Liquid crystal thermography based study on melting dynamics and the effect of mushy zone constant in numerical modeling of melting of a phase change material

Abstract

Melt front tracking is vital in a solid–liquid phase change process to understand the melting process and quantify the system’s liquid faction, sensible and latent energies. This study presents a method to track the solid–liquid interface during the melting of a phase change material using liquid crystal thermography. The melt front movement is captured simultaneously through temperature influenced color variation in Thermochromic Liquid Crystal (TLC) sheet and direct visualization. Experiments have been performed for the cases of (i) heating from the bottom and (ii) heating from the top. Further, three-dimensional numerical simulations have been performed to validate the mushy zone temperatures and understand the effect of the mushy zone constant in the mushy zone temperature and liquid fraction. The results show that the TLC easily captures the dynamic motion of the solid–liquid interface during melting. From numerical simulations, it is found that the mushy zone constant affects the numerical prediction of melting in the bottom heating case with the low and high mushy zone constants, respectively, over predicting and under predicting the mushy zone temperatures during melting. Additionally, in this case, it is seen that the Rayleigh–Benard convection creates a wavy interface and accelerates the melting rate of the PCM. In the case of heating from the top, the numerical prediction of melting is independent of the mushy zone constant. Besides, a flat interface is observed in this case due to the absence of convection in the PCM during melting. Additionally, in the case of heating from the top, the combination of the PCM’s low thermal conductivity and heat diffusion through conduction leads to the self insulation effect of the PCM during melting. The convection-driven melting of PCM maintains the heater temperature lower by up to 35%, reduces the melting thermal resistance up to 78%, and increases the average volumetric melting to 92% over the case of melting without convection in the PCM.

Introduction

High latent heats associated with solid–liquid phase change processes enable the use of phase change materials(PCMs) in different applications, namely thermal energy storage, waste heat recovery, food storage containers, building cooling, and transient high power electronics [1]. Despite the high latent heat, PCMs are associated with low thermal conductivities. In view of this, to augment the heat diffusion into the PCM, different thermal conductivity enhancers are invariably used, as for example fins, metal foams, mixing of nano-particles and heat pipes [2], [3], [4], [5]. The efficient and effective design of thermal energy storage systems involves understanding and augmenting the thermophysical properties of PCMs and a knowledge of heat transfer characteristics and melting dynamics of the PCM under consideration. In the past few decades, experimental and numerical studies have been conducted to investigate and understand the melt front movement and heat transfer mechanisms during the melting and solidification process in PCMs. Gau and Viskanta [6], experimentally, studied the effect of natural convection on the movement of the solid–liquid interface during melting from the bottom and solidification from the top and melting through a vertical wall [7], for the case of a pure metal (gallium). The investigations have been carried out through probe measurements and photographic visualization and, the studies reveal that the natural convection in the liquid significantly distorts the melt front and escalates the melting rate. Wolf and Viskanta [8], experimentally, investigated the melting of a metal (tin) in a rectangular cavity. The results showed that, during melting, natural convection is the dominant mode of the heat transfer mechanism. However, as metals have a higher thermal conductivity compared to ordinary liquids, the convection in the melting of liquid metals is not the same as that which occurs in the melting of nonmetallic materials. From the investigations, it is clear that the thermal conductivity of the PCM plays a vital role in the thermal transport mechanisms, melt front shape and its rate of movement and, the latent energy exploitation. In view of above, researchers started exploring melting heat transfer in nonmetallic PCMs. Hale and Viskanta [9], and Gao et al. [10] experimentally, studied the melting of n-octadecane from the bottom and investigated the effect of buoyancy-driven convection on the shape of the melt front through photographic visualization. Ho and Viskanta [11] and Webb and Visanta [12], experimentally, studied the melting of n-octadecane from the vertical wall and at different inclinations, respectively. The above studies reported that an increase in the inclination angle from the vertical creates three-dimensional vortices, which grow as Benard convection patterns. The convection cells rapidly transport the energy to the melt front, compared to heating from a vertical wall. Zhang et al. [13], experimentally, studied the melting of an n-octadecane in a rectangular cavity with discrete heating through a recording of the transient solid–liquid interface via photography. The results showed that the effect of natural convection is more pronounced on the melt front shape with an increase in the Stefan number. Debabrata and Joshi [14], experimentally, investigated melting of n-triacontane through a vertical wall. The same problem was investigated numerically by Jones et al. [15] in a cylindrical enclosure, with n-eicosane as the PCM. Numerical results were validated with experimental liquid fraction visualization photographs and were also compared with the results of Brent et al. [16]. The results showed that the strength of natural convection in PCM diminishes gradually, with an increase in melt fraction. Shokouhmand and Kamkari [17], experimentally, investigated the melting of lauric acid in a rectangular container through a vertical wall and later by Kamkari et al. [18] for different inclination angles. The authors visualized the melting interface and measured the transient temperature of PCM at various locations through thermocouples. The results showed the effect of natural convection at different stages of melting. The heat transfer was seen to be augmented more than two times in a horizontal enclosure compared to the vertical one. Assis et al. [19] performed experimental and numerical simulations on the melting of a PCM(RT27) in a spherical shell. The melting of PCM was studied experimentally through direct photographic visualization. The numerical model was validated against experimental results. The constrained (arresting the movement of solid PCM) melting and unconstrained (allowing the movement of solid PCM due to gravity) melting of PCM (n-octadecane, paraffin wax) in a spherical shell was experimentally investigated by Tan [20] and Tan et al. [21] through a photographic visualization. The results showed that in constrained melting, initially there is melting due to heat conduction, following which remaining solid PCM melts due to convection in the liquid PCM surrounded by it. However, in unconstrained melting, the movement of solid PCM due to gravity pushes the liquid PCM to the top. Hence, the solid PCM at the bottom region melts due to heat conduction, and the PCM at the top melts due to convection in the liquid PCM. The direct photographic visualization method helps better visualize the melting and solidification process of PCM to distinguish the solid, liquid phases and the propagation of the melt front. However, it is tough to understand and quantify the flow patterns in detail with photographic visualization. Hence, in the literature, flow details have generally been explored numerically using the enthalpy porosity method in different geometries and different applications.[22], [23], [24], [25], [26], [27], [28], [29], [30], As the phase transition region (i.e., mushy zone) is confined to a tiny portion (a few mm thick) during the melting of a PCM, it is difficult to investigate this with the macro-scale direct visualization method. To circumvent this, in the numerical modeling of the melting and solidification processes using the enthalpy porosity method, the phase transition region is modeled as a porous zone and the flow is mimicked in this region to match up with the photographic melt front position (temporally and spatially) through a process of iteration of the permeability constant or mushy zone constant. Table 1 shows a summary of mushy zone constants adopted in literature for different PCMs and in various geometries and applications. More recently, Yang et al. [31], experimentally, investigated the phase transition region (mushy zone) through microscopic visualization during melting and solidification of PCM. The authors also performed numerical simulations using the enthalpy porosity method. These studies have clearly established that the mushy zone constant depends on the local liquid fraction and temperature. Even so, an average value of the mushy zone constant simplifies the macro modeling of the melting and solidification process. Mohamed and Philip [32] carried out numerical simulations to study the effect of mushy zone constant on the heat transfer characteristics during melting of a PCM in a rectangular cavity. The authors concluded that (i) lower values of the mushy zone constant lead to an unrealistic prediction of solid–liquid interface, (ii) higher values of the mushy zone constant lead to slow melting of PCM, and (iii) the effect of the mushy zone constant is negligible in the conduction dominated regions. Ebrahimi et al. [33] studied the sensitivity of permeability constant through numerical simulations of melting and solidification. From the above studies, it is seen that the permeability constant plays a vital role in the numerical simulation of non-isothermal phase change process (melting or solidification) and the simulation of isothermal phase change process is independent of the permeability constant. Li et al. [34] revisited the melting of a nano-enhanced PCM with a temperature-based indirect visualization method using liquid crystal thermography. The authors performed experiments on a PCM with different loading levels of nano-particles, and numerical simulations have also been performed using the enthalpy porosity model to understand the flow details in the PCM. The study concluded that high loading of nano-particles in the PCM deteriorates the melting. This was also confirmed with a flattened melt front, captured through a thermochromic liquid crystal sheet (TLC) as a result of decelerated convection in the PCM, due to an increase in the viscosity of the liquid PCM.

From the above review of literature, it is seen that studies on the dynamic movement of melt front (transient and spatial) and understanding of the melting dynamics are essential to reliably and accurately model melting heat transfer. Direct-visualization tracking, a conventional experimental technique, became popular for tracking the dynamic solid–liquid interface during melting of PCMs. However, this method bypasses the interlink between the phase change temperature and physical state of the PCM. Moreover, it is not easy to use the direct-visualization tracking method when the solid and liquid phases are visually indistinguishable for the cases such as when nano-particles are mixed in the PCM (i.e., Nano-enhanced PCMs). The use of a set of thermocouples in the PCM container is another conventional method to track the liquid–solid interface during phase change [35]. However, the spatial resolution of temperature is constrained by the number of thermocouples, and an increase in the number of thermocouples may significantly alter the heat transfer and melting dynamics in the PCM. Thermal imaging is yet another technique to study the solid–liquid interface during phase change [36]. However, the accuracy of the thermal imaging technique mostly depends on the emissivity of the material. For solid–liquid phase change, assigning the dynamically changing emissivity values with the phase of the material is quite challenging. The liquid crystal thermography technique seems a more reliable technique to track the melt front with temperatures for the problem under consideration. However, the limitation of the useful temperature range restricts its use in situation with a large temperature range. This technique also helps in the understanding of the phase transition region with the temperatures of the mushy zone, for a better numerical prediction of the phase change process. Li et al. [34], recently, used this technique to study the melting of nano-enhanced PCM in a differentially heated cavity. Even so, they could not explore much in the phase transition region due to the opaqueness of the nano-enhanced PCM.

In this study, liquid crystal thermography technique is used to track the solid–liquid interface during the melting of PCM (Tetracosane). A thermochromic liquid crystal (TLC) sheet is used to capture the PCM temperatures for various time instants. Experiments are conducted to track the solid–liquid interface of a PCM in a rectangular transparent acrylic container for the cases of (i) top heating (i.e., without convection in the PCM) (ii) bottom heating (i.e., with convection in the PCM). Three-dimensional numerical simulations have also been performed with different mushy zone constants to study the effect of the constant on mushy zone characteristics and the heater temperature and these simulations have been validated against in-house experimental results.