maximum RUE
and with cooling


420



400 -



380 -

a

E 360
aI


Boiler exit vapor
mass fraction


Boiler


Boiler inlet


0.30


0.25



0.20 c
o


0.15



-0.10 .


- 0.05


320 i i I.i 0.00
340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)


Fig. 4.16 Working fluid temperatures and vapor fractions in boiler: at maximum RUE
with pure work output


A .


Boiler exit vapor
mass fraction


4-
/J Boiler Exit


Bubble Point


I I









promote low vapor fraction in the boiler. Consequently, there is a large temperature

difference at the boiler exit (between heat source state II and vapor at state 5) and the

result is poor thermal matching in the boiler. A large temperature glide would be needed

for good thermal matching in the boiler, which only occurs at large vapor fractions.

From Fig. 4.1, it can be seen that the exergy in the heat source fluid leaving the

boiler is not utilized elsewhere. In order to remove as much of the exergy out of the heat

source as possible, the temperature of the heat source should be dropped to the maximum

extent possible in the boiler.

Since the fluid enters the boiler at a condition where it is beginning to boil, the

bubble point of the strong solution should be low. This is achieved by having a high

basic (strong) solution concentration and lower boiler pressures. However when

operating at these conditions, the pressure ratios are lower resulting in a lower

temperature drop in the turbine.

Figure 4.17 clearly shows that the pressure ratios are lower in the RUE optimized

results compared to the exergy efficiency optimized results. Interestingly, it is seen that

setting a lower limit for recovery heat exchanger effectiveness results in a substantial

reduction in pressure ratio in the optimized exergy efficiency results. With ammonia-

water mixtures, lower absorber pressures result in higher pressure ratios. However, the

basic (strong) solution concentration then becomes smaller limiting the vapor fractions in

the boiler. With the resulting increase in the weak solution flow, the load on the recovery

heat exchanger goes up. A reduction in the effectiveness of the recovery unit pushes the

optimum towards higher absorber pressures and lower pressure ratios.














22-

20 -

18 -

16-

.* 14-

12-

uI 10-
,l


6-

4-

2-

0


- exergy effrcrency optimized
- -- RUE optimized


340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)


Fig.4.17 Cycle pressure ratios and the influence of solution heat exchanger effectiveness




1.2
--- energy efficiency optimized
: ---- RUE optimized


qlnsef=0.3






O 0.6 -

S llrere=11




I--r------ -0
0.4


0.2 ---- i ---- i ---- i ---- i ---- ----- i----- i---
0.2 .
340 360 380 400 420 440 460 480 500

Heat Source Temperature (K)


Fig.4.18 Cooling to work output ratios at optimum conditions










83


Figure 4.18 shows the cooling to work output ratio at optimum conditions using the

basic cycle configuration. Clearly, assigning a larger weight to the refrigeration output

results in a larger cooling output at optimum conditions in the cooling domain. Unlike

classic refrigeration cycles, the cold fluid is in the form of dry or slightly wet vapor. The

cooling is by sensible heating of the vapor, and not by the vaporization of a two-phase

mixture as in a typical evaporator. When weight assigned to cooling is larger, in some

cases, the turbine output temperature drops well below the set limit of 270 K in the

simulations.

The corresponding first law efficiency of the cycle at optimum exergy efficiency

and optimum RUE conditions is plotted in Fig. 4.19 and 4.20 respectively. Since the heat

source temperature is low, the corresponding first law efficiency is generally low.



30

a-*-- nEq, (2.17)
25 re, Eq. (2.41), rllref=0.4
Onlywork output

3 20


r 15 --

5 -
*r 10
A-
LL




0 I I
340 360 380 400 420 440 460 480 500
Heat Source Temperature (K)


Fig. 4.19 First law efficiency at optimized exergy efficiency conditions