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Analysis of a novel combined thermal power and cooling cycle using ammonia-water mixture as working fluid

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Title:
Analysis of a novel combined thermal power and cooling cycle using ammonia-water mixture as working fluid
Creator:
Xu, Feng, 1967-
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Language:
English
Physical Description:
x, 157 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Ammonia ( jstor )
Boilers ( jstor )
Cooling ( jstor )
Exergy ( jstor )
Heat ( jstor )
Inlet temperature ( jstor )
Liquids ( jstor )
Turbines ( jstor )
Vapors ( jstor )
Working fluids ( jstor )
Dissertations, Academic -- Mechanical Engineering -- UF ( lcsh )
Mechanical Engineering thesis, Ph. D ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1997.
Bibliography:
Includes bibliographical references (leaves 152-156).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Feng Xu.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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ANALYSIS OF A NOVEL COMBINED THERMAL POWER AND COOLING CYCLE
USING AMMONIA-WATER MIXTURE AS A WORKING FLUID














By

FENG XU













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
1997













ACKNOWLEDGMENTS


I would like to sincerely thank my advisor Dr. D. Yogi Goswami for his constant

support, assistance and suggestions, which encouraged me throughout my work. The

encouragement and advice provided by Dr. S. A. Sherif are greatly appreciated. I owe a

great deal of thanks to Dr. J. E. Peterson, C. K. Hsieh and B. L. Capehart for their time

and effort devoted as part of the dissertation review committee. I would also like to thank

Ms. Barbara Walker, Mr. Charles Garretson and Mr. John West for all the help and

support they have rendered during my study at the Solar Energy and Energy Conversion

Laboratory.

Deep appreciation is extended to my family for the support and inspiration they have

always provided. Finally, I am grateful to my wife Hong and son Tom. This would not

have been possible solely by myself.














TABLE OF CONTENTS


page

ACKNOWLEDGMENTS ------------------------------------- ---- ii

NOMENCLATURE------------------------------------ ----------- vi

ABSTRACT ------------------------------------------------------- ix

CHAPTERS

1 INTRODUCTION-------------------------------- -------------------- 1

1.1 Power Cycle ------------------------------------------------- 2
1.2 Vapor Power Cycle----------------------------------- ----- 4
1.3 Multi-Component Working Fluid Research ---------------------------- 6
1.4 Combined Cycle ------------------------------------- ---------- 8
1.5 The Proposed Cycle ------------------------------------ -------- 9
1.5.1 Rankine Cycle Processes ------------------------------------- 10
1.5.2 Ammonia-Absorption Refrigeration Cycle Processes----------- 10
1.5.3 Combined Power and Cooling Cycle Processes------------- 10
1.6 Thermodynamic Properties of Ammonia-Water Mixtures ---------- 11

2 THERMODYNAMIC PROPERTIES OF AMMONIA-WATER
MIXTURES ---------------------------------------------- ---- 14

2.1 Introduction-------------------------------------- -- ------- 14
2.2 El-Sayed and Tribus Method------------------------------------- 16
2.2.1 Computational Procedure--------------------------------- 17
2.2.2 Ammonia-Water Mixture------------------------------ --- 24
2.2.3 Discussion -------------------------------------------- 26
2.3 Thermodynamic Properties of Ammonia-Water Mixtures by
Gibbs Free Energy Method---------------------------------- 26
2.3.1 Gibbs Free Energy for Pure Component ------------------------- 26
2.3.2 Thermodynamic Properties of a Pure Component ------------- 28








2.3.3 Ammonia-Water Liquid Mixtures------------------------ 29
2.3.4 Ammonia-Water Vapor Mixtures ----------------------------- 32
2.3.5 Vapor-Liquid Equilibrium----------------------------- 32
2.3.6 Discussion --------------- ----------------------- 33
2.4 Method by Park and Sonntag ----------------------------------- 33
2.5 An Alternative Method: Using Gibbs Free Energy Method for Pure
Components, and Bubble and Dew Point Temperature Equations
for Equilibrium Composition---------------------- ---- 36
2.6 Results and Comparision With Literature Data ------------------- 37
2.6.1 Comparison of Bubble and Dew Point Temperature ---------- 38
2.6.2 Comparison of Saturation Pressure at Constant Temperature- 39
2.6.3 Comparison of Saturated Liquid and Vapor Enthalpy--------- 39
2.6.4 Comparison of Saturated Liquid and Vapor Entropy------- 40
2.7 Conclusion--------------------------------------- 41

3 AMMONIA-BASED COMBINED POWER/COOLING CYCLE -------- 67

3.1 Introduction--------------------------------------- 67
3.2 Characteristics of the Novel Cycle as a Bottoming Cycle -------- 71
3.3 Thermodynamic Analysis of the Proposed Cycle------------------ 74
3.4 Thermodynamic Property Calculation-------------------------- 75
3.5 A New Improved Design Cycle -------------------------------- 79
3.6 Conclusion---------------------------------------- 84

4 THE SECOND LAW THERMODYNAMIC ANALYSIS------------- 85

4.1 Introduction-------------------------- 85
4.2 Work and Availability ------------------------------------- 85
4.3 Thermodynamic Processes and Cycles ---------- ------------------ 87
4.4 Exergy------------------------------------------ 87
4.5 Background of Dead State-------------------------------- 88
4.6 Exergy Analysis of the Proposed Cycle --------------------------- 92
4.7 Discussion -------------------------------------- 97
4.8 Conclusion--------------------------------------- 98

5 A THERORECTICAL COMPARISON OF THE PROPOSED CYCLE
AND THE RANKINE CYCLE--------------------------------- 99

5.1 Introduction-------------------------------------- 99
5.2 Cycle Description--------------------------------- 100
5.3 Thermal Boundary Condtions ------------------------------- 101
5.4 Temperature Limitation in the Heat Addition Exchanger -------- 101
5.5 Cycle Analysis -------------------------------------- 110
5.6 Conclusion--------------------------------------- 115








6 SYSTEM SIMULATION AND PARAMETRIC ANALYSIS --------------- 116

6.1 Introduction------------ -------------------------------- 116
6.2 Thermodanymic Analysis of the Proposed Cycle----------------- 116
6.3 Basic Equation ----------------------------------------- 118
6.4 Results and Discussion ------------------------------------------- 119
6.5 Conclusion---------------------------- --------------------124

7 CONCLUTIONS AND FUTURE WORK ------------------------------------148

REFERENCES----------------------------------------------------------- 152

BIOGRAPHICAL SKETCH------------------------------- ------ 157














NOMENCLATURE


A Helmholtz free energy

C, Specific heat

Ex Exergy

f Fugacity

G Gibbs free energy

H Enthalpy

h Enthalpy per unit mass

m Polarity factor

n Index

P Pressure

PB Reference pressure, PB= 10 bar

R Gas constant

S Entropy

s Entropy per unit mass

T Temperature

TB Reference temperature, TB = 100 K

V Volume

v Specific volume








w Eccentric factor

x Ammonia mass fraction

x' Ammonia mole fraction

y Ammonia vapor mass fraction

y' Ammonia vapor mole fraction

Z Compressiblity factor



Subscripts

0 Reference state

Ideal gas state

a Ammonia

b Bubble point

c Critical point

cw Critical point of water

cm Critical point of mixture

d Dew point

f Saturated liquid

g Saturated vapor

m Mixture

r Reduced property

v Vaporization

w Water








Supscript

E Excess property

g Vapor state

L Liquid state














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

ANALYSIS OF A NOVEL COMBINED THERMAL POWER AND COOLING CYCLE
USING AMMONIA-WATER MIXTURE AS A WORKING FLUID

By

Feng Xu

August 1997


Chairman: D. Yogi Goswami
Major Department: Mechanical Engineering

A combined thermal power and cooling cycle is proposed. Ammonia-water mixture

is used as a working fluid. The proposed cycle combines Rankine cycle and absorption

refrigeration cycle. It can provide power output as well as refrigeration with power

generation as a primary goal. The concept of this cycle is based on the varying

temperature boiling of a multi-component working fluid. The boiling temperature of the

ammonia-water mixture increases as the boiling process proceeds until all liquid is

vaporized, so that a better thermal match is obtained in the boiler. The proposed cycle

takes advantage of the low boiling temperature of ammonia vapor so that it can be

expanded to a low temperature while it is still in a vapor state or a high quality two phase

state. This cycle can be used as a bottoming cycle using waste heat from a topping cycle








and can be used as an independent cycle using low temperature sources such as

geothermal and solar energy.

Thermodynamic properties of the ammonia-water mixture are of technical

importance to predict the performance of the proposed cycle. A new method is developed

using Gibbs free energy equations to compute the pure component of ammonia and water

properties, using bubble and dew point temperature equations developed from the

experimental data in the literature for the mixture phase equilibrium calculations. Results

have shown very good agreement with the experimental data and other literature data.

This study has also conducted the first and second law thermodynamic analyses of

the proposed cycle. The mass composition of binary working fluid is considered in the

second law analysis while most of the studies in the literature treat a binary working fluid

as a simple fluid in the second law analysis. A comparison of the proposed cycle and the

conventional Rankine cycle under the same thermal boundary conditions shows the

advantage of the proposed cycle using ammonia-water mixture as a working fluid.

A completed cycle simulation program is developed and shows the performance of

the proposed cycle with different parameters.













CHAPTER 1
INTRODUCTION



Thermal power cycle efficiencies have been steadily improving over the past 100

years. A number of methods have been used to improve the thermal efficiency of a

power cycle. Raising the temperature of the heat source, using different working fluids,

improving the system design and lowering the temperature of heat rejection are the most

common ways.

The second law of thermodynamics sets an upper limit on the efficiencies of power

cycles operating between fixed temperatures. The main reason that the maximum

efficiency of a power cycle can not equal the efficiency of a Carot cycle is due to

irreversibilities in the system. Therefore, one way to increase the efficiency of a cycle

with a fixed temperature heat source and sink is to reduce the cycle irreversibilities.

Considering the limitation of the second law of thermodynamics, a new power cycle

combined with a cooling cycle has been proposed. Ammonia-water mixture is used as a

working fluid in this cycle. A new system design will exploit the unique thermodynamic

properties of ammonia-water mixtures to reduce the system irreversibilities. The

proposed cycle will produce power while providing cooling as well. This cycle will be

able to use low quality heat sources such as solar energy, geothermal heat and waste heat









while achieving high thermal efficiency. It may be used as an independent cycle or as a

bottoming cycle in a combined cycle system.






1.1 Power Cycle




A thermal power cycle can be generally categorized by the working fluid as a vapor

power cycle or a gas power cycle. In a vapor power cycle, the working fluid usually

changes its phase from liquid to vapor and back to liquid in the cycle. In a gas power

cycle, the working fluid remains a gas.

A typical vapor power cycle using steam as a working fluid is the Rankine Cycle as

shown in figure 1-1:








to,




Cooling Wate
Pump

"P


Figure 1-1 Rankine cycle











2 3
Heat exchanger

Win Won
Conpres-sor Turbine

Heat xchanger 4







Figure 1-2 Brayton cycle




A typical gas power cycle using air as a working fluid is Brayton cycle as shown in

figure 1-2. Both cycles have similar working theories: heat is added to the working fluid

at the boiler or combustion chamber; the high temperature, high pressure working fluid

passes through a turbine and becomes low temperature and low pressure fluid; the result

is power output from the turbine. The fluid from the turbine goes through a heat

exchanger to further lower its temperature before going through a pump or compressor to

elevate its pressure.

It is well known that the higher the temperature of the working fluid at the turbine

inlet, the more efficiently the power cycle performs. There are limits of temperature and

pressure range for a vapor power cycle, which needs to operate between the ranges of two

phases. High temperature vapor causes high pressure which requires piping that can

withstand great stresses at elevated temperatures. For a gas power cycle, the high gas

temperature is also restricted by metallurgical limitations imposed by the materials used

to fabricate the turbine and other components.








Various modifications of the basic cycles are usually incorporated to improve the

overall performance under the allowable material conditions and other limitations.

Superheat, reheat and regeneration are the common modifications for vapor power cycles.

Reheat, regeneration and compression with intercooling are the common modifications

for gas power cycles.

An advantage of using a gas power system is that gas turbines tend to be lighter and

more compact than the vapor power systems. In addition, the favorable power output-to-

weight ratio and much higher turbine inlet temperatures make them well suited for certain

applications. But a high turbine inlet temperature also results in a high turbine outlet

temperature (i.e. a lot of heat has to be rejected). This is the main reason that makes a gas

power system function at a low second law efficiency. To solve this problem a combined

cycle is introduced. A combined cycle uses a gas power cycle as a topping cycle and a

vapor power cycle as the bottoming cycle to utilize the waste energy in the relatively

high temperature exhaust gas from the gas power cycle.

In this work, we are focusing on a vapor power cycle as an independent power cycle

or as a bottoming cycle.



1.2 Vapor Power Cycle



Since the first electric generating station in the United States, the Brush Electric

Light Company in Philadelphia, went into service in 1881, engineers have been working

to improve the efficiency of the Rankine Cycle for power production (Babcock & Wilcox,

1978). The additions of superheat, multiple reheat and supercritical cycles have helped








push the thermal efficiency from 7% to approximately 38% (Bejan, 1988). The

introduction and improvement of equipment such as air heaters, economizers and

regenerative feedwater heaters have also contributed to an increase in thermal efficiency.

Advances in metallurgy coupled with the previously mentioned improvements in cycle

and equipment have raised the steam generator outlet conditions from 10x106 Pa

(140psig) and 500 K (440 F) in the 1880s, to today's 2.4x 10 Pa (3500psig) and 865 K

(1100 F) range typical of units such as the Cleveland Electric Illuminating Company's

Avon Lake Station Unit #8 (Bannister and Silvestri., 1989; Duffy, 1964). However one

item has remained constant since the Hero of Alexandria's engine, the use of water as the

working fluid.

One of the methods of increasing the thermal efficiency of a vapor power cycle is the

binary cycle. In this system the heat exchanger with the higher boiling point fluid serves

as the boiler for the lower boiling point fluid. As early as the 1920s several binary cycles

were being explored. Some of the fluids being looked at were mercury, aluminum

bromide, zinc ammonium chloride and diphenyloxide (Gaffert, 1946). Mercury/water

binary cycles have the most operating experience. It should be noted that the New

Hampshire Public Service Shiller plant went on line in the early 1950s with a heat rate

commendable by today's standards, 9700 kJ/kWh (9200 Btu/kWh) (Zerban and Nye,

1957). It was decommissioned in the late 1970s. Metallurgical and safety concerns on

the mercury portion curtailed further development. A similar cycle receiving attention

lately is the patented Anderson Power Cycle(Patent No. 4,660,511, 1987; Patent No.

4,346,561, 1982). In the Anderson cycle the water condenser serves as boiler for the R-








22 refrigerant. It is important to remember that in these binary cycles the two

components are totally segregated.

The multi-component working fluid power cycle that this investigation is developing

is different from the previously mentioned binary cycles in that the working fluids

progress through the cycle; compression, vaporization, expansion and condensation;

together in the same flow stream. More than two fluids can be employed.



1.3 Multi-Component Working Fluid Research



A review of the literature shows that the studies of multi-component cycles are very

recent as compared to the conventional Rankine cycle. Kalina is recognized for

introducing the multi-component working fluid power cycle and for bringing it to it's

current state(Kalina, 1983, 1984; Kalina and Tribus, 1990; Kalina et al., 1986). However,

Back in 1953, Maloney and Robertson (1953) from Oak Ridge National Laboratory

studied an absorption-type power cycle using a mixture of ammonia and water as the

working fluid. Avery (1980) investigated ammonia-water mixtures as the heat exchange

media for power generation in the Ocean Thermal Energy Conversion (OTEC). Maloney

and Robertson, and Avery encountered difficulties in getting the thermodynamic

properties of ammonia-water mixtures in their systems analysis.

Kalina, Tribus and El-Sayed have collaborated on several publications. A

comparison of the multi-component cycle to the Rankine cycle by El-Sayed and Tribus

shows a 10% to 20% improvement in thermal efficiency (El-Sayed and Tribus, 1985b).






7

Marston (1990) conducted a detailed discussion of multi-component cycle behavior

to date. It includes the effect of turbine inlet NH3 mass fraction on cycle efficiency as

well as the associated change in mass fraction in separator flow. Also investigated was

the effect of varying the separator temperature on the cycle efficiency and separator inlet

flow. All work was done at one separator pressure. Turbine inlet conditions were 773.15

K and 1.0x 107 Pa. Marston found that the temperature at the separator and composition

at the turbine inlet are the key parameters for optimizing the Kalina cycle.

Ibrahim and Klein (1996), and Park and Sonntag (1990a) also analyzed the Kalina

cycle. Their studies show the advantages of Kalina cycle over the conventional Rankine

cycle under certain conditions. Park and Sonntag pointed out that since the Kalina cycle

uses many heat exchangers and separators for the distillation condensation process, the

parameters ( such as temperatures and pressures between heat exchangers) have small

differences. This makes the simulation of Kalina cycle very difficult. Ibrahim and Klein

(1996) concluded that Kalina cycle will have advantage over the conventional Rankine

cycle only when heat exchanger NTU is greater that 5.

Since Kalina cycle uses the conventional condensation process by exchanging heat

with the environment, it puts a constraint on the lowest temperature of the working fluid

exiting the turbine. This constraint can be relaxed if absorption condensation process is

employed.

Rogdakis and Antonopoulos (1991) proposed a triple stage power cycle which is

similar to the Kalina cycle. However, they replaced the distillation condensation of the

Kalina cycle with the absorption condensation process. Kouremenos el al. (1994) applied

this absorption type of power cycle as a bottoming cycle in connection with a gas turbine






8

topping cycle. The absorption condensation process in this power cycle removes the need

to use too many heat exchangers and simplifies the ammonia-water power cycle. Since

this cycle still uses ammonia-water vapor mixtures going through turbine, the exit

temperature must be relatively high in order to avoid condensation in the turbine. In their

cycle, Rogdakis and Antonopoulos (1991) used about 400 C heat source and triple stage

turbines to achieve high efficiency.

In this study a new cycle as proposed by Goswami (1995, 1996) is analyzed, that

retains the advantages of the Kalina cycle but removes the constraints of the Kalina cycle

and the Rogdakis and Antonopoulos cycle as identified above. The new cycle uses

ammonia-water mixtures as the working fluids but uses very high concentration ammonia

vapor in the turbine which allows it to expand the fluid in the turbine to a much lower

temperature without condensation. The new cycle also uses absorption condensation

process with its advantages as explained before.



1.4 Combined Cycle



A combined cycle is a synergistic combination of cycles operating at different

temperatures, in which each cycle could operate independently. The cycle which operates

at the higher temperature is called a topping cycle and the cycle which operates at the

lower temperature is called a bottoming cycle. The topping cycle rejects heat at a high

enough temperature to drive the bottoming cycle. The heat rejected from the topping

cycle is recovered and used by the bottoming cycle to produce additional power to

improve the overall efficiency of the combined cycle. Combined cycles which have been






9

proposed or commercialized include several combinations: diesel-steam, mercury-steam,

gas-steam, steam-organic fluid, gas-organic fluid, and MHD-steam.

Combined cycle systems have been recognized as efficient power systems. A typical

combined cycle system consists of a gas turbine cycle and a steam Rankine cycle which

uses the exhaust gas from the gas turbine as the high temperature source. The exhaust gas

provides the available energy for the bottoming cycle (the Rankine cycle) to improve the

efficiency of the combined cycle system over the gas turbine cycle alone.

The efficiency of the overall system is a function of the temperature and pressure of

the exhaust gas, the sink temperature of the bottoming cycle, and the type of the

bottoming cycle itself.



1.5 The Proposed Cycle

The proposed ammonia-based power/cooling cycle, first suggested by Dr. Yogi

Goswami(1995, 1996), combines two thermodynamic cycles, the Rankine cycle and the

ammonia-absorption refrigeration cycle. This novel cycle uses a mixed working fluid

(such as ammonia-water) with different compositions at different stages, therefore, it

cannot be shown on a single thermodynamic diagram (i.e. pressure-enthalpy chart).

However, by evaluating the features of the individual Rankine and ammonia-absorption

refrigeration cycles, the features that apply to the overall cycle can be discussed.



1.5.1 Rankine Cycle Processes

An ideal Rankine cycle, shown in Figure 1-1, is a power generating cycle that has

been used in steam power plants. The process involves pumping a liquid to a high






10

pressure, heating it to a superheated vapor state in a boiler, expanding it through a turbine

to generate power while at the same time bringing the vapor to a saturated state,

condensing the fluid back to a saturated liquid, and finally pumping the liquid back to the

boiler.



1.5.2 Ammonia Absorption Refrigeration Cycle Processes

An ideal cycle for the vapor compression refrigeration is essentially a Rankine cycle

in reverse. The ammonia-absorption refrigeration cycle differs from the vapor-

compression cycle in the manner in which compression is achieved. In the ammonia-

absorption refrigeration cycle(Figure 1-3), low-pressure ammonia vapor from the

evaporator is absorbed in water and the liquid solution is pumped to a high pressure. The

liquid solution is then heated and ammonia vapor is separated from the water. The

ammonia vapor passes through a condenser where it is converted to a liquid and then

through an expansion valve to reduce its pressure. At this point the liquid enters an

evaporator, draws heat, and exits as a low pressure ammonia vapor.



1.5.3 Combined Power and Cooling Cycle Processes

The similarities in the Rankine and ammonia-absorption refrigeration cycle to the

proposed ammonia-based power and cooling cycle are evident as seen in Figure 1-4.

Within this one cycle, the Rankine cycle process of expanding a superheated vapor to

produce work is present, as are most of the absorption refrigeration cycle processes.










Boler Condenser



Heat Expanion
Exchanger al




Pump Absorber Evaporator










Figure 1-3 Ammonia-absorption refrigeration cycle




1.6 Thermodynamic Properties of Ammonia-Water Mixtures




Ammonia-water mixtures have been in use for several decades as working fluids of

absorption-refrigeration cycles where ammonia is the refrigerant and water is the

absorbent. Since 1980, ammonia-water mixtures have been investigated as potential

working fluids for power cycles.

Consistent and accurate thermodynamic properties data of ammonia-water mixtures

are very important for the power cycle analysis. In the past, properties of ammonia-water

mixtures were of interest in the operating range of the absorption refrigeration cycle. As

ammonia-water mixtures become attractive as power cycle working fluids, we need to

extend their properties data to a high pressure and temperature range. Computer






12

programs are also needed to generate these properties. The important properties required

are vapor pressure, equilibrium composition of the components, bubble and dew point

temperature, saturation enthalpy and entropy. Data over the region of compressed liquid

and superheated vapor are also required.

The literature survey shows that there are mainly three methods to compute the pure

ammonia and water properties: 1. free energy method(Gibbs or Helmholtz free energy);

2. a generalized equation method; and 3. use of basic thermodynamic relationships (El-

Sayed and Tribus method).

In chapter 2, these three methods are studied and evaluated. A method is developed

which combines the advantages of the available methods. This new method is faster than

the existing methods because it requires less iterations and it also provides a better match

with the available experimental data. The results from this study are compared with the

most recent experimental data.
















































A/V /XAl Supedwed Ammorna po,
V / // Song Aquamona Soton
S-Weak Aqa-amonia Solu-on


Figure 1-4 Ammonia-based combined power/cooling cycle













CHAPTER 2
THERMODYNAMIC PROPERTIES OF AMMONIA-WATER MIXTURES





2.1 Introduction



The thermodynamic properties of ammonia and water mixtures are of technical

importance since ammonia-water mixtures have been in use for several decades as

working fluids in absorption-refrigeration cycles. Use of multi-component working fluids

for power cycles has been investigated more recently over the last two decades.

Ammonia-water mixtures have been considered as potential working fluids for this

purpose because of relatively high expected coefficients of performance for this

combination.

For the power cycle analysis, the temperature and pressure range is much higher than

that of absorption-refrigeration cycles. So a consistent and extended set of

thermodynamic data for ammonia-water mixtures at higher temperatures and pressures is

required. The motive of this study is a lack of enthalpy and entropy data over the range of

variables needed. Also, it is necessary to use computer simulation to investigate

ammonia-water mixtures as potential working fluids for a power cycle.








Many studies of the vapor-liquid equilibrium and thermodynamic properties of

ammonia-water mixtures are cited in the literature. The temperature and pressure ranges

of thermodynamic properties of the majority of the data in the literature are suitable for

absorption-refrigeration cycle applications. Institute of Gas Technology (IGT) tables

(Macriss et al. 1964) cover the range up to a pressure of 34 bar and its corresponding

saturation temperature. Using the IGT data, Schultz (1972) developed equations of state

for a pressure range of 0.01 to 25 bar and a temperature range of 200 to 450 K. Ziegler

and Trepp (1984) presented a new correlation of equilibrium properties of ammonia-

water mixtures. They used an equation of state that is based on that developed by Schultz

and extended the range of applicability to 500 K and 50 bar. Ibrahim and Klein (1993)

used the form of the equation of state given by Ziegler and Trepp for pure ammonia and

pure water. They modified the correlation given by Ziegler and Trepp for the Gibbs

excess energy to include Gillespie et al. (1987) experimental data at higher temperatures

and pressures. The correlations by Ibrahim and Klein (1993) cover vapor-liquid

equilibrium pressures of 0.2 to 110 bar and temperatures of 230 to 600 K.

A study of power cycles using ammonia-water mixtures was recently initiated by

Kalina (1983). For power cycles, thermodynamic data of ammonia-water mixtures at

higher temperatures and pressures than those presented by IGT are required. Gillespie et

al. (1987) published vapor-liquid equilibrium measurements for five isotherms between

313 and 588 K. Corresponding pressures ranged from 0.1 to 210 bar. Herold et al.

(1988) developed a computer program for calculation of the thermodynamic properties of

ammonia-water mixtures using the Ziegler and Trepp correlation. El-Sayed and Tribus

(1985a) presented a method for computing the thermodynamic properties of mixtures








from the properties of pure components to extend the property correlation to higher

temperatures and pressures. Derived properties cover pressures of 0.1 to 110 bar and

temperatures between 300 and 770 K. Kalina et al. (1986) presented a similar method to

predict the thermodynamic properties of two miscible-component mixtures for the

purpose of power-cycle analysis. Park and Sonntag (1990b) published a set of

thermodynamic data of ammonia-water mixtures based on a generalized equation of state.

The pressure and temperature ranges are extended to 200 bar and 650 K respectively.

Based on the above discussion it is clear that methods developed by Ibrahim and

Klein (1993), Park and Sonntag (1990b) and El-Sayed and Tribus (1985a) cover all of the

modeling efforts reported in the literature. The following section gives detailed

discussions of these methods.



2.2 El-Saved and Tribus method



El-Sayed and Tribus method starts with the thermodynamic properties of pure

components, and mixes them according to certain assumptions. In the liquid region,

below the bubble point temperature, and in the vapor region, above the dew point

temperature, the enthalpy and entropy of the mixture are calculated by summing the

product of the thermodynamic properties and mass fractions of the pure components.

The bubble point temperature is defined as the temperature at which the first bubbles

of gas appear. The dew point temperature is the temperature at which condensate first

appears.






17

El-Sayed and Tribus use a group of equations developed exclusively for ammonia-

water mixtures based on vapor-liquid equilibrium data of Gillespie et al. (1987). The

advantage of these equations is that they allow us to determine the start and end of the

phase change of the mixture and compute the mass fractions of ammonia and water liquid

and vapor phase respectively. This avoids the complicated method of calculating fugacity

coefficient of a component in a mixture to determine the bubble and dew point

temperatures.



2.2.1 Computational Procedure



The basic equations are given below.

Bubble temperature Tb = T(P, x) 2-1

Dew temperature Td = T(P, x) 2-2

Equation of state P = P( T) 2-3


Tb = T, (C, + x)(ln( ))' 2-4
i=l j=l

where

4
T T_=T a.x 2-5
i=l


Pc = P exp(Ybix') 2-6


P in psia and T in F


Ta = T, (a, + A,,(in(1.0001 x))'(ln(-))' 2-7
i j-P








P in psia and T in OF.

Since El-sayed and Tribus used English units in their research, their equations are

kept in English units in this study. In the program, English units are converted to SI

units.



