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Performance analysis of a bittern-based solar pond
Solar Energy. Vol. 40. No. 5, pp. 469-475, 1988 Printed in the U.S.A.
0038-092X/88 $3.00 + .00 Copyright © 1988 Pergamon Press plc
PERFORMANCE ANALYSIS OF A BITTERN-BASED SOLAR POND A. S. MEHTA, N. PATHAK,B. M. SHAH, and S. D. GOMKALE Central Salt & Marine Chemicals Research Institute, Bhavnagar 364 002, India Abstract--An attempt has been made to analyze the performance of the bittern-based solar pond of a 1600-m: area located in Bhavnagar, India (latitude 21°, 45'N and longitude 72°, 12'E). Solar radiation transmission in the pond has been measured with a silicon solar cell module and the results are used in the calculation. Thermal efficiency of the pond is worked out by the correlations proposed by Kooi and Hull. Its value is very very low and reasons for this are discussed in the text. Theoretical temperature profiles in the NCZ and optimum thickness of the NCZ are calculated based on the correlations developed by Kooi. Calculated temperature profiles and observed profiles in NCZ match quite satisfactorily.
Kooi[8] in brief, along with the ground heat loss term as suggested by Hull[l l]. A brief description of the CSMCRI pond is presented in Section 3. Methods adopted to withdraw brine samples, temperature measurement in the pond, and density gradient corrections in the gradient zone are also described. In Section 4 results regarding thermal efficiency of the pond and heat balance calculation are presented and they are discussed with respect to steady-state behavior of the pond, optimum thickness of the gradient zone, and temperature profiles in the pond. In Section 5, conclusions based on the results and discussion are mentioned regarding the behavior of the pond.
1. I N T R O D U C T I O N
Salt gradient solar ponds (SGSP) have attracted worldwide attention after their successful exploitation in Israel for power generation. A good number of solar ponds are constructed all over the world and have been under observation during the last decade. A number of investigators have proposed mathematical models for the SGSP and have carried out simulation studies by assuming ideal conditions[l-5]. Only a few models have been checked with the actual performance data obtained on experimental ponds of moderate size. The lack of experimental confirmation is especially true in the case of bittern-based ponds. A few investigators, based on their practical experience[6,7], have reported that the actual conditions in the pond differ significantly from those predicted in the theoretical analysis whereby the final results, say for example, storage zone temperature and thermal energy stored, are much lower when compared with the theoretical analysis. One such case is the bittern-based solar pond under investigation in Bhavnagar. The main factors responsible for the steady-state behavior of the pond are discussed by C. F. Kooi[8], Newell and Boehm[9] and Kishore and Veena[10]. According to their analysis: (1) the thermal mass of the pond is so large that diurnal temperature variations are normally less than I°C; (2) when the season changes the effective change in pond temperature is immediately observed; (3) at high latitudes, steady state would vary considerably throughout the year, but at low latitudes (as is the case of Bhavnagar) it is likely that a nearly constant steady state could he maintained throughout the year. In short, if environmental conditions do not change very much with time, and pond parameters result in fast response time, pond behavior can be considered safely in a steady state. Actually, the steady-state model is not applicable to most of the ponds and time-varying analysis is required, but it appears that the steady-state model is applicable to CSMCRI pond, as discussed later. Section 2 describes the steady-state model of
2. T H E O R E T I C A L
MODEL
TRANSMISSION
AND RADIATION
IN THE POND
Considering the solar pond, to be similar to the fiat-plate collector, Kooi[8] expressed the efficiency of the solar pond as = F R [aT - (UL A T ~ H ) ]
(1)
where FR is the heat removal factor as defined by Duffle and Beckman[12] and its value is assumed as 0.95. Absorptance transmittance product is defined as
ar =
(x)dx
x2 - xl)
(2)
where H is solar insolation in W / m 2 and h(x) is the fraction of insolation that remains at a depth x. UL is the top loss coefficient expressed as Ut. = k / ( x 2 - x O
(3)
where k is thermal conductivity of pond brine. Xl and x 2 are the depth of upper convecting zone (UCZ), nonconvecting zone (NCZ) boundary, and nonconvecting lower convecting zone (LCZ) boundary from
469
470
A. S. MEHTAet al.
the surface, respectively. A T is the temperature difference between LCZ and UCZ temperature. In eqn (1), Kooi has not considered ground heat loss, whereas H u l l [ l l ] included this term and modified eqn (1) as
sions are available[4,5,8.13] to evaluate h(x). In the present case, solar radiation transmission is measured by silicon solar cell module and the results are correlated by the following expression[8], h(x) = a - b In(x/cos r)
= FR [et "r - (UL A T ~ H ) - (Qo/H)]
where Qb is the heat loss from the bottom of the solar pond. Hull has developed a method to calculate Qb in which ground water movement is also considered. Based on Hull's procedure, Kishore and Veena[10] have suggested the following simple equation to calculate ground heat loss Qt, = Ub (Tb - Tg)
(5)
where a and b are empirical Constants and r is" the refraction angle that depends on the incidence angle of the sun rays and refractive index of the pond brine. Incidence angle is calculated based on the time of measurement of radiation transmission. Refractive index of the pond brine is measured in the laboratory by Abbrs refractometer. It varies from 1.33 to 1.39 depending on the salt concentration and temperature of the brine. In the calculation, an average value of 1.36 has been used.
where Tb and Tg are the pond bottom and underground water temperature, respectively. Ub is the ground heat transfer coefficient defined as Ub = 0.99 [kg/l s] + 0.9kg ( S / A )
(6)
Here, kg is soil thermal conductivity, lg is water table depth, and S and A are the pond bottom perimeter and area, respectively. Differentiating eqn (1) with respect to x2 and setting equal to zero, Kooi obtained the following expression to calculate optimum depth of the N C Z LCZ boundary for maximum efficiency of the pond. f X2h(x) dx - (x~
-
xl) h(x~_) = K A T / H
(7)
I
Substituting eqns (7), (2), and (3) in eqns (1) and (4), the maximum efficiency is defined without considering ground heat loss and with ground heat loss as "q"
= FRh(XT)
(8)
and ~q'~ = FR[h(xT) - (Qb/H)]
(9)
The vertical temperature distribution in the UCZ and LCZ are constant at T(x~) and T(x,), respectively. Integrating a one-dimensional, steady-state heat conduction equation between the limits x~ and x2, the following expression for temperature distribution in NCZ is obtained[8]
~
3. CSMCRI SOLAR POND
The Central Salt and Marine Chemicals Research Institute, Bhavnagar, has constructed a solar pond in the Institute's Experimental Salt Farm, which is 8 km away from the Institute. Details of construction of this pond are available in earlier publications[ 14,15]. The pond was designed to provide 1 million kcal of thermal energy per day at 80°C by assuming 15% heat collection efficiency. The solar pond dimensions are 40 m x 40 m at the surface and 35 m x 35 m at the bottom, and it is 2.3 m deep at the center as shown in Fig. 1. The solar pond was filled up to 1 m depth with sea bittern collected from the experimental salt farm. It contains about 400 g dissolved salts in 1 liter. The rest of the pond was filled up with fresh sea water in April 1981. During the construction of the pond, copper constantan thermocouples were installed at various depths in the ground, side walls of the pond, and in the pond brine to monitor temperature profile in the pond. In 1982, there was a severe cyclonic storm in Bhavnagar and the original thermocouple network was totally destroyed. Later on, temperature measurements were carried out only in pond brine with the help of platinum thermistor sensor attached to a movable support. Temperature measurement was carried out at 2.5, 5.0, and 10.0 cm intervals in the pond brine from the surface to the 1.6 m depth. Pond brine samples were collected by using a graduated scale along with a flexible tube at I0 cm intervals. A vacuum was applied at one end of the tube and a sample was
x
T(x) = ( H / k )
(11)
(4)
"aO,mxaow~
h(x)dx + [T(x2) - T(xO
PONDTOP
,/x I
- (H/k)
h(x)dxl [(x - xO/(x2 - xOl
(10)
2.1 Solar radiation transmission The attenuation function h(x) depends mainly on the transparency of the pond water. Many expres-
WORKING~J PLATFORM ~
~,
'~
~.l[
L/~ N.OPE.LINER .......
