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Heat extraction from Non-Convective and Lower Convective Zones of the solar pond: A transient study
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ScienceDirect Solar Energy 97 (2013) 517–528 www.elsevier.com/locate/solener
Heat extraction from Non-Convective and Lower Convective Zones of the solar pond: A transient study Abhijit Date a,⇑, Yusli Yaakob a, Ashwin Date a, Shankar Krishnapillai b, Aliakbar Akbarzadeh a a
School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box 71, Bundoora, Victoria 3083, Australia b Indian Institute of Technology Madras, Chennai, India Received 11 June 2013; received in revised form 10 August 2013; accepted 7 September 2013
Communicated by: Associate Editor Yogi Goswami
Abstract Heat extraction from the Non-Convective Zone (NCZ) or gradient layer and Lower Convective Zone (LCZ) of the solar pond has been investigated through one-dimensional finite difference transient model. Instantaneous efficiency of the solar pond is introduced and defined in this paper. The solar pond considered in the present study is assumed to have an in-pond heat exchanger for heat extraction. The rate of heat transfer is controlled by the mass flux of heat transfer fluid in this model. As in reality mass flux of heat transfer fluid is the simplest and most practical way to control the rate of heat extraction. In this model for an ideal situation it is assumed that the heat transfer fluid is initially at the local daily average ambient temperature and the in-pond heat exchanger has heat transfer effectiveness equal to unity. With these assumptions the model can predict the thermal performance of the solar pond with maximum heat extraction for a desired mass flux of the heat transfer fluid. This paper presents the comparison of the transient thermal performance of solar pond with heat extraction from LCZ alone and that with combined heat extraction from LCZ and NCZ. It is shown how the efficiency of the solar pond increases when heat is extracted from both NCZ and LCZ. The main objective of this study is to offer a simple method to predict transient thermal performance of a solar pond with heat extraction from NCZ and to estimate the mass flux of heat transfer fluid used in an in-pond heat exchanger for heat extraction from different layers of solar pond. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Solar pond; Heat extraction; Transient performance
1. Introduction A solar pond is a large body of saline water whose salinity increases with depth. These ponds are used as solar thermal energy collectors that can simultaneously store heat for long period, so they are suitable for sessional solar thermal energy storage. In case of fresh water ponds almost all the solar radiation that falls on the surface is absorbed by top 3 m of fresh water and this thermal energy is rapidly lost to the atmosphere through natural convection heat transfer. ⇑ Corresponding author. Tel.: +61 3 9925 0612; fax: +61 3 9925 6108.
E-mail address: [email protected] (A. Date). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.09.013
So the temperature of a fresh water pond never rises and is almost constant throughout the fresh water pond depth. Practical heat extraction from Lower Convective Zone (LCZ) for different applications is very common. In past heat has been extracted from LCZ using two methods, in the first method hot saline water is extracted from the LCZ and passed through an external heat exchanger as used at Kutch in India (Kumar and Kishore, 1999) and Beith Ha’arava in Israel (Tabor and Doron, 1990). In the second method an in-pond heat exchanger is used for heat extraction from the LCZ as used at Pyramid Hill, Victoria (Leblanc et al., 2011) and Marshad in Iran (Jaefarzadeh, 2006). Tabor (Tabor, 1981) has discussed both of these
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Nomenclature Asp cp DE h Hhs H(X) jmf k Lr q00e q00 S s T X DX
surface area of solar pond (m2) specific heat capacity (J/kg °C) instantaneous change in the energy content (J) solar radiation flux absorbed (W/m2) global solar radiation flux incident on the horizontal surface (W/m2) solar radiation flux that reaches to X (m) of depth of solar pond (W/m2) mass flux of heat transfer fluid (kg/m2/s) thermal conductivity (W/m °C) solar radiation reflective losses (%) heat flux extracted by heat transfer fluid (W/m2) conductive heat flux (W/m2) salinity (%) salinity (kg/m3) temperature of node (°C) path length of light in solar pond to the end of the respective division (m) thickness of the division (m)
methods in his review of solar pond technology, and stressed that both method have convenient practical merit. The main limitation to the full scale application of solar ponds in industry has been the low solar thermal efficiency and in many cases lowers temperature heat available (below 60 °C) as discussed by Leblanc et al. (2011) and Andrews and Akbarzadeh (2005). Researchers have proposed many different ways of improving the thermal performance of solar ponds, which include improving the water clarity (Gasulla et al., 2011; Wang and Seyed-Yagoobi, 1995; Malik et al., 2011), increasing the thickness of LCZ and reducing the thickness of Upper Convective Zone (UCZ) Wang and Akbarzadeh, 1982a, introducing an additional upper Non-Convective Zone (NCZ) Husain et al., 2012, putting an external reflector to reflect additional solar radiation into solar pond (Aboul-Enein et al., 2004), by integrating a solar pond with flat plate solar collectors (Bozkurt and Karakilcik, 2012), etc. Researchers have proposed of extracting/utilizing the heat stored in the NCZ to improve the overall thermal performance of the solar ponds and have claimed to improve the solar pond efficiency by up to 50% using a steady state theoretical model (Leblanc et al., 2011; Andrews and Akbarzadeh, 2005; Yaakob et al., 2011). To date all the studies have used steady state theoretical model and its unknown if similar improvement in the solar pond efficiency is achievable for real solar pond using a transient model. Present paper investigates the transient thermal performance of the solar pond with heat extraction from both NCZ and LCZ. Through this paper efforts have been made to further develop the one-dimensional finite difference model of the solar pond for predicting the mass flux of heat transfer fluid flowing through an in-pond heat
q gsp in gsp avg
density (kg/m3) instantaneous efficiency of solar pond (%) average annual solar pond efficiency (%)
Subscripts e extraction i inlet or initial n nth layer/node in solar pond and ground n 1 Layer/node above the nth node n + 1 Layer/node below the nth node g ground ucz Upper Convective Zone ncz Non-Convective Zone lcz Lower Convective Zone s present time (s) Ds time increment (s) f heat transfer fluid fw fresh water
exchanger in a solar pond. This new model can predict transient behaviour of such solar pond while neglecting the shading and wall effects. Effects on the temperature profile of the solar pond for different heat extraction rates from NCZ and LCZ have been discussed and the best mix of heat extraction has been presented. 2. Solar pond Fig. 1 shows the schematic of salinity gradient solar pond, which consists of three regions. The cold upper layer or Upper Convective Zone (UCZ) is a homogeneous thin layer of low salinity brine or fresh water. The middle gradient layer or Non-Convective Zone (NCZ) has salinity gradient with salinity increasing from top of NCZ to the bottom of NCZ, this helps suppress the heat loss by natural convection. The bottom layer or Lower Convective Zone (LCZ) has high salinity (some cases close to saturation) that absorbs and stores solar radiation that reaches the LCZ in form of thermal energy. If Hhs amount of solar radiation is incident on the horizontal top surface of the solar pond and around Lr percentage of solar radiation is reflected back to the atmosphere, then (Hhs Lr Hhs) amount of solar radiation penetrates the top surface of the solar pond. And this amount of solar radiation is gradually absorbed by the water along the depth of the solar pond. As shown in Fig. 1, hucz is the amount of solar radiation that is absorbed by the water in the UCZ, hncz is the amount of solar radiation that is absorbed by the water in the NCZ and hlcz is the amount of solar radiation that is absorbed in the LCZ. The solar radiation that is absorbed in the three layers of the solar pond is converted to heat. Part of this heat is lost
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Fig. 1. Schematic diagram of salinity gradient solar pond.
to the atmosphere and part is lost to the ground. The amount of heat that is stored in the LCZ and NCZ is available for extraction and this amount of heat is responsible for the temperature gradient formation in the solar pond. 3. Theoretical modelling To predict thermal performance of large solar ponds, the thermal process in these solar ponds can be treated as one-dimensional unsteady conduction loss, with heat generation from incoming solar radiation as used by many researchers in the past (Wang and Akbarzadeh, 1982a; Aboul-Enein et al., 2004; Bansal and Kaushik, 1981). Here efforts are made to develop a transient thermal performance model of a solar pond with heat extraction from NCZ and LCZ following the steady state model developed by Andrews and Akbarzadeh(2005) and the finite difference method discussed by Wang and Akbarzadeh (1982a). It is assumed that the main mode of heat transfer in the NCZ is only by conduction and convection is suppressed by the available density gradient. As shown in Fig. 2 a solar pond is assumed to have two thermal boundaries (Upper and Lower). The upper boundary is at the interface of the UCZ and the NCZ. The temperature of the UCZ is assumed to the equal to the monthly average local daily
Fig. 2. Schematic diagram of zone interfaces.
