## Publications

165 results found

Guzmán-Iñigo J, Morgans AS, 2024, Designing the edges of holes (with bias flow) to maximise acoustic damping, *Journal of Sound and Vibration*, Vol: 575, ISSN: 0022-460X

Circular holes with a mean bias flow passing through them can amplify or damp acoustic energy and this property is relevant for many industrial applications. In this work, we propose a methodology to design the edges of such holes so that the acoustic damping is maximised. The approach relies on a Bayesian optimisation framework and is illustrated in a short circular hole with a mean laminar bias flow. The acoustic response of the perforation is characterised numerically using a two-step approach where, first, a steady mean flow is computed as the solution of the incompressible Navier–Stokes equations. Second, small-amplitude acoustic perturbations are superimposed on this mean flow and their dynamics are obtained as the solution of the linearised compressible Navier–Stokes equations. Both the upstream and downstream edges of the hole are modified with 45°chamfers. The sizes of these two chamfers are the control parameters optimised to maximise the acoustic absorption coefficient. The results of this letter show that the careful design of the edges can dramatically increase the acoustic energy that holes can damp: the hole investigated here goes from one generating 55% more acoustic energy than incident upon it at a given frequency to one that damps 46% of this acoustic energy.

Tian Y, Yang L, Morgans AS,
et al., 2023, On the flame transfer function models for laminar premixed conical and V- flames considering the stretch effect, *Combustion and Flame*, Vol: 258, ISSN: 0010-2180

This paper investigates a predictive model that considers the impact of stretch on the dynamic responseof laminar premixed conical and V- flames; the flame stretch consists of two components: the flamecurvature and flow strain. The steady and perturbed flame fronts are determined via the linearized Gequation associated with the flame stretch model. Parameter analyses of the effects of Markstein lengthL, flame radius R and unstretched flame aspect ratio β are also conducted. Results show that the flamestretch reduces the steady flame height, with this effect being more significant for larger Marksteinlengths and smaller flame sizes. The effects of flame stretch on perturbed flames are evaluated by comparing the flame transfer function (FTF) considering the flame stretch and not. For flames of differentsizes, the impact of flame stretch on FTF gain can be divided into three regions. When both β and Rare relatively small, due to the decrease in steady flame height and the impact of flow strain, the FTFgain increases. As β and R gradually increase, the FTF gain of the conical flame oscillates periodicallywhile the FTF gain of the V-flame decreases, primarily due to the flame curvature enhancing the flamefront disturbance and the wrinkle counteracting effect. When β and R are large, a disruption in wrinklecounteracting effect ensues, leading to a significant increase in FTF gain. Furthermore, as the actual flameheight is reduced, the flame stretch also reduces the FTF phase lag which is related to the disturbancepropagation time from the flame root to the tip.

Ahmed D, Morgans AS, 2023, Wake bi-modality: the effect of upstream boundary layer dynamics, *Journal of Fluid Mechanics*, Vol: 975, ISSN: 0022-1120

The turbulent wake past a square-back Ahmed body in close proximity to the ground experiences random side-to-side switching between two asymmetric positions, a phenomenon known as bi-modality. It has been observed to be sensitive to the dynamics of the upstream boundary layers formed along the body surfaces. Close to the body fore end, these separate and reattach, with hairpin vortices emanating from the reattachment points and growing along the surfaces before breaking down upstream of the base. This study uses wall-resolved large eddy simulations to investigate the effect of using suction to suppress these upstream boundary layer separations on the wake bi-modality. It is seen that, in the unforced flow (in the absence of suction), the smaller top and side surface vortices resulting from breakdown interact as they convect downstream. Steady suction is confirmed to suppress the boundary layer separations on the different body surfaces. When the boundary layer separations on the two side (vertical) surfaces are suppressed, it is found that horizontal bi-modality is completely inhibited with weak vertical asymmetry preserved. The interaction of the small top/side surface vortices is interrupted, damping boundary layer fluctuations just upstream of the base. Applying suction on different combinations of side/top/bottom boundary layer separations is found to have different effects on the underbody flow and the wake vertical balance, with bi-modality suppression dependent on side surface suction. This confirms that bi-modality is triggered, at least in part, by boundary layer disturbances on the surfaces perpendicular to the switching direction.