ELEVATION Fig. 1. The CSMCRI solar pond.
Bittern-based solar pond first collected in the tube and then transferred to the sampling bottles. M e a s u r e m e n t of brine specific gravity, salinity, pH, turbidity, etc. were carried out in the laboratory. T e m p e r a t u r e and density profiles were monitored twice in a week, whereas other data such as solar insolation, wind velocity, relative humidity, and m a x i m u m m i n i m u m temperature were recorded continuously round the clock. Solar radiation transmission m e a s u r e m e n t was c a r d e d out by solar cell module twice in a week. In order to c o m p e n s a t e evaporation losses and to clean the pond surface, flushing operation was carried out three times in a week through a 7.5 c m diameter and 30 m long perforated pipe. Sea water is p u m p e d from the adjoining creek during high tides, which are not very frequent in a m o n t h , and stored to flush the pond. In the sea water reservoir, sea brine density increased due to evaporation. As a result, less a m o u n t o f sea water of specific gravity less than 1.03 was available for flushing purposes. This imposed the limitation on the extent o f flushing operation and in maintaining density gradient across the NCZ. Regular doses o f copper sulphate and alum were added in the pond brine to m i n i m i z e the algal growth and to settle d o w n the suspended silt from the brine. S o m e t i m e s small intermediate c o n v e c t i v e layers develop in the NCZ. They are modified or corrected by injecting dilute seabrine or dense sea bittern using a 50 c m diameter diffuser fabricated from a 12.5 m m thick P V C sheet. Diffuser slit width is adjusted by Teflon gaskets 1 to 3 m m thick. Sea bittern is also charged in the pond bottom through the diffuser w h e n e v e r bottom layer density decreases below the desired level. Sea bittern is available from the experimental salt farm during April and M a y (the prem o n s o o n months) w h e n there is normally very high wind velocity. Due to high winds, U C Z thickness increases at the cost of N C Z thickness. As a result,
471
pond performance deteriorates in these months. Generally, L C Z density correction is carried out by adding sea bittern during this period. It was expected that in the stabilized pond, the b o t t o m temperature would be around 80°C with 1 m thick L C Z , 1.0 to 1.1 m thick N C Z and 0.2 to 0.3 m thick U C Z . Surprisingly, it was observed that the L C Z temperature has n e v e r exceeded 75°C and the o b s e r v e d variations in thicknesses of three zones are (1) L C Z 0.8 to 1.0 m, (2) N C Z 0.3 to 0.8 m and (3) U C Z 0.2 to 0.8 m.
4. RESULTS AND DISCUSSION Data for the solar pond are g i v e n in Tables 1 and 2 as fortnightly average values for a period of two years. Calculated and o b s e r v e d temperature profiles in the pond are s h o w n in Fig. 2. The percentage deviation between the calculated and observed temperature profile in N C Z is about 8 to 10%. This indicates the extent up to w h i c h the theoretical model can fit experimental data o f a moderate size pond.
4.1 Steady-state behavior o f the pond F r o m the data given in Table 1, one can see that the pond temperature continuously increased from N o v e m b e r 16 to 30, 1984 to M a r c h 1985. A separate heat balance calculation has been worked out for the L C Z for this period and results are given in Table 3. For the heat balance calculation the ground temperature data are not available and hence water sink temperature is considered as pond surface temperature. A b o u t three years back, a bore well was dug half a kilometer away from the pond site and at that time the water table depth was recorded as l 0 m. This value has been used as a depth of water sink from the pond bottom. Based on the rise in temperature of LCZ, thermal energy stored in it is calculated. Prod-
Table 1. Solar pond performance data Temperature,°C Date
S t . no. I.
NOV.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
Dec. Dec. Jan. Oct. Nov. Dec. Jan. Feb. Feb. Mar.
Apr. Apr. June Sept. Oct. Nov. Dec.
16-30/83 1-15/83 16-31/83 16-31/84 1-15/84 16- 30/84 1-15/84 16-31/85 1-14/85 15-28/85 1-15/85 1-15/85 6-30/85 16-30/85 1-15/85 16-31/85 16-30/85 16-31/85
Thickness, m
Specific Gravity
Insolation H w/m:
UCZ
LCZ
UCZ
NCZ
Ti
T2
x~
x2 - xt
UCZ Pl
LCZ P_-
201 197 193 211 272 205 194 207 243 246 278 302 298 238 206 260 199 190
23.3 19.5 19.3 21.5 37.0 20.0 22.8 20.3 20.0 22.0 26.0 29.5 27.5 28.5 29.5 27.2 22.8 23.1
48.5 45.0 45.8 46.3 67.0 47.8 51.3 52.0 56.5 62.0 65.7 65.8 63.8 62.5 59.8 69.0 58.6 53.1
0.50 0.50 0.50 0.60 0.60 0.20 0.23 0.28 0.30 0.30 0.35 0.27 0.45 0.77 0.70 0.24 0.25 0.30
0.42 0.50 0.50 0.40 0.55 0.40 0.52 0.53 0.55 0.50 0.60 0.53 0.70 0.53 0.63 0.51 0.50 0.45
1.063 1.064 1.064 1.053 1. 100 1.060 1.063 1.063 1.057 1.058 1.060 1.071 1.095 1.090 1.103 1.029 1.050 1.047
1.184 1.196 1.179 1.888 1.237 1. 229 1.221 1.239 1.238 1.236 1.233 1.232 1.223 1.250 1.249 1.245 1.245 1.234
A. S. MEHTA et
472
Table 2. Values of empirical constants a and b based on the solar radiation transmission data correlated by the expression h(x) = a - b In (x/cos r) along with the correlation coefficient based on regression analysis a
b
Correlation coefficient
0.1123 0.1554 0.1545 0.1725 0.1785 0.1425 0.1695 0.1523 0.1825 0.1895 0.1335 0.1635 0.1675 0.1985 0.1145 0.1435 0.1863 0.1625
0.1938 0.1383 0.1383 0.1392 0.2034 0.1900 0.1730 0.2120 0.1778 0.1762 0.1720 0.1134 0.1178 0.2020 0.1980 0.2010 0.1942 0.1808
0.9988 0.9895 0.9868 0.9925 0.9875 0.9835 0.9915 0.9905 0.9875 0.9939 0.9962 0.9985 0.9897 0.9912 0.9968 0.9925 0.9969 0.9943
Date Nov. Dec. Dec. Jan. Oct. Nov. Dec. Jan. Feb. Feb. Mar. Apr. Apr. June Sept. Oct. Nov. Dec.
