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Numerical and experimental analysis of a salt gradient solar pond performance with or without reflective covered surface
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APPLIED ENERGY Applied Energy 85 (2008) 1102–1112 www.elsevier.com/locate/apenergy
Numerical and experimental analysis of a salt gradient solar pond performance with or without reflective covered surface ¨ zek a Nalan C ¸ . Bezir a, Orhan Do¨nmez b, Refik Kayali b,*, Nuri O a
Department of Physics, Faculty of Art and Science, Su¨leyman Demirel University, 32260 Isparta, Turkey b Department of Physics, Faculty of Art and Science, Nig˘de University, 51200 Nig˘de, Turkey Received 21 September 2007; received in revised form 21 February 2008; accepted 21 February 2008 Available online 3 April 2008
Abstract An experimental salt gradient solar pond having a surface area of 3.5 3.5 m2 and depth of 2 m has been built. Two covers, which are collapsible, have been used for reducing the thermal energy loses from the surface of the solar pond during the night and increasing the thermal efficiency of the pond solar energy harvesting during daytime. These covers having reflective properties can be rotated between 0° and 180° by an electric motor and they can be fixed at any angle automatically. A mathematical formulation which calculates the amount of the solar energy harvested by the covers has been developed and it is adapted into a mathematical model capable of giving the temporal temperature variation at any point inside or outside the pond at any time. From these calculations, hourly air and daily soil temperature values calculated from analytical functions are used. These analytic functions are derived by using the average hourly and daily temperature values for air and soil data obtained from the local meteorological station in Isparta region. The computational modeling has been carried out for the determination of the performance of insulated and uninsulated solar ponds having different sizes with or without covers and reflectors. Reflectors increase the performance of the solar ponds by about 25%. Finally, this model has been employed for the prediction of temperature variations of an experimental salt gradient solar pond. Numerical results are in good agreement with the experiments. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Solar pond; Analytical function; Daily and hourly temperatures; Performance; Reflector
1. Introduction A salt-gradient solar pond (SGSP) which consists of three distinct zones: an upper convecting zone (UCZ), a non-convecting zone (NCZ), and a lower convecting zone (LCZ), is an inexpensive solar energy collection and storage system for low-temperature heat-sources. The concept of the solar pond appears very simple:
*
Corresponding author. Tel.: +90 388 2252152. E-mail address: refi[email protected] (R. Kayali).
0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.02.015
N.C¸. Bezir et al. / Applied Energy 85 (2008) 1102–1112
1103
Nomenclature
Z1Y1 Z2Y2 M1L1 C SM1 a G1
pond area, m2 amount of solar energy falling on one-meter square area perpendicular to the incident light per unit time on LHS reflector amount of solar energy falling on one-meter square area perpendicular to the incident light per unit time on RHS reflector term representing time lower convective zone day number non-convective zone the hourly air temperature at any time of the day of the year upper convective zone thickness of the first layer, m distance between the pond surface and the top layer of the storage region, m distance between the pond surface and bottom of the storage region, m the amount of solar energy which will fall on one meter square area of the solar pond per unit time incoming from LHS reflector the amount of solar energy which will fall on one meter square area of the solar pond per unit time incoming from RHS reflector front side of the projection area of LHS reflector normal to the incident light front side of the projection area of RHS reflector normal to the incident light the side length of the first reflector the angle between Z1Y1 and the reflector at any time and M1L1 projection area of the reflector normal to the incident light the length of one side of the pond or the length of the reflector the amount of the solar energy which will be reflected by the reflector into the solar pond
Greek b1 b2
angles with horizontal of first cover angles with horizontal of second cover
A B1 B2 K LCZ n NCZ TSH UCZ X1 X2 X3 U1 U2
a body of water harvests the incident solar energy and stores it for a long period of time. This long-term store provides an alternative for conventional energy-source [1–3]. Solar ponds have been studied by many researchers because of their excellent heat collection and storage performances. There have been considerable theoretical and experimental studies [4–8] on SGSPs. Many experimental solar ponds [9–18] have been constructed, instrumented and operated, and various numerical models [19–30] have been developed for analyzing SGSP performance in the literature. Theoretical studies have concentrated on modeling and predicting solar pond performance. Early studies of these types of works [31–33] were performed on one-dimensional models that did not account in a detailed way for the dynamical thermal interactions between the solar pond and the surrounding soil. Later researchers [34,35] developed more detailed models which account for the two-dimensional interactions within the soil. Recently, studies on non-stable solar ponds have appeared [6,36]. Kanayama et al. considered a cylindrical solar pond, 44 m in diameter. They used average hourly values of the horizontal solar radiation, and represented the monthly average temperature variation by a sine curve evaluated from the monthly average ambient temperatures in their simulations. Kayali et al. have developed empirical functions for air and soil temperatures obtained from meteorological data and used them for the calculations of the temperature variations in a rectangular type of solar pond [37,38]. Hawladar [39] did similar studies on the performance of the solar ponds operating at different latitudes and under different physical and operational conditions and used
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hourly ambient temperatures obtained from meteorology stations in his simulations. He also described the influence of the extinction coefficient on the effectiveness of solar ponds in his other study [40]. This paper reports the summary of the results of the numerical modeling developed for a salt gradient solar pond having covers used for preventing heat loss and reflecting the sun light into solar pond and how these covers affect performance of the solar pond. An experimental salt gradient solar pond with a surface area of 3.5 3.5 m2 and depth of 2 m has been built for supplying hot water to a leather workshop on the campus area of the Vocational College of Isparta/Yalvacß. A cover system for the surface of the pond was designed and used firstly to reduce the thermal energy loses from the top to air during night-time and to increase the thermal efficiency of solar energy harvesting during daytime. Simulations have been carried out using the mathematical formulation, which calculates the amount of the solar energy harvested by the covers, adapted into the model developed in [37] to see the affect of the covers on the performance of the solar pond. In order to get the best performance from the covers, one of them is kept at a fixed position and the other is rotated it from 0° to 180° to following the sun. This system is controlled by an electric motor and these covers have insulation and reflection properties. Analytical soil and air temperature functions used in the theoretical model simulations were developed using meteorological data obtained from the local meteorological station of Isparta region. Results obtained from theoretical and experimental studies showed that these kinds of salt gradient solar ponds can be used as a source for the warm water required at a leather workshop and for domestic applications. It was also found that covers have little effect on thermal losses during nights, but they are very effective for increasing the daytime harvesting performance. 2. Theory and experiment 2.1. Formulation of the air temperature function In theoretical model simulations, variable air temperature values are obtained from analytical functions. To obtain the analytic function which gives the temperature corresponding to any day of the year and any hour of that day, firstly the average air temperature of each day of each year was calculated and the average values of these values corresponding to six years were obtained using the data taken from measurements at the local Isparta meteorological station. Then plotting these values, the curve shown in Fig. 1 was obtained and another continuous curve was fitted to it. Fitting this curve yielded the following expression for the average air temperature T SH1 of the nth day of the year
30
measured calculated
25
Air temperature (ºC)
20 15 10 5 0 0 -5
30
60
90 120 150 180 210 240 270 300 330 360 Days
Fig. 1. The curve obtained using the measured daily average air temperatures.
N.C¸. Bezir et al. / Applied Energy 85 (2008) 1102–1112
T SH1 ¼ 19 þ 8 sin
1105
360 n 103 365
ð1Þ
This equation gives only the average values, but the ambient temperature changes hour by hour. To overcome this problem, the maximum and minimum deviations from these daily average temperatures resulting from the difference between day and night were found. These calculated deviations were found to be within ±5 °C for each day of the year. Thus, a suitable equation giving the hourly air temperature deviations T SH2 from the daily average temperature is 360 T SH2 ¼ 5 sin t ð2Þ 24 where t is any hour of the day varying from 1 to 24. Combining Eqs. (1) and (2) a general equation for the hourly air temperature TSH at any hour of any day of the year is obtained: 360 360 T SH ðn; tÞ ¼ 19 þ 8 sin n 103 þ 5 sin t ð3Þ 365 24 2.2. Formulation of soil temperature functions A similar procedure, applied to obtain the analytical function which gives the air temperature, was also followed to derive an expression giving the average daily soil temperature at any depth and any day of the year. For this purpose the daily average soil temperatures obtained from the local meteorological station were used. The curves obtained as mentioned above for different depths were used to obtain the expressions for the average temperature of the soil at any day of the year. These fitted curves defined by cosine functions are given in Table 1. As an example, the curve obtained using the measured daily average soil temperatures at 10 cm corresponding different days of the year and the fitted curve to these values are shown in Fig. 2. Similar fits were employed for the other soil temperatures corresponding to the other depths. 2.3. Experimental solar pond and mathematical modeling An experimental salt gradient solar pond with a surface area of 3.5 3.5 m2 and depth of 2 m has been built for supplying hot water to a leather workshop on the campus area of Vocational College of Isparta/Yalvacß. The thickness of the concrete walls and bottom are 0.2 m. The thicknesses of the NCZ and the LCZ are 1.4 m and 0.5 m, respectively. Salty layers were formed by pouring the salt solution prepared with a required amount of salt (NaCl) on a floating wood plate on the layer formed before. The solar pond began to operate after establishing the salt gradient. The stability of the salt gradient is provided by a salt gradient preventing system, explained in Ref. [37]. Temperature variations in the inside and outside of the solar pond at different points were recorded continuously by means of thermocouples associated with a computer system.
Table 1 Equations for the average daily soil temperature at different depths Depth (cm)
Equation
10 20 30 40 50 60 70 80 90 100
T = 22 + 12cos (0.98n + 161) T = 22 + 12cos (0.98n + 161) T = 22 + 11cos (1.170n + 140) T = 22 + 11cos (0.91n + 158) T = 22 + 10cos (0.91n + 158) T = 22 + 10.2cos (0.91n + 164) T = 22 + 10.2cos (0.91n + 164) T = 22 + 10.6cos (0.91n + 153) T = 22 + 10.6cos (0.91n + 153) T = 22 + 9.4cos (0.98n + 142)
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35
calculated
Soil temperature (ºC)
30 25 20 15 10 5 0 0
40
80
120
-5
160 200 Days
240
280
320
360
Fig. 2. The curve obtained using the measured daily average soil temperatures at 10 cm corresponding to different days of the year and the fitted curve.
