© The Author(s), 2025. Published by Cambridge University Press.This paper presents an experimental application of reactive control to jet installation noise based on destructive interference. The work is motivated by the success of previous studies in applying this control approach to mixing layers (Sasaki et al. Theor. 2018b Comput. Fluid Dyn. 32, 765-788), boundary layers (Brito et al. 2021 Exp. Fluids 62, 1-13; Audiffred et al. 2023 Phys. Rev. Fluids 8, 073902), flow over a backward-facing step (Martini et al. 2022 J. Fluid Mech. 937, A19) and, more recently, to turbulent jets (Maia et al. 2021 Phys. Rev. Fluids 6, 123901; Maia et al. 2022 Phys. Rev. Fluids 7, 033903; Audiffred et al. 2024b J. Fluid Mech. 994, A15). We exploit the fact that jet-surface interaction noise is underpinned by wavepackets that can be modelled in a linear framework and develop a linear control strategy where piezoelectric actuators situated at the edge of a scattering surface are driven in real time by sensor measurements in the near field of the jet, the objective being to reduce noise radiated in the acoustic field. The control mechanism involves imposition of an anti-dipole at the trailing edge to cancel the scattering dipole that arises due to an incident wavepacket perturbation. We explore two different control strategies: (i) the inverse feed-forward approach, where causality is imposed by truncating the control kernel, and (ii) the Wiener-Hopf approach, where causality is optimally enforced in building the control kernel. We show that the Wiener-Hopf approach has better performance than that obtained using the truncated inverse feed-forward kernel. We also explore different positions of the near-field sensors and show that control performance is better for sensors installed for streamwise positions downstream in the jet plume, where the signature of hydrodynamic wavepacket is better captured by the sensors. Broadband noise reductions of up to 50 % are achieved.

© The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article,In a combined experimental and numerical effort, we investigate the generation and reduction of airfoil tonal noise. The means of noise control are streak generators in the form of cylindrical roughness elements. These elements are placed periodically along the span of the airfoil at the mid-chord streamwise position. Experiments are performed for a wide range of Reynolds numbers and angles of attack in a companion work (Alva et al., AIAA Aviation Forum, 2023). In the present work, we concentrate on numerical investigations for a further investigation of selected cases. We have performed wall-resolved large-eddy simulations for a NACA 0012 airfoil at zero angle of attack and Mach 0.3. Two Reynolds numbers (0.8 × 105 and 1.0 × 105) have been investigated, showing acoustic results consistent with experiments at the same Reynolds but lower Mach numbers. Roughness elements attenuate tones in the acoustic field and, for the higher Reynolds number, suppress them. Through Fourier decomposition and spectral proper orthogonal decomposition analysis of streamwise velocity data, dominating structures have been identified. Further, the coupling between the structures generated by the surface roughness and the instability modes (Kelvin–Helmholtz) of the shear layer has been identified through stability analysis, suggesting stabilisation mechanisms by which the sound generation by the airfoil is reduced by the roughness elements.

© The Author(s), 2025. Published by Cambridge University Press.We explore a reduced-order model (ROM) of plane Couette flow with a view to performing near-wall turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier–Stokes system onto a basis of controllability modes. Such ROMs were found to reproduce key aspects of turbulence dynamics in Couette flow with only a few hundred degrees of freedom, and here we use them to devise a control strategy. We consider a ROM with an extra forcing term whose structure is given by a combination of eigenfunctions of a linear viscous diffusion equation, optimised in order to minimise the total fluctuation energy. The optimisation is performed at Reynolds numbers Re = 1000, 2000, 3000, and produces a novel control mechanism wherein the optimal forcing leads the flow to laminarisation in all cases. The forcing acts by reducing the shear in a large portion of the channel, hindering the main energy input mechanism. The forced flow possesses a new laminar solution which is linearly stable at Re = 1000 and unstable at higher Re, but whose transient growth of streaky structures is substantially lower than that of laminar Couette flow, leading the flow to full laminarisation when the forcing is removed. Forcings optimised in the ROM are subsequently applied in direct numerical simulations (DNS). The same control mechanisms are observed in the DNS, where laminarisation is also achieved. We show that the ROMs provide an effective framework to design turbulence control strategies, despite the high degree of truncation, which opens up interesting possibilities for turbulence control.

© 2025 Acoustical Society of America.This study explores the use of parabolized stability equations (PSEs) for predicting sound propagation in ducts, a novel application in computational duct acoustics. The PSE, formulated in a general duct-fitted coordinate system, was validated against several test cases, including uniform flow, axial temperature gradients, and laminar/turbulent flows, demonstrating close agreement with existing literature. This paper highlights limitations of the PSE, particularly when the local Helmholtz number decreases, potentially causing mode cutoff, and suggests remedies for mitigating phase and amplitude errors. The efficiency of the PSE is further demonstrated through a comparison with linearized Euler equations for forward fan noise propagation in a turbofan inlet, showing 75.8% reduced computational time and 98.2% reduced memory usage. These computational advantages become more significant as problem size increases, with the PSE outperforming traditional finite element and parabolic approximation methods, especially in cases involving viscous shear flow effects. This makes the PSE particularly well-suited for applications such as boundary layer shielding and liner-boundary layer interactions. The study provides a promising avenue for future acoustic research and practical engineering applications, emphasizing the efficiency and accuracy of PSE in complex duct acoustics.

© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.This work aims to provide a more complete understanding of the resonance mechanisms that occur in turbulent jets at high subsonic Mach number, as shown by Towne et al. (J. Fluid Mech., vol. 825, 2017, pp. 1113-1152). Resonance was suggested by that study to exist between upstream- and downstream-travelling guided waves. Five possible resonance mechanisms were postulated, each involving different families of guided waves that reflect in the nozzle exit plane and at a number of downstream turning points. However, that study did not identify which of the five resonance mechanisms underpin the observed spectral peaks. In this work, the waves underpinning resonance are identified via a biorthogonal projection of Large Eddy Simulation data on eigenbases provided by a locally parallel linear stability analysis. Two of the five scenarios postulated by Towne et al. are thus confirmed to exist in the turbulent jet. The reflection-coefficients in the nozzle exit and turning-point planes are, furthermore, identified. Such information is required as input for simplified resonance-modelling strategies such as developed in Jordan et al. (J. Fluid Mech., vol. 853, 2018, pp. 333-358) for jet-edge resonance, and in Mancinelli et al. (Exp. Fluids, vol. 60, 2019, pp. 1-9) for supersonic screech.

© 2025 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.The Actuator Line Method (ALM) is a technique that replaces the detailed airfoil geometry with distributed body forces to predict the flow field. ALM has been widely employed for simulating rotating blade wakes due to its flexibility and accuracy in the far field. In this study, the applicability of ALM for unsteady aerodynamics and acoustic field prediction is evaluated. The case study considered is the harmonic transverse oscillation of a thin airfoil in uniform flow. The ALM body forces are distributed over a few grid points following a Gaussian function, with a range of smearing ratio of ε/c (smearing parameter over the chord length) between 0.4 and 1. These forces are computed using thin airfoil theory with the Prandtl-Glauert correction for compressible regime. Based on these computations, the compressible Navier-Stokes equations are numerically solved, yielding the velocity and pressure fields. ALM lift results are validated against unsteady aerodynamic theory in the subsonic regime. Moreover, results demonstrate an acoustic field consistent with a dipole distribution and a spectrum exhibiting a frequency corresponding to the plunging motion. Furthermore, the acoustic results are validated through an acoustic analogy approach, involving the prediction of the acoustic field via Green’s function. The prediction of the acoustic far-field using ALM is expected to significantly reduce the computational cost of compressible simulations applied to propeller and wind turbine aeroacoustics.

© The Author(s), 2024.Guided-jet waves have been shown to close resonance loops in a myriad of problems such as screech and impingement tones in jets. These discrete, upstream-travelling waves have long been identified in linear-stability models of jet flows, but in this work they are instead considered in the context of an acoustic-scattering problem. It is shown that the guided-jet mode results from total internal reflection and transmission of acoustic waves, arising from the shear layer behaving like a duct with some given wall impedance. After total reflection, only discrete streamwise wavenumbers may be supported by the flow, with these wavenumbers dictated by the fact that the standing wave formed inside of the jet must fit between the two shear layers. Close to the sonic line, the transmission of this mode to the outside is maximum, leading to a net-energy flux directed upstream, which dictates the direction of propagation of this mode, providing a clear connection to the better understood soft-duct mode (Towne et al., J. Fluid Mech., vol. 825, 2017, pp. 1113-1152). The model also indicates that these waves are generated in the core of the flow and can only be efficiently transmitted to the quiescent region under certain conditions, providing an explanation as to why screech is only observed at conditions where the discrete mode is supported by the flow. The present results explain, for the first time, the nature and characteristics of the guided-jet waves.

© The Author(s), 2024. Published by Cambridge University Press.We present an experimental study of reactive control of turbulent jets, in which we target axisymmetric coherent structures, known to play a key role in the generation of sound. We first consider a forced jet, in which coherent structures are amplified above background levels, facilitating their detection, estimation and control. We then consider the more challenging case of an unforced jet. The linear control targets coherent structures in the region just downstream of the nozzle exit plane, where linear models are known to be appropriate for description of the lowest-order azimuthal modes of the turbulence. The control law is constructed in frequency space, based on empirically determined transfer functions. And the Wiener–Hopf formalism is used to enforce causality and to provide an optimal controller, as opposed to the sub-optimal control laws provided by simpler wave-cancellation methods. Significant improvements are demonstrated in the control of both forced and unforced jets. In the former case, order-of-magnitude reductions are achieved; and in the latter, turbulence levels are reduced by up to 60 %. The results open new perspectives for the control of turbulent flow at high Reynolds number.

© The Author(s), under exclusive licence to Springer Nature B.V. 2023.A comparative study of the acoustic far-field radiation of a subsonic jet near a folded plate with an opening, intended to represent a flapped wing with thrust gate, is presented in this work. Three openings with different widths were used to evaluate experimentally the influence of the gaps in the far-field noise radiation, for two folding angles. Boundary Element Method simulations with a wavepacket model which represents the jet acoustic source are used to calculate the far-field noise. Numerical simulation results are compared with experimental measurements and show similar trends in terms of acoustic radiation. Through parametric simulations, it was also possible to estimate that opening widths greater than one jet diameter do not contribute significantly to reducing the far-field noise. The results show that even the smallest tested openings were able to reduce the far-field noise for the tested positions.

© The Author(s), 2024. Published by Cambridge University Press.The low-frequency modal and non-modal linear dynamics of an incompressible, pressure-gradient-induced turbulent separation bubble (TSB) are investigated, with the objective of studying the mechanism responsible for the low-frequency contraction and expansion (breathing) commonly observed in experimental studies. The configuration of interest is a TSB generated on a flat test surface by a succession of adverse and favourable pressure gradients. The base flow selected for the analysis is the average TSB from the direct numerical simulation of Coleman et al. (J. Fluid Mech., vol. 847, 2018, pp. 28-70). Global mode analysis reveals that the eigenmodes of the linear operator are damped for all frequencies and wavenumbers. Furthermore, the least damped eigenmode appears to occur at zero frequency and low, non-zero spanwise wavenumber when scaled with the separation length. Resolvent analysis is then employed to examine the forced dynamics of the flow. At low frequency, a region of low, non-zero spanwise wavenumber is also discernible, where the receptivity appears to be driven by the identified weakly damped global mode. The corresponding optimal energy gain is shown to have the shape of a first-order, low-pass filter with a cut-off frequency consistent with the low-frequency unsteadiness in TSBs. The results from resolvent analysis are compared to the unsteady experimental database of Le Floc'h et al. (J. Fluid Mech., vol. 902, 2020, A13) in a similar TSB flow. The alignment between the optimal response and the first spectral proper orthogonal decomposition mode computed from the experiments is shown to be close to, while the spanwise wavenumber of the optimal response is consistent with that of the low-frequency breathing motion captured experimentally. This indicates that the fluctuations observed experimentally at low frequency closely match the response computed from resolvent analysis. Based on these results, we propose that the forced dynamics of the flow, driven by the weakly damped global mode, serve as a plausible mechanism for the origin of the low-frequency breathing motion commonly observed in experimental studies of TSBs.

© 2024 American Physical Society.Most of the studies on pressure fluctuations in wall-bounded turbulent flows aim at obtaining statistics as power spectra and scaling laws, especially at the walls. In the present study we study energetic coherent pressure structures of turbulent channel flows, aiming at a characterization of dominant coherent structures throughout the channel. Coherent structures are detected using spectral proper orthogonal decomposition (SPOD) and modeled using resolvent analysis, similarly to related works dealing with velocity fluctuations but this time using pressure fluctuations as the output of interest. The resolvent operator was considered with and without the Cess eddy-viscosity model. Direct numerical simulations (DNSs) of incompressible turbulent channel flows at friction Reynolds numbers of approximately 180 and 550 were employed as databases in this study. Three representative dominant structures emerged from a preliminary spectral analysis: near-wall, large-scale, and spanwise-coherent structures. For frequency-wave number combinations corresponding to these three representative structures, SPOD results show a strong dominance of the leading mode, highlighting low-rank behavior of pressure fluctuations. The leading resolvent mode closely agrees with the first SPOD mode, providing support to studies that showed better performance of resolvent-based estimators when predicting pressure fluctuations compared to velocity fluctuations [Amaral, J. Fluid Mech. 927, A17 (2021)JFLSA70022-112010.1017/jfm.2021.764]. The dominant mechanisms of the analyzed modes are seen to be the generation of quasistreamwise vortices with pressure fluctuations appearing close to vortex centers. A study on the individual contributions of the nonlinear terms (treated as forcing in resolvent analysis) to the pressure output reveals that each forcing component plays a constructive role to the input-output formulation, which also helps understanding the weaker role of forcing "color"in driving pressure fluctuations.

© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.Abstract: We study generalised quasilinear (GQL) approximations applied to turbulent plane Couette flow. The GQL framework is explored in conjunction with a Galerkin reduced-order model (ROM) recently developed by Cavalieri and Nogueira (Phys Rev Fluids 7:102601, 2022), which considers controllability modes of the linearised Navier–Stokes system as basis functions, representing coherent structures in the flow. The velocity field is decomposed into two groups: one composed by high-controllability modes and the other by low-controllability modes. The former group is solved with the full nonlinear equations, whereas the equations for the latter are linearised. We also consider a new GQL framework wherein the linearised equations for the low-controllability modes are driven by nonlinear interactions of modes in the first group, which are characterised by large-scale coherent structures. It is shown that GQL-ROMs successfully recover the statistics of the full model with relatively high controllability thresholds and sparser nonlinear operators. Driven GQL-ROMs were found to converge more rapidly than standard GQL approximations, providing accurate description of the statistics with a larger number of linearised modes. This indicates that the forcing of linearised flow structures by large-scale coherent structures is an important feature of turbulence dynamics that should be considered in GQL models. The results presented here reveal that further model reductions are attainable with GQL-ROMs, which can be valuable to extend these models to larger Reynolds numbers. Graphical abstract: (Figure presented.)

© The Author(s), 2024. Published by Cambridge University Press.We study the stability of a zero-pressure gradient boundary layer subjected to free-stream disturbances by means of local stability analysis. The dataset under study corresponds to a direct numerical simulation (DNS) of a flat plate with a sharp leading edge in realistic wind tunnel conditions, with a turbulence level of 3.45 % at the leading edge. We present a method to track the convective evolution of the secondary instabilities of streaks by performing sequential stability calculations following the wave packet, connecting successive unstable eigenfunctions. A scattered nature, in time and space, of secondary instabilities is seen in the stability calculations. These instabilities can be detected before they reach finite amplitude in the DNS, preceding the nucleation of turbulent spots, and whose appearance is well correlated to the transition onset. This represents further evidence regarding the relevance of secondary instabilities of streaks in the bypass transition in realistic flow conditions. Consistent with the spatio-temporal nature of this problem, our approach allows us to integrate directly the local growth rates to obtain the spatial amplification ratio of the individual instabilities, where it is shown that instabilities reaching an -factor in the range [2.5,4] can be directly correlated to more than 65 % of the nucleation events. Interestingly, it is found that high amplification is not only attained by modes with high growth rates, but also by instabilities with sustained low growth rates for a long time.

© The Author(s), 2024. Published by Cambridge University Press.Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude free stream disturbances is investigated using direct numerical simulations. The flow is practically indistinguishable from clean inflow simulations in the literature for turbulence intensities at the leading edge of. At slightly higher turbulence intensities of, the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex (DSV). This phenomenon is considered in more detail by analysing its appearance in an ensemble of simulations comprising statistically independent realisations of the flow, thus proving its statistical relevance. In order to extract the transient dynamics of the vortex shedding, the classical proper orthogonal decomposition method is generalised to include time in the energy measure and applied to the time-resolved simulation data of incipient dynamic stall. Using this technique, the dominant transient spatiotemporally correlated features are distilled and the wave train of the vortex shedding prior to the emergence of the main DSV is reconstructed from the flow data exhibiting dynamics of large-scale coherent growth and decay within the turbulent boundary layer.

© The Author(s) 2024.Abstract: This study presents a physics-based, low-order model for the trailing edge (TE) noise generated by an airfoil at low angle of attack. The approach employs incompressible resolvent analysis of the mean flow to extract relevant spanwise-coherent structures in the transitional boundary layer and near wake. These structures are integrated into Curle’s solution to Lighthill’s acoustic analogy to obtain the scattered acoustic field. The model has the advantage of predicting surface pressure fluctuations from first principles, avoiding reliance on empirical models, but with a free amplitude set by simulation data. The model is evaluated for the transitional flow (Re=5e4) around a NACA0012 airfoil at 3 deg angle of attack, which features TE noise with multiple tones. The mean flow is obtained from a compressible large eddy simulation, and spectral proper orthogonal decomposition (SPOD) is employed to extract the main hydrodynamic and acoustic features of the flow. Comparisons between resolvent and SPOD demonstrate that the physics-based model accurately captures the leading coherent structures at the main tones’ frequencies, resulting in a good agreement of the reconstructed acoustic power with that of the SPOD (within 4 dB). Discrepancies are observed at high frequencies, likely linked to nonlinearities that are not considered in the resolvent analysis. The model’s directivity aligns well with the data at low Helmholtz numbers, but it fails at high frequencies where the back-scattered pressure plays a significant role in directivity. This modeling approach opens the way for efficient optimization of airfoil shapes in combination with low-fidelity mean flow solvers to reduce TE noise. Graphical abstract: (Figure presented.)

© The Author(s), 2024. Published by Cambridge University Press.Plane Couette flow at Reynolds number Re = 1200 (based on the channel half-height and half the velocity difference between the top and bottom plates) is investigated with a spatial domain designed to retain only two spanwise integral length scales. In this system, the computation of invariant solutions that are physically representative of the turbulent state has been understood to be challenging. To address this challenge, our approach is to employ an accurate reduced-order model with 600 degrees of freedom (Cavalieri & Nogueira, Phys. Rev. Fluids, vol. 7, 2022, L102601). Using the two-scale energy budget and the temporal cross-correlation of key observables, it is first demonstrated that the model contains most of the multi-scale physical processes identified recently (Doohan et al., J. Fluid Mech., vol. 913, 2021, A8); i.e. the large- and small-scale self-sustaining processes, the energy cascade for turbulent dissipation, and an energy-cascade mediated small-scale production mechanism. Invariant solutions of the reduced-order model are subsequently computed, including 96 equilibria and 43 periodic orbits. It is found that none of the computed equilibrium solutions are able to reproduce an accurate energy balance associated with the multi-scale dynamics of the turbulent state. Incorporation of unsteadiness into invariant solutions is seen to be essential for a sensible description of the multi-scale turbulent dynamics and the related energetics, at least in this type of flow, as periodic orbits with a sufficiently long period are mainly able to describe the complex spatio-temporal dynamics associated with the known multi-scale phenomena.

© 2024 Author(s).The widest spanwise scales in turbulent channel flows are studied through the use of three periodic channel-flow simulations at friction Reynolds number Re τ = 550 . The length and height of the channels are the same in all cases ( L x / h = 8 π and L y / h = 2 , respectively), while the width is progressively doubled: L z / h = { 4 π , 8 π , 16 π } . The effects of increasing the domain width cannot be determined with statistical significance in our simulations, since the difference in the statistics between the simulations is of the same order as the errors of convergence. A channel flow similar to the smaller one [Del Álamo et al., “Scaling of the energy spectra of turbulent channels,” J. Fluid Mech. 500, 135-144 (2004)], which was averaged over a very long time, was used as a reference. The one-dimensional spanwise spectrum of the streamwise velocity is computed with the aim of assessing the domain-size effect on the widest scales. Our results indicate that 90% of the total streamwise energetic fluctuations is recovered without a significant influence of the size of the domain. The remaining 10% of the energy reflects that the widest scales in the outer layer are the ones most significantly affected by the spanwise length of the domain. The power-spectral density for kz = 0 remains constant even if the size of the domain in the spanwise direction is increased up to four times the standard spanwise length, indicating that wide, spanwise coherent structures are not an artifact of domain truncation.

© The Author(s) 2023.Abstract: An adjoint-based method is presented for determining manufacturing tolerances for aerodynamic surfaces with natural laminar flow subjected to wavy excrescences. The growth of convective unstable disturbances is computed by solving Euler, boundary layer, and parabolized stability equations. The gradient of the kinetic energy of disturbances in the boundary layer (E) with respect to surface grid points is calculated by solving adjoints of the governing equations. The accuracy of approximations of ΔE, using gradients obtained from adjoint, is investigated for several waviness heights. It is also shown how second-order derivatives increase the accuracy of approximations of ΔE when surface deformations are large. Then, for specific flight conditions, using the steepest ascent and the sequential least squares programming methodologies, the waviness profile with minimum L2-norm that causes a specific increase in the maximum value of N- factor, ΔN, is found. Finally, numerical tests are performed using the NLF(2)-0415 airfoil to specify tolerance levels for ΔN up to 2.0 for different flight conditions. Most simulations are carried out for a Mach number and angle of attack equal to 0.5 and 1.25∘, respectively, and with Reynolds numbers between 9×106 and 15×106 and for waviness profiles with different ranges of wavelengths. Finally, some additional studies are presented for different angles of attack and Mach numbers to show their effects on the computed tolerances. Graphic abstract: (Figure presented.).

© The Author(s), 2024. Published by Cambridge University Press.Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free-stream turbulence are considered in the present work. Within an input–output model, where nonlinear terms of the incompressible Navier–Stokes equations are treated as an external forcing, we manage to separate inputs related to perturbations coming through the intake of the numerical domain, whose evolution represents a linear mechanism, and the volumetric nonlinear forcing due to triadic interactions. With these, we perform the full reconstruction of the statistics of the flow, as measured in the simulations, to quantify pairs of wavenumbers and frequencies more affected by either linear or nonlinear receptivity mechanisms. Inside the boundary layer, different wavenumbers at near-zero frequency reveal streaky structures. Those that are amplified predominantly via linear interactions with the incoming vorticity occur upstream and display transient growth, while those generated by the nonlinear forcing are the most energetic and appear in more downstream positions. The latter feature vortices growing proportionally to the laminar boundary layer thickness, along with a velocity profile that agrees with the optimal amplification obtained by linear transient growth theory. The numerical approach presented is general and could potentially be extended to any simulation for which receptivity to incoming perturbations needs to be assessed.

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We aim to reduce the noise emitted by high-speed turbulent jets using recently developed resolvent-based estimation and control tools. Our approach relies on detecting noise-generating wavepackets and canceling them via actuation. This paper reports on our progress toward this objective in the form of (i) implementation and validation of these resolvent-based tools in a large-scale CFD solver and (ii) preliminary estimation results for a subsonic jet. We validate our implementation via comparisons to the literature for a laminar channel flow, the acoustic response to a monopole forcing in a freestream, a trailing-line vortex problem, an airfoil wake, and resolvent modes for a jet. The preliminary estimation study for the subsonic jet shows that operator-based and data-driven versions of the methods yield similar estimation kernels and results. Future work will focus on extending this study to a series of supersonic jets and systematically exploring the selection and placement of sensors, actuators, and targets to mitigate noise-generating wavepackets most effectively

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We present the results from a physics-based model of the trailing-edge (TE) noise radiated by an airfoil, obtained from resolvent analysis of the turbulent mean flow. In our approach, the acoustic model input is reduced to the optimal coherent structures identified by the resolvent. This method has the advantage of isolating the main mechanisms generating noise in the turbulent flow and, unlike empirical models, is applicable to a wide variety of cases. We investigate a NACA0012 airfoil at 3 deg angle of attack, equipped with a zigzag trip to trigger a turbulent boundary layer, which results in broadband TE noise. The analysis is based on a large eddy simulation (LES) for a chord-based Reynolds number Re = 2.105 . The time-averaged flow is used to construct the linear operator underlying resolvent analysis, and a spectral proper orthogonal decomposition (SPOD) of the snapshots is used to extract the main hydrodynamic and acoustic features of the flow, used as a reference for the resolvent model. The results demonstrate that the resolvent-based model can accurately reproduce both the coherent structures associated with TE noise and the directivity of the radiated sound field when low-rank dynamics are identified with SPOD. Although the region of low-rank dynamics corresponds to the peak of acoustic power, a significant portion of the spectrum is associated with high-rank dynamics, which we do not attempt to model here. Nevertheless, the resolvent model identifies a wavepacket on the suction side of the trailing edge as the main driver of TE noise, and allows us to investigate spanwise wavenumbers which are not resolved in the LES.