16-30/83 1-15/83 16-31/83 16-31/84 1-15/84 16-30/84 1-15/84 16-31/85 1-14/85 15-28/85 1-15/85 1-15/85 16-30/85 16-30/85 1-15/85 16-31/85 16-30/85 16-31/85
al.
uct of specific gravity and specific heat of bittern is taken as 0.98. The average thickness o f L C Z works out to be 1.5 m and equivalent v o l u m e of L C Z is 1334 m 3. Average pond area is a s s u m e d to be 1400 m 2 for the calculation o f conduction heat losses from L C Z to U C Z and a m o u n t o f radiation reaching in the LCZ. Soil and brine thermal conductivity used in the calculation are 1.00 and 0 . 6 0 W / m . C ° respectively. F r o m the results given in Table 3, the following observations can be made on the behavior of the pond. (1) Considering field conditions and various assumptions made in the calculation, deviation in heat balance is comparatively low. (2) A b o u t 75 to 80% of the insolation reaching the L C Z is lost as conduction heat loss from L C Z to UCZ. Ground heat loss is about 10 to 12% and actual gain in thermal energy of L C Z is negligible. (3) U n d e r the present conditions, input and output of thermal energy is almost of the same magnitude. Hence, even though heat extraction experiments are not carried out, the pond can be safely considered in a steady state. (4) T h e main reason for large conduction loss from L C Z to U C Z m a y be the
0 0.5
0.5 i
Cm
h
1.0
II
1.5 2.0 0
1"0f 1.5
1
I
25
35
II
II
L5
5'5
2.0
15
o 18-30/11,}84 , 16-31/1,}85 A 1G-28/2,~85 i
25
3'5
, 55
,
45
~0.5
,.E =
1.0
o I iiJ:iiiiil '
,1
lo1_
1,5
2.0
/
20
30
40
50
20
60
0.5
30
t,lO
510
60
0.5-
1.0
1'0
o 16-30/6,/85
Ill 2.0
25
J 35
,
45
l
55
I.
65
2.0
25
~
35
~
45
T EMPERATURE'C
Fig. 2. Temperature profiles of the CSMCRI solar pond.
i
55
, ,,
65
Bittern-based solar pond
473
Table 3. Heat balance across LCZ of the pond q is in w / m 2 Sr. no.
Date
q,
qb
q~
qc
Qr
Percentage Deviation
1. 2. 3. 4. 5. 6.
Nov. 16--30/84 Dec. 1-15/84 Jan. 16-31/85 Feb. 1-14/85 Feb. 15-28/85 Mar. 1-15/85
37.9 40.3 41.3 54.0 56.3 47.8
5.61 5.75 6.40 7.36 8.07 8.01
-0.011 0.002 0.013 0.017 0.011
41.7 32.9 35.9 39.8 48.0 39.7
-38.7 42.3 47.2 56.1 47.7
-÷ 3.97 - 2.42 -'- 12.59 + 0.35 ÷ 0.21
q~ = heat input in the LCZ. qb = heat loss to the ground. q~ = heat gain in the LCZ. qc = heat loss through conduction from LCZ to UCZ. Qr = qb + qg + qc. large temperature gradient across the N C Z because o f a thin NCZ. If the thickness o f N C Z is 1 m, the conduction loss will c o m e d o w n to 30 to 35% o f the heat stored in the LCZ. (5) One o f the reasons for the small N C Z thickness is fluctuation in the U C Z N C Z boundary. In this pond, large U C Z up to 80 c m thick are observed because o f high wind velocity. 4.2 O p t i m u m t h i c k n e s s o f t h e N C Z An attempt has been made to calculate the optim u m thickness o f the N C Z based on the observed performance o f the pond and eqn (7). Results o f Ihe calculation are presented in Table 4. It can be seen from Table 4 that in each case o p t i m u m thickness is more than the observed value o f the NCZ. Percentage deviation varies b e t w e e n 34 to 64. Out o f 18 sets o f observations in 8 sets, percentage deviation is more than 50% between the calculated NCZ and observed value o f NCZ. Moreover, calculated optimum thickness o f N C Z for all the sets o f observation s h o w s that it should be about 1 m in order to obtain m a x i m u m
efficiency in the pond under the observed conditions. This tallies with the thickness o f NCZ suggested by various investigators. It may be mentioned here that during s u m m e r period, when UCZ increases up to 0.70 m, it is difficult to maintain a 1 m thick NCZ. Suppose the NCZ is maintained at 1.1 m thickness (e.g., Sr. No. 13 and 14 o f Table 4), the N C Z - L C Z boundary will start at 1.8 m depth from the surface. At this depth, the amount o f radiation reaching the boundary will be very low and hence it will affect the pond performance in a reverse way. In the winter months (i.e., N o v e m b e r to March), U C Z thickness can be maintained less than 0.30 m by using wave breakers. But in the s u m m e r months (i.e., April to September), it is difficult to maintain a UCZ thickness even around 0.40 m. A simple criterion by Newell and Boehm[9] shows that one needs to maintain a ratio o f N C Z salt difference to temperature difference greater than 3.9 × l03 (kg salt)/(kg solution K) for sodium chloride ponds. Using this criterion and estimating tempera-
Table 4. Calculated and observed thickness of NCZ in the pond. Thermal efficiency of the pond without considering ground heat loss and with the ground heat loss Thermal efficiency of the pond%
Sr. no.
