Bifurcation analysis of combustion instability in a Rijke burner with an improved third-order saturated flame model

The bifurcation analysis of nonlinear combustion instability in a Rijke burner is studied numerically. First, a saturated flame model and a third-order saturated flame model are proposed, and the mode truncation effects are investigated by studying their influences on system eigenvalues. Then, bifurcation analysis on the flame location, average flame intensity, damping, and time delay in the flame model is conducted with the new flame models. Results show that the burner driven by the saturated model loses stability via supercritical Hopf bifurcations, whereas the system driven by the third-order saturated model shows the characteristic of subcritical Hopf bifurcations, accompanied by bistable regimes emerging in the bifurcation diagrams. Finally, the effects of velocity perturbations are analyzed further, and the results show that a given system may oscillates with different frequencies if the disturbance is imposed to different Galerkin modes. This study reveals that the process of the combustion system's transition to instability depends strongly on the nonlinear term in the flame model.