A nonlinear frequency domain model for limit cycles in thermoacoustic systems with modal coupling

For prediction of limit cycle oscillations of linearly unstable thermo-acoustic systems, a frequency-domain, low-order system with explicit modal coupling is developed. To this purpose, a model for the nonlinear heat source dynamics is obtained from unsteady computational fluid dynamics in combination with feed-forward neural network identification. From the neural network, an equivalent representation for the input-output relation in Volterra series form is derived, where Volterra kernels are computed in terms of the weights of the neural network. Then the kernels are transformed into the frequency domain to obtain the higher order transfer functions, through which the modes are coupled. In this way nonlinear energy exchange among the modes can be described explicitly. Comparison with a Galerkin time domain simulation shows that deviations from purely sinusoidal behaviour in the limit cycle are captured correctly, while the computational cost is drastically reduced.