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PergamonEnergy Vol. 21, No. IO, pp. 939-946, 1996Copyr igh t 0 1996 Elsev ier Sc ience LtdPII: SO360-5442(96)00040-O Pr inted in Great Br i ta in . Al l r ights reserved0360.5442/96 $15.00 + 0.00

PARAMETRIC STUDY OF A SOLAR POND FOR NORTHERNJORDAN

K. AL-JAMAL+ and S. KHASHANMechanical Engineering Department, Jordan University of Science and Technology, Irbid, Jordan

(Received 31 August 1995)

Abstract-A mathematical model is developed to determine the various parame ters affecting theperformance of a salt-gradient solar pond (SG SP). We use the finite difference method for solution.Monthly average meteorological data for the Irbid region are used. Our results indicate that thethickness of the non-convection zone (NCZ) has a significant effect on the storage-zone tempera-ture. The optimum value of this thickness is found to be one meter. Storage-temperature fluctu-ations due to wea ther change s ma y be minimized by increasing the thickness o f the storage zone.This result may also be achieved by assuming that the rate of heat extraction is proportional tothe intensity of the incoming solar radiation. C opyright 0 1996 Elsevier Science Ltd.

INTRODUCTION

A salt-gradient solar pond (SGS P) is an excellent design for solar energy collection, as well as forlong term energy storage . The SG SP is an attractive facility for seasonal storage and may provide userswith energy for an entire year. Theoretical and experimental studies on SGS P were perform ed duringthe last two deca des with encouraging results.-9

The aim of our investigation is to determine design param eters of an SG SP for long-term storage .A numerical metho d was used because an analytical appr oach r equires many simplifications.- One ofthe simplifications mad e is to assume that the tempe rature of the upper convective zone (UCZ ) equalsthe ambient tem perature. This assumption eliminates convective heat exchan ge a nd evaporation losses.A finite difference meth od was applied by Atkinson and Harlem an to investigate the effect of windspeed , which is site-specific and cannot be totally eliminated because of wav e generation in the UCZeven at low wind speeds. T he effects of storage-zone thickness and of extracted heat energy on thestorage temp erature are discussed. The optimum storage-zon e thickness fo r maintaining the requiredstability in each zone has been determined and associate d surface losse s were estimated numerically.Many investigators have neglected these losses.,

SGSP CALCULATION PARAMETERS

Design parametersAn SGSP consists of three zones (see Fig. 1): the upper convective zone (UCZ) with low salt

concentration, the non-convection zone (NC Z) with linearly increasing salt concentration down ward s,and the lower convective zone (LCZ) (storage zone) with nearly saturated saline water. The SGSP isassum ed to have a large surface area with negligible side-wall heat losses.Stability criteria

The SG SP is stable against convective heat transfer if the density gradient of the salt concentrationin the NC Z is greater than the negative density gradient produc ed by the tempe rature gradient, i.e.

(dp/dS) (as/az) I=- - (t3pldT) (fmdZ), (la)

tAuthor for correspondence.939

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940 K. AI-Jamal and S. Khashan

uczNCZ dZ c____________________------------------

LCZ

-G Z. .tzz,1z3c

Fig. 1. Schematic of the SGSP ; Z, = UCZ thickness, Z , = NCZ thickness, Z 3 = LCZ thickness.

(apI > (a,lp) (anaz), (lb)where p and S are the density and salt concentration of the salt water, respectively, Z is the verticalaxis (positive downward), and (Y,and p are the thermal and salt expansion coefficients, respectively,which are defined by (Y,= - (l/p) (ap/aT) and p = (l/p) (+/6S). If AT is the temperature differencebetween two points at different d epths, the minim um required concentration difference ( AS),i" for staticstability between these two points is

(AS),, = LU,AT/p. (2)In spite of being statically stable, the pond is susceptible to an oscillation disturbance that propagatesvertically, grows w ith time and leads to hydrodynamic instability. The dynam ic stability criterion is

