Transverse mean flows and transverse acoustic perturbations are factors that may influence the flame response, and thus change the frequency, growth rate and mode nature (standing, spinning or mixed) of the azimuthal thermoacoustic modes in annular combustors. Previous analytical and low-order network models for annular combustors usually consider only axial flame response. This work identifies the linear response of an asymmetric planar Bunsen flame under simultaneous axial and transverse perturbations. A linearized analytical method for studying the response of an inclined flame under perturbations using G-equation is applied. The relation between the flame responses under a 2-D perturbation and separate axial/transverse perturbations is studied to identify a linear 2-D flame response superposition, with the response under simultaneous perturbations being equal to the sum of two responses under each single perturbation. The effect of this linear 2-D flame response on the azimuthal thermoacoustic modes is then investigated by incorporating it into a linear low-order network methodology [19]. An annular combustor both with and without mixing burners and transverse mean flows is studied. The results are verified by comparing with FEM (Helmholtz solver) simulations. It is found that even though the transverse flame response is usually much smaller than the axial flame response, it may strongly affect the spin ratio of the azimuthal thermoacoustic modes. The asymmetries (e.g. due to burner difference) in both the transverse and axial flame response, and the effect of transverse mean flow on the acoustic propagation may all significantly change the spin ratio of the azimuthal modes, and thus need to be considered simultaneously.

横向平均流量和横向声扰动是可能影响火焰响应，从而改变环形燃烧器中方位热声模的频率，增长率和模态性质（直立，旋转或混合）的因素。先前用于环形燃烧器的分析和低阶网络模型通常仅考虑轴向火焰响应。这项工作确定了不对称平面本生火焰在同时的轴向和横向扰动下的线性响应。用G研究扰动下倾斜火焰响应的线性分析方法。-等式被应用。研究了二维扰动下火焰响应与单独的轴向/横向扰动之间的关系，以确定线性二维火焰响应叠加，同时摄动下的响应等于每个摄动下两个响应的总和。然后，通过将线性二维火焰响应并入线性低阶网络方法中，研究该线性二维火焰响应对方位角热声模式的影响[19]。研究了带有和不带有混合燃烧器和横向平均流量的环形燃烧器。通过与FEM（Helmholtz求解器）仿真进行比较来验证结果。发现即使横向火焰响应通常比轴向火焰响应小得多，它也可能强烈影响方位角热声模的自旋比。横向和轴向火焰响应中的不对称性（例如，由于燃烧器的不同）以及横向平均流量对火焰响应的影响声传播都可能显着改变方位模的自旋比，因此需要同时考虑。