## Publications

151 results found

Nan J, Li J, Morgans AS,
et al., 2022, Theoretical analysis of sound propagation and entropy generation across a distributed steady heat source, *Journal of Sound and Vibration*, Vol: 536, Pages: 117170-117170, ISSN: 0022-460X

Acoustic and entropy waves interacting in a duct with a steady heat source and mean flow are analysed using an asymptotic expansion (AE) for low frequencies. The analytical AE solutions are obtained by taking advantage of flow invariants and applying a multi-step strategy. The proposed solutions provide first-order corrections to the compact model in the form of integrals of mean flow variables. An eigenvalue system is then built to predict the thermoacoustic modes of a duct containing a distributed heat source or sink. Predictions from the AE solutions agree well with the numerical results of the linearised Euler equations for both frequencies and growth rates, as long as the low-frequency condition is satisfied. The AE solutions are able to accurately reconstruct the acoustic and entropy waves and correct the significant errors in the predicted entropy wave associated with the compact model. The analysis illustrates that the thermoacoustic system needs to account for the entropy wave generated by the interaction of acoustic wave and the distributed steady heat source, especially when density- or entropy-dependent boundary conditions are prescribed at the duct ends. Furthermore, a combination of the AE method and the modified WKB approximation method is discussed for a cooling case. The AE solutions remedy the disadvantage of the WKB solution in the low and very low-frequency domain and facilitate full-frequency theoretical analyses of sound propagation and entropy generation in inhomogeneous duct flow fields.

Guzmán-Iñigo J, Yang D, Gaudron R,
et al., 2022, On the scattering of entropy waves at sudden area expansions, *Journal of Sound and Vibration*, Pages: 117261-117261, ISSN: 0022-460X

Ahmed D, Morgans AS, 2022, Nonlinear feedback control of bimodality in the wake of a three-dimensional bluff body, *Physical Review Fluids*, Vol: 7, Pages: 1-29, ISSN: 2469-990X

The turbulent wake behind a square-back Ahmed body in close proximity to the ground exhibits bimodal switching. This manifests as the center of the wake switching between one of two asymmetric positions, either horizontally or vertically. Switches occur over random timescales, with the wake recovering symmetry in the long time average. The present work employs wall-resolved large eddy simulations to investigate feedback control for suppressing horizontal (lateral) wake bimodality of a square-back Ahmed body at Reynolds number, ReH∼3.3×104 based on the body height. Base-mounted pressure sensors are used to estimate the position of the wake as an input signal for the controller, while actuation targets the near-wake region via synthetic jets emanating from a gap around the perimeter of the Ahmed body base. A nonlinear feedback controller based on a Langevin model of the wake dynamics is synthesized. This successfully suppresses the wake lateral bimodal switching. However, this switching is replaced by a time-periodic streamwise motion of the large coherent structure occupying the near-wake region, leading to amplification of the higher frequency dynamical wake modes. The action of feedback control also leads to base pressure recovery and a reduction in pressure drag. Upon varying the controller parameters, a trade-off between the degree of bimodality suppression and drag reduction is observed. A maximum drag reduction of 7.4% is achieved for a semisymmetrized wake, with a fully symmetrized wake achieving 2.5% reduction. Bimodality suppression is proposed to have an indirect link to drag reduction through the effect of the wake state on the separated free shear layers and the upstream boundary layers.

Hu X, Morgans AS, 2022, Attenuation of the unsteady loading on a high-rise building using feedback control, *Journal of Fluid Mechanics*, Vol: 944, ISSN: 0022-1120

The unsteady wind loading on high-rise buildings has the potential to influence stronglytheir structural performance in terms of serviceability, habitability and occupant comfort.This paper investigates numerically the flow structures around a canonical high-risebuilding immersed in an atmospheric boundary layer, using wall-resolved large eddysimulations. The switching between two vortex shedding modes is explored, and theinfluence of the atmospheric boundary layer on suppressing symmetric vortex sheddingis identified. It is shown that the antisymmetric vortex shedding mode is prevalent in thenear wake behind the building, with strong coherence between the periodic fluctuations ofthe building side force and the antisymmetric vortex shedding mode demonstrated. Twofeedback control strategies, exploiting this idea, are designed to alleviate the aerodynamicside-force fluctuations, using pressure sensing on just a single building wall. The sensorresponse to synthetic jet actuation along the two ‘leading edges’ of the building ischaracterised using system identification. Both the designed linear controller and the leastmean square adaptive controller attenuate successfully the side-force fluctuations whenimplemented in simulations. The linear controller exhibits a better performance, and itseffect on the flow field is to delay the formation of dominant vortices and increase theextent of the recirculation region. Feedback control that requires a smaller sensing area isthen explored, with a comparable control effect achieved in the attenuation of the unsteadyloading. This study could motivate future attempts to understand and control the unsteadyloading of a high-rise building exposed to oncoming wind variations.

