Modeling the influences of a phase change material and the Dufour effect on thermal performance of a salt gradient solar pond

doi:10.1016/j.ijthermalsci.2021.106979

International Journal of Thermal Sciences

Volume 166, August 2021, 106979

https://doi.org/10.1016/j.ijthermalsci.2021.106979 Get rights and content

Highlights

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The Finite Volume Method is adopted to solve the transfer equations.
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The influences of a PCM layer and the Dufour effect on a SGSP are studied.
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The PCM layer decreases the SGSP temperature and its thermal efficiency.
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The PCM layer increases the heat losses via the SGSP free surface.
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The Dufour effect is mitigated in the SGSP with the PCM layer.

Abstract

The influences of a layer of a Phase Change Material (PCM) and the Dufour effect on thermal performance of a Salt Gradient Solar Pond (SGSP) are investigated numerically. The enthalpy model is used to model the heat transfer in the PCM layer. The transfer equations in the SGSP are solved using the implicit Finite Volume Method, the Gauss method and the SIMPLE algorithm. The explicit Finite Volume Method is retained for the heat transfer equation of the PCM layer. The developed numerical model that has been validated experimentally and numerically is used to simulate the operation of the SGSP during ten days under the meteorological data of Tangier in Morocco. Two cases are considered for analysis; the first one is the SGSP without the PCM layer (case 1) and the second one is the SGSP with the PCM layer disposed at its bottom (case 2). The simulation results showed that the temperature, the thermal efficiency of the SGSP with the PCM layer are inferior and the amount of heat losses across the saline water free surface is superior to those of the SGSP without the PCM layer. Furthermore, the increase of the dimensionless Dufour coefficient from 0 to 0.8 leads to decrease, in case 1, the dimensionless temperature of the storage zone from 0.894 to 0.764 and the thermal storage efficiency from 37.41 % to 31.85 %. For the same range of variation of the dimensionless Dufour coefficient, the dimensionless temperature of the storage zone decreases from 0.800 to 0.688 and the thermal storage efficiency reduces from 33.32 % to 28.66 % in case 2. Thus, the Dufour effect is mitigated in the SGSP with the PCM compared to the SGSP without the PCM.

Introduction

Solar energy is the safest, cleanest and most sustainable energy source. It offers significant environmental advantages over conventional energy sources. However, the key disadvantage of this energy is its intermittency, causing limitations in various applications. Thus, the best way to ensure the continuity of this energy is its storage by using Thermal Energy Storage systems (TES). These systems are based on Sensible Heat storage (SH) by raising the temperature of a material, Latent Heat storage (LH) by changing the phase of a material or a combination between SH and LH.

One efficient and economical device for SH solar energy storage is the Salt Gradient Solar Pond (SGSP). This last one can be used as a thermal energy collector that can store an amount of sensible heat for a long period of time. Typically, a SGSP is an artificial lake of water with a salt concentration gradient (Fig. 1). It consists of two convective zones and an insulating zone. The first convective zone is called the Lower Convective Zone (LCZ) or storage zone, which is located at the SGSP bottom. It is a concentrated salt zone in which the thermal energy is stored as sensible heat. This energy can be used for many applications [1] such as electricity production [[2], [3], [4], [5]], industrial processes [[6], [7], [8], [9]], space heating [[10], [11], [12]] or water desalination [[13], [14], [15], [16]]. The second convective zone is the Upper Convective Zone (UCZ) that is the top zone of the SGSP. It is the least salt concentrated zone in order to protect the SGSP from outside perturbation such as wind. The insulating zone is located between the two convective zones to prevent convection between them and is called the Non-Convective Zone (NCZ). In this zone, the salt concentration increases as depth increases, creating a salt concentration gradient (Fig. 1). The Sodium Chloride (NaCl) is the most common salt used to produce the salt concentration gradient in the SGSPs, due to its low economic cost and weak environmental impact. However, other salts have also shown their capability to form the salt concentration gradient in the SGSPs, such as Calcium Chloride (CaCl₂) [17].

