Characterizing premixed laminar flame–acoustics nonlinear interaction

• Premixed flame–acoustics interaction is studied.
• Premixed flame is found to respond strongly to lower-frequency perturbations.
• Higher-frequency flow disturbances pass through the flame smoothly.
• Linear and nonlinear transfer functions are determined.
• Hammerstein–Wiener model can provide a better agreement.

Self-excited thermoacoustic oscillations, also known as combustion instability is generated by the coupling between unsteady combustion and acoustic perturbations. If such combustion instability occurs, then pressure fluctuations may become so intense that they can cause overheating and/or engine structural damage. Thus it is necessary to understand the dynamic coupling physics between acoustic perturbations and unsteady combustion, and to identify a measure to characterize the interaction between a heat source and oncoming acoustic perturbations. The present work investigates linear and nonlinear responses of a conical premixed laminar flame to oncoming acoustic disturbances. Unsteady heat release from the premixed flame is assumed to be caused by its surface area variation. And the area variation results from the fluctuations of the oncoming acoustic flow velocity. In order to track the flame front variation in real-time, the classical G-equation is applied. Second-order finite difference (FD) method is then used to expand the dynamic flame model. Time evolution of the flame surface under the periodic acoustics forcing is successfully captured. Finally, system identification is then conducted to estimate the linear and nonlinear flame transfer function to quantify the dynamic response of the flame to oncoming acoustic disturbances. Good agreement is obtained.