Observed thickness of NCZ meter (x2 - x,)
Calculated thickness of NCZ meter (x~ - x,)
Without ground heat loss
With ground heat loss
Observed x2
Optimum x7
Observed x2
Optimum .~
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
0.42 0.50 0.50 0.40 0.55 0.40 0.52 0.53 0.55 0.50 0.60 0.53 0.70 0.53 0.65 0.51 0.50 0.45
0.89 1.15 1.20 1.14 0.85 1.12 0.86 0.81 0.92 0.98 0.95 1.20 1.10 1.10 1.10 0.83 0.94 0.94
0.25 4.05 3.05 2.74 -0.49 -6.96 - 1.20 11.08 3.33 10.10 4.12 9.82 8.87 3.06 -2.17 10.02 10.82 7.07
4.60 8.20 7.70 9.10 9.80 8.50 14.70 12.70 14.00 13.90 8.40 11.40 11.00 6.80 -0.20 12.34 14.50 11.74
-3.46 0.25 - 1.03 -0.78 -3.53 - 10.95 -5.57 6.53 - 1.14 5.25 -0.15 6.21 5.26 - 1.22 -6.54 5.27 5.50 2.41
0.90 4.38 3.62 5.52 6.77 4.54 10.32 8.17 9.51 9.03 4.12 7.77 7.40 2.57 -4.57 7.59 9.17 7.09
474
A. S. MEHTA et al.
ture difference from Table 1 to be 30°C across the NCZ, salt concentration difference works out to be 0.12 (kg salt)/(kg solution). Actually, the salt coneentration difference maintained across the NCZ ranges between 0.13 to 0.24 as shown in Table 5. This value is higher than the value obtained by the above criterion. With this much salt difference across the NCZ, the pond bottom temperature should rise to as high as 80°C. As shown in Table 5, this ratio works out in the range 4 to 7.3 x 103 kg salt/(kg solution) K. for the data given in Table 1. These points when plotted do not fall on a smooth curve. Moreover, the pond is also not showing the best performance, and hence based on results given in Table 5 similar criterion for a bittern-based pond cannot be suggested. 4.3 Thermal efficiency of the pond By using eqns (1), (4), (8), and (9) and data given in Table 1, thermal efficiency of the pond is calculated for observed and calculated optimum thickness of NCZ. Results are given in Table 4. If ground heat losses are not considered, then average efficiency works out as 4.69% and with ground heat losses it drops down to 0.13% for the observed NCZ thickness. When the same exercise is repeated for calculated optimum thickness of NCZ, the average thermal efficiency works out as 10.55 and 5.77% without and with ground heat losses, respectively. In both cases, difference between the efficiency of the pond with ground heat loss and without ground heat loss is approximately 4.65, which indicates the extent of heat losses in the ground from LCZ. This value is based on the total insolation falling on the pond surface.
Table 5. Determination of stability of the pond based on the Newell and Boehm criteria [9] Temperature and salt concentration difference across NCZ
Sr. no.
Date
.AT, °C
AC kg salt kg soln
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
Nov. 16-30/83 Dec. 1-15/83 Dec. 16-31/83 Jan. 16-31/84 Oct. 1-15/84 Nov. 16-30/84 Dec. 1-15/84 Jan. 16-31/85 Feb. 1-14/85 Feb. 15-28/85 Mar. 1-15/85 Apr. 1-15/85 Apr. 16-30/85 June 16-30/85 Sept. 1-15/85 Oct. 16-31/85 Nov. 16-30/85 Dec. 16-31/85
25.2 25.5 26.5 24.8 30.0 27.8 28.5 31.7 36.5 40.0 39.7 36.3 36.3 34.0 30.3 41.8 35.8 30.0
0.153 0.163 0.144 0.168 0.130 0.199 0.192 0.203 0.207 0.205 0.202 0.185 0.149 0.170 0.153 0.247 0.220 0.218
AT AC × I0 3 6.07 6.39 5.43 6.77 4.33 7.16 6.74 6.40 5.67 5.13 5.09 5.10 4.10 5.00 5.05 5.91 6.15 7.27
The very low value of thermal efficiency can be explained by the following points: (1) a lesser amount of radiation is reaching the LCZ because of a higher depth of the N C Z - L C Z boundary and higher conduction losses from LCZ to UCZ and (2) poor transparency of the pond. Frequent dust storms are observed during the summer months in the afternoon hours. As a result, a lot of dust falls on the pond surface, which affects the transparency of the pond. As mentioned earlier, this pond was designed to provide I million kcal thermal energy per day at 15% heat collection efficiency. Against this, if the pond is operated under optimum conditions, it will deliver heat only at 5.77% efficiency. 4.4 Temperature profiles in the NCZ So far, heat extraction experiments have not been carried out, and therefore it has not been possible to check the actual efficiency of the pond with the calculated values. As a result, only temperature profiles in the NCZ were correlated with the actual observed performance of the pond. Considering various assumptions made by Kooi and practical limitations in the measurements, especially solar radiation transmission in the pond, the percentage deviation between calculated and observed temperature profile seems tolerable. Zangdrando[16] has shown polynominal curves for temperature and density variations in the NCZ for the pond stability analysis. Kooi has assumed that the density profile in the NCZ should be appropriate to assure stabilities and no specific forms were assumed. According to Kooi's analysis, the temperature gradient becomes zero at a particular depth when efficiency becomes maximum. If the actual thickness of NCZ is less than the optimum value, the temperture gradient shows positive value at the N C Z - L C Z boundary. This is the case for all the observations given in Table 4. If the actual thickness of the NCZ is more than the optimum value of the NCZ, the temperature gradient will still decrease further and will show negative value at the N C Z - L C Z boundary. Sometimes in a monsoon, a negative temperature gradient is observed in the LCZ. This may be because of the rising water table and increased heat losses due to the wet soil. 5. CONCLUSION Thermal performance of the bittern-based solar pond is analyzed baed on two years' observations. A steady state model developed by C. F, Kooi for salt gradient solar pond and modified by J. R. Hull for ground heat loss is used for the analysis. It is observed that thermal energy input and output from the LCZ of the pond are almost equal and hence a steady-state model is applicable to this pond. It has been shown that calculated optimum thickness is more than the observed thickness of NCZ. This observation leads us to state that one of the reasons for not attaining, higher ternperature in the LCZ is the smaller thickness of the
Bittern-based solar pond N C Z . resulting mainly due to instabilities occurring at the U C Z - N C Z boundaries.
Acknowledgments--The authors wish to acknowledge the guidance and encouragement provided by Prof. M. M. Taqui Khan, the Director of Central Salt & Marine Chemicals Research Institute, Bhavnagar.
8. 9. 10.
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16.
