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Theoretical Analysis of Solar Driven Flash Desalination System Based on Passive Vacuum Generation

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THERORETICAL ANALYSIS OF SOLAR DRIVEN FLASH DESALINATION SYSTEM BASED ON PASSIVE VACUUM GENERATION By SHALABH CHANDRA MAROO A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by SHALABH CHANDRA MAROO

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To the loving memory of my grandfathe r and grandmother, whom I shall always remember

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ACKNOWLEDGMENTS I would like to express my gr atitude and respect towards my advisor, Prof. D. Yogi Goswami, for his invaluable suggestions a nd comments during the course of this work, without which it would have been an exercise in futility. I would also like to than k my committee members for their comments and help. Many thanks go to the staff working at the solar energy and energy conversion laboratory. The support and help of my fa mily are highly appreciated. iv

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TABLE OF CONTENTS page ACKNOWLEDGEMENTS....iv LIST OF TABLES.....vii LIST OF FIGURES..viii NOMENCLATURE....x ABSTRACT.xiii CHAPTER 1 INTRODUCTION AND LI TERATURE REVIEW... Introduction.. Desalination Processes.2 Multi-Effect Distillation (MED)..2 Multi-Stage Flash (MSF).3 Electrodialysis (ED).4 Reverse Osmosis (RO).5 Freezing Humidification-De humidification (HD)..9 Desalination using Heat Pumps.10 Thermal vapor compression (TVC)...11 Mechanical vapor compression (MVC).....11 Adsorption vapor compression (ADVC)...12 Absorption vapor compression (ABVC)...13 Solar Desalination..14 Indirect solar desalination systems....15 Direct solar desalination systems...18 2 PROPOSED DESALINATION SYSTEM Single-Stage System..23 Two-Stage System.24 v

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3 THEORETICAL ANALYSIS...27 Evaporator..27 Flashing Process.28 Concentrated Brine Column..30 Vapor Space...31 Condenser..33 Distillate Column...35 Pressure in the System...36 Boiling Point Elevation (BPE)...38 Heat Source....38 Pumping Power..41 Performance Ratio.....41 Method of Analysis Single-Stage...42 Two-Stage..44 4 RESULTS AND DISCUSSION45 Single-stage System with Consta nt Temperature Heat Source..46 Variation of Inlet Sa line Water Temperature. Variation of Saline Water Mass Flow Rate... Variation of Length of Condenser. Variation of Ambient Water Temperature. System Output Two Stage System with Constant Temperature Heat Source....51 Solar Collector Specifications....52 Single-stage System Coupled with Solar Collector...53 Two-stage System Coupled with Solar Collector..57 5 CONCLUSION AND FUTURE WORK..64 APPENDIX A PHYSICAL PROPERTIES...66 B COMPUTER PROGRAM FOR SINGLE-STAGE SYSTEM..70 C COMPUTER PROGRAM FO R TWO-STAGE SYSTEM...88 LIST OF REFERENCES.114 BIOGRAPHICAL SKETCH...119 vi

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LIST OF TABLES Table page 1.1 Energy consumption of some desalination processes 1.2 Types of solar collectors 1.3 Indirect solar desa lination systems16 1.4 Suggested variations in solar still..20 3.1 Nusselt number for laminar flow in circular tube annulus ...34 3.2 Concentration of main gases dissolved in sea water..37 3.3 Average values of k and C for 21 st day of each month for the United States vii

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LIST OF FIGURES Figure page 1-1 Schematic of a multi-effect distillation system 1-2 Schematic of a multi-stage flash system..4 1-3 Typical electrodialys is configuration...5 1-4 Schematic of a RO system...6 1-5 Schematic of indirect freezing method8 1-6 Schematic of the HD process.10 1-7 Schematic of thermal vapor compression system..11 1-8 Schematic of MVC Desa lination Process..12 1-9 Schematic of single-effect adso rption vapor compression system 1-10 Schematic of absorption vapor compression system 1-11 Schematic of a conventional solar still..19 2-1 Proposed single stage desalination system 2-2 Proposed two-stage desalination system 3-1 Schematic of flashing process 3-2 Schematic of the concentrated brine column.31 3-3 Control volume of vapor space..32 3-4 Horizontal annular flow.33 3-5 Control volume of the distillate column 4-1 Variation of output with inle t saline water temperature viii

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4-2 Variation of system pressure with inlet saline water temperature.47 4-3 Effect on distillate output with ch ange in saline water flow rate...48 4-4 System pressure variatio n with condenser length..48 4-5 Variation of system saturation temperature with ambient water temperature...49 4-6 Effect of ambient water temp erature on distillate output...49 4-7 Hourly output for single-stage system w ith constant temperature heat source.50 4-8 Hourly output for two-stage system with constant temperature heat source.51 4-9 Insolation on the tilted solar collector surface on May 21 at Gainesville, FL...53 4-10 Variation of single-stage system temper atures coupled with solar collector.54 4-11 Single stage system pressure c oupled with solar collector 4-12 Pressure change due to NC gases in single-stage system with collector...55 4-13 Water column height variation for single-stage coupled with solar collector...55 4-14 Hourly output of single stage system coupled with solar collector...56 4-15 Feed water temperature for two stag e system coupled with collector...57 4-16 Two-stage system pressure c oupled with solar collector..58 4-17 Saturation temperature curves for twostage system with solar collector.59 4-18 Condenser outlet temperature of two-st age system coupled with collector..60 4-19 Pressure increase due to NC gases in two-stage system w ith solar collector 4-20 Brine height in the first stage of the two-stage system with collectors.61 4-21 Brine column height in second stage of the two-stage system with collector...62 4-22 Hourly output from two-stage system with solar collector ix

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NOMENCLATURE A: Area of cross-section (m 2 ) BPE: Boiling point elevation ( o C) C: Sky diffuse factor C n : Sky clearness factor C ps : Specific heat of seawater (J/kg.K) C pv : Specific heat of vapor (J/kg.K) C pw : Specific heat of water (J/kg.K) D: Diameter (m) g: gravitational accel eration constant h: Enthalpy (J/kg), Heat transfer coefficient (W/m 2 .K) h fg : Latent heat of vapora tization of water (J/kg) h s : Hour angle I: Solar insolation intensity (W/m 2 ) i: Solar incidence angle k: Thermal conductivity (W/m.K), Atmospheric optical depth L: Latitude l: Longitude M: Mass (kg) M : Mass flow rate (kg/s) Nu: Nusselt number x

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n: Number of moles, Day of the year P: System pressure (Pa) PR: Performance ratio Pr: Prandtl number Q : Heat transfer rate between c ondenser and cooling seawater (W) R: Universal gas constant Re: Reynolds number T: Temperature ( o C) t : Differential time element (s) U: Overall heat transfer coefficient (W/m 2 .K) X: Salt concentration (g/kg) Greek Symbols : Solar altitude angle s : Solar azimuth angle w : Surface azimuth angle : Surface tilt angle s : Solar declination angle : Efficiency : Dynamic viscosity (Pa.s) : Kinematic viscosity (m 2 /s) : Density (kg/m 3 ) Subscripts xi

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a: Ambient b: Brine cs: Condenser surface c,in: Condenser inlet c,out: Condenser outlet d: Distillate ev: Evaporator water column i: Inner l: Liquid o: Outer ps: Distillate column s: Surface sat: Saturation sc: Solar collector sc,in: Solar collector inlet sc,out: Solar collector outlet sw: Seawater u: Useful v: Vapor vs: Vapor space v,eq: Vapor at equilibrium Superscripts t, : Value of the parameter at this time instant t+ t xii

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Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science THERORETICAL ANALYSIS OF SOLAR DRIVEN FLASH DESALINATION SYSTEM BASED ON PASSIVE VACUUM GENERATION By Shalabh Chandra Maroo May 2006 Chair: D. Yogi Goswami Major Department: Mechanic al and Aerospace Engineering An innovative solar driven flash desalina tion system is proposed. The system uses the natural forces of gravity and atmospheri c pressure to create a vacuum. Single-stage and two-stage concepts have been outlined. Th e main components include evaporator(s), condenser(s), collection tanks, heat source a nd seawater circulati on pump. Partial heat recovery is attained by first passing the feedwater through the condenser(s), followed by the heat source. Additional distillate output is obtained in the second stage of the twostage system without any extra heat additi on, since the high temperature brine from the first stage is passed and flashed in the second stage. Theoretical analysis of the single-stage and two-stage concepts is done for the system when coupled with constant temper ature heat source and solar collector. The single-stage and two-stage systems are s hown to produce 11.3 kg and 13.9 kg of water respectively in a 12 hour duration with a c onstant temperature heat source. When coupled with a solar collector of 1 m 2 area, a single stage system produces 5.54 kg of xiii

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water in 7.83 hours, while the two-stage system produces 8.66 kg in 7.7 hours. The performance ratios obtained, including the e fficiency of solar collectors, are 0.48 and 0.75 for a single-stage and two-stage system respectively, or 0.748 and 1.350 if only the useful heat collected by the so lar collector is considered. xiv

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CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW Introduction Global resources of freshwater are beco ming scarce and unevenly distributed with increasing population. The world population is growing approximately at a rate of 1.2 % annually resulting in a net addition of about 77 million people every year. The population is expected to increase to around 8.9 billi on by 2050 [1]. The earths water supply is nearly 1370 million km 3 out of which nearly 3% constitutes freshwater. Nearly 29 million cubic kilometers of freshwater is frozen in the form of glaciers and ice. Ground water, lakes and rivers together constitute just a little over 8 million cubic kilometers of freshwater. The critical water level to satisfy basic human needs is estimated to be 1000 m 3 /capita annually. It is proj ected that by 2050 about 1.7 billion people in 39 countries will fall below this level [2]. According to the World Health Organizat ion, the permissible limit of salinity in water is 500 parts per million (ppm) and for special cases up to 1000 ppm of total dissolved salts, while most of the water available has a salinity up to 10,000 ppm and seawater normally has a salin ity in the range of 35,000 45,000 ppm. Desalination has evolved over the past few decades as a pr omising technology to counteract the water scarcity. There are about 15,000 desalinati on plants around the world with a total production capacity of 32 million m 3 per day [3]. The conventional desalination technologies include multi-stage flash, multieffect distillation, reverse osmosis, electrodialysis and freezing. 1

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2 Desalination is an energy intensive pro cess. With the total installed capacity expected to increase drastically in the coming decades, the energy consumption for desalination will continue to rise and hen ce the amount of fossil fuel required will substantially go up. This trend does not match with the decreasing fossil fuel reserves. In terms of oil consumption, it is estimated that about 203 million tons of oil per year is required to produce 22 million m 3 per day of desalinated wa ter [3]. With conventional hydrocarbon fuel shortages being inevitable unl ess radical changes occur in demand or in the supply of non-conventional hydrocarbons [4], the energy water link cannot be overlooked. In addition, the usage of fossil fuel s continues to pollute the environment and adds to the cause of global warming. A feasible and promising solution is the use of renewable energy resources for desalination, as will be further discussed in this chapter. Desalination Processes The desalination processes can be broke n down into two parts: Phase change processes (which include multi-effect distillation, multi-stage flash, freezing, humidification-dehumidification) and Me mbrane processes (reverse osmosis, electrodialysis). The phase change pro cesses are economical for water having high salinity (10000-50000 ppm) whereas membrane pr ocesses are suitable for brackish water with salinity ranging between 1000-10000 ppm. Multi-Effect Distillation (MED) The distillation process is the oldest pro cess in desalination. Sea water, after being pre-heated by the heat recovery from the exi ting distillate, is introduced in the first stage of the system where some of it is evaporat ed by the motive steam from the external source (here depicted as the flash vessel in which the motive steam is produced). The

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3 vapor produced in the first stag e is used as the heating source in the next stage generating additional vapor while condensing itself to add to the distillate output. Vapor formation in the stages can be accomplished by either surf ace evaporation or by boiling. In order to attain boiling, the pressure maintained in each stage should be lower than the previous stage. Figure 1-1. Schematic of a multi-effect distillation system [3]. There have been variations in the dis tillation systems depending on the flowsheet arrangement and heat transfer configurations which can be broadly classified into the submerged tube, horizontal tube falling film and vertical tube falling film designs. The performance ratio of typical MED plants is about 10, and can reach as high as 12-14 [3]. Multi-Stage Flash (MSF) MSF is the most widely used desalination process in terms of capacity. The feed sea water is passed through a set of heat exchangers on the outside of which the vapor generated in each flash chamber is condensed, in turn pre-heating the feed sea water. The sea water is then heated up to a temp erature above the saturation temperature

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4 corresponding to the maximum system pressure by an external heat source (here shown as solar collectors). It then enters into the first stage th rough an orifice, and a small fraction of it flashes generating vapor. Th e subsequent stages are maintained at successively lower pressures using vacuum pumps. The brine from the first stage is injected into the second stag e causing additional flashing. This process is repeated throughout the plant. Figure 1-2. Schematic of a multi-stage flash system [3] A conventional MSF plant is divided into two sections: heat r ecovery section and the heat rejection system. The performance ratio of the MSF plant typi cally varies from 6 10 [3]. Electrodialysis (ED) Electrodialysis is an ion-exchange memb rane separation process. This process works on the principle that when electrical potential difference is applied to seawater separated by a certain configuration of selective membrane s, ions are transferred from the seawater thus reducing its salinity. A typical ED configuration is shown in figure 1.3. Feed seawater is passed through the sections separated by membranes from the bottom.

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5 The cation-exchange membrane (CEM) allows Na+ ions present in seawater to pass through, while the anion exchange membra ne (AEM) allows Clions thus reducing the salinity in sections (c). The concentration of dissolved salts in the seawater increase in sections (b), whereas electrode reaction products are present in secti ons (a). Such cells are arranged in stacks, therefore produc ing fresh water in sections (c). Figure 1-3. Typical electrodi alysis configuration [5]. In an actual electrodialysis plant, al ternating CEM and AEM are used. Inverters are used to reverse the polar ity of the electric field about every 20 minutes to prevent scaling. This is called electrod ialysis reversal (EDR) proce ss. Electrodialysis is more practical on feedwater with salinity not more then 6000 ppm due to the high energy requirements at higher salinity, and this process is not suitable to produce water containing less than 400 ppm of dissolved solids [3]. Reverse Osmosis (RO) When a pure solvent (water) and a soluti on (seawater) are separated by an ideal semi-permeable membrane (one that is perm eable to solvent but not the solute), the solvent passes through the membrane to the solution side. The transport happens due to

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6 the chemical potential driving force created by the presence of the solute. If a pressure greater than the osmotic pressure is applie d to seawater, pure wate r will pass through the membrane and can be collected. This is th e basis of desalination by reverse osmosis (RO). A schematic of the RO system is given in figure 1.4. Figure 1-4. Schematic of a RO system [3]. The separation of fresh water from the seawat er happens in an RO plant as depicted in the above figure. Theoretically, the only energy requirement is that to drive the pump. It can be also economically feasible to rec over the rejected brine energy with a suitable turbine. Such systems are called energy recovery reverse osmosis (ER-RO). The performance of the membrane and hence th e production rate of freshwater strongly depends on the following ma jor operating variables: a) Seawater Concentration With increasing seawater concentr ation, the osmotic pressure increases and hence greater pressure must be ap plied to the seawater side to attain the same fresh water production rate. Thus, RO is favorable over other processes in the desalination of brackish water. b) Operating Pressure Increase in the operating pressure increases the driving force for the solvent (water) and only marginally affects the driving force for solute (salt). c) Feed Flow Rate The primary effect of th e feed flow rate is to change the mixing at the solution side, and thus altering the mass transfer coefficient at the membrane.

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7 Prevention of membrane fouling is a very important aspect in RO systems. Fouling can lead to reduction in produc tion rate, lowering of membra ne lifetime, difficulty in predicting various operation para meters, etc. It can be cau sed by many reasons, including concentration polarizatio n, plugging of membrane pores by suspended matter, precipitation of solute at the membrane surf ace, biological fouling, and degradation of the membrane itself. Fouling can be largely minimized by the pr e-treatment of seawater before it is pressurized in the membrane modules. Studies have shown that par ticles larger than 5 m in size have no effect on the overall fouling pr ocess, and that the particles smaller than 0.45 um in size [6], including colloids and dissolved solids caused fouling more often than other materials. Filtration can include coarse particle scre ening, followed by finer cartridge filtration, and extra fine sand f iltration. Compounds which foul by scaling can be treated either by removal of the ion before processing, inhibiting the crystal growth or reducing system recovery, with anti-scalants being used for this purpose. Membranes are also affected by acid/base hydrolysis, and t hus the pH of the seawater has to be maintained within certain limits. Seawater containing calcium carbonate is treated with acid to yield more soluble bi carbonate and carbon dioxide which can be removed in posttreatment by lime softening and degassing respectively. Freezing Freezing is a separation process based on the solid-liquid phase change phenomenon. When salt water is reduced to it s freezing point, ice crystals of pure water are formed within the salt solution which can be mechanically separated and melted to obtain fresh water. If the temperature of th e salt solution is further reduced it reaches a

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8 point, called the eutectic temperature, wher e salt crystals start forming. Thus the operating temperature of the freezing chamber in the desalination plant should be above the eutectic temperature. The basic indi rect freezing method is shown in figure 1.5. Figure 1-5. Schematic of i ndirect freezing method [7]. The inlet salt water, after passing th rough the heat exchanger to reduce its temperature, is cooled in the freezing ch amber by means of a separate refrigeration system to form ice crystals. The ice is then separated from the brine in a wash column and transferred to a melting unit where ice is melted by the heat of condensation released by the refrigeration system. Both the releas ed brine and the fresh water are passed through the heat exch anger before being taken out of the desalination unit. The direct freezing method is a modificati on of the above technique, in which use of an external refrigerant is eliminated and water itself is used as a refrigerant. Here the freezing chamber is maintained at a water vapo r pressure equal to or below the triple

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9 point of the water thus causi ng partial flashing as the salt water is introdu ced. The vapor generated due to flashing is compressed (and thus heated) and discharged to the melting unit where it melts the ice crys tals and in turn itself gets condensed. This method is also called the vacuum-freezing vapor compression method. A modification to this method is the vapor-absorption method in which the va por produced is absorbed rather than compressed. An interesting variation, called the secondary refrigerant method, is the use of an immiscible refrigerant, like isobutane, in contact directly with salt water which makes the operating pressure of the system to be much higher than the triple point of water. Another variation to the secondary refrigerant method is the hydrate process in which a hydrate is added to salt water where a crystal lattice of water and the hydrating agent are formed at higher temperatures and pressures than pure ice. The main attractions of the freezing de salination process are the low energy requirements since the latent heat of fusion is about one seventh the latent heat of vaporization, minimal corrosion of proce ss equipment and allowing the usage of inexpensive plastics due to the low temper atures involved. The disadvantages of this process are the problems related to physically separating the i ce crystals from the brine, high vacuum requirements, removal of refrig erant from the outgoing streams, need for external refrigeration units. Humidification-Dehumidification (HD) The HD process is based on the fact that air can be mixed with quantities of vapor. When an airflow is in contact with salt water, air extracts some amount of vapor at the expense of sensitive heat of salt wa ter, causing cooling. On the other hand, the

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10 distilled water is recovered by maintaining hum id air in contact with the cooling surface, causing the condensation of a part of vapor mixed with air. Figure 1-6. Schematic of the HD process [8]. The basic cycle consists of a heat sour ce, air humidifiers (1) and dehumidifiers (2). The brine is passed through a heater (3) where its te mperature rises, then through packed towers where water vapor and heat ar e given up to the counter-current air stream, reducing the brine temperature. The air stream is then passed over the dehumidifier which genereally use fresh or sea water as cooling phase. Heat exchangers are present for heat recovery. Desalination using Heat Pumps The combination of multi-effect evaporation (MEE) and heat pumps have become attractive in the past decade to reduce the energy costs required in desalination. These hybrid systems are predicted to increase th e performance ratio from low values of 1020% to higher values of close to 200% [9]. Four such desa lination systems are: thermal

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11 vapor compression (TVC), mechanical va por compression (MVC), adsorption vapor compression (ADVC) and absorption vapor compression (ABVC). Thermal Vapor Compression (TVC) The TVC system uses a steam ejector to compress and heat the vapor generated from the evaporator. The inlet sea water is pre-heated in the heat exchanger shown as condenser and introduced into the evaporator. The generated vapor is passed into the steam ejector. Figure 1-7. Schematic of therma l vapor compression system [10]. The superheated vapor resulting from the st eam ejector is fed into the evaporator tubes evaporating the inlet sea water, and itself getting conde nsed into the product water. A portion of the superheated vapor coming out fr om the ejector is by-passed into the heat exchanger to pre-heat the inlet sea water. Mechanical Vapor Compression (MVC) The MVC system is driven by the use of electrical energy and does not require any external heating source. The inlet sea water is pre-heated in the feed pre-heater and passed on to the evaporator where vapors ar e formed. These vapors are taken in by the

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12 compressor where it is superheated to a temperature higher th an the saturation temperature of the seawater. The superheate d vapor is introduced into the evaporator tubes where it condenses by evaporating the f eed sea water and colle cted. The rejected brine and the product water are passed through the preheater before being taken out of the system. Figure 1-8. Schematic of MV C Desalination Process [9]. The MVC system requires no cooling water. The main drawbacks of this system are the need of electrical energy and the inclusion of compressor. Adsorption Vapor Compression (ADVC) This system comprises of two adsorption be ds (e.g. zeolite), evaporator/condenser single unit, and heat exchangers. Figure 1.9 depicts the schematic of ADVC system. Initially, bed I is assumed to be cold and at a temperature T a less than the temperature of the water adsorbed in the bed, while bed II is dry and hot with its temperature being the same as the temperature of the heating steam T g

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13 Figure 1-9. Schematic of single-effect adsorption vapor compression system [9]. The circulating fluid starts to transfer heat between the be ds, and during this period no heat is exchanged be tween the absorbers and any external source or sink. This process is stopped when bed I re aches a certain temperature T e1 and bed II has been cooled to T e2 Now, bed I is heated from T e1 to T g by the external source of the heating steam and bed II is cooled from T e2 to T a by the cooling water. During the heating process, when the pressure in bed I become s higher than the condenser pressure, it is opened to the evaporator tubes where th e vapors generated from the bed condense. Similarly, when the pressure in bed II is lowe r than the evaporator pr essure it is opened to the evaporator adsorbing the vapors. This comp letes the first half of the cycle. In the second half, the roles of the ad sorbent beds are reversed with bed I adsorbing vapors from the evaporator and bed II generati ng vapor to the evaporator tubes. This system does not include any moving pa rts, and has high performance ratios. Absorption Vapor Compression (ABVC) The ABVC system shown in Figure 1.10 comprises of generator, absorber, evaporator-condenser single unit and heat exchangers. The vapor formed in the

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14 evaporator is absorbed in the absorber genera ting heat which is rejected by the cooling water. The absorption solution (absorbent depi cted here by LiBr) is circulated between the absorber and the generator. The motive steam heats the diluted solution in the generator generating steam which is passed into the evaporator tubes and condenses into product water. Figure 1-10. Schematic of absorp tion vapor compression system [9]. The advantages of this system are similar to that of the ADVC system. The performance ratio of ABVC is better than ADVC at lower boiling temperatures, being as high as 5 for a single effect system [9]. Solar Desalination The conventional desalination systems consume significant fuel to produce potable water. A rough estimate of the energy consumption of desalination processes is given in Table 1.1. Since energy costs is one of the most important parameters in determining water costs, desalination using solar energy is increasingly becoming an

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15 attractive option due to continuous rise in conventional fuel costs and harm to the environment. Table 1-1. Energy consumption of some desalination processes Process Heat input (kJ/kg) Mechanical power Input (kWh/m 3 of product) Prime energy consumption (kJ/kg of product) a MSF 294 2.5-4 (3.7) b 338.4 MEB 123 2.2 149.4 VC 8-16 (16) 192 RO 5-13 (10) 120 ER-RO 4-6 (5) 60 ED 12 144 Solar Still 2330 0.3 2333.6 a Assumed conversion efficiency of electricity generation of 30 % b Figure used for prime energy consump tion estimation shown in last column adapted from Kalogirou [3] Desalination systems using solar energy can be classified as indirect collection systems and direct collection systems. Indirect collection systems can be seen as a combination of two systems, a collector to convert solar energy and the actual desalination plant to which the collected ener gy is supplied. Direct collection systems are those where heat collection a nd desalination process takes place in the same system. Table 1.3 provides a brief summary of the so me of the indirect collection systems. Indirect Solar Desalination Systems Solar energy can be used as a source of heat or power for any desalination process. Solar systems which are co mmonly used for this purpose are: Solar Collectors The principle of operation of solar collect ors is to absorb the solar radiation, convert it into heat and transf er this heat to the fluid fl owing through the collector. They can be classified into non-concentrating or c oncentrating type, and stationary or tracking. A list of collectors is shown in Table 1.2.

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16 Solar Ponds Solar ponds are used as both solar energy co llectors and heat storage system. The water in the pond gets heated up by the solar radiation. Water at the bottom of the pond is made denser by dissolving salt in it, and there exists a salt concentration gradient from the bottom to the top. This eliminates the natural tendency of mixing if the density gradient is adequate. Thus, h eat is collected and stored in the bottom water layer of the pond. Table 1-2. Solar Collectors Motion Collector type Absorber type Concentration ratio Indicative temperature range (oC) Flat plate collector Flat 1 30-80 Evacuated tube collector Flat 1 50-200 Stationary Compound parabolic collect or Tubular 1-5 60-240 Compound parabolic collect or Tubular 5-15 60-300 Linear Fresnel reflector Tubular 10-40 60-250 Parabolic trough collector Tubular 15-45 60-300 Single-axis tracking Cylindrical trough collector Tubular 10-50 60-300 Parabolic dish reflector Point 100-1000 100-500 Two-axes tracking Heliostat field collector Point 100-1500 150-2000 adapted from Kalogirou [3] Photovoltaic Cells PV cells are used to convert solar energy directly into electrical energy which can be used to power various components in desa lination processes such as reverse osmosis, electrodialysis, freezing a nd vapor compression. These cel ls have low conversion efficiency ranging around 10-15 %. Table 1-3. Indirect sola r desalination systems. Description Author(s) Comments Combination of a (MED) with an open cycle adsorptive heat pump using internal heat recovery. The heat transfer fluid flowing through tubes in the adsorbent beds is heated up by PTC Zejli et al. [11] Theoretical modeling was done. Variation of energy consumption and PR with the number of effects is shown.

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17 Table 1-3. Continued Hawaj and Darwish [12] Simulation shows that it is a viable option in an arid environment with performance ratio reaching more than twice the conventional system Multi-effect distillation coupled with a solar pond Tabor [13] Optimizes the size of the pond and the number of effects used, taking into account the large variation of pond heat output between summer and winter. Solar parabolic trough collector field coupled to a conventional MSF plant. Garcia-Rodriguez and Gomez-Camacho [14] Conclusion was that use of solar energy could compete with a conventional energy supply in MSF distillation processes in some climatic conditions. A small multi-effect, multi-stage flash distillation (MEMS) unit and a brine concentration and recovery system (BCRS) coupled with a solar pond Lu et al. [15] Experimental study. Aimed at reaching zerodischarge desalination. Single-effect solar assisted heat pump desalination system incorporating both flash and distillation techniques Hawlader et al. [16] Experimental study. A single stage flash desalination system working on flat plate solar collectors Joseph et. al. [17] Experimental study, maximum distillate yield of 8.5 l/d is obtained with collector area of 2 m 2 Multi-stage flash desalination system using two types of solar collectors Farwati [18] Experimental study. Yield from CPC was better than FPC Thomson and Infield [19] Experimental study. Shows substantial cost reduction to other PV-RO systems. Photovoltaic-powered seawater reverse-osmosis desalination system Laborde et al. [20] E xperimental study with mathematical modeling. Different parameters optimized with regard to power needs and energy consumption.

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18 Table 1-3. Continued Electrodialysis process operated with photovoltaic cells AlMadani [21] Experimental study Humidification-dehumidification method with an eight-stage air solar collector heatinghumidifying system Amara et al. [22] Experimental study. Principal operating parameters were optimized Dai et al. [23] Mathematical model with experimental validation. Humidification-dehumidification using flat plate collectors Fath and Ghazy [24] Numerical analysis. Shows that the dehumidifier effectiveness has an insignificant influence on system productivity. Direct Solar Desalination Systems The solar still is the simplest desalination system in terms of operation. It is an air tight basin, usually constructe d out of concrete/cement, galvanized iron sheet or fibre reinforced plastic (FRP) with a top cover of transparent material like glass or plastic. The inner surface of the ba se known as base liner is blackened to efficiently absorb the solar radiation incident on it. There is a provision to collect distil late output at the lower ends of top cover. The saline water evaporates on getting heated by solar radiation and the vapor moves to the glass cover, rejecting heat to the ambient and condensing. The condensed droplets flow along the glass cove r and get collected in the troughs from where they run down to the product tank. On the basis of various modifications and mode of operations introduced in conventional solar stills, thes e solar distillation systems ar e classified as passive and active solar stills. In the case of active solar stills, extra-thermal energy by an external mode is fed into the basin of passive solar st ill for faster evaporation. The external mode

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19 may be collector/concentrator pa nel, waste thermal energy source, etc. If no such external mode is used then that type of so lar still is a passive solar still. Figure 1-11. Schematic of a conventional solar still. A typical still efficiency, defined as the ra tio of the energy used in vaporization to the energy incident on the glass cover, is 35 % with the daily produc tion of about 3-4 l/m 2 [3]. The meteorological parameters name ly wind velocity, solar radiation, sky temperature, ambient temperature, salt co ncentration, algae formation on water and mineral layers on basin liner significantly a ffect the performance of solar stills. The design parameters are the brine depth, vapor le akage from the still, thermal insulation, cover slope, shape of the still a nd the material of construction. In order to improve the performance of a conventional sola r still, several modifications have been sugge sted in many studies and have been listed in Table 1-4.

