Eigenmode Analysis of the Thermoacoustic Combustion Instabilities Using a Hybrid Technique Based on the Finite Element Method and the Transfer Matrix Method

Thermoacoustic combustion instabilities affect modern gas turbines equipped with lean premixed dry low emission combustion systems. In the case of annular combustion chambers, experimental test cases carried out on small scale test rigs equipped with single burner arrangements fail to give adequate indications for the design of the full scale combustion chamber, since they are unable to reproduce the interaction of the flame fluctuation with the azimuthal pressure waves. Therefore there is a large interest in developing techniques able to make use of data gathered from tests carried out on a single burner for predicting the thermoacoustic behavior of the combustion chamber at full scale with its actual geometry. A hybrid technique based on the use of the finite elements method and the transfer matrix method is used to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability, under the hypothesis of linear behavior of the acoustic waves. This approach is able to model complex geometries such as annular combustion chambers equipped with several burners. Heat release fluctuations are modeled through a classical n-τ Flame Transfer Function (FTF). In order to model the acoustic behavior of the burners, the computational domain corresponding to each burner is substituted by a mathematical function, that is the Burner Transfer Matrix (BTM), that relates, one to each other, pressure and velocity oscillations at either sides of the burner. Both the FTF and the BTM can be obtained from experimental tests or from CFD simulations. The use of the transfer matrix permits us to take into account parameters, such as the flow velocity and the viscous losses, which are not directly included in the model. This paper describes the introduction of the burner transfer matrix in the combustion chamber model. Different geometries of combustion chamber and burner are tested. The influence of the parameters characterizing the transfer matrix is investigated. Finally the application of the BTM to an actual annular combustion chamber is shown.