Analytical Models for Time-Averaged Slit Flame Dynamics with Axial and Transverse Disturbances

The paper investigates two-dimensional slit flame front dynamics subjected to transverse and axial perturbations simultaneously, addressing the practical importance of azimuthal and longitudinal thermoacoustic oscillations occurring in annular combustion chambers. Specifically, responses of time-averaged flame fronts to two-way perturbations are theoretically investigated and analyzed using different disturbance propagation velocity models. Analytical solutions of time-averaged flame fronts with two-way flow disturbances are derived using the [Formula: see text]-equation model and perturbation method, which incorporate undisturbed steady properties and disturbed zero-frequency properties. Time-averaged properties of flame configurations cannot be assumed as undisturbed steady properties, acknowledging the nonlinear nature of flame dynamics. The physical mechanisms of competing and coupling behaviors between transverse disturbance and axial disturbance have been investigated. Results highlight the substantial impact of the transverse-to-axial disturbance ratio on time-averaged flame fronts and heat release rates. Time-averaged flame heat release rate can be enhanced as the slit flame becomes longer, indicating that flame aspect ratio plays a pivotal role in shaping time-averaged flame front dynamics. Moreover, the disturbance propagation velocity model becomes a critical factor affecting time-averaged flame heat release rates, which will be enhanced with increasing transverse mean flow velocity.