Hu X, Morgans A, 2023, Attenuation of the unsteady loading on a high-rise building using top-surface open-loop control, *Journal of Fluid Mechanics*, Vol: 968, Pages: 1-23, ISSN: 0022-1120

With the severity and frequency of significant weather events increasing, methods for alleviating unsteady wind loading for high-rise buildings are gaining interest. This study numerically investigates the three-dimensional flow structures around a canonical high-rise building immersed in an atmospheric boundary layer at different oncoming wind angles, using wall-resolved large eddy simulations. A synthetic jet located on the top surface is used as open-loop active actuation with the aim of suppressing the building's side-force fluctuations when exposed to oncoming wind variations. Three different frequencies of jet forcing are considered, all half an order of magnitude larger than the vortex shedding frequency. The behaviour of the synthetic jet and its effect on the building's unsteady side force, time-averaged flow fields and unsteady flow structures are investigated numerically. The synthetic jet actuation is found to reduce the side-force fluctuation of the building, enhance the downwash flow and successfully attenuate the antisymmetric vortex shedding. This was achieved to different extents across the range of oncoming wind angles considered and may motivate future attempts to explore experimental active control strategies for attenuation of unsteady wind loading.

Hesse F, Morgans AS, 2023, Characterization of the unsteady wake aerodynamics for an industry relevant road vehicle geometry using LES, *Flow, Turbulence and Combustion*, Vol: 110, Pages: 855-887, ISSN: 1386-6184

A wall-resolved large eddy simulation (WRLES) study of the flow around a 15% scale model of the Nissan NDP, an electric concept vehicle developed by Nissan, at ReH=100,000 is presented. First, wake asymmetries and the associated possibility of wake bimodality occurring are investigated by comparing the flow fields around “squareback” and cavity variants of the Nissan NDP. It is highlighted that there is no noteworthy long-term wake asymmetry in the spanwise direction for both configurations and that there is, instead, symmetric spanwise vortex shedding, as highlighted through the use of proper orthogonal decomposition (POD) post-processing. One can, therefore, exclude the existence of classical wake bimodality in the spanwise direction that has been observed for the Ahmed body. However, the wake does explore the vehicle’s rear space in the spanwise direction rapidly over non-dimensional time intervals of O(10). Meanwhile, there is a strong wake tilt in the vertical direction due to the presence of a ground, the vehicle geometry’s vertical asymmetry, and the detachment of a powerful hairpin vortex from the vehicle’s roof. When looking at POD of the flow field in a vertical plane, asymmetric vortex shedding, similar to that observed for the Ahmed body by Hesse and Morgans (2021) in the spanwise plane, is found. This suggests that wake bimodality in the vertical direction could occur for the Nissan NDP—the presented results are not conclusive, as the provided non-dimensional simulation duration of t∗∼60 is insufficient for the bimodal phenomenon that occurs at t∗∼1000. Additionally, the discernible impact of having a cavity at the rear of the NDP is to allow the wake to explore a larger vehicle base space (i.e. the wake is able to move more freely). This, coupled to a 5% reduction in rear base area, translates to a drag reduction compared to the “squareback” variant of 13.6%. Second, in a more qualit

Brokof P, Guzmán-Iñigo J, Morgans AS,
et al., 2023, Injection-coupling instabilities in the BKD combustor: acoustic analysis of the isolated injectors, *AIAA Journal*, Vol: 61, Pages: 2581-2590, ISSN: 0001-1452

Injection coupling is a well-known cause of high-frequency combustion instability in hydrogen/liquid oxygen (H2/LOX) rocket engines. This type of instability is commonly explained by the two-way coupling between the dynamics of the combustion chamber and the injection system. Recent experimental studies of the BKD combustor, however, suggest that the LOX injector could be self-excited and driving the acoustic mode of the combustion chamber. To assess the feasibility of this mechanism, here, we study both experimentally and theoretically the acoustic stability of the LOX injector isolated from the combustion chamber. The experimental study was performed in a water facility mimicking the conditions of a single LOX injector. The water injector was then modeled using an acoustic network analysis, where the transfer matrix of the LOX injector inlet orifice was computed numerically using a linear approach. The analysis successfully predicts the experimental peak in unsteady pressure, revealing that the LOX injector can be self-excited. The instability was found to be driven by the whistling of the orifice at the inlet of the injector coupled with the second longitudinal acoustic mode of the LOX post tube.