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20 Table 1-4. Suggested vari ations in solar still. Description Author(s) Comments Double-basin solar still coupled to a flat-plate solar collector in the thermo-siphon mode. Yadav and Jha [25] Transient analysis shows it to be slightly less efficient if coupled to a collector in forced-circulation mode. Significant improvement in performance over that of the conventional double-basin solar still. Improved heat and mass transfer correlations in basin type solar stills Hongfei et al. [26] Validated with an experimental set up. Can provide better predictions for the evaporation rate of basin type solar stills at a wide range of Rayleigh numbers and temperatures Vertical multiple-effect diffusion-type solar still consisting of a flat-plate mirror Tanaka and Nakatake [27] Theoretically predicted to produce 29.2 and 34.5 kg/m 2 -d on the spring equinox and winter solstice days respectively, on the equator. Single-stage, basin-type solar still couple with flat plate collector Badran et al. [28] Experimental study. An increase in production of 52% was noticed when the still was connected with the collector over that of the still alone. Adding an outside passive condenser to a single-basin-type solar still Bahi and Inan [29] Experimental study. Efficiency was improved by more than 70%, and the distilled fresh water was up to 7 l/m 2 .d Inclined solar water desalination system Aybar et al. [30] Experimental study. Tested with bare plate, black-cloth wick and black-fleece wick. Conventional type solar still connected with a wick-type solar still Minasian and Al-Karaghouli [31] Experimental study. Overall efficiency of this new still was higher than the other two individual stills Study of different water depths in the basin on the heat and mass transfer coefficients Tripathi and Tiwari [32] Experimental study Effect of wind speed on solar still productivity El-Sebaii [33] Numerical study Vacuum solar stil l Al-Hussaini and Smith [34] Theoretical study. Shown to enhance the efficiency by 100 %. Solar still with an indirect evaporator-condenser Tchinda et al. [35] Numerical analysis Solar still with charcoal particles as absorber medium Naim and Abd El Kawi [36] Experimental study. Has a 15% improvement in productivity over wick-type stills.

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21 Table 1-4. Continued Optimization of glass cover inclination for maximum yield in a solar still Tiwari et al. [37] Numerical analysis Solar still with reflectors and black dye Tamimi [38] Experimental study. Authors advise to operate the still with the reflectors only, without adding the black dye. Single and double basin solar-stills Al-Karaghouli and Alnaser [39] Experimental study. The daily average still production for the double-basin still is around 40% higher than the production of the single-basin still. Triple-basin solar still E1-Sebaii [40] Numerical analysis optimized various parameters which affect the performance of the still Spherical solar still Dhiman [41] Mathematical modeling. Authors show efficiency of a spherical solar still is 30% greater than that of a conventional still. stepped solar still with built-in latent heat thermal energy storage Radhwan [42] Storage material paraffin wax, and the efficiency obtained was 57 % Water film cooling over the glass cover of solar still Abu-Hijleh and Mousa [43] Authors infer increase in the still efficiency by up to 20%

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CHAPTER 2 PROPOSED DESALINATION SYSTEM In the proposed flash desalination syst em, an innovative passive gravity based method is used for the production of vacuum The concept was proposed by Sharma and Goswami [44]. A standing column of water is allowed to drop generating very low pressures in the headspace created. Conventi onal desalination system s require the use of vacuum pumps or steam ejectors to attain the same purpose. Based on this concept, a desalination system was investigated by [45] which incorporated surface evaporation in the vacuum chamber. Simulated performa nce of that system matched well with experimental results. However, the evaporator size for a practical output in such a system is large. Further, with change in pressure in the evaporator the water level fluctuation is large which poses difficulty in heat addition. The system bei ng proposed here uses a flash evaporator, which reduces the size of the system. Heat input is provided using a solar collector. The concept can be implemented as a single-stage unit as well as a multi-stage system design. Single-stage and two-stage systems have been proposed in this study. These systems can work on low grade heat source li ke solar energy. The obj ective is to develop theoretical models for the proposed single stag e and two-stage systems, and analyze them to obtain the desired potable water output. A thermodynamic analysis of each component and the whole system was done, and a mathematical model was formulated. 22

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23 Single-Stage System Referring to the Figure 2.1, the system cons ists of a flash chamber (A), condenser (B), low grade heat source (C), feed wate r pump (D), product water tank (E), and brine collection tank (F) arranged as shown. The evaporator and c ondenser have to be located at a height of 10 m or more a bove the collection tanks at the bottom of the figure, such as roof tops of buildings. The vacuum is created by letting a column of water fall in a closed space under gravity creating low pressures in the head space at the top. One possible implementation is as follows: valves V1 and V2 are open wh ile valves V3, V4, and V5 are closed. Brine is pumped into the system using the feed water pump until all the air inside the system in vented out through valve V2. When the system is completely filled with water, the pump is turned off, and valves V1 and V2 are closed. Valves V4 and V5 are then opened causing the water to drain down, creating a vacu um in the space above (i.e. in the flash chamber and condenser). A water column of approximately 10 m is formed which is balanced by atmospheric pressure. During operation, heated brine is pumped into the evaporator where it flashes because of lower pressure, producing vapor and a higher concentration brine solution. The vapor is condensed rejecting heat that is used to preheat the brine. The brine can be heated by using solar heat from a collector. Other low grade heat sources can also be used. The concentrated brine and the product wa ter drain out of the system due to gravity, and hence no pumps are required for these pur poses. The levels in the brine collection tank and the product water tank can be maintained using float valves.

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24 Figure 2-1. Proposed Single Stag e Flash Desalination System. Two-Stage System For more effective utilization of the heat input, multi-stage systems can be used that flash the brine at successively lower pressures with effective heat recovery, increasing the production of vapor. Figure 2.2 shows an example of the implementation of a two-stage flash system. Referring to the figure 2.2, the two stages are in a stack as shown, with the requirement that the second stage flash chamber (A2) and condenser (B2) be located at a minimum height of 10 m or more over the brin e and freshwater reservoirs shown at the bottom. (Note that these reservoirs could be located below ground level while being open to the atmosphere). The method of creating the vacuum is sim ilar to that for a single-stage system. Vacuum in the two stages is created inde pendently. The two stages are only connected

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25 via valve V7 and the orifice. Valve V6 is now similar to valve V2. Thus for the creation of vacuum, stage 2 is filled up first with seawater follo wed by stage 1. Seawater from stage 1 is allowed to drain down before stage 2. This ensures that valve V7 remains closed. After vacuum is created in stage 1, va lve V9 is closed and it remains closed while the system is in operation. Hence seawater af ter being flashed in A1 has to flow through valve V7 to A2. The connecting pipe between A1 and F will become filled with seawater when the system begins to operate (as shown in figure 2-2). Figure 2-2. Proposed Two-St age desalination system. The initial pressure in both the stages will be the same (the vapor pressure of water at its temperature). The system bei ng ready for operation, heated feedwater is flashed in A1 and the brine begins to accumu late in A1. After a certain amount of brine

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26 has accumulated in A1, valve V7 is opened. Due to the pressure difference in the two stages, the accumulated brine in A1 flows in to A2 and is further flashed at a lower pressure. The flow rate of seawater from A1 to A2 is controlled by the pressure in each stage and the connecting arrangement.

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CHAPTER 3 THEORETICAL ANALYSIS The mathematical modeling of the proposed desalination system comprised the analysis of each component of the system. Mass and solute conservation equations along with energy balance equations were formulat ed, and a computer program written in C++ was developed to solve the equations. This chapte r starts with the transient analysis of the components of the system followed by the met hod adopted to solve the set of equations and the algorithm used. Two versions of the computer program were developed, the first one assumed a constant heat source temp erature while the second one took into consideration a solar collector as the source of heat. Evaporator The evaporator is that component of the system where pure water vapor is generated from the saline water. The method in corporated in this system to generate vapor is flashing. After the feed saline water is heated by the heat source, it is throttled to the evaporator which is at a lower pressure than that corresponding to its temperature leaving the heat source. It s hould also be noted that the f eed saline water is prevented from boiling by keeping its pressure throughout the heat source and piping above the saturation pressure corresponding to its temperature. Flash evaporation occurs when saline wate r is exposed to a sudden pressure drop (the evaporator being under low pressure conditions) below the saturation vapor pressure corresponding to the waters temperature. To regain equilibrium, part of the saline water vaporizes by drawing its late nt heat of vaporization from the remaining liquid, whose 27

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28 temperature drops towards the saturation temperature correspondi ng to the lowered pressure. Distillate formation also lead s to an increase of water salinity. More commonly three flashing methods are used to achieve flash evaporation: pool liquid exposed to a sudden pressure drop in a container, supe rheated liquid flowing in a low pressure open channel (usually inco rporated in a conventional MSF evaporator) and superheated liquid jet ejected from a simple tubular nozzle or a circ ular orifice into a low pressure zone. Miyatake [46] experimenta lly compared these methods with regard to the coefficient of flash evaporation, and determ ined that this coefficient for the flashing liquid jet was 10 times more th an that of superheated pool liquid or superheated flowing liquid. In the proposed desalination syst em, flashing is achieved by ejecting the superheated saline water into the evaporator using an orifice. Flashing process The evaporator is broken down into two control volumes; first one where the flashing process happens (near th e orifice) and the other bei ng the brine collected in the evaporator and water column. The flashing efficiency is also taken into account. Figure 3-1. Schematic of flashing process. Mass Balance Mass flow rate ofMass flow rate ofMass flow rate feed saline water vapor generatedof falling brine

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29 tt t s wv b M MM ..... EQ 1 Salt Balance Salt in feed saline waterSalt in fallingbrine ttt t s wswbb M XMX t t sw b tt swvM t s w X X MM ..... EQ 2 Energy Balance Energy of feedEnergy of vaporEnergy of saline watergeneratedfalling brine 000000 0 ()ttt sw v vtttttt swswvvbb TTT ttttttt sw ps v ps fgb ps TTT ttt swvbMhMhMh MhCdTMhCdThMhCdT hMMM 00 00 tt tt sw v v vTT TT tttttttt swps ps vfgvps ps TT TT M CdTCdTMhMCdTCdT t sw t vT tt swps T t v t fg M CdT M h ..... EQ 3 Ideally the temperature attained by the va por after flashing should be equal to the saturation temperature correspond ing to the pressure in the evaporator. But this depends on the amount of time given for the flashing pr ocess in the system, and since this time is finite the actual temperature of the vapor generated is highe r than what it should ideally attain. Thus a flashing efficiency is defined. Flashing Efficiency: Actual vapor generation rate Maximum possible vapor generation rateflash

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30 ,, ,max ,() ()t sw t v t sw t veqT ttt t psfgv T vactual t flash t T ttt v psfgveq TCdThT M M CdThT ..... EQ 4 Miyatake et. al. [47] proposed the follo wing empirical relationship for flashing efficiency for aqueous NaCl solution, and also mentioned that it does not depend on the other experimental conditi ons except the superheat: 1111.53.0tt t flash swsatTT ..... EQ 5 Concentrated Brine Column The height of the brine column depe nds only on the difference between the pressure in the evaporator and the atmospheri c pressure. As the brine level in the brine tank is constant, the amount of brine rejected from the system will be the sum of the brine falling after flashing and the brine water lo ss due to the pressure increase in the evaporator. The temperature and salt gradient s in the brine column are neglected. The initial mass, salt concentation and temperature of saline water in the column are known. Mass Balance ChangeinpressureChangeinmass of in the systemwaterin the column ep ttt ttt ev evA M MP g P ..... EQ 6 Salt Balance Salt in the brine Salt in the brine Saltadded due to Salt in brine rejected column at time t+tcolumn at time tfalling brine in tfrom the system in t tttttttt tttttt evevevevbb evbevA M XMXMXtPPXMXt g

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31 () (ttttt ttt evev ev bbevMXX MXX t ) ..... EQ 7 Figure 3-2. Schematic of th e concentrated brine column. Energy Balance Energy of the brine Energy of the brine Energy added by Energy of brine rejected column at time t+tcolumn at time tfalling brine in tfrom the system in t tttttttt tttttt evevevevbb evbevA M hMhMhtPPhMht g tt ev t t v ev t evT ttt ev ps T T tt bps TMCdT M CdT t ..... EQ 8 Vapor Space The vapor space comprises that of the w hole system which is mainly the vapor space of the evaporator and of the condenser. Th e temperature gradient is neglected in the vapor space. It is also assumed that the vapor is condensed at the saturation temperature, and that sensible cooling is neglected. The heat of condensation is rejected to the condenser from the vapor space. The initial mass of vapor in the vapor space is equal to

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32 the volume of vapor space times the density of vapor at the ambient saline water temperature. Mass Balance Mass of vaporMass of vaporMass of vapor Mass of vapor at time t+tat time tadded in tcondensed in t ttttt vs vsv d M MMtM t ttt t vs vs vMM t d M M t ..... EQ 9 Figure 3-3. Control volume of vapor space. Energy Balance Energy of vaporEnergy of vapor Energy of Energy of vapor Energy rejected in vapor spacein vapor space condensed added in t to conden at time t+tat time t water in t ser ttttttttttt vsvsvsvsvvdd M hMhMhtMhtQt ,tttttt ttttt vsvsvsvs vvdd dsatMhMh M hMhQ t HereTT tt t sat v t sat satt T tttttt vs ps dfg vpv TTM CdTMhQMCdT t tT .... EQ 10 Also, the mass of vapor in the vapor space at any instant t can be found out as:

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33 (Volume of Space)(Volume of Space)()tt vs v satMf tT .... EQ 11 Condenser The vapor condenses to give the desire d product after rejec ting the heat of condensation in the condenser. The condenser is water cooled in order to obtain better heat removal rates. The heat of condensati on pre-heats the feed saline water passing through the condenser, thus recove ring heat in the system. The type of condenser used in the system is a horizontal tube -in-tube type condenser vapor condensing in the inner tube and feed saline water (cooling water) flowing in the annulus. Figure 3-4. Horiz ontal annular flow. In horizontal tubes at low vapor velocities, low condens ation rates and/or short tube lengths, which is the case here, liquid that condensed on the upper portion of the inside tube wall tends to run down the wall towards the bottom resulting in a stratified annular flow condition, as depicted in figure 3.4. For lo w vapor velocities (Re<35,000) the condensation heat transfer coefficient is given by [48]

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34 1/4 3() 0.555 ()llvlfg i lsatsgkh h TTD where, the modified latent heat is ,3 () 8 f gfgplsatshhCTT The heat transfer coefficient in the annul us will depend on the nature of the flow, and hence on the volume flow rate of the cooling saline water. The Reynolds number can be found out using the hydraulic diameter D h (for circular tube annulus): Hydraulic diameter 2244 4oi ho oiDD A DD PDD iD Reynolds number Re s wh DVD If Re <2300 then the flow is laminar, or else the flow is turbulent. The Nusselt number for fully developed laminar flow in a circular tube annulus with one surface insulated and the other at constant temper ature can be obtained from table 3.1. For turbulent flow, the Nusselt number can be calculated from [48]: 4/50.40.023RePriDNu (for Re D > 2300) The heat transfer coefficient can be obtained as: l oi hk hN D u Table 3-1. Nusselt number for lamina r flow in circul ar tube annulus. io D D i N u 0 0.05 17.46 0.10 11.56 0.25 7.37 0.50 5.74 1.00 4.86 adapted from Incropera and DeWitt [48]

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35 Overall heat transfer coefficient t io iohh U hh .... EQ 12 The rate of heat transfer from the conde nsing vapors to the c ooling saline water is: ,,() ( lntt tt ttt outin cs swpscoutcin tt satin tt satoutTT QUA MCTT TT TT ) .... EQ 13 ,,()t cs t s wpsUA MC tttt coutsatsatcinTTTTe .... EQ 14 Distillate Column The distillate column, like th e brine column, depends on th e difference in pressure of the system and the atmospheric pressure. The amount of distillate coming out from the system will be the sum of the distillate added to the distillate tube after condensation and the distillate rejection due to the pressure increase in the evaporator. The temperature gradient in the distillate column is neglected. The initial mass and temperature of the water in the column are known. Mass Balance ChangeinpressureChangeinmass of in the systemwaterin the column p tttttt ps psA M MP g P .... EQ 15 Energy Balance Energy of the Energy of distillate Energy of the distillate Energy added by distillate column rejected from the column at time tcondensed distillate in t at time t+t system in t p tttttttt tttttt pspspspsdd psdpsA M hMhMhtPPhMht g

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36 tt ps t t sat ps t psT ttt ps pw T T tt dpw TMCdT M CdT t .... EQ 16 Figure 3-5. Control volume of the distillate column. Pressure in the System The pressure is one of the most importan t parameter in this system design. The initial low pressure in the system is created by using the natural forces of gravity and atmospheric pressure, resulting in the formati on of the saline water co lumn. The height of the water column is mainly dependent on the sy stem pressure as the atmospheric pressure can be treated as a constant. Thus, any increase in system pressure will lead to a decrease in the water column height and vice versa. Initially when the system is started, the pr essure in the system will be equal to the saturation pressure at the ambient temperature of the saline water. The pressure change in the system relates directly w ith the rate of evaporation a nd rate of condensation. The pressure increase in the system is due to the combined effect of vapor and noncondensable gases accumulation. The e ffect of continuous accumulation of non-

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37 condensable gases is taken into account in the system design as it is assumed that no vacuum pump or steam ejector is used to remove these gases from the system. Oxygen and nitrogen and small amounts of othe r gases are absorbed in sea water only in molecular form, and they are released without changing the chemical composition of sea water. However, the liberation of carbon-dioxide impairs the equilibrium between carbon-dioxide CO 2 bicarbonate and carbonate The physico-chemical equilibrium depends essentially on temperature, pressure, salin ity and pH-value of the sea water []. In order to compensate for the removal of CO 3HCO 23CO 2 decomposes to produce new CO 3HCO 2 molecules. The dissolved gases content of sea water is given in Table 3.2. Table 3-2. Concentration of main gases dissolved in sea water. Gas Concentration mole/m 3 Parts per million (ppm) CO2 0.005 0.22 O2 0.24 7.7 N2 0.45 12.6 Ar 0.01 0.4 3HCO 3.062 187.1 adapted from Seifert and Genthner [49] Thus, the pressure in the system at any time instant t can be written as: ()ttttt vaporgassatgasPPPfTP .... EQ 17 The irreversible increase in pressure caused by the non-condensable gases can be found out using Daltons law of partial pressu re, and by considering them to behave as ideal gases: , igas t gasigasnRT PP V .... EQ 18

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38 It is also assumed here that the moles of gases released in time are directly proportional to the concentration of the gas in the sea water and the amount of vapor being generated. t swConcentration of gas iigas vnM ttE Boiling Point Elevation (BPE) The vapor pressure of sea water is approximately 1.84 %less than that of fresh water in the temperature range of 0 o C 100 o C [50]. Thus, if two vessels containing fresh water and sea water at the same temperatur e (within the above mentioned temperature range) have their vapor space connected, fresh water will distill into the sea water vessel. In other words, the lower vapor pressure fo r the sea water manifests itself as a boiling point elevation which is a function of the dissolved solids concentration. tt veqsatTTBP .... EQ 19 Heat Source Flat plate solar colle ctors are used to convert a re newable energy source to drive the system. The saline water, after being preheated in the condens er, is passed through the solar collector to increase its temperature in the desired range and then flashed in the evaporator. A heat exchanger between the collector loop and the desalination system has been omitted as the sea water flows direc tly through the collector absorbers. This increases the efficiency and simultaneously redu ces costs. But this al so leads to the risk of scale formation and corrosion in the metalli c absorbers of the conventional flat plate solar collector. A possible solution has been suggested by Hermann et. al. [51]: collectors which have corrosion-free absorbers. In their design, selectively coated glass tubes acted

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39 as absorbers with silicone hoses reinforced with aramid fibers acting as headers. The efficiency was increased by adding a specially shaped reflector. Operating temperatures as high as 90 o C can be reached with effi ciencies of about 50 %. The efficiency of a flat plat solar coll ector mainly depends on the solar insolation and the inlet fluid-ambient temperature di fference once constructed. The analysis, explained next is used to determine the solar insolation incident on the collector. For a given location with latitude L, longitude and its standard time meridian being at a longitude locall s tl the solar declination can be estimated by: 23.45sin360284365oo sn where n is the day number during the year with January 1 being n = 1 Declinations north of equator are positive, and south are negative. The hour angle is defined as minutes from local solar noon 4 min/degreesh where values east of due south are negative and west of due south are positive. The relationship between the local solar tim e and the local standard time (LST) is: Solar Time = LST + ET + ()4min/degree where, ET (in mins) = 9.87 sin 2B 7.53cos B 1.5 sin B and B = 360(n-81)/364 degreesstlocalll The solar altitude angle is obtained from sinsinsincoscoscosh s ssLL The solar azimuth angle s a can be found as sin cossinh/cossssa with the corrections as mentioned in [52] if, computationally, s a comes out greater than 90 o Sunrise and sunset times can be determ ined from their re spective hour angles: 1 or costantan s ssr shhL

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40 Solar radiation on a tilted surface is the su m of the beam radiation, sky diffuse radiation and ground reflected radiation. ,, cbcdcr c I III Beam radiation: ,,cosbcbN I Ii Diffuse radiation: 2 ,,cos2dcbNICI Ground reflected radiation: 2 ,.sinsin2rcgrbNIIC where, /sin k bNnICIe 010.034cos360365.25oII n g r is the ground reflectance and is the surface tilt angle. The angle of coincidence I can be calculated from: coscoscossinsincosswiaa where, is the surface azimuth angle. wa The average values of atmospheric optical depth k and sky diffuse factor C can be determined from Table 3.3, whereas C n is the clearness number. Table 3-3. Average values of k and C for 21 st day of each month for United States [52]. Month 1 2 3 4 5 6 7 8 9 10 11 12 k 0.142 0.144 0.156 0.180 0.196 0.205 0.207 0.201 0.177 0.160 0.149 0.142 C 0.058 0.060 0.071 0.097 0.121 0.134 0.136 0.122 0.092 0.073 0.063 0.057 Thus from the sunrise and sunset time, the time and the number of hours for operation of the desalination system can be determined. The temperature of the saline water exiting the collector can be calculated from: ,, s cscc scoutscin s wps A I TT M C .... EQ 20

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41 where s cinT is the inlet collector saline water temperature which is equivalent to its exit temperature from the condenser, s cA is the solar collector area and s c is the solar collector efficiency. Pumping Power The pump is used to circulate the sali ne water through the condenser and solar collectors to the evaporator. The pressure to which the saline water should be pumped before it enters the evaporator depends on th e fact that it should be greater than the saturation pressure correspondi ng to its temperature to prevent boiling within the circulating tubes. The power required by the pump can be determined as: Pump Power = frictionatm pumpPgHPPV where, P is the final desired pressure, is the atmospheric pressure, H is the height of the system from the ground, atmP f rictionP is the frictional pressure drop, V is the volume flow rate of saline water and pump is the pump efficiency. Performance Ratio The performance ratio (PR) can be define d as the ratio between heat used to evaporate saline water into fresh water and the heat added to the system. In context with the present system two performance ratios can be stated, one where th e heat added is only the useful heat extracted from the heat source and the other efficiency being the total heat incident on the solar collectors.

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42 1Heat used for evaporation Useful heat addeddfg t u tmh PR tQ 2Heat used for evaporation Energy incident on collectordfg t tmh PR tQ Method of Analysis The procedure followed in this analysis was to first write the equations in their differential form. All system component equations were written in the differential form, and the ideal way was to integrate all the e quations simultaneously. The difficulty then would be in solving them, as the equations in their partial derivative form are not linear. Hence, another approach is followed here where all the component s of the system are assumed to move from one static state at time t to another static state at time . In this method all the differential terms are appr oximated in finite differential form and the equations are solved simultaneously and iterati vely till convergence is obtained. All the system parameters are solved for time t, and then input parameters for time are updated to those obtained from the previ ous iterations at time t, and so on. t+t t+t Single Stage 0000000,,,,,,,evpsvsevpsatevKnownInitialConditionsMMMPTTTX 0 0,,, s wcwins w K nownfortMMTX For iteration at any time beginning from 0, t 0: t ,1) 19 45t veq t vCalculateTfromEQ CalculateTfromEQandEQ 2) is known for constant te mperature case, and can be calculated from EQ 20 for the solar collector caseswT

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43 3) 3t vCalculateMfromEQ 4) 1t bCalculateMfromEQ 5) 2t bCalculateXfromEQ ,6) 12 14t t coutCalculateUusingEQ CalculateTfromEQ 7) 13tCalculateQfromEQ 18) 910 11t s atSimultaneouslysolveEQandEQutilizingEQtoobtainT 1 11 19) 18 7 17t gas tt vapor sat tCalculatePfromEQ CalculatePusingTcalculatedinstep CalculatePfromEQ 1110) 8tt satCalculateactualTfromPfoundinstep 1111) 11 8tt vs satCalculateMMassofvaporfromEQusingTcalculatedinstepMassof noncondesablegasesaddedusingtheidealgasequation ,112) 9 11tt t dv sCalculateMfromEQwhereMarecaluclatedfromEQ 13) Calculatethenewheightoftheseawatercoloumnandnewvolume ofvaporspace 114) 6t evCalculateMfromEQ 115) 8t evCalculateTfromEQ 116) 7t evCalculateXfromEQ 117) 15t psCalculateMfromEQ 118) 16t pCalculateTfromEQ 19) 11 Gotostepforttandrepeattheprocess

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44 Two Stage The basic algorithm for the two stage system is similar to the single stage with the main difference here being two evaporators, two condensers and tw o distillate column. The component equations of mass, salt and energy balance are the same. The following changes in the algorithm can be mentioned for the two stage system: 1) The inlet saline water temperature for condenser of stage 1 is the exit temperature from condenser of stage 2 2) The mass flow rate of saline water from evaporator of stage 1 to that of stage 2 depends on the pressure difference in the two stages and the orifice size 3) The amount of saline water in evaporator 1 depends on the mass flow rate as mentioned in (2) above and the unevaporated saline water4) The heat source only heats up the saline water entering in stage 1 5) The temperature of saline water entering stage 2 is equivalent to the temperature of saline water in evaporator of stage 1

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CHAPTER 4 RESULTS AND DISCUSSION The theoretical results presented in this chapter were obtained by mathematical analysis of the system using the equations fo rmulated in the earlie r chapter. The results presented here are for the cases of the syst em (single-stage and two-stage) operating on a constant temperature heat source and a solar collector. The assumpti ons made here are: the heat loss from the system, the thermal capacity of the system material and the effect of non-condensable gases on c ondensation is neglected. In this chapter, changes in the system performance are first studied by variations in different system parameters for a single-st age system with a constant temperature heat source. This is followed by the simulation results obtained for opera ting the system on a constant heat source for a period of 12 hour s. Single-stage system performance using solar collector is presented along with the tw o-stage system results using constant heat source (period of operation being 12 hours) and solar collector. The system parameters which are taken as constants for all the cases are: Inner diameter of condenser tube 0.0762 m (= 3 inch) Outer diameter of condenser tube 0.1016 (= 4 inch) Circular cross-sectional area of evaporator 0.2 m 2 Length of collections tanks 0.2 m Cross-sectional area of collection tanks 0.1 m 2 Diameter of connecting pipes 0.0254 m (= 1 inch) Volume of the initial sp ace in the system 0.03 m 3 Salinity 35 g/kg 45

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46 Single-stage system with constant temperature heat source The main input parameters in the system are the temperature of the heated saline water (T sw ), the saline water mass flow rate (M sw ) and length of the condenser (L c ). The ambient temperature (T a ) also has some effect on the system output. For the simulation, the time interval is taken to be 5 seconds. t Variation of inlet saline water temperature The effect of variation of temperature of the inlet saline water on the distillate output is shown in figure 4.1. M sw was set to 20 kg/hr and L c was 1 m. The output is for 1 hour of operation, and it can be noticed that with the in crease in the saline water temperature the output increases. The reason for th is increase is that as the initial system pressure (hence the saturation temperature) is same in all the cases, more flashing occurs and hence more vapors are generated with increasing temperature since flashing is directly proportional to the superheat of the saline water i.e. () s wsatTT It should also be noted that the temperatures obtained strict ly depend on the heat source available. Figure 4-1. Variation of output with inlet saline water temperature.