475
start up performance of the Miamisburg salt gradient solar pond. J Solar Energy Eng. 103, 11 (1981). C. F. Kooi, The steady state salt gradient solar pond. Solar Energy 23, 37 (1979). T. A. Newell and R. F. Boehm, Gradient zone constraints in a salt stratified solar pond. J. Solar Energy Eng. 104, 280 (1982). V. V. N. Kishore and Veena Joshi, A practical collector efficiency equation for non convecting solar ponds. Solar Energy 33, 391 (1984). J. R. Hull. Solar pond ground heat loss to a moving water table. Solar Energy 35, 211 (1985). J. A. Duffle and W. A. Beckman. Solar Energy Thermal Processes. Chap. 7, Wiley, New York (1974). J. R. Hull, Computer simulation of solar pond thermal behavior. Solar Energy 25, 33 (1980). A. S. Mehta and S. D. Gomkale, Solar Pond at Central Salt and Marine Chemicals Research Institute, Bhavnagar, India. International Solar Pond Letters 1, 21 (1983). A. S. Mehta, K. K. Bokil, S. D. Gomkale, and K. S. Rao, Construction and performance of CSMCRI bittern based pond. Proc. International Symposium Workshop on Renewable Energy Sources, Lahore, Pakistan, March 1983, p. 221. F. Zangrando, Heat and mass extraction from solar pond: Analysis and development of a laboratory facility. Report prepared under task No. 1216.01 WPA No.279 for U.S. Department of Energy, April 1982.
0038-092X/88 $3.00 + .00 Copyright © 1988 Pergamon Press plc
PERFORMANCE ANALYSIS OF A BITTERN-BASED SOLAR POND A. S. MEHTA, N. PATHAK,B. M. SHAH, and S. D. GOMKALE Central Salt & Marine Chemicals Research Institute, Bhavnagar 364 002, India Abstract--An attempt has been made to analyze the performance of the bittern-based solar pond of a 1600-m: area located in Bhavnagar, India (latitude 21°, 45'N and longitude 72°, 12'E). Solar radiation transmission in the pond has been measured with a silicon solar cell module and the results are used in the calculation. Thermal efficiency of the pond is worked out by the correlations proposed by Kooi and Hull. Its value is very very low and reasons for this are discussed in the text. Theoretical temperature profiles in the NCZ and optimum thickness of the NCZ are calculated based on the correlations developed by Kooi. Calculated temperature profiles and observed profiles in NCZ match quite satisfactorily.
Kooi[8] in brief, along with the ground heat loss term as suggested by Hull[l l]. A brief description of the CSMCRI pond is presented in Section 3. Methods adopted to withdraw brine samples, temperature measurement in the pond, and density gradient corrections in the gradient zone are also described. In Section 4 results regarding thermal efficiency of the pond and heat balance calculation are presented and they are discussed with respect to steady-state behavior of the pond, optimum thickness of the gradient zone, and temperature profiles in the pond. In Section 5, conclusions based on the results and discussion are mentioned regarding the behavior of the pond.
1. I N T R O D U C T I O N
Salt gradient solar ponds (SGSP) have attracted worldwide attention after their successful exploitation in Israel for power generation. A good number of solar ponds are constructed all over the world and have been under observation during the last decade. A number of investigators have proposed mathematical models for the SGSP and have carried out simulation studies by assuming ideal conditions[l-5]. Only a few models have been checked with the actual performance data obtained on experimental ponds of moderate size. The lack of experimental confirmation is especially true in the case of bittern-based ponds. A few investigators, based on their practical experience[6,7], have reported that the actual conditions in the pond differ significantly from those predicted in the theoretical analysis whereby the final results, say for example, storage zone temperature and thermal energy stored, are much lower when compared with the theoretical analysis. One such case is the bittern-based solar pond under investigation in Bhavnagar. The main factors responsible for the steady-state behavior of the pond are discussed by C. F. Kooi[8], Newell and Boehm[9] and Kishore and Veena[10]. According to their analysis: (1) the thermal mass of the pond is so large that diurnal temperature variations are normally less than I°C; (2) when the season changes the effective change in pond temperature is immediately observed; (3) at high latitudes, steady state would vary considerably throughout the year, but at low latitudes (as is the case of Bhavnagar) it is likely that a nearly constant steady state could he maintained throughout the year. In short, if environmental conditions do not change very much with time, and pond parameters result in fast response time, pond behavior can be considered safely in a steady state. Actually, the steady-state model is not applicable to most of the ponds and time-varying analysis is required, but it appears that the steady-state model is applicable to CSMCRI pond, as discussed later. Section 2 describes the steady-state model of
2. T H E O R E T I C A L
MODEL
TRANSMISSION
AND RADIATION
IN THE POND
Considering the solar pond, to be similar to the fiat-plate collector, Kooi[8] expressed the efficiency of the solar pond as = F R [aT - (UL A T ~ H ) ]
(1)
where FR is the heat removal factor as defined by Duffle and Beckman[12] and its value is assumed as 0.95. Absorptance transmittance product is defined as
ar =
(x)dx
x2 - xl)
(2)
where H is solar insolation in W / m 2 and h(x) is the fraction of insolation that remains at a depth x. UL is the top loss coefficient expressed as Ut. = k / ( x 2 - x O
(3)
where k is thermal conductivity of pond brine. Xl and x 2 are the depth of upper convecting zone (UCZ), nonconvecting zone (NCZ) boundary, and nonconvecting lower convecting zone (LCZ) boundary from
469
470
A. S. MEHTAet al.
the surface, respectively. A T is the temperature difference between LCZ and UCZ temperature. In eqn (1), Kooi has not considered ground heat loss, whereas H u l l [ l l ] included this term and modified eqn (1) as
sions are available[4,5,8.13] to evaluate h(x). In the present case, solar radiation transmission is measured by silicon solar cell module and the results are correlated by the following expression[8], h(x) = a - b In(x/cos r)
= FR [et "r - (UL A T ~ H ) - (Qo/H)]
where Qb is the heat loss from the bottom of the solar pond. Hull has developed a method to calculate Qb in which ground water movement is also considered. Based on Hull's procedure, Kishore and Veena[10] have suggested the following simple equation to calculate ground heat loss Qt, = Ub (Tb - Tg)
(5)
where a and b are empirical Constants and r is" the refraction angle that depends on the incidence angle of the sun rays and refractive index of the pond brine. Incidence angle is calculated based on the time of measurement of radiation transmission. Refractive index of the pond brine is measured in the laboratory by Abbrs refractometer. It varies from 1.33 to 1.39 depending on the salt concentration and temperature of the brine. In the calculation, an average value of 1.36 has been used.
