Combining analytical models and LES data to determine the transfer function from swirled premixed flames

A methodology is developed where the acoustic response of a swirl stabilized flame is obtained from a reduced set of simulations. Building upon previous analytical flame transfer functions, a parametriza- tion of the flame response is first proposed, based on six independent physical parameters: a Strouhal number, the mean flame angle with respect to the main flow direction, the vortical structures convection speed, a swirl intensity parameter, a time delay between acoustic and vortical perturbations, as well as a phase shift between bulk and local velocity signals. It is then shown how these parameters can be de- duced from steady and unsteady simulations. The methodology is applied to a laboratory scale premixed swirl stabilized flame exhibiting features representative of real aero-engines. In this matter, cold and re- active flow Large Eddy Simulations are first validated by comparing results with reference data from experiments. The high fidelity simulations are seen to be able to capture the flame structure and velocity profiles at different locations while forced flame dynamics for the frequency range of interest also match the experimental data. From the same analytical transfer function model, three methodologies of increas- ing complexity are presented for the determination of the model parameters, depending on the available data or computational resources. A first estimation of the flame acoustic response is obtained by evalu- ating parameters from a single stationary flame simulation in conjunction with analytical estimations for the acoustic-convective time delay. Flame dynamics and swirl related parameters can then be determined from a series of robust treatments on pulsed simulations data to improve the model accuracy. It is shown that good qualitative agreement for the flame transfer function can be obtained from a single non-forced simulation while quantitative agreement over the frequency range of interest can be obtained using ad- ditional reactive or non-reactive pulsed simulations at one single forcing frequency corresponding to a local gain minimum. The method also naturally handles different perturbation levels