Flame response to transverse velocity excitation leading to frequency doubling and modal coupling

Transverse thermoacoustic modes may occur in gas turbines, aero-engines, and rocket engines. Various scenarios of flame excitation can be observed, depending on the type of transverse mode and the location of the flame relative to the mode shape. If an acoustically compact, symmetric flame is exposed to transverse velocity fluctuations of uniform strength and direction, the resulting modulation of the overall heat release rate is invariant to the direction of the velocity perturbation. It follows that the dominant flame response occurs at twice the forcing frequency, even for an infinitesimally small oscillation amplitude. The present study proposes a modeling framework for this inherently non-linear phenomenon, which relies on a second-order kernel of the Volterra series. As a possible realization of the Volterra series, an ad-hoc model is proposed and validated with CFD for mono-frequency forcing. Furthermore, a mechanism of modal interaction is established by which frequency doubling in the flame response causes an unstable transverse mode to drive a higher order stable mode, such that at near-resonance conditions the higher order mode exhibits elevated amplitude. This mechanism can explain the observations made by Urbano et al. (2016) in a small-scale rocket thrust chamber, where a radial mode appears at exactly twice the frequency of the dominant transverse mode. A simple representative setup of a cylindrical combustion chamber is used to explain this mechanism analytically.