Keywords

2.1 Introduction

Due to fluctuation in solar heat flux owing to adverse weather conditions, storage of solar thermal energy is necessary and it provides a means to utilize the thermal energy for nocturnal use. Directions of research involving latent heat thermal energy storage (LHS) have become manifold ascribed to its many practically relevant applications which include building heating, providing hot water for domestic needs, refrigeration applications, drying equipment and waste heat recovery. It has innumerous advantages comparable to sensible energy storage (SES) device in terms of effectiveness and storage capacity. Study by Sharma et al. [1] revealed that energy storing capacity of LHS is 14 times higher than SES. There are various types of storage media for LHS out of which, paraffin wax is cheap and easily available.

Agarwal and Sarviya [2] investigated a shell and tube type latent heat storage (LHS) for solar drying application using paraffin wax as the storage medium. In their study, the effect of flow rate and temperature of heat transfer fluid (HTF) during charging and discharging process were also analyzed. Kabeel et al. [3] conducted an experimental study and evaluated the energy yield and performance of a solar desalination system by comparing a conventional system with an improved LHS-based system. The result indicated that the LHS-based system showed an improved performance in terms of daily freshwater yield. Melting and solidification in a double pipe heat exchanger were investigated by Jesumathy et al. [4] using paraffin wax as the means of storage. They reported that charging is dominated by natural convection and discharging is dominated by conduction. Performance of a finned solar air heater is experimentally studied by Kabeel et al. [5]. The effects of variation in mass flow rate on daily and instantaneous efficiency were measured. The result revealed that the efficiency increased by 10.8–13.6%. Hu et al. [6] performed a wide investigation on PCMs for investigating the thermal management of electronic devices and emphasized on using the modularized thermal storage unit as an improvement over current PCM-based heat sinks for cooling applications in high duty electronic equipment.

Korti and Tlemsani [7] researched a latent heat-based energy storage system with various types of paraffin and the effect of inlet temperature and flow rate of HTF were studied. It was also noted that addition of engine oil to paraffin improved the charging and discharging process by 42.4 and 66%, respectively. Experimental investigations have been performed by Sobolčiak et al. [8] for various compositions of linear low-density polyethylene, paraffin wax and expanded graphite using both conventional and non-conventional methods. From the testing, it is found that thermal conductivity was improved by adding extended graphite. Melting process of industrial grade paraffin wax-based energy storage was studied by Saraswat et al. [9] both experimentally and numerically (using OpenFOAM). They highlighted about using the copper pipes along with the PCM to enhance heat dissipation rate. Salunkhe and Krishna [10] reviewed the recent works on latent heat storage materials (LHSMs) and their thermophysical properties. Further, they discussed in detail the various factors affecting the life of a LHSM. Experimental studies involving paraffin wax-based latent heat storage with an application in forced convection solar dryer was reported by Rabha and Muthukumar [11] and the exergy and energy efficiencies were reported as 18.3–20.5% and 43.6–49.8%, respectively. Wahid et al. [12] provided a comprehensive review of literatures based on the various features of the PCMs, their latest developments and future directions with an application towards the building architecture. Naghavi et al. [13] analyzed a solar water heating system by implementing an evacuated tube heat pipe solar collector along with latent heat storage (LHS). Results indicated that the system efficiency in the summer was found to be 38–42% and it showed a fluctuation of about 8% in the rainy season. Németh et al. [14] prepared microcapsules containing paraffin wax and studied the various process parameters. Khan et al. [15] performed parametric investigation in a shell and tube-based thermal energy storage to study the performance of LHS. It was observed that increase in inlet temperature increases the efficiency of the storage. Comparison study between a naturally cooled and a storage-based latent heat cooled PV solar panels conducted by Tana et al. [16] was found that the panel temperature of the latent heat cooled shell reduced by 15 °C in comparison with a naturally cooled PV panel. It is observed from the above literatures that most of the studies were either numerical or experimental. However, studies including both methods were a few.

