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Technical Brief

# Effectiveness of Bottom Insulation of a Salinity Gradient Solar PondOPEN ACCESS

[+] Author and Article Information
Sayantan Ganguly

Environmental Hydrogeology Group,
Department of Earth Sciences,
Utrecht University,
Princetonplein 9,
Utrecht 3584CC, The Netherlands
e-mail: s.ganguly@uu.nl

Abhijit Date

Energy Conservation and Renewable Energy Group,
School of Engineering,
RMIT University,
P.O. Box 71,
Bundoora 3083, Victoria, Australia
e-mail: abhijit.date@rmit.edu.au

Energy Conservation and Renewable Energy Group,
School of Engineering,
RMIT University,
P.O. Box 71,
Bundoora 3083, Victoria, Australia
e-mail: akbar@rmit.edu.au

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received December 21, 2017; final manuscript received February 8, 2018; published online March 13, 2018. Assoc. Editor: M. Keith Sharp.

J. Sol. Energy Eng 140(4), 044502 (Mar 13, 2018) (5 pages) Paper No: SOL-17-1500; doi: 10.1115/1.4039416 History: Received December 21, 2017; Revised February 08, 2018

## Abstract

This technical brief presents a study on the effectiveness of the bottom insulation of a salinity gradient solar pond (SGSP) in Melbourne, Australia. Insulation is applied at the bottom of a SGSP in order to minimize the heat loss from the SGSP to the ground underneath. But selection of optimum thickness of the insulation to extract the best thermal performance of an SGSP is a challenge as insulation involves significant investment. Hence, modeling heat loss from SGSP to the ground before and after applying the insulation is thus very essential. In this study, a layer of polystyrene is used as insulation at the bottom of SGSP. The temperature distribution in the SGSP and ground below it, the efficiency of the SGSP and the heat removal from SGSP are estimated for the SGSP without insulation and with insulation of different thicknesses. The results show that the insulation definitely reduces the heat loss from the SGSP to the ground, but to a certain extent. Insulation beyond a certain thickness is proved to be ineffective in increasing the efficiency or reducing the heat loss to ground and thus unable to enhance the thermal performance of the SGSP.

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## Introduction

A salinity gradient solar pond (SGSP) is a large but relatively shallow body of water which is used as a solar thermal energy collector with an inbuilt thermal storage. The solar insolation incident on a body of water is converted to heat which is lost rapidly to atmosphere due to natural convection. In SGSP salinity gradient in the middle zone which is also known as nonconvective zone (NCZ) is used to suppress the natural convection to store solar heat in the heat storage zone at the bottom also known as lower-convective zone (LCZ). The top layer which is known as the upper-convective zone (UCZ) has the minimum salinity and often the temperature in this zone is assumed to be equal to the ambient temperature [13].

The solar radiation which is incident on the SGSP penetrates the water surface and attenuates rapidly. A part of the heat generated by the solar radiation is lost to the atmosphere by reflection and another part to the ground below and sides by conduction. The rest of the heat is stored in the LCZ and available for recovery. Insulations of low thermal conductivity materials such as polystyrene [4,5], clay [6,7], glass-wool [8,9] are used at the bottom and sides of the SGSP to minimize the heat loss. To the best of our knowledge, there is hardly any study which investigates the transient thermal performance of a SGSP with thermal insulations of different thicknesses and tries to find the optimum insulation thickness for the best thermal performance. This study predicts the thermal performance of a SGSP without insulation and with insulation of different thicknesses and tries to find out the best insulation thickness. As the insulation involves considerable expenditure, finding an optimum thickness for it is necessary, and thus, modeling the transient thermal performance of SGSP in terms of efficiency and heat extraction is utmost important, before applying it practically. The present SGSP which is used here for modeling is located in Melbourne, Australia. The SGSP with a layer of insulation at the bottom is schematically shown in Fig. 1.