temperature as suggested by Hull (1979) and Weinberger (1964). This assumption has been made to simplify the solar pond analysis. For accurate performance prediction of the solar pond it is important to consider the energy balance between UCZ and the air interface as discussed by Bansal and Kaushik (1981). The lower boundary is at the interface of the LCZ and the ground below the pond. The temperature of the ground below the pond will be affected by the temperature of LCZ. For the purpose of one-dimensional finite difference model the NCZ is divided into number of divisions each with a thickness of DX, while LCZ is considered to be single layer with temperature at the top of the LCZ equal to the bottom temperature of LCZ. It is not necessary for these divisions to have equal thickness, but in the present study for simplicity these divisions are assumed to have equal thickness. And the nodes are located at the centre of each division. Eq. (1) provides a generalised energy balance equation for the solar pond. 00s 00s DEnsþDs ¼ hsn Ds þ q00s n1 Ds þ qnþ1 Ds qe n Ds
ð1Þ
here DEsþDs represents the change in the energy content of n nth layer (i.e. layer under investigation) in solar pond after time Ds, hsn represents the solar radiation energy absorbed by nth layer in solar pond at time s, q00s n1 represents the conductive heat transfer to or from the division above the nth layer in solar pond at time s, q00s nþ1 represents the conductive heat transfer to or from the division below the nth layer in solar pond at time s and q00s e n represents the heat extracted from the nth layer in solar pond at time s. The solar radiation flux h (W/m2) that is absorbed by each layer is equal to the solar radiation transmitted through the layer above minus the solar radiation that reaches the top of the layer below. If hourly solar radiation data is available then the reflective losses from the surface of the solar pond can be estimated as discussed by Kooi (1979) and Kaushik et al. (1980). In Eq. (2) the percentage reflective losses are represented by Lr and the sun light
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attenuation equation as discussed by Bryant and Colbeck (1977) is used to estimate the solar radiation flux that reaches the nth layer in solar pond at time s . H sn ¼ H shs H shs Lr ð0:36 0:08 ln½X n Þ ð2Þ hsn ¼ Asp ðH sn1 H snþ1 Þ ! T sn T sn1 00s qn1 ¼ DX n DX n1 þ 2kn1 2k n ! s s T T n nþ1 q00s nþ1 ¼ DX nþ1 DX n þ 2k 2k n nþ1
ð3Þ ð4Þ ð5Þ
s s q00s e n ¼ jmf cpf ðT n T f n1 Þ
DEsþDs n
¼ qn Asp DX n cpn
ð6Þ ðT sþDs n
T sn Þ
ð7Þ
As shown in Fig. 3 the first temperature node in the NCZ is only DX/2 distance away from the adjacent temperature node in UCZ and similarly the last temperature node in NCZ is only DX/2 distance away from the adjacent temperature node in LCZ. So when writing the equation for the conductive heat loss or gain from the first temperature node in NCZ to the adjacent temperature node in UCZ it should be noted that only one thickness and thermal conductivity term will appear in the denominator of the Eq. (4). Similarly when writing the equation for the conductive heat loss or gain from the temperature node in the NCZ to the adjacent temperature node in LCZ it should be noted that only one thickness and thermal conductivity term will appear in the denominator of the Eq. (5). Similar one-dimensional finite method is used for thermal analysis of the ground below the pond. Wang and
Akbarzadeh (1982a) have suggested that ground temperature beyond 5 m below the solar pond floor can be assumed to be equal to the yearly average ambient temperature. So 5 m of ground below the solar pond floor is divided into number of sub divisions each with a thickness of DXg. There is no heat generation in the ground as the solar radiation does not reach there and there is no heat extraction from the ground. When analysing the energy balance of a division in the ground below solar pond there is only conductive heat loss or gain from the layer above and below. Following equation provides the generalised energy balance for ground below the solar pond. 00s DEgsþDs ¼ q00s n g n1 Ds þ qg nþ1 Ds
ð8Þ
here DEsþDs represents the change in the energy content of gn nth layer in ground below solar pond after time Ds, q00s g n1 represents the conductive heat transfer to or from the division above the nth layer in the ground at time s and q00s g nþ1 represents the conductive heat transfer to or from the division below the nth layer in the ground at time s. 0 1 s s T T g n g n1 @ A ð9Þ q00s g n1 ¼ DX g n1 DX g n þ 2k g n 2k g n1 0 1 T sg n T sg nþ1 00s ð10Þ qg nþ1 ¼ @ DX g n DX g nþ1 A þ 2k g n 2k g nþ1 sþDs s DEg n ¼ qg n Asp DX g n cpg n T sþ1 T ð11Þ gn gn
Fig. 3. Schematic of symmetrical section of solar pond – NCZ, LCZ and ground divisions, node positions and NCZ–LCZ heat extraction systems.
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The initial temperature of the solar pond is assumed to be equal to the monthly average ambient. Knowing this initial temperature and the incoming solar radiation the and repeatedly solving Eqs. (1)–(9), (11), (12) for different divisions and the interfaces the final temperatures of all divisions at the end of each time increment can be obtained node by node. 3.1. Transient model convergence criteria In all the above equations s is the initial time that is used to predict the thermal performance after a time increment of Ds. The time increment and the thickness of the each sub division of the solar pond zones can be of any size, but they should satisfy the stability condition shown in Eq. (13) as discussed by Wang and Akbarzadeh (1982a). ! 1 1 Ds þ DX 61 ð12Þ DX n1 DX nþ1 DX n n q DX þ 2kn1 2kn þ 2k n cp n n 2k n nþ1
521
the heat loss or gain from the LCZ of the solar pond in a time interval of Ds. DEsg ¼
0 X
X g n Asp qg n cpg n T sg n T s1 gn
ð15Þ
n
and hence the instantaneous efficiency of the solar pond can be calculated by using Eq. (17). ginst SP ¼
DEslcz þ DEsncz þ DEsg Asp H shs H shs Lr Ds
ð16Þ
Average annual solar pond efficiency is expressed as the ratio of sum of change in energy content of LCZ, NCZ and ground per year divided by the total solar radiation that penetrates the top surface of the solar pond per year and is shown by Eq. (17). Here the first day is the when the solar pond operation begins. i Pday¼1 h s s s DE þ DE þ DE lcz ncz g day¼360 gsolar pond ¼ Pday¼1 ð17Þ s s day¼360 Asp H hs H hs Lr Ds
3.2. Efficiency of solar pond 3.3. Solar salinity gradient stability criteria Solar pond efficiency would have meaning only when heat is extracted from the solar pond. Conventionally heat has been extracted from the LCZ of the solar pond. As the solar pond has got large thermal mass, the rate of heat extraction can be varied to suit the application without compromising the stability of the solar pond. Although using the instantaneous heat extraction rate alone to estimate the instantaneous efficiency of the solar pond can be very misleading. This is because in some applications the instantaneous rate of heat extraction can be larger than the solar radiation that penetrates the top surface of the pond. So here the instantaneous efficiency of the solar pond is defined as ratio of instantaneous change in energy content of the solar pond plus ground below the solar pond divided by the amount of solar radiation that penetrates the top surface of the solar pond. The instantaneous change in the energy content of LCZ is shown by Eq. (14) as the sum of the energy extracted (heat extracted) and solar energy absorbed in a time interval of Ds. DEslcz ¼ jmf lcz cpf lcz T slcz T sf i Ds þ X lcz ð13Þ Asp qlcz cplcz T slcz T s1 lcz The instantaneous change in the energy content of NCZ is shown by Eq. (15) as the sum of the energy extracted (heat extracted) and solar energy absorbed in a time interval of Ds. X0 h DEsncz ¼ j cpf ðT sn T sf n Þ Ds þ X n Asp n mf ncz ð14Þ qn cpn T sn T s1 n The instantaneous change in the energy content of ground below the solar pond is shown by Eq. (16) and is equal to
The stability of the salinity gradient layer (non-convecting layer) has been discussed in a number of articles (Wang andAkbarzadeh (1982a,b). The following relations for stability of the solar pond have been used for the present study and earlier it has been used by Wang and Akbarzadeh (1982a,b). ds dT > 0:44 for the surface condition dX dX ds dT > 1:18 for the bottom condition dX dX
ð18Þ ð19Þ
In the above equation s is salinity (kg/m3), T temperature dS (°C) and x is the pond depth (m). Further, dX is salinity gradT dient and dX is the temperature gradient in the pond. In the first few cm below the surface of the pond, the available solar radiation decreases very sharply. At a depth of 0.3 m, the intensity of solar radiation is close to half of its original value and, if there is no convection at this depth, then as discussed by Wang and Akbarzadeh(1982a) the corresponding temperature gradient can be expected to be as high as 200 °C/m. For a top convective layer with 0.3 m thickness the density gradient should be such that it can suppress convection caused by the temperature gradient. Substituting the value of 200 °C/m for the temperature gradient in Eq. (18), a value of 88 kg/m3/m is obtained for the corresponding minimum salinity gradient to prevent erosion. For a bottom convective layer if no heat is extracted the minimum temperature gradient that can be present would be 60 °C/m. To support this temperature gradient at the bottom, a salinity density gradient of at least 70.8 kg/m3/m is required to ensure stability as estimated by using Eq. (19). A stable solar pond phenomenon can only exist if a minimum salinity gradient of 88 kg/m3/m is
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present at the interface of the UCZ and NCZ. And at least 70.8 kg/m3/m of salinity gradient is present at interface of NCZ and LCZ. 4. Simulation boundary conditions and assumptions For the present study a reference solar pond in Melbourne with large enough surface area to neglect heat loss through wall is used and the salt is sodium chloride. The temperature development is predicted for a three year period. The solar pond starts operation on 1st October (i.e. early spring in southern hemisphere), and the heat removal operation starts after 60 days. This solar pond is assumed to have 0.3 m thick UCZ and for the purpose solving the finite difference model the UCZ is considered to be a single layer. The salinity of the water in the UCZ is assumed to be 2% and the temperature of UCZ is assumed to be equal to the monthly average ambient temperature. This assumption is to simplify the analysis. The NCZ is assumed to be 1.2 m thick and is divided into eight sub divisions for the purpose of solving the finite difference model to estimate the temperatures of the nodes assumed to be located at the centre of each layer in the NCZ (i.e. n = 8). It is assumed that the LCZ has constant salinity and hence this layer always has same temperature throughout its thickness. The LCZ is assumed to be 1.5 m thick with a uniform salinity of 20%. So the solar pond under investigation has a total depth of 3 m which is very commonly used. The properties of the salt water are calculated using the following relations as discussed by Wang and Akbarzadeh (1982a). Sn k n ¼ 0:5553 0:0000813 qfw þ 0:0008 100 ðT sn 20Þ
Sn qfw 0:4 ðT sn 20Þ 100 Sn cpn ¼ 4180 4:396 qfw þ 0:0048 100 2 Sn qfw 100 qn ¼ 998 þ 0:65
ð17Þ
solar radiation is always normal to the solar pond surface. This assumption is made only to simplify the analysis for the purpose of the present study. For accurate performance prediction the reflective losses from the surface of the solar pond due to varying angle of incidence should be estimated as discussed by Kooi (1979) and Kaushik et al. (1980). As discussed in the previous section Bryant and Colbeck solar radiation attenuation equation is used with path length X as the real vertical distance that sun light has travelled after it penetrates the water surface. For the present study both solar radiation and ambient temperature are adequately approximated by sinusoidal functions based on statistical data of monthly average values as shown in Fig. 4. The solar pond is assumed to have an in-pond heat exchanger installed around the peripheral wall of the solar pond for heat extraction from the NCZ and on the bottom of solar pond for heat extraction from LCZ. The rate of heat extraction from the solar pond is controlled by the mass flux of heat transfer fluid flowing through the in-pond heat exchangers. While in operation controlling flow rate is the simplest and most practical way to control the heat extraction. It is assumed that the heat transfer fluid is initially at the same temperature as the temperature of UCZ or average ambient temperature. Further both the heat exchangers in NCZ and LCZ are assumed to have heat transfer effectiveness equal to 1, i.e. the heat transfer fluid will always get heated to the temperature corresponding solar pond division. This assumption is made to simplify the heat transfer analysis. For more accurate performance prediction more realistic value of heat exchanger effectiveness must be used. Further any effect if present due to the heat extraction from the NCZ on the stability of the salinity gradient is not considered in the present study. This study investigates following two ways of heat extraction,
ð18Þ
ð19Þ
here Sn is the salinity if of the water in nth layer of the solar pond and qfw is the density of fresh water and is assumed to be 1000 kg/m3. The ground below the solar pond is assumed to have uniform thermal properties. As explained by earlier researchers the underground conditions have strong influence on the thermal performance of the solar pond (Aboul-Enein et al., 2004; Wang and Akbarzadeh, 1983). In this simulation it is assumed that the solar pond is lined with plastic liner under which there is 5 m of clay liner. The thermal properties of the clay under the pond liner are assumed based on the work by Zhang and Wang (1990), kg = 1.28 W/m K; qg = 1460 kg/m3; cpg ¼ 880 J=kg K. It is assumed that all solar radiation (diffused and direct) comes from sun and angle of incidence is equal to zero i.e.,
Transient thermal performance prediction of pond while extraction heat at different rates LCZ alone. Transient thermal performance prediction of pond while extraction heat at different rates both NCZ and LCZ.
