Desalination 288 (2012) 80–92

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Desalination

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Performance analysis of an evacuated multi-stage solar water desalination system

K.S. Reddy a,⁎, K. Ravi Kumar a, Tadhg S. O'Donovan b, T.K. Mallick b

a Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600 036, Indiab Mechanical Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK

⁎ Corresponding author. Tel.: +91 44 22574702; fax:E-mail addresses: ksreddy@iitm.ac.in, dr_k_s_reddy@

0011-9164/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.desal.2011.12.016

a b s t r a c t

a r t i c l e i n f o

Article history:Received 20 September 2011Received in revised form 29 November 2011Accepted 15 December 2011Available online 20 January 2012

Keywords:DesalinationSolar energyMulti-stage evaporatorSaline waterFlat plate collectorYear round performance

In this paper, a novel multi-stage evacuated solar desalination system is developed by utilizing latent heat recov-ery. A transient model is proposed for the solar desalination system. The effect of various design and operatingparameters on the system performance is studied to optimize the configuration. The distillate yield increases ini-tially due to enhanced evaporation caused by the presence of a thin layer of water in the stages. The distillateyield decreases with increase in salinity of water due to an increase in ion activity and the reduction of thermo-dynamically spontaneous change from liquid to vapor. The optimum number of stages, gap between the stagesand the supplied mass flow rate for the system were found to be 4, 100 mm and 55 kg/m2/day respectivelythroughout the year. The overall thermal efficiency of the system is found to be 53.9% and 29.6% for the monthsMarch and December respectively in India. The maximum yield of 53.2 kg/m2/day is found in March at an oper-ating pressure of 0.03 bar. The multi-stage evacuated solar desalination system is a viable option to meet theneeds of rural and urban communities.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Water is one of the most important natural resources on the earth.All our day-to-day activities: agricultural, industrial and domesticdirectly or indirectly depend on the usage ofwater. The combined effectof continuous increase in world population, changes in life style,increases in ground water salinity and infrequent rainfall togetherwith the increasing industrial and agricultural activities all over theworld contributes to the depletion and pollution of fresh waterresources. Thus, industrial desalination of seawater is amajor contenderfor providing a sustainable source of fresh water for arid zones andduring drought periods. There are number of methods available totreat brackish water but every method has its own advantages anddisadvantages. It is estimated by Kalogirou [1] that the production of1000 m3/day of freshwater requires 10,000 tons of oil per year. Consid-ering the increase in energy costs of recent years and that this trend islikely to continue, it is very important to look for alternative energypowering sources for the economic production of fresh water. Solardesalination is a green energy method of producing potable water,specifically in remote rural locations.

A simple basin solar still is the oldest known method and numberof attempts has been made to improve its efficiency by several authors[2–10]. Rai and Tiwari [11] found that, the daily distillate production of acoupled single basin still with a flat plate collector is 24% higher thanthat of an uncoupled design. Tiwari et al. [12] presented a parametric

+91 44 22574652.yahoo.co.in (K.S. Reddy).

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study of passive and active solar stills integrated with a flat plate collec-tor. Yadav [13] studied the performance of a solar still coupled with aflat plate collector using natural and forced circulation modes. Tiris etal. [14] analyzed the active solar stills with two flat plate solar collectorsintegrated with a basin type solar still. The average daily production ofdistilledwaterwas found to be two times of simple basin type solar still.

The requirement for higher yields from passive solar stills is a realchallenge for researchers around the world and necessitates the devel-opment of more advanced concepts of solar stills, focusing on multi-stage and evacuated solar stills coupled to solar thermal collectors.Fernandez and Chargoy [15] investigated the multi-stage solar still,which consists of a stacked array of w-shaped distillation trays thatact as a condenser for the tray below. Kumar and Reddy [16] designedand evaluated the performance of the solar desalination system forhigher performance. Abakr and Ismail [17] and Ahmed et al. [18]analyzed the multi-stage evacuated solar desalination systems coupledwith a flat plate collector. The results show that the total daily yield wasfound to be about three times that of the maximum yield of the basin-type solar still. Shatat and Mahkamov [19] investigated the perfor-mance of multi-stage active water desalination still with “V” shapedtrays. The test results demonstrate that system produces about 9 kg/m2/day of freshwater and has a solar collector efficiency of 68% approx-imately. Simulation of condensation and evaporation process inside themulti-stage solar still is also carried out. Schwarzer et al. [20] developeda multi-stage solar desalination system with heat recovery. The resultsshow that, the system produces about 15–18 l/m2/day, which is 5–6times higher than a simple still. It is clear that multi-stage evacuatedsolar stills with heat recovery are proven to have higher performancethan all other thermally driven systems. The earlier studies dealt with

