Inherently high-speed manifold-based modeling of supersonic turbulent combustion

Manifold-based turbulent combustion models were developed in the low Mach number limit where thermodynamic pressure variation and viscous heating are assumed to be negligible. Various approaches have attempted to account for compressibility effects through the addition of ad hoc correction terms that introduce thermodynamic inconsistencies between model and flow solver, and, although a more recent iterative approach allows for complete thermodynamic consistency between model and flow solver, all of these models still ultimately rely on solutions to the low Mach manifold equations. In this work, high-fidelity data from a high-speed turbulent reacting flow in a scramjet-like geometry is used to inform an inherently high-speed manifold model that includes the high-speed terms directly in the manifold equations, avoiding the need for ad hoc correction terms or iterative approaches. The inclusion of these terms also allows the model to capture local compressibility effects such as shockwaves. Multiple datasets are then analyzed to understand how errors in accounting for compressibility effects compare to other manifold-based modeling errors, specifically the modality of the combustion processes.