where Tb and Tg are the pond bottom and underground water temperature, respectively. Ub is the ground heat transfer coefficient defined as Ub = 0.99 [kg/l s] + 0.9kg ( S / A )
(6)
Here, kg is soil thermal conductivity, lg is water table depth, and S and A are the pond bottom perimeter and area, respectively. Differentiating eqn (1) with respect to x2 and setting equal to zero, Kooi obtained the following expression to calculate optimum depth of the N C Z LCZ boundary for maximum efficiency of the pond. f X2h(x) dx - (x~
-
xl) h(x~_) = K A T / H
(7)
I
Substituting eqns (7), (2), and (3) in eqns (1) and (4), the maximum efficiency is defined without considering ground heat loss and with ground heat loss as "q"
= FRh(XT)
(8)
and ~q'~ = FR[h(xT) - (Qb/H)]
(9)
The vertical temperature distribution in the UCZ and LCZ are constant at T(x~) and T(x,), respectively. Integrating a one-dimensional, steady-state heat conduction equation between the limits x~ and x2, the following expression for temperature distribution in NCZ is obtained[8]
~
3. CSMCRI SOLAR POND
The Central Salt and Marine Chemicals Research Institute, Bhavnagar, has constructed a solar pond in the Institute's Experimental Salt Farm, which is 8 km away from the Institute. Details of construction of this pond are available in earlier publications[ 14,15]. The pond was designed to provide 1 million kcal of thermal energy per day at 80°C by assuming 15% heat collection efficiency. The solar pond dimensions are 40 m x 40 m at the surface and 35 m x 35 m at the bottom, and it is 2.3 m deep at the center as shown in Fig. 1. The solar pond was filled up to 1 m depth with sea bittern collected from the experimental salt farm. It contains about 400 g dissolved salts in 1 liter. The rest of the pond was filled up with fresh sea water in April 1981. During the construction of the pond, copper constantan thermocouples were installed at various depths in the ground, side walls of the pond, and in the pond brine to monitor temperature profile in the pond. In 1982, there was a severe cyclonic storm in Bhavnagar and the original thermocouple network was totally destroyed. Later on, temperature measurements were carried out only in pond brine with the help of platinum thermistor sensor attached to a movable support. Temperature measurement was carried out at 2.5, 5.0, and 10.0 cm intervals in the pond brine from the surface to the 1.6 m depth. Pond brine samples were collected by using a graduated scale along with a flexible tube at I0 cm intervals. A vacuum was applied at one end of the tube and a sample was
x
T(x) = ( H / k )
(11)
(4)
"aO,mxaow~
h(x)dx + [T(x2) - T(xO
PONDTOP
,/x I
- (H/k)
h(x)dxl [(x - xO/(x2 - xOl
(10)
2.1 Solar radiation transmission The attenuation function h(x) depends mainly on the transparency of the pond water. Many expres-
WORKING~J PLATFORM ~
~,
'~
~.l[
L/~ N.OPE.LINER .......
ELEVATION Fig. 1. The CSMCRI solar pond.
Bittern-based solar pond first collected in the tube and then transferred to the sampling bottles. M e a s u r e m e n t of brine specific gravity, salinity, pH, turbidity, etc. were carried out in the laboratory. T e m p e r a t u r e and density profiles were monitored twice in a week, whereas other data such as solar insolation, wind velocity, relative humidity, and m a x i m u m m i n i m u m temperature were recorded continuously round the clock. Solar radiation transmission m e a s u r e m e n t was c a r d e d out by solar cell module twice in a week. In order to c o m p e n s a t e evaporation losses and to clean the pond surface, flushing operation was carried out three times in a week through a 7.5 c m diameter and 30 m long perforated pipe. Sea water is p u m p e d from the adjoining creek during high tides, which are not very frequent in a m o n t h , and stored to flush the pond. In the sea water reservoir, sea brine density increased due to evaporation. As a result, less a m o u n t o f sea water of specific gravity less than 1.03 was available for flushing purposes. This imposed the limitation on the extent o f flushing operation and in maintaining density gradient across the NCZ. Regular doses o f copper sulphate and alum were added in the pond brine to m i n i m i z e the algal growth and to settle d o w n the suspended silt from the brine. S o m e t i m e s small intermediate c o n v e c t i v e layers develop in the NCZ. They are modified or corrected by injecting dilute seabrine or dense sea bittern using a 50 c m diameter diffuser fabricated from a 12.5 m m thick P V C sheet. Diffuser slit width is adjusted by Teflon gaskets 1 to 3 m m thick. Sea bittern is also charged in the pond bottom through the diffuser w h e n e v e r bottom layer density decreases below the desired level. Sea bittern is available from the experimental salt farm during April and M a y (the prem o n s o o n months) w h e n there is normally very high wind velocity. Due to high winds, U C Z thickness increases at the cost of N C Z thickness. As a result,
471
pond performance deteriorates in these months. Generally, L C Z density correction is carried out by adding sea bittern during this period. It was expected that in the stabilized pond, the b o t t o m temperature would be around 80°C with 1 m thick L C Z , 1.0 to 1.1 m thick N C Z and 0.2 to 0.3 m thick U C Z . Surprisingly, it was observed that the L C Z temperature has n e v e r exceeded 75°C and the o b s e r v e d variations in thicknesses of three zones are (1) L C Z 0.8 to 1.0 m, (2) N C Z 0.3 to 0.8 m and (3) U C Z 0.2 to 0.8 m.
4. RESULTS AND DISCUSSION Data for the solar pond are g i v e n in Tables 1 and 2 as fortnightly average values for a period of two years. Calculated and o b s e r v e d temperature profiles in the pond are s h o w n in Fig. 2. The percentage deviation between the calculated and observed temperature profile in N C Z is about 8 to 10%. This indicates the extent up to w h i c h the theoretical model can fit experimental data o f a moderate size pond.
4.1 Steady-state behavior o f the pond F r o m the data given in Table 1, one can see that the pond temperature continuously increased from N o v e m b e r 16 to 30, 1984 to M a r c h 1985. A separate heat balance calculation has been worked out for the L C Z for this period and results are given in Table 3. For the heat balance calculation the ground temperature data are not available and hence water sink temperature is considered as pond surface temperature. A b o u t three years back, a bore well was dug half a kilometer away from the pond site and at that time the water table depth was recorded as l 0 m. This value has been used as a depth of water sink from the pond bottom. Based on the rise in temperature of LCZ, thermal energy stored in it is calculated. Prod-
Table 1. Solar pond performance data Temperature,°C Date
S t . no. I.
NOV.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
Dec. Dec. Jan. Oct. Nov. Dec. Jan. Feb. Feb. Mar.
Apr. Apr. June Sept. Oct. Nov. Dec.
