Simulation of the flame describing function of a turbulent premixed flame using an open-source LES solver

Numerical simulations were used to characterise the non-linear response of a turbulent premixed flame to acoustic velocity fluctuations. The test flame simulated was the bluff body stabilised flame which has been the subject of a detailed experimental study (Balachandran et al., 2005). Simulations were performed using Large Eddy Simulation (LES) via the open source Computational Fluid Dynamics (CFD) software, Code_Saturne, with combustion modelled by combining a Flame Surface Density (FSD) method with a fractal approach for the wrinkling factor. The cold flow field and the unforced reacting flow were used for preliminary code validation. In order to characterise the non-linear response of the unsteady heat release rate to acoustic forcing, a harmonically varying velocity fluctuation, for which both the forcing frequency and normalised forcing amplitude were varied, was imposed. The flame response was characterised via a Flame Describing Function (FDF), also known as a non-linear flame transfer function, for which the gain and phase shift depend on forcing amplitude as well as forcing frequency. The response at four frequencies was compared to experimental data in detail, confirming that the LES results captured both the qualitative flame dynamics and the quantitative response of the heat release rate with very reasonable accuracy. The full FDF was then obtained across more frequencies, again showing a good fit with the experimental data, other than for a slight under-prediction in gain, most probably due to neglecting the effect of wall heat loss and the effect of combustion modelling. The agreement was significantly better than has been obtained previously for this test case using numerical simulations. Finally, it was found that increasing combustor length had little affect on the flame response, which may prove useful for future long combustor stability and limit cycle analysis. This work thus confirms that LES, in this case via the open source Code_Saturne, provides a useful tool for characterising the response of lean premixed turbulent flames.