Detonation propagation in weakly confined gases

This study investigates the propagation of detonations along a layered configuration where a reactive gas is weakly confined by a hotter inert layer. Computational Fluid Dynamics (CFD) simulations are performed using a single-step, non-Arrhenius reaction model designed to intentionally suppress cellular instabilities, thereby enabling the formulation of a theoretical framework that can be directly compared with the simulation results. The simulations reach a quasi-steady state, revealing distinct flowfield regimes that depend on the acoustic impedance ratio and relative layer thicknesses, with some detonations exhibiting velocity deficits while others propagate above the ideal Chapman–Jouguet (CJ) speed. Analytical models are developed to interpret these regimes. When a precursor shock is observed in the inert layer, the detonation is overdriven; this phenomenon is modeled using shock-polar analysis and velocity estimates based on the approach of Mitrofanov (Acta Astronaut 3:995–1004, 1976). An analytical criterion for the onset of the precursor shock is proposed. In underdriven scenarios, the detonation front exhibits positive curvature, which is analyzed using a geometric construction approach, wherein the relationship between wave speed and front curvature is evaluated a priori. In underdriven cases, a simplified characteristic-based model is introduced to capture the decay of the shock wave in the inert layer, after which a shock-polar analysis is applied to determine the resulting wave interaction. The predictions from these analytical models are assembled into a phase map that delineates regions of overdriven and underdriven behavior, along with the corresponding shock interactions, in the space of acoustic impedance and area ratios. This map is then compared directly with the CFD results. The combined numerical–theoretical framework presented in this paper clarifies transition mechanisms that govern layered detonations and provides insights into detonation dynamics relevant to rotating detonation engines in which the detonation is bounded by the hotter combustion products formed from a previous cycle.