COMBUSTION MODELING OF COMPOSITE SOLID PROPELLANTS (PEM)

A theoretical model for the combustion of composite solid propellants is described. This model, the Petite Ensemble Model (PEM), is based upon a combination of a unique statistical treatment of the burning surface of a composite solid propellant and a comprehensive, multiple-flame, physio-chemical combustion model. Due to this statistical treatment, the PEM can account for both oxidizer particle size and size distribution effects on propellant burning rate behavior. A scenario for the behavior of aluminum particles burning within the surface/near surface environment of a composite solid propellant is postulated. Calculations indicate the importance of considering aluminum particle size distribution within the framework of this aluminum PEM, or ALPEM. The augmentation of propellant burning rate due to an imposed acceleration field is shown to have an aluminum particle size dependency. Propellant erosive burning is modeled through a coupling of the steady state PEM with an approximate, transpired boundary layer analysis. Erosive burning results from this model agree with traditionally observed experimental trends. That is, a threshold velocity is predicted that decreases with increasing pressure. Also, erosive burning sensitivity is calculated to be greater for slower burning propellants. Finally, a small perturbation analysis is performed on the equations representing both the nonerosive and the erosive PEM. These analyses yield two nonsteady response models; one for the pressure coupled response function and another for the velocity coupled response function, both applicable to composite solid propellants. Pressure coupled and velocity coupled response models are also formulated based on a Zeldovich/Novoshilov methodology in which the nonsteady response of a propellant is directly related to its steady state response characteristics. Results indicate that the magnitude of the pressure coupled response is highly dependent on oxidizer particle size as is the frequency at which the response peaks. As combustion pressure is increased, both the magnitude of the pressure coupled response as well as the peak frequency increase. Finally, the tendency for a propellant to yield to velocity coupling is shown to be directly related to the degree of erosive burning sensitivity exhibited by the propellant