Modélisation des changements de phase solide-liquide : effet de la variation de la densité avec la phase et du couplage thermomécanique

Authors: Dallaire, Jonathan
Advisor: Gosselin, Louis
Abstract: Phase change materials (PCM) are commonly used in a vast range of engineering applications in which they can serve, for example, as a way of storing thermal energy in the form of latent energy. Solid-liquid phase change has been the subject of many studies in the past decades both experimentally and numerically. Due to the different ways in which matter is organized at the molecular level, the physical properties of the solid and liquid phases are different. In particular, the density variations during phase change leads to volume variations, i.e., the PCM will either expand or shrink, depending on the relative density of each phase. In most studies, however, volume variations during solid-liquid phase change were deemed negligible and were not taken into account. The additional complexity and the challenges associated with the mathematical and numerical modeling of solid-liquid phase change with variable density are such that only a handful of studies on the topic may be found in literature, especially in the case where the PCM interacts with its physical boundaries (thermo-mechanical coupling). The goal of this thesis is therefore to contribute to the state of the art in terms of mathematical and numerical modeling of solid-liquid phase change when both density variations and thermo-mechanical coupling between the PCM and its container are taken into account. First, a new set of conservation equations is derived for solid-liquid phase change with different properties for each phase, especially the density. By representing the mushy region of the PCM as a porous medium (similarly to the well-known enthalpy-porosity model), macroscopic average conservation equations are developed by applying a method of volume averaging to the exact conservation equations for the solid and liquid phases at the pore level. The choice of the assumption regarding the velocity of the solid phase within the mushy region (stationary or moving) is achieved by the use of a single numerical parameter. Numerical simulations of a 1D solidification problem were performed with a finite volume code on Matlab to outline the differences between the new model and the existing enthalpy-porosity model. Then, the mathematical model developed in the first part of this thesis was extended in order to account for the interaction of the PCM with its physical boundaries. Two new models for the thermo-mechanical coupling were introduced. In the first model, it was assumed that the PCM expansion was constrained by an elastic wall and that the pressure rise within the PCM followed a modified Hooke’s law. In the second model, an air gap was introduced on top of the PCM in order to allow the latter to expand more easily. Analytical correlations were derived to predict relevant physical quantities at equilibrium, such as the pressure rise within the system, the melting temperature, the height of the PCM slab, etc. The finite volume code developed during the first part of this work was extended with a moving mesh technique to accommodate the volume variations of the PCM. The problem studied was the solidification of a 1D PCM slab of finite height. The numerical results were compared against the analytical predictions at equilibrium and showed good agreement. Finally, the elastic wall model introduced in the previous part of the thesis was applied to the problem of solidification of water near its density extremum in a 2D cavity with natural convection. The complete model was implemented in commercial software package (Fluent). A new methodology was developed in order to improve the capabilities of the software and the thermo-mechanical coupling was achieved with the help of a set of User-Defined Functions (UDF). The effect of the confinement of water as it solidifies inside the cavity was studied by varying the stiffness of the elastic wall. It was shown that the pressure rise resulting from the thermo-mechanical coupling significantly influences the flow pattern and the solidification rate of the PCM.
Document Type: Thèse de doctorat
Issue Date: 2017
Open Access Date: 24 April 2018
Grantor: Université Laval
Collection:Thèses et mémoires

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