An analytical model for acoustic induced aluminum combustion fluctuations in solid rocket motors

International audienceIn a Solid Rocket Motor, the combustion of aluminum droplets released by the solid propellant is often used to increase the thrust. The dynamics of this distributed combustion can drive thermo-acoustic instabilities. An analytical model for the local heat release rate fluctuations of the burning droplet cloud is derived and compared with previous low order models and with numerical flow simulations. This new model leads to close agreement with simulations and improve our understanding of the pressure oscillation source. Two contributions to heat release rate fluctuations are identified. The first one originates from the burning droplet cloud within the combustion volume and the second one lies at the combustion volume boundary between the burning cloud and the inert zone. The first contribution is the consequence of the response of the individual droplet dynamics to the flow oscillations and the second one is due to droplet lifetime oscillations. Both contributions depend on the droplet diameter, droplet velocity and gas velocity fluctuations. Models for diameter and droplet velocity fluctuations are derived by considering the peculiar structure of the acoustic boundary layer along the solid propellant surface with mass injection. The expressions for heat release rate fluctuations derived in this study can be used to predict the linear stability of a solid rocket motor at reduced computational costs