Thesis defense: Min Lin [UL]




Monsieur Min Li

Le mercredi 30 août 2017 à 14 h 30

à la salle 3370, Pavillon Adrien-Pouliot

Numerical Model Building Based on XFEM/Level Set Method to Simulate Ledge Freezing/Melting in Hall‐Héroult Cell

Président: Monsieur Jean Côté Département de génie civil et de génie des eaux Université Laval

Examinateurs :

Monsieur Mario Fafard (directeur de recherche) Département de génie civil et de génie des eaux Université Laval

Monsieur Jean‐Loup Robert (codirecteur de recherche) Département de géologie et de génie géologique Université Laval

Monsieur Louis Gosselin Département de génie mécanique Université Laval

Monsieur Hicham Chaouki Département de génie civil et de génie des eaux Université Laval

Monsieur Mohamed Rachik (examinateur externe)Université de Technologie de Compiègne



During the Hall‐Héroult process for smelting aluminium, the ledge formed by freezing the molten

bath plays a significant role in maintaining the internal working condition of the cell at stable state.

The present work aims at building a vertically two‐dimensional numerical model to predict the

ledge profile in the bath‐ledge two‐phase system through solving three interactive physical

problems including the phase change problem (Stefan problem), the variation of bath composition

and the bath motion. For the sake of simplicity, the molten bath is regarded as a binary system in

chemical composition. Solving the three involved problems characterized by the free moving

internal boundary and the presence of discontinuities at the free boundary is always a challenge to

the conventional continuum‐based methods. Therefore, as an alternative method, the extended

finite element method (XFEM) is used to handle the local discontinuities in each solution space

while the interface between phases is captured implicitly by the level set method.

In the course of model building, the following subjects: 1) one‐phase density driven flow 2) Stefan

problem without convection mechanism in the binary system 3) Stefan problem with ensuing melt

flow in pure material, are investigated by coupling each two of the problems mentioned above. The

accuracy of the corresponding sub‐models is verified by the analytical solutions or those obtained

by the conventional methods. Finally, the model by coupling three physics is applied to simulate the

freezing/melting of the bath‐ledge system under certain scenarios. In the final application, the bath

flow is described by Stokes equations and induced either by the density jump between different

phases or by the buoyancy forces produced by the temperature or/and compositional gradients.

The present model is characterized by the coupling of multiple physics, especially the liquid density

and the melting point are dependent on the species concentration. XFEM also exhibits its accuracy

and flexibility in dealing with different types of discontinuity based on a fixed mesh.

Bienvenue à tous !