The stability of an unsustained salt gradient solar pond

Renewable Eneryy, Vol. 13, No. 4, pp. 543 548, 1998

~

~.C' 1998 Elsevier Science Ltd. All rights reserved Printed in G r e a t Britain

Pergamon

PII : S0960-1481(98)00016-0

TECHNICAL

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NOTE

The stability of an unsustained salt gradient solar pond R. JAYAPRAKASH* and K. PERUMAL Department of Physics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, 641020, Tamilnadu, India

(Received 10 May 1997;accepted21 January 1998)

Abstract--A

solar pond of area 5.712 m 2 was constructed. It was filled with water to a height of 87.5 cm. The stability of density and temperature profile, variation of salt flux due to temperature and depth, temperature loss during night time, and the evaporation losses at the surface were analyzed. © 1998 Elsevier Science Ltd. All rights reserved.

NOMENCLATURE s

P Z

T

~,K~ v

q

concentration (kg m 3) density (kg m - 3 ) depth (m) temperature CC) coefficients of temperature and salt diffusivities (m 2 s-~) viscosity (m 2 s ~) salt flux (kg s -~ m -2)

INTRODUCTION A solar pond is nothing but a body of water collecting the solar radiation and storing it for a long period of time in its bottom layers. The energy stored is prevented from the convection loss by maintaining the salt gradient layer floating over the high concentration layer. Here the high concentration layer acts as the Lower Convective Zone (LCZ) and the gradient zone acts as a Non Convective Zone (NCZ). Fresh water maintained over the NCZ, acts as an Upper Convective Zone (UCZ). This gradient zone is formed by the distribution of salt concentration solution from the surface to the storage zone. In this case salt from the storage zone diffuses continuously but slowly, tending to homogenize the pond. To study the stability of the salt gradient solar pond, the density and temperature gradient of the pond is regularly monitored. The fluid motion in the gradient zone is stabilized by density changes due to increase in salt concentration with depth. But the fluid motion in the gradient zone is destabilized by the density changes due to increase in temperature and by decrease in depth. In the pond the density gradient and stability criterion are related to the temperature, salinity distribution and depth. The stability of this pond is mainly maintained with only one constituent of salt (NaC1). The presence of another constituent of the salt would affect the stability.

* Author to whom correspondence should be addressed. 543

544

Technical Note

The distribution of solar energy absorbed, the resultant heating of the pond and the exchange of heat with the earth beneath have all been discussed by Tabor [1]. Weinberger discussed mathematically the physics of the solar pond [2]. A further study on the theory of falling pond is made by Wang and Akbarzadeh [3]. The stability and maintenance of the gradient layer of the hydrodynamics of salt gradient solar ponds as a function was analyzed by Zangrando [4]. The quantity of salt required per day for replenishment was studied by Tabor and Weinberger for constant temperature and depth [5]. In this work the pond is studied unsustainity and the quantity of salt flux diffusion is also analyzed theoretically and experimentally due to change in temperature and depth. THE STABILITY CONDITION FOR SOLAR POND The stability of a solar pond warmed by solar radiation is maintained by salt concentration gradient. According to Rayleigh analysis, the concentration gradient required for maintaining stability is given by [5] - (v

ap

c~

(v+g~) CONSTRUCTION OF THE POND A solar pond of area 5.712 m 2 and depth 0.9 m was constructed to investigate its performance with respect to temperature and salinity. The bottom of the pond was well insulated using clay, sand and saw dust. This insulation was laid in the form of layers which were separated by LDPE (low density polyethylene) liner. The side wall was built using bricks and cement mortar. Figure 1 shows a cross section of the pond. FILLING THE POND Solar ponds are filled in layered sections with small concentration differences between adjacent layers. The top layer of the upper convective zone (UCZ) has 0% concentration and vertical convection takes place due to effects of wind evaporation. The Non convective zone is 60 cm and it is split into six layers 10 cm thickness each. The concentration of the layers in NCZ are 17, 14, 11, 8, 5, and 3%, respectively. The separation of the pond into six layers suppresses the convection loss and so it is called Non convective zone. This layer is Non convecting, even though the temperature may

"

CZ LCZ

I

"60m~/~.j/~

~

I

.~j0m

T.w

I. LLIPE

L~Der

2. Brlcl~ w~ll j. ~and /~. c l a y

S. Saw du$|

Fig. 1.

