Measurement of transfer matrices and source terms of premixed flames

An experimental method to determine the thermoacoustic properties of a gas turbine combustor using a lean-premixed low emission swirl stabilized burner is presented. To model thermoacoustic oscillations, a combustion system can be described as a network of acoustic elements, representing for example fuel and-air supply, burner and flame, combustor, cooling channels, suitable terminations, etc. For most of these elements, simple analytical models provide an adequate description of their thermoacoustic properties. However, the complex response of burner and flame (involving a three-dimensional flow field, recirculation zones, flow instabilities and heat release) to acoustic perturbations has - at least in a first step - to be determined by experiment. In our approach, we describe the burner as an active acoustical two-port, where the state variables pressure and velocity at the inlet and the outlet of the two port are coupled via a four element transfer matrix. This approach is similar to the "black box" theory in communication engineering. To determine all four transfer matrix coefficients, two test states, which are independent in the state vectors, have to be created. This is achieved by using acoustic excitation by loudspeakers upstream and downstream of the burner, respectively. In addition, the burner might act as an acoustic source, emitting acoustic waves due to an unsteady combustion process. The source characteristics were determined by using a third test state, which again must be independent from the two other state vectors. In application to a full size gas turbine burner, the method's accuracy was tested in a first step without combustion and the results were compared to an analytical model for the burner's acoustic properties. Then the method was used to determine the burner transfer matrix with combustion. An experimental swirl stabilized premixed gas-turbine burner was used for this purpose. The treatment of burners as acoustic two-ports with feedback including a source term and the experimental determination of the burner transfer matrix is novel.