Hypersonic combustion with shock waves in turbulent reacting flows

This paper describes preliminary results of the research toward hypersonic external flows and supersonic internal flows of high speed aerospace vehicles in general. Interactions of shock waves, turbulence, and chemical reactions are the focus of the investigation. Shock-turbulence boundary layers in reacting flows occur in both external and internal flows. All speed regeimes of supersonic, and hypersonic flows, compressible and incompressible flows, viscous and inviscid flows are included. Computational schemes dealing with these physical complexities require innovative strategies. To this end we invoke the mixed explicit/implicit schemes with adjustable implicitness parameters in Taylor-Galerkin formulations to provide flexibilities toward widely disparate length and time scales invloved in shock thicknesses, turbulence microscales, and chemical reaction rates of different species. Although our ultimate goal is the direct numerical simulation via unstructured adaptive h-p methods, the purpose of the present paper addresses an intermediate step - to gun experience in resolving the physical aspect of interactions involved in shock waves, turbulence and chemical reactions. The k- ϵ medel is used for turbulence. The theory and computational strategies are demonstrated for the supersonic hydrogen-air flame holder combustion aa an example. It is shown that consideration of shock wave boundary layer interactions with viscosity, turbulence, and chemical reactions is important. Details of these physical phenomena are investigated in this paper.