Abstract
The present work gives a description and comparison of recent methods for the direct numerical simulation of droplet vaporization using a two-scalar approach for energy and species equations. Those methods require a choice of modelling for the phase change process. The comparison relies on the work of Palmore at al. in the context of Volume of fluid and on the phase change procedure of Rueda Villegas et al. [2] in the Level set framework. Both approaches have been implemented and coupled to the same two-phase low Mach solver. A quantitative analysis is given on the canonical Stefan flow problem where analytical solutions are available. First the 1D planar Stefan problem is performed to avoid any errors associated to topology. Then, the 3D spherical Stefan problem is tested to evaluate both methodologies on a multidimensional case where the choice of interface representation is prevalent. Finally, a 2D droplet convected in a quiescent ambient gas is presented. This last test case aims to demon- strate robustness of the solver on a more demanding test case implying convection, interface deformation and non homogeneous vaporization.
Highlights
Direct numerical simulation (DNS) of droplet evaporation has been a growing subject of interest in the last decades with the emergence of multiple DNS solvers and various associated numerical methods
This work compares Volume of fluid (VOF) and Level set (LS) strategies adapted to the same low Mach solver
The Stefan flow test cases presented here show that VOF has a regression following d2 law even for the most under-resolved test cases
Summary
Direct numerical simulation (DNS) of droplet evaporation has been a growing subject of interest in the last decades with the emergence of multiple DNS solvers and various associated numerical methods. With ul and ug the liquid and gas velocities respectively and nΓ the interface normal pointing outward the liquid phase This leads to uΓ = ul − ρl nΓ and uΓ = ug − ρg nΓ. Definition of the vaporization rate The evaporation rate has two definitions based on the heat and mass flux jumps at the interface (9) and (10). A methodology is proposed in [5] to address this issue by switching between both vaporization regimes when a critical temperature close to Tsat is reached Another way to deal with this issue is to always use equation (11) for mcomputation and to provide a closure for TΓ which can be very different from Tsat as in [1] and [2]. Closure for YΓ and TΓ Considering that the pressure is at saturation at the interface, TΓ and YΓ are related through the Clausius-Clayperon relation
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