the solar from the the solar from the
5. Results and discussion Fig. 5 shows the temperature development of the solar pond under investigation without heat extraction over a period of 3 years. The boiling of the water in LCZ in the second and third year is ignored in Fig. 5 to simplify the heat transfer model used for temperature development. It should be noted that in reality the LCZ temperature will never go beyond the local boiling temperature of the saline water. It can be seen that the LCZ temperature increases significantly in the first year. It is interesting to see from Fig. 5
A. Date et al. / Solar Energy 97 (2013) 517–528
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Average solar radiation and ambient temperatures for Melbourne 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0
Average global daily irradiance on horizontal surface
30 25 20 15 10 5
0
Sollar Radiation (MJ/m²/day)
Temperature ( C)
Monthly Average Ambient Temp
0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 1020 1080 Dec June Mid-Winter
Mid-Summer
Days
Fig. 4. Melbourne climate data – Monthaly average of daily global solar radiation on horizontal surface and montly average temperature.
Temperature profile of solar pond without heat extraction (Heat extrated = 0 MJ/m²/year) UCZ Temp
NCZ Temp -0.55m depth
NCZ Temp -0.83m depth
NCZ Temp -1.1m depth
NCZ Temp -1.36m depth
LCZ Temp
Instantaneous efficiency
Tem mperature (°C)
90
Layer
Thickness
UCZ NCZ LCZ
0.3m 1.2m 1.5m
50% 40% 30%
80
20%
70
10%
60
0%
50
-10%
40
-20%
30
-30%
20
-40%
10
-50%
0 0
Instantan neous efficiency (%)
110 100
-60% 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 10201080
Dec June Mid-Summer Mid-Winter
Days
Fig. 5. Temperature development of solar pond in Melbourne without heat extration.
how the instantaneous efficiency starts to decreases as the temperature of the pond starts to increases in first couple of months from the start of the solar pond operation. Instantaneous efficiency is a measure of the energy absorbed and/or extracted and energy lost, if the value of instantaneous efficiency falls below 0% then this means the instantaneous energy loss is more than the instantaneous energy absorbed and/or extracted. Further it interesting to see that the maximum and minimum LCZ temperature corresponds to 0% instantaneous efficiency and it does not correspond to the maximum and minimum instantaneous efficiency points, the main reason for this is the thermal inertia of the solar pond. For the first year the average annual solar pond efficiency is about 9%, while for the second and third year the average annual efficiency of the solar pond is 1% and 0.1% respectively. In the second and third year the low average
annual solar pond efficiency can be attributed to the higher solar pond temperatures and no heat extraction. 5.1. Heat extraction from LCZ alone Fig. 6 shows the temperature development of the solar pond under investigation with heat extraction from LCZ alone over a period of 3 years. The heat extraction starts on 60th day from the start of the operation of the solar pond. Heat transfer fluid initially at UCZ temperature (i.e. equal to the ambient temperature) flows through the in-pond heat exchanger in the LCZ. By varying the mass flux of the heat transfer fluid the rate of heat extraction can be controlled. To extract heat from solar pond at least 5 °C of driving temperature difference would be required between LCZ and heat transfer fluid. Further 5 °C of driving temperature
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A. Date et al. / Solar Energy 97 (2013) 517–528 LCZ 0.00015 kg/m²/s
LCZ 0.0002 kg/m²/s
LCZ 0.00025 kg/m²/s
LCZ 0.0003 kg/m²/s
UCZ - Temp
Solar Radiation
70
70
50
Temperature (°C)
50 40
40
38°C 33°C 29°C
30
30
29°C
26°C
20
20
ΔT= 20°C 19°C 9°C
9°C
10 0 0
Solar Radiation (MJ/m²/day)
60
59°C
60
10
0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 10201080
June
Dec
Mid-Summer
Days
Mid - Winter
Fig. 6. Temperature development of the solar pond with heat extraction from LCZ.
Eff - LCZ 0.00015 kg/m²/s Eff - LCZ 0.00025 kg/m²/s Heat extracted @ 0.00015 kg/m²/s Heat extracted @ 0.00025 kg/m²/s
Eff - LCZ 0.0002 kg/m²/s Eff - LCZ 0.0003 kg/m²/s Heat extracted @ 0.0002 kg/m²/s Heat extracted @ 0.0003 kg/m²/s
50%
50
40 35
30%
30 20%
25 20
10%
15
Heat extracted (W/m²)
Instantenous Efficiency (%)
45 40%
10
0%
5 -10% 0
120
Dec Mid-Summer
240
360
480
June
600
720
840
960
0 1080
Days
Mid-Winter
Fig. 7. Instanteneous efficiency of solar pond for heat extraction from LCZ with different mass flux of heat transfer fluid.
difference would be required for heat transfer between heat transfer fluid and the end use application such as heating of air. So for any meaningful use of the available heat in the solar pond, it is assumed that a minimum 20 °C temperature difference must be present between the LCZ temperature and the heat transfer fluid inlet temperature (average ambient temperature). Further it is assumed that the inlet temperature of the heat transfer fluid is maintained at the same temperature as UCZ (i.e. ambient temperature). Fig. 6 shows the LCZ temperature development profile for a solar pond with heat extraction from LCZ alone and constant heat transfer fluid mass flux between 0.00015 kg/m2/s and 0.0003 kg/m2/s. It is found that the 0.00025 kg/m2/s is the limiting mass flux of the heat transfer fluid to maintain a minimum temperature difference of 20 °C between LCZ and inlet
temperature of the heat transfer fluid for the solar pond under investigation located in Melbourne. If the mass flux is increased beyond 0.00025 kg/m2/s the solar pond efficiency will improve but the available temperature difference will fall below 20 °C and this will limit the application of available heat. Further from Fig. 6, it can also be seen that for the limiting mass flux the highest temperature of 59 °C appears at the end of February with a lag of about 2 months behind the maximum insolation and there is a minimum temperature of 29 °C, this is mainly due to large thermal mass of the solar pond and suppressed convective heat loss by the NCZ. The yearly average LCZ temperature for the limiting mass flow of heat transfer fluid of 0.00025 kg/m2/s is 44 °C, which is about 30 °C above the annual mean
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Eff - NCZ & LCZ 0.0001 kg/m²/s
Eff - NCZ & LCZ 0.0002 kg/m²/s
Eff - NCZ & LCZ 0.00015 kg/m²/s
Heat Extracted from NCZ & LCZ @ 0.0001 kg/m²/s
Heat Extracted from NCZ & LCZ @ 0.0002 kg/m²/s
Heat Extracted from NCZ & LCZ @ 0.00015 kg/m²/s
50%
60
40%
50
30%
40
20%
30
10%
20
0%
10
-10% 0
120 Dec Mid -Summer
240 June
Mid- Winter
360
480
600
720
840
960
Heat extracted (W/m²)
Instantenous Efficiency (%)
Fig. 8. LCZ temperature development profiles with constant heat transfer fluid mass flux through NCZ and LCZ heat exchanger.
