Impact of heat release global fluctuations and flame motion on transverse acoustic wave stability

The interaction between transverse acoustic modes and flames in a combustion chamber is investigated by considering the impact of two different mechanisms on the stability of the system. The first mechanism is generally taken into account in the acoustic energy balance of the system. It relates to the temporal fluctuations of heat release rate mainly due to the geometrical modifications of the flame structure (creation and destruction of flame surface). The method used to predict the system stability is well established and has been successfully applied in many studies. It involves an acoustic solver and a Flame Transfer (or Describing) Function (FTF/FDF) obtained experimentally or numerically by longitudinal excitation of the flame. The coupling of these two elements yields complex eigenfrequencies giving access to the stability of the system. The second mechanism, overlooked in most studies, deals with the transverse motion of the flame particularly when located near a velocity anti-node. A model (E-FAME) is developed in this article to take into account this effect. The method is mainly analytical and does not necessitate numerical or experimental data. It can be implemented easily for simple or more complex configurations. The two mechanisms are implemented in the same simple case to allow comparison. It is shown that the flame motion effect is moderate in many configurations but should not be overlooked especially when the Helmholtz number of the combustion chamber is small or when the global heat release rate is high.