Dynamics and stability of lean-premixed swirl-stabilized combustion

Combustion instability has become a major issue for gas turbine manufacturers. Stricter emission regulations, particularly on nitrogen oxides, have led to the development of new combustion methods, such as lean premixed prevaporized(LPP)combustion,to replacethetraditionaldiffusion e ame.However,LPPcombustionismuchmore liable to generate strong oscillations, which can damage equipment and limit operating conditions. As a tutorial, methods to investigate combustion instabilities are reviewed. Theemphasis is on gas turbine applications and LPP combustion. The e ow is modeled as a one-dimensional mean with linear perturbations. Calculations are typically done in the frequency domain. The techniques described lead to predictions for the frequencies of oscillations and the susceptibility to instabilities for which linear disturbances grow expotentially in time. Appropriate boundary conditions are discussed, as is the change in the linearized e ow across zones of heat addition and/or area change. Many of the key concepts are e rst introduced by considering one-dimensional perturbations. Later higher-order modes, particularly circumferential waves, are introduced, and modal coupling is discussed. The modeling of a simplie ed combustion system, from compressor outlet to turbine inlet, is described. The approaches are simple and fast enough to be used at the design stage.

Acoustic Analysis of Gas Turbine Combustors

Experimental investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations

Advances in global linear instability analysis of nonparallel and three-dimensional flows

Analysis of combustion instabilities relies in most cases on linear analysis but most observations of these processes are carried out in the nonlinear regime where the system oscillates at a limit cycle. The objective of this paper is to deal with these two manifestations of combustion instabilities in a unified framework. The flame is recognized as the main nonlinear element in the system and its response to perturbations is characterized in terms of generalized transfer functions which assume that the gain and phase depend on the amplitude level of the input. This 'describing function' framework implies that the fundamental frequency is predominant and that the higher harmonics generated in the nonlinear element are weak because the higher frequencies are filtered out by the other components of the system. Based on this idea, a methodology is proposed to investigate the nonlinear stability of burners by associating the flame describing function with a frequency-domain analysis of the burner acoustics. These elements yield a nonlinear dispersion relation which can be solved, yielding growth rates and eigenfrequencies, which depend on the amplitude level of perturbations impinging on the flame. This method is used to investigate the regimes of oscillation of a well-controlled experiment. The system includes a resonant upstream manifold formed by a duct having a continuously adjustable length and a combustion region comprising a large number of flames stabilized on a multipoint injection system. The growth rates and eigenfrequencies are determined for a wide range of duct lengths. For certain values of this parameter we find a positive growth rate for vanishingly small amplitude levels, indicating that the system is linearly unstable. The growth rate then changes as the amplitude is increased and eventually vanishes for a finite amplitude, indicating the existence of a limit cycle. For other values of the length, the growth rate is initially negative, becomes positive for a finite amplitude and drops to zero for a higher value. This indicates that the system is linearly stable but nonlinearly unstable. Using calculated growth rates it is possible to predict amplitudes of oscillation when the system operates on a limit cycle. Mode switching and instability triggering may also be anticipated by comparing the growth rate curves. Theoretical results are found to be in excellent agreement with measurements, indicating that the flame describing function (FDF) methodology constitutes a suitable framework for nonlinear instability analysis.

A unified framework for nonlinear combustion instability analysis based on the flame describing function

Small perturbations of a choked flow through a thin annular nozzle are investigated. Two cases are considered, corresponding to a ‘choked outlet’ and a ‘choked inlet’ respectively. For the first case, either an acoustic or entropy or vorticity wave is assumed to be travelling downstream towards the nozzle contraction. An asymptotic analysis for low frequency is used to find the reflected acoustic wave that is created. The boundary condition found by Marble & Candel (1977) for a compact choked nozzle is shown to apply to first order, even for circumferentially varying waves. The next-order correction can be expressed as an ‘effective length’ dependent on the mean flow (and hence the particular geometry of the nozzle) in a quantifiable way.For the second case, an acoustic wave propagates upstream and is reflected from a convergent–divergent nozzle. A normal shock is assumed to be present. By considering the interaction of the shock's position and flow perturbations, the reflected propagating waves are found for a compact nozzle. It is shown that a significant entropy disturbance is produced even when the shock is weak, and that for circumferential modes a vorticity wave is also present. Numerical calculations are conducted using a sample geometry and good agreement with the analysis is found at low frequency in both cases, and the range of validity of the asymptotic theory is determined.

Reflection of circumferential modes in a choked nozzle

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. Acoustic waves produce fluctuations in heat release, for instance by perturbing the fuel–air ratio or flame shape. These heat fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can result.A linear model for thermoacoustic oscillations in LPP combustors is described. A thin annular combustor is assumed and so circumferential modes are included but radial dependence is ignored. The geometry consists of straight ducts joined by short regions of area change. Perturbations to the flow can be thought of as a combination of acoustic, entropy and vorticity waves. The development of these waves along the straight ducts is found using a propagation matrix approach. At the entrance to the combustion chamber, a flame model is used in which the unsteady heat release is related to fluctuations in fuel–air ratio. Various possible inlet and outlet conditions are described. The model is then applied to a simplified example based on a sector rig. The resonant modes are found numerically and compared with the frequencies that occurred in experiments.Copyright © 2001 by ASME

Thermoacoustic Oscillations in an Annular Combustor

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. Acoustic waves produce fluctuations in heat release, for instance by perturbing the fuel-air ratio. These heat fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can form. The resulting limit cycles can have large amplitude causing structural damage. Thermoacoustic oscillations will have a low amplitude initially. Thus linear models can give stability predictions. An unstable linear mode will grow in amplitude until nonlinear effects become important and a limit cycle is achieved. While the frequency of the linear mode can provide a good approximation to that of the resulting limit cycle, linear theories give no prediction of its amplitude. A low-order model for thermoacoustic limit cycles in LPP combustors is described. The approach is based on the fact that the main nonlinearity is in the combustion response to flow perturbations. In LPP combustion, fluctuations in the inlet fuel-air ratio have been shown to be the dominant cause of unsteady combustion: these occur because velocity perturbations in the premix ducts cause a time-varying fuel-air ratio, which then convects downstream. If the velocity perturbation becomes comparable to the mean flow, there will be an amplitude-dependent effect on the equivalence ratio fluctuations entering the combustor and hence on the rate of heat release. A simple nonlinear flame model for this dependence is developed and is assumed to be the major non-linear effect on the limit cycle. Since the Mach number is low, the velocity perturbation can be comparable to the mean flow, with even reverse flow occurring, while the disturbances are still acoustically linear in that the pressure perturbation is still much smaller than the mean. Hence elsewhere the perturbations are treated as linear. In this nonlinear flame model, the flame transfer function describing the combustion response to changes in inlet flow is a function of both frequency and amplitude. The nonlinear flame transfer function is incorporated into a linear thermoacoustic network model for plane waves. Frequency, amplitude and modeshape predictions are compared with results from an atmospheric test rig. The approach is extended to circumferential waves in a thin annular geometry, where the nonlinearity leads to modal coupling.Copyright © 2004 by ASME

Simon R. Stow

Papers

Acoustic Analysis of Gas Turbine Combustors

Reflection of circumferential modes in a choked nozzle

Thermoacoustic Oscillations in an Annular Combustor

Low-Order Modelling of Thermoacoustic Limit Cycles

Model-Based Control of Combustion Instabilities in Annular Combustors