Coupled problem of modeling the internal ballistics of nozzleless solid rocket motors

A physicomathematical formulation of the coupled gas-dynamic and geometric problem of modeling intrachamber processes and calculating the internal ballistics of nozzleless solid rocket motors is given, and a method and algorithm for solving the problem are developed. The parameters in the forward section of the motor are calculated using averaged unsteady equations of internal ballistics, and the parameters of the grain channel and the exit cone are determined using one-dimensional gas-dynamic equations in a quasi-steady formulation. The software package is verified by calculating the internal ballistics of a motor which is utilized without nozzle cluster and simulates intrachamber processes in a nozzleless solid rocket motor during the full-duration firing. The design features, motor operating parameters, and the composition characteristics influencing the energetics of propellants in nozzleless solid rocket motors are calculated. It is shown that, depending on comparison conditions (identical expansion ratios and identical profiles of the nozzle and exit cone), the specific impulse of nozzleless solid rocket motors (the main energy parameter) is slightly smaller than or nearly comparable to that of conventional solid rocket motors.