1. Pure ammonia liquid:


C,= A+BT+C(T T)-"2


h = [AT +0.5BT- 2C(T T)1"2]


where A =3.14894

B = -0.0006386

C = 16.66345

T, = ammonia critical temperature, 405.5 K

T = temperature, K

Ti = Reference temperature, 195.40 K

T2 = Final temperature, K

Coefficients A, B and C were found in Haar and Gallagher (1978).


ds
C ,p = T -
dT

1/2 ds
A+BT+C(T -T)-1/2 =T
c dT









AnT+BT+ CI (T T)"2 (TC)12 1 2-12
s =,T:2 (T T)'2 +(T)12 ,



2. Ammonia vaporization




H,2 = H, [ 2-13


where HvI = Known enthalpy of vaporization at a reference temperature TI,

cal/g mole

Hy2 = Enthalpy of vaporization, cal/g mole

T = Ammonia critical temperature, 405.5 K

Tr, = Reduced temperature, at temperature T1

Tr2 = Reduced temperature, at temperature T2

n =Constant

Equation 2-13 is transformed as follows:

H, = C(1-T,2)" 2-14

where


C, =
S (1- T,,)



The above equation can be set up in the form y = a + bx

InH2 =lnC + nln( -T,2) 2-15

where y = lnHv2








a= nCl

b=n

x = ln(1 Tr2)

Values of Hv2 and Tr2 from 0.1 bar to 112 bar were taken from published

literature(Haar and Gallagher, 1978) to find n as 0.38939. Ci is found by

InC = lnH2 -nln(1- Tr2) 2-16

The value of C used in this investigation was taken by averaging 11 values over the

previously mentioned range of pressures. It is

Ci = 7906.555

The enthalpy of vaporization equation used was found by using known values of C1

and n in equation 2-14.

Hv = 7906.555 x (1 T/Te)038939 2-17

The entropy of vaporization is

Sv = Hv / T 2-18



3. Ammonia vapor

Integrating the heat capacity equation 2-19 and comparing the results with published

enthalpy data did not yield good agreement.

C = A + BT + CT2 +DT3 2-19

As the pressure increased the agreement worsened. Therefore, a pressure

compensation term was added to obtain equation 2-20. In addition, the original

coefficients (A, B, C and D) were changed as reflected in equation 2-21. Coefficients

were taken from Haar and Gallagher (1978).








Cp= C, +EPT0

where C, = A + BT + CT2+ DT

A = 3.70315

B = 2.8074 x 10-"

C = 4.4199 x 10-6

D=-6.3441 x 10"9

E= 1.73447 x 1010

G= 4.3314

P = pressure, bar

T = temperature, K


S[ AT+ BT2 C DT EPT'-G+
h= AT+-C+-+--+--
2 3 4 (1-G) 1J

1 EPT-G T2
s= AlnT+ BT+ CT +DT' ---
L IT|


where Ti = Saturation temperature, K

T2 = Final temperature, K



4. Water liquid

The liquid enthalpy is found using the enthalpy of vaporization of H20 and the H20

vapor enthalpy. Figure 2-1 illustrates the use of these two values in finding the liquid

enthalpy.

Temperature Ti in figure 2-1 is the reference temperature, chosen for this work to be

273.15 K. The straight, horizontal segment, line 1-2, is the enthalpy of vaporization.








This now places the computations on the saturated vapor curve. Liquid enthalpies at

other temperatures are found by first "traveling" the H20 saturated vapor curve. Segment

2-3 is the H20 vapor enthalpy difference between the reference temperature and the

temperature of interest, T2. Point 3 is the H20 vapor enthalpy at temperature T2. The

liquid enthalpy is found by subtracting the enthalpy of vaporization from the saturated

vapor enthalpy. This is point 4 in figure 2-1. Point 5 is the critical temperature. Segment

5-6 is superheated vapor.

The liquid entropy of H20 was found in a manner similar to the enthalpy. In this

case the entropy of vaporization was used with the vapor entropy to find the liquid

entropy. Again use figure 2-1 as a reference.



5. Water vaporization

Enthalpy of vaporization Hv2 at temperature T2 is found from the following equation:


H2 = Tc T2 2-24
H,, T T,

In this equation, the known enthalpy of vaporization, H.i at temperature TI, and the

power coefficient, n, were found from Reid et al. 1987, resulting in the following

equation:


H2 C ( Tc 2-25


where C1 = 13468.42

C2 = 0.380

T, = H20 critical temperature, 647.3 K



























Ti 1
T1


Property


Figure 2-1 A generic diagram of water property (enthalpy or entropy) against temperature








6. Water vapor

C =A+BT+CT2 +DT3 2-26

where A = 32.24

B = 1.924 x 10-3

C =1.056 x 10-5

D = -3.596 x 10"9






[AT+ BT2 CT3 DT4]1V 2-27

= AT+-T+ + 2-28


2 3
TI

where TI = Saturation temperature, K

T2 = Final temperature, K



2.2.2 Ammonia-Water Mixtures



1. Liquid

The ammonia-water mixture is in the liquid phase when the temperature is below its

bubble point temperature.

hm = hNH3,f + (1 x)hH20,f 2-29

m = XSNH3f + (1 x)sH2o,f Rm(x'lnx' + (1 x')ln(l x') 2-30

where x = ammonia mass fraction








x' = ammonia mole fraction

Rm= gas constant of the mixture



2. Two phase region

The two phase region is the region between the bubble point and dew point.

hm = amv x XghNH3,g + amv(1 xg)hH2o,g

+ aml x XfhNH3,f + aml(1 Xf)hH2o,f 2-31




m = amv x XgSNH3.g + amv(l Xg)sH2o,g

+ aml xfSNH3,f + aml(1 xf)SH20,f

Rm(xg'ln x' + (1 xg')ln(1 Xg'))

R(xf'lnxi + (1 xf)ln(1 x/)) 2-32

where aml, amy = mass fractions of liquid and vapor in the mixture

x, and x,' = mass and mole fraction of ammonia of vapor

mixture

xf and xi = mass and mole fraction of ammonia of liquid

mixture



3. Vapor

The ammonia-water mixture is in the vapor phase when temperature is above its dew

point temperature.

hm = xhNH3,g + (1 X)hH2,g 2-33

Sm = XSNH3,g + (1 X)SH20,g Rm(x'lnx' + (1 x')ln(l x')) 2-34








2.2.3 Discussion



The advantage of using the El-Sayed and Tribus method is that it is very convenient

to calculate the bubble and dew temperatures, without having to compute the fugacity to

determine the two phase region. The disadvantage is that it needs to calculate the

saturation temperature to compute the enthalpy and entropy. And the saturation

temperatures of pure components are different from the saturation temperatures of the

mixtures, because the saturation temperature of a mixture changes even at the same

pressure. Also, the coefficients of heat capacity equations can not fit a wide range. In the

liquid region, the properties of two pure components cannot simply be mixed. Gibbs free

energy is still needed to calculate the difference from the ideal condition.





2.3 Thermodynamic Properties of Ammonia-Water Mixtures by
Gibbs Free Energy Method


2.3.1 Gibbs Free Energy for Pure Component



The fundamental equation of the Gibbs energy, G, of a pure component can be

derived from known relations for volume and heat capacity as a function of temperature

and pressure. The fundamental equation of the Gibbs energy is given in an integral form

as

T P TC
G = ho -Tso + JCdT+ vdP T dT 2-35
To Po To








where ho, so, To and Po are the enthalpy, entropy, temperature, and pressure at the

reference state. The volume, v, and the heat capacity at constant pressure, Cp, for liquid

phase are assumed to fit the following empirical relations proposed by Ziegler and

Trepp(1984);

v = al + a2P + a3T + a4T2 2-36

CpL = b + b2T + b3T2 2-37

For the gas phase, the corresponding empirical relations are




v = +c,+c2 + T c4p2 2-38
P T' T"

Cp,0 = d + d2T + d3T2 2-39

where the superscripts are L for liquid, g for gas, and o for the ideal gas state.

Integration leads to the following equations for the Gibbs energy for the pure

components.



Liquid phase:

G = h T,s, + B,(T, -T,,o)+ (T,2 T2) + -(T3 T3)- BT, In(
2 3 T".

-B2T,(T, -T,,) 3-(T2 T,) + (A, + A3T, + A4)(P, P,,o) + A(P, Po)
2 2

2-40


Gas phase:








D2 T D 3 DT(T2 T )+D(T T )-DT n(
G' = ho Ts, + D,(T, -T,,) + (T,2 + 3 roDT

-D2T,(T, -T,o))- (T, To)+T,n( r)
P P P, T, P P, PT
+C,(P,- P.) +C,( 4 +3 3( -12 + 11 )
o T I TI.o TT,

+o 12 +11
3 T," T;;, T,2,

2-41

where the reduced thermodynamic properties are defined as

T = T/TB

P, =P/PB

G, = G/RTB

hr = h/RT

s, =s/R

v,= vPs/RTB

The reference values for the reduced properties are R = 8.314 kJ/kmole-K, TB = 100

K and PB = 10 bar.


2.3.2 Thermodynamic Properties of a Pure Component


The molar specific enthalpy, entropy, and volume are related to Gibbs free energy by


h= -T2a (G/ T)


LT
J G
aT]









S= J 2-44


In terms of reduced variables


h =-RTBT,[ (G,/ T,) 2-45



s=-R G, 2-46



v -RT T, 2-47
P, OPr AT



2.3.3 Ammonia-Water Liquid Mixtures



The Gibbs excess energy for liquid mixtures allows for deviation from ideal solution

behavior. The Gibbs excess energy of the liquid mixture is expressed by the relation

proposed by Redlich and Kister(Reid et al. 1987; Ziegler and Trepp 1984), which is

limited to three terms and is given by

G = F, +F (2x -1)+ F(2x- 1)2(1 x) 2-48

where

FI = El + E2P, + (E3 + E4P,)Tr + Es/T4 + E/T,2

F2 = E4 + EP4 + (E9 + EioPr)Tr + EIl/Tr + E12/T,2

F3 E13 + E14Pr + E15/T, + E6/T,2








Table 2-1 Coefficients of equations 2-40 and 2-41

Coefficient Ammonia Water

A1 3.971423 102 2.748796 10-

A2 -1.790557 105 -1.016665 10-

A3 -1.308905 102 -4.452025 103

A4 3.752836 103 8.389246 104

B1 1.634519 10'1 1.214557 10+l

B2 -6.508119 -1.898065

B3 1.448937 2.911966 10"

C1 -1.049377 102 2.136131 10-2

C2 -8.288224 -3.169291 10+1

C3 -6.647257 10+ -4.634611 10O

C4 -3.045352 10+ 0.0

D1 3.673647 4.019170

D2 9.989629 102 -5.175550 10-

D3 3.617622 10-2 1.951939 10-2

hro 4.878573 21.821141

hr,o 26.468873 60.965058

Sro 1.644773 5.733498

Sro 8.339026 13.453430

Tro 3.2252 5.0705

P,o 2.000 3.000










Table 2-2 Coefficients of equation 2-48

El -41.733398 E9 0.387983

E2 0.02414 Elo 0.004772

E3 6.702285 El -4.648107

E4 -0.011475 E12 0.836376

Es 63.608967 E13 -3.553627

E6 -62.490768 E14 0.000904

E7 1.761064 E15 24.361723

Es 0.008626 E16 -20.736547


The excess enthalpy, entropy, and volume for the liquid mixtures are given as


hE = -RTBT2 -i (G" / T) 2-4
Tr ,x


r JP, ,


vE RTB GF
PB L JT,


The enthalpy, entropy, and volume of a liquid mixture are computed by

hm= xh +( -x,)h,+hE 2-


SL = xsL +(1 -xf)s +SE +smix








sm- = -R{xfln(x,)+(1-x,)ln(1-x,)} 2-54

v= Xf,v +(1- Xf)v+v 2-55



2.3.4 Ammonia-Water Vapor Mixture

Ammonia-water vapor mixtures are assumed to be ideal solutions. The enthalpy,

entropy, and volume of the vapor mixture are computed by

h, = x,h +(1-x- )h 2-56

s- = xgs + (1 Xg)sl + smx 2-57

v = xv + (1- x)v 2-58



2.3.5 Vapor-Liquid Equilibrium



At equilibrium, binary mixtures must have the same temperature and pressure.

Moreover, the partial fugacity of each component in the liquid and gas mixtures must be

equal.

TL = T T 2-59

pL = p = 2-60

f.L = 2-61

i = f 2-62

where P and T are the equilibrium pressure and temperature of the mixture, and f is the

fugacity of each component in the mixture at equilibrium.

The fugacities of ammonia and water in liquid mixtures are given by Walas(1985)








f =yfxS. 2-63

f= yf(1-x)65 2-64

where y = activity coefficient

fo = standard state fugacity of pure liquid

component corrected to zero pressure

6 = Poynting correction factor from zero pressure to

saturation pressure of mixture

assuming an ideal mixture in the vapor phase, the fugacities of the pure components in

the vapor mixtures are given by

f. = aPy 2-65

f = wP(1-y) 2-66

where: 4 = fugacity coefficient



2.3.6 Discussion



The Gibbs free energy method is relatively simple for calculation of the pure

component thermodynamic properties. The reference temperature and pressure are fixed,

you only need to know the temperature and pressure of interest to determine the mixtures

properties.


2.4 Method by Park and Sonntag








The generalized equation of state approach is useful in predicting thermodynamic

and volumetric properties of substances for which experimental data are scarce and a

minimum number of data are available: critical temperature, critical pressure, critical

volume, and eccentric factor.

In this study, thermodynamic and volumetric properties of ammonia-water mixtures

are derived from three basic equations:

1. Helmholtz free energy equation for the ideal gas properties of water:


A'= R + 461n(T) -1011.249 T2-67
Li'= t -

where t= 1000/T

constants of ideal gas equation for water


Table 2-3


Coefficients of equation 2-67


a, 1857.065 a3 -419.465 as -20.5516

a2 3329.12 a4 36.6649 a6 4.85233


Similarly, for ammonia


A R= ai ln(T) + aT' +n(4.8180T)- 1 2-68




2. The generalized equation of state based on a four-parameter corresponding state

principle, which is expressed in terms of Zo, Z1, Z2; functions of T, and P,; eccentric

factor, w; and polarity factor, m, with appropriate correction term:








Z=Z +wZ +mZ2 2-

Z' =- -(Z' Z) 2-
ww
S= Z- Z + Z ZO)} 2-


where Z' and Z2 are the nonspherical and polar corrections, respectively.



Table 2-4 Coefficients of equation 2-68

a, -3.872727 a7 0.36893175 10-'0

a2 0.64463724 as -0.35034664 10"1

a3 3.2238759 as 0.2056303 10-16

a4 -0.00213769925 alo -0.6853420 10-20

a5 0.86890833 10- all 0.9939243 10-24

a6 -0.24085149 10-


3. The pseudocritical constants method:

Tm = Z ,TE, + eo,ot,


where subscript cm refers to critical property of mixture.

V. = CZev + e,o,v,


i iV
Sx i 2/3
O'- Ex,V ,3








p Z ZRTm 2-75
V.e

Zc = 02901 0.0879wm 0.0266m. 2-76

w = x,w, 2-77


mm = x,m 2-78




4. Discussion

Park and Sonntag claim that using the generalized equation method provides a

consistent way to calculate the thermodynamic properties of ammonia-water mixtures.

But in the high pressure range, they don't have experimental data to verify the reliability

of this method. This method needs to be further investigated.





2.5 An Alternative Method: Using Gibbs Free Energy Method for Pure Components,
and Bubble and Dew Point Temperature Equations for Equilibrium Composition



The Gibbs free energy of the mixture is a function of temperature, pressure and mixture

composition. The property data derived from such an equation of state are very

consistent and convenient. One can easily calculate the thermodynamic properties of

interest such as enthalpy, entropy, specific volume and vapor pressure without

considering the phase state. Most of the researchers tend to use equation of state model

in their properties calculation.








The criteria of phase equilibrium in a binary system is that the liquid fagucity (or

chemical potential) of a pure component equals the vapor fagucity (or chemical potential)

of that pure component. This requires several iterations to get the composition of each

component of phase equilibrium. The accuracy and convergent time vary at different

points. In a power cycle simulation, these iterations should be avoided for the accuracy

and the computation time of the simulations. El-Sayed and Tribus (1985) developed

bubble and dew point temperatures equations to calculate phase equilibrium. These

equations reduce iterations during phase equilibrium calculations and their temperature

ranges up to 770 K.

In the present study, a method that combines the advantages of Gibbs free energy

method and bubble and dew point temperatures equations is presented. The results show

a very good agreement with the available data based on experimental measurements and

the computation time is reduced.



2.6 Results and Comparisons with Literature Data



The properties of pure ammonia and water can be calculated very precisely by using the

Gibbs free energy equation. In order to calculate the properties of the mixtures it is very

important to predict equilibrium state of vapor-liquid mixture.

For the vapor-liquid equilibrium, experimental data are used. Most experiments

were done in the early 30s. IGT conducted their experiments in the 60s and combined

most of the data from the early experiments to produce vapor-liquid equilibrium data and

mixture properties data for temperature up to 500 K and pressure up to 34.45 bar. The






38

IGT data is accepted as a reliable source, and most computational data are compared with

it.

Wiltec Research Co. (Gillespie et al. 1987) conducted measurements of the

ammonia-water mixtures vapor-liquid equilibrium in the early 80s from 313 K and 589

K. Their data is used to extend the ammonia-water mixtures data to temperature up to

600 K and pressure up to 110 bar by Ibrahim and Klein (1993).

IGT and Wiltec data are used to make correlations to predict ammonia-water

mixtures equilibrium state. The accuracy of computation depends on the mathematical

models used to generate correlations, and computational methods used to compute the

thermodynamic properties of ammonia-water mixtures. It is not surprising that studies

reported in the literature have varying degrees of agreement with the IGT properties data.



2.6.1 Comparison of Bubble and Dew Point Temperatures



Figures 2-2 to 2-5 show that the bubble and dew point temperatures generated by

this study compares favorably with the IGT data.

For the bubble point temperature at constant pressure, IGT has a complete set of data

for pressures from 1 psia to 500 psia and ammonia mass concentration from 0 to 1

incremented by 0.1. The differences between our computed values and the IGT data are

less than 0.3%. Ziegler and Trepp, Ibrahim and Klein reported to have differences up to

2% with the IGT data.

IGT data has dew point temperatures with only four different ammonia mass

fractions of 0.9641, 0.9824, 0.9907 and 0.9953. The data for small moisture








concentrations are used primarily for the moisture effects of absorption refrigeration

cycle. Our results match equally well for the bubble temperatures. An advantage of this

comparison is that the working fluid used in the proposed power cycle also has a very

small percentage of moisture content.



2.6.2 Comparison of Saturation Pressure at Constant Temperature

Figures 2-6 to 2-10 show the saturation vapor and liquid pressures of ammonia-

water mixtures as compared with Gillespie et al. data.

For temperatures less than 406 K, the computation results fit the experimental data

well, except at saturated liquid pressure. At higher temperatures, our computed values

are within 5% of the Gillespie et al. (1987) data even at pressures higher than 110 bar,

while Ziegler and Trepp have reported more than 15% difference. Ibrahim and Klein

reported a less than 5% error under 110 bar and higher errors over 110 bar.



2.6.3 Comparison of Saturated Liquid and Vapor Enthalpy

1. Saturated liquid enthalpy

The enthalpy of saturated liquid of this work is compared with IGT data, as shown in

figures 2-11 to 2-14. The differences are less than 2% for all the data.

2. Saturated vapor enthalpy

The saturated vapor enthalpy at constant pressure is shown in figures 2-15 to 2-18.

The agreement with IGT data is within 3%. Ibrahim and Klein's model reported about a

5% maximum difference.








The ammonia mass fractions shown in these figures are not ammonia vapor

concentrations. In fact, these are ammonia liquid mass fractions when the mixtures reach

a saturated state. So in order to compute the saturated vapor enthalpy, the ammonia vapor

mass fraction has to be determined first. This means that the model has to be accurate in

predicting the ammonia compositions in saturated liquid and vapor.



2.6.4 Comparison of Saturated Liquid and Vapor Entropy

The value of entropy is very important in predicting the performance of a turbine in a

power cycle. Entropy data is also essential to the second law analysis of thermal systems.

Scatchard et al. (1947) published saturated liquid and vapor entropy data based on

experimental data from Zinner (1934), Wucherer (1932) and Perman (1901). Park and

Sonntag(1990b) published calculated entropy data based on their models and compared

with the Scatchard et al. data. In the present study, saturated liquid entropy data are

compared with Scatchard et al., and Park and Sonntag computational data. However,

saturated vapor data are compared with Scatchard et al. data only.



1. Saturated liquid entropy

Figures 2-19 to 2-22 show saturated liquid entropy data as compared with Scatchard

et al. data. Our data agree with the experimental data very well except in the region of

ammonia mass fraction from 0.3 to 0.6. In figures 2-19, 2-21 and 2-22, computed data

from Park and Sonntag (1990b) are also compared. It can be seen that the magnitude of

Park and Sonntag's data are very low as compared to Scatchard's data; it is more than

50% lower at ammonia mass fraction of 0.5.








2. Saturated vapor entropy

Excellent agreement of our computed values with the Scatchard et al. data of the

saturated vapor entropy is shown in figures 2-23 to 2-26. Data reported by Park and

Sonntag (1990b) are consistently lower than the Scatchard's data. Since it is very

difficult to identify Park and Sonntag's saturated vapor entropy data from the literature,

we didn't compare our results with them. Since the behavior of ammonia-water mixtures

in the vapor state is close to the ideal gas mixture, this results in a good match for our

mixture vapor model.



2.7 Conclusion

Different methods for calculating the ammonia-water mixture properties are studied.

A practical and accurate method is used in this study. This method uses Gibbs free

energy equations for pure ammonia and water properties, and bubble and dew point

temperature equations for vapor-liquid equilibrium. The iterations necessary for

calculating the bubble and dew point temperatures by the fugacity method are avoided.

This method is much faster than method of using fugacities or chemical potentials. The

computational results have been compared with the accepted experimental data and show

very good agreement.

With consistent and accurate thermodynamic properties data of ammonia-water

mixtures, we can perform the first and second law analyses of the proposed power cycle.
















400
This Work
380 0- IGT Data

360 P = 1.38 bar


340

2 320

0 300

280

260

240

220
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia Mass Fraction


Figure 2-2 Bubble and dew point temperatures at a pressure of 1.38 bar
















460
-- This Work
440 O IGT Data

420 P = 6.89 bar

400 -

380

S360 -

E
S340
I-

320

300

280

260
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia Mass Fraction


Figure 2-3 Bubble and dew point temperatures at a pressure of 6.89 bar
















480
-- This Work
460 0 IGT Data

440 P= 13.79 bar


420

T 400

S380 -
E

360 -

340 -

320

300
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia Mass Fraction


Figure 2-4 Bubble and dew point temperatures at a pressure of 13.79 bar
















540

52- This Work
5 0 IGT Data
500
500 P = 34.47 bar
480

460 -

S440

I 420
E
- 400

380

360

340

320
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia Mass Fraction


Figure 2-5 Bubble and dew point temperatures at a pressure of 34.47 bar


















30-


This work
25 0 Gillespie et al.



20







1a 10



5-








0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-6 Saturated pressures of ammonia-water mixtures at 333.15 K


















120

-- This work
100 0 Gillespie et al.



80 / 0






S40-



20-



0




0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-7 Saturated pressures of ammonia-water mixtures at 394.15 K

















140 -I


--This work
120 -
120 0 Gillespie et al.


100


80 -0


60 -
a-o


40


20


0



0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-8 Saturated pressures of ammonia-water mixtures at 405.95 K


















200

180 This work
0 Gillespie et al.
160

140


- 120-




a. 80 -

60 -

40

20 -
20



0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-9 Saturated pressures of ammonia-water mixtures at 449.85 K


















250 1 i i

SThis work
O Gillespie et al.
200 /




S150 -









50






0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Ammonia mass fraction


Figure 2-10 Saturated pressures of ammonia-water mixtures at 519.26 K


















500

SThis work
400 0 IGT data


300 -


200 -


100 -

0 -


-100 -


-200 -


-300


-400 I -
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-11 Saturated liquid enthalpy of ammonia-water mixtures at 1.38 bar


















800 I

This work
0 IGT data

600




i 400-


a-

ui 200




0-




-200 I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-12 Saturated liquid enthalpy of ammonia-water mixtures at 6.89 bar


















900

-- This work
800 \ 0 IGT data

700


600


500 -


400


300


200


100


0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-13 Saturated liquid enthalpy of ammonia-water mixtures at 13.79 bar


















1100 '
This work
1000 0 IGTdata


900 -


800 -


S700-


6 600 -


500 -


400-


300 -


200
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-14 Saturated liquid enthalpy of ammonia-water mixtures at 34.47 bar


















2800

SThis work
2600- 0 IGT data


2400


2200


3 2000 -


| 1800


1600


1400


1200


1000 -I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-15 Saturated vapor enthalpy of ammonia-water mixtures at 1.38 bar


















2800

-- This work
2600 0 IGT data


2400


2200


S2000
_Q- ~
, 1800-


1600


1400


1200


1000 -I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-16 Saturated vapor enthalpy of ammonia-water mixtures at 6.89 bar


















3000- I I

-- This work
2800 0 IGT data


2600


2400


2200


S2000


1800


1600


1400


1200
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-17 Saturated vapor enthalpy of ammonia-water mixture at 13.79 bar


















3000 I II

This work
2800 0 IGT data


2600


2400


| 2200


| 2000


1800


1600


1400


1200
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction


Figure 2-18 Saturated vapor enthalpy of ammonia-water mixtures at 34.47 bar



















0.7
0 Scatchard et al.
-- This work
0.6 Park and Sonntag



0.5-








0.3 -


0.2 O




0.1 I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-19 Entropy of Saturated liquid at 310.9 K



















0.90 -I

o Scatchard et al.
0.85 This work



0.80



' 0.75



2 0.70-



0.65



0.60
0 0


0.55 I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-20 Entropy of Saturated liquid at 327.6 K





















1.1
SScatchard et al.
-- This work
1.0 0 Parketal.



0.9



| 0.8 :



o 0.7 -
w LJ


0.6 -


0 0
0.5 -



0.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-21 Entropy of Saturated liquid at 338.7 K




















1.6
D Scatchard et al.
This work
1.5 0 Park et al.


1.4


1.3-


S1.2
(D 0





1.0-




0.9
0.8 -------- i ----------- I------

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-22 Entropy of Saturated liquid at 366.5 K




















10.0

9.5-
o Scatchard et al.
9.0 --- This work

8.5

8.0

7.5 -

o, 7.0

6.5 -

2 6.0

5.5

5.0

4.5

4.0 -

3.5

3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-23 Entropy of Saturated vapor at 310.9 K




















10.0-

9.5
Scatchard et al.
9.0 This work

8.5

8.0

7.5

0 7.0



j 6.0
5.5 -
6.0 -
C
W
5.5

5.0

4.5

4.0

3.5

3.0 -
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-24 Entropy of Saturated vapor at 327.6 K



















10.0

9.5
9.5 Scatchard et al.
9.0 -- This work

8.5

8.0

7.5

7.0 -

6.5

S6.0

5.5

5.0

4.5

4.0

3.5

3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-25 Entropy of Saturated vapor at 338.7 K



















10.0

9.5
o Scatchard et al.
9.0 This work

8.5

8.0

7.5

' 7.0

S6.5

2 6.0

5.5 -

5.0

4.5

4.0

3.5

3.0 il -i
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ammonia mass fraction in saturated liquid


Figure 2-26 Entropy of Saturated vapor at 366.5 K













CHAPTER 3
AMMONIA-BASED COMBINED POWER/COOLING CYCLE





3.1 Introduction



Combined cycle systems have been recognized as efficient power systems. A typical

combined cycle system consists of the gas turbine cycle(the Brayton cycle), which

produces the base load, and the Rankine cycle, which uses the exhaust gas from the gas

turbine as the high temperature source. The exhaust gas provides the available energy to

the bottoming cycle (the Rankine cycle) to improve the efficiency of the combined cycle

system over the gas turbine cycle alone.

The efficiency of the overall system is a function of the temperature and pressure of

the exhaust gas, the sink temperature of the bottoming cycle, and the type of the

bottoming cycle itself.

Most heat sources available to the bottoming cycles, such as hot exhaust gases, are

sensible-heat sources because the temperature of the source is varying during the heat

transfer process. The amount of the cooling medium at the sink temperature in reality is

also limited so that the heat sink is sensible as well. This sensible heat does not satisfy








the isothermal process of the ideal cycle (the Carnot cycle). The ideal cycle to convert

sensible heat to mechanical or electrical energy is therefore not the Camot cycle.