0 1080
Days
Fig. 9. Instanteneous efficiency profiles with constant mass flux of heat transfer fluid through NCZ and LCZ heat exchanger.
ambient temperature. The yearly LCZ temperature fluctuation is about 30 °C, which means that with the pond supplying heat at a constant rate the quality of the heat varies substantially with the season. From Fig. 7 it can be seen that for the limiting mass flux of 0.00025 kg/m2/s the average annual solar pond efficiency in the second and the third year is about 17% and this corresponds to a heat extraction of about 970 MJ/m2/year from LCZ alone. 5.2. Heat extraction from NCZ and LCZ Here the performance of the solar pond with heat extraction simultaneously from NCZ and LCZ is investigated. Here two scenarios are considered, first with a constant heat transfer fluid mass flux flowing through both
NCZ and LCZ heat exchangers. And second, with different mass flux of heat transfer fluid flowing through NCZ and LCZ heat exchangers. Figs. 8 and 9 show the thermal performance of the solar pond for the first scenario with constant mass flux of the heat transfer fluid ranging from 0.0001 kg/m2/s to 0.0002 kg/m2/s. It can be seen from Fig. 8 that 0.00015 kg/m2/s is the limiting mass flux of the heat transfer fluid to maintain a temperature difference of more than 20 °C between LCZ and heat transfer fluid inlet temperature for the solar pond under investigation. It can be seen from Fig. 9 that the average annual efficiency of the solar pond for limiting mass flux of 0.00015 kg/m2/s in the second and the third year is about 22% and this corresponds to a combined heat extraction from NCZ and LCZ of
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Fig. 10. LCZ temperature development profiles with different mass flux of heat transfer fluid flowing through NCZ and LCZ heat exchanger.
Eff - NCZ 0.00025 kg/m²/s & LCZ 0.0001 kg/m²/s Eff - NCZ 0.0002 kg/m²/s & LCZ 0.0001 kg/m²/s Eff - NCZ 0.0001 kg/m²/s & LCZ 0.0002 kg/m²/s Heat Extracted - NCZ 0.00025 & LCZ 0.0001 kg/m²/s Heat Extracted - NCZ 0.0002 & LCZ 0.0001 kg/m²/s Heat Extracted - NCZ 0.0001 & LCZ 0.0002 kg/m²/s
60
40%
50
30%
40
20%
30
10%
20
0%
10
-10% 0
120 Dec
Mid-Summer
240
360
480
June
Mid-Winter
600
720
840
960
Heat extracted (W/m²)
Instantenous Efficiency (%)
50%
0 1080
Days
Fig. 11. Instanteneous efficiency profiles with different mass flux of heat transfer fluid flowing through NCZ and LCZ heat exchanger.
about 1200 MJ/m2/year. This is about 30% improvement in the efficiency of the solar pond as compared with solar pond with heat extraction from LCZ only. This improvement is achieved while maintaining the minimum temperature difference of 20 °C between LCZ and inlet temperature of the heat transfer fluid for the solar pond under investigation. Figs. 10 and 11 show the thermal performance of the solar pond for the second scenario with different mass flux of heat transfer fluid flowing through NCZ and LCZ heat exchanger. A wide range of mass flux combinations have been tried with the transient model and the combination with highest average annual efficiency is determined while maintaining the limiting temperature difference. It can be said from Fig. 10 that to maintain higher LCZ tempera-
tures, the mass flux of heat transfer fluid in the NCZ heat exchanger should always be greater than or equal to mass flux of heat transfer fluid that flow through the LCZ heat exchanger. It can be seen from Figs. 10 and 11 that maximum efficiency could be achieved while maintaining a temperature difference of 20 C between LCZ and heat transfer fluid inlet temperature when a mass flux of 0.00025 kg/m2/s is applied to NCZ and a mass flux 0.0001 kg/m2/s is applied to LCZ. It can be seen from Fig. 11 that for this operating condition the average annual efficiency of the solar pond in the second and the third year is about 25% and this corresponds to a combined heat extraction from NCZ and LCZ of about 1330 MJ/m2/year. This represents an improvement of about 47% (i.e. (25–17)/17 = 47%) in the efficiency of the solar pond as compared with solar
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pond with heat extraction from LCZ only, while maintaining the minimum temperature difference of 20 °C between LCZ and inlet heat transfer fluid temperature. The average annual efficiency of the solar pond could be further improved by reducing the available temperature difference between the LCZ and heat transfer fluid inlet temperature. It is seen from Figs. 8–11 that if the mass flux of the heat transfer fluid is kept constant throughout the year then the instantaneous efficiency of the solar pond drops to minimum value during the mid-winter and reaches a maximum value during the start of summer and stays high till the mid-summer. This strategy of keeping the mass flux of heat transfer fluid constant would be most practical. The present numerical investigation of solar pond under investigation satisfies the stability criteria as explained under Section 3.3. 6. Summary/conclusion This study has found that the temperature of LCZ and the average annual solar pond efficiency is very sensitive to the mass flux of the heat transfer fluid that flows through the in-pond heat exchangers. This investigation shows that there is a sharp decrease in the LCZ temperature if the rate of heat extracted from LCZ is higher than that from NCZ. Hence the mass flux of heat transfer fluid that flows through the NCZ heat exchanger should always be greater than or equal that mass flux that flows through LCZ heat exchanger. It is also found that the instantaneous efficiency curves tend to flatten out with increased heat extraction for both LCZ alone and combined NCZ and LCZ heat extraction. The maximum average annual solar pond efficiency of about 25% could be achieved while maintaining a minimum temperature difference of 20 °C between LCZ and UCZ. Higher average annual solar pond efficiencies could be achieved with smaller minimum temperature difference between LCZ and inlet temperature of the heat transfer fluid. And the average annual efficiency of the solar pond is improved by about 47% for simultaneous heat extraction from NCZ and LCZ as compared to solar pond with heat extraction from LCZ only, while maintaining a minimum temperature difference of 20 °C between LCZ and inlet temperature of heat transfer fluid. For a temperature difference of 20 °C between LCZ and inlet temperature of heat transfer fluid, a solar pond in Melbourne could be operated at 17% average annual efficiency with an optimum heat transfer fluid mass flux of 0.00025 kg/m2/s for heat extraction from LCZ alone. Further for same temperature difference between LCZ and inlet temperature of heat transfer fluid, the average annual efficiency of this solar pond could be increased to 22% with simultaneous heat extraction from both NCZ and LCZ for a constant heat transfer fluid mass flux of 0.00015 kg/m2/s.
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Furthermore for same temperature difference between LCZ and inlet temperature of heat transfer fluid, the average annual efficiency of this solar pond could be improved to 25% by extracting heat from both NCZ and LCZ with different mass flux rates of 0.00025 kg/m2/s and 0.0001 kg/m2/s respectively. It is shown that the proposed finite difference model could be used to predict the mass flux of heat transfer fluid for in-pond heat exchangers. While for practical use more realistic heat transfer effectiveness should be considered for the in-pond heat exchanger. Further development of this model is required in order to predict the mass flux of saline water withdrawal and injection when using a series of external heat exchangers. To achieve this, the finite difference transient model has to be two dimensional that would allow considering the effect saline water withdrawal and injection on the stability of the gradient layer (NCZ). Nevertheless the present study has provided an improved transient model to predict the thermal performance of solar pond as compared to the earlier studies. It is suggested that in future applications of this numerical model effect of salt content on the scattering of sun light should be considered for more detailed performance prediction. References Aboul-Enein, S., El-Sebaii, A.A., Ramadan, M.R.I., Khallaf, A.M., 2004. Parametric study of a shallow solar-pond under the batch mode of heat extraction. Applied Energy 78 (2), 159–177. Andrews, J., Akbarzadeh, A., 2005. Enhancing the thermal efficiency of solar ponds by extracting heat from the gradient layer. Solar Energy 78 (6), 704–716. Bansal, P.K., Kaushik, N.D., 1981. Salt gradient stabilized solar pond collector. Energy Conversion and Management 21 (1), 81–95. Bozkurt, I., Karakilcik, M., 2012. The daily performance of a solar pond integrated with solar collectors. Solar Energy 86 (5), 1611–1620. Bryant, H.C., Colbeck, I., 1977. A solar pond for London? Solar Energy 19 (3), 321–322. Gasulla, N., Yaakob, Y., Leblanc, J., Akbarzadeh, A., Cortina, J.L., 2011. Brine clarity maintenance in salinity-gradient solar ponds. Solar Energy 85 (11), 2894–2902. Hull, J.R., 1979. Physics of The Solar Pond. Iowa State University of Science and Technology. Husain, M., Sharma, G., Samdarshi, S.K., 2012. Innovative design of nonconvective zone of salt gradient solar pond for optimum thermal performance and stability. Applied Energy 93, 357–363. Jaefarzadeh, M.R., 2006. Heat extraction from a salinity-gradient solar pond using in pond heat exchanger. Applied Thermal Engineering 26 (16), 1858–1865. Kaushik, N.D., Bansal, P.K., Sodha, M.S., 1980. Partitioned solar pond collector/storage system. Applied Energy 7 (1–3), 169–190. Kooi, C.F., 1979. The steady state salt gradient solar pond. Solar Energy 23 (1), 37–45. Kumar, A., Kishore, V.V.N., 1999. Construction and operational experience of a 6000 m2 solar pond at Kutch, India. Solar Energy 65 (4), 237–249. Leblanc, J., Akbarzadeh, A., Andrews, J., Lu, H., Golding, P., 2011. Heat extraction methods from salinity-gradient solar ponds and introduction of a novel system of heat extraction for improved efficiency. Solar Energy 85 (12), 3103–3142.
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Malik, N., Date, A., Leblanc, J., Akbarzadeh, A., Meehan, B., 2011. Monitoring and maintaining the water clarity of salinity gradient solar ponds. Solar Energy 85 (11), 2987–2996. Tabor, H., 1981. Solar ponds. Solar Energy 27 (3), 181–194. Tabor, H.Z., Doron, B., 1990. The Beith Ha’Arava 5 MW(e) Solar Pond Power Plant (SPPP) progress report. Solar Energy 45 (4), 247–253. Wang, Y.F., Akbarzadeh, A., 1982a. A study on the transient behaviour of solar ponds. Energy 7 (12), 1005–1017. Wang, Y.F., Akbarzadeh, A., 1982b. A further study on the theory of “falling ponds”. Solar Energy 29 (6), 557–563. Wang, Y.F., Akbarzadeh, A., 1983. A parametric study on solar ponds. Solar Energy 30 (6), 555–562.
