experimental and numerical analysis of sodium-carbonate salt gradient solar-pond performance under...

PPLIED
A
Applied Energy 83 (2006) 324–342

www.elsevier.com/locate/apenergy

ENERGY

Experimental and numerical analysis ofsodium-carbonate salt gradient solar-pondperformance under simulated solar-radiation

Huseyin Kurt a,*, Mehmet Ozkaymak a, A. Korhan Binark b,1

a Zonguldak Karaelmas University, Technical Education Faculty, 78200 Karabuk, Turkeyb Marmara University, Technical Education Faculty, 34722 Kuyubasi-Istanbul, Turkey

Available online 13 June 2005

Abstract

The objective of this study is to investigate experimentally and theoretically whether

sodium carbonate (Na2CO3) salt is suitable for establishing a salinity gradient in a salt-gradi-

ent solar-pond (SGSP). For this purpose, a small-scale prismatic solar-pond was constructed.

Experiments were conducted in the laboratory under the incident radiation from two halogen-

lamps acting as a solar simulator. Furthermore, a one-dimensional transient mathematical

model that describes the heat and mass transfer behaviour of the SGSP was developed. The

differential equations obtained were solved numerically using a finite-difference method. It

was found from the experiments that the density gradient, achieved using sodium carbonate

salt, can suppress convection from the bottom to the surface of the pond.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Salt-gradient solar-pond; Sodium-carbonate; Indoor experiment; Solar simulator; Transient

heat-and-mass transfer model

0306-2619/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.apenergy.2005.03.001

* Corresponding author. Tel.: +90 370 4338200; fax:+90 370 4338204.

E-mail address: [email protected] (H. Kurt).1 Tel.: +90 216 3365770/666; fax: +90 216 3378987.

mailto:[email protected]

Nomenclature

a reflection factor of pond�s surface (Albedo) (%)

Ca specific heat of air (J/kg �C)Cp specific heat of the solution (J/kg �C)D coefficient of salt diffusion (m2/s)

hc convective heat-transfer coefficient (W/m2 �C)he latent heat of evaporation of water (J/kg)

I solar-radiation intensity (W/m2)

I(x) solar-radiation intensity at depth x (W/m2)

I0 available solar-energy below surface after reflection from pond�s sur-

face (W/m2)

Ir reflected solar-radiation intensity from the pond�s surface (W/m2)

Is incident solar-radiation intensity at the pond�s surface (W/m2)

J diffusion flux (kg/m2s)

k thermal conductivity of the solution (W/m �C)L depth of the pond (m)

N number of cells in the NCZ

P1 partial pressure of water vapor in ambient air (Pa)

Patm atmospheric pressure (Pa)

Ps vapor pressure of water at the surface�s temperature Ts (Pa)

q heat flux (W/m2)

Qc heat loss by convection (W/m2)

Qe heat loss by evaporation (W/m2)

Qr heat loss by radiation (W/m2)

Qt total heat-losses from the pond�s surface (W/m2)

QU heat extracted from the storage zone

Rh relative humidity (%)

t time (s)

T temperature (�C)T1 ambient temperature (�C)TLCZ LCZ temperature (�C)Ts pond�s surface temperature (�C)Tsky sky temperature (�C)TUCZ UCZ temperature (�C)Vr wind velocity (m/s)

x depth (m)

XLCZ thickness of the LCZ (m)

XNCZ thickness of the NCZ (m)

XUCZ thickness of the UCZ (m)

_q internal heat-generation rate (W/m3)

b fraction of energy absorbed at the pond�s surface (%)

Dt time step (s)

H. Kurt et al. / Applied Energy 83 (2006) 324–342 325

Dx thickness of layer (m)

ew emissivity of water

l absorption coefficient (m�1)

hg radiation incident-angle over pond�s surface (�)hk angle of refraction at the pond�s surface (�)q density of solution (kg/m3)

r Stefan–Boltzman constant (W/m2 K4)

326 H. Kurt et al. / Applied Energy 83 (2006) 324–342

1. Introduction

A salt-gradient solar-pond (SGSP) is an inexpensive solar-energy collection and

storage system for low-temperature heat-sources. It has a shallow, large body of

water in which a stable salinity-gradient is artificially established in order to prevent

thermal convection induced by the absorption of solar radiation. Thus, the pond acts

as a trap for solar radiation. Thermal energy is collected and stored in the lower lay-

ers of the pond, and the capacity for long-term energy storage is a major attractivefeature of a SGSP. This long-term store provides an alternative for conventional en-

ergy-sources [1–3].

