Consistent Coupling of Compressibility Effects in Manifold-Based Models for Supersonic Combustion

Manifold-based models are an efficient modeling framework for turbulent combustion but, in their basic formulation, do not account for the compressibility effects of high-speed flows. To include the effects of com-pressibility, ad hoc corrections have been proposed but result in an inconsistent thermodynamic state between the manifold and flow simulation. In this work, an iterative algorithm to consistently incorporate compressibility effects into manifold-based models is developed. The manifold inputs (fuel and oxidizer temperatures and pressure) are determined iteratively to reflect the nonnegligible variations in thermodynamic state (expressed in terms of density and internal energy in flow simulations) that are characteristic of supersonic combustion. The algorithm is demonstrated on data from simulations of high-speed reacting mixing layers and is significantly more accurate than established approaches that only partially couple the manifold in compressible flow simulations. The proposed approach eliminates partial coupling approximation errors in excess of 10 and 20% for temperature and water source term.