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47 The pressure in the system builds up with vapor generation and the release of noncondensable gases. As there are no means of venting, the system pressure strongly depends on the amount of vapor generation and the rate of condensation. Figure 4.2 shows the effect of variation of inlet saline water temperatur e on the system pressure. As seen in the figure, the system pressure rapi dly increases initially as no condensation is occurring. It takes a small dip for three cases (60 o C, 70 o C and 80 o C) as condensation starts, whereas for T sw = 90 o C, the rate of condensation is exceeded by the rate of vapor generation and the pressure further increases. Figure 4-2. Variation of system pressure with inlet saline water temperature. Variation of saline water mass flow rate The saline water mass flow rate was varied for constant L c = 1 m and T sw = 90 o C. Figure 4.3 shows the increase in output with increasing mass flow rate, since the amount of vapor generated during flashing is di rectly proportional to the feed rate.

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48 Figure 4-3. Effect on distillate output with change in saline water flow rate. Variation of length of condenser The length of the condenser and hence th e condensation rate is an important parameter in the pressure build up in the system. Increasing the condenser length leads to higher condensation rate and lesser pre ssure increase in the system. For M sw = 20 kg/hr and T sw = 90 o C, the system pressure vari ation is shown in figure 4.4. Figure 4-4. System pressure va riation with c ondenser length.

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49 Variation of ambient water temperature The initial pressure in the system is th e saturation pressure corresponding to the ambient water temperature. Hence with a cool er ambient water temperature, the initial pressure of the system will be lower which will result in increased vapor generation. The variation of the system saturation temperature is shown in figure 4.5. Figure 4-5. Variation of syst em saturation temperature with ambient water temperature. Figure 4-6. Effect of ambient wate r temperature on distillate output

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50 Also, the condensation rate will be greater for lower water temperature leading to increase in distillate output as shown in figure 4.6. Values of M sw = 20 kg/hr, T sw = 90 o C and L c = 1 m are taken. System Output The system was simulated for a 12 hour duration run. The input parameters were M sw = 20kg/hr, L c = 1 m and T sw = 90 o C with T a = 23.8 o C. The output of the system is shown in figure 4.7. The total di stillate output at the end of 12 hrs was 11.31 kg. The net pressure and saturation temperature conti nued to increase thr oughout the duration, and reached values of 22.3 kPa and 62.8 o C. Due to the pressure rise the brine and distillate water column fell to 7.94 m fr om the initial 9.87 m. The pre ssure increase due to noncondensable gases was 1.1% of the total pressure increase. Figure 4-7. Hourly output for single-stage system with consta nt temperature heat source.

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51 From the figure 4.7, it can be noticed that the hourly output continues to decrease due to the increase in the saturation temp erature thus decreasing the superheat for flashing. The salinity of the br ine rejected from the brine co lumn at the end of the run was 36.7 g/kg. The performance ratio of the system for the 12 hour run was 0.746. Two stage system with consta nt temperature heat source The two stage system specifics were taken as: M sw = 20kg/hr, L c = 1 m for both condensers and T sw = 90 o C for the first stage. The simu lation was run for 12 hours with taken as 1 second. Figure 4.8 shows the hour ly output of both the stages in the duration. The total distillate output obtained was 13.9 kg, with 7.1 kg from the first stage and 6.8 kg from the second stage. The perfor mance ratio of this system was 1.42. The other reason, except for the system being a tw o-stage one, for this increase is that the saline water is now pre-heated in two condensers and thus the heat required to reach a temperature of 90 t o C reduces. Figure 4-8. Hourly output for two-stage system with constant temperature heat source.

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52 As seen from the above figure, the output from the first stage continues to decrease due to the increasing pressure. The second stage is assumed to become operational when the height of brine accumula ted in the first stage is over 5 cm. The second stage operation starts midway through the first hour with th e output increasing initially and then decreasing. The pressure at the end of 12 hrs in the first and second stages reached about 39.9 kPa and 17.5 kPa re spectively. The saturation temperature in the first stage was 76.3 o C, and in the second stage was 57.6 o C. The pressure increase due to non-condensable gases was nearly 1.14% of the total pressure in the first stage and 0.82% in the second stage. The brine accumulation height in the first stage was 12.6 cm, while the brine column height drop in second stage was 1.47 m. Solar collector specifications In the simulation using solar collector clear sky conditions are assumed, and the location is taken to be Gain esville, Florida (Latitude 29.68 o N, Longitude 82.27 o W) with the collector facing south and tilted at an an gle equal to the latitude of Gainesville (Latitude 29.68 o N) from the horizontal. The collec tor efficiency is given by: c() 0.754.87 I s cina scTT Figure 4.9 shows the solar insolation on the surf ace of a collector oriented as mentioned. The area of the collector was taken to be 1 m 2 for all the cases. The collector was operated only when the incident angle on th e solar collector surface was less than 60 o

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53 Figure 4-9. Insolation on a tilted solar coll ector surface on May 21 fo r a clear day at Gainesville, FL. Single-stage system coupled with solar collector A single stage system coupled with a solar collector was simulated for May 21 with the M sw = 20 kg/hr and L c = 1 m. The time interval t was set as 5 seconds. The simulation ran for a system time of 7.83 hrs. The temperature of the inlet saline water increased as the insolation on the collector surface increased. It attained a maximum value of 83.7 o C. Figure 4.10 shows the variation of temperature with time. The system saturation temperat ure reached a maximum of 58 o C. The insolation decreased after reaching a maximum, and thus decreasing the inlet saline water temperature and the saturation temperature. With the increasing saturation temperatur e, more vapors are generated and hence the system pressure increases. The pressure also follows the same trend, reaching a maximum of 17.8 kPa with insolation. The variat ion of pressure is shown in figure 4.11.

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54 Figure 4-10. Variation of singl e-stage system temperatures c oupled with solar collector. Figure 4-11. Single stage system pre ssure coupled with solar collector The pressure increase due to the accumul ation of non-condensable gases is shown in figure 4.12. It depends on th e rate of release of the non-condensable gases and hence the vapor generation rate.

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55 Figure 4-12. Pressure change due to non condensable (NC) ga ses in single-stage system with collector. Here only oxygen and nitrogen are taken into account as they make up the major portion of the total dissolved ga ses in seawater. The pressure increase due to the gases at the end of duration is about 117 Pa. Figure 4-13. Water column height variation fo r single-stage coupled w ith solar collector.

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56 The height of the brine column also fluctu ates as it depends on the pressure in the system. It attains a minimum of 8.38 m. Figure 4.13 shows the variation of the brine water column height with time. The maximum distillate output rate reached is 42.410 kg/s. The net output obtained after 7.83 hours is 5.54 kg. The hourly out put is shown in figure 4.14. As per the performance ratios defined in the previous chapter, the efficiency obtained are: and 10.748 PR 20.480 PR Figure 4-14. Hourly output of single stage system coupled with solar collector. Two-stage system coupled with solar collector The performance of the two-stage system is simulated for the same day i.e. May 21 with the input values as M sw = 20 kg/hr and L c = 1 m. The time interval taken here is 1 second as it provides better iteration va lues. The second stage is assumed to become operational when the height of brine accumu lated in the first stage is over 5 cm. t

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57 The temperature of inlet seawater varies with time due to the change in solar insolation, and is shown in figure 4.15. The ma ximum temperature attained by the saline water is higher than that of single-stage as the saline water is pre-heated in two condensers before passing through the solar coll ector. The value of this temperature is 99 o C, which would require high efficiency flat plate solar collectors or parabolic trough collectors for operation and thus such temperatures are achievable. The inlet saline water to the second stage is from the first st age, and the maximum value attained is 77.3 o C. Figure 4-15. Feed water temperature for two stage system coupled with collector It is also seen here that this maximum value for the second stage is reached after the temperature in the first stage has peaked. The reason is that the high inlet temperature in the first stage takes a finite amount of time to reflect in the brine accumulating in first stage, which is the feed water for the sec ond stage. The sudden jump seen in the inlet seawater temperature in the first stage is when the second stage becomes operational and its condenser starts pre-heating the feed water.

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58 The increase in the inlet seawater temper ature leads to an increase in the vapor generation rate and hence an increase in the system pressure. Figure 4.16 shows the variation of system pressure with time. The pressure in th e first stage reaches a maximum value of 44.5 kPa and in the second stage a value of 15.9 kPa. The pressure decreases henceforth due to the decrease in in solation and vapor generation rate. Figure 4-16. Two-stage system pre ssure coupled with solar collector. The peak pressure reached in the second stag e is after the peak reached in the first stage because of the difference in the peaks for maximum inlet seawater temperature in both the stages. Again, the jump in the pressure curve for the first stage is due to the jump in the inlet seawater temperature. With the increase in pressure, the saturation temperatures of both the stages follow the same pattern. The maximum va lue reached in the first stage is 78.9 o C and in the second stage is 55.6 o C. The variation of saturation temperature is shown in figure 4.17.

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59 Figure 4-17. Saturation temperature curves for two-stage system with solar collector. The variation of condenser outlet temperatures with time is shown in figure 4.18. The high temperatures as shown are obtained due to the low mass flow rate of the saline water. The maximum is reached when the sa turation temperature peak is attained. The pressure increases due to non-condensab le gases in the two stages are shown in figure 4.19. The increase in the second stag e is significantly lower because of the low vapor generation rate, and also due to the fact that a small fraction of the gases dissolved in the seawater has been liberated in th e first stage leading to lower dissolved concentrations of gases in the seawater en tering the second stage. At the end of the system run, the increase in pressure due to non-condensable gases in the first stage is 955.8 Pa and in the second stage is 81.9 Pa.

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60 Figure 4-18. Condenser outlet temperature of two-stage system coupled with collector. Figure 4-19. Pressure increase due to NC gases in two-stage system with solar collector. The pressure changes also lead to cha nges in the brine column height in the second stage and the brine accumulation height in the first stage. These are shown in figures 4.20 and 4.21. The final brin e height attained in the evaporator in stage 1 is 13.4 cm. The curve shown in figure 4.20 shows that the brine height increases to a certain value, decreases slightly and then again st arts increasing. The decrease is due to the

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61 increase in the pressure in the first stage due to which more brine flows from the first stage to the second than the am ount of brine getting accumulated. Figure 4-20. Brine height in the first stage of the two-st age system with collectors. The brine column follows the same trend as that of the single-stage system. It varies with the pressure change and reaches a minimum when the pressure in the system reaches a maximum. The minimum height to which the column drops is 8.57 m. The diameter of the orifice connecting the two stages is an important parameter in the two-stage system analysis. A very large di ameter would result in all the brine draining from the first stage to the second, thus equa lizing the pressures and making the two-stage concept non-operational. A sma ll diameter would lead to very small flow rates from the first stage to the second thus re sulting in negligible output from the second stage, and also leading to large accumulation of brine in the first stage. The diameter here was taken as 1.24 mm.

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62 Figure 4-21. Brine column height in second st age of the two-stage system with collector Figure 4-22. Hourly output from twostage system with solar collector. Figure 4.22 shows the hourly distillate out put from each of the stages. The total yield for 7.7 hours of operation was 8.66 kg, w ith the first stage output as 4.76 kg and second stage output as 3.90 kg. The perfor mance ratios of the system were:

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63 121.35, 0.75 PR PR The high efficiency is due to the combined e ffects of pre-heating of feed saline water in the condenser and due to the utilization of the second stage by producing more distillate without using any ex tra heat source.

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CHAPTER 5 CONCLUSION AND FUTURE WORK Conclusion An innovative desalination system is proposed which makes use of natural forces of gravity and atmospheric pres sure to create vacuum under wh ich saline water is flashed. The system can be coupled with low grade heat source like sola r collectors to produce potable water. Single-stage and two-stage concepts of the desalination system were outlined. Mathematical models of the concepts were formulated and developed, and the results were presented for the systems coupled with: a) constant temperature heat source, and b) solar collector. The analysis shows the following: For the case of constant temperature heat source, the single-stage system was shown to produce 11.31 kg of distillate with a performance ratio of 0.746 and the two-stage system produced 13.9 kg with performance ratio of 1.42 in 12 hours of operation under the same initial conditions When coupled with a solar collector of 1 m 2 area, the single-stage system had a distillate output of 5.54 kg in 7.83 hrs with a performance ratio of 0.748 (based on only the useful energy extracted from the collector) or 0.48 (based on the solar insolation incident on the collector). The two-stage system produced 8.66 kg in 7.7 hrs with performance ratio of 1.35 (based on only the useful energy extracted from the collector) or 0.75 (based on the solar insolation incident on the collect or). The mass flow ra te of feed saline water for all the cases was 20 kg/hr. Thus the system performance obtained is better than that of a conventional solar still. Effect of different parameters on the system output was studied. The system produces more output with higher saline water mass flow rate, higher feed saline water temperature and with more condenser surface area. The orifice diameter is an important additional parameter in the two-stage system. 64

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65 When coupled with solar collector, the increase in pressure due to noncondensable gases was negligible as comp ared to the pressure increase due to vapor accumulation. Thus, the system can be operated for a number of days without a need to re-establish the vacuum if the pressure increase due to vapor accumulation can be kept low. This can be achieved by additional condensation (without vapor generation) and/or by night-cooling. Future Work The future work, in the order shown, includes: 1) Fabricating and experimental ly testing the concepts. 2) Validating the theoretical model after ta king into account the heat loss from the system and including the thermal capacity of the system. 3) Performing an economic analysis of the syst em to determine the cost of distillate produced.

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APPENDIX A PHYSICAL PROPERTIES Sea Water Density [53] 32 3 0021502200 10 150160ijj i ijSt cTT where is in kg/m 3 Salinity S is in g/kg, temperature t is in o C, denotes a summation, the first term of which is ha lved and Tk(x) represents a Chebyshev polynomial of degree k which are defined as: T o (x) = 1; T 1 (x) = x; T r+1 (x) = 2xT r (x) T r-1 (x) The Chebyshev coefficients c ij are as follows: i = 0 i = 1 i = 2 i = 3 j = 0 4.032219 -0.108199 -0.012247 0.000692 j = 1 0.115313 0.001571 0.001740 -0.000087 j = 2 0.000326 -0.000423 -0.000009 -0.000053 Heat Capacity [54] 222 2 123123123 123 pCaaSaSbbSbSTccScSTddSdST 2 3 where is in kJ/kg pC o C, S is the salinity in g/kg and T is the temperature in o K. The coefficients are defined as follows: a 1 = 5.328 b 1 = 36.91310 a 2 = 29.7610 b 2 = 47.35110 a 3 = 44.0410 b 3 = 63.1510 c 1 = 69.610 d 1 = 92.510 c 2 = 61.92710 d 2 = 91.66610 c 3 = 98.2310 d 3 = 127.12510 66

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67 Thermal Conductivity [7] k = (577 + 1.522 t 0.00581 t 2 )10 -3 where t is in o C, and k is in W/m.K Dynamic Viscosity [55] 22 20 10 12 12 o2 20 2 12 o220 log 1 1 20 109 where viscosity of solution at 20, mNs m = 1.002 viscosity of solution at t, mNs m t AaSaSBbSbSt t C cScS C S = salinity in g/kg The equation constants are: A = 1.37060 B = 0.000832 a1 = -0.000619 a2 = -0.000003 b1 = 0.006102 b2 = -0.000015 c1 = 0.001652 c2 = 0.0000083 Vapor Pressure [56] 2 10 4 7 olog where h = 2.160910 j = 3.501210 S = salinity in g/kg Here, p is the vapor pressure of pure water at the same temperature, and is defined as:op hSjS p 21 2 510 2-11log 10110 where x = z, c = 1.386910 y = 344.11, d = 1.196510 z = t + 273.16, e = 4.4000dx fy obcx pa e zz g t 3 03 5 35 010 t = temperature f = 5.714810 a = 5.432368, g = 2.937010 b = 2.005110, p is in units of 10/ C Nm 4 2

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68 Boiling Point Elevation (BPE) 2 2 2565.7579.815591.54739log337.1786.419810.922753log 32.6810.553680.079022log 266919.6379.6690.334169 S where c = 19.819 1 S = salinity in kg/kg TT c T cT ct T BPE TT S T = temperature in K T Water Density 32 63 94 3 3o999.8395216.9451767.98704011046.17046110105.5630210 116.87985010 where, is in kg/m and T is temperature in TTT T C T Dynamic Viscosity 52 10 21792.5 log10.21580.017731.263110 where T is temperature in K and is in Ns/m TT T m Specific Heat [57] 34 26 3 oo p4.21743.720283101.412855102.654387102.09323610 where T is temperature in and C is in kJ/kgpCTTT CC 8 4TT Thermal Conductivity 620.27580.0046125.539110 where T is temperature in K and is inW/m.K kT k Latent Heat of Vaporization fg31462.36 where T is temperature in K and h is in kJ/kgfghT

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69 Vapor Density 3460.5 10 0 2 Vapor Pressure of sea water at T where T is temperature in K and is inkg/m T Specific Heat 73 2 o p100.00010.03021.1804 where T is temperature in K and C is in kJ/kgpCTTT C

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APPENDIX B COMPUTER PROGRAM FOR SINGLE-STAGE SYSTEM #include #include #include #include double k_sw(double); double cp_sw(double, double); double cp_v(double); double mu_sw(double, double); double vp_sw(double, double); double rho_sw(double, double); double cheby_poly(double,int); double rho_v(double); double bpe(double); double hfg(double); double condenser(double,double); double rho_w(double); double mu_w(double); double cp_w(double); double k_w(double); int insolation(int); double int_cpsw(double); double int_cpv(double); struct sc { double tfout; double qu; }; sc collector(double, double, double, double); double dt = 5; double s = 35; double pi = 3.142; //Input Parameters double lc = 1; double msw = 0.005556; double asc = 1; 70

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71 // Condenser double di= 0.0762; double dou= 0.1016; double ac = pi*di*lc; double dh = dou di; double across = (pi/4)*(dou*dou di*di); int month, day; double mcw = msw; void main() { //Input parameter double vos = 0.03; ofstream st1; st1.open("Msw=20 Lc=1 VOS= 0.03 Asc=1 Month=12.xls"); // Enter month and day of the year cout<<"Enter the month numb er of the year : "; cin>>month; cout<<"Enter the day of the month : "; cin>>day; // Define Salinity and Ambient Water and Air Temperature double tv0, ta; double tmonth[12] = {10.6, 12.2, 16.0, 20.2, 23.8, 25.4, 27.3, 26.3, 25.3, 21.4, 16.2, 11.9}; tv0 = tmonth[month-1]; ta = tv0; //Hours of Insolation int count1, dj = 5; count1 = insolation(dj); int n = count1*dj*60/dt; cout<<"n = "<
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72 //Tank and connecting tubes Dimensions lt = 0.2; lp = (100000-p0)/(rho_sw(tv0,s)*9.81) lev; at = 0.1; ap = 0.00051; double mev0,mvs0,mps0; // Define Initial mass of flui ds in evaporator, product water tube and vapor space mev0 = (lp*ap+lt*at+lev*aev)*rho_sw(tv0,s); mps0 = ((lev+lp)*ap+lt*at)*rho_sw(tv0,s); mvs0 = vos*rho_v(tv0); double quc; double mv,mb,md; double mev,mps,mvs; double tsw,tveq,tv,tsat,tev,tout,tin,tp,tsatr,tsatv; double p,pgas; double xsw,xb,xev; double q,u; double x,dx; double mev2,mps2,mvs2; double tsat2,tev2,tp2, tsatr2,tsatv2; double p2,pgas2; double xev2; double x2,dx2; double feff; double time; mv = 0.0; mb = 0.0; md = 0.0; tsw = 0.0; tv = 0.0; tout = 0.0; tin = tv0; pgas = 0.0; xb = 0.0; q = 0; u=0; quc = 0; time = 0; int w, i, timecheck; double a1,a2;

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73 mev = mev0; mps = mps0; mvs = mvs0; tsat = tv0; tev = tv0; tp = tv0; tsatv = tv0; xev = 35; xsw = 35; p = p0; pgas = 0; dx = lev; x = lev+lp+lt; int chk = 0; double ins; ifstream insol; insol.open("insolation.txt"); st1<<"tv[i]"<<"\t"<<"tveq[i]"<<"\t"<<"Feff[i ]"<<"\t"<<"tsw[i]"<<"\t"<<"Ins[i]"<<"\t"< <"quc[i]"<<"\t"<<"mv[i]"<<"\t "<<"mb[i]"<<"\t"<<"xb[i]"<<" \t"<<"u[i]"<<"\t"<<"tout[i] "<<"\t"<<"q[i]"<<"\t"<<"md[i]"<<"\t"<<"\t"<<"Time[i]"<<"\t"<<"\t"<<"tsat[i]"<<"\t"<< "tsatv[i]"<<"\t"<<"mvs[i]"<<" \t"<<"pgas[i]"<<"\t"<<"p[i]" <<"\t"<<"mev[i]"<<"\t"<<"te v[i]"<<"\t"<<"xev[i]"<<"\t"<<"mps[i] "<<"\t"<<"tp[i]"<<" \t"<<"x[i]"<>ins; // Inlet Cooling water temperature tin = tv0; // Temperature of vapor produced tveq = tsat + bpe(tsat); // Overall HTC at saturation temperature u = condenser(tsat,tv0); // Outlet temperature of the cooling water

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74 tout = tsat (tsat-tin)*ex p(-(u*ac/(mcw*cp_sw(tin,s)))); // Heat rejected from condenser q = mcw*(int_cpsw(tout)-int_cpsw(tin)); s1 = collector(msw,tout,ta,ins); tsw = s1.tfout; quc = s1.qu; if(tsw>90) break; if(tswa2) tv = tv 0.001; else tv = tv + 0.001; } while(fabs(a1-a2)>0.01); // Mass flow rate if vapor produced mv = msw*(int_cpsw(tsw) int_cpsw(tv))/hfg(tv); // Mass flow rate of falling brine mb = msw-mv; // Salt concentration of falling brine xb = msw*xsw/(msw-mv); // Saturation temperature of the vapor space (only vapor) w = 0; tsat2 = tsat + 0.001; do

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75 { a1 = mvs*(int_cpsw(tsat2) int_cpsw(tsat))/dt; a2 = (mv-vos*(rho_v(tsat2)-rho_v(tsat))/dt)*hf g(tv)-q+mv*(int_cpv(tv )-int_cpv(tsat)); if(fabs(a1-a2)<1) { w=1; } else { if(a1>a2) tsat2 = tsat2 0.001; else tsat2 = tsat2 + 0.001; } } while(w==0); // Pressure in evaportor (vapor+gases) pgas2 = 0.7*mv*dt*8.314*(tsat+273)/(rho_sw(tsw,s)*vos); pgas2 = pgas2 + pgas; p2 = vp_sw(tsat2,s)+pgas2; // Actual saturation temperat ure corresponding to pressure w=0; tsatr2 = tsat2 + 0.001; do { if (fabs(p2-vp_sw(tsatr2,s))<1) w=1; else if(p2>vp_sw(tsatr2,s)) tsatr2 = tsatr2 + 0.001; else tsatr2 = tsatr2 0.001; } while(w==0); tsatv2 = tsat2; tsat2 = tsatr2; // Mass of vapor + gases in the vapor space mvs2 = vos*rho_v(tsatv2) + 0.45*mv*dt*0.028/(rho_sw(tsw,s)*vos) + 0.24*mv*dt*0.032/(rho_sw(tsw,s)*vos); // Product water flow rate if(i==0) md = 0;

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76 else md = mv vos*(rho_v(tsatv2)-rho_v(tsatv))/dt; // Mass of seawater in ev aportor and new vapor space dx2 = dx (p2-p)/(9.81*rho_sw(tev,s)); if(dx>0 && dx2<0) { mev2 = mev dx*aev*rho_sw(tev,s ) ((p2-p)/(9.81*rho_sw(tev,s))dx)*ap*rho_sw(tev,s); x2 = lp + lt ((p2-p)/(9.81*rho_sw(tev,s))-dx); vos = vos2+lev*aev; } else { if(dx2>0) { mev2 = mev aev*(p2-p)/9.81; vos = vos + aev*(p2-p)/(9.81*rho_sw(tev,s)); if (vos>(vos2+lev*aev)) vos = vos2+lev*aev; x2 = x (p2-p)/(9.81*rho_sw(tev,s)); } else { if(dx2<0) { mev2 = mev ap*(p2-p)/9.81; x2 = x (p2-p)/(9.81*rho_sw(tev,s)); } else { if(dx<0 && dx2>0) { mev2 = mev + dx2*aev*rho_sw(tev, s) dx*ap*rho_sw(tev,s); x2 = lp + lt ((p2-p)/(9.81*rho_sw(tev,s))-dx); vos = vos2+(lev-dx2)*aev; } } } } // Temperature of seawater in evaportor tev2 = tev + 0.00001; a2 = (int_cpsw(tv)-int_cpsw(tev))*md; do

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77 { a1 = mev2*(int_cpsw(tev2)-int_cpsw(tev))/dt; if(a1>a2) tev2 = tev2 0.00001; else tev2 = tev2 + 0.00001; } while(fabs(a1-a2)>1); // Salt concentration of seawater in evaporator xev2 = xev + mb*(xb-xev)*dt/mev2; // Mass of product water in the product pipe mps2 = mps ap*(p2-p)/9.81; // Temperature of product water in the product pipe tp2 = tp + 0.00001; a2 = (int_cpsw(tsat)-int_cpsw(tp))*md1; do { a1 = mps2*(int_cpsw(tp2)-int_cpsw(tp))/dt; if(a1>a2) tp2 = tp2 0.00001; else tp2 = tp2 + 0.00001; } while(fabs(a1-a2)>1); //st1<
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78 dx = dx2; x = x2; time = time + dt; if(chk==1) break; } st1.close(); } // Thermal Conductivity of Seawater double k_sw(double t) { return (577 + 1.522*t 0.00581*t*t)/1000; } // Heat Capacity of seawater double cp_sw(double t, double s) { double a1, a2, a3, b1, b2, b3, c1, c2, c3, d1, d2 ,d3, cp; t = t + 273; a1 = 5.328; a2 = -0.0976; a3 = 0.000404; b1 = -0.006913; b2 = 0.0007351; b3 = -0.00000315; c1 = 9.6*pow(10,-6); c2 = -1.927*pow(10,-6); c3 = 8.23*pow(10,-9); d1 = 2.5*pow(10,-9); d2 = 1.666*pow(10,-9); d3 = -7.125*pow(10,-12); cp = ((a1 + a2*s + a3*s*s) + (b1 + b2*s + b3*s *s)*t + (c1 + c2*s + c3*s*s)*t*t + (d1 + d2*s + d3*s*s)*t*t*t)*1000; return cp; } double int_cpsw(double t) { double a1, a2, a3, b1, b2, b3, c1, c2, c3, d1, d2 ,d3, cpt; t = t + 273; a1 = 5.328; a2 = -0.0976; a3 = 0.000404; b1 = -0.006913;

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79 b2 = 0.0007351; b3 = -0.00000315; c1 = 9.6*pow(10,-6); c2 = -1.927*pow(10,-6); c3 = 8.23*pow(10,-9); d1 = 2.5*pow(10,-9); d2 = 1.666*pow(10,-9); d3 = -7.125*pow(10,-12); cpt = ((a1 + a2*s + a3*s*s)*t + (b1 + b2*s + b3*s*s)*t*t/2 + (c1 + c2*s + c3*s*s)*t*t*t/3 + (d1 + d 2*s + d3*s*s)*t*t*t*t/4)*1000; return cpt; } double cp_v(double t) { return ((pow(10,-7)*pow(t,3) 0.0001*t*t + 0.0302*t 1.1804)*1000); } double int_cpv(double t) { return ((pow(10,-7)*pow(t,4)/4 0.0001*t*t*t/3 + 0.0302*t*t/2 1.1804*t)*1000); } // Dynamic Viscosity of Seawater double mu_sw(double t, double s) { double a,a1,a2,b,b1,b2,c1,c2,vis_20,z,vis; a = 1.3722; a1 = -0.001015; a2 = 0.000005; b = 0.000813; b1 = 0.000102; b2 = -0.00004; c1 = 0.001550; c2 = 0.0000093; vis_20 = 1.002 + c1*s + c2*s*s; z = ((t-20)/(t+109))*(a*(1+a1*s+a2* s*s) + b*(1+b1*s+b2*s*s)*(t-20)); vis = (vis_20/pow(10,z))*pow(10,-3); return vis; } // Vapor pressure of seawater double vp_sw(double t, double s) { double z,g,x,y,a,b,c,d,e,f,h,j,q,po,p;