The SGSP generally consists of three distinct zones: the upper convective zone

(UCZ), non-convective zone (NCZ), and the lower convective zone (LCZ), as shown

in Fig. 1. The UCZ is the topmost layer and usually a thin layer of fresh water. The

NCZ is just below the UCZ and has linearly increasing salinity gradient downwards.


It acts as transparent insulation to prevent heat loss due to convection from the

LCZ. The LCZ is the bottom layer, with a nearly constant and uniform high density.

Because of serving as the solar-energy collection and heat storage medium, it is also

called the storage zone.

Solar radiation is transmitted through the UCZ and NCZ and then trapped in theLCZ. As a result of solar-radiation absorption, a gradient of temperature is estab-

lished. In the NCZ, the density decreases due to the temperature gradient producing

an upward buoyancy force. This force in counterbalanced by the increase in the den-

sity due to the salinity gradient increasing in the downward direction. Thus convec-

tion currents are suppressed and prevent convection heat-loss from the LCZ by the

artificially established salinity gradient. Heat stored in the LCZ only escapes by con-

duction. Since water has a low thermal-conductivity, the NCZ acts as a transparent

insulator, so allowing a considerable amount of incident solar radiation beingtrapped and stored in the form of heat in the LCZ [1–3].

SGSPs have been extensively studied because of their excellent heat collection and

storage performances. There have been considerable theoretical and experimental

studies [3–12] on SGSPs, which include analytical and numerical model treatments,

laboratory testing and construction and economic analyses, to gain a better

understanding of the mechanism of their operation and applications. Many

experimental solar ponds [13–19] have been constructed, instrumented and operated,

and various numerical models [20–30] have been developed for analysing SGSPperformance in the literature. The numerical models initially were generally one-

dimensional (1D) and treated the problem of transient heat conduction and

mass diffusion. The 1D transient heat-and-mass transfer equations were solved

using a finite-difference method to predict the time-dependent temperature and

density.

Tasdemiroglu [1] reported salt availability and solar pond utilization in Turkey.

Kurt et al. [2,3], Bozdemir and Kayali [4] investigated the performance of the so-

dium-chloride SGSP experimentally and theoretically. Kanayama et al. [5] have ana-lyzed practical-scale sodium chloride SGSP performance. Leshuk et al. [6]

investigated experimentally the stability of the salinity gradient, with established

potassium nitrates salt, under a solar simulator. Keren et al. [7] carried out an indoor

experiment and a numerical analysis on a small-scale model of a magnesium-chloride

SGSP under a solar simulator. Xiang et al. [8,9] conducted an indoor experiment and

a numerical analysis of a small-scale SGSP using NaCl salt, and examined the ero-

sion phenomenon on the NCZ under incident radiation from a solar simulator. Kho

et al. [10] studied the design and performance evaluation of a solar pond, containingsodium chloride salt, for industrial process-heating experimentally and numerically.

Tahat et al. [11] investigated experimentally and theoretically the performance of a

portable mini solar-pond. Kumar and Kishore [12] constructed a 6000 m2 solar pond

for a milk-processing dairy plant to supply process heat, and demonstrated the tech-

nical and economic viability of solar-pond technology in India.

Subhakar and Murthy [13,14] investigated a saturated solar-pond, with magne-

sium chloride (MgCl2) and potassium nitrate (KNO3) salts, theoretically and exper-

imentally. Banat et al. [15] studied experimentally the temperature and salinity


profiles in the pond in which a salinity gradient is established using carnalite salt.

Pawar and Chapgaon [16], as well as Murthy and Pandey [17] have evaluated exper-

imentally the performances of solar ponds using fertilizer salt under simulated

conditions. Hassairi et al. [18] experimentally investigated the performance of

small-scale solar pond of natural brine. Lund et al. [19] measured the spectral trans-mittances of magnesium chloride (MgCl2), sodium sulphate (Na2SO4), sodium

nitrate (NaNO3), potassium nitrate (KNO3) and sodium carbonate (Na2CO3) salt-

solutions under a solar simulator.

