simulatin and model validation of an horizontal shallow basin solar concentrator

8/9/2019 Simulatin and Model Validation of an Horizontal Shallow Basin Solar Concentrator

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employ phytoremediation strategies to reduce salinityimpacts through sequential reuse of water on increasinglysalt tolerant crops (Cervinka et al., 1999) with eventual saltremoval. In current IFDM designs, mixed salts are pro-duced via final stage physical evaporation of water, usually

in a solar evaporation basin although other concepts are in

development. Recovery of purified salts might improve theoverall economics of salt management. A critical element inthis last stage is final concentration of the drainage water.The behavior of a horizontal shallow basin solar concen-trator which can be used for concentrating salts and dispos-

ing brine is investigated.

Nomenclature

A evaporation surface area, m2

Ac collector area, m2

cpb specific heat of brine in the collector, J kg1 K1

cpc specific heat of collector, J kg

1

K

1

cpmu specific heat of makeup brine, J kg1 K1

c1 salt concentration in bulk solution, kg saltkg solution1

di difference between ith estimated and ith mea-sured values

Esal saline evaporation, m period1

Fev volumetric flow rate of water evaporated, m3 s1

Fmu volumetric flow rate of makeup brine into theconcentrator, m3 s1

hb specific enthalpy of brine, J kg1

hconv,b-a convection coefficient between the air and thebrine, W m2 K1

hfg latent heat of vaporization of water, J kg1Gb beam component of radiation on horizontal sur-

face, W m2

Gd diffuse component of radiation on horizontalsurface, W m2

hconv,c-b convection coefficient between the collector andthe brine, 170 W m2 K1

hmu specific enthalpy of makeup brine, J kg1

hvapor specific enthalpy of vapor, J kg1

kG transport coefficient, kg s1 m2 mm Hg1

l brine depth, cmmb mass of brine in the collector, kg

mc mass of collector, kg_mmu mass flow rate of makeup brine flowing into thecollector, kg s1

_mev evaporation rate, kg s1

n number of data pairsnair index of refraction of air, 1.00nwater index of refraction of water, 1.33pa partial pressure of water in air, mm Hgpb brine vapor pressure, mm Hgpsat saturation water vapor pressure, mbarp0w saturation vapor pressure of pure water,

mm Hgqsolar absorb rate of solar energy absorbed by the brine,

W m2

qconv,c-b rate of convection heat transfer from the collec-tor to the brine, W m2

qrad,b-sky net rate of radiation heat transfer with the low-er atmosphere, W m2

qconv,b-a rate of convective heat transfer from the brineto the air, W m2

re evaporative mass flux, kg h1 m2

rw reflection loss coefficient for water for beamradiationrwd reflection loss coefficient for water for diffuse

radiationS salinity weight, %Ta ambient air temperature, CTb brine temperature, CTc collector temperature, CTd dew point temperature, CTmu temperature of makeup brine flowing into the

collector, CTsky effective sky (lower atmosphere) temperature, Ct time, s

V wind speed, m s1xb mass fraction of salt in the brine, kg salt kg

1

brinexmu mass fraction of salt in the makeup solution, kg

salt kg1 fresh brineXi ith estimated valueYi ith measured valueab absorptance of brine for beam radiationad absorptance of brine for diffuse radiationasd diffuse solar absorptance of collector surfaceb activity coefficient of water dimensionlesse emissivity of brine surface

gi rate energy distributionhref angle of refraction, degreeshref_diff effective angle of refraction for diffuse radiation,

degreeshz zenith angle of sun, degreesli extinction coefficient, cm

1

qev density of water evaporated, kg m3

qmu density of makeup brine, kg m3

r StefanBoltzmann constant, 5.6697 108,W m2 K4

s transmittancesw transmittance of water for beam radiationswd transmittance of water for diffuse radiation

(sa)b beam transmittanceabsorptance product forthe collectorbrine system

(sa)d diffuse transmittanceabsorptance product forthe collectorbrine system

/ relative humidity decimal

464 D.H. Kim et al. / Solar Energy 81 (2007) 463475


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Physical characteristics of shallow solar ponds have pre-viously been described empirically (Bowen, 1926; Penmam,1948; Bonython, 1958; Ferguson, 1952). Pancharatnam(1972) improved Fergusons energy balance equation fora shallow solar pond by considering an additional termof heat transfer between the water and the bottom surface.

Model validation by comparing numerical results withexperimental data has also been performed (Manganaroand Schwartz, 1985; Losordo and Piedrahita, 1991; Alagaoet al., 1994; Newell et al., 1994; Gao and Merrick, 1996;Jacobs et al., 1998). The study described here was con-ducted to develop a simulation model for design, andobtain experimental data for model validation.

2. Mathematical models

To predict evaporation rate, a model of an open typeshallow basin horizontal concentrator was developed.

The general simulation system is schematically shown inFig. 1. The model consists of the basin structure along witha shallow liquid layer maintained at constant depth bymakeup solution.

Two coupled components are considered in the model:the brine in the basin and the basin structure. The twocomponents are coupled through the heat exchange pro-cesses between the basin and the brine and the absorptionof solar radiation by the brine before reaching the basinsurface.

