Chemical relaxation in a viscous shock

Abstract

We consider the flow of a nonequilibrium dissociating diatomic gas in a normal compression shock with account for viscosity and heat conductivity. The distribution of gas parameters in the flow is found by numerically solving the Navier-Stokes and chemical kinetics equations. The greatest difficulty in numerical integration comes from the singular points of this system at which the initial conditions are given. These points lead to instability of the numerical results when the problem is solved by standard numerical methods. An integration method is proposed that yields stable numerical results-continuous profiles of the distribution of the basic gas parameters in the shock are obtained. We consider steady one-dimensional flow in which the gas passes from equilibrium state 1 to another equilibrium state 2, which has higher values for temperature, density, and pressure. Such a flow is termed a normal compression shock. The parameter distribution in normal shock for nonequilibrium chemical processes has usually been calculated [1–3] without account for the transport phenomena (viscosity, heat conduction, and diffusion). The presence of an infinitely thin shock front perpendicular to the flow velocity direction was postulated. It was assumed that the flow is undisturbed ahead of the shock front. The gas parameters (velocity, density, and temperature) change discontinuously across the shock front, but the gas composition does not change. The composition change due to reactions takes place behind the shock front. The gas parameter distribution behind the front was calculated by solving the system of gasdynamic and chemical kinetics equations using the initial values determined from the Hugoniot conditions at the front to state 2 far downstream. Several studies (for example, [4, 5]) do account for transport phenomena in calculating parameter distribution in a compression shock, but not for nonequilibrium chemical reactions. These problems are solved by integrating the Navier-Stokes equations continuously from state 1 in the oncoming flow to state 2 downstream. We present a solution to the problem of normal compression shock in nonequilibrium dissociating oxygen with account for viscosity and heat conduction using the Navier-Stokes equations.