Mansour et al. [20] investigated numerically the transient behaviours of the

thermal and salinity fields, and the stability of the SGSP. Jubran et al. [21] devel-

oped a three-dimensional finite-volume method for modelling the convective lay-

ers in the solar pond. Hongfei et al. [22] studied the performance of heat

collection and storage of a SGSP based on similar methods to analyse and calcu-late the flat-plate solar-collector performance. Angeli and Leonardi [23] developed

a 1D transient mathematical model for investigating the salt diffusion and stabil-

ity of the density gradient in a solar pond. Husain et al. [24] studied the estima-

tion of radiation flux in solar ponds and proposed a simple empirical

formulation. E1-Refaee et al. [25] developed a 1D transient mathematical-model

for predicting the thermal performance of the SGSP and the obtained results

from the model are compared with those from an experimental study. Alkhalaileh

et al. [26] developed a computer simulation model, and analysis of a solar-pondfloor heating system. Hawlader et al. [27] solved the basic energy-equation numer-

ically and studied the pond�s behaviour. Antonopoulos and Rogdakis [28] devel-

oped simple correlations that express the maximum useful-heat received from a

SGSP throughout the year. Subhakar and Murthy [29] described a 1D simulation

procedure for a saturated solar-pond. Alagao [30] developed a 1D simulation

model, which simulates the transient behaviour of the pond using a finite-differ-

ence method, for a closed-cycle SGSP.

Solar ponds normally employ sodium-chloride salt (NaCl). Various salts, likemagnesium chloride (MgCl2), potassium nitrate (KNO3), ammonium nitrate

(NH4NO3), sodium nitrate (NaNO3), fertilizer salts as urea (NH2CO Æ NH2), sat-

isfy the stability criterion and hence are considered suitable for a solar pond.

After reviewing the literature, it is seen that establishing the SGSP�s density-

gradient with sodium carbonate salt has not been tested. Hence, for this purpose,

a small-scale pond in laboratory conditions was constructed for the experimental

work and also a 1D mathematical model for the SGSPs heat and mass transfer

was developed.

2. A mathematical model for the SGSP

A model of transient behaviours of the heat and mass transfers in a SGSP was

developed. Fig. 2 shows the configuration of the pond under consideration. The

mathematical model is based upon energy and mass balances over a horizontal fluid

layer in the vertical direction. Because of various processes occurring in and out of

Fig. 2. Salt-gradient solar-pond model configuration for heat flux.


the pond, the operation of the pond is usually complicated. Therefore, some assump-

tions were made for simplifying the analysis as follows:

� The temperature variation along the y-direction is considered small enough so

that it is negligible. Therefore, the temperature and salinity distributions within

the pond are 1D.

� The pond has three distinct zones, which are the LCZ, NCZ, and UCZ, and the

coordinates of the zone boundaries are fixed.� Heat losses through the pond�s sidewalls are considered small enough, due to all

the sides of the pond being well insulated, to be considered negligible. Heat loss

only occurs from the pond�s surface due to convection, evaporation and radiation.

� The bottom surface is blackened in order to maximize the radiation absorption.

Therefore, the radiation energy reaching the LCZ is completely absorbed by

the solution and the bottom of the pond.

� The pond is artificially stabilized by a density gradient, so that the convection cur-

rents can be considered negligible and remain as such during the period ofoperation.

� The physical properties of the salt solution like density, specific heat, ther-

mal conductivity and salt diffusivity, do not vary with temperature and

salinity.

� Due to the presence of convection, the temperatures of the UCZ and LCZ are

likely to be uniform. Therefore, the UCZ and LCZ are considered as a single cell,

and which have thicknesses of XUCZ and XLCZ. The NCZ is divided into five equal

finite cells, each of size Dx. Conservation of energy and mass apply for each cell.The total depth of the pond is L.


