Hydrodynamic instabilities and acoustic velocity fluctuations form an integral component of the velocity coupling mechanism of the combustion instability process. This paper extends a prior study on the response of flames to non-axisy mmetric disturbances. There are at least two important sources of non-axisymmetry in transversely excited flames. First, transverse acoustic fluctuations are intrinsically non-axisymmetric. Second, non-axisymmetric helical modes are dominant downstream of the potential core in non-swirling jets and are often dominant in swirling jets. 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'_i ∞ exp(imθ) and m denotes the helical mode number. Results are derived for local flame wrinkling and heat release fluctuations, showing that they 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'_i, translate into heat release oscillations. Thus, the helical mode, m, with the dominant contribution to local flame wrinkling, m=m_0, and spatially integrated heat release fluctuations, m=m_1, is generally different.For example, the helical mode, m, leading to the largest amplitude of local flame wrinkling and heat release in a solid body swirl flow field is given by m_0σ= U_(t,f)/ U_c - 1, where σ is the ratio of swirl angular rotation rate to forcing frequency,U_(t,f) is the component of mean tangential velocity along the forcing direction and U_c is the phase speed of the convecting vortex. In contrast, only the axisymmetric m=m_1=0 mode leads to global surface area fluctuations in axisymmetric flames, which are also completely insensitive to swirl number. Since the maximum amplitude of local flame wrinkling is, in general, excited by helical modes with m≠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.
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