The ideal cycle to convert sensible heat to mechanical or electrical energy is the

Lorenz cycle (Lorenz 1894). This cycle has a triangular shape on a temperature and

entropy diagram, generating the least entropy during the heat transfer process (Kalina

1984). The least production of entropy yields the highest thermodynamic efficiency. It is

interesting to note that with respect to the combined cycle efficiency, the Carot cycle is

still the ideal cycle to produce overall maximum work at a given source temperature since

the bottoming cycle of a triangular shape leads the overall combined cycle to the Camot

cycle, as seen in figure 3-1.

To increase the efficiency of the Rankine cycle working with sensible heat, two

conventional ways have been proposed:

(1) Incorporation of a multi-pressure boiler

(2) Implementation of the supercritical cycle

The multi-pressure boiler is widely used in industry, but results in only moderate

improvement in efficiency unless the number of boiler steps is very large. For the

exhaust gas temperature range from 900-1000 0F(755 811 K), the cycle efficiency is 20-

22% with a single pressure boiler and 23-25% with tri-pressure boiler (Foster-Pegg

1978). Since a significant increase in the number of boiler steps is technically and

economically not feasible, the number of such steps does not usually exceed three (Kalina

1984). The implementation of a supercritical cycle can theoretically achieve a triangular

shape cycle and thus high efficiency, but requires extremely high pressure in the boiler,








which in turn adversely affects the turbine performance (Kalina 1984). Milora and

Tester (1976) have given a detailed discussion of the supercritical cycle.











T













Ranklne Cycle



Q



S


Figure 3-1 Schematic diagram of the Rankine cycle
in connection with a combined cycle








An alternative way to increase the efficiency of the Rankine cycle working with a

sensible heat source is to use a multi-component working fluid. A multi-component

working fluid boils at a variable temperature with a change in the liquid composition of

the components. This variable temperature boiling process yields a better thermal match

with the sensible heat source than the constant temperature boiling process, and is close

to a triangular shape. The better thermal match contributes to the improvement of

thermodynamic efficiency in the boiler. Since the multi-component working fluid

condenses at a variable temperature as well, a part of the gain of the variable temperature

boiling is lost in the condenser. To reduce this loss, the simple condensation process is

complemented by an absorption distillation process (Babcock and Wilcox, 1978).

Our novel power cycle is proposed by Goswami(1995, 1996). The cycle uses a

multi-component working fluid and the condensing process of the Rankine cycle is

replaced by the absorption process. This cycle meets both conditions for higher

thermodynamic efficiency--a better thermal match in the boiler and a heat rejection

system complemented by the absorption system.

The purpose of this work is to conduct a study of the novel power cycle system in

connection with a combined cycle system as in Figure 3-2, comparing the novel cycle and

the Rankine cycle at the same thermal boundary conditions with different internal

conditions for the best performance of each cycle. This study is performed using the

thermodynamic properties of ammonia-water mixtures developed in Chapter 2 in this

study.








3.2 Characteristics of the Novel Cycle as a Bottoming Cycle



A bottoming cycle is a cycle which operates between the high temperature heat

rejected by a topping cycle and the ambient. The cycle utilizes the available heat of the

exhaust gas from the topping cycle. Most heat available to the bottoming cycle is

sensible; the temperature varies during the heat transfer process. This sensible heat can

not realize the isothermal heat supply process of the ideal cycle, the Carnot cycle.

Therefore, the Carot cycle is not the ideal bottoming cycle to convert sensible heat to

mechanical energy or electrical energy. Rather, the ideal cycle working with sensible heat

is the Lorenz cycle(Lorenz, 1894), which has a triangular shape in the temperature and

entropy coordinates.

The Lorenz cycle is composed of four processes, as shown in Figure 3-2

(1) Heat supply at a variable temperature(I-2)

(2) Isentropic expansion(2-3)

(3) Isothermal heat rejection(3-4)

(4) Isentropic compression(4-1)

The Lorenz cycle is exactly the same as the Camot cycle except for the process(l-2).

Possible ways to realize the Lorenz cycle are:

(1) Multi-pressure boiler

(2) Supercritical cycle

(3) The Kalina cycle

(4) The novel ammonia-based combined power/cooling cycle











T
2






1 Equivalnent
proposed cycle


4 QL 3







Figure 3-2 Schematic diagram of the novel cycle in connection with a combined cycle



The novel cycle combines two thermodynamic cycles, the Rankine cycle and the

ammonia-absorption refrigeration cycle, as seen in figure 1-4. In Rankine cycle,

ammonia-water mixture is pumped to a high pressure. The mixture is heated to boil off

ammonia, and ammonia is separated from water. After expanding through a turbine to

generate power, ammonia is brought to absorption refrigeration cycle. Low temperature

ammonia provides cooling in the evaporator and then it is absorbed by water in an








absorber and becomes ammonia-water mixture liquid. As seen in figure 3-3, the novel

cycle provides extra work (shade area) over Rankine cycle.

The novel cycle as a bottoming cycle is a creative way to realize the triangular shape

of the T-S diagram. The concept of this cycle is based on the varying temperature boiling

of a multi-component working fluid. The boiling temperature of the multi-component

working fluid increases as the boiling process proceeds until all liquid is vaporized, so

that a better thermal match is obtained in the boiler. This better thermal match yields a





T












Rankine Cycle



Q



S


Figure 3-3 T-S diagram showing advantage of the novel cycle
over a conventional Rankine cycle








better thermodynamic efficiency. The higher thermodynamic efficiency of the novel

cycle as the bottoming cycle results from

(1) The multi-component working fluid, having a variable boiling temperature, provides

significantly less available energy loss in the boiler, as the heat source has a variable

temperature in the boiler as well.

(2) The working fluid starts boiling almost immediately after entering the evaporator,

which increases the efficiency of the heat exchanger(boiler).

(3) The amount of heat rejected in the condenser is significantly smaller than that in the in

the Rankine cycle arrangement.





3.3 Thermodynamic Analysis of the Proposed Cycle



As seen in Figure 3-3 the proposed ammonia-based cycle is a combination of the

Rankine and the ammonia-absorption refrigeration cycles. Within this one cycle, the

Rankine cycle process of expanding a superheated vapor to produce work is present, as is

part of the ammonia-absorption refrigeration cycle. A difference between this cycle and

the ammonia-absorption refrigeration cycle is that ammonia vapor is not condensed and

then expanded to provide refrigeration, but the ammonia vapor is used as the working

fluid in a turbine.

This section gives a thermodynamic analysis of this novel cycle with assumed

thermal boundary conditions as








1. Power output: 2.5 kW

2. Turbine inlet temperature: 400 K 500 K

3. Turbine inlet pressure: 18 bar 32 bar

At this stage, the thermodynamic state conditions of the proposed combined cycle

are evaluated assuming a idealized cycle (that is irreversibilities associated with real

apparatus were neglected.) The idealized cycle does provide the analytical maximum

limits for real processes and is necessary in determining the efficiency limits of a real

system. The following list of assumptions was used in the initial analysis of the proposed

cycle.





3.4 Thermodynamic Property Calculation



The thermodynamic properties of the working fluids were evaluated using the

methods developed in Chapter 2. The following paragraphs explain the techniques used

to determine the thermodynamic properties at each state in the cycle.

Three working fluids were considered, ammonia vapor, strong ammonia/water

solution, and a weak ammonia water solution. Strong ammonia/water solution refers to

the condition where ammonia vapor and the weak ammonia/water solution have been

combined. Likewise, when the ammonia vapor is boiled off from the strong

ammonia/water solution, the remaining solution is considered the weak ammonia/water










Table 3-1 Assumptions and parameters of the proposed cycle

Assumptions State characteristics
a Strong ammonia/water mixture is pumped P2 = 27.6,
to 27.6 bar and heated to 466 K T4 = T7 = 466 K
b Superheated ammonia vapor is expanded P5 =2.1bar
through a turbine to 2.1 bar
c ammonia vapor exiting the turbine is used in T6 = 277 K
a refrigeration application which brings its
temperature to 277 K
d Neglect pressure drops in components and P2 = P3= P4 = P7 = P8 = 27.6 bar
pipelines. Ps = P6 = P9 = P1 = 2.1 bar

e Liquid solutions at states 1, 3, and 7 are
saturated liquids

f Pump process is assumed to be reversible h2 h = (P2- PI)VI
and adiabatic

g Steady state, steady flow.
h Pure ammonia vapor leaves boiler. xa = 1.0
i Turbine expansion is isentrophic (reversible, S4 = S5
adiabatic)

j The pressure reducing valve is an adiabatic h = h9
process
k Mass flow of weak aqua-ammonia solution
is assumed
1 Temperature of strong aqua-ammonia T3 = 373 K
solution is 373 K after leaving the heat
exchanger.








solution. Subscripts a, s, and w for the thermodynamic properties refer to the

ammonia vapor, strong ammonia/water solution, and weak ammonia/water solution,

respectively.

Since pressure drops in the components and pipelines are neglected, all pressures are

established from the given assumptions; States between the pump and the turbine, or the

pump and pressure relief valve are at 27.6 bar and the states between the turbine or

pressure relief valve and the pump are at 2.1 bar.

The concentrations of ammonia in the aqua-ammonia mixtures are determined using

the assumptions that the strong and weak liquids would be saturated at states 3 and 7,

respectively. The concentrations are assumed as x, = 0.54, xw = 0.125 and xa = 1.0.

Mass balance equations were used to determine the mass flow rates through the

cycle. With the following two equations:

ms = mw + ma,

msxs = mwxw + maxa

and assuming a value for one of the mass flow rates, the values of the other two flow rates

can be determined.

Table 3-2 shows the thermodynamic state including enthalpy at each point.

Table 3-3 shows the energy balance of each component.













Table 3-2 Example of operating conditions for the proposed cycle

State Description Fluid Phase Temp Pressure Enthalpy Concentration Flowrate
K bar kJ/kg kg NH3/kg mix kg/s
1 Absorber Exit / strong aqua- saturated 280 2.1 -209.16 0.540 0.01141
Pump Inlet ammonia liquid
solution
2 Pump Exit/ HEX strong aqua- liquid 280 27.6 -206.59 0.540 0.01141
Inlet ammonia
solution
3 HEX Exit / Boiler strong aqua- saturated 373 27.6 223.22 .540 0.01141
Inlet ammonia liquid
solution
4 Boiler Exit / Turbine ammonia superheated 466 27.6 1682.37 1.000 0.00541
Inlet vapor
5 Turbine Exit/ ammonia superheated 262 2.1 1256.28 1.000 0.00541
Cooler Inlet vapor
6 Cooler Exit / ammonia superheated 277 2.1 1290.98 1.000 0.00541
Absorber Inlet vapor
7 Boiler Exit / HEX weak aqua- saturated 466 27.6 760.95 0.125 0.006
inlet ammonia liquid
solution
8 HEX Exit /PRV weak aqua- subcooled 288 27.6 -15.5 0.125 0.006
Inlet ammonia liquid
solution
9 PRV Exit /Absorber weak aqua- subcooled 288 2.1 -15.5 0.125 0.006
Inlet ammonia liquid
solution








Table 3-3 Energy balance of each component

Component Energy equations Energy (kW)
Pump W= ms(h2 hi) 0.030
Boiler Qb = mah4 + mh7 msh3 11.120
Turbine Wt = m(hs h4) -2.305
Cooler Qc= m(h6 hs) 0.188
Absorber Qa = mah6 + mwh9 msh -9.278


Turbine power output:

Refrigeration:


First law efficiency:


W, = ma(h4 hs) = 2.305 kW

Qc= ma(he h5) 0.188 kW

W+Q 2.305+0.188
S+ Q, 2.305 + 0.188 x00% = 22.42%
Qb 11.12


3.5 A New Improved Design Cycle


The previous section has described the advantage of the conceptual proposed cycle

as shown in figure 1-4. In that section it was assumed that the boiler produced pure

ammonia vapor, however, the figure does not show how to generate highly concentrated

ammonia vapor. Usually, the boiler generates vapor with about 90% ammonia mass

fraction. At this ammonia mass fraction, vapor can not be expanded in a turbine to a very

low temperature because a certain amount of condensation will be generated in the

turbine. For an absorption refrigeration cycle, a condenser or rectifier is used to condense








part of the water vapor from the boiler. After the condenser, a highly concentrated

ammonia vapor is generated. The ammonia composition after the condenser can be over

99%.

Since water vapor is condensed in the condenser/rectifier, heat of condensation is

released. But this heat is not wasted, instead it is used to preheat the basic solution from

the absorber.

Figure 3-4 shows a more detailed design of the proposed cycle. In this system, the

boiler generates ammonia rich vapor (state 5). Before the vapor is superheated in a

superheater (state 7), it passes through a condenser or rectifier (state 6) to get a higher

concentration ammonia vapor. After expansion in the turbine, the ammonia vapor drops

to a very low temperature. The cold ammonia vapor provides cooling by passing through

the cooler (state 9). The ammonia vapor is then reunited with the weak solution from the

boiler in the absorber to regenerate the basic solution (state 1). The basic solution is then

pumped to a high pressure (state 2) to complete the loop. The basic solution coming out

of the absorber is used as the cooling fluid for the condenser. At state 2, part of the

solution goes through a solution heat exchanger, and another part goes to the condenser.

These two streams mix before the boiler. So no heat is wasted while a highly

concentrated ammonia vapor is obtained as a working fluid.

Table 3-4 shows typical operating conditions of the proposed cycle. Table 3-5

shows the performance of each component based on a unit mass of the basic solution at

the conditions of table 3-4.

















































Figure 3-4 A modified ammonia-based combined power/cooling cycle



















Table 3-4 Typical operating conditions

State T p h s x Flow rate
(K) (bar) (kJ/kg) (kJ/kg K) m/ml
1 280.0 2.0 -214.1 -0.1060 0.5300 1.0000
2 280.0 30.0 -211.4 -0.1083 0.5300 1.0000
3 378.1 30.0 246.3 1.2907 0.5300 1.0000
4 400.0 30.0 1547.2 4.6102 0.9432 0.2363
5 360.0 30.0 205.8 1.1185 0.6763 0.0366
6 360.0 30.0 1373.2 4.1520 0.9921 0.1997
7 410.0 30.0 1529.7 4.5556 0.9921 0.1997
8 257.0 2.0 1148.9 4.5558 0.9921 0.1997
9 280.0 2.0 1278.7 5.0461 0.9921 0.1997
10 400.0 30.0 348.2 1.5544 0.4147 0.8003
11 300.0 30.0 -119.0 0.2125 0.4147 0.8003
12 300.0 2.0 -104.5 0.2718 0.4147 0.8003



















Table 3-5 Results from the table 3-4 state conditions

cycle high temperature and pressure are 410.0 K and 30.0 bar
cycle low temperature and pressure are 257.0 K and 2.0 bar
boiler heat input = 390.4
super heat input = 31.3
condenser heat reject = -83.8
absorber heat reject = -358.8
cooler cooling load = 25.9
turbine work output = 76.0
turbine liquid fraction = 0.0692
turbine vapor fraction = 0.9308
pump work input = 2.7

total heat input = 421.6
total work output = 73.33
cycle efficiency = 23.54%
All energy units are kW/kg basic solution








3.6 Conclusion



The initial thermodynamic analysis has shown that the ammonia-based combined

power/cooling cycle has a promising application. In the case study of turbine inlet

condition of 466 K and 27.6 bar, we obtain a pretty good first law system efficiency of

20.7%. At this condition, the steam is still a condensed liquid which means that the

steam Rankine cycle can't even be used for such low temperature application. Further

study with different turbine inlet temperature will also show that the proposed cycle will

have better first law efficiency. The proposed cycle can be applied to many low

temperature heat sources such as geothermal and solar energy heat sources.

An improved design of the proposed cycle is also presented in this chapter with

detailed information. A second law analysis and system simulation based on this design

are discussed in the following chapter.














CHAPTER 4
THE SECOND LAW THERMODYNAMIC ANALYSIS




4.1 Introduction



With the increasing cost of our most widely used fuels and the potential decrease in

their availability in the future, the importance of effective use of our available energy

resources is now receiving more and more attention. The location and degree of

inefficient use of energy in our energy systems should be a primary factor in the design

and performance analysis of the system. The second law analysis is directed to providing

this information by a systematic approach.

To evaluate the effectiveness of energy use in different systems, a realistic measure

of energy utilization must be applied. The exergy method of analysis will provide this

true measure of effective energy use through its application of principles of both the first

and second laws of thermodynamics.



4.2 Work and Availability



The final product of interest from the expenditure of energy resources is work which

is used to perform tasks such as generating electricity, pumping water and moving






86

objects. Work is made available from the energy resources in many forms. For example,

the combustion of oil or gas in a power plant provides high-pressure, high-temperature

steam that is available to do work through a turbine and generator system. When the

temperature and pressure of the steam are near the conditions of the surrounding

environment(condensed liquid near ambient temperature), the work available in the steam

has essentially disappeared. Another example is that, the water behind a dam on a river

is available to do work by driving a hydraulic turbine and an electric generator. The

available work in the water behind the dam reverts to zero when the water level falls to

the level in front of the dam. So when the mass comes into equilibrium with the

environment, no more changes of state will occur and the mass will not be capable of

doing any work. Therefore, the steady-state condition of our surrounding environment is

a reference state which a mass at a given state(such as high temperature and high pressure

steam, water held in a dam) can achieve after a process to perform maximum available

work. This concept of available work referenced to the surrounding environment is the

basis of the exergy method of energy-systems analysis.

It is also a realistic method of comparing the efficient use of our energy resources. It

should be noted that a fluid or gas that is not in equilibrium with the ambient

surroundings has the potential to perform work as its condition reverts to the ambient

surrounding conditions, as everything will do naturally. This means that a fluid that is

colder than the ambient surroundings will be available to perform work as it warms up to

the ambient surroundings just as a warm fluid is available to perform work in its passage

to the ambient surrounding conditions.








4.3 Thermodynamic Processes and Cycles



Energy systems are made up of a series of individual processes that form closed or

open cycles. Each process in a system or cycle can be analyzed separately from the

system by performing a first-law energy balance around the component involved in the

process.

As the available work in a system working fluid decreases through energy-related

processes, there are losses in the available work since no transfer of heat or conversion

between mechanical work and heat can be performed without some irreversibility in the

process. In a system in which many processes are involved, the loss of work in the

system will be distributed throughout the individual processes. It is important to establish

the relative losses in each process if we are to effectively improve the system efficiency.

It should be noted that the conventional heat-balance method of evaluating system

losses and system efficiency is misleading and not a true representation of system

effectiveness. Only through an evaluation of the available work throughout the system

can we have a true measure of the losses in the system processes, which is necessary for

effective energy conservation in system design and operation.



4.4 Exergy



Exergy is defined as the work that is available in a mass as a result of conditions

nonequilibrium relative to some reference condition. As we have described in the








previous paragraph, atmospheric condition generally is a reference condition. Useful

work can be recovered during the cooling and expansion processes of steam through a

steam engine or turbine and heat exchangers. The exergy that is not recovered as useful

work is lost.

Exergy is an explicit property at steady-state conditions. Its value can be calculated

at any point in an energy system from the other properties that are determined from an

energy balance on each process in the system. Exergy is calculated at a point in the

system relative to the reference condition by the following general equation:



Exergy = (u uo) To(s so) + Po(v vo) + V2/2g + g(z zo) + Z(ti pio)x, 4-1

Internal Entropy Work Momentum Gravity Chemical
Energy Potential

Where the subscript 0 denotes the reference condition and i denotes as i-th

composition. There are variations of this general exergy equation, and in most systems

analyses some, but not all, of the terms shown in equation 4-1 would be used. Since

exergy is the work available from any source, terms can also be developed using electrical

current flow, magnetic fields, and diffusion flow of materials.



4.5 Background of Dead State



The exergy method of analysis is a particular approach to application of the second

law of thermodynamics to engineering systems. Another frequently used term is








availability analysis, which is often found in classical thermodynamic text books

(Sonntag et al, 1994; Moran and Shapiro, 1992).

"Exergy is the maximum theoretical work that can be extracted from a combined

system or system and environment as the system passes from a given state to equilibrium

with the environment-that is, passes to the dead state." (Moran and Sciubba, 1994).

Environment or surroundings are often used as a reference state for availability

analysis. When the mass comes into equilibrium with the environment, no change of

state will occur. So the mass is incapable of doing any work or is in a dead state.

One standard atmospheric pressure is normally used as a reference pressure.

Different reference environment temperature have been used by researchers such as 293

K (Aphorratana and Eames, 1995), 298 K (Egrican, 1988) and 300 K (Waked, 1991).

Krakow(1991) proposed a dead-state definition. He indicated that the reservoir of a

system that is not the environment is defined as the system reservoir. The system

reservoir serves as the source for engines and coolers and as the sink for heat pumps. The

environment serves as the sink for engines and coolers and as the source for heat pumps.

So instead of using universal ambient condition as a dead state, he proposed that one of

the high-temperature and low-temperature reservoirs of the system to be considered as a

reference state.

Since reservoirs of real systems are finite, their temperatures change during any heat

transfer process. Therefore, the dead state temperature in a real process changes during

the process. To account for the change in the dead state temperature in real processes,








Krakow defined an effective reservoir temperature for heat sources and sinks which is

essentially the same as the entropic average temperature used by Herold (1989).

The effective reservoir temperature, which is used as the dead state for the reservoir,

is defined as the temperature that will make its initial exergy equal to the final exergy.

Neglecting the momentum, gravity and chemical exergies, the initial and final exergies of

a reservoir are

Ex, = (hi hef) Te(sI sef) 4-2

Ex2 = (h2 hf) Tf(2 Sef) 4-3

where subscripts 1 and 2 stand for the initial and final conditions of the reservoir, and ef

stands for the effective temperature condition.

Tef is defined such that Exl = EX2.

The entropic average temperature of a reservoir is defined as


T, =Q = Q 4-4

IT

where QI-2 is the heat exchanged with the reservoir.

Above methods and definitions can be used easily for single working fluids such as

steam. However, it is difficult to define the dead state for mixtures such as LiBr/water

and ammonia/water. Since a dead state composition must also be defined. In other

words, it is important to know what work will be done by changing mixture composition

at the same temperature and pressure, or will the composition change at all under the

same temperature and pressure.




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ANALYSIS OF A NOVEL COl\IBINED THERMAL POWER AND COOLING CYCLE USING AMMONIA-WATER MIXTURE AS A WORKJNG FLUID By FENG XU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILL11ENT OF THE REQU1REMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1997

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ACKNOWLEDGJ\1ENTS I would like to sincerely thank my advisor Dr. D. Yogi Goswami for his constant support, assistance and suggestions, which e11couraged me throughout my work. The encouragement and advice provided by Dr. S. A. Sherif are greatly appreciated. I owe a great deal of thanks to Dr. J.E. Peterson C. K. Hsieh and B. L. Capehart for theit time and effort devoted as part of the dissertation review committee I would also like to thank Ms. Barbara Walker Mr. Charles Garretson and Mr. John West for all the help and suppo11 they have rendered dtrring my study at the Solar Energy and E11ergy Conversion Laboratory. Deep appreciation is extended to my family for the support and inspiration they have always provided Finally, I am giateful to my wife Hong and son Tom. This would not have been possible solely by myself. .. 11

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TABLE OF CONTENTS page A CKN O WLEDG:MENTS----------------------------------------------------------ii NO:MENCLATURE----------------------------------------------------------------vi ABSTRACT-------------------------------------------------------------------------ix CHAPTERS 1 IN"TRODUCTION-----------------------------------------------------------------1 1.1 Power Cycle ------------------------------------------------------------------2 1.2 Vapor Power Cycle----------------------------------------------------------4 1.3 Multi-Component Working Fluid Research-----------------------------6 1.4 Combined Cycle-------------------------------------------------------------8 1.5 The Proposed Cycle---------------------------------------------------------9 I. 5 .1 Rankine Cycle Processes -------------------------------------------10 1.5.2 Ammonia-Absorption Refrigeration Cycle Processes----------10 1.5 .3 Combined Power and Cooling Cycle Processes-----------------I 0 1.6 Thermodynamic Properties of Ammonia-Water Mixtures ----------11 2 THERMODYNAMIC PROPERTIES OF M1MONIA-WATER MIXTURES-----------------------------------------------------------------14 2.1 Introduction-----------------------------------------------------------------14 2.2 El-Sayed and Tribus Method---------------------------------------------16 2.2.1 Computational Procedtire-------------------------------------------17 2.2.2 Ammonia-Water Mixture-------------------------------------------24 2.2.3 Discussion ------------------------------------------------------------26 2.3 Thern1odynamic Properties of Ammonia-Water Mixtures by Gibbs Free Energy Method--------------------------------------------26 2.3 .1 Gibbs Free Energy for Pwe Component -------------------------26 2.3.2 The1nodynamic Prope1ties of a Puie Component--------------28 111

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2 3 .3 Ammonia-Water Liquid Mixtures---------------------------------29 2.3 4 Ammonia-Water Vapor Mixtures---------------------------------32 2. 3. 5 VaporLiquid Equili bri t1m------------------------------------------3 2 2.3 .6 Discussion -----------------------------------------------------------33 2.4 Method by Park and Sonntag-------------------------------------------33 2.5 An Alternative Method: Using Gibbs Free Energy Method for Pure Components, and Bubble and Dew Point Temperature Equations for Equilibrium Composition-----------------------------------------36 2.6 Results and Comparision With Literatwe Data-----------------------37 2.6.1 Comparison of Bubble and Dew Point Temperature-----------38 2.6.2 Comparison of Saturation Pressure at Constant Temperature-39 2.6.3 Comparison of Saturated Liquid and Vapor Enthalpy----------39 2.6.4 Comparison of Saturated Liquid and Vapor Entropy-----------40 2. 7 Conclusion------------------------------------------------------------------41 3 ANl:MONIA-BASED CO:MBINED POWER/COOLING CYCLE -------------67 3 1 Introduction-----------------------------------------------------------------67 3.2 Characteristics of the Novel Cycle as a Bottoming Cycle-----------71 3.3 Thermodynamic Analysis of the Proposed Cycle---------------------74 3 .4 Thermodynamic Property Calculation----------------------------------75 3 .5 A New Improved Design Cycle -----------------------------------------79 3. 6 Conclt1sion------------------------------------------------------------------84 4 THE SECOND LAW THERMODYNAMIC ANALYSIS-----------------------85 4 .1 Introdt1cti on-----------------------------------------------------------------8 5 4.2 Work and Availability----------------------------------------------------85 4.3 Thertnodynamic Proce ss es and Cycles---------------------------------8 7 4 .4 Exergy-----------------------------------------------------------------------87 4 .5 Background of Dead State------------------------------------------------88 4.6 Exergy Analy s is of the Proposed Cycle--------------------------------92 4. 7 Discussion ------------------------------------------------------------------97 4. 8 Conclusion------------------------------------------------------------------9 8 5 A THERORECTICAL COMPARISON OF THE PROPOSED CYCLE AND THE ~1 CYCLE---------------------------------------------------99 5 .1 Introduction-----------------------------------------------------------------99 5 .2 Cycle Description---------------------------------------------------------100 5 .3 Thermal Boundary Condtions ------------------------------------------101 5 4 Temperature Limitation in the Heat Addition Exchanger ----------101 5 .5 Cycle Analysis ------------------------------------------------------------110 5. 6 Conclusion-----------------------------------------------------------------115 J V

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6 SYSTEM SIMULATION AND PARANIBTRIC ANALYSIS------------------116 6 .1 Introduction----------------------------------------------------------------116 6 .2 Thertnodanymic Analysis of the Proposed Cycle--------------------116 6.3 Basic Equation------------------------------------------------------------118 6.4 Results and Discussion --------------------------------------------------119 6 .5 Conclusion-----------------------------------------------------------------124 7 CONCLUTIONS AND FUTURE WORK ----------------------------------------148 REFERENCES ---------------------------------------------------------------------------15 2 BIOGRAPI-IlCAL SKETCH-----------------------------------------------------------157 V

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NO:MENCLA TURE A Helmholtz free energy Cp Specific heat Ex Exergy f Fugacity G Gibb s free energy H Enthalpy h Enthalpy per unit mass m Polarity factor n Index P Pres s ure P B Reference pressure, P 8 = 10 bar R Gas constant S Entropy s Entropy per unit mass T Temperature T 8 Reference temperature T a = 100 K V Volume v Specific volume V I

