Instability of a premix burner with nonmonotonic pressure drop characteristic

Instabilities in combustion systems 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-flow rate characteristic locally displays a negative slope. In the limit of low frequencies (Helmholtz mode), it is then straightforward to show that ah oscillatory instability can result from such behavior. An analytical stability criterion is derived, relating the nondimensionalized gradient of the pressure drop characteristic to the Helmholtz number of the burner. The physical mechanism of the instability is explained, and it is observed that the Rayleigh criterion need not be satisfied for this kind of instability to occur. In order to extend the stability analysis to higher frequencies, the transfer matrix for a burner with nonmonotonic pressure drop is derived in the limit of low Mach number and negligible fluctuations of the rate of heat release. The transfer matrix is employed in stability analysis based on a linear acoustic model of a combustion system. 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 the model predictions very well.