Fig. 3. Schematic model of the solar pond.
A solar pond model is shown in Fig. 3 [37]. According to this model the solar pond is divided into two regions. The first region consists of the pond itself, plus the soil within a certain thickness under it. The second region is the soil which surrounds the first region. To apply the finite difference method, the first region where the temperature varies only with depth and time, is divided into I number of layers having the equal thicknesses of Dx. However the situation in the second region is more complex than in the first region. There is no mass transfer horizontal in this region. Hence temperature varies horizontally and with the depth at the same time. Therefore, the second region has been divided into I layers of thickness Dx and J columns, each of width Dy. Furthermore, the temperature in both region is also a function of time. So the time parameter has been expressed as a third variable indexed by K. As a non-homogeneous system, the pond is analyzed most simply by writing heat balances in individual elements within each zone and a computer simulation model has been developed by Kayali [38].
2.4. Formulation of cover system used as a reflector For overcoming heat loss due to heat transfer from the surface of the solar pond to the atmosphere during nights and also for increasing the solar energy harnessing area during days, a surface cover system as shown in Fig. 4 was designed and used. It consists of two parts which can be collapsible by means of an electrical con-
N.C¸. Bezir et al. / Applied Energy 85 (2008) 1102–1112
B1 Z1 M1
B1
1107
Incident Beam
B1
Y2
C
θ i1 θ r1
First Cover (LHS)
α
D
Y1
θr2
γ2
β1
B2
Fi
O1 L1
UCZ
β2
O2
α
θi2
B2
B2
Z2 M2
Second Cover (RHS)
L2
a NCZ
LCZ
Fig. 4. Schematic diagram of the reflectors.
trolled driving system. They act as an insulator and as a reflector. In this section, a mathematical formulation of this system will be given. For calculating the amount of the sun light energy which is reflected by the reflectors, a mathematical formulation was carried out. In the derivation of the equations, the model seen in Fig. 4 was used. As seen from this figure, cover1 (LHS reflector) and cover2 (RHS reflector) make b1 and b2 angles with horizontal, respectively, and these two angles are the adjustable angles. In this model, the reflectors were considered as two different light sources. a is the angle between the horizontal surface and the incident light arriving at any hour of any day of the year. To obtain the expression which gives the amount of the solar energy which will be reflected by the first reflector, the following procedure is followed; to find the amount of the solar energy incident on the surface of this reflector, the front side of the projected area of the reflector normal to the incident light Z1Y1 is given by Z 1 Y 1 ¼ M 1 L1 cos C
ð4Þ
where C is the angle between Z1Y1 and the reflector and it is a function of time. M1L1 is the side length of the reflector. C is given by C ¼ 90 ½180 a b1 ¼ 90 180 þ a þ b1 ¼ 90 þ a þ b1
ð5Þ
Substituting C in Eq. (4), the length of Z1Y1 in the triangle, Z1Y1O1, is Z 1 Y 1 ¼ M 1 L1 cosð90 þ a þ b1 Þ
ð6Þ
The projection area of the reflector normal to the incident light, SM1, is SM 1 ¼ Z 1 Y 1 a
ð7Þ
where a is the length of one side of the pond or the length of the reflector. Substituting the value of Z1Y1 given in Eq. (6) into Eq. (7), SM1 is SM 1 ¼ M 1 L1 cosð90 þ a þ b1 Þ a The amount of the solar energy which will be reflected by the first reflector into the solar pond is
ð8Þ
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G1 ¼ SM 1 B1
ð9Þ
where B1 is amount of the solar energy falling on one-meter square area perpendicular to the incident light per unit time and it is equal to B2. The amount of the solar energy which will fall on one-meter square area of the solar pond in per unit time, U1, is obtained using G1 U 1 ¼ G1 =a2
ð10Þ
U 1 ¼ M 1 L1 cosð90 þ a þ b1 Þ B1 =a
ð11Þ
or
Following the similar way an expression which will give the amount of the energy to be reflected from the other reflector, U2, is U 2 ¼ M 1 L1 cosð90 a þ b2 Þ B1 =a
ð12Þ
where M1L1 is equal to M2L2. In the computational modeling, it is necessary to know the angles between the light beams coming from reflectors and the normal of the surface of the solar pond. These angles were denoted by c1 and c2, respectively, and their expressions have been obtained using the geometry of the system shown in Fig. 4 in terms of a, b1 and b2 c1 ¼ 90 þ a 2b1
ð13Þ
c2 ¼ 270 2b2 a
ð14Þ
and
These equations have been used in the theoretical model calculations. In order to model the solar pond with covers, numerical solution of the equations, defining how much energy is incoming from reflectors to the pond surface, is implemented to our existing code [37,38]. 3. Results and discussion In this section, the results obtained from the model and experiment will be discussed and compared with each other, and then the effects of the various parameters will be examined. To see the effect of pond size on the performance of the solar pond, model simulations have been carried out using the thermal parameters
Fig. 5. Comparisons of the temperature distributions in the storage region of the solar pond without covers, only covers, and covers and reflectors (b1 = 30° and b2 = 89°).