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w Eccentric factor x Ammonia mass fraction x' Ammonia mole fraction y Ammonia vapor mass fraction y' Ammonia vapor mole fraction Z Compressiblity factor Subscripts 0 a b C cw cm d f g m r V w Reference state Ideal gas state Ammonia Bubble point Critical point Critical point of water Critical point of mixtt11e Dew point Saturated liquid Saturated vapor Mixture Reduced prope1ty Vaporization Water .. Vll

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Sup script E Excess property g Vapor state L Liquid state Vlll

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Abstract of Dissertation Presented to the Graduate School of the University of Florida h1 Patiia1 Fulfillment of the Requiren1ents for the Degree of Doctor of Philosophy ANALYSIS OF A NOVEL CO:MBINED THERMAL POWER AND COOLING CYCLE USING AMMONIA-WATER l\1IXTURE AS A WORKING FLUID By Fe11g Xu August 1997 Chairman: D. Yogi Goswami Major Department: Mechanical Engineering A combined thennal power and cooling cycle is proposed. Ammonia-water mixture is used as a working fluid. The proposed cycle combines Rankine cycle and absorption refrigeration cycle. It can provide power output as well as refrigeration with power generation as a primary goal. Tl1e concept of this cycle is based on the varying temperature boilir1g of a mt1lti-component working fluid. The boiling temperature of the ammonia-water mixture increases as the boiling process proceeds until alJ liquid is vaporized, so that a better thermal match is obtained in the boiler. The proposed cycle takes advantage of the low boiling temperature of ammonia vapor so that it can be expanded to a low temperature while it is still in a vapor state or a high quality two phase state. This cycle can be used as a bottoming cycle using waste heat from a topping cycle lX

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and can be used as an independent cycle using low temperature sources st1ch as geothermal and solar energy. Thermodynamic properties of the am1nonia-water mixture are of technical importance to predict the performance of the proposed cycle. A new method is developed using Gibbs free energy equations to compute the pure compo11ent of ammonia ru1d water properties, using bubble and dew point temperature equations developed from the experimental data in the literature for the mixture phase equilibritlDl calculations. Results have shown very good agreement with the experimental data and other literature data. This study has also conducted the frrst and second law thermodynamic analyses of the proposed cycle. The mass composition of binary working fluid is considered in the second law analysis while most of the studies in the literature treat a binary working fluid as a simple fluid in the second law analysis. A compruison of the proposed cycle and the conventional Rankine cycle under the same thermal boundary conditions shows the advantage of the proposed cycle using ammonia-water mixture as a working fluid. A completed cycle simulation program is developed and shows the performance of the proposed cycle with different parameters. X

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CHAPTER 1 INTRODUCTION Thermal power cycle efficiencies have been steadily improving over the past 100 years. A number of methods have been used to improve the thermal efficiency of a power cycle. Raising the temperature of the heat source, using different working fluids improving the system design and lowering the temperature of heat rejection are the most common ways The second law of thermodynamics sets an upper limit on the efficiencies of power cycles operating between fixed temperatures. The main reason that the maximum efficiency of a power cycle can not equal the efficiency of a Carnot cycle is due to irreversibilities in the system. Therefore one way to increase the efficiency of a cycle with a fixed temperature heat source and sink is to reduce the cycle irreversibilities Considering the limitation of the second law of thermodynamics, a new power cycle combined with a cooling cycle has been proposed. Ammonia-water mixture is used as a working fluid in this cycle. A new system design will exploit the unique thermodynamic properties of ammonia-water mixtures to reduce the system irreversibilities. The proposed cycle will produce power while providing cooling as well. This cycle will be able to use low quality heat sources such as solar energy, geothermal heat and waste heat 1 l

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while achieving high thermal efficiency It may be used as an independent cycle or as a bottoming cycle in a combined cycle system. 1 1 Power Cycle 2 A thermal power cycle can be generally categorized by the working fluid as a vapor power cycle or a gas power cycle. In a vapor power cycle, the working fluid usually changes its phase from liquid to vapor and back to liquid in the cycle In a gas power cycle, the working fluid remains a gas. A typical vapor power cycle using steam as a working fluid is the Rankine Cycle as shown in figure 1-1 : 1 T urbine c:t==~....._ W l Bolle r I > C ondenser 4 C oollng W ete r 3 Figure 1-1 Rankine cycle

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3 3 Heat ex c hanger Wjn Wo u t c===-:::::;:> C ompre s sor 1------------i Turbine 1 { Heat e xc ha n ge r 4 c C J, Clo u t J Figure 12 Brayton cycle A typical ga s power cycle u s ing air as a working fluid i s Brayton cycle as shown it1 figure 1-2. Both c ycles have sirnilru: workin g tl1eorie s: heat is added to the working fluid at the boiler or combustion chamber; the high temperature high pressw e working fluid passes through a turbine and become s low temperature and low pressure fluid ; the result i s power output from the turbine. The fluid from the turbine goe s through a heat exchanger to further lower it s temperatu1 e before g oing through a pump or compre ss or to elevate its pres s ure It is well known that the higher the temperature of the working fluid at the turbine inlet the n1ore efficiently the power cycle perform s. There are limit s of temperatw e and pressw e range for a vapor power cycle which needs to operate between the ranges of two phases. High temperature vapor causes hi g h pres s ure which require s piping that can with s tand great s tres s es at elevated temperatures. Fo1 a gas power cycle the high g a s temperature is al s o restricted by metallurgical limitations imposed by the material s used to fabricate the turbine and other c omponent s.

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4 Various modifications of tl1e basic cycles are usually incorporated to improve the overall performance W1der the allowable material conditions and other limitations. Superheat, reheat and regeneration are the common modifications for vapor power cycles. Reheat regeneration and compression with intercooling are the common modifications for gas power cycles. An advantage of using a gas power system is that gas turbines tend to be lighter and more compact than the vapor power systems. In addition, the favorable power output-to weight ratio and much higher turbine inlet temperatures make them well suited for certain applications. But a high turbine inlet temperature also results in a high turbine outlet temperature (i.e. a lot of heat has to be rejected). This is the main reason that makes a gas power sy stem function at a low second law efficiency. To solve this problem a combined cycle is introduced A combined cycle uses a gas power cycle as a topping cycle and a vapor power cycle as the bottoming cycle to t1tilize the waste energy in the relatively high temperature exhaust gas fro1n the ga s power cycle. In this work, we are focusing on a vapor power cycle as an independent power cycle or as a bottoming cycle. 1.2 Vapor Power Cycle Since the fust electric ge11erating station in the United States, the Brush Electric Light Company in Philadelphia went into service in 1881 engineers l1ave been working to improve the efficiency of the Rankine Cycle for power production (Babcock & Wilcox 1978). The additions of superheat, multiple reheat and superc1itical cycles have helped

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5 push the thermal efficiency from 7 o/ o to approximately 38 % (Bejan, 1988). TI1e introduction and improvement of equipment such as air beaters, economizers and regenerative feedwater heaters have also contributed to an increase in thermal efficiency. Advances in metallurgy coupled with the previously mentioned improvements in cycle and equipment have raised the steam generator outlet conditions from 1O x 10 6 Pa (140psig) and 500 K (440 F) in the 1880s, to today's 2.4 x l0 7 Pa (3500psig) and 865 K ( 1100 F) range typical of units such as the Cleveland Electric Illuminating Company s Avon Lake Station Unit # 8 (Bannister and Silvestri. 1989; Duffy 1964). However one item has remained constant since the Hero of Alexandria's engine, the use of water as the working fluid. One of the methods of increasing the thermal efficiency of a vapor power cycle is the binary cycle. In this system the heat exchanger with the higher boiling point fluid serves as the boiler for the lower boiling point fluid. As early as the l 920s several binary cycles were being explored. Some of the fluids being looked at were me1cU1y, aluminum bromide, zinc ammonium chloride and diphenyloxide (Gaffert, 1946). Mercury / water binary cycles have the most operating experience. It should be noted that the New Hampshire Public Service Shiller plant went on line it1 the early 1950s with a heat rate comn1endable by today s standards, 9700 kJ / kWh (9200 Btu/kWh) (Zerban and Nye, 1957). It was decommissioned in the late 1970s. Metallurgical and safety concern s on the mercury portion cu1iailed further development A similar cycle receiving attention lately is the patented Anderson Power Cycle(Patent No. 4,660,511, 1987 ; Patent No. 4,346,561, 1982). In the Anderson cycle the water condenser serves as boiler for the R

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6 22 refrigerant. It is important to remember that in these binary cyc l es the two components are totally segregated. The multi-component working fluid power cycle that this investigation is developing is different from the previously mentioned binary cycles in that the working fluids progress through the cycle; compression, vaporization, expansion and condensatio11; togetl1er in the same flow streao1. More than two fluids can be employed 1.3 Multi-Component Working Fluid Research A review of the literature shows that the studies of multi-component cycles are very recent as compared to the conventional Rankine cycle. Kalina is recognized for introducing the multi-component working fluid power cycle and for bringing it to it's current state(Kalina, 1983, 1984; Kalina and Tribus, 1990; Kalina et al 1986). However, Back in 1953, Maloney and Robertson (1953) from Oak Ridge National Laboratory studied an absorption-type power cycle using a mixture of ammonia and water as the working fluid. A very (1980) investigated ammonia-water mixtures as the heat exchange media for power generation in the Ocean Thermal Energy Conversion (OTEC). Maloney and Robe1tson, and A very encountered difficulties in getting the thermodynamic properties of ammonia-water nuxtures in their systems analysis. Kalina, Tribus and El-Sayed have collaborated on several publications. A comparison of tl1e multi-component cycle to the Rankine cycle by El-Sayed and Tri bus shows a 10% to 20% improvement in thennal efficiency (El-Sayed and Tri bus, 1985b ).

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7 Marston ( 1990) conducted a detailed discussion of multi-component cycle behavior to date. It includes the effect of turbine inlet NH 3 mass fraction on cycle efficiency as well as the associated change in mass fraction in separator flow. Also investigated was the effect of varying the separator temperature on the cycle efficiency and separator inlet flow. All work was done at one separator pressure. TU1bine inlet conditions were 773.15 K and l .O x 10 7 Pa. Marston found that the temperature at the separator and composition at the turbine inlet are the key parameters for optimizing the Kalina cycle. Ibrahim and Klein (1996), and Park and Sonntag (1990a) also analyzed the Kalina cycle Their studies show the advantages of Kalina cycle over the conventional Rankine cycle under certain conditions. Park and Sonntag pointed out that since the Kalina cycle uses many heat exchangers and sepruators for the distillation condensation process the parameters ( such as temperatures and pressures between heat exchangers) have small differences. This make s the simulation of Kalina cycle very difficult. Ibrahim and Klein (1996) concluded that Kalina cycle will have advantage over the conventional Rankine cycle only when heat exchanger NTU is gieater that 5. Since Kalina cycle uses the conventional condensation process by exchanging heat with the environment, it puts a constraint on the lowest temperature of the working fluid exiting the turbine. This constraint can be relaxed if absorption conde11sation process is employed Rogdakis and Antonopoulos (1991) proposed a triple stage power cycle which is similru to the Kalina cycle. However they replaced the distillation condensation of the Kalina cycle with the absorption condensation process. KoU1 emenos el al (1994) applied this absorption type of power cycle as a bottoming cycle in connection with a gas turbine

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8 topping cycle. The absorption condensation process in this power cycle removes the need to use too many heat exchangers and simplifies the arrunonia-water power cycle Since this cycle st ill uses ammonia-water vapor mixtures going tht ough turbine, the exit temperatwe mtist be relatively high in order to avoid condensation in the turbine. In their cycle, Rogdakis and Antonopoulos ( 1991) used about 400 C heat source and triple stage turbines to achieve high efficiency. In this study a new cycle as proposed by Goswami (1995 1996) is analyzed, that retains the advantages of the Kalina cycle but removes the constraints of the Kalina cycle and the Rogdakis and Antonopoulos cycle as identified above. The new cycle uses ammonia -w ater mixture s as the working flt1ids but uses very high concentration ammonia vapor in the turbine which allows it to expand the fluid in the turbine to a much lower temperatut e without condensation. The new cycle also uses abso1ption condensation proces s with its advantages a s explained before 1.4 Combined Cycle A combined cyc le is a synergistic combination of cycles operating at different temperatures in which each cycle could operate independently The cycle which operates at the higher temperature is called a topping cycle and the cycle which operat es at the lower temperature is called a bottoming cycle. The topping cycle rejects heat at a high enough temperature to drive the bottoming cyc le The heat rejected from the topping cyc le is recovered and used by the bottoming cycle to produce additional power to improve the overall efficiency of the combined cycle. Combined cycles which have been

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9 proposed or commercialized include several con1binations: diesel-steam, mercury-steam, gas-steam, steam-organic fluid, gas-organic fluid, and MI-ID-steam. Combined cycle systems have been recognized as effic i ent power systems. A typical combined cycle system consists of a gas turbine cycle and a steam Rankine cycle which uses the exhaust gas from tl1e gas turbine as the high temperature source. The exhaust gas provides the available energy for the bottoming cycle (the Rankine cycle) to improve the efficiency of the combined cycle system over the gas turbine cycle a l o11e. The efficiency of the overall system is a function of the temperature and pressure of the exhaust gas, the sink temperature of the bottoming cycle, and the type of the bottoming cycle itself. 1.5 The Proposed Cycle The proposed ammonia-based power / cooling cycle, first suggested by Dr. Yogi Goswami(1995, 1996), combines two thermodynamic cycles, tl1e Rankine cycle and the ammo11ia-absorption refrigeration cycle. This novel cycle uses a mixed working fluid (such as ammonia-water) with different compositions at different stages, therefore, it cannot be shown on a single thermodynamic diagram (i.e. pressure-enthalpy chart). However, by evaluating the features of the individual Rankine and ammorua-absorption refrigeration cycles, the features that apply to the overall cycle can be discussed 1.5 1 Rankine Cycle Processes An ideal Rankine cycle shown in Figure 1-1, is a power generating cycle that has been used in steam power plants. The process involves pumping a liquid to a high

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1 0 pressure heating it to a superheated vapor state in a boiler expanding it through a turbine to generate power while at the same time bringing the vapor to a saturated state condensing the fluid back to a saturated liquid and finally pumping the liquid back to the boiler 1 5.2 Ammonia Ab s orpt i on Refrigeration Cycle Processes An ideal cy c le for the vapor c ompre ss ion refrigeration is e s sentially a Rankine cy cle in rever s e. The ammonia-absorption refrigeration cycle differ s from the vapor compre s sion cycle in the manner in which compre s sion is achieved. In the ammonia absorption refrigeration cycle(Figure 1-3 ), l ow pre ss ure ammonia vapor from the evaporator is absorbed in water and the liquid s olution i s pumped to a high pre s sure The liquid s olution i s then heated and ammonia vapor is s eparated from the water The ammonia vapor pas s es through a condenser where it i s converted to a liquid and then through an expan s ion valve to reduce it s pressure At this point the liquid enters an evaporator draw s heat and exit s as a low pre ss w e ammonia vapor. 1 .5 3 C ombined Power and Cooling Cycle Proce s se s The similaritie s in the Rankine and ammonia ab s orption refrigeration c y cle to the proposed ammonia-based powe1 and cooling cycle are evident as seen in Figure 1-4 Within this one cycle the Rankine cycle proce s s of expanding a superheated vapor to produce work i s pre s ent as are most of the ab s orption refrigeration cycle proces s e s.

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Heat Exchange r ( Boller J ( ) C ...... Pump +-1Con d enser Expans1on valve .. 17 Absorber Figure 1-3 Ammonia-absorption refrigeration cycle 1.6 Thermodynamic Prope11ies of Ammonia-Water Mixtures 11 Ammonia-water mixtures have been in use for several decades as working fluids of absorption-refrigeration cycles where an1monia is the refi:igerant and water is the absorbent. Since 1980, ammonia-water mixtmes have been investigated as potential working fluids for power cycles. Consistent and acctu ate thermodynamic properties data of ammonia-water mixttues are very important for the power cycle analysis. In the past, properties of ammonia-water mixtures were of interest in the operating range of the absorption refrigeration cycle. As ammonia-water mixtures become attractive as power cycle working fluids, we need to extend their properties data to a high p1essure and temperature range. Computer

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1 2 programs are also needed to generate these properties. The important propertie s required are vapor pressure equilibrium composition of the components bt1bble and dew point temperature saturation e11thalpy and entropy Data over the region of compres s ed liquid ru1d superheated vapor are also required The literature s urvey show s that there are mainly three methods to compute the pw e ammonia and water propertie s : 1 free energy metl1od(Gibbs or Helmholt z free ener gy ) ; 2. a generalized equation method ; and 3. u s e of ba s ic thermodynatnic relationship s (E Sayed and Tribu s method). In chapter 2 the s e tlu ee method s are s tudied and evaluated. A method is developed which combine s the advantage s of the available method s This new method i s fa s ter than the e x i s ting methods because it require s les s iterations and it also provide s a better match with the available experimental data The result s from this study are compared with the mo s t recent experimental data.

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WP Pump 1 Absorber 2 a Pressure Reducing Valve 9 Heat Exchanger 8 WYXXZ7X&1 v 77 77 771 3 7 Cooler Superheated Ammonia Vapor Stron_g Aqua~mmonla Solution Weak Aqua~mmonia Solution Boiler Turbine 5 Figure 1-4 An1monia-based combined power /c ooling cyc le 13 4 Ws C ,_

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CHAPTER2 THERMODYNAMIC PROPERTIES OF AMMONIA-WATER MIXTURES 2.1 Introduction The thermodynamic propertie s of ammonia and water mixtures are of technical impo11ance since ammonia-water mixtures have been in use for several decades as working fluids in absorpt ion-refri geration cycles. Use of multi-component working fluids for power cycles has been investigated more recently over the last two decades Ammonia-water mixtures have been considered as potential working fluids for this purpose because of relatively high expected coefficients of perforn1ance for tl1is combination For the power cyc le analysis, the temperature ru1d pressure range is much higher than that of absorption-refrigeration cycles. So a cons i ste nt and extended set of thermodynamic data for ammonia-water mixtures at higher temperatures and pressures is required. The motive of this study is a lack of enthalpy and entropy data over the range of variables needed. Also, it is necessary to use computer simulation to investigate ammonia-water mixtures as potential working fluids for a power cycle. 14

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15 Many studies of the vapor-liquid equilibrium and thermodynamic properties of ammonia-water mixtures are cited in the literature. The temperature and pressure ranges of thermodynamic properties of the majority of the data in the literature are suitable for absorption-refrigeration cycle applications. Institute of Gas Technology (IGT ) tables (Macriss et al. 1964) cover the range up to a pressure of 34 bar and its corresponding saturation temperature. Using the IGT data Schultz (1972) developed equations of s tate for a pressure range of 0.01 to 25 bar and a temperature range of 200 to 450 K. Ziegler and Trepp (1984 ) presented a new correlation of equilibrium properties of ammonia water mixtures. They used an equation of state that is based on that developed by Schultz and extended the range of applicability to 500 Kand 50 bar. Ibrahim and Klein (1993) used the f 01m of the equation of state given by Ziegler and Trepp for pure ammonia and pure water They modified the correlation given by Ziegler and Trepp for the Gibb s excess energy to include Gillespie et al. ( 1987) experimental data at higher temperatures and presstrre s The correlations by Ibrahim and Klein ( 1993) cover vapor-liquid equilibrium pres s ures of 0.2 to 110 bar and te1nperature s of 230 to 600 K. A study of power cycles using ammonia-water mixtures was recently initiated by Kalina (1983). For power cycles thermodynamic data of ammonia water mixture s at higher temperatures and pressure s than those pre s ented by IGT are required Gillespie et al. ( 1987) publi s hed vapor-liquid equilibrium measurements for five isotherm s between 313 and 588 K Correspondingp1 es s ures ranged frotn 0 1 to 210 bar. Herold et al ( 1988) developed a computer program for calculation of the thermodynamic properties of ammonia-water mixtures using the Ziegler and Trepp cotTelation El-Sayed and Tribu s ( 1985a ) presented a method for computing the thermodynamic properties of mixture s

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1 6 from the prope1ties of pu1e components to extend the property conelation to higher temperatures and pressures Derived properties cover pressures of 0 1 to 110 bar and temperature s between 300 and 770 K Kalina et al. (1986 ) presented a similar method to predict the thermodynamic prope1tie s of two miscible component mixtures for the purpose of power cycle analysis Park and Sonntag (1990b) published a set of thermodynamic data of ammonia-water mixtures based on a generalized equation of state The pressure and temperature ranges are extended to 200 bar and 650 K respectivel y. Based on the above discu s sion it i s c l ear that methods developed by Ibrahim and Klein (1993) Park and Sonntag ( 1990b) and El-Sayed and Tribus ( 1985a ) cover all of the modeling effo11 s reported in the literature. The following s ection give s detailed discus s ion s of the s e method s 2.2 E lSa y ed and Tribus method El-Sayed and Tribus method starts with the thermodynamic properties of pure component s, and mi x es them according to certain a ss umption s. In the liquid region below the bubble point temperature and in the vapor region above the dew point temperature the enthalpy and entJ:opy of the mixture are calculated by summing the product of the thermodynamic propertie s and mas s fractions of the pure components. The bubble point temperature is defined as the temperature at which the fir s t bubbles of gas appear The dew point temperature i s the temperature at which condensate first appears

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17 El-Sayed and Tribus use a group of equations developed exclusively for ammoniawater mixtures based on vapor-liquid equilibrium data of Gillespie et al. (1987) The advantage of these equations is that they allow us to determine the start and end of the phase change of the mixture and compute tl1e mass fractions of ammonia and water liquid and vapor phase respectively. This avoids the comp licated method of ca lculating fugacity coefficient of a component in a mixture to determine the bubble and dew point temperatures. 2.2 .1 Computational Procedure The basic equations are given below. Bubble temperature T b= T(P x) Dew temperature T d = T(P x) Equation of state P = P( T ) where 4 T c = T ew L a. XI 1 1 l= 8 P c = P ew exp(L b ixj) i= I P in psia and T in F 2-1 2-2 2-3 2-4 2-5 2-6 2-7

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Pin psia and Tin F. Since El-sayed and Tribus used English units in their research, their equations are kept in English units in this study. In the program, English WJits are converted to SI units. 1. Pure ammonia liquid: T h = [AT+ 0.5BT 2 2C(T c T) '' 2 ] 2 T1 where A = 3.14894 B = -0.0006386 C = 16.66345 T c= ammonia critical temperature, 405.5 K T = temperature, K T 1 = Reference temperature 195.40 K T 2 = Final temperature, K Coefficients A Band C were found in Haar and Gallagher (1978). C =T ds P dT A + BT+ C(T T) l / 2 = T ds C dT 2-8 2-9 2-10 2-11 18

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2-12 2. Ammonia vaporization H H l T r2 v2 = vi 1 -Trl n 2-13 where H v 1 = Known enthalpy of vaporization at a reference temperature T 1, cal / g mole H v 2 = Enthalpy of vaporization cal / g mole T c= Ammonia critical temperature 405.5 K Tr i= Reduced temperature at temperature T 1 Tr 2 = Reduced temperature at temperature T 2 n = Constant Equation 2-13 is transformed as follows: where The above equation can be set up in the form y = a + bx where y = lnHv 2 2-14 2-15 19

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20 a = lnC1 b = n X = ln(l Tr 2 ) Values ofHv 2 and Tr 2 from 0.1 bai to 112 bar were taken from published literature(Haar and Gallagher 1978) to fmd n as 0.38939. C 1 is found by lnC1 = lnH v2 nln(l T r2 ) 2-16 The value of C 1 used in this investigation was taken by averaging 11 values over the previously mentioned range of pressures. It is C1 = 7906.555 The enthalpy of vaporization equation used was found by using known values of C1 and n in equation 2-14. H v = 7906.555 X (1 T / T c ) 0 38939 The entropy of vaporization is Sv = Hv / T 3. Ammonia vapor 2-17 2-18 Integrating the heat capacity equation 2-19 and comparing the results with pt1blished enthalpy data did not yield good agreement. Cp = A + BT + CT 2 + DT 3 2-19 As the pressure increased the agreement worsened. Therefore, a p1essure compensation term was added to obtain equation 2-20. 1n addition, the original coefficients (A B C and D) were changed as reflected in equatio11 2-21. Coefficient s were taken from Haar and Gallagher (1978).

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where Cp o = A + BT + CT 2 + DT 3 A = 3.70315 B = 2.8074 x 10 3 C = 4.4199 x 10 6 D = -6 3441 x 10 9 E = 1. 7 3447 X 10 1 0 G = 4. 33 14 P = pre ss u1 e, bar T = temperature K BT 2 CT 3 DT4 EP1' 1 -G) AT+ --+ + +--T2 h = 2 3 4 (1G) Tl T2 s = AlnT + BT + CT 2 + DT 3 EPT -G G Tl where T 1 = Saturation temperature K T2 = Final temperature K 4 Water liquid 22 0 2-21 2-22 2 -2 3 21 The liquid enthalpy is found using the enthalpy of vaporization ofH 2 0 and the H 2 0 vapor enthalpy Figure 2-1 illustrates the use of these two va lue s in finding the liquid enthalpy. Temperatut e T 1 in figure 2-1 is the reference temperature chosen for this work to be 273.15 K. The straight, horizontal segment, line 1-2 i s the enthalpy of vaporization

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22 This now places the computations on the saturated vapor cUI ve. Liquid enthalpies at other temperatures are found by first '' traveling ' tl1e H 2 0 saturated vapor curve. Segment 2-3 is the H 2 0 vapor enthalpy difference between the reference temperature and the temperature of interest, T 2 Point 3 is the H 2 0 vapor enthalpy at temperature T 2 The liquid enthalpy is found by subtt acting the enthalpy of vaporization from the saturated vapor enthalpy This is point 4 in figure 2-1. Point 5 is the critical temperature. Segment 5-6 is superheated vapor. The liqt1id entropy of H 2 0 was found in a manner similar to the enthalpy. In thi s case the entropy of vaporization was used with the vapor entropy to fmd the liquid entropy Again use figure 2-1 as a reference. 5. Water vaporization Enthalpy of vaporization H v2 at temperattrre T 2 is found from the following equation: n 2-24 In this equation, the known enthalpy of vaporization, H v I at temperature T 1 and the power coefficient n, were found from Reid et al. 198 7, resulting in the following equatio11: where C1 = 13468.42 C 2 = 0.380 T c= H 2 0 critical temperatw e 647.3 K 2-25

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23 6 a) ;... 5 H a) T2 4 A 3 5 Tl ---1------------\ 2 --------------.-----,---~----,---~Figure 2-1 A ge 11eric diagram of water propert y ( enthalpy or entropy) against temperature

PAGE 34

6. Water vapor CP =A+BT+CT 2 + DT 3 where A = 32.24 B = 1.924 x 10 3 C = 1.056 x 10 5 D = -3.596 x 10 9 h = 'T4 T, AT+BT 2 + CT 3 + D1 2 3 4 T2 s= AlnT+BT + CT 2 + DT 3 2 3 Tl where T 1 = Saturation temperatme K T 2 = Final temperature K 2.2.2 Ammonia-Water Mixtures 1. Liquid 24 2-26 2-27 2-28 The ammonia-water mixture is in the liquid phase when the temperahrre is below its bubble point temperature. h m = xh NH3 f + (1 x)hmo f Sm = XSNH 3,f+ (1 x)sH 20,r Rm(x'lnx' + (1 x')ln(l x') where x = ammonia mass fraction 2-29 2-30

PAGE 35

x' = am monia mole fraction R m= ga s constant of the mixture 2. Two phase region The two phase region is the region between the bubble point and dew point hm = amv x X g h NID,g + amv( 1 X g )h mo g + aml x xth NHJ f + aml(l x r )h mo r Sn1 = amv x X g S NH3 g + amv(l X g )S H20 g + am.I x XfS NHJ f + aml(l x r )sH2 0 f R m (X g 'ln X g 1 + (1 X g ')ln(l X g ')) R m (xr'lnx r' + ( 1 xr')ln(l xr')) where 3. Vapor aml, amv = mass fractions of liquid and vapor in the mixture X g and x g = mass and mole fraction of ammonia of vapor mixture x r and X f = mass and mole fraction of amn1onia of liquid mixtwe 2-31 2-32 25 The ammonia-water mixture is in the vapor phase when temperature is above its dew point temperature. hm = xh NH3 g + (1 x)hm o g S n1 = XS NID g + (1 x)s H20 g Rm(x'lnx' + (1 x')ln( 1 x')) 2-33 2-34

