Combustion instability modeling using multi-mode flame transfer functions and a nonlinear Euler solver

Abstract

Modern methods for predicting combustion dynamics in high-pressure combustors range from high-fidelity simulations of sub-scale model combustors, mostly for validation purposes or detailed investigations of physics, to linearized, acoustics-based analysis of full-scale practical combustors. Whereas the high-fidelity simulations presumably capture the detailed physics of mixing and heat addition, computational requirements preclude their application for practical design analysis. The linear models that are used during design typically use flame transfer functions that relate the unsteady heat addition q ′ to oscillations in velocity and pressure ( u ′ and p ′ ) that are obtained from the wave equation. These flame transfer functions can be empirically determined from measurements or derived from theory and analysis. This paper describes a hybrid approach that uses high-fidelity simulations to generate flame transfer functions along with nonlinear Euler CFD to predict the combustor flowfield. A model rocket combustor that presented a self-excited combustion instability with pressure oscillations on the order of 10% of mean pressure is used for demonstration. Spatially distributed flame transfer functions are extracted from a high-fidelity simulation of the combustor and then used in a nonlinear Euler CFD model of the combustor to verify the approach. It is shown that the reduced-fidelity model can reproduce the unsteady behavior of the single element combustor that was both measured in the experiment and predicted by a high-fidelity simulation reasonably well.