N.C¸. Bezir et al. / Applied Energy 85 (2008) 1102–1112
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of the solar ponds whose depth, storage region depth and height of the NCZ are 2.5 m, 1 m and 1.4 m, respectively. To see the effect of reflectors and covers on the performance of the solar ponds, the model solar pond started to operate on the 1st of January for 360 days. In these calculations, the analytical functions derived for air and soil temperatures mentioned above were used in our code. Only the temperature of water in the solar pond and the concrete bottom under the LCZ are taken as 15 °C. Fig. 5 shows the comparisons of the temperature distributions in the storage region of solar pond having no covers, only covers, or covers and reflectors (b1 = 30° and b2 = 89°). The effect of the covers is very small when they are used as covers for closing the surface of the solar pond at nights. In this case, the average temperature difference between solar pond having no cover and having cover is 1 °C. This is due to the sufficiently large thickness of the NCZ. Covers would become more effective for small NCZ thicknesses. On the other hand, the average tem-
Fig. 6. Annual temperature variations in the LCZ when the RHS reflector is kept at fixed angle 89° and the LHS reflector is changed from 30° to 80° with 10° intervals.
Fig. 7. Annual temperature distributions in the LCZ when LHS reflector is kept at a fixed angle 30° and RHS reflector is changed from 20° to 80° with 10° intervals.
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perature difference the between solar pond having a cover and a reflector is about 10 °C. This means that reflectors play a vital role on the performance of solar ponds contributing to harvesting much more solar energy and increasing the energy harvesting area. To see the effect of the reflectors depending on their positions, simulations have been carried out in two different ways. Firstly, the angle between the horizontal axes and RHS reflector was kept at 89° and the angle between the horizontal axes and LHS reflector was changed from 30° to 80° with 10° intervals. As seen from Fig. 6, the performance of the solar pond reaches a maximum and a minimum when the angles are 30–89° and at 80–89°, respectively. A similar simulation is carried out keeping the LHS reflector at a fixed 30° angle and changing the angle of RHS reflector from 20° to 80° with 10° intervals. As seen from Fig. 7, maximum and minimum performances of the solar pond occur when the angles are at 30–80° and at 30–20°, respectively. An important result is obtained if these two results are compared with each other. While the temperature of the LCZ corresponding to the first condition changing from 58 °C to (63–4) °C it changes 50 °C to (62–3) °C for the second condition.
Fig. 8. Annually temperature distributions in the LCZ of the solar pond having different sizes (b1 = 30° and b2 = 89°).
Fig. 9. Comparison of numerical and experimental temperature variations of the LCZ of the solar pond vs. days.
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1111
56
Temperature (ºC)
51 46 41 36 31 26 21 6
8
28.05.2001 07.06.2001 13.08.2001 Theoretical values
10 Layers
12
14
28.05.2001 01.07.2001 13.08.2001
07.06.2001 01.07.2001 Experiment
Fig. 10. Theoretical and experimental temperature variations at different layers in the NCZ with cover corresponding to different dates.
Fig. 8 depicts the annual temperature variations in the LCZ of the solar ponds having different sizes. As seen from this figure, the performance of the solar pond increases with the increasing size. The reason is that the heat loss rate per unit area from the walls and bottom of the solar pond decreases with increase in the size. Experimental and theoretical results will be given for the experimental solar pond having no covers and reflectors. Fig. 9 shows the comparison of numerical and experimental temperature variations of the LCZ of the experimental solar pond having no cover and reflector. As seen from this figure, the average value of experimental results is in a good agreement with the numerical results. Comparisons of theoretical and experimental temperature variations in different layers of solar pond starting to operate on 28.05.2001 for different dates are seen in Fig. 10. As seen from this figure, the experimental expectation has similar behavior with the numerical one. 4. Conclusion The mathematical model developed by Refs. [37] and [38] is modified and supplemented with additional subroutines in order to simulate how the performance of the solar pond is affected by covers. Analytical functions derived for air and soil temperatures using the local meteorological data were used in simulations and the parameters effecting on the solar ponds were determined. It was found that a cover affects little the performance of the solar pond when it is used only as a cover during nights; this is due to the small height of the NCZ (1.4 m). However, covers are very effective when they are used as reflectors. The temperature of the LCZ in the solar pond increases by about 25% when compared with the uncovered case. It can be concluded that the best performance of the pond can be achieved when the covers are employed as reflectors. The performance of the solar pond increases very much with increasing solar pond size; this is due to the decrease in the heat loss from the side walls falling per unit area of the solar pond. Experimental and theoretical model results, obtained for the solar pond without a cover, are in a good agreement with each other. The demonstration of the value of the theoretical modeling of solar pond will be crucial in deciding the future course of experiments and technology development. A more detailed study of comparison of the results obtained from experiments and the theoretical model will be presented in a forthcoming paper for the covers used as a reflectors. References [1] Zangrando F. On the hydrodynamics of salt-gradient solar ponds. Sol Energy 1991;46:6–323.