PAGE 36

26 2.2.3 Disci1ssion The advantage of using the El-Sayed and Tribus method is that it is very convenient to calculate the bubble and dew temperatures, without having to compute the fugacity to determine the two phase region. The disadvantage is that it needs to calculate the saturation temperature to compute the enthalpy and entropy. And the saturation temperattrres of pure components are different fron1 the saturation temperatures of the mixtures, because the satwation temperature of a mixture changes even at the same pressure. Also, the coefficients of heat capacity eqt1ations can not fit a wide range. In the liquid region, the properties of two pure components cannot simply be mixed. Gibbs free energy is still needed to calculate the difference from the ideal condition. 2.3 Thermodynamic Ptoperties of Ammonia-Water Mixtures by Gibbs Free E11ergy Method 2.3.1 Gibbs Free Ene rgy for Ptrre Component The fundamental equation of the Gibbs energy G, of a pure component can be derived from known relations for volume and heat capacity as a function of temperatwe and pressure. The fundamental equation of the Gibbs energy is given in an integral form as T P T C G = h 0 Ts 0 + f C P dT + f vdP T f ; dT T o P o T o 2-35

PAGE 37

27 where h o, s o T o and P o are the enthalpy, entropy temperature, and pressure at the reference state. The volume, v and the heat capacity at constant pressure Cp, for liquid phase are as s umed to fit the following empirical relations proposed by Ziegler and Trepp(l 984); For the gas phase the corresponding empirical relations are RT C C P 2 v & =-+c + 2 + c T 11 + -4-'--p I T 3 3 T l I 2-36 2-37 2-38 2 39 where the s uperscripts are L for liquid g for gas, and o for the ideal gas state. Integration leads to the following equations for the Gibbs energy for the pure components. Liquid phase : 2-40 Gas phase:

PAGE 38

28 P P PT P P PT +C (P p ) + C ( r 4 r o + 3 r o r) + C ( r 1 2 r o + l l r o r) I r r ,o 2 T 3 T 3 't' 3 T l I Tl I T l2 r r o r o r r o r o C p 3 p 3 p 3 T + 4 ( r 12 r o + l l r ,o r ) 3 T l) T l) T l2 r r o r o 2-41 where the reduced thermodynamic properties are defined as Gr = G/RT s Sr = s / R V r = vPs/RT a The reference values for the reduced properties are R = 8.314 kJ / kmole-K, Ta = 100 Kand Pa = 10 bar. 2.3 .2 Thermodynamic Propertie s of a Pure Component The molar specific enthalpy entropy and volume are related to Gibbs free energy by h =T 2 a (G I T) 8T s = B G 8T p 2-42 p 2-43

PAGE 39

v = 8 G 8 P T In terms of reduced variables 2.3.3 Ammonia-Water Liquid Mixtures 29 2-44 2-45 2-46 2-47 The Gibbs excess energy for liquid mixtures allows for deviation from ideal solution behavior. The Gibbs excess energy of the liquid mixture i s expres s ed by the relation proposed by Redlich and Kister ( Reid et al 1987; Ziegler and Trepp 1984) which is limited to three term s and i s given by 2-48 where

PAGE 40

30 Table 2-1 Coefficients of equations 2-40 and 2-41 Coefficient Ammonia Water A1 3.971423 102 2. 7 48796 10 2 A 2 -1.790557 103 -1.016665 10 -:> A 3 -1.308905 102 -4.452025 1 oj A4 3.752836 103 8.389246 104 Bi 1.634519 10 + 1 1.214557 10 + 1 B 2 -6.508119 -1.89806 5 B 3 1.448937 2.911966 10 Ct -1.049377 102 2 .13 6131 102 C 2 -8.288224 -3.169291 10 + 1 C 3 -6.64 7257 10 + 2 -4.634611 10 + 4 C4 -3.0 45352 10 +_; 0.0 D1 3.673647 4.019170 D 2 9.989629 102 -5.175550 10-L D 3 3.617622 10 2 1 9 519 3 9 1 0 2 hroL 4.878573 21.821141 hr ,og 26.468873 60.965058 L 1.644773 5.733498 Sr o g 8.339026 13.453430 Sr o Tro 3.2252 5 .0 705 Pro 2 .000 3.000

PAGE 41

31 Table 2-2 Coefficients of equation 2-48 E1 -41.733398 E 9 0.387983 E 2 0.02414 E1 0 0.004772 E 3 6 702285 E1 I -4.648107 E4 -0.0114 75 E1 2 0.836376 Es 63.608967 E13 -3.5 53627 E 6 -62.490768 E14 0.000904 E1 1.761064 Ei s 24.361723 Es 0.008626 E16 -20.736547 The excess enthalpy, entropy, and volume for the liquid mixtures are given as a (G E; r) 8 T r r r Pr x 2-49 2-50 2-51 The enthalpy entropy and volume of a liquid mixture are computed by 2-52 2-53

PAGE 42

2-54 2-55 2.3 .4 Ammonia-Water Vapor Mixture Ammonia-water vapor mixtures are assumed to be ideal solutions. The enthalpy, entropy and volume of the vapor mixture are computed by 2-56 S g = X S g + ( 1 X )s g + Sm ix m g a g w 2-57 2-58 2.3.5 Vapor-Liquid Equilibrium At equilibrium binary mixture s must have the same tempe1 ature and pres s ure. 3 2 Moreover the partial fugacity of each component in the liquid and gas mixtures mu s t be equal. 2-59 2-60 2-61 2-62 "' where P and T a1 e the equilibrium pressure and temperature of the mixture and f i s the fugacity of each component in the mixtu1 e at equilibrium. The fugacitie s of ammonia and water in liquid mixtures are given by Walas(1985 )

PAGE 43

where y = activity coefficient f = standard state fugacity of pUte liquid component conected to zero pressure 8 = Poynting correction factor from zero pressure to satlrration pressure of mixture 33 2-63 2-64 assuming an ideal mixture in the vapor phase, the fugacities of the pure components in the vapor mixtures are given by 2-65 2-66 where: = fugacity coefficient 2.3.6 Discussion The Gibbs free energy method is relatively simple for calculation of the pure component thermodynamic properties. The reference temperatUte and pressure are fixed, you only need to know the temperatu1 e and pressure of interest to determine the mixtures properties. 2.4 Method by Park and Sonntag

PAGE 44

The generalized equation of state approach is useful in predicting thermodynamic and volumetric properties of substances for which experimental data are scarce and a minimum number of data are available: critical temperature, critical pressure, critical volume, and eccentric factor. 34 In this study the1modynamic and volumetric properties of ammonia-water mixtures are derived from three basic equations: 1. Helmholtz free energy equation for the ideal gas properties of water: A. = R ~ i + 46ln(T) 101 l.249 ln(T) t I t = I 2-67 where t = 1000 / T constants of ideal gas equation for water Table 2-3 Coefficients of equation 2-67 a1 1857.065 a 3 -419.465 as -20.5516 a 2 3329.12 a4 36.6649 a6 4.85233 Similarly, for ammonia I I = RT a 1 ln(T) + La i T i 3 + ln(4.8180T) l 2-68 i=2 2. The generalized equation of state based on a four-parameter corresponding state principle which is expressed in terms of z 0 Z 1 Z 2 ; functions of Tr and Pr; eccentric factor w; and polarity factor, m, with appropriate correction term:

PAGE 45

35 2 = z o +WZ 1 +mZ 2 2-69 2-70 w z 2 = z w z o + w (Zr z o ) wr 2-71 where Z 1 and Z 2 are the nonsphe1ical and polar corrections, respectively. Table 2-4 Coefficients of equation 2-68 a1 -3 872727 a 1 0.36893175 } oI U a 2 0.64463724 ag -0.35034664 10 1 3 a 3 3.2238759 a 9 0.2056303 10 1 6 a4 -0.00213769925 a10 -0.6853420 1 oLU a s 0.86890833 10 5 a11 0.9939243 10 24 a 6 -0.24085149 10 7 3. The pseudocritical constants method: 2-72 . I I J where subscript cm refers to c11tical prope1ty of mixture. 2-73 . I I J V 2/3 e = x i ci 2-74 "x V ~13 I Ct

PAGE 46

36 2-75 z cm = 0.2901 0.0879w m 0.0266m m 2-76 2-77 I m = ""'x m m L..,; I I 2-78 I 4. Discussion Park and Sonntag claim that using the generalized equation method provides a consistent way to calculate the thermodynamic properties of ammonia-water mixtures. But in the high pressure range, they don t have expe11m.ental data to verify the reliability of this method. This method needs to be further investigated. 2.5 An Alternative Method : Using Gibbs Free Energy Method for Pm e Components, and Bubble and Dew Point Temperature Equations for Equilibrium Composition The Gibbs free energy of the mixture is a function of temperature, pressure and mixture composition. The property data derived from such an equation of state are very consistent and convenient. One can easily calculate the thermodynamic properties of interest such as enthalpy entropy, specific volume and vapor pressure without considering the phase state. Most of the researchers tend to use equation of state model in their properties calculation.

PAGE 47

37 The criteria of phase equilibrium in a binary system is that the liquid fagucity ( or chemical potential) of a pure component equals the vapor fagucity ( or chemical potential) of that pu1e component. This requires several iterations to get the composition of each component of phase equilibrium. The accuracy and convergent time vary at different points. In a power cycle simulation these iterations should be avoided for the accuracy and the computation time of the simu lation s. El-Sayed and Tribus (1985) developed bubble and dew point temperatw:es equations to calculate phase equilibrium. These equations reduce iterations during phase equilibrium calculations and their temperature ranges up to 770 K. In the present study a method that combines the advantages of Gibbs free energy method and bubble and dew point temperatures equations is presented. The results show a very good agreement with the available data based on experimental measurements and the computation time is reduced. 2.6 Results and Comparisons with Literature Data The properties of pure ammonia and water can be calculated very precisely by using the Gibbs free energy equation. In order to calct1late the properties of the mixtures it is very important to predict equilibrium state of vapor-liquid mixture. For the vapor-liqu id equilibrium, experimental data are used. Most experiments were done in the early 30s IGT conducted their experiments in the 60s and combined most of the data from the ea1ly expe1 iments to prodt1ce vapor-liquid equilibrium data and mixture properties data for temperature up to 500 Kand pressure up to 34.45 bar. The

PAGE 48

3 8 IGT data i s accept e d as a reliable source, and most computational data are compared with it Wiltec Research Co (Gillespie et al. 1987) conducted measureme11ts of the amn1onia-water mixtures vapor-liquid equilibrium in the early 80s fro111 313 Kand 589 K. Their data is u s ed to extend the ammonia-water mixtures data to temperature up to 600 Kand pre ss ure up to 110 bar by Ibrahim and Klein (1993 ) IGT and Wiltec data are u s ed to make correlations to predict ammonia-water mixtures equilibrium state. The accuracy of co1nputation depends on the mathemati c al model s used to generate correlations and computational methods used to compute the thermodynamic properties of ammonia-water mixtures. It is not s urprising that s tudies reported in the literature have varying degree s of agreement with the IGT prope11:ie s data 2 .6 1 Comparison of Bubble and Dew Point Temperatw e s Figure s 22 to 2 -5 s how that the bubble and dew point temperature s generated b y this study compares favorably with the IGT data. For the bubble point temperature at constant pressure IGT has a complete set of data for pressures from 1 psia to 500 psia and ammonia mass concentration from O to 1 incremented b y 0.1. The differences between our computed value s and the IGT data are les s than 0. 3% Z iegler and Trepp Ibrahim and Klein reported to have difference s up to 2% with the IG T data IGT data ha s dew point temperature s with only four different ammonia mas s fractions of 0 96 4 1 0 9824 0.990 7 and 0 99 5 3 The data for small moi s ture

PAGE 49

39 concentrations are used primarily for the moisture effects of absorption refrigeration cycle. Our results match equally well for the bubble temperatures. An advantage of this comparison is that the working fluid used in the proposed power cycle also has a very small percentage of moisture content. 2.6 2 Comparison of Sattrration Pressure at Constant Temperature Figures 2-6 to 2-10 show the saturation vapor and liquid pressures of ammonia water mixtures as compared with Gillespie et al. data. For temperatures less than 406 K, the computation results fit the experimental data well, except at saturated liquid pressure. At higher temperatures, our computed values are within 5o/o of the Gillespie et al. (1987) data even at pressures higher than 110 bat', while Ziegler and Trepp have reported more than 15% difference. Ibrahim and Klein reported a less than 5% error under 110 bar and higher errors over 110 bar 2.6.3 Comparison of Saturated Liquid and Vapor Enthalpy 1 Saturated liquid entl1alpy The enthalpy of saturated liquid of this work is compared with IGT data as shown in figures 2-11 to 2-14. The differences are less than 2% for all the data. 2. Saturated vapor enthalpy The saturated vapor enthalpy at constant p1essure is shown in figures 2-15 to 2-18. The agreement with IGT data is within 3%. Ibrahim and Klein's model reported about a 5% maximum difference.

PAGE 50

40 The ammonia mass fractions shown in these figures are not ammonia vapor concentrations. In fact, these are ammonia liquid mass fractions when the mixtures reach a saturated state. So in order to compute the saturated vapor enthalpy, the ammonia vapor mass fraction has to be determined first. This means that the model has to be accurate in predicting the ammonia compositions in saturated liquid and vapor. 2.6.4 Comparison of Saturated Liquid and Vapor Entropy The value of entropy is very important in predicting the performance of a turbine in a power cycle. Entropy data is also essential to the second law analysis of thermal systems. Scatchard et al. ( 194 7) published saturated liquid and vapor entropy data based on experimental data from Zinner (1934), Wucherer (1932) and Perman (1901). Park and Sonntag( 1990b) published calculated entropy data based on their models and compared with the Scatcha1 d et al. data. In the present study, saturated liquid entropy data are compared with Scatchard et al and Park and Sonntag computational data. However saturated vapor data are compared with Scatchard et al data only 1. Saturated liquid entropy Figures 2-19 to 2-22 show saturated liquid entropy data as compared with Scatchard et al. data. Our data agree with the experimental data very well except in the region of ammonia mass fraction from 0.3 to 0.6. In figures 2-19, 2-21 and 2-22, computed data from Park and Sonntag (1990b) are also compared. It can be seen that the magnitude of Park and Sonntag's data are very low as compared to Scatchard's data ; it is more than 50o/o lower at ammonia mass fraction of 0 .5.

PAGE 51

41 2. Saturated vapor entropy Excellent agree1nent of our computed values with the Scatchard et al. data of the satwated vapor entropy is shown in figures 2-23 to 2-26. Data reported by Park and Sonntag (1990b) are consistently lower than the Scatchard's data. Since it is very difficult to identify Park and Sonntag's saturated vapor entropy data from the literature, we didn't compare our results with them. Since the behavior of ammonia-water mixtures in the vapor state is close to the ideal gas mixture, this results in a good match for our mixtw e vapor model. 2. 7 Conclusion Different methods for calculating the ammonia-water mixture properties are studied. A practical and accurate method is used in this study. This method uses Gibbs free energy equations for pure ammonia and water properties, and bubble and dew point temperature equations for vapor-liquid equilibrium. The iterations necessary for calculating the bubble and dew point temperatwes by tl1e fugacity method are avoided. This method is much faster than method of using fugacities or chemical potentials. The computational results have been compared with the accepted experimental data and show very good agreement. With consistent and accurate thermodynamic properties data of ammonia-water mixtw es, we can perform fue first and second law analyses of the proposed power cycle.

PAGE 52

42 ~This Work 380 0 IGT Data 360 340 320 ::s +J ro s..... 300 E (1) r280 260 240 P = 1 38 bar 0 0 0 1 0.2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Ammonia Mass Fraction Fi g ure 2-2 B u b b le and dew point temperahrre s at a pre s strre of 1.38 bar

PAGE 53

-Q) s... ::J +J ro s... Q) 0. E Q) I420 400 380 360 340 320 300 280 43 This Work 0 IGT Data P = 6.89 bar 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0.9 1 0 Ammonia Mass Fraction Figure 2 3 Bubb l e and dew point t e mperature s at a pre ss w e of 6.89 bar

PAGE 54

460 440 420 400 :l ...... ro "380 E (1) ._ 360 340 320 -This Work 0 IGT Data P=13.79bar 44 0 0 0 1 0.2 0.3 0 4 0 5 0 6 0 7 0 8 0 9 1.0 Ammonia Mass Fraction Figure 2 4 Bubble and d e w point temperature s a t a pre ss ur e of 1 3.7 9 bar

PAGE 55

.-. .___. (1) i.... :J ...., ro i.... (1) a. E (1) I520 500 480 460 440 420 400 380 360 340 _ This Work 0 IGT Data P = 34 47 bar 45 320 --+~~ .---.---.----.----.--.--.---.-..----.--.---.--,-.----.-~ -,--I 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Ammonia Mass Fraction F i gUI e 2 -5 Bubb l e and dew point temperature s at a pre ss ure of 34 4 7 bar

PAGE 56

Iro .0 ...__ (1) ':::J Cl) Cl) (1) I0.. 46 30 --,-----,,---......----.----.------,-----.-----.----,--------.-----, 25 20 15 10 5 -This work 0 Gillespie et al. 0 0 0 1 0.2 0 .3 0 4 0 5 0 .6 0 .7 0 8 0 .9 1 0 Ammonia mass fraction Figure 2-6 Saturated presswes of ammonia-water mixtures at 333 .1 5 K

PAGE 57

4 7 120 --r-----,-----,-----,----.----.--,----.---r-----r------, 100 L.. 80 i 60 ::J (/) (/) 40 0... 20 0 -This work 0 Gillespie et al. 0 0 0 0 0 0 1 0.2 0 3 0 4 0 5 0.6 0.7 0 8 0 9 1 0 Ammonia mass fraction Figure 2 -7 Saturated pressures of ammonia-water mixhrres at 394 15 K

PAGE 58

48 140 -.-----,------,---------,----,------r--.--------.....-----.-----r-------... 120 100 80 Q) :5 60 (/) (/) Q) I... 0.. 40 20 0 -This work 0 Gillespie et al. 0 0 0 0.0 0 1 0 2 0.3 0 4 0.5 0 6 0.7 0 8 0 9 1 0 Ammonia mass fraction F igw e 2 -8 Saturated pres s trres of amn1onia-water mixture s at 405.95 K

PAGE 59

49 200 ----~---~-----~--~~ 180 160 140 "i:"120 co .n 100 :::::J en en Q) "0.. 80 60 40 20 -This work 0 Gillespie et al. 0 0 -4--~-~~-~-~-~-~----,I 0.0 0 1 0.2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Ammonia mass fraction Figure 2-9 Saturated pre ss ures of ammonia-water mixture s at 449.85 K

PAGE 60

50 250 ~----~--~-~----.-----.-----r----. 200 "2150 ro ..0 ...__ Q) ::J (/) (/) Q) a.. 100 50 This work 0 Gillespie et al. 0 0 0 --+---------,-----r-----.-----r------.--~-------1 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 Ammonia mass fraction Figure 210 Saturated pres s ures of ammonia-water mixttrres at 519 .2 6 K

PAGE 61

.......... 0) .::t::.. -, .::t::.. ....__ >0.. cu .c ....., C w 51 500 ~ -~--.---,----.---.--,r---.----~--,----, 400 300 200 100 0 -100 -200 -300 -This work 0 IGT data -400 --------,---,----,------.----.------.---1 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1.0 Ammonia mass fraction Figure 2-11 Saturated liquid enthalpy of ammonia-water mixtures at 1 .3 8 bar

PAGE 62

0) -, >, C. ro ..c ... C w 52 800 -----,-----,-----,----,-------.-------,----,-----.-------.-----, -This work 0 IGT data 600 400 200 0 -200 -1-------,------,----,----,----,----,----,----,---,-------i 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Ammonia mass fraction Figui e 21 2 Saturated liquid enthalpy of ammonia-water mixture s at 6.89 bar

PAGE 63

Q. 53 900 ~--.----.----.----.-------------.----------.------.----.----.-----, 800 700 600 -This work 0 IGT data 400 +-' C w 300 200 100 0 --+----.----.----.---.----.----.-----.----.---.----1 0 0 0.1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1.0 Ammonia mass fraction Figw e 2-13 Saturated liquid enthalpy of ammonia-water mixtures at 13. 79 bar

PAGE 64

.......... 0) .::: -.. 54 1100 ~----.-----.-----.-----,--------.----------.-------,----,----,---, 1000 900 800 -This work 0 IGT data 700 ..._... >a. ro ..c: ..... C w 600 500 400 300 200 -+-----.----.----.---,---,--------.-----r-----,-----,--0 0 0 1 0 2 0.3 0 4 0.5 0 6 0.7 0.8 0 9 1 0 Ammonia mass fraction Figure 2-14 Saturated liquid enthalpy of ammonia-wate1 mixture s at 34.47 bar

PAGE 65

0) ...., ...__., >, a. cu .c ...... C w 55 2800 ---,----,-----,-----,-----,-----.---,----,----,----, 2600 2400 2200 2000 1800 1600 1400 1200 -This work 0 IGT data 1000 -+----,-----,-----,-----,-----,-----,----,----,----,-------i 0 0 0 1 0 2 0 3 0.4 0.5 0 6 0 7 0 8 0 9 1 0 Ammonia mass fraction Figure 2 -1 5 Saturated vapor enthalpy of ammonia-water mixture s at 1 .3 8 bar

PAGE 66

....-0) .:::s::. ........ -, .:::s::. ->, C. ro .c +-' C UJ 56 2800 ~--.---.-------.-------.----,---,----,-----,----,---, 2600 2400 2200 2000 1800 1600 1400 1200 -This work 0 IGT data 1000 -4---.-------,----,------,-----.---,---.--.---,--I 0.0 0 1 0.2 0 3 0 4 0 5 0.6 0 7 0 8 0 9 1.0 Ammonia mass fraction Figure 2-16 Saturated vapor enthalpy of amn1onia-water mixtures at 6.89 bar

PAGE 67

,.--... 0) 57 3000 ~--,---,----,------r-----r---,r---~---,----.----, This work 0 IGT data 2600 2400 2200 a. 2000 ..... C w 1800 1600 1400 1200 --+---.---.----,----.----,-----,----.----.----.----; 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Ammonia mass fraction Figure 2 -1 7 Saturated vapor enthalpy of ammonia -wa ter mixture at 13. 79 bar

PAGE 68

O> .:: 58 3000 ---,------,------,----,---,---,---,---,----r----r-----, 2600 2400 -This work 0 IGT data 2200 >. a. 1 2000 ..... C w 1800 1600 1400 1200 -l------,------,------,---,---.-------.---------.-----,-----,---1 0.0 0 1 0 .2 0.3 0 4 0 5 0 6 0 7 0 8 0.9 1 0 Ammonia mass fraction Figure 2-18 Saturated vapor enthalpy of ammonia-wate1 mixtures at 34.4 7 bar

PAGE 69

0) ....... -, 59 0 7 ~-~---.------,---,---,-----.----r--~--,-----, 0 Scatchard et al This work 0 6 0 Park and Sonntag 0 5 -0.4 0 0 0 >0. 0 L.. ..... C w 0 0 0 0 0 3 0 0 0 0 2 0 0 0 0 1 --+---,----,---,---.,---,--------,----,---,---,-------l 0 0 0 1 0 2 0 3 0 4 0.5 0 6 0 7 0 8 0 9 1 0 Ammonia mass fraction in saturated liquid Figure 2 -19 Entrop y of Saturated liquid at 310.9 K

PAGE 70

.....--.. 0) ---, ....__ >a. 0 L.. +-' C w 60 0.90 -~ ----.----.----,---,--------.----,--~ -----, 0.85 0 80 0.75 0 70 0 65 0 60 0 Scatchard et al -This work 0 0 0 0.55 ---1-~------.----,----.--~ ---,--~----1 0 0 0 1 0.2 0 3 0 4 0 5 0 6 0.7 0 8 0.9 1 0 Ammonia mass fraction in saturated liquid Fig ure 2-20 Entropy of Saturated liquid at 327 .6 K

PAGE 71

1 1 1 0 0 9 0 0 Scatchard et al -This work 0 Park et al 0 0 6 1 0. 0 .!:; 0 7 C w 0 0 0 6 0 0 0 0 0 0 5 0 4 -1------..----.------.----.----.-----.-~----.--.----1 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Ammonia mass fraction in saturated liquid Figure 2 2 1 Entrop y of Saturated liquid at 3 3 8.7 K

PAGE 72

...-0) .::: --, .::: ..__., >. 0. 0 I... ..... C LU 62 1 6 ---.---~---r---;---------,------r-----r---r-----, 1 5 1 4 1.3 1.2 1.1 0 1.0 0 0 9 0 Scatchard et al -This work 0 Park et al. 0 0 0 0 0 0 8 -+----.-------.-------.-------.----~-~-~-~-~---1 0.0 0 1 0.2 0 3 0.4 0 5 0.6 0 7 0 8 0 9 1 0 Ammonia mass fraction in saturated liquid Figure 2 22 Entropy of Saturated liquid at 366.5 K

PAGE 73

0) ----, ...__... >0. 0 L.. ..... C w 63 1 0 0 ~---.-----------r----.---------.-----.----,-----,----,----,-----, 9 5 9 0 8 5 8 0 7 5 7 0 6 5 6 0 5.5 5 0 4 5 4.0 3.5 0 Scatchard et al. This work 3 0 -1-----.------.-----------r-----.----.-------.-----,-----,--------r-----l 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0.8 0 9 1 0 Ammonia mass fraction in saturated liquid Figure 22 3 Entropy ofSatt1rated vapor at 310.9 K

PAGE 74

...--... O> -.... -, .!II:: ....__ >. a. 0 L.. +-' C w 64 10. 0 -,-------,----,-----,------,----,-----,-----.--.-------.-------, 9.5 9.0 8 5 8 0 7 5 7 0 6.5 6 0 5 5 5.0 4 5 4 0 3.5 0 Scatchard et al. -This work 3 0 -1----.---.--------y---.----.----.--,---,-------..--1 0.0 0 1 0.2 0 3 0 4 0 5 0.6 0 7 0.8 0 9 1 0 Ammonia mass fraction in saturated liquid Figure 2-24 Entropy of Saturated vapor at 327 .6 K

PAGE 75

Q' 0) ..!J:::'. ..._ J ..!J:::'. ......... >,. a. 0 ,._ +-' C w 65 10 0 ---,-----,-----y-----,--------.----y-----,---.---.---------i---, 9 5 9 0 8 5 8.0 7.5 7 0 6.5 6 0 5 5 5.0 4.5 4 0 3.5 0 Scatchard et al. -This work 3 0 -+----r----,------.-----,-----,-----,-----,....----,....---r------1 0 0 0 1 0 2 0.3 0 4 0 5 0 6 0 7 0.8 0 9 1 0 Ammonia mass fraction in saturated liquid F igure 2 25 E ntropy of Saturated vapor at 3 3 8 7 K

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0) -.. -, ...__ >. C. 0 L.. +-' C w 66 10 0 --,------.-----.----.-----.----,-----,-----r------r---.-----, 9 5 9 0 8 5 8.0 7.5 7 0 6 5 6 0 5.5 5 0 4.5 4 0 3.5 0 Scatchard et al This work 3.0 ~----. --.----,---.---.---------,--r----,---y----1 0 0 0 1 0.2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Ammonia mass fraction in saturated liquid Figwe 2 2 6 E ntropy of Saturated vapor at 366.5 K

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CHAPTER3 AMMONIA-BASED COMBINED POWER/COOLING CYCLE 3.1 Introduction Combined cycle systems have been recognized a s efficient power systems. A typical combined cycle system consists of the gas turbine cycle(the Brayton cycle), which produce s the ba s e load and the Rankine cycle, which uses the exhaust gas from the gas tui bine as the high temperature source. The exhau s t gas provides the available energy to the bottoming cycle (the Rankine cycle) to improve the efficiency of the combined cycle system over the gas turbine cycle alone. The efficiency of the overall sys tem i s a function of tl1e temperature and pressure of the exhaust gas, th e s ink temperatw e of tl1e bottoming cycle, and tl1e type of the bottoming cycle it se lf. Mo s t heat so urce s available to the bottoming cycles, such as hot exhat1st gases, are sensible-heat sources because the temperature of the source is va1 ying during the heat transfer proces s. The amotmt of the cooling medium at the sink temperatu1 e i11 reality is also limited so that the heat s ink is se n s ible a s well. This s ensible heat doe s not satisfy 67

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68 the isothermal process of the ideal cycle (the Carnot cycle). The ideal cycle to convert sensible heat to n1echanical or electrical energy is therefore not the Ca1not cycle. The ideal cycle to convert sensible heat to mechanical or electrical energy is the Lorenz cycle (Lorenz 1894). This cycle has a triangular shape on a temperattrre and entropy diagram, generating the lea st entropy during the heat transfer process (Kalina 1984). The lea st production of entropy yields the highest thermodynamic efficiency. It is interesting to note that with respect to the combined cycle efficiency, the Carnot cycle is still the ideal cycle to produce overall maximum work at a given source temperature since the bottoming cycle of a triangular shape leads the overall combined cycle to the Carnot cycle, as seen in figure 3-1. To increase the efficiency of the Rankine cycle working with sensible heat, two conventional ways have been proposed: ( 1) Incorporation of a multi-pressure boiler (2) Implementation of the supe1critical cycle The multi-pressure boiler is widely used in industry, but results in only moderate improvement in efficiency tmless the number of boiler steps is very large. For the exhaust gas temperatu1e range from 900-1000 F(7 5 5 811 K), the cycle efficiency is 2022% with a single pressure boiler and 23-25% with tri-pressure boiler (Foster-Pegg 1978). Since a significant increase in the number of boiler steps is technically and economically not feasible, the nun1ber of such steps does not usually exceed three (Kalina 1984 ). The implementation of a supercritical cycle can theoretically achieve a triangulru: shape cycle and thus high efficiency, but requires extremely high pressure in the boiler,

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which in turn adversely affects the turbine performance (Kalina 1984). Milora and Tester ( 1976) have given a detailed discussion of the supercritical cycle. T Q Rankine Cycle Q s Figure 3-1 Schematic diagram of the Rankine cycle in connection with a c ombined cycle 69

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70 An alternative way to increase the efficiency of the Rail.kine cycle working with a sensible heat sot1rce is to use a multi-component working fluid. A multi-component working fluid boils at a variable temperature with a change in the liquid composition of the co1nponents. This variable temperature boiling process yields a better thermal 1natch with the sensible heat source than the constant temperature boiling process, and is close to a triangular shape. The better thermal match contributes to the improvement of thermodynamic efficiency in the boiler. Si.t1ce the multi-component working fluid condenses at a variable temperature as well, a part of the gain of the variable temperature boiling is lost in the condenser To reduce this loss, the sin1ple condensation process is complemented by an absorption distillation process (Babcock and Wilcox, 1978). Otrr novel power cycle is proposed by Goswami(1995, 1996). The cycle uses a multi-component working fluid and the condensing process of the Ranki11e cycle is replaced by the absorption process. This cycle meets both conditions for higl1er thermodynamic efficiency--a better thermal match in the boiler and a l1eat rejection system complemented by the absorption system. The purpose of this work is to condt1ct a s tudy of the novel power cycle system in connection with a combined cycle system as in Figure 3-2 comparing the novel cycle and the Rankine cycle at the same thermal boundary conditions with different internal conditions fo1 the best performance of each cycle. This stt1dy is performed using the tl1ermodynamic properties of ammonia-water mixtures developed in Chapter 2 in this study.