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The dynamics of wavepackets in an elliptical jets are studied using direct numerical simulation (DNS) data of an AR = 2 incompressible elliptical jet at Reynolds number Re = 400. Analysis of the numerical data displays several complex features, the most striking being axis switching, a phenomenon that strongly affects the development of coherent structures in the flow. By applying spectral proper orthogonal decomposition (SPOD), it was found that modes in the SA symmetry were dominated by the Se1 flapping geometry in the upstream region. After the axis-switching point, the mode structure becomes more complex and multi-modal at mid-frequencies, while the mode structure remains largely unchanged for very low frequencies. Linear parabolised stability equations (PSE) are also used to evaluate the development of the different Kelvin-Helmholtz wavepackets in this elliptical jet showing excellent agreement with the SPOD modes.

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Upstream-travelling guided jet waves have been shown to be one of the key elements in many resonance processes underpinned in high-speed jets. Despite its importance, many of its characteristics, including how these waves are generated and how it can travel subsonically, have not been detailed in the literature. In this work, we aim to provide a clarification about the dynamics of this mode. With the aid of an acoustic scattering formulation, we are able to show that the guided-jet mode results from total-internal-reflection and transmission to decaying waves, arising from the shear layer behaving like a hard duct. After total reflection, only discrete streamwise wavenumbers may be supported by the flow, with these wavenumbers dictated by the fact that the standing wave formed inside of the jet must fit between the two shear layers. Close to the sonic line, the transmission of this mode to the outside is maximum, leading to a net-energy flux directed upstream, which dictates the direction of propagation of this mode in the eigenspectrum, providing a clear connection to the better understood soft-duct mode.

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The present paper is a follow up of a previous study on the effect of streaky-generating cylindrical tabs located on the inner surface of a round nozzle on jet aeroacoustics (Amaral et al., AIAA AVIATION 2023 Forum, p. 4516, 2023). The aim is to identify coherent structures through stereoscopic particle image velocimetry (stereo PIV) measurements obtained in crossstream planes parallel to the jet nozzle exit. As the tabbed nozzle has L-fold symmetry, Floquet exponents are used to perform Fourier decomposition in the azimuthal direction. Spectral proper orthogonal decomposition (SPOD) is employed to extract coherent structures. Comparison of the structures obtained for nozzles with and without tabs show the strong enhancement of streaks produced by the tabbed nozzle.

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.In the last few years, flow control has become increasingly important for the aeronautical field, since it is seen as a promising tool to design safer and more efficient aircraft. In this regard, noise emission is still a major concern in the aviation industry. Specifically, for the under-wing configuration currently adopted in civil aircraft. When the jet interacts with a nearby surface, such as the wing, hydrodynamic structures are scattered into the acoustic field, drastically increasing the emitted noise. Within this context, a feed-forward control scheme is considered for the attenuation of jet installation noise in the far field. Since non-causality is observed in several flow control problems solved in the frequency domain, we compare a wave-cancelling approach, where causality is imposed via the truncation of the control kernel, to the Wiener-Hopf approach, where the causality constraint is imposed a priori. The latter provides an optimal causal solution, and with this, prevents the drop in performance that may be observed in flow control applications that use a truncated solution. The results presented here show a significantly better performance of the Wiener-Hopf method with respect to that of a truncated Kernel, where the control was performed based on microphones measurements, which provided the axisymmetric mode in the near field of the jet as the input signal for the controller. An attenuation of up to 5dB of the broadband spectral hump related to installation effects is obtained.

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Coherence decay has been understood to be a key quantity to predict acoustic noise emitted by wavepackets in subsonic turbulent jets. Frequency-domain frameworks such as input-output and resolvent analyses are able to predict accurately the spatial structure of wavepackets turbulent flows compared to coherent structures educed from simulation data (as for example identified using spectral proper orthogonal, SPOD). However, at least at reduced-order, they are unable to capture two-point statistics such as coherence. A missing piece is the modelling of variability induced by the turbulence, which jitters (disorganises) the coherent structures and leads to stronger noise radiation. The aim of the present study is to consider the impact of turbulence on jet wavepackets through stochastic modelling under location uncertainty. This framework considers the conservation of mass and momentum of fluid parcels submitted to a stochastic transport, representing here the effect of turbulence. By linearising the resulting generalised stochastic Navier–Stokes equations and expressing it in the Fourier domain, a stochastic linear model (SLM) is obtained. We explore in this paper that ability of SLM to predict the two point coherence of the wavepackets in turbulent jets, and show its impact on acoustic emissions.

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.A current area of interest within jet noise is the installed-jet configuration, being a representation of interactions between the aircraft exhaust and the wing. This work considers a previously presented dataset (Amaral et al. AIAA paper 2023-3830) where a simplified configuration involving a round jet and a rectangular plate was studied, and explores the different tonal regimes that are observed across jet Mach number and plate radial offset (R/D) for constant plate axial offset and angle. These are, broadband, transitional, linear frequency-selection (LFS), LFS with non-linearities, and non-linear frequency-selection (NLFS). Results also suggested a transition from LFS to NLFS tone as R/D is decreased, and that for the case of NLFS, triadic interactions between two frequencies may produce all other tones within the spectrum.

© 2024, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The aim of present work is to investigate trailing-edge noise generation mechanisms to improve prediction tools and control strategies. We focus on a NACA 0012 airfoil at 3 degrees angle of attack with zigzag tripping elements close to the leading edge to generate a turbulent boundary layer. A compressible implicit large eddy simulation (LES), using the open-source high-order numerical framework PyFR, is performed for collecting data for our analysis. For comparison, we use data from an experimental campaign performed in parallel at the facility in TU Berlin. The comparison of velocity and sound pressure statistics shows good agreement between simulations and experiments. Further, spectral proper orthogonal decomposition (SPOD) is applied to the LES dataset to investigate dominant feature of the turbulent boundary layer and its relation to sound radiation. SPOD analysis is applied to different spanwise wavenumbers in order to understand their contribution to noise generation. Leading SPOD modes for the first spanwise wavenumbers, which dominate acoustic radiation, are shown to correspond to wavepackets. The contribution of such coherent structures in the radiated sound field is examined, clarifying their contribution to trailing-edge noise for a wide range of frequencies.

© TSFP 2024.All rights reserved.The low-frequency receptivity of an incompressible, pressure-gradient-induced turbulent separation bubble (TSB) is investigated with the aim of studying the mechanism responsible for the low-frequency unsteadiness commonly observed in experimental studies. The investigated flow consists of a TSB generated on a flat plate by means of adverse and favorable pressure gradients. The direct numerical simulation of Coleman et al. (2018) is used for the linear analysis and compared to the unsteady flow database of Le Floc’h et al. (2018, 2020). Resolvent analysis (RA) reveals receptivity to external forcing at low frequency and low, non-zero spanwise wavenumber. This low-frequency receptivity can be related to the experimentally observed low-frequency “breathing” of the bubble through the alignment metric, which exceeds 94 %. Finally, the strong similarities between the least stable mode of the global linear stability analysis and the optimal response of RA suggests that the low-frequency breathing motion might be caused by a modal mechanism, driven by this weakly damped global mode.

© TSFP 2024.All rights reserved.We present the results of a physics-based model of the trailing-edge noise radiated by a NACA0012 airfoil at low angle of attack, obtained from resolvent analysis of the turbulent mean flow. Most aeroacoustic models require turbulent spectra of surface pressure fluctuations to reconstruct the acoustic field, which are often derived from empirical models. In our approach, the acoustic model input is reduced to the optimal coherent structures identified by the resolvent. This method has the advantage of isolating the main mechanisms generating noise in the turbulent flow and, unlike empirical models, is applicable to a wide variety of cases. The model is evaluated for two different configurations: (i) an airfoil with a smooth surface at transitional Reynolds number (Re = 5.104), resulting in tonal noise; and (ii) the same airfoil with a zigzag trip near the leading edge at higher Reynolds number (Re = 2.105), resulting in broadband noise. Large eddy simulations (LES) were performed for both cases to obtain the mean flow, which is used to construct the linear operator underlying the resolvent analysis. A spectral proper orthogonal decomposition (SPOD) of the LES snapshots was used to extract the main hydrodynamic and acoustic features of the flow, which served as a reference for the physics-based model. Results for the tonal case show an excellent agreement between the resolvent and the SPOD modes at the frequency of the main tones in terms of dominant coherent structures and acoustic directivity. For the broadband case, a good agreement is also obtained for St < 10, where low-rank dynamics are identified by the SPOD. This match is improved when considering a simple model of eddy viscosity in the resolvent, and even small changes to the mode shapes have a visible influence on the acoustic directivity. This suggests that a resolvent-based model could be a valuable tool in optimisation methods for the control of trailing-edge noise.

© 2023 American Physical Society.A resolvent-based methodology is employed to obtain spatiotemporal estimates of turbulent pipe flow from probe measurements of wall shear-stress fluctuations. Direct numerical simulations (DNSs) and large-eddy simulations (LESs) of turbulent pipe flow at a friction Reynolds number of 550 are used as databases. We consider a DNS database as the true spatiotemporal flow field, from which wall shear-stress fluctuations are extracted and considered as measurements. A resolvent-based estimator is built following our earlier work [Amaral, J. Fluid Mech. 927, A17 (2021)0022-112010.1017/jfm.2021.764], requiring a model for the nonlinear (or forcing) terms of the Navier-Stokes equations system, which are obtained from another DNS database, as in our earlier work, and from a series of computationally cheaper LES databases with coarser grids; the underlying idea is that LESs may provide accurate statistics of nonlinear terms related to large-scale structures at a low computational cost. Comparisons between the DNS and the estimates indicate that sufficiently accurate results can be achieved with estimators built with statistics from LESs with an order of magnitude fewer grid points than the DNSs, with estimates closely matching the reference DNS results up to the buffer layer and reasonable agreement up to the beginning of the log layer.

© 2023 American Physical Society.Reactive flow control has been shown to be a promising tool to improve, among other aspects, the aerodynamic characteristics of an aircraft. This paper focuses on the use of reactive flow control to attenuate Tollmien-Schlichting (TS) waves over a wing profile. TS waves are an instability mechanism that is one of the first stages of boundary layer transition to turbulence. The Wiener-Hopf technique was used in this work for the experimental boundary layer control. The approach improves previous wave-cancellation techniques that, by constructing control kernels in the frequency domain, lead to control kernels with a noncausal part, i.e., actuation would need future sensor information to be constructed. In practical applications, it is unfeasible to access this type of information. Ignoring the noncausal part of the kernel leads to suboptimal solutions that might significantly degrade the performance of the controller. The Wiener-Hopf formalism allows us to take into account causality constraints in the formulation of the control problem, leading to an optimal realistic solution and a control kernel that is causal by construction. Moreover, it is possible to construct the control strategy based only on the power and cross-spectra obtained experimentally in a data-driven approach. The present work shows how to apply experimentally the Wiener-Hopf resolvent-based formalism using signals from a wind tunnel experiment, demonstrating that the TS waves can be effectively attenuated via a Wiener-Hopf-based controller, which yielded better results than a typical wave-cancellation approach.

© The Author(s), 2023. Published by Cambridge University Press.We present the results of direct numerical simulations of a NACA 0012 airfoil, with Mach number 0.3 and angle of attack of, examining the dynamics of the flow with increasing Reynolds numbers. Two-dimensional simulation results are obtained with chord-based Reynolds numbers in the range, where each simulation uses the last time step of the previous one as a starting point, to capture the evolution of dynamics as a function of. The development of the pressure fluctuations with time shows a transition from periodic to quasi-periodic attractor for, leading to the emergence of secondary tones in the wall and acoustic field pressure spectra, different from peaks related to the fundamental frequency and the respective harmonics; a second, incommensurate frequency appears, leading to several secondary tones with frequency, with and integers. Further increase of the Reynolds number leads to the emergence of a tertiary frequency, indicating a route to chaos of the Ruelle-Takens-Newhouse type. Such a mechanism is related to the ladder-type characteristic structure of the tones, indicating that dynamic systems theory is an important tool for understanding airfoil tonal noise.

© 2023 by the American Institute of Aeronautics and Astronautics, Inc..In this work, a kinematic wave-packet model is used to predict installed-jet noise. Large-eddy simulation results of freejets, for Mach numbers 0.4 and 0.9, are used to obtain parameters of wave packets representing large-scale turbulent structures, which were used to provide a model source for the Lighthill analogy used to predict far-field noise spectra. The source amplitude in the model is calibrated using noise measurements for a freejet, and such a wave-packet source is used to predict noise of the same jet in an installed configuration using a tailored Green’s function. Results from the prediction model are compared to installed-jet experimental data for four different observer positions and a large range of frequencies. Overall, the model predicts both directivities and amplitudes similar to the experimental data, with a hump in the generated noise for lower Strouhal numbers and a clear peak near a Strouhal number of 0.2. This low-order model is fast and flexible, and it is expected to be helpful in preliminary aircraft design.

© 2023 American Physical Society. Stochastic linear modeling proposed in Tissot, Mémin, and Cavalieri [J. Fluid Mech. 912, A51 (2021)0022-112010.1017/jfm.2020.1168] is based on classical conservation laws subject to a stochastic transport. Once linearized around the mean flow and expressed in the Fourier domain, the model has proven its efficiency to predict the structure of the streaks of streamwise velocity in turbulent channel flows. It has been in particular demonstrated that the stochastic transport by unresolved incoherent turbulence allows us to better reproduce the streaks through lift-up mechanism. In the present paper, we focus on the study of streamwise-elongated structures, energetic in the buffer and logarithmic layers. In the buffer layer, elongated streamwise vortices, named rolls, are seen to result from coherent wave-wave nonlinear interactions, which have been neglected in the stochastic linear framework. We propose a way to account for the effect of these interactions in the stochastic model by introducing a stochastic forcing, which replaces the missing nonlinear terms. In addition, we propose an iterative strategy in order to ensure that the stochastic noise is decorrelated from the solution, as prescribed by the modeling hypotheses. We explore the prediction abilities of this more complete model in the buffer and logarithmic layers of channel flows at Reτ=180, Reτ=550, and Reτ=1000. We show an improvement of predictions compared to resolvent analysis with eddy viscosity, especially in the logarithmic layer.

© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Colistin remains one of the few available options for the treatment of infections caused by resistant bacteria. Pharmacokinetic (PK) studies have been successful in estimating the appropriate colistin methanesulfonate (CMS) dose to achieve a target colistin concentration. Currently, there is a consensus that the dose of CMS should vary according to the patient renal function since CMS is mainly eliminated by renal route. For this same reason, the loading dose should vary according to the patient's renal capacity; however, this is not the current clinical practice. In this study we develop a framework to determine two key parameters for the loading dose regimen: (1) the optimal dose according to the characteristics (renal function and weight) of the patient; (2) the waiting time before the maintenance dose. Based on a previous PK model, our framework allows a fast parameter sweep so as to select optimal loading dose and waiting time minimizing the deviation between the plasma concentration and a target value. The results showed that patients presenting low creatinine clearance (CrCL) should receive a lower CMS loading dose with longer interval to start maintenance treatment to avoid nephrotoxic colistin concentrations. In cases of high CrCL, the dose should be higher and the interval to the next dose shorter to avoid subtherapeutic concentrations. Optimization of the loading dose should considerably improve colistin therapy, as the target concentration is reached more quickly, without reaching toxic values.

© 2023, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.In recent years, flow control has become increasingly important for the aeronautical field, as it is seen as a promising tool to design safer, quieter and more efficient aircraft. Since non-causality is observed in several flow control problems solved in the frequency domain, we consider here the use of the Wiener-Hopf technique for the control of a forced turbulent jet. Such approach allows us to enforce causality when obtaining the control kernel, which provides an optimal causal solution, and with this, prevents the drop in performance that may be observed in flow control applications that use a truncated solution. The experimental results presented here shows a significantly better performance of the Wiener-Hopf method with respect to that of a truncated kernel obtained using a wave-cancellation approach.

© 2023, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Large-eddy simulations of a Blasius boundary layer over a flat plate, without a leading edge, at multiple levels of incoming free stream turbulence are considered. The data from the saved snapshots are then applied to an input-output model where non-linear terms of the Navier-Stokes equations are treated as an external forcing. By separating the inputs corresponding to the perturbations coming through the inflow boundary and non-linear forcing, we can perform the full reconstruction of the statistics of the flow observed in the simulations and discriminate which frequencies and wavenumbers are more affected by either linear or non-linear dynamics. Different frequency-wavenumber combinations reveal streaks that grow predominantly through linear or non-linear mechanisms, the former occurring upstream and the latter at downstream stations of the boundary layer.

© 2023, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.This paper reports aeroacoustic experiments on round jets containing tab elements adhered to the nozzle internal surface with the purpose of generating steady streaks in the nozzle boundary-layer. Such streaks are theoretically expected to reduce growth rates associated with the Kelvin-Helmholtz mechanism and, in turn, to reduce jet noise. Nozzle configurations with and without a boundary-layer transition trigger element (carborundum trip), were studied. Stereo particle image velocimetry (stereo PIV) was employed to measure the three components of the velocity for a series of planes parallel to the nozzle exit at Mj = 0.7 in the 0.03 xD 10 streamwise range, where x is the streamwise distance and D is the jet diameter. Such measurements clearly show alternating regions of high and low speed flow due to the streaks that were induced by the tabs on the nozzle boundary-layer and are sustained in the jet shear-layer up to at least xD = 3. The acoustic experiments were performed in an anechoic facility, using an azimuthal array containing 18 equally-spaced microphones to characterize the acoustic field. The antenna was employed to conduct measurements at 15 streamwise stations in the 20 deg θ 90 deg polar range. All acoustic experiments were conducted in the 0.4 Mj 0.9 Mach number range. The presence of the tab elements leads to noise reductions of up to 6 dB/St, observed for Strouhal numbers in the 0.1 St 0.5 range, Mj = 0.4, axisymmetric azimuthal mode and untripped boundary-layer case. When the trip mechanism is present, the noise reduction is up to 3 dB/St. An overall sound pressure level (OASPL) reduction of up to 3 dB was measured for axisymmetric mode of the tabbed case for Mj = 0.4. As the tabs were designed based on boundary-layer measurements at Mj = 0.4, the noise reduction decreases with increasing Mach number. Nevertheless, significant noise reductions of up to 1.5 dB are still observed up to Mj = 0.9 and axisymmetric mode. Moreover, the noise reduction is up to 6 dB for the two first helical modes. The noise reduction was measured at both lower and higher polar angles and for almost the entire frequency range, up to at least St 2. Streak-inducing devices such as the present tabs are thus a promising approach to reduce jet noise

© 2023, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.In a combined experimental and numerical effort we investigate aerofoil tonal noise generation and reduction. The means of noise control are streak generators in form of cylindrical roughness elements. These elements are placed periodically along the span of aerofoil at the mid chord streamwise position. Experiments are performed for a wide range of Reynolds number and angle of attack. In the present work we concentrate on our numerical investigations. We have performed wall-resolved large-eddy simulations for a given angle of attack of 0 degree and Mach 0.3. Two Reynolds numbers 0.8 × 105 and 1.0 × 105 have been investigated, showing acoustic results consistent with experiments at the same Reynolds but lower Mach numbers. Roughness elements attenuate tones in the acoustic field, and, for the higher Reynolds number, suppress them. Through Fourier decomposition and POD analysis of streamwise velocity data, dominating structures have been identified. Further, the coupling between structures generated by surface roughness and instability modes (Kelvin-Helmholtz) of shear layer has been identified, suggesting stabilisation mechanisms by which the sound generation by the airfoil is reduced by the roughness elements.

© 2023, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.This experimental work investigates the trailing-edge (TE) noise from a NACA0012 airfoil in an open-jet wind tunnel, for chord-Reynolds numbers between 105 and 4.6 × 105 and angles of attack between 0° and 6°. The range of parameters for which TE noise is either tonal or broadband in the present experiments is in good agreement with existing literature results. One of the main objectives of this work is to test the assumption of recent modelling approaches based on the linearised Navier-Stokes operator. These studies focus on spanwise coherent structures in the turbulent boundary layer to investigate the mechanisms responsible for trailing edge noise, as they always satisfy the trailing edge scattering condition. However, numerical simulations routinely use a narrow numerical domain and periodic lateral boundary conditions, which could favour spanwise coherent dynamics. Therefore, particular emphasis is placed on the experimental characterisation of the spanwise wavenumber content of the pressure fluctuations on the airfoil surface and in the acoustic field. A good agreement with theoretical and numerical observations is found, as the spanwise wavenumber contents of the acoustic field are in good agreement with the edge scattering condition. Furthermore, the coherence between the surface pressure fluctuations and the acoustic fields is significantly improved when considering spanwise-coherent structures by spanwise averaging of the temporal signals, even in the case of broadband noise.

© 2023, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.An array of cylindrical roughness elements was used to reduce the tonal noise introduced by the separation bubble over a NACA 0012 airfoil at low angles of attack. Experiments were performed for four configurations: a baseline smooth airfoils, two with roughness elements at only one of the airfoil surfaces (pressure side or suction side), and the other with roughness elements at both airfoil surfaces. Arowof spanwise periodically spaced cylinderswas placed close to the mid-chord position in order to induce streaks that render the bubble three-dimensional, decreasing separation and stabilizing the Kelvin-Helmholtz instability of the separated shear layer, which is related to tonal noise. Our results show a decrease, and in some cases the total suppression, of the tonal noise at Reynolds numbers ranging from 0.6×105 to 2.5×105, and angles of attack ranging from 0 to 4 degrees.

© 2023 Elsevier Masson SAS. All rights reserved.An attempt to improve the accuracy of resolvent-based predictions by including velocity correlations in the linear model is developed here. Closure assumptions for unresolved nonlinearities are thus pushed back to a higher order. Turbulent channel flow is considered as a test case: response and forcing modes obtained from singular value decomposition of the new resolvent model are compared to Spectral Proper Orthogonal Decomposition (SPOD) modes extracted from a Direct Numerical Simulation (DNS) database. The performance of the approach is also measured against previous resolvent-based models. The new model does not yield significant global improvement, but does improve predictions in some regions. Further work on the method should target the linear modeling of the velocity-pressure gradient correlation tensor.

© Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to response modes from resolvent analysis. The SPOD, coupled with the Welch method for spectral estimation, may require long time-resolved datasets. In this work, a linearised Ginzburg-Landau model is considered in order to study the method's convergence. Spectral proper orthogonal decomposition modes of the white-noise forced equation are computed and compared with corresponding response resolvent modes. The quantified error is shown to be related to the time length of Welch blocks (spectral window size) normalised by a convective time. Subsequently, an algorithm based on a temporal data shift is devised to further improve SPOD convergence and is applied to the Ginzburg-Landau system. Next, its efficacy is demonstrated in a numerical database of a boundary layer subject to bypass transition. The proposed approach achieves substantial improvement in mode convergence with smaller spectral window sizes with respect to the standard method. Furthermore, SPOD modes display growing wall-normal and spanwise velocity components along the streamwise direction, a feature which had not yet been observed and is also predicted by a global resolvent calculation. The shifting algorithm for the SPOD opens the possibility for using the method on datasets with time series of moderate duration, often produced by large simulations.

© 2022 American Physical Society.Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearized Navier-Stokes system for a few low wave numbers. Resulting Galerkin systems comprise ordinary differential equations, with a number of degrees of freedom ranging from 144 to 600, which may be integrated to large times without any indication of numerical instability. The reduced-order models so obtained are also found to match statistics of direct numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy, despite a truncation of orders of magnitude in the degrees of freedom of the system. The present models offer thus an interesting compromise between simplicity and accuracy in a canonical wall-bounded flow, with relatively few modes representing coherent structures in the flow and their dominant dynamics.

© 2022 authors. Published by the American Physical Society.Resolvent analysis has found applications in several areas of fluid mechanics, providing physical insight into both laminar and turbulent flows. In spite of such fact, the global (3D) resolvent is computationally expensive, which limits the size of the domain and the Reynolds number of the flows which can be considered. In this work, we derive a parabolic resolvent approach, which enables a significant increase in the computational efficiency of the calculation, for streaky structures in boundary layer flows. The computational speedup depends on the size of the problem and could be of more than one order of magnitude for the same accuracy as the global calculation. The method is derived based on an optimization method via the Lagrange multipliers over the linearized boundary layer equations and it is coupled to a Krylov-Arnoldi decomposition to the computation of suboptimals. The application of the method is exemplified for two problems: A Falkner-Skan boundary layer, where we obtain trends for both the optimals and suboptimals, and a turbulent boundary layer, where characteristics such as the double peak in the spectrum and the characteristic inner and outer length scales can be recovered when a variable eddy viscosity is considered. In both cases, a scaling is found for the dominant gain, given in terms of the fourth power of the Reynolds number, defined in terms of the relevant scale for the problem, the displacement thickness, and the modified Rotta-Clauser parameter for the laminar and turbulent boundary layers, respectively. For the laminar case, we further demonstrate that a forcing limited to the free-stream region is capable of generating streaky structures inside the boundary layer, a relevant feature for free-stream turbulence-induced transition.

