A coupled numerical approach is investigated for predicting combustion instability limit cycle characteristics when the combustor contains a long flame. The test case is the ORACLES combustor, with a turbulent premixed flame a metre long: it exhibits limit cycle oscillations at ∼ 50 Hz and normalised velocity amplitude ahead of the flame of ∼ 0.29. The approach obtains the flame response to acoustic excitation using Large Eddy Simulations (LES), and couples this with a low-order wave-based network representation for the acoustic waves within the combustor. The flame cannot be treated as acoustically compact; the spatial distribution of both its response and the subsequent effect on the acoustics must be accounted for. The long flame is uniformly segmented axially, each segment being much shorter than the flow wavelengths at play. A series of “local” flame describing functions, one for the heat release rate response within each segment to velocity forcing at a fixed reference location, are extracted from the LES. These use the Computational Fluid Dynamics toolbox, OpenFOAM, with an incompressible approximation for the flow-field and combustion modelled using the Partially Stirred Reactor model with a global onestep reaction mechanism. For coupling with the low-order acoustic network modelling, compact acoustic jump conditions are derived and applied across each flame segment, while between flame segments, wave propagation occurs. Limit cycle predictions from the proposed coupled method agree well with those predicted using the continuous 1-D linearised Euler equations, validating the flame segmentation implementation. Limit cycle predictions (frequency 51.6 Hz and amplitude 0.38) also agree well with experimental measurements, validating the low-order coupled method as a prediction tool for combustors with long flames. A sensitivity analysis shows that the predicted limit cycle amplitude decreases rapidly when acoustic losses at boundaries are accounted for, and increases if combustor heat losses downstream of the flame are accounted for. This motivates more accurate determination of combustor boundary and temperature behaviour for thermoacoustic predictions

For annular combustors, the interactions between different modal structures (longitudinal, azimuthal spinning, standing, and slanted) remain a challenge in ongoing studies of thermoacoustic instabilities. The present work develops an annular combustor named TurboCombo, similar to the multiple-injector annular combustor named MICCA, but with a convergent turbine section connected to the combustor outlet. A Helmholtz solver provides a proper estimate of the modal frequencies and reveals the spatial structures for both two rigs. The experimental results present the consistencies of frequency domains between the acoustic pressure signals and the hydroxyl (OH^*) radicals emission signal. The high-speed flame images are processed by the dynamic mode decomposition method, statistically showing longitudinal, azimuthal spinning, or standing nature in different cases. The stability maps of the two combustors show slight differences under atmospheric conditions. In the TurboCombo rig, there are two types of interaction behaviors between the 1/4 wave longitudinal mode of the chamber and the 1st order azimuthal mode of the plenum. Unlike the prevalent “dual-mode coexistence” characteristics, an interesting behavior of “intermittent switching” is revealed, which manifests as conspicuous two-way jumps between the two modes with different frequencies. Such intermittent switching occurs randomly between two stable limit cycles in a long-time observation without any external excitation, but is driven by the turbulence-induced stochastic process. Moreover, there still exist some weak azimuthal oscillations while the longitudinal mode is dominated. The standing or spinning bias of the azimuthal mode also features intermittent transition, corresponding to the occasions dominated by longitudinal mode or azimuthal mode, respectively.

Combustion instability is one significant issue in the development of aero-engines and gas turbines. In practical combustors, the exit boundary of the combustion chamber is complex and the mechanisms of thermoacoustic coupling become more complicated. In order to study the effect of outlet boundary on combustion instabilities, the premixed swirling combustor was built and several different damping rings were adopted to obtain the outlet contraction of combustion chamber. Acoustic impedances corresponding to different configurations were measured in cold flow, and reactive experiments were conducted in different conditions. The results show that combustion instabilities were tightly related to both the equivalence ratio and exit boundary. The quarter wave mode would be triggered at a certain interval of equivalence ratio and suppressed in different levels while applying various damping rings. The outlet contraction left an effect on both the frequency and amplitude of thermoacoustic mode. It affected the resonant frequency by influencing the gas temperature and modifying the acoustic boundary. Oscillation amplitudes were weakened due to the change in acoustic energy generated from unstable heat release. Moreover, the helical mode corresponding to the precessing vortex core was detected, which was also affected by the outlet boundary. These results are rarely reported in previous work and may provide useful ideas in the prediction and control of combustion instabilities.

Combustion instabilities arise owing to a two-way coupling between acoustic waves and unsteady heat release. Oscillation amplitudes successively grow, until nonlinear effects cause saturation into limit cycle oscillations. Feedback control, in which an actuator modifies some combustor input in response to a sensor measurement, can suppress combustion instabilities. Linear feedback controllers are typically designed, using linear combustor models. However, when activated from within limit cycle, the linear model is invalid, and such controllers are not guaranteed to stabilize. This work develops a feedback control strategy guaranteed to stabilize from within limit cycle oscillations. A low-order model of a simple combustor, exhibiting the essential features of more complex systems, is presented. Linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame. The latter is determined numerically using a level set approach. Its implication is that the open-loop transfer function (OLTF) needed for controller design varies with oscillation level. The difference between the mean and the rest of the OLTFs is characterized using the ν -gap metric, providing the minimum required ‘robustness margin’ for an H ∞ loop-shaping controller. Such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations.