Stability Analysis of Solid Rocket Motor Combustion by Computational Fluid Dynamics

The acoustic combustion instability of a solid rocket motor is investigated by computational fluid dynamics and compared with theoretical results. The quasi-one-dimensional Euler equations for the unsteady flow inside the combustion chamber and the equation for the thermal conduction inside the solid propellant are simultaneously solved with a quasi-steady flame model near the burning surface. The Runge-Kutta discontinuous Galerkin method is used as the platform for the flow simulation, and a numerical accuracy study is carried out The conventional second-order finite volume method is verified to give accurate results by comparison with the third-order Runge-Kutta discontinuous Galerkin method. The growth rate versus the nozzle entrance Mach number for the attenuation case shows good agreement with the linear theory. For the growing case, it is shown that agreement is good for small Mach numbers. The results of the stability limit show good agreement with the theory for low Mach numbers. For higher Mach numbers, the stability-limit curve of the present simulation shows a dependency on the imaginary part of the response function. Extension to the axisymmetric problem is straightforward, and preliminary results are obtained.