Technical Note

545

increase with depth, because the higher salt concentration with increasing depth negates thermal buoyancy forces. The bottom convective layer has 15 cm thickness with uniform concentration of 20% called lower convective zone (LCZ). The fresh water with 0% concentration is filled initially in the pond and acts as UCZ. Then the layer of 3% concentration of NaC1 solution is introduced at the bottom of the pond. Similarly, 5, 8, 11, 14, and 17% are introduced step by step in the increasing order of concentration. These six layers setup in the pond acts as NCZ. Finally 20% concentration layer is introduced at the bottom and it acts as the LCZ. Generally, in this pond all lighter denser layers float on the high denser layer. EXPERIMENTAL AND THEORETICAL STUDY In this study, the periodic salt replenishment and surface washing were not done. The pond was protected from algae formation using CuSo4. The daily surface evaporation of the pond and hourly solar radiation were recorded. The temperature of the pond was recorded at different depths at regular intervals of time after exposure of the pond. Similarly the fall in concentration gradient of the pond was recorded. The basic assumptions for the theoretical study made in this work using the eqns (2), and (4), below are as follows : (1) The initial concentration of the LCZ is 20%. (2) The change in salt flux due to the rise and fall of temperature in the steps of 0.5°C. (3) The decrease in water level due to evaporation is constant. PARAMETRIC STUDY ON THE UNSUSTAINED POND

The theoretical prediction for diffusion coefficient is linearly dependent upon temperature [5] and given by

Ks(T) =

Ds[1 +hAT]

(2)

w h e r e D s = 1.39×10 - g i n 2s l a n d h = 0 . 0 2 9 The mass balance equation is given by ~2s

as

K'(T)~z2 = ~t

(3)

A computer model is developed by solving the above mass balance eqn (3), with the help of finite difference method. For this purpose, the UCZ and LCZ are considered as single layers. The NCZ is divided into layers of N equal sizes. A space step of Ax and time step of At are used. The 8 layers are used in this model with a depth of 85 cm. A time step of 1 h is used for predicting the variation of concentration and it is applied in eqn (4) for theoretical prediction. The quantity of salt flux required by the salt gradient solar pond due to the variation of temperature and depth is given by q = Ks(t)[l + hAT] ( ~ ) K g s -1 m -2

(4)

The change in the quantity of salt flux is analyzed by using eqns (2) and (4). The bottom concentration of the pond is assumed at 20%. The variation of salt flux due to temperature and depth is computed numerically. Figures 2 and 3, show the experimental temperature gradient and density gradient of the solar pond under the unsustained condition. Figure 4 predicts theoretically the variation of salt flux with respect to depth at constant temperature. Figure 5 shows the variation of the salt flux due to temperature both theoretically and experimentally during the time of rise in temperature. Figure 6 shows the variation of the salt flux due to fall in temperature due to decrease in depth. The density and temperature variations of the pond were recorded daily. The surface evaporation was at the rate of 0.4 cm/day. The variations in thickness of the upper convective zone (UCZ), non convective zone (NCZ) and lower convective zone (LCZ) were shown in Figs. 2 and 3. The maximum

546

Technical Note 1"1t_ " ' • • " * * •

.~ 1,0412-~--" ~ i~~'~8~k_k~._._.___vr~~ , : =

0

10

20

30

4Q

60

60

70

II! day 1Xth day 30th day 45th day 6Oth day ?Sth day 90th d,by 110th day

80

Depth (cm)

Fig. 2. Variation of density with depth.