© Self-similarity of wall-attached coherent structures in a turbulent channel at is explored by means of resolvent analysis. In this modelling framework, coherent structures are understood to arise as a response of the linearised mean-flow operator to generalised frequency-dependent Reynolds stresses, considered to act as an endogenous forcing. We assess the self-similarity of both the wall-attached flow structures and the associated forcing. The former are educed from direct numerical simulation data by finding the flow field correlated with the wall shear, whereas the latter is identified using a frequency space version of extended proper orthogonal decomposition (Borée, Exp. Fluids, vol. 35, issue 2, 2003, pp. 188-192). The forcing structures identified are compared to those obtained using the resolvent-based estimation introduced by Towne et al. (J. Fluid Mech., vol. 883, 2020, A17). The analysis reveals self-similarity of both wall-attached structures - in quantitative agreement with Townsend's hypothesis of self-similar attached eddies - and the underlying forcing, at least in certain components.

© The Author(s), 2022.The publisher apologises that upon publication of the article Martini, E., Jung, J., Cavalieri, A., Jordan, P. & Towne, A. (2022), two author affiliations were switched around. The full and correct author affiliations are: Eduardo Martini1,2, Junoh Jung3, André V.G. Cavalieri1, Peter Jordan2 and Aaron Towne3 1Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos/SP, Brazil 2Département Fluides, Thermique et Combustion, Institut Pprime, CNRS, Université de Poitiers, ENSMA, 86000 Poitiers, France 3University of Michigan, Ann Arbor, MI 48109, USA The online version of this article has been updated.

© The Author(s), 2022. Published by Cambridge University PressThe application of control tools to complex flows frequently requires approximations, such as reduced-order models and/or simplified forcing assumptions, where these may be considered low rank or defined in terms of simplified statistics (e.g. white noise). In this work we propose a resolvent-based control methodology with causality imposed via a Wiener-Hopf formalism. Linear optimal causal estimation and control laws are obtained directly from full-rank, globally stable systems with arbitrary disturbance statistics, circumventing many drawbacks of alternative methods. We use efficient, matrix-free methods to construct the matrix Wiener-Hopf problem, and we implement a tailored method to solve the problem numerically. The approach naturally handles forcing terms with space-time colour; it allows inexpensive parametric investigation of sensor/actuator placement in scenarios where disturbances/targets are low rank; it is directly applicable to complex flows disturbed by high-rank forcing; it has lower cost in comparison to standard methods; it can be used in scenarios where an adjoint solver is not available; or it can be based exclusively on experimental data. The method is particularly well suited for the control of amplifier flows, for which optimal control approaches are typically robust. Validation of the approach is performed using the linearized Ginzburg-Landau equation. Flow over a backward-facing step perturbed by high-rank forcing is then considered. Sensor and actuator placement are investigated for this case, and we show that while the flow response downstream of the step is dominated by the Kelvin-Helmholtz mechanism, it has a complex, high-rank receptivity to incoming upstream perturbations, requiring multiple sensors for control.

© 2022 American Physical Society.This paper presents a study on wave cancellation in forced jets. Building on recent work on real-time control of forced turbulent jets by Maia et al. [Phys. Rev. Fluids 6, 123901 (2021)10.1103/PhysRevFluids.6.123901], we here assess the effect of jet upstream conditions and nonlinearity on wave-cancellation performance. The experiments are performed in jets with laminar and turbulent boundary layers inside the nozzle. An open-loop campaign is first conducted, in which the goal is to analyze the jet response to stochastic forcing with variable bandwidth. The upstream conditions of the jet are found to have a strong influence on the jet response. For narrow forcing bandwidths, both jets present a clear response regime. However, in the initially laminar jet, as bandwidth is increased, high growth rates and transition to turbulence in the initial region underpin the onset of nonlinear effects in jet response. In the initially turbulent jet, on the other hand, lower growth rates allow a linear response regime to be maintained for a broader range of forcing parameters. As the wave cancellation strategy is linear, reactive control is found to be more effective in the initially turbulent jet, consistent with the results of the open-loop analysis.

© 2021 The Author(s). Published by Cambridge University Press.The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira & Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier-Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin-Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira & Cavalieri. Further increase of leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher, leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets.

© The Author(s), 2021. Published by Cambridge University Press.We present an analysis of the linear stability characteristics of shock-containing jets. The flow is linearised around a spatially periodic mean, which acts as a surrogate for a mean flow with a shock-cell structure, leading to a set of partial differential equations with periodic coefficients in space. Disturbances are written using the Floquet ansatz and Fourier modes in the streamwise direction, leading to an eigenvalue problem for the Floquet exponent. The characteristics of the solution are directly compared with the locally parallel case, and some of the features are similar. The inclusion of periodicity induces minor changes in the growth rate and phase velocity of the relevant modes for small shock amplitudes. On the other hand, the eigenfunctions are now subject to modulation related to the periodicity of the flow. Analysis of the spatiooral growth rates led to the identification of a saddle point between the Kelvin-Helmholtz mode and the guided jet mode, characterising an absolute instability mechanism. Frequencies and mode shapes related to the saddle points for two conditions (associated with axisymmetric and helical modes) are compared with screech frequencies and the most energetic coherent structures of screeching jets, resulting in a good agreement for both. The analysis shows that a periodic shock-cell structure has an impulse response that grows upstream, leading to oscillator behaviour. The results suggest that screech can occur in the absence of a nozzle, and that the upstream reflection condition is not essential for screech frequency selection. Connections to previous models are also discussed.

© 2022 12th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2022. All rights reserved.A resolvent-based methodology is employed to obtain non-causal spatio-temporal estimates of turbulent pipe flow from low-rank probe measurements of wall shear-stress fluctuations. DNS and LES pipe flow numerical simulations at friction Reynolds number of 550 are used as databases. We consider one of the DNS databases as the true spatio-temporal flow field, from which the low-rank measurements are extracted. Such database is also employed to verify the accuracy of the linear estimators. The estimator needs a model for the nonlinear (or forcing) terms of the Navier-Stokes equations system, which are obtained from a DNS database and from a series of computationally cheaper LES databases with grids coarser than the DNS. Comparisons between the reference DNS and the estimates indicate that sufficiently accurate results can be achieved with cheaper LES containing up to 10% of the number of grid points of the DNS, with estimates closely matching the reference DNS results up to the buffer-layer and reasonable agreement up to the beginning of the log layer.

© 2022 12th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2022. All rights reserved.Coherent structures are found in many different turbulent flows, and they are known to drive self-sustaining processes in minimal-unit turbulence. Identifying the triadic interactions between coherent structures can provide insights beyond what is possible in the framework of linearised models. There are infinite possible interactions that may generate a given structure, and thus a method to systematically study those, ranking them in terms of their contribution, is of interest. We here use the resolvent-based extended spectral proper orthogonal decomposition (RESPOD) approach (Karban, U. et al. 2022 Self-similar mechanisms in wall turbulence studied using resolvent analysis. Journal of Fluid Mechanics 969, A36) to identify the relevant triadic interactions for a minimal Couette flow at Reτ = 34, studying the interactions that give rise to wall-attached structures, obtained by measuring the wall-shear. Our analysis reveals that there are six triadic interactions that dominate the most-energetic wall-attached structure.

© 2022 12th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2022. All rights reserved.We propose a formulation to study the effect of streaks in the spatial development of wavepackets. To this end, a modified version of the parabolised stability equations (PSE) linearized around a streak-containing mean flow is used, which considers a series of azimuthal wavenumbers in the solution. In the present case, streaks are obtained from experiments using spectral proper orthogonal decomposition applied to particle image velocimetry data, and extrapolated in the radial direction using a Gaussian fit. Streaks and rolls predicted by resolvent analysis are also used in the analysis to evaluate the effect of streamwise vortices in the development of the noise-generating structures. Results show that streaks non-trivially modify the spatial support of the Kelvin-Helmholtz wavepackets and their phase velocity, which may lead to changes in the sound generation efficiency of the jet. New structures across the shear layer induced by the presence of streaks are also observed further downstream for high streak amplitudes.

© 2022, AIAA International. All rights reserved.The present work is dedicated to the modeling of the low-frequency part of the jet installation noise (JIN) in flight conditions. It is known that the properties of JIN can be predicted based on the characteristics of the near field of an isolated jet. Unlike the static case, in the presence of a coflow, it is difficult to directly measure the structure of the pressure perturbations in the jet near field. To overcome this problem, we propose a technique based on hot-wire measurements on the jet axis, suitable both for static and flight conditions. The well-known agreement between a parabolized stability equations (PSEs) model and experimentally measured velocity fluctuations on the jet axis allows using the PSE approach for the reconstruction of the axisymmetric pressure fluctuations in the vicinity of the wing trailing-edge location. The first helical mode, which is also important for the jet installation noise prediction, is approximately reconstructed based on the fact that its properties are close to those of the axisymmetric mode. These pressure characteristics are then used as input in an analytical jet installation noise model. To confirm this approach, acoustic measurements of JIN in static and flight conditions are conducted for a laboratory subsonic jet installed near a flat plate simulating a wing. It is shown that the analytical model informed by the PSE-reconstructed pressure field is capable of capturing the main features of the low-frequency jet–plate interaction noise both in static conditions and in the presence of coflow.

© 2022, AIAA International. All rights reserved.The effect of addition of viscoelastic plies on the acoustic scattering quadrupoles near the trailing edge of laminated plates is evaluated. A numerical method is applied to compute the acoustic field scattered by finite flexible plates. For a two-dimensional problem whereby a cantilevered plate scatters sound from a point quadrupole near the free edge, results show that adding viscoelastic layers to a composite plate can modify the far-field sound. Parametric investigations show that this treatment reduces scattered noise near resonance frequencies. Discussions on the positioning and thickness of the viscoelastic layers and operating temperature are provided. The use of outer viscoelastic layers in composite plates is predicted to significantly reduce acoustic scattering near resonances due to structural damping.

© 2021 Acoustical Society of America.Parabolized stability equations (PSE) have been shown to model wavepackets and, consequently, the near-field of turbulent jets with reasonable accuracy. In this work, PSE were employed to obtain a reduced-order model that could estimate both the fluid-dynamic and the acoustic fields of a supersonic jet in a computationally efficient approximation for resolvent-based estimation based on a single input. From the unsteady pressure data at an input position, the time-domain pressure field was estimated using transfer functions obtained using PSE and a data-driven method based on a well-validated large-eddy simulation (LES). The prediction scheme employed is a single-input single-output, linear model. The unsteady pressure predicted by the PSE showed good agreement with the LES results, especially if the input position is outside the mixing layer, where the prediction capabilities of the PSE are comparable to those of the data-driven transfer functions. The good agreement indicates that PSE could not only be used to predict the sound generation but also to open up different potentialities to attenuate the noise by flow control. The exploration of the regions where the method displayed good agreement, which are presented in this work, can guide the positioning of the sensors for experimental implementation of closed-loop control in a jet.

© 2021 American Physical Society.In this work we perform reactive control of stochastic disturbances in forced turbulent jets based on destructive interference. The study is motivated by the success of recent studies in applying this type of control on instability waves in transitional boundary layers and free-shear flows. Linear convective mechanisms in the initial region of turbulent jets are explored in order to perform reactive control, wherein the actuation signal is updated in real time based on sensor measurements performed upstream, resulting in an inverse feedforward approach. The control law is based on empirical transfer functions of the jet response to stochastic forcing and actuation, which are measured experimentally. Since turbulent jets have energy content spread in a number of azimuthal wave numbers, we apply axisymmetric forcing at the nozzle lip in order to be able to perform control using a reduced number of sensors and actuators. The external forcing produces axisymmetric wave packets which possess stochastic phases and amplitudes, akin to turbulent fluctuations found in unforced jets. We demonstrate the successful implementation of real-time reactive control of these disturbances, achieving order-of-magnitude attenuations of associated velocity fluctuations. Control is shown to reduce fluctuation levels over an extensive streamwise range.

© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Optimization of antibiotic administration helps minimizing cases of bacterial resistance. Dosages are often selected by trial and error using a pharmacokinetic (PK) model. However, this is limited to the range of tested dosages, restraining possible treatment choices, especially for the loading doses. Colistin is a last-resort antibiotic with a narrow therapeutic window; therefore, its administration should avoid subtherapeutic or toxic concentrations. This study formulates an optimal control problem for dosage selection of colistin based on a PK model, minimizing deviations of colistin concentration to a target value and allowing a specific dosage optimization for a given individual. An adjoint model was used to provide the sensitivity of concentration deviations to dose changes. A three-compartment PK model was adopted. The standard deviation between colistin plasma concentrations and a target set at 2 mg/L was minimized for some chosen treatments and sample patients. Significantly lower deviations from the target concentration are obtained for shorter administration intervals (e.g. every 8 h) compared to longer ones (e.g. every 24 h). For patients with normal or altered renal function, the optimal loading dose regimen should be divided into two or more administrations to attain the target concentration quickly, with a high first loading dose followed by much lower ones. This regimen is not easily obtained by trial and error, highlighting advantages of the method. The present method is a refined optimization of antibiotic dosage for the treatment of infections. Results for colistin suggest significant improvement in treatment avoiding subtherapeutic or toxic concentrations.

© Authors 2021We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. Martini et al. (J. Fluid Mech., vol. 900, 2021, p. A2) showed that the resolvent-based estimator is optimal when the true space-Time forcing statistics are utilised, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterise these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models-an eddy-viscosity model and white-noise forcing-and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer layer, but only using the true forcing statistics allows accurate estimation of large-scale logarithmic-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-Attached structures enables accurate estimations through the logarithmic layer.

© We investigate spanwise-coherent structures in the turbulent flow around airfoils, motivated by their connection with trailing-edge noise. We analyse well-resolved large-eddy simulations (LES) of the flow around NACA 0012 and NACA 4412 airfoils, both at a Reynolds number of 400 000 based on the chord length. Spectral proper orthogonal decomposition performed on the data reveals that the most energetic coherent structures are hydrodynamic waves, extending over the turbulent boundary layers around the airfoils with significant amplitudes near the trailing edge. Resolvent analysis was used to model such structures, using the mean field as a base flow. We then focus on evaluating the dependence of such structures on the domain size, to ensure that they are not an artefact of periodic boundary conditions in small computational boxes. To this end, we performed incompressible LES of a zero-pressure-gradient turbulent boundary layer, for three different spanwise sizes, with the momentum-thickness Reynolds number matching those near the airfoils trailing edge. The same coherent hydrodynamic waves were observed for the three domains. Such waves are accurately modelled as the most amplified flow response from resolvent analysis. The signature of such wide structures is seen in non-premultiplied spanwise wavenumber spectra, which collapse for the three computational domains. These results suggest that the spanwise-elongated structures are not domain-size dependent for the studied simulations, indicating thus the presence of very wide structures in wall-bounded turbulent flows.

© 2021 American Physical Society.In shock wave/boundary layer interactions, two mechanisms have been recognized to drive the low-frequency unsteadiness of the reflected shock: upstream boundary layer forcing and downstream feedback. The current work presents a quantitative analysis of the causal mechanisms underlying such flow unsteadiness. The analysis is based on a large-eddy simulation database covering approximately 300 cycles of the low-frequency shock fluctuations in a Mach 2 turbulent boundary layer. This time span enables the accurate application of frequency-domain system identification methods targeting such low frequencies. The evaluation of the spectrum in the interaction zone indicates that the broadband low-frequency unsteadiness is predominantly two-dimensional and can be isolated via spanwise averaging. Empirically derived transfer functions are computed using the averaged flow field and indicate the occurrence of a feedback between the locations downstream of the flow separation and the shock fluctuations. The results indicate that this mechanism dominates over the upstream forcing of the interaction region. Accordingly, the computed transfer functions are also used as an estimation tool to predict the shock motion accurately; for the largest streamwise separation between input and output signals, correlations above 0.6 are observed between predictions and raw data. Computation of spectral proper orthogonal decomposition modes reveals the existence of upstream traveling waves in the leading spectral mode at the main shock frequency; higher frequencies do not exhibit this trend. Furthermore, the spectral modes obtained using selected flow regions downstream of the shock enable the reconstruction of a significant portion of the energy in the interaction zone. Finally, a linear stability analysis is conducted using the mean turbulent flow, showing the existence of upstream traveling waves. Evaluation of a vortex sheet model indicates that these upstream traveling modes are of acoustic nature. The predicted modes from this local analysis present a compelling match against the spectral modes, both in terms of the shape and phase speed of the fluctuations. The combined analysis of the techniques indicates that downstream disturbances are the dominant cause of shock oscillations in the present configuration, leading to shock motion by upstream traveling acoustic modes.

© 2021 American Physical Society. New reduced-order models (ROMs) are derived for sinusoidal shear flow (also known as Waleffe flow) and plane Couette flow in small periodic domains. A first derivation for Waleffe flow exploits Fourier modes that form a natural orthonormal basis for the problem. A ROM for such basis is obtained by a Galerkin projection of the Navier-Stokes equation. A large basis was reduced to 12 modes that contribute significantly in maintaining chaotic, turbulent dynamics. A key difference from earlier ROMs is the inclusion of two roll-streak structures, with spanwise wavelengths equal to Lz and Lz/2, where Lz is the spanwise length of the computational box. The resulting system was adapted to Couette flow by rewriting the Galerkin system for the same 12 modes, modified so as to satisfy no-slip conditions on the walls. The resulting dynamical systems lead to turbulence with finite lifetimes, in agreement with earlier ROMs and simulations in small domains. However, the present models display lifetimes that are much longer than in earlier ROMs, with differences of more than an order of magnitude. The Couette-flow model is compared to results of direct numerical simulation (DNS), with statistics displaying fair agreement. The inclusion of the Lz and Lz/2 length scales is seen to be a key feature for longer turbulence lifetimes: Neglecting any of the roll modes, or their nonlinear interaction, leads to drastic reductions of turbulence lifetimes. The present ROMs thus highlight some of the dominant nonlinear interactions that are relevant in maintaining turbulence for long lifetimes.

© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.This manuscript presents a successful application of the inverse feed-forward control (IFFC) technique for control of the Tollmien–Schlichting (TS) waves over a wing profile placed in an open-circuit wind tunnel. Active cancellation of two-dimensional broadband TS disturbances is performed using a single dielectric barrier discharge (DBD) plasma actuator. The measurements required for the IFFC are performed with microphones, instead of hot wires often used for this purpose, in order to reduce the space occupied by the sensors and assess the suitability of simpler and cheaper devices. An attenuation of the TS-wave amplitude of one order of magnitude is achieved. Direct numerical simulations (DNS) are also performed and compared to the outcome of the experiments. The plasma-actuator model used in DNS is a mapping of the force field used by Fabbiane et al. (In: Proceedings of TSFP-9, Melbourne, 2015a) to the actual geometry, whereas the sensors (microphones) are modeled as pressure probes. Despite these modelling choices, a good agreement between the results of DNS and the experiments is achieved. However, the control performance is better in the DNS, with attenuation of three orders of magnitude of TS-wave amplitude. Further analysis of experiments and simulations shows that the limiting factor in the experiments is the ambient low-frequency acoustic waves in the wind tunnel. These waves are sensed by the microphones and act as noise in the analysis of TS-wave evolution and thus leading to lower coherence between sensors and actuators. This in turn leads to a suboptimal control kernel in the experiment.Please confirm if the inserted city and country are correct in Affiliations [Aff1, Aff2]. Amend if necessary.Confirmed. It is correct.Please confirm if the corresponding author is correctly identified. Amend if necessary.Confirmed. The corresponding author is Pedro P. C. Brito. Graphic abstract: [Figure not available: see fulltext.]

© 2021 American Physical Society.A method is proposed in order to optimally decompose the trace of cross-covariances of flow fluctuations, such as Reynolds stresses. Such method, referred to as cross proper orthogonal decomposition (CPOD), leads to a basis of modes extracted from a flow database that are optimal in representing an inner product related to the cross-covariance of interest. A sample application is shown for the representation of Reynolds shear stress in a turbulent channel flow with friction Reynolds number equal to 179. Leading modes are shown to comprise streamwise vortices and streaks with phase opposition between streamwise (u′) and wall-normal (v′) velocities, representing ejections and sweeps, and higher-order modes show similar structures, but with u′ and v′ in phase. A combination of such structures leads to an accurate reconstruction of the Reynolds stress, and consequently of the mean flow, with a reasonable near-wall reconstruction with the leading CPOD mode pair (even and odd modes) for each considered wave number, and a close match of the profiles with the five leading CPOD mode pairs. The present method is thus a valuable modal decomposition technique targeting cross-covariances of flow quantities such as Reynolds stresses.

© The Author(s), 2021.The presence of elongated streaks of high and low streamwise velocity in the shear layer of circular jets breaks the axisymmetry of their steady-state solution. If the streaks are considered to be part of the base flow, for the purpose of linear instability analysis, the instability eigenmodes are thus affected by their presence. The resulting changes of growth rate and spatial shapes of eigenmodes, related to the shear instability in jets, are investigated here for parallel base flows. Optimal streamwise vortices ('rolls') with prescribed azimuthal periodicity are computed, such that the transient temporal growth of the streaks that they produce is maximal. The presence of finite-amplitude streaks requires the formulation of eigenvalue problems in a two-dimensional cross-plane. Sinuous rolls and streaks are found to have a stabilising effect on the Kelvin-Helmholtz instability, whereas the varicose rolls and streaks have a destabilising effect. Absolute instability is not found to occur. This work shows that the effects of rolls and streaks need to be taken into account for more precise modelling of jet instability.

© 2021, American Institute of Aeronautics and Astronautics Inc.. All rights reserved.Experimental observations of laminar separation bubbles show that the dynamics of the separated shear layer are dominated by the amplification of external disturbances. For low-to-moderate levels of free-stream turbulence intensity, the laminar-to-turbulent transition process is initiated by the formation of spanwise-aligned vortices associated with inflectional instability. The spanwise coherence of such structures varies strongly depending on the intensity of the flow recirculation and the amplitude of the external disturbances. On the other hand, two-dimensional laminar separation bubbles are intrinsically unstable and tend to become distorted along the spanwise direction even in the absence of external disturbances. This three-dimensional distortion can affect qualitatively and quantitatively the flow receptivity to external disturbances and their subsequent amplification, and thus it needs to be accounted for in the modeling of separation bubbles. This work addresses the receptivity of two-dimensional and three-dimensional separation bubbles to three-dimensional disturbances by analyzing the optimal inputs and outputs via the resolvent operator. A novel matrix-free strategy is used, which provides optimal gains and modes for all frequencies using a single iterative scheme, resulting in total costs an order of magnitude lower than previous methods. Results show that three-dimensional distortion of bubbles may enhance amplification of external disturbances by more than an order of magnitude.

© 2021, American Institute of Aeronautics and Astronautics Inc.. All rights reserved.We introduce a new algorithm for computing resolvent modes of large systems based on randomized singular value decomposition (RSVD) combined with a time-marching method. The most expensive steps of the RSVD algorithm in the context of resolvent analysis, which constitute a bottleneck in its application to large systems, are replaced by leveraging the time-domain equations that have given rise to the resolvent operator. Specifically, the actions of the resolvent operator and its adjoint on a vector are obtained by equivalent direct and adjoint marching operations in the time domain. Our algorithm exploits streaming calculations to alleviate memory issues emerging for large systems, and we develop strategies to minimize the time-stepping cost while maintaining a desired level of accuracy. We validated our proposed algorithm by comparing the resolvent modes and gains of a Ginzburg-Landau model problem to those obtained from RSVD. Then, we use an axisymmetric jet and a three-dimensional extension thereof to assess and demonstrate the accuracy, cost, and memory efficiency of our new algorithm when applied to a high-dimensional system. In the three-dimensional case, we achieve orders-of-magnitude reduction in both CPU and memory usage compared to a direct application of RSVD.

© We study a turbulent jet issuing from a cylindrical nozzle to characterise coherent structures evolving in the turbulent boundary layer. The analysis is performed using data from a large-eddy simulation of a Mach 0.4 jet. Azimuthal decomposition of the velocity field in the nozzle shows that turbulent kinetic energy predominantly resides in high azimuthal wavenumbers; the first three azimuthal wavenumbers, that are important for sound generation, contain much lower, but non-zero amplitudes. Using two-point statistics, low azimuthal modes in the nozzle boundary layer are shown to exhibit significant correlations with modes of the same order in the free-jet region. Spectral proper orthogonal decomposition is used to distill a low-rank approximation of the flow dynamics. This reveals the existence of tilted coherent structures within the nozzle boundary layer and shows that these are coupled with wavepackets in the jet. The educed nozzle boundary-layer structures are modelled using a global resolvent analysis of the mean flow inside the nozzle to determine the most amplified flow responses using the linearised Navier-Stokes system. It is shown that the most-energetic nozzle structures can be successfully described with optimal resolvent response modes, whose associated forcing modes are observed to tilt against the nozzle boundary layer, suggesting that the Orr mechanism underpins these organised, turbulent, boundary-layer structures.