Nomenclature

Ac Collector area (m2)cp Specific heat capacity (J/kg K)D Diffusion coefficient (m2/s)F′ Collector efficiency factorg Acceleration due to gravity (m/s2)Gr Grashof numberGr∗ Modified Grashof numberhc Convective heat transfer coefficient (W/m2 K)hfg Latent heat of vaporization (J/kg)hfg* Modified latent heat of vaporization (J/kg)I Radiation (W/m2)k Thermal conductivity (W/m K)Le Lewis numberL Length (m)Ma Molar mass of dry air (kg/k mol)Med Daily distillate yield (kg/day)Mv Molar mass of water vapor (kg/k mol)_m Mass flow inlet of salt water (kg/s)_me Mass flow rate of distillate water at outlet (kg/s)Nc Number of collectorsNs Number of stagesNu Nusselt numberP Pressure (N/m2)Pr Prandtl numberQ Heat energy (W)r Tilt factorS Incident flux absorbed by the absorber plate (W/m2)T Temperature (K)Ul Overall heat loss coefficient (W/m2 K)XH20 Water molar fraction

Greek lettersα Thermal diffusivity (m2/s)β Thermal expansion coefficient (1/K)η Efficiency (%)μ Dynamic viscosity (Ns/m2)ν Kinematic viscosity (m2/s)ρ Density (kg/m3)τα Transmissivity–absorptivity product

Subscriptsa ambient airAM Arithmetic meanb Beambw Brine waterc Collectord Diffusedis Distillatee Evaporationfi Fluid inletfo Fluid outletfw Fresh wateri Stage (or) evaporating surface of ith stagei+1 Condensing surface of ith stagein Inletio Stage drain outflowm Mixtureo TotalOth Overall thermalr Reflected

s Salt waterv Vaporw Water

81K.S. Reddy et al. / Desalination 288 (2012) 80–92

active solar stills andmulti-stage solar stills for different configurations.The multi-stage active solar still geometry has to be optimized in orderto improve the performance. Therefore, the present study deals withidentification of better configuration ofmulti-stage solar still for variousoperating parameters and year round transient analysis of performanceand distillate yield for different salinity of water.

2. Description of the multi-stage evacuated solardesalination system

A multi-stage evacuated solar desalination system is a combinationof flat plate collectors and an evaporative-condenser unit. The systemis supplied with additional heat through flat plate collectors thus mak-ing it “active” to enhance the distillate yield. Each evaporative-condenser unit is a combination of bottom and top trays which act asevaporator and condenser surfaces. One such unit is called as a stage;themulti-stage des\alination systemconsists of a number of such stagesstacked one over the other. The condenser surface at the bottom of onestage acts as the evaporator surface for the stage above. The system con-sists of two flat plate collectors connected either in series or in parallelto the multi-stage desalination unit as shown in Fig. 1. If connected inseries, the outlet from the saline tank is given as an inlet to the firstcollector. The outlet of the first collector is inlet to the second collectorand so on up to the Ncth collector. Thus, the outlet temperature of thelast collector is taken as the oulet temperature of the series configura-tion. In a parallel configuration, the outlet from the saline tank is distrib-uted to the inlet of each of the collectors through a common header andthe outlet from all of them are connected separately through anothercommon header. Thus, the net cumulative outlet temperature of allthe collectors is taken as the outlet temperature of the parallel configu-ration. Each flat plate collector has an area of 1.35 m2 and is inclined atan angle equal to the latitude of Chennai facing due south for maximumyear round performance. Each evaporator and condenser tray has anarea of 1 m2 inclined at an angle of 16°.

At the top of last stage, there is a 150 l capacity water tank whichstores the saline water. The saline water from the tank flows throughthe flat plate collectors and thus gets heated. The heated saline waterenters each stage of the desalination system with a controlled massflow rate using flow control valves. The evaporator surface of eachstage is covered with a porous silk cloth so that the incoming salinewater is spread across the surface of the tray, thus ensuring maximumevaporation owing to this minimum depth of water. The evaporatedwater in the first stage condenses on the bottom side of the top traythus releasing the latent heat of condensation to the second stage. Thesecond stage is additionally heated by this latent heat apart from the in-coming hot water, thus leading to more evaporation and condensation.The top stages therefore yield higher distillate compared to the bottomstages. The condensed water falls into the collection trough located be-neath the condenser surface. The condensed fresh water and left overdrain water from each stage are collected separately.

3. Mathematical modeling

The analysis of the solar flat plate collector and the multi-stage de-salination system is carried out using MATLAB 7.0.1.

3.1. Solar flat plate collector

The heat losses from the solar flat plate collector to the surroundingsare important in the study of the collector performance. A detailed

Fig. 1. Multi-stage evacuated solar desalination system coupled with flat plate collectors.

82 K.S. Reddy et al. / Desalination 288 (2012) 80–92

thermal analysis of the flat plate collector is carried out by consideringheat losses from the collector. The heat lost to the surroundings fromthe absorber plate through the glass cover by conduction, convectionand radiation is calculated using energy balance equations. The heatlosses from the flat plate collector are shown in Fig. 2.

