Combustion Instability: Acoustic Interaction with a Burning Propellant Surface

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Abstract
A theory of the response of a burning solid to a sound wave is developed, based on time‐dependent solutions of the transport equations relevant to a combustible having idealized physical and chemical properties. The development is restricted to small perturbations about the steady‐state conditions for a rather simple model whose parameters have either a direct physical significance, or are experimentally determinable. The introduction of ad hoc time delays, or other phenomenological parameters has been entirely avoided. Time‐dependent reaction rate chemistry also has been avoided, by considering only sufficiently fast reactions that the volumetric rate of reaction corresponds to the steady‐state rate appropriate to the instantaneous local conditions as described by solution of the time‐dependent transport equations. The predictions of the theory are discussed briefly, and several rather general observations are made. However, in view of the complexity inherent in the phenomenon and the present state of inadequate available empirical knowledge regarding this phenomenon, it is not yet possible to make a quantitative comparison between the theory and experiment.

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