Using CFD for Time-Delay Modeling of Premix Flames

This paper presents a refined model of the transfer function of a premix burner, compares the model with experiments, and discusses how the model can be used to map stability characteristics of a combustion system. The model is based on the assumption that acoustic velocity fluctuations cause modulations of fuel concentration at the fuel injector which, after a time delay, result in fluctuating heat release rates at the flame. Here, the time delay is modeled as a multitude of single time delays. The distribution of these time delays can be found either from model fitting to experimental data, or can be obtained directly from numerical simulations of the burner. The effect of distributed time delays is caused by axially distributed fuel injectors, turbulent diffusion, and a non-planar flame shape. As a consequence, heat release fluctuations at higher frequencies cancel, an effect which is also observed experimentally. It is found that the model is generally in good agreement with experiments. It is also demonstrated that the model can be used to map the burner stability charactistics for various operating conditions, e.g. for variations in power and flame temperature. A stability analysis is performed by incorporating the flame model into a combustor network model.