Application of the Boltzmann equation for determining the aerodynamic characteristics of aircrafts

Abstract

In this paper we present the derivation of new one-dimensional non-stationary nonlinear system of moment equations and an approximation of the microscopic boundary condition when part of molecules reflect from the surface specularly and part diffusive with Maxwell’s distribution. Macroscopic boundary conditions for the system of moment equations depend on the evenness and oddness of the approximation , where is the partial sum of expansion of the distribution function of molecules  into eigenfunctions of the linearized collision operator. The formulation of the initial and boundary value problem for the system of moment equations in the third approximation under the Maxwell-Auzhan macroscopic boundary conditions is given. To analyze aerodynamic characteristics of aircraft in transient regime was used complete integro-differential Boltzmann equation, which contains a term depending on the moving speed of aircraft, and under Maxwell's microscopic boundary conditions, depending on the surface temperature.