Phase change materials (PCM) present great potential for energy efficiency gains in thermal systems by storing solar energy or waste heat in industrial processes. This is due to the great amount of energy stored per mass unit within a small temperature range. In this paper we focus, by means of the numerical investigation, on the solidification process of the PCM erythritol in spheres, having 10, 20, 30 and 40 mm diameter, under wall temperatures of 10, 15, 20, 25, 30 and 40 K below the phase change temperature of the material. The problem is considered two-dimensional in geometry and transient in time. The numerical model here adopted consists of mass, momentum, energy and volume fraction equations. The results have been initially validated by comparison with data found in literature. Afterwards, analysis of the convective streams on the liquid PCM, liquid fraction, heat flux in the sphere wall and total solidification times have been widely illustrated. The liquid fraction suffers a sharp reduction at the beginning of the solidification process due to the high heat flux at the initial times. As the solid layer adjacent to the shell increases, it causes an augmentation of thermal resistance, significantly reducing the heat flux. The shape of the curve representing the solid fraction shows similarity with the S-curve pattern of solidification. The total solidification time proved to be dependent on both the diameter length and the temperature difference ΔT (between phase change material and wall temperature), being its influence reduced for lower temperature values. Finally, the liquid 2 fraction results, as a function of Fourier and Stefan numbers, have been employed to amend a dimensionless correlation found in literature.
Phase change materials (PCMs) are classified according to their phase change process, temperature, and composition. The utilization of PCMs lies mainly in the field of solar energy and building applications as well as in industrial processes. The main advantage of such materials is the use of latent heat, which allows the storage of a large amount of thermal energy with small temperature variation, improving the energy efficiency of the system. The study of PCMs using computational fluid dynamics (CFD) is widespread and has been documented in several papers, following the tendency that CFD nowadays tends to become increasingly widespread. Numerical studies of solidification and melting processes use a combination of formulations to describe the physical phenomena related to such processes, these being mainly the latent heat and the velocity transition between the liquid and the solid phases. The methods used to describe the latent heat are divided into three main groups: source term methods (E-STM), enthalpy methods (E-EM), and temperature-transforming models (E-TTM). The description of the velocity transition is, in turn, divided into three main groups: switch-off methods (SOM), source term methods (STM), and variable viscosity methods (VVM). Since a full numerical model uses a combination of at least one of the methods for each phenomenon, several combinations are possible. The main objective of the present paper was to review the numerical approaches used to describe solidification and melting processes in fixed grid models. In the first part of the present review, we focus on the PCM classification and applications, as well as analyze the main features of solidification and melting processes in different container shapes and boundary conditions. Regarding numerical models adopted in phase-change processes, the review is focused on the fixed grid methods used to describe both latent heat and velocity transition between the phases. Additionally, we discuss the most common simplifications and boundary conditions used when studying solidification and melting processes, as well as the impact of such simplifications on computational cost. Afterwards, we compare the combinations of formulations used in numerical studies of solidification and melting processes, concluding that “enthalpy–porosity” is the most widespread numerical model used in PCM studies. Moreover, several combinations of formulations are barely explored. Regarding the simulation performance, we also show a new basic method that can be employed to evaluate the computing performance in transient numerical simulations.
The demand for renewable energy resources and the need for the development of components which increase how it collects, transforms, stores and distributes this energy, emphasizes the importance of improving current technological systems to meet these demands. Phase change materials (PCM) offer great potential in this area. as they can increase energy efficiency in thermal systems as well as save energy by storing solar energy or waste heat from industrial processes, which is made possible by the high amount of energy stored per mass and volume unit, with low temperature variation. Therefore, it is of high importance that the suggested mathematical and numerical models are capable of analyzing its energy performance. The present work uses a mathematical and numerical model of Computational Fluid Dynamics (CFD), capable of reproducing the solidification process of erythritol in spheres of 10, 20, 30 and 40 mm diameters, with temperature differences of 10, 15, 20, 25, 30 and 40 K between the sphere wall and the phase change temperature of the material. The problem is considered twodimensional and transient. The model consists of mass, energy, momentum and volume fraction equations. The mathematical and numerical model is validated with experimental results from the literature, presenting good agreement between them. After space and time discretization tests, we analyze liquid fraction over time and heat flux at the sphere wall. The results show that liquid fraction suffers a strong reduction in the beginning of the solidification process due to the high heat flux in the early stages. As the solid layer near the wall increases, it causes an increase in thermal resistance, causing a significant reduction in heat flux.
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