基于分子平均自由程的热流计算壁面网格准则

A WALL GRID SCALE CRITERION BASED ON THE MOLECULE MEAN FREE PATH FOR THE WALL HEAT FLUX COMPUTATIONS BY THE NAVIER-STOKES EQUATIONS

面向壁面热流Navier-Stokes方程数值计算的应用,研究了壁面法向网格尺度问题.从气体分子物理学角度,对壁面热流进行了微观统计分析,指出壁面热流与气体分子平均自由程之间的内在联系是壁面法向网格尺度存在最优下限的原因.据此建立了一个新的壁面法向网格尺度准则,即MFP准则.该准则简单、实用,具有清晰的热力学物理意义,且只依赖于壁面局部参数.并以多种对比算例验证了MFP准则的准确性和适用性.

The wall heat flux is a very important physical parameter for the heat protection system design of high-speed vehicles, and its accurate prediction is one of difficult problems in computational fluid dynamics. In this paper, the wall normal grid scale is discussed for the Stokes equations. Firstly, the wall heat flux is analyzed physics, and the analysis shows that the coherent relation accurate computation of wall heat flux by the Navierusing the micro statistical approach in gas molecule between the wall heat flux and the gas molecule mean free path results in the optimal critical limit of the wall normal grid scale. Secondly, a new wall normal grid scale criterion, called MFP （mean free path） criterion for short, is given based on the foregoing theoretical analysis. This criterion with clear thermodynamics sense is simple and easy to be applied, and it only depends on the wall local parameters. Finally, a few different numerical examples are chosen for comparisons to validate the accuracy and the validity of the MFP criterion, namely, a hypersonic flow around a blunt cone at zero angle-of-attack, a hypersonic flow around a blunt bi-cone with and without angle-of-attack, and a hypersonic flow around a double ellipsoid at different angle-of-attacks. The considered numerical methods are finite difference, finite volume, and finite element, and the considered numerical schemes are TVD, WENO, NND, and AUSM-DV. The wall heat fluxes based on the MFP criterion are in well agreement with the relevant experiment data for all of the numerical methods and numerical schemes.