Premixed Flames Excited by Helical Disturbances: Flame Wrinkling and Heat Release Oscillations

This paper describes an analysis of the response of swirling premixed flames to helical disturbances, i.e., where the flow fluctuations have an azimuthal dependence of the form (u) over cap (')(i)infinity exp(im theta) and m denotes the helical mode number. Results elaborate the nature of local flame wrinkling and heat release fluctuations. Significantly, these results show that these different induced fluctuations exhibit very different sensitivities to helical mode number m, swirl strength, and dimensionless frequency. In addition, the degree of axisymmetry of the time averaged flame plays a crucial role in these interactions, particularly in how flow disturbances (u) over cap (')(i) translate into heat release oscillations. Thus, the helical modem, with the dominant contribution to local flame wrinkling and heat release, m = m(0), and spatially integrated heat release fluctuations, m = m(1), is generally different. For example, helical mode m, leading to the largest amplitude of local flame wrinkling and heat release in a solid body swirl flowfield, is given by m(0)sigma = U-t,U-f/U-c - 1, where sigma is the ratio of swirl angular rotation rate to forcing frequency,U-t,U-f is the component of mean tangential velocity resolved along the axial forcing direction, and U-c is the phase speed of the convecting vortex. In contrast, only the axisymmetric mode, m(1) = 0, leads to global surface area fluctuations in axisymmetric flames, which are also completely insensitive to swirl number. Because the maximum amplitude of local flame wrinkling is, in general, excited by helical modes with m not equal 0, care must be taken in interpreting the significance of large scale helical flame flapping, as often is captured from planar experimental data or visualized in computations.