The literature revue highlights that numerous numerical models have been spotted describing the transient modeling of the SGSPs. In this sense, Aramesh et al. [18] carried out a numerical study in order to predict the thermal behavior of a rectangular type SGSP during the heat extraction process. This study is based on transient differential heat equations in the LCZ and inside the heat exchanger tube. These equations are solved using the Alternating Direction Implicit (ADI) technique and the Crank-Nicolson method. The numerical model is validated with experimental results of a literature survey regarding the heat stored in the SGSP. The maximum observed percentage error is around 2.03 %, which confirmed that the model developed can predict the transient thermal behavior of the SGSP during the heat extraction process with a good accuracy [18]. These authors also presented another transient model, basing on the differential heat equations, to simulate the SGSP heat extraction process by nanofluids in the transient step [19]. The capacity of this model to describe the heat extraction process by nanofluids in the transient step is confirmed, with a maximum error percentage related to the amount of the heat stored around 5.35 % [19]. Another numerical model has been developed to study the transient hydrodynamic, heat and mass transfer in a two-dimensional SGSP [20]. This model is tackled using the dimensionless equations of Navier-Stokes, thermal energy and mass transfer. The numerical resolution of this model by the finite volume method gives remarkable local information about the transient evolution of the temperature, concentration and velocity fields for different values of the internal Rayleigh number and aspect ratio [20].

Moreover, the literature revue also points out that the main aims of the most numerical and experimental SGSP studies are the search for methods allowing to increase the temperature of the storage zone, to decrease the amount of the SGSP heat losses and to improve its thermal stability. It has been shown that the SGSP configuration [21,22], the climate conditions [[23], [24], [25], [26]], the amount of heat losses via its saline water interface especially by evaporation [27], the heat extraction mode [28], the thermo-diffusion [29] and the Soret and Dufour effects [[30], [31], [32]] significantly affect the thermal performance of the SGSP and its storage capability. In this sense, numerous concepts have been introduced in order to minimize the effects of the negative phenomena (heat losses, salt diffusion …) on the thermal performance of the SGSPs and therefore improve their thermal efficiency by using, for instance, transparent covers (mica, glass and polycarbonate) [33], a glazing plastic cover [22], floating discs [34], a liquid layer [35], a porous medium [36] or external heat sources [37].

In a further development, the thermal performance of SGSPs can be improved by combining the SH storage and LH storage in the same device by integrating a PCM into the SGSP as it has been proposed by Assari et al. [38], Amirifard el al. [39], Ines et al. [40] and Beik et al. [41]. In this context, two SGSPs have been built in Jundi Shapour University of Technology in Dezful (Iran) to study their thermal performance [38]. The SGSPs have a surface area of 3.4 m², a depth of 1 m and one of them contains, in its LCZ, horizontal cylindrical capsules containing Paraffin Wax as a PCM. The results obtained show that the PCM inside the SGSP leads to a reduction of the maximum average temperature of the SGSP, of its thermal efficiency and of the outlet water temperature of the heat exchanger. Hence, the SGSP with the PCM is the most thermally stable against environmental conditions (temporary reduction of solar radiation). In addition, it is more thermally stable during heat extraction than that without the PCM. On the other hand, Amirifard et al. [39] carried out a numerical investigation, basing on the SGSP energy balance, of the effect of a PCM placed in a SGSP on its thermal performance. Their study showed that the average discharging efficiency is increased by 6.1 % and 5.4 % for the series and parallel layouts, respectively, compared to the efficiency of the SGSP without PCM. Further, Ines et al. [40] carried out an experimental study of a SGSP inside a climatic chamber at the Environmental Energy Laboratory at the Marche Polytechnic University in Italy. Results display that the integration of the PCM in the SGSP allowed to provide hot water for longer periods of time, even without an exterior energy supply. In addition, the SGSP with PCM can be used as a hot water source for domestic applications as it collects and stores solar energy. Moreover, Beik et al. [41] confirmed experimentally and numerically that the use of a PCM in a SGSP leads to a more stable temperature in the SGSP during the heat extraction.