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71 3.2 Characteristics of the Novel Cycle as a Bottoming Cycle A bottoming cycle is a cycle which operates between the high temperature heat rejected by a topping cyc le and the ambient. The cycle utilize s the available heat of the exhaust gas from the topping cycle. Most l1eat available to the bottoming cycle is sens ible ; the temperature varies during the heat transfer process. This sensib le heat can not realize the isothermal heat supply process of the ideal cycle, the Carnot cycle. Therefore, the Carnot cyc le is not the ideal bottoming cycle to convert sensib le heat to mechanical energy or electrical energy. Rather, the ideal cycle working with sensible heat is the Lorenz cycle(Lorenz, 1894 ), which has a triangular shape in the temperature and entropy coordinates. The Lorenz cycle i s composed of four processes, as shown in Figure 3-2 (1) Heat supply at a variab le temperatuie(l-2) (2) Isentropic expansion(2-3) (3) Isothermal heat rejection(3-4) ( 4) Isentropic compress ion ( 4-1) The Lorenz cyc l e is exactly the same as the Carnot cycle except for the process(l-2). Possible ways to realize the Lorenz cycle are: ( 1) Multi-pressure boiler (2) Supe1critical cycle (3) The Kalina cycle (4) The novel ammonia-based combined power / coo lin g cycle

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T 1 4 E quivalnent propo s ed c yc le 72 2 3 C> s Figure 3-2 Schematic diagram of the novel cyc l e in connect i on with a combined cycle The nove l cycle combines two thermodynamic cycles, the Rankine cycle and tl1e ammonia-absorption refrigerat i on cyc l e as seen in figure 1-4. In Rankine cycle, ammonia-water mixture is pumped to a l1igh presswe. The mixture is heated to boi l off an1monia, and ammonia is separated from wate1. After expanding through a tw bine to generate power, ammonia is brought to absorptio11 refrigeration cycle. Low temperature ammonia provides cooling in t h e evaporator and then it is abso r bed by water in an

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73 absorber and becomes ammonia-water mixture liquid. A s see n in figure 3-3, the 11ovel cycle provides extra work (s hade area) over Rankine cycle. The novel cycle as a bottoming cycle is a creative way to realize the triangular s hape of the T-S diagram. The concept of this cycle is ba s ed on the va1ying temperature boiling of a multi-component working fluid The boiling temperature of the multi-component working fluid increa ses as the boiling proce ss proceed s until all liquid is vaporized so that a better the1mal match i s obtai11ed in the boiler. This better thermal match yields a T L~ a Rankine Cycle J Q V -I> s Figure 3-3 T-S diagram s howin g advantage of the novel cycle over a conventional Rankine cycle

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74 better thermodynamic efficiency. The higher thermodynamic efficiency of the novel cycle as the bottoming cycle results from ( 1) The multi-component working fluid, having a variable boiling temperature provides significantly less available energy lo ss in the boiler, as the heat source has a variable temperature in the boiler as well (2) The working fluid starts boiling almost immediately after entering the evaporator which increases the efficiency of the heat exchanger(boiler). (3) The amount of heat rejected in the condenser is significant ly sma ller than that in the in the Rankine cycle ru.Tangement. 3 3 The1modynamic Analysis of the Proposed Cycle A s seen in Figure 3-3 the proposed ammonia-based cycle i s a combination of the Rankine and the ammonia-absorption refrigeration cycles. Within this one cycle, the Rankine cycle process of expanding a superheated vapor to produce work is present, as is part of the ammonia-absorption refrigeration cycle. A difference between this cycle and the ammonia-absorption refrigeration cycle is that ammonia vapor is not condensed and then expanded to provide refrigeration but the ammonia vapor is used as the working fluid in a turbine. This section gives a thermodynamic analysis of this novel cycle with assumed thermal boundary condit ion s as

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1 Power output : 2. Turbine inlet temperature: 3. Turbine inlet pressure: 2.5 kW 400 K500 K 18 bar 32 bar 75 At this stage, the thermodynamic state conditions of the proposed combined cycle are evaluated assuming a idealized cycle ( that is irreversibilities associated with real apparatus were neglected.) The idealized cycle does provide the analytical n1aximum limit s for real processes and is necessary in determining the efficiency limits of a real system. The following list of assumptions was used in the initial analysis of the proposed cycle. 3 .4 Thermodynamic Property Calculation The thermodynamic properties of the working fluids were evaluated using the methods developed in Chapter 2. The following pai agraphs explain the techniques used to determine the thermodynamic properties at each s tate in the cycle. Three working fluids were considered ammonia vapor, strong ammonia/water so lution, and a weak ammonia water so lution. Strong ammonia/water so lution refers to the condition where ammo11ia vapor and the weak ammonia/water so lution have been combined. Likewise when the ammonia vapor is boiled off fi om the strong ammonia/water solution, the remaining solution is considered the weak ammonia/water

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76 Table 31 A ss umption s and parameter s of the proposed cycle As s umption s State characteristic s Stron g a mmonia/water mi x ture pumped P 2 = 27 .6 a l S to 27 .6 b ar and heated to 466 K T 4 = T 1 = 466 K b Superheated ammonia vapor expanded P s = 2 .1 bar I S throu g h a turbine to 2. 1 bar C ammoni a va por e x itin g the n1rbin e i s u se d in T 6=277 K a r e fri ge r a tion appli c ation whi c h brin gs it s temperatur e to 2 77 K d Neglect pre ss w e drop s in c omponent s and P 2 = P 3 = P 4 = P 1 = P s = 27 6 bar pipeline s. P s = P 6 = P 9 = P 1 = 2. 1 bar e Liquid s olution s at s tate s 1 3, and 7 are s aturated l i quid s f Pump pr o ce ss is a s sum e d to be rever s ible h 2 h 1 = (P 2 P1 ) V 1 and adiab a ti c g Steady s t at e s tead y flow h Pur e ammo nia vap o r lea v e s boil e r Xa = 1 0 Turbine ex pan s ion i s i s en t rophi c ( rev e r s ible 1 S4 = S5 a di a bati c) The pre ss ure redu c in g v a l v e i s an adiab a ti c h s = h 9 J pro c e ss k Ma ss flo w o f weak aqua ammonia s olution i s a ss um e d I T emper at ure of s tron g T 3= 373 K aqt1 a -ammon1a s olution i s 37 3 K after l e a v in g the h e at e x chan g er

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77 sol utio11 Subscript s a, s, and w for the thermodynan1ic properties refer to the ammonia vapo1 strong ammonia/water so lution and weak ammonia/water solution respectively. Since pre ss ure drops in the components and pipelines are neglected all pressures are e s tablished from the given assumption s; State s between the pump and the turbine, or the pump and pressure relief valve are at 27 6 bar and the states between tl1e turbine or pre ss ure relief valve and the pump are at 2. 1 bar. The concentrations of ammonia in the aqua-ammonia mixture s are determined u s ing the assumptions that the strong and weak liquids would be s aturated at s tates 3 and 7, re s pectively. The concentrations are as s umed as Xs = 0.54 Xw = 0.125 and Xa = 1.0. Ma ss balance equations were used to determine the ma ss flow rate s through the cycle. With the following two equatio11s: m s = m w + m a, and a ss umin g a value for one of th e m ass flow r ates the values of the other two flow rates can be determined. Table 3-2 shows the thermodynamic s tate including enthalpy at each point Table 3-3 shows tl1e energy balance of each component.

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State Description 1 Absorber Exit I Pump Inlet 2 Pump Exit / HEX Inlet 3 HEX Exit I Boiler Inlet 4 Boiler Exit / Turbine Inlet 5 Turbine Exit I Cooler Inlet 6 Cooler Exit I Absorber Inlet 7 Boiler Exit / HEX inlet 8 HEX Exit I PRV Inlet 9 PRV Exit I Absorber Inlet Table 3-2 Example of operating conditions for the proposed cycle Fluid Phas e Temp Presswe Enthalpy Concentration K bar kJ/kg ke: NH 3 /kg mix strong aquasaturated 280 2.1 -209.16 0.540 liquid ammorua solution strong aqualiquid 280 27.6 -206.59 0.540 ammorua solution strong aquasaturated 373 27.6 223.22 .540 liquid amm orua solution superheated 466 27.6 1682.37 1.000 ammorna va oor superheated 262 2.1 1256.28 1.000 ammorua vaoor super h eated 277 2.1 1290 .98 1.000 ammorua vaoor weak aquasaturated 466 27.6 760.95 0.125 liquid ammorua sol ution weak aquas ub cooled 288 27.6 -15.5 0.125 liquid anunorua so lution weak aquasubcooled 288 2.1 -15.5 0.125 liquid airunorua solution Flowrate ke/s 0.01141 0.01141 0 01141 0.00541 0.00541 0.00541 0.006 0.006 0.006 -...) 00

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Table 3-3 Energy bala11ce of eacl1 component Component Pump Boiler Turbine Cooler Ab s orber Turbine power output: Refrigeration : Fir s t law effi c ienc y: Energy equations W p = m s (h 2 h 1 ) Q b = m a ~ + m w h 7 m s l1 3 W t= m a ( h s lui ) Q c = m a ( l1 6 } 1 5 ) Q a = m a h 6 + m w h 9 m s h 1 W t = m a Ch4 h s ) = 2.3 0 5 kW Q c = m a Che h s ) = 0 188 kW Energy (kW) 0.030 11 1 2 0 2 3 0 5 0.188 -9. 27 8 11 = w l + Q C = 2.305 + 0.188 x 100 % = 2 2.42 % Q b 11.1 2 3 5 A New Impro v ed De s ign Cycle 79 The previous s ection has des c ribed the advantage of the conceptual propo s ed cycle as shown in figure 1 -4. In that s ection it wa s a s sumed that the boiler produced pure ammonia vapor however the fi g ure doe s not s how how to generate highly concentrated ammonia v apor. Us ually the boiler generate s vapor witl1 about 90 3/o ammonia mas s fraction At thi s animonia ma ss fra c tion vapor can not be expanded in a turbine to a v ery low temperature be c au s e a certain amount of conden s ation will be gene1 ated in the turbine For an ab s orption refrigeration cycle a condenser or rectifier i s u s ed to condense

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80 part of the water vapor from the boiler. After the condenser, a highly concentrated ammonia vapor is generated. The ammonia composition after the co11denser can be over 99%. Since water vapor is condensed in the condenser / rectifier heat of condensation is released. But this heat is not wasted instead it is used to preheat the basic solution from the absorber. Figure 3-4 shows a more detailed design of the proposed cycle. In tlris system, tl1e boiler generates ammonia rich vapor (s tate 5). Before the vapor is superheated in a superl1eater (state 7), it passes througl1 a condenser or rectifier (state 6) to get a higher concentration ammonia vapor. After expansion in the turbine, the ammonia vapor drops to a very low temperature. The cold ammonia vapor provides cooling by passing through the cooler (state 9). The ammonia vapor is then reunited with the weak solutio11 from the boiler in the absorber to regenerate the basic solution (state 1 ). The basic solution is then pumped to a high pressure (state 2) to complete the loop. The basic solution coming out of the absorber is used as the cooling fluid for the condenser. At state 2, part of tlie solution goes through a solution heat excl1anger and another part goes to the condenser. These two streams mix before the boiler. So no heat is wasted while a highly concentrated ammonia vapor is obtained as a working fluid. Table 3-4 shows typical operating conditions of the proposed cycle. Table 3-5 shows the perfonnance of each compo11ent based on a tmit mass of the basic solution at the conditions of table 3-4.

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81 Condense r / e Rectifier I 3 4 5 Boiler I I 13 2 S H 10 14 H E. I.: J 2 1 11 Pump Turbine X 1 12 8 Cooler Absorber VVV\/ Figm e 3 4 A modified a 1 nmonia-based combined power / cooling cycle

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82 Table 3-4 Typical operating conditions State T p h s X Flow rate (K) (bar) (kJ/kg) (kJ / kg K) mlm1 1 280.0 2.0 -214.1 -0.1060 0.5300 1.0000 2 280.0 30.0 -211.4 -0.1083 0.5300 1.0000 3 378.1 30.0 246.3 1.2907 0.5300 1.0000 4 400.0 30.0 1547.2 4.6102 0.9432 0.2363 5 360.0 30.0 205.8 1.1185 0.6763 0.0366 6 360.0 30.0 1373.2 4.1520 0.9921 0.1997 7 410.0 30.0 1529.7 4 5556 0.9921 0.1997 8 257.0 2.0 1148.9 4.5558 0.9921 0.1997 9 2 80.0 2 0 1 278 7 5.0461 0.9921 0.1997 10 400.0 30.0 348.2 1.5544 0.4147 0.8003 11 300.0 30.0 -119.0 0.2125 0.4147 0.8003 12 300 .0 2.0 -104.5 0.2718 0.4147 0.8003

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83 Table 3-5 Results from the table 3-4 state conditions cycle high temperature and pressure are 410.0 K and 30.0 bar cycle low temperature and pressure a1e 257.0 Kand 2.0 bar boiler heat input = 390.4 super heat input 31.3 condenser heat reject = -83.8 absorber heat reject = -358.8 cooler cooling load = 25.9 turbine work output 76.0 turbine liquid fraction = 0.0692 turbine vapor fraction = 0.9308 pu1np work input 2.7 total heat input = 421.6 total work output = 73.33 cycle efficiency = 23.54% All energy units are kW / kg basic solution

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84 3 .6 Conclusion The initial thermodyna mic analysis has shown that the ammonia-ba s ed combined power / cooling cycle has a promising application In the case study of turbine inlet condition of 466 Kand 27.6 bar, we obtain a pretty good frrst law system efficiency of 20 .73/o At this condition, the steam is still a condensed liquid which means that the steam Rankine cycle can't even be used for such low temperature application. Further study with different t1ubine inlet temperature will also show that the proposed cycle will have better fust law efficiency. The proposed cycle can be applied to many low temperature heat sources such as geothermal and solar energy heat s0U1ces. An improved design of the proposed cycle is also presented in this chapter with detailed information. A second law analysis and system simulation based on this design are discussed in the foil owing chapter.

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CHAPTER4 THE SECOND LAW THERMODYNAWC ANALYSIS 4 .1 Introduction With the increasing cost of our most widely used fuels and the potential decrease in their availability in the future, the importance of effective use of our available energy resources is now receiving more and more attention. The location and degiee of inefficient use of e11ergy in ow energy systems should be a primary factor in the design and pe1fo1mance analysis of the system. The second law analysis is directed to providing this information by a sys ten1atic approach. To eva l uate the effectiveness of energy Li s e in different systems, a realistic mea s ure of energy utilization mt1st be applied. The exergy method of analysis will provide this true measure of effective energy use througl1 its application of principles of both the frrst and second law s of thermodynamics. 4 2 Work and Availability The final product of intere s t from the expenditure of energy resou1 es is work which is used to perform tasks st1ch as generating electricity, pumping water and moving 85

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86 objects. Work is made available from the energy resources in many forms. For example, the combustion of oil or gas in a power plant provides high-presswe, high-temperature steam that is available to do work through a turbi11e and ge11erator system When the temperature and pressure of the steam are near the conditions of the surrounding environment( condensed liquid near ambient temperature), the work available in the steam has essentially disappeared. Another example is that, the water behind a dam on a river i s available to do work by driving a hydrat1lic turbine and an electric generator. The available work in the water behind the dam reve11 s to zero when the wate1 level falls to the level in front of the dam So when the mass comes into equilibrium with the environment, no more changes of state will occur and the mass will not be capable of doing any work. Therefore, the steady-state condition of ow surrounding environment is a reference state which a mass at a given state( such as high temperature and l1i gh pressure steam, water held in a dam) can achieve after a process to perform maximum available work. This concept of available work referenced to the surrounding environment is the basis of tl1e exergy method of energy-systems analysis. It is also a reali stic method of comparing the efficie11t use of our energy resowces. It s hould be noted that a fluid or gas that is not in equilibrium with the ambient sur roundings has the potential to perform work as its condition reverts to the ambient stUTounding conditions, as everything will do naturally. This means that a fluid that is colder than the ambient su rroundings will be available to perform work as it warms up to the ambient sm1oundings just as a warm fluid is available to perform work in its passage to the ambient swTounding conditions.

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87 4.3 Thermodynan1ic Processes and Cycles Energy systems are made up of a series of individual processes that fo1m closed or open cycles. Each process in a system or cycle can be analyzed separately from the system by performing a first-law energy ba l ance around the component involved in the process As the available work in a system working fluid decreases through energy related processes there are losses in the available work since no transfer of heat or conversion between mechanical work and heat can be pe1formed without some i1reversibility in the process. fu a system in which n1any processes are involved, the loss of work in the system will be dist11buted throughout the individua l processes. It is impo1iant to establish the relative losses in each process if we are to effectively improve the system efficiency. It should be noted that the conventional heat-balance method of eva l uating system losses and system efficiency is misleading and not a true representation of system effectiveness. Only through an evaluation of the availab l e work throughout the system can we have a t1ue measure of the losses in the system processes, which is necessary for effective energy conservation in system design and operation. 4.4 Exergy Exergy is defmed as the work that is available in a mass as a result of conditions noneqt1ilibr i um relative to some reference condition. As we have described in the

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88 previot1 s paiagraph atmospheric condition generally is a reference condition. Useful work can be recovered during the cooling and expansion processes of steam through a s team engine or turbine and heat exchangers. The exergy that is not recovered as useful work is lost Exergy is an explicit property at steady-state conditions. Its value can be calculated at any point in an energy system from the other prope1ties that are determined from an energy balance on each process in the system. Exergy is calct1lated at a point in the sys ten1 relative to the reference condition by the following general equation: Exergy = (u Uo) To{s so)+ P o (v v o ) + V 2 / 2g + g(z zo) + i2{i io)Xi 4-1 Internal Entropy Work Momentum Gravity Chemical Energy Potential W11ere the s ubscript O denote s the reference condition and i denote s a s i-th composition. Tl1ere a1 e va1iation s of this general exergy equation and in mo s t systems analy s es some, but not all of the terms s hown in equation 4-1 would be used Since exergy is the work available from any s ource terms can also be developed using electrical current flow, magnetic fields and diffusion flow of materials. 4.5 Background of Dead State The exergy method of analy s i s i s a particular approach to application of the second law of ther1nodynamics to enginee1 ing systems. Another frequently used term is

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89 availability analysis, which is often found in classical thermodynamic text books (Sonntag et al, 1994; Moran and Shapiro, 1992). ''Exergy is the maximum theoretical work that can be extracted from a combined system or system and environment as the system passes fi. on1 a given state to equilibrium with the environment-that is, passes to tl1e dead state.'' (Moran and Sciubba, 1994). Environment or sw1.oundings are often used as a reference state for availability analysis. When the mass comes into equilibrium with the environment, no change of state will occw. So the mass is incapable of doing any work or is in a dead state. One standard atmospheric pressure is normally used as a reference pressure. Different reference environment temperature have been used by 1esearchers such as 293 K (Aphornratana and Eames, 1995), 298 K (Egrican, 1988) and 300 K (Waked, 1991). Krakow( 1991) proposed a dead-state definition. He indicated that the reservoir of a system that is not the environment is defmed as the system 1 eservoir. The system reservoir serves as the source for engines and coolers and as the sink for heat pumps. The environment serves as the sink for engine s and coolers and as the source for heat pumps. So instead of using universal ambient condition as a dead state, he proposed that one of the high-temperature and low-temperature reservoirs of the system to be considered as a reference state. Since reservoirs of real systems are fmite their temperatures change during any heat transfer process. Therefore, the dead state ten1pe1ature in a real process changes during the process. To account for the change in the dead state temperature in real processes,

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90 Krakow defined an effective reservoir te1nperatwe for heat sources and sinks which is essentially the same as the entropic average temperatwe t1sed by Herold (1989). The effective reservoir temperature, which is used as the dead state for the reservoi1 is defined as the temperature that will make its initial exergy equal to the fmal exergy. Neglecting the 1nomentum, gravity and chemical exergies, the initial and fmal exergies of a reservorr are Ex1 = (h1 he f) T et(s1 Ser) 4-2 4-3 where subscripts 1 and 2 stand for the initial and fmal conditions of the reservoir, and ef stands for the effective temperature condition. Tef is defined such that Ex 1 = Ex 2 The entropic average temperatwe of a reservoir is defined as 4-4 where Q i-2 is the heat exchanged with the reservoir. Above methods and defmitions can be used easily for sing le working fluids such as steam. However, it is difficult to defme the dead state for mixtures such as LiBr / water and ammonia/water. Since a dead state composition must also be defmed. In other words, it is important to know wl1at work will be done by changing mixture co1nposition at the same temperature and pressure, or will the composition change at all under the same temperature and pressure

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Koehler et al. ( 1988) propo s ed the following method to consider the mixture composition factor in exergy calculations for the LiB1 / water mixtures. Ex = Ex ( T P, x ) = Ex(T P) + Ex o ( x ) 45 Ex ( T P) denotes the temperature and pressure dependent part of the exergy of 1nixtures at a given composition x, and Ex o (x ) depends on x at the reference state 91 To find E x o (x) imagine mixtures at T o P o W1der g oing a c hange of s tate from a g i v en x to the dead state at saturated mixtures s tate X s by adding an amount of s olution at T o P o. And we have following equation s: Ex(T P ) = (h(T P x ) h o (T o P o x) ) T o (s( T P x ) s o ( T o P o x) ) 4-6 X S -x m s m x where ---------1 X S m x subscript 0 2 stands for the solute or solution bein g added s ub s cript s s and x stand for the s aturated and actual concentration The exergy of the pure component can be obtained a s 4-8 There are two main problems with thi s n1ethod First, when a s oll1tion from a state T P pa ss e s to a de a d s tate T o P o the s olt1tion concentration n1ay be over the level of s aturation concentration Then an amount of s olute mu s t be taken out from the s olution Koehler et al. did not mention thi s point Secondly equation 4-8 is not the equation for

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the pure cycle wo1king fluid exergy analysis ru:1d therefore it should not be used for a pure component e x ergy calculation. 4.6 Exergy Analysis for the Proposed Cycle The reservoir in a system that serves as the environment state should be t1sed as a refere11ce state. Our new cycle is a combined power and refrigeration cycle, the ref ore both boiler and cooler are system reservoirs. The main purpose of thi s cycle i s power generation, and the absorber serves as a condenser of the power cycle. Heat is rejected during the absorption process. 92 It is inappropriate to u s e water at ambient state as a reference for a mixture solution Koehler et al.(1988) consider the mixttrre effect, but his method will create many reference state s in the system a s there are s everal different mixture compo s itions. Therefore theit method does not provide a common ground for exergy analy s is. Szargut et al. ( 1988) suggested a 1ule for the choice of reference levels for calculating exergy of mixtures If the proce ss es tmder con s ideration are only physical a refere11ce level can be assumed s eparately for each constituent involved in the proce ss For a cyclic ph ys ical proce s s involving a s olution of changing composition the following equation can be used for the thermal exergy related to the arbitrarily a s sumed reference level: 4-9 For a binary s olution ammonia-water mixtures equation 4 9 can be written a s :

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Ex = h T o S (h ow T o S o w)Xw (h oa T o S oa )Xa X w = 1 X a Substituting 4-11 in 4-10 gives Ex = h T o s + [-(h ow T o s ow )] + [(h ow T o s ow) (h oa T o s oa )]xa Equation 4 12 can be written as Ex = h T o s + a + bx where a = -Ch ow T osow ) b = Ch ow T o S ow ) (h oa T o s oa) 4-10 4-11 4-12 4-13 9 3 In Equation 4-13, xis the ammonia mass fraction a and bare constants that depend on the choice of the dead state For a closed cycle, the values of a and b will not have any effect on the exergy analysis since eventual l y they will be canceled out. So a and b can be chosen such that all the exergies in a cycle are positive. For pure component analysis xis either O or 1 In that case equation 4-12 takes the following form : Ex= h-T o s + c where c is a constant. 4-14 Equation 4-11 is a general form for a pure component exergy analysis. The following is an exergy analysis of the proposed cycle as shown in figure 3-4. Assumptions used in the study are: 1. Ammonia-water solutions in the boiler and the absorber were assumed to be in equilibrium at their respective temperatures and pressures

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94 2. Pressure losses due to the friction in heat exchangers and pipe lines are neglected. 3. The reference temperature T O has been cl1osen as 280 K which is the absorber temperature usually used in thi s study Co1istants a and b are chosen as 10 kJ / kg and 536 kJ/kg so that all the point s have po s itive exergy Boiler exergy change: ~ bo il e r = 11'4E4 + m 1 oE10 m 3 E 3 m s E s Condenser exergy change: ~E cond = msE s + m ~6 + ID 3 E 3 tl'4E 4 m 3 E 2 Superheater exergy change: ~E s H. = m 1 E 1 m 6 E 6 Cooler exergy change: Absorber exergy change: i1E absorber = ffi 1 E 1 m 9 E 9 ID 12 E 1 2 Solution heat exchanger exergy change: ~E H .E. = m 2 E 2 + m11E11 m 2 E 2 m1 0 E 10 4-15 4-16 4-17 4-18 4-19

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Throttling valve exergy change: Exergy change due to mixing at point 3: L\Emixing = m 3 E 3 m 2 E2 m 3 E 3 Turbine exergy change: ~Erurbin e = m 3 E s + m 7 E 7 Pump exergy change: L\Epump = m 2 E 2 + m1E1 95 4-20 4-21 4 22 4-23

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96 Ta bl e 1 T ypi ca l state point s State Temperature P r essure Enthalpy Entropy Ammonia Flow rate Exergy (K) (bar) (k J /kg) (kJ/kg K) mass frac. m/m1 (kJ/kg) 1 280.0 2.0 -209.7 -0.0636 0.5000 1 .0000 86. l 2 280 0 23 0 -207.6 -0.0649 0.5000 1 .0000 88.6 2' 374.0 23.0 263.5 1 .4282 0 5000 0.7299 141.6 3 372.5 23.0 234.5 1.3441 0.5000 1 0000 136.1 3' 360.0 23.0 156.0 1.0761 0.5000 0 270 1 1 32.7 4 400.0 23.0 1590.7 4 8285 0.9227 0.2784 743.3 5 360.0 23.0 168.6 1.0992 0.5738 0.0436 1 78.4 6 360 0 23.0 1409.5 4.3613 0.9876 0.2347 727.6 7 500.0 23.0 1793.4 5 2631 0.9876 0.2347 859. 1 8 276.1 2.0 1250.5 5.2631 0.9876 0.2347 316.2 9 280.0 2.0 1264.1 5.3159 0.9876 0.2347 315.0 1 0 400.0 23.0 357.2 1 5718 0.3504 0.7653 115.0 1 1 300.0 23.0 -92.1 0.2826 0.3504 0.7653 26.7 12 300.0 2.0 -94.0 0.2838 0.3504 0.7653 24.4

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97 Table 2 Exergy change of each compone11t Exergy Exergy Exergy lo ss Exergy lo ss(o/o) Work Change input Output Boiler 151.0 1 5 1 0 S uperheater 30.8 30.8 Condenser -16.4 16.4 28 97 /o Ab so rber -6.5 6.5 l l .49o/o Solution H.E. -28.9 28 9 51.06% Tlu ottling Valve -1.8 1.8 3 18 % Mixing -3.0 3 .0 5 30% Turbine -127.4 1 27.4 Cooler -0.3 0.3 Pump 2 5 -2.5 Total 0 181.8 56.6 100 % 125 .2 The second law efficiency is 11 0 = ( exergy output) / ( exergy input ) = 125 .5 / 181 8 = 68.9o/o 4. 7 Di sc u ss ion It can be seen that the condenser solutio11 heat exchanger and absorber are the three 1najor components that lo se exergy. While absorber and condenser lose about the same amount of exer gy, so lution heat exchanger make s up the bigge s t lo ss of exergy. The exergy analysis ha s identified the components of the cycle that must be targeted for

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98 further improvement in the cycle efficiency. To reduce the amount of exergy loss in condenser the condenser temperattrre must be increased so that less vapor is condensed. But this will increase the moisture content in the ammonia vapor and cause problems in the turbine expansion process. The condenser temperat1rre can be increased to reduce the exergy loss in the condenser, as long as the turbine exit condition of less than 1 Oo/o moisture(liquid) can be maintained. 4.8 Conclusion A second law analysis of the new power cycle is presented. This analysis has used the thermodynamics prope11ies of ammonia-water mixtures developed in this research. Different methods proposed in the literature to cl1oose dead state conditions for exergy analysis are discussed. This paper proposes a reference state at ambient pressure and saturated liquid state of the basic solution in the cycle, so that the mixture effect is considered in the reference state. Performances of the proposed cycle are evaluated. The exergy analysis shows more detailed information than the frrst law analysis. The exergy analysis shows how the energy is utilized a nd which components waste the available energy, so that improve1nents in system design can be recommended.

