The flame describing function and flame dynamics under self-sustained oscillations

International audienceTransfer function concepts that appear in many areas and most notably in control systems have been extensively used to represent the flame response in low order models of combustion instability. Much of the theoretical work is based on flame transfer functions (FTF). In recent years the nonlinear extension of the flame transfer function, namely the flame describing function (FDF), was used to get a more accurate representation of the flame response when the level of oscillation becomes large and the system reaches a limit cycle. Despite their wide use, the validity of using FTF/FDF to represent flame response still remains to be experimentally substantiated. This article is aimed at providing a direct assessment of the capacity of the FDF to suitably describe the flame behavior under self-sustained oscillations (SSO). This is accomplished by making use of an experimental combustion configuration which exhibits unstable oscillations but which can also be used to modulate the flame using a set of driver units. The flame dynamics and response are determined under well established oscillations. The chamber length is then modified to obtain a stable regime and the flame is modulated externally at the frequency of the self-sustained oscillation observed in the first stage. The amplitude of incident velocity modulations is then progressively varied until it coincides with that found under self-sustained oscillations. This allows a direct comparison of the flame dynamics in these two situations. Gain and phase of the describing function are measured for the various input levels and found to approximately match those measured under SSO. It is shown that the best match is obtained when the amplitude of external modulation induces a level of velocity oscillations that is closest to that prevailing under SSO demonstrating that the FDF suitably captures the nonlinearity of the flame response, at least in the configuration investigated in this research