Yang D, Guzmán-Iñigo J, Morgans AS, 2022, Sound generated by axisymmetric non-plane entropy waves passing through flow contractions, *International Journal of Aeroacoustics*, Pages: 1475472X2211073-1475472X2211073, ISSN: 1475-472X

For a single-component perfect gas, entropy perturbations are associated with the difference between the overall density fluctuation and that coming from the acoustic perturbation. Entropy perturbations can generate sound when accelerated/decelerated by a non-uniform flow and this is highly relevant to thermoacoustic instabilities for gas turbines and rocket engines, and to noise emission for aero-engines. Widely used theories to model this entropy-generated sound rely on quasi-1D assumptions for which questions of validity were raised recently from both numerical and experimental studies. In the present work, we build upon an acoustic analogy theory for this problem. This theory was initiated by Morfey (J. Sound Vib. 1973) and Ffowcs Williams and Howe (J. Fluid Mech. 1975) about 50 years ago and extended recently by Yang, Guzmán-Iñigo and Morgans (J. Fluid Mech. 2020) to study the effect of non-plane entropy waves at the inlet of a flow contraction on its sound generation. Comparisons against both numerical simulations and previous theory are performed to validate the results.

Gaudron R, Morgans AS, 2022, Thermoacoustic stability prediction using classification algorithms, *Data-Centric Engineering*, Vol: 3, ISSN: 2632-6736

Predicting the occurrence of thermoacoustic instabilities is of major interest in a variety of engineering applications such as aircraft propulsion, power generation, and industrial heating. Predictive methodologies based on a physical approach have been developed in the past decades, but have a moderate-to-high computational cost when exploring a large number of designs. In this study, the stability prediction capabilities and computational cost of four well-established classification algorithms—the K-Nearest Neighbors, Decision Tree (DT), Random Forest (RF), and Multilayer Perceptron (MLP) algorithms—are investigated. These algorithms are trained using an in-house physics-based low-order network model tool called OSCILOS. All four algorithms are able to predict which configurations are thermoacoustically unstable with a very high accuracy and a very low runtime. Furthermore, the frequency intervals containing unstable modes for a given configuration are also accurately predicted using multilabel classification. The RF algorithm correctly predicts the overall stability and finds all frequency intervals containing unstable modes for 99.6 and 98.3% of all configurations, respectively, which makes it the most accurate algorithm when a large number of training examples is available. For smaller training sets, the MLP algorithm becomes the most accurate algorithm. The DT algorithm is found to be slightly less accurate, but can be trained extremely quickly and runs about a million times faster than a traditional physics-based low-order network model tool. These findings could be used to devise a new generation of combustor optimization tools that would run much faster than existing codes while retaining a similar accuracy.

Yeddula SR, Guzmán-Iñigo J, Morgans AS, 2022, A solution for the quasi-one-dimensional linearised Euler equations with heat transfer, *Journal of Fluid Mechanics*, Vol: 936, ISSN: 0022-1120

The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three variables, namely the dimensionless mass, stagnation temperature and entropy fluctuations, which are invariants of the system at zero frequency and with no heat transfer. The resulting first-order system of differential equations is then solved using the Magnus expansion method, where the perturbation parameters are the normalised frequency and the volumetric heat transfer. In this work, a measure of the flow non-isentropicity (in this case the steady heat transfer) is used for the first time as an expansion parameter. The solution method was applied to a converging–diverging nozzle with constant heat transfer for both subcritical and supercritical flow cases, showing good agreement with numerical predictions. It was observed that the acoustic and entropy transfer functions of the nozzle strongly depend on the frequency and heat transfer.

