Task 3.2 Nonlinear coupling of thermoacoustic modes modelled by a Green's function approach
This task will build on the work by Heckl (2013) who has applied a Green's function approach to Lighthill's acoustic analogy equation and derived a simple governing differential equation for a single thermoacoustic mode. The approach will be extended to several modes of a prototype thermoacoustic system. It is expected that the governing equation for each mode is a damped oscillator equation with a forcing term (due to the dependence of the heat release on the acoustic field), and that the oscillator equations are nonlinearly coupled by the forcing terms. Once the governing equations have been established, they will be analysed with a combination of methods from nonlinear dynamics. Parameter studies will be conducted to explore where bifurcations occur, and to identify the parameter regimes that favour a predominant mode.