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80 z = 273.16 + t; g = 2.9370*pow(10,5); x = z*z g; y = 344.11 t; a = 5.432368; b = -2.0051*1000; c = 1.3869*pow(10,-4); d = 1.1965*pow(10,-11); e = -0.0044; f = -0.0057148; h = -0.00021609; j = -3.5012*pow(10,-7); q = a + b/z + c*x*(pow(10,d*x*x) 1)/z + e*pow(10,f*pow(y,1.25)); po = pow(10,q); p = po*pow(10,(h*s+j*s*s))*pow(10,5); return p; } // Density of Seawater double rho_sw(double t, double s) { double m,n,sumj=0,sumi=0,density; double c[4][3] = { {4.032219, 0.115313, 0.000326}, {-0.108199, 0.001571, -0.000423}, {-0.012247, 0.001740, -0.000009}, {0.000692, -0.000087, -0.000053} }; m = (2*s 150)/150; n = (2*t 200)/160; for (int i=0; i<4; i++) { for(int j=0; j<3; j++) { if (j==0) sumj = sumj + c[i][j]*cheby_poly(m,j)/2; else sumj = sumj + c[i][j]*cheby_poly(m,j); } if (i==0) sumi = sumi + sumj*cheby_poly(n,i)/2; else sumi = sumi + sumj*cheby_poly(n,i); sumj = 0; }

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81 density = sumi*1000; return density; } double cheby_poly(double x, int i) { double T; if (i==0) T = 1; if (i==1) T = x; if (i==2) T = 2*x*x 1; if (i==3) T = 4*x*x*x 3*x; return T; } // Density of Vapor double rho_v(double t) { double v; v = 4.605*(t+273.15)*100/(vp_sw(t,35)) 0.02; return (1/v); } // Boiling point elevation of seawater double bpe(double t) { t = t + 273; double c, elv; double cb = 0.035; c = 19.819*cb/(1-cb); elv = c*t*t*(565.757/t 9.81559 + 1.54739*l og(t) c*(337.178/t 6.41981 + 0.922753*log(t)) + c*c*(32.681/t 0.55368 + 0.079022*log(t)))/(266919.6 379.669*t + 0.334169*t*t); return elv; } //Latent heat of vaporization of water double hfg(double t) { return 1000*(3146 2.36*(t+273)); }

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82 double condenser(double tsat, double tinn) { double ts,hi,ho,u,e1,e2,hfg_n,Red,Nuo,t out,tavg,tin,Pr_sw,tdt; tin = tinn; ts = tsat 0.001; tout = ts; int e = 1; if(tsat==tin) { u=0; tout=tin; tdt=0; ts=tin; tavg=tin; } else { do { tavg = (tout+tin)/2; hfg_n = hfg(tsat) + (3 /8)*cp_w(tsat)*(tsat-ts); hi = 0.555*pow((9.81*rho_w(tsat)*(rho_w(tsat) rho_v(tsat))*pow(k_w(tsat),3)*hfg_n/(mu_w(tsat)*( tsat-ts)*di)),0.25); Red = mcw*dh/(across*mu_sw(tavg,s)); if (Red<2300) { Nuo = 5.58; } else { Pr_sw = mu_sw(tavg,s)*cp_sw(tavg,s)/k_sw(tavg); Nuo = 0.023*pow(Red,0.8)*pow(Pr_sw,0.4); } ho = Nuo*k_sw(tavg)/dh; e1 = hi*ac*(tsat-ts); tout = tin + e1/(mcw*cp_sw(tavg,s)); tdt = (tout-tin)/log((tsat-tin)/(tsat-tout)); u = hi*ho/(hi+ho); e2 = u*ac*dt; if(fabs(e1-e2)<0.1) {

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83 e=0; } else { if(e1>e2) ts = ts + 0.000001; else ts = ts 0.000001; } } while(e==1); } return u; } // Density of Water double rho_w(double t) { return ((999.83952 + 16.945176*t 7.9870401*pow(10,-3)*t*t 46.170461*pow(10,-6)*t*t*t + 105.56302*pow( 10,-9)*t*t*t*t 280.5423*pow(10,12)*t*t*t*t*t)/(1 + 16.879850*pow(10,-3)*t)); } // Dynamic Viscosity of Water double mu_w(double t) { t = t + 273; double w; w = -10.2158+1792.5/t+0.01773*t-1.2631*pow(10,-5)*t*t; return (pow(10,w)/1000); } // Specific Heat of Water double cp_w(double t) { return (1000*(4.2174 3.720283*pow( 10,-3)*t + 1.412855*pow(10,-4)*t*t 2.654387*pow(10,-6)*t*t*t + 2.093 236*pow(10,-8)*t*t*t*t)); } // Thermal Conductivity of Water double k_w(double t) { t = t + 273; return (-0.2758+0.004612*t-5.5391*pow(10,-6)*t*t); }

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84 int insolation(int dj) { double pi = 3.1415926535; double lat, lon, lst; double p; lat = 29.68; lon = 82.27; lst = 75; p = pi/180; double n; int mo[12] = {0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334}; n = day + mo[month-1]; double delta_s; delta_s = 23.45*sin(360*(284+n)*p/365); double b, et, det; b = 360*(n-81)/364; et = 9.87*sin(2*b*p) 7 .53*cos(b*p) 1.5*sin(b*p); det = et + (lst-lon)*4; double dsn; dsn = 4*acos(-(tan(lat* p)*tan(delta_s*p)))/p; int dsni, deti; dsni = dsn; if((dsn-dsni)>0.5) dsni = ceil(dsn); else dsni = floor(dsn); deti = det; if(fabs(det-deti)>0.5) deti = ceil(det); else deti = floor(det); int deth, detm; if(deti>60) { detm = deti%60; deth = deti/60; } else { detm = deti; deth = 0; }

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85 int min, hour, ssrh, ssrm, sssh, sssm; min = dsni%60; hour = abs(dsni/60); ssrh = 11-hour; ssrm = 60-min; sssh = hour; sssm = min; int lsrh, lsrm, lssh, lssm; char rm, sm; rm = '; sm = '; lsrh = ssrh deth; lsrm = ssrm detm; if(lsrm<0) { lsrm = 60 + lsrm; lsrh = lsrh 1; } if(lsrm>60) { lsrm = lsrm 60; lsrh = lsrh + 1; } lssh = sssh deth; lssm = sssm detm; if(lssm<0) { lssm = 60 + lssm; lssh = lssh 1; } if(lssm>60) { lssm = lssm 60; lssh = lssh + 1; } if(lsrm<10) rm = '0'; if(lssm<10) sm = '0'; cout<<"Sunrise time = "<
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86 ofstream inso_file("insolation.txt"); int hs; hs = sssh*60+sssm; double alpha_w = 0, alpha_s, alpha, ia; double beta; beta = fabs(lat); int io = 1377; double i; i = io*(1 + 0.034*cos(360*n*p/365.25)); double ibn, ibc, idc, irc, ic, jhs; int j, cn=1; double rho = 0.2; double te, tw; double k[12] = {0.142, 0.144, 0.156, 0.18, 0.196, 0.205, 0.207, 0.201, 0.177, 0.16, 0.149, 0.142}; double c[12] = {0.058, 0.06, 0.071, 0.097, 0.121, 0.134, 0.136, 0.122, 0.092, 0.073, 0.063, 0.057}; char ch; ch = 'A'; int count=0, llsrh; double llsrm, l1, l2; for (j=-hs+1; j=12) { ch = 'P'; if(lsrh>12) llsrh = lsrh 12; } else llsrh = lsrh; jhs = j/4; alpha = asin(sin(lat*p)*sin(delta_s*p) + cos(lat*p)*cos(delta_s*p)*cos(jhs*p))/p;

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87 alpha_s = asin(cos(delta_s *p)*sin(jhs*p)/cos(alpha*p))/p; te = -acos(tan(delta_ s*p)/tan(lat*p))*60/(p*15); tw = -te; if(lat>delta_s) { if(tej) alpha_s = (180 fabs(alpha_s)); } if(lat<=delta_s) alpha_s = 180 fabs(alpha_s); if(j<0) alpha_s = -alpha_s; ia = acos(cos(alpha*p)*cos((al pha_s-alpha_w)*p)*sin(beta*p) + sin(alpha*p)*cos(beta*p))/p; ibn = cn*i*exp(-k[month-1]/sin(alpha*p)); if(ia>90) ibc=0; else ibc = ibn*cos(ia*p); idc = c[month-1]*ibn*pow(cos(beta*p/2),2); irc = rho*ibn*(sin(alpha*p)+c [month-1])*pow(sin(beta*p/2),2); ic = ibc+idc+irc; llsrm = lsrm; l1 = lsrh; l2 = l1+llsrm/60; if(ia<=60) { inso_file<
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APPENDIX C COMPUTER PROGRAM FOR TWO-STAGE SYSTEM #include #include #include #include double k_sw(double); double cp_sw(double, double); double mu_sw(double, double); double vp_sw(double, double); double rho_sw(double, double); double cheby_poly(double,int); double rho_v(double); double cp_v(double); double bpe(double); double hfg(double); double condenser1(double,double); double condenser2(double,double); double rho_w(double); double mu_w(double); double cp_w(double); double k_w(double); int insolation(int); double int_cpsw(double); double int_cpv(double); struct sc { double tfout; double qu; }; sc collector(double, double, double, double); double dt = 1; double s = 35; double pi = 3.142; // Condenser 1 88

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89 double di1= 0.0762; double dou1= 0.1016; double lc1 = 1; double ac1 = pi*di1*lc1; double dh1 = dou1 di1; double across1 = (pi/4)*(dou1*dou1 di1*di1); //Condenser 2 double di2 = 0.0762; double dou2 = 0.1016; double lc2 = 1; double ac2 = pi*di2*lc2; double dh2 = dou2 di2; double across2 = (pi/4)*(dou2*dou2 di2*di2); double msw = 0.005556; double mcw = msw; int month, day; void main() { // Enter month and day of the year cout<<"Enter the month numb er of the year : "; cin>>month; cout<<"Enter the day of the month : "; cin>>day; // Define Salinity and Ambient Water and Air Temperature double tv0, ta; double tmonth[12] = {10.6, 12.2, 16.0, 20.2, 23.8, 25.4, 27.3, 26.3, 25.3, 21.4, 16.2, 11.9}; tv0 = tmonth[month-1]; ta = tv0; //Hours of Insolation; dj in minutes int count1, dj = 5; count1 = insolation(dj); cout<<"count1 = "<>ins;

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94 } // Set Cooling water flow rate = Inlet feedwater flow rate msw1 = msw; // Temperature of vapor produced tveq1 = tsat1 + bpe(tsat1); //Inlet cooling water temp erature to condenser 1 if(ychk==0) tin1 = tv0; else tin1 = tout2; // Overall HTC at saturation temperature u1 = condenser1(tsat1,tin1); // Outlet temperature of the cooling water tout1 = tsat1 (tsat1-tin1)*e xp(-(u1*ac1/(mcw*cp_sw(tin1,s)))); // Heat rejected from condenser q1 = mcw*(int_cpsw(tout1)-int_cpsw(tin1)); s1 = collector(msw 1,tout1,ta,ins); tsw1 = s1.tfout; quc1 = s1.qu; if(tsw1a2) tv1 = tv1 0.00001; else tv1 = tv1 + 0.00001; }

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95 while(fabs(a1-a2)>0.01); // Mass flow rate if vapor produced mv1 = msw*(int_cpsw(tsw1) int_cpsw(tv1))/hfg(tv1); // Mass flow rate of falling brine mb1 = msw1-mv1; // Salt concentration of falling brine xb1 = msw1*xsw1/(msw1-mv1); // Saturation temperature of the vapor space (only vapor) w = 0; tsat1n= tsat1 + 0.0001; do { a1 = mvs1*(int_cpsw(tsat1n) int_cpsw(tsat1))/dt; a2 = (mv1-vos1*(rho_v(tsat1n)-rho_v(tsat1) )/dt)*hfg(tv1)-q1+mv1*(int_cpv(tv1)int_cpv(tsat1)); if(fabs(a1-a2)<1) { w=1; } else { if(a1>a2) tsat1n = tsat1n 0.0001; else tsat1n = tsat1n + 0.0001; } } while(w==0); // Pressure in evaporator (vapor+gases) pgas1n = 0.7*mv1*dt*8.314*(tsat1+273) /(rho_sw(tsw1,s)*vos1); pgas1n = pgas1n + pgas1; p1n = vp_sw(tsat1n,s)+pgas1n; // Actual saturation temperat ure corresponding to pressure w=0; tsatr1n = tsat1n + 0.0001; do { if (fabs(p1n-vp_sw(tsatr1n,s))<1) w=1; else

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96 if(p1n>vp_sw(tsatr1n,s)) tsatr1n = tsatr1n + 0.0001; else tsatr1n = tsatr1n 0.0001; } while(w==0); tsatv1n = tsat1n; tsat1n = tsatr1n; // Mass of vapor + gases in the vapor space mgas1 = mgas1 + 0.45*mv1*dt*0.028/(rho_sw(tsw1,s)*vos1) + 0.24*mv1*dt*0.032/(rho_sw(tsw1,s)*vos1); mvs1n = vos1*rho_v(tsatv1n) + mgas1; // Product water flow rate if(i==0) md1 = 0; else md1 = mv1 vos1*(rho_v(tsatv1n)-rho_v(tsatv1))/dt; // Mass of seawater in ev aportor and new vapor space x1 = mev1/(rho_sw(tev1,s)*aev1); if(x1>y) ychk=1; if(ychk==1) msw2 = 0.6*aorf*pow(2*rho_sw(te v1,s)*(p1+rho_sw(tev1,s)*9.81*x1-p2),0.5); else msw2 = 0; mev1n = mev1 + (mb1 msw2)*dt; if(i==0) tev1 = tv1; // Temperature of seawater in evaporator tev1n = tev1 + 0.00001; a2 = (int_cpsw(tv1)-i nt_cpsw(tev1))*md1; do { a1 = mev1n*(int_cpsw(tev1n)-int_cpsw(tev1))/dt; if(a1>a2) tev1n = tev1n 0.00001; else tev1n = tev1n + 0.00001; }

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97 while(fabs(a1-a2)>1); // New Vapor Space if(x1>0) { vos1 = vos11 mev1n/rho_sw(tev1n,s); } // Salt concentration of seawater in evaporator xev1n = (mev1*xev1 + (mb1*xb1 msw2*xev1)*dt)/mev1n; // Mass of product water in the product pipe mps1n = mps1 ap*(p1n-p1)/9.81; // Temperature of product water in the product pipe tp1n = tp1 + 0.00001; a2 = (int_cpsw(tsat1) -int_cpsw(tp1))*md1; do { a1 = mps1n*(int_cpsw(tp1n)-int_cpsw(tp1))/dt; if(a1>a2) tp1n = tp1n 0.00001; else tp1n = tp1n + 0.00001; } while(fabs(a1-a2)>1); cout<
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98 // Temperature of vapor produced tveq2 = tsat2 + bpe(tsat2); // Overall HTC at saturation temperature u2 = condenser2(tsat2,tv0); // Outlet temperature of the cooling water tout2 = tsat2 (tsat2-tin2)*e xp(-(u2*ac2/(mcw*cp_sw(tin2,s)))); // Temperature of feed seawater tsw2 = tev1; // Heat rejected from condenser q2 = mcw*(int_cpsw(tout2)-int_cpsw(tin2)); xsw2 = xev1; // Non-Equilibrium Allowance (Flashing efficieny) feff2 = 1 1/(1+1.5*(tsw2-tsat2-3)); // Actual Vapor temperature tv2 = tveq2 + 0.00001; a1 = feff2*(int_cpsw(tsw2)-int_cpsw(tveq2))/hfg(tveq2); do { a2 = (int_cpsw(tsw2)-int_cpsw(tv2))/hfg(tv2); if(a1>a2) tv2 = tv2 0.00001; else tv2 = tv2 + 0.00001; } while(fabs(a1-a2)>0.01); // Mass flow rate if vapor produced mv2 = msw2*(int_cpsw(tsw2) int_cpsw(tv2))/hfg(tv2); //cout<
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99 do { a1 = mvs2*(int_cpsw(tsat2n) int_cpsw(tsat2))/dt; a2 = (mv2-vos2*(rho_v(tsat2n)-rho_v(tsat2) )/dt)*hfg(tv2)-q2+mv2*(int_cpv(tv2)int_cpv(tsat2)); if(fabs(a1-a2)<1) { w=1; } else { if(a1>a2) tsat2n = tsat2n 0.0001; else tsat2n = tsat2n + 0.0001; } } while(w==0); // Pressure in evaportor (vapor+gases) pgas2n = 0.7*mv2*dt*8.314*(tsat2+273) /(rho_sw(tsw2,s)*vos2); pgas2n = pgas2n + pgas2; p2n = vp_sw(tsat2n,s)+pgas2n; // Actual saturation temperat ure corresponding to pressure w=0; tsatr2n = tsat2n + 0.0001; do { if (fabs(p2n-vp_sw(tsatr2n,s))<1) w=1; else if(p2n>vp_sw(tsatr2n,s)) tsatr2n = tsatr2n + 0.0001; else tsatr2n = tsatr2n 0.0001; } while(w==0); tsatv2n = tsat2n; tsat2n = tsatr2n; // Mass of vapor + gases in the vapor space mgas2 = mgas2 + 0.45*mv2*dt*0.028/(rho_sw(tsw2,s)*vos2) + 0.24*mv2*dt*0.032/(rho_sw(tsw2,s)*vos2); mvs2n = vos2*rho_v(tsatv2n) + mgas2;

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100 // Product water flow rate if(i<2) md2 = 0; else md2 = mv2 vos2*(rho_v(tsatv2n)-rho_v(tsatv2))/dt; // Mass of seawater in ev aportor and new vapor space dx2n = dx2 (p2n-p2)/(9.81*rho_sw(tev2,s)); if(dx2>0 && dx2n<0) { mev2n = mev2 dx2*aev2*rho_sw(tev2,s) ((p2n-p2)/(9.81*rho_sw(tev2,s))dx2)*ap*rho_sw(tev2,s); x2n = lp + lt ((p2n-p2)/(9.81*rho_sw(tev2,s))-dx2); vos2 = vos21+lev2*aev2; } else { if(dx2n>0) { mev2n = mev2 aev2*(p2n-p2)/9.81; vos2 = vos2 + aev2*(p2n-p2)/(9.81*rho_sw(tev2,s)); if (vos2>(vos21+lev2*aev2)) vos2 = vos21+lev2*aev2; x2n = x2 (p2n-p2)/(9.81*rho_sw(tev2,s)); } else { if(dx2n<0) { mev2n = mev2 ap*(p2n-p2)/9.81; x2n = x2 (p2n-p2)/(9.81*rho_sw(tev2,s)); } else { if(dx2<0 && dx2n>0) { mev2n = mev2 + dx2n*aev2*rho_sw(tev2,s) dx2*ap*rho_sw(tev2,s); x2n = lp + lt ((p2n-p2)/(9.81*rho_sw(tev2,s))-dx2); vos2 = vos21+(lev2-dx2n)*aev2; } } } } // Temperature of seawater in evaportor tev2n = tev2 + 0.00001;

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101 a2 = (int_cpsw(tv2)-i nt_cpsw(tev2))*md2; do { a1 = mev2n*(int_cpsw(tev2n)-int_cpsw(tev2))/dt; if(a1>a2) tev2n = tev2n 0.00001; else tev2n = tev2n + 0.00001; } while(fabs(a1-a2)>1); // Salt concentration of seawater in evaporator xev2n = xev2 + mb2*(xb2-xev2)*dt/mev2n; // Mass of product water in the product pipe mps2n = mps2 ap*(p2n-p2)/9.81; // Temperature of product water in the product pipe tp2n = tp2 + 0.00001; a2 = (int_cpsw(tsat2) -int_cpsw(tp2))*md2; do { a1 = mps2n*(int_cpsw(tp2n)-int_cpsw(tp2))/dt; if(a1>a2) tp2n = tp2n 0.00001; else tp2n = tp2n + 0.00001; } while(fabs(a1-a2)>1); st2<
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102 tp2 = tp2n; dx2 = dx2n; x2 = x2n; } if(chk==1) break; tsat1 = tsat1n; pgas1 = pgas1n; p1 = p1n; tsatv1 = tsatv1n; tsatr1 = tsatr1n; mvs1 = mvs1n; mev1 = mev1n; tev1 = tev1n; xev1 = xev1n; mps1 = mps1n; tp1 = tp1n; } st1.close(); st2.close(); } // Thermal Conductivity of Seawater double k_sw(double t) { return (577 + 1.522*t 0.00581*t*t)/1000; } // Heat Capacity of seawater double cp_sw(double t, double s) { double a1, a2, a3, b1, b2, b3, c1, c2, c3, d1, d2 ,d3, cp; t = t + 273; a1 = 5.328; a2 = -0.0976; a3 = 0.000404; b1 = -0.006913; b2 = 0.0007351; b3 = -0.00000315; c1 = 9.6*pow(10,-6); c2 = -1.927*pow(10,-6);

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103 c3 = 8.23*pow(10,-9); d1 = 2.5*pow(10,-9); d2 = 1.666*pow(10,-9); d3 = -7.125*pow(10,-12); cp = ((a1 + a2*s + a3*s*s) + (b1 + b2*s + b3*s *s)*t + (c1 + c2*s + c3*s*s)*t*t + (d1 + d2*s + d3*s*s)*t*t*t)*1000; return cp; } double int_cpsw(double t) { double a1, a2, a3, b1, b2, b3, c1, c2, c3, d1, d2 ,d3, cpt; t = t + 273; a1 = 5.328; a2 = -0.0976; a3 = 0.000404; b1 = -0.006913; b2 = 0.0007351; b3 = -0.00000315; c1 = 9.6*pow(10,-6); c2 = -1.927*pow(10,-6); c3 = 8.23*pow(10,-9); d1 = 2.5*pow(10,-9); d2 = 1.666*pow(10,-9); d3 = -7.125*pow(10,-12); cpt = ((a1 + a2*s + a3*s*s)*t + (b1 + b2*s + b3*s*s)*t*t/2 + (c1 + c2*s + c3*s*s)*t*t*t/3 + (d1 + d 2*s + d3*s*s)*t*t*t*t/4)*1000; return cpt; } double cp_v(double t) { return ((pow(10,-7)*pow(t,3) 0.0001*t*t + 0.0302*t 1.1804)*1000); } double int_cpv(double t) { return ((pow(10,-7)*pow(t,4)/4 0.0001*t*t*t/3 + 0.0302*t*t/2 1.1804*t)*1000); } // Dynamic Viscosity of Seawater double mu_sw(double t, double s) { double a,a1,a2,b,b1,b2,c1,c2,vis_20,z,vis; a = 1.3722; a1 = -0.001015;

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104 a2 = 0.000005; b = 0.000813; b1 = 0.000102; b2 = -0.00004; c1 = 0.001550; c2 = 0.0000093; vis_20 = 1.002 + c1*s + c2*s*s; z = ((t-20)/(t+109))*(a*(1+a1*s+a2* s*s) + b*(1+b1*s+b2*s*s)*(t-20)); vis = (vis_20/pow(10,z))*pow(10,-3); return vis; } // Vapor pressure of seawater double vp_sw(double t, double s) { double z,g,x,y,a,b,c,d,e,f,h,j,q,po,p; z = 273.16 + t; g = 2.9370*pow(10,5); x = z*z g; y = 344.11 t; a = 5.432368; b = -2.0051*1000; c = 1.3869*pow(10,-4); d = 1.1965*pow(10,-11); e = -0.0044; f = -0.0057148; h = -0.00021609; j = -3.5012*pow(10,-7); q = a + b/z + c*x*(pow(10,d*x*x) 1)/z + e*pow(10,f*pow(y,1.25)); po = pow(10,q); p = po*pow(10,(h*s+j*s*s))*pow(10,5); return p; } // Density of Seawater double rho_sw(double t, double s) { double m,n,sumj=0,sumi=0,density; double c[4][3] = { {4.032219, 0.115313, 0.000326}, {-0.108199, 0.001571, -0.000423}, {-0.012247, 0.001740, -0.000009}, {0.000692, -0.000087, -0.000053} }; m = (2*s 150)/150;

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105 n = (2*t 200)/160; for (int i=0; i<4; i++) { for(int j=0; j<3; j++) { if (j==0) sumj = sumj + c[i][j]*cheby_poly(m,j)/2; else sumj = sumj + c[i][j]*cheby_poly(m,j); } if (i==0) sumi = sumi + sumj*cheby_poly(n,i)/2; else sumi = sumi + sumj*cheby_poly(n,i); sumj = 0; } density = sumi*1000; return density; } double cheby_poly(double x, int i) { double T; if (i==0) T = 1; if (i==1) T = x; if (i==2) T = 2*x*x 1; if (i==3) T = 4*x*x*x 3*x; return T; } // Density of Vapor double rho_v(double t) { double v; v = 4.605*(t+273.15)*100/(vp_sw(t,35)) 0.02; return (1/v); } // Boiling point elevation of seawater double bpe(double t) {

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106 t = t + 273; double c, elv; double cb = 0.035; c = 19.819*cb/(1-cb); elv = c*t*t*(565.757/t 9.81559 + 1.54739*l og(t) c*(337.178/t 6.41981 + 0.922753*log(t)) + c*c*(32.681/t 0.55368 + 0.079022*log(t)))/(266919.6 379.669*t + 0.334169*t*t); return elv; } //Latent heat of vaporization of water double hfg(double t) { return 1000*(3146 2.36*(t+273)); } // Condenser Analysis for overall HTC double condenser1(double tsat, double tinn) { double ts,hi,ho,u,e1,e2,hfg_n,Red,Nuo,t out,tavg,tin,Pr_sw,tdt; tin = tinn; ts = tsat 0.001; tout = ts; int e = 1; if(tsat==tin) { u=0; tout=tin; tdt=0; ts=tin; tavg=tin; } else { do { tavg = (tout+tin)/2; hfg_n = hfg(tsat) + (3 /8)*cp_w(tsat)*(tsat-ts); hi = 0.555*pow((9.81*rho_w(tsat)*(rho_w(tsat) rho_v(tsat))*pow(k_w(tsat),3)*hfg_n/(mu_w(tsat)*( tsat-ts)*di1)),0.25); Red = mcw*dh1/(across1*mu_sw(tavg,s)); if (Red<2300) { Nuo = 5.58; }

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107 else { Pr_sw = mu_sw(tavg,s)*cp_sw(tavg,s)/k_sw(tavg); Nuo = 0.023*pow(Red,0.8)*pow(Pr_sw,0.4); } ho = Nuo*k_sw(tavg)/dh1; e1 = hi*ac1*(tsat-ts); tout = tin + e1/(mcw*cp_sw(tavg,s)); tdt = (tout-tin)/log((tsat-tin)/(tsat-tout)); u = hi*ho/(hi+ho); e2 = u*ac1*dt; if(fabs(e1-e2)<0.1) { e=0; } else { if(e1>e2) ts = ts + 0.000001; else ts = ts 0.000001; } } while(e==1); } return u; } double condenser2(double tsat, double tinn2) { double ts,hi,ho,u,e1,e2,hfg_n,Red,Nuo,t out,tavg,tin,Pr_sw,tdt; tin = tinn2; ts = tsat 0.001; tout = ts; int e = 1; if(tsat==tin) { u=0; tout=tin; tdt=0; ts=tin; tavg=tin; }

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108 else { do { tavg = (tout+tin)/2; hfg_n = hfg(tsat) + (3 /8)*cp_w(tsat)*(tsat-ts); hi = 0.555*pow((9.81*rho_w(tsat)*(rho_w(tsat) rho_v(tsat))*pow(k_w(tsat),3)*hfg_n/(mu_w(tsat)*( tsat-ts)*di2)),0.25); Red = mcw*dh2/(across2*mu_sw(tavg,s)); if (Red<2300) { Nuo = 5.58; } else { Pr_sw = mu_sw(tavg,s)*cp_sw(tavg,s)/k_sw(tavg); Nuo = 0.023*pow(Red,0.8)*pow(Pr_sw,0.4); } ho = Nuo*k_sw(tavg)/dh2; e1 = hi*ac1*(tsat-ts); tout = tin + e1/(mcw*cp_sw(tavg,s)); tdt = (tout-tin)/log((tsat-tin)/(tsat-tout)); u = hi*ho/(hi+ho); e2 = u*ac2*dt; if(fabs(e1-e2)<0.1) { e=0; } else { if(e1>e2) ts = ts + 0.000001; else ts = ts 0.000001; } } while(e==1); } return u; } // Density of Water

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109 double rho_w(double t) { return ((999.83952 + 16.945176*t 7.9870401*pow(10,-3)*t*t 46.170461*pow(10,-6)*t*t*t + 105.56302*pow( 10,-9)*t*t*t*t 280.5423*pow(10,12)*t*t*t*t*t)/(1 + 16.879850*pow(10,-3)*t)); } // Dynamic Viscosity of Water double mu_w(double t) { t = t + 273; double w; w = -10.2158+1792.5/t+0.01773*t-1.2631*pow(10,-5)*t*t; return (pow(10,w)/1000); } // Specific Heat of Water double cp_w(double t) { return (1000*(4.2174 3.720283*pow( 10,-3)*t + 1.412855*pow(10,-4)*t*t 2.654387*pow(10,-6)*t*t*t + 2.093 236*pow(10,-8)*t*t*t*t)); } // Thermal Conductivity of Water double k_w(double t) { t = t + 273; return (-0.2758+0.004612*t-5.5391*pow(10,-6)*t*t); } int insolation(int dj) { double pi = 3.1415926535; double lat, lon, lst; double p; lat = 29.68; lon = 82.27; lst = 75; p = pi/180; double n; int mo[12] = {0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334}; n = day + mo[month-1];

