Comparison and extension of methods for acoustic identification of burners

The prediction and the control of combustion instabilities require the identification of the combustion chamber response. This identification is usually performed by forcing the combustor (for example, modulating its inlet velocity) and measuring its response. Two methods may be found in the literature to analyze this response: identification of transfer matrices (ITM) and flame transfer functions (FTF). In ITM approaches, the burner is considered as a “black box” and a two-port formulation (based on acoustic pressure and velocity perturbations) is used to construct a transfer matrix linking acoustic fluctuations on both sides of the burner. A drawback of this method is that in experiments, the measurement of unsteady pressure and velocity in burnt gases can be difficult. In FTF approaches, pressure measurements are replaced by a global heat release measurement (usually based on optical methods). The heat release fluctuations are then related to the flow velocity modulations at a reference point (usually the combustor inlet) through a transfer function. This paper uses a compressible numerical simulation of a forced laminar Bunsen flame to analyze FTF and ITM methods. Results show that FTF approaches lead to an ill-defined problem as soon as the reference point is not close enough to the chamber. This “compactness” limit is quantified here in terms of distance between the reference point and the local chamber. The source of the problem is that FTF approaches correlate heat release fluctuations to velocity oscillations only: extended FTF models are then proposed using the local unsteady pressure as well as the velocity upstream of the flame to predict the heat release oscillations. These models are tested numerically and provide consistent values when the reference point location changes or when upstream and downstream conditions are varied. These results lead to simple recommendations for system identification.