Simon R. Stow

Acoustic analysis of gas turbine combustors

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.

Reflection of circumferential modes in a choked nozzle

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 shocks 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.

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 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

Low-order modelling of thermoacoustic limit cycles

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

Modelling of Circumferential Modal Coupling Due to Helmholtz Resonators

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 geometry is assumed and so circumferential modes are included but radial dependence is ignored. The formulation is in terms of a network of modules such as straight ducts and area changes. At certain operating conditions, the flow is predicted to be unstable, with linear waves growing in amplitude. Helmholtz resonators can be used to absorb acoustic energy and, when carefully designed and installed at appropriate locations, can stabilise the flow. Helmholtz resonators are included in the model. Connecting a Helmholtz resonator to an annular duct destroys the axisymmetry of the geometry. This results in coupling of the circumferential modes which must be calculated. The model is used to investigate the best arrangement of resonators around the circumference of an annular duct to achieve maximum damping of a circumferential oscillation.Copyright

MEASUREMENT AND ANALYSIS OF FLAME TRANSFER FUNCTION IN A SECTOR COMBUSTOR UNDER HIGH PRESSURE CONDITIONS

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. A flame transfer function describes the change in the rate of heat release in response to perturbations in the inlet flow as a function of frequency. It is a quantitative assessment of the susceptibility of combustion to disturbances. The resulting fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can result. Flame transfer functions for LPP combustion are poorly understood at present but are crucial for predicting combustion oscillations. This paper describes an experiment designed to measure the flame transfer function of a simple combustor incorporating realistic components. Tests were conducted initially on this combustor at atmospheric pressure (1.2 bar and 550 K) to make an early demonstration of the combustion system. The test rig consisted of a plenum chamber with an inline siren, followed by a single LPP premixer/duct and a combustion chamber with a silencer to prevent natural instabilities. The siren was used to induce variable frequency pressure/acoustic signals into the air approaching the combustor. Both unsteady pressure and heat release measurements were undertaken. There was good coherence between the pressure and heat release signals. At each test frequency, two unsteady pressure measurements in the plenum were used to calculate the acoustic waves in this chamber and hence estimate the mass-flow perturbation at the fuel injection point inside the LPP duct. The flame transfer function relating the heat release perturbation to this mass flow was found as a function of frequency. The same combustor hardware and associated instrumentation were then used for the high pressure (15 bar and 800 K) tests. Flame transfer function measurements were taken at three combustion conditions that simulated the staging point conditions (Idle, Approach and Take-off) of a large turbofan gas turbine. There was good coherence between pressure and heat release signals at Idle, indicating a close relationship between acoustic and heat release processes. Problems were encountered at high frequencies for the Approach and Take-off conditions, but the flame transfer function for the Idle case had very good qualitative agreement with the atmospheric-pressure tests. The flame transfer functions calculated here could be used directly for predicting combustion oscillations in gas turbine using the same LPP duct at the same operating conditions. More importantly they can guide work to produce a general analytical model.Copyright

Flame transfer function for swirled LPP combustion from experiments and CFD

Combustion oscillations that arise in gas turbines can lead to plant damage. One method used to predict these oscillations is to analyse the acoustics using a simple linear model. This model requires a transfer function to describe the response of the heat release to flow perturbations. A transfer function has been obtained for a swirled premixed combustion system using experiments under atmospheric conditions and CFD. These results have been compared with analytical models. The experimental and computational transfer functions both indicate a low frequency zero. A time-delay spread model gives a good representation of the computational transfer function. The experimental transfer function is described well by a model that combines a time-delay spread with a constant gain.Copyright

Three-dimensional extensions to Jeffery?Hamel flow

We consider two viscous flows, both of which are in a class of three-dimensional flow states that are closely related to the classical Jeffery–Hamel solutions. In the first configuration, we consider a flow between two planes, intersecting at an angle α, and driven by a line-source-like solution in the neighbourhood of the apex of intersection (just as in classical, two-dimensional, Jeffery–Hamel flow). However, in addition we allow for a flow in the direction of the line of intersection of the planes (in order to capture the broader class of three-dimensional solutions). In this flow, two solution scenarios are possible; the first of these originates as a bifurcation from Jeffery–Hamel flow, whilst the second scenario describes a radial velocity of the classical Jeffery–Hamel form (also with a zero azimuthal velocity component), but with an axial velocity determined from the radial flow. Both of these solutions are exact within the Navier–Stokes framework. In the second configuration, we consider the high Reynolds number, three-dimensional flow in a diverging channel, with (generally) non-straight walls close to a plane of symmetry, and driven by a pressure gradient. Similarity solutions are found, and a connection with Jeffery–Hamel flows is established for the particular case of a flow through straight (but non-parallel) channel walls, and again, additional three-dimensional solutions are found. One member of this general class (corresponding to the flow through a straight-walled channel, driven by linearly increasing pressure in both the axial and cross-channel directions), leads to a further family of exact Navier–Stokes solutions.

Boundary-layer flow along a ridge: alternatives to the Falkner-Skan solutions

We consider the laminar boundary–layer flow past a semi–infinite plate with a streamwise ridge. We seek similarity solutions to the problem, when the freestream velocity takes the form x*n, where x* denotes the distance from the leading edge of the plate; such solutions may exist if the transverse and lateral scales of the ridge develop in the streamwise direction at the same rate as the boundary–layer thickness grows. In deriving the necessary far–field boundary conditions for these calculations, we are led to a consideration of a class of flows of the Falkner–Skan type, but which may possess a cross–flow component of velocity (which grows linearly in the cross–flow direction). This new class of flow is a three–dimensional alternative to the FalknerSkan family. Wall transpiration effects are also addressed and portions of the solution curves correspond to separated flows. Solutions for the flow along a ridge for both the aforementioned classes of far–field behaviour are presented. A study of the effects of relaxing the similarity constraint on both the classical solution and new families of solution is also made. It is found that the problem is (frequently) complicated by the existence of spatially developing eigensolutions (originating from the leading edge), which have the effect of rendering standard parabolic marching procedures ill posed.

Conditional Moment Closure LES Modelling of an Aero-Engine Combustor at Relight Conditions

A Conditional Moment Closure (CMC) approach embedded in an LES CFD framework is presented for simulation of the reactive flow field of an aero-engine combustor operating at altitude relight conditions. Before application to the combustor geometry, the CMC model was validated on the standard lab-scale Sandia flame D. For the combustor simulation, a global mechanism for n-heptane was used along with a Lagrangian approach for the spray, to which a secondary break-up model was applied. The simulation modelled a multi-sector sub-atmospheric rig that was used to verify the altitude relight capability of the combustor. A comprehensive suite of diagnostics was applied to the rig test, including high-speed OH and kerosene PLIF as well as high speed OH* chemiluminescence. The CMC-based CFD simulation was able to predict well the position of the flame front and fuel distribution at the low pressure, low temperature conditions typical of altitude relight. Furthermore, the simulation of the ignition showed strong similarities with OH* chemiluminescence measurements of the event. An EBU-based LES was run too and showed to be unable to capture the flame front as well as the CMC model could. This work demonstrates that CMC LES can be an effective tool to support assessment of the relight capability of aero-engine combustors.Copyright