## Numerical Modeling

The mathematical model for the SGSP is based on the energy balance equation [1,10] given by Display Formula

(1)$ΔEnτ+Δτ=hnτ×Δτ+qn−1τ×Δτ+qn+1τ×Δτ−qeτ×Δτ$

where $ΔEnτ+Δτ$ is the change in the energy content of nth layer (i.e., layer under investigation) in SGSP after time $Δτ$; $hnτ$ is the solar radiation energy absorbed by nth layer in SGSP at time $τ$; $qn−1τ$ is the conductive heat transfer to or from the division above the nth layer in SGSP at time $τ$; $qn+1τ$ is the conductive heat transfer to or from the division below the nth layer in SGSP at time $τ$ and $qeτ$ represents the heat extracted from the LCZ at time $τ$. The different zones and boundaries of SGSP considered for modeling are shown here schematically in Fig. 2.

The operation of the SGSP in Melbourne starts on 1st October which is early spring season. The removal of heat starts 60 days after the start of operation. The SGSP under consideration is 3 m deep in which the thicknesses of the UCZ, NCZ, and LCZ are assumed to be equal to 0.3 m, 1.2 m, and 1.5 m, respectively [13]. The data of monthly average daily temperature and the monthly solar radiation in Melbourne are adequately approximated here by sinusoidal expressions and presented in Fig. 3. The numerical model similar to that discussed in Refs. [1] and [2] is further developed for this study with a layer of polystyrene insulation of different thicknesses at the bottom of the SGSP. The numerical model here is one-dimensional finite difference unsteady heat conduction model, as done by many researchers in the past [1,11,12]. The heat loss from the sides of the SGSP is assumed negligible compared to that from the bottom since the bottom area is large enough compared to the sides. Solar insolation is absorbed by different layers of the SGSP and is converted to heat. A part of that is lost to the atmosphere and the ground, and the rest is available for extraction. The target of insulating the bottom is to minimize the part of heat lost to the ground such that more heat is available for recovery. The ground temperature beyond 5 m below a SGSP can be assumed to be equal to the yearly average ambient temperature [1]. Hence, the heat which is lost from the SGSP to the ground is considered to be stored in the depth of 5 m from SGSP bottom [3]. The 5 m thickness of ground is divided into 20 sublayers for numerical simulations to evaluate the temperature at the nodes which are at the center of each layer, while the gradient layer NCZ is divided into eight sublayers. UCZ and LCZ are assumed to be single layers with uniform temperatures due to convective mixing. The temperature of the UCZ and the initial temperature of the heat transfer fluid (HTF) are assumed to be equal to the monthly average local daily temperature [1,2] of Melbourne. Heat is removed from the storage zone of LCZ by flux of HTF through in-pond heat exchangers in the LCZ. Hence, the easiest way to control the heat removal is to control the HTF flux through the heat exchangers. Effectiveness of heat transfer of the heat exchangers has been assumed to be equal to one. The thermal performance of the SGSP without insulation and with polystyrene insulation of different thicknesses is evaluated here in terms of temperature development in LCZ, heat removal from SGSP, and thermal efficiency of the SGSP. The density, thermal conductivity, and specific heat of polystyrene used for insulation are 35 kg/m3, 0.03 W/m·K and 1400 J/kg·K, respectively [5].

## Temperature Developments in Lower-Convective Zone and Ground Underneath

The temperature development in the LCZ and three depths of ground over 3 years is shown in Fig. 4 for a SGSP without insulation at the bottom and with insulation of four thicknesses (5, 10, 20, and 25 cm). Solar radiation data are also plotted in the same figure which shows that the maximum and minimum temperature points in the sinusoidal temperature distribution plots of SGSP and ground lags behind the solar radiation maximum and minimum. This happens due to the thermal inertia of the SGSP and ground. For any worthwhile use of the heat recovered from SGSP, a minimum difference ($ΔTmin$) of 20 °C should be present between initial temperature of HTF and LCZ temperature [1]. To maintain the $ΔTmin$ here the HTF flux through the LCZ heat exchangers is fixed as 0.0003 kg/m2/s. Note that the temperature of ground at a depth of 4.5 m or more, falls below the ambient temperature sometimes during summer. It is evident from Figs. 4(a)4(e) that after applying insulation at the bottom of the SGSP, the temperature profiles in LCZ and the ground are affected. The overall LCZ temperature has increased, and the ground temperature has fallen after using insulation. Hence, the insulation has successfully reduced the heat loss from the SGSP to ground. For instance, the annual average LCZ temperature for a SGSP without insulation is 42.3 °C, which is about 28 °C higher than the annual average ambient temperature in Melbourne (14.3 °C), whereas the same for a SGSP with 5 cm and 10 cm bottom insulation at the bottom is 44.6 °C and 46.5 °C, respectively, which is 30.3 °C and 32.3 °C higher than the annual average ambient temperature in Melbourne. But interestingly this situation does not improve for a thickness of insulation more than 10 cm. The difference between annual average ambient temperature in Melbourne and annual average LCZ temperature is about 32.4 °C and 32.5 °C, respectively, when insulation thickness at the bottom of SGSP is increased to 20 cm and 25 cm, respectively.

