Thermoacoustic Instabilities arising from secondary modes, an analytical and experimental declaration

Abstract

It is well known that the secondary dynamic modes of thermoacoustic systems come to prominence during the modal stabilization attempts. To this date; however, there has been no exhaustive analytical explanation given for this interesting phenomenon. In this work we examine a Rijke tube with a passive Helmholtz resonator and perform an active feedback control to suppress instabilities. The core dynamics is represented by a linear time-invariant multiple time delay system of neutral type. Non-conservative stability of this infinite-dimensional dynamics is investigated using a recent analytical tool: cluster treatment of characteristic roots (CTCR) paradigm. First, we examine the parametric stability outlook with the Helmholtz resonator using a holistic approach in contrast to conventional modal studies. We then select an unstable operating point and impose a time-delayed integral feedback control over this structure and inquire the stabilizing controller parameters using the CTCR methodology. This procedure also declares the potential unexpected instabilities caused by the secondary modes. Analytical work is presented with validations using an experimental Rijke tube set-up.