Brokof P, Guzmán-Iñigo J, Yang D,
et al., 2023, The acoustics of short circular holes with reattached bias flow, *Journal of Sound and Vibration*, Vol: 546, Pages: 1-17, ISSN: 0022-460X

One of the most important parameters influencing the acoustic response of holes that sustaina low-Mach-number bias flow is their length-to-diameter ratio. For sufficiently short holes, thebias flow is detached within the hole’s length, while in long holes the bias flow reattaches.The acoustic behaviour of each class is different and separate modelling approaches exist inthe literature. For many technical applications, however, the length-to-diameter ratio falls inthe range 1.5 < 𝐿ℎ∕𝐷ℎ < 3.0, where is not clear if the holes behave acoustically as short orlong holes. In this work, the acoustics of such medium holes are explored numerically andanalytically. The numerical approach is based on the linearisation of the compressible Navier–Stokes equations (LNSE) around a Reynolds-averaged mean flow. Medium holes are shown towhistle at higher Strouhal numbers than short holes although the mean flow reattaches withinthem. The underlying physics are further investigated by incorporating selected flow featuresof the LNSE results into a semi-analytical model accounting for vortex-sound interaction. It isshown that the perturbation field is determined by the three-way coupling of the two vortexsheets shed from the inlet and outlet edges of the hole with the acoustic field. Furthermore, themodelling of the growth of vorticity inside the hole is shown to be crucial to enable whistlingin the semi-analytical model.

Wang D, Nan J, Yang L,
et al., 2023, Analytical solutions for the acoustic field in thin annular combustion chambers with linear gradients of cross-sectional area and mean temperature, *Aerospace Science and Technology*, Vol: 132, Pages: 1-14, ISSN: 1270-9638

Predictions of thermoacoustic instabilities in annular combustors are essential but difficult. Axial variations of flow and thermal parameters increase the cost of numerical simulations and restrict the application of analytical solutions. This work aims to find approximate analytical solutions for the acoustic field in annular ducts with linear gradients of axially non-uniform cross-sectional area and mean temperature. These solutions can be applied in low-order acoustic network models and enhance the ability of analytical methods to solve thermoacoustic instability problems in real annular chambers. A modified WKB method is used to solve the wave equation for the acoustic field, and an analytical solution with a wide range of applications is derived. The derivation of the equations requires assumptions such as low Mach number, high frequency and small non-uniformity. Cases with arbitrary distributions of cross-sectional surface area and mean temperature can be solved by the piecewise method as long as the assumptions are satisfied along the entire chamber.

Duarte Nunes C, Morgans A, 2023, The acoustic response of hydrogen/ammonia flames, *Journal of Ammonia Energy*, Vol: 1, Pages: 33-45, ISSN: 2752-7735

Ammonia is a carbon-free fuel which could be used in gas turbines. Ammonia’s potential as a fuel can be improved when mixed with hydrogen. However, this could cause an increased propensity to thermoacoustic oscillations in the combustor. The acoustic response of hydrogen/ammonia flames was evaluated by calculating the flame transfer functions (FTFs). A local level set approach, combined with an incompressible velocity perturbation model, was used to calculate the flame front response to different frequencies of acoustic oscillations. The unsteady heat release rate was calculated from the flame front surface area, obtained by solving the G-equation, thereby calculating the gain and phase of the FTF. The unstretched flame speed, was obtained from experimental values and two chemical kinetic models: CRECK-NH3 and GRI-Mech3.0. The models’ accuracy was assessed by comparing the modelled to experimental values from literature. CRECK-NH3 was fitter for ammonia/hydrogen modelling, as it was always within 12% of experimental values, compared to GRI-Mech3.0 which always differed by over 35%. The FTFs suggested an increase in hydrogen enrichment led to an increase in the flame acoustic response, as the gain drop off occurred at a higher frequency with higher hydrogen content. The flame acts as a low-pass filter to acoustic waves and the bandwidth of this filter (the frequency at which the gain drops off) increases with hydrogen content. This was due to higher flame speeds with higher hydrogen content. These FTFs were also compared to those of hydrogen/methane flames and the non-linear response was briefly analysed.