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110 double delta_s; delta_s = 23.45*sin(360*(284+n)*p/365); double b, et, det; b = 360*(n-81)/364; et = 9.87*sin(2*b*p) 7 .53*cos(b*p) 1.5*sin(b*p); det = et + (lst-lon)*4; double dsn; dsn = 4*acos(-(tan(lat* p)*tan(delta_s*p)))/p; int dsni, deti; dsni = dsn; if((dsn-dsni)>0.5) dsni = ceil(dsn); else dsni = floor(dsn); deti = det; if(fabs(det-deti)>0.5) deti = ceil(det); else deti = floor(det); int deth, detm; if(deti>60) { detm = deti%60; deth = deti/60; } else { detm = deti; deth = 0; } int min, hour, ssrh, ssrm, sssh, sssm; min = dsni%60; hour = abs(dsni/60); ssrh = 11-hour; ssrm = 60-min; sssh = hour; sssm = min; int lsrh, lsrm, lssh, lssm; char rm, sm; rm = '; sm = ';

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111 lsrh = ssrh deth; lsrm = ssrm detm; if(lsrm<0) { lsrm = 60 + lsrm; lsrh = lsrh 1; } if(lsrm>60) { lsrm = lsrm 60; lsrh = lsrh + 1; } lssh = sssh deth; lssm = sssm detm; if(lssm<0) { lssm = 60 + lssm; lssh = lssh 1; } if(lssm>60) { lssm = lssm 60; lssh = lssh + 1; } if(lsrm<10) rm = '0'; if(lssm<10) sm = '0'; cout<<"Sunrise time = "<
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112 double te, tw; double k[12] = {0.142, 0.144, 0.156, 0.18, 0.196, 0.205, 0.207, 0.201, 0.177, 0.16, 0.149, 0.142}; double c[12] = {0.058, 0.06, 0.071, 0.097, 0.121, 0.134, 0.136, 0.122, 0.092, 0.073, 0.063, 0.057}; char ch; ch = 'A'; int count=0, llsrh; double llsrm, l1, l2; for (j=-hs+1; j=12) { ch = 'P'; if(lsrh>12) llsrh = lsrh 12; } else llsrh = lsrh; jhs = j/4; alpha = asin(sin(lat*p)*sin(delta_s*p) + cos(lat*p)*cos(delta_s*p)*cos(jhs*p))/p; alpha_s = asin(cos(delta_s *p)*sin(jhs*p)/cos(alpha*p))/p; te = -acos(tan(delta_ s*p)/tan(lat*p))*60/(p*15); tw = -te; if(lat>delta_s) { if(tej) alpha_s = (180 fabs(alpha_s)); } if(lat<=delta_s) alpha_s = 180 fabs(alpha_s);

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113 if(j<0) alpha_s = -alpha_s; ia = acos(cos(alpha*p)*cos((al pha_s-alpha_w)*p)*sin(beta*p) + sin(alpha*p)*cos(beta*p))/p; ibn = cn*i*exp(-k[month-1]/sin(alpha*p)); if(ia>90) ibc=0; else ibc = ibn*cos(ia*p); idc = c[month-1]*ibn*pow(cos(beta*p/2),2); irc = rho*ibn*(sin(alpha*p)+c [month-1])*pow(sin(beta*p/2),2); ic = ibc+idc+irc; llsrm = lsrm; l1 = lsrh; l2 = l1+llsrm/60; if(ia<60) { inso_file<
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116 26. Hongfei, Z., Xiaoyan, Z., Jing, Z., an d Yuyuan, W., 2002, "A group of improved heat and mass transfer correlations in solar stills," Energy Conversion and Management, 43, pp. 2469-2478. 27. Tanaka, H., and Nakatake, Y., 2005, "A si mple and highly productive solar still: a vertical multiple-effect diffusion-type sola r still coupled with a fiat-plate mirror," Desalination, 173, pp. 287-300. 28. Badran, A.A., A1-Hallaq, A.A., Eyal Salman, I. A., and Odat, M. Z., 2005, "A solar still augmented with a flat-plate collector," Desalination, 172, pp. 227-234. 29. E1-Bahi, A., and Inan, D., 1993, "A solar still with minimum inclination, coupled to an outside condenser," Desalination, 123, pp. 79-83. 30. Aybar, H.S., Egelioglu, F., and Atikol U., 2005, "An experimental study on an inclined solar water distil lation system," Desalination, 180, pp. 285-289. 31. Minasian A. N. and Al-Karaghouli A. A., 1995, An improved solar still: The wick-basin type, Energy Convers ion and Management, 36(3), pp. 213-217. 32. Tripathi R. and Tiwari G. N., 2005, "Eff ect of water depth on intemal heat and mass transfer for active solar dist illation," Desalination, 173, pp. 187-200. 33. El-Sebaii, A.A., 2004, "Effect of wind speed on active and passive solar stills," Energy Conversion and Management, 45, pp. 1187-1204. 34. Al-Hussaini, H., and Smith, I.K., 1995, "Enhancing of solar still productivity using vacuum technology," Ener gy Conversion and Management, 36(11), pp. 1047-1051. 35. Tchindaa, R., Kaptouoma, E., and Njom o, D., 1999, "Heat and mass transfer processes in a solar still with an indirect evaporator-condenser," Energy Conversion & Management, 41, pp. 93-107. 36. Naim, M.M., and Abd El Kawi, M.A., 2002, "Non-conventional solar stills: Part 1. Non-conventional solar sti lls with charcoal particle s as absorber medium," Desalination, 153, pp. 55-64. 37. Tiwari, G.N., Thomas, J.M., and Khan, E., 1994, Optimization of glass cover inclination for maximum yield in a solar still, Heat Recovery Systems and CHP, 14(4), pp. 447-455. 38. Tamimi, A., 1987, Performance of a solar still with reflectors and black dye, Solar and Wind Technology, 4(4), pp. 443-446.

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117 39. Al-Karaghouli, A.A., and Alnaserb, W.E., 2004, "Performances of single and double basin solar-stills," Applied Energy, 78, pp. 347-354. 40. E1-Sebaii, A.A., 2005, "Thermal performa nce of a triple-bas in solar still," Desalination, 174, pp. 23-37. 41. Dhiman, N.K., 1988, Transient analysis of a spherical solar still, Desalination, 69, pp. 47-55. 42. Radhwan, A.M., 2004, "Transient performance of a stepped solar still with builtin latent heat thermal energy storage," Desalination, 171, pp. 61-76. 43. Abu-Hijleh, B., and Mousa, H.A., 1997, Wat er film cooling over the glass cover of a solar still including ev aporation effects, Energy, 22(1), pp. 43-48. 44. Sharma, S.K., and Goswami, D.Y, 1 994, Low temperature energy conversion system, unpublished document, Solar Energy and Energy Conversion Laboratory, University of Florida. 45. Al-Kharabsheh, S., and Goswami, D.Y., 2003, "Analysis of an innovative water desalination system using low-grade sola r heat," Desalination, 156(1-3), pp. 323332. 46. Miyatake, O., 1994, "Comparative study of fl ash evaporation rates," Desalination, 96, pp. 163-171. 47. Miyatake, O., Koito, Y., Tagawa, K ., and Maruta, Y., 2001, "Transient characteristics and performance of a novel desalination system based on heat storage and spray flashing," Desalination, 137(1-3), pp. 157-166. 48. Incropera, F.P. and DeWitt, D.P., 2002, Fundamentals of Heat and Mass transfer fifth edition, John Wiley & Sons, New York. 49. Seifert, A., and Genthner, K., 1991, "A model for stagewise calculation of noncondensable gases in multi-stage ev aporators," Desalination, 81(1-3), pp. 333347. 50. Bemporad, G.A., 1995, Basic hydrodynamic aspects of a solar energy based desalination process, Desalination, 54(2), pp. 125-134. 51. Hermann, M., Koschikowski, J., and Ro mmel, M., 2002, "Corrosion-free solar collectors for thermally dr iven seawater desalination," Solar Energy, 72(5), pp. 415-426. 52. Goswami, D.Y., Kreith, F., and Kreider, J.F., 2000, Principles of Solar Engineering second edition, Taylor & Francis, Philadelphia.

PAGE 132

118 53. Isdale, J.D., and R. Morris, R., 1972, "Phys ical properties of sea water solutions: density," Desalination, 10(4), pp. 329-339. 54. Jamieson, D.T., Tudhope, J.S., Morris, R., and Cartwright, G., 1969, "Physical properties of sea water solutions: heat capacity," Desalination, 7(1), pp. 23-30. 55. Isdale, J.D., Spence, C.M., and Tudhope, J.S., 1972, "Physical properties of sea water solutions: viscosity," Desalination, 10(4), pp. 319-328. 56. Emerson, W.H., and Jamieson, D.T., 1967, "Some physical properties of sea water in various concentrations," Desalination, 3(2), pp. 213-224.

PAGE 133

BIOGRAPHICAL SKETCH Shalabh Maroo received his bachelors degree in mechanical engineering in 2003 from the Indian Institute of Technology Bomb ay, India. He joined the University of Florida in the same year to pursue his gradua te studies under the guida nce of Dr. D. Yogi Goswami. He is currently working towa rds his doctorate degree in mechanical engineering at the same university. 119


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Copyright Date: 2008

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THEORETICAL ANALYSIS OF SOLAR DRIVEN FLASH DESALINATION
SYSTEM BASED ON PASSIVE VACUUM GENERATION
















By

SHALABH CHANDRA MAROO


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2006

































Copyright 2006

by

SHALABH CHANDRA MAROO




































To the loving memory of my grandfather and grandmother, whom I shall always
remember















ACKNOWLEDGMENTS

I would like to express my gratitude and respect towards my advisor, Prof. D. Yogi

Goswami, for his invaluable suggestions and comments during the course of this work,

without which it would have been an exercise in futility.

I would also like to thank my committee members for their comments and help.

Many thanks go to the staff working at the solar energy and energy conversion

laboratory.

The support and help of my family are highly appreciated.
















TABLE OF CONTENTS



ACKNOW LEDGEM ENTS .................. .................. .....................iv

LIST OF TABLES.................. ...................................... ......... ......vii

LIST OF FIGU RE S................... .................................. ... ...... viii

NOM ENCLATURE................... ...........................................x

ABSTRACT.................................. .......................... xiii

CHAPTER

1 INTRODUCTION AND LITERATURE REVIEW..................................1

Introdu action ...................................... ........................ ............ 1
D esalination Processes....................... ........... ................... .......... 2
Multi-Effect Distillation (MED) ................. ........... ...........2
M ulti-Stage Flash (M SF)................... ................. .... .............. 3
Electrodialysis (ED )................................ ............ ............ .4
Reverse Osmosis (RO)............... .......................... ...............5
Freezing........... ................................................. 7
Humidification-Dehumidification (HD)..................................... 9
Desalination using Heat Pumps ............................ ...............10
Thermal vapor compression (TVC)....................................11
Mechanical vapor compression (MVC)............ ............. 11
Adsorption vapor compression (ADVC)..........................12
Absorption vapor compression (ABVC).......................... 13
Solar D esalination................... .. ......................................14
Indirect solar desalination systems.............. ... ............... 15
Direct solar desalination systems ........... ................. 18

2 PROPOSED DESALINATION SYSTEM ........................... ...........22

Single-Stage System ................. ...... ......................... ............23
Two-Stage System ........... ........................ ............. .......... 24









3 THEORETICAL ANALYSIS .................... ...... ................27

Evaporator................... .................... ... .................. .. ......... 27
F lashing P rocess........................................................ ..........2 8
Concentrated Brine Column .............. .................. ..............30
V apor Space........... ............................ ................... ... ... ..... 31
Condenser................... .................... ... .................. .. ......... 33
Distillate Column ................. ........................ .................. 35
Pressure in the System ................................. ................. ............ 36
Boiling Point Elevation (BPE) .................. .............................38
Heat Source.............................................................. .. .......... 38
Pumping Power................... .................. ........................... 41
Perform ance Ratio............ ..... .................................. .......... 41
Method of Analysis ................... ........................................ 42
Single-Stage ................. ..... ........................ ...............42
Tw o-Stage.................................................................. 44

4 RESULTS AND DISCUSSION ............ ..................... ............... 45

Single-stage System with Constant Temperature Heat Source.......................46
Variation of Inlet Saline Water Temperature............................46
Variation of Saline Water Mass Flow Rate...................................47
Variation of Length of Condenser........ ................................. 48
Variation of Ambient Water Temperature................................... 49
System Output....................................... ........... .......... 50
Two Stage System with Constant Temperature Heat Source............ ............51
Solar Collector Specifications....................................... ............... 52
Single-stage System Coupled with Solar Collector..................................53
Two-stage System Coupled with Solar Collector ...................................57

5 CONCLUSION AND FUTURE WORK........................................... 64

APPENDIX

A PHYSICAL PROPERTIES ............................................. .............. 66

B COMPUTER PROGRAM FOR SINGLE-STAGE SYSTEM......................70

C COMPUTER PROGRAM FOR TWO-STAGE SYSTEM.......................88

L IST O F R EFER EN CE S ......................................................... ........... 114

BIOGRAPHICAL SKETCH........................ ..............................119
















LIST OF TABLES


Table p

1.1 Energy consumption of some desalination processes........................... 15

1.2 Types of solar collectors................ .................. ....................... 16

1.3 Indirect solar desalination system s..................................... ...............16

1.4 Suggested variations in solar still .............................. .............. 20

3.1 Nusselt number for laminar flow in circular tube annulus .........................34

3.2 Concentration of main gases dissolved in sea water.................................37

3.3 Average values of k and C for 21st day of each month for the United States......40
















LIST OF FIGURES

Figure page

1-1 Schematic of a multi-effect distillation system........................................ 3

1-2 Schematic of a multi-stage flash system ............... ............. ............4

1-3 Typical electrodialysis configuration ...................... ......... ...... .............5

1-4 Schem atic of a RO system ................................. ............. ............6

1-5 Schematic of indirect freezing method ........... ............... .................8

1-6 Schem atic of the HD process ............ ............................................. 10

1-7 Schematic of thermal vapor compression system .................................. 11

1-8 Schematic of MVC Desalination Process............ ...........................12

1-9 Schematic of single-effect adsorption vapor compression system............... 13

1-10 Schematic of absorption vapor compression system........................... 14

1-11 Schematic of a conventional solar still............... ........ ..................... 19

2-1 Proposed single stage desalination system........... ........................24

2-2 Proposed two-stage desalination system........................ ...............25

3-1 Schematic of flashing process..................... ........... ... ... ..............28

3-2 Schematic of the concentrated brine column..........................................31

3-3 Control volume of vapor space................................ ................. 32

3-4 Horizontal annular flow .............. .. ........................ .............. 33

3-5 Control volume of the distillate column................. .................. ..............36

4-1 Variation of output with inlet saline water temperature......................... 46










4-2 Variation of system pressure with inlet saline water temperature..................47

4-3 Effect on distillate output with change in saline water flow rate .....................48

4-4 System pressure variation with condenser length .................................. 48

4-5 Variation of system saturation temperature with ambient water temperature......49

4-6 Effect of ambient water temperature on distillate output.........................49

4-7 Hourly output for single-stage system with constant temperature heat source....50

4-8 Hourly output for two-stage system with constant temperature heat source.......51

4-9 Insolation on the tilted solar collector surface on May 21 at Gainesville, FL......53

4-10 Variation of single-stage system temperatures coupled with solar collector.......54

4-11 Single stage system pressure coupled with solar collector.......................54

4-12 Pressure change due to NC gases in single-stage system with collector ...........55

4-13 Water column height variation for single-stage coupled with solar collector......55

4-14 Hourly output of single stage system coupled with solar collector ...............56

4-15 Feed water temperature for two stage system coupled with collector ..............57

4-16 Two-stage system pressure coupled with solar collector.......................58

4-17 Saturation temperature curves for two-stage system with solar collector..........59

4-18 Condenser outlet temperature of two-stage system coupled with collector........60

4-19 Pressure increase due to NC gases in two-stage system with solar collector......60

4-20 Brine height in the first stage of the two-stage system with collectors ...........61

4-21 Brine column height in second stage of the two-stage system with collector......62

4-22 Hourly output from two-stage system with solar collector........................62















NOMENCLATURE


A: Area of cross-section (m2)

BPE: Boiling point elevation (C)

C: Sky diffuse factor

Cn: Sky clearness factor

Cps: Specific heat of seawater (J/kg.K)

Cpv: Specific heat of vapor (J/kg.K)

Cpw: Specific heat of water (J/kg.K)

D: Diameter (m)

g: gravitational acceleration constant

h: Enthalpy (J/kg), Heat transfer coefficient (W/m2.K)

hfg: Latent heat of vaporatization of water (J/kg)

hs: Hour angle

I: Solar insolation intensity (W/m2)

i: Solar incidence angle

k: Thermal conductivity (W/m.K), Atmospheric optical depth

L: Latitude

1: Longitude

M: Mass (kg)

M : Mass flow rate (kg/s)

Nu: Nusselt number










n: Number of moles, Day of the year

P: System pressure (Pa)

PR: Performance ratio

Pr: Prandtl number

Q: Heat transfer rate between condenser and cooling seawater (W)

R: Universal gas constant

Re: Reynolds number

T: Temperature (C)

At: Differential time element (s)

U: Overall heat transfer coefficient (W/m2.K)

X: Salt concentration (g/kg)

Greek Symbols

a: Solar altitude angle

as: Solar azimuth angle

, : Surface azimuth angle

P : Surface tilt angle

6s: Solar declination angle

Tr: Efficiency

ji: Dynamic viscosity (Pa.s)

v: Kinematic viscosity (m2/s)

p : Density (kg/m3)

Subscripts









a: Ambient

b: Brine

cs: Condenser surface

c,in: Condenser inlet

c,out: Condenser outlet

d: Distillate

ev: Evaporator water column

i: Inner

1: Liquid

o: Outer

ps: Distillate column

s: Surface

sat: Saturation

sc: Solar collector

sc,in: Solar collector inlet

sc,out: Solar collector outlet

sw: Seawater

u: Useful

v: Vapor

vs: Vapor space

v,eq: Vapor at equilibrium

Superscripts

t, t+At : Value of the parameter at this time instant















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

THEORETICAL ANALYSIS OF SOLAR DRIVEN FLASH DESALINATION
SYSTEM BASED ON PASSIVE VACUUM GENERATION

By

Shalabh Chandra Maroo

May 2006

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

An innovative solar driven flash desalination system is proposed. The system uses

the natural forces of gravity and atmospheric pressure to create a vacuum. Single-stage

and two-stage concepts have been outlined. The main components include evaporator(s),

condenser(s), collection tanks, heat source and seawater circulation pump. Partial heat

recovery is attained by first passing the feedwater through the condenser(s), followed by

the heat source. Additional distillate output is obtained in the second stage of the two-

stage system without any extra heat addition, since the high temperature brine from the

first stage is passed and flashed in the second stage.

Theoretical analysis of the single-stage and two-stage concepts is done for the

system when coupled with constant temperature heat source and solar collector. The

single-stage and two-stage systems are shown to produce 11.3 kg and 13.9 kg of water

respectively in a 12 hour duration with a constant temperature heat source. When

coupled with a solar collector of 1 m2 area, a single stage system produces 5.54 kg of









water in 7.83 hours, while the two-stage system produces 8.66 kg in 7.7 hours. The

performance ratios obtained, including the efficiency of solar collectors, are 0.48 and

0.75 for a single-stage and two-stage system respectively, or 0.748 and 1.350 if only the

useful heat collected by the solar collector is considered.














CHAPTER 1
INTRODUCTION AND LITERATURE REVIEW

Introduction

Global resources of freshwater are becoming scarce and unevenly distributed with

increasing population. The world population is growing approximately at a rate of 1.2 %

annually resulting in a net addition of about 77 million people every year. The population

is expected to increase to around 8.9 billion by 2050 [1]. The earth's water supply is

nearly 1370 million km3 out of which nearly 3% constitutes freshwater. Nearly 29 million

cubic kilometers of freshwater is frozen in the form of glaciers and ice. Ground water,

lakes and rivers together constitute just a little over 8 million cubic kilometers of

freshwater. The critical water level to satisfy basic human needs is estimated to be 1000

m3/capita annually. It is projected that by 2050 about 1.7 billion people in 39 countries

will fall below this level [2].

According to the World Health Organization, the permissible limit of salinity in

water is 500 parts per million (ppm) and for special cases up to 1000 ppm of total

dissolved salts, while most of the water available has a salinity up to 10,000 ppm and

seawater normally has a salinity in the range of 35,000 45,000 ppm. Desalination has

evolved over the past few decades as a promising technology to counteract the water

scarcity. There are about 15,000 desalination plants around the world with a total

production capacity of 32 million m3 per day [3]. The conventional desalination

technologies include multi-stage flash, multi-effect distillation, reverse osmosis,

electrodialysis and freezing.









Desalination is an energy intensive process. With the total installed capacity

expected to increase drastically in the coming decades, the energy consumption for

desalination will continue to rise and hence the amount of fossil fuel required will

substantially go up. This trend does not match with the decreasing fossil fuel reserves. In

terms of oil consumption, it is estimated that about 203 million tons of oil per year is

required to produce 22 million m3 per day of desalinated water [3]. With conventional

hydrocarbon fuel shortages being inevitable unless radical changes occur in demand or in

the supply of non-conventional hydrocarbons [4], the energy water link cannot be

overlooked. In addition, the usage of fossil fuels continues to pollute the environment and

adds to the cause of global warming. A feasible and promising solution is the use of

renewable energy resources for desalination, as will be further discussed in this chapter.

Desalination Processes

The desalination processes can be broken down into two parts: Phase change

processes (which include multi-effect distillation, multi-stage flash, freezing,

humidification-dehumidification) and Membrane processes (reverse osmosis,

electrodialysis). The phase change processes are economical for water having high

salinity (10000-50000 ppm) whereas membrane processes are suitable for brackish water

with salinity ranging between 1000-10000 ppm.

Multi-Effect Distillation (MED)

The distillation process is the oldest process in desalination. Sea water, after being

pre-heated by the heat recovery from the exiting distillate, is introduced in the first stage

of the system where some of it is evaporated by the motive steam from the external

source (here depicted as the flash vessel in which the motive steam is produced). The






3


vapor produced in the first stage is used as the heating source in the next stage generating

additional vapor while condensing itself to add to the distillate output. Vapor formation in

the stages can be accomplished by either surface evaporation or by boiling. In order to

attain boiling, the pressure maintained in each stage should be lower than the previous

stage.



STEAM VACCUM



FLASH
VESSEL "







SLOWDOWN
SEA-WATER
DISTILLATE


Figure 1-1. Schematic of a multi-effect distillation system [3].

There have been variations in the distillation systems depending on the flowsheet

arrangement and heat transfer configurations, which can be broadly classified into the

submerged tube, horizontal tube falling film and vertical tube falling film designs. The

performance ratio of typical MED plants is about 10, and can reach as high as 12-14 [3].

Multi-Stage Flash (MSF)

MSF is the most widely used desalination process in terms of capacity. The feed

sea water is passed through a set of heat exchangers on the outside of which the vapor

generated in each flash chamber is condensed, in turn pre-heating the feed sea water. The

sea water is then heated up to a temperature above the saturation temperature







4


corresponding to the maximum system pressure by an external heat source (here shown

as solar collectors). It then enters into the first stage through an orifice, and a small

fraction of it flashes generating vapor. The subsequent stages are maintained at

successively lower pressures using vacuum pumps. The brine from the first stage is

injected into the second stage causing additional flashing. This process is repeated

throughout the plant.

VACCUM


SEA-WATER

-- -"- -' DISTILLATE
DEMISTER
ES-------------- -------------- -----------------E




SLOWDOWN


Figure 1-2. Schematic of a multi-stage flash system [3]

A conventional MSF plant is divided into two sections: heat recovery section and

the heat rejection system. The performance ratio of the MSF plant typically varies from 6

- 10 [3].

Electrodialysis (ED)

Electrodialysis is an ion-exchange membrane separation process. This process

works on the principle that when electrical potential difference is applied to seawater

separated by a certain configuration of selective membranes, ions are transferred from the

seawater thus reducing its salinity. A typical ED configuration is shown in figure 1.3.

Feed seawater is passed through the sections separated by membranes from the bottom.








The cation-exchange membrane (CEM) allows Na+ ions present in seawater to

pass through, while the anion exchange membrane (AEM) allows Cl- ions thus reducing

the salinity in sections (c). The concentration of dissolved salts in the seawater increase in

sections (b), whereas electrode reaction products are present in sections (a). Such cells

are arranged in stacks, therefore producing fresh water in sections (c).


tCEM t AEM t CEM AEM CEM


0-


-0


I .1 .. -I !i I "
SN& ._ ....N
H'.O, D" Cf' low, 4

HaO


A t T IA T T t--


T T T T T T
(a) (b) (c) (b) (c) (a)

Figure 1-3. Typical electrodialysis configuration [5].

In an actual electrodialysis plant, alternating CEM and AEM are used. Inverters

are used to reverse the polarity of the electric field about every 20 minutes to prevent

scaling. This is called electrodialysis reversal (EDR) process. Electrodialysis is more

practical on feedwater with salinity not more then 6000 ppm due to the high energy

requirements at higher salinity, and this process is not suitable to produce water

containing less than 400 ppm of dissolved solids [3].

Reverse Osmosis (RO)

When a pure solvent (water) and a solution (seawater) are separated by an ideal

semi-permeable membrane (one that is permeable to solvent but not the solute), the

solvent passes through the membrane to the solution side. The transport happens due to










the chemical potential driving force created by the presence of the solute. If a pressure

greater than the osmotic pressure is applied to seawater, pure water will pass through the

membrane and can be collected. This is the basis of desalination by reverse osmosis

(RO). A schematic of the RO system is given in figure 1.4.

HIGH PRESSURE
PUMP RO PLANT

SEA-WATER CARTRIDGE
FILTER
DUAL
MEDmIA _
MODIj lPOST-TREATMENT

PRETREATMENT B----- D
BRINE TO
WASTE ---
ENERGY RECOVERY
TURBINE (IF FITTED)
PRODUCT


Figure 1-4. Schematic of a RO system [3].

The separation of fresh water from the seawater happens in an RO plant as depicted

in the above figure. Theoretically, the only energy requirement is that to drive the pump.

It can be also economically feasible to recover the rejected brine energy with a suitable

turbine. Such systems are called energy recovery reverse osmosis (ER-RO). The

performance of the membrane and hence the production rate of freshwater strongly

depends on the following major operating variables:

a) Seawater Concentration With increasing seawater concentration, the osmotic
pressure increases and hence greater pressure must be applied to the seawater side
to attain the same fresh water production rate. Thus, RO is favorable over other
processes in the desalination of brackish water.

b) Operating Pressure Increase in the operating pressure increases the driving force
for the solvent (water) and only marginally affects the driving force for solute
(salt).

c) Feed Flow Rate The primary effect of the feed flow rate is to change the mixing
at the solution side, and thus altering the mass transfer coefficient at the
membrane.









Prevention of membrane fouling is a very important aspect in RO systems. Fouling

can lead to reduction in production rate, lowering of membrane lifetime, difficulty in

predicting various operation parameters, etc. It can be caused by many reasons, including

concentration polarization, plugging of membrane pores by suspended matter,

precipitation of solute at the membrane surface, biological fouling, and degradation of the

membrane itself.

Fouling can be largely minimized by the pre-treatment of seawater before it is

pressurized in the membrane modules. Studies have shown that particles larger than 5 [tm

in size have no effect on the overall fouling process, and that the particles smaller than

0.45 um in size [6], including colloids and dissolved solids caused fouling more often

than other materials. Filtration can include coarse particle screening, followed by finer

cartridge filtration, and extra fine sand filtration. Compounds which foul by scaling can

be treated either by removal of the ion before processing, inhibiting the crystal growth or

reducing system recovery, with anti-scalants being used for this purpose. Membranes are

also affected by acid/base hydrolysis, and thus the pH of the seawater has to be

maintained within certain limits. Seawater containing calcium carbonate is treated with

acid to yield more soluble bicarbonate and carbon dioxide which can be removed in post-

treatment by lime softening and degassing respectively.

Freezing

Freezing is a separation process based on the solid-liquid phase change

phenomenon. When salt water is reduced to its freezing point, ice crystals of pure water

are formed within the salt solution which can be mechanically separated and melted to

obtain fresh water. If the temperature of the salt solution is further reduced it reaches a










point, called the eutectic temperature, where salt crystals start forming. Thus the

operating temperature of the freezing chamber in the desalination plant should be above

the eutectic temperature. The basic indirect freezing method is shown in figure 1.5.


