Aluminum combustion instabilities: Dimensionless numbers controlling the instability in solid rocket motors

Abstract

This article is focused on the analysis of the aluminum combustion dynamics, induced by acoustic oscillations, in solid rocket motors. This dynamics is expected to drive self-sustained pressure oscillations which can lead to structural damages of the rocket. In order to control this thermoacoustic instability, theoretical developments are presented in this paper to highlight the main parameters of the thermoacoustic source. These new theoretical developments are based on a linear model of the thermoacoustic source which has been verified with a numerical simulation in a previously published work. With some assumptions and reductions, this article clearly demonstrates that (i) the thermoacoustic source depends on 4 dimensionless numbers (Sherwood number, Stokes number, combustion Strouhal number, flow Strouhal number), (ii) if the source can be split into two contributions (flame dynamics around an evaporating droplet and droplet combustion end-dynamics), both contributions have different tendencies, (iii) the acceleration of the mean flow along the motor leads to this thermoacoustic instability. Under some assumptions (aluminum combustion model, linear or weakly nonlinear dynamics), these results make it possible to control this instability in a solid rocket motor.