2.1. Total mass balance

A mass balance on the brine in the concentrator can bewritten as

dmbdt

qmuFmu qevFev 1

Under normal conditions, the feed rate into the concentra-tor is controlled such that the level of brine is constant. Ifwater flows into the concentrator from precipitation orcondensation, the makeup flow is reduced or stoppeddepending on the magnitude of influx. The solution inthe basin becomes diluted. We model the experimental set

up by assuming that the makeup volumetric flow rateequals the rate that water is evaporated

Fmu Fev; Fev> 0

0; Fev 6 0

2

Therefore the total mass balance becomes

dmbdt

Fevqmu qev; Fev> 0

qevFev; Fev 6 0

3

The volumetric evaporation rate is calculated from theevaporation mass flow rate and density

Fev _mev

qev4

2.2. Component mass balance on salt

The component mass balance on the salt in the basin canbe written as

dmbxb

dt qmuFmuxmu 5

Expanding the left-hand side

mbdxbdt

xbdmb

dt qmuFmuxmu 6

Combining Eqs.(3) and (6):For Fev> 0

mbdxbdt x

bFevqmu qev Fmuqmuxmu 7

For Fev< 0

mbdxbdt

xbqevFev 0 8

Simplifying gives the equation for the mass fractions of sol-ids in the brine

dxbdt

Fevmb

qmuxmu xb qmuqev ; Fev> 0

Fevmb

qevxb ; Fev 6 0

( 9

Brine solution

Basin (collector)Convection

brine to basin

Convection with

ambient air

Energy and mass out

with evaporation

Energy and mass in

with makeup solutionLong wave radiation

brine/skySolar radiation

direct & diffuse

Fig. 1. Horizontal concentrator and components considered in mass and energy balances.

D.H. Kim et al. / Solar Energy 81 (2007) 463475 465


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2.3. Energy balance on brine

Energy is received by the concentrator as direct radia-tion from the sun and indirectly from the atmosphere. Partof this energy is reflected, part absorbed, and the rest istransmitted to the collector bottom surface of the concen-

trator. Some of the energy absorbed by the collector istransferred to the brine via convective heat transfer, someis lost to the ambient environment by convection and radi-ation. The brine in the basin also receives energy from themake-up solution whose temperature is assumed to be thesame as the ambient air temperature although this is notnecessarily the case in practice especially where brine isstored in-ground such as in a drainage sump. The brineloses energy by radiation exchange with the environment(lower atmosphere), by convection with the air, and byevaporation of water. The energy balance on the brine isshown schematically inFig. 2.

The brine is assumed to be well-mixed with respect to

temperature and composition and brine depth is assumedto remain constant by make-up solution over the time per-iod. The specific heat of the brine is assumed to be indepen-dent of brine concentration, surface dust has no effect, andthe heat transfer is one-dimensional. The overall energybalance on the brine is

dmbhb

dt qsolar absorbAc qconv;c-bAc qrad;b-skyAc

qconv;b-aAc _mevhvapor _mmuhmu 10

The energy balance equation is simplified as follows:

dm

bh

bdt hb

dmb

dt mb

dhb

dt

and

dmbdt

qmuFmuqevFev _mmu _mev

The specific enthalpies of the brine and makeup solu-tions are

hbcpbTb and hmu cpmuTmu

dhbdt

dhbdTb

dTbdt

cpbdTbdt

dmbhb

dt cpbTb_mmu _mev mbcpbdTbdt

Substituting this into the energy balance on the brine, Eq.(10):

mbcpbdTbdt

qsolar absorbAc qconv;c-bAcqrad;b-skyAc

qconv;b-aAc _mevhvapor cpbTb

_mmucpmuTmu cpbTb 11Models are presented for each of the energy flux terms inthe energy balance.

2.3.1. Solar radiation absorbed by the brine

Net solar radiation absorbed by the brine per unit areais written as

qsolar absorbabGbadGd 12

The absorptance of the brine for beam radiation wasdetermined using the net radiation method (Tsilingiris,1998)

ab 1rw

1rwdswd1asdswd

1swdsw1asd asdsw 13

ad 1rwd

1rwdswd1asdswd

1 swdswd1 asd asdswd 14

The reflectance at the water surface, rw, is given byFresnels equation with the angle of refraction calculatedfrom Snells law and the angle of incidence in this case isthe zenith angle of the sun

rw12

sin2href hz

sin2href hz

tan2href hztan2href hz

" #;

hrefsin1 nair

nwatersin hz

15

The reflectance for the diffuse radiation is a constant andis calculated by assuming the incidence angle is 60(Tsilingiris, 1997, 1998)

rwd1

2

sin2href diff 60

sin2href diff 60

tan2href diff 60

tan2href diff 60

" #;

href diffsin1 nair

nwater sin60

16

The zenith angle, Gb, and Gd are calculated from Duffieand Beckman (1991).

The transmittance of the brine for beam radiation is cal-culated using the model developed by Tsilingiris (1988,1998)for pure water

sw s l

cos href

X5i1

gielil= cos href 17

The transmittance for diffuse radiation reflected fromthe bottom absorbing surface is treated as beam radiation

with an equivalent incidence angle of 60(Tsilingiris, 1998)

Brine solution

Basin (collector)qconv,c-b

qsolarabsorb qrad,b-sky vaporevhm. .

makeupmuhm

qconv,b-a

Fig. 2. Energy balance on brine.