Su J, Yang D, Morgans AS, 2022, Low-frequency acoustic radiation from a flanged circular pipe at an inclined angle, *The Journal of the Acoustical Society of America*, Vol: 151, Pages: 1142-1157, ISSN: 0001-4966

The generic problem of low-frequency acoustic radiation through quiescent air from a circular pipe that is inclined with respect to its exit flange is studied in this work. The exit flange is taken to extend as an infinite plane away from the pipe opening. The analysis implements a hybrid method that combines modal expansions with the boundary element method. The reflection coefficient and pipe end correction for Helmholtz numbers (based on the pipe radius) less than 2.5 are calculated for various inclination angles up to 75°. Calculations are validated using simulations from the finite-element solver of the commercial software package COMSOL. The reflection coefficient and end correction predictions agree closely with the validation simulations yet differ notably from the results available in the literature. The solution obtained from the hybrid method is subsequently used to analyse the acoustic field at the pipe exit and in the downstream space. The key aspects of the governing physics pertaining to practical engineering applications at low frequencies are captured in a low-order approximation, which significantly reduces the degrees of freedom of the problem and provides generally good estimates of the reflection coefficient and end correction, as well as the downstream acoustic field.

Surendran A, Na W, Boakes C,
et al., 2022, A low frequency model for the aeroacoustic scattering of cylindrical tube rows in cross-flow, *Journal of Sound and Vibration*, Vol: 527, Pages: 116806-116806, ISSN: 0022-460X

Heat exchanger tube rows can influence the thermoacoustic instability behaviour of combustion systems since they act as both acoustic scatterers and unsteady heat sinks. Therefore, with careful tuning of their thermoacoustic properties, heat exchangers have the potential to act as passive control devices. In this work, we focus on (only) the acoustic scattering behaviour of heat exchanger tubes. We present a comparison of existing acoustic models for tube rows and slits, models for the latter having the advantage of incorporating frequency dependence. We then propose a new model that enables the adaptation of slit models for tube rows. This model is validated against experiments and Linearised Navier–Stokes Equations (LNSE) predictions for the transmission and reflection coefficients, including phase information. The model predictions show very good agreement with the experimental and numerical validations, especially for low frequencies (Strouhal number , based on tube radius and excitation frequency), with mean differences less than 2% for the transmission coefficients (the reflection coefficient errors are somewhat larger since their magnitudes are very close to zero).

Yeddula SR, Gaudron R, Morgans AS, 2021, Acoustic absorption and generation in ducts of smoothly varying area sustaining a mean flow and a mean temperature gradient, *Journal of Sound and Vibration*, Vol: 515, ISSN: 0022-460X

In ducts with varying cross-sectional area and sustaining a subsonic non-isentropic mean flow, the axially varying flow conditions affect the acoustic energy balance of the system. This is significant in understanding and controlling thermo-acoustic phenomena, particularly in combustors. This work aims at quantifying the acoustic energy change in such configurations, using the acoustic absorption coefficient, . The acoustic response of the duct to acoustic forcing is determined using an analytical model, neglecting the effect of entropy fluctuations on the acoustic field, and subsequently, is estimated. The model predictions of are validated using a linearised Euler equations (LEEs) solver. The model was found to be accurate for Mach numbers below 0.25, provided the lower frequency limit set by the analytical solution is satisfied. For conically varying area ducts with linear mean temperature gradient, it was observed that showed very little dependence on frequency, and that the absolute value of tended to be maximised when the upstream boundary was anechoic rather than non-anechoic. More importantly, was also observed to show stronger dependence on the mean temperature gradient than area gradient variation for such configurations. Further parametric and optimisation studies for revealed a crucial finding that a positive mean temperature gradient, representing a heated duct caused acoustic energy absorption. Similarly, a negative mean temperature gradient, representing a cooled duct caused acoustic energy generation – a key result of this analysis. This behaviour was shown to be consistent with a simplified analysis of the acoustic energy balance. Based on this finding, a linearly proportional reduction in acoustic energy generation was achieved by changing the mean temperature gradient.

Guzman Inigo J, Duran I, Morgans AS, 2021, Scattering of entropy waves into sound by isolated aerofoils, *Journal of Fluid Mechanics*, Vol: 923, Pages: 1-38, ISSN: 0022-1120

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. Mean flow variations of velocity and density are accounted for in the source term, but are neglected in the sound propagation. 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 places no restrictions on the entropy wavelength, while assuming that the acoustic wavelength is large compared to the profile chord and spacing. The source term is further simplified by assuming that the steady flow is a small perturbation to a uniform flow. The model is illustrated using a symmetric aerofoil and its performance is assessed against numerical simulations of the compressible Euler equations. Good agreement is found for all the frequencies of validity of the theory and for all the range of subsonic Mach numbers. The solution for a symmetric aerofoil interacting with plane entropy waves corresponds to the combination of a dipole along the horizontal axis and a monopole. The dipole originates from the unsteady drag experienced by the aerofoil owing to the fluctuations of density and the monopole from the strong local acceleration of the flow at the leading edge. The monopole term becomes negligible for low Mach numbers.

