Swirling flame instability analysis based on the flame describing function methodology

International audienceThermoacoustic instabilities are analyzed by making use of a nonlinear representation of flame dynamics based on the describing function. In this framework, the flame response is determined as a function of frequency and amplitude of perturbations impinging on the combustion region. This methodology is applied to confined swirling flames in a laboratory scale setup (2.5 to 4 kW) comprising an upstream manifold, an injection unit equipped with a swirler (swirl number = 0.55) and a cylindrical flame tube. The flame describing function is experimentally determined and is combined with an acoustic transfer matrix representation of the system to provide growth rates and oscillation frequencies as a function of perturbation amplitude. These data can be used to determine regions of instability, frequency shifts with respect to the acoustic eigenfrequencies and they also yield amplitude levels when self-sustained oscillations of the system have reached a limit cycle. This equilibrium is obtained when the amplitude dependent growth rate equals the damping rate in the system. This requires an independent determination of this last quantity which is here based on measurements of the resonance response curve. Results obtained are compared with observations from systematic experiments carried out by varying the test combustor geometry. The demonstration of the FDF framework in a generic configuration indicates that this can be used in more general situations of technological interest