-- t Compressor to Cooler -

Liquid Refrigerant


Freezing relting
Charnber Unit

Fresh
Water


Separation
Ice & Brine Unit
Incoming
Sea water

Fresh Waler
1_. __- _-_-- ----_- k
Brine Heat Exchanger
^----------- BrneRair
Brine Return



Figure 1-5. Schematic of indirect freezing method [7].

The inlet salt water, after passing through the heat exchanger to reduce its

temperature, is cooled in the freezing chamber by means of a separate refrigeration

system to form ice crystals. The ice is then separated from the brine in a wash column

and transferred to a melting unit where ice is melted by the heat of condensation released

by the refrigeration system. Both the released brine and the fresh water are passed

through the heat exchanger before being taken out of the desalination unit.

The direct freezing method is a modification of the above technique, in which use

of an external refrigerant is eliminated and water itself is used as a refrigerant. Here the

freezing chamber is maintained at a water vapor pressure equal to or below the triple









point of the water thus causing partial flashing as the salt water is introduced. The vapor

generated due to flashing is compressed (and thus heated) and discharged to the melting

unit where it melts the ice crystals and in turn itself gets condensed. This method is also

called the vacuum-freezing vapor compression method. A modification to this method is

the vapor-absorption method in which the vapor produced is absorbed rather than

compressed. An interesting variation, called the secondary refrigerant method, is the use

of an immiscible refrigerant, like isobutane, in contact directly with salt water which

makes the operating pressure of the system to be much higher than the triple point of

water. Another variation to the secondary refrigerant method is the hydrate process in

which a hydrate is added to salt water where a crystal lattice of water and the hydrating

agent are formed at higher temperatures and pressures than pure ice.

The main attractions of the freezing desalination process are the low energy

requirements since the latent heat of fusion is about one seventh the latent heat of

vaporization, minimal corrosion of process equipment and allowing the usage of

inexpensive plastics due to the low temperatures involved. The disadvantages of this

process are the problems related to physically separating the ice crystals from the brine,

high vacuum requirements, removal of refrigerant from the outgoing streams, need for

external refrigeration units.

Humidification-Dehumidification (HD)

The HD process is based on the fact that air can be mixed with quantities of

vapor. When an airflow is in contact with salt water, air extracts some amount of vapor at

the expense of sensitive heat of salt water, causing cooling. On the other hand, the









distilled water is recovered by maintaining humid air in contact with the cooling surface,

causing the condensation of a part of vapor mixed with air.

*C L WC



















Figure 1-6. Schematic of the HD process [8].

The basic cycle consists of a heat source, air humidifiers (1) and dehumidifiers

(2). The brine is passed through a heater (3) where its temperature rises, then through

packed towers where water vapor and heat are given up to the counter-current air stream,

reducing the brine temperature. The air stream is then passed over the dehumidifier which

generally use fresh or sea water as cooling phase. Heat exchangers are present for heat

recovery.

Desalination using Heat Pumps

The combination of multi-effect evaporation (MEE) and heat pumps have become

attractive in the past decade to reduce the energy costs required in desalination. These

hybrid systems are predicted to increase the performance ratio from low values of 10-

20% to higher values of close to 200% [9]. Four such desalination systems are: thermal










vapor compression (TVC), mechanical vapor compression (MVC), adsorption vapor

compression (ADVC) and absorption vapor compression (ABVC).

Thermal Vapor Compression (TVC)

The TVC system uses a steam ejector to compress and heat the vapor generated

from the evaporator. The inlet sea water is pre-heated in the heat exchanger shown as

condenser and introduced into the evaporator. The generated vapor is passed into the

steam ejector.


td) Tld-~ L Boiler ___e

Feed F
Ef Dr
F
(e) U TJf


Condenser

Condensale (c) Mc =F
S-Dr TV1 D
l(df) !
r Horizontal tube evaporator HTE Distillate
Brine blowdown


Figure 1-7. Schematic of thermal vapor compression system [10].

The superheated vapor resulting from the steam ejector is fed into the evaporator

tubes evaporating the inlet sea water, and itself getting condensed into the product water.

A portion of the superheated vapor coming out from the ejector is by-passed into the heat

exchanger to pre-heat the inlet sea water.

Mechanical Vapor Compression (MVC)

The MVC system is driven by the use of electrical energy and does not require

any external heating source. The inlet sea water is pre-heated in the feed pre-heater and

passed on to the evaporator where vapors are formed. These vapors are taken in by the










compressor where it is superheated to a temperature higher than the saturation

temperature of the seawater. The superheated vapor is introduced into the evaporator

tubes where it condenses by evaporating the feed sea water and collected. The rejected

brine and the product water are passed through the preheater before being taken out of the

system.


Evaporator


= Feed Seawater
VwrSuction Tube '

Mechanical
Compressor Intake Seawater
Product Mr t Product
Md, Td t-Md-, To
Rejected Brine Bri
Mb Tb Feed Preheater Mb, To


Figure 1-8. Schematic of MVC Desalination Process [9].




The MVC system requires no cooling water. The main drawbacks of this system are the

need of electrical energy and the inclusion of compressor.

Adsorption Vapor Compression (ADVC)

This system comprises of two adsorption beds (e.g. zeolite), evaporator/condenser

single unit, and heat exchangers. Figure 1.9 depicts the schematic of ADVC system.

Initially, bed I is assumed to be cold and at a temperature Ta less than the temperature of

the water adsorbed in the bed, while bed II is dry and hot with its temperature being the

same as the temperature of the heating steam Tg.















Adsorptivon < .ke Sew ter



Fluid N


Bed Bed II HE] Ms, Tc.


HE2

Figure 1-9. Schematic of single-effect adsorption vapor compression system [9].

The circulating fluid starts to transfer heat between the beds, and during this

period no heat is exchanged between the absorbers and any external source or sink. This

process is stopped when bed I reaches a certain temperature Tel and bed II has been

cooled to Te2. Now, bed I is heated from Tei to Tg by the external source of the heating

steam and bed II is cooled from Te2 to Ta by the cooling water. During the heating

process, when the pressure in bed I becomes higher than the condenser pressure, it is

opened to the evaporator tubes where the vapors generated from the bed condense.

Similarly, when the pressure in bed II is lower than the evaporator pressure it is opened to

the evaporator adsorbing the vapors. This completes the first half of the cycle. In the

second half, the roles of the adsorbent beds are reversed with bed I adsorbing vapors from

the evaporator and bed II generating vapor to the evaporator tubes.

This system does not include any moving parts, and has high performance ratios.

Absorption Vapor Compression (ABVC)

The ABVC system shown in Figure 1.10 comprises of generator, absorber,

evaporator-condenser single unit and heat exchangers. The vapor formed in the










evaporator is absorbed in the absorber generating heat which is rejected by the cooling

water. The absorption solution (absorbent depicted here by LiBr) is circulated between

the absorber and the generator. The motive steam heats the diluted solution in the

generator generating steam which is passed into the evaporator tubes and condenses into

product water.

Formed Vapor Demister Spray Nozes
Md,T, V.

Compressed Vapor ", -. -,.
\ &'WVA" k FeedSawater

Motive Steam M ,
MM, T.

Product
Reject Brine Md Md, T.
Circulat ng Mb, Tb Reject Brine
LiBr Soluti HE3

Intake Seawater
Absorber RE1 Mr, Tc.

Mew, TT,,
HE2

Figure 1-10. Schematic of absorption vapor compression system [9].

The advantages of this system are similar to that of the ADVC system. The

performance ratio of ABVC is better than ADVC at lower boiling temperatures, being as

high as 5 for a single effect system [9].

Solar Desalination

The conventional desalination systems consume significant fuel to produce

potable water. A rough estimate of the energy consumption of desalination processes is

given in Table 1.1. Since energy costs is one of the most important parameters in

determining water costs, desalination using solar energy is increasingly becoming an









attractive option due to continuous rise in conventional fuel costs and harm to the

environment.

Table 1-1. Energy consumption of some desalination processes
Process Heat input Mechanical power Prime energy
(kJ/kg) Input (kWh/m3 of consumption (kJ/kg
product) of product)a
MSF 294 2.5-4 (3.7)b 338.4
MEB 123 2.2 149.4
VC 8-16 (16) 192
RO 5-13 (10) 120
ER-RO 4-6 (5) 60
ED 12 144
Solar Still 2330 0.3 2333.6
a Assumed conversion efficiency of electricity generation of 30 %
b Figure used for prime energy consumption estimation shown in last column
adapted from Kalogirou [3]

Desalination systems using solar energy can be classified as indirect collection

systems and direct collection systems. Indirect collection systems can be seen as a

combination of two systems, a collector to convert solar energy and the actual

desalination plant to which the collected energy is supplied. Direct collection systems are

those where heat collection and desalination process takes place in the same system.

Table 1.3 provides a brief summary of the some of the indirect collection systems.

Indirect Solar Desalination Systems

Solar energy can be used as a source of heat or power for any desalination

process. Solar systems which are commonly used for this purpose are:

Solar Collectors

The principle of operation of solar collectors is to absorb the solar radiation,

convert it into heat and transfer this heat to the fluid flowing through the collector. They

can be classified into non-concentrating or concentrating type, and stationary or tracking.

A list of collectors is shown in Table 1.2.









Solar Ponds

Solar ponds are used as both solar energy collectors and heat storage system. The

water in the pond gets heated up by the solar radiation. Water at the bottom of the pond is

made denser by dissolving salt in it, and there exists a salt concentration gradient from

the bottom to the top. This eliminates the natural tendency of mixing if the density

gradient is adequate. Thus, heat is collected and stored in the bottom water layer of the

pond.

Table 1-2. Solar Collectors
Motion Collector type Absorber Concentr- Indicative
type ation ratio temperature
range (oC)
Stationary Flat plate collector Flat 1 30-80
Evacuated tube collector Flat 1 50-200
Compound parabolic collector Tubular 1-5 60-240
Single-axis Compound parabolic collector Tubular 5-15 60-300
tracking Linear Fresnel reflector Tubular 10-40 60-250
Parabolic trough collector Tubular 15-45 60-300
Cylindrical trough collector Tubular 10-50 60-300
Two-axes Parabolic dish reflector Point 100-1000 100-500
tracking Heliostat field collector Point 100-1500 150-2000
adapted from Kalogirou [3]

Photovoltaic Cells

PV cells are used to convert solar energy directly into electrical energy which can

be used to power various components in desalination processes such as reverse osmosis,

electrodialysis, freezing and vapor compression. These cells have low conversion

efficiency ranging around 10-15 %.

Table 1-3. Indirect solar desalination systems.
Description Author(s) Comments
Combination of a (MED) with an open Zejli et al. [11] Theoretical modeling was
cycle adsorptive heat pump using done. Variation of energy
internal heat recovery. The heat consumption and PR with
transfer fluid flowing through tubes the number of effects is
in the adsorbent beds is heated up by shown.
PTCshown.
PTC









Table 1-3. Continued
Multi-effect distillation coupled
with a solar pond


Hawaj and Darwish
[12]


Tabor [13]


Simulation shows that it is
a viable option in an arid
environment with
performance ratio reaching
more than twice the
conventional system


Optimizes the size of the
pond and the number of
effects used, taking into
account the large variation
of pond heat output
between summer and
winter.


Solar parabolic trough collector Garcia-Rodriguez and Conclusion was that use of
field coupled to a conventional Gomez-Camacho [14] solar energy could
MSF plant. compete with a
conventional energy
supply in MSF distillation
processes in some climatic
conditions.
A small multi-effect, multi-stage flash Lu et al. [15] Experimental study.
distillation (MEMS) unit and a brine Aimed at reaching zero-
concentration and recovery system discharge desalination.
(BCRS) coupled with a solar pond
Single-effect solar assisted heat Hawlader et al. [16] Experimental study.
pump desalination system
incorporating both flash and
distillation techniques
A single stage flash desalination Joseph et. al. [17] Experimental study,
system working on flat plate solar maximum distillate yield
collectors of 8.5 1/d is obtained with
collector area of 2 m2
Multi-stage flash desalination Experimental study. Yield
system using two types of solar Farwati [18] from CPC was better than
collectors FPC
Photovoltaic-powered seawater Thomson and Infield Experimental study.
reverse-osmosis desalination [19] Shows substantial cost
system reduction to other PV-RO
systems.
Laborde et al. [20] Experimental study with
mathematical modeling.
Different parameters
optimized with regard to
power needs and energy
consumption.


I









Table 1-3. Continued
Electrodialysis process operated AlMadani [21] Experimental study
with photovoltaic cells
Humidification-dehumidification Amara et al. [22] Experimental study.
method with an eight-stage air Principal operating
solar collector heating- parameters were
humidifying system optimized
Humidification-dehumidification Dai et al. [23] Mathematical model with
using flat plate collectors experimental validation.
Fath and Ghazy [24] Numerical analysis.
Shows that the
dehumidifier effectiveness
has an insignificant
influence on system
productivity .


Direct Solar Desalination Systems

The solar still is the simplest desalination system in terms of operation. It is an air

tight basin, usually constructed out of concrete/cement, galvanized iron sheet or fibre

reinforced plastic (FRP) with a top cover of transparent material like glass or plastic. The

inner surface of the base known as base liner is blackened to efficiently absorb the solar

radiation incident on it. There is a provision to collect distillate output at the lower ends

of top cover. The saline water evaporates on getting heated by solar radiation and the

vapor moves to the glass cover, rejecting heat to the ambient and condensing. The

condensed droplets flow along the glass cover and get collected in the troughs from

where they run down to the product tank.

On the basis of various modifications and mode of operations introduced in

conventional solar stills, these solar distillation systems are classified as passive and

active solar stills. In the case of active solar stills, extra-thermal energy by an external

mode is fed into the basin of passive solar still for faster evaporation. The external mode







19


may be collector/concentrator panel, waste thermal energy source, etc. If no such external

mode is used then that type of solar still is a passive solar still.


Sun


h t.t
Condenm& dmpk-ts flow
Along the inside of the ss
Cover an collect in the gutter
% t Gass Cover
Distilled water
tro u g h

Heatedby the su, water Outlet
\ r evporates and condese s



inet ..-


-^^..--l-f I l -,J- :]" r,




Figure 1-11. Schematic of a conventional solar still.

A typical still efficiency, defined as the ratio of the energy used in vaporization to

the energy incident on the glass cover, is 35 % with the daily production of about 3-4 1/m2

[3]. The meteorological parameters namely wind velocity, solar radiation, sky

temperature, ambient temperature, salt concentration, algae formation on water and

mineral layers on basin liner significantly affect the performance of solar stills. The

design parameters are the brine depth, vapor leakage from the still, thermal insulation,

cover slope, shape of the still and the material of construction.

In order to improve the performance of a conventional solar still, several

modifications have been suggested in many studies and have been listed in Table 1-4.









Table 1-4. Suggested variations in solar still.
Description Author(s) Comments
Double-basin solar still coupled Yadav and Jha Transient analysis shows it to be
to a flat-plate solar collector in [25] slightly less efficient if coupled to a
the thermo-siphon mode. collector in forced-circulation
mode. Significant improvement in
performance over that of the
conventional double-basin solar
still.
Improved heat and mass Hongfei et al. Validated with an experimental set
transfer correlations in basin [26] up. Can provide better predictions
type solar stills for the evaporation rate of basin
type solar stills at a wide range of
Rayleigh numbers and temperatures
Vertical multiple-effect Tanaka and Theoretically predicted to produce
diffusion-type solar still Nakatake [27] 29.2 and 34.5 kg/m2-d on the spring
consisting of a flat-plate mirror equinox and winter solstice days
respectively, on the equator.
Single-stage, basin-type solar Badran et al. Experimental study. An increase in
still couple with flat plate [28] production of 52% was noticed
collector when the still was connected with
the collector over that of the still
alone.
Adding an outside passive Bahi and Inan Experimental study. Efficiency was
condenser to a single-basin-type [29] improved by more than 70%, and
solar still the distilled fresh water was
up to 7 l/m2.d
Inclined solar water desalination Aybar et al. Experimental study. Tested with
system [30] bare plate, black-cloth wick and
black-fleece wick.
Conventional type solar still Minasian and Experimental study. Overall
connected with a wick-type Al-Karaghouli efficiency of this new still was
solar still [31] higher than the other two individual
stills
Study of different water depths Tripathi and Experimental study
in the basin on the heat and Tiwari [32]
mass transfer coefficients
Effect of wind speed on solar El-Sebaii [33] Numerical study
still productivity
Vacuum solar still Al-Hussaini and Theoretical study. Shown to
Smith [34] enhance the efficiency by 100 %.
Solar still with an indirect Tchinda et al. Numerical analysis
evaporator-condenser [35]
Solar still with charcoal Naim and Abd Experimental study. Has a 15%
particles as absorber medium El Kawi [36] improvement in productivity over
wick-type stills.









Table 1-4. Continued
Optimization of glass cover Tiwari et al. Numerical analysis
inclination for maximum yield [37]
in a solar still
Solar still with reflectors and Tamimi [38] Experimental study. Authors advise
black dye to operate the still with the reflectors
only, without adding the black dye.
Single and double basin Al-Karaghouli Experimental study. The daily
solar-stills and Alnaser average still production for the
[39] double-basin still is around 40%
higher than the production of the
single-basin still.
Triple-basin solar still E1-Sebaii [40] Numerical analysis optimized various
parameters which affect the
performance of the still
Spherical solar still Dhiman [41] Mathematical modeling. Authors
show efficiency of a spherical solar
still is 30% greater than that of a
conventional still.
stepped solar still with Radhwan [42] Storage material paraffin wax, and
built-in latent heat thermal the efficiency obtained was 57 %
energy storage

Water film cooling over the Abu-Hijleh and Authors infer increase in the still
glass cover of solar still Mousa [43] efficiency by up to 20%














CHAPTER 2
PROPOSED DESALINATION SYSTEM

In the proposed flash desalination system, an innovative passive gravity based

method is used for the production of vacuum. The concept was proposed by Sharma and

Goswami [44]. A standing column of water is allowed to drop generating very low

pressures in the headspace created. Conventional desalination systems require the use of

vacuum pumps or steam ejectors to attain the same purpose. Based on this concept, a

desalination system was investigated by [45] which incorporated surface evaporation in

the vacuum chamber. Simulated performance of that system matched well with

experimental results. However, the evaporator size for a practical output in such a system

is large. Further, with change in pressure in the evaporator, the water level fluctuation is

large which poses difficulty in heat addition. The system being proposed here uses a flash

evaporator, which reduces the size of the system. Heat input is provided using a solar

collector. The concept can be implemented as a single-stage unit as well as a multi-stage

system design.

Single-stage and two-stage systems have been proposed in this study. These

systems can work on low grade heat source like solar energy. The objective is to develop

theoretical models for the proposed single stage and two-stage systems, and analyze them

to obtain the desired potable water output. A thermodynamic analysis of each component

and the whole system was done, and a mathematical model was formulated.









Single-Stage System

Referring to the Figure 2.1, the system consists of a flash chamber (A), condenser

(B), low grade heat source (C), feed water pump (D), product water tank (E), and brine

collection tank (F) arranged as shown. The evaporator and condenser have to be located

at a height of 10 m or more above the collection tanks at the bottom of the figure, such as

rooftops of buildings.

The vacuum is created by letting a column of water fall in a closed space under

gravity creating low pressures in the head space at the top. One possible implementation

is as follows: valves VI and V2 are open while valves V3, V4, and V5 are closed. Brine

is pumped into the system using the feed water pump until all the air inside the system in

vented out through valve V2. When the system is completely filled with water, the pump

is turned off, and valves VI and V2 are closed. Valves V4 and V5 are then opened

causing the water to drain down, creating a vacuum in the space above (i.e. in the flash

chamber and condenser). A water column of approximately 10 m is formed which is

balanced by atmospheric pressure.

During operation, heated brine is pumped into the evaporator where it flashes

because of lower pressure, producing vapor and a higher concentration brine solution.

The vapor is condensed rejecting heat that is used to preheat the brine. The brine can be

heated by using solar heat from a collector. Other low grade heat sources can also be

used. The concentrated brine and the product water drain out of the system due to gravity,

and hence no pumps are required for these purposes. The levels in the brine collection

tank and the product water tank can be maintained using float valves.










Seawater heated in condenser


S Orifice Vapor

C -A B:


A Evaporator Structure of height
B: Condenser greater than 10 m
C: Heat Source (e.g. Buildings,
D: Feedwater Pump homes, etc)
E: Product Water Tank
F: Brine Collection Tank

V1, V2, V3, V4, V5 : Valves
V1 V3

V4 V5 F- To Freshwater
To Brine I I Storaqe Tank
Storage Tank F E



Figure 2-1. Proposed Single Stage Flash Desalination System.

Two-Stage System

For more effective utilization of the heat input, multi-stage systems can be used

that flash the brine at successively lower pressures with effective heat recovery,

increasing the production of vapor. Figure 2.2 shows an example of the implementation

of a two-stage flash system.

Referring to the figure 2.2, the two stages are in a stack as shown, with the

requirement that the second stage flash chamber (A2) and condenser (B2) be located at a

minimum height of 10 m or more over the brine and freshwater reservoirs shown at the

bottom. (Note that these reservoirs could be located below ground level while being open

to the atmosphere).

The method of creating the vacuum is similar to that for a single-stage system.

Vacuum in the two stages is created independently. The two stages are only connected










via valve V7 and the orifice. Valve V6 is now similar to valve V2. Thus for the creation

of vacuum, stage 2 is filled up first with seawater followed by stage 1. Seawater from

stage 1 is allowed to drain down before stage 2. This ensures that valve V7 remains

closed. After vacuum is created in stage 1, valve V9 is closed and it remains closed while

the system is in operation. Hence seawater after being flashed in Al has to flow through

valve V7 to A2. The connecting pipe between Al and F will become filled with seawater

when the system begins to operate (as shown in figure 2-2).


Seawater heated in condensers


Orifice V2 Vapor

C BI
Al
/ v
VT

A: Evaporator -V
B: Condenser B2
C: Heat Source A2
D: Feedwater Pump Vapor
E : Product Water Tank
F: Brine Collection Tank
Structure of height
1: Stage 1 greater than 10 m
2: Stage 2 (e.g. Buildings,
homes, etc)
V1 -10: Valves
Valve V9 remains
closed after vacuum
v10
is created
V1 V3

V9- V4 4 V5 V- V8 To Freshwater
To Brine Storaqe Tank
Storage Tank --F E



Figure 2-2. Proposed Two-Stage desalination system.

The initial pressure in both the stages will be the same (the vapor pressure of

water at its temperature). The system being ready for operation, heated feedwater is

flashed in Al and the brine begins to accumulate in Al. After a certain amount of brine






26


has accumulated in Al, valve V7 is opened. Due to the pressure difference in the two

stages, the accumulated brine in Al flows into A2 and is further flashed at a lower

pressure. The flow rate of seawater from Al to A2 is controlled by the pressure in each

stage and the connecting arrangement.














CHAPTER 3
THEORETICAL ANALYSIS

The mathematical modeling of the proposed desalination system comprised the

analysis of each component of the system. Mass and solute conservation equations along

with energy balance equations were formulated, and a computer program written in C++

was developed to solve the equations. This chapter starts with the transient analysis of the

components of the system followed by the method adopted to solve the set of equations

and the algorithm used. Two versions of the computer program were developed, the first

one assumed a constant heat source temperature while the second one took into

consideration a solar collector as the source of heat.

Evaporator

The evaporator is that component of the system where pure water vapor is

generated from the saline water. The method incorporated in this system to generate

vapor is flashing. After the feed saline water is heated by the heat source, it is throttled to

the evaporator which is at a lower pressure than that corresponding to its temperature

leaving the heat source. It should also be noted that the feed saline water is prevented

from boiling by keeping its pressure throughout the heat source and piping above the

saturation pressure corresponding to its temperature.

Flash evaporation occurs when saline water is exposed to a sudden pressure drop

(the evaporator being under low pressure conditions) below the saturation vapor pressure

corresponding to the water's temperature. To regain equilibrium, part of the saline water

vaporizes by drawing its latent heat of vaporization from the remaining liquid, whose









temperature drops towards the saturation temperature corresponding to the lowered

pressure. Distillate formation also leads to an increase of water salinity.

More commonly three flashing methods are used to achieve flash evaporation:

pool liquid exposed to a sudden pressure drop in a container, superheated liquid flowing

in a low pressure open channel (usually incorporated in a conventional MSF evaporator)

and superheated liquid jet ejected from a simple tubular nozzle or a circular orifice into a

low pressure zone. Miyatake [46] experimentally compared these methods with regard to

the coefficient of flash evaporation, and determined that this coefficient for the flashing

liquid jet was 10 times more than that of superheated pool liquid or superheated flowing

liquid. In the proposed desalination system, flashing is achieved by ejecting the

superheated saline water into the evaporator using an orifice.

Flashing process

The evaporator is broken down into two control volumes; first one where the

flashing process happens (near the orifice) and the other being the brine collected in the

evaporator and water column. The flashing efficiency is also taken into account.


MMTY
SW r---

Tsw

M'T
b V


Figure 3-1. Schematic of flashing process.

Mass Balance

Mass flow rate of Mass flow rate of] Mass flow rate
feed saline water vapor generated of falling brine









> M,, = M,' +Mbt ........... EQ1

Salt Balance

[Salt in feed saline water] = [Salt in falling brine]

-> MX = M[XE


X" = A, X ........... EQ2


Energy Balance

Energy of feed Energy of vapor Energy of
saline water ] generated ] falling brine

'wh = hh +httht

ha ^+ C dT =M[ha + C,' dT+h +Mh++ CdT

- ha +A fL ) 't" C dT CL dT = Lf h +A
s t bdT
zth.M. k + CT fT- C' dT + +c + t


v J C ..... EQ 3


Ideally the temperature attained by the vapor after flashing should be equal to the

saturation temperature corresponding to the pressure in the evaporator. But this depends

on the amount of time given for the flashing process in the system, and since this time is

finite the actual temperature of the vapor generated is higher than what it should ideally

attain. Thus a flashing efficiency is defined.

Flashing Efficiency:
Actual vapor generation rate
flash Maximum possible vapor generation rate









M, CC' hdTh )
S_ actual T ( )
M..max f Cp' d hT h (T' )
v,eq


........... EQ 4


Miyatake et. al. [47] proposed the following empirical relationship for flashing

efficiency for aqueous NaCl solution, and also mentioned that it does not depend on the

other experimental conditions except the superheat:


h = 1- 1+1.5 ) 3.0 ........... EQ 5

Concentrated Brine Column

The height of the brine column depends only on the difference between the

pressure in the evaporator and the atmospheric pressure. As the brine level in the brine

tank is constant, the amount of brine rejected from the system will be the sum of the brine

falling after flashing and the brine water loss due to the pressure increase in the

evaporator. The temperature and salt gradients in the brine column are neglected. The

initial mass, salt concentration and temperature of saline water in the column are known.

Mass Balance

Change in pressure FChangein mass of
oc
in the system water in the column


........... EQ 6


A M +' ^ A M t_ Aep pAt pt
g


Salt Balance

Salt in the brine Salt in the brine +Salt added due to Salt in brine rejected
column at time t+At column at time t falling brine in At] from the system in At

t> At'Xt At MtX +MAt XAt A [t+At -pt] +MAtX: At
bL J









iM A t (X ^ IV+ X __
SA V = ,bt Xt Xev)
At


........... EQ 7


Figure 3-2. Schematic of the concentrated brine column.

Energy Balance

Energy of the brine Energy of the brine 1 Energy added by Energy of brine rejected
column at time t+At column at time t Ifalling brine in At from the system in At

> ht =Mht +A>hh hAt- [Pt At-Pt]ht +AMthAt



> ev t ,b C pst dT ........... EQ 8


Vapor Space

The vapor space comprises that of the whole system which is mainly the vapor

space of the evaporator and of the condenser. The temperature gradient is neglected in the

vapor space. It is also assumed that the vapor is condensed at the saturation temperature,

and that sensible cooling is neglected. The heat of condensation is rejected to the

condenser from the vapor space. The initial mass of vapor in the vapor space is equal to









the volume of vapor space times the density of vapor at the ambient saline water

temperature.

Mass Balance

Mass of vapor Mass of vaporr Mass of vapor Mass of vapor
at time t+At at time t added in At condensed in At


->' M' = M, + M,'At -MAidtt


M ^A-Mt
At


M s Tsat
Vapor Space


........... EQ 9


Md
Td


Figure 3-3. Control volume of vapor space.


Energy Balance


Energy of vapor Energy of vapor Energy vapor
in vapor space = in vapor space +
added in At
at time t+At at time t
M AathAt t =Mt h + thth Atht -Q

At At

Here, Td = T


I-, ;,' ., 'C dT=M 'h '-' +M: C dT
At C dT d fgs dT


Energy of
condensed
water in At


Energy rejected
to condenser


.......... EQ 10


Also, the mass of vapor in the vapor space at any instant t can be found out as:


M
TV









M,, = (Volume of Space) p, = (Volume of Space) f(T, at)


Condenser

The vapor condenses to give the desired product after rejecting the heat of

condensation in the condenser. The condenser is water cooled in order to obtain better

heat removal rates. The heat of condensation pre-heats the feed saline water passing

through the condenser, thus recovering heat in the system. The type of condenser used in

the system is a horizontal tube-in-tube type condenser vapor condensing in the inner tube

and feed saline water (cooling water) flowing in the annulus.