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swd s l

cos 60

X5i1

gielil= cos60 18

Parameter values for Eq. (18) are listed in Table 1. Theexperimental data for solar radiation is in the form of totalradiation (beam plus diffuse) on a horizontal surface. Anempirical correlation is used to separate the beam and dif-fuse components (Reindl et al., 1990).

2.3.2. Convection from collector to brine

Convection between the collector surface and the brineis modeled by

qconv;c-b hconv;c-bTc Tb W m2 19

The heat transfer coefficient is based on turbulent convec-tion arising from wind and from the temperature differencebetween the collector surface and the brine (Pancharatnam,1972). For turbulent convection, the convection coefficientis 170 (W m2 C1) or higher (McAdams, 1954).

2.3.3. Convection from brine to ambient airThe rate of convective heat transfer from the brine to theair depends on the temperature difference between the brineand the air as well as the wind speed. The effect of windspeed is modeled as a linear dependence over the rangeof wind speeds of interest (Duffie and Beckman, 1991)

qconv;b-a hconv;b-aTb Ta W m2 20

hconv;b-a 2:83:0V W m2 C2 21

2.3.4. Longwave radiation exchange between the brine

surface and the sky

The energy transferred by long-wave radiation exchangewith the lower atmosphere can be expressed as

qrad;b-sky erTb273:154 Tsky273:15

4 W m2

22

The effective sky temperature, Tsky, is(Sartori, 1996)

Tsky Ta273:15 Td200

250

1=4273:15 23

2.3.5. Evaporation

Only a few evaporation models consider a change of

salinity in the pond.Manganaro and Schwartz (1985) for-

mulated equations for an evaporative solar salt pond sys-tem. In their study, evaporation rate was expressed asfollows:

re 0:0416Cpb pa1 0:224V 24

pb p0w1 0:7c1 25

p0w 31:82exp 17:42 1:8T 545:41:8T 0:6

26

Newell et al. (1994)investigated a brine reconcentrationsystem by spraying and exposing brine to ambient air.Evaporation occurred as the brine flowed down the waterdroplet area. They used Pancharatnams (1972) formula-tion for the heat lost by evaporation. The overall energybalance for this system was the same as that used by Panch-aratnam (1972)except for the addition of ground conduc-tion. The evaporation rate is expressed as

_mev kGApbpa 27

pbp0w

1:00:01158S 28

Alagao et al. (1994)modeled a closed-cycle salt-gradientpond. In their study, evaporation rate was related to thedissolved salt concentration. Salts dissolved in waterdecrease water evaporation by lowering the free energy ofsolution. In addition, the saturation vapor pressure at thebrine surface is decreased as salinity increases due to theinterfering presence of salts. The energy lost by evapora-tion was then formulated as

Esal ffVgfbSpsatT upsatTag 29

psatT 10expf5:8002206 103

T5:5162560 4:8640239102T4:1764768 105T2

1:4452093108T3 6:5459673 lnTg

30

bS 10:00309S0:000039S2 31

The coefficient f(V) is usually empirical and is a linearfunction of wind speed. Meyer (1915), Rohwer (1931),Penmam (1948), Pancharatnam (1972) and Duffie andBeckman (1991)proposed similar forms of the mass trans-port coefficient for calculating evaporation rate and for thisstudy, the Duffie and Beckman coefficients were used as

follows:

fV 2:83:0V 32

The curve for activity coefficient, (b(S)), is within 0.02%accuracy by comparing the calculated results with mea-sured activity coefficient at different salinities (Alagaoet al., 1994).

2.4. Energy balance on collector

The energy balance on the collector shown in Fig. 3 ismade assuming the collector can be modeled using the

lumped capacity method (Cengel, 1998)

Table 1Parameter values for wavelength intervals of Eq.(18)(source:Tsilingiris,1998)

Wavelengthband (i)

Wavelength(lm)

gi li(cm1)

1 0.20.60 0.237 0.000322 0.600.75 0.193 0.0045

3 0.750.90 0.167 0.034 0.901.20 0.179 0.355 1.203.00 0.224 18



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mccpcdTcdt

sabGb sadGd hconv;c-bTcTbAc

33

The transmittanceabsorptance product for the beamradiation was found using the net radiation method (Duffieand Beckman, 1991)

sab asdsw1rw

1rwdswd1 asdsw34

and the product for diffuse radiation is

sad asdswd1rwd

1rwdswd1 asdswd35

2.5. Final model equations for horizontal concentrator

The energy equations are solved along with the massbalances to yield the brine and collector temperaturesand the evaporation rate. The three evaporation methodsdescribed above were incorporated into the energy andmass balances to compare predictions. For example, inthe case of the Newell model, the final energy equations are

