Linear combustion stabiliy analysis of oxidizer-rich staged combustion engines

This thesis concerns the consistent linear acoustic stability analysis of an engine modeled on the RD-170, a prototypical example of an Oxidizer Rich Staged Combustion (ORSC) engine. Both the preburner-turbine assembly as well as the main combustion chamber are studied. The theoretical basis for the stability analysis is an inhomogeneous acoustic wave equation in the pressure. Boundary effects are accounted for by means of impedance boundary conditions. Theoretical impedance models are employed to describe the physics of various components: the turbine inlet blade row in the preburner assembly, and the flow distributor in the main chamber. In the main chamber, mean flow and combustion response effects are accounted for by means of right hand side source terms in the wave equation. Two cases are considered for mean flow: piecewise uniform and swirl flow. The swirl flow is generated by time averaging the results from LES of the main chamber injectors. It is found that the mean flow contributes significant damping to the system by means of convecting acoustic energy out of the domain. The swirl flow additionally provides acoustic refraction which further increases the damping. Overall the mean flow is found to far eclipse the other sources of damping. The response of the combustion to acoustic perturbations is quantified by means of a Flame Transfer Function (FTF). Spatially distributed fields for both the FTF gain and phase are computed from LES data using POD reduction for three different injector recess lengths. A chamber-level response field is constructed as a superposition of fields for individual injectors. It is found that as the recess length decreases, the system becomes more unstable, due to the fact that the base of the injector nonpremixed flame becomes more exposed to the transverse oscillations in the main chamber. A sensitivity analysis is conducted on a reduced set of scalar quantities which characterize the distributed combustion response fields. The eigenvalue results are found to be most sensitive to the maximum of the gain field, the axial spread of the gain about this maximum value, and the maximum axial slope of the phase field. The radial location of the maximum gain also affects the stability to a lesser extent. The results suggest that to maximize the stability margin of the engine the recess length of the injector should be maximized and the fluid conditions should be such that the flame is wide and combustion is distributed over as large an axial extent as possible.Ph.D