Linear Response of Laminar Premixed Flames to Flow Oscillations: Unsteady Stretch Effects

This paper describes the linear response of a laminar premixed flame to harmonic velocity disturbances. It generalizes previous studies by considering the influence of unsteady stretch effects, manifested as variations in the local burning velocity along the wrinkled flame front. Results are derived from analytical solutions of the G equation and used to interpret the relative impact of unsteady curvature and hydrodynamic strain. It is shown that the overall linear flame response depends upon two Strouhal numbers, St(2) and St(c), related to the amount of time taken for a flow (St(c)) and flame front (St(2)) disturbance to propagate the flame length, normalized by the acoustic period. Stretch effects are shown to be characterized by two frequency-dependent Markstein numbers, sigma(c)* and sigma(s)*, for curvature and hydrodynamic strain, respectively. Unsteady curvature effects on the flame surface area become significant when vertical bar sigma(c)*vertical bar St(2)(2) similar to O(1) and are responsible for the experimentally observed reduction in the flame front wrinkle size in the flow direction [referred to as filtering by Bourehla and Baillot (Bourehla, A., and Baillot, F., Appearance and Stability of a Laminar Conical Premixed Flame Subjected to an Acoustic Perturbation, Combustion and Flame, Vol. 1143-4,1998, pp. 303-318.doi:10.1016/S0010-2180(97)00323-4)].