3. Heat-transfer model

Under the prescribed assumptions, application of the energy balance for a small

layer in the NCZ, then

½ðqxÞi � ðqxþDxÞi� þ ½ðIxÞi � ðIxþDxÞi� ¼ qCp

oT ðx; tÞot

Dx; ð1Þ

qx � qx þdqxdx

Dx� ��

þ IðxÞ � IðxÞ þ dIðxÞdx

Dx� ��

¼ qCp

oT ðx; tÞot

Dx; ð2Þ

and

o

oxkoT ðx; tÞ

ox

� �þ _q ¼ qCp

oT ðx; tÞot

; ð3Þ

where _q, internal heat-generation term, which represents the absorption rate of thesolar radiation per unit volume at a depth x from the pond�s surface. It is given by

_q ¼ � oIðxÞox

; ð4Þ

where I(x) is the solar energy radiation intensity at depth x, in the solution, which is

a time and depth dependent function. Radiation attenuation in the pond is calcu-

lated as an exponential decay, following a simplified equation of Beer�s Law

IðxÞ ¼ ð1� aÞð1� bÞI se�lx for x > 0; ð5Þwhere I(x) is the solar-radiation intensity at depth x, Is is the incident solar-radiation

intensity at the pond�s surface, a is the reflectance of solar radiation at the surface, brepresents the long-wave fraction of Is which is absorbed very close to the surface,

and where l is the attenuation or extinction coefficient. The extinction coefficient

normally depends on the wavelength of the radiation. A single extinction coefficientis used to describe the absorption of radiation. It is assumed that a fraction, b, of theradiation, is absorbed within a depth d (=5 mm) from the surface of the pond and,

the remaining radiation is absorbed within a depth d from the surface of the pond

and the remaining radiation follows an exponential decay. For the present tests,

a = 3–10%, b = 0.5 and l = 0.7 were used.

The thermal process in the SGSP can be treated as a 1D unsteady-conduction

problem with heat generation in to the proposed mathematical model. The solution

of this equation requires an initial and two boundary conditions. The initial condi-tion is the initial pond-temperature, which equals the ambient temperature at the

time of initiating the pond�s operation. The first boundary-condition is specified at

x = L1 (UCZ–NCZ interface) and the second boundary-condition is specified at

x = L2 (NCZ–LCZ interface). For both boundary-conditions, an energy balance

was applied at each pond depth. The first boundary-condition is obtained from en-

ergy balance over the UCZ as

koT ðx; tÞ

ox

��x¼L1

þ I jx¼0 � I jx¼L1� Qt

� �¼ qCp

oT ðx; tÞot

xUCZ; ð6Þ


where Qt is the heat loss from the pond�s surface by convection, evaporation and

radiation. The second boundary condition is obtained from an energy balance over

the LCZ as given by

�koT ðx; tÞ

ox

��x¼L2

þ I jx¼L2� I jx¼L3

� �¼ qCp

oT ðx; tÞot

xLCZ. ð7Þ

4. Heat-loss calculation

The model solar-pond is assumed to be well insulated: heat loss from the pond�ssurface occurs due to convection, evaporation and radiation. Thus, the total heat-loss can be calculated as follows [2,3,20]:

Qt ¼ Qc þ Qe þ Qr. ð8ÞThe convective heat-loss is given by

Qc ¼ hcðT y � T1Þ; ð9Þwhere hc is the wind convection heat-transfer coefficient, which depends on the veloc-ity of wind, is given by

hc ¼ 5.7þ 3.8V r. ð10ÞThe heat loss due to evaporation is proportional to the wind-induced convective

heat-transfer coefficient hc and the difference between the vapour pressure of the free

surface and the partial pressure of the water vapour in the atmosphere. The evapo-

rative heat loss can be expressed as follows:

Qe ¼hehcðP s � P1Þ1.6CaP atm

; ð11Þ

where Ps is the vapour pressure evaluated at the surface temperature

P s ¼ exp 18.403� 3885

T s þ 230

� �ð12Þ

and P1 is the partial pressure of water vapour in the ambient air obtained at the

ambient temperature

P1 ¼ Rh exp 18.403� 3885

T1 þ 230

� �. ð13Þ

Heat loss due to radiation from the pond�s surface to the sky can be calculated from

the following expression:

Qr ¼ ewr ðT s þ 273.15Þ4 � ðT sky þ 273.15Þ4� �

. ð14Þ

The sky temperature is estimated as follows:

T sky ¼ T1 þ ð0.55þ 0.704ðffiffiffiffiffiffiffiP1

pÞÞ0.25. ð15Þ


5. Mass-transfer model

There are several physical processes occurring in the operation of a solar pond.

