Effects of variable-area compressible boundary on detonation propagation

Detonation propagation in partially confined channels involves lateral expansion at the material interface, leading to energy loss and velocity deficits. We employ quasi-two-dimensional Euler equations to simulate this process and introduce the open-area ratio (α) to quantify the degree of lateral confinement. In the conventional partially confined channel (α = 1.0), the detonation ultimately fails. For α < 1.0, three propagation modes emerge as α decreases: intermittent transverse detonation, large-cellular detonation, and small-cellular detonation. For large α, combustion products can freely expand into the inert gas layer, resulting in energy loss and velocity deficit. With decreasing α, the narrowed lateral opening restricts expansion at the material interface, suppressing energy loss. In the limiting case (α tends to 0), the fluid behavior approaches the flow under the solid wall constraint, which is similar to the rigid wall. Two triple-point generation mechanisms are identified: (i) formation of new triple points induced by a highly curved Mach front associated with transverse detonation, and (ii) generation of new triple points through the interaction between the incident shock wave and material interface. A quasi-one-dimensional model that accounts for transverse area divergence and adopts the straight streamline approximation accurately predicts the velocity deficit of a detonation weakly confined by inert gases. The velocity deficit scales almost linearly with the open-area ratio, and the velocity deficit predicted by the quasi-one-dimensional model is in good agreement with the velocity deficit measured by numerical simulation.