The chemical-gas dynamic mechanisms of pulsating detonation wave instability

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Abstract
The chemical–gas dynamic mechanisms behind the instability and failure of a one–dimensional pulsating detonation wave driven by a three–step chain–branching reaction are revealed by direct numerical simulation. Two types of pulsating instability observed experimentally are explained. The first involves regular oscillations of the detonation front, where the instability is driven by low–frequency finite–amplitude compression and expansion waves in the chain–branching induction zone between the main reaction layer and the detonation shock. For irregular oscillations of the front, the instability mechanism first involves a decoupling between the shock and main reaction layer. Subsequently, the main reaction layer accelerates, drives a compression wave ahead of it, and undergoes a transition to detonation. This internal detonation wave overtakes the lead detonation shock, generating a new high–pressure detonation, which rapidly decays. A smaller–amplitude pressure oscillation occurs during the decay with a mechanism reminiscent of that observed for the previous regular oscillation, before the detonation and main reaction layer once again decouple and the instability cycle is repeated. For failure scenarios, the shock temperature is observed to drop to the cross–over temperature for the chain–branching reaction, causing the main reaction layer to decouple and retreat indefinitely from the detonation shock.
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