Convective mass-transfer occurs in the LCZ and UCZ and diffusive mass-transfer

in the NCZ. The density gradient could develop by molecular diffusion. In thismodel, the total mass of the system in the control volume is constant, and the mass

transfer takes place as a result of molecular diffusion. The mass-transfer processes

are independent of the thermal processes. Based upon these assumptions, 1D mass

diffusion in the x-direction for a differential volume-element of thickness, Dx, as illus-trated in Fig. 6, is given as follows:

ðJx � JxþDxÞ ¼oqðx; tÞ

ot

� �Dx; ð16Þ

� ðJ jxþDx � J jxÞDx

� �¼ oqðx; tÞ

ot; ð17Þ

� oJox

¼ oqðx; tÞot

. ð18Þ

By Fick�s law of diffusion, the diffusion flux J is related to the density gradient by

J ¼ �Doqðx; tÞ

ox. ð19Þ

Substituting from Eq. (19) into Eq. (18) and assuming a constant D, the followingequation. can be obtained,

o

oxDoqðx; tÞ

ox

� �¼ oqðx; tÞ

ot. ð20Þ

The solution of the mass diffusion equation needs an initial condition and two

boundary conditions. The initial condition is specified by a linear density-gradient

of the form, as follows:

q ¼ q1; 0 6 x < L1; ð21Þ

q ¼ q2; L2 < x 6 L3. ð22ÞThe first boundary-condition is specified at x = L1 (UCZ–NCZ interface) and the

second at x = L2 (NCZ–LCZ interface). For both boundary-conditions, a mass bal-

ance was applied at each point. A mass balance at the UCZ gives the first boundary

condition, as follows:

Doqðx; tÞ

ox¼ oqðx; tÞ

otXUCZ; x ¼ L1; t > 0. ð23Þ

A mass balance at the LCZ gives the second boundary-condition, as follows:

�Doqðx; tÞ

ox¼ oqðx; tÞ

otX LCZ; x ¼ L2; t > 0. ð24Þ

Fig. 3. Salt-gradient solar-pond model configuration for mass transfer.


Equation (24) is of exactly the same form as the 1D unsteady heat-conduction equa-

tion: the same mathematical techniques are applicable for its solution.

The equations obtained from the heat and mass transfers are solved numerically

to determine the temperature and density profiles within the pond. The method used

in generating solutions to the 1D temperature and density finite-difference equations

is explicit because unknown nodal variables for a new time are calculated using theknown values of the parameters at a previous time. A finite-difference form of the

differential equation is derived by integration over the control volume surrounding

the typical node i, as shown in the grid of Figs. 2 and 3. A Fortran computer-

program has been developed for the aforementioned reasons. A layer increment of

5 cm and a time step of 1 h were used in the model. The stability criterion of explicit

formulation is Dt < qCp(Dx)2/2k.

6. Experimental study

Experiments were carried out under the laboratory conditions using a scale solar-

pond of dimensions 60 · 50 cm2 and 60 cm deep as shown in Fig. 4. This pond wasconstructed from 1.5 mm galvanized metal sheet. Inside of the pond was painted

black to ensure absorption of the radiation, while the outside was insulated with

20 mm thick glass–wool and 30 mm thick styrofoam to reduce the rate of heat loss.

The pond was subjected to a simulator solar-radiation spectrum close to that of

solar radiation. A low-cost solar simulator, which has 2 · 1000 W, 220–230 V,

6.5 A and 25,000 ml Philips halogen lamps, adjustable on the vertical axis above

the pond�s surface, was designed. The simulator was installed 35 cm above the pond�ssurface. The incident radiation intensity was measured with a Solar-130 type pyra-nometer of accuracy ±1.5 W/m2. The corresponding radiant-flux intensity is

750 W/m2.

Fig. 4. Cross-section of experimental solar pond.


The temperatures were measured by chromel–alumel (K-type) thermojunctions,

fixed at 8 points on a vertical side wall of the pond, with an accuracy of ±0.3 �C.The thermojunctions are spaced 10 cm apart from top to bottom of the pond: they

provide a clear temperature profile by connecting the thermocouples to a digital mul-

timeter (Mastech MY-64 type).

Density profiles were determined by analyzing the densities of small samples ex-

tracted from the solar pond at the same level as the thermojunctions. Flexible plas-

tic tubes, attached 10 cm apart, acted as sampling vents at the other sidewall of thepond. The density of the withdrawn solution was determined by measuring the

mass of a given volume to an accuracy of ±10�4 g. The volume was measured with

a 10 ml pycnometer to an accuracy of ±0.2 ml. Density profiles were taken twice a

day while the pond was subjected to radiation, and at regular intervals while

cooling.

The pond was filled layer by layer, starting with the layer of highest concentrated

solution to fill the LCZ. Next, the NCZ was established by painstakingly pouring

slowly a decreasingly less-concentrated solution from a floating plastic can. TheNCZ is formed of five layers. Lastly, the UCZ is filled with fresh water on top of

the NCZ in the same way as the NCZ. The thicknesses the UCZ, NCZ and LCZ

are 10, 25 and 25 cm, respectively.

Then the pond was covered by a non-transparent plastic sheet to prevent radia-

tion from heating up the solution. The pond remained covered for three days to al-

low molecular diffusion of the salt to take place and to achieve a linear salt-gradient.

Subsequently, the pond was subjected to solar simulator radiation.


7. Results and discussion

After reviewing the literature, it is seen that achieving the SGSP density-gradient

with sodium-carbonate salt has not previously been tested. So, four experiments with

the solar pond having different ranges of density gradient have been conducted. InTables 1–4, the distributions of salinity and density of sodium carbonate solutions

Table 1

The distributions of salinity and density in the pond zones for the first experiment

Pond zone Pond zone

thickness (cm)

Salinity (%) Density (kg/m3)

UCZ 10 0 998

NCZ 25 5 2 1036.8

5 4 1052.6

5 4 1052.6

5 6 1068.3

5 6 1068.3

LCZ 25 8 1081

Table 2

The distributions of salinity and density in the pond zones for the second experiment

Pond zone Pond zone

thickness (cm)


UCZ 10 0 998

NCZ 25 5 2 1036.8

5 4 1052.6

5 4 1052.6

5 6 1068.3

5 8 1081

LCZ 25 10 1108

Table 3

The distributions of salinity and density in the pond zones for the third experiment

Pond zone Pond zone

thickness (cm)


UCZ 10 0 998

NCZ 25 5 3 1042

5 5 1063

5 5 1063

5 7 1079.5

5 7 1079.5

LCZ 25 12 1120

Table 4

The distributions of salinity and density in the pond zones for the fourth experiment

Pond zone Pond zone

thickness (cm)


UCZ 10 0 998

NCZ 25 5 3 1042

5 5 1063

5 8 1081

5 10 1108

5 12 1120

LCZ 25 16 1157


that filled the pond are seen. As seen from the tables, the salinity difference between

the surface and the bottom of the pond amount to 8% for first experiment, 10% for

second experiment, 12% for third experiment and 16% for last experiment. A higher

salinity range cannot be achieved because thin crystal solid layers, then form at the

base of the pond.

The density and temperature profiles as functions of the pond�s depth are shown

in Figs. 5 and 6, respectively. In Fig. 5, the density profile initially looks like stair

steps, then it starts to turn to a shape like the SGSP density profile after the firstday. After the fourth day, a stable density-gradient was formed as a result of salt dif-

fusion from the bottom to the surface. The temperature profile after the pond is sub-

jected to the solar simulator radiation for a day is illustrated in Fig. 6.

Figs. 7 and 8 show the density and temperature profiles for the second experiment.

In the first experiment, the density gradient with a 10% of salinity range cannot be

enough to suppress convection currents that occur as a result of the radiation

absorption in the LCZ. However, when a comparison has made between the first

and fourth day�s experimental results, the temperature profile has tended to theSGSP temperature profile.

Fig. 5. Density profile in experiment 1.

Fig. 6. Temperature profile in experiment 1.