GS/tiZ > - [(Pr + l)/(Pr + ~,)](a,/~)(~T/8Z), (3)where Pr = v/KT is the Prandtl number, TV KS/K, is the inverse Lewis number, [(Pr + l)/(Pr + T,)]is called the dynam ic instability factor, v = kinematic viscosity, K,y coefficient of salt diffusivity, andK7. = coefficient of thermal diffusivity. Equation (3) may be rewritten as

(AS), = [(Pr + l)/(Pr + rV>](~,/P> AT. (4)The d ensity p is a function of the salt concentration and temperature of the saline water.Weather parameters

Weather data are given in Table 1 and are based on meteorological findings from the YarmoukUniversity site. Hourly solar radiation (H) used in SGSP performance calculation is based on the modelgiven by Hawalder and Brinkworth* as

H = / 3 ' Hs (- F) exp[ p(Z - G)/cos @ .I, (5)where H is the part of solar radiation that penetrates a thin layer 6, H, = Z/24 (where I is defined inTable 1 , F measures the radiation absorbed within 6, p is the coefficient of transmission (= 1 O -reflective losses), 0,. the refractive angle, an d p the extinction coefficient wh ich is used to describe theabsorbance of radiation for the range of optical depth* 6 = 0.06 m and F = 0.4.Propert ies of salt w ater

The thermal conductivity (k) in W/m -K and the specific heat capacity (C ) in kJ/kg-K of the NaC lsolution are functions of the water temperature and salt concentration and are given by I3

k = 0.5553 - 0.0008 133 S + 0.0008( T - 20), (6)

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Parametric study of a solar pond for northern Jordan 941

Table 1. Meteorological data for Irbid; Tamb average daily ambient temperature, I = total daily solar radi-ation, V = average daily wind speed, e = total daily evaporation rate.

MonthI

(kWhr/m*)V

(m/s)e

(mm/day)

JanFe bM arAprMayMyA%SeptOttNovDC C

9.0 3.22 3.81 3.19.9 3.89 3.81 3.6

12.2 4.94 3.91 4.416.2 5.86 3.86 6.120.4 6.98 3.70 8.323.7 7.61 4.63 9.625.0 7.63 5.14 8.825.4 7.13 4.63 8.423.9 6.17 3.65 7.720.1 4.94 2.83 7.015.4 3.17 3.03 5.610.6 3.07 3.45 3.5

C = 4180 - 4.396 S p + 0.0048 s2p2, (7 )where S is the salt concentration in each 6 of SGSP-w ater.

ENERGY BALANCEFOR THE POND

Since the temp eratures within both the UCZ and LCZ are uniform, the governing equation isaTi at =( k l pC) ( a2i " / aZ2)( akqazyac, ( 8)

where T s the tempe rature at depth Z (see Fig. l), t the time, and Hz he net radiative solar energy atdepth Z and is given by H, (Hi): (Hr)z,here Hi s the transmitted solar radiation from the SGS P-surface and H, he reflected radiation from the bottom of the pond. Both the incident radiation at thesurface and the reflected radiation from the bottom are transmitted through the water in the pond andsuffer exponential decays as follows:

(Hi)?Hs 1 -F) exp[-p(Z - S)/cos@],(H,), Hs ( - F) ( 1 - a) exp [-p(D - G)/cos& ]exp[- ~.L(D Z)/cos&],

(9 )

(10)where F, , f?,,nd S are defined in the nomenclature. 6'HJdZs then calculated from

aH?/ az [ Hs 1 - F)pk0se,) (exp[- p(Z - syc0se,l +( 1 - a) exp[-p( 20 - s)k0se,l exp(pzkose,)). (11)

Substituting Eqn. (11) in Eqn. (8) yields

anat =(kipc)aWaz 2) + {Hs 1 -F)pi(pcc0se,))x {exp[-p(Z - syc0se,] + (1 - a) exp[- ~(20 - tqk0se,lx ex p (Gic0se,)]. (12)

Solution of the preceding equation requires an initial condition and two boundary conditions. The

