Thermoacoustic modal instability and its suppression with locally resonant flexible membranes

Thermoacoustic oscillation and instability are a common occurrence in many industrial problems. Investigations on the interplay among different types of modes, their evolution process and coupling with add-on control devices are of vital importance to guide the development of proper control strategies. Using a linear heat release n-τ model inside a duct, these issues are investigated in this paper based on a fully coupled energy-based model. Studies allow the classification and quantification of different types of eigen-modes, as well as their stability and controllability features. Using flush-mounted flexible membranes over the duct wall, possible suppressions of unstable modes and the underlying control mechanisms are revealed with particular focus on cases involving small time delay and interaction indices. Numerical analyses show that thermoacoustic instability of the system can be controlled via creating strong vibro-acoustic coupling, via two different physical processes for acoustic and intrinsic modes. For the former, the acoustic modal pressure distribution should be positively altered in the vicinity of the heat source to create a favorable pressure state scenario, in agreement with Rayleigh criterion. For the latter, control is achieved indirectly through a proper alteration of the nearby acoustic modes, thus affecting their coupling with the targeted intrinsic mode. In both cases, a successful suppression of the thermoacoustic modal instability can be materialized through a proper adjustment of the physical parameters of the membranes and their installation locations.