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, $f_1$ and $f_2$, a notable flame response can also be identified at the difference frequency, $f_d$. The $f_d$ response is particularly significant in the high-frequency regime, characterized by multiple wavelengths of both $f_1$ and $f_2$ 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 $f_1$ or $f_2$, the nonlinear effect suppresses the responses of the upper-part flame at both $f_1$ and $f_2$ while promoting the bulk flame response at $f_d$. 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.