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APPLIED ENERGY Applied Energy 85 (2008) 1102–1112 www.elsevier.com/locate/apenergy
Numerical and experimental analysis of a salt gradient solar pond performance with or without reflective covered surface ¨ zek a Nalan C ¸ . Bezir a, Orhan Do¨nmez b, Refik Kayali b,*, Nuri O a
Department of Physics, Faculty of Art and Science, Su¨leyman Demirel University, 32260 Isparta, Turkey b Department of Physics, Faculty of Art and Science, Nig˘de University, 51200 Nig˘de, Turkey Received 21 September 2007; received in revised form 21 February 2008; accepted 21 February 2008 Available online 3 April 2008
Abstract An experimental salt gradient solar pond having a surface area of 3.5 3.5 m2 and depth of 2 m has been built. Two covers, which are collapsible, have been used for reducing the thermal energy loses from the surface of the solar pond during the night and increasing the thermal efficiency of the pond solar energy harvesting during daytime. These covers having reflective properties can be rotated between 0° and 180° by an electric motor and they can be fixed at any angle automatically. A mathematical formulation which calculates the amount of the solar energy harvested by the covers has been developed and it is adapted into a mathematical model capable of giving the temporal temperature variation at any point inside or outside the pond at any time. From these calculations, hourly air and daily soil temperature values calculated from analytical functions are used. These analytic functions are derived by using the average hourly and daily temperature values for air and soil data obtained from the local meteorological station in Isparta region. The computational modeling has been carried out for the determination of the performance of insulated and uninsulated solar ponds having different sizes with or without covers and reflectors. Reflectors increase the performance of the solar ponds by about 25%. Finally, this model has been employed for the prediction of temperature variations of an experimental salt gradient solar pond. Numerical results are in good agreement with the experiments. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Solar pond; Analytical function; Daily and hourly temperatures; Performance; Reflector
1. Introduction A salt-gradient solar pond (SGSP) which consists of three distinct zones: an upper convecting zone (UCZ), a non-convecting zone (NCZ), and a lower convecting zone (LCZ), is an inexpensive solar energy collection and storage system for low-temperature heat-sources. The concept of the solar pond appears very simple:
*
Corresponding author. Tel.: +90 388 2252152. E-mail address: refi[email protected] (R. Kayali).
0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.02.015
N.C¸. Bezir et al. / Applied Energy 85 (2008) 1102–1112
1103
Nomenclature
Z1Y1 Z2Y2 M1L1 C SM1 a G1
pond area, m2 amount of solar energy falling on one-meter square area perpendicular to the incident light per unit time on LHS reflector amount of solar energy falling on one-meter square area perpendicular to the incident light per unit time on RHS reflector term representing time lower convective zone day number non-convective zone the hourly air temperature at any time of the day of the year upper convective zone thickness of the first layer, m distance between the pond surface and the top layer of the storage region, m distance between the pond surface and bottom of the storage region, m the amount of solar energy which will fall on one meter square area of the solar pond per unit time incoming from LHS reflector the amount of solar energy which will fall on one meter square area of the solar pond per unit time incoming from RHS reflector front side of the projection area of LHS reflector normal to the incident light front side of the projection area of RHS reflector normal to the incident light the side length of the first reflector the angle between Z1Y1 and the reflector at any time and M1L1 projection area of the reflector normal to the incident light the length of one side of the pond or the length of the reflector the amount of the solar energy which will be reflected by the reflector into the solar pond
Greek b1 b2
angles with horizontal of first cover angles with horizontal of second cover
A B1 B2 K LCZ n NCZ TSH UCZ X1 X2 X3 U1 U2
a body of water harvests the incident solar energy and stores it for a long period of time. This long-term store provides an alternative for conventional energy-source [1–3]. Solar ponds have been studied by many researchers because of their excellent heat collection and storage performances. There have been considerable theoretical and experimental studies [4–8] on SGSPs. Many experimental solar ponds [9–18] have been constructed, instrumented and operated, and various numerical models [19–30] have been developed for analyzing SGSP performance in the literature. Theoretical studies have concentrated on modeling and predicting solar pond performance. Early studies of these types of works [31–33] were performed on one-dimensional models that did not account in a detailed way for the dynamical thermal interactions between the solar pond and the surrounding soil. Later researchers [34,35] developed more detailed models which account for the two-dimensional interactions within the soil. Recently, studies on non-stable solar ponds have appeared [6,36]. Kanayama et al. considered a cylindrical solar pond, 44 m in diameter. They used average hourly values of the horizontal solar radiation, and represented the monthly average temperature variation by a sine curve evaluated from the monthly average ambient temperatures in their simulations. Kayali et al. have developed empirical functions for air and soil temperatures obtained from meteorological data and used them for the calculations of the temperature variations in a rectangular type of solar pond [37,38]. Hawladar [39] did similar studies on the performance of the solar ponds operating at different latitudes and under different physical and operational conditions and used
