## Publications

109 results found

Guzman Inigo J, Baddoo PJ, Ayton LJ, et al., 2019, Noise generated by entropic and compositional inhomogeneities interacting with a cascade of airfoils, 25th AIAA/CEAS Aeroacoustics Conference, Publisher: American Institute of Aeronautics and Astronautics

Dalla Longa L, Evstafyeva O, Morgans A, 2019, Simulations of the bi-modal wake past three-dimensional blunt bluff bodies, *Journal of Fluid Mechanics*, Vol: 866, Pages: 791-809, ISSN: 0022-1120

The bi-modal behaviour of the turbulent flow past three-dimensional blunt bluff bodies is simulated using wall-resolved large eddy simulations. Bi-modality (also called bi-stability) is a phenomenon that occurs in the wakes of three-dimensional bluff bodies. It manifests as a random displacement of the wake between preferred off-centre locations. Two bluff bodies are considered in this work: a conventional square-back Ahmed body representative of road cars, and a simplified lorry, which is taller than it is wide, with its aspect ratio corresponding to a 15 % European lorry scale model. To our knowledge, this is the first time that the asymmetric bi-modal switching behaviour of the wake, observed experimentally, has been captured in simulations. The resulting unsteady flow fields are then analysed, revealing instantaneous topological changes in the wake experiencing bi-modal switching. The best-resolved case, the simplified lorry geometry, is then studied in greater detail using modal decomposition to gain insights into the energy content and the dominant frequencies of the wake flow structures associated with the asymmetric states. High-frequency snapshots of the switching sequence allow us to propose that large hairpin vortices are responsible for the triggering of the switching.

Yang D, Laera D, Morgans AS, 2019, A systematic study of nonlinear coupling of thermoacoustic modes in annular combustors, *Journal of Sound and Vibration*, ISSN: 0022-460X

Thermoacoustic instabilities in annular gas turbine combustors often involve modes which vary in both the longitudinal and circumferential directions. Recent experimental studies show that during limit cycle oscillations, different thermoacoustic modes may be uncoupled, as is the case in purely longitudinal or circumferential spinning modes. They may also be coupled, for example two counter-rotating circumferential modes combining to give standing or mixed modes, and coupling between circumferential and longitudinal modes giving rise to the slanted mode. Accurately predicting such modal couplings and the resulting spatial pattern of limit cycle oscillations remains an open challenge. This work uses a 2-D low-order network model based on modal expansions, validated against a full 3-D Helmholtz solver, to systematically investigate these couplings. For the first time, low-order network modelling is shown to capture limit cycle oscillations exhibiting both uncoupled and nonlinearly coupled modes, the latter including coupling between counter-rotating circumferential modes and between longitudinal and circumferential modes. It is shown that limit cycle solutions with totally different mode patterns (longitudinal, circumferential spinning, circumferential standing and slanted) can all exist in a given thermoacoustic system, with switches between modal patterns arising from slight changes in parameters such as the flame time delay.

Yang D, Sogaro FM, Morgans AS,
et al., 2019, Optimising the acoustic damping of multiple Helmholtz resonators attached to a thin annular duct, *Journal of Sound and Vibration*, Vol: 444, Pages: 69-84, ISSN: 0022-460X

Helmholtz resonators (HRs) are widely used to damp acoustic oscillations, including in the combustors of aero-engines and power gas turbines where they damp thermoacoustic oscillations. The geometries of such combustors are often annular in shape, which means that low frequency acoustic modes exhibit both longitudinal and circumferential modeshapes, the latter across different circumferential wave numbers. For linear acoustic disturbances downstream of the flame, the presence of HRs leads to modal coupling and mode shape shifts, which makes design and placement of multiple HRs very complicated. A procedure which ensures that the design and placement of the HRs can be optimised for good acoustic damping performance would be very valuable, and such a procedure is presented in this work. A simplified linear, low-dimensional model for the acoustic behaviour in a hot annular duct sustaining a mean flow is extended to account for the attachment of multiple HRs. The HRs are assumed to sustain a cooling mean bias flow through them, towards the combustor, such that they can be modelled using linear, lumped element Rayleigh conductivity models. An optimisation method based on the gradient derived from adjoint sensitivity analysis is then applied to the low order network acoustic modelling framework for hot annular ducts incorporating HR models, for the first time. It is used to optimise over multiple HR geometry and placement parameters, to obtain optimum acoustic damping over all acoustic modes in a given frequency range. These optimisation procedures are validated via multi-dimensional parameter sweep results. Thus a novel and efficient tool for HR optimisation for thin annular ducts is presented.