Wang, J., Seyed-Yagoobi, J., 1995. Effect of water turbidity on thermal performance of a salt-gradient solar pond. Solar Energy 54 (5), 301– 308. Weinberger, H., 1964. The physics of the solar pond. Solar Energy 8 (2), 45–56. Yaakob, Y., Date, A., Akbarzadeh, A., 2011. Heat extraction from gradient layer using external heat exchangers to enhance the overall efficiency of solar ponds. in: IEEE First Conference on Clean Energy and Technology (CET). Zhang, Z.M., Wang, Y.F., 1990. A study on the thermal storage of the ground beneath solar ponds by computer simulation. Solar Energy 44 (5), 243–248.
ScienceDirect Solar Energy 97 (2013) 517–528 www.elsevier.com/locate/solener
Heat extraction from Non-Convective and Lower Convective Zones of the solar pond: A transient study Abhijit Date a,⇑, Yusli Yaakob a, Ashwin Date a, Shankar Krishnapillai b, Aliakbar Akbarzadeh a a
School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box 71, Bundoora, Victoria 3083, Australia b Indian Institute of Technology Madras, Chennai, India Received 11 June 2013; received in revised form 10 August 2013; accepted 7 September 2013
Communicated by: Associate Editor Yogi Goswami
Abstract Heat extraction from the Non-Convective Zone (NCZ) or gradient layer and Lower Convective Zone (LCZ) of the solar pond has been investigated through one-dimensional finite difference transient model. Instantaneous efficiency of the solar pond is introduced and defined in this paper. The solar pond considered in the present study is assumed to have an in-pond heat exchanger for heat extraction. The rate of heat transfer is controlled by the mass flux of heat transfer fluid in this model. As in reality mass flux of heat transfer fluid is the simplest and most practical way to control the rate of heat extraction. In this model for an ideal situation it is assumed that the heat transfer fluid is initially at the local daily average ambient temperature and the in-pond heat exchanger has heat transfer effectiveness equal to unity. With these assumptions the model can predict the thermal performance of the solar pond with maximum heat extraction for a desired mass flux of the heat transfer fluid. This paper presents the comparison of the transient thermal performance of solar pond with heat extraction from LCZ alone and that with combined heat extraction from LCZ and NCZ. It is shown how the efficiency of the solar pond increases when heat is extracted from both NCZ and LCZ. The main objective of this study is to offer a simple method to predict transient thermal performance of a solar pond with heat extraction from NCZ and to estimate the mass flux of heat transfer fluid used in an in-pond heat exchanger for heat extraction from different layers of solar pond. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Solar pond; Heat extraction; Transient performance
1. Introduction A solar pond is a large body of saline water whose salinity increases with depth. These ponds are used as solar thermal energy collectors that can simultaneously store heat for long period, so they are suitable for sessional solar thermal energy storage. In case of fresh water ponds almost all the solar radiation that falls on the surface is absorbed by top 3 m of fresh water and this thermal energy is rapidly lost to the atmosphere through natural convection heat transfer. ⇑ Corresponding author. Tel.: +61 3 9925 0612; fax: +61 3 9925 6108.
E-mail address: [email protected] (A. Date). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.09.013
So the temperature of a fresh water pond never rises and is almost constant throughout the fresh water pond depth. Practical heat extraction from Lower Convective Zone (LCZ) for different applications is very common. In past heat has been extracted from LCZ using two methods, in the first method hot saline water is extracted from the LCZ and passed through an external heat exchanger as used at Kutch in India (Kumar and Kishore, 1999) and Beith Ha’arava in Israel (Tabor and Doron, 1990). In the second method an in-pond heat exchanger is used for heat extraction from the LCZ as used at Pyramid Hill, Victoria (Leblanc et al., 2011) and Marshad in Iran (Jaefarzadeh, 2006). Tabor (Tabor, 1981) has discussed both of these
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Nomenclature Asp cp DE h Hhs H(X) jmf k Lr q00e q00 S s T X DX
surface area of solar pond (m2) specific heat capacity (J/kg °C) instantaneous change in the energy content (J) solar radiation flux absorbed (W/m2) global solar radiation flux incident on the horizontal surface (W/m2) solar radiation flux that reaches to X (m) of depth of solar pond (W/m2) mass flux of heat transfer fluid (kg/m2/s) thermal conductivity (W/m °C) solar radiation reflective losses (%) heat flux extracted by heat transfer fluid (W/m2) conductive heat flux (W/m2) salinity (%) salinity (kg/m3) temperature of node (°C) path length of light in solar pond to the end of the respective division (m) thickness of the division (m)
methods in his review of solar pond technology, and stressed that both method have convenient practical merit. The main limitation to the full scale application of solar ponds in industry has been the low solar thermal efficiency and in many cases lowers temperature heat available (below 60 °C) as discussed by Leblanc et al. (2011) and Andrews and Akbarzadeh (2005). Researchers have proposed many different ways of improving the thermal performance of solar ponds, which include improving the water clarity (Gasulla et al., 2011; Wang and Seyed-Yagoobi, 1995; Malik et al., 2011), increasing the thickness of LCZ and reducing the thickness of Upper Convective Zone (UCZ) Wang and Akbarzadeh, 1982a, introducing an additional upper Non-Convective Zone (NCZ) Husain et al., 2012, putting an external reflector to reflect additional solar radiation into solar pond (Aboul-Enein et al., 2004), by integrating a solar pond with flat plate solar collectors (Bozkurt and Karakilcik, 2012), etc. Researchers have proposed of extracting/utilizing the heat stored in the NCZ to improve the overall thermal performance of the solar ponds and have claimed to improve the solar pond efficiency by up to 50% using a steady state theoretical model (Leblanc et al., 2011; Andrews and Akbarzadeh, 2005; Yaakob et al., 2011). To date all the studies have used steady state theoretical model and its unknown if similar improvement in the solar pond efficiency is achievable for real solar pond using a transient model. Present paper investigates the transient thermal performance of the solar pond with heat extraction from both NCZ and LCZ. Through this paper efforts have been made to further develop the one-dimensional finite difference model of the solar pond for predicting the mass flux of heat transfer fluid flowing through an in-pond heat
q gsp in gsp avg
density (kg/m3) instantaneous efficiency of solar pond (%) average annual solar pond efficiency (%)
Subscripts e extraction i inlet or initial n nth layer/node in solar pond and ground n 1 Layer/node above the nth node n + 1 Layer/node below the nth node g ground ucz Upper Convective Zone ncz Non-Convective Zone lcz Lower Convective Zone s present time (s) Ds time increment (s) f heat transfer fluid fw fresh water
exchanger in a solar pond. This new model can predict transient behaviour of such solar pond while neglecting the shading and wall effects. Effects on the temperature profile of the solar pond for different heat extraction rates from NCZ and LCZ have been discussed and the best mix of heat extraction has been presented. 2. Solar pond Fig. 1 shows the schematic of salinity gradient solar pond, which consists of three regions. The cold upper layer or Upper Convective Zone (UCZ) is a homogeneous thin layer of low salinity brine or fresh water. The middle gradient layer or Non-Convective Zone (NCZ) has salinity gradient with salinity increasing from top of NCZ to the bottom of NCZ, this helps suppress the heat loss by natural convection. The bottom layer or Lower Convective Zone (LCZ) has high salinity (some cases close to saturation) that absorbs and stores solar radiation that reaches the LCZ in form of thermal energy. If Hhs amount of solar radiation is incident on the horizontal top surface of the solar pond and around Lr percentage of solar radiation is reflected back to the atmosphere, then (Hhs Lr Hhs) amount of solar radiation penetrates the top surface of the solar pond. And this amount of solar radiation is gradually absorbed by the water along the depth of the solar pond. As shown in Fig. 1, hucz is the amount of solar radiation that is absorbed by the water in the UCZ, hncz is the amount of solar radiation that is absorbed by the water in the NCZ and hlcz is the amount of solar radiation that is absorbed in the LCZ. The solar radiation that is absorbed in the three layers of the solar pond is converted to heat. Part of this heat is lost
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519
Fig. 1. Schematic diagram of salinity gradient solar pond.
to the atmosphere and part is lost to the ground. The amount of heat that is stored in the LCZ and NCZ is available for extraction and this amount of heat is responsible for the temperature gradient formation in the solar pond. 3. Theoretical modelling To predict thermal performance of large solar ponds, the thermal process in these solar ponds can be treated as one-dimensional unsteady conduction loss, with heat generation from incoming solar radiation as used by many researchers in the past (Wang and Akbarzadeh, 1982a; Aboul-Enein et al., 2004; Bansal and Kaushik, 1981). Here efforts are made to develop a transient thermal performance model of a solar pond with heat extraction from NCZ and LCZ following the steady state model developed by Andrews and Akbarzadeh(2005) and the finite difference method discussed by Wang and Akbarzadeh (1982a). It is assumed that the main mode of heat transfer in the NCZ is only by conduction and convection is suppressed by the available density gradient. As shown in Fig. 2 a solar pond is assumed to have two thermal boundaries (Upper and Lower). The upper boundary is at the interface of the UCZ and the NCZ. The temperature of the UCZ is assumed to the equal to the monthly average local daily
Fig. 2. Schematic diagram of zone interfaces.