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hourly ambient temperatures obtained from meteorology stations in his simulations. He also described the influence of the extinction coefficient on the effectiveness of solar ponds in his other study [40]. This paper reports the summary of the results of the numerical modeling developed for a salt gradient solar pond having covers used for preventing heat loss and reflecting the sun light into solar pond and how these covers affect performance of the solar pond. An experimental salt gradient solar pond with a surface area of 3.5 3.5 m2 and depth of 2 m has been built for supplying hot water to a leather workshop on the campus area of the Vocational College of Isparta/Yalvacß. A cover system for the surface of the pond was designed and used firstly to reduce the thermal energy loses from the top to air during night-time and to increase the thermal efficiency of solar energy harvesting during daytime. Simulations have been carried out using the mathematical formulation, which calculates the amount of the solar energy harvested by the covers, adapted into the model developed in [37] to see the affect of the covers on the performance of the solar pond. In order to get the best performance from the covers, one of them is kept at a fixed position and the other is rotated it from 0° to 180° to following the sun. This system is controlled by an electric motor and these covers have insulation and reflection properties. Analytical soil and air temperature functions used in the theoretical model simulations were developed using meteorological data obtained from the local meteorological station of Isparta region. Results obtained from theoretical and experimental studies showed that these kinds of salt gradient solar ponds can be used as a source for the warm water required at a leather workshop and for domestic applications. It was also found that covers have little effect on thermal losses during nights, but they are very effective for increasing the daytime harvesting performance. 2. Theory and experiment 2.1. Formulation of the air temperature function In theoretical model simulations, variable air temperature values are obtained from analytical functions. To obtain the analytic function which gives the temperature corresponding to any day of the year and any hour of that day, firstly the average air temperature of each day of each year was calculated and the average values of these values corresponding to six years were obtained using the data taken from measurements at the local Isparta meteorological station. Then plotting these values, the curve shown in Fig. 1 was obtained and another continuous curve was fitted to it. Fitting this curve yielded the following expression for the average air temperature T SH1 of the nth day of the year
30
measured calculated
25
Air temperature (ºC)
20 15 10 5 0 0 -5
30
60
90 120 150 180 210 240 270 300 330 360 Days
Fig. 1. The curve obtained using the measured daily average air temperatures.
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T SH1 ¼ 19 þ 8 sin
1105
360 n 103 365
ð1Þ
This equation gives only the average values, but the ambient temperature changes hour by hour. To overcome this problem, the maximum and minimum deviations from these daily average temperatures resulting from the difference between day and night were found. These calculated deviations were found to be within ±5 °C for each day of the year. Thus, a suitable equation giving the hourly air temperature deviations T SH2 from the daily average temperature is 360 T SH2 ¼ 5 sin t ð2Þ 24 where t is any hour of the day varying from 1 to 24. Combining Eqs. (1) and (2) a general equation for the hourly air temperature TSH at any hour of any day of the year is obtained: 360 360 T SH ðn; tÞ ¼ 19 þ 8 sin n 103 þ 5 sin t ð3Þ 365 24 2.2. Formulation of soil temperature functions A similar procedure, applied to obtain the analytical function which gives the air temperature, was also followed to derive an expression giving the average daily soil temperature at any depth and any day of the year. For this purpose the daily average soil temperatures obtained from the local meteorological station were used. The curves obtained as mentioned above for different depths were used to obtain the expressions for the average temperature of the soil at any day of the year. These fitted curves defined by cosine functions are given in Table 1. As an example, the curve obtained using the measured daily average soil temperatures at 10 cm corresponding different days of the year and the fitted curve to these values are shown in Fig. 2. Similar fits were employed for the other soil temperatures corresponding to the other depths. 2.3. Experimental solar pond and mathematical modeling An experimental salt gradient solar pond with a surface area of 3.5 3.5 m2 and depth of 2 m has been built for supplying hot water to a leather workshop on the campus area of Vocational College of Isparta/Yalvacß. The thickness of the concrete walls and bottom are 0.2 m. The thicknesses of the NCZ and the LCZ are 1.4 m and 0.5 m, respectively. Salty layers were formed by pouring the salt solution prepared with a required amount of salt (NaCl) on a floating wood plate on the layer formed before. The solar pond began to operate after establishing the salt gradient. The stability of the salt gradient is provided by a salt gradient preventing system, explained in Ref. [37]. Temperature variations in the inside and outside of the solar pond at different points were recorded continuously by means of thermocouples associated with a computer system.
Table 1 Equations for the average daily soil temperature at different depths Depth (cm)
Equation
10 20 30 40 50 60 70 80 90 100
T = 22 + 12cos (0.98n + 161) T = 22 + 12cos (0.98n + 161) T = 22 + 11cos (1.170n + 140) T = 22 + 11cos (0.91n + 158) T = 22 + 10cos (0.91n + 158) T = 22 + 10.2cos (0.91n + 164) T = 22 + 10.2cos (0.91n + 164) T = 22 + 10.6cos (0.91n + 153) T = 22 + 10.6cos (0.91n + 153) T = 22 + 9.4cos (0.98n + 142)
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35
calculated
Soil temperature (ºC)
30 25 20 15 10 5 0 0
40
80
120
-5
160 200 Days
240
280
320
360
Fig. 2. The curve obtained using the measured daily average soil temperatures at 10 cm corresponding to different days of the year and the fitted curve.