Su J, Yang D, Morgans AS, 2021, Modelling of sound-vortex interaction for the flow through an annular aperture, *Journal of Sound and Vibration*, Vol: 509, Pages: 1-25, ISSN: 0022-460X

The acoustic characteristics of bluff-body burners play a critical role in the combustion stability for combustors using this type of burners. The acoustic modelling of an axisymmetric bluff-body burner entails properly capturing the sound-vortex interaction for the flow through the annular aperture of the burner. Such a problem pertaining to annular apertures can also be of relevance to other engineering applications, such as acoustic dampers or turbofan duct systems. The methodology of combining suitable acoustic Green’s functions with a vortex sheet model has been applied extensively in previous theoretical studies of the acoustic response of a short circular orifice with a mean flow passing through it. In this work, the Green’s function and vortex sheet model theory is generalised in order to efficiently predict the acoustic characteristics of thin annular apertures sustaining a mean flow, which effectively emulate the typical axisymmetric bluff-body burner configurations in realistic combustors. This requires the incorporation of multiple Kutta conditions for modelling the vortex shedding and multiple vortex sheets for modelling the interaction of the shed vorticity and the acoustics. A high-resolution compressible Large Eddy Simulation (LES) of a simplified representative geometry is performed for validation; the analytical prediction and numerical findings show very good agreement, and the LES further provides key insights into the speed with which vortical disturbances convect downstream.

Li J, Wang D, Morgans AS,
et al., 2021, Analytical solutions of acoustic field in annular combustion chambers with non-uniform cross-sectional surface area and mean flow, *Journal of Sound and Vibration*, Vol: 506, Pages: 1-12, ISSN: 0022-460X

Low-order acoustic network models, treating the complex combustor geometry as a network of simple geometry elements, are typically used to analyse circumferential combustion instabilities in annular combustion chambers. These elements are typically assumed to have uniform cross-sectional surface area and average radius so that the analytical solutions of the acoustic field within them can be directly obtained. However, this may lead to errors in the combustion instability analyses. The present work derives the analytical solutions of the acoustic field in annular combustion chambers with both varying cross-sectional surface area and average radius sustaining a mean flow. A wave equation for the pressure perturbation is firstly derived based on very few assumptions. Analytical solutions of the acoustic field are then derived based on a modified WKB approximation. These solutions are then validated by comparing them to results by numerically resolving the linearised Euler equations. Results show that accurate predictions can always be obtained for a smooth change of the cross-sectional surface area and small-to-moderate subsonic axial Mach numbers as long as the frequency is larger than a certain value.

Lim Z, Li J, Morgans AS, 2021, The effect of hydrogen enrichment on the forced response of CH4/H2/Air laminar flames, *International Journal of Hydrogen Energy*, Vol: 46, Pages: 23943-23953, ISSN: 0360-3199

Hesse F, Morgans AS, 2021, Simulation of wake bimodality behind squareback bluff-bodies using LES, *Computers & Fluids*, Vol: 223, Pages: 1-17, ISSN: 0045-7930

A large eddy simulation (LES) study of the flow around a 1/4 scale squareback Ahmed body at Re H = 33 , 333 is presented. The study consists of both wall-resolved (WRLES) and wall-modelled (WMLES) simu- lations, and investigates the bimodal switching of the wake between different horizontal positions. Within a non-dimensional time-window of 1050 convective flow units, both WRLES and WMLES simulations, for which only the near-wall region of the turbulent boundary layer is treated in a Reynolds-averaged sense, are able to capture horizontal (spanwise) shifts in the wake’s cross-stream orientation. Equilib- rium wall-models in the form of Spalding’s law and the log-law of the wall are successfully used. Once these wall-models are, however, applied to a very coarse near-wall WMLES mesh, in which a portion of the turbulent boundary layer’s outer region dynamics is treated in a Reynolds-averaged manner as well, large-scale horizontal shifts in the wake’s orientation are no longer detected. This suggests larger-scale flow structures found within the turbulent boundary layer’s outer domain are responsible for generat- ing the critical amount of flow intermittency needed to trigger a bimodal switching event. By looking at mean flow structures, instantaneous flow features and their associated turbulent kinetic energy (TKE) production, it becomes clear that the front separation bubbles just aft of the Ahmed body nose generate high levels of TKE through the shedding of large hairpin vortices. Only in the reference WRLES and (rela- tively) fine near-wall mesh WMLES simulations are these features present, exemplifying their importance in triggering a bimodal event. This motivates studies on the suppression of wake bimodality by acting upon the front separation bubbles.

