Application of the finite volume method for the supersonic flow around the axisymmetric cone body placed in a free stream

摘要

The aim of this study is to determine the supersonic flow parameters around the axisymmetric cone body by finite volume methods. A code is written to capture the oblique shock wave behind a cone placed in supersonic free stream. The numerical method uses the Flux Vector Splitting method of Van Leer (Flux Vector Splitting for the Euler Equations, Lecture Notes in Physics, 170, pp. 507-512, 1982). Time stepping is used as a parameter to ensure the convergence of the solution. The CFL coefficient and the mesh size are the other two parameters used to steady the convergence (Haoui et al. Condition de convergence appliquee a unecoulement reactif axisymetrique, 16eme CFM, n°738, Nice, France, 2003). The shock wave is detached when the point angle is large or the Mach number is weak. The Mach-contours show the evolution of the flow well from the infinite one to after the body. The precision of calculations is an order 10~(-8). For the same infinite Mach number, when the point angle increases, the detached shock back away. The computer code also collects also the waves of relaxation on the convex part of the body.