Vapor



Liquid


Flow





Figure 3-4. Horizontal annular flow.

In horizontal tubes at low vapor velocities, low condensation rates and/or short

tube lengths, which is the case here, liquid that condensed on the upper portion of the

inside tube wall tends to run down the wall towards the bottom resulting in a stratified

annular flow condition, as depicted in figure 3.4. For low vapor velocities (Re<35,000)

the condensation heat transfer coefficient is given by [48]


.......... EQ 11









3 1/4
h 0.555gp( )kh
L 1(T, T)D


where, the modified latent heat is h = h +3-C (T1 -T).
8

The heat transfer coefficient in the annulus will depend on the nature of the flow,

and hence on the volume flow rate of the cooling saline water. The Reynolds number can

be found out using the hydraulic diameter Dh (for circular tube annulus):

4A 4(r/4)(D -D2
Hydraulic diameter Dh =4 = ; =D ( D, -D
P 0Do + :D


Reynolds number


ReD = Dh
V


If Re <2300 then the flow is laminar, or else the flow is turbulent. The Nusselt

number for fully developed laminar flow in a circular tube annulus with one surface

insulated and the other at constant temperature can be obtained from table 3.1. For

turbulent flow, the Nusselt number can be calculated from [48]:

Nu = 0.023 Re4/5 Pr04 (for ReD > 2300)


The heat transfer coefficient can be obtained as:


k
h= Nu,
Dh


Table 3-1. Nusselt number for laminar flow in circular tube annulus.
D, IDo Nu,

0.05 17.46
0.10 11.56
0.25 7.37
0.50 5.74
1.00 4.86
adapted from Incropera and DeWitt [48]









hh
Overall heat transfer coefficient Ut = .......... EQ 12
h,+

The rate of heat transfer from the condensing vapors to the cooling saline water is:

(T 'CT '
Qt' UAc t t 1v ( t c ) .......... EQ13
c s t t w ptt court can
In satr
[T'-T
sat out

Ut'Acs
T = T (Ttt Tc- )e swn .......... EQ 14

Distillate Column

The distillate column, like the brine column, depends on the difference in pressure

of the system and the atmospheric pressure. The amount of distillate coming out from the

system will be the sum of the distillate added to the distillate tube after condensation and

the distillate rejection due to the pressure increase in the evaporator. The temperature

gradient in the distillate column is neglected. The initial mass and temperature of the

water in the column are known.

Mass Balance

Change in pressure Change in mass of
in the system water in the column


->M^ M P ^ -Pt ..........EQ15


Energy Balance

Energy of the Energy of distillate
distillate column = rejected from the
SLcolumn at time t condensed distillate in At
at time t+At system in At

> /Y h =t M ht +MAIth At-i P^ Pt h +pM h pAt
PS P ddt L[ hP P










M' AtP' C1 C 'dT
PS t pw ,
-t" =Aj= CP dT .......... EQ16
At p'


Md Td



M ps





d TpS


Figure 3-5. Control volume of the distillate column.

Pressure in the System

The pressure is one of the most important parameter in this system design. The

initial low pressure in the system is created by using the natural forces of gravity and

atmospheric pressure, resulting in the formation of the saline water column. The height of

the water column is mainly dependent on the system pressure as the atmospheric pressure

can be treated as a constant. Thus, any increase in system pressure will lead to a decrease

in the water column height and vice versa.

Initially when the system is started, the pressure in the system will be equal to the

saturation pressure at the ambient temperature of the saline water. The pressure change in

the system relates directly with the rate of evaporation and rate of condensation. The

pressure increase in the system is due to the combined effect of vapor and non-

condensable gases accumulation. The effect of continuous accumulation of non-










condensable gases is taken into account in the system design as it is assumed that no

vacuum pump or steam ejector is used to remove these gases from the system.

Oxygen and nitrogen and small amounts of other gases are absorbed in sea water only in

molecular form, and they are released without changing the chemical composition of sea

water. However, the liberation of carbon-dioxide impairs the equilibrium between

carbon-dioxide C02, bicarbonate HCO3 and carbonate CO' The physico-chemical

equilibrium depends essentially on temperature, pressure, salinity and pH-value of the sea

water []. In order to compensate for the removal of C02, HCO; decomposes to produce

new CO2 molecules. The dissolved gases content of sea water is given in Table 3.2.

Table 3-2. Concentration of main gases dissolved in sea water.
Gas Concentration mole/m3 Parts per million (ppm)
CO2 0.005 0.22
02 0.24 7.7
N2 0.45 12.6
Ar 0.01 0.4
HCO3 3.062 187.1


adapted from Seifert and Genthner [49]

Thus, the pressure in the system at any time instant t can be written as:

S= P +P =f(Ta)+ .......... EQ 17
vapor gas sat gas

The irreversible increase in pressure caused by the non-condensable gases can be

found out using Dalton's law of partial pressure, and by considering them to behave as

ideal gases:

tn gas RT
P =gas I .. ....... EQ 18
gas ga


7



>









It is also assumed here that the moles of gases released in time At are directly

proportional to the concentration of the gas in the sea water and the amount of vapor

being generated.

(Concentration of gas i) ~A
n =as M- At
Psw

Boiling Point Elevation (BPE)

The vapor pressure of sea water is approximately 1.84 % less than that of fresh

water in the temperature range of OC 100C [50]. Thus, if two vessels containing fresh

water and sea water at the same temperature (within the above mentioned temperature

range) have their vapor space connected, fresh water will distill into the sea water vessel.

In other words, the lower vapor pressure for the sea water manifests itself as a boiling

point elevation which is a function of the dissolved solids concentration.

STeT = t +BPE' .......... EQ 19

Heat Source

Flat plate solar collectors are used to convert a renewable energy source to drive

the system. The saline water, after being pre-heated in the condenser, is passed through

the solar collector to increase its temperature in the desired range and then flashed in the

evaporator. A heat exchanger between the collector loop and the desalination system has

been omitted as the sea water flows directly through the collector absorbers. This

increases the efficiency and simultaneously reduces costs. But this also leads to the risk

of scale formation and corrosion in the metallic absorbers of the conventional flat plate

solar collector. A possible solution has been suggested by Hermann et. al. [51]: collectors

which have corrosion-free absorbers. In their design, selectively coated glass tubes acted









as absorbers with silicone hoses reinforced with aramid fibers acting as headers. The

efficiency was increased by adding a specially shaped reflector. Operating temperatures

as high as 90C can be reached with efficiencies of about 50 %.

The efficiency of a flat plat solar collector mainly depends on the solar insolation

and the inlet fluid-ambient temperature difference once constructed. The analysis,

explained next, is used to determine the solar insolation incident on the collector.

For a given location with latitude L, longitude local and its standard time meridian

being at a longitude/,, the solar declination can be estimated by:

8, =23.45 sin[360(284+ n)/365]

where n is the day number during the year with January 1 being n = 1. Declinations north

of equator are positive, and south are negative.

minutes from local solar noon
The hour angle is defined as h = s f l s where values
4 min/degree

east of due south are negative and west of due south are positive.

The relationship between the local solar time and the local standard time (LST) is:

Solar Time = LST + ET + (/, -1oc )- 4 min /degree
where, ET (in mins) = 9.87 sin 2B 7.53 cos B 1.5 sin B
and B = 360(n-81)/364 degrees

The solar altitude angle a is obtained from sin a = sinL sin3 + cosL cos 6 cosh,

The solar azimuth angle a, can be found as sin a = cos sin hj/ cos a with the

corrections as mentioned in [52] if, computationally, a comes out greater than 90.

Sunrise and sunset times can be determined from their respective hour angles:

h or k = cos [- tan L tan ,]









Solar radiation on a tilted surface is the sum of the beam radiation, sky diffuse

radiation and ground reflected radiation.

Ic =I +I + Ir.


Beam radiation:

Diffuse radiation:

Ground reflected radiation:


Ib,c= Ib,N COSi

dc =CIb,N Cos2 (,/2)


I, = Pgrb N (sina +C) sin2 (,/2)


where, Ib,N =CJe s, I = 011 +0.034cos(360n/365.25) p,,is the ground


reflectance and / is the surface tilt angle.

The angle of coincidence I can be calculated from:

cosi os a cos(a, a)sin f + sin a cos f

where, aw is the surface azimuth angle.

The average values of atmospheric optical depth k and sky diffuse factor C can be

determined from Table 3.3, whereas Cn is the clearness number.

Table 3-3. Average values of k and C for 21st day of each month for United States [52].
Month 1 2 3 4 5 6 7 8 9 10 11 12
k 0.142 0.144 0.156 0.180 0.196 0.205 0.207 0.201 0.177 0.160 0.149 0.142
C 0.058 0.060 0.071 0.097 0.121 0.134 0.136 0.122 0.092 0.073 0.063 0.057


Thus from the sunrise and sunset time, the time and the number of hours for

operation of the desalination system can be determined. The temperature of the saline

water exiting the collector can be calculated from:


t c A=T Acin .......... EQ 20
Msw ps









where T ,,, is the inlet collector saline water temperature which is equivalent to its exit

temperature from the condenser, A, is the solar collector area and r7, is the solar

collector efficiency.

Pumping Power

The pump is used to circulate the saline water through the condenser and solar

collectors to the evaporator. The pressure to which the saline water should be pumped

before it enters the evaporator depends on the fact that it should be greater than the

saturation pressure corresponding to its temperature to prevent boiling within the

circulating tubes.

The power required by the pump can be determined as:

[(P +pgH +APIf )-Pm]
Pump Power = )-
I pump

where, P is the final desired pressure, 1P is the atmospheric pressure, H is the height of

the system from the ground, APfn,,on is the frictional pressure drop, -F-is the volume flow

rate of saline water and p7ump is the pump efficiency.

Performance Ratio

The performance ratio (PR) can be defined as the ratio between heat used to

evaporate saline water into fresh water and the heat added to the system. In context with

the present system two performance ratios can be stated, one where the heat added is only

the useful heat extracted from the heat source and the other efficiency being the total heat

incident on the solar collectors.










C mdhf
Heat used for evaporation At
PR, = -
Useful heat added At YQ
At

Y mdhfg
Heat used for evaporation At_
PR2
Energy incident on collector At Q
At

Method of Analysis

The procedure followed in this analysis was to first write the equations in their

differential form. All system component equations were written in the differential form,

and the ideal way was to integrate all the equations simultaneously. The difficulty then

would be in solving them, as the equations in their partial derivative form are not linear.

Hence, another approach is followed here where all the components of the system are

assumed to move from one static state at time 't' to another static state at time 't+At'. In

this method all the differential terms are approximated in finite differential form and the

equations are solved simultaneously and iteratively till convergence is obtained. All the

system parameters are solved for time t, and then input parameters for time t+At are

updated to those obtained from the previous iterations at time t, and so on.

Single Stage

Known Initial Conditions ->Mo,Mo MM, po ,T, ToT X
evv P sat ev

Known for t > 0 -MAs,Mw, ,,, X

For iteration at any time t > 0, beginning from t = 0:

1) Calculate Teq from EQ19
Calculate Tt from EQ 4 and EQ 5

2) T, is known for constant temperature case, and can be calculated from EQ 20 for
the solar collector case









3) Calculate MA from EQ 3

4) Calculate MA from EQ

5) Calculate Xt from EQ 2

6) Calculate Ut using EQ 12
Calculate T0, from EQ 14

7) Calculate Q' from EQ 13

8) Simultaneously solve EQ9 and EQ10 utilizing EQ1 to obtain Tt,+t

9) Calculate P~ from EQ 18
Calculate P1ZO, using T' calculated in step 7
Calculate Pt from EQ 17

10) Calculate actual TIf from Pt+ found in step 8

11) Calculate M = Mass of vapor from EQ 11 using Tst calculated in step 8 +Mass of
non condesable gases added using the ideal gas equation
12) Calculate Md from EQ 9 where M "t are caluclated from EQ 11

13) Calculate the new height of the seawater column, and new volume
of vapor space

14) Calculate Mt + from EQ6

15) Calculate Ti, from EQ 8

16) Calculate Xt1 from EQ7

17) Calculate Mt1 from EQ 15

18) Calculate T' from EQ16

19) Go to step 1 for t = t +1 and repeat the process









Two Stage

The basic algorithm for the two stage system is similar to the single stage with the

main difference here being two evaporators, two condensers and two distillate column.

The component equations of mass, salt and energy balance are the same. The following

changes in the algorithm can be mentioned for the two stage system:

1) The inlet saline water temperature for condenser of stage 1 is the exit temperature
from condenser of stage 2

2) The mass flow rate of saline water from evaporator of stage 1 to that of stage 2
depends on the pressure difference in the two stages and the orifice size

3) The amount of saline water in evaporator 1 depends on the mass flow rate as mentioned
in (2) above and the unevaporated saline water
4) The heat source only heats up the saline water entering in stage 1

5) The temperature of saline water entering stage 2 is equivalent to the temperature
of saline water in evaporator of stage 1














CHAPTER 4
RESULTS AND DISCUSSION

The theoretical results presented in this chapter were obtained by mathematical

analysis of the system using the equations formulated in the earlier chapter. The results

presented here are for the cases of the system (single-stage and two-stage) operating on a

constant temperature heat source and a solar collector. The assumptions made here are:

the heat loss from the system, the thermal capacity of the system material and the effect

of non-condensable gases on condensation is neglected.

In this chapter, changes in the system performance are first studied by variations

in different system parameters for a single-stage system with a constant temperature heat

source. This is followed by the simulation results obtained for operating the system on a

constant heat source for a period of 12 hours. Single-stage system performance using

solar collector is presented along with the two-stage system results using constant heat

source (period of operation being 12 hours) and solar collector.

The system parameters which are taken as constants for all the cases are:

Inner diameter of condenser tube 0.0762 m (= 3 inch)
Outer diameter of condenser tube 0.1016 (= 4 inch)
Circular cross-sectional area of evaporator 0.2 m
Length of collections tanks 0.2 m
Cross-sectional area of collection tanks 0.1 m
Diameter of connecting pipes 0.0254 m (= 1 inch)
Volume of the initial space in the system 0.03 m3
Salinity 35 g/kg










Single-stage system with constant temperature heat source

The main input parameters in the system are the temperature of the heated saline

water (Tsw), the saline water mass flow rate (Msw) and length of the condenser (L,). The

ambient temperature (Ta) also has some effect on the system output. For the simulation,

the time interval At is taken to be 5 seconds.

Variation of inlet saline water temperature

The effect of variation of temperature of the inlet saline water on the distillate

output is shown in figure 4.1. Msw was set to 20 kg/hr and L, was 1 m. The output is for 1

hour of operation, and it can be noticed that with the increase in the saline water

temperature the output increases. The reason for this increase is that as the initial system

pressure (hence the saturation temperature) is same in all the cases, more flashing occurs

and hence more vapors are generated with increasing temperature since flashing is

directly proportional to the superheat of the saline water i.e. (T, T,) It should also be


noted that the temperatures obtained strictly depend on the heat source available.


Figure 4-1. Variation of output with inlet saline water temperature.


1.2
In duration of I hour
1
S


O 0.6

- 0.4

0.2


60 70 80
Sea Water T em perat u re {C )













The pressure in the system builds up with vapor generation and the release of non-

condensable gases. As there are no means of venting, the system pressure strongly

depends on the amount of vapor generation and the rate of condensation. Figure 4.2

shows the effect of variation of inlet saline water temperature on the system pressure. As

seen in the figure, the system pressure rapidly increases initially as no condensation is

occurring. It takes a small dip for three cases (60C, 70C and 80C) as condensation

starts, whereas for Tsw = 90C, the rate of condensation is exceeded by the rate of vapor

generation and the pressure further increases.


25000 -


20000 X--X-x-x- x-x-x-x-x-x-x--X-X-







--T sw= 60 C
---Tsw= 70 C
5000f ---Tsw= 8 C
-;i -x-Ts~= 90 C
0
0 -------- i -------- i -------- --X-------- i ------

0 20 40 50 80 NO
Time (sect


Figure 4-2. Variation of system pressure with inlet saline water temperature.

Variation of saline water mass flow rate

The saline water mass flow rate was varied for constant L, = 1 m and Tsw = 90C.

Figure 4.3 shows the increase in output with increasing mass flow rate, since the amount

of vapor generated during flashing is directly proportional to the feed rate.














1.4
m In duration of 1 hour
1.2

I

C

0.6

0.4

0.2

0
10 20 30
M ass flow rate of sea water (kglhrl



Figure 4-3. Effect on distillate output with change in saline water flow rate.


Variation of length of condenser


The length of the condenser and hence the condensation rate is an important


parameter in the pressure build up in the system. Increasing the condenser length leads to


higher condensation rate and lesser pressure increase in the system. For Msw = 20 kg/hr


and Tsw = 900C, the system pressure variation is shown in figure 4.4.



30000 -


25000 -


20000
._______ /____-----

15000 -- Condenser Length = 0.5 m
1 -- Condenser Length = I m
0 10000 -- Condenser Length = 1.5 m


5000



0 50 100 150 200 250 300
Time (sec)


Figure 4-4. System pressure variation with condenser length.












Variation of ambient water temperature


The initial pressure in the system is the saturation pressure corresponding to the


ambient water temperature. Hence with a cooler ambient water temperature, the initial


pressure of the system will be lower which will result in increased vapor generation. The


variation of the system saturation temperature is shown in figure 4.5.



70





S- Ta =10. C
40 Ta =1.0 C
Si---Ta =23.8 C
so

s 20

0lo

0
0 20 40 0s 80 100
Time 6tecm



Figure 4-5. Variation of system saturation temperature with ambient water temperature.


1.2

11i In duration of

e 11

r 1,05





0Am5


10 1i
Amblent temperature |C)


Figure 4-6. Effect of ambient water temperature on distillate output


23 8


1 hour








Also, the condensation rate will be greater for lower water temperature leading to

increase in distillate output as shown in figure 4.6. Values ofMsw = 20 kg/hr, Tsw = 900C

and L, = 1 m are taken.

System Output

The system was simulated for a 12 hour duration run. The input parameters were

Msw = 20kg/hr, L, = 1 m and Tsw = 900C with Ta= 23.80C. The output of the system is

shown in figure 4.7. The total distillate output at the end of 12 hrs was 11.31 kg. The net

pressure and saturation temperature continued to increase throughout the duration, and

reached values of 22.3 kPa and 62.80C. Due to the pressure rise, the brine and distillate

water column fell to 7.94 m from the initial 9.87 m. The pressure increase due to non-

condensable gases was 1.1% of the total pressure increase.


Figure 4-7. Hourly output for single-stage system with constant temperature heat source.


0.96 -
Hourly distillate output

0.95
.9 0.9



0.91

0.88
1 2 3 4 5 6 7 s 9 10 11 12
Nth hour of system operation


I










From the figure 4.7, it can be noticed that the hourly output continues to decrease

due to the increase in the saturation temperature thus decreasing the superheat for

flashing. The salinity of the brine rejected from the brine column at the end of the run

was 36.7 g/kg. The performance ratio of the system for the 12 hour run was 0.746.

Two stage system with constant temperature heat source

The two stage system specifics were taken as: Msw = 20kg/hr, L, = 1 m for both

condensers and Tsw = 90C for the first stage. The simulation was run for 12 hours with

At taken as 1 second. Figure 4.8 shows the hourly output of both the stages in the

duration. The total distillate output obtained was 13.9 kg, with 7.1 kg from the first stage

and 6.8 kg from the second stage. The performance ratio of this system was 1.42. The

other reason, except for the system being a two-stage one, for this increase is that the

saline water is now pre-heated in two condensers and thus the heat required to reach a

temperature of 90C reduces.


0.9 -
Stage 1 hourly output
0.8
Stage 2 hourly output
0.7 -




0.3

0.2

0.i


1 2 3 4 5 6 7 8 9 10 11 12
Time {Nth hour)


Figure 4-8. Hourly output for two-stage system with constant temperature heat source.









As seen from the above figure, the output from the first stage continues to

decrease due to the increasing pressure. The second stage is assumed to become

operational when the height of brine accumulated in the first stage is over 5 cm. The

second stage operation starts midway through the first hour with the output increasing

initially and then decreasing. The pressure at the end of 12 hrs in the first and second

stages reached about 39.9 kPa and 17.5 kPa respectively. The saturation temperature in

the first stage was 76.3C, and in the second stage was 57.6C. The pressure increase due

to non-condensable gases was nearly 1.14% of the total pressure in the first stage and

0.82% in the second stage. The brine accumulation height in the first stage was 12.6 cm,

while the brine column height drop in second stage was 1.47 m.

Solar collector specifications

In the simulation using solar collector clear sky conditions are assumed, and the

location is taken to be Gainesville, Florida (Latitude 29.68N, Longitude 82.27W) with

the collector facing south and tilted at an angle equal to the latitude of Gainesville

(Latitude 29.68N) from the horizontal. The collector efficiency is given by:




r/ = 0.75-4.87 (c -T)




Figure 4.9 shows the solar insolation on the surface of a collector oriented as mentioned.

The area of the collector was taken to be 1 m2 for all the cases. The collector was

operated only when the incident angle on the solar collector surface was less than 60.





























500 700 900 1100 1300 1500 1700 1900
Timre{Hourofthedaye.g. 1300 hours = 1 PM)


Figure 4-9. Insolation on a tilted solar collector surface on May 21 for a clear day at
Gainesville, FL.



Single-stage system coupled with solar collector

A single stage system coupled with a solar collector was simulated for May 21

with the Msw = 20 kg/hr and L, = 1 m. The time interval At was set as 5 seconds. The

simulation ran for a system time of 7.83 hrs. The temperature of the inlet saline water

increased as the insolation on the collector surface increased. It attained a maximum

value of 83.7C. Figure 4.10 shows the variation of temperature with time.

The system saturation temperature reached a maximum of 58C. The insolation

decreased after reaching a maximum, and thus decreasing the inlet saline water

temperature and the saturation temperature.

With the increasing saturation temperature, more vapors are generated and hence

the system pressure increases. The pressure also follows the same trend, reaching a

maximum of 17.8 kPa with insolation. The variation of pressure is shown in figure 4.11.


1400

1200

Oa0



800
600
0



200

0


_- Insolation on May 21 at Gainesville, FL












90







5 50
S40
S-- System saturation temperature
30 -
Condenser outlet temperature
20 Saline water temperature from solar collector

10 1


0 1 2 3 4 5 6 7 8 9
Time{hours)


Figure 4-10. Variation of single-stage system temperatures coupled with solar collector.


0 1 2 3 4 5 6 7 8 9
Time {hour)


Figure 4-11. Single stage system pressure coupled with solar collector


The pressure increase due to the accumulation of non-condensable gases is shown


in figure 4.12. It depends on the rate of release of the non-condensable gases and hence


the vapor generation rate.


20000

18000
16000

14000
. 12000

I 10000

8 a000
6000

4000
2000



































Figure 4-12. Pressure change due to non condensable (NC) gases in single-stage system
with collector.



Here only oxygen and nitrogen are taken into account as they make up the major


portion of the total dissolved gases in seawater. The pressure increase due to the gases at


the end of duration is about 117 Pa.


Figure 4-13. Water column height variation for single-stage coupled with solar collector.


40 -

120 -



NO
100 -

80 -

i 60 -

40 -

20 -

0 -


- Pressure due to NC gases


4 5 6 7 a
Time (hour)


10
9.8
9.6
9.4

9.2


a8.

a.6
a.4
8.2


-- Water Column Height


0 1 2 3 4 5 6 7 8 9
Time [hours)










The height of the brine column also fluctuates as it depends on the pressure in the

system. It attains a minimum of 8.38 m. Figure 4.13 shows the variation of the brine

water column height with time.

The maximum distillate output rate reached is 2.4 x 10 4 kg/s. The net output

obtained after 7.83 hours is 5.54 kg. The hourly output is shown in figure 4.14. As per the

performance ratios defined in the previous chapter, the efficiency obtained are:

PR = 0.748 and PR, = 0.480.







1-
0.9 1 Hourly Output

0.7-

0.5 -
OA -
0.3-
02


1 2 3 4 5 6 7 723
Time (Nth Hour)


Figure 4-14. Hourly output of single stage system coupled with solar collector.

Two-stage system coupled with solar collector

The performance of the two-stage system is simulated for the same day i.e. May

21 with the input values as Msw = 20 kg/hr and L, = 1 m. The time interval At taken here

is 1 second as it provides better iteration values. The second stage is assumed to become

operational when the height of brine accumulated in the first stage is over 5 cm.










The temperature of inlet seawater varies with time due to the change in solar

insolation, and is shown in figure 4.15. The maximum temperature attained by the saline

water is higher than that of single-stage as the saline water is pre-heated in two

condensers before passing through the solar collector. The value of this temperature is

990C, which would require high efficiency flat plate solar collectors or parabolic trough

collectors for operation and thus such temperatures are achievable. The inlet saline water

to the second stage is from the first stage, and the maximum value attained is 77.3C.





120 -

Goa



S0 -s



S40 -
Stage I inlet seawater temperature
20 Stage 2 inlet seawater temperature


0 1 2 3 4 5 6 7 8 9
Time houri


Figure 4-15. Feed water temperature for two stage system coupled with collector

It is also seen here that this maximum value for the second stage is reached after

the temperature in the first stage has peaked. The reason is that the high inlet temperature

in the first stage takes a finite amount of time to reflect in the brine accumulating in first

stage, which is the feed water for the second stage. The sudden jump seen in the inlet

seawater temperature in the first stage is when the second stage becomes operational and

its condenser starts pre-heating the feed water.











The increase in the inlet seawater temperature leads to an increase in the vapor

generation rate and hence an increase in the system pressure. Figure 4.16 shows the

variation of system pressure with time. The pressure in the first stage reaches a maximum

value of 44.5 kPa and in the second stage a value of 15.9 kPa. The pressure decreases

henceforth due to the decrease in insolation and vapor generation rate.


50000 -
-0 Stage 2 Pressure
45000
Stage 1 Pressure
40000 _
35000
30000
25000
S20000
15000
10000
5000

0 1 2 3 4 5 6 7 8 9
Time{hoursl


Figure 4-16. Two-stage system pressure coupled with solar collector.

The peak pressure reached in the second stage is after the peak reached in the first

stage because of the difference in the peaks for maximum inlet seawater temperature in

both the stages. Again, the jump in the pressure curve for the first stage is due to the jump

in the inlet seawater temperature.

With the increase in pressure, the saturation temperatures of both the stages

follow the same pattern. The maximum value reached in the first stage is 78.90C and in

the second stage is 55.6C. The variation of saturation temperature is shown in figure

4.17.



























0 1 2 3 4 5 6 7 8 9
Time I hour)


Figure 4-17. Saturation temperature curves for two-stage system with solar collector.

The variation of condenser outlet temperatures with time is shown in figure 4.18.

The high temperatures as shown are obtained due to the low mass flow rate of the saline

water. The maximum is reached when the saturation temperature peak is attained.

The pressure increases due to non-condensable gases in the two stages are shown

in figure 4.19. The increase in the second stage is significantly lower because of the low

vapor generation rate, and also due to the fact that a small fraction of the gases dissolved

in the seawater has been liberated in the first stage leading to lower dissolved

concentrations of gases in the seawater entering the second stage. At the end of the

system run, the increase in pressure due to non-condensable gases in the first stage is

955.8 Pa and in the second stage is 81.9 Pa.


90
30
a7
Ssa
; 50
S40
30
20
10












B0

70--



50
IL
40

E 30
I -- Condenser 1 outlet temperature
20
-- Condenser 2 outlet temperature



0 1 2 3 4 5 6 7 8 9
Time [hour)


Figure 4-18. Condenser outlet temperature of two-stage system coupled with collector.


1200
Pressure due to NC gases in Stage 1

1000 Pressure due to NC gases in Stage 2

S800 -




.L 400

200


0 1 2 3 4 5 6 7 8 9
Time (hour)


Figure 4-19. Pressure increase due to NC gases in two-stage system with solar collector.


The pressure changes also lead to changes in the brine column height in the


second stage and the brine accumulation height in the first stage. These are shown in


figures 4.20 and 4.21. The final brine height attained in the evaporator in stage 1 is 13.4


cm. The curve shown in figure 4.20 shows that the brine height increases to a certain


value, decreases slightly and then again starts increasing. The decrease is due to the










increase in the pressure in the first stage due to which more brine flows from the first

stage to the second than the amount of brine getting accumulated.




0.6 -

0. -



? 0.1
0.0 -



0.04 Height of Water in Eavporator 1

0.02 -

0 2 3 4 5 6 7 8 9
Time (hoursT


Figure 4-20. Brine height in the first stage of the two-stage system with collectors.

