Systematic modulation of the flame transfer function and its effect on thermoacoustic stability

We investigate the thermoacoustic response of a simple laboratory combustor where the flame response is varied systematically by combining hydrogen enrichment with coherent vortex shedding to introduce modulations in the gain and phase of the flame transfer function (FTF). Previous work showed that the modulations in the FTF were produced by superposition of two convective disturbances with different time-delays: a convective time-delay from the flame base to the center of heat release rate and a convective time-delay due to controlled vortex shedding upstream of the flame. Although the latter can be independently controlled by geometry, the former depends on the combustion properties of the flame which determines the center of heat release rate. In this paper we take advantage of the combustion properties of different H2/CH4/air blends that produce flames with a different flame speed and center of heat release rate but have the same equivalence ratio, adiabatic flame temperature, thermal power, as well as bulk velocity. Since the flame temperature is proportional to the acoustic amplification of the flame, fixing this enables fully independent control of both time-delays that modify the gain and phase of the flame response enabling a systematic investigation into the thermoacoustic response of the system. To interpret the effect these modifications have on the thermoacoustic system response, a Distributed Time Lag (DTL) model is used to generalize and describe the FTF in terms of the two convective time delays, which are linked to physical parameters. The DTL model is then implemented into an elementary 1D network model of the system, and results from a linear stability analysis are compared with measurements of self-excited instabilities. Changes to the growth rate are shown to be consistent with the experimentally observed limit cycle when the time delay related to the modulations is varied. The relative importance of gain or phase modulations on the change in growth rate is then discussed. We find that a modification to the gain extends the initial eigenvalue trajectory, whereas a change in the phase leads to a rotation in the complex plane. Furthermore, the overall effect on the growth rate depends on the initial location of the eigenvalue in the complex plane, which is determined by the operating conditions. The influence of strong mode veering due to exceptional points on the eigenvalue trajectories is shown to play an important role when modulations are introduced.