Fig. 3. Schematic model of the solar pond.
A solar pond model is shown in Fig. 3 [37]. According to this model the solar pond is divided into two regions. The first region consists of the pond itself, plus the soil within a certain thickness under it. The second region is the soil which surrounds the first region. To apply the finite difference method, the first region where the temperature varies only with depth and time, is divided into I number of layers having the equal thicknesses of Dx. However the situation in the second region is more complex than in the first region. There is no mass transfer horizontal in this region. Hence temperature varies horizontally and with the depth at the same time. Therefore, the second region has been divided into I layers of thickness Dx and J columns, each of width Dy. Furthermore, the temperature in both region is also a function of time. So the time parameter has been expressed as a third variable indexed by K. As a non-homogeneous system, the pond is analyzed most simply by writing heat balances in individual elements within each zone and a computer simulation model has been developed by Kayali [38].
2.4. Formulation of cover system used as a reflector For overcoming heat loss due to heat transfer from the surface of the solar pond to the atmosphere during nights and also for increasing the solar energy harnessing area during days, a surface cover system as shown in Fig. 4 was designed and used. It consists of two parts which can be collapsible by means of an electrical con-
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B1 Z1 M1
B1
1107
Incident Beam
B1
Y2
C
θ i1 θ r1
First Cover (LHS)
α
D
Y1
θr2
γ2
β1
B2
Fi
O1 L1
UCZ
β2
O2
α
θi2
B2
B2
Z2 M2
Second Cover (RHS)
L2
a NCZ
LCZ
Fig. 4. Schematic diagram of the reflectors.
trolled driving system. They act as an insulator and as a reflector. In this section, a mathematical formulation of this system will be given. For calculating the amount of the sun light energy which is reflected by the reflectors, a mathematical formulation was carried out. In the derivation of the equations, the model seen in Fig. 4 was used. As seen from this figure, cover1 (LHS reflector) and cover2 (RHS reflector) make b1 and b2 angles with horizontal, respectively, and these two angles are the adjustable angles. In this model, the reflectors were considered as two different light sources. a is the angle between the horizontal surface and the incident light arriving at any hour of any day of the year. To obtain the expression which gives the amount of the solar energy which will be reflected by the first reflector, the following procedure is followed; to find the amount of the solar energy incident on the surface of this reflector, the front side of the projected area of the reflector normal to the incident light Z1Y1 is given by Z 1 Y 1 ¼ M 1 L1 cos C
ð4Þ
where C is the angle between Z1Y1 and the reflector and it is a function of time. M1L1 is the side length of the reflector. C is given by C ¼ 90 ½180 a b1 ¼ 90 180 þ a þ b1 ¼ 90 þ a þ b1
ð5Þ
Substituting C in Eq. (4), the length of Z1Y1 in the triangle, Z1Y1O1, is Z 1 Y 1 ¼ M 1 L1 cosð90 þ a þ b1 Þ
ð6Þ
The projection area of the reflector normal to the incident light, SM1, is SM 1 ¼ Z 1 Y 1 a
ð7Þ
where a is the length of one side of the pond or the length of the reflector. Substituting the value of Z1Y1 given in Eq. (6) into Eq. (7), SM1 is SM 1 ¼ M 1 L1 cosð90 þ a þ b1 Þ a The amount of the solar energy which will be reflected by the first reflector into the solar pond is
ð8Þ
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G1 ¼ SM 1 B1
ð9Þ
where B1 is amount of the solar energy falling on one-meter square area perpendicular to the incident light per unit time and it is equal to B2. The amount of the solar energy which will fall on one-meter square area of the solar pond in per unit time, U1, is obtained using G1 U 1 ¼ G1 =a2
ð10Þ
U 1 ¼ M 1 L1 cosð90 þ a þ b1 Þ B1 =a
ð11Þ
or
Following the similar way an expression which will give the amount of the energy to be reflected from the other reflector, U2, is U 2 ¼ M 1 L1 cosð90 a þ b2 Þ B1 =a
ð12Þ
where M1L1 is equal to M2L2. In the computational modeling, it is necessary to know the angles between the light beams coming from reflectors and the normal of the surface of the solar pond. These angles were denoted by c1 and c2, respectively, and their expressions have been obtained using the geometry of the system shown in Fig. 4 in terms of a, b1 and b2 c1 ¼ 90 þ a 2b1
ð13Þ
c2 ¼ 270 2b2 a
ð14Þ
and
These equations have been used in the theoretical model calculations. In order to model the solar pond with covers, numerical solution of the equations, defining how much energy is incoming from reflectors to the pond surface, is implemented to our existing code [37,38]. 3. Results and discussion In this section, the results obtained from the model and experiment will be discussed and compared with each other, and then the effects of the various parameters will be examined. To see the effect of pond size on the performance of the solar pond, model simulations have been carried out using the thermal parameters
Fig. 5. Comparisons of the temperature distributions in the storage region of the solar pond without covers, only covers, and covers and reflectors (b1 = 30° and b2 = 89°).