Brine:

mbcpbdTbdt

abGb adGdAchconv;c-bAc

er Tb273:154 Tsky273:15

4h i

Ac

hconv;b-aTb TaAc kGAcpbpa

hvaporcpbTb _mmucpmuTmu cpbTb

36

Collector:

mccpc dTcdt

sabGb sadGd hconv;c-bTcTbAc

37

2.6. Solution procedure and model assumptions

The model equations were coded into Matlab v.6.5.0.(Mathworks Inc., 2002). Ambient meteorological condi-tions were measured at one minute intervals and averagedand recorded over 30 minutes. Wind speed was measuredby a MetOne 014A three cup anemometer (MetOne,Grants Pass, Oregon). Air temperature and relative humid-

ity were measured by a Campbell Scientific CS500 sensor

(Campbell Scientific, Logan, Utah). Horizontal solar radi-ation was measured with a LiCor LI-200SA pyranometer(LI-COR, Lincoln, Nebraska). All sensors were locatedadjacent to the experimental collector system on thewhite-surfaced roof of a three-story office building inDavis, California. Data were collected and recorded onan electronic datalogger (Model CR21X, Campbell Scien-tific, Logan, Utah). The experiment was performed from06/22 to 6/28/2003.

Density data for brine as a function of both temperatureand salt concentration were obtained from the literature.Several data sets are compared in Fig. 4. For the results

reported here, density data (Table 2) for sodium sulfatesolutions were used (Sohnel and Novotny, 1985).

3. Experimental methods and procedure

A small-scale prototype horizontal concentrator wasbuilt and used to test the predictions of the model. Brinewas maintained in the basin as a quiescent liquid. A con-stant head brine supply system maintained a constantdepth of brine in the basin.

The concentrator included the basin, water supply sys-tem, and instrumentation (Fig. 5), all located on the openroof of a large three-story building. The basin was con-structed of plastic-coated 19 mm thick plywood lined onthe inside with black polyethylene plastic film. The basinwas 1.5 m2 with a maximum allowable depth of 35 mm.The basin was supported level at a height of 0.9 m abovethe roof surface. The brine supply system was composedof an inverted brine tank suspended from a load cell tomeasure the weight and situated so as to maintain a con-stant depth of brine.

Salt concentration of agricultural drainage water from amodel farm in the Central Valley, California is approxi-mately 1%. Batches of brine with the same concentration

as the drainage water were prepared by mixing pre-weighed

Brine solution

Basin (collector)qconv,c-b

( )bG b ( )dGd

Fig. 3. Energy balance on collector.

Fig. 4. Density versus concentration for various salt solutions at 20 C.



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amounts of salt obtained from a solar pond at RainbowRanch (now Andrews Agriculture), California, with de-ionized and distilled water.

Makeup brine was added daily into the reservoir. Tankweight and hence evaporation rate was measured using acalibrated load cell and recorded electronically. In additionto the mass balance, salt concentration was also monitoredby electrical conductivity (Model 30, YSI, Inc, YellowSprings, OH) twice daily, at the beginning and end of thepeak evaporation period (i.e., 9 a.m. and 6 p.m.). Brinetemperature in the basin and the collector surface (bottomsurface of the basin) temperature were measured by type Tthermocouples shielded from direct solar radiation.

4. Results and discussion

Experimental results were compared with predicted val-ues under the same meteorological conditions and basincharacteristics. For calculating evaporation rates, the mod-els of Manganaro and Schwartz (1985), Newell et al.

(1994), andAlagao et al. (1994)were used.

Predicted temperatures and evaporation rates from theuncalibrated model utilizing the original published coeffi-cients generally follow the experimental results but deviateby more than 5 C and 0.4 kg m2 h1 during the peakevaporation periods of the day (Figs. 68). Although thecoefficients fromNewell et al. (1994)consistently predictedhigher collector and brine temperatures than measured, thepredicted evaporation rates were lower than measured dur-ing the peak because the Newell model gives the lowest sen-sitivity of the transport coefficients on wind speed amongthree models so that heat transfer from the brine body tothe ambient air by evaporation is relatively low, therefore,

higher brine temperatures were predicted.

Table 2Density of sodium sulfate solutions (Sohnel and Novotny, 1985)

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32%

100 C 958 976 994 1011 1030 1048 1067 1086 1105 1125 1145 1165 1186 1207 122895 C 962 979 997 1015 1033 1051 1070 1089 1108 1128 1148 1168 1189 1210 123290 C 965 983 1000 1018 1036 1054 1073 1092 1111 1131 1151 1171 1192 1213 123585 C 969 986 1003 1021 1039 1057 1076 1095 1114 1134 1154 1175 1195 1217 1238 1261