Xia Y, Laera D, Jones WP,
et al., 2019, Numerical Prediction of the Flame Describing Function and Thermoacoustic Limit Cycle for a Pressurized Gas Turbine Combustor, *Combustion Science and Technology*, ISSN: 0010-2202

© 2019, © 2019 Taylor & Francis Group, LLC. The forced flame responses in a pressurized gas turbine combustor are predicted using numerical reacting flow simulations. Two incompressible 11 Incompressible does not imply constant density but rather that the density is independent of pressure variations throughout the flow, i.e., not able to be compressed. large eddy simulation solvers are used, applying two combustion models and two reaction schemes (4-step and 15-step) at two operating pressures (3 and 6 bar). Although the combustor flow field is little affected by these factors, the flame length and heat release rate are found to depend on combustion model, reaction scheme, and combustor pressure. The flame responses to an upstream velocity perturbation are used to construct the flame describing functions (FDFs). The FDFs exhibit smaller dependence on the combustion model and reaction chemistry than the flame shape and mean heat release rate. The FDFs are validated by predicting combustor thermoacoustic stability at 3 and 6 bar and, for the unstable 6 bar case, also by predicting the frequency and oscillation amplitude of the resulting limit cycle oscillation. All of these numerical predictions are in very good agreement with experimental measurements.

Han X, Laera D, Morgans AS,
et al., 2018, The Effect of Stratification Ratio on the Macrostructure of Stratified Swirl Flames: Experimental and Numerical Study, *JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER-TRANSACTIONS OF THE ASME*, Vol: 140, ISSN: 0742-4795

Li J, Yang D, Morgans A, 2018, The effect of an axial mean temperature gradient on communication between one-dimensional acoustic and entropy waves, *International Journal of Spray and Combustion Dynamics*, Vol: 10, Pages: 131-153, ISSN: 1756-8277

This work performs a theoretical and numerical analysis of the communication between one-dimensional acoustic and entropy waves in a duct with a mean temperature gradient. Such a situation is highly relevant to combustor flows where the mean temperature drops axially due to heat losses. A duct containing a compact heating element followed by an axial temperature gradient and choked end is considered. The proposed jump conditions linking acoustic and entropy waves on either side of the flame show that the generated entropy wave is generally proportional to the mean temperature ratio across the flame and the ratio (F-1), where F is the flame transfer function. It is inversely proportional to the Mach number immediately downstream of the flame M2. The acoustic and entropy fields in the region of axial mean temperature gradient are calculated using four approaches: (1) using the full three linearised Euler equations as the reference; (2) using two linearised Euler equations in which the acoustic and entropy waves are assumed independent (thus allowing the extent of communication between the acoustic and entropy wave to be evaluated); (3) using a Helmholtz solver which neglects mean flow effects and (4) using a recently developed analytical solution. It is found that the communication between the acoustic and entropy waves is small at low Mach numbers; it rises with increasing Mach number and cannot be neglected when the mean Mach number downstream of the heating element exceeds 0.1. Predictions from the analytical method generally match those from the full three linearised Euler equations, and the Helmholtz solver accurately determines the acoustic field when M2≤0.1.

