Time Periodic Solution of Thermo-Acoustic System

It is well known that some nonlinear phenomena in thermo-acoustic system can't be explained by using linear thermo-acoustic theory. The purpose of this paper is to obtain the nonlinear solution of the thermo-acoustic system. The nonlinear time periodic solution of a thermo-acoustic system was found by using Gaierkin' low spectrum mode and solving the ordinary differential equations, in this paper. A technique called phase space analysis was employed to depict the evolutionary characteristics of a thermo-acoustic system in phase plane, and the phase space analysis method is a powerful tool in the investigation of open systems. These phase diagrams of the pressure signals and the temperature signals were plotted in phase planes by means of reconstructing pressure and temperature trails. The results show that the stable solution for a thermo-acoustic system is a stable nonlinear periodic oscillation with a limit cycle. The results obtained herein may be useful for understanding the mechanism of thermo-acoustic effect.