This paper describes the response of a swirling premixed flame with constant burning velocity to non-axisymmetric harmonic excitation. This work extends prior studies of axisymmetric forcing, which have shown that wrinkles are excited on the flame that propagate downstream along the mean flame surface at a speed given by U(o)cos psi, where U-o is the mean flow velocity and psi is the flame angle. The swirl component in the flow field introduces an azimuthal transport mechanism for disturbances on the flame. As such, the flame response at any given position is a superposition of flame wrinkles excited at earlier times, upstream axial locations, and different azimuthal positions. These swirl transport effects do not arise in problems where axisymmetric flames are subjected to axisymmetric excitation, but enter quite prominently in the presence of non-axisymmetries, such as when the flame is subjected to transverse excitation. The solution characteristics are strongly dependent upon the ratio of angular rotation rate to excitation frequency, denoted by sigma = Omega/omega, which describes the fraction of azimuthal rotation a disturbance makes in one acoustic period. When sigma << 1 and sigma >> 1, the axial wavelength of flame wrinkles scales with the convective wavelength, lambda(o) but becomes much longer for sigma similar to O(1). The spatial variation in phase of flame wrinkling is also strongly dependent upon sigma. Regardless of swirl number, flame wrinkles propagate in helical spirals along the solution characteristics at a phase speed equal to the local tangential velocity. The axial phase characteristics of flame wrinkling at a fixed azimuthal location, as would be measured by laser sheet imaging, are much more complex. For sigma < 1, the wrinkles exhibit the familiar negative roll-off character for the phase with axial downstream distance, indicative of an axially convecting disturbance. The slope of this phase roll-off decreases with increasing sigma, however, and becomes zero at sigma = 1 for a compact flame. For sigma > 1, the wrinkles actually have a positive roll-off character for the phase with axial downstream distance, indicating a flame wrinkle with a negative trace velocity, but whose actual propagation velocity is positive. Finally, these results show that while the flame response to transverse acoustic excitation is quite strong locally, its spatially integrated effect is much smaller for acoustically compact flames. This suggests that the dominant mechanism through which the flame responds globally to transverse excitation is the induced vortical and longitudinal acoustic fluctuations. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
