Model for acoustic induced aluminum combustion fluctuations in solid rocket motors

Combustion of aluminum droplets released by the solid propellant is widely used to increase the thrust in solid rocket motors. The combustion dynamics of the released droplet cloud in the unsteady flow is however susceptible to trigger thermoacoustic instabilities. A theoretical analysis is conducted to determine the heat release rate fluctuations produced by the burning droplet cloud for small acoustic disturbances. Two contributions to heat release fluctuations are identified. The first originates from fluctuations of the evaporation rate due to the oscillating flow around the droplets. This leads to local fluctuations of the volumetric rate of heat release within the droplet cloud. The second one originates from the motion of the boundary of the burning droplet cloud at the end of the combustion process. This motion is due to droplet lifetime oscillations leading to an additional source of heat release disturbances. Both contributions to heat release disturbances take place within the acoustic boundary layer along the solid propellant surface. Quasi-steady models for the response of the droplet diameter fluctuations and droplet velocity fluctuations are derived. Combined with a model for the gas velocity fluctuations within the acoustic boundary layer they lead to expressions for the resulting heat release rate disturbances within the droplet cloud and at its boundary. Results are compared to a previous low order model and to numerical flow simulations. It is shown that the new model leads to close agreement with simulations over the entire flow. The derived expressions yield a better understanding on heat release disturbances and can be used to predict the linear stability of a solid rocket motor at reduced computational costs