The Origin of Secondary Peaks with Active Control of Thermoacoustic Instability

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Abstract
This paper deals with the generation of new peaks in the pressure spectrum in controlled combustors in experimental investigations of active control of thermoacoustic instabilities. Typically, the reported experiments have demonstrated that the dominant thermoacoustic instability can be suppressed, but secondary peaks at different frequencies which were not excited in the uncontrolled combustor appear. We develop a physically-based model of an actively controlled premixed laminar combustor which takes into account (a) laminar flame kinematics, (b) linear acoustic dynamics with coupling between the acoustic modes, and (c) actuation using side-mounted and end-mounted loudspeakers. Using this model, we analyze some of the experimental controllers proposed in the literature and explain the origin of secondary peaks observed in these studies. Secondary peaks are created while using these controllers due to resonant coupling between various mechanisms in the combustor that are distinct from those responsible for thermoacoustic resonance and mechanisms in the controller other than those that enable suppression of thermoacoustic instability. Other than at acoustic frequencies, premixed laminar combustors respond at lower frequencies due to flame dynamics, and at higher frequencies due to antiresonance. The experimental controllers are usually implemented using analog electronic circuitry whose components are designed so as to provide the functionalities of a phase-shifter, a filter, and an amplifier. Since analog filters tend to provide a phase compensation over a wide range of frequencies and not just at the isolated (unstable) frequency, they can initiate resonances by coupling with various mechanisms present in the combustor. Low frequency secondary peaks are typically due to coupling between the flame dynamics and the filter components in the controller, while high frequency peaks are due to either the interaction between various components of the active controller themselves, or the interaction between the controller components and antiresonance. Such phenomena clearly underscore the need for an active control design which accounts for the combustor dynamics over a range of frequencies with the goal of obtaining the desired performance over this entire range.