3.1.1. For a single flat plate collectorThe outlet temperature from a single flat plate collector is given as

[21]:

Tfo ¼ SUl

þ Ta

� �1− exp −AcUlF

′

_mccp

( )( )þ Tfi exp −AcUlF

′

_mccp

( )ð1Þ

Fig. 2. Detailed heat losses from the abs

3.1.2. For series configuration of flat plate collectorsFor a system of Nc collectors connected in series, the outlet fluid

temperature from the Ncth collector can be expressed in terms ofinlet temperature of the first collector given as [21]:

TfoNc¼ S

Ulþ Ta

� �1− exp −NcAcUlF

′

_mccp

( )( )þ Tfi exp −NcAcUlF

′

_mccp

( )ð2Þ

3.1.3. For parallel configurations of collectorsAssuming the outlet from saline tank is equally split into Nc collec-

tors, the fluid outlet temperature from the Ncth collector in parallelconfiguration can be expressed in terms of inlet temperature of the

orber plate of a flat plate collector.

83K.S. Reddy et al. / Desalination 288 (2012) 80–92

first collector by dividing the mass flow rate term in Eq. (2) with thenumber of collectors. The incident flux absorbed by tilted absorbersurface plate of a flat plate collector is given as [22]:

S ¼ Ibrb ταð Þb þ Idrd þ Ib þ Idð Þrrf g ταð Þd ð3Þ

3.2. Multi-stage evacuated solar desalination system

In multi-stage desalination system, due to the low temperaturedifference between the adjacent stages and the absence of non-condensable gases, heat transfer by radiation and natural convectionis negligible. Heat transfer between the hot saline water bed andthe condensation surface in every stage is mainly conveyed by evap-oration and condensation processes [18]. The temperature of waterand yield of the still can be obtained by applying an energy balancefor various stages of the still and it is shown in Fig. 3.

Stage-1:Energy balance for first stage can be written as

Qin1−Qe1−Qbw1

−Qfw1¼ 0 ð4Þ

Also

_ms1cps1Tfo−me1cpfw1Tfw1

−me1h�fg1−mbw1

cps1dT1dt

¼ 0 ð5Þ

Rewritten as

_ms1cps1Tfo−me1 cpfw1Tfw1

þ h�fg1

� �¼ mbw1

cps1dT1dt

ð6Þ

Fig. 3. Schematic of energy balance diagra

Stages-2:Energy balance for second stage can be written as

Qin2þ Qe1−Qe2−Qbw2

−Qfw2¼ 0 ð7Þ

Also

_ms2cps2Tfo þ _me1

h�f g1 þ _me1cpfw1

Tfw1� Ts2

� �� _me2

h�f g2

� _me2cpfw2

Tfw2�mbw2

cps2dT2

dt¼ 0

ð8Þ

Rewritten as

_ms2cps2Tfo þ _me1 h�fg1 þ cpfw1Tfw1

−Ts2

� �� �− _me2 h�fg2 þ cpfw2

Tfw2

� �¼ mbw2

cps2dT2dt

ð9Þ

Stages-3 to Ns:Energy balance for 3 to Ns stages can be written as

Qini−1þ Qei−1

−Qei−Qbwi−Qfwi

¼ 0 ð10Þ

Also

_msicpsiTfo þ _mei−1h�fgi−1

þ _mei−1cpfwi−1

Tfwi−1−Tsi

� �− _meih

�fgi

− _meicpfwiTfwi

−mbwicpsi

dTidt

¼ 0

ð11Þ

m for multistage desalination system.

84 K.S. Reddy et al. / Desalination 288 (2012) 80–92

Rewritten as

_msicpsiTfo þ _mei−1h�fgi−1

þ cpfwi−1Tfwi−1

−Tsi

� �� �− _mei h�fgi þ cpfwi

Tfwi

� �¼ mbwi

cpsidTidt

ð12Þ

The refined latent heat of vaporization of water for each stageused in Eqs. (5) to (12) can be determined by the following ex-pression [23]:For i=1 to Ns−1

h�

fgi ¼ hfgi þ 0:68� cpwiTi−Tiþ1� � ð13Þ

For the Nsth stage

h�fgNs ¼ hfgNs þ 0:68� cpwNs TNs−Tað Þ ð14Þ

The latent heat of vaporization of water for each stage can be de-termined by [24]:

hfgi ¼ 1000� 3161:5−2:41Tavð Þ ð15Þ

For i=1 to Ns−1

Tav¼Tiþ Tiþ1

2ð16Þ

For the Nsth stage

Tav¼TNsþ Ta

2ð17Þ

The specific heat capacity of water for each stage used in Eqs. (5)to (12) can be computed as a function of liquid–air interface temper-ature inside the stage [25].

cpwi ¼ 1000� 4:2101−0:0022Ti þ 5� 10−5T2i−3� 10−7T3i

h ið18Þ

The specific heat of salt water at constant pressure for each stageused in Eqs. (5) to (12) can be determined as [26]:

cps ¼ Aþ BTav þ CTav2 þ DTav

3� �

ð19Þ

where the variables A, B, C and D are evaluated as a function of watersalinity.