The brine column follows the same trend as that of the single-stage system. It

varies with the pressure change and reaches a minimum when the pressure in the system

reaches a maximum. The minimum height to which the column drops is 8.57 m.

The diameter of the orifice connecting the two stages is an important parameter in

the two-stage system analysis. A very large diameter would result in all the brine draining

from the first stage to the second, thus equalizing the pressures and making the two-stage

concept non-operational. A small diameter would lead to very small flow rates from the

first stage to the second thus resulting in negligible output from the second stage, and also

leading to large accumulation of brine in the first stage. The diameter here was taken as

1.24 mm.













10



D.6- Height of water c

-.4





8.8

8.6

8.4
0 1 2 3 4 5
Time (hDurl


columnn in stage 2


6 7 8 9


Figure 4-21. Brine column height in second stage of the two-stage system with collector


0.8 Stage I hourly output

0.8 U Stage 2 hourly output

0.7

iD0.6
0.5

a0.4

0.3

0.2

0.1


1 2 3 4 5 6 7 7.7
Time (Nth hour]





Figure 4-22. Hourly output from two-stage system with solar collector.





Figure 4.22 shows the hourly distillate output from each of the stages. The total


yield for 7.7 hours of operation was 8.66 kg, with the first stage output as 4.76 kg and


second stage output as 3.90 kg. The performance ratios of the system were:






63


PR, =1.35, PR2= 0.75

The high efficiency is due to the combined effects of pre-heating of feed saline water in

the condenser and due to the utilization of the second stage by producing more distillate

without using any extra heat source.














CHAPTER 5
CONCLUSION AND FUTURE WORK

Conclusion

An innovative desalination system is proposed which makes use of natural forces

of gravity and atmospheric pressure to create vacuum under which saline water is flashed.

The system can be coupled with low grade heat source like solar collectors to produce

potable water.

Single-stage and two-stage concepts of the desalination system were outlined.

Mathematical models of the concepts were formulated and developed, and the results

were presented for the systems coupled with: a) constant temperature heat source, and b)

solar collector.

The analysis shows the following:

For the case of constant temperature heat source, the single-stage system was
shown to produce 11.31 kg of distillate with a performance ratio of 0.746 and the
two-stage system produced 13.9 kg with performance ratio of 1.42 in 12 hours of
operation under the same initial conditions. When coupled with a solar collector
of 1 m2 area, the single-stage system had a distillate output of 5.54 kg in 7.83 hrs
with a performance ratio of 0.748 (based on only the useful energy extracted from
the collector) or 0.48 (based on the solar insolation incident on the collector).

The two-stage system produced 8.66 kg in 7.7 hrs with performance ratio of 1.35
(based on only the useful energy extracted from the collector) or 0.75 (based on
the solar insolation incident on the collector). The mass flow rate of feed saline
water for all the cases was 20 kg/hr. Thus, the system performance obtained is
better than that of a conventional solar still.

Effect of different parameters on the system output was studied. The system
produces more output with higher saline water mass flow rate, higher feed saline
water temperature and with more condenser surface area. The orifice diameter is
an important additional parameter in the two-stage system.









*When coupled with solar collector, the increase in pressure due to non-
condensable gases was negligible as compared to the pressure increase due to
vapor accumulation. Thus, the system can be operated for a number of days
without a need to re-establish the vacuum if the pressure increase due to vapor
accumulation can be kept low. This can be achieved by additional condensation
(without vapor generation) and/or by night-cooling.

Future Work

The future work, in the order shown, includes:

1) Fabricating and experimentally testing the concepts.

2) Validating the theoretical model after taking into account the heat loss from the

system and including the thermal capacity of the system.

3) Performing an economic analysis of the system to determine the cost of distillate


produced.














APPENDIX A
PHYSICAL PROPERTIES

Sea Water

Density [53]


1 33 2 2S-150 ( 2t-200 >
1=0i 0 = 150 160

where p is in kg/m3, Salinity S is in g/kg, temperature t is in C, Y denotes a

summation, the first term of which is halved and Tk(x) represents a Chebyshev

polynomial of degree k which are defined as:


To(x) = 1; Ti(x) = x; Tr+l(x) = 2xTr(x)

The Chebyshev coefficients ci are as follows:


Tr-l(x)


i=0 i=l i=2 i=3
j= 0 4.032219 -0.108199 -0.012247 0.000692
S=1 0.115313 0.001571 0.001740 -0.000087
= 2 0.000326 -0.000423 -0.000009 -0.000053

Heat Capacity [54]
C, = (a + a2S +aS2)+(b, +b2S+bS2 )T+(c, +cS + cS2 ) T2 +(d, +d2S+dS2 ) T3

where C is in kJ/kgC, S is the salinity in g/kg and T is the temperature in K.

The coefficients are defined as follows:

al = 5.328 bl = -6.913x10-3
a2 = -9.76x10-2 b2= 7.351x10-4
a3= 4.04 x10-4 b3= 3.15 x10-6
cl= 9.6x10-6 di= 2.5x10-9
c2 = -1.927 x10-6 d2= 1.666 x10-9
C3 = 8.23 x10-9 d3 = -7.125 x1012









Thermal Conductivity [7]

k= (577 + 1.522 t- 0.00581 t2)10-3

where t is in C, and k is in W/m.K

Dynamic Viscosity [55]


lg10 t= +109 [A(iS+a2S2)+B ( bS+b2S2 t) 20)]

where 720 = viscosity of solution at 200C, mNs m-2
= 1.002 + cS + 2S2
1 22
7 = viscosity of solution at toC, mNs m-2
S = salinity in g/kg


The equation constants are:
A= 1.37060 B = 0.000832
al = -0.000619 a2 = -0.000003
bl = 0.006102 b2= -0.000015
cl= 0.001652 c2 = 0.0000083


Vapor Pressure [56]


\logo P=hS+ jS2

where h= -2.1609x10-4
j = -3.5012x107
S = salinity in g/kg
Here, p. is the vapor pressure of pure water at the same temperature, and is defined as:


b ex (I _,2
log0 P= a+--+-10 -
zz
where x =z2g,
y = 344.1 t,
z =t + 273.16,
t = temperature C,
a =5.432368,
b= -2.0051x103,


l)+el0'125
1) + e 10 1 25

c = 1.3869 x 10-4
d= 1.1965 x101
e = 4.4000 x103
f = -5.7148x10 3
g = 2.9370 x105

P0 is in units of 105 N/m2









Boiling Point Elevation (BPE)

2565.757/T -9.81559+1.547391ogT- c(337.178/T 6.41981+0.922753logT)

+ c2 (32.68 /t- 0.55368 + 0.079022log T)
(266919.6 -379.669T + 0.334169T2

where c= 19.819 S
1-S
S = salinity in kg/kg
T = temperature in K


Water

Density

999.83952 +16.945176T 7.9870401 x 103 32 -46.170461 x 106 T3 +105.56302 x 109 T4
1+16.879850x10-3T
where, p is in kg/m3 and T is temperature in C


Dynamic Viscosity

1792.5
logo1 r= -10.2158+ 2- +0.01773T 1.2631x 105 T2
T
where T is temperature in K and 7 is in mNs/m2

Specific Heat [57]

C = 4.2174 -3.720283 x10 3T+1.412855 x104T2 -2.654387 x106 T3 +2.093236 x10 T4
where T is temperature in oC and Cp is in kJ/kgC

Thermal Conductivity

k = -0.2758 + 0.004612T- 5.5391x 10-6T2
where T is temperature in K and k is in W/m.K

Latent Heat of Vaporization

hfg =3146-2.36T
where T is temperature in K and hf is in kJ/kg









Vapor

Density



1/p 460.5T
Vapor Pressure
of sea water at T
where T is temperature in K and p is in kg/m3

Specific Heat

Cp = 107T3 -0.0001T2 +0.0302T -1.1804
where T is temperature in K and C, is in kJ/kgC














APPENDIX B
COMPUTER PROGRAM FOR SINGLE-STAGE SYSTEM

#include
#include
#include
#include

double ksw(double);
double cp_sw(double, double);
double cp v(double);
double mu_sw(double, double);
double vp_sw(double, double);
double rhosw(double, double);
double cheby_poly(double,int);
double rho v(double);
double bpe(double);
double hfg(double);
double condenser(double,double);
double rhow(double);
double mu w(double);
double cp w(double);
double k w(double);
int insolation(int);
double int cpsw(double);
double intcpv(double);

struct sc
{
double tfout;
double qu;
};
sc collector(double, double, double, double);

double dt = 5;
double s = 35;
double pi = 3.142;

//Input Parameters
double Ic = 1;
double msw = 0.005556;
double asc = 1;










// Condenser
double di= 0.0762;
double dou= 0.1016;
double ac = pi*di*lc;
double dh = dou di;
double across = (pi/4)*(dou*dou di*di);
int month, day;
double mew = msw;

void main()
{
//Input parameter
double vos = 0.03;

ofstream stl;
stl.open("Msw=20 Lc=l VOS=0.03 Asc=l Month=12.xls");

// Enter month and day of the year
cout<<"Enter the month number of the year : ";
cin>>month;
cout<<"Enter the day of the month : ";
cin>>day;

// Define Salinity and Ambient Water and Air Temperature
double tv0, ta;
double tmonth[12] = {10.6, 12.2, 16.0, 20.2, 23.8, 25.4, 27.3, 26.3, 25.3, 21.4, 16.2,
11.9};
tv0 = tmonth[month-1];
ta = tv0;

//Hours of Insolation
int county, dj = 5;
county = insolation(dj);
int n = countl*dj*60/dt;
cout<<"n = "<
double vos2;
double lp,ap,lt,at,lev,aev;
double pO;

// Define the Initial Pressure pO
pO = vp_sw(tv0,s);
lev= 0.3;
aev = 0.2;
vos2 = vos;











//Tank and connecting tubes Dimensions
It =0.2;
lp =(100000-p0)/(rho_sw(tv0,s)*9.81) lev;
at =0.1;
ap= 0.00051;
double mev0,mvs0,mps0;

// Define Initial mass of fluids in evaporator, product water tube and vapor space
mev0 = (lp*ap+lt*at+lev*aev)*rho_sw(tv0,s);
mpsO = ((lev+lp)*ap+lt*at)*rho_sw(tv0,s);
mvs0 = vos*rho v(tv0);

double quc;
double mv,mb,md;
double mev,mps,mvs;
double tsw,tveq,tv,tsat,tev,tout,tin,tp,tsatr,tsatv;
double p,pgas;
double xsw,xb,xev;
double q,u;
double x,dx;
double mev2,mps2,mvs2;
double tsat2,tev2,tp2,tsatr2,tsatv2;
double p2,pgas2;
double xev2;
double x2,dx2;
double feff;
double time;

my = 0.0;
mb = 0.0;
md = 0.0;
tsw = 0.0;
tv = 0.0;
tout = 0.0;
tin = tvO;
pgas = 0.0;
xb = 0.0;
q = 0;
u=O;
quc = 0;
time = 0;

int w, i, timecheck;
double al,a2;









mev = mev0;
mps = mps0;
mvs = mvs0;
tsat = tvO;
tev = tvO;
tp = tvO;
tsatv = tvO;
xev = 35;
xsw = 35;
p = pO;
pgas = 0;
dx = lev;
x = lev+lp+lt;

int chk = 0;

double ins;
ifstream insol;
insol. open("insolation.txt");

stl<<"tv[i]"<<"\t"<<"tveq[i] "<<"\t"<<"Feff[i]"<<"\t"<<"tsw[i] "<<"\t"<<"Ins[i]"<<"\t"<
<"quc[i] "<<"\t"<<"mv[i]"<<"\t"<<"mb[i]"<<"\t"<<"xb[i]"<<"\t"<<"u[i]"<<"\t"<<"tout[i]
"<<"\t"<<"q[i]"<<"\t"<<"md[i]"<<"\t"<<"\t"<<"Time[i]"<<"\t"<<"\t"<<"tsat[i]"<<"\t"<<
"tsatv[i] "<<"\t"<<"mvs[i] "<<"\t"<<"pgas[i] "<<"\t"<<"p[i] "<<"\t"<<"mev[i]"<<"\t"<<"te
v[i]"<<"\t"<<"xev[i]"<<"\t"<<"mps[i]"<<"\t"<<"tp[i]"<<"\t"<<"x[i]"<
mew = msw;
sc sl;

for(i=0; i {
timecheck = time;
if(timecheck%300 == 0)
insol>>ins;


// Inlet Cooling water temperature
tin = tv0;

// Temperature of vapor produced
tveq = tsat + bpe(tsat);

// Overall HTC at saturation temperature
u = condenser(tsat,tv0);


// Outlet temperature of the cooling water









tout = tsat (tsat-tin)*exp(-(u*ac/(mcw*cp_sw(tin,s))));

// Heat rejected from condenser
q = mcw*(intcpsw(tout)-intcpsw(tin));
sl = collector(msw,tout,ta,ins);
tsw = sl.tfout;
quc = sl.qu;

if(tsw>90)
break;

if(tsw {
chk = 1;
}

// Non-Equilibrium Allowance (Flashing efficiency)
feff= 1 1/(1+1.5*(tsw-tsat-3));

// Actual Vapor temperature
tv = tveq 0.0001;
al = feff*(intcpsw(tsw)-intcpsw(tveq))/hfg(tveq);
do
{
a2 = (intcpsw(tsw)-intcpsw(tv))/hfg(tv);
if(al>a2)
tv = tv- 0.001;
else
tv = tv + 0.001;
}
while(fabs(al-a2)>0.01);


// Mass flow rate if vapor produced
my = msw*(intcpsw(tsw) intcpsw(tv))/hfg(tv);

// Mass flow rate of falling brine
mb = msw-mv;

// Salt concentration of falling brine
xb = msw*xsw/(msw-mv);

// Saturation temperature of the vapor space (only vapor)
w =0;
tsat2 = tsat + 0.001;
do









{
al = mvs*(intcpsw(tsat2) intcpsw(tsat))/dt;
a2 = (mv-vos*(rho v(tsat2)-rho v(tsat))/dt)*hfg(tv)-q+mv*(intcpv(tv)-intcpv(tsat));
if(fabs(al-a2)<1)
{
w=l;
}
else
{
if(al>a2)
tsat2 = tsat2 0.001;
else
tsat2 = tsat2 + 0.001;
}
}
while(w==0);

// Pressure in evaportor (vapor+gases)
pgas2 = 0.7*mv*dt*8.314*(tsat+273)/(rho_sw(tsw,s)*vos);
pgas2 = pgas2 + pgas;
p2 = vp_sw(tsat2,s)+pgas2;

// Actual saturation temperature corresponding to pressure
w=0;
tsatr2 = tsat2 + 0.001;
do
{
if (fabs(p2-vp_sw(tsatr2,s)) w=l;
else
if(p2>vp_sw(tsatr2,s))
tsatr2 = tsatr2 + 0.001;
else
tsatr2 = tsatr2 0.001;
}
while(w==0);
tsatv2 = tsat2;
tsat2 = tsatr2;

// Mass of vapor + gases in the vapor space
mvs2 = vos*rho v(tsatv2) + 0.45*mv*dt*0.028/(rho_sw(tsw,s)*vos) +
0.24*mv*dt*0.032/(rho_sw(tsw,s)*vos);

// Product water flow rate
if(i==0)
md = 0;









else
md = my vos*(rho v(tsatv2)-rho v(tsatv))/dt;


// Mass of seawater in evaportor and new vapor space
dx2 = dx (p2-p)/(9.81 *rho_sw(tev,s));
if(dx>0 && dx2<0)
{
mev2 = mev dx*aev*rhosw(tev,s) ((p2-p)/(9.81*rho_sw(tev,s))-
dx)*ap*rho_sw(tev,s);
x2 = lp + It ((p2-p)/(9.81*rho_sw(tev,s))-dx);
vos = vos2+lev*aev;
}
else
{
if(dx2>0)
{
mev2 = mev aev*(p2-p)/9.81;
vos = vos + aev*(p2-p)/(9.81*rho_sw(tev,s));
if (vos>(vos2+lev*aev))
vos = vos2+lev*aev;
x2 = x (p2-p)/(9.81 *rho_sw(tev,s));
}
else
{
if(dx2<0)
{
mev2 = mev ap*(p2-p)/9.81;
x2 = x (p2-p)/(9.81 *rho_sw(tev,s));
}
else
{
if(dx<0 && dx2>0)
{
mev2 = mev + dx2*aev*rho_sw(tev,s) dx*ap*rho_sw(tev,s);
x2 = lp + It ((p2-p)/(9.81*rho_sw(tev,s))-dx);
vos = vos2+(lev-dx2)*aev;
}
}
}
}

// Temperature of seawater in evaportor
tev2 = tev + 0.00001;
a2 = (int cpsw(tv)-int cpsw(tev))*md;









{
al = mev2*(intcpsw(tev2)-intcpsw(tev))/dt;
if(al>a2)
tev2 = tev2 0.00001;
else
tev2 = tev2 + 0.00001;
}
while(fabs(al-a2)>1);

// Salt concentration of seawater in evaporator
xev2 = xev + mb*(xb-xev)*dt/mev2;

// Mass of product water in the product pipe
mps2 = mps ap*(p2-p)/9.81;

// Temperature of product water in the product pipe
tp2 = tp + 0.00001;
a2 = (intcpsw(tsat)-intcpsw(tp))*mdl;
do
{
al = mps2*(intcpsw(tp2)-intcpsw(tp))/dt;
if(al>a2)
tp2 = tp2 0.00001;
else
tp2 = tp2 + 0.00001;
}
while(fabs(al-a2)>1);

//st < st < "\t"< me<<"\t"<<"\t"< "\t"< stl<
tsat = tsat2;
pgas = pgas2;
p = p2;
tsatv = tsatv2;
tsatr = tsatr2;
mvs = mvs2;
mev = mev2;
tev = tev2;
xev = xev2;
mps = mps2;
tp= tp2;









dx = dx2;
x = x2;

time = time + dt;
if(chk==1)
break;
}
stl.close();
}

// Thermal Conductivity of Seawater
double ksw(double t)
{
return (577 + 1.522*t 0.00581*t*t)/1000;
}

// Heat Capacity of seawater
double cp_sw(double t, double s)
{
double al, a2, a3, bl, b2, b3, cl, c2, c3, dl, d2 ,d3, cp;
t = t + 273;
al = 5.328;
a2 = -0.0976;
a3 = 0.000404;
bl =-0.006913;
b2 = 0.0007351;
b3 = -0.00000315;
cl = 9.6*pow(10,-6);
c2 = -1.927*pow(10,-6);
c3 = 8.23*pow(10,-9);
dl = 2.5*pow(10,-9);
d2 = 1.666*pow(10,-9);
d3 = -7.125*pow(10,-12);
cp = ((al + a2*s + a3*s*s) + (bl + b2*s + b3*s*s)*t + (cl + c2*s + c3*s*s)*t*t + (dl +
d2*s + d3*s*s)*t*t*t)*1000;
return cp;
}

double int cpsw(double t)
{
double al, a2, a3, bl, b2, b3, cl, c2, c3, dl, d2 ,d3, cpt;
t = t + 273;
al = 5.328;
a2 = -0.0976;
a3 = 0.000404;
bl =-0.006913;









b2 = 0.0007351;
b3 = -0.00000315;
cl = 9.6*pow(10,-6);
c2 = -1.927*pow(10,-6);
c3 = 8.23*pow(10,-9);
dl = 2.5*pow(10,-9);
d2 = 1.666*pow(10,-9);
d3 = -7.125*pow(10,-12);
cpt = ((al + a2*s + a3*s*s)*t + (bl + b2*s + b3*s*s)*t*t/2 + (cl + c2*s +
c3*s*s)*t*t*t/3 + (dl + d2*s + d3*s*s)*t*t*t*t/4)*1000;
return cpt;
}

double cp v(double t)
{
return ((pow(10,-7)*pow(t,3) 0.0001*t*t + 0.0302*t 1.1804)*1000);
}

double intcpv(double t)
{
return ((pow(10,-7)*pow(t,4)/4 0.0001*t*t*t/3 + 0.0302*t*t/2 -
1.1804*t)*1000);
}

// Dynamic Viscosity of Seawater
double mu_sw(double t, double s)
{
double a,al,a2,b,bl,b2,cl,c2,vis 20,z,vis;
a =1.3722;
al =-0.001015;
a2 = 0.000005;
b = 0.000813;
bl = 0.000102;
b2 = -0.00004;
cl = 0.001550;
c2 = 0.0000093;
vis 20 = 1.002 + cl*s + c2*s*s;
z = ((t-20)/(t+109))*(a*(l+al*s+a2*s*s) + b*(l+bl*s+b2*s*s)*(t-20));
vis = (vis_20/pow(10,z))*pow(10,-3);
return vis;
}

// Vapor pressure of seawater
double vp_sw(double t, double s)
{
double z,g,x,y,a,b,c,d,e,f,h,j,q,po,p;









z = 273.16 + t;
g = 2.9370*pow(10,5);
x = z*z g;
y = 344.11 t;
a = 5.432368;
b = -2.0051*1000;
c= 1.3869*pow(10,-4);
d = 1.1965*pow(10,-11);
e = -0.0044;
f= -0.0057148;
h =-0.00021609;
j= -3.5012*pow(10,-7);
q = a + b/z + c*x*(pow(10,d*x*x) 1)/z + e*pow(1O,f*pow(y,1.25));
po = pow(10,q);
p = po*pow(10,(h*s+j*s*s))*pow(10,5);
return p;
}

// Density of Seawater
double rho_sw(double t, double s)
{
double m,n,sumj =0,sumi=0,density;
double c[4][3] = { {4.032219, 0.115313, 0.000326},
{-0.108199, 0.001571, -0.000423},
{-0.012247, 0.001740, -0.000009},
{0.000692, -0.000087, -0.000053} };

m =(2*s- 150)/150;
n =(2*t 200)/160;
for (int i=0; i<4; i++)
{
for(int j=0; j<3; j++)
{
if(j==0)
sumj = sumj + c[i][j]*cheby_poly(m,j)/2;
else
sumj = sumj + c[i][j]*cheby_poly(m,j);
}

if(i==0)
sumi = sumi + sumj*cheby_poly(n,i)/2;
else
sumi = sumi + sumj*cheby_poly(n,i);

sumj = 0;










density = sumi*1000;
return density;
}

double cheby_poly(double x, int i)
{
double T;
if (i==0)
T= 1;
if (i== 1)
T = x;
if (i==2)
T = 2*x*x 1;
if (i==3)
T = 4*x*x*x 3*x;
return T;
}

// Density of Vapor
double rho v(double t)
{
double v;
v = 4.605*(t+273.15)*100/(vp_sw(t,35)) 0.02;
return (1/v);
}


// Boiling point elevation of seawater
double bpe(double t)
{
t = t + 273;
double c, elv;
double cb = 0.035;
c =19.819*cb/(1-cb);
elv = c*t*t*(565.757/t 9.81559 + 1.54739*log(t) c*(337.178/t 6.41981 +
0.922753*log(t)) + c*c*(32.681/t 0.55368 + 0.079022*log(t)))/(266919.6 379.669*t +
0.334169*t*t);
return elv;
}

//Latent heat of vaporization of water
double hfg(double t)
{
return 1000*(3146 2.36*(t+273));










double condenser(double tsat, double tinn)
{
double ts,hi,ho,u,el,e2,hfgn,Red,Nuo,tout,tavg,tin,Prsw,tdt;
tin = tinn;
ts = tsat 0.001;
tout = ts;
int e = 1;
if(tsat==tin)
{
u=0;
tout=tin;
tdt=0;
ts=tin;
tavg=tin;
}
else
{
do
{
tavg = (tout+tin)/2;
hfgn = hfg(tsat) + (3/8)*cp w(tsat)*(tsat-ts);
hi = 0.555*pow((9.81*rho w(tsat)*(rho w(tsat) -
rho v(tsat))*pow(k w(tsat),3)*hfg_n/(mu w(tsat)*(tsat-ts)*di)),0.25);

Red = mcw*dh/(across*mu_sw(tavg,s));
if(Red<2300)
{
Nuo = 5.58;
}
else
{
Prsw = mu_sw(tavg,s)*cp_sw(tavg,s)/ksw(tavg);
Nuo = 0.023*pow(Red,0.8)*pow(Prsw,0.4);
}

ho = Nuo*ksw(tavg)/dh;

el = hi*ac*(tsat-ts);
tout = tin + el/(mcw*cp_sw(tavg,s));
tdt = (tout-tin)/log((tsat-tin)/(tsat-tout));
u = hi*ho/(hi+ho);
e2 = u*ac*dt;

if(fabs(el-e2)<0. 1)









e=0;
}
else
{
if(el>e2)
ts = ts + 0.000001;
else
ts = ts- 0.000001;
}
}
while(e== );
}
return u;
}

//Density of Water
double rho w(double t)
{
return ((999.83952 + 16.945176*t 7.9870401*pow(10,-3)*t*t -
46.170461 *pow(10,-6)*t*t*t + 105.56302*pow(10,-9)*t*t*t*t 280.5423*pow(10,-
12)*t*t*t*t*t)/(1 + 16.879850*pow(10,-3)*t));
}

// Dynamic Viscosity of Water
double mu w(double t)
{
t = t + 273;
double w;
w = -10.2158+1792.5/t+0.01773*t-1.2631 *pow(10,-5)*t*t;
return (pow(10,w)/1000);
}

// Specific Heat of Water
double cp w(double t)
{
return (1000*(4.2174 3.720283*pow(10,-3)*t + 1.412855*pow(10,-4)*t*t -
2.654387*pow(10,-6)*t*t*t + 2.093236*pow(10,-8)*t*t*t*t));
}

// Thermal Conductivity of Water
double k w(double t)
{
t = t + 273;
return (-0.2758+0.004612*t-5.5391*pow(10,-6)*t*t);









int insolation(int dj)
{
double pi = 3.1415926535;
double lat, Ion, 1st;
double p;
lat = 29.68;
Ion = 82.27;
1st = 75;
p = pi/180;

double n;

int mo[12] = {0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334};
n = day + mo[month-1];

double delta s;
delta s = 23.45*sin(360*(284+n)*p/365);
double b, et, det;
b =360*(n-81)/364;
et = 9.87*sin(2*b*p) 7.53*cos(b*p) 1.5*sin(b*p);
det = et + (lst-lon)*4;
double dsn;
dsn = 4*acos(-(tan(lat*p)*tan(deltas*p)))/p;
int dsni, deti;
dsni = dsn;
if((dsn-dsni)>0.5)
dsni = ceil(dsn);
else
dsni = floor(dsn);

deti = det;
if(fabs(det-deti)>0.5)
deti = ceil(det);
else
deti = floor(det);
int deth, detm;
if(deti>60)
{
detm = deti%60;
deth = deti/60;
}
else
{
detm = deti;
deth = 0;










int min, hour, ssrh, ssrm, sssh, sssm;
min = dsni%60;
hour = abs(dsni/60);
ssrh= 11-hour;
ssrm = 60-min;
sssh = hour;
sssm = min;

int Isrh, Isrm, Issh, Issm;
char rm, sm;
rm =
sm =
Isrh = ssrh deth;
Isrm = ssrm detm;
if(lsrm<0)
{
Isrm = 60 + Isrm;
Isrh = Isrh 1;
}
if(lsrm>60)
{
Isrm = Isrm 60;
Isrh = Isrh + 1;
}

Issh = sssh deth;
Issm = sssm detm;
if(lssm<0)
{
Issm = 60 + Issm;
Issh= ssh 1;
}
if(lssm>60)
{
Issm = Issm 60;
Issh= ssh + 1;
}
if(lsrm<10)
rm = '0';
if(lssm<10)
sm = '0';

cout<<"Sunrise time = "< cout<<" Sunset time = "<








ofstream inso_file("insolation.txt");
int hs;
hs = sssh*60+sssm;
double alpha w = 0, alphas, alpha, ia;
double beta;
beta = fabs(lat);
int io = 1377;
double i;
i = io*(1 + 0.034*cos(360*n*p/365.25));
double ibn, ibc, idc, ire, ic, jhs;
intj, cn=l;
double rho = 0.2;
double te, tw;
double k[12] = {0.142, 0.144, 0.156, 0.18, 0.196, 0.205, 0.207, 0.201, 0.177, 0.16,
0.149, 0.142};
double c[12] = {0.058, 0.06, 0.071, 0.097, 0.121, 0.134, 0.136, 0.122, 0.092,
0.073, 0.063, 0.057};

char ch;
ch = 'A';
int count=0, llsrh;
double llsrm, 11, 12;
for (j=-hs+l; j {
Isrm = Isrm + dj;
if(lsrm<60)
{
Isrh = Isrh;
}
else
{
Isrh = Isrh + 1;
Isrm = Isrm 60;
}
if(lsrh>= 12)
{
ch = 'P';
if(lsrh>12)
llsrh = Isrh 12;
}
else
llsrh = Isrh;

jhs =j/4;
alpha = asin(sin(lat*p)*sin(deltas*p) +
cos(lat*p)*cos(deltas*p)*cos(jhs*p))/p;