Mean Flame Shape Effects on the Non-linear Response of Premixed Flames to Helical Flow Disturbances

This work considers a model swirl-stabilized premixed flame responding to helical disturbances in swirling flows. Hydrodynamic instabilities manifest themselves with an axisymmetric mode (m = 0) and/or with helical modes (m ≠ 0) where the mode number m is a signed integer. Prior research considered an axisymmetric framework, showing both the linear and non-linear response of premixed flames to the m = 0 mode. Majority of swirling flows show dominant amplitudes for helical modes. Prior work has shown that the linear response is determined purely by the m = 0 mode for axisymmetric mean flames regardless of their strength compared to helical modes. This work was extended to the non-linear regime to show that one or more helical modes can interact under certain conditions to result in a non-zero flame response. In multi-nozzle can combustor configurations, flame-flame interactions result in asymmetric mean flame shapes. In contrast with axisymmetric flames in the linear regime, when mean flame asymmetries are introduced, helical modes in the flow interact with asymmetric modes in the mean flame shape to result in non-zero flame response. In this study, we extend the framework to show that mean flame asymmetries have a strong impact on non-linear flame response.