The foregoing correlation is valid over salinity and temperatureranges of 20,000–160,000 ppm (or 20–160 g/kg) and 20 °C to180 °C. In each stage of the still, there are interrelated combinedheat and mass transfer phenomena owing to the presence of complextemperature and concentration dependent thermo-physical proper-ties of humid air. Both liquid and vapor phases are in thermal equilib-rium at the interface between liquid layer and air in each stage.Therefore, vapor pressure at the interface must be equal to the satu-ration vapor pressure corresponding to the liquid phase at that tem-perature. Each stage condensing surface temperature is lower thanthat of liquid interface temperature. Water vapor diffuses upwardsby continuous evaporation from the liquid interface because of thevapor pressure difference. Higher concentration water vapor–dry airmixture moves away from the liquid surface which is replaced bythe lower concentration mixture from the condensing surface. Themass transfer phenomenon caused by a fluid density difference insideeach stage of a multi-stage evacuated solar desalination system is afunction of both temperature and composition. The Grashof numberdetermines the natural convection heat transfer due to temperaturedifferential alone; the complicated phenomenon of combined heat

and mass transfer inside multi-stage still leads to the definition of amodified Grashof number.

The working fluid in multi-stage solar still is assumed as a binarymixture of two gaseous components in equilibrium, namely dry airand water vapor. The modified Grashof number can be determinedas [27]:

Gri� ¼ gβiρ

2miL

3ΔTi�

μ2mi

ð20Þ

For i=1 to Ns−1

βi¼1

Tiþ1ð21Þ

ΔTi� ¼ Ti−Tiþ1

� �þ Pv;iþ1−Pv;i� �

Mv−Mað ÞTiMaPo þ Pv;i Mv−Mað Þ ð22Þ

For the Nsth stage

βNsþ1¼1Ta

ð23Þ

ΔTNs� ¼ TNs−Tað Þ þ

Pv;Nsþ1−Pv;Ns� �

Mv−Mað ÞTNsMaPo þ Pv;Ns Mv−Mað Þ ð24Þ

The Nusselt number correlation in an enclosed space is given as[28]:

Nu ¼ C GrPrð Þn ð25Þ

Assuming the values of C and n to be 0.2 and 0.26 respectivelywhich can be applied for a fairly wide range of Rayleigh number(3.5×103bRab106), McAdams [28] relation modifies to each stageof a multi-stage evacuated solar desalination system as:

Nui¼ hcviL

kmi

¼ 0:2 Gri�Pri

� �0:26 ð26Þ

where

Pri ¼νmi

αmi

ð27Þ

Thus, using Eqs. (20) to (27), the convective heat transfer coefficientfor each stage is given by the following expression:For i=1 to Ns−1

hcvi ¼ 0:2kmiL3n−1 gρmiβi

μmiαmi

� � Ti−Tiþ1� �þ Ti Pv;i−Pv;iþ1

� �Ma−Mvð Þ

MaPo−Pv;i Ma−Mvð Þ

24

350:26

ð28Þ

For the Nsth stage

hcvNs ¼ 0:2kmNsL3n−1 gρmNsβNs

μmNsαmNs

� �

×TNs−Tað Þ þ TNs Pv;Ns−Pv;Nsþ1

� �Ma−Mvð Þ

MaPo−Pv;Ns Ma−Mvð Þ

24

350:26

ð29Þ

85K.S. Reddy et al. / Desalination 288 (2012) 80–92

Thus, using Eqs. (28) and (29), the distillate mass outflow fromeach stage of a multi-stage evacuated solar desalination system isgiven as [29]:For i=1 to Ns−1

_mei ¼hcvi

ρmicpmi

� � PoPAM;i

Mv

RPv;iTi

−Pv;iþ1

Tiþ1

� �Lei

−2=3 ð30Þ

For the Nsth stage

_meNs ¼hcvNs

ρmNscpmNs

� � PoPAM;Ns

Mv

RPv;NsTNs

−Pv;Nsþ1

Ta

� �LeNs

−2=3 ð31Þ

where

PAM;i ¼ Po−Pv;i−Pv;iþ1

2ð32Þ

Lei ¼αmi

Dið33Þ

The difference in evaporation of saline water and fresh water isbecause of salt concentration. The evaporation rate can be linked tothe salinity by introducing the water molar fraction, X H2o as an effec-tive variable for a salt solution. Saturated vapor pressure of salt waterinside each stage can be calculated using the following expression:

Pvsi ¼ PviXH2O ð34Þ

Hourly supplied mass flow rate (Mi) to the ith stage is given as:

