Stability of hypersonic flow of a detonable gas mixture in the stagnation region of a blunt body and a forward facing step

The time-dependent characteristics of the hypersonic flow of a detonable gas mixture in the stagnation region of a blunt-nosed body and blunt face of a forward facing step are studied using approximations based on inviscid analysis. In this investigation the approximation that at hypersonic speeds the flow in the stagnation region, behind the normal shock wave which is established in front of the blunt face of the model, can be considered to be at 'constant density' is used. Both of these approximations may be justified for very high Reynolds number flow at hypersonic speeds. In this analysis, it is shown that using the time-dependent flow equations which include the heat addition due to the chemical reactions, it is possible to develop a second-order differential equation for the instantaneous temperature. The stability characteristics of this governing equation are analyzed for the zero-order and first-order chemical reaction cases so as to determine the stability boundaries of the detonation phenomena in terms of the flow and the chemical reaction parameters. These dynamic characteristics are studied by the examination of the phase diagrams. The stability characteristics are determined by the analysis of the linearized equations. The calculated eigenvalues of the solutions are used to define both the stability boundaries and the oscillation frequencies.