A thermodynamically consistent manifold model for premixed deflagrations & detonations

Accurate modeling of compressible premixed flames, encompassing both deflagrations and detonations, remains a significant challenge for predictive Large Eddy Simulation (LES) due to the strong coupling between the thermochemical state and the local thermodynamic state. This work presents a manifold-based turbulent combustion model that ensures a fully consistent thermodynamic state between model and flow solver through an iterative procedure. The framework reproduces critical quantities including temperature, radical species, and source term profiles, addressing limitations of existing approaches that rely on low-Mach perturbations or tabulated ZND detonations without thermodynamic consistency. Validation is performed against one-dimensional and high-fidelity RDE-like data, demonstrating that the thermodynamically consistent model consistently outperforms existing approaches across a broad range of compressible flame regimes — including both deflagration and detonation. The results highlight the importance of fully accounting for the thermodynamic state to achieve accurate predictions. By capturing both deflagrative and detonative behavior within a single framework, the model provides a unified, versatile tool for LES of high-speed reacting flows and offers a foundation for future studies of compressible reacting flows, including applications to rotating detonation engines and other supersonic combustion systems. Novelty and significance statement Current manifold-based models for compressible premixed flames are based on a partial coupling of the thermodynamic state with the thermochemical state. This leads to inaccurate predictions of key quantities such as chemical source terms and radical species, particularly in the presence of large thermodynamic fluctuations characteristic of high-speed compressible flows, due to their very strong sensitivity to the thermodynamic state. This work presents a novel manifold-based turbulent combustion model that fully incorporates the thermodynamic state and spans all regimes of premixed combustion from deflagration to detonation, for the first time in one unified model. The new model enables the study of the coupling between chemical kinetics, heat release, and compressible wave dynamics governing combustion processes featuring deflagration and detonation, including deflagration-to-detonation transition and rotating detonation engines, at reduced computational cost compared to detailed chemistry with higher physical accuracy compared to existing models.