16-30/83 1-15/83 16-31/83 16-31/84 1-15/84 16- 30/84 1-15/84 16-31/85 1-14/85 15-28/85 1-15/85 1-15/85 6-30/85 16-30/85 1-15/85 16-31/85 16-30/85 16-31/85
Thickness, m
Specific Gravity
Insolation H w/m:
UCZ
LCZ
UCZ
NCZ
Ti
T2
x~
x2 - xt
UCZ Pl
LCZ P_-
201 197 193 211 272 205 194 207 243 246 278 302 298 238 206 260 199 190
23.3 19.5 19.3 21.5 37.0 20.0 22.8 20.3 20.0 22.0 26.0 29.5 27.5 28.5 29.5 27.2 22.8 23.1
48.5 45.0 45.8 46.3 67.0 47.8 51.3 52.0 56.5 62.0 65.7 65.8 63.8 62.5 59.8 69.0 58.6 53.1
0.50 0.50 0.50 0.60 0.60 0.20 0.23 0.28 0.30 0.30 0.35 0.27 0.45 0.77 0.70 0.24 0.25 0.30
0.42 0.50 0.50 0.40 0.55 0.40 0.52 0.53 0.55 0.50 0.60 0.53 0.70 0.53 0.63 0.51 0.50 0.45
1.063 1.064 1.064 1.053 1. 100 1.060 1.063 1.063 1.057 1.058 1.060 1.071 1.095 1.090 1.103 1.029 1.050 1.047
1.184 1.196 1.179 1.888 1.237 1. 229 1.221 1.239 1.238 1.236 1.233 1.232 1.223 1.250 1.249 1.245 1.245 1.234
A. S. MEHTA et
472
Table 2. Values of empirical constants a and b based on the solar radiation transmission data correlated by the expression h(x) = a - b In (x/cos r) along with the correlation coefficient based on regression analysis a
b
Correlation coefficient
0.1123 0.1554 0.1545 0.1725 0.1785 0.1425 0.1695 0.1523 0.1825 0.1895 0.1335 0.1635 0.1675 0.1985 0.1145 0.1435 0.1863 0.1625
0.1938 0.1383 0.1383 0.1392 0.2034 0.1900 0.1730 0.2120 0.1778 0.1762 0.1720 0.1134 0.1178 0.2020 0.1980 0.2010 0.1942 0.1808
0.9988 0.9895 0.9868 0.9925 0.9875 0.9835 0.9915 0.9905 0.9875 0.9939 0.9962 0.9985 0.9897 0.9912 0.9968 0.9925 0.9969 0.9943
Date Nov. Dec. Dec. Jan. Oct. Nov. Dec. Jan. Feb. Feb. Mar. Apr. Apr. June Sept. Oct. Nov. Dec.
16-30/83 1-15/83 16-31/83 16-31/84 1-15/84 16-30/84 1-15/84 16-31/85 1-14/85 15-28/85 1-15/85 1-15/85 16-30/85 16-30/85 1-15/85 16-31/85 16-30/85 16-31/85
al.
uct of specific gravity and specific heat of bittern is taken as 0.98. The average thickness o f L C Z works out to be 1.5 m and equivalent v o l u m e of L C Z is 1334 m 3. Average pond area is a s s u m e d to be 1400 m 2 for the calculation o f conduction heat losses from L C Z to U C Z and a m o u n t o f radiation reaching in the LCZ. Soil and brine thermal conductivity used in the calculation are 1.00 and 0 . 6 0 W / m . C ° respectively. F r o m the results given in Table 3, the following observations can be made on the behavior of the pond. (1) Considering field conditions and various assumptions made in the calculation, deviation in heat balance is comparatively low. (2) A b o u t 75 to 80% of the insolation reaching the L C Z is lost as conduction heat loss from L C Z to UCZ. Ground heat loss is about 10 to 12% and actual gain in thermal energy of L C Z is negligible. (3) U n d e r the present conditions, input and output of thermal energy is almost of the same magnitude. Hence, even though heat extraction experiments are not carried out, the pond can be safely considered in a steady state. (4) T h e main reason for large conduction loss from L C Z to U C Z m a y be the
0 0.5
0.5 i
Cm
h
1.0
II
1.5 2.0 0
1"0f 1.5
1
I
25
35
II
II
L5
5'5
2.0
15
o 18-30/11,}84 , 16-31/1,}85 A 1G-28/2,~85 i
25
3'5
, 55
,
45
~0.5
,.E =
1.0
o I iiJ:iiiiil '
,1
lo1_
1,5
2.0
/
20
30
40
50
20
60
0.5
30
t,lO
510
60
0.5-
1.0
1'0
o 16-30/6,/85
Ill 2.0
25
J 35
,
45
l
55
I.
65
2.0
25
~
35
~
45
T EMPERATURE'C
Fig. 2. Temperature profiles of the CSMCRI solar pond.
i
55
, ,,
65
Bittern-based solar pond
473
Table 3. Heat balance across LCZ of the pond q is in w / m 2 Sr. no.
Date
q,
qb
q~
qc
Qr
Percentage Deviation
1. 2. 3. 4. 5. 6.
Nov. 16--30/84 Dec. 1-15/84 Jan. 16-31/85 Feb. 1-14/85 Feb. 15-28/85 Mar. 1-15/85
37.9 40.3 41.3 54.0 56.3 47.8
5.61 5.75 6.40 7.36 8.07 8.01
-0.011 0.002 0.013 0.017 0.011
41.7 32.9 35.9 39.8 48.0 39.7
-38.7 42.3 47.2 56.1 47.7
-÷ 3.97 - 2.42 -'- 12.59 + 0.35 ÷ 0.21
q~ = heat input in the LCZ. qb = heat loss to the ground. q~ = heat gain in the LCZ. qc = heat loss through conduction from LCZ to UCZ. Qr = qb + qg + qc. large temperature gradient across the N C Z because o f a thin NCZ. If the thickness o f N C Z is 1 m, the conduction loss will c o m e d o w n to 30 to 35% o f the heat stored in the LCZ. (5) One o f the reasons for the small N C Z thickness is fluctuation in the U C Z N C Z boundary. In this pond, large U C Z up to 80 c m thick are observed because o f high wind velocity. 4.2 O p t i m u m t h i c k n e s s o f t h e N C Z An attempt has been made to calculate the optim u m thickness o f the N C Z based on the observed performance o f the pond and eqn (7). Results o f Ihe calculation are presented in Table 4. It can be seen from Table 4 that in each case o p t i m u m thickness is more than the observed value o f the NCZ. Percentage deviation varies b e t w e e n 34 to 64. Out o f 18 sets o f observations in 8 sets, percentage deviation is more than 50% between the calculated NCZ and observed value o f NCZ. Moreover, calculated optimum thickness o f N C Z for all the sets o f observation s h o w s that it should be about 1 m in order to obtain m a x i m u m
efficiency in the pond under the observed conditions. This tallies with the thickness o f NCZ suggested by various investigators. It may be mentioned here that during s u m m e r period, when UCZ increases up to 0.70 m, it is difficult to maintain a 1 m thick NCZ. Suppose the NCZ is maintained at 1.1 m thickness (e.g., Sr. No. 13 and 14 o f Table 4), the N C Z - L C Z boundary will start at 1.8 m depth from the surface. At this depth, the amount o f radiation reaching the boundary will be very low and hence it will affect the pond performance in a reverse way. In the winter months (i.e., N o v e m b e r to March), U C Z thickness can be maintained less than 0.30 m by using wave breakers. But in the s u m m e r months (i.e., April to September), it is difficult to maintain a UCZ thickness even around 0.40 m. A simple criterion by Newell and Boehm[9] shows that one needs to maintain a ratio o f N C Z salt difference to temperature difference greater than 3.9 × l03 (kg salt)/(kg solution K) for sodium chloride ponds. Using this criterion and estimating tempera-
Table 4. Calculated and observed thickness of NCZ in the pond. Thermal efficiency of the pond without considering ground heat loss and with the ground heat loss Thermal efficiency of the pond%
Sr. no.
