Combustion instability is known to be a result of interaction between pressure fluctuations and unsteady heat release. Many processes in the combustion chamber lead to unsteady heat release. Among them are fluctuations in equivalence ratio, periodic shedding of vortices from the flame holders, inherent instability of the flames, pressure fluctuations themselves affecting the burning process, etc. The instability is observed if the Rayleigh criterion is met. Since, during instability, the pressure undergoes sinusoidal variation in time (with multiple dominant frequencies), it is useful to study the effect of such pressure oscillations on the burning process i.e., the flame, and to see if the Rayleigh criterion is met. Most researchers have performed frequency response analysis on premixed flames and some have on non-premixed flames, both theoretically (linear framework) and experimentally. In this seminar, we present a numerical study of "partially premixed flames" (PPFs) and their responses to sinusoidal modulation of the flow.

A rectangular coflow burner with fuel inlet at the center is considered for the analysis. A cold flow through the burner sets up different profiles of equivalence ratio, characterized by the premixedness value (0-1), along the length of the burner. With these profiles as the inlet conditions to the burner, flames with varying premixedness can be observed. The response of the flames is then obtained by subjecting them to the flow modulation and performing a Fourier transform on the net heat release signal. The numerical analysis was performed using a sixth order accurate compact scheme for spatial discretization and fourth order accurate Runge-Kutta scheme for integration in time. In the results, we observe a low-pass filter like response of the flames with low premixedness, consistent with the literature. But as the premixedness is increased, a resonance like response is seen. An attempt is made to analytically extract the value of natural frequency and to explain the existence of it.