Gaudron R, Yang D, Morgans A, 2021, Acoustic energy balance during the onset, growth and saturation of thermoacoustic instabilities, *Journal of Engineering for Gas Turbines and Power*, Vol: 143, Pages: 1-10, ISSN: 0742-4795

Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh's criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Delta and the cycle-to-cycle acoustic energy ratio lambda, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles (rest of the abstract in the article).

Yeddula SR, Morgans AS, 2021, A semi-analytical solution for acoustic wave propagation in varying area ducts with mean flow, *Journal of Sound and Vibration*, Vol: 492, Pages: 115770-115770, ISSN: 0022-460X

A semi-analytical solution is developed for the propagation of plane acoustic waves in a varying area duct, sustaining a 1-D mean flow with a temperature gradient. The mean flow can be non-isentropic, such that the axial variation of the flow area and temperature can be prescribed independently. The case of an isentropic mean flow, for which the flow area and mean temperature variation are linked, is discussed. A second order differential equation (ODE) for acoustic pressure is derived from the linearised Euler equations in the frequency domain, neglecting the communication between acoustic and entropy disturbances. This ODE has axially varying coefficients and is solved using an iterative WKB approximation method. The obtained wave-like solution is expressed as the superposition of downstream and upstream propagating plane wave amplitudes. The solution thus obtained is, at any location, a function of upstream thermodynamic and mean-flow properties and wave-number, and can be applied to ducts with arbitrarily varying area and temperature profiles. For validation of the model, two shapes of area variation with linear temperature gradient are considered, and the solution is further simplified to depend only on local spatial coordinate and inlet conditions. The semi-analytical solutions are valid at “high” frequencies, thus the frequencies considered must be both low enough for a predominantly one-dimensional acoustic field, and large enough for validity of the solutions. For each geometry, the analytical solution is presented along with the frequency range of its validity. The analytical predictions are compared to numerical solutions of the linearised Euler equations (LEEs), which can either account for or neglect the acoustic - entropy wave coupling; this further allows the coupling effect to be evaluated. Within the frequency ranges of their validity, the simplified semi-analytical solutions perform well up to flow Mach-numbers around 0.3. For inlet tem

MacLaren A, Morgans AS, Gaudron R, 2021, Oscilos brass - An open-source acoustic solver for brass instruments

The characteristic sound quality of brass wind instruments is determined by the frequency and amplitude distribution of their resonant modes. Each instrument has a unique spectral fingerprint, which depends primarily on the geometry of the bore cavity. The ability to predict accurately the modal frequencies of a given bore geometry is an essential component of ongoing brass-wind acoustics research, and of commercial instrument design and optimisation, but remains a nontrivial task. In this work, an existing thermoacoustic solver, OSCILOS, is repurposed to predict the modal frequencies of brass instruments. OSCILOS_brass incorporates new user-configurable boundary conditions from existing musical-acoustical models, and a powerful framework for describing bore geometry, both analytically and from measurements. Modal inharmonicity is determined from Equivalent Fundamental Pitch deviation. Close agreement with both measured input impedance spectra, and those calculated by existing techniques, is demonstrated for four bore profiles from published work. The code is open-source, lightweight, user-friendly, and written in MATLAB R2020a. Extensive documentation is provided by the accompanying technical report and user guide.

Yeddula SR, Morgans AS, 2021, The two-dimensional acoustic field in an annular duct with axially varying area, sustaining an isentropic mean flow

This paper develops an analytical solution for the two-dimensional (both axial and azimuthal variations of the perturbed flow) acoustic field in an annular duct whose cross-sectional area varies axially. The duct sustains an isentropic axial and azimuthal mean flow. For the first time, the effects of axial variations in both the mean radius and the width of the annular duct are accounted for. The mean flow is numerically resolved from the conservation equations for a perfect, inviscid gas in both the meridional and azimuthal directions of the annular duct. Mean flow variations in the radial direction are neglected. For linear flow perturbations in the axial and azimuthal directions, the linearized Euler equations are recast into a first-order system of differential equations and solved using the Magnus expansion. The analytical predictions are validated against numerical simulations of the linearized Euler equations. The model can capture the acoustic field accurately at low frequencies, at both low and high flow Mach numbers, even when the Magnus expansion is truncated to a limited number of terms.

Yang D, Guzman-Inigo J, Morgans AS, 2020, Sound generation by entropy perturbations passing through a sudden flow expansion, *Journal of Fluid Mechanics*, Vol: 905, ISSN: 0022-1120

Entropy perturbations generate sound when accelerated/decelerated by a non-uniform flow. Current analytical models provide a good prediction of this entropy noise when the flow cross-sectional area changes are gradual, as is the case for nozzle flows. However, they typically rely on quasi-1-D and isentropic assumptions, and their predictions differ significantly from experimental measurements when sudden area increases are involved. This work uses a theoretical approach to quantitatively identify the main mechanisms responsible for the mismatch. A new form of the acoustic analogy is derived in which the entropy-related source terms are systematically identified for the first time. The theory includes three-dimensional and non-isentropic effects. The approach is applied to the flow through a sudden area expansion, for which the large-scale flow separation creates a recirculation zone. The derived acoustic analogy is simplified for low Mach numbers and frequencies, and solved using a Green's function method. The results provide the first quantitative evidence that the presence and spatial extent of the recirculation zone, rather than the flow non-isentropicity, is the dominant factor causing deviation from predictions from quasi-1-D, isentropic theory.

Han X, Laera D, Yang D,
et al., 2020, Flame interactions in a stratified swirl burner: Flame stabilization, combustion instabilities and beating oscillations, *Combustion and Flame*, Vol: 212, Pages: 500-509, ISSN: 0010-2180

The present article investigates the interactions between the pilot and main flames in a novel stratified swirl burner using both experimental and numerical methods. Experiments are conducted in a test rig operating at atmospheric conditions. The system is equipped with the BASIS (Beihang Axial Swirler Independently-Stratified) burner fuelled with premixed methane-air mixtures. To illustrate the interactions between the pilot and main flames, three operating modes are studied, where the burner works with: (i) only the pilot flame, (ii) only the main flame, and (iii) the stratified flame (with both the pilot and main flames). We found that: (1) in the pilot flame mode, the flame changes from V-shape to M-shape when the main stage is switched from closed to supplying a pure air stream. Strong oscillations in the M-shape flame are found due to the dilution of the main air to the pilot methane flame. (2) In the main flame mode, the main flame is lifted off from the burner if the pilot stage is supplied with air. The temperature of the primary recirculation zone drops substantially and the unsteady heat release is intensified. (3) In the stratified flame mode, unique beating oscillations exhibiting dual closely-spaced frequencies in the pressure spectrum is found. This is observed within over narrow window of equivalence ratio combinations between the pilot and main stages. Detailed analysis of the experimental data shows that flame dynamics and thermoacoustic couplings at these two frequencies are similar to those of the unstable pilot flame and the attached main flame cases, respectively. Large Eddy Simulations (LESs) are carried out with OpenFOAM to understand the mechanisms of the time-averaged flame shapes in different operating modes. Finally, a simple acoustic analysis is proposed to understand the acoustic mode nature of the beating oscillations.

Li J, Morgans AS, Yang L, 2020, The three-dimensional acoustic field in cylindrical and annular ducts with an axially varying mean temperature, *Aerospace Science and Technology*, Vol: 99, Pages: 1-9, ISSN: 1270-9638

This paper presents analytical solutions for the three dimensional acoustic field in cylindrical and annular ducts with dependence of mean temperature on axial position. A wave equation for the pressure perturbation is constructed in cylindrical coordinates, applying a zero mean flow condition. Separation of variables is used to express the pressure perturbation as a product of functions which vary only axially, radially and circumferentially. The axial dependence of the mean temperature means that a general analytical solution for the axial second order ordinary differential equation (ODE) cannot be obtained. Variable transformation is applied, yielding a standard second order ODE with known solutions for linear and quadratic axial mean temperature dependence. The acoustic field and resonant frequencies for an annular duct with linear/quadratic axial mean temperature variation predicted using these solutions match perfectly with those calculated using the linearised Euler equations. The analytical solution for the linear mean temperature profile is applied 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 and resonant frequency are predicted very accurately even when very few axial segments are used.

