## Publications

140 results found

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

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.

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.

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.

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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- Citations: 19

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)

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, 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.

Gaudron R, Morgans AS, 2019, Acoustic absorption in a subsonic mean flow at a sudden cross section area change, 26th International Congress on Sound and Vibration (ICSV26)

Gaudron R, Morgans AS, 2019, Acoustic absorption in a subsonic mean flow at a sudden cross section area change

Acoustic waves propagating within a duct containing a subsonic mean flow are of interest in many practical applications such as aeroengines or gas turbines. In these systems, sudden cross section area increases where flow separation occurs are widespread and the acoustic energy balance is known to be affected for such conditions. On the other hand, sudden cross section area decreases are usually assumed to be isentropic and the acoustic energy balance is unaffected. The objective of this work is to determine the acoustic absorption coefficient for various models of sudden cross section area increase and decrease commonly implemented in low order network tools used for thermoacoustic stability prediction. Analytical expressions in the low Mach number limit are also provided and compared with numerical predictions. It is shown that for a sudden cross section area increase with flow separation, the acoustic absorption coefficient depends on the upstream Mach number, cross section area ratio and boundary acoustic reflection coefficient only. For certain values of these parameters, all of the acoustic energy is damped across the area change. On the other hand, the acoustic energy is amplified across the area change for other values of these parameters

Surendran A, Boakes C, Yang D, et al., 2019, Thermoacoustic response of heat exchanger tubes in future aero-propulsion engines

© Proceedings of the 26th International Congress on Sound and Vibration, ICSV 2019. All rights reserved. Cylindrical heat exchanger tubes can act as active or passive acoustic elements that influence the thermoacoustic stability of combustion systems. They can act as both unsteady heat sinks and acoustic dampers. The present work is motivated by heat exchangers in future aero-propulsion engines. One significant difference to heat exchanger tubes in domestic boiler systems is that rather than being tightly spaced, their spacing is likely to be of the same order as their diameter. The heat transfer behaviour can change depending on the tube spacing. The contributions of this work are twofold. Firstly, to build acoustic scattering models for heat sinks and simple area jump conditions, and secondly, to include them in 1D network models to study the influence of the spatial positioning of these models within the network. Preliminary results indicate that there is significant variation in the thermoacoustic behaviour if one were to consider an approximated model with a heat sink followed by an area jump, as compared to the one where an area jump is followed by a heat sink

Yeddula SR, Morgans AS, 2019, A semi-analytical solution for acoustic wave propagation in varying area ducts with mean flow, Pages: 5633-5640, ISSN: 2226-7808

A semi-analytical solution for the propagation of plane acoustic waves in a varying area duct, sustaining a mean isentropic flow with axial gas property gradients, is developed. A second order differential equation (ODE) for acoustic pressure is derived from the linearised Euler equations in the frequency domain, by neglecting the communication between acoustic and entropy disturbances. This ODE has axially varying coefficients and is solved using an adaptive WKB approximation method, so that the obtained wave-like solution consists of separate amplitude and phase factors, expressed as the superposition of downstream and upstream propagating wave components. This solution is valid at sufficiently large frequencies, meaning the frequencies considered must be low enough to ensure a predominantly one-dimensional acoustic field with negligible diffusive effects, but large enough for WKB method validity. A test case representing a typical industrial gas turbine combustor outlet converging section with a high mean-flow acceleration is considered for validation. Analytical results are compared to numerical solutions of linearised Euler equations neglecting acoustic-entropy coupling (2LEE). When the limiting frequency criteria are satisfied, the semi-analytical solution agrees well with the 2LEE results at even flow Mach-numbers around 0.5.

Boakes C, Surendran A, Yang D, et al., 2019, Acoustic scattering in arrays of orifices, slits and tube rows with mean flow: A comparison, Pages: 2126-2133, ISSN: 2226-7808

Thermoacoustic oscillations result from positive feedback between acoustic fluctuations and unsteady heat transfer into or out of the system. The thermoacoustic response of combustion system heat exchangers in cross flow is assumed to be dominated by two effects: acoustic scattering at the heat exchanger tube row and unsteady heat transfer from the tube row. While the latter causes a significant reduction in the net energy of the oscillations, the influence of both the effects on the acoustic fluctuations needs to be addressed carefully to predict the thermoacoustic response of the heat exchanger. To this end, we adopt a sequential approach where the acoustic scattering and the heat transfer are assumed to be independent of each other. In the present work, we focus on the acoustic scattering behaviour of heat exchanger tubes (only) by comparing existing acoustic models for orifices, slits and tube rows and identifying those operating regimes where the different models are valid and overlap. This will enable us to formulate appropriate acoustic models for the various operating regimes of the heat exchanger tube rows.

Na W, Boij S, Surendran A, et al., 2019, Prediction of acoustic response on tube-rows with bias-flow using linearized Navier-Stokes equations in frequency domain, Pages: 2134-2141, ISSN: 2226-7808

Heat exchangers are widely used in industries where heat needs to be transferred from one fluid to another fluid. For example, there are plate-fin heat exchangers in gas turbine engines, shell and tube heat exchangers in oil refineries and tube bundle heat exchangers in domestic boilers. Among the different types of exchangers, tube bundle exchangers are the most commonly used heat exchange equipments. In this paper, heat exchanger with the structure of tube rows with bias flow and possible acoustic interaction at the tube row is studied for the acoustic reflection and transmission. The numerical methodology solving the linearized Navier-Stokes equation in the frequency domain is used. It has the advantage of taking into account the flow effects, viscous losses as well as thermal losses in the acoustic propagation. The simplified geometry for the heat exchanger investigated in this paper is a two-dimensional rectangular duct with two half cylinders with a bias flow going through the gap between the cylinders. In the current study, the acoustic response is predicted numerically with the cold flow only and compared to the experimental data, as a preparation for the next study with the hot flow.

Surendran A, Boakes C, Yang D, et al., 2019, Thermoacoustic response of heat exchanger tubes in future aero-propulsion engines

Cylindrical heat exchanger tubes can act as active or passive acoustic elements that influence the thermoacoustic stability of combustion systems. They can act as both unsteady heat sinks and acoustic dampers. The present work is motivated by heat exchangers in future aero-propulsion engines. One significant difference to heat exchanger tubes in domestic boiler systems is that rather than being tightly spaced, their spacing is likely to be of the same order as their diameter. The heat transfer behaviour can change depending on the tube spacing. The contributions of this work are twofold. Firstly, to build acoustic scattering models for heat sinks and simple area jump conditions, and secondly, to include them in 1D network models to study the influence of the spatial positioning of these models within the network. Preliminary results indicate that there is significant variation in the thermoacoustic behaviour if one were to consider an approximated model with a heat sink followed by an area jump, as compared to the one where an area jump is followed by a heat sink

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

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