Han X, Laera D, Morgans A,
et al., 2018, Flame macrostructures and thermoacoustic instabilities in strati fied swirling flames, *Proceedings of the Combustion Institute*, ISSN: 1540-7489

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 novel double-swirled combustion system developed by adapting an industrial lean premixed prevaporized (LPP) combustor. At first, the flame macrostructures are investigated and discussed for various total equivalence ratios (ϕtotal) and stratification ratios (SRs). Depending on operating conditions, three different flame types are stabilized in the combustor: two attached flames comprising a stratified flame and a V-shaped flame (V-flame), as well as a lifted flame. Thermoacoustic instabilities are then investigated. The amplitude of the oscillations is found to be more sensitive to SR than the ϕtotal. Large amplitude limit cycles are found for low and high values of SR, for which the V-flame and the lifted flame are observed in the combustor, respectively. The flame dynamics are also investigated using local Rayleigh index maps. It is found that for both the lifted flame and V-flame, the major driving force comes from the flame-to-wall impingement region. Coherent structures associated with flame wrinkling are found along the flame brushes of the V-flame. On the contrary, the stratified flame is found to be more thermo-acoustically stable. Finally, incompressible Large Eddy Simulations is used to obtain the flame responses to forcing at 300 Hz, which is very close to the frequencies at which limit cycle oscillations occur. The results show that the global heat release rate response of the stratified flame exhibits a significant phase shift compared to the responses of the other two flame types, and this is the most likely cause of thermoacoustic stabilization.

Yang D, Guzman J, Johnson H, et al., 2018, On the sensitivity of the acoustics of short circular holes to inletedge geometries, AIAA/CEAS Aeroacoustics Conference, Publisher: AIAA

Short circular holes with a low Mach number mean bias flow passing through them can absorb or generate acoustics. A recent semi-analytical model (Yang & Morgans, Journal of Sound and Vibration, 384 (2016) pp. 294-311 & 393 (2017) pp. 41-61) based on the Green’s function method has been shown to be able to capture both the acoustic absorption and gen-eration. The model indicates the importance of accurately capturing the path of the shedvorticity from the hole inlet edge. In the present work, the effect of this vorticity path on thehole acoustics is first studied systematically using the semi-analytical model. As the vorticitypath is sensitive to the sharpness of the hole inlet edge, CFD tools are then used to obtain thevortex sheet shape after slightly changing the hole inlet edge shape. The acoustic responses ofthese modified holes are obtained using the semi-analytical model. A slightly chamfered edge case and a small ellipse edge case are considered to show that a very small change to the shape of the hole inlet edge can give a significant difference in the hole acoustic response.

Xia Y, Laera D, Morgans AS, et al., Thermoacoustic limit cycle predictions of a pressurised longitudinal industrial gas turbine combustor, ASME Turbo Expo 2018, Publisher: American Society of Mechanical Engineers

Morgans AS, 2018, Advective disturbances in combustor thermoacoustics, *International Journal of Spray and Combustion Dynamics*, Vol: 10, Pages: 101-102, ISSN: 1756-8277

Xia Y, Laera D, Morgans A, Effect of flame-to-flame interaction on the flame describing function of a turbulent swirling flame in an annular combustor, The 25th International Congress on Sound and Vibration (ICSV25)

Yang D, Morgans A, LOW-ORDER NETWORK MODELING FOR ANNULAR COMBUSTORS EXHIBITING LONGITUDINAL AND CIRCUMFERENTIAL MODES, ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition

Sogaro F, Schmid P, Morgans AS, 2018, Sensitivity analysis of thermoacoustic instabilities, Pages: 2063-2070

Copyright © (2018) by International Institute of Acoustics & Vibration.All rights reserved. Thermoacoustic instability is a phenomenon that occurs in numerous combustion systems, from rockets to land-based gas turbines. The thermoacoustic oscillations of these systems are of significant importance as they can result in severe vibrations, thrust oscillations, thermal stresses and mechanical loads that lead to fatigue or even failure. In this work we use a low-order network model representation of a combustor where linear acoustics are solved together with appropriate boundary conditions and flame jump conditions. Special emphasis is directed towards the interaction between instabilities associated with acoustic modes and flame-intrinsic modes. Adjoint methods are used to perform a receptivity and sensitivity analysis of the spectral properties of the system to changes in the parameters involved. To better analyse the extreme sensitivities that arise in the neighbourhood of a modal interaction, we compare the results with a time domain model that allows us to perform a pseudospectra analysis. The results provide key insights into the interplay between mode types.