The density and temperature profiles provided from the third experiment are gi-

ven in Figs. 9 and 10. It is more stable than the first and second density profiles

and more suitable for a SGSP. A similar situation was observed in the fourth exper-

iment. A salinity range with a 12% density gradient is enough to store the radiation

absorbed in the form of heat at the LCZ. After seven days� observations, the temper-ature difference was measured between the pond�s bottom and its surface as 10 �C.The experiment ceased at the seventh day due to the storage temperature remaining

unchanged. The density gradient with 12% salinity range prevented convection from

the bottom to the surface. The pond�s temperature-profile during the cooling period,

which shows a similar characteristic as with the SGSP was kept for a long time.

From the results, at least a 12% salinity range to establish a worthwhile density gra-

dient between the pond�s bottom and surface is needed to store heat in the SGSP

containing a sodium-carbonate solution.




Fig. 11 shows a stable density-gradient. The temperature profile remained un-

changed after the sixth day and a 12 �C temperature difference ensued on the seventh

day (see Fig. 12).

The comparisons of density and temperature profiles for the fourth experiment

with the results of the model are shown in Figs. 13 and 14. The results are qualita-tively in good agreement, but a small difference was seen quantitatively due to the

physics of the solar pond. The model storage temperature was higher than the mea-

sured storage temperature due to the temperature values measured in the NCZ and

UCZ being larger than the corresponding temperatures provided from the model.

This is a result of solar simulator radiation being used as the energy source in the

experiments. The simulator spectrum has a bias towards the long-wavelength (infra-

red) radiation compared with that of the Sun. The long wavelength range of



Fig. 13. The comparison of model-experiment temperature profiles.

Fig. 14. The comparison of model and experiment density profiles.


simulator radiation is mostly absorbed by the UCZ, and the temperature rise of the

UCZ occurs quickly. On the contrary, only small part of the simulator radiation is

transmitted to the LCZ, so that the temperature rise of the LCZ occurs slowly.

8. Conclusions

Sodium-carbonate salt has been used in the establishment of salinity gradients in

the SGSP.

Four different density-gradients with sodium-carbonate solution were initially

established in the pond with salinity ranges of 8%, 10%, 12% and 16%. In the first

experiment, a temperature-gradient similar to that of SGSP in the pond was not ob-tained. However, a slow conversion to a temperature gradient similar to the SGSP


temperature-gradient was observed in the second experiment. In the third experi-

ment, temperature differences were observed between the bottom and the surface

of the pond of around 10 �C. In fourth experiment, this difference became 12 �C.In order to be able to store heat in the SGSP with sodium carbonate solution, a den-

sity gradient with a salinity range of 12% between the bottom and surface of thepond is necessary.

In order to verify the validity of the experimental results, a 1D time-dependent

mathematical model for heat-and-mass transfers, based on energy and mass bal-

ances, was developed. Differential equations constituting the model were solved

using a finite-difference method. The numerical results were compared with the

experimental results. It is seen that experimental and numerical results were well cor-

related. The results are in harmony, but small differences between the surface and

bottom of the pond in the model became higher than the experimental temperaturedifferences. The solar simulator radiation that is used as the energy source in the

experiments causes this dissimilarity the between model and experiment profiles. If

a suitable density-gradient with sodium-carbonate salt is established, a considerable

amount of the incident solar radiation can be trapped and stored as heat energy in

the LCZ over a long time-period.

References

[1] Tas�demiroglu E. Salt availability in Turkey and its potential use in solar ponds. Resour Conser

1987;15:215–28.

[2] Kurt H, Binark AK, Halici F. Mathematical modelling of salt-gradient solar-pond as a solar energy

store. In: TIEES-98, second Trabzon international energy and environment symposium, Trabzon;

1998. p. 187–91.

[3] Kurt H, Halici F, Binark AK. Solar-pond conception: experimental and theoretical studies. Energ

Convers Manage 2000;41:939–51.

[4] Bozdemir S, Kayah R. Mathematical modelling of solar ponds and comparison with experimental

data. J Environ Sci 1987;7(3):387–97.

[5] Kanayama K, Inaba H, Baba H, Fukuda T. Experiment and analysis of practical-scale solar-pond

stabilized with a salt gradient. Sol Energy 1993;46(6):353–9.

[6] Leshuk JP, Zaworski RJ, Styris DL, Harling OK. Solar-pond stability experiment. Sol Energy

1978;21:237–44.

[7] Keren Y, Rubin H, Atkinson J, Priven M, Bemporad GA. Theoretical and experimental comparison

of conventional and advanced solar-pond performance. Sol Energy 1993;51(4):255–70.