Mi ¼ ∫t

0

_midt ð35Þ

Daily supplied mass flow (Mdi)to the ith stage is given as:

Mdi¼ ∫

12

t¼1

Mi dt ð36Þ

The cumulative distillate efficiency for each stage is defined as theratio of total cumulative daily distillate yield from each stage to thatof the total supplied mass flow rate to that stage throughout theday. It can thus be calculated by the following expression:

ηdisi ¼Medi

Mdi

ð37Þ

Cumulative distillate efficiency for the multi-stage evacuated solardesalination system is defined as the ratio of total cumulative dailydistillate yield from all the stages to that of the total supplied massflow rate to all the stages throughout the day. Overall thermal effi-ciency for each stage is defined as the ratio of total heat content out-put from the stage by the cumulative daily distillate yield of that stageto that of the total heat content supplied to that stage throughout theday. For the first stage, the total heat content input is only through theflat plate collectors. Whereas, for the second to Ns stages, there is anadditional heat input through latent heat of condensation. The outlettemperature from the flat plate collectors, latent heat and refined la-tent heat of vaporization of water from each stage and specific heatcapacity of water from each stage are averaged over the day. Thus,

the overall thermal efficiency can be calculated by the followingexpression:

For the first stage (i=1)

ηothi¼ Medi

hfgiavMdi

cpsiavTfoavð38Þ

For i=2 to Ns

ηothi¼ Medi

hfgiavMdi

cpsiavTfoav þMdi−1h�fgi−1av þ cpwi−1av

Ti−1av−Tiav

� �h i ð39Þ

The overall thermal efficiency for the multi-stage evacuated solardesalination system is defined as the ratio of total heat output fromall the stages by cumulative daily distillate yield of all the stages tothat of the total heat content supplied to system throughout theday. For the entire system, the total heat input is only through flatplate collectors. The latent heat of vaporization of water and specificheat of water is averaged over the entire system. Thus, the overallthermal efficiency can be calculated by the following expression:

ηothms¼ Medms

hfgMdms

cpsTfoavð40Þ

4. Results and discussion

The proposed model can accurately predict the distillate yield for amulti-stage evacuated solar desalination system operating at high tem-peratures. The model accounts for the variation of thermo-physicalproperties of humid air, the partial vapor pressure at the watersurface and the condensing surface. The model also considers theinfluence of the average distance between the water surface andcondensing surface. The proposed model has been validated withShatat and Mahkamov model [19] for stage temperature and distillateyield. The comparison of stage temperature and cumulative distillateyield of the present model with Shatat and Mahkamov [19] is shownin Figs. 4 and 5 respectively. The cumulative distillate yield predictedby the present model deviates a maximum of 10.5% compared to thatof Shatat and Mahkamov [19]. The variation of distillate yield withShatat and Mahkamov [19] may be due to consideration properties ofhumid air and water vapor. There are various design and operatingparameters which affect the performance characteristics and distillateyield of the multi-stage evacuated desalination system; these are ana-lyzed in this section.

4.1. Variation of global solar radiation and ambient temperature

The variation of global solar radiation and ambient temperature isshown in Fig. 6. The maximum radiation and ambient temperature isobserved as 956W/m2 and 36.1 °C in the months of March and Mayrespectively.

4.2. Effect of series and parallel configuration of flat plate collectors

The configuration of flat plate collectors in both series and parallelare considered and its effect on the outlet temperature of the collectoris shown in Fig. 7. In series configuration, the outlet temperature ofthe first collector is the inlet to the next collector leading to moreheat losses from the second collector and thus energy collectedfrom the series configuration is lower. In parallel configuration, theinlet to both the collectors is ambient thus heat losses will be less. Ad-ditionally the mass flow rate supplied is distributed equally amongthe two collectors leading to an increase in the collector outlet tem-perature. The optimum distillate yield is found to be 21.77 kg/m2/

Fig. 4. Comparison of stage temperatures of present model with Shatat and Mahkamov [19].

86 K.S. Reddy et al. / Desalination 288 (2012) 80–92

day and 24.13 kg/m2/day for series and parallel configuration respec-tively. Thus, from the foregoing analysis, it is found that parallel con-figuration is better and further analysis is carried out based onparallel configuration.

4.3. Effect of number of stages on the distillate yield

This analysis is carried out by considering a mass flow rate of150 kg/day through the collector. For 150 kg/day, the outlet tempera-ture from the flat plate collector is computed and is fed into the stagesof the desalination unit where the gap between the stages is fixed at250 mm. The preliminary year round analysis is done for fresh waterfeeding into the evaporative-condenser unit which is operating at at-mospheric pressure. The effect of number of stages on cumulative dis-tillate yield is computed and is shown in Fig. 8. It is found that byincreasing in number of stages beyond 5, the temperature differencebetween the stages decreases, thus there is no improvement in thedistillate yield. For the month of March, the analysis was carried outand observed that by varying the number of stages, the temperaturedifference between the evaporator and condenser surface for eachstage decreases. The effect of number of stages on the temperaturedifference is shown in Fig. 9. The optimum number of stages isfound to be four for the maximum year round performance.

