Natural co-ordinates and high speed flows, a numerical method for reactive gases

A new high resolution, space marching, numerical method, based on operator splitting, for high speed, steady, planar two dimensional, Inviscid, chemically reacting (real gas) flow fields as described. A simple model for chemical non-equilibrium was used based on Lighthill's ideal dissociating gas model for diatomic Oxygen. The method is formulated within the natural co-ordinate space consisting of streamlines and their normals. Boundaries are treated exactly and the variation of the chemistry shown to be along the streamline co-ordinate. Operator splitting is used to split the full problem up into two consisting of the wave and chemical contributions. We use the Riemann problem based Random Choice Method (RCM) for solving the homogeneous Euler equations with frozen initial data for the wave contribution. The definition of the Riemann problem for the natural co-ordinate space is described. The RCM does not suffer from numerical smearing or spurious oscillations like other methods and this will be a positive advantage for chemical non-equilibrium due to the sudden rise in temperature across a shock wave. The flow field changes due to the chemical non-equilibrium are included by solving numerically a system of stiff ordinary differential equations. This was done using the stiff solver LSODE. The algorithm is first validated for inert flow fields. This is done by making comparisons between theoretical and experimental results for several classic high speed configurations. The method is then validated for chemical non-equilibrium by making comparisons with results from other numerical methods. Finally, the qualitative effect of these real gas effects on the aerodynamic characteristics of s simple re-entry profile (modelling the Space Shuttle) was investigated.