▪ Abstract  Early work and recent advances in feedback control of combustion oscillations are described. The physics of combustion oscillations, most commonly caused by a coupling between acoustic waves and unsteady heat release, are discussed, and the concept of using feedback control to interrupt these interactions is introduced. Factors affecting practical implementation of feedback control, including sensors, actuators, and controller design are described, and the historical development of control strategy for combustion oscillations is reviewed. Finally, demonstrations of feedback control on full-scale combustion systems are described, and it is concluded that there is potential to apply more systematic controller designs at full scale.

The coherent structures of a turbulent wake generated behind a bluff three-dimensional axisymmetric body are investigated experimentally at a diameter based Reynolds number ∼ 2×10 5 . Proper orthogonal decomposition of base pressure measurements indicates that the most energetic coherent structures retain the structure of the symmetry-breaking laminar instabilities and manifest as unsteady vortex shedding with azimuthal wavenumber m = ±1. In a rotating reference frame, the shedding preserves the reflectional symmetry and is linked with a reflectionally symmetric mean pressure distribution on the base. Due to a slow rotation of symmetry plane of the turbulent wake around the axis of the body, statistical axisymmetry is recovered in the time average. The ratio of the timescales associated with the slow rotation of the symmetry plane and the vortex shedding is of order 100.

This paper considers the effect of flow advection on entropy waves. The interest is in whether entropy waves persist in gas turbine combustors, between the flame, where they are generated, and the combustor exit, where their acceleration generates acoustic waves (known as ‘entropy noise’ or ‘indirect combustion noise’). Entropy wave advection within a simplified fully developed turbulent channel-flow simulation is investigated. Entropy wave dissipation is found to be negligible, with loss of entropy wave strength caused predominantly by mean flow shear dispersion. The impulse response of entropy perturbations downstream of where they are generated is shown to be well modelled by a Gaussian profile in time. This yields a (different) Gaussian form for the inlet–outlet transfer function of entropy perturbations. For representative gas turbine flows, the magnitude of this transfer function is such that significant entropy wave strength will remain at the combustor exit, confirming that entropy-generated acoustic waves are likely to be important.

A modelling methodology to reproduce the experimental measurements of a turbulent flow in the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries that occur in the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.

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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.

Combustion noise comprises two components: direct combustion noise and indirect combustion noise. The latter is the lesser studied, with entropy noise believed to be its main component. Entropy noise is generated via a sequence involving diverse flow physics. It has enjoyed a resurgence of interest over recent years, because of its increasing importance to aero-engine exhaust noise and a recognition that it can affect gas turbine combustion instabilities. Entropy noise occurs when unsteady heat release rate generates temperature fluctuations (entropy waves), and these subsequently undergo acceleration. Five stages of flow physics have been identified as being important, these being (a) generation of entropy waves by unsteady heat release rate; (b) advection of entropy waves through the combustor; (c) acceleration of entropy waves through either a nozzle or blade row, to generate entropy noise; (d) passage of entropy noise through a succession of turbine blade rows to appear at the turbine exit; and (e) reflection of entropy noise back into the combustor, where it may further perturb the flame, influencing the combustor thermoacoustics. This article reviews the underlying theory, recent progress and outstanding challenges pertaining to each of these stages.

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.