Role of compressibility effects in manifold models for supersonic turbulent combustion

At low Mach number, the kinetic energy of the flow is negligible compared to the heat release from combustion, and one can treat the background thermodynamic state as uniform. However, at high Mach number, the addition of compressibility effects couples the thermodynamic state to the combustion processes – a challenge for supersonic turbulent combustion models. Many high-speed reacting flow simulations rely on manifold-based models due to their low computational cost compared to other turbulent combustion models, but manifold models typically either do not account for compressibility effects or rely on partial coupling between the manifold model and the thermodynamic state. Notably, manifold models typically assume a linear relationship between enthalpy and mixture fraction, valid strictly only at low Mach numbers. In this work, an a priori analysis is performed to analyze the role of compressibility effects in manifold models for supersonic turbulent combustion. Specifically, the influence of enforcing a nonlinear enthalpy profile is compared to using a (locally) linear enthalpy profile. This analysis is applied to data from the Direct Numerical Simulation (DNS) of a supersonic reacting mixing layer allowing for insight into the impact of compressibility on turbulent combustion.