A one-dimensional theoretical model, incorporating the Noble-Abel dense gas law, has been developed to describe the transient model combustion phenomena inside a propellant crack. The theoretical model can be used to predict wave phenomena, heat transfer from the gas to the propellant surface and associated thermal penetration, flame propagation, and resultant pressurization at various locations along the propellant cavity. Calculations made with the current theoretical model revealed that the internal pressurization rate, pressure gradient, and flame velocity in propellant cracks (for which gases can penetrate) decrease as: the gap width increases, the rocket chamber pressurization rate decreases, and the propellant gasification temperature increases. Additionally, the predicted flame spreading was found to decelerate in a region near the crack tip; this phenomena has been experimentally observed by others.

This report is a facsimile of a report submitted by Systems Associates, Pennsylvania State University, under Contract N60530-79C-0006 and maintains the original format. It includes the study of dynamic burning effects in the combustion of solid propellants with cracks, and the use of granular bed combustion codes for solving hazard problems in rocket propulsion systems. The Zeldovich quasi-steady flame model was used in the evaluation of the dynamic burning effect. The dynamic burning rate was obtained by solving the transient heat conduction equation for the solid propellant and using the Zeldovich map for determining the heat feedback. Results indicate a stronger dynamic burning response for a higher pressurization rate, larger energy storage in the propellant, and lower initial pressure. A dynamic burning-rate augmentation function was developed to facilitate the incorporation of the transient burning effect into the crack combustion code. The augmentation function is in close correlation with results obtained from the finite difference method over the broad range of conditions studied. The mobile and fixed granular bed combustion codes (MGBC and FGBC), users manuals for these two programs, sample input data, and output listing were delivered to NWC.

This report presents results of a study of combustion processes in solid propellant cracks. As might be expected, under moderate chamber pressurization rates (10,000 atm/s), the theoretical predictions, as well as the experimental observations, indicate that the ignition front propagates from the entrance of the crack to the tip. However, under rapid chamber pressurization rates (100,000 atm/s or higher), the tip region of the crack was observed to ignite before the arrival of the convective ignition front. (Ignition is defined here as the onset of emission of luminous light from the propellant surface with some material loss. A theoretical model has been developed to explain the tip ignition phenomena. The model considers: a one-dimensional transient heat conduction equation for the solid phase; and one-dimensional, unsteady mass and energy conservation equations for the gas phase near the crack tip. Both experimental and theoretical results indicate that the ignition delay time decreases as the pressurization rate is increased.