Flame transfer functions of asymmetric conical and V-shaped flames

Transfer functions of asymmetric flames subjected to incident flow perturbations are explored using the classical kinematic model, the G-equation, parameterized by flame tip angle alpha, flame-base incline angle beta, and eccentricity e. With perturbations of various frequencies, we analyze perturbed asymmetric flames and derive analytical formulations of Flame Transfer Functions (FTF) for various flame conditions. It is observed that the gain of the asymmetric conical flame is increased compared to the symmetric case. Meanwhile, the amplification effect of the V-shaped flame is considerably suppressed as the flame becomes asymmetric. That means with a proper asymmetric geometry setting, the V-shaped flame no longer tends to amplify the perturbation and in other words becomes less susceptible to combustion instability. These findings have significant value for the future design and optimization of propulsion systems, where improving flame stability and reducing thermoacoustic instabilities are critical. Subsequently, a numerical study is conducted to verify the FTF results and examine the response of asymmetric flames under various perturbation levels. It has been demonstrated that the asymmetric conical flame is minimally affected by the amplitude of these perturbations, and the asymmetric V-shaped flame is highly sensitive to the convective amplitudes.