80 C 972 989 1007 1024 1042 1060 1079 1098 1117 1137 1157 1178 1199 1220 1242 126475 C 975 992 1010 1027 1045 1063 1082 1101 1120 1140 1160 1181 1202 1223 1245 126870 C 978 995 1013 1030 1048 1066 1085 1104 1123 1143 1163 1184 1205 1227 1249 127165 C 981 998 1015 1033 1051 1069 1088 1107 1126 1146 1166 1187 1208 1230 1252 127460 C 983 1001 1018 1036 1054 1072 1091 1110 1129 1149 1170 1190 1211 1233 1255 127855 C 986 1003 1021 1038 1056 1075 1094 1113 1132 1152 1173 1193 1215 1236 1258 128150 C 988 1006 1023 1041 1059 1078 1096 1116 1135 1155 1176 1196 1218 1239 1262 128445 C 990 1008 1025 1043 1062 1080 1099 1118 1138 1158 1179 1199 1221 1242 1265 1287 131040 C 992 1010 1028 1046 1064 1083 1102 1121 1141 1161 1181 1202 1224 1246 1268 1290 131435 C 994 1012 1030 1048 1066 1085 1104 1124 1143 1164 1184 1205 1227 1249 1271 1294 131730 C 996 1014 1032 1050 1068 1087 1107 1126 1146 1166 1187 1208 1229 1251 127425 C 997 1015 1033 1052 1071 1089 1109 1128 1148 1169 119020 C 998 1017 1035 1054 1072 1091 1111 1131 115115 C 999 1018 1036 1055 1074 109310 C 1000 1019 1037 1056 1075

5 C 1000 1019 1038 10570 C 1000 1019 1038

V

V V

LC

Horizontal

concentrator

Concentrated

brine

Data logger

Brine tank

Makeup brine

Air vent when new

makeup brine added New makeup brine inlet

LC: Load cell

V: Valve

Fig. 5. Schematic of horizontal concentrator.

Fig. 6. Comparison of measured and predicted surface temperatures fromthe uncalibrated models.



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4.1. Uncertainty of measurements and predictions

The uncertainty associated with the measurements wasevaluated according toColeman and Glenn Steele (1989).The uncertainty is given by

wrXji1

hiwxi2

" #1=238

where the wxi are the uncertainties in the variables xiandhi o

roxi

where the result, r=r(x1, x2, . . . , xj) is the experi-mental result dependent on the xi.

The uncertainty in the measurement of the evaporationrate depends on the individual uncertainties associated withthe calibration of the load cell and the time at which

makeup brine is discharged from the reservoir into thebasin. The makeup discharge is not continuous, but insteadoccurs intermittently as the liquid level in the basin declinessufficiently for the head in the reservoir to overcome theatmospheric pressure force. At such time, an unmeteredamount of water is discharged from the reservoir. In someinstances this discharge occurs in a data sampling intervalfollowing the primary period of evaporation; hence therecorded evaporation rate in an interval may either beunder- or over-estimated. The relative error associated withthis intermittency decreases with the frequency of dischargeand so is lower during the peak evaporation period. Thisuncertainty in the evaporation rate measurement is greater

than that associated with the calibration of the load cellused to record reservoir weight.

The experimental uncertainty in the predicted values isassociated with the measurements of the meteorologicaland concentration parameters used in the model. Theparameters needed in Eq. (38) for both the experimentaland predicted evaporation rates, _mev, are listed inTable 3.

The uncertainties in the predicted rates range from 0.12to 0.22 kg m2 h1 with a mean of 0.16 kg m2 h1 for thesampling period (Table 3). By comparison, the uncertain-ties in the experimental evaporation rates are0.27 kg m2 h1 over the same period. The absolute uncer-

tainties in the measurement are 0.27 kg m2

h1

, mainly bythe frequency of discharge from the reservoir involved.Relative uncertainties are high (>50%) when experimentalevaporation rate is near zero (i.e., at night) but decreaseto as low as 14% during periods of peak evaporation. With-out calibration, predicted peak evaporation ranged from1.1 to 1.3 kg m2 h1 compared with measurements yield-ing 1.3 to 1.6 kg m2 h1 (Table 4). The model was cali-brated against the experimental data in order to reducethe deviation between predicted and measured evaporationrate.

4.2. Calibration of model

A number of statistical indicators have been proposedand used to evaluate models.Stone (1993)discussed severalindicators including the root mean square error

Fig. 7. Comparison of measured and predicted brine temperatures fromthe uncalibrated models.

Fig. 8. Comparison of measured and predicted evaporation rates from theuncalibrated models.

Table 3Uncertainty (kg m2 h1) in maximum daily evaporation rate for 7 days

Day 1 2 3 4 5 6 7

Meteorological parameters (Ta, Tb, RHa, wind speed) 0.18 0.14 0.12 0.14 0.18 0.22 0.14

Load cell 5 104 5 104 5 104 5 104 6 104 5 104 7 104

Discharge 0.27 0.27 0.27 0.27 0.27 0.27 0.27

a

RH relative humidity.



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RMSE1 1

n

Xni1

d2i

!1=239

The smaller the RMSE1, the better the model fit. A draw-back of this statistic is that a few large errors in the sum canproduce a significant increase in RMSE1. According toStone (1993), another measure using the relative root meansquare normalized deviation can be applied

RMSE2 1

n

Xni1

diYi

2

!1=2

40

RMSE2 for _mev is calculated only for times during whichthe evaporation rate is non-zero to avoid normalizationerrors.

There is another parameter to evaluate models:R-squared (r2)

r2 n

Pni1XiYi

Pn

i1Xi Pn

i1Yi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffinPni1X2i Pni1Xi 2h i nPni1Y2i Pni1Yi 2h ir

2

664

3

775

2

41

r2 becomes 1 in the absence of error and zero if there is norelationship between measured and estimated values.