The objective of the present study is to perform the numerical analysis of a latent heat storage system (LHS) and, subsequently, to compare the results with the experimental model of 10 MJ capacities using paraffin wax as PCM. Various performance parameters have been analyzed during the charging/discharging process and are reported in terms of energy stored/released, variation of melt fraction, etc.

2.2 Numerical Details

2.2.1 Modelling and Assumptions

The three-dimensional sectional view of a shell and tube heat exchanger is presented with paraffin wax as the phase change material (PCM) and water as the heat transfer fluid (HTF). The tube radial-thickness and tube internal diameter are maintained as 4 mm and 14 mm, respectively, whereas the shell length and diameter are maintained as 1000 mm and 300 mm, respectively. The data related to the thermophysical properties of paraffin wax are taken from Niyas et al. [15] and are mentioned as follows. The properties of PCM, namely, thermal conductivity (k), specific heat capacity (Cp), density (ρ), dynamic viscosity (μ) and latent heat of fusion (L) are maintained as 0.25 W m−1 K−1, 2000 J kg−1 K−1, 780 kg m−3, 0.0041 kg m−1 s−1 and 168 kJ kg−1, respectively. The melting temperature and the melting range are maintained at 315.15 K and 3 K, respectively. While simulating the model, the following assumptions were considered (Fig. 2.1).

Fig. 2.1
figure 1

Flow domain

Full size image
  1. 1.

    HTF is an incompressible and Newtonian fluid.

  2. 2.

    PCM is homogeneous and isotropic, its initial temperature is assumed to be uniform throughout the domain.

  3. 3.

    Viscous dissipation is neglected in the flow and phase change is assumed to occur in a temperature range.

2.2.2 Governing Equations

The model considers conjugate heat transfer across the thickness of the tube which involves the heat transfer in heat transfer fluid (HTF) as well as in the phase change material (PCM). For incorporating the effect of latent heat, an effective heat capacity (EHC) method is used in which CP, EFF is calculated keeping into consideration the latent heat of fusion. The governing equation for mass conservation, momentum conservation and energy conservation are written in Eqs. (2.1)–(2.3) as follows. The quantities are in their dimensional form.

$$\frac{\partial U}{\partial x} + \frac{\partial V}{\partial y} = 0$$
(2.1)
$$\frac{\partial U}{\partial t} + U\frac{\partial U}{\partial x} + V\frac{\partial U}{\partial y} = \frac{1}{\rho }\left\{ {\begin{array}{*{20}l} { - \frac{\partial p}{\partial x} + \mu \left( {\frac{{\partial^{2} U}}{{\partial x^{2} }} + \frac{{\partial^{2} U}}{{\partial y^{2} }}} \right)} \hfill \\ {+ \rho g\beta (T - T_{\infty } ) + \frac{{(1 - \theta )^{2} }}{{(\theta^{3} + \varepsilon )}}A_{\text{MUSH}} V} \hfill \\ \end{array} } \right\}$$
(2.2)
$$\rho C_{p} \left( {\frac{\partial T}{\partial t} + U\frac{\partial T}{\partial x} + V\frac{\partial T}{\partial y}} \right) = k\left( {\frac{{\partial^{2} T}}{{\partial x^{2} }} + \frac{{\partial^{2} T}}{{\partial y^{2} }}} \right)$$
(2.3)

In the above equations, U, V, T, β, θ, AMUSH and p, etc., represent stream wise velocity component (m/s), span wise velocity component (m/s), temperature (K), volume expansion coefficient, melt fraction, mushy zone constant and pressure (Pa), respectively.

2.2.3 Initial and Boundary Conditions

The initial temperature for HTF and PCM are set as 298 K, whereas no flow boundary condition is set for velocity. At the inlet, boundary condition for HTF is set to be U = 0.05 m/s and T = 333 K. In order to avoid heat losses to the atmosphere, adiabatic boundary condition is set at the shell outer surface and the heat losses to the ambient through this surface are assumed to be negligible. While solving, only one-fourth of the flow domain is solved and symmetry boundary condition is used to reduce the number of mesh elements.