© 2021 Cambridge University Press. All rights reserved.Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into the dynamics of transitional and turbulent flows and can provide a model for the dominant coherent structures within the flow, particularly for flows where the linear operator selectively amplifies one particular force component, known as the optimal force mode. Force and response modes are typically obtained from a singular-value decomposition of the resolvent operator. Despite recent progress, the cost of resolvent analysis for complex flows remains considerable, and explicit construction of the resolvent operator is feasible only for simplified problems with a small number of degrees of freedom. In this paper we propose two new matrix-free methods for computing resolvent modes based on the integration of the linearized equations and the corresponding adjoint system in the time domain. Our approach achieves an order of magnitude speedup when compared with previous matrix-free time-stepping methods by enabling all frequencies of interest to be computed simultaneously. Two different methods are presented: one based on analysis of the transient response, providing leading modes with fine frequency discretization; and another based on the steady-state response to periodic forcing, providing optimal and suboptimal modes for a discrete set of frequencies. The methods are validated using a linearized Ginzburg-Landau equation and applied to the three-dimensional flow around a parabolic body.

© The Author(s), 2021. Published by Cambridge University Press.We present a two-point model to investigate the underlying source mechanisms for broadband shock-associated noise (BBSAN) in shock-containing supersonic jets. In the model presented, the generation of BBSAN is assumed to arise from the nonlinear interaction between downstream-propagating coherent structures with the quasi-periodic shock cells in the jet plume. The turbulent perturbations are represented as axially extended wavepackets and the shock cells are modelled as a set of stationary waveguide modes. Unlike previous BBSAN models, the physical parameters describing the hydrodynamic components are not scaled using the acoustic field. Instead, the source characteristics of both the turbulent and shock components are extracted from the hydrodynamic region of large-eddy simulation and particle image velocimetry datasets. Apart from using extracted data, a reduced-order description of the wavepacket structure is obtained using parabolised stability equations. The validity of the model is tested by comparing far-field sound pressure level predictions to azimuthally decomposed experimental acoustic data from a cold Mach 1.5 underexpanded jet. At polar angles and frequencies where BBSAN dominates, encouraging comparisons of the radiated noise spectra for the first three azimuthal modes, in both frequency and amplitude (at peak frequency), reinforce the suitability of using reduced-order wavepacket sources for predicting BBSAN peaks. On the other hand, wavepacket jitter is found to have a critical role in recovering sound amplitude at interpeak frequencies. The paper presents a quantitative demonstration that the wavepacket-shock interaction, carefully reconstructed by extracting components from data or linearised models, contains the correct essential flow physics that accounts for most features of the far-field BBSAN spectra.

© 2021 The Author(s). Published by Cambridge University Press.This study is focused on the prediction of coherent structures, propagating within a turbulent channel flow. We propose a derivation of the linearised problem based on a stochastic formulation of the Navier-Stokes equations. It consists in considering the transport of quantities by a resolved velocity (i.e. solution of the model) perturbed by a Brownian motion which models the unresolved turbulent fluctuations over the time-averaged field, here thought of as the underlying background turbulence. The associated linearised model, considering the mean velocity profile as given, predicts linear solutions evolving within a corrected mean velocity field and perturbed by modelled background turbulence. Two ways to define the statistics of the Brownian motion are proposed and compared: One based on full simulation data, and the second, data free, based on preliminary predictions from resolvent analysis. The technique is applied on turbulent channel flows at friction Reynolds numbers and, and predictions are compared with direct numerical simulation results. We show that the principal components of an ensemble of solutions of this stochastic linearised system are able to represent the leading spectral proper orthogonal decomposition modes with a similar accuracy to optimal responses coming from resolvent analysis with an eddy-viscosity model at scales where strong production occurs. For the other scales, receiving energy by nonlinear redistribution, the present strategy improves the prediction. Moreover, the second mode is systematically well predicted over all scales. This behaviour is understood by the ability of the stochastic modelling to model positive and negative inter-scale energy transfers through stochastic diffusion and random stochastic transport, while the eddy-viscosity term in resolvent analysis is purely diffusive.

© 2020 by The Authors. Published by the American Institute of Aeronautics and Astronautics, Inc.This paper studies the amplitude of large-scale coherent wave-packet structures in jets, modeled by the parabolized stability equations (PSEs). Linear PSEs can retrieve the shape of the wave packets, but linearity leads to solutions with a free amplitude, which has traditionally been obtained in an ad hoc manner using limited data. We systematically determine the free amplitude as a function of frequency and azimuthal wave number by comparing the fluctuation fields retrieved from PSEs with coherent structures educed from large-eddy simulation data using spectral proper orthogonal decomposition. The wave-packet amplitude is shown to decay exponentially with the Strouhal number for axisymmetric and helical modes at both Mach numbers considered in the study: 0.4 and 0.9. Analytical fit functions are proposed, and the scaled wave packets provide reasonable reconstructions of pressure and velocity spectra on the jet centerline and lip line over a range of streamwise positions.

© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.This work deals with the characterization of the closed-loop control performance aiming at the delay of transition. We focus on convective wavepackets, typical of the initial stages of transition to turbulence, starting with the linearized Kuramoto–Sivashinsky equation as a model problem representative of the transitional 2D boundary layer; its simplified structure and reduced order provide a manageable framework for the study of fundamental concepts involving the control of linear wavepackets. The characterization is then extended to the 2D Blasius boundary layer. The objective of this study is to explore how the sensor–actuator placement affects the optimal control problem, formulated using linear quadratic Gaussian (LQG) regulators. This is carried out by evaluating errors of the optimal estimator at positions where control gains are significant, through a proposed metric, labelled as γ. Results show, in quantitative manner, why some choices of sensor–actuator placement are more effective than others for flow control: good (respectively, bad) closed-loop performance is obtained when estimation errors are low (respectively, high) in the regions with significant gains in the full-state-feedback problem. Unsatisfactory performance is further understood as dominant estimation error modes that overlap spatially with control gains, which shows directions for improvement of a given set-up by moving sensors or actuators. The proposed metric and analysis explain most trends in closed-loop performance as a function of sensor and actuator position, obtained for the model problem and for the 2D Blasius boundary layer. The spatial characterization of the γ-metric provides thus a valuable and intuitive tool for the problem of sensor–actuator placement, targeting here transition delay but possibly extending to other amplifier-type flows.

© 2020 Elsevier Inc.Turbulent channel flow was analysed using direct numerical simulations at friction Reynolds numbers Reτ=180 and 550. The databases were studied using spectral proper orthogonal decomposition (SPOD) to identify dominant near-wall coherent structures, most of which turn out to be streaks and streamwise vortices. Resolvent analysis was used as a theoretical approach to model such structures, as it allows the identification of the optimal forcing and most amplified flow response; the latter may be related to the observed relevant structures obtained by SPOD, especially if the gain between forcing and response is much larger than what is found for suboptimal forcings or if the non-linear forcing is white noise. Results from SPOD and resolvent analysis were compared for several combinations of frequencies and wavenumbers. For both Reynolds numbers, the best agreement between SPOD and resolvent modes was observed for the cases where the lift-up mechanism from resolvent analysis is present, which are also the cases where the optimal resolvent gain is dominant. These results confirm the outcomes in our previous studies (Abreu et al., 2019; Abreu et al., 2020), where we used a DNS database of a pipe flow for the same Reynolds numbers.

© The Author(s), 2020.Linearisation of the Navier-Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier-Stokes equations can be equivalently written using many different sets of dependent variables, we show that the properties of the linear operator obtained via linearisation about the mean depend on the variables in which the equations are written prior to linearisation, and can be modified under nonlinear transformation of variables. For example, we show that using primitive and conservative variables leads to differences in the singular values and modes of the resolvent operator for turbulent jets, and that the differences become more severe as variable-density effects increase. This lack of uniqueness of mean-flow-based linear analysis provides new opportunities for optimising models by specific choice of variables while also highlighting the importance of carefully accounting for the nonlinear terms that act as a forcing on the resolvent operator.

© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.The problem of finding optimal forcing and response for unbounded base flows, exemplified by the Blasius boundary layer, is assessed by means of a locally parallel resolvent analysis. A new analysis of previous results in the literature, which stated that a maximum resolvent gain occurs for spanwise wavenumber kz≈ 0.2 , revealed that this result was not domain converged, and larger domains lead to peak amplification for kz→ 0 ; this result is seen to depend strongly on domain size. It is seen that forcing and response modes for low frequency and wavenumber tend to be extended throughout the computational domain, with substantial support in the free stream. Free-stream modes and their gains are found analytically by considering the resolvent operator for uniform flow, and it is seen that low frequencies and wavenumbers lead to a dominance of such free-stream modes in the resolvent analysis of boundary layers. The lack of domain convergence is explained by the analysis, as gains scale with the square of the domain height. We then propose a new approach to evaluate the resolvent gains for this kind of unbounded flows, by means of a weighting function for the chosen norm that neglects response modes above a cut-off height yp, typically placed outside the boundary layer thickness; this ensures that relevant responses will only be sought in a region of interest, which here corresponds to the boundary layer. The method proved to solve the problem raised by the presence of free-stream modes, resulting in domain-converged forcing and response modes with the shape of streamwise vortices and streaks, respectively. The results were also shown to be independent of the choice of the filter parameters, leading to converged gains for the whole spectrum.

© The Author(s), 2020.In resolvent analyses of turbulent channel flows it has been common practice to neglect or model the nonlinear forcing term that forms the input of the resolvent. However, the spatiotemporal structure of this term is mostly unknown. Here, this nonlinear forcing term is quantified. The Fourier transform of its two-point space-time correlation, its cross-spectral density (CSD), is computed. The CSD is evaluated for two channel flows at friction Reynolds numbers Reτ = 179 and Reτ = 543 via direct numerical simulations (DNS). The CSDs are computed for energetic structures typical of buffer-layer and large-scale motions, for different temporal frequencies. It is found that the forcing is structured and that its solenoidal part, which is the only one affecting the velocity field, is the combination of an oblique streamwise vortical forcing and a streamwise component that counteract each other, as in a destructive interference. It is shown that a rank-2 approximation of the forcing, with only the most energetic spectral proper orthogonal decomposition (SPOD) modes, leads to the bulk of the response. Moreover, it is found that the nonlinear forcing term has a non-negligible projection onto the linear sub-optimal forcings of resolvent analysis, which demonstrates that the linear optimal forcing is not representative of the nonlinear forcing. Finally, it is clarified that the Cess eddy-viscosity-modelled forcing improves the accuracy of resolvent analysis prediction because the modelled forcing projects onto the linear sub-optimal forcings similarly to DNS data.

© The Author(s), 2020. Published by Cambridge University Press.Direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers and. The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing the mapping out of similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing is dominated by the wall-normal and azimuthal components, and associated response corresponds to streaks of streamwise velocity. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism, here understood as nonlinear forcing terms leading to the appearance of streamwise vortices, which in turn form high-amplitude streaks. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.

© The Author(s), 2020. Published by Cambridge University Press.A model problem for analysing the interaction between coherent structures in shear flows with the presence of a convective instability is proposed in this work. Starting from Couette flow, a permanent forcing in the shape of a hyperbolic tangent is introduced in the laminar equations, leading to a wall-bounded flow with an inflection point, which triggers a hydrodynamic instability. Temporal linear stability analysis applied to this new flow model shows that this flow is unstable at low Reynolds numbers, giving rise to Kelvin-Helmholtz-like vortices. Due to the presence of shear, streaks and rolls (streamwise vortices), predicted by resolvent analysis, are also present in the flow, and these structures will interact with vortices via oblique waves. Results of locally parallel analysis inspired the design of a computational box for a direct numerical simulation of such flow and the numerical results exhibit a limit cycle involving streaks, vortices, rolls, oblique waves and the mean flow, so that the flow becomes periodically unstable for the present case. The flow dynamics is shown to reproduce some of the features of jets and mixing layers, such as jitter and translational instability, showing that the present model can potentially clarify some of the phenomena involved in the turbulent dynamics of such flows.

© © The Author(s), 2020. Published by Cambridge University Press.Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin-Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211-237) at low Strouhal number and non-zero azimuthal wavenumbers . In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency-wavenumber space where each dominates, finding lift-up to be dominant as. Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core.

© The Author(s), 2020. Published by Cambridge University Press.An analysis of the statistics of the nonlinear terms in resolvent analysis is performed in this work for turbulent Couette flow at Reynolds number 400. Data from a direct numerical simulation of a minimal flow unit is used to compute the covariance matrix of the velocity. From the same data, we computed the nonlinear terms of the Navier-Stokes equations (treated as forcing), which allowed us to compute the covariance matrix of the forcing. The quantitative relation between the two covariances via the resolvent operator is confirmed here for the first time, accounting for relevant signal processing issues related to the windowing procedure for frequency-domain quantities. Such exact correspondence allowed the eduction of the most relevant force components for the dominant structures in this flow, which participate in the self-sustaining cycle of turbulence: (i) streamwise vortices and streaks, and (ii) spanwise-coherent fluctuations of spanwise velocity. The results show a dominance by a subset of the nonlinear terms for the prediction of the full statistics of streamwise vortices and streaks; a single term is seen to be dominant for spanwise motions. A relevant feature observed in these cases is that the forcing covariance is dominated by its first eigenfunction, showing that nonlinear terms also have a coherent structure at low frequencies in this flow. Different forcing components are also coherent between them, which leads to constructive and destructive interferences that greatly modify the flow response. These are key features of forcing 'colour' for the present flow.

© 2020, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.A comparative study of the acoustic far-field radiation of a subsonic jet near a folded plate with an opening, intended to represent a flapped wing with thrust gate, is presented in this work. Three openings with different widths were used to evaluate experimentally the influence of the gaps in the far-field noise radiation, for two folding angles. Boundary Element Method (BEM) simulations with a wavepacket model to represent the jet acoustic source were both used to calculate the noise far-field for comparison with the patterns found experimentally and for investigating the acoustic field at others points. The BEM simulations showed trends similar to those found experimentally. Through parametric simulations, it was also possible to estimate that openings widths greater than one diameter do not contribute significantly to reducing the far-field noise. The results show that even the smallest tested openings were able to reduce the noise in the far-field for the tested positions.

© American Institute of Aeronautics and Astronautics Inc.. All rights reserved.An investigation is carried out to evaluate how an external uniform stream affects turbulent-jet coherent structures. The presence of this uniform stream outside the jet represents the effect of forward flight on the velocity field. Coherent structures are modelled as wave packets, and the flight effect is studied using the parabolized stability equations (PSEs). Measurements of mean base flows and axial velocity fluctuations on the jet centerline at assumed flight conditions are described. The velocity fields were supplied to a PSE model to retrieve the wave packet signatures of axial velocity fluctuations. Overall results are in good agreement with experimental measurements. There is an observed increase in wave packet wavelengths and phase velocities (with respect to the nozzle) as flight velocity increases. Also, axial amplification rates are determined and show stabilization in the near-nozzle region, which is confirmed by experimental power spectral densities on the jet centerline. This tendency holds as the freestream velocity increases.

© The Author(s), 2020. Published by Cambridge University Press.We extend the resolvent-based estimation approach recently introduced by Towne etal. (J. Fluid Mech., vol. 883, 2020, A17) to obtain optimal, non-causal estimates of time-varying flow quantities from low-rank measurements. We derive optimal transfer functions between the measurements and certain nonlinear terms that act as a forcing on the linearised Navier-Stokes equations, and show that the resulting transfer function to the flow state is equivalent to a multiple-input, multiple-output Wiener filter if the colour of the forcing statistics is known. A matrix-free implementation is developed based on integration of the direct and adjoint linearised Navier-Stokes operators, enabling application to the large systems encountered for transitional and turbulent flows without the need for a priori model reduction. Using a linearised Ginzburg-Landau problem, we show that the non-casual resolvent-based method outperforms a casual Kalman filter for general sensor configurations and recovers the Kalman filter transfer function in specific cases, leading to causal estimates at a significantly reduced computational cost. Additionally, our method is shown to be more accurate and robust than popular approaches based on truncation of the resolvent operator to its leading modes. The applicability of the method to transitional and turbulent flows is demonstrated via application to a (linearised) transitional boundary layer and a (nonlinear) turbulent channel flow. Errors on the order of 2A are achieved for the boundary layer, and the channel flow case highlights the need to account for the forcing colour to achieve accurate flow estimates. In practice, our method can be used as a post-processing tool to reconstruct unmeasured quantities from limited experimental data, and, in cases where the transfer function can be accurately truncated to its causal components, as a low-cost estimator for flow control.

© 2019 Acoustical Society of America.An investigation of a wavepacket model for free-jet and jet-surface interaction noise was conducted. The source term for the axisymmetric mode was extracted from a Mach 0.9 jet large eddy simulation and employed to adjust the parameters of a simple source model. Streamwise coherence decay, in particular, was considered. The source model was propagated with both the free-field and tailored Green's function for a semi-infinite flat plate positioned at a distance of r/D = 1 from the jet axis. Significant deviations were observed in the prediction of the low-Angle directivity of the isolated jet as well as in the reproduction of the characteristics of the source field. However, the effects of trailing edge noise were well reproduced. The installed jet case, at the region dominated by trailing-edge scattering, showed very little sensitivity to the coherence decay, a crucial feature in the isolated jet case. In this sense, the modelling of the installed-jet case proved to be much simpler.

© 2019 Cambridge University Press.The linear stability of high-Reynolds-number corrugated jets is investigated by solving the compressible Rayleigh equation linearized about the time-averaged flow field. A Floquet ansatz is used to account for periodicity of this base flow in the azimuthal direction. The origin of multiple unstable solutions, which are known to appear in these non-circular configurations, is traced through gradual perturbations of a parametrized base-flow profile. It is shown that all unstable modes are corrugated jet continuations of the classical Kelvin-Helmholtz modes of circular jets, highlighting that the same instability mechanism, modified by corrugations, leads to the growth of disturbances in such flows. It is found that under certain conditions the eigenvalues may form saddles in the complex plane and display axis switching in their eigenfunctions. A parametric study is also conducted to understand how penetration and number of corrugations impact stability. The effect of these geometric properties on growth rates and phase speeds of the multiple unstable modes is explored, and the results provide guidelines for the development of nozzle configurations that more effectively modify the Kelvin-Helmholtz instability.

© 2019 American Physical Society.A large-eddy simulation of turbulent, compressible flow around a NACA 0012 airfoil at zero angle of attack and Mach number 0.115 is used to study mechanisms of trailing-edge noise. The boundary layers at both sides of the airfoil have a forced transition near the airfoil leading edge, and are turbulent near the trailing-edge. Flow-acoustic correlations and spectral (frequency-domain) proper orthogonal decomposition (SPOD) are used to evaluate turbulent structures that are relevant for the radiated sound. Homogeneity in the spanwise direction allows application of a Fourier decomposition in span prior to both correlations and SPOD. It is known that acoustic theory, based on an analysis of the tailored Green's function modeling trailing-edge scattering, shows that only spanwise wave numbers kz satisfying kz<k, where k is the acoustic wave number, lead to radiated sound; two-dimensional disturbances (kz=0) always satisfy this criterion, and thus spanwise-coherent structures are expected to be important for trailing-edge noise. Analysis of turbulence statistics of the boundary layer close to the trailing edge shows that the well-known, dominant streaky structures have kz>k and thus should not contribute to the radiated sound. To investigate this further using simulation data, flow-acoustic correlations are obtained using either the standard two-point analysis or considering two-dimensional disturbances in velocity and pressure fields, and results show significant correlation coefficients (of about 0.5) once two-dimensional disturbances near the trailing edge are isolated. A further increase of correlation peaks (up to 0.7) is obtained once the antisymmetric parts of the fields is considered, reflecting the classical antisymmetric nature of trailing-edge scattering. SPOD is then used for frequencies around the peak radiated sound to examine the structure of two-dimensional disturbances in the trailing-edge region and their contribution to radiated sound. Leading SPOD modes show coherent hydrodynamic waves propagating from the region of boundary-layer tripping toward the trailing edge, characterizing a noncompact source akin to wave packets seen in turbulent jets. These leading SPOD modes have significant contribution to the radiated sound, as two modes lead to 50% of the acoustic intensity for the lower studied frequencies. The present results point to the scattering of spanwise-coherent boundary-layer structures as the dominant mechanism of trailing-edge noise in this flow.

© 2019 Cambridge University Press.Streaks have been found to be an important part of wall-turbulence dynamics. In this paper, we extend the analysis for unbounded shear flows, in particular a Mach 0.4 round jet, using measurements taken using dual-plane, time-resolved, stereoscopic particle image velocimetry (PIV) taken at pairs of jet cross-sections, allowing the evaluation of the cross-spectral density of streamwise velocity fluctuations resolved into azimuthal Fourier modes. From the streamwise velocity results, two analyses are performed: the evaluation of wavenumber spectra (assuming Taylor's hypothesis for the streamwise coordinate) and a spectral proper orthogonal decomposition (SPOD) of the velocity field using PIV planes in several axial stations. The methods complement each other, leading to the conclusion that large-scale streaky structures are also present in turbulent jets where they experience large growth in the streamwise direction, energetic structures extending up to eight diameters from the nozzle exit. Leading SPOD modes highlight the large-scale, streaky shape of the structures, whose aspect ratio (streamwise over azimuthal length) is approximately 15. The data were further analysed using SPOD, resolvent and transient growth analyses, good agreement being observed between the models and the leading SPOD mode for the wavenumbers considered. The models also indicate that the lift-up mechanism is active in turbulent jets, with streamwise vortices leading to streaks. The results show that large-scale streaks are a relevant part of the jet dynamics.

© 2019 The Author(s) Published by the Royal Society. All rights reserved.This paper is focused on the study of a kinematic wavepacket model for jet noise based on two-point statistics. The model contains physical parameters that define its structure in terms of wavenumber, envelope shape and coherence decay. These parameters, which are necessary to estimate the sound pressure levels radiated by the source, were educed from a largeeddy simulation database of a Mach 0.4, fully turbulent jet. The sound pressure levels predicted by the model were compared with acoustic data and the results show that when the parameters are carefully educed from the data, the sound pressure levels generated are in good agreement with experimentally measured values for low Strouhal numbers and polar angles. Furthermore, here we show that a correct representation of both coherence decay and wavepacket envelope shape are key aspects to an accurate sound prediction. A Spectral Proper Orthogonal Decomposition (SPOD) of the model source was also performed motivated by the search for a low-rank model capable of capturing the acoustic efficiency of the full source. It is shown that only a few SPODmodes are necessary to recover acoustically important wavepacket traits.

© 2019 Acoustical Society of America.Acoustic measurements of turbulent jets in the vicinity of a flat plate, mimicking a neighbouring wing, were compared to results from two wavepacket-based source models previously studied in the literature: the Tailored Green's Function method, which considers the radiation of the turbulent structure in the vicinity of a semi-infinite flat plate, and the Boundary Element Method, which can represent the full geometry of the plate used in the experiments. Particular interest is given to analysing how the angle of attack of the plate (α) affects the sound radiated by an installed jet with trailing edge 6 diameters away from the nozzle and 1 diameter away from the centerline for 0° ≤ α ≤ 45°. The results herein confirm the behaviour identified by the models: the scattered acoustic field follows the rotation of the plate, shifting a silence region with negligible scattered sound, and creating regions with lower noise levels in positions that correspond to the ground for an aircraft with engines under its wings. This is further explored by means of a Mach number analysis for M = 0.5, 0.7, and 0.9, showing that this trend is present whenever trailing-edge scattering of jet disturbances is dominant in the acoustic field.

© 2019 American Physical Society.Coherent turbulent wave-packet structures in a jet at Reynolds number 460000 and Mach number 0.4 are extracted from experimental measurements and are modeled as linear fluctuations around the mean flow. The linear model is based on harmonic optimal forcing structures and their associated flow response at individual Strouhal numbers, obtained from analysis of the global linear resolvent operator. These forcing-response wave packets ("resolvent modes") are first discussed with regard to relevant physical mechanisms that provide energy gain of flow perturbations in the jet. Modal shear instability and the nonmodal Orr mechanism are identified as dominant elements, cleanly separated between the optimal and suboptimal forcing-response pairs. A theoretical development in the framework of spectral covariance dynamics then explicates the link between linear harmonic forcing-response structures and the cross-spectral density (CSD) of stochastic turbulent fluctuations. A low-rank model of the CSD at given Strouhal number is formulated from a truncated set of linear resolvent modes. Corresponding experimental CSD matrices are constructed from extensive two-point velocity measurements. Their eigenmodes (spectral proper orthogonal or SPOD modes) represent coherent wave-packet structures, and these are compared to their counterparts obtained from the linear model. Close agreement is demonstrated in the range of "preferred mode" Strouhal numbers, around a value of 0.4, between the leading coherent wave-packet structures as educed from the experiment and from the linear resolvent-based model.

