Detonation propagation in weakly confined gases

Abstract

This study investigates the propagation of detonations along a layered configuration where a reactive gas is weakly confined by a hotter inert layer. CFD simulations are performed using a single-step, non-Arrhenius reaction model designed to suppress cellular instabilities, enabling formulation of a theoretical framework directly compared with 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 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 precursor shock onset is proposed. In underdriven scenarios, the detonation front exhibits positive curvature, analyzed using a geometric construction wherein the relationship between wave speed and front curvature is evaluated a priori. A simplified characteristic-based model captures the decay of the shock wave in the inert layer, after which shock-polar analysis determines the resulting wave interaction. Predictions from these models are assembled into a phase map delineating regions of overdriven and underdriven behavior, along with corresponding shock interactions, in the space of acoustic impedance and area ratios. This map is compared directly with CFD results. The combined numerical-theoretical framework clarifies transition mechanisms governing layered detonations and provides insights into detonation dynamics relevant to rotating detonation engines in which the detonation is bounded by hotter combustion products from a previous cycle.

Figures (42)

• Figure 1: Schematic representation of the problem, showing terminal shock structures relative to the detonation front: (a) attached shock (behind the front); (b) precursor shock (ahead of the front).
• Figure 2: Initial conditions showing abrupt initiation via a high-pressure, high-temperature region.
• Figure 3: Representative flowfields with wave-fixed Mach number overlaid on numerical schlieren for $A_2/A_1 = 1$. (a) Underdriven cases, $\kappa > 0$: i) $Z = 0.80$ (Case A), ii) $Z = 0.70$ (Case B). (b) Precursor shock cases, $\kappa < 0$: i) $Z = 0.45$ (Case C), ii) $Z = 0.30$ (Case D). (c) Detached shock, $A_2/A_1 = 11$, $Z = 0.40$ (Case E).
• Figure 4: Example flowfield of wave-fixed Mach number overlay with schlieren for (a) $\kappa > 0$ for $A_2/A_1 = 1$ and $Z = 0.80$ (Case A from Fig. \ref{['fig:mach_schlieren_A2A1_1']}), and (b) $\kappa < 0$ for $A_2/A_1 = 1$ and $Z = 0.45$ (Case C from Fig. \ref{['fig:mach_schlieren_A2A1_1']}). Wave-fixed Mach number profiles are extracted along the top and bottom boundaries are shown above and below the flowfield. Dashed lines indicate $M = 1$ on the Mach number plots, while dotted lines project from the plots onto the flowfield to mark approximate locations where flow becomes sonic.
• Figure 5: Closeup of the schlieren image of the detonation structure in Fig. \ref{['fig:mach_overlay']}, showing (a) the underdriven case ($\kappa > 0$) and (b) the overdriven case ($\kappa < 0$), with the sonic locus overlay and corresponding simplified schematics on the right.