Scaling considerations for aluminum agglomeration in solid rocket propellants

Aluminum agglomeration during solid rocket propellant combustion decreases rocket motor performance. Previous works have generally been unsuccessful in determining consistent trends between propellant formulation and agglomerate size on or near the propellant surface. In this work, scaling considerations are presented to provide physical insight to identify trends based upon propellant formulation and operating conditions. A modified Weber number, W e m , presents the ratio of drag and adhesive forces whereas a second dimensionless parameter, τ , quantifies relevant time scales (i.e., ignition delay and particle time of arrival). Initial aluminum particle size influences the agglomeration tendency only through the force competition quantified by W e m and not in terms of particle heating time. When the total contact surface area between a particle and melt layer is considered, a consistent trend is observed with the adjusted Weber number and agglomerate size normalized with initial aluminum particle diameter. The burning rate exponent, n , was determined to be critical in identifying pressure scaling trends from considerations of the forces ( W e m ∝ P n − 1 for R e < 5 ) and time scales ( τ ∝ P n , indirectly through the heat flux). The effects of pressure, propellant formulation, and microstructure on agglomeration are manifested in the ballistics of the propellant and the statistical distribution of heat flux from the change in flame structure. Incorporation of mesoscale propellant simulation data into the scaling arguments indicated qualitative agreement with the literature. Comparison to other previous studies and extension of the scaling arguments to more detailed models is discussed.