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942 K. Al-Jamal and S. Khashan

initial condition is that the initial temperature equals the ambient temperature at the time of initiatingpond operation. The first boundary condition is specified at Z = 0 (pond surface) and the second at Z= Z, + Z, + Z3 (pond bottom). For both b oundary conditions, an energy balance was applied at eachpond depth. The first boundary condition is

qcondrZ, - %ss+ Hs Hz, = PC& (aTslat), (13)whereqcond.2,s the rate of conductive heat transfer at Z = Z, from N CZ , g loss qr + qc + qe is heattransfer from the pond surface by infrared radiation to the sky (q r ) , convection (qc) and evaporation(q. ) , H , is the net solar radiation energy received at Z = 0, H z , the net solar radiation penetrating theUCZ, and T , is the temperature at Z = 0. The second boundary condition is

Hz2 qcond,Z2 qg qu = PC z,w,m (14)where H z2 is the net solar radiation penetrating the NCZ, q_d,Z2 the rate of conduction of energy toNCZ from LCZ, qg the rate of energy loss to the ground from LCZ, qu the extracted load from LCZ,an d Ts,, he uniform temperature in the LCZ. A numerical formulation is used to solve the governingequations using a backw ard, implicit, finite-difference method. Stability is verified for each calcu-lation step.

RESULTS AND DISCUSSIONThe LCZ-temperature T , has been calculated for various conditions.

Cons tan t pond - l aye r th i c knessThe reference pond is assumed to have Z, = 0.1 m, Z, = 1.0 m, an d Zs = 1.5 m. Th e absorption

coefficient at the pond bottom is 0.85. Total monthly heat extraction of 1 4.4 kW hr/m2 w as begun inJune. The calculation was performed for the data in Table 1. Beginning in March, TsP nd T , as wellas Tamb re shown in Fig. 2 as functions of the month of the year for two years. Warm-up lasts fromMarch to May of the first year. Ts, shows a continuous rise between March and September. During

20 2

11

3100' I IMl M J S N I 1 I I I IA J A 0 ID F A J A 0 D

IJI MI M( JI Sl NI JIFMonth of the Year

Fig. 2. Sto rage zone (curve l), pond surface (curve 3), and daily average ambient (curve 2) temperatures asfunctions of the month of the year.

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Parametric study of a solar pond for northern Jordan 943

the fall and winter seasons, heat losses from the pond exceeded the absorbed energy and T,, wasreduced. The highest Ts, of 92C occurred in September and the minimum temperature of 51C inJanuary. The yearly average rr,, was 71C, which exceeded the yearly average of Tamb by 54C. It isevident that both T Y and energy supply vary substantially with the seasons. T, = 8C in February and19C in August, as shown in Fig. 2.

Annual variations of energy compo nents in the storage zone are shown in Fig. 3. Maxim um solarenergy (HH ) utilization occurre d in June and July and led to substantial stored energy. The HH cannot cover the energy demand from Decem ber to February. This demand is met, in part, by stored heat.The total monthly averag e qn is - 10 kWhr/m2; the maximum qK s - 14 kWhr/m2 during September.Conduction heat loss is transferred from the storage zone to the NCZ from m id-August to Marc h ofthe following year with a maximum of about 5 kWhr/m2 during December. There is heat gain fromthe NC Z in the storage zone during the remainder of the year. The he at loss or gain by conduction qLCfrom the storage zone upw ards or downwards to the NCZ depends on the temperature gradient at theinterface betwe en the zones. This boundary-tem perature gradient is approxim ately zero in Ma rch, nega-tive in June, and positive in Septem ber (see Fig. 4), which serves to explain the variations of the qLcat the interface between the storage zone and the NC Z. Figure 4 show s the pond-tem perature distributionfor March, June, and September of the second year. The upper convective and storage zones are iso-thermal and the tempe rature profiles w ithin the NC Z are non-linear. These fea tures have the positiveeffect of reducing the temperature gradient at the interface between the storage zone and the NCZ.Effect of pond-l ayer t hi ckness on TsP

T, is plotted in Fig. 5 as a function of the month of the year for Z, = 0.01, 0.1, 0.2, and 0.3 m. Themaximum TFp s obtained at Z, = 0.01 m when Z, = 1.0 m and Z, = 1.5 m. The difference between theT,,, maxima for Z, between 0.01 and 0.3 m is about 34C. The annual average 7,,, decreases withincreasing Z,, as shown in Fig. 6, whe re the annual averag e T, is plotted as a function of NC Z thickne ss.For all Z,, the maxim a of the annual averag e T, occur at Z, = lm, in agreement with Ref. 8. Properselection of Z, is important for the design of an SGS P.

The storage-zone thickness depends on application of the SGSP. The highest T, is achieved at Z3= 0.5 m (see Fig. 7). For long-term energy storage, Z, must be greater than 0.5 m when the maximumT,,,at Z, = 2.5 m is 87C i.e. about 27C less than that for Z, = 0.5 m.

=340

30

20

10

0

-10

Month of the YearFig. 3. The total monthly energy gain or loss from the storage zone as a function of the month of the year.Curve I = solar energy gain, curve 2 = monthly stored energy within the LCZ, curve 3 = energy loss to the

ground, curve 4 = conduction heat from or to the LCZ.

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K. Al-Jamal and S. Khashan90 280 - 370 -

30-20 -

10 -

0 I I I I I,, I, I I I I I I I I I I I0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Depth Z (m)

Fig. 4. The temperature distribution within the solar pond as a function of pond depth during March (curveI), June (curve 2). and September (curve 3) of the second year.

140

130

120

11010 0

9080

70

60

50

40

30

1

20 I I I I I I I I I I I IMI MI JI Sl NI Jj MI M J S N JA J A 0 D F A J A 0 ID IFMonth of the YearFig. 5. Storage-zone temperature as a function of the month of the year for a pond with Z, = I .O m, Z, =1.5 m, and different Z, [Z, = 0.01 m (curve I), Z, = 0.1 m (curve 2). Z, = 0.2 m (curve 3), and Z, = 0.3 m

(curve 4)].

2, is the major p aram eter affecting dynamic stability of the NC Z because of tempe rature and salinitygradients. We need to verify stability in order to determine Z, and 5. The pond is ultimately stablefor all NC Z thicknesses of 1 m or less, irrespective of changes in the other zon e thicknesses. If Z,increases to 1.4 m, Z3 must be 5 1 m. Any furthe r increase in Z, may m ake the pond unstable.

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100

Parametric study of a solar pond for northern Jordan

190 -

80 -

t 70 -aiif 80-f

50 -

40 -

30 1 I I I1 I t I I I I I@ II 11 11 110.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5

NC2 - Thlckncsr (m)Fig. 6. The average annual storage temperature as a function of the NCZ thickness Z, for ZS = 1.5 m anddifferent Z, [Z, = 0.0 m (curve l), Z, = 0.1 m (curve 2). Z, = 0.2 m (curve 3), and Z, = 0.3 m (curve 4)].

110.100

90

80 .

70

60

50

40

30

20 I IMAR. 1 JULY I I INOV. 1 MAR. 1 JULYINOV.

MAY SE JAN. MAYMonth of the YccrJ!N.

Fig. 7. The storage temperature as a function of the month of the year for Z, = 0.2 m, Z, = I .Om and differentZ, [Z, = 0.5 m (curve I ), Z, = I.0 m (curve 2). Z, = 1.5 m (curve 3). Z, = 2.0 m (curve 4). and 2, = 2.5 m

(curve S)].

945

Effect of extracted heat on TY,,T,,, depends on the extracted load, as shown in Table 2. The highest TV,, s achieved at low heat

extraction with minimal fluctuations in TV,,when the extracted load is 10% of the annual average solarradiation, the maximum TV,, s greater than when the extracted heat load equals 10% of the monthly

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946 K. Al-Jamal and S. KhashanTable 2. Th e influence of heat-extraction ra te qw on ry,,,.