4.4. Effect of mass flow rate on the distillate yield

The effect of mass flow rate on the distillate yield is shown inFig. 10. It is found that by decreasing the mass flow rate from

Fig. 5. Comparison of cumulative distillate yield of present model w

150 kg/m2/day to 55 kg/m2/day the yield increases but if decreasedfurther from 55 kg/m2/day to 30 kg/m2/day, the distillate yield alsodecreases. Initially, as the mass flow rate decreases from 150 kg/m2/day to 55 kg/m2/day, the thickness of water layer in the stages de-crease; thus it enhances evaporation and condensation phenomenaleading to more stage water temperature. As the water temperaturein the stages increases, because of recovery of latent heat of conden-sation, the distillate yield from the stages increase. But a further de-crease in mass flow rate from 55 kg/m2/day to 30 kg/m2/day resultsin reduction of stage temperature which leads to a decrease in distil-late yield.

4.5. Effect of gap between the trays on the distillate yield

The year round analysis is performed on the desalination systemwith the optimum 4 stages and mass flow rate of 55 kg/m2/day byvarying the gap between the trays is shown in Fig. 11. It is foundthat by decreasing the gap between the trays, the distillate yield in-creases. This is attributed to the increase in temperature differencebetween the stages which is due to the reduction in vapor leakage.As the distillate yield increases with a decrease in gap between thetrays, the optimum gap is fixed as 100 mm beyond which it is practi-cally not feasible to keep a very small distance between the trays.Thus, the complete year round analysis is performed for the optimumconfiguration of the multi-tray solar desalination system consisting offour stages with a 100 mm gap and a flow rate of 55 kg/m2/day equal-ly distributed among them.

ith the theoretical distillate yield of Shatat and Mahkamov [19].

Fig. 6. Mean monthly hourly variation of global solar radiation and ambient temperature at Chennai.

87K.S. Reddy et al. / Desalination 288 (2012) 80–92

4.6. Effect of salinity on the distillate yield

Salinity is a technical term used to describe the saltiness or dis-solved salt content in a water body. Based on salinity content inwater, it is classified as: fresh water (b0.05% or b0.5 ppt), brackishwater (0.05–3% or 0.5–30 ppt), saline water (3–5% or 30–50 ppt)and brine (>5% or >50 ppt). With the increase in salinity, the evapo-ration of water decreases due to the increase in ion activity and thereduction of thermodynamically spontaneous change of evaporation.The presence of dissolved salts in the evaporating water reduces thewater evaporation by as much as 20% because of salt effects on theevaporation layer and reduction of the water vapor pressure at thesurface. Increasing the water salinity increases the boiling point ele-vation, which reduces the temperature of the evaporated water andits vapor pressure. It should be noted that evaporation from thewater surface would result in an increase of the local salt concentra-tion in the surface layer. This would reduce further the water vaporpressure at the water surface or the driving force for evaporation.

The year round variation of cumulative distillate yield of freshwater, brackish water, saline water and brine solution for mass flowrate of 55 kg/m2/day and 100 mm gap between the trays operatingunder atmospheric pressure for a 4 stage desalination system isshown in Fig. 12. The maximum yield for fresh water is 28.044 kg/

Fig. 7. Effect of series and parallel combination of flat plate collectors on the outlettemperature.

m2/day in March and it is decreased to 25.721 kg/m2/day for brackishwater, 22.553 kg/m2/day for saline water and 18.614 kg/m2/day forbrine solution. While for the month of December, the distillate yieldis a minimum of 13.335 kg/m2/day for fresh water and it decreasedto 12.543 kg/m2/day for brackish water, 11.382 kg/m2/day for salinewater and 9.791 kg/m2/day for brine solution. The year round varia-tion of distillate efficiency with salinity is shown in Fig. 13. The max-imum distillate efficiency for fresh water is 51% in March, 46.76% forbrackish water, 40.46% for saline water and 33.84% for brine solution.While in the month of December, the distillate yield is a minimum of24.24% for fresh water, 22.81% for brackish water, 20.69% for salinewater and 17.8% for brine solution.