Guzman-Inigo J, Yang D, Gaudron R,
et al., 2022, On the scattering of entropy waves at sudden area expansions, *Journal of Sound and Vibration*, Vol: 540, ISSN: 0022-460X

In this work, we investigate both numerically and theoretically the sound generated by entropy waves passing through sudden area expansions. This is a canonical configuration representing internal flows with flow separation and stagnation pressure losses. The numerical approach is based on a triple decomposition of the flow variables into a steady mean, a small-amplitude coherent part, and a stochastic turbulent part. The coherent part contains acoustic, vortical, and entropy waves. The mean flow is obtained as the solution of the Reynolds-Averaged Navier–Stokes (RANS) equations. The equations governing the coherent perturbations are linearised and solved in the frequency domain. To account for the effect of turbulence on the coherent perturbations, a frozen eddy viscosity model is employed. When entropy fluctuations pass through the area expansion, the generated entropy noise behaves as a low-pass filter. The numerical predictions of the noise at low frequencies are compared to the predictions of compact, quasi-one-dimensional, and isentropic theory and large discrepancies are observed. An alternative model for the generated entropy noise tailored for area expansions is then proposed. Such model is based on the conservation of mass, momentum, and energy written in integral form. The model assumes zero frequency and the one-dimensionality of the flow variables far upstream and downstream of the expansion. The predictions of this model agree well with the numerical simulations across a range of finite subsonic Mach numbers including low, intermediate, and high Mach numbers. The contributions of this work are both numerical and theoretical. Numerically, a triple decomposition adapted to high-Mach-number, compressible flows is introduced for the first time in the context of acoustic simulations. From a theoretical point of view, the quasi-steady model proposed here correctly captures the low-frequency entropy noise generated at sudden area expansions, including a

Gaudron R, Guzmán Iñigo J, Morgans AS, 2022, Variation of acoustic energy across sudden area expansions sustaining a subsonic flow, *AIAA Journal*, Vol: 61, Pages: 1-12, ISSN: 0001-1452

The acoustic energy balance of a sudden area expansion is known to be altered in the presence of a mean flow. In this work, Ronneberger’s quasi-steady model describing the acoustic response of a sudden area expansion sustaining a subsonic mean flow of arbitrary Mach number is revisited using the acoustic absorption coefficient, shown to be a function of the inlet Mach number Mu, cross-sectional area ratio θ, and upstream acoustic reflection coefficient Ru. These analytical predictions are tested using a two-step numerical strategy, whereby the mean flow variables are obtained using Reynolds-averaged Navier–Stokes simulations and the fluctuating variables are computed using in-house linearized Navier–Stokes equations solvers. The agreement between the analytical model and the numerical results is found to be excellent for all geometries, mean flows, and acoustic boundary conditions investigated. The generation of acoustic energy by the flow expansion is observed analytically and numerically for high-Mach-number flows undergoing a slight sudden area increase for given acoustic boundary conditions. Conversely, it is found that substantial acoustic energy damping occurs across sudden area expansions characterized by a wide range of parameters (Mu,θ,Ru). Moreover, entropy and vorticity fluctuations are found to be generated at the sudden area expansion, but entropy fluctuations are shown to have a negligible impact on the acoustic response of the area expansion at low and intermediate Mach numbers. Finally, the analytical model is found to be reasonably accurate up to Helmholtz numbers He∼0.05–0.1, corresponding to the frequency range of many industrial applications.

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.

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*, Vol: 21, Pages: 521-536, 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.

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).

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.

Hirschberg L, Guzman-Iñigo J, Aulitto A, et al., 2022, Linear Theory and Experiments for Laminar Bias Flow Impedance: Orifice Shape Effect

Axisymmetric orifices with neck diameter equal to the plate thickness have been investigated. The influence of orifice geometry on the transfer impedance in presence of bias flow was predicted for laminar-flow conditions by means of a compressible Linearized-Navier-Stokes-Equations model. The results are compared to those for an incompressible-flow model and to measurements of the transfer impedance. The effect of confinement on the transfer impedance appears to be negligible for the resistance. The effect of confinement on the inertance (or reactance) can be estimated by means of Fok’s classical result for thin orifices. The experimental results agree qualitatively with the predicted impedances. The Strouhal numbers for minima of the resistance are slightly higher than predicted. Negative minima indicating a whistling potentiality correspond to hydrodynamic modes of the orifice. The predicted inertance is at higher Strouhal numbers significantly larger than the measured one. The results indicate how whistling potentiality of a certain hydrodynamic mode can be promoted. The amplitude of the acoustical forcing was varied permitting to delimit the conditions under which the orifice response is linear. As the acoustic velocity amplitude approaches the steady flow velocity, the whistling potentiality of the orifices disappears.