As noted earlier, uncalibrated model predictions under-estimate actual evaporation rates during periods of highevaporation (Fig. 8). Model evaporation is dependent onassumed values for the convective heat transfer coefficientsbetween ambient air and brine and the brine and collector,the emissivity for long-wave radiation, the evaporativemass transfer coefficient, the absorptance of the collectorsurface for solar radiation, specific heat of the brine, and

the temperature of the makeup brine (Table 5). Daily max-imum heat convection between the air and the brine variesbetween 80 and 120 W m2 or about 15% of total heat loss.Maximum long-wave radiation is between 120 and180 W m2 and accounts for about 20% of total heat trans-ferred from the solar concentrator which is approximately1000 W m2 at maximum evaporation (Fig. 9). Evapora-tion accounts for more than 60% of the total heat loss dur-ing this time. The absorptance of the collector is the most

important factor for this analysis relative to the energyinput to the system by solar radiation. The evapora-tive mass transfer coefficient and the absorptance of the

Table 5Initial model assumptions

asd Diffuse solar absorptance of collector surface 0.8a

k Mass transfer coefficient (kg m2 s1 mm Hg1) 1.35623 106 (1.9 + 1.065V)b

e Emissivity of brine surface 0.95a

hconv,b-a Convection coefficient between the brine and the air (W m2

C1) 2.8+3.0Va

hconv,c-b Convection coefficient between the collector and the brine (W m2

C1) 170c

cpb Specific heat of brine in the collector (J kg1

C1) Same as sea waterd

Tmu Temperature of makeup brine (C) Same as air temperature

a Duffie and Beckman (1991).b Newell et al. (1994).c McAdams (1954).d

Bromley et al. (1967).

Fig. 9. Heat transfer rates by evaporation, long-wave radiation, andconvection between brine and air as estimated from the uncalibratedmodel.

Table 4Mean and range of measured and predicted peak evaporation rate over a 7 day sampling period

Day 1 2 3 4 5 6 7

Maximum evaporation (kg m2 h1) Predicted Mean 1.11 1.17 1.17 1.19 1.27 1.27 1.31Min. 0.93 1.03 1.05 1.05 1.09 1.05 1.17Max. 1.29 1.31 1.29 1.33 1.45 1.49 1.45

Experiment Mean 1.31 1.45 1.38 1.41 1.52 1.40 1.64

Min. 1.04 1.18 1.11 1.14 1.25 1.13 1.37Max. 1.58 1.72 1.64 1.68 1.79 1.65 1.90



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collector are the most influential factors in determiningevaporation rate.

Model calibration was performed by minimizing RMSE(Fig. 10). For both absorptance and the evaporative masstransfer coefficient, initial calibration values were derivedas the average of the RMSE1and RMSE2values individu-ally minimized. Final calibration values were then obtainedby minimizing RMSE1for simultaneous changes in absorp-tance and mass transfer coefficient (Table 6).

The numbers in parentheses in Table 7 are the datapoints used for calculation. The Newell model is the mostimproved through calibration, showing the greatest reduc-tion in RMSE values, from 2.53 to 1.43 in RMSE 1 for thebrine temperature (Table 7). However, RMSE1 andRMSE2values for the brine temperature from the Alagao

model have increased from 2.16 to 2.56, and 0.08 to 0.09respectively after calibration. Because of the uncertaintyin terms of frequency of discharge, r2 for _mevwas calculatedusing the daytime data which had relatively lower uncer-tainty. Although the calibrated mass transport coefficientfor the Alagao model increased RMSE values anddecreased r2 for brine temperature, the calibrated modeldecreased RMSE values and increased r2 for the evapora-tion rate. RMSE values for the evaporation rate from allthree models were reduced.

4.3. Validation of calibrated model

The calibrated model was tested using an independentexperimental data set collected from 07/06/03 to 07/11/03but using the same horizontal shallow basin solar concen-trator and sensors.

Most RMSE values for brine temperatures and evapora-tion rate found using the original literature models werehigher than those using the calibrated models, and the val-ues for the validation data set were generally lower than thefinal values after calibration for the calibration data set

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

Absorptance

RMSE01

collector temperature

brine temperature

Fig. 10. Sensitivity of RMSE1 to collector surface absorptance.

Table 6Calibrated model coefficients

Original value Calibrated value

Diffuse solar absorptance of collector surface 0.8a 0.61

Mass transfer coefficient 1.36 106 (1.9 + 1.065V) (kg m2 s1 mm Hg1)b 1.70 106

(1.84 + 1.0V)0.0208(1 + 0.224V) (kg m2 h1 mm Hg1)c 0.0233(1 + 0.214V)2.8 + 3.0V(W m2 C1)a 3.0 + 3.33V

a Duffie and Beckman (1991).b Pancharatnam (1972).c Manganaro and Schwartz (1985).