" • * • " • * s

30? 11' t ll'.lr:t, e,-.t~e * *-*-~.~ . E

aol i

i 0 !. . . . . . . . . . . . . . . . . . . o 10 20 30

Is! duy 12th day 15th day 30th O., 45th day 60th day 7Sth day 80th day

• 11thh day 40

60

60

?0

80

Depth (cnt)

Fig. 3. Variation of temperature with depth.

The~,-o'e( i~lo| ~rve ;tO

6

0

~

c X,,i

i°" 114, DEPTH c"'

Fig. 4.

Technical Note ~O

°

547

I. T.~, of let I ca! Curve ~ . ~ perim#nekl curve

I& 2. 12

At

kg

bll

60

T E M P ~ R A T U ~ "C

Fig. 5.

I. Ttworet tcal curve 2. £al~rirhamlel GW'Ve it

1

TF~I~C3F.~ UXE "C

Fig. 6.

temperature obtained in this pond was 62.4°C. The maximum storage temperature was 58.4°C. The temperature of the LCZ decreased from 62.4°C to 58.4°C during night time. The temperature loss during night time was predicted by our pond as 4°C. The variation of the density profile gives the decay of NCZ and LCZ in 110 days. Figure 4 shows that the quantity of salt flux increases with the increase of temperature, assuming that the depth of the water level in the pond goes on decreasing in steps of 0.4 cm/day due to evaporation throughout the period of study. The quantity of salt flux is analyzed with respect to variation of depth with temperature as constant. This is also performed for the various temperatures keeping them as constant. Owing to this, the quantity of salt flux diffusion is decreased due to increase in depth and the stability of the pond is also increased even at the higher temperatures. So the pond requires suitable depth of water to maintain its stability. Figure 5 shows the increase in salt flux due to increase in temperature. The experimental and theoretical results are compared with each other and the same trend is achieved with small deviation owing to a slight mixing of the adjacent layers at the time of pond filling. This small deviation is studied statistically using eqn (5) for finding the mean percentage error and analyzed as 7.17%. The mean percentage error is defined by

548

Technical Note

Id, I MPE = n/-~-1 Hv x t00

(5)

where, d~is the difference between the ith experimental value and ith theoretical value, n is the number of data and Hv is theoretical value. Similarly, Fig. 6 shows the change in salt flux due to decrease in temperature with unsustainity of depth. Hence the stability change in the pond is also due to temperature. The theoretical and experimental values of the quantity of salt flux are calculated at 60°C as 1.4 × 1 0 - 6 kg s -t m -2 and 1.3 × 1 0 - 6 kg s -~ m -2 respectively. CONCLUSION The storage temperature of the LCZ was increased at the rate of l°C/day. The thermal storage capacity was raised by the increase of depth of the pond. The quantity of salt flux diffusion decreases for the large depth and it is useful for maintaining more temperature at the LCZ. The experimental data had achieved the same trend as the numerical data. This analysis revealed that the quantity of salt flux varied due to rise in temperature. The erosion of the upper convective zone (UCZ) and non convective zone (NCZ) due to evaporation, without surface washing and replenishment of salt in the pond, was the factor behind the poor performance. REFERENCES

1. Tabor, H., Solar Ponds. Solar Energy, 1969, 7, 189-194. 2. Weinberger, H., The Physics of the solar pond. Solar Energy, 1964, 8, 45-56. 3. Wang, Y. F. and Akbarzadeh, A., A further study on the theory of Falling Pond. Solar Energy, 1982, 29, 557-563. 4. Zangrando, F., On the hydrodynamics of salt gradient solar ponds. Solar Energy, 1991, 46, 323341. 5. Tabor, H. and Weinberger, Z., Non convecting solar ponds. In Solar Energy Hand Book, ed. Krieder and Kreith. McGraw-Hill, New York, 1981, Chapter 10.