Supersonic Flow Around the Axisymmetric Cone Placed in Shock Tube

Abstract

The aim of this study is to determine the supersonic flow parameters around the axisymetric cone body by the finite volume method. A code is written to capture both the incident and reflected oblique shock wave in the shock tube. The numerical method uses the split flow method [1]. Time stepping method is used to ensure convergence. The CFL coefficient and the mesh size are the other two parameters used to steady the convergence [3]. Introduction A numerical technique is proposed to predict a supersonic flow around an axisymetric cone body placed in shock tube. An explicit formulation with the finite volume method is used for this purpose. The oblique shock is attached to the cone and reflected on the tube wall where a sudden increase of the pressure takes place. The goal is to determine the pressure distribution both around the cone body model and along the shock tube. Figure.1 shows the setup of the cone and the computational domain. M=4 Cone body Figure 1: Configuration of the cone in shock tube, ° = 20 θ . Equations The basic equations are the Euler equations written in a vector form as follow: ( ) Ω = + ∂ ∂ + ∂ ∂ + ∂ ∂ y H y yG y x F t W 1 Where 14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA 2006-8149 Copyright © 2006 by haoui rabah. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.