A finite element approach to response function calculations including multi-dimensional radiative heat transfer

Response function calculations for the solid propellant rocket motor are carried out using finite elements. The formulation is based on the Arrhenius law with a single step forward chemical reaction and the pressure coupling impressed by a harmonic acoustic disturbance of arbitrary wave incidence. Multi-dimensional nonlinear time dependent equations are employed with analytical boundary conditions at the flame and decomposition zones implemented by means of the Lagrange multipliers. Radiative heat transfer in participating media is included. The numerical results show that an oscillatory behavior of all variables (pressure, density, velocity, temperature, and mass fraction) is pronounced at upstream and gradually diminishes toward downstream. It is also shown that the radiative heat transfer contributes to damping at low frequencies, whereas it enhances the responses at high frequencies.