A nonlinearly kinematic model of the asymmetrically turbulent premixed slit flame subjected to two-way harmonic disturbances

Transversal and longitudinal combustion instabilities typically occur in gas turbines and rocket engines. Quantifying the nonlinear flame dynamic response of turbulent premixed flames subjected to the two-way disturbances and mean bulk flows is significant to understand the complex nonlinear combustion instability phenomena. A Two-way Nonlinear Unforced Flame Speed Modeling (2W-NUFSM) approach was proposed in this study. The turbulent effects were accounted for in the flame propagation speed term and the steady flame term in the kinematic equation of the flame front; an expansion method was then used to obtain the nonlinear solutions corresponding to the transverse and longitudinal acoustic disturbances. The turbulent effect on the flame consumption speed was also considered in the heat release rate calculation of the perturbed flame. Validations of this approach were conducted by comparing its results to the former credible results obtained from other methods and good agreements were obtained. The influence of turbulent effects on the flame dynamic response in an asymmetrical premixed flame was investigated in detail. The coupling effect of the turbulence and harmonic flow disturbances on the flame nonlinear dynamic response was also quantified.