Gaudron R, Yang D, Morgans AS, 2020, Acoustic energy balance during the onset, growth and saturation of thermoacoustic instabilities

Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh’s criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient ∆ and the cycle-to-cycle acoustic energy ratio λ, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles, 2) the acoustic energy transfers occurring at the combustor’s boundaries and 3) the sources and sinks of acoustic energy located within the combustor. The acoustic energy balance of the well-documented Palies burner is then analyzed during the onset, growth and saturation of thermoacoustic instabilities using this new methodology. It is demonstrated that this new approach allows a deeper understanding of the physical mechanisms

Han X, Laera D, Morgans AS,
et al., 2019, Inlet temperature driven supercritical bifurcation of combustion instabilities in a lean premixed prevaporized combustor, *Experimental Thermal and Fluid Science*, Vol: 109, ISSN: 0894-1777

The present article reports experimental observation and analyses of a supercritical bifurcation of combustion instabilities triggered by the air inlet temperature (). The studies are performed with a pressurised kerosene fuelled Lean Premixed Prevaporized (LPP) combustor operated under elevated temperature. Unlike some previous studies, starting from an unstable condition of the system, the amplitude of combustion instabilities suddenly decrease when exceeds a critical value of = 570 K. When the temperature is lowered back the system returns to being unstable without featuring any hysteresis behaviour, as expected in case of a supercritical bifurcation. The unstable flames feature a periodic axial motion of lift-off and re-ignition, characterized as Helmholtz mode. The phase difference between chemiluminescence and pressure signals is found to increase with , exceeding 90 degrees (out of phase) for temperatures higher than 570 K. A low order network framework is conducted, illustrating that when is increased a stability shift of this mode is predicted at near 570 K, in good agreement with the experimental observations. The impact of on the spray characteristics is also examined, finding that higher promotes fuel evaporation and reduces equivalence ratio fluctuation at the exit of the swirler.

Guzmán-Iñigo J, Yang D, Johnson HG,
et al., 2019, Sensitivity of the acoustics of short circular holes with bias flow to inlet edge geometries, *AIAA Journal*, Vol: 57, Pages: 4835-4844, ISSN: 0001-1452

Short circular holes with a mean bias flow passing through them can absorb or generate acoustic energy depending on frequency. A recently proposed semi-analytical model (Yang and Morgans, Journal of Sound and Vibration, Vol. 384, 2016 pp. 294–311) based on the Green’s function method successfully captured this acoustic absorption and generation. The model pointed to the importance of accurately capturing the path followed by the unsteady vorticity shed from the hole inlet edge. In the present work, the effect of the path of the shed vorticity on the hole acoustics is systematically studied. The above model is combined with computational fluid dynamics tools for capturing how the path of the shed vorticity varies for small modifications in the hole inlet edge shape. A chamfered edge, a rounded edge, and two elliptical edge cases are considered to show that a very small change to the shape of the hole inlet edge can give rise to significant differences in the hole acoustic response.

Sogaro FM, Schmid PJ, Morgans AS, 2019, Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities, *Journal of Fluid Mechanics*, Vol: 878, Pages: 190-220, ISSN: 0022-1120

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.

Yang D, Laera D, Morgans AS, 2019, A systematic study of nonlinear coupling of thermoacoustic modes in annular combustors, *Journal of Sound and Vibration*, Vol: 456, Pages: 137-161, 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, GUZMÁN-IÑIGO J, Morgans A, 2019, Sound generation by entropy perturbations passing through short circular holes, The 23rd International Congress on Acoustics

Xia Y, Laera D, Jones WP,
et al., 2019, Numerical prediction of the Flame Describing Function and thermoacoustic limit cycle for a pressurised gas turbine combustor, *Combustion Science and Technology*, Vol: 191, Pages: 979-1002, ISSN: 0010-2202

The forced flame responses in a pressurized gas turbine combustor are predicted using numerical reacting flow simulations. Two incompressible1 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.

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Gaudron R, Morgans AS, 2019, The acoustic absorption coefficient of short circular holes sustaining a high Reynolds number bias flow, 23rd International Congress on Acoustics (ICA 2019)

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