Simulation numérique de l'ébullition sur maillages non structurés Numerical simulation of boiling on unstructured gridsThèse soutenue publiquement le 18 décembre 2019, devant le jury composé de :

In this study, we present different numerical methods for the simulation of liquid-vapor phase change (boiling). We use a Level Set formalism to capture the liquid-vapor interface. Such a formalism requires a reinitialization (aka redistancing) step of the Level Set function after advection. This step is critical for phase change simulation as it must neither move the interface nor induce perturbations in the Level Set function profile, otherwise the normal vector to the interface and its curvature, two quantities that are crucial to define respectively the interface velocity due to phase change and the pressure jump at the interface due to surface tension, would be in turn affected by too large numerical errors. Here we present a comparison of different reinitialization algorithms of the Level Set function for boiling simulations, on structured and unstructured grids. These methods are then validated against the analytical case of a static growing bubble with a fixed mass transfer rate. In particular, we observe that at the time corresponding to a doubled bubble radius, the error on the bubble radius decreases with the grid cell size for all presented methods.

Two-phase flows are characterized by the existence of an interface between the two phases. Therefore, numerical simulations of two-phase flows require high accuracy on the methods used to model the interface motion. Different families of methods exist to keep track of the interface, among them are Front Tracking [1], Volume Of Fluid [2] and Level Set methods [3]. We have developed a solver in the finite volume-based YALES2 framework [4] for numerical simulations of boiling. We use a Level Set method where the liquid-vapor interface is defined as the 0-level of the Signed Distance Function to the interface. The advantages of using the Level Set method compared to the Front Tracking and Volume of Fluid methods are the easier computation of the interface geometrical properties such as normal vector and curvature, and the ability to inherently handle interface topological changes such as coalescence and atomization. The Level Set field is continuous at the interface, thus no interface reconstruction procedure is needed after advection. The interface motion is then represented by the advection of the Level Set function by the fluid velocity. One notorious problem is that the advected Level Set function is no longer the signed distance function to the advected interface, and so a reinitialization step is needed. On structured cartesian grids, two well-known methods exist to reinitialize the signed distance function: the Fast Marching Method (FMM) [5] and Hamilton-Jacobi's method (HJ) [6]. The FMM updates node lists to solve the Eikonal equation