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CHAPTERS A THEORETICAL COMPARISON OF THE PROPOSED CYCLE AND ......... CYCLE 5 1 Introduction The new power cycle using ammonia-water mixtures as a working fluid was introduced in the chapter 3. The new power cycle can operate as an independent cycle as well as a bottoming cycle. Most heat sources available to the bottoming cycles such as hot exhaust gases, are sensible-heat sources because the temperature of the source varies during the heat transfer. The amount of cooling medium at the sink temperature in reality is also limited so that the heat sink is sensible as well. This sensible heat transfer does not fit the isothermal process of the conventional Rankine cycle using a pure working fluid because there is a pinch point during the heat transfer process. In this chapter, a detailed performance of the new cycle and the RankiI1e cycle will be investigated and contrasted. An objective of this study is to determine under what circumstances one cycle has an advantage over the other. Maloney and Robertson(1953) studied a similar ammonia-water power cycle using ammo11ia-water mixtures as a working fluid. They compared the ammonia-water power cycle with Rankine cycle and concluded that the efficiency of the ammonia-water cycle is less than that of a steam cycle. 99

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100 5 .2 Cycle Description In the Rankine cycle the heat rejection occurs in a simp le heat exchanger(condenser) and the heat addition also occurs in a simp le heat exchanger(boiler or steam generator). In the proposed cycle the heat rejection occurs in an absorber, and the heat addition includes so lution l1eat exchanger boiler and rectifier. When comparing different power cycles, regardless of the details of the balance of the system, heat so1-1rce and heat sink are the two major criteria for comparison. The ability to add heat in the cycle at the heat source temperatUIe and reject heat at the heat sink temperature is a decisive factor in achieving a better cycle efficiency. Figure 5-1 shows a simplified power cycle model used to compare the proposed cycle and the Rankine cyc le. Heatin g fluid ........ .. .. .. .. .. .. .. .. . .. ........... Heat add ition Vapor Turbine ...... Wor k output Liquid Heat r ejection .. .. .. .. .. .. .. .. .. ... Coolant Figure 5-1 A simp lified power cycle

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101 The working fluid is heated to a vapor state in the heat addition heat exchanger. The vapor expands in the ttubine and produces useful work. The fluid condenses to liquid state in the heat rejection heat exchanger. The liquid is pumped to a higl1 pressure to complete the cycle. In the following paragraph, a theoretical comparison of using ammonia-water mixtures and steam as working fluids in this cycle is stud ied The results will show the advantage of the proposed cycle over the Rankine cycle. 5 .3 Thermal Boundary Conditions As 1nentioned in the chapter 3 this cycle can be used as a bottoming cycle as well as an independent power cycle using low temperature heat sotuces such as so lar energy and geothermal energy. The heating fluid is taken to be at 520 Kand the cooling sink is taken to be at 280 K. The heating fluid has a constant thermal capacity of 1 kJ / kg K. If a stream of hot gases is taken to flow without friction and is cooled to sink temperature under constant composition, it is found that the maximum mechanical power that could be produced is 220 kJ/kg of gases. This is referred to as 1003/o of the exergy. The destruction of this exergy will be investigated in both the cyc le s. 5 .4 Temperature Limitation in the Heat Addition Exchanger The first limitation is due to thermal properties and heat transfer. If water at 280 K and 20 bar is introduced in the steam generator and if the heat transfer surface is infinite

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102 in area, it is found that the temperature profile of water can not match the temperatt1re profile of the hot gases. At one point in the heat exchanger, the water boiling point temperature can at most be equal to the hot fluid temperature. Tltls is the so-called ''pinch point'' Figure 5-2 shows the heat transfer profile of a steam generator of Rankine cycle. At the exit the temperature can at most be equal to the inlet temperature of the hot gases. If the maximum pressure of steam is 20 bar and the water inlet temperature is 280 K, it is found that a large amount of hot fluid energy re1nains unused in the heat exchanger. The exit temperature of hot gases will be 470 K, which means 67.5% of the availability remains unused and therefore wasted. The availability gained by the steam is 27.9%, and 4.6% availability is destroyed during the heat transfer process Figure 5-4 shows the exergy diagram of a steam generator assuming the outlet steam temperature equals the inlet hot fluid temperature and pinch point te1nperature difference is zero. In the proposed cycle ammonia-water mixture is a working fluid. When the mixture enters the vapor generator, light substance ammonia tends to boil off early. The mixture composition changes during the heating process and the boiling point rises. Figure 5-3 shows a typical temperature profile of ammonia-water mixtures and hot gases in a heat exchanger.

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103 500 450 .......... Q) ":l ..... 400 ro "Q) 0. E Q) 350 l300 0 1 Location Figure 5 2 Temperatw e profile of a steam g enerator 500 sz 450 ...__ Q) ":l ..... 400 ro "Q) 0. E Q) l350 300 0 1 Location Figure 53 Temperatw e profile of a NH3/H20 vapor generator

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Hot fluid 470 K 67.5% 520 K 100% 4----l W------4.6% ---+1 1-------+ 280K 520 K 27.9% Steam Figure 5-4 Performance of a steam generator assuming infmite heat transfer area at 20 bar 104 Tab le 5-1 Properties at state points of Figure 5-4 State points T(K) P (bar) h (kJ / kg) s (kJ / kg K) m/1n gas e (kJ/kg) Hot fluid inlet 520 1 247 0.6444 1 66.7 Hot fluid outlet 470 1 197 0.5433 1 45.0 Hot fluid pinch 485.3 1 212.3 0.5754 1 51 3 Water pinch 485.3 20 907.5 2.4479 0 017 3.9 Water inlet 280 20 30.5 0.1058 0.017 0.0 Steam outlet 520 20 2890 6.5263 0.017 18.6

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105 If the pinch point and exit temperature differences are assumed zero, the leaving gas will have been cooled to 345 Kand wi l l only carry 7.8% of the original exergy. Thi s shows s ignificant improvement due to a better temperature match using ammonia-water mixtures. Ammonia-water working fluid will catzy 84.4 % of the original exergy as compared with only 27.93/o by the steam a s a working fluid Figtue 5-5 s hows the exergy distribution in a ammonia-water vapor gene1ator. Since it is unrealistic to have an infinite heat t1 ansfer area in a heat exchanger there will be a temperatw e difference between the hot gases and the working fluid. There also exists a temperatu1 e difference at the pinch point Assuming a good heat exchanger and no friction lo ss, it is assumed that there is a 10 K temperatw e difference between the hot gas inlet and the working fluid ex i t. It is al s o a ss umed a 5 K temperature difference exist s at the pinch point. By doing this the performance of a steam generator will be mi se rable. Figure s 5-6 and 5 -7 s how tl1e exergy profi l e assuming a finite heat tran sfe r area in the heat exchanger. For a steam generator, It i s possible to lower the pinch point by reducing the pre ss ure But it s till does not compare will with an ammonia-wate1 vapor generator. Figw:e 5-8 shows the improvement of a steam generator by reducing the pressure from 20 bar to 10 bar.

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337.3K 7 8 % 520 K 1 00% . . . . . . . . . . . . . . . . . Hot fluid 7.8% . . . . . . . . . . . . . . . . 280K 520 K 84.4 % Figure 5-5 Performance of a NH 3 /H 2 0 vapor generator assuming infinite heat transfer area at 20 bar Table 5-2 Propertie s at state points of Figme 5-5 State points T(K) P (bar) h (kJ / kg) s (kJ / kg K) m/m gas e (kJ / kg) Hot fluid inlet 520 1 247 0.6444 1 66.7 Hot fluid outlet 337.3 1 64 .3 0.2116 1 5.2 Hot fluid pinch 364.8 1 91.8 0.2899 1 10.7 NH 3 /H 2 0 pinch 364.8 20 178.8 1.1400 0.071 3.6 NH 3 /H 2 0 inlet 280 20 -207.9 -0.0647 0.071 0.1 NH 3 /H 2 0 outlet 520 20 2363.9 6.2900 0.071 56.4 106

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107 Hot fluid 436.7 K 7 1 8 % 520 K 100% . . . . . . . . . . . . . . ' 4 .3% . . . . . . . . . . . . . . . . . 280K St e am 510 K 2 3.9 % Figure 5 -6 Performance of a steam ge nerator assuming finite heat transfer area at 20 bar Table 5 -3 Properti es at state point s of Figure 5-6 State point s T(K) P (bru) h (k J / k g) s (kJ / k g K) m/1n gas e (kJ / kg) Hot fluid inlet 520 1 2 4 7 0.6444 1 66.7 Hot fluid outlet 477 1 204 0.5581 1 47.9 Hot fluid pinch 490.3 1 2 1 7.3 0. 5 856 I 53.4 Water pin c h 485 3 20 907.5 2.4479 0.015 3.4 Water inlet 280 20 30 5 0.1058 0.015 0.0 Ste a m outlet 520 20 2890 6.5263 0.015 16.0

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Hot fluid 343 K 9 2 % 520 K 100 % . . . . . . . . . . . . . . . . . . "' 9.3 % . . . . . . . . . . . . . . . . . 280K 510K 81.4% Figure 5 7 Performance of a NH 3 /H 2 0 vapor ge nerator assuming fmite heat transfer area at 20 bar Table 5 -4 Propertie s at state points of Figure 5-7 State point s T(K) P (bar) h (kJ / kg ) s (kJ/kg K) m/m gas e (k J / kg) Hot fluid inlet 520 1 247 0.6444 1 66.7 Hot fluid outlet 342.9 1 69.9 0.2280 1 6.2 Hot fluid pinch 369.8 1 96.8 0.3035 1 11.9 NH3/H 2 0 pinch 364.8 20 178.8 1.1400 0.070 3.5 NH 3 /H 2 0 inlet 280 20 -207.9 -0.0647 0.070 0.1 NH 3 /H 2 0 outlet 520 20 2363 .9 6.2900 0.070 54.4 108

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Hot fluid 520 K 100% 8.8 % -----M .,__----+ 1 .,___ _____ _____. 520 K 46.2% 280K Steam Figure 5-8 Performance of a steam generator assuming infinite heat transfer area at 10 bar Table 5-5 Prope1iies at state points of F i gure 5-8 State points T(K) P (bar) h (kJ/kg) s (kJ/kg K) m/m gas e (kJ/kg) Hot flu i d inlet 520 1 247 0.6444 1 66.7 Hot fluid outlet 430.3 1 157.3 0.4550 1 30.0 Hot fluid pinch 452.9 1 179.9 0.5063 1 38.3 Water pit1ch 452.9 10 762.7 2.1415 0.031 5.1 Water inlet 280 10 29.5 0.1059 0.031 0.0 Steam outlet 520 10 2931.3 6.9068 0.031 30.9 109

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110 5.5 Cycle Analysis The previous section shows a superior performance of ammonia-water mixture in a finite heat capacitance heat addition process as compared with water. In this section, the performance of the boiler will be incorporated in a cycle, together with a turbine and a condenser. For simplicity, an adiabatic efficiency of 100% is used in the calculations for both cycles. Studies show that exergy loss in a turbine due to iITeversibility in expansion is about the same in both cycles, or less than 0.2 % The selection of turbine back pressure is based on two c1iteria: 1 The condensation at the turbine exit should be less than 10 %. 2. The working fluid can be condensed at 300K. For hot gases at a temperature of 520 K a 10 K temperature difference is a ss umed between the hot gas inlet and the working fluid exit Also a 5 K temperatwe difference is assun1ed at the pinch point. The Rankine cycle is taken to operate between 10 bar and 0.63 bar, so that the boiler may get the high output from hot gas and 903/o quality at tl1e turbine exit. At the presst1re of 0.63 bar steam can be condensed at 360 K. The ainmonia-water cycle is taken to operate between 15 bar and 2 bar. An ammonia-water mixtures with 0.5 ammonia mass fraction and a 2 bar pressure can be condensed at 300 K That is a 5 K degree difference with the coolant iitlet temperatt1re. Figures 5-9 and 5-10 show the performance of a Rankine cycle and an an1n1onia water cycle.

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446.4 K 53.7% ? 3 1 520 K 100 % . . . . . . . . . . . . I. 5. 2 % 510 K 4 1 1 % 5 4 Vapor Liquid 3 60 K Turbine P ump 8 7 18.5 % . ... . ... . . . . . . . . . . . ....... Co olant F i gure 5 9 P e r fo rman ce of a Rankine cyc l e F ir s t l aw efficiency of th e above cycle i s w t 17 1 =8 -_ 8 -= 19 0 o/ o 2 I an d th e seco nd l aw ef fi cie n cy i s 17 n = 2 2.6%. 111 22 6 % . Wor k output

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112 Table 5-6 Properties at state points of Figure 5-9 State points T(K) P (bar) h (kJ / kg) s (kJ / kg K) kg/kg gas e (kJ / kg gas) 1 520 1 247 0.6444 1 66.7 2 446.4 1 173.4 0.4918 1 35.8 3 pinch point 457 9 1 184.9 0.5173 1 40.2 4 pinch point 452.9 10 762.7 2.1415 0.029 4.7 5 360 10 364.7 1.1591 0.029 1.2 6 510 10 2909 0 6.8635 0.029 28 6 7 360 0.63 2426 6.8635 0.029 14.6 8 360 0.63 364.3 1.1576 0.029 1.2

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335 .1 K 7.2% 2 3 1 52 0 K 100 % . . . . . . . . ......... 10 7 % 510 K 82.1 % 5 4 Vapor Liquid 300K Turbine Pump 8 7 , 3 2 .9 % . . . . . . . . . . .. .. C o olant Figu1 e 5-10 Performance of a ammonia-water cycle First law efficiency of the above is w t ) / 111 =H --H -= 17.2~o 2 1 and the second law efficiency is 11 11 = 49.2% 113 49. 2 % . Wor k output

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114 Table 5-7 Properties of state points ofFigwe 5-10 State points T(K) P (bar) h (kJ / kg) s (kJ/kg K) kg / kg gas e (kJ / kg gas) 1 520 1 247 0.6444 1 66.7 2 335.1 1 62.1 0.2049 1 4.8 3 pinch point 357.3 1 84.3 0.2691 1 9.0 4 pinch point 352.3 15 119.4 0 9763 0.073 2.7 5 285 15 -185.8 0.0155 0.073 0.1 6 510 15 2352.3 6.3977 0.073 54 8 7 370.7 2 1915.5 6.3979 0.073 23.7 8 285 2 -187 .1 0.0164 0.073 0.0

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11 5 5.6 Conclusion Chapter 3 has qualitatively shown that ammonia-water mixture has favorable heat tra11sfer characteristics. In this Chapter, we have demonstrated quantitatively that ammonia-water mixture has a big advantage over steam in a bottoming cycle. An interestin g point shown here is that the first law analysis is misleading In figure 9 a Rankine cycle has a frrst law efficiency of 19 0 % while from figure 5-10 an ammonia-water cycle has a first law efficiency of 17.2 o/ o under identical source and sink conditions. But ammonia-water cycle has a 49 .2 % second law efficiency as compared with only 22.6 % for the Rankine cycle. In Rankine cycle, most of the available heat in the source is wasted and only a small amount of heat is input into the cycle The first law thermodynamic efficiency is ba s ed on only the amount of heat inpt1t and the work output The second law analysi s show s how well the available energy is used. An ammonia water cycle certainly makes a good u s e of the available energy as shown in thi s chapter If the heat tran s fer effectivenes s from the heat sow ce i s not considered, an ammonia water cycle may s eem les s favorable than a Rankine cycle Most heat sources available to the bottoming cycles are sensible-heat sources so the temperature of the sow ce varies during the heat transfer process. A con s tant boiling temperatwe of a Rankine cycle mismatcl1es the heat transfer proce ss which generate s irreversibility.

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CHAPTER6 SYSTEM SIMULATION AND PARA.METRIC ANALYSIS 6.1 lntrodt1ction The novel ammonia based power / cooling cycle was simulated as descried in chapter 3 figure 3-4 This chapter describes the results of computer simulation of the cycle The results are presented as a parametric analysis to conduct a systematic study of the effect of turbine inlet vapor temperature, turbine presswe ratio, bo i ler and condenser temperature and absorber temperature. 6.2 Thermodynamic Analysis of the Proposed Cycle This section gives a thermodynamic analysis of this novel cycle with assumed thermal boundru:y conditions as 1. Boiler temperature: 400 K 450 K 2. Turbine inlet temperatUIe: 400 K 500 K 3. Turbine inlet pressure: 18 bar 32 bar 4. Ammonia concentration in basic solution: 0.20 0.55 by mass 116

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117 The thermodynami c state condition s of the proposed combit1ed cycle were evaluated assuming an idealized cycle ( that is irreversibilities associated with real apparatt1s were neglected.) The idealized cycle does provide the analytical maximum limits for the real cycle and is neces sary in dete1mining the efficiency limits of a real syste m A computer program for ammonia-water mixture thermodynamic properties ha s been developed for the cycle analysis. The program u ses Gibbs free energy method and has shown good agreement of thermodynamic properties with published literature data. Following are the assumptions for the cycle analy s is. l At point l, the working fluid is s aturated liquid at low pressme. Temperature is set at 280 K to keep fluid at liquid s tate at a 2 ba1 pressure. 2. At point 2, saturated liquid i s pumped to a high pres s ure at 20-30 bar. 3. Mixture pa sses tht ough a preheat heat exchanger and the temperature is raised to abot1t 350 K as s umit1g that the boiler temperature i s 400 K 4 Basic solution of ammonia-water mixture enters the boiler where it is heated to 400 K. NH 3/H2 0 mixtures will evaporate with a higher concentration ofNH 3 So at point 4 ammonia ma ss concentration i s expected to be over 0.90. At point 10 weak aqua returns to the absorber via a heat exchanger. 5 Because we need high concentration mixture(pure ammonia is ideal but it is impos s ible ), pati of the moi s ture is condensed in the condenser. The condenser te1nperatt1re is se t at abot1t 360 K 6. After the condenser the ammonia concentration in the mixture can be as high as 0.99.

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118 7. The mixture is superheated before it enters the turbine. S uperheater ten1perature is set at 410 K. 8. T11e mixture with high presswe, temperature and ammonia concentration expands in the turbine and transfers output work to a generator. We can expand the mixture to a very low temperature and still maintain a vapor state A very small amount of moisture may condense after the turbine. Based on the operating experience of steam twbines in the literature it is assumed that less than 1 O o/ o moisture after the turbine exit won't affect turbine's perfo1mance. 6.3 Basic Equations Boiler heat transfer: qb o il er = m 4 h4 + m1 o h 10 m 3 h 3 m s h s Condenser heat transfer: q con d = m s h s + mJl. 6 + m h 3 0 m 3 h 2 St1perl1eat input: q s up e rb eater = ID 6 ( h 7 11 6 ) Absorber heat rejection: qab so rb e r = m1h1 m1 2 h1 2 m 9 h 9 Cooling capacity: q coo l = m g (h 9 hs)

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Turbine work output and pump work input: Wn et = WtWp The thermal efficiency is: W net + q coo l 11 = q sup erberter + q boi I er 6.4 Results and Discussion 1. Effect of turbine inlet pressure 119 With boiler temperature at 400 K and co11denser temperature at 360 K, figure 6-1 shows thermal efficiency changes witl1 tw bine inlet pressttre and ammonia mass fraction. The turbine exit pressure is maintained at 2 bar Figure 6-2 shows that vapor production goes linearly down as the turbine inlet pressure increases. Figure 6-3 s hows that turbine power output goes almost linearly down as the pressure increases, this figwe matches figure 6-2. It is known that the enthalpy d1op across the turbine is increased as the presstire ratio increases. But tl1e enthalpy gains from high pressuie ratio do not make up the vapor flow rate drops so the turbine work output decrease s. Cooling capacity increases frrst as the pressure goes up Then due to the low vapor flow rate the cooling capacity goes down at a pressure of about 28

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120 bar. Figure 6-4 shows this trend The maxim1un point of cooling capacity cl1anges with the basic solution ammonia mass fraction. It occtrrs at a higher turbine inlet presstlfe for a higher ammonia mass fraction. Although turbine work output decreases as the pressure increases, the thermal efficiency goes 11p fir s t to a maxin1um and then decrease s This result is s hown in figure 6-1. This figUI e is s in1jlar to figure 6-4 s howing the cycle cooling capacity, however the maximum point of thermal efficiency does not coincide with the maximum cycle cooling capacity. The ma xim um thermal efficiency increase s as the ammonia mas s fraction increases. There is a limit to the increase in ammonia composition at a given absorber pressure and temperature. In a later section, the limitation of the absorber condition on the cycle perfortnance will be discussed 2. Effect of boiler temperatUIe The effe c t of boiler temperature is shown in figures 6-5 to 6-8 at a turbine pre ss ure ratio of 12. 5, a condenser temperature of 360 K and a su perheater temperature of 410 K. Since the tUI bine pressure ratio and inlet temperature are fixed the enthalpy drop will remain the same regardless of the boiler temperature. What is affected by the boiler temperature i s the vapor flow rate. Figure 6-6 s hows that the vapor flow rate goes up almost linearly as boiler temperature goes 11p. It i s easy to explain this re s ult since the higher the boiler temperature the more vapor will be generated. Consequently turbine work output and cooling capacity follow the vapor flow rate changes. Curves of turbine

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121 work output in figure 67 and cooling capacity in figure 6-8 show trends similar to the curves of vapor flow rate in figure 6-6. The heat input increases rapidly as the boiler temperature increases. So the thetmal efficiency will reach a limit even though the turbine power output and cooling capacity increase. To chai1ge this limit tl1e condenser temperature ha s to increase as the boiler temperature goes up so that n1ore vapor will remain available to the turbine. 3. Effect of condenser temperature The condenser temperature controls the vapor ammonia concentration. Low condenser temperatw e will condense more moisture from the vapor thereby increasing the ammonia concentration vapor and vice versa. The advantage of low condenser temperature is that the system will produce ammonia vapor with very small amount of moisture so that the vapor can be allowed to d1op to low temperatt1re in turbine. The disadvantage i s that the vapor flow rate will also drop. Figure 6-9 shows tl1at the cooling capacity dtops as the condenser temperature increases. There is no cooling available when the condenser ten1peratwe is greater than 390 K. Figures 6-10 and 6-11 show that the vapor flow rate and turbine work output increase as tl1e condenser temperature goes up. Figure 6-12 shows the change it1 thermal efficiency with the condense r temperature, which is due to the combined effect of tl1e results shown in figuies 6-9 to 6-11. In figure 6-12, the tl1ermal efficiency drops fust as the condenser temperature increa ses, but the efficiency increases when condenser temperature i s greater than 390 K where no cooling capacity is available. When the

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122 condenser temperatu1e is less than 3 90 K the cooling capacity drops faster than the h1rbine work output increases, so the thermal efficiency decreases while the turbine work output increases. When conde11ser temperature is greater than 390 K no cooling capacity is available, the thermal efficiency increases as the turbine work output increases. 4. Effect of superheater temperature Figure 6-13 shows that thermal efficiency drops first and then goes up as the superheat temperature increases. Vapor flow rate is not affected by the superheat temperature, as can be seen from figure 6-14. From figure 6 15, it is expected that turbine work output would increase with higher superheat temperature. The cooling capacity drops as the superheat temperature increases as shown in figwe 6-16. There is no cooling capacity available when the superheat temperature is greater than 4 70 K The reason is that the turbine inlet vapor entropy is higher at a higher inlet temperature, with the same pressure ratio, therefore the turbine exit temperature is higher also. In a conventional Rankine cycle, the thermal efficiency increases as the superheat temperature increases since most of the superheat is converted to work ot1tput. In the novel cycle, cooling capacity is a factor in ther1nal efficiency. With an increase in superheat temperature, the cooling capacity drops steeper than the increase in turbine work output. That is why the therrr1al efficiency drops steadily against the superheat temperature. However, the thermal efficiency increases when the superheat temperature is greater that 470 K where the cycle stops providing coo l ing capacity.

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12 3 5. Effect of absorber temperature The absorber in the proposed cycle act s as a condenser in a conventional Rankine cycle. The absorber temperattrre is decided by the cooling media. The lower the ab s orber temperature tl1e higher the thermal efficiency will be In the propo s ed cycle with the same ammo11ia concentration the turbine exit pre s sure has to be increased as the absorber temperature increases in order to condense the solution Figures 6-1 7 to 6-20 show the effect of absorber te1npe1 ature for an ammonia mass fraction of 0 5 When the ab s orber temperature is 3 2 0 K there is no cooling effect. At 300 K no coolin g effect is ob s erved when the twbine inlet pressure is less than 2 5 bar. 6 Other con s iderations From figure 6-17 the therrr1al efficiency drops s ubstantially when tl1e ab s orber temperature increa s es at 0.50 ammonia ma s s fraction. At a high absorber temperature ab s orber pre ss ure ha s to be maintained at a high level in order to condense the ammonia water mixture this require s a higher turbine exit pressure which bring s the thermal efficiency down. In order to operate at a low turbine exit pressm e and consequently a low turbine exit temperature the ammonia ma ss c oncentration of the ba s ic solution must be low al s o A lower ammonia concentration s olution ha s a higher boiling temperature. Figure 62 1 shows the effect of turbine inlet pre ss ure on the thermal efficiency for ammonia concentrations of 0.20 0 25 0. 3 0 and the conesponding turbine exit pressure that would allow c ondensation in the ab s orber Ba s ic s olutions with 0.25 and 0 30 ammonia mass fraction are able to maintain 16 % -18 % thermal efficiency while a ba s ic

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124 solution with 0.20 ammonia 1nass fraction performs poorly. Figttres 6-22 and 6-23 show the vapor flow rate and turbine work output respectively at the conditions of figure 6-21. Figure 6-21 may not reflect the best perfor1nance range for each ammonia mass fraction in the basic solution. In fact, the basic solution with lower ammonia mass fraction performs well in a lower pressure range. In figtrre 6-21, it can be told that which ammonia mass fraction in the basic solution is before right at and after its best operation range. The orde1 in this case is 0.3, 0.25 and 0.2 of anunonia mass fraction in tl1e basic solution. 6.5 Conc l usion A combined power / cooling cycle using ammonia-water mixtmes as a working fluid is proposed. The cycle is a combination of the Rankine and absorption refrigeration cycles. It will not only produce power bttt also provide certain amount of cooling. Initial simulation results show that the power output is limited by cycle pressme and temperature. Thi s cycle certainly has flexibility for various applications. We can have a multi-stage turbine system for high pressttre and temperature applications. For multi stage expansion systetn, we can discard condenser and let the ammonia-water mixture go through the expansion directly Because of high pressure and temperature ammonia water mixture will still be in a vapor state after the first stage turbine or we can condense some of the moisture at each stage. That will allow t1s to expand the working fluid to very low temperature while maintaining condensation at less than 10 % level in each turbine stage.

