Extracting flame describing functions in the presence of self-excited thermoacoustic oscillations

One of the key elements in the prediction of thermoacoustic oscillations is the determination of the acoustic response of flames as an element in an acoustic network, in the form of a flame describing function (FDF). In order to obtain a response, flames often have to be confined into a system with its own acoustic response. Separating the pure flame response and that of the system can be complicated by the non-linear effects that the flame can have on the overall system response. In this paper, we investigate whether it is possible to obtain a flame response via the usual methods of dynamic chemiluminescence and pressure measurements, starting from an unforced system with incipient self-excitations at a given frequency fs, in the form of a stabilized flame at atmospheric pressure with a 700 mm tube as a combustor. The flame is forced at discrete frequencies from 20 to 400 Hz, away from the self-excitation, and the response of the flame is measured using OH* chemiluminescence. This response was compared to a flame response measured in a short tube with no other excitations. The results show that both the gain and phase can be entirely dominated by the behavior of the self-excitation, so that in general it is not possible to extract reliable gain and phase information as if the forced and self-excited modes acted independently and linearly. Although the gain in this particular case was not significantly affected, the phase information of the original flame became dominated by the triggered self-excitation. Boundary conditions and systems used for flame acoustic forcing therefore need to be carefully controlled whenever there is a possibility of self-excitation