Premixed flame response to helical disturbances: Mean flame non-axisymmetry effects

A key component of the thermoacoustic instability feedback mechanism is the excitation of hydrodynamic flow disturbances by narrowband acoustic fluctuations. In earlier work, we considered the response of time-averaged axisymmetric flames to helical disturbances. That study showed that although all helical modes cause local flame wrinkling, only the axisymmetric hydrodynamic mode, m = 0, contributes to the global heat release rate fluctuations. This paper extends this work to consider time-averaged flames that are non-axisymmetric. We show that distortions of the unforced flame shape changes its receptivity to helical disturbances, as it does not allow for the perfect destructive interference seen in axisymmetric flames. This results in a non-zero global flame response contribution from helical modes. Given that helical modes often have the largest amplitudes in jet flows, particularly those with swirl, these results show that the degree of non-axisymmetry of the flame has an important influence in determining which hydrodynamic modes, axisymmetric or helical, control the global heat release response of the flame. These points have been illustrated with example calculations that show how different control parameters and the degree of time-averaged non-axisymmetry influence the global flame response. An important implication of these results relates to scaling results from simplified geometries where a round jet is placed inside a round enclosure, to more realistic ones (such as where multiple jets are placed next to each other) where the flame shape will be distorted from being perfectly circular.