Table 7Relative errors forTb and _mev before and after model calibration (number of data points shown in parentheses)

Tb _mev

Original Calibrated Original Calibrated

Newell RMSE1 2.53 (336) 1.43 (336) 0.20 (336) 0.19 (168)RMSE2 0.08 (336) 0.06 (336) 0.67 (148) 0.66 (73)R-square 0.9834 (336) 0.9837 (336) 0.7598 (148) 0.7735 (148)

Manganaro RMSE1 2.29 (336) 2.18 (336) 0.19 (336) 0.18 (168)RMSE2 0.10 (336) 0.08 (336) 0.73 (148) 0.69 (73)R-square 0.9844 (336) 0.9847 (336) 0.7804 (148) 0.7883 (148)

Alagao RMSE1 2.16 (336) 2.56 (336) 0.21 (336) 0.19 (168)RMSE2 0.08 (336) 0.09 (336) 0.68 (148) 0.66 (73)

R-square 0.9709 (336) 0.9688 (336) 0.7395 (148) 0.7572 (148)



11/13

(compare Tables 7 and 8). Maximum deviation betweenmeasured and predicted brine temperatures using the cali-

brated models differ by no more than 3 C(Fig. 12), andthere is no apparent bias between the predicted and mea-sured brine temperature for the uncalibrated models (com-pare Figs. 11 and 13). The measured and predicted peakevaporation rate is between 1.2 and 1.4 kg m2 h1

(Fig. 14). The larger deviation in evaporation rate inFig. 15is due to the rapid transients in the morning andlate afternoons indicating the effect of the frequency of dis-charge on the experimental evaporation rates. The makeupdischarge from the brine tank occurs intermittently byaccumulating water evaporated in the basin. At such time,no experimental evaporation is recorded especially from

evening to next day morning although predictions of evap-oration are continuous. The large deviation in Fig. 15,hence, is a result of the limited resolution of the experimen-tal detection of evaporation.

5. Model application

The calibrated Newell model was applied to predictevaporation rates and accumulated evaporation rates (pro-ductivity) at Five Points, California using hourly CIMISdata from January through December 2004 (CaliforniaIrrigation Management Information System, Departmentof Water Resources, http://wwwcimis.water.ca.gov/cimis)assuming 1% salt concentration of the agricultural drain-age water.Table 9gives the hourly productivity expressedas mass of water evaporated per unit area and per monthpredicted along with the predicted average daily maximumevaporation rate for each month and compares it with astandard pan measuring evapotranspiration (ETo) whichis the sum of evaporation and plant transpiration obtained

from CIMIS data.

Fig. 11. Measured and predicted brine temperature from the uncalibrated

models. Lines are 1:1.

Table 8Relative errors for Tb and _mev with the calibrated model run on thevalidation data (number of data points shown in parentheses)

Tb _mev

NewellRMSE1 1.48 (288) 0.17 (288)RMSE2 0.04 (288) 0.89 (129)

R-square 0.9846 (288) 0.7690 (129)

ManganaroRMSE1 1.34 (288) 0.16 (288)RMSE2 0.04 (288) 0.85 (129)

R-square 0.9904 (288) 0.8049 (129)

AlagaoRMSE1 2.25 (288) 0.17 (288)RMSE2 0.06 (288) 0.82 (129)R-square 0.9722 (288) 0.7444 (129)

Fig. 12. Comparison of measured and predicted brine temperature fromthe calibrated models.

Fig. 13. Measured and predicted brine temperature from the calibratedmodels. Lines are 1:1.

http://wwwcimis.water.ca.gov/cimishttp://wwwcimis.water.ca.gov/cimis


12/13

Seasonal productivity is an important considerationfor concentrator operation. AsTable 9shows, there is lit-tle evaporation at this site during the winter months of

November to February. About 81% of the total evapora-tion occurs between April and September, with 94% ofevaporation occurring between March and October(Table 10). Comparing the total productivity with theannual ETo in Table 9, the horizontal concentrator hasa productivity about 20% higher than ETo due to thesolar energy gain by the collector.

6. Conclusions

Parameter calibration of the shallow basin brine con-centration model improved the predictions of peak tem-

peratures and evaporation rates by as much as 10%

Fig. 14. Comparison of measured and predicted evaporation rate fromthe calibrated models.

Fig. 15. Measured and predicted evaporation rate from the calibratedmodels. Lines are 1:1.

T

able9

Predictedmonthlyproductivityanddailyma

ximumevaporationrateatFivePoints,

CA

M

onth

January

February

March

April

May

June

July

August

September

October

November

December

Total

Productivity(kgm2

mo

1)

16

48

150

227

285

282

280

250

220

110

33

12

1913

D

ailypeakevaporationrate

(kgm2

h

1)

0.1

6

0.3

4

0.6

7

0.9

1

1.0

2

1.0

1

0.9

9

0.9

3

0.8

7

0.5

4

0.2

6

0.1

2

0.6

6(annual

avg)

E

To(mmmo

1)

22

52

122

179

219

213

214

195

164

93

40

21

1534



13/13

compared to original published values of heat and masstransfer coefficients. Deviations between predicted andmeasured peak brine temperatures and evaporation rateswere reduced from 5 C and 0.4 kg m2 h1 to less than3 C and 0.2 kg m2 h1, respectively.

