Novel frequency-domain Dixon approach for analyzing the stability range of the Rijke tube

This study addresses the crucial issue of thermoacoustic instability, an undesirable phenomenon that severely impacts combustion chambers. The mathematical dynamic model of the Rijke tube has been reassessed as a linear time-invariant multi-time-delay system (LTI-MTDS). To analyze its stability characteristics, a precise approximation of the quasi-polynomial was performed. Subsequently, a new theoretical framework based on the Dixon discriminant method was established to derive the critical frequency range. The curves that represent the stability transition points are clearly depicted through comprehensive frequency scanning. This method reveals important information about the stable operating regions of the tube within the parameter space, including delays and geometric dimensions.