© 2019 Cambridge University Press.Motivated by recent studies that have revealed the existence of trapped acoustic waves in subsonic jets (Towne et al., J. Fluid Mech., vol. 825, 2017, pp. 1113-1152), we undertake a more general exploration of the physics associated with acoustic modes in jets and wakes, using a double vortex-sheet model. These acoustic modes are associated with eigenvalues of the vortex-sheet dispersion relation; they are discrete modes, guided by the vortex sheet; they may be either propagative or evanescent; and under certain conditions they behave in the manner of acoustic-duct modes. By analysing these modes we show how jets and wakes may both behave as waveguides under certain conditions, emulating ducts with soft or hard walls, with the vortex-sheet impedance providing effective 'wall' conditions. We consider, in particular, the role that upstream-travelling acoustic modes play in the dispersion-relation saddle points that underpin the onset of absolute instability. The analysis illustrates how departure from duct-like behaviour is a necessary condition for absolute instability, and this provides a new perspective on the stabilising and destabilising effects of reverse flow, temperature ratio and compressibility; it also clarifies the differing symmetries of jet (symmetric) and wake (antisymmetric) instabilities. An energy balance, based on the vortex-sheet impedance, is used to determine stability conditions for the acoustic modes: these may become unstable in supersonic flow due to an energy influx through the shear layers. Finally, we construct the impulse response of flows with zero and finite shear-layer thickness. This allows us to show how the long-time wavepacket behaviour is indeed determined by interaction between Kelvin-Helmholtz and acoustic modes.

© 2019 Cambridge University Press.Three methods are evaluated to estimate the streamwise velocity fluctuations of a zero-pressure-gradient turbulent boundary layer of momentum-Thickness-based Reynolds number up to , using as input velocity fluctuations at different wall-normal positions. A system identification approach is considered where large-eddy simulation data are used to build single and multiple-input linear and nonlinear transfer functions. Such transfer functions are then treated as convolution kernels and may be used as models for the prediction of the fluctuations. Good agreement between predicted and reference data is observed when the streamwise velocity in the near-wall region is estimated from fluctuations in the outer region. Both the unsteady behaviour of the fluctuations and the spectral content of the data are properly predicted. It is shown that approximately 45Â % of the energy in the near-wall peak is linearly correlated with the outer-layer structures, for the reference case . These identified transfer functions allow insight into the causality between the different wall-normal locations in a turbulent boundary layer along with an estimation of the tilting angle of the large-scale structures. Differences in accuracy of the methods (single-and multiple-input linear and nonlinear) are assessed by evaluating the coherence of the structures between wall-normally separated positions. It is shown that the large-scale fluctuations are coherent between the outer and inner layers, by means of an interactions which strengthens with increasing Reynolds number, whereas the finer-scale fluctuations are only coherent within the near-wall region. This enables the possibility of considering the wall-shear stress as an input measurement, which would more easily allow the implementation of these methods in experimental applications. A parametric study was also performed by evaluating the effect of the Reynolds number, wall-normal positions and input quantities considered in the model. Since the methods vary in terms of their complexity for implementation, computational expense and accuracy, the technique of choice will depend on the application under consideration. We also assessed the possibility of designing and testing the models at different Reynolds numbers, where it is shown that the prediction of the near-wall peak from wall-shear-stress measurements is practically unaffected even for a one order of magnitude change in the corresponding Reynolds number of the design and test, indicating that the interaction between the near-wall peak fluctuations and the wall is approximately Reynolds-number independent. Furthermore, given the performance of such methods in the prediction of flow features in turbulent boundary layers, they have a good potential for implementation in experiments and realistic flow control applications, where the prediction of the near-wall peak led to correlations above 0.80 when wall-shear stress was used in a multiple-input or nonlinear scheme. Errors of the order of 20Â % were also observed in the determination of the near-wall spectral peak, depending on the employed method.

© The Author(s) 2018.In the present work, a numerical and experimental study of the thermoacoustic instabilities of a combustor is performed. The numerical model is represented by the one-dimensional linearised Euler Equation and an n-τ formulation for flame transfer function that describes the unsteady combustion response to these acoustic disturbances. This approach is similar to other simplified models present in the literature. However, most theoretical works assume a constant density and speed of sound in the medium, which is not realistic for combustion chambers, as the mean temperature is expected to decrease spatially as one moves away from the combustion area. Hence, to compare with experiments where chamber temperature is spatially varying, we developed a numerical solution procedure, seeking eigenvalues (complex-valued frequencies ω) indicating the stability characteristics of a given mode. Due to the non-linear dependence of the flame transfer function with ω, eigenvalues are found with a non-linear root-finding method. The acquired results met those obtained experimentally, indicating that the proposed model is capable of predicting the thermoacoustic behaviour of the combustion chamber.

Copyright © 2019 by ASME.Organized structures in turbulent jets can be modeled as wavepackets. These are characterized by spatial amplification and decay, both of which are related to stability mechanisms, and they are coherent over several jet diameters, thereby constituting a noncompact acoustic source that produces a distinctive directivity in the acoustic field. In this review, we use simplified model problems to discuss the salient features of turbulentjet wavepackets and their modeling frameworks. Two classes of model are considered. The first, that we refer to as kinematic, is based on Lighthill's acoustic analogy, and allows an evaluation of the radiation properties of sound-source functions postulated following observation of jets. The second, referred to as dynamic, is based on the linearized, inhomogeneous Ginzburg-Landau equation, which we use as a surrogate for the linearized, inhomogeneous Navier-Stokes system. Both models are elaborated in the framework of resolvent analysis, which allows the dynamics to be viewed in terms of an input-ouput system, the input being either sound-source or nonlinear forcing term, and the output, correspondingly, either farfield acoustic pressure fluctuations or nearfield flow fluctuations. Emphasis is placed on the extension of resolvent analysis to stochastic systems, which allows for the treatment of wavepacket jitter, a feature known to be relevant for subsonic jet noise. Despite the simplicity of the models, they are found to qualitatively reproduce many of the features of turbulent jets observed in experiment and simulation. Sample scripts are provided and allow calculation of most of the presented results.

© 2019 Cambridge University Press. All rights reserved.The current work presents a realizable method to control streaky disturbances in boundary layer flows and delay transition to turbulence by means of active flow control. Numerical simulations of the nonlinear transitional regime in a Blasius boundary layer are performed where streaks are excited in the boundary layer by means of a high level of free-stream turbulence. The occurring disturbances are measured by means of localized wall-shear-stress sensors and damped out using near-wall actuators, which resemble ring plasma actuators. Each actuator is powered by a time-varying signal whose amplitude is computed by processing signals from the sensors. The processed signal is the result of two control laws: The linear quadratic Gaussian regulator (LQG) and the inverse feed-forward control technique (IFFC). The use of the first control method, LQG, requires a state-space representation of the system dynamics, so the flow is described by means of a linear time-invariant operator that captures only the most relevant information of the dynamics and results in a reduced-order model (ROM). The ROM is computed by means of the eigensystem realization algorithm (ERA), which is based on the impulse responses of the real system. Collecting such impulse responses may be unfeasible when considering free-stream turbulence because of the high dimensionality of the input forcing needed for a precise description of such a phenomenon. Here, a new method to identify the relevant system dynamics and generate the needed impulse responses is proposed, based on additional shear-stress measurements in an upstream location. Transfer functions between such measurements and other downstream sensors are obtained and allow the derivation of the ERA system, in a data-driven approach that would be realizable in experiments. Finally, in order to discuss the advantages of the LQG based on the ROM and analyse its performance, the implemented LQG is compared to the IFFC, which consists of wave cancellation. The work (i) presents a systematic and straightforward way to deal with high-dimensional disturbances in order to build ROMs for a feasible control technique, and (ii) shows that even when considering practical constraints, such as the type and size of actuators and sensors, it is possible to achieve at least as large delay of bypass transition as that obtained in more idealized cases found in the literature.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.In this work we investigate the use of multiple-input, multiple-output (MIMO) transfer functions obtained empirically from a large-eddy simulation of a turbulent jet. We compare the MIMO performance with single-input-single-output (SISO) transfer functions used in previous studies. The choice of sensor placement has been made based on results of linear stability analysis from the literature. The results show that MIMO transfer functions improve on SISO results where both single-and two-point statistics are concerned. It is also found that the number of sensors necessary to converge the estimates depends strongly on Strouhal number.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Azimuthally coherent low-energy structures in the form of wavepackets are documented to play dominant role in sound radiation by subsonic turbulent jets. In earlier work, we have shown evidence of a coupling between the turbulent nozzle boundary-layer (NBL) disturbances and wavepackets in a M=0.9 turbulent jet, by means of two point statistics.1 The purpose of this study is to characterise the structures within the NBL using a high-fidelity large-eddy simulation of a M=0.4 turbulent jet. We first employ Spectral Proper Orthogonal Decomposition (SPOD) to the axisymmetric component of the flow in order to distill a low-rank approximation of the flow dynamics. This reveals the existence of coherent structures within the NBL and shows that these are correlated with wavepackets in the jet. We then model the NBL structures via a mean-flow stability analysis. Projection of the leading SPOD modes on the stability eigenmodes shows that the organised boundary layer structures can be modelled using a small number of stable eigenmodes. Finally local resolvent analysis of the mean-flow is performed. It is shown that the most-energetic nozzle structures can be succesfully modelled with optimal resolvent response modes.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Large scale, elongated structures, similar those ones widely studied in wall-bounded flows, are also present in turbulent jets. Several characteristics of these streaks can be identified via reduced order models such as resolvent analysis. The present work involves a resolvent-based study of these structures in turbulent jets. We focus on obtaining the optimal forcing that generates these energetic coherent structures. Results are compared with experimental data post-processed using spectral proper orthogonal decomposition, allowing us to draw conclusions about the nature of the non-linear forcing, since the two analyses should provide equivalent results if this term is modelled as spatially white. By identifying streaks in a global framework, we expect to better understand the mechanism by which they are generated.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.�Wavepacket models have been used extensively to predict the noise produced by turbulent subsonic and supersonic jets. Such wavepackets, which represent the organised structures of the flow, are solutions to the linearised Navier-Stokes equations. Using a kinematic two-point model, Wong et al. [1] have indicated the importance of incorporating coherence decay in modelling broadband shock-associated noise (BBSAN) in supersonic jets. In this work, we aim to improve the shock-noise model by using solutions from linear parabolised stability equations (PSE) to model the wavepacket part of the BBSAN source. The two-point coherence of the wavepackets is obtained from large-eddy simulation (LES) data of a Mj = 1.5 fully-expanded isothermal supersonic jet [2]. The aim is to build a dynamic sound-source model for BBSAN that would improve on the simplified line-source model proposed by Wong et al. [3]. We find that a frequency dependent coherence decay length scale is important in order to suppress the higher-order harmonic peaks [4] and to obtain the correct BBSAN peak shape. Moderate agreement up to St = 1 was found between the current noise predictions and those from experimental data.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The Parabolized Stability Equations (PSE) method has been extensively employed to compute the evolution of hydrodynamic instabilities in sheared flows. In its compressible-flow formulation, this method may also be used to compute sound propagation. Duct acoustics, in particular, may greatly benefit from its use, because complex boundary conditions and base-flows, including acoustic liners and developing boundary-layers, could be incorporated in the method. Furthermore, the PSE method is much less computationally demanding than standard numerical duct acoustics techniques. Aiming at unveiling this untapped potential, this work assessed the capabilities of PSE to predict sound propagation in cylindrical ducts. The acoustic field predicted with the PSE method for several simple duct models was compared with literature results. There was close agreement for ducts with uniform flow/constant wall impedance, sheared flow and axially varying base-flow temperature. The acoustic field predicted by the PSE for a duct with axially varying impedance displayed the expected trends and demonstrated that the method is able to account for such variation. Finally, prediction of acoustic propagation in a duct with turbulent boundary-layer showed that the PSE method can capture refraction and viscous dissipation of sound. These results showed that the method is able to accurately predict sound propagation through realistic duct models and is frugal with computational resources. We expect that the unveiled potentialities of the PSE method pave the way for faster acoustic liner design/optimization and deeper understanding on phenomena like liner instability.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We present a numerical method to compute the acoustic scattering by an arbitrary geometry through resolvent analysis, allowing a classification of source distributions into optimal and suboptimal with respect to their acoustic radiation. A boundary element method (BEM) is applied to solve the Helmholtz equation for a discretisation of a source distribution, and the computed pressure for each source element is used to construct the resolvent operator, which is the product of a tailored Green’s function GT and quadrature weights. To understand how the acoustic field can be modelled, the optimal harmonic forcing and the associated linear response of the flow are obtained using a singular value decomposition of the linear resolvent operator. This was performed for two different cases. The first case is a semi-infinite flat plate, a case that has an analytical tailored Green’s function available in the literature, so a numerical approximation of the resolvent operator is directly obtained by multiplying the integration weights by a discretisation of GT. Results show the optimal forcing for sources close to the plate as a quadrupole distribution concentrated at the vicinity of the trailing edge. The associated responses have the expected cardioid directivity in the far field, with variations of this for higher-order resolvent modes. In the second case we analyse three different NACA airfoils, 0012, 4412 and 0018, where the tailored Green’s function was obtained numerically, and used to build the resolvent operator. Results for three different acoustic wavenumbers k0 show that the optimal forcing has dominant contributions from the leading and trailing edge regions, as well as a relevant region near the upper and lower surfaces, where typical boundary-layer fluctuations would act. The associated response for the largest k0 in the acoustic field is a scattering cardioid with secondary scattering due to the presence of a leading edge, as expected. Resolvent analysis can also be used to decompose model sources into forcing-mode components, which lead to far-field sound given by the response modes weighted by the gains; this is carried out here for a sample harmonic source. The present methods can be used as a novel analysis tool for aeroacoustic problems, isolating clearly dominant source mechanisms with high acoustic efficiency.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The effect of addition of viscoelastic layers on the acoustic scattering quadrupoles near the trailing edge of composite plates is evaluated. For modelling of the viscoelastic material the complex modulus approach was used in combination with the frequency-temperature correspondence principle. The computation of laminate stiffness is based on Classical Lamination Theory. We employ a numerical method to compute the acoustic field scattered by finite elastic plates. Based on a Boundary Element Method, this procedure solves the Helmholtz equation subject to boundary conditions related to the vibration of the plate. These conditions are recast in terms of the vibration modes of a rectangular plate. Results show that by adding viscoelastic plies to a composite plate we modify the far-field sound scattered by turbulence near an edge of the plate. Parametric studies show that this approach reduces scattered noise at resonance frequencies. Discussions on the operating temperature, positioning and thickness of the viscoelastic layers are provided.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Hydrodynamic instabilities are directly related to large-scale coherent structures that are correlated with jet noise emission. Unravelling and accurately predicting their fundamental dynamics shows a promising direction for designing quieter jet engines. In this study, we analyze high-fidelity large-eddy simulation data of a turbulent Mach 0.4 round jet and a Mach 1.5 chevron jet. Using spectral proper orthogonal decomposition we identify, beyond the well-known1 Kelvin–Helmoholtz and Orr mechanisms, elongated alternating streamwise streaks of high and low-speed fluid that have been associated with a non-modal lift-up effect in wall-bounded shear flows. In the global three-dimensional domain, the most energetic streaks manifest for azimuthal wavenumber m = 1 and frequency St → 0. Furthermore, for the chevron jet, streaks and streamwise vortices appear due to the presence of the serrated nozzle, and they inherit the periodicity of the nozzle geometry. Finally, local (planar) spectral proper orthogonal decomposition is used to analyze the coherent structures of the chevron jet flow. Near the nozzle exit, antisymmetric and symmetric modes appear to be amplified and linked to the presence of the chevrons/streaks. Further downstream, the most energetic modes share similar characteristics to the ones observed in round jets.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The present work is dedicated to the modelling of the low-frequency part of the jet-plate interaction noise in flight conditions. An analytical model used in the work is based on the scattering of jet near-filed hydrodynamic pulsations, represented in terms of azimuthal modes, by the plate trailing edge. Unlike the static case, in the presence of a co-flow it is difficult to measure directly the azimuthal structure of the pressure in the jet near-field. In the present work, we use the technique based on the hot-wire measurements on the jet axis. This approach allows measuring velocity fluctuations related to the axisymmetric mode. The agreement found between a parabolized stability equations (PSE) model and experimentally measured velocity fluctuations on the jet axis allows using the PSE approach for reconstruction of the pressure field of the axisymmetric mode in the vicinity of the plate trailing edge in static and flight conditions. These pressure characteristics are then used as input in the analytic jet-plate interaction noise model. It is shown that this analytic model informed by PSE-reconstructed pressure field is capable to capture the main features of low-frequency jet-plate interaction noise in the presence of co-flow.

© 2019 Cambridge University Press. All rights reserved.This work deals with the closed-loop control of streaky structures induced by free-stream turbulence (FST), at the levels of 3.0Â % and 3.5Â %, in a zero-pressure-gradient transitional boundary layer, by means of localized sensors and actuators. A linear quadratic Gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator that aims to induce the exact structures that are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition (SPOD) mode, and an actuator that maximizes the energy of induced downstream structures. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the FST levels. Integrated total drag reductions observed were up to 21Â % and 19Â % for turbulence intensity levels of 3.0Â % and 3.5Â %, respectively, depending on the considered actuator. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme when a cancellation of disturbances is considered along the wall-normal direction. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer.

© 2019 International Symposium on Turbulence and Shear Flow Phenomena, TSFP. All rights reserved.Fully resolved direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers Reτ = 180 and 550 (El Khoury et al., 2013). The database was analysed using spectral proper orthogonal decomposition (SPOD) so as to identify dominant coherent structures, most of which are of streaky shape. As a reduced-order model for such structures, the linearised flow response to harmonic forcing was computed, and the analysed singular modes of the resolvent operator were analysed. For turbulent flows, this approach amounts to considering the non-linear terms in the Navier–Stokes system as an unknown forcing, treated convenienty as external. Resolvent analysis then allows an identification of the optimal forcing and most amplified flow response; the latter may be related to observed relevant structures obtained by SPOD, especially if the gain between forcing and response is much larger than what is found for suboptimal forcings or if the non-linear forcing is white noise. Results from SPOD and resolvent analysis were extracted for several combinations of frequencies, streamwise and azimuthal wavenumbers. For both Reynolds numbers, good agreement between SPOD and resolvent modes was observed for parameter combinations where the lift-up mechanism is present: optimal forcing from resolvent analysis represents streamwise vortices and the associated response are streaky structures.

© Proceedings of the 26th International Congress on Sound and Vibration, ICSV 2019. All rights reserved.This work has as main objective to analyse experimentally the influence of the effects of the flexibility in the sound emissions of trailing-edge extensions in aeronautical structures. For this, an experimental apparatus installed in a cavitation tunnel was used, whose working fluid is water. Flow was studied around a rigid NACA 0012 profile with interchangeable flexible trailing edge extensions. Two flat metal plates with different thicknesses were used as extensions, leading therefore to different values of flexural stiffness. The purpose of such tests is to obtain high Reynolds numbers, low Mach numbers and high fluid-structure loading factors (related to the ratio of fluid and solid densities). Which enhances fluid-structural interactions; acoustic effects are captured with a hydrophone installed in acoustic chamber in the section of tests. This analysis allows to make comparisons of the experimental results with predictions from aeroacoustic theory. Increasing the flexibility of the trailing edge, according to this theory, reduces aeroacoustic and hydroacoustic emissions. However, the experimental results obtained show the opposite effect: the more flexible trailing edge led to a greater sound radiation. The results suggest that there is significant changes in turbulence due to the effect of the trailing edge vibrations; a possible increase in turbulent kinetic energy due to surface vibration could explain the present results

© 2019 The Author(s) Published by the Royal Society. All rights reserved.We investigate the effects of structural damping on the interaction of a turbulent eddy with flexible plates with respect to the efficiency of aerodynamic noise generation. Potential benefits are studied using a model based on a point-reacting compliant semiinfinite plate on a spring-damper foundation. This scattering problem is solved using the Wiener- Hopf technique. We compare results for semi-infinite compliant plates with finite ones. In both cases, plate vibration lead to reductions of sound radiation, especially at resonance; damping tends to reduce such acoustic benefits. We also present a formulation that considers the effect of structural damping on the acoustic properties of finite elastic plates. Numerical results are obtained by applying a boundary element method to solve the Helmholtz equation subject to the boundary conditions imposed by the plate vibration. Under specific conditions, such as high fluid loading factor and low bending-wave Mach number, the acoustic power scattered by an edge tends to be smaller than that which propagates over the plate as bending waves. Results show that structural damping attenuates these waves and may modify the far-field acoustic pressure, mostly by reducing the scattered sound at structural resonances. All models show that large damping coefficients lead to locally overdamped responses. There is thus an ideal range of structural damping to reduce both plate vibration and acoustic scattering.

© 2019 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.The dominant acoustic radiation from turbulent jets has been associated with coherent wave-packet structures in the plume. Jet noise models are therefore often designed using the statistics of decomposed coherent fluctuations, which display wave-packet attributes. In the absence of a universal definition for wave-packet fluctuation components, several approaches have evolved to educe wave packets. These include pressure and velocity variables that are typically processed through azimuthal and/or proper orthogonal decompositions to yield different models. Large-eddy simulation database of a Mach 0.9 jet is used to suggest a unifying candidate field to obtain wave-packet statistics. The statistical properties of this acoustic mode, which comprises the irrotational-isentropic constituent of momentum fluctuations, are tested to show that it properly reproduces wave-packet statistics known to be crucial for acoustic modeling. Compared to raw pressure fluctuations, the acoustic wave packet essentially filters out the high-energy hydrodynamic fluctuations, optimally reconstructs the near- and far-field acoustic radiation, and recovers wave-packet properties with superior spatiotemporal coherence and radiative efficiency. The inherent difference between the acoustic wave packet and the pressure field is related to the distribution of phase speeds of the respective signals. These features of the acoustic mode are then used to generate a two-point wave-packet model for downstream radiation from this jet.

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.In this study the parabolized stability equations (PSE) are used to build reduced-order-models (ROMs) given in terms of frequency and time-domain transfer functions (TFs) for application in closed-loop control. The control law is defined in two steps; first it is necessary to estimate the open-loop behaviour of the system from measurements, and subsequently the response of the flow to an actuation signal is determined. The theoretically derived PSE TFs are used to account for both of these effects. Besides its capability to derive simplified models of the flow dynamics, we explore the use of the TFs to provide an a priori determination of adequate positions for efficiently forcing along the direction transverse to the mean flow. The PSE TFs are also used to account for the relative position between sensors and actuators which defines two schemes, feedback and feedforward, the former presenting a lower effectiveness. Differences are understood in terms of the evaluation of the causality of the resulting gain, which is made without the need to perform computationally demanding simulations for each configuration. The ROMs are applied to a direct numerical simulation of a convectively unstable 2D mixing layer. The derived feedforward control law is shown to lead to a reduction in the mean square values of the objective fluctuation of more than one order of magnitude, at the output position, in the nonlinear simulation, which is accompanied by a significant delay in the vortex pairing and roll-up. A study of the robustness of the control law demonstrates that it is fairly insensitive to the amplitude of inflow perturbations and model uncertainties given in terms of Reynolds number variations.

© 2018 Elsevier Inc.We present a fast numerical framework for the computation of acoustic scattering by poroelastic plates of arbitrary geometries. A boundary element method, BEM, is applied to solve the Helmholtz equation subjected to boundary conditions related to structural vibrations. This analysis is performed by rewriting the BEM boundary conditions in terms of a modal basis of the poroelastic plate which is computed by the finite element method, FEM. The current formulation allows a direct solution of the fully coupled fluid-structure interaction problem. In order to accelerate the solution of the large dense linear systems from the BEM formulation in three-dimensional problems, a wideband adaptive multi-level fast multipole method, FMM, is employed. A parametric study is carried out for the trailing-edge scattering of sample acoustic sources, representative of either uncorrelated turbulent eddies or a non-compact turbulent jet. Firstly, the noise scattering by a compact quadrupole source is analyzed for low and high frequencies for square and trapezoidal plates. Results show that geometric features such as trailing-edge sweep and serrations are very effective in the reduction of noise scattering. Moreover, it is shown that finite elastic plates are more effective in reducing the scattered noise at higher frequencies. On the other hand, porosity is more effective in reducing the radiated sound for lower frequencies. Results demonstrate that elasticity and porosity can be combined with trailing-edge sweep and serrations to reduce the scattered noise at a broader range of frequencies for poroelastic plates.

© 2018 Cambridge University Press.Motivated by the problem of jet-flap interaction noise, we study the tonal dynamics that occurs when an isothermal turbulent jet grazes a sharp edge. We perform hydrodynamic and acoustic pressure measurements to characterise the tones as a function of Mach number and streamwise edge position. The observed distribution of spectral peaks cannot be explained using the usual edge-tone model, in which resonance is underpinned by coupling between downstream-travelling Kelvin-Helmholtz wavepackets and upstream-travelling sound waves. We show, rather, that the strongest tones are due to coupling between Kelvin-Helmholtz wavepackets and a family of trapped, upstream-travelling acoustic modes in the potential core, recently studied by Towne et al. (J. Fluid Mech. vol. 825, 2017) and Schmidt et al. (J. Fluid Mech. vol. 825, 2017). We also study the band-limited nature of the resonance, showing the high-frequency cutoff to be due to the frequency dependence of the upstream-travelling waves. Specifically, at high Mach number, these modes become evanescent above a certain frequency, whereas at low Mach number they become progressively trapped with increasing frequency, which inhibits their reflection in the nozzle plane.