Qw(W/m*) ma x Storage-zone temperature Cmin mean fluctuation0.0 114.40 72.80 100.20 41.6020.0 97.45 55.96 81.61 41.490. K,n..vg 88.60 47.22 71.90 41.380. lHmon.svg. 83.0 52.70 72.40 30.30

average solar radiation. The extracted heat in the second case is not constant and depends on the availablesolar energy reaching the solar pond. At constant extrac ted heat, the Tsp fluctuation is around 41S C,whereas it drops to 30.3C when the load is varied. For both cases, the mean Tsp remains around 72C.Hea t extraction at constant rate results in an exce ss of energy collected during the hot season and a mark edfluctuation in Tsp. In order to avoid this fluctuation, the extracted load should be proportional to themonthly average of solar radiation to achieve good pond performance. A higher thermal efficiency maythen be achieved at variable load than for constant extracted heat, since the thermal efficiency is definedas the extracted heat divided by the incident solar radiation reaching the SGSP.

REFERENCES

1. S. Abughres, M. Mashena, and K. Agha, Modeling the Performance of Solar Ponds, Center for Solar EnergyStudies, Tripolis, Libya (1989).2. N. Chepumity and S. Savage, Sol. Energy 17, 203 (1975).3. J. Hull, Sun-Worl d 2, 1000 (1980).4. A. Akbarzadeh and G. Ahamadi, Sol. Energy 24, 143 (1980).5. 2. Panahi, J. C. Batty, and J. P. Riley, Transacti ons of the ASME, J. Sol. Energy Eng. 105, 63 (1983).6. T. A. Newell, Transacti ons of t he ASME, J. Sol. Energy Eng. 105, 363 (1983).7. P. Vadasz, D. Weiner, and Y. Zvirin, Transact i ons of the ASM E, J. Sol. Energy Eng. 105, 48 (1983).8. A. Akbarzadeh, R . Macdonald, and Y. Wang, Sol. Energy 31, 337 (1983).9. J. Atkinson and D. Harlem an, S ol. Energy 31, 243 (1983).10. K. Meyer, J. Sol . Energy Eng. 105, 41 ( 1983).11. S. A. Khashan, C omputer Simulation of a Solar Pond , MS Thesis, Jordan University of Science and Tech-nology, Mech. Eng. Dept. Irbid, Jordan (1993).12. M. Hawalder and B. Brinkworth, Sol. Energy 27, 195 (1981).13. R. Perry and C. Chillon, Chemical Engineering Handbook, 5th edn., McGraw-Hill, New York (1973).

NOMENCLATUREC = Specific heat of brineD = Depth of the solar pond = Z, + Z,

+ Z,e = Rate of wa ter evaporation from thepond surfaceF = Constant = 0.4I = Total daily solar radiationH i = Transmitted solar radiation throughthe pondH, = Reflected radiation from the bottomH,$ Incident insolation at the pondsurfaceH_ = Radiative energy reaching depth Zk = Therm al conductivity of brine

K, = Coefficient of salt diffusivityK7 = Coefficient of thermal diffusivityPr = Prandtl numberqk = Heat loss from LCZ to NCZ byconductionqL, = Heat extracted from the storagezone

q,Y Total heat stored in the storage zoneqz = Heat conducted at depth ZS = Salt concentration (salinity)T = Temperature

Tamb Ambient temperatureT, = Surface temperatureTv p= Storage-zone temperatureV= Wind speedZ= Coordinate (positive downward)Z, = Thickness of UCZZ, = Thickness of NCZZ3 = Thickness of L CZ(Y Bottom reflectivitycu ,= Therm al expansion coefficient/3 = Salt-expansion coefficient13, Angle of refraction0, = Incident angle (solar zenith angle)8 = Constant = 0.06 mp = Brine densityv = Kinematic viscosity of brinep = Extinction coefficient