An adjoint Green’s function approach for thermoacoustic instabilities in a duct with mean flow

• DOI: 10.1016/j.jsv.2024.118673
• Publication Date: 2024-08-11T21:38:25Z
• Authors: Jiasen Wei; Sadaf Arabi; Jan O. Pralits; Alessandro Bottaro; Maria A. Heckl
• Keywords: Thermoacoustics; Thermoacoustic heat engine; Mean flow

Thermoacoustic instabilities arise from the feedback between an acoustic field and unsteady heat released in a burner, yielding self-sustained oscillations. A fundamental framework for modelling thermoacoustic systems where mean flow is present introduced, based on definition of adjoint Green's function which permits to convert analogy equation into integral equation. The problem produces sensitivity functions quantify response system initial, boundary or other forcing terms. simple one-dimensional examined; it includes steady uniform nonlinear source with amplitude-dependent time-delay release model. versatility approach demonstrated by applying two resonators characterized different conditions: Rijke tube quarter-wave resonator. control parameters are: position, heater power length. results reveal that proposed analytical successfully captures limit cycles, triggering phenomena, hystereses, Hopf bifurcations observed experiments. We show velocity cannot be discarded study such systems; increasing it, stabilization generally ensues, modification bistability characteristics system.