Observed thickness of NCZ meter (x2 - x,)
Calculated thickness of NCZ meter (x~ - x,)
Without ground heat loss
With ground heat loss
Observed x2
Optimum x7
Observed x2
Optimum .~
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
0.42 0.50 0.50 0.40 0.55 0.40 0.52 0.53 0.55 0.50 0.60 0.53 0.70 0.53 0.65 0.51 0.50 0.45
0.89 1.15 1.20 1.14 0.85 1.12 0.86 0.81 0.92 0.98 0.95 1.20 1.10 1.10 1.10 0.83 0.94 0.94
0.25 4.05 3.05 2.74 -0.49 -6.96 - 1.20 11.08 3.33 10.10 4.12 9.82 8.87 3.06 -2.17 10.02 10.82 7.07
4.60 8.20 7.70 9.10 9.80 8.50 14.70 12.70 14.00 13.90 8.40 11.40 11.00 6.80 -0.20 12.34 14.50 11.74
-3.46 0.25 - 1.03 -0.78 -3.53 - 10.95 -5.57 6.53 - 1.14 5.25 -0.15 6.21 5.26 - 1.22 -6.54 5.27 5.50 2.41
0.90 4.38 3.62 5.52 6.77 4.54 10.32 8.17 9.51 9.03 4.12 7.77 7.40 2.57 -4.57 7.59 9.17 7.09
474
A. S. MEHTA et al.
ture difference from Table 1 to be 30°C across the NCZ, salt concentration difference works out to be 0.12 (kg salt)/(kg solution). Actually, the salt coneentration difference maintained across the NCZ ranges between 0.13 to 0.24 as shown in Table 5. This value is higher than the value obtained by the above criterion. With this much salt difference across the NCZ, the pond bottom temperature should rise to as high as 80°C. As shown in Table 5, this ratio works out in the range 4 to 7.3 x 103 kg salt/(kg solution) K. for the data given in Table 1. These points when plotted do not fall on a smooth curve. Moreover, the pond is also not showing the best performance, and hence based on results given in Table 5 similar criterion for a bittern-based pond cannot be suggested. 4.3 Thermal efficiency of the pond By using eqns (1), (4), (8), and (9) and data given in Table 1, thermal efficiency of the pond is calculated for observed and calculated optimum thickness of NCZ. Results are given in Table 4. If ground heat losses are not considered, then average efficiency works out as 4.69% and with ground heat losses it drops down to 0.13% for the observed NCZ thickness. When the same exercise is repeated for calculated optimum thickness of NCZ, the average thermal efficiency works out as 10.55 and 5.77% without and with ground heat losses, respectively. In both cases, difference between the efficiency of the pond with ground heat loss and without ground heat loss is approximately 4.65, which indicates the extent of heat losses in the ground from LCZ. This value is based on the total insolation falling on the pond surface.
Table 5. Determination of stability of the pond based on the Newell and Boehm criteria [9] Temperature and salt concentration difference across NCZ
Sr. no.
Date
.AT, °C
AC kg salt kg soln
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
Nov. 16-30/83 Dec. 1-15/83 Dec. 16-31/83 Jan. 16-31/84 Oct. 1-15/84 Nov. 16-30/84 Dec. 1-15/84 Jan. 16-31/85 Feb. 1-14/85 Feb. 15-28/85 Mar. 1-15/85 Apr. 1-15/85 Apr. 16-30/85 June 16-30/85 Sept. 1-15/85 Oct. 16-31/85 Nov. 16-30/85 Dec. 16-31/85
25.2 25.5 26.5 24.8 30.0 27.8 28.5 31.7 36.5 40.0 39.7 36.3 36.3 34.0 30.3 41.8 35.8 30.0
0.153 0.163 0.144 0.168 0.130 0.199 0.192 0.203 0.207 0.205 0.202 0.185 0.149 0.170 0.153 0.247 0.220 0.218
AT AC × I0 3 6.07 6.39 5.43 6.77 4.33 7.16 6.74 6.40 5.67 5.13 5.09 5.10 4.10 5.00 5.05 5.91 6.15 7.27
The very low value of thermal efficiency can be explained by the following points: (1) a lesser amount of radiation is reaching the LCZ because of a higher depth of the N C Z - L C Z boundary and higher conduction losses from LCZ to UCZ and (2) poor transparency of the pond. Frequent dust storms are observed during the summer months in the afternoon hours. As a result, a lot of dust falls on the pond surface, which affects the transparency of the pond. As mentioned earlier, this pond was designed to provide I million kcal thermal energy per day at 15% heat collection efficiency. Against this, if the pond is operated under optimum conditions, it will deliver heat only at 5.77% efficiency. 4.4 Temperature profiles in the NCZ So far, heat extraction experiments have not been carried out, and therefore it has not been possible to check the actual efficiency of the pond with the calculated values. As a result, only temperature profiles in the NCZ were correlated with the actual observed performance of the pond. Considering various assumptions made by Kooi and practical limitations in the measurements, especially solar radiation transmission in the pond, the percentage deviation between calculated and observed temperature profile seems tolerable. Zangdrando[16] has shown polynominal curves for temperature and density variations in the NCZ for the pond stability analysis. Kooi has assumed that the density profile in the NCZ should be appropriate to assure stabilities and no specific forms were assumed. According to Kooi's analysis, the temperature gradient becomes zero at a particular depth when efficiency becomes maximum. If the actual thickness of NCZ is less than the optimum value, the temperture gradient shows positive value at the N C Z - L C Z boundary. This is the case for all the observations given in Table 4. If the actual thickness of the NCZ is more than the optimum value of the NCZ, the temperature gradient will still decrease further and will show negative value at the N C Z - L C Z boundary. Sometimes in a monsoon, a negative temperature gradient is observed in the LCZ. This may be because of the rising water table and increased heat losses due to the wet soil. 5. CONCLUSION Thermal performance of the bittern-based solar pond is analyzed baed on two years' observations. A steady state model developed by C. F, Kooi for salt gradient solar pond and modified by J. R. Hull for ground heat loss is used for the analysis. It is observed that thermal energy input and output from the LCZ of the pond are almost equal and hence a steady-state model is applicable to this pond. It has been shown that calculated optimum thickness is more than the observed thickness of NCZ. This observation leads us to state that one of the reasons for not attaining, higher ternperature in the LCZ is the smaller thickness of the
Bittern-based solar pond N C Z . resulting mainly due to instabilities occurring at the U C Z - N C Z boundaries.
Acknowledgments--The authors wish to acknowledge the guidance and encouragement provided by Prof. M. M. Taqui Khan, the Director of Central Salt & Marine Chemicals Research Institute, Bhavnagar.
8. 9. 10.
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