temperature as suggested by Hull (1979) and Weinberger (1964). This assumption has been made to simplify the solar pond analysis. For accurate performance prediction of the solar pond it is important to consider the energy balance between UCZ and the air interface as discussed by Bansal and Kaushik (1981). The lower boundary is at the interface of the LCZ and the ground below the pond. The temperature of the ground below the pond will be affected by the temperature of LCZ. For the purpose of one-dimensional finite difference model the NCZ is divided into number of divisions each with a thickness of DX, while LCZ is considered to be single layer with temperature at the top of the LCZ equal to the bottom temperature of LCZ. It is not necessary for these divisions to have equal thickness, but in the present study for simplicity these divisions are assumed to have equal thickness. And the nodes are located at the centre of each division. Eq. (1) provides a generalised energy balance equation for the solar pond. 00s 00s DEnsþDs ¼ hsn Ds þ q00s n1 Ds þ qnþ1 Ds qe n Ds
ð1Þ
here DEsþDs represents the change in the energy content of n nth layer (i.e. layer under investigation) in solar pond after time Ds, hsn represents the solar radiation energy absorbed by nth layer in solar pond at time s, q00s n1 represents the conductive heat transfer to or from the division above the nth layer in solar pond at time s, q00s nþ1 represents the conductive heat transfer to or from the division below the nth layer in solar pond at time s and q00s e n represents the heat extracted from the nth layer in solar pond at time s. The solar radiation flux h (W/m2) that is absorbed by each layer is equal to the solar radiation transmitted through the layer above minus the solar radiation that reaches the top of the layer below. If hourly solar radiation data is available then the reflective losses from the surface of the solar pond can be estimated as discussed by Kooi (1979) and Kaushik et al. (1980). In Eq. (2) the percentage reflective losses are represented by Lr and the sun light
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attenuation equation as discussed by Bryant and Colbeck (1977) is used to estimate the solar radiation flux that reaches the nth layer in solar pond at time s . H sn ¼ H shs H shs Lr ð0:36 0:08 ln½X n Þ ð2Þ hsn ¼ Asp ðH sn1 H snþ1 Þ ! T sn T sn1 00s qn1 ¼ DX n DX n1 þ 2kn1 2k n ! s s T T n nþ1 q00s nþ1 ¼ DX nþ1 DX n þ 2k 2k n nþ1
ð3Þ ð4Þ ð5Þ
s s q00s e n ¼ jmf cpf ðT n T f n1 Þ
DEsþDs n
¼ qn Asp DX n cpn
ð6Þ ðT sþDs n
T sn Þ
ð7Þ
As shown in Fig. 3 the first temperature node in the NCZ is only DX/2 distance away from the adjacent temperature node in UCZ and similarly the last temperature node in NCZ is only DX/2 distance away from the adjacent temperature node in LCZ. So when writing the equation for the conductive heat loss or gain from the first temperature node in NCZ to the adjacent temperature node in UCZ it should be noted that only one thickness and thermal conductivity term will appear in the denominator of the Eq. (4). Similarly when writing the equation for the conductive heat loss or gain from the temperature node in the NCZ to the adjacent temperature node in LCZ it should be noted that only one thickness and thermal conductivity term will appear in the denominator of the Eq. (5). Similar one-dimensional finite method is used for thermal analysis of the ground below the pond. Wang and
Akbarzadeh (1982a) have suggested that ground temperature beyond 5 m below the solar pond floor can be assumed to be equal to the yearly average ambient temperature. So 5 m of ground below the solar pond floor is divided into number of sub divisions each with a thickness of DXg. There is no heat generation in the ground as the solar radiation does not reach there and there is no heat extraction from the ground. When analysing the energy balance of a division in the ground below solar pond there is only conductive heat loss or gain from the layer above and below. Following equation provides the generalised energy balance for ground below the solar pond. 00s DEgsþDs ¼ q00s n g n1 Ds þ qg nþ1 Ds
ð8Þ
here DEsþDs represents the change in the energy content of gn nth layer in ground below solar pond after time Ds, q00s g n1 represents the conductive heat transfer to or from the division above the nth layer in the ground at time s and q00s g nþ1 represents the conductive heat transfer to or from the division below the nth layer in the ground at time s. 0 1 s s T T g n g n1 @ A ð9Þ q00s g n1 ¼ DX g n1 DX g n þ 2k g n 2k g n1 0 1 T sg n T sg nþ1 00s ð10Þ qg nþ1 ¼ @ DX g n DX g nþ1 A þ 2k g n 2k g nþ1 sþDs s DEg n ¼ qg n Asp DX g n cpg n T sþ1 T ð11Þ gn gn
Fig. 3. Schematic of symmetrical section of solar pond – NCZ, LCZ and ground divisions, node positions and NCZ–LCZ heat extraction systems.
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The initial temperature of the solar pond is assumed to be equal to the monthly average ambient. Knowing this initial temperature and the incoming solar radiation the and repeatedly solving Eqs. (1)–(9), (11), (12) for different divisions and the interfaces the final temperatures of all divisions at the end of each time increment can be obtained node by node. 3.1. Transient model convergence criteria In all the above equations s is the initial time that is used to predict the thermal performance after a time increment of Ds. The time increment and the thickness of the each sub division of the solar pond zones can be of any size, but they should satisfy the stability condition shown in Eq. (13) as discussed by Wang and Akbarzadeh (1982a). ! 1 1 Ds þ DX 61 ð12Þ DX n1 DX nþ1 DX n n q DX þ 2kn1 2kn þ 2k n cp n n 2k n nþ1
521
the heat loss or gain from the LCZ of the solar pond in a time interval of Ds. DEsg ¼
0 X
X g n Asp qg n cpg n T sg n T s1 gn
ð15Þ
n
and hence the instantaneous efficiency of the solar pond can be calculated by using Eq. (17). ginst SP ¼
DEslcz þ DEsncz þ DEsg Asp H shs H shs Lr Ds
ð16Þ
Average annual solar pond efficiency is expressed as the ratio of sum of change in energy content of LCZ, NCZ and ground per year divided by the total solar radiation that penetrates the top surface of the solar pond per year and is shown by Eq. (17). Here the first day is the when the solar pond operation begins. i Pday¼1 h s s s DE þ DE þ DE lcz ncz g day¼360 gsolar pond ¼ Pday¼1 ð17Þ s s day¼360 Asp H hs H hs Lr Ds
3.2. Efficiency of solar pond 3.3. Solar salinity gradient stability criteria Solar pond efficiency would have meaning only when heat is extracted from the solar pond. Conventionally heat has been extracted from the LCZ of the solar pond. As the solar pond has got large thermal mass, the rate of heat extraction can be varied to suit the application without compromising the stability of the solar pond. Although using the instantaneous heat extraction rate alone to estimate the instantaneous efficiency of the solar pond can be very misleading. This is because in some applications the instantaneous rate of heat extraction can be larger than the solar radiation that penetrates the top surface of the pond. So here the instantaneous efficiency of the solar pond is defined as ratio of instantaneous change in energy content of the solar pond plus ground below the solar pond divided by the amount of solar radiation that penetrates the top surface of the solar pond. The instantaneous change in the energy content of LCZ is shown by Eq. (14) as the sum of the energy extracted (heat extracted) and solar energy absorbed in a time interval of Ds. DEslcz ¼ jmf lcz cpf lcz T slcz T sf i Ds þ X lcz ð13Þ Asp qlcz cplcz T slcz T s1 lcz The instantaneous change in the energy content of NCZ is shown by Eq. (15) as the sum of the energy extracted (heat extracted) and solar energy absorbed in a time interval of Ds. X0 h DEsncz ¼ j cpf ðT sn T sf n Þ Ds þ X n Asp n mf ncz ð14Þ qn cpn T sn T s1 n The instantaneous change in the energy content of ground below the solar pond is shown by Eq. (16) and is equal to
The stability of the salinity gradient layer (non-convecting layer) has been discussed in a number of articles (Wang andAkbarzadeh (1982a,b). The following relations for stability of the solar pond have been used for the present study and earlier it has been used by Wang and Akbarzadeh (1982a,b). ds dT > 0:44 for the surface condition dX dX ds dT > 1:18 for the bottom condition dX dX
ð18Þ ð19Þ
In the above equation s is salinity (kg/m3), T temperature dS (°C) and x is the pond depth (m). Further, dX is salinity gradT dient and dX is the temperature gradient in the pond. In the first few cm below the surface of the pond, the available solar radiation decreases very sharply. At a depth of 0.3 m, the intensity of solar radiation is close to half of its original value and, if there is no convection at this depth, then as discussed by Wang and Akbarzadeh(1982a) the corresponding temperature gradient can be expected to be as high as 200 °C/m. For a top convective layer with 0.3 m thickness the density gradient should be such that it can suppress convection caused by the temperature gradient. Substituting the value of 200 °C/m for the temperature gradient in Eq. (18), a value of 88 kg/m3/m is obtained for the corresponding minimum salinity gradient to prevent erosion. For a bottom convective layer if no heat is extracted the minimum temperature gradient that can be present would be 60 °C/m. To support this temperature gradient at the bottom, a salinity density gradient of at least 70.8 kg/m3/m is required to ensure stability as estimated by using Eq. (19). A stable solar pond phenomenon can only exist if a minimum salinity gradient of 88 kg/m3/m is
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present at the interface of the UCZ and NCZ. And at least 70.8 kg/m3/m of salinity gradient is present at interface of NCZ and LCZ. 4. Simulation boundary conditions and assumptions For the present study a reference solar pond in Melbourne with large enough surface area to neglect heat loss through wall is used and the salt is sodium chloride. The temperature development is predicted for a three year period. The solar pond starts operation on 1st October (i.e. early spring in southern hemisphere), and the heat removal operation starts after 60 days. This solar pond is assumed to have 0.3 m thick UCZ and for the purpose solving the finite difference model the UCZ is considered to be a single layer. The salinity of the water in the UCZ is assumed to be 2% and the temperature of UCZ is assumed to be equal to the monthly average ambient temperature. This assumption is to simplify the analysis. The NCZ is assumed to be 1.2 m thick and is divided into eight sub divisions for the purpose of solving the finite difference model to estimate the temperatures of the nodes assumed to be located at the centre of each layer in the NCZ (i.e. n = 8). It is assumed that the LCZ has constant salinity and hence this layer always has same temperature throughout its thickness. The LCZ is assumed to be 1.5 m thick with a uniform salinity of 20%. So the solar pond under investigation has a total depth of 3 m which is very commonly used. The properties of the salt water are calculated using the following relations as discussed by Wang and Akbarzadeh (1982a). Sn k n ¼ 0:5553 0:0000813 qfw þ 0:0008 100 ðT sn 20Þ