Guzmán-Iñigo J, Morgans AS, Durán I, 2018, A model for the sound generated by entropy disturbances interacting with isolated blades

© 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. This article presents a modelling approach to predict the low-frequency sound generated by entropy fluctuations interacting with isolated aerofoils. A model of the acoustic field is obtained based on a linearisation of the compressible Euler equations about a steady potential compressible mean flow. Neglecting the mean flow variations of velocity and density in the propagation of sound, but not in the source term, and using a Lorentz-type transformation, the problem is reduced to solving a Helmholtz equation. This equation is recast in integral form and a solution is obtained using a compact Green’s function method. This approach assumes that the acoustic wavelength is large compared to the profile chord and spacing, while no restrictions are made on the entropy wavelengths. The source term is further simplified by assuming that the steady flow is a small perturbation to an uniform flow. The model is illustrated using a symmetric aerofoil and its performance is assessed with numerical simulations of the compressible Euler equations.

Xia Y, Laera D, Morgans AS, et al., 2018, Thermoacoustic limit cycle predictions of a pressurised longitudinal industrial gas turbine combustor

Copyright © 2018 Siemens AG This article presents numerical prediction of a thermoacoustic limit cycle in an industrial gas turbine combustor. The case corresponds to an experimental high pressure test rig equipped with the full-scale Siemens SGT-100 combustor operated at two mean pressure levels of 3 bar and 6 bar. The Flame Transfer Function (FTF) characterising the global unsteady response of the flame to velocity perturbations is obtained for both operating pressures by means of incompressible Large Eddy Simulations (LES). A linear stability analysis is then performed by coupling the FTFs with a wave-based low order thermoacoustic network solver. All the thermoacoustic modes predicted at 3 bar pressure are stable; whereas one of the modes at 6 bar is found to be unstable at a frequency of 231 Hz, which agrees with the experiments. A weakly nonlinear stability analysis is carried out by combining the Flame Describing Function (FDF) predicted by LES with the low order thermoacoustic network solver. The frequency, mode shape and velocity amplitude corresponding to the predicted limit cycle at 209 Hz are used to compute the absolute pressure fluctuation amplitude in the combustor. The numerically reconstructed amplitude is found to be reasonably close to the measured dynamics.

Han X, Laera D, Morgans AS, et al., 2018, THE EFFECT OF STRATIFICATION RATIO ON THE MACROSTRUCTURE OF STRATIFIED SWIRL FLAMES: EXPERIMENTAL AND NUMERICAL STUDY, ASME Turbo Expo: Turbomachinery Technical Conference and Exposition, Publisher: AMER SOC MECHANICAL ENGINEERS

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Han X, Morgans A, 2017, Non-linear Interactions of Two Premixed Flames Explored by Large Eddy Simulation with External Acoustic Forcing, *Combustion Science and Technology*, Vol: 190, Pages: 424-435, ISSN: 0010-2202

This article describes a numerical study of the interactions between two lean premixed flames subjected to external acoustic forcing. This provides insights into the flame-to-flame interactions that may occur during combustion instability in annular combustors. Experimental measurements for comparison are available from the target combustor developed at Cambridge University (Worth and Dawson, 2012). Large eddy simulation is applied using the open source computational fluid dynamics toolbox, OpenFOAM, with the combustion modeled using the partially stirred reactor model with a four-step chemical reaction mechanism for methane/air. Harmonic velocity oscillations are imposed at the inlet; the flame responses are studied based on heat release rate signals in different combustion regions. The effect of the flame separation distance (Sd) on both the flame dynamics and unsteady heat release responses is analyzed. The results show that the flame-to-flame interactions are nonlinear for the flame separations studied. The spatial variation of the unsteady heat release rate demonstrates that flame-wall interactions play an important role, becoming even more important than flame-to-flame interactions for closely spaced flames (Sd < 2.00D). These findings imply that for the flame separation distances studied, any flame model used in the low-order annular combustion instability prediction should account for both nonlinearity and flame-to-flame interactions.