© 2018, The Author(s).This work deals with the feedforward active control of Tollmien–Schlichting instability waves over incompressible 2D and 3D boundary layers. Through an extensive numerical study, two strategies are evaluated; the optimal linear–quadratic–Gaussian (LQG) controller, designed using the Eigensystem realization algorithm, is compared to a wave-cancellation scheme, which is obtained using the direct inversion of frequency-domain transfer functions of the system. For the evaluated cases, it is shown that LQG leads to a similar control law and presents a comparable performance to the simpler, wave-cancellation scheme, indicating that the former acts via a destructive interference of the incoming wavepacket downstream of actuation. The results allow further insight into the physics behind flow control of convectively unstable flows permitting, for instance, the optimization of the transverse position for actuation. Using concepts of linear stability theory and the derived transfer function, a more efficient actuation for flow control is chosen, leading to similar attenuation of Tollmien–Schlichting waves with only about 10% of the actuation power in the baseline case.

© 2018 Cambridge University Press.To investigate the effects of the nozzle-exit conditions on jet flow and sound fields, large-eddy simulations of an isothermal Mach 0.9 jet issued from a convergent-straight nozzle are performed at a diameter-based Reynolds number of. The simulations feature near-wall adaptive mesh refinement, synthetic turbulence and wall modelling inside the nozzle. This leads to fully turbulent nozzle-exit boundary layers and results in significant improvements for the flow field and sound predictions compared with those obtained from the typical approach based on laminar flow in the nozzle. The far-field pressure spectra for the turbulent jet match companion experimental measurements, which use a boundary-layer trip to ensure a turbulent nozzle-exit boundary layer to within 0.5 dB for all relevant angles and frequencies. By contrast, the initially laminar jet results in greater high-frequency noise. For both initially laminar and turbulent jets, decomposition of the radiated noise into azimuthal Fourier modes is performed, and the results show similar azimuthal characteristics for the two jets. The axisymmetric mode is the dominant source of sound at the peak radiation angles and frequencies. The first three azimuthal modes recover more than 97 % of the total acoustic energy at these angles and more than 65 % (i.e. error less than 2 dB) for all angles. For the main azimuthal modes, linear stability analysis of the near-nozzle mean-velocity profiles is conducted in both jets. The analysis suggests that the differences in radiated noise between the initially laminar and turbulent jets are related to the differences in growth rate of the Kelvin-Helmholtz mode in the near-nozzle region.

© 2018 Acoustical Society of America.Trailing edge scattering is a significant source of sound, and elasticity is known to decrease the radiated sound by a process involving coupled acoustic and bending waves. Most of the analysis available in the literature to deal with this problem is limited to structures of isotropic material. A numerical method is extended, based on the solution of a boundary element method with boundary conditions given by the structural problem, to account for anisotropic composite plates, restricted to symmetric laminates. These conditions are recast in terms of the vibration modes of a rectangular plate. To obtain these modes, the hierarchical finite element method is used to model an elastic flat plate. Expressions for bending waves propagating in such plates are derived, and how the solution of the problem is modified to account for these effects is shown. Results show modifications in the scattered sound as a function of ply orientation and stacking sequence. Composite materials are shown to be advantageous, since laminates lead to lower acoustic scattering when compared to structurally equivalent metallic plates. This is due to a lower specific mass, leading to higher coupling between fluid and solid, and thus to more significant elasticity effects, decreasing substantially the radiated sound.

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.We study a modified backwards-facing step flow, with the addition of two different plates; one is a baseline, impermeable plate and the second a perforated one. An experimental investigation is carried out for a turbulent reattaching shear layer downstream of the two plates. The proposed setup is a model configuration to study how the plate characteristics affect the separated shear layer and how turbulent kinetic energies and large-scale coherent structures are modified. Measurements show that the perforated plate changes the mean flow field, mostly by reducing the intensity of reverse flow close to the bottom wall. Disturbance amplitudes are significantly reduced up to five step heights downstream of the trailing edge of the plate, more specifically in the recirculation region. A loudspeaker is then used to introduce phase-locked, low-amplitude perturbations upstream of the plates, and phase-averaged measurements allow a quantitative study of large-scale structures in the shear-layer. The evolution of such coherent structures is evaluated in light of linear stability theory, comparing the eigenfunction of the Kelvin–Helmholtz mode to the experimental results. We observe a close match of linear-stability eigenfunctions with phase-averaged amplitudes for the two tested Strouhal numbers. The perforated plate is found to reduce the amplitude of the Kelvin–Helmholtz coherent structures in comparison to the baseline, impermeable plate, a behavior consistent with the predicted amplification trends from linear stability.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.This work deals with the feedforward active control of velocity fluctuations over incompressible 3D boundary layers. Two strategies are evaluated, the Linear Quadratic Gaussian (LQG) controller, built using the eigensystem realization algorithm (ERA), is compared to a wave-cancellation scheme, obtained via the direct inversion of the frequency-domain transfer functions of the system. For the evaluated cases, it is shown that LQG leads to a wave-cancelling signal of the incoming Tollmien-Schlichting wavepacket. Such result allows further insight into the physics behind the active control of convectively unstable flows permitting, for instance, the optimization of the transverse position for actuation via a linear stability approach.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.This work deals with the characterization of the control of convective wavepackets, typical of the initial stages of transition to turbulence, using the Kuramoto-Sivashinsky equation [1] as a model problem representative of the transitional 2D boundary layer. Its simplified structure and reduced order provide a manageable framework for the study of fundamental concepts involving the control of linear wavepackets. The objective of this paper is to explore how the sensor-actuator placement interferes in the control problem. This is carried out by evaluating errors of the optimal estimator at positions where control gains are significant. Results show, in quantitative manner, why some choices of sensor/actuator placement are more effective than others for flow control.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.The present work considers control of perturbations in the boundary layer over a flat plate by means of adaptive methods. In particular, we focus our attention on a control law based on a multi-input-multi-output (MIMO) filtered-x least-mean-square (fxLMS) adaptive algorithm. The studies are performed through direct numerical simulations. The perturbation field studied here mimics those generated by freestream turbulence with different amplitude and scales. Plasma actuators and shear-stress sensors are considered to mimic a real case scenario.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.In the present work, we investigate efficient placement of sensors and actuators for closed-loop control of boundary-layer flows. The focus of this work is on the transitional flow cases where perturbation field is dominated by streaks. This is done using a reduced-order model based on resolvent analysis, an approach that also allows us to analyse the sensitivity of the flow response to control. A numerical sensitivity analysis was performed in this first approach, leading to conclusions about best choices of velocity components to be sensed and directions to be forced. Afterwards, we compared the performance between gaussian and shear sensors at the wall, focusing on the damping of the first resolvent gain using these devices. We close the work with the analysis of a plasma actuator, a configuration closer to standard choices for this kind of problem in both simulations and experiments.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved. Turbulent flow over a NACA 4412 airfoil with an angle of attack AoA = 5 ◦ was analysed using an incompressible direct numerical simulation (DNS) at chord Reynolds number of Re c = 4 · 10 5 . Snapshots of the flow field were analysed using the method of Spectral Proper Orthogonal Decomposition (SPOD) in frequency domain, in order to extract the dominant coherent structures of the flow. Focus is given to two-dimensional disturbances, known to be most relevant for aeroacoustics. The leading SPOD modes show coherent structures forming a wavepacket, with significant amplitudes in the trailing-edge boundary layer and in the wake. To model coherent structures in the turbulent boundary layer, the optimal harmonic forcing and the associated linear response of the flow were obtained using the singular value decomposition of the linear resolvent operator. The resolvent analysis shows that the leading SPOD modes can be associated to most amplified, linearised flow responses. Furthermore, coherent structures in the wake are modelled as the Kelvin-Helmholtz mode from linear stability theory (LST).

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.Unstable flows can be classified as absolutely unstable, when perturbations grow throughout the domain, and convectively unstable, where amplified perturbations are convected downstream, the flow locally returning to its equilibrium position. Absolute instabilities can be understood as a feedback loop, which can be long-ranged, as in impinging jets, or local, as in wakes and hot jets. Local feed-back mechanism involves an upstream- and a downstream-traveling mode. It is well know in the literature that in sheared flows the latter is typically a Kelvin-Helmholtz mode; however little is found on the former. Inspired by recent findings in high Mach subsonic jets, that identified trapped acoustic waves in the jet core, we examine the role of such acoustic modes on the stability of jets and wakes. Using a Double Vortex-Sheet (DVS) model, we derive conditions for which these flows behave as wave-guides, emulating acoustic ducts. We show that the upstream-traveling mode that leads to absolute instability is acoustic in essence, explaining differences in hot jets (symmetric) and cold wakes (antisymmetric) instabilities. Moreover, to evaluate the occurrence of such acoustic modes in turbulent flows, two-point correlations for a 0.4 Mach jet LES are constructed, highlighting that upstream influence in the flow is due to an acoustic mode. This novel way to understand jet and wake instabilities can lead to novel control methods which can be used, for instance, to reduce aircraft noise and drag, and minimize cyclic loads in civil and maritime structures, and might be expanded as to explain other jet/wake behaviors, as instability trends with compressibility and with instability modes other then than Kelvin-Helmoltz.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.In this work we deal with the problem of trailing edge noise scattered by a flat elastic plate. We use a model based on a boundary element method that couples the acoustic problem with the fluid-structure interaction and takes into account structural damping. The solution is obtained using the modal basis of the free vibration problem. The objective of this paper is to expand the acoustic scattering analysis for different damped plates to increase knowledge about the effects of structural damping and to identify potential benefits of using inherently damped structures, such as viscoelastic materials. It is found that there is a range of damping coefficients, capable of reducing peaks in the acoustic spectra associated with structural resonance, while mantaining the reduction of scattered sound due to elasticity. When the damping coefficient is increased above this range, the rigid-plate limit is recovered and acoustic benefits are reduced. The present results allow the selection of optimally-damped structures with respect to acoustic radiation.

© 2018, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.An experimental investigation has been undertaken to study the wavy leading edge phenomena on rectangular wing of aspect ratio 4 with a NACA 0020 airfoil at Reynolds number range from 700,000 to 3,000,000. Force measurements for various shapes of sinusoidal leading edge indicate smaller amplitude and shorter wavelength configuration (A3λ11) presenting a substantial increase in aerodynamic performance at entire range of Reynolds number tested when compared to baseline configuration, as result achieving 28.3 % of increasing in maximum lift coefficient. Oil flow visualizations reveal that tubercles with smaller amplitude have the role of delaying trailing edge flow separation. At high angles of attack, the A3 λ 11 configuration is shown to present spanwise wavelengths for which the optimal generation of streaks in turbulent boundary layers is expected according to previous experimental works. The appearance of such streaky boundary layers is a possible reason for the delay in flow separation and increase of maximum lift coefficient.

© 2018, Journal of Aerospace Technology and Management. All rights reserved.The flow patterns over a finite square cylinder of aspect ratio of 3 were analyzed experimentally in a subsonic wind tunnel using the time-resolved particle image velocimetry (TR - PIV) techniques. The near wake flow structures and vortex shedding characteristics were investigated using mean flow analysis, spectral analysis and proper orthogonal decomposition (POD). The cylinders were fixed on a elliptical leading edge flat plate, creating a boundary layer which interacted with the cylinder wake. The 2D PIV measurements were conducted at a low horizontal plane, z/h = 0.3, to investigate possible boundary layer interactions. Due to the complexity of the phenomena, the flow was characterized both in terms of average behavior and time-resolved velocity fields. Both symmetrical and anti-symmetrical vortices structures occur in the cylinder wake, which can be identified based on the coefficients of the first four POD modes. The results indicated that the alternating Karman vortex structures are dominant, described by the first two POD modes.

© 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.The dominant acoustic radiation from turbulent jets has been associated with coherent wavepacket structures in the core. Predictive models for jet noise are therefore often designed using the statistics of decomposed coherent fluctuations, which display wavepacket attributes. In the absence of a universal definition for the wavepacket component of fluctuations, there exist various approaches to educe wavepackets using different techniques, such as azimuthal and/or proper orthogonal decompositions, on variables including pressure and velocity. This yields distinct models that differ from each other. In this work, we suggest a candidate field, comprised of the irrotational and isentropic component of momentum fluctuations, termed the acoustic component/mode, to obtain wavepacket statistics. We test the statistical properties of this mode to show that it reproduces wavepacket statistics known to be crucial for acoustic field modeling, and smoothly degenerates to the pressure field (scaled by the ambient speed of sound) outside of the turbulent core. A Large-Eddy Simulation of a turbulent Mach 0.9 jet is considered. The acoustic component extracts the wavepacket form of turbulent momentum density in the turbulent jet by effectively filtering out the high-energy hydrodynamic fluctuations. Wavepacket properties, including local spatio-temporal coherence and radiative efficiency, are demonstrated through several statistical analyses. Cross-spectral-density maps and amplitude envelopes of the acoustic mode show higher spatio-temporal coherence than axisymmetric components of raw fluctuations, which are typically used to define traditional wavepacket structures. The fluctuation amplitude of the acoustic mode scales directly according to a homogeneous wave propagator. Furthermore, compared to the raw pressure fluctuations, it optimally reconstructs the near and farfield acoustic radiation. The inherent difference between the acoustic mode and the pressure field is related to the distribution of phase speeds: at all jet Mach numbers, the former successfully filters out the convective hydrodynamic component, thus correctly isolating those components that are efficient at radiating sound.

© 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.A study of the influence of the incidence angle in the acoustics of installed jets is presented here. Acoustic measurements of turbulent jets in the vicinity of a _at plate, mimicking a neighbouring wing, were compared to results from two models previously studied in the literature, both based on a wavepacket source: the Tailored Green's Function method, which considers the radiation of the turbulent structure in the vicinity of a semi-infinite flat plate, and the Boundary Element Method, which can represent the full geometry of the plate used in the experiments. Particular interest is given to analysing how the angle of attack of the plate affects the sound radiated by this installed jet configuration. The results herein confirm the behaviour identified by the said models: the scattered acoustic field follows the rotation of the plate, shifting the silence region and creating regions with lower noise levels in positions that, for an aircraft with engines under its wings, correspond to the ground. The robustness of this phenomenon is assessed by means of a Mach number analysis with the experimental approach, showing that this trend is present whenever the acoustic scattering is dominant.

© 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.This work presents a study of acoustic scattering by 3D elastic plates made of composite materials. A fast multipole boundary element method is employed to solve the Helmholtz equation subject to boundary conditions consisting of the vibration of the elastic plate. Such boundary conditions are obtained by the solution of a structural modal basis which satisfies the free vibration problem of plates composed of orthotropic materials. The fluid-structure interaction problem is coupled through the linearized Euler equation. An important difference between the composite and aluminum plates is observed in terms of the specific mass, which impacts the fluid-structure coupling. Results demonstrate that the higher frequency propagation of bending waves along composite plates leads to a further noise reduction when compared to elastic aluminum plates. Solutions obtained by twodimensional plates are compared to those obtained by fully three-dimensional ones. It is shown that the 2D models of composite plates cannot recover the directional aspects of trailing-edge noise scattering by 3D plates due to the spanwise effects of propagation of bending waves that impact on the acoustic solution.

© 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.The proximity of the source and an edge can make the acoustic scattering by wings a significant source of aerodynamic sound. Theoretical results have shown that elastic edges lead to reductions of acoustic scattering; however, experimental confirmation of theoretical trends is difficult, since surface vibrations modify both the source structure and the scattering properties. A simplified, controlled setting for measurements of acoustic scattering, allowing the evaluation of fluid-structure interactions, would thus be desirable to study how elastic edges modify the radiated sound. We present an experimental procedure to isolate the scattered field using a loudspeaker in the vicinity of at plates. The methodology is applied to three different plates, made of steel, aluminum and carbon fiber, as a demonstration. The responses of these elastic plates are studied for a sound source of dipole type near the trailing edge. The method is based on the experimental determination of frequency response functions between source and radiated sound for experiments with and without the plate; subtraction of results, accounting for amplitude and phase, isolates the scattered field. Experimental results treated with the developed procedure were compared with predictions made by numerical simulations performed with a Boundary Element Method (BEM), coupling the acoustic problem with the plate vibration. The comparison between experimental and numerical results revealed that a two-dimensional model can predict satisfactorily the reductions in scattered field by elastic plates observed in the experiment. The present methods can be used to support the choice between different materials for edges focusing on their respective acoustic benefit.

© 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.Measurements of the sound radiated by subsonic jets with Mach numbers ranging from 0.3 to 0.9 are carried out, with a view to examining the two-point statistics of the far-field sound, and, in particular, the two-point coherence. It is seen that the cross-correlation between neighbouring microphones in a polar arc decreases with increasing Mach number. The same happens with the two-point coherence, a feature predicted by wave-packet models including jitter.1 The far-field coherence results are shown to be consistent with the mentioned wave-packet model. In particular, a collapse of coherence results for all Mach numbers is obtained once measurements are plotted as a function of the angular dependence expected by the model. The results show that the far-field is consistent with a jittering wave-packet source model, which explains the observed decrease of coherence for higher Mach numbers.

© 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.Wavepackets modelling large-scale coherent structures are related to the peak noise ra- diation by subsonic jets. Such wavepacket models are well developed in the literature, and are often based on a linearization of the Navier-Stokes system; solutions of the resulting linear problem have a free amplitude, which can be obtained by comparison with experi-ments or simulations. In this work we determine amplitudes of turbulent-jet wavepackets by comparing large-eddy simulation (LES) data from Brès et al.2, 4 of a Mach 0.9 jet and fluctuation fields using the parabolized stability equations (PSE) model (Sasaki et al.18). Projection of the leading mode from spectral proper orthogonal decomposition (SPOD), applied to the LES data, onto the PSE model solutions is a way to determine the free am- plitude, and by analyzing such amplitudes for different Strouhal numbers and azimuthal modes of the turbulent jet, it is possible to notice a clear pattern of the scaling factor with varying St. Azimuthal wavenumbers m = 0, 1 and 2 show an exponential dependence of wavepacket amplitude with Strouhal number. This sheds light on how wavepackets amplitudes behave and how they are excited upstream.

© 2017 American Physical Society.This paper details the statistical and time-resolved analysis of the relationship between the near-field pressure fluctuations of unforced, subsonic free jets (0.4≤M≤0.6) and their far-field sound emissions. Near-field and far-field microphone measurements were taken on a conical array close to the jets and an azimuthal ring at 20 to the jet axis, respectively. Recent velocity and pressure measurements indicate the presence of linear wave packets in the near field by closely matching predictions from the linear homogenous parabolized stability equations, but the agreement breaks down both beyond the end of the potential core and when considering higher order statistical moments, such as the two-point coherence. Proper orthogonal decomposition (POD), interpreted in terms of inhomogeneous linear models using the resolvent framework allows us to understand these discrepancies. A new technique is developed for projecting time-domain pressure measurements onto a statistically obtained POD basis, yielding the time-resolved activity of each POD mode and its correlation with the far field. A single POD mode, interpreted as an optimal high-gain structure that arises due to turbulent forcing, captures the salient near-field-far-field correlation signature; further, the signatures of the next two modes, understood as suboptimally forced structures, suggest that these POD modes represent higher order, acoustically important near-field behavior. An existing Green's-function-based technique is used to make far-field predictions, and results are interpreted in terms of POD/resolvent modes, indicating the acoustic importance of this higher order behavior. The technique is extended to provide time-domain far-field predictions.

© 2017 Cambridge University Press.Wavepackets obtained as solutions of the flow equations linearised around the mean flow have been shown in recent work to yield good agreement, in terms of amplitude and phase, with those educed from turbulent jets. Compelling agreement has been demonstrated, for the axisymmetric and first helical mode, up to Strouhal numbers close to unity. We here extend the range of validity of wavepacket models to Strouhal number and azimuthal wavenumber by comparing solutions of the parabolised stability equations with a well-validated large-eddy simulation of a Mach 0.9 turbulent jet. The results show that the near-nozzle dynamics can be correctly described by the homogeneous linear model, the initial growth rates being accurately predicted for the entire range of frequencies and azimuthal wavenumbers considered. Similarly to the lower-frequency wavepackets reported prior to this work, the high-frequency linear waves deviate from the data downstream of their stabilisation locations, which move progressively upstream as the frequency increases.

© 2017 American Physical Society.Instability waves traveling within subsonic turbulent jets have a modal linear growth until approximatively the end of the potential core. At these stations it is believed that nonlinear and/or nonmodal effects become important and a mismatch appears between experimental measurements and linear models. In this paper the response of the linearized operator to nonlinearities treated here as an external forcing is found to be consistent with a simplified model of the Orr mechanism, supporting the idea that a nonmodal growth of disturbances occurs in the downstream region of the jet in response to the modeled nonlinear forcing.

© 2017 Cambridge University PressÂ.Coherent features of a turbulent Mach 0.9, Reynolds number jet are educed from a high-fidelity large eddy simulation. Besides the well-known Kelvin-Helmholtz instabilities of the shear layer, a new class of trapped acoustic waves is identified in the potential core. A global linear stability analysis based on the turbulent mean flow is conducted. The trapped acoustic waves form branches of discrete eigenvalues in the global spectrum, and the corresponding global modes accurately match the educed structures. Discrete trapped acoustic modes occur in a hierarchy determined by their radial and axial order. A local dispersion relation is constructed from the global modes and found to agree favourably with an empirical dispersion relation educed from the simulation data. The product between direct and adjoint modes is then used to isolate the trapped waves. Under certain conditions, resonance in the form of a beating occurs between trapped acoustic waves of positive and negative group velocities. This resonance explains why the trapped modes are prominently observed in the simulation and as tones in previous experimental studies. In the past, these tones were attributed to external factors. Here, we show that they are an intrinsic feature of high-subsonic jets that can be unambiguously identified by a global linear stability analysis.

© 2017 Cambridge University PressÂ.The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and relate them to previously observed tones in the near-nozzle region. The waves are detected in data from a large-eddy simulation of a Mach 0.9 isothermal jet and modelled using parallel and weakly non-parallel linear modal analysis of the Euler equations linearized about the turbulent mean flow, as well as simplified models based on a cylindrical vortex sheet and the acoustic modes of a cylindrical soft duct. In addition to the Kelvin-Helmholtz instability waves, three types of waves with negative phase velocities are identified in the potential core: Upstream-A nd downstream-propagating duct-like acoustic modes that experience the shear layer as a pressure-release surface and are therefore radially confined to the potential core, and upstream-propagating acoustic modes that represent a weak coupling between the jet core and the free stream. The slow streamwise contraction of the potential core imposes a frequency-dependent end condition on the waves that is modelled as the turning points of a weakly non-parallel approximation of the waves. These turning points provide a mechanism by which the upstream-A nd downstream-travelling waves can interact and exchange energy through reflection and transmission processes. Paired with a second end condition provided by the nozzle, this leads to the possibility of resonance in limited frequency bands that are bound by two saddle points in the complex wavenumber plane. The predicted frequencies closely match the observed tones detected outside of the jet. The vortex-sheet model is then used to systematically explore the Mach number and temperature ratio dependence of the phenomenon. For isothermal jets, the model suggests that resonance is likely to occur in a narrow range of Mach number, <![CDATA[$0.82<M.

© 2017 Cambridge University Press.Three methods are considered for estimating the downstream evolution of wavepackets in turbulent jets based on upstream measurements. The parabolised stability equations are used to compute a transfer function between axially and radially separated points in the flow, and the performance of this theoretical model is compared with that of two empirical approaches, direct transfer function calculation and autoregressive moving-average exogenous system identification, both of which require unsteady experimental data. The three approaches, which perform equally well, prove suitable for estimation of the downstream evolution of wavepackets using pressure data measured in the near-nozzle region. Over distances of the order of a couple of jet diameters, correlations of up to 80 % are observed between estimation and measurement. The performance deteriorates as axial separation between input and output is increased. While the two empirical approaches are limited in terms of both the number of input-output pairs and the number of flow variables that can be reasonably considered, the parabolised stability equations-based approach has no such limitation and can be used to perform full-field estimates comprising all of the dependent variables; in this it constitutes a potentially formidable means by which to perform single-input-multiple-output estimation. It has the further advantage of not requiring unsteady data for its construction, the only necessary ingredients being the mean flow and the linearised equations of motion.

© 2017 American Physical Society.Sound radiation from a subsonic turbulent jet is examined after a hypothetical removal of the near-field coherent structures in the axisymmetric component of the velocity fluctuations. With the help of a well-validated database of large-eddy simulation, the near-field coherent structures are extracted using a discrete wavelet transform (DWT), and their spatial structures are examined using a proper orthogonal decomposition (POD). The acoustic far field is calculated using Lighthill's acoustic analogy. It is shown that the coherent part extracted by DWT accounts for most of the fluctuation energy in the axisymmetric component of axial velocity, whereas the incoherent part, assumed to have a Gaussian probability distribution, has little energy. After the coherent part is removed, the axisymmetric component of the sound is found to be significantly reduced, around 7 dB in the overall sound pressure level at 30 deg with respect to the jet axis. The reduction is mostly at low Strouhal numbers (St<0.4, based on the speed of sound and the nozzle exit diameter). The first few POD modes of the near-field coherent part, which capture most of the fluctuation energy, are found to be characterized by large-scale wavy structures. After these POD modes are removed, the axisymmetric component of the sound pressure level is also reduced considerably, by around 5 dB/St at St=0.2. The results suggest that there is a causal link between the axisymmetric components of the near-field hydrodynamic fluctuations and far-field low-angle jet noise, although the axisymmetric mode constitutes only a small proportion of total fluctuation energy. It is also suggested that not only the large-scale wavy structures in low POD modes but also the smaller scale structures in higher POD modes need to be included for jet noise modeling, because they are both shown to be efficient at sound radiation.

