The effect of dichromatic forcing on the linear and nonlinear response of premixed flames

This paper investigates dichromatic (two-frequency) forcing to retrieve flame describing functions (FDFs) from measurements, where the effects of frequency separation and forcing amplitude are investigated systematically. At low forcing amplitudes, both standard monochromatic and dichromatic methods produce similar results in terms of gain and phase. However, significant differences appear when the forcing amplitude is increased, and dichromatic forcing tends to produce lower gains and a shift in the phase, indicative of nonlinear saturation. Saturation effects were associated with the redistribution of heat release rate (HRR) fluctuations from the forcing frequencies into combinational harmonics. Moreover, the amplitude at these combinational harmonics is shown to increase exponentially with the forcing frequency, and as the FDFs gain saturate, a cross-over frequency was defined at which the combinational harmonics begin to dominate the global response. The effect of forcing amplitude is shown to reduce this cross-over frequency, whereas a similar but significantly less prominent trend is found for varying frequency separation at fixed amplitude. Although the global response appears dominated by the combinational harmonics at lower frequencies, image analysis shows that significant energy appears at the two forcing frequencies. However, the energy in the global HRR oscillations is significantly reduced at the forcing frequencies due to phase cancellation, and the HRR mode at the frequency difference is shown to follow the modulation envelope of the acoustic velocity. These results highlight the importance of nonlinear interactions in the measurement of FDF, especially in the case of broadband (more than one) frequency forcing. It also highlights that global measurements may miss high-frequency modes, due to global phase cancellation.