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of the solar ponds whose depth, storage region depth and height of the NCZ are 2.5 m, 1 m and 1.4 m, respectively. To see the effect of reflectors and covers on the performance of the solar ponds, the model solar pond started to operate on the 1st of January for 360 days. In these calculations, the analytical functions derived for air and soil temperatures mentioned above were used in our code. Only the temperature of water in the solar pond and the concrete bottom under the LCZ are taken as 15 °C. Fig. 5 shows the comparisons of the temperature distributions in the storage region of solar pond having no covers, only covers, or covers and reflectors (b1 = 30° and b2 = 89°). The effect of the covers is very small when they are used as covers for closing the surface of the solar pond at nights. In this case, the average temperature difference between solar pond having no cover and having cover is 1 °C. This is due to the sufficiently large thickness of the NCZ. Covers would become more effective for small NCZ thicknesses. On the other hand, the average tem-
Fig. 6. Annual temperature variations in the LCZ when the RHS reflector is kept at fixed angle 89° and the LHS reflector is changed from 30° to 80° with 10° intervals.
Fig. 7. Annual temperature distributions in the LCZ when LHS reflector is kept at a fixed angle 30° and RHS reflector is changed from 20° to 80° with 10° intervals.
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perature difference the between solar pond having a cover and a reflector is about 10 °C. This means that reflectors play a vital role on the performance of solar ponds contributing to harvesting much more solar energy and increasing the energy harvesting area. To see the effect of the reflectors depending on their positions, simulations have been carried out in two different ways. Firstly, the angle between the horizontal axes and RHS reflector was kept at 89° and the angle between the horizontal axes and LHS reflector was changed from 30° to 80° with 10° intervals. As seen from Fig. 6, the performance of the solar pond reaches a maximum and a minimum when the angles are 30–89° and at 80–89°, respectively. A similar simulation is carried out keeping the LHS reflector at a fixed 30° angle and changing the angle of RHS reflector from 20° to 80° with 10° intervals. As seen from Fig. 7, maximum and minimum performances of the solar pond occur when the angles are at 30–80° and at 30–20°, respectively. An important result is obtained if these two results are compared with each other. While the temperature of the LCZ corresponding to the first condition changing from 58 °C to (63–4) °C it changes 50 °C to (62–3) °C for the second condition.
Fig. 8. Annually temperature distributions in the LCZ of the solar pond having different sizes (b1 = 30° and b2 = 89°).
Fig. 9. Comparison of numerical and experimental temperature variations of the LCZ of the solar pond vs. days.
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1111
56
Temperature (ºC)
51 46 41 36 31 26 21 6
8
28.05.2001 07.06.2001 13.08.2001 Theoretical values
10 Layers
12
14
28.05.2001 01.07.2001 13.08.2001
07.06.2001 01.07.2001 Experiment
Fig. 10. Theoretical and experimental temperature variations at different layers in the NCZ with cover corresponding to different dates.
Fig. 8 depicts the annual temperature variations in the LCZ of the solar ponds having different sizes. As seen from this figure, the performance of the solar pond increases with the increasing size. The reason is that the heat loss rate per unit area from the walls and bottom of the solar pond decreases with increase in the size. Experimental and theoretical results will be given for the experimental solar pond having no covers and reflectors. Fig. 9 shows the comparison of numerical and experimental temperature variations of the LCZ of the experimental solar pond having no cover and reflector. As seen from this figure, the average value of experimental results is in a good agreement with the numerical results. Comparisons of theoretical and experimental temperature variations in different layers of solar pond starting to operate on 28.05.2001 for different dates are seen in Fig. 10. As seen from this figure, the experimental expectation has similar behavior with the numerical one. 4. Conclusion The mathematical model developed by Refs. [37] and [38] is modified and supplemented with additional subroutines in order to simulate how the performance of the solar pond is affected by covers. Analytical functions derived for air and soil temperatures using the local meteorological data were used in simulations and the parameters effecting on the solar ponds were determined. It was found that a cover affects little the performance of the solar pond when it is used only as a cover during nights; this is due to the small height of the NCZ (1.4 m). However, covers are very effective when they are used as reflectors. The temperature of the LCZ in the solar pond increases by about 25% when compared with the uncovered case. It can be concluded that the best performance of the pond can be achieved when the covers are employed as reflectors. The performance of the solar pond increases very much with increasing solar pond size; this is due to the decrease in the heat loss from the side walls falling per unit area of the solar pond. Experimental and theoretical model results, obtained for the solar pond without a cover, are in a good agreement with each other. The demonstration of the value of the theoretical modeling of solar pond will be crucial in deciding the future course of experiments and technology development. A more detailed study of comparison of the results obtained from experiments and the theoretical model will be presented in a forthcoming paper for the covers used as a reflectors. References [1] Zangrando F. On the hydrodynamics of salt-gradient solar ponds. Sol Energy 1991;46:6–323.
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