Xia Y, Duran I, Morgans AS,
et al., 2017, Dispersion of entropy perturbations transporting through an industrial gas turbine combustor, *Flow, Turbulence and Combustion*, Vol: 100, Pages: 481-502, ISSN: 1386-6184

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.

Li J, Morgans A, 2017, Commentary on manuscript “Comment on ‘The one-dimensional acoustic field with arbitrary mean axial temperature gradient and mean flow’ (J. Li and A. S. Morgans, Journal of Sound and Vibration 400 (2017) 248–269)”, *Journal of Sound and Vibration*, Vol: 410, Pages: 488-494, ISSN: 0022-460X

Davide L, Morgans AS, 2017, Large eddy simulations for the flame describing functionof apremixed turbulent swirling flame, 24th International Congress on Sound and Vibration (ICSV24)

Computational prediction of thermoacoustic instabilities arising in gas turbine and aeroengine combustors is an ongoing challenge. Approaches which couple separate treatments for the acoustic waves and the flame all rely on a model for the response of the flame to oncoming acoustic perturbations. In the frequency domain, in the limit of small perturbations, this function is usually given in terms of the so-called Flame Transfer Function (FTF), i.e., a function that relates the heat release rate perturbation at the flame location with longitudinal velocity fluctuations taken at an upstream reference point. With the increase of the amplitude of oscillations, nonlinear combustion process controls the dynamics of the systems. A flame describing function (FDF) is so-defined introducing a dependence of the gain and phase of the FTF on velocity fluctuations amplitude |u'/ū|. The present work uses numerical simulations to obtain the FDF of a turbulent premixed swirling flame. The swirled burner developed at NTNU university is considered in a longitudinal combustor setup. Simulations are performed using Large Eddy Simulations (LES) via the open source Computational Fluid Dynamics (CFD) code, OpenFOAM. The predicted unperturbed flame structure is at first presented and discussed. Subsequently, the nonlinear flame response is characterised submitting the flame to a harmonically varying longitudinal velocity fluctuation, for which the forcing frequency is varied from 300 Hz to 1900 Hz considering two forcing amplitude levels, |u'/ū|=0.1 and |u'/ū|=0.2. The shape of the gain and the phase of the full FDF is discussed and the main characteristics are investigated.

Iñigo JG, Morgans A, Durán I, 2017, Sound generated by blades interacting with entropy waves, 24th International Congress on Sound and Vibration 2017 (ICSV 24)

This paper deals with the theoretical modelling of the sound generated by convected entropic perturbations interacting with blades. A model is obtained for inviscid small perturbations evolving around a potential steady flow past an aerofoil. Neglecting the mean flow variations of velocity and density in the propagation of sound and using a Lorentz-type transformation, the equation governing the acoustics is reduced to the Helmholtz equation with a modified source term. The simplified problem is recast in integral form and solved using compact Green's function method. This approach assumes that the acoustic wavelength is large compared to the profile chord and spacing, while no restrictions are made on the entropy wavelengths. The aerofoil thickness, camber and angle of attack are restricted such that the steady flow is a small perturbation to a uniform flow. For a symmetric profile, it is found that the main contribution to the radiated sound arises from the deceleration of the flow at the stagnation point of the leading-edge.

