a b s t r a c t Accurate prediction of limit cycle oscillations resulting from combustion instability has been a long-standing challenge. The present work uses a coupled approach to predict the limit cycle characteristics of a combustor, developed at Cambridge University, for which experimental data are available (Balachandran, Ph.D. thesis, 2005). The combustor flame is bluff-body stabilised, turbulent and partially-premixed. The coupled approach combines Large Eddy Simulation (LES) in order to characterise the weakly non-linear response of the flame to acoustic perturbations (the Flame Describing Function (FDF)), with a low order thermoacoustic network model for capturing the acoustic wave behaviour. The LES utilises the open source Computational Fluid Dynamics (CFD) toolbox, OpenFOAM, with a low Mach number approximation for the flow-field and combustion modelled using the PaSR (Partially Stirred Reactor) model with a global one-step chemical reaction mechanism for ethylene/air. LES has not previously been applied to this partially-premixed flame, to our knowledge. Code validation against experimental data for unreacting and partially-premixed reacting flows without and with inlet velocity perturbations confirmed that both the qualitative flame dynamics and the quantitative response of the heat release rate were captured with very reasonable accuracy. The LES was then used to obtain the full FDF at conditions corresponding to combustion instability, using harmonic velocity forcing across six frequencies and four forcing amplitudes. The low order thermoacoustic network modelling tool used was the open source OSCILOS (http://www.oscilos.com). Validation of its use for limit cycle prediction was performed for a well-documented experimental configuration, for which both experimental FDF data and limit cycle data were available. The FDF data from the LES for the present test case was then imported into the OSCILOS geometry network and limit cycle oscillations of frequency 342 Hz and normalised velocity amplitude of 0.26 were predicted. These were in good agreement with the experimental values of 348 Hz and 0.21 respectively. This work thus confirms that a coupled numerical prediction of limit cycle behaviour is possible using an entirely open source numerical framework.

Numerical simulations were used to characterise the non-linear response of a turbulent premixed flame to acoustic velocity fluctuations. The test flame simulated was the bluff body stabilised flame which has been the subject of a detailed experimental study (Balachandran et al., 2005, Combustion & Flame). Simulations were performed using Large Eddy Simulation (LES) via the open source Computational Fluid Dynamics (CFD) software, Code S aturne, with combustion modelled by combining a Flame Surface Density (FSD) method with a fractal approach for the wrinkling factor. The cold flow field and the unforced reacting flow were used for preliminary code validation. In order to characterise the non-linear response of the unsteady heat release rate to acoustic forcing, a harmonically varying velocity fluctuation, for which both the forcing frequency and normalised forcing amplitude were varied, was imposed. The flame response was characterised via a Flame Describing Function (FDF), also known as a nonlinear flame transfer function, for which the gain and phase shift depend on forcing amplitude as well as forcing frequency. The response at four frequencies was compared to experimental data in detail, confirming that the LES results captured both the qualitative flame dynamics and the quantitative response of the heat release rate with very reasonable accuracy. The full FDF was then obtained across more frequencies, again showing a good fit with the experimental data, other than for a slight under-prediction in gain, most probably due to neglecting the effect of wall heat loss and the effect of combustion modelling. The agreement was significantly better than has been obtained previously for this test case using numerical simulations. Finally, it was found that increasing combustor length had little affect on the flame response, which may prove useful for future long combustor stability and limit cycle analysis. This work thus confirms that LES, in this case via the open source Code S aturne, provides a useful tool for characterising the response of lean premixed turbulent flames.

SUMMARYAmong the various hybrid methodologies, Speziale's very large eddy simulation (VLES) is one that was proposed very early. It is a unified simulation approach that can change seamlessly from Reynolds Averaged Navier–Stokes (RANS) to direct numerical simulation (DNS) depending on the numerical resolution. The present study proposes a new improved variant of the original VLES model. The advantages are achieved in two ways: (i) RANS simulation can be recovered near the wall which is similar to the detached eddy simulation concept; (ii) a LES subgrid scale model can be reached by the introduction of a third length scale, that is, the integral turbulence length scale. Thus, the new model can provide a proper LES mode between the RANS and DNS limits. This new methodology is implemented in the standard k − ϵ model. Applications are conducted for the turbulent channel flow at Reynolds number of Reτ = 395, periodic hill flow at Re = 10,595, and turbulent flow past a square cylinder at Re = 22,000. In comparison with the available experimental data, DNS or LES, the new VLES model produces better predictions than the original VLES model. Furthermore, it is demonstrated that the new method is quite efficient in resolving the large flow structures and can give satisfactory predictions on a coarse mesh. Copyright © 2012 John Wiley & Sons, Ltd.

In the context of combustion noise and combustion instabilities, the transport of entropy perturbations through highly simplified turbulent flows has received much recent attention. This work performs the first systematic study into the transport of entropy perturbations through a realistic gas turbine combustor flow-field, exhibiting large-scale hydrodynamic flow features in the form of swirl, separation, recirculation zones and vortex cores, these being ubiquitous in real combustor flows. The reacting flow-field is simulated using low Mach number large eddy simulations, with simulations validated by comparison to available experimental data. A generic artificial entropy source, impulsive in time and spatially localized at the flame-front location, is injected. The conservation equation describing entropy transport is simulated, superimposed on the underlying flow-field simulation. It is found that the transport of entropy perturbations is dominated by advection, with both thermal diffusion and viscous production being negligible. It is furthermore found that both the mean flow-field and the large-scale unsteady flow features contribute significantly to advective dispersion — neither can be neglected. The time-variation of entropy perturbation amplitude at combustor exit is well-modelled by a Gaussian profile, whose dispersion exceeds that corresponding to a fully-developed pipe mean flow profile roughly by a factor of three. Finally, despite the attenuation in entropy perturbation amplitude caused by advective dispersion, sufficient entropy perturbation strength is likely to remain at combustor exit for entropy noise to make a meaningful contribution at low frequencies.

The present article investigates the correlation between flame macrostructures and thermoacoustic combustion instabilities in stratified swirling flames. Experiments are carried out in a laboratory scale longitudinal test rig equipped with the Beihang Axial Swirler Independently-Stratified (BASIS) burner, a

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

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