Three-dimensional nonlinear thermoacoustic instability analysis based on Green's function approach

In this work, nonlinear thermoacoustic instability analysis is made in a hard-walled box to investigate the limit cycle of thermoacoustic oscillation and the interplay of two modes. We model the flame as an acoustically compact source described by a generic Flame Describing Function, i.e. an amplitude-dependent Flame Transfer Function. The acoustic field in the hard-wall box could be described by an integral equation using a Green's function tailored to a three-dimensional (3-D) rectangular box with hard-wall boundary conditions. The integral equation is solved by two methods. Firstly, an iteration method, stepping forward in time, is used to give the time history of the acoustic velocity. The other method is done in the frequency domain to determine the thermoacoustic eigenfrequency and growth rate of thermoacoustic modes. We could observe the phenomenon of modes "jump" after two different time windows of the time history operated with the Fourier transformation. This result reveals that there are two modes in the system, the interference between modes will occur. In the early stage, the two modes work together. After reaching the limit cycle oscillation, the role of one mode is dominant and the other mode basically disappears.