The year round variation of overall thermal efficiency with salinityis shown in Fig. 14. The maximum distillate efficiency for fresh wateris 81.17% in March and it is decreased to 74.45% for brackish water,65.28% for saline water and 53.88% for brine solution. While for themonth of December, the distillate yield is a minimum of 40.36% forfresh water and it decreased to 37.96% for brackish water, 34.45%for saline water and 29.63% for brine solution. The year round varia-tion of cumulative distillate yield salinity is computed for all thestages. The year round distillate yield variation for all the four stagesfor fresh water, brackish water, saline water and brine solutions is an-alyzed. It is found that by increasing the salt content in the solution,the distillate yield decreases. The maximum yield for fresh water,brackish water, saline water and brine solution is found in themonth of March for the fourth stage of 13.58 kg/m2/day, 12.2 kg/m2/day, 10.37 kg/m2/day and 8.21 kg/m2/day respectively whilethat for the first stage, it is 0.85 kg/m2/day, 0.84 kg/m2/day, 0.82 kg/m2/day and 0.78 kg/m2/day respectively. The minimum yield forfresh water, brackish water, saline water and brine solution is foundin the month of December for the fourth stage of 6.24 kg/m2/day,5.77 kg/m2/day, 5.11 kg/m2/day and 4.25 kg/m2/day respectivelywhile that for the first stage, it is of 0.52 kg/m2/day, 0.51 kg/m2/day,0.5 kg/m2/day and 0.47 kg/m2/day respectively.

The year round variation of distillate efficiency is computed for allthe stages. The year round variation of distillate efficiency for all thefour stages for fresh water, brackish water, saline water and brine so-lutions is also computed. The maximum distillate efficiency for freshwater, brackish water, saline water and brine solution is found inthe month of March for the fourth stage of 98.73%, 88.72%, 75.45%and 59.7% respectively while that for the first stage, it is 6.15%,6.09%, 5.95% and 5.65% respectively. The minimum distillate efficien-cy for fresh water, brackish water, saline water and brine solution isfound in the month of December for the fourth stage to be 45.38%,

Fig. 8. Effect of number of stages on the cumulative distillate yield.

Fig. 9. Variation of evaporator and condenser surfaces temperature difference for four stage desalination system with time.

88 K.S. Reddy et al. / Desalination 288 (2012) 80–92

42%, 37.19% and 30.93% respectively while that for the first stage, it isof 3.74%, 3.70%, 3.63% and 3.45% respectively.

The maximum distillate efficiency for fresh water, brackish water,saline water and brine solution is found in the month of March for thefourth stage to be 74.43%, 70.02%, 63.69% and 55.3% respectivelywhile that for the first stage, it is 9.79%, 9.7%, 9.48% and 9% respective-ly. The minimum distillate efficiency for fresh water, brackish water,saline water and brine solution is found in the month of Decemberfor the fourth stage to be 50.86%, 48.14%, 44.15% and 38.65%

Fig. 10. Effect of mass flow rate on the distillate yield.

respectively while that for the first stage 6.23%, 6.17%, 6.04% and5.74% respectively. Based on the previous analysis, it is found thatfor the month of March, the distillate yield, distillate efficiency andoverall thermal efficiency are at a maximum. Thus, further analysesare carried out for different wind velocities, evaporative-condenserinternal pressure, heat input by distributing unequal mass flow ratefor the month of March.

Fig. 11. Effect of gap between the trays on the distillate yield.

Fig. 12. Year round variation of distillate yield with salinity.

Fig. 13. Year round variation of distillate efficiency with salinity.

89K.S. Reddy et al. / Desalination 288 (2012) 80–92

4.7. Variation of cumulative distillate yield with time

For fresh water, the yield from all the stages is computed at everyhour and the hourly individual yield is summed up and the variationin cumulative distillate yield at every hour is calculated and it isshown in Fig. 15. Even after 13:00 h beyond which the solar radiation

Fig. 14. Year round variation of overal

drops, the cumulative yield increases because of the existence ofstage temperature difference, which is due to hot collector outlettemperature but the increment is less. But, at the end of the day be-cause of insufficient heat source to the first stage which is due toless outlet temperature from the flat plate collector combination (al-most equal to ambient), the evaporation of water in the stage

l thermal efficiency with salinity.

Fig. 15. Variation of cumulative distillate yield with time.

90 K.S. Reddy et al. / Desalination 288 (2012) 80–92

decreases leading to a decrease in the latent heat of condensationwhich leads to a decrease in temperature difference between thestages. Thus, there is no increment in cumulative distillate yield andit attains almost steady state. The cumulative distillate yield at theend of the day for the individual stages are 0.85 kg/m2/day for firststage, 4.17 kg/m2/day for second stage, 9.45 kg/m2/day for thirdstage and 13.58 kg/m2/day for the fourth stage. The overall cumula-tive distillate yield at the day for the multi-stage solar desalinationsystem is found to be 28.04 kg/m2/day.

4.8. Effect of temperature difference between the stages on distillate yield

The effect of temperature difference between the stages on thedistillate yield is computed for all the stages. When the temperaturedifference between the evaporating and condensing surfaces in-creases, the distillate yield increases owing to higher evporation andthus higher condensation. It is found that the maximum hourly distil-late yield for the first stage is 0.14 kg/m2/h for a temperature differ-ence of 1.51 °C between the condensing and evaporating surface. Itis found that the maximum hourly distillate yield is found to be0.69 kg/m2/h for a temperature difference of 4.91 °C between thecondensing and evaporating surface for the second stage.

