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

摘要

Transverse thermoacoustic modes may occur in gas turbines, aero-engines, and rocket engines. Variousscenarios of flame excitation can be observed, depending on the type of transverse mode and the locationof the flame relative to the mode shape. If an acoustically compact, symmetric flame is exposed to transversevelocity fluctuations of uniform strength and direction, the resulting modulation of the overall heatrelease rate is invariant to the direction of the velocity perturbation. It follows that the dominant flameresponse 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, whichrelies on a second-order kernel of the Volterra series. As a possible realization of the Volterra series, anad-hoc model is proposed and validated with CFD for mono-frequency forcing. Furthermore, a mechanismof modal interaction is established by which frequency doubling in the flame response causes an unstabletransverse mode to drive a higher order stable mode, such that at near-resonance conditions the higherorder mode exhibits elevated amplitude. This mechanism can explain the observations made by Urbanoet al. (2016) in a small-scale rocket thrust chamber, where a radial mode appears at exactly twice thefrequency of the dominant transverse mode. A simple representative setup of a cylindrical combustionchamber is used to explain this mechanism analytically.