This article investigates passive stabilization of thermoacoustic dynamics in a Rijke tube by using a Helmholtz resonator. Under certain assumptions, the mathematical model of the dynamics is shown to fall into the linear time-invariant multiple time delay systems class of neutral type. To study the thermoacoustic instability phenomenon and its passive suppression, the cluster treatment of characteristic roots (CTCR) paradigm is implemented. This effort reveals the placement of Helmholtz resonator along the Rijke tube for stabilizing the unstable dynamics. The analytically obtained results are compared with experiments conducted on a laboratory scale Rijke tube. In addition, the effect of resonator’s design parameters on its stabilization capability is investigated.
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