Modélisation de la dynamique de la croissance dendritique des corps purs à la rupture de surfusion

Abstract

Nowadays, energy storage becomes essential in order to adjust the production of energy to the consumption. Among the available techniques of energy storage, the latent heat storage has received much attention from both scientific and industrial points of view. The main idea behind this type of storage is the use of the energy transfer taking place when a material changes phase. The performance of latent heat storage systems depends strongly on the crystallization process. For pure substances, different behaviors can be observed according to the supercooling degree of the liquid phase, the difference between the solid-liquid equilibrium temperature and the liquid temperature at the nucleation instant. When the supercooling degree is low, the solidification is characterized by a stable interface (i.e. Stefan problem). However, when it is high enough, dendritic pattern dominates and a complex unstable interface develops as soon as crystallization begins. Experimental visualizations have shown that during the dendritic growth, the supercooled liquid temperature returns to the equilibrium temperature and then the complete solidification occurs at this temperature. Dendritic growth is due to the complex interaction between the stabilizing and destabilizing effects at the solid-liquid interface. Despite the large volume of literature dealing with dendritic growth, the problem is still not completely understood, and many questions remain without clear answers. Although this Ph.D., collaboration between the Laboratory of thermal, energetics and processes, and the Industrial Research Group in energy technologies and energy efficiency (t3e), does not deal specifically with phase change materials, it constitutes the first step of the research project dedicated to study the dendritic growth during solidification processes of some selected phase change materials. The Ph.D. has two major parts, the first is experimental and the second is numerical. The numerical study is based on a code written in C++, which solves the dendritic growth problem and simulates the two-dimensional evolution of the liquid-solid interface taking into account all the involved effects. The numerical method is based on a front-tracking approach and a finite-volume scheme. The interface evolution is then tracked explicitly using an independent set of marker points which evolves over the fixed background describing the whole medium. Firstly, numerical techniques are described, and the behavior of the code is tested through the critical radius concept of homogeneous nucleation, and an isotropic circular stable case of solidification, where a good agreement with analytical solutions for similar cases are found. Unstable cases of solidification, considering four-fold and six-fold symmetry modes of anisotropy are performed next. Finally, interface evolution, providing realistic dendritic features as tip-splitting and side-branching, is described, showing the ability of the code to deal with complicated dendritic growth. Secondly, the effect of non-homogeneous temperature field in a supercooled liquid on dendritic growth of pure substances is investigated. It has been found that the initial supercooling degree affects the size and the structure of the interface and that the macroscopic gradient (imposed by different temperatures at the domain boundaries) leads to an asymmetrical dendritic growth. The higher the macroscopic gradient is, the more visible the asymmetrical of dendritic growth is. The obtained quantitative results indicate that dendritic velocities depend only on the local supercooling degree. In this context, a local competition between the interface dynamics and the transfer rate of the associated latent heat in liquid phase is shown: when the interface grows rapidly, it moves to a region which is not yet influenced by the heat release and then it keeps growing. Otherwise, when the interface movement is slow, it gets influenced by the heat release and then moves slower. Finally, it has been found that the variation of both total length of the interface and total solid phase surface are independent on the imposed macroscopic gradient and that their ratio tends in all simulations to the same constant. The experimental part consists of the design and the installation of a bench able to visualize dendritic phase under different thermal and geometrical conditions. Indeed, it is designed in a manner that, from the one hand, the thickness of liquid could be modified in order to allow several types of study, and from the other hand, the thermal gradient created in the liquid by the cooling system could be controlled. Although the design of this bench has allowed for the determination of the assumptions on which the numerical study is based, no experimental result has been obtained.

Date	23 Sept 2016
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Daniel Rousse (Supervisor) & Jean Pierre Bédécarrats (Co-supervisor)