A wall grid scale criterion based on the molecule mean free path for the wall heat flux computations by the navier-stokes equations

The wall heat flux is a very important physical parameterfor the heat protection system design of high-speed vehicles, and itsaccurate prediction is one of difficult problems in computational fluiddynamics. In this paper, the wall normal grid scale is discussed for theaccurate computation of wall heat flux by the Navier-Stokes equations.Firstly, the wall heat flux is analyzed using the micro statistical approachin gas molecule physics, and the analysis shows that the coherent relationbetween the wall heat flux and the gas molecule mean free path results inthe optimal critical limit of the wall normal grid scale. Secondly, a newwall normal grid scale criterion, called MFP (mean free path) criterion forshort, is given based on the foregoing theoretical analysis. This criterionwith clear thermodynamics sense is simple and easy to be applied, and itonly depends on the wall local parameters. Finally, a few differentnumerical examples are chosen for comparisons to validate the accuracy andthe validity of the MFP criterion, namely, a hypersonic flow around a bluntcone at zero angle-of-attack, a hypersonic flow around a blunt bi-cone withand without angle-of-attack, and a hypersonic flow around a doubleellipsoid at different angle-of-attacks. The considered numerical methodsare finite difference, finite volume, and finite element, and the considerednumerical schemes are TVD, WENO, NND, and AUSM-DV. The wall heat fluxesbased on the MFP criterion are in well agreement with the relevantexperiment data for all of the numerical methods and numerical schemes.