Seminars on Numerical Algorithms, Analyses, and Applications：Evaporation and binary solidification model for phase change flows: A sharp and conservative method based on the geometrical VOF approach-Tianyuan Mathematical Center in Southeast China (TMSE)

Seminars on Numerical Algorithms, Analyses, and Applications：Evaporation and binary solidification model for phase change flows: A sharp and conservative method based on the geometrical VOF approach

Dec 19, 2022

Tencent Meeting ID：846-918-793（No Password）

Jie Zhang（Xi’an Jiaotong University）

Speaker：Jie Zhang（Xi’an Jiaotong University）

Time：2022-12-19, 10:00

Location：Tencent Meeting ID：846-918-793（No Password）

Abstract:

Liquid-vapor and liquid-solid phase changes are ubiquitous in natural and industrial process, such as the falling rainfall, the vaporization of the spraying fuel droplets, and the solidification of metallic materials in metallurgical industry. The relevant physical phenomena of phase change is always complex owing to the exchange of mass, momentum and thermal energy across the interface, and correspondingly, the experimental technique cannot yield a comprehensive understanding of this problem that the direct numerical simulations (DNS) could provide more detailed information. To design such numerical schemes, the first difficulty comes from the singular distribution of the mass source, which only exists in those interfacial cells during the phase change. Clearly, such singularity is a probable origination of the numerical instability, especially when solving the velocity - pressure coupling equations with high mass transfer. The second challenge requires careful treatment is about the strong coupling of the temperature and the concentration fields, either of vapor or solute in different phase change problem, at the interface. We propose a sharp phase change model on basis of the VOF method is proposed to solve the evaporation and the binary solidification flows, and the equations are discretized in the finite volume (FV) framework so that their conservative properties are well preserved. Then the embedded boundary method (EBM) is implemented to construct a second-order accurate interpolation scheme within the FV framework, and this sharp scheme enables the two phases to be solved separately, while the two regions are correlated through the jump conditions at the interface. This numerical methodology is validated through conducting a series of benchmark problems. In particular, two very challenging numerical tests are simulated: a droplet levitating above a hot plate whose temperature is much higher than the boiling temperature, known as the Leidenfrost effect; and the binary solidification of the Bi-Cu alloy driven by the temperature and the concentration simultaneously. We show that the newly implemented numerical methods can accurately reproduce experimental and theoretical results, serving as convincing evidence of the superiority of our method.