## Heat Extraction and Efficiency

The heat extraction from LCZ and the instantaneous efficiency is studied here to investigate the thermal performance of the SGSP with and without insulation. The instantaneous efficiency here is estimated as the ratio of instantaneous change in energy content of the SGSP (LCZ and NCZ) plus ground underneath (up to a depth of 5 m) divided by the amount of solar radiation that penetrates the top surface of the SGSP [1] Display Formula

(2)$ηinstsp=ΔElczτ+ΔEnczτ+ΔEgτAsp×(Hτ−Hτ×L)×Δτ$

where ηinst sp is the instantaneous efficiency of the solar SGSP; $ΔElczτ$, $ΔEnczτ$, and $ΔEgτ$ are the changes in the energy content of LCZ, NCZ, and ground, respectively; $Asp$ is the surface area of the SGSP; $Hτ$ is the global solar radiation flux incident on the horizontal surface at instant $τ$, and $L$ is the percentage of solar radiation that is reflected back to the atmosphere.

Figure 5 shows instantaneous efficiency of the SGSP with and without bottom insulation. From Fig. 5, it is again evident that the instantaneous efficiency and the heat removal from the SGSP enhances after applying the insulation. The annual average efficiency (ηan) for the SGSP in Melbourne in second and third year (first year is ignored here since the heat removal from SGSP started 60 days after the start of operation) without insulation is 20.6%. This means 20.6% of all the solar radiation that is incident on the SGSP surface has been converted to recoverable thermal energy in the SGSP. The ηan for the SGSP with bottom insulation of 5 cm and 10 cm thickness are 21.5% and 23.6%, respectively, which is an improvement of 4.4% and 14.5%, respectively. Increasing the insulation thickness to 20 cm and 25 cm produces an annual average efficiency of about 23.7% which is a negligible improvement over an SGSP with 10 cm bottom insulation. Note that instantaneous efficiency of SGSP drops down drastically after midsummer and attains negative value in winter for all the cases of SGSP with insulations. Instantaneous efficiency is a measure of energy extracted/absorbed from/by the SGSP to the instantaneous energy loss. Negative values indicate that the loss of heat is exceeding the heat absorbed/removed. Due to application of insulation, as the temperature of the SGSP increases, heat loss from the SGSP increases simultaneously. When sufficient heat is not removed from the SGSP, the efficiency falls, reaching subzero values during winter. When the heat removal is increased from the SGSP by increasing the HTF flux through heat exchangers, the efficiency is increased. Figure 5 also shows the instantaneous efficiency of the SGSP when the HTF flux increased to 0.0004 kg/m2/s. From Fig. 5, it can be estimated that ηan for a SGSP with 10 cm bottom insulation, for a HTF flux of 0.0004 kg/m2/s increases to 25.2% (compared to 23.6% with HTF flux of 0.0003 kg/m2/s). But the HTF flux also has to be increased carefully as increasing it may violate the minimum temperature difference ($ΔTmin$) criterion [1], meaning that higher amount of heat can be extracted from the SGSP but at a lower temperature, compromising the quality of the heat and thus limiting the application of it.