Yeddula SR, Guzmán-Iñigo J, Morgans AS, et al., 2022, A Magnus-expansion-based model for the sound generated by non-plane entropy perturbations passing through nozzles

This paper presents an analytical model based on the Magnus-expansion method to predict the sound generated by the acceleration/deceleration of non-planar entropy perturbations in nozzles. Previous models assume that entropy perturbations reaching the inlet of the nozzle are one-dimensional, plane waves and remain plane inside the nozzle. However, studies of the convection of entropy waves throughout the combustor have confirmed that effects, such as shear dispersion and turbulent mixing, deform and attenuate the entropy perturbations as they propagate. It is thus very unlikely that entropy waves have a uniform distribution at the inlet and/or inside the nozzles but, instead, a more complex shape is expected. This alters the acoustic response significantly, particularly at higher frequencies. In this work, we adapt an existing model for entropy noise to account for non-plane effects at both the inlet and/or within the nozzle. To this end, we use the Magnus-expansion-based analytical model to solve the linearised form of the Euler equations of an inviscid, perfect, compressible gas flowing inside an isentropic nozzle. The three-dimensional entropy wave profile is sampled from numerical simulations across various frequencies. This profile is then fed to the model to capture the acoustic response. The model predictions of the nozzle’s acoustic transmission and reflection coefficients are successfully validated against numerical simulations across a wide range of frequencies.

Guzmán-Iñigo J, Morgans AS, 2022, Influence of the shape of a short circular hole with bias flow its acoustic response

Short circular holes with a mean bias flow passing through them can absorb or generate acoustic energy. This property is relevant for many industrial applications containing holes, such as liners or Helmholtz resonators. A recent theoretical study suggested that the acoustic response of such perforations could be strongly sensitive to small modifications of the geometry of their lips. In this work, we study this sensitivity numerically. To this end, we use a two-step approach, where a steady mean flow is computed first as the solution of the incompressible Reynolds-Averaged Navier-Stokes (RANS) equations. Small-amplitude acoustic perturbations are then superimposed on this mean flow and their dynamics are obtained as the solution of the linearised Navier-Stokes equations (LNSE) with frozen eddy viscosity. The approach is compared with experimental results for a straight hole (with sharp edges) and an excellent agreement is obtained. Two cases with modified edges are then investigated: (i) a hole with a chamfered upstream edge (sharp downstream edge) and (ii) the inverse configuration (chamfered dowstream edge). The chamfer at the upstream edge strongly modifies the acoustic response of the perforation over the range of frequencies investigated. The chamfer at the downstream edge, on the other hand, does not significantly alter it. This work confirms the sensitivity of the acoustic response of the holes to modifications of the upstream-edge geometries and proposes an efficient numerical tool that can be used to design bespoke geometries to leverage this property in industrial applications.

Yeddula SR, Guzmán-Iñigo J, Morgans AS, 2022, Effect of steady and unsteady heat interactions on the acoustic and entropy transfer functions of a nozzle

This paper presents an analytical framework to investigate the effect of both steady (mean) and unsteady (fluctuating) heat release rate on the acoustic response of a quasi-one-dimensional nozzle sustaining a mean flow. Previous models consider either steady or unsteady heat release separately, and established independently that these phenomena can significantly alter the acoustic response of the nozzles. In this work, we develop a new model to account for the effect of both steady and unsteady heat release rate with arbitrary spatial distribution. To this end, we propose a Magnus-expansion-based solution of a linearised form of the Euler equations for a perfect, compressible gas flowing inside such a non-isentropic nozzle. The solution requires an additional constraint that relates the fluctuating unsteady heat release with acoustic oscillations, i.e. a closure model. A simple linear flame transfer function (FTF) with constant gain and phase-lag was considered but the analysis can be extended to consider non-linear flame describing functions. The model predictions of the nozzle’s acoustic response is successfully validated against numerical solutions of the linearised Euler equations for different steady and unsteady heat release rate distributions inside the nozzle. It is observed that both steady and unsteady heat release rates significantly affect the unsteady nozzle response.

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).

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