Sn qfw 0:4 ðT sn 20Þ 100 Sn cpn ¼ 4180 4:396 qfw þ 0:0048 100 2 Sn qfw 100 qn ¼ 998 þ 0:65
ð17Þ
solar radiation is always normal to the solar pond surface. This assumption is made only to simplify the analysis for the purpose of the present study. For accurate performance prediction the reflective losses from the surface of the solar pond due to varying angle of incidence should be estimated as discussed by Kooi (1979) and Kaushik et al. (1980). As discussed in the previous section Bryant and Colbeck solar radiation attenuation equation is used with path length X as the real vertical distance that sun light has travelled after it penetrates the water surface. For the present study both solar radiation and ambient temperature are adequately approximated by sinusoidal functions based on statistical data of monthly average values as shown in Fig. 4. The solar pond is assumed to have an in-pond heat exchanger installed around the peripheral wall of the solar pond for heat extraction from the NCZ and on the bottom of solar pond for heat extraction from LCZ. The rate of heat extraction from the solar pond is controlled by the mass flux of heat transfer fluid flowing through the in-pond heat exchangers. While in operation controlling flow rate is the simplest and most practical way to control the heat extraction. It is assumed that the heat transfer fluid is initially at the same temperature as the temperature of UCZ or average ambient temperature. Further both the heat exchangers in NCZ and LCZ are assumed to have heat transfer effectiveness equal to 1, i.e. the heat transfer fluid will always get heated to the temperature corresponding solar pond division. This assumption is made to simplify the heat transfer analysis. For more accurate performance prediction more realistic value of heat exchanger effectiveness must be used. Further any effect if present due to the heat extraction from the NCZ on the stability of the salinity gradient is not considered in the present study. This study investigates following two ways of heat extraction,
ð18Þ
ð19Þ
here Sn is the salinity if of the water in nth layer of the solar pond and qfw is the density of fresh water and is assumed to be 1000 kg/m3. The ground below the solar pond is assumed to have uniform thermal properties. As explained by earlier researchers the underground conditions have strong influence on the thermal performance of the solar pond (Aboul-Enein et al., 2004; Wang and Akbarzadeh, 1983). In this simulation it is assumed that the solar pond is lined with plastic liner under which there is 5 m of clay liner. The thermal properties of the clay under the pond liner are assumed based on the work by Zhang and Wang (1990), kg = 1.28 W/m K; qg = 1460 kg/m3; cpg ¼ 880 J=kg K. It is assumed that all solar radiation (diffused and direct) comes from sun and angle of incidence is equal to zero i.e.,
Transient thermal performance prediction of pond while extraction heat at different rates LCZ alone. Transient thermal performance prediction of pond while extraction heat at different rates both NCZ and LCZ.
the solar from the the solar from the
5. Results and discussion Fig. 5 shows the temperature development of the solar pond under investigation without heat extraction over a period of 3 years. The boiling of the water in LCZ in the second and third year is ignored in Fig. 5 to simplify the heat transfer model used for temperature development. It should be noted that in reality the LCZ temperature will never go beyond the local boiling temperature of the saline water. It can be seen that the LCZ temperature increases significantly in the first year. It is interesting to see from Fig. 5
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Average solar radiation and ambient temperatures for Melbourne 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0
Average global daily irradiance on horizontal surface
30 25 20 15 10 5
0
Sollar Radiation (MJ/m²/day)
Temperature ( C)
Monthly Average Ambient Temp
0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 1020 1080 Dec June Mid-Winter
Mid-Summer
Days
Fig. 4. Melbourne climate data – Monthaly average of daily global solar radiation on horizontal surface and montly average temperature.
Temperature profile of solar pond without heat extraction (Heat extrated = 0 MJ/m²/year) UCZ Temp
NCZ Temp -0.55m depth
NCZ Temp -0.83m depth
NCZ Temp -1.1m depth
NCZ Temp -1.36m depth
LCZ Temp
Instantaneous efficiency
Tem mperature (°C)
90
Layer
Thickness
UCZ NCZ LCZ
0.3m 1.2m 1.5m
50% 40% 30%
80
20%
70
10%
60
0%
50
-10%
40
-20%
30
-30%
20
-40%
10
-50%
0 0
Instantan neous efficiency (%)
110 100
-60% 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 10201080
Dec June Mid-Summer Mid-Winter
Days
Fig. 5. Temperature development of solar pond in Melbourne without heat extration.
how the instantaneous efficiency starts to decreases as the temperature of the pond starts to increases in first couple of months from the start of the solar pond operation. Instantaneous efficiency is a measure of the energy absorbed and/or extracted and energy lost, if the value of instantaneous efficiency falls below 0% then this means the instantaneous energy loss is more than the instantaneous energy absorbed and/or extracted. Further it interesting to see that the maximum and minimum LCZ temperature corresponds to 0% instantaneous efficiency and it does not correspond to the maximum and minimum instantaneous efficiency points, the main reason for this is the thermal inertia of the solar pond. For the first year the average annual solar pond efficiency is about 9%, while for the second and third year the average annual efficiency of the solar pond is 1% and 0.1% respectively. In the second and third year the low average
annual solar pond efficiency can be attributed to the higher solar pond temperatures and no heat extraction. 5.1. Heat extraction from LCZ alone Fig. 6 shows the temperature development of the solar pond under investigation with heat extraction from LCZ alone over a period of 3 years. The heat extraction starts on 60th day from the start of the operation of the solar pond. Heat transfer fluid initially at UCZ temperature (i.e. equal to the ambient temperature) flows through the in-pond heat exchanger in the LCZ. By varying the mass flux of the heat transfer fluid the rate of heat extraction can be controlled. To extract heat from solar pond at least 5 °C of driving temperature difference would be required between LCZ and heat transfer fluid. Further 5 °C of driving temperature
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A. Date et al. / Solar Energy 97 (2013) 517–528 LCZ 0.00015 kg/m²/s
LCZ 0.0002 kg/m²/s
LCZ 0.00025 kg/m²/s
LCZ 0.0003 kg/m²/s
UCZ - Temp
Solar Radiation
70
70
50
Temperature (°C)
50 40
40
38°C 33°C 29°C
30
30
29°C
26°C
20
20
ΔT= 20°C 19°C 9°C
9°C
10 0 0
Solar Radiation (MJ/m²/day)
60
59°C
60
10
0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 10201080
June
Dec
Mid-Summer
Days
Mid - Winter
Fig. 6. Temperature development of the solar pond with heat extraction from LCZ.
Eff - LCZ 0.00015 kg/m²/s Eff - LCZ 0.00025 kg/m²/s Heat extracted @ 0.00015 kg/m²/s Heat extracted @ 0.00025 kg/m²/s
Eff - LCZ 0.0002 kg/m²/s Eff - LCZ 0.0003 kg/m²/s Heat extracted @ 0.0002 kg/m²/s Heat extracted @ 0.0003 kg/m²/s
50%
50
40 35
30%
30 20%
25 20
10%
15
Heat extracted (W/m²)
Instantenous Efficiency (%)
45 40%
10
0%
5 -10% 0
120
Dec Mid-Summer
240
360
480
June
600
720
840
960
0 1080
Days
Mid-Winter
Fig. 7. Instanteneous efficiency of solar pond for heat extraction from LCZ with different mass flux of heat transfer fluid.
difference would be required for heat transfer between heat transfer fluid and the end use application such as heating of air. So for any meaningful use of the available heat in the solar pond, it is assumed that a minimum 20 °C temperature difference must be present between the LCZ temperature and the heat transfer fluid inlet temperature (average ambient temperature). Further it is assumed that the inlet temperature of the heat transfer fluid is maintained at the same temperature as UCZ (i.e. ambient temperature). Fig. 6 shows the LCZ temperature development profile for a solar pond with heat extraction from LCZ alone and constant heat transfer fluid mass flux between 0.00015 kg/m2/s and 0.0003 kg/m2/s. It is found that the 0.00025 kg/m2/s is the limiting mass flux of the heat transfer fluid to maintain a minimum temperature difference of 20 °C between LCZ and inlet
temperature of the heat transfer fluid for the solar pond under investigation located in Melbourne. If the mass flux is increased beyond 0.00025 kg/m2/s the solar pond efficiency will improve but the available temperature difference will fall below 20 °C and this will limit the application of available heat. Further from Fig. 6, it can also be seen that for the limiting mass flux the highest temperature of 59 °C appears at the end of February with a lag of about 2 months behind the maximum insolation and there is a minimum temperature of 29 °C, this is mainly due to large thermal mass of the solar pond and suppressed convective heat loss by the NCZ. The yearly average LCZ temperature for the limiting mass flow of heat transfer fluid of 0.00025 kg/m2/s is 44 °C, which is about 30 °C above the annual mean
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Eff - NCZ & LCZ 0.0001 kg/m²/s
Eff - NCZ & LCZ 0.0002 kg/m²/s
Eff - NCZ & LCZ 0.00015 kg/m²/s
Heat Extracted from NCZ & LCZ @ 0.0001 kg/m²/s
Heat Extracted from NCZ & LCZ @ 0.0002 kg/m²/s
Heat Extracted from NCZ & LCZ @ 0.00015 kg/m²/s
50%
60
40%
50
30%
40
20%
30
10%
20
0%
10
-10% 0
120 Dec Mid -Summer
240 June
Mid- Winter
360
480
600
720
840
960
Heat extracted (W/m²)
Instantenous Efficiency (%)
Fig. 8. LCZ temperature development profiles with constant heat transfer fluid mass flux through NCZ and LCZ heat exchanger.
