Gas-dynamic flow in a spinning, coning solid rocket motor

A numerical study was performed to calculate the moment induced by gas-dynamic flow through a spinning, coning payload assist module (PAM). Although the flow is three-dimensional, the solution is achieved by solving two sets of two-dimension al equations. The flow field in a spinning, nonconing motor is first obtained. Then, the spatially periodic perturbation about the axisymmetric flow is computed to account for the vehicle's coning motion. Inviscid, single-phase simulations were performed with geometries corresponding to the grain configurations near the beginning, middle, and end of the burn. For all cases a stabilizing moment is predicted. However, the numerical study predicts a moment that is only 40-80% of the commonly used jet-damping value obtained from a one-dimensional flow theory. The simulations using the two earlier grain configurations agree with flight data; the vehicle exhibits stable motion for approximately the first three-quarters of the firing. However, the analysis for the grain configuration near the end of burn predicts stability but an exponential increase in the cone angle is observed in flight. The model was improved by including the aluminum oxide particles and viscous effects separately. The two-phase flow calculation predicts a slightly larger stabilizing moment than the inviscid solution. The predicted moment for the turbulent simulation is nearly equal to that calculated in the inviscid analysis. These simulations indicate that gas-dynamic flow is not the cause of the instability observed on the PAM.