A Thermodynamically Consistent Manifold-based Combustion Model for Premixed Detonations and Deflagrations

In low-Mach flows, the kinetic energy of the flow is negligible, so the background thermodynamic state is approximately uniform. The local changes in the thermochemical state – temperature, composition, etc. – are then solely a function of transport and chemistry. Manifold-based models take advantage of this decoupling by solving for the thermochemical state separately from CFD as a function of a reduced set of manifold coordinates, such that during CFD only the manifold coordinates must be transported, with the local thermochemical state simply retrieved. In compressible flows, the conversion between kinetic energy and internal energy is non-negligible and changes the local thermodynamic state. This coupling poses a challenge for manifold-based models since the local thermodynamic state must be known to determine the thermochemical state and vice-versa (e.g., evaluation of the ideal gas law). Recent work for nonpremixed combustion solves this issue by iterating the thermodynamic state and the manifold model solution to ensure thermodynamic consistency between CFD and model. This work leverages this approach for premixed combustion. Accuracy of the approach is demonstrated for both premixed deflagrations and detonations. For implementation of the model in CFD, two additional dimensions for manifold solutions (enthalpy and pressure) require coupling with In-Situ Adaptive Manifolds (ISAM), which solves the manifold equations during the simulation only if necessary and intelligently stores and reuses prior model evaluations. Together, the new model paired with ISAM presents a leap in fidelity for simulations with supersonic premixed flames such as those investigating deflagration-to-detonation (DDT) transition, rotating detonation engines (RDEs), and more.