Johnson HG, Morgans AS, 2017, Optimising the acoustics of short circular holes with mean flow, 24th International Congress on Sound and Vibration 2017 (ICSV 24)

Short circular holes with a high Reynolds mean flow passing through them are a common occurrence in applications such as Helmholtz resonators, perforated plates or liners and fuel injectors. The acoustic response of such holes has been shown to be strongly dependent on the path followed by the vorticity which is shed at the hole inlet and convected downstream to form a vortex sheet. Coupling between this vorticity and the acoustic waves has the potential either to absorb or to generate acoustic energy in the low frequency region. A semi-analytical model based on Green's function method (The acoustics of short circular holes opening to confined and unconfined spaces, Yang & Morgans, Journal of Sound and Vibration, 2017) is combined with a gradient-based optimisation technique to determine the optimal vortex sheet shapes for absorption or amplification of noise. As the shape of the vortex sheet depends directly on the geometry of the hole inlet, finding the optimal shape provides information on the geometry required to achieve the desired acoustic effect.

Li J, Morgans AS, 2017, Analytical solutions of the one-dimensional acoustic waves in a duct, 24th International Congress on Sound and Vibration 2017 (ICSV 24)

Wave-based models for one-dimensional duct acoustics are widely used in thermoacoustic network models. However, they currently assume a constant mean temperature and mean flow within each duct module, while in practice many ducts of relevance sustain a significant axial temperature gradient or mean flow gradient. This paper presents an analytical solution for the one-dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow. A wave equation for the pressure perturbation is derived which relies on very few assumptions. An analytical solution for this is derived using an adapted WKB approximation. The proposed solution is applied to ducts with a mean temperature profile which varies axially with (i) a linear and (ii) a partial sine wave profile. The analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate-to-high subsonic Mach numbers. It always performs well when the frequency exceeds a certain value; when the mean temperature profile is linear, it also performs well to very low frequencies. This increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner, axially segmenting the temperature profile into regions that can be approximated as linear. The acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied: |k0| > |α|, where k0 is the local wave number when there is no mean flow and α is the normalised mean density gradient.

Sogaro F, Schmid P, Morgans AS, 2017, Sensitivity analysis of thermoacoustic instabilities, 24th International Congress on Sound and Vibration 2017 (ICSV 24)

Thermoacoustic instability is a phenomenon that occurs in numerous combustion systems, from rockets to land based gas turbines. The resulting acoustic oscillations can result in severe vibrations, thrust oscillations, thermal stresses and mechanical loads that lead to fatigue or even failure. This propensity to instability has been found to occur much more frequently in lean premixed combustion, one of the recent methods used in the gas turbine industry of aeroengines and power gas turbines to reduce NOx emissions. In this work we consider a simplified combustion system, and analyse the sensitivity of its thermoacoustic modes to small changes in the flame and combustor geometry parameters. Such a sensitivity analysis offers insights on how best to change the combustion system so as to "design-out" instability. The simplified combustor is modelled using a low order network representation: linear plane acoustic waves are combined with the appropriate acoustic boundary and flame jump conditions and a linear n-tau flame model. A sensitivity analysis is then performed using adjoint methods, with special focus on the sensitivity of the modes to parameters, such as reflection coefficients and flame model gain and time delay. The gradient information obtained reveals how the thermoacoustic modes of the system respond to changes to the various parameters. The results offer key insights into the behaviour and coupling of different types of modes - for example acoustic modes and so-called "intrinsic" modes associated with the flame model. They also provide insights into the optimal configuration for the design of such combustors.

Yang D, Morgans AS, Luciano E, et al., 2017, Vortex-sound interaction for an annular duct opening, International Congress on Sound and Vibration, Publisher: Curran Associates, Inc.

The sound associated with an annular duct opening is relevant to many engineering applications, such as the fuel injectors of gas turbine combustors or turbofan duct systems. In the absence of a mean flow, the annular duct opening reflects and transmits low frequency (plane) acoustic waves without significant acoustic energy loss. In the presence of a mean flow, however, energy conversion between acoustic waves and shed vorticity may be significant. In the present work, we use an analytical model based on the Green's function method to study the vortex-sound interaction for an annular duct opening, with a low Mach number mean flow inside the annular duct. An annular duct opening towards a coaxial annular duct upstream and a cylindrical duct downstream is considered, for cases both with and without mean flows. Comparisons with previous models and preliminary experimental measurements are provided.

