| dc.description.abstract | In the analysis of thermoacoustic systems, a flame is usually characterised
by the way its heat release responds to acoustic forcing. This
response depends on the hydrodynamic stability of the flame. Some
flames, such as a premixed bunsen flame, are hydrodynamically globally
stable. They respond only at the forcing frequency. Other flames,
such as a jet diffusion flame, are hydrodynamically globally unstable.
They oscillate at their own natural frequencies and are often assumed
to be insensitive to low-amplitude forcing at other frequencies.
If a hydrodynamically globally unstable flame really is insensitive to
forcing at other frequencies, then it should be possible to weaken
thermoacoustic oscillations by detuning the frequency of the natural
hydrodynamic mode from that of the natural acoustic modes. This
would be very beneficial for industrial combustors.
In this thesis, that assumption of insensitivity to forcing is tested
experimentally. This is done by acoustically forcing two different selfexcited
flows: a non-reacting jet and a reacting jet. Both jets have
regions of absolute instability at their base and this causes them to
exhibit varicose oscillations at discrete natural frequencies. The forcing
is applied around these frequencies, at varying amplitudes, and
the response examined over a range of frequencies (not just at the
forcing frequency). The overall system is then modelled as a forced
van der Pol oscillator.
The results show that, contrary to some expectations, a hydrodynamically
self-excited jet oscillating at one frequency is sensitive to
forcing at other frequencies. When forced at low amplitudes, the jet
responds at both frequencies as well as at several nearby frequencies,
and there is beating, indicating quasiperiodicity. When forced at
high amplitudes, however, it locks into the forcing. The critical forcing
amplitude required for lock-in increases with the deviation of the
forcing frequency from the natural frequency. This increase is linear,
indicating a Hopf bifurcation to a global mode.
The lock-in curve has a characteristic ∨ shape, but with two subtle
asymmetries about the natural frequency. The first asymmetry concerns
the forcing amplitude required for lock-in. In the non-reacting
jet, higher amplitudes are required when the forcing frequency is above
the natural frequency. In the reacting jet, lower amplitudes are required
when the forcing frequency is above the natural frequency. The
second asymmetry concerns the broadband response at lock-in. In the
non-reacting jet, this response is always weaker than the unforced response,
regardless of whether the forcing frequency is above or below
the natural frequency. In the reacting jet, that response is weaker
than the unforced response when the forcing frequency is above the
natural frequency, but is stronger than it when the forcing frequency
is below the natural frequency.
In the reacting jet, weakening the global instability – by adding coflow
or by diluting the fuel mixture – causes the flame to lock in at lower
forcing amplitudes. This finding, however, cannot be detected in the
flame describing function. That is because the flame describing function
captures the response at only the forcing frequency and ignores all
other frequencies, most notably those arising from the natural mode
and from its interactions with the forcing. Nevertheless, the flame describing
function does show a rise in gain below the natural frequency
and a drop above it, consistent with the broadband response.
Many of these features can be predicted by the forced van der Pol
oscillator. They include (i) the coexistence of the natural and forcing
frequencies before lock-in; (ii) the presence of multiple spectral peaks
around these competing frequencies, indicating quasiperiodicity; (iii)
the occurrence of lock-in above a critical forcing amplitude; (iv) the
∨-shaped lock-in curve; and (v) the reduced broadband response at
lock-in. There are, however, some features that cannot be predicted.
They include (i) the asymmetry of the forcing amplitude required
for lock-in, found in both jets; (ii) the asymmetry of the response at
lock-in, found in the reacting jet; and (iii) the interactions between
the fundamental and harmonics of both the natural and forcing frequencies,
found in both jets. | |
