Toward Large-eddy/reynolds-averaged Simulation of Supersonic Combustion

While flamelet-based progress variable models have matured to production-level in recent years for incompressible flows, little development toward compressible formulations of the flamelet model has ensued. For supersonic and hypersonic flows exhibiting combustion, an applicable flamelet-based combustion model must reflect the compressible nature of the flow, the tight coupling of the flow and flamelet equations, and the problem of multiple flamelet boundary conditions This paper describes recent work toward developing a compressible formulation for use with large-eddy/Reynolds-averaged simulations and implementing flamelet-based progress variable models in a production-level research code frequently used to simulate high-speed reacting flows. The proposed model relies on first solving transport equations for momentum, species mass fraction, and temperature for an axisymmetric opposed-flow diffusion flame for a range of strains and pressures. The solution space is tabulated and subsequently parameterized by mixture fraction, progress variable, and pressure. At runtime, transport equations for mass, momentum, energy, mixture fraction, and progress variable are solved, and at each time step, relevant chemical properties are retrieved from the flamelet table. By mapping the chemistry to a small set of tracking scalars, finite-rate simulations of high-speed reacting flows are made comparable in computational cost to a frozen-chemistry simulation.