2.2.4 Meshing and Numerical Treatment

Computational domain for the current investigation consists of 406,380 volume elements. Finite elements method based COMSOL Multiphysics 4.3a is used to solve continuity, momentum and energy equation. BDF time discretization scheme is used in conjunction with a nonlinear time-dependent PARADISO solver. Convergence criteria for velocity and temperature are set to a prescribed limit of 10−3.

2.3 Experimental Setup

The LHS system comprises of 17 copper tubes with a shell that is made up of stainless steel. Thermo-foam insulation is provided at the shell outer surface to reduce heat loss to the ambient. T-type thermocouples were used to measure the temperature at the different location of the LHS (Fig. 2.2).

Fig. 2.2
figure 2

Experimental setup depicting various components and their arrangement

Full size image

2.4 Result and Discussions

2.4.1 Validation Study

Validation study is performed for the present investigation in terms of temporal variation of volumetric-averaged temperature, with the experimental results for charging/discharging process and the results are revealed in Figs. 2.3. Numerical results provided a reasonably good comparison with the experimental data and moreover, the profile showed a similar trend with the reported results of Niyas et al. [17].

Fig. 2.3
figure 3

Variation of volumetric-averaged temperature with time a charging and b discharging

Full size image

After performing this validation, results are reported in terms of variation of volume-averaged temperature, melt fraction, sensible, latent and total energy stored/released with time as obtained in the simulation.

2.4.2 Contours of Average Melt Fraction

Instantaneous melt fraction contours of PCM are presented at different time instances as depicted in Fig. 2.4. As charging is a convection dominated process, faster melting rate is observed compared to a relatively slower rate of solidification during discharging. Simulation data substantiates that time taken for complete melting is t = 110 min (6600 s), whereas complete solidification of paraffin wax is obtained at t = 150 min (9000 s).

Fig. 2.4
figure 4

Instantaneous contour of melt fraction during charge (as shown in a, b, c, d and e) and discharge (as shown in f, g, h, i and j)

Full size image

2.4.3 Variation of Average Temperature and Melt Fraction During Charging and Discharging

The HTF is circulated through the pipe at 333 K/298 K during charging/discharging process and the variation of average temperature is recorded with time as shown in Fig. 2.5. It can be comprehended from the figures that the average temperature varies smoothly over time for charging process, whereas during release of energy, the average temperature profile followed a steep decrease in the beginning which is followed by a flat slope. Further, volume-averaged melt fraction is also plotted, as seen in Fig. 2.6, to understand the melting and solidification process comprehensively. When melt fraction becomes zero, it suggests pure solid paraffin wax and when its value becomes one, it represents pure liquid paraffin suggesting complete melt.

Fig. 2.5
figure 5

Variation of average temperature with time during a charging and b discharging

Full size image
Fig. 2.6
figure 6

Variation of average melt fraction with time during a charging and b discharging

Full size image

2.4.4 Energy Stored/Released

The change in sensible, latent and total energy in both charging and discharging process are shown in Fig. 2.7. During charging process, when HTF passes through the tubes, PCM starts melting. In the initial phase, sensible heat transfer occurs which follows a latent transfer of heat during phase change and, subsequently, sensible transfer of heat from liquid paraffin. When the PCM reached 333 K, the sensible, latent and total energy stored are found to be 3.152 MJ, 7.5 MJ and 10.71 MJ, respectively. Similarly, while discharging, when averaged temperature of PCM reached 302 K the sensible, latent and total energy released are found to be 2.751 MJ, 7.5 MJ and 10.2 MJ, respectively.

Fig. 2.7
figure 7

Variation of energy stored/released with time during charging/discharging

Full size image

2.5 Conclusions

Numerical analysis of a 3D shell and tube type LHS was studied and the storage characteristics are analyzed for both the charging and discharging process. After performing validation study with the experimental results, reasonably good agreement is found. Further, performance parameters of the LHS system are evaluated in terms of volume-averaged temperature, melt fraction, energy stored/released and a few key findings are summarized below.

  • Time taken for complete charging and discharging are found to be 110 min and 150 min, respectively.

  • Charging, being convection dominated process, is faster than discharging.

  • The total energy stored and released during the process are 10.71 MJ and 10.2 MJ, respectively.