Nonlinear acoustic processes in solid rocket engines

A study is made of flow dynamics in a model solid rocket engine chamber flow induced by strong sidewall mass injection. The system is subjected to either a large endwall transient disturbance, or a to large sidewall transient disturbance which mimics unsteady mass addition due to irregular propellant burning.Perturbation methods are used to derive systematic approximations to the complete compressible Navier-Stokes equations. An initial-boundary value approach is used to formulate a generalized unsteady mathematical model capable of describing both non-resonant and resonant time histories of solutions. Fourier series representations of the velocity and pressure are obtained in terms of eigenfunctions that satisfy all the prescribed boundary conditions. Finite difference schemes have been adopted to solve the final nonlinear diffusive equations in order to obtain the explicit results. In addition, in the case of endwall forcing, systems of truncated, time dependent, nonlinear coupled ordinary differential equations have been solved to evaluate the validity of the modal approach for different frequencies.Axial waves, generated directly by an endwall forcing or indirectly by a sidewall forcing, propagate through the basically inviscid shear flow field, and perhaps unexpectedly, create significant vorticity at the surface of the porous cylinder. The radial component of the injected flow field carries vorticity into the entire cylinder.The formulation and analysis describe the transport and time-history of the spatial distribution of vorticity within the cylinder on the time scale for axial acoustic waves to traverse the cylinder length. Finally, results show that transient rotational flow effects are crucial to the evolution and stability of internal fluid dynamics when the characteristic cylinder Reynolds number (Re) and axial Mach number (M) are very large and small, respectively.