Kinetic Model Solution for Microscale Gas Flows

Abstract

A kinetic theory analysis is made of low-speed gas flows around microscale flat plates. The Boltzmann equation simplified by a collision model is solved by means of a finite difference approximation together with the discrete ordinate method. The advantage of the present method is that it does not suffer from statistical noise, which is common in particle-based methods. Calculations are made for flows around a flat plate with zero thickness and a5 %flat plate. Results for the 5% flat plate at a freestream Mach number 0.5 showed good agreement with those from the direct simulation Monte Carlo method. It is shown that strong rarefaction effects exist around the leading and trailing edges. Results from the present method at a freestream Mach number 0.087 also showed similar nonequilibrium effects. Comparison of results with those from the information preservation method and numerical solutions of the Navier‐Stokes equations showed some differences in details near the leading and trailing edges. Nomenclature Ac = collision frequency d = characteristic length of the flowfield F = Maxwell‐Boltzmann distribution f = distribution function g, h = reduced distribution functions Kn = Knudsen number L = length of flat plate l = normal distance from plate surface R =g as constant t = thickness of flat plate U∞ = free stream velocity Vx =v elocity of molecule in the x direction Vy =v elocity of molecule in the y direction Vz =v elocity of molecule in the z direction λ = mean free path I. Introduction