Travelling Wave Solution of a Riemann Problem and Shock Structure in an Unsteady Flow of a Perfect Gas under Viscosity

Abstract

Travelling wave solution of one-dimensional unsteady flow of a perfect gas with the effect of viscosity under Riemann condition is investigated. The system of gas dynamic equations are reduced into a single ordinary differential equation for non-dimensional velocity and Riemann condition is transformed into boundary conditions. The exact solution is obtained for the gas velocity, pressure, temperature and change-in-entropy under the constant boundary conditions taking the origin at inflection point of the gas velocity profile. It is found that the travelling wave is a shock transition zone of the thickness of order 10^(-6) meter. The viscosity of the gas, Mach number, ratio of specific heats, and Riemann condition has significant effects on the shock structure.