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>-. a.> ..... <) a.> ...... s 0.) ..c E--c 26 2 4 22 20 18 16 T a b so rb e r = 2 80 K T su perh e at = 410 K T bo il e r = 400 K T co nd e n se r = 36 0 K P l o w = 2 bar e X = 0.47 -aX = 0 50 A X = 0 53 125 14 --1-~ -~~ ~-~ -~ -~----l 16 18 20 22 24 26 28 30 32 34 Turbine inlet pre ss ure ( bar ) Figure 6-1 Effect of turbine inlet pre ss ure on thermal efficiency

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0 40 0 35 0 30 8 s 0.25 c,j 0 0 20 '-< 0 ro > 0 15 0 10 0.05 16 T 280 K T = 410 K T = 400 K abso r ber superheat boiler T 360 K p 2 bar co nd e n ser low 18 20 22 24 26 28 Turbine inlet pres s ure (bar) e X = 0 47 -IIX = 0.50 .t. X = 0 53 30 32 Fi g ur e 6 2 Effect o f turbine inlet pre ss ure on vapor flow rate 1 2 6 34

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120 100 --oJ) c 80 +-' ;::, & ;:j 0 0 60 Q) 9 .D ;:j 40 20 16 T 280 K T = 410 K T = 400 K abso rbe r s u pe rh ea L boi l e r T co nd e n se r = 36 0 K P 1 o w = 2 bar 18 20 22 2 4 2 6 28 Turbin e inl e t pr ess ure ( bar ) I X = 0.47 --X = 0.50 6 X = 0 5 3 30 32 Fi gu re 6-3 Effe c t of turbine inlet pre ss ure o n turbine work o utput 127 34

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1 2 8 T 280 K T = 410 K T = 400 K absorber superheat bo il er T = 360 K p = 2 bar co nd enser l ow 30 e X = 0 47 -IIX = 0.50 25 X = 0.53 ,.-... 20 bJ:) -..__ c ..... 15 CJ "1 Clj u bJ:) .s ,......, 0 0 10 u 5 o ~--~--------~-----~--~--~-----1 16 18 20 22 24 26 28 30 32 34 Turbine inlet pres s ure (bar) Figure 6 4 Effect of turbine inlet pre s sure on cooling capacity

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24 22 20 >-, <.} Q..) 18 <.} 4--t Q..) s i-. 16 Q..) ..c E--4 14 12 10 370 T ab so rb e r = 28 0 K T s uperhea t = 4 lO K T co nde n s er = 36 0 K p hi g h = 25 bar P i o w = 2 bar e X = 0.47 -aX = 0 50 A X = 0 53 380 390 400 410 420 B o iler temperatur e ( K ) Figure 6 5 Effect o f boiler temperature o n thermal efficiency 1 2 9 430

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0 .3 5 0 .3 0 0 2 5 s \0 S 0 20 0 10 0 05 0 00 3 7 0 T a b so rber = 28 0 K T su perh ea t = 41 O K T co nd e ns e r = 36 0 K p hi g h = 25 bar P 1 o w = 2 bar e X = 0 47 --X = 0 50 __,._ X = 0 53 3 8 0 3 90 400 410 420 B o iler t e mp e ratur e (K) Fi g ur e 6 6 Effe c t o f b o il e r t e mp e r a ture o n v ap o r fl ow rat e 1 30 430

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,,,......_ bJ:) c ..... & ;:::s 0 0 0.) .9 .,D '""' ;:::s E-c 140 120 100 80 60 40 20 T absorber = 28 0 K' T s uperheat = 41 O K T condenser = 3 6 0 K P rugh = 25 bar ~ ow = 2 bar e X = 0.47 --X = 0.50 .._ X = 0 53 1 31 0 --+---,-----,------,------,-----,------1 370 380 390 400 410 420 430 Boiler temperature (K) Figure 6-7 Effect of boiler t e mperature on turbine w o rk output

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,,-... '-" .... ....
PAGE 143

,......._ bO >-. c..) 0.. c..) bO .8 0 0 u T ab s o r ber = 28 0 K T superheat = 41 O K T boiler = 4 00 K ph igb = 25 bar Pi o w = 2 bar 133 30 --------------------------, 25 20 15 10 5 0 340 350 360 370 380 Conden s er temperature ( K ) e X = 0.47 -IIX = 0.50 X = 0.53 390 400 Figure 6 9 Effect of condenser temperature on cooling capacity 410

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0.30 0.28 0.26 8 -. 0.24 \0 8 0.22 0 l;:: H 0.20 > 0.18 0.16 0.14 340 T b b = 280 K, T h c = 410 K, T boiler= 400 K a sor er s uper ea p hig h = 25 bar, P iow = 2 bar e X = 0.47 -ItX = 0.50 X = 0.53 350 360 370 380 Condenser temperature (K) 390 400 Figure 6 10 Effect of condense1 temperature on vapor flow rate 134 410

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135 T = 280 K T = 410 K T = 400 K absorber superheat boiler p high = 2 5 bar P 1ow = 2 bat 120 e X = 0.47 110 ---X = 0 50 A X = 0 53 100 --OJ) --90 ..... ;:I & ;:I 0 1-, 0 80 <1) s .D 1-, ;:I 70 60 50 340 350 360 370 380 390 400 410 Condenser te1nperature (K ) Fi g ure 6 11 Effect o f condenser temperature o n turbine work o utput

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1 3 6 T absorber = 28 0 K T supe r heat = 41 O K T boile r = 4 00 K Pl h = 25 bar n = 2 bar 11 g rt ow 23 22 I X = 0.47 -aX = 0.50 A X = 0 53 21 ;;:,,-_ 20 C.) (1.) ..... C.) !+:: <.+-. 19 (1.) ....... e Q) 18 17 16 15 340 350 360 370 380 390 400 410 Conden s er temperature (K) Figure 6 12 Effect of conden s er temperature on thermal efficiency

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23 22 2 1 >-, 8 Q.) 20 .... CJ b:= Q.) s I-< 19 Q.) ..cl 1 8 17 16 380 T absorber = 28 0 K T boiler = 4 00 K T condenser = 36 0 K P high = 25 bar P 10 w = 2 bar X = 0 47 --X = 0 50 6 X = 0 53 400 420 440 460 480 500 Superheat te1nperature (K) 1 37 520 Figure 6 13 Effect of s up er heat temperature o n thermal efficiency

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0 .3 0 0 28 0.26 ...... 8 0.24 s Q..) ..... 0 .22 0 H 0 ~0 20 > 0 18 0 16 0.14 380 T absorber = 28 0 K T boiler = 4 00 K T condenser = 36 0 K P high = 25 bar P 1 0 w = 2 bar X = 0 47 --X = 0.50 X = 0.53 400 420 440 460 480 500 Superheat temperature (K ) Figure 6-14 Effect of s uperheat temperature on vapor flow rate 138 520

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130 120 110 00 100 c ..... & ;:j 0 90 H 0 Q) s 80 .0 1--1 ;:j 70 60 50 380 T = 280 K T = 400 K T = 360 K absorber boiler condenser P bigh = 25 bar P 10 w = 2 ba1 X = 0 47 -9X = 0 50 .6 X = 0.53 400 420 440 460 Superheat temperature ( K ) 480 500 139 520 Figure 6 15 Effect of s uperheat temperature on turbine work output

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14 0 T = 280 K T = 400 K T = 360 K absorber boiler co nden s er P high = 25 bar p low = 2 bar 3 0 X = 0 47 25 -aX = 0.50 X = 0 53 20 ,,,-.... 0/) "15 0 (.) (.) 10 0/) ..... 0 0 u 5 0 380 400 420 440 460 480 500 520 Superheat temp e ratur e (K ) F i g ure 6 16 E ff ec t o f s up e rh e at t e mp e rature o n coo lin g c apa c i ty

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(.) Q) C) !+:: (I) Q) ,..c::: 24 22 2 0 18 16 14 12 10 T superheat = 4 lO K T boiler = 4 00 K T condenser = 36 0 K P = 2 bar x = 0 50 low T absorber = 2 8 0 K --T absorber = 3 00 K T = 320 K absorber 14 1 8 --+------,-----,----...-----...------.-----.---~-~-----l 16 18 20 22 24 26 28 30 32 34 Turbine inlet pre s s u re (bar) Fi g ure 6 17 Effect of ab s orber temperature on thermal efficienc y

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0.40 0.35 0.30 ...... E -s 0.25 Q) ....;I ro 0 0.20 ~ H 0 0.. ro > 0.15 0.10 0.05 16 T superheat = 41 O K T boiler = 4 00 K' T condenser = 3 6 0 K P = 2 bar x = 0 50 l ow 18 20 22 T absorber = 28 0 K T ab so rber = 3 00K T absorber = 32 0 K 24 26 28 Turbine inlet pressure (bar) 30 32 Figure 6 18 Effect of absorber temperature on vapor flow rate 142 34

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110 100 90 ,,-.... OJ) 80 ..._,, & 70 ;:j 0 60 H 0 0 S ,D 50 ;:j 40 30 20 16 T = 410 K T = 400 K T = 360 K superheat bo il er co nd e n ser P 1ow = 2 bar X = 0. 50 18 20 22 24 T absorber = 28 0 K T absorbe r = 3 00 K T absorber = 32 0 K 26 28 30 Turbine inlet pre ss ure (bar) 143 32 34 Figure 6 19 Effect of absorbe1 temperature on turbine work output

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144 T = 410 K, T = 400 K T = 360 K superheat bo il er condenser P = 2 bar x = 0. 50 low 25 T = 280 K absorber 20 T = 300 K abso r be r T = 320 K absorber ,-... bO 15 ....._, c ~ 10 (.) ro 0.. ro <) .... 0 0 5 u 0 16 18 20 22 24 26 28 30 32 34 Turbine inlet pressure (bar) Figure 6 20 Effect of absorber temperature o n cooling capacity

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1 8 16 14 ;;;:,-.., u c:= Q) ..... u lE 12 Q.) ro Q) ..c: 10 8 17 x = 0 20 l? o w = 1.03 bar -ax = 0 25 l? o w = 1 5 bar X = 0 .3 0 l? o w =2. 1 bar T ab so rber = 320 K T = 460 K sup e rh e at T b 1 = 440 K 0 1 e r T co nd e n se r = 41 O K 18 19 20 21 22 23 24 2 5 Turbine inlet pre ss ure ( bar ) F i gu re 6 21 Effe c t of turbin e inlet pre ss ur e on thermal e fficienc y f o r different turbin e exit pre ss ure 145 26

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0.25 0.20 ,-, s -0.15 8 0 1-. 0 1-. 0.10 0 > 0.05 0.00 17 I X = 0.20, I? ow = 1.03 bar T absorber = 320 K --X = 0.25, l? ow = 1.5 bar T = 460 K supe rh eat x = 0.30 B ow = 2.1 bar T boiler = 440 K T = 410 K condenser 18 19 20 21 22 23 24 25 Turbine inlet pressure ( bar) Figure 6 -22 Effect of turbine inlet pre ss ure on vapor flow rate for different turbine exit pressure 146 26

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80 70 20 10 17 147 x = 0 20 I? o w = 1.03 bar -11x = 0 25 I? ow = 1 5 bar A x = 0 30 I? ow =2 .1 bar T absorber = 320 K T = 460K superheat T b 1 = 440 K 01 er T condenser = 41 O K 18 19 20 21 22 23 24 2 5 26 Turbine inlet pre ss ure (bar) Figure 6 23 Effect of turbine outlet pre ss ure on tu1bine work output f o r different turbine exit pre ss ure

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CHAPTER 7 CONCLUSIONS AND FUTURE WORK This thesis consists of two different but stro11gly related topics: the1modynamic properties of ammonia-water mixtures and a study of a novel cycle with multicomponent working fluid integrated with absorption refrigeration cycle. The thermodynamic analysis entails the thermodynamic properties of ammonia-water mixtures, which are the working fluids of our proposed power system. The thermodynamic properties of ammonia-water mixtures are of fundamental importance for the proposed power cycle analysis. A few models for the thermodynamic properties of these mixtures have been proposed. The criteria for a successful computer program for predicting the thermodynamic properties is accuracy, a wide range of conditions, reliability and computing time. Therefore the previot1s works have been critically reviewed and a new approach is developed using Gibbs free energy method. This method is based on extensive experimental data, avoiding some suspect assumptions. However, because of the nattrre of the experiments and the data from different sources, it is necessary to fu1iher investigate the coefficients of the computing equation. Theoretical approach should be investigated in order to validate the experimental data. This sounds odd. The reason for doing this is that the reported 148

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149 experimental data were taken by different individuals at different times and with different equipment resulting in lack of consistency. A generalized equation of state method by Park and Sonntag (1990b) is so far the most complete theoretical approach to calct1late the thermodynamic properties of ammonia-water mixtures. Although they claim that this method provides a con s istent way without combining or mosaicking equilibrium data and without discontinuities or gaps some researchers have expressed (Ibrahim and Klein 1993)their doubts about this method in the high presswe range because of lack of experimental data. The thermodynamic properties of ammonia-water mixture based on the model used in this study were compared with most recent experiment data. The results agree with the experimental data very well This model was based on Macriss et al. (1964) data developed by Schulz ( 1971 ). Zieger and Trepp (1984) extended Schulz s con elations to a higher temperature and pressure range. Using Gillespie et al. (1987) VLE data Ibrahim and Klein (1993) generated correlations for the liquid mixtures. In the 90s, several researchers in Germany have condt1cted measurement on ammonia-water mixtures. They are Harms-Watzenberg (1995) Prup and Wagner (1995), Kurz (1994) Peters (1994) and Zimmermann (1991) Using these 1 ecent data, it is possible to develop new correlations to extend the ammonia-water mixtures properties data to a hig}1er temperature and pressure range. The second part of this thesis i s an investigation of a new power cycle proposed by Goswami ( 199 5, 1996). It is a new concept of a power cycle. Kalina cycle which uses ammonia-water mixture as a working fluid is somewhat siinilar to this cycle. But there is

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1 50 a major difference. The heat rejection of our cycle is a part of absorption refrigeration cycle and the working fluid for the power generation(i.e. fluid flowing through the turbine) is pure ammonia. Kalina cycle tends to apply to a higher temperatt1re source (above 700 K) while the proposed cycle focuses on low temperature application (about 500 K) producing both power and refrigeration. A second law analysis method has been developed for a binary system. Most s tt1dies in the literature neglect the effect of the composition of a binary mixture in the second law analysis The method used in this study incorporates the effect of ammonia ma s s fraction on exergy calculations The proposed cycle has been compared with Rankine cycle quantitatively and qualitatively The results s how that ammonia-water cycle has a 15 % -20 % advantage over a Rankine cycle. An ammonia-water cycle may not be favorable over a Rankine cycle if the type of heat source is not considered. A Rankine cycle is excellent with a con s tant temperature heat s ource. Unforttmately most heat sources have a variable temperature. A s imulation program has been used for the analysis of the proposed s y s tem Simulation of the boiling and condensation processes taking place in the boiler / rectifier and absorber and the a s sociated heat transfer processes has been also conducted Result s from the s imulation study have been pre s ented in Chapter 6. The effect s of ma s s concentration of ammonia in the s trong and weak ammonia-water mixture s, the temperatures and pressures in the turbine absorber and the boiler on the cycle performance ha v e been studied

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The first part of this thesis in which the thermodynamic properties of ammoniawater mixtures are investigated lay down a solid foundation for the second part of this thesis. Accurate property data of the mixtures is the key for the system simulation analysis. 151 An experimental study of the proposed syste1n is needed for future study. The experimental study will be conducted on a system based on a single stage turbine. Since the turbine design, the boiler size and the absorber design will limit the operational conditions, the data obtained will be limited. However, even a limited amount of data will be helpful in validating the results obtained fi om the simulation program.

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LIST OF REFERENCES Alefeld, G., 1989 ''Second Law Analysis for an Absorption Chiller," Newsletter of the IEA Heat Pump Center, Vol. 7 No. 2, pp. 54-57. Amrane, K. and Radermacher, R., 1994 '' Second-Law Analysis of Vapor Compression Heat Pumps with Solution Cu:cuit," J. Eng. for Gas Turbines and Power, Vol. 116, pp. 453-461. Anand D. K. Lindler K. W., Schweitzer, S. and Kennish W. J ., 1984 '' Second Law Analysis of Solar Powered Absorption Cooling Cycles and Systems ," J. of Solar Energy Eng Vol 106, pp. 291-298. Anderson J. H., 1989 ''The Anderson Power Cycle," Pollution Engineering, Vol. 21, pp. 94-97. Apho1nratana, S. and Eames, I. W., 1995 ''Thermodynamic Analysis of Absorption Refrigeration Cycles using the Second Law of Thermodynamics Method,' Int. J. Refrig., Vol 18, No.4, pp 244-252. Avery, K. A. 1980 ''An Evaluation of the Use of the Binary Mixture 'Ammonia-Water' as the Heat Exchange Medium for Power Generation in the Ocean Thermal Energy Conversion Power Plant,'' Master Thesis, University of Rhode Island. Babcock & Wilcox, 1978 ''Steam/Its Generation and Use," 39th edition. New York, Babcock & Wilcock. Bannister R. L. and Silvestri G. J. Jr., 1989 '' The Evolution of Central Station Turbines,'' Mechanical Engineering, Vol. 111, pp. 7078. Bejan A., 1988 ''Advanced Engineering Thennodynamics," New York, John Wiley and Sons. Best, R., Islas, J. and Martinez, M. 1993 ''Exergy Efficiency of an Ammonia-Water Absorption System for Ice Production ," Applied Energy, Vol. 45, pp. 241-256 Bosnjakovic, F., Knoche, K. F. and Stehmeier D. 1986 ''Exergetic Analysis of Ammonia/Water Absorption Heat Pumps ,'' Computer-Aided Engineering of Energy Systems, AES-Vol. 3, pp. 93-104. 152

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153 Duffy J. W., 1964 ''Power, Prime Mover of Technology," Bloomington, IL, McKnight & McKnight. Egrican, N., 1988 '' The Second Law Analysis of Absorption Cooling Cycles, Heat Recovery Systems & CHP, Vol. 8, No. 6 pp. 549-558. El-Sayed Y. M. and Trib11s M. 1985a '' The1modynamic Properties of Water-Ammonia Mixtures: Theoertical Implementation for Use in Power Cycle Analysis ," ASME Special Publication, AES-Vol. 1, pp. 89-95. El-Sayed Y. M. and Tribus M ., 1985 b '' A Theoretical Comparison of the Rankine and Kalina Cycles," ASME Special Publication, AES-Vol. 1, pp. 97-102 Foster-Pegg R. W ., 1978 ''Steam Bottoming Plants for Combined Cycles ," J Eng. for Power, Vol. 100 pp. 124-130. Gaffert G. A., 1946 '' Steam Power Stations," New York, McGraw-Hill. Gillespie, P. C., Wilding W V. and Wilson G. M. 1987 '' Vapor-Liquid Equilibrium Measurements on the Ammonia-Water System from 313K to 589K," AICHE Symposium Series Vol. 83, No. 256, pp. 97-127. Goswami, D. Y. 1995 "Solar Thermal Power-Status and Future Directions," Proceedings of the 2nd ASME-ISHMT Heat and Mass Transfer Conference, Mangalore, India, Dec 1995. Goswami, D. Y. 1996 Plenary Lecture at the ENERGEX'96, Beijing, China, June 1996 To appear in Energy Sources Journal Harms-Watzenberg, F. 1995 '' Messung und Konelation der thermodynamischen Eigenschaften von W asser-Ammoniak-Gemischen'' F ortschr. -Ber VD I-Ver lag Dtisseldorf VDI 3, No. 380. Haar, L. and Gallagher J. S. 1978 '' Thermodynamic Properties of Ammonia ,'' Journal of Physical and Chemical Reference Data, Vol. 7, pp. 635792. Herold K. E Han K. and Moran M. J 1988, ''AMMW AT: A Computer Program for Calcu latin g the Thermodynamic Properties of Ammonia and Water Mixtures Using a Gibbs Free Energy Formu lation ," ASME Proceedings Vol. 4, pp. 65-75. Herold, K. E. and Moran, M. J ., 1987 '' Recent Advances in the Thermodynamic Analysis of Absorption Heat Pumps ,'' The Fowih Inte1national Symposium on Second Law Analysis of Thermal Systems Rome, Italy May, 1987, pp. 97-103.

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1 54 Ibrahim 0. M. and Klein S. A. 1993 '' Thermodynamic P1 operties of Ammonia-Water Mixtures ASHRAE Transaction s Vol. 99 pp.1495-1502. Ibrahim M. B. and Kovach R M ., 1993 '' A Kalina Cycle Application for Power Gereration Energy Vol. 18 No 9 pp. 961-969 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 ,'' ASME Paper 83-JPGC-GT-3. Kalina A I. 1984 '' Combined Cycle Syste1n with Novel Bottoming Cycle ,'' ASME J. Eng Ga s Turbine s and Power Vol. 106 pp 7377 4 2 Kalina A. I. and Tribus M. 1990 '' Advance s in Kalina Cycle Technology ( 1980-1991 ) : Part I Development of a Practical Cycle ," Ene1 gy for the Transition Age Proceedin gs of the Florence World Energy Research Symposium Firenze Italy pp. 97-110. Kalina A. I. and Tribus M. 1990 '' Advan c e s in Kalina Cycle Technolo gy( 1980-1991 ) : Part II Iterative Improvements ' Energy for the Transition Age, Proceedings of the Florence World Energy Research Symposium, Firenze, Italy, pp. 111-124. Kalina A. I. Tribus M. and El-Sayed Y. M. 1986 '' A Theoretical Approach to the Thermophysical Properties of Two-Miscible-Component Mixtures for the Purpose of Power-Cycle Anal y sis, ASME Paper 86-WA/HT5 4 Koehler W J. Ibele W. E ., Solte s, J and Winter E. R ., 1988 '' Availability Simulation of a Lithium Bromide Absorption Heat Pump ,'' Heat Recovery System s & CHP Vol 8 No. 2 pp. 15 7 -1 7 1 Koremenos D. A. Rogdakis E D and Antonopoulos K. A. 1994 '' Cogeneration with Combined Ga s and Aqua-Ammonia Ab s orption Cycles ,'' In Thermodynamics and The Design Analysis and Improvement of Energy Sy s tems, (Ed.) R.J Krane AES-Vol 33 New York AS:ME pp. 231-238. Krakow K. I. 1991 '' Exergy Analysis: Dead-State Definition ," ASHRAE Transactions Vol. 97 pp. 3 2 83 36. Kurz F. 1994 ''U ntersuchungen zur simultanen Losung von Ammoniak und Kohlendioxid in Wasser und s alzhaltigen wa~rigen Losungen '' Dissertation Univer s itat Kaiserslaute1n Lorenz, V. H ., 1894 '' Die Ausnutzun g der Brennstoffe in den Kiihlmaschinen ,'' Zeit s chrift fiir die gesammte Kfilte-Industrie Vol. 1 pp. 10-15.

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155 Macriss, R. A., Eakine, B. E., Ellington, R. T. and Huebler, J. 1964, ''Physical and Thermodynamic Properties of Ammonia-Water Mixtures,'' Chicago Institute of Gas Technology, Research Bulletin No. 34. Maloney, J. D. and Robertson R. C., 1953 ''Thermodynamic Study of Ammonia-Wate1 Heat Power Cycles,'' ORNL Report CF 53-8-43, Oak Ridge TN. Marston C.H., 1990 ''Parametric Analysis of the Kalina Cycle,'' J. Eng. for Gas Turbines and Power Vol. 112, pp. 107-116. Marston C.H., 1990 ''A Family of Ammonia-Water Adjustable Proportion Fluid Mixtwe Cycles," Proceedings of the 25th h1tersociety Energy Conversion Engineering Conference, Vol 2, pp. 160-165. Milora S. T. and Tester J. W., 1976 ''Geothermal Energy as a Source of Electric Power Thermodynamic and Economic Design Criteria," Cambridge, The MIT Press. Moran M. J. and Sciubba, E., 1994 ''Exe rgy Analysis: Principles and Practice, J. Eng. for Gas Turbines and Power Vol. 116 pp 285-290. Mumah, S. N Adefila, S S. and Arinze E. A., 1994 ''Properties Generation ProcedUIe s for First and Second Law Analyses of Ammonia-Water Heat Pump System, Ene1 gy Convers. Mgmt. Vol. 35, No. 8 pp. 727-736. Park Y. M. and Sonntag R. E., 1990a '' A Preliminary Study of the Kalina Power Cycle in Connection with a Combined Cycle System ," Int. J. of Energy Res., Vol. 14 pp. 153-162. Park Y. M. and Sonntag R. E., 1990b ''Thermodynamic Properties of Ammonia-Water Mixtures: A Generalized Equation-of-State Approach," ASHRAE Transactions Vol. 96 pp. 150-159 Peng D. Y. and Robinson D. B. 1976 '' A New Two-Constant Equation of State ," Fundementals of Industrial Engineering Chemistry, Vol. 15 No. 1, pp. 59-64. Pe1man E. P ., 1901 ''Vapour Pressure of Aqueous Ammonia Solution ," Part I, J. Chem. Soc., Vol 79,pp. 718 725; Peters, R 1994 '' Dampf-Fltissgkeits-Phasengleichgewichte im Stoffsystem Ammoniak Wasser-Lthiumbromid, '' PhD thesis Universitat Siegen. Reid R. C., Prausnitz J. M. and Poling B. E., 1987 '' The Properties of Gases and Liquids," 4th ed. New York McGraw-Hill. Rogdakis E. D. and Antonopoulos K. A ., 1991 '' A High Efficiency NH 3 /H 2 0 Absorption Power Cycle," Heat Recovery Systems Vol. II pp. 263-275.

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BIOGRAPHICAL SKETCH Feng Xu was born on June 11, 1967 in Quanzhou city, P.R. China. He completed his bachelor's degree in flying vehicle design and applied mechanics in July 1988 and master's degree in low temperature engineering and refrigeration technology in January 1991 from Beijing University of Aeronautics and Astronautics Beijing, P.R. China, where he met his wife. Feng Xu enrolled in the Department of Mechanical Engineering, University of Florida in Spring of 1994 working for his Ph.D. degree. His wife also got her Ph.D. degree from the Department of Aerospace Engineering, Mechanics and Engineering Science University of Florida. During their stay at UF, they had their first child, Tom. 157

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality as a dissertation for the degree of Doctor of Philo s ophy. D. Y gi Goswami Chairman Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ( C. H s iel1 Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to accept a ble standards of scholarly presentation and is fully adequate, in scope and quality as a dissertation for the degree of Doctor of Philosophy. ( E Peterson ssociate Professor of Mechanical Engineering

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scl1olarly presentation and is fully adequate, in scope and qt1ality as a dis se rtation for the degree of Doctor of Philosophy. Sherif A. Sherif Associate Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it confortns to acceptable standards of scholarly presentation and is fully adequate in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Barney L. peha Professor of Industrial and System s Engineering This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August, 1997 Winfred M. Phillips Dean, College of Engineering Karen A. Holbrook Dean, Graduate School

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1780 1 9 9.7 .)( 4q9 UNIVERSITY OF FLORID A II I 1111111 11 111 I 3 1262 08554 9078


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