Heat extraction from the LCZ over 3 years is shown in Fig. 6. The annual average heat extraction (AAHE) without bottom insulation is 36 W/m2 amounting to a total annual heat removal of 1135.3 MJ/m2/yr. The AAHE for the SGSP with bottom insulations of 5 cm and 10 cm thickness are 40 W/m2 and 41.2 W/m2, respectively. This amounts to a total annual heat removal of 1261.4 MJ/m2/yr and 1299.3 MJ/m2/yr, respectively, which is an improvement of about 11.1% and 14.4%, respectively. The AAHE for and SGSP with bottom insulation of 20 cm and 25 cm are almost same (41.25 and 41.3 W/m2, respectively) as that with 10 cm insulation. Hence, for the SGSP in Melbourne, a bottom insulation of 10 cm polystyrene layer is evidently optimum for the best thermal performance.

## Conclusions

This study aims to investigate the thermal performance of a SGSP with and without insulation at the bottom which is meant for minimizing the heat loss from the SGSP to the ground beneath. The study finds that the bottom insulation definitely enhances the thermal performance of the SGSP in terms of the efficiency and heat extraction from it. But this improvement is limited to a certain thickness of the insulation. Beyond that the increasing the insulation thickness does not improve the thermal performance. Hence, optimizing the insulation thickness for a SGSP is very important, since the insulation involves considerable cost. This study finds the optimum thickness of polystyrene insulation for the SGSP in Melbourne, to extract the best thermal performance.

## Nomenclature

• A =

area (m2)

• E =

energy content (J/m2)

• h =

solar radiation flux absorbed by SGSP layers (W/m2)

• H =

global solar radiation flux incident on the horizontal surface (W/m2)

• L =

percentage of solar radiation reflected back to the atmosphere

• q =

conductive heat flux (W/m2)

• T =

temperature (°C)

Greek Symbols
• Δ =

difference

• $Δτ$ =

time increment (s)

• η =

efficiency

• $τ$ =

present time (s)

Subscripts
• an =

annual

• g =

ground

• inst =

instantaneous

• LCZ =

lower-convective zone

• min =

minimum

• 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

• NCZ =

nonconvective zone

• sp =

solar pond

## References

Date, A. , Yaakob, Y. , Date, A. , Krishnapillai, S. , and Akbarzadeh, A. , 2013, “Heat Extraction From Non-Convective and Lower Convective Zones of the Solar Pond: A Transient Study,” Sol. Energy, 97, pp. 517–528.
Ganguly, S. , Jain, R. , Date, S. , and Akbarzadeh, A. , 2017, “On the Addition of Heat to Solar Pond From External Sources,” Sol. Energy, 144, pp. 111–116.
Ganguly, S. , Date, S. , and Akbarzadeh, A. , 2017, “Heat Recovery From Ground Below the Solar Pond,” Sol. Energy, 155, pp. 1254–1260.
Andrews, J. , and Akbarzadeh, A. , 2005, “Enhancing the Thermal Efficiency of Solar Ponds by Extracting Heat From the Gradient Layer,” Sol. Energy, 78(6), pp. 704–716.
Leblanc, J. , Akbarzadeh, A. , Andrews, J. , Lu, H. , and Golding, P. , 2011, “Heat Extraction Methods From Salinity-Gradient Solar Ponds and Introduction of a Novel System of Heat Extraction for Improved Efficiency,” Sol. Energy, 85(12), pp. 3103–3142.
Silva, G. , and Almanza, R. , 2009, “Use of Clays as Liners in Solar Ponds,” Sol. Energy, 83(6), pp. 905–919.
Jubran, B. A. , El-Baz, A. R. , Hamdan, M. A. , and Badran, A. A. , 1996, “Experimental Investigation of Local Clays and Clay Schemes as Liners for Solar Ponds,” Int. J. Energy Res., 20(7), pp. 637–642.
Karakilcik, M. , Kıymac, K. , and Dincer, I. , 2006, “Experimental and Theoretical Temperature Distributions in a Solar Pond,” Int. J. Heat Mass Transfer, 49(5–6), pp. 825–835.
Kurt, H. , Ozkaymak, M. , and Binark, A. K. , 2006, “Experimental and Numerical Analysis of Sodium-Carbonate Salt Gradient Solar-Pond Performance Under Simulated Solar-Radiation,” Appl. Energy, 83(4), pp. 324–342.
Ganguly, S. , Date, S. , and Akbarzadeh, A. , 2018, “Investigation of Thermal Performance of a Solar Pond With External Heat Addition,” ASME J. Sol. Energy. Eng., 140(2), p. 024501.
Wang, Y. F. , and Akbarzadeh, A. , 1983, “A Parametric Study on Solar Ponds,” Sol. Energy, 30(6), pp. 555–562.
Aboul-Enein, S. , El-Sebaii, A. A. , Ramadan, M. R. I. , and Khallaf, A. M. , 2004, “Parametric Study of a Shallow Solar-Pond Under the Batch Mode of Heat Extraction,” Appl. Energy, 78(2), pp. 159–177.
View article in PDF format.

