Reduced-Fidelity Detonation Model Using Multistate Approximation for Rotating Detonation Combustors

Rotating detonation engines (RDEs) provide a practical approach to pressure-gain combustion. Recent studies have shown that the interaction between the wave and flow path components such as turbines, compressors, inlets, and nozzles are critical for understanding the realizable efficiency. In order to facilitate the design of such systems, reliable and predictive computational tools are needed. Currently, available approaches are computationally expensive as they rely on resolving the detonation wave using an Eulerian grid-based representation. In order to reduce the computational cost, a reduced-order modeling approach is proposed here. This study will focus on the feasibility of approximating a detonation wave as an infinitely thin interface using numerical approaches similar to those used to describe multiphase fluids where a computational cell contains mixed sub-states. To ensure numerical stability, non-conservative flux source terms are incorporated across the detonation wave front in a multistate computational cell. The proposed method is demonstrated using a canonical one-dimensional detonation tube configuration and a two-dimensional rotating detonation combustor (RDC) geometry, and the results are compared against detailed chemistry calculations.