© 2016 Elsevier LtdA model for sound generation by a jet in the vicinity of a flat plate, mimicking an exhaust jet installed near an aircraft wing, is presented. An earlier model (Cavalieri et al. J. Sound Vib. 333 (2014) 6516—6531) is further simplified by considering that the sound source is an axially-extended, cylindrical wavepacket concentrated on the jet lipline, and that this source is scattered by the trailing edge of a semi-infinite flat plate; the model is shown to match earlier results and considerably simplifies the analysis. It is used to evaluate how the parameters of the problem influence sound radiation by subsonic jets. We show that the axisymmetric mode of the source is the most acoustically efficient, similarly to what is seen for free jets; but unlike the latter problem, the sound scattered by the trailing edge is only weakly dependent on the details of the wavepacket envelope and on the two-point coherence of the source, the wavepacket phase speed being the salient feature for installed jet noise. We then use the model to evaluate how geometrical parameters of jet-plate configurations modify the radiated sound. The acoustic radiation is particularly sensitive to the jet-plate distance due to the exponential radial decay of near-field disturbances; the relative axial position of jet and trailing edge is shown to play a comparably minor role. Finally, changes in the angle of attack of the plate and in the sweep angle of the trailing edge considerably modify the radiated sound, leading to significant reductions of the acoustic intensity in some directions. The various properties of installed jet noise are further explored by appealing to the wavenumber transform of the tailored Green's function used to compute the scattered field; insight is thus provided on how jet-wing configurations might be designed so as to reduce installation noise.

© 2017 American Physical Society.An experiment has been performed in order to provide support for wave-packet jet-noise modeling efforts. Recent work has shown that the nonlinear effects responsible for the two-point coherence of wave packets must be correctly accounted for if accurate sound prediction is to be achieved for subsonic turbulent jets. We therefore consider the same Mach 0.4 turbulent jet studied by Cavalieri et al. [Cavalieri, J. Fluid Mech. 730, 559 (2013)JFLSA70022-112010.1017/jfm.2013.346], but this time using two independent but synchronized, time-resolved stereo particle-image velocimetry systems. Each system can be moved independently, allowing simultaneous measurement of velocity in two, axially separated, crossflow planes, enabling eduction of the two-point coherence of wave packets. This and the associated length scales and phase speeds are studied and compared with those of the energy-containing turbulent eddies. The study illustrates how the two-point behavior of wave packets is fundamentally different from that of the more usually studied bulk two-point behavior, suggesting that sound-source modeling efforts should be reconsidered in the framework of wave packets. The study furthermore identifies two families of two-point-coherence behavior, respectively upstream and downstream of the end of the potential core, regions where linear theory is, respectively, successful and unsuccessful in predicting the axial evolution of wave-packets fluctuation energy.

© 2016 Cambridge University Press.Linear instability waves, or wavepackets, are key building blocks for the jet-noise problem. It has been shown in previous work that linear models correctly predict the evolution of axisymmetric wavepackets up to the end of the potential core of subsonic turbulent jets. Beyond this station, linear models fail, and nonlinearity is the likely missing piece. The essential underlying nonlinear mechanisms are unknown, and it remains unclear how these should be incorporated in a reduced-order model. The nonlinear interactions are considered in this work as an 'external' harmonic forcing added to the standard linear model. This modelling framework is explored using a locally parallel resolvent analysis to determine optimal forcing and associated responses, and a global approach based on 4D-Var data assimilation aimed at finding the optimal forcing of the parabolised stability equations that would minimise errors in the predictions of wavepackets. In all of the problems considered, the critical layer is found to be relevant: it is the position where sensitivity of wavepackets to nonlinearity is greatest. It is seen that disturbances are forced around the critical layer, and tilted by shear as they are advected, in a manner suggestive of an Orr-like mechanism. The ensemble of results suggests that critical-layer effects play a central role in the dynamics of wavepackets in subsonic turbulent jets, and that inclusion of such effects may remedy the shortcomings of linear reduced-order models.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.It has been previously demonstrated in several works that the dynamics of jets important for sound radiation are dominated by low-energy and coherent azimuthal structures, wavepackets. However, the link between these and the nozzle dynamics has received less attention. It is not clear, for instance, if wavepacket amplitudes are determined by mechanisms upstream or downstream of the nozzle exit plane. In this work, a statistical analysis of a Mach 0.9 isothermal turbulent round jet is carried out with a focus on the nozzle dynamics. High-fidelity large eddy simulation data are used in the analysis. First, the azimuthal, axial and radial structures of fluctuations in the nozzle are presented. Distinct hydrodynamic and acoustic components are identified within the nozzle, and a model for the latter, based on duct acoustics, is explored. Two-point statistics of pressure and velocity fields are computed between the upstream and the downstream of the jet exit, with an aim to identify casual relation and coupling in these domains. It is seen that acoustic modes within the nozzle are linked with similar, acoustic disturbances downstream of the jet exit. Moreover, boundary-layer velocity fluctuations are shown to present significant cross-spectral densities with the downstream hydrodynamic wavepackets, suggesting that these boundary-layer disturbances excite the Kelvin-Helmholtz instability in the jet mixing layer.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.A formulation to evaluate the mean flow field of an assumed jet embedded by an outer coaxial stream is used to extrapolate measured mean-flow velocity profiles from static to flight conditions. This velocity field was then input in a parabolized stability equations (PSE) model, based on the same code of Sasaki et al.18 (2015), in order to retrieve the wavepacket signatures of axial velocity fluctuations. Overall results are in good agreement with experimental measurements. There is an observed increase in wavepacket wavelengths and phase velocities. Also, axial amplification rates are determined and show stabilization in the near-nozzle region, which is confirmed by experimental power spectral densities on the jet centreline. This tendency holds as the free-stream velocity increases.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Parabolized Stability Equations (PSE) have been shown to model wavepackets and, consequently, the near field of turbulent jets with reasonable accuracy. Because of these capabilities, PSE is a promising reduced-order model to derive control laws that could be employed to reduce the sound generation of a jet. The purpose of this work is to apply PSE to obtain time-domain transfer functions that could estimate both the fluid-dynamic and the acoustic fields of a supersonic jet. The results of this model were compared to results obtained from a database of a well-validated large-eddy simulation of a supersonic jet. Based on the unsteady pressure data at a input position, the time-domain pressure field was estimated using transfer functions obtained using PSE and an empirical method based on the LES data. The prediction scheme employed is a single-input-single-output (SISO), linear model. The unsteady pressure predicted by PSE showed good agreement with the LES results, especially if the input position is outside the mixing layer. For this region, the prediction capabilities of PSE are comparable to those of empirical transfer functions. The agreement is good even for output points taken in the acoustic field, showing that it is possible to estimate the time-domain behaviour of Mach-wave radiation using transfer functions. This indicates that PSE could not only be used to predict the sound generation, but also to open up new potentialities to attenuate noise by means of closed-loop control of the flow. The exploration of the regions where the method displayed good agreement, presented in this work, can guide the positioning of sensors and actuators for experimental implementation of closed-loop control in a jet.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.This paper is focused on the investigation of the effect of coherence decay on the acoustic field generated by a wavepacket source. Coherence decay, which is the statistical signature of jitter in the time domain, has been identified by several studies as a key parameter for the acoustic effciency of jet-noise sources.1-3, 27 Here we study its effect using the model source proposed by Cavalieri and Agarwal1 which is based on two-point statistics. This source comprises a linear wavepacket with modulated growth and coherence. The wavepacket parameters necessary to estimate the sound pressure levels radiated by the source were educed from a dual-plane-time-resolved PIV experiment. The jet Mach number was Ma = 0.4. The sound pressure levels computed were compared with the acoustic m = 0 mode obtained experimentally and the results show that when coherence decay is correctly accounted, the sound-pressure levels generated are in reasonable agreement with experimentally measured values, especially for low Strouhal numbers. A Proper Orthogonal Decomposition of the model source was also performed motivated by the relationship between POD modes and turbulent forcing and coherence decay established by other studies.29, 35, 36 It is shown that only a few POD modes are necessary to recover acoustically important wavepacket traits.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We develop a reduced-order-model framework using the parabolized stability equations and identification techniques for the closed-loop control of unsteady fluctuations along fluidic systems. These models had been successfully applied to a turbulent jet as estimation techniques and to an incompressible shear-layer for the development of closed-loop control laws. Through this paper, we propose a further investigation of the PSE-based transfer functions, exploring its flexibility to educe different control schemes and to determine the most effective sensor/actuator positions. Emphasis is be given to the feedforward and feedback configurations for flow control, and differences are understood in terms of causality. A study of the robustness to uncertainties in Reynolds and mean flow velocity, along with external perturbations is also presented. These topics allow deeper insight into the active closed-loop flow control problem and therefore may lead to more effective schemes, particularly on what concerns the experimental implementation of closed-loop control.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We perform acoustic scattering calculations by 3D poroelastic plates with swept trailing edges. A boundary element method (BEM) is applied to solve the Helmholtz equation subjected to boundary conditions related to the vibration of trapezoidal plates. This analysis is performed by rewriting the BEM boundary conditions in terms of the structural modes of the plate, which allows a direct solution of the coupled fluid-structure interaction problem. In order to accelerate the solution of the large dense linear systems from the BEM formulation, a wideband adaptive fast multipole method (FMM) is employed. The structural modes of the plate are computed either by a pseudo-spectral method or a finite element method. A parametric study is carried out for the 3D acoustic scattering problem where a model source is placed close to a swept trailing edge. Firstly, the noise scattering by a compact quadrupole source is analyzed for low and high frequencies. Results are shown for different plate configurations including rigid, porous-rigid, impermeable-elastic and poroelastic plates. Then, acoustic scattering by a jet-installation problem is presented where a turbulent jet wavepacket is placed under a poroelastic plate with a swept trailing edge.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The flow patterns over a finite square cylinder of aspect ratio H/d = 3 were analyzed experimentally. The measurements were carried out in a subsonic wind tunnel using the technique of Time Resolved Particle Image Velocimetry (TR-PIV). The near wake flow structures and vortex shedding characteristics were investigated using instant velocity maps and proper orthogonal decomposition (POD). Tests were performed at a speed of 20m/s, resulting in Re = 65300, with the cylinder facing the flow at 90°. For the wind tunnel tests, the cylinders were fixed on flat plate, creating a boundary layer which interacted with the cylinder wake. The 2D PIV measurements were conducted at three horizontal planes (z/H = 0.3, z/H = 0.5, z/H = 1) and the symmetry x-z plane. Due to the complexity of the phenomena, the flow was characterized both in terms of average behavior and time-resolved velocity fields. Both symmetrical and anti-symmetrical vortices structures occur in the cylinder wake, which can be identified based on the coefficients of the first four POD modes. The results indicated that the alternating Karman vortex structures are dominant, described by the two first POD modes. However, this structure is sometimes suppressed, leading to periods of symmetrical vortex shedding.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We perform data-driven analyses in order to explore some well-documented discrepancies between linear models and observed wavepacket dynamics in turbulent jets. The paper asks if these discrepancies may be due to non-modal effects that are not usually incorporated in linear models. A locally parallel, spatial transient-growth analysis is first performed, the objective being to address differences between linear model and data in the region downstream of the potential core. The results show how in this region, following stabilisation of the KelviHelmholtz mode, non-modal effects become important in terms of both the streamwise and radial wavepacket organisation. LES data is then used in conjunction with the linearised Euler equations, where linearisation is about the global, non-parallel, mean flow. The objective is to explore two further questions. (i) Are the mechanisms identified in the optimal, locally parallel, transient-growth study present in the real flow, which is non-parallel and does not necessarily contain optimally excited structures? (ii) Are non-modal mechanisms important for two-point coherence decay? The answers to both questions are affirmative: non-modal phenomena are shown to be a key feature of turbulent-jet wavepacket dynamics. The study further-more suggests that these mechanisms are activated by non-linear interactions distributed throughout the flow and that might be modelled as a volume forcing of the linear operator.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We study a modified backwards-facing step flow, with the addition of two different splitter plates; one is a baseline, impermeable plate and the second a perforated one. An experimental investigation is carried out for a turbulent reattaching shear layer downstream of the two plates. The proposed setup is a model configuration to study how the plate characteristics affect the separated shear layer, and also how turbulent kinetic energies and large-scale coherent structures are modified. Hot-wire measurements show that the perforated plate changes the mean profile, mostly by reducing the intensity of backflow close to the bottom wall. Disturbance amplitudes are significantly reduced up to 5 step-heights downstream the trailing edge of the plate, more specifically in the recirculation region. A loudspeaker is then used to introduce phase-locked, low-amplitude perturbations up- stream of the splitter plates, and phase averaged measurements allow a quantitative study of large-scale structures in the reattaching shear-layer. The evolution of such coherent structures are evaluated in light of linear stability theory, comparing the eigenfunction of the Kelvin-Helmholtz mode to the experimental results. We observe a close match of linear- stability eigenfunctions with phase-averaged amplitudes for all tested Strouhal numbers. The perforated plate is found to reduce the amplitude of the Kelvin-Helmholtz coherent structures in comparison to the baseline, impermeable plate, a behavior consistent with the predicted amplification trends from linear stability.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.A numerical method to compute the acoustic field scattered by finite perforated elastic plates is extended to include structural damping typical of viscoelastic materials. We employ a boundary element method to solve the Helmholtz equation subject to boundary conditions related to the vibration of the plate. In order to enable our investigation of the effect of damping, we rewrite the equations considering the terms responsible for the structural damping. Results show that by adding damping to the problem formulation, the flexural waves in the plate are attenuated and thus can modify the far-field sound scattered by turbulence near an edge of the plate. Parametric studies also show that structural damping tends to reduce scattered sound at structural ressonances. The combined effects of elasticity, porosity and damping may be more appropriate to represent the behavior of realistic materials.

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The turbulent flow over a NACA 0012 airfoil at zero angle of attack was analysed numerically using a compressible-flow large-eddy simulation for Mach number M∞ = 0:115. Snapshots of the flow field were analysed using Proper Orthogonal Decomposition (POD) in frequency domain, in order to extract the dominant coherent structures of the flow. Homogeneity in the spanwise direction allows application of a Fourier decomposition in span prior to POD, and focus is given to two-dimensional disturbances since these are expected to dominate acoustic scattering. The POD results show, in general, coherent hydrodynamics waves propagating from the region of boundary-layer tripping towards the trailing-edge, characterising a non-compact source akin to wavepackets seen in turbulent jets. The results also show the high contribution of the first POD mode in the acoustic field for each analysed frequency. To understand how coherent structures in the turbulent field can be modelled, the optimal harmonic forcing and the associated linear response of the flow using the singular value decomposition of the linear resolvent operator was performed in a locally parallel analysis. Such resolvent analysis shows that the leading POD modes can be associated to optimal, linearised flow responses.

© 2016 Acoustical Society of America.Installed jet noise is studied by means of a simplified configuration comprising a flat plate in the vicinity of a round jet. The effects of Mach number, jet-plate radial distance, and trailing-edge sweep angle are explored. Acoustic measurements are performed using a traversable 18-microphone azimuthal array, providing pressure data at 360 points on a cylindrical surface surrounding the jet-plate system. Key observations include a decrease, with increasing Mach number, of the relative level of the scattered field in comparison to the uninstalled jet; an exponential dependence of the scattered sound pressure level on the radial jet-plate separation; and considerable sideline noise reductions with increasing sweep angle, with which there is an overall reduction in acoustic efficiency. The measurements are compared with results obtained using a kinematic wavepacket source model, whose radiation is computed in two ways. A TGF for a semi-infinite flat plate is used to provide a low-order approximation of the scattering effect. Use of a more computationally intensive boundary element method provides additional precision. Good agreement between model predictions and experiment, encouraging from the perspective of low-cost prediction strategies, demonstrates that the models comprise the essential sound generation mechanisms.

© 2015, Springer-Verlag Berlin Heidelberg.A large eddy simulation of flow over a forward-facing plate is performed and the resulting database analyzed with respect to sound radiation. Aeroacoustic analysis motivates an initial data compression comprising eduction of the zeroth-order spanwise Fourier mode. The space–time structure of this component of the flow is then analyzed using POD and DMD in order to probe both the energetics and dynamics of the sound-producing flow skeleton. Both data processing techniques educe flapping and shedding modes and identify a nonlinear interaction between the two. POD shows the flapping mode to be energetically unimportant, while DMD highlights its dynamic importance. The difference mode—vortex shedding modulated by flapping of the separation bubble—is found to be the most acoustically important feature of the flow.

© 2016 The Author(s) Published by the Royal Society. All rights reserved.We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates.

© 2016 Cambridge University Press.We present a study of the turbulent and acoustic fields of subsonic jets, controlled by means of a novel actuator that introduces perturbations via steady-fluidic actuation from a rotating centrebody. The actuation can produce louder or quieter jets, and these are analysed using time-resolved stereoscopic particle image velocimetry and a hot-wire anemometer. We place the analysis in the framework of wavepackets and linear stability theory, whence we show, using solutions of the linear parabolised stability equations, that the quieter flows can be understood to result from a mean-flow deformation that modifies wavepacket dynamics, and in particular their phase velocities, which are significantly reduced. The mean-flow deformation is shown, by a triple decomposition, to be due to the generation of Reynolds stresses associated with incoherent turbulence (rather than coherent structures) which arises when the actuation energises the flow with a frequency-azimuthal wavenumber (-) combination to which the mean flow is stable. When the actuation excites the flow with an-combination to which the mean flow is unstable, the response is dominated by coherent structures, whose rapid growth takes them beyond the linear limit, where they undergo quadratic wave interactions and lead, consequently, to a louder flow.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Linear instability waves, wavepackets, are key building blocks for the jet-noise problem. It has been shown in previous work that linear models correctly predict the evolution of axisymmetric wavepackets up to the end of the potential core. Beyond this station linear models fail to predict single-point statistics; they fail more broadly in the prediction of two-point properties such as coherence; and their underprediction of the radiated noise is believed to be associated with these errors. Non-linearity is the likely missing piece. But how might it be incorporated? What are the essential underlying mechanisms? Might it be amenable to a reduced-order modelling methodology? The work described in this paper is concerned with these questions. The non-linear interactions are considered as an “external” harmonic forcing of the standard linear model; the forcing can be viewed as comprising those Fourier components of the non-linear term of the Navier-Stokes equations which are most amplified by the linear wavepackets. This modelling framework is explored using three complementary problems in which we try to understand the relationship between “external” forcing, linear system and flow response. The response of an incompressible, two-dimensional, locally parallel, shear-flow to direct, spatially localised, harmonic forcing is first considered. A resolvant analysis is then performed, again in a locally parallel context, both for the incompressible, 2D problem and for a compressible axisymmetric shear-flow where the mean flow is taken from experiments. Finally, in order to incorporate the slow axial variation of the real jet, a novel approach is considered where 4D-Var data assimilation is applied using experimental data and the Parabolised Stability Equations (PSE-4D-Var). The objective of this third, data-driven, approach is to search for an optimal forcing that might improve the match between wavepaket solutions and measurements. In all of the problems considered the critical layer, where the phase speed of the wave is equal to the local mean velocity, is found to be relevant. It is at this point that the sensitivity of the linear waves to non-linearity is greatest. In the 2D, incompressible, problem the largest response is produced when the flow is forced in the vicinity of the critical layer. The resolvant analyses show optimal forcing modes that peak on the critical layer and the optimal response modes have a critical-layer structure. The PSE-4D-Var approach shows highest sensitivity near the critical layer. Furthermore, the structure of the forced perturbations are tilted in a manner that suggests an Orr-like mechanism. The ensemble of results suggest that the critical layer may play a central role in the modelling of wavepackets in subsonic turbulent jets, and indeed may be the key to remedying the deficiencies evoked above.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Three methods are considered for estimating the downstream evolution of wavepackets in turbulent jets based on upstream measurements. The Parabolised Stability Equations are used to compute a transfer function between axially and radially separated points in the flow, and the performance of this theoretical model is compared with that of two empirical approaches, direct transfer-function calculation and Auto-Regressive Moving-Average eXogneous (ARMAX) system identification, both of which require unsteady experimental data. The three approaches, which perform equally well, prove suitable for estimation of the downstream evolution of wavepackets using pressure data measured in the near-nozzle region. Over distances of the order of a couple of jet diameters correlations of up to 80% are observed between estimation and measurement. The performance deteriorates as axial separation between input and output is increased. While the two empirical approaches are limited in terms of both the number of input- output pairs and the number of flow variables that can be reasonably considered, the PSE-based approach has no such limitation and can be used to perform full-field estimates comprising all of the dependent variables; in this it constitutes a potentially formidable means by which to perform Single-Input-Multiple-Output (SIMO) estimation. It has the further advantage of not requiring unsteady data for its construction, the only necessary ingredients being the mean flow and the linearised equations of motion.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.A formulation to evaluate the sound generated by a jet in the vicinity of a semi-infinite flat plate based on a PSE (Parabolised Stability Equations) code is proposed. Complexity is added to the model used in Cavalieri et al.,1 where the flat plate is considered semiinfinite, focusing on the trailing edge scattering of the acoustic source, by exchanging the sound source, previously considered as a semi-empirical wavepacket, for linear PSE solutions, which are based on a linearisation of the Navier-Stokes equations and avoid thus the empiricism of the previous approach. The calculation reproduces the main trends expected for this case, such as the superdirectivity at low polar angles for the free jet and the cardioid shape of the acoustic field for the installed jet, although the amplitudes reached are yet to be validated. We first study the influence of the radial distance between jet and plate, considering that this analysis is only weakly dependent on the two-point coherence of the source. We expect that, although the hydrodynamic field from the PSE has differences in comparison to the semi-empirical wavepacket, the main features observed using the previous model should be identified. This work will lead to a more reliable tool, based on first principles, to study the characteristics of the sound generated by a jet near a trailing edge.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We explore the stability characteristics of non-circular jets, by means of the direct numerical solution of a compressible Rayleigh equation considering a parallel base flow which is a function of radius and azimuth. The formulation is based on the Floquet theory of differential equations with periodic coefficients. In this sense, solutions of eigenfunctions, growth rates and phase speeds are possible for arbitrarily shaped base-flows, with azimuthal periodicity. For validation purposes, previous results for chevrons and elliptical jets were reproduced. Base flows representative of jets with chevrons and micro-jets were then fitted using an extended version of Michalke’s1 hyperbolic tangent profile, allowing here azimuthal inhomogeneities in the base flow. Sample velocity profiles in the near-nozzle region can be described by an azimuthal variation of the mixing layer position R and momentum thickness Θ. The effect of these parameters is studied so as to discern their instability properties, and it is seen that the combined azimuthal variations of R and Θ produces significant reductions of growth rates for a profile representative of chevrons; micro-jets induce mainly changes in R, with consequent reductions of spatial amplifications, but less significant than the chevron case. The influence of the number of lobes in the base-flow is also investigated, and growth rates for different numbers of chevrons collapse once the afore mentioned base-flow parameters (with the same values obtained for the chevron case) are preserved in the representative piece of the base-flow.

© American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. Acoustic waves trapped in the potential core of subsonic turbulent jets have recently been observed and explained by Towne et al. 11, 13, 14 We show that these waves also radiate outside the jet, primarily into the upstream arc. We provide an experimental identification of the Mach-number dependence of the phenomenon, which indicates that the modes are active even when evanescent, probably due to turbulent forcing. Finally, we show that for Mach numbers lower than about 0.8, the strong tonal dynamics and sound radiation (up to 170dB) that occur when a sharp edge is placed close to the jet are related to a resonance mechanism involving convective hydrodynamic wavepackets and a ‘slow’, upstream-propagating, trapped acoustic mode. A Helmholtz scaling of the resonance at higher Mach number suggests involvement of the ‘fast’ trapped modes in the range 0.8 ≤ M ≤ 1.