0 1080
Days
Fig. 9. Instanteneous efficiency profiles with constant mass flux of heat transfer fluid through NCZ and LCZ heat exchanger.
ambient temperature. The yearly LCZ temperature fluctuation is about 30 °C, which means that with the pond supplying heat at a constant rate the quality of the heat varies substantially with the season. From Fig. 7 it can be seen that for the limiting mass flux of 0.00025 kg/m2/s the average annual solar pond efficiency in the second and the third year is about 17% and this corresponds to a heat extraction of about 970 MJ/m2/year from LCZ alone. 5.2. Heat extraction from NCZ and LCZ Here the performance of the solar pond with heat extraction simultaneously from NCZ and LCZ is investigated. Here two scenarios are considered, first with a constant heat transfer fluid mass flux flowing through both
NCZ and LCZ heat exchangers. And second, with different mass flux of heat transfer fluid flowing through NCZ and LCZ heat exchangers. Figs. 8 and 9 show the thermal performance of the solar pond for the first scenario with constant mass flux of the heat transfer fluid ranging from 0.0001 kg/m2/s to 0.0002 kg/m2/s. It can be seen from Fig. 8 that 0.00015 kg/m2/s is the limiting mass flux of the heat transfer fluid to maintain a temperature difference of more than 20 °C between LCZ and heat transfer fluid inlet temperature for the solar pond under investigation. It can be seen from Fig. 9 that the average annual efficiency of the solar pond for limiting mass flux of 0.00015 kg/m2/s in the second and the third year is about 22% and this corresponds to a combined heat extraction from NCZ and LCZ of
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Fig. 10. LCZ temperature development profiles with different mass flux of heat transfer fluid flowing through NCZ and LCZ heat exchanger.
Eff - NCZ 0.00025 kg/m²/s & LCZ 0.0001 kg/m²/s Eff - NCZ 0.0002 kg/m²/s & LCZ 0.0001 kg/m²/s Eff - NCZ 0.0001 kg/m²/s & LCZ 0.0002 kg/m²/s Heat Extracted - NCZ 0.00025 & LCZ 0.0001 kg/m²/s Heat Extracted - NCZ 0.0002 & LCZ 0.0001 kg/m²/s Heat Extracted - NCZ 0.0001 & LCZ 0.0002 kg/m²/s
60
40%
50
30%
40
20%
30
10%
20
0%
10
-10% 0
120 Dec
Mid-Summer
240
360
480
June
Mid-Winter
600
720
840
960
Heat extracted (W/m²)
Instantenous Efficiency (%)
50%
0 1080
Days
Fig. 11. Instanteneous efficiency profiles with different mass flux of heat transfer fluid flowing through NCZ and LCZ heat exchanger.
about 1200 MJ/m2/year. This is about 30% improvement in the efficiency of the solar pond as compared with solar pond with heat extraction from LCZ only. This improvement is achieved while maintaining the minimum temperature difference of 20 °C between LCZ and inlet temperature of the heat transfer fluid for the solar pond under investigation. Figs. 10 and 11 show the thermal performance of the solar pond for the second scenario with different mass flux of heat transfer fluid flowing through NCZ and LCZ heat exchanger. A wide range of mass flux combinations have been tried with the transient model and the combination with highest average annual efficiency is determined while maintaining the limiting temperature difference. It can be said from Fig. 10 that to maintain higher LCZ tempera-
tures, the mass flux of heat transfer fluid in the NCZ heat exchanger should always be greater than or equal to mass flux of heat transfer fluid that flow through the LCZ heat exchanger. It can be seen from Figs. 10 and 11 that maximum efficiency could be achieved while maintaining a temperature difference of 20 C between LCZ and heat transfer fluid inlet temperature when a mass flux of 0.00025 kg/m2/s is applied to NCZ and a mass flux 0.0001 kg/m2/s is applied to LCZ. It can be seen from Fig. 11 that for this operating condition the average annual efficiency of the solar pond in the second and the third year is about 25% and this corresponds to a combined heat extraction from NCZ and LCZ of about 1330 MJ/m2/year. This represents an improvement of about 47% (i.e. (25–17)/17 = 47%) in the efficiency of the solar pond as compared with solar
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pond with heat extraction from LCZ only, while maintaining the minimum temperature difference of 20 °C between LCZ and inlet heat transfer fluid temperature. The average annual efficiency of the solar pond could be further improved by reducing the available temperature difference between the LCZ and heat transfer fluid inlet temperature. It is seen from Figs. 8–11 that if the mass flux of the heat transfer fluid is kept constant throughout the year then the instantaneous efficiency of the solar pond drops to minimum value during the mid-winter and reaches a maximum value during the start of summer and stays high till the mid-summer. This strategy of keeping the mass flux of heat transfer fluid constant would be most practical. The present numerical investigation of solar pond under investigation satisfies the stability criteria as explained under Section 3.3. 6. Summary/conclusion This study has found that the temperature of LCZ and the average annual solar pond efficiency is very sensitive to the mass flux of the heat transfer fluid that flows through the in-pond heat exchangers. This investigation shows that there is a sharp decrease in the LCZ temperature if the rate of heat extracted from LCZ is higher than that from NCZ. Hence the mass flux of heat transfer fluid that flows through the NCZ heat exchanger should always be greater than or equal that mass flux that flows through LCZ heat exchanger. It is also found that the instantaneous efficiency curves tend to flatten out with increased heat extraction for both LCZ alone and combined NCZ and LCZ heat extraction. The maximum average annual solar pond efficiency of about 25% could be achieved while maintaining a minimum temperature difference of 20 °C between LCZ and UCZ. Higher average annual solar pond efficiencies could be achieved with smaller minimum temperature difference between LCZ and inlet temperature of the heat transfer fluid. And the average annual efficiency of the solar pond is improved by about 47% for simultaneous heat extraction from NCZ and LCZ as compared to solar pond with heat extraction from LCZ only, while maintaining a minimum temperature difference of 20 °C between LCZ and inlet temperature of heat transfer fluid. For a temperature difference of 20 °C between LCZ and inlet temperature of heat transfer fluid, a solar pond in Melbourne could be operated at 17% average annual efficiency with an optimum heat transfer fluid mass flux of 0.00025 kg/m2/s for heat extraction from LCZ alone. Further for same temperature difference between LCZ and inlet temperature of heat transfer fluid, the average annual efficiency of this solar pond could be increased to 22% with simultaneous heat extraction from both NCZ and LCZ for a constant heat transfer fluid mass flux of 0.00015 kg/m2/s.
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Furthermore for same temperature difference between LCZ and inlet temperature of heat transfer fluid, the average annual efficiency of this solar pond could be improved to 25% by extracting heat from both NCZ and LCZ with different mass flux rates of 0.00025 kg/m2/s and 0.0001 kg/m2/s respectively. It is shown that the proposed finite difference model could be used to predict the mass flux of heat transfer fluid for in-pond heat exchangers. While for practical use more realistic heat transfer effectiveness should be considered for the in-pond heat exchanger. Further development of this model is required in order to predict the mass flux of saline water withdrawal and injection when using a series of external heat exchangers. To achieve this, the finite difference transient model has to be two dimensional that would allow considering the effect saline water withdrawal and injection on the stability of the gradient layer (NCZ). Nevertheless the present study has provided an improved transient model to predict the thermal performance of solar pond as compared to the earlier studies. It is suggested that in future applications of this numerical model effect of salt content on the scattering of sun light should be considered for more detailed performance prediction. References Aboul-Enein, S., El-Sebaii, A.A., Ramadan, M.R.I., Khallaf, A.M., 2004. Parametric study of a shallow solar-pond under the batch mode of heat extraction. Applied Energy 78 (2), 159–177. Andrews, J., Akbarzadeh, A., 2005. Enhancing the thermal efficiency of solar ponds by extracting heat from the gradient layer. Solar Energy 78 (6), 704–716. Bansal, P.K., Kaushik, N.D., 1981. Salt gradient stabilized solar pond collector. Energy Conversion and Management 21 (1), 81–95. Bozkurt, I., Karakilcik, M., 2012. The daily performance of a solar pond integrated with solar collectors. Solar Energy 86 (5), 1611–1620. Bryant, H.C., Colbeck, I., 1977. A solar pond for London? Solar Energy 19 (3), 321–322. Gasulla, N., Yaakob, Y., Leblanc, J., Akbarzadeh, A., Cortina, J.L., 2011. Brine clarity maintenance in salinity-gradient solar ponds. Solar Energy 85 (11), 2894–2902. Hull, J.R., 1979. Physics of The Solar Pond. Iowa State University of Science and Technology. Husain, M., Sharma, G., Samdarshi, S.K., 2012. Innovative design of nonconvective zone of salt gradient solar pond for optimum thermal performance and stability. Applied Energy 93, 357–363. Jaefarzadeh, M.R., 2006. Heat extraction from a salinity-gradient solar pond using in pond heat exchanger. Applied Thermal Engineering 26 (16), 1858–1865. Kaushik, N.D., Bansal, P.K., Sodha, M.S., 1980. Partitioned solar pond collector/storage system. Applied Energy 7 (1–3), 169–190. Kooi, C.F., 1979. The steady state salt gradient solar pond. Solar Energy 23 (1), 37–45. Kumar, A., Kishore, V.V.N., 1999. Construction and operational experience of a 6000 m2 solar pond at Kutch, India. Solar Energy 65 (4), 237–249. Leblanc, J., Akbarzadeh, A., Andrews, J., Lu, H., Golding, P., 2011. Heat extraction methods from salinity-gradient solar ponds and introduction of a novel system of heat extraction for improved efficiency. Solar Energy 85 (12), 3103–3142.
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