Rijke Tube Thermoacoustic Instability Nonlinear Dynamics Study|Bifurcation Analysis

The thermoacoustic model of a horizontal Rijke tube is established. The governing equations are expanded and solved by using the Galerkin method. The convergence order of Galerkin modes is determined as 10. The bifurcation analysis of the system is carried out by using nonlinear dynamics theory. The bifurcation behaviors of the horizontal Rijke tube thermoacoustic system is found to be subcritical Hopf bifurcation. The system stability regions are divided into globally stable region, globally unstable region and bistable region. The bifurcation diagrams of the non-dimensional heater power (K), the position of the heater (x_f), the damping coefficient (c₁) and the time delay (τ) are obtained, and the bifurcation diagram of the position of the heater (x_f) has two Hopf bifurcation points. In linear unstable region, the amplitude of the oscillation firstly increases and then decreases with the increase of time lag (τ).