Models of the time-averaged heat release rate of the two-dimensional laminar premixed slit flame subjected to the transverse disturbance

A two-dimensional laminar premixed slit flame subjected to the transverse oncoming flow disturbance has been modelled in this work. The time-averaged flame heat release rate is theoretically studied. The time-averaged flame fronts can be assumed to be constant as the oncoming flow disturbance is weak. This assumption is not appropriate as the nonlinear flame dynamics are accounted for in the present work. The G-equation method is applied to capture the flame front dynamic evolutions. The perturbation method is used to conduct the nonlinear dynamics analysis. Analytical solutions of responses of time-averaged heat release rates of the slit flame to transverse perturbations are derived using different velocity perturbation models. Results show that the time-averaged flame fronts can be perturbed by the second order nonlinear term at different forcing frequencies in the perturbation analysis. The time-averaged flame fronts therefore include the unperturbed flame fronts and the perturbed zero order flame fronts. The flame aspect ratio has a significant effect on the transfer function of the time-averaged slit flame front surface area (TFSF). The velocity perturbation model has a significant effect on the TFSF and the TFSF using the uniform model has two states: the expanded state and the contracted state. The transverse bulk mean flow velocity has an important effect on the response of the time-averaged slit flame heat release rate to the transverse disturbance.