Li J, Xia Y, Morgans AS,
et al., 2017, Numerical prediction of combustion instability limit cycle oscillations for a combustor with a long flame, *Combustion and Flame*, Vol: 185, Pages: 28-43, ISSN: 0010-2180

A coupled numerical approach is investigated for predicting combustion instability limit cycle characteristicswhen the combustor contains a long flame. The test case is the ORACLES combustor, with aturbulent premixed flame a metre long: it exhibits limit cycle oscillations at ∼ 50 Hz and normalisedvelocity amplitude ahead of the flame of ∼ 0.29. The approach obtains the flame response to acousticexcitation using Large Eddy Simulations (LES), and couples this with a low-order wave-based networkrepresentation for the acoustic waves within the combustor. The flame cannot be treated as acousticallycompact; the spatial distribution of both its response and the subsequent effect on the acoustics mustbe accounted for. The long flame is uniformly segmented axially, each segment being much shorter thanthe flow wavelengths at play. A series of “local” flame describing functions, one for the heat release rateresponse 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 approximationfor the flow-field and combustion modelled using the Partially Stirred Reactor model with a global onestepreaction mechanism. For coupling with the low-order acoustic network modelling, compact acousticjump 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 withthose predicted using the continuous 1-D linearised Euler equations, validating the flame segmentationimplementation. Limit cycle predictions (frequency 51.6 Hz and amplitude 0.38) also agree well with experimentalmeasurements, validating the low-order coupled method as a prediction tool for combustorswith long flames. A sensitivity analysis shows that the predicted limit cycle amplitude decreases rapidlywhen acoustic losses at boundaries are accounted for, and inc

XIA Y, Morgans AS, Jones WP, et al., 2017, Predicting thermoacoustic instability in an industrial gas turbine combustor: combining a low-order network model with flame LES, ASME TURBO EXPO 2017, Publisher: ASME

The thermoacoustic modes of a full scale industrial gas turbine combustor have been predicted numerically. The predictive approach combines low order network modelling of the acoustic waves in a simplified geometry, with a weakly nonlinear flame describing function, obtained from incompressible large eddy simulations of the flame region under upstream forced velocity perturbations, incorporating reduced chemistry mechanisms. Two incompressible solvers, each employing different numbers of reduced chemistry mechanism steps, are used to simulate the turbulent reacting flowfield to predict the flame describing functions. The predictions differ slightly between reduced chemistry approximations, indicating the need for more involved chemistry. These are then incorporated into a low order thermoacoustic solver to predict thermoacoustic modes. For the combustor operating at two different pressures, most thermoacoustic modes are predicted to be stable, in agreement with the experiments. The predicted modal frequencies are in good agreement with the measurements, although some mismatches in the predicted modal growth rates and hence modal stabilities are observed. Overall, these findings lend confidence in this coupled approach for real industrial gas turbine combustors.

Yang D, Morgans A, 2017, The acoustics of cooled Helmholtz resonators, *AIAA Journal*, Vol: 55, Pages: 3120-3127, ISSN: 1533-385X

Helmholtz resonators (HRs) are commonly used to damp thermoacous-tic oscillations in aero-engine and gas turbine combustors. In practice theHR is often maintained at a cooler temperature than the combustor, butthis tends to be neglected when modelling. In this work, we derive ananalytical model for both the acoustic damping and the effect on the com-bustor thermoacoustics of HRs whose volume is at a different temperatureto the combustor. The energy conservation equation based on stagnationenthalpy, together with the mass and momentum conservation equations, isincorporated into a linear HR sound absorption model. These are coupledwith linear wave-based models for the plane acoustic waves in the systemto which the HR is attached – here a combustor. The temperature differ-ence is found to generate an entropy wave which advects downstream of theresonator (and may generate further acoustic waves if accelerated), and tochange the acoustic damping near the resonant frequency. This model forthe HR acoustics is then incorporated into a low-order network model forcombustor thermoacoustics. The importance of capturing the effect of theHR temperature difference on the overall thermoacoustic modes is clearlydemonstrated.

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