[8] Xiang YL, Kanayama K, Baba H. Spectral calculation of thermal performance of a solar pond and

comparison of the results with experiments. Renew Energ 2000;20:371–87.

[9] Xiang YL, Kanayama K, Baba H, Maeda Y. Experimental study about erosion in a salt-gradient

solar-pond. Renew Energ 2001;23(2):207–17.

[10] Kho TH, Hawlader MNA, Ho JC, Wijeysundera NE. Design and performance evaluation of a solar

pond for industrial process-heating. Int J Sol Energ 1991;10:83–101.

[11] Tahat MA, Kodah ZH, Probert SD, Al-Tahaineh H. Performance of a portable mini solar-pond.

Appl Energ 2000;66(4):299–310.

[12] Kumar A, Kishore VVN. Construction and operation experience of a 6000 m2 solar-pond at Kutch,

India. Sol Energy 1999;65(4):237–49.

[13] Subhaker D, Murthy SS. Experiments on a magnesium-chloride saturated solar-pond. Renew Energ

1991;1(5–6):655–60.


[14] Subhaker D, Murthy SS. Saturated solar ponds: 3. Experimental verification. Sol Energy

1994;53(6):469–72.

[15] Banat FA, El-Sayed SE, El-Temtamy. Carnalite salt-gradient solar-ponds: an experimental study.

Renew Energ 1994;4(2):265–9.

[16] Pawar SH, Chapgaon AN. Fertilizer solar-ponds as a clean source of energy: some observations from

small-scale experiments. Sol Energy 1995;55(6):537–42.

[17] Murthy GRR, Pandey KP. Comparative performance evaluation of a fertiliser solar-pond under

simulated conditions. Renew Energ 2003;28(3):455–66.

[18] Hassairi M, Safi MJ, Chibani S. Natural-brine solar-pond: an experimental study. Sol Energy

2001;70:45–50.

[19] Lund PD, Keinonen RS. Radiation–transmission measurements for solar ponds. Sol Energy

1984;33(3-4):237–40.

[20] Mansour RB, Nguyen CT, Galanis N. Numerical study of transient heat-and-mass transfers and

stability in a salt-gradient solar-pond. Int J Therm Sci 2004;43:779–90.

[21] Jubran BA, Al-Abdali H, Al-Hiddabi S, Al-Hinai H, Zurigat Y. Numerical modelling of convective

layers in solar ponds. Sol Energy 2004;77(3):339–45.

[22] Hongfei Z, Hua J, Lianying Z, Yuyuan W. Mathematical model of the thermal-utilization coefficient

of a salt-gradient solar-pond. Energ Convers Manage 2002;43:2009–17.

[23] Angeli C, Leonardi E. A one-dimensional numerical study of the salt diffusion in a salinity-gradient

solar-pond. Int J Heat Mass Trans A 2004;47(1):1–10.

[24] Husain M, Patil PS, Patil SR, Samdarshi SK. Computer simulation of salt-gradient solar-pond�sthermal behaviour. Renew Energ 2003;28(5):769–802.

[25] E1-Refaee MM, Al-Marafie AM. Numerical simulation of the performance of the Kuwait

experimental salt-gradient solar-pond. Energ Sources 1993;15:145–8.

[26] Alkhalaileh MT, Atieh KA, Nasser NG, Jubran BA. Modelling and simulation of solar-pond floor-

heating system. Renew Energ 1999;18(1–2):1–14.

[27] Hawlader MNA, Brinkworth BJ. An analysis of the non-convecting solar pond. Sol Energy

1981;27:195–204.

[28] Antonopoulos KA, Rogdakis ED. Correlations for the yearly or seasonally optimum salt-gradient

solar-pond in Greece. Sol Energy 1993;50(5):417–24.

[29] Subhakar D, Murthy SS. Saturated solar-ponds: 1. Simulation procedure. Sol Energy

1993;50(3):275–82.

[30] Alagao FB. Simulation of the transient behaviour of a closed-cycle salt-gradient solar-pond. Sol

Energy 1996;56(3):245–60.

experimental and numerical analysis of sodium-carbonate salt gradient solar-pond performance under...

Documents