Response of a Burning Solid to Small-Amplitude Pressure Oscillations

Publisher Website
Google Scholar
Abstract
The acoustic response for waves normally incident upon a burning surface region is analyzed. The combustion process involves heat conduction within the solid, an irreversible surface pyrolysis process, and a distributed gas-phase reaction zone with conduction and diffusion. Linear differential equations determining the acoustic response are derived for arbitrary frequencies and simplified to a single second-order equation for the case in which the frequency is small compared to the reciprocal of a characteristic gaseous reaction time. An approximate analytical solution to this last equation, valid when the over-all activation energy for the gaseous reaction is large, is shown to yield a simple formula for the admittance, which determines the acoustic response. This admittance formula implies that sound waves are attenuated at low frequencies and, in most cases, amplified only when the frequency approaches the reciprocal of the reaction time. In particular, it is inferred that a pure solid ammonium perchlorate deflagration will not amplify acoustic vibrations, and therefore, presumably, will not experience oscillatory combustion.

This publication has 3 references indexed in Scilit: