Bifurcation measurement and analysis of a nonlinear Rijke-type thermoacoustic system

Thermoacoustic systems are typically nonlinear, which are characterized by limit cycle pressure oscillations. In present work, we conduct bifurcation analysis to a nonlinear thermoacoustic system by using the method of multiple scales to gain insight on the system's asymptotic behaviors. Both theoretical and experimental studies are performed. To de- scribe/characterize the unsteady heat release from an acoustically compact heat source in the system, two different models are proposed to approximate experimental measurements. Model A is formulated with 3rd order polynomial equation, while model B is 5th order one. Comparison is made between the results obtained from these two models. Model A is shown to be associated with supercritical Hopf bifurcation. However, subcritical Hopf bifurcation occurs in the higher-order nonlinear thermoacoustic system, i.e. model B. Furthermore, hysteresis and bistable zones are observed. In addition, the effects of 1) the heating power K, 2) the axial location of the heat source x_f/L and 3) the overall acoustic damping/loss ξ on supercritical and subcritical bifurcation are studied one at a time. To validate our theoretical findings on supercritical and subcritical bifurcation, experimental investigation on a Rijke tube is conducted. Both super- and subcritical bifurcation are experimentally observed, as the fuel flow rate m_f or the flame axial location x_f/L is varied. The experimental measurements are more consistent with the prediction from Model B. This confirms that it is more accurate to predict subcritical bifurcation behaviors by modelling the thermoacoustic system with a higher order nonlinear model.