A one-dimensional, mathematical model is adopted to investigate, numerically, the instabilities experienced inside a hybrid rocket propulsion system. The presumption is that such oscillations feed into combustion instabilities and result in poor performance of the propulsion system and/or result in mechanical vibrations that lead to failure of the rocket motor. The model adopted for the numerical study is a one-dimensional, multi-node representation of a subscale hybrid rocket propulsion system. A one dimensional channel with circular cross-section is configured to simulate a combustion chamber of a rocket hybrid rocket motor and is connected to a converging–diverging nozzle in the downstream and to a plenum with a flow straightener in the upstream side. The working fluid is supplied from a pressurized storage tank to the upstream plenum through a throttle valve. A multi-component approach is used to model, mathematically, the propulsion system. In this integrated-component model, the unsteady flow through the throttle valve and the nozzle is assumed to be one-dimensional and isentropic whereas the flow in the forward plenum and in the combustion chamber is assumed to be a one-dimensional, unsteady, compressible, turbulent, and subsonic. The physics based mathematical model of the flow in the channel consists of conservation of mass, momentum and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations of the compressible flow in the combustion chamber are discretized using the second order accurate MacCormack finite difference scheme. Convergence and grid independence studies were done to determine the optimum mesh size and computational time increment needed for the present simulations. Furthermore, steady state results of the proposed model are compared to the results of the isentropic, Fanno (viscous 1-D flow), and Rayleigh (1-D flow with heat input) case studies to verify the accuracy of the numerical predictions. Numerical experiments were then carried out to simulate the flow oscillations in the combustion chamber of a sample subscale hybrid rocket motor. Experiments were repeated for various operating conditions (Re numbers between 104 and 106) to determine the flow regions where these oscillations are sustained. The numerical simulation results indicate that the proposed mathematical model predicts the expected unsteady axial distributions of temperature, velocity, and pressure in the combustion chamber and the general characteristics of the experimentally observed instabilities associated with hybrid rocket propulsion systems.