The literature survey on the integration of PCM in a SGSP shows that the main objective of these studies is, on the one hand, to maintain the temperature of the storage zone (LCZ) stable even during the extraction of the amount of heat stored and, on the other hand, to improve the thermal average discharging efficiency of the SGSP. Hence, the present study proposes a numerical investigation in order to analyze the influences of a PCM layer disposed at a SGSP bottom and the Dufour effect (the heat transfer caused by the salt concentration gradient) that is neglected in previous SGSP studies on its thermal performance. Transfers in the SGSP are governed by the Navier-Stokes equations and those of thermal energy and mass transfer. Furthermore, the enthalpy model approach is adopted to model the heat transfer in the PCM layer.

Section snippets

Physical model

Fig. 2 shows the physical model proposed in this study. It consists a square salt gradient solar pond (SGSP) of a size equal to 1 m (H_SGSP = L = 1 m) in which its vertical and bottom walls are thermally insulated (Fig. 2-a). This SGSP, filled with a mixture of water and salt (NaCl), is composed of three zones (Fig. 2-b): the lower convective zone (LCZ) of a thickness h₁ (h₁ = 0.4 m), the non-convective zone (NCZ) of a thickness h₂ (h₂ = 0.4 m) and the upper convective zone (UCZ) of a thickness h

Numerical method

The dimensionless equations of the SGSP (equations (34)–(38)) subjected to initial and boundary conditions are solved numerically using the Implicit Finite Volume Method (FVM) [47], the Gauss algorithm and an iterative procedure. The link between the velocity and the pressure fields is assumed by the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations). The explicit Finite Volume Method is used for the dimensionless equations of the PCM layer (equations (39) and (40)). The central

Results and discussion

The computations were performed for a square SGSP of a size equal to 1 m in which the thicknesses of its three zones are reported in Fig. 2-b, for A = 1, Ra = 10¹², N = 10, Pr = 6, Le = 75, Δτ = 6 × 10⁻⁹ and for four values of the dimensionless Dufour coefficient D_f = 0, 0.2, 0.6 and 0.8. These values of D_f are selected basing on our published work [32]. Furthermore, the thermo-physical properties of the PCM (paraffin wax) are reported in Table 1. In addition, the simulations of the SGSP

Conclusion

The influences of a layer of phase change material and the Dufour effect on the thermal performance of a square salt gradient solar pond are investigated numerically. Transfers in the SGSP are governed by the Navier-Stokes equations and the thermal energy and mass transfer equations. The enthalpy model is used to model the heat transfer in the PCM layer. The transfer equations of the SGSP are solved using the implicit Finite Volume scheme, the Gauss method and the SIMPLE algorithm. The explicit

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors gratefully acknowledge the National Center for Scientific and Technical Research of Morocco (CNRST) for providing us with the access to the HPC-MARWAN calculation service.

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Modeling the influences of a phase change material and the Dufour effect on thermal performance of a salt gradient solar pond

Highlights

Abstract

Introduction

Section snippets

Physical model

Numerical method

Results and discussion

Conclusion

Declaration of competing interest

Acknowledgments

Renew. Sustain. Energy Rev.

Sol. Energy

Energy Procedia

Energy Convers. Manag.

Renew. Sustain. Energy Rev.

Sol. Energy

Sol. Energy

Sol. Energy

Sol. Energy

Sol. Energy

Sol. Energy

Desalination

Renew. Energy

Desalination

Energy

Sol. Energy

Energy Convers. Manag.

Sol. Energy

Energy Convers. Manag.

Sol. Energy

Sol. Energy

Sol. Energy

Sol. Energy

Sol. Energy