Instability of a premix burner with non-monotonic pressure drop characteristic

Thermo-acoustic combustion instabilities have frequently been reported to occur when slight changes in operating conditions lead to significant and abrupt changes in flame shape or flame position, i.e. changes in the mode of flame stabilization. The present paper offers an explanation and mathematical model of this observation. The analysis rests on the assumption that changes in the mode of flame stabilization are accompanied by a significant variation of the pressure drop across burner and flame, such that the pressure drop-flowrate characteristic locally displays a negative slope. In the limit of lowfrequencies (Helmholtz mode), it is then straightforward to show that an oscillatory instability can result from such behavior. A stability criterion is derived, relating the non-dimensionalized gradient of the pressure drop characteristic to the Helmholtz number of the burner. The physics of the instability mechanism is explained, and it is observed that the Rayleigh criterion need not be satisfied for this kind of instability to occur. The analysis is then extended to higher frequencies and the transfer matrix for a burner with non-monotonic pressure drop is derived in the limit of low Mach number and negligible fluctuations of the rate of heat release. Experimental results obtained with an externally premixed swirl burner are presented. The pressure drop characteristic, the observed onset of instability and the instability frequency match very well the analytical predictions.