Nonlinear response of conical flame to dual-frequency excitation

This work investigates the nonlinear response of a conical premixed flame to dual-frequency excitation through experiments and G-equation analysis. In addition to the responses at excitation frequencies, f1 and f2, a notable flame response can also be identified at the difference frequency, fd. The fd response is particularly significant in the high-frequency regime, characterized by multiple wavelengths of both f1 and f2 on the flame front. This distinct behavior of difference-frequency response can be attributed to the spatial superposition of the intensified flame fluctuation waves at the two forcing frequencies. As the excitation enhances at either f1 or f2, the nonlinear effect suppresses the responses of the upper-part flame at both f1 and f2 while promoting the bulk flame response at fd. Based on a third-order expansion of the G-equation, it is shown that the nonlinear flame dynamics necessarily generate the observed interaction component when the flame is perturbed by dual-frequency excitations. The present results emphasize the importance of nonlinear flame dynamics in inducing flame responses at interaction frequencies, offering insights into thermoacoustic oscillations of multiple frequencies.