4.9. Effect of wind velocity on the distillate yield

The effect of wind velocity on the distillate yield is computed andthe variation is shown in Fig. 16. It is found that the distillate yield in-creases when the wind velocity decreases because of less heat lossesfrom the flat plate collector leading to higher temperature input to

Fig. 16. Effect of wind velocity on the distillate yield.

the first stage and thus high stage temperature which leads to hightemperature between the stages. Increase in temperature differencebetween the stages leads to increase in evaporation and condensationand increases the distillate yield. The maximum yield is found to be8.28 kg/m2/h at a wind velocity of 3.25 m/s.

4.10. Effect of distribution of mass flow rate on the distillate yield

The effect of variation of distillate yield with optimum mass flowrate of 55 kg/m2/day is computed by distributing it equally and un-equally into the stages and is shown in Fig. 17. It is found that withthe increase in mass flow rate to the first stage, the distillate yield de-creases which is due to thickness of water layer, whereas by increas-ing the mass flow rate to the fourth stage, the cumulative yield isfound to increase. This is due to more evaporation and yield in thefourth stage and thus increase in the yield in successive stages below.

4.11. Effect of pressure on the distillate yield

The internal pressure of the evaporative-condenser unit is variedand its effect on distillate yield is shown in Fig. 18. Distillate yield in-creases with decreasing pressure, due to the increase in temperaturedifference between the stages. By further decreasing pressure, thetemperature difference between the stages decreases due to en-hanced evaporation in all the stages simultaneously leading to a de-crease in distillate yield. At very high vacuum pressure, all thesupplied water gets evaporated immediately from all the stages andthus condensation phenomena will not happen. It is seen that de-crease in pressure beyond a certain limit, the top stages are attaininghigher temperature than the stages below, thus stopping condensa-tion phenomena occuring which leads to a sudden drop in distillateyield. It is found that the distillate yield and distillate efficiency in-creases from 28.04 kg/m2/day and 51% at atmospheric pressure to53.21 kg/m2/day and 96.75% respectively at 0.03 bar pressure forfresh water. Whereas for brackish water, the yield and efficiency in-creased from 24.34 kg/m2/day and 42.44% at atmospheric pressureto 42.04 kg/m2/day and 76.44% at 0.02 bar respectively. For salinewater, it is found that yield and efficiency increases from 19.35 kg/m2/day and 35.18% to 40.26 kg/m2/day and 73.13% by decreasingthe pressure from atmospheric to 0.02 bar respectively. In case ofbrine solution, the yield and efficiency increased from 13.25 kg/m2day and 24.08% at atmospheric pressure to 33.05 kg/m2/day and60.09% at 0.02 bar respectively.

5. Conclusions

A transient model was developed for the multi-stage evacuatedsolar desalination system coupled with a flat plate collector to deter-mine the optimum design configuration and system performance. The

Fig. 17. Effect of distribution of mass flow rate on the distillate yield for the month of March.

Fig. 18. Effect of evaporative-condenser pressure on the distillate yield.

91K.S. Reddy et al. / Desalination 288 (2012) 80–92

effects of various design and operating parameters have been studied topredict the optimum yield. Parallel combination of collectors has beenfound to be better compared to series combination. The optimum num-ber of stages and the suppliedmass flow rate for the systemwere foundto be 4 and 55 kg/m2/day irrespective of the climatic conditions. Thedistillate yield increases with a decrease in mass flow rate from150 kg/m2/day to 55 kg/m2/day due to enhanced evaporation whichis due to the thin layer of water in the stages. But, by further decreasingthe mass flow rate from 55 kg/m2/day to 30 kg/m2/day, the distillateyield decreases which is due to decrease in stage temperature and tem-perature difference between the stages.

The distillate yield is found to increase with decreasing gap be-tween the stages. The distillate yield decreases with increase in salin-ity. The fourth stage yielded the highest distillate while that of stageone being the minimum irrespective of climatic conditions and salin-ity. The collector outlet temperature and the distillate yield increaseswith decreasing wind velocity. The increase in heat input to the firststage by varying the mass flow rate decreases the distillate yield inthe first stage because of decreasing stage water temperature due tothicker water layers, but by increasing the flow rate to the fourthstage, results in more distillate yield due to more evaporation. The ef-fect of pressure was found to be very significant on the distillate yield.The optimum design conditions gave a maximum yield of 28.04 kg/m2/day and a minimum of 13.33 kg/m2/day. The multi-stage solar de-salination system can meet the fresh water needs of rural and urbancommunities to necessitate 10 to 30 kg/m2/day.

Acknowledgement

The financial support provided by DST-UKIERI, New Delhi to theresearch project is duly acknowledged.

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