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

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;