Nonlinear Self-excited Thermoacoustic Oscillations of a Ducted Premixed Flame: Bifurcations and Routes to Chaos

We study the bifurcations of a ducted two-dimensional premixed flame using numerical simulations of the coupled dynamical system. When the flame position in the duct is changed the system undergoes transition to period-1, quasi-periodic, period-2, frequencylocked and chaotic oscillations via different bifurcations. For certain parameter ranges multiple stable solutions exist and the ultimate state reached depends on the initial conditions. Hence there is hysteresis and mode switching is possible. Often the system traverses through intermediate states before reaching its final stable state. Two routes to chaos are established for this system: the period-doubling route and the Ruelle-Takens-Newhouse route. Flame images show that the flame wrinkles have multiple time and length scales, which reflect the nonlinear behaviour seen in the time series. This study complements recent experiments by providing a reduced order model with approximately 5000 degrees of freedom that captures much of the complex nonlinear dynamics observed in the laboratory.