Calibration was accomplished by minimizing root meansquare error (RMSE) between predicted and measuredtemperatures and evaporation rate. RMSE on collectorsurface absorptance was reduced by roughly 0.2 and masstransfer coefficients were increased by minimizing RMSE1through simultaneous calibration of concentrator surfaceabsorptance and heat and mass transfer coefficients. Vali-

dation of the calibrated models was performed using anindependent experimental data set.

Predicted seasonal productivity (Table 10) suggests thatconcentrator designs oversized by only 20% compared withfull year operation would be sufficient to handle summer-time irrigated agricultural drainage flows within the pri-mary six month growing season. Although horizontalbasins of the type modeled here may not be the preferreddesign choice due to environmental considerations, theseconclusions are likely to extend to other solar concentratordesigns handling agricultural drainage brines that are thesubject of related papers.

References

Alagao, F.B., Akbarzadeh, A., Johnson, P.W., 1994. The design,construction, and initial operation of a closed-cycle, salt-gradientsolar pond. Solar Energy 53 (4), 343351.

Bonython, C.W., 1958. The influence of salinity upon the rate of naturalevaporation. Climatology and microclimatology. In: Proceedings ofCanberra Symposium, pp. 6570.

Bowen, I.S., 1926. The ratio of heat losses by conduction and byevaporation from any water surface. Physical Review 27, 779787.

Bromley, L.A., Desaussure, V.A., Clipp, J.C., Wright, J.S., 1967. Heatcapacities of sea water solutions at salinities of 1 to 12% andtemperatures of 2 to 80 C. Journal of Chemical and Engineering Data12 (2), 202206.

Cengel, Y.A., 1998. Heat Transfer, Practical Approach. WCB McGraw-Hill, Boston.

Cervinka, V., Diener, J., Erickson, J., Finch, C., Martin, M., Menezes, F.,Peters, D., Shelton, J., 1999. Integrated system for agriculturaldrainage management on irrigated farmland. Bureau of Reclamation,US Department of the Intrior, Final Research Report, 4-FG-20-11920.

Coleman, H.W., Glenn Steele Jr., W., 1989. Experimentation andUncertainty Analysis for Engineers. John Wiley & Sons, Inc.

Duffie, J.A., Beckman, W.A., 1991. Solar Engineering of ThermalProcesses, second ed. John Wiley & Sons, Inc., New York.

Ferguson, J., 1952. The rate of natural evaporation from shallow ponds.Australian Journal of Scientific Research 5, 315330.

Gao, J., Merrick, N.P., 1996. Simulation of temperature and salinity in afully mixed pond. Environmental Software 11 (13), 173178.

Jacobs, A.F.G., Heusinkveld, B.G., Lucassen, D.C., 1998. Temperaturevariation in a class A evaporation pan. Journal of Hydrology 206, 7583.

Losordo, T.M., Piedrahita, R.H., 1991. Modeling temperature variationand thermal stratification in shallow aquaculture ponds. EcologicalModeling 54, 189226.

Manganaro, J.L., Schwartz, J.C., 1985. Simulation of an evaporative solarsalt pond. Industrial & Engineering Chemistry Process Design andDevelopment 24, 12451251.

McAdams, W.H., 1954. Heat Transmission, third ed. McGraw-Hill, NewYork, NY.

Meyer, A.F., 1915. Computing run-off from rainfall and other physicaldata. Transactions of ASCE 79, 10561224.

Newell, T.A., Smith, M.K., Cowie, R.G., Upper, J.M., Cler, C.L., 1994.Characteristics of a solar pond brine reconcentration system. Journalof Solar Energy Engineering 116 (2), 6973.

Pancharatnam, S., 1972. Transient behavior of a solar pond andprediction of evaporation rates. Industrial & Engineering ChemistryProcess Design and Development 11 (2), 287292.

Penmam, H.L., 1948. Natural evaporation from open water, bare soil andgrass. Proceedings of the Royal Society of London. Series A,Mathematical and Physical Sciences 193 (1032), 120145.

Reindl, D.T., Beckman, W.A., Duffie, J.A., 1990. Diffuse fractioncorrelations. Solar Energy 45 (1), 17.

Rohwer, C., 1931. Evaporation from free water surfaces. US DepartmentAgricultural Technical Bulletin 271, 96.

Sartori, E., 1996. Solar still versus solar evaporator: a comparative studybetween their thermal behaviors. Solar Energy 56 (2), 199206.

Sohnel, O., Novotny, P., 1985. Densities of aqueous solutions of inorganicsubstancesPhysical Sciences Data, vol. 22. Elsevier, Amsterdam.

Stone, R.J., 1993. Improved statistical procedure for the evaluation ofsolar radiation estimation models. Solar Energy 51 (4), 289291.

Tsilingiris, P.T., 1988. An accurate upper estimate for the transmission ofsolar radiation in salt gradient ponds. Solar Energy 40 (1), 4148.

Tsilingiris, P.T., 1997. Design, analysis and performance of low-costplastic film large solar water heating systems. Solar Energy 60 (5), 245256.

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Table 10Seasonal productivity

Total April to September March to October

Productivity (kg m2) 1913 1544 1804Percent (%) 100 80.7 94.3


simulatin and model validation of an horizontal shallow basin solar concentrator

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