## References

Date, A. , Yaakob, Y. , Date, A. , Krishnapillai, S. , and Akbarzadeh, A. , 2013, “Heat Extraction From Non-Convective and Lower Convective Zones of the Solar Pond: A Transient Study,” Sol. Energy, 97, pp. 517–528.
Ganguly, S. , Jain, R. , Date, S. , and Akbarzadeh, A. , 2017, “On the Addition of Heat to Solar Pond From External Sources,” Sol. Energy, 144, pp. 111–116.
Ganguly, S. , Date, S. , and Akbarzadeh, A. , 2017, “Heat Recovery From Ground Below the Solar Pond,” Sol. Energy, 155, pp. 1254–1260.
Andrews, J. , and Akbarzadeh, A. , 2005, “Enhancing the Thermal Efficiency of Solar Ponds by Extracting Heat From the Gradient Layer,” Sol. Energy, 78(6), pp. 704–716.
Leblanc, J. , Akbarzadeh, A. , Andrews, J. , Lu, H. , and Golding, P. , 2011, “Heat Extraction Methods From Salinity-Gradient Solar Ponds and Introduction of a Novel System of Heat Extraction for Improved Efficiency,” Sol. Energy, 85(12), pp. 3103–3142.
Silva, G. , and Almanza, R. , 2009, “Use of Clays as Liners in Solar Ponds,” Sol. Energy, 83(6), pp. 905–919.
Jubran, B. A. , El-Baz, A. R. , Hamdan, M. A. , and Badran, A. A. , 1996, “Experimental Investigation of Local Clays and Clay Schemes as Liners for Solar Ponds,” Int. J. Energy Res., 20(7), pp. 637–642.
Karakilcik, M. , Kıymac, K. , and Dincer, I. , 2006, “Experimental and Theoretical Temperature Distributions in a Solar Pond,” Int. J. Heat Mass Transfer, 49(5–6), pp. 825–835.
Kurt, H. , Ozkaymak, M. , and Binark, A. K. , 2006, “Experimental and Numerical Analysis of Sodium-Carbonate Salt Gradient Solar-Pond Performance Under Simulated Solar-Radiation,” Appl. Energy, 83(4), pp. 324–342.
Ganguly, S. , Date, S. , and Akbarzadeh, A. , 2018, “Investigation of Thermal Performance of a Solar Pond With External Heat Addition,” ASME J. Sol. Energy. Eng., 140(2), p. 024501.
Wang, Y. F. , and Akbarzadeh, A. , 1983, “A Parametric Study on Solar Ponds,” Sol. Energy, 30(6), pp. 555–562.
Aboul-Enein, S. , El-Sebaii, A. A. , Ramadan, M. R. I. , and Khallaf, A. M. , 2004, “Parametric Study of a Shallow Solar-Pond Under the Batch Mode of Heat Extraction,” Appl. Energy, 78(2), pp. 159–177.

## Figures

Fig. 1

Schematic diagram of SGSP with insulation at bottom

Fig. 2

Schematic diagram of the SGSP showing the different zones and boundaries with the numerical grid

Fig. 3

Monthly average of daily solar radiation on a horizontal surface in Melbourne and monthly average temperature in Melbourne

Fig. 4

Temperature development in the LCZ of solar pond and ground for (a) no insulation, (b) insulation of 5 cm at bottom, (c) insulation of 10 cm at bottom, (d) insulations of 20 cm at bottom, and (e) insulation of 25 cm at bottom

Fig. 5

Instantaneous efficiency of the Melbourne SGSP without insulation and with insulation of different thicknesses

Fig. 6

Heat removed from the Melbourne SGSP without insulation and with insulation of different thicknesses

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