© American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Wavepackets obtained as solutions of the flow equations linearised around the mean flow have been shown in recent work to yield good agreement with the amplitudes and phases of turbulent fluctuations in jets. Compelling agreement has been demonstrated up to Strouhal numbers, St ≈ 1. We extend the range of validity of wavepacket models to higher values, 1.0 < St < 4.0, by comparing Parabolised Stability Equation solutions with well resolved large-eddy simulation data. The initial growth rates of the high-frequency fluctuations continue to be well predicted, but saturation occurs earlier and agreement with simulation begins to deteriorate upstream of the end of the potential core of the jet. Results show that near-nozzle dynamics for a broad range of frequencies can be modelled using linearised models, which capture well the spatial growth of Kelvin-Helmholtz wavepackets for all the studied Strouhal numbers.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.An investigation of a semi-empirical wavepacket model for free-jet and jet-surface in- teraction noise was conducted. The source term for the axisymmetric mode was extracted from a Mach 0:9 jet Large Eddy Simulation (LES) and employed to adjust the parameters of a simple line source wavepacket model. Streamwise coherence decay, in particular, was considered. The source model was propagated with both the free-field and tailored Green’s function for a semi-infinite at plate positioned at a distance of r=D = 1 from the jet axis. For the free jet, the original unit-coherence source produced a sound field with 40dB errors in comparison with experimental data. When the coherence decay extracted from the LES was used in the line source, noise levels presented very good agreement with experimental data at all polar angles. With the tailored function, at the polar angles most affected by the trailing-edge scattering, the unit-coherence source presented noise levels about 10dB lower than the experiments. Inclusion of the coherence decay extracted from the LES improved the results in the whole directivity range. These results not only confirms the importance of matching source coherence in addition to amplitude and phases of the real source, but also that the installed case is somehow less sensitive to source coherence than is the free jet.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.This study aims at the attenuation of the unsteady fluctuations along a two-dimensional mixing layer which may be considered as a prototypical problem for the evaluation of estimation and control techniques, and also a canonical problem, when compressibility is considered, for sound radiation by low-Reynolds-number free shear flows. Two strategies are proposed for the estimation of the time evolution of wavepackets based on upstream data of the simulation: a Parabolised-stability-equation (PSE) based transfer function between two positions and an empirical-transfer-function identification technique, which relies on the theoretical background established by the PSE. Both techniques present a similar performance for prediction of the fluctuations between streamwise-separated input and output positions. Furthermore, the identification method is used to determine the response of the flow to a body force actuation which allows for the elaboration of a Feedforward control framework for the fluctuations via a phase-opposition actuation. This strategy, which is evaluated with three di erent control laws, presents encouraging results both for the linearized system (i.e. described in terms of transfer functions) and for the non-linear, direct numerical simulation of the mixing layer, in which significant delays of vortex pairing are observed. The established framework is thus seen as a promising technique for real-time flow control aiming at the attenuation of wavepackets, and the corresponding reduction of the radiated sound.

© 2016 by The Authors.Coherent fluctuations in a turbulent jet at Ma = 0.4 and Re = 4.6 × 105 are analysed by combining experiments and linear stability analysis. Following the work by Dergham et al,1 we explore the connection between singular modes of the resolvent operator and the measured covariance, within the framework introduced by Farrell and Ioannou.2 Instantaneous velocity fields are measured by means of time-resolved, stereoscopic PIV, in the radial-azimuthal plane at different locations along the streamwise direction. Proper orthogonal decomposition of the cross-spectral density covariance is applied for extracting coherent wavepackets, at a given frequency. The mean flow field is used for the linear stability analysis. We compute the singular value decomposition of the linear resolvent operator, derived from the fully compressible Navier-Stokes equations, in order to identify the optimal harmonic forcing and the associated linear flow response. The analysis shows a remarkable agreement between the modal structures computed by linear analysis and the wavepackets extracted by statistical analysis of experimental measurements. These results suggest that the stochastic framework may help in shedding light on the structure of the non-linear forcing responsible for the wavepackets as observed in experiments.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The mean flow stability of a Mach 0.9 turbulent jet is investigated by means of global linear theory with a focus on acoustic effects. A novel class of resonant acoustic modes that are trapped within the potential core, and whose eigenvalues appear as discrete branches in the global stability spectrum, is studied in detail. A dispersion relation is reconstructed from the global modes, and shown to accurately predict energy bands observed in the PSD of a high-fidelity LES. Similarly, the acoustic far-field radiation patterns of the trapped modes are compared to the LES. A favorable agreement between the global mode waveforms and coherent structures educed from the LES is found for both the trapped acoustic wave component inside the core and the far-field radiation.

© 2016 by The Authors.An experiment has been designed in order to address the questions that remain open following the experiments, analysis and modelling reported in Cavalieri et al (2013). The same Mach 0.4 turbulent jet is considered, but this time using two independent-but-synchronised, time-resolved, stereo PIV systems. Each system can be moved independently, allowing simultaneous measurement of velocity in two, axially separated, cross-flow planes, enabling eduction of the two-point coherence of wavepackets. This and the associated lengthscales are studied and compared with those of the energy containing turbulent eddies. Different scaling behaviours are observed which have important implications for jet-noise modelling.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Sound radiation from a subsonic turbulent jet is examined after a hypothetical removal of near-field coherent structures in the low azimuthal components of the velocity fluctuations. With the help of a well-validated database of large-eddy simulation, the near-field coherent structures are extracted using discrete wavelet transform (DWT), and their spatial structures are examined using proper orthogonal decomposition (POD). The acoustic far field is calculated using Lighthill’s acoustic analogy. It is shown that the coherent part extracted by DWT accounts for most of the fluctuation energy of axial velocity, whereas the incoherent part, assumed to have a Gaussian probability distribution, has little energy. After the coherent part is removed, the axisymmetric component of the sound is found to be significantly reduced by around 7 dB in the overall sound pressure level at 30 degrees with respect to the jet axis. The reduction is mostly at low Strouhal numbers (St < 0.4, based on the speed of sound and the nozzle exit diameter). The first few POD modes of the near-field coherent part, which capture most of the fluctuation energy, are found to be characterised by large-scale wavy structures. After these POD modes are removed, the axisymmetric component of the sound pressure level is also reduced considerably, by around 5 dB/St at St = 0.2. When velocity components in the first and second helical azimuthal modes are removed, the overall sound pressure levels are reduced for a wide range of polar angles. The results also show that axial velocity fluctuations in the second helical mode are closely associated with sound radiation at high polar angles. Far-field azimuthal decomposition indicates that the sound reduction takes place in multiple azimuthal modes. The results suggest that there is a causal link between the axisymmetric components of the near-field coherent fluctuations and far-field low-angle jet noise. On the other hand, velocity components in near-field helical azimuthal modes are coupled for sound radiation in helical azimuthal modes. It is also suggested that not only the large-scale wavy structures in low POD modes, but also the smaller-scale coherent structures in higher POD modes need to be included for jet noise modelling, because they are both shown to be efficient at sound radiation.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Installed jet noise is studied by means of a simplified configuration comprising flat rectangular plates situated in the nearfield of a round jet. Acoustic measurements are performed using a traversable 18-microphone azimuthal array, providing pressure data at 360 points on a cylindrical surface surrounding the jet-plate system. A rigid aluminium plate and a flexible, composite plate were tested to assess the influence of the plate stiffness on the scattered sound. The numerical predictions are confirmed by experiments and suggest that a reduction in the scattered sound level can be achieved as the flexibility of the plate is increased.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.It is well known that large-scale coherent structures play a crucial role in sound radiation from jets. Their acoustic efficiency is believed to be associated with their interaction with smaller-scale structures. This study conducts numerical experiments on a low Reynolds number jet where smaller-scale structures are artificially suppressed by increasing the eddy viscosity in a subgrid model. It is found that when the smaller-scale structures are sup- pressed, the fluctuation energy of the large-scale structures around the most unstable Strouhal numbers (0.25 < St < 0.4, based on jet exit velocity and nozzle diameter) remains at almost the same level as the original. The coherence length scales of the large-scale structures (at 0.3 < St < 0.6) generally increase after the flow transitions into turbulence. A proper orthogonal decomposition (POD) shows that the first POD mode at low Strouhal numbers have wavelike patterns, and that the peak energy and convection speed of these wavepackets are not influenced much by the increasing eddy viscosity. The radiated sound is shown to decrease significantly at high Strouhal numbers at various polar angles, but to remain approximately the same at low Strouhal numbers (St < 0.4). It is suggested that the instability waves at the most unstable Strouhal numbers (St ≈ 0.35) are not significantly affected by the structures at high Strouhal numbers (St > 0.6), and that the sound radiation at low Strouhal numbers (0.25 < St < 0.35) at various polar angles possibly comes from the large-scale structures in the similar Strouhal number range.

© American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.To improve understanding and modeling of jet-noise source mechanisms, extensive experimental and numerical databases are generated for an isothermal Mach 0.9 turbulent jet at Reynolds number Re = 106. The large eddy simulations (LES) feature localized adaptive mesh refinement, synthetic turbulence and wall modeling inside the nozzle to match the fully turbulent nozzle-exit boundary layers in the experiments. Long LES databases are collected for two grids with different mesh resolutions in the jet plume. Comparisons with the experimental measurements show good agreement for the flow and sound predictions, with the far-field noise spectra matching microphone data to within 0.5 dB for most relevant angles and frequencies. Preliminary results on the radiated noise azimuthal decomposition and temporal intermittency are also discussed. The azimuthal analysis shows that the axisymmetric mode is dominant at the peak radiation angles and that the first 3 Fourier azimuthal modes of the LES data recover more than 97% of the total acoustic energy at these angles. The temporal analysis highlights the presence of recurring intermittency in the radiated sound for the low-frequency range and main downstream angles. At these frequencies and angles, temporally-localized bursts of noise can reach levels up to 3 or 4 dB higher (or lower) than the long-time average.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and that have been previously detected as tones in the near-nozzle region. Using three models (the linearized Euler equations, a cylindrical vortex sheet, and a cylindrical duct with pressure release boundary conditions), we show that these waves can be described by linear modes of the jet and correspond to acoustic waves that are trapped within the potential core. At certain frequencies, these trapped waves resonate due to repeated reflection between end conditions provided by the nozzle and the streamwise contraction of the potential core. Our models accurately capture numerous aspects the potential core waves that are extracted from large-eddy-simulation data of a Mach 0.9 isothermal jet. Furthermore, the vortex sheet model indicates that this behavior is possible for only a limited range of Mach numbers that is consistent with previous experimental observations.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.A model for sound generation by a jet in the vicinity of a flat plate, mimicking an exhaust jet installed near an aircraft wing, is presented. An earlier model (Cavalieri et al. J. Sound Vib. 333 (2014) 6516—6531) is further simplified by considering that the sound source is an axially-extended, cylindrical wavepacket concentrated on the jet lipline, and that this source is scattered by the trailing edge of a semi-infinite flat plate; the model is shown to match earlier results and considerably simplifies the analysis. It is used to evaluate how the parameters of the problem influence sound radiation by subsonic jets. We use the model to evaluate how geometrical parameters of jet-plate configurations modify the radiated sound. The acoustic radiation is particularly sensitive to the jet-plate distance due to the exponential radial decay of near-field disturbances; the relative axial position of jet and trailing edge is shown to play a comparably minor role. Finally, changes in the sweep angle of the trailing edge considerably modify the radiated sound, leading to significant reductions of the acoustic intensity in some directions. The sweep-angle dependency of installed jet noise is further explored by appealing to the wavenumber transform of the tailored Green’s function used to compute the scattered field; insight is thus provided on how jet-wing configurations might be designed so as to reduce installation noise.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.We study mechanisms of noise generation by an airfoil at zero angle of attack using flow-acoustic correlations. We use a large-eddy simulation (LES) of the compressible flow around a NACA0012 airfoil for M∞ = 0.115 and Rec = 408000. With this simulation we analyse flow fluctuations around the airfoil, such as pressure and velocity, and relate them to the far-field sound using standard correlation techniques. Similar to the results of Cava- lieri et al.,3 who have obtained more significant flow-acoustic correlation for turbulent jets when the axisymmetric mode was isolated, we have noticed much higher correlations in the present problem when the two-dimensional mode, i.e. spanwise-averaged uctuations, was isolated from the turbulent flow and subsequently correlated to the acoustic pressure. This result is justified theoretically by an analysis of the tailored Green's function for a half plane, where we find that a necessary condition for trailing edge scattering is ǀkzǀ < k, where kz is the spanwise wavenumber of turbulent disturbances and k is the acoustic wave number. Two-dimensional perturbations, associated to kz = 0, are always radiating. Isolation of spanwise-coherent disturbances is thus a means of filtering non-radiating structures. Another feature that tends to increase correlation coefficients is the use of the difference between uctuations in the upper and lower surfaces of the airfoil, which again is in line with theory: when disturbances are in phase opposition between the two sides of the airfoil acoustic scattering is maximal.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Recent studies have shown that while linear wavepacket models accurately reproduce experimentally observed, low azimuthal-wavenumber pressure fluctuations in the near field of turbulent jets, they significantly under-predict the intensity of the acoustic radiation produced in the subsonic case. In a linear context, “jittering” of the wavepackets, which can arise due to both stochastic and nonlinear interactions that force the wavepackets, has been hypothesized as a mechanism by which the radiation efficiency of wavepackets is greatly increased. We use data from a carefully validated large-eddy-simulation of a Mach 0.9 turbulent jet to explore this hypothesis. We analyze the LES data in frequency space using windowed segments of a set of snapshots spanning two thousand acoustic time units. We apply the linearized Navier-Stokes operator to this data in order to compute the non- linear forcing field that occurred in the LES simulations, and propose several techniques for educing the relation between the forcing and the observed flow fields. In particular, we employ empirical techniques to identify high energy modes (via proper orthogonal decomposition) in both the flow and acoustic fields, as well as a set of empirical resolvent modes that maximize either the gain between the forcing and flow fields, or the gain between the forcing and acoustic fields. The high gain modes are similar to the high energy modes in both cases, suggesting that the forcing fields are nearly uncorrelated in each realization. Both flow and acoustic fields appear to be driven by largely incoherent forcing corresponding to turbulence in the region of strong shear and, in particular, close to the critical layer. With the caveat that we have thus far only analyzed the axisymmetric mode of the disturbance fields, the results suggest that accurate linear wavepacket models that capture both the coherent flow and acoustic fields can be constructed if appropriate parameterizations of the stochastic forcing can be found, i.e. such forcings will excite the high gain modes to produce the observed coherent structures in both the near and far field.

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The mechanism of sound generation in the downstream direction of jets is often associated with large-scale structures, or wavepackets. These are often modelled using frequency-domain models based on the linearisation of the Navier-Stokes system. A closed-loop control formulation requires a time-domain model in order to calculate appropriate gains between sensors and actuators so as to minimise a given objective. In the present work, we address how such a control scheme can be developed using time-domain transfer functions, derived from corresponding frequency-domain models. We first exemplify the application of the present technique for a simplified 1D problem based on the nonlinear Burgers’ equation. The proposed method is then applied for time-domain transfer functions obtained using wave-packet models for jets, as an attempt to control large-scale structures in such flows and consequently reduce their sound radiation.

© 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.An experiment has been designed to help answer the questions that remained unan- swered following the experiments, analysis and modelling reported in Cavalieri et al. [1]. The same Mach 0.4 turbulent jet is here considered, but this time using two independent- but-synchronised, time-resolved, stereo PIV systems. Each system can be moved indepen- dently, allowing the simultaneous measurement of three velocity components in two, axially separated, cross-ow planes. This note outlines the motivation, describes the experiment and shows some preliminary results.

© 2015, American Institute of Aeronautics and Astronautics Inc, AIAA. All Rights Reserved.We present a fast numerical framework to compute the acoustic scattering by 3D poroe-lastic plates. A boundary element method (BEM) is applied to solve the Helmholtz equation subjected to boundary conditions related to the vibration of the plate. This analysis is performed by rewriting the boundary conditions in terms of the structural modes of the plate, which allows a direct solution of the coupled problem. In order to accelerate the solution of the large dense linear systems from the BEM formulation, a wideband adaptive fast multipole method (FMM) is employed. A pseudo-spectral method is applied to compute the structural modes of the plate. A parametric study is carried out for a 3D acoustic scattering problem where a model source is placed close to the trailing edge of a plate with finite span and chord. The current study presents results for plates with a clamped leading edge and free trailing and lateral edges. Results are shown for different configurations including rigid, porous-rigid, impermeable-elastic and poroelastic plates. The effects of plate aspect ratio are evaluated for different ranges of acoustic and plate vibration frequencies. A study of trailing edge scattering by 2D and 3D acoustic sources is also presented. It is shown that the combination of elasticity and porosity can reduce the intensity of the far-field sound scattered by turbulence near an edge of the plate.

© 2015 by The Authors, Airbus.Installed jet noise is studied by means of a simplified configuration comprising a flat plate in the vicinity of a round jet. The effects of jet Mach number, jet-plate radial distance and trailing-edge sweep angle are explored. Acoustic measurements are performed using a traversable 18-microphone azimuthal array, providing pressure data at 360 points on a cylindrical surface surrounding the jet-plate system. Key obsevations include: a decrease, with increasing Mach number, of the relative level of the scattered field in comparison to the uninstalled jet; an exponential dependence of the scattered sound pressure level on the radial jet-plate separation (consistent with a wavepacket source), provided the plate is not in a region of strong mean flow; and, perhaps most interestingly, considerable sideline noise reductions with increasing sweep angle—an evaluation of the integrated sound power radiated by the system shows that this is more than just a directivity modification, the acoustic efficiency of the system decreasing as the sweep angle is increased. The measurements are compared with results obtained using a kinematic wavepacket source model—previously identified from uninstalled measurements—whose radiation is computed in two ways. The tailored Green’s function for a semi-infinite flat plate is used to provide a low-order approximation of the scattering effect; the computation is fast and straightforward, and good agreement with measurements demonstrates that much of the essential source and scattering mechanisms are correctly captured. Use of a more computationally intensive Boundary Element Method provides additional precision, lobes associated with secondary scattering from the other edges and corners being correctly predicted. That such simplified models can reproduce so much of the aeroacoustic behaviour of this high-Reynolds-number, fully turbulent, installed jet, is not only encouraging from the perspective of low-cost prediction strategies, it is first and foremost a demonstration that the models comprise the essential sound generation mechanisms.

© 2015, American Institute of Aeronautics and Astronautics Inc, AIAA. All Rights Reserved.Trailing edge scattering is a significant source of sound in aeroacoustics, and elasticity is known to decrease the radiated sound by a process involving coupled acoustic and bending waves. Most of the analysis in the literature is appropriate for metallic plates, which are isotropic. We extend a numerical method, based on the solution of a boundary element method (BEM) with boundary conditions given by the structural problem, to account for anisotropic, composite plates. We perform a comparison between composite and metallic plates with the same thickness and similar bending stiffness. For both cases, elasticity is seen to reduce the scattered sound; composite plates lead to greater reductions of far-field sound due to their lower specific mass and consequent higher fluid loading factor. Results also show that orientation of laminae can be used so as to optimise plates for acoustic radiation at specific Helmholtz numbers k0 of interest: different lay-ups present changes in structural resonance frequencies, and higher acoustic benefits can be obtained by ensuring that a given k0 is between two resonances, in a situation where acoustic excitation and elastic response are in phase opposition.

An investigation of jet-surface interaction noise was conducted. Simulations of an isothermal jet flow with Mach number M = 0.4 close to a flat plate were carried out using Large-Eddy Simulation based on the Lattice-Boltzmann Method (LBM). Far-field acoustic results were obtained via the Ffowcs Williams and Hawkings (FW-H) surface integral method. Analyzed cases included a jet in isolation and other configurations including jet-plate interaction with two distances (r/D = 1 and 0.6) between plate and jet axis, and validation with experimental results is provided. The influences in the far-field sound caused by a sweep angle, between the plate trailing edge and the jet axis, were also investigated. Results for the isolated jet and plate at r/D = 1 showed reasonable agreement with experimental data. The trends of the sweep effect were well captured by the simulation model. Results for the plate at r/D = 0.6 showed an increase in noise levels in the St range affected by the installation. Comparisons of the Power Spectral Density (PSD) of the axial velocity with the solution of linear Parabolized Stability Equations (PSE) showed that even in the case of the closest plate position, the evolution of the axisymmetric mode in the centerline was not significantly affected by the presence of the surface.

This paper examines the impact of removing coherent structures (CS) on jet noise. By applying discrete wavelet transform (DWT) and Fourier transform in azimuth, the jet flow is decomposed into wave packets (WP), coherent eddies (CE), and incoherent structures (IS). It is shown that CS which consist of WP and CE constitute most of the fluctuation energy, and that IS have small coherence length scale and account for almost all the fluctuation energy in the high Strouhal number range. When a similar decomposition is applied to the far field and CS are removed from the low azimuthal modes, a significant sound reduction is obtained compared with the original jet. When viewed in the frequency domain, removal of the CS reduces acoustic energy only at low Strouhal numbers (St, based on jet exit velocity and diameter). The values of the correlations between the CS in the axisymmetric modes of the near and far field are significantly higher than those reported for flow-acoustic correlations of the axisymmetric mode. This suggests a link connecting the near-field and far-field CS, and that most of the low St acoustic energy is reduced by removing WP. It is discussed that the sound reduction obtained by removing CS from the low azimuthal modes of the acoustic field is an over-estimation of what could be achieved for the jet-without WP in the velocity field.

Copyright © 2014 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.Aeroacoustic predictions of a model airframe noise problem are conducted to assess the effects of wake interaction on flow and acoustic fields. Simulations of unsteady low Reynolds number flows, including both noise generation and its subsequent propagation to the far field, are performed for a configuration composed of a cylinder placed above a NACA 0012 airfoil. An assessment of cylinder position and freestream Mach number effects on sound radiation is presented. It is observed that intense interference among cylinder and airfoil dipoles occurs for all configurations analyzed. In this case, each body scatters the sound emitted by the other. For moderate Mach number flows with wake interaction, quadrupole sources become important to the total acoustic prediction, specially for the downward noise radiation. In order to investigate how wake interaction affects noise radiation, a comparison between the current model problem with a single cylinder case is presented. Results show that wake interaction becomes a major feature of the airfoil-cylinder flow, causing a faster downstream decay of convecting disturbances when compared to the isolated cylinder case. This issue is further studied using a linear stability calculation for the wake interaction problem, which shows that for higher Mach numbers, compressibility effects lead to the formation of a wave-packet structure in the wake with higher maximum amplitude, higher convection Mach number and a sudden spatial decay. Therefore, wake interaction and compressibility effects play a key role in the present model problem and are proposed as responsible for the increase of quadrupole noise radiation.

© 2014 Elsevier Masson SAS. All rights reserved.Locally-parallel linear stability theory (LST) of jet velocity profiles is revisited to study the evolution of the wavepackets and the manner in which the parabolized stability equations (PSE) approach models them. An adjoint-based eigenmode decomposition technique is used to project cross-sectional velocity profiles measured using time-resolved particle image velocimetry (PIV) on the different families of eigenmodes present in the LST eigenspectrum. Attention is focused on the evolution of the Kelvin-Helmholtz (K-H) eigenmode and the projection of experimental fluctuations on it, since in subsonic jets the inflectional K-H instability is the only possible mechanism for linear amplification of the large-scale fluctuations, and governs the wavepacket evolution. Comparisons of the fluctuations extracted by projection onto K-H eigenmode with PSE solutions and PIV measurements are made. We show that the jet can be divided into three main regions, classified with respect to the LST eigenspectrum. Near the jet exit, there is significant amplification of the K-H mode; the PSE solution is shown to comprise almost exclusively the K-H mode, and the agreement with experiments shows that the evolution of this mode dominates the near-nozzle fluctuations. For downstream positions, the Kelvin-Helmholtz mode becomes stable and eventually merges with other branches of the eigenspectrum. The comparison between PSE, experiment and the projection onto the K-H mode for downstream positions suggests that the mechanism of saturation and decay of wavepackets is related to a combination of several marginally stable modes, which is reasonably well modeled by linear PSE, but cannot be obtained in the usual application of locally-parallel stability dealing exclusively with the K-H mode. In addition, the projection of empirical data on the K-H eigenmode at a near-nozzle cross-section is shown to be a well-founded method for the determination of the amplitudes of the linear wavepacket models.

© 2014 Elsevier Ltd.We present an investigation of the acoustic scattering due to the presence of a flat plate in the vicinity of a turbulent subsonic jet. Experiments have been performed to measure changes in the velocity and sound fields for Mach numbers ranging from 0.4 to 0.6, and for distances between the plate and the jet axis ranging from 1 to 2 jet diameters. Results show only very slight changes in the mean flow induced by the plate, and no differences in the velocity fluctuation amplitudes on the jet centreline, suggesting that wave-packet models derived for jets without installation effects may be representative of the installed case, at least for the jet-plate distances considered here. The acoustic results, on the other hand, include a significant increase in the low-frequency sound radiation, and phase opposition between the shielded and unshielded sides of the plate. There is an exponential decay of the scattered sound with increasing jet-plate distance, suggesting that low-frequency radiation is due to the scattering of evanescent hydrodynamic wavepackets in the jet near field. To model this phenomenon, we calculate sound generation from wave-packet sources in two ways: on one hand we use a tailored Greens function that accounts for the presence of a semi-infinite, rigid flat plate; and, on the other, we solve numerically the Helmholtz equation, with boundary conditions representative of a finite flat plate, using a fast multipole boundary element method. In agreement with the experimental measurements, numerical calculations capture the phase opposition between shielded and unshielded sides, and the scattered sound depends exponentially on the position of the plate. This exponential dependence is related to non-compact effects associated with wavepackets, as compact sources would lead to an algebraic dependence. Acoustic pressure directivities computed for the finite and semi-infinite flat plates agree well where acoustic reflection and diffraction from the trailing edge of the plates are concerned. However, additional diffraction effects associated with the leading and lateral edges of the finite plate, and which take the form of multiple lobes in the directivity, are illustrated by the comparison. As the plate dimensions are increased, i.e. the Helmholtz number is increased, the solution approaches that obtained for the semi-infinite plate.

© 2014 Cambridge University Press.Wavepackets obtained by a linear stability analysis of the turbulent mean flow were shown in recent works to agree closely with some relevant statistics of turbulent jets, such as power spectral densities and averaged phases of flow fluctuations. However, when such wavepacket models were used to calculate the far-field sound, satisfactory agreement was only obtained for flows that were supersonic relative to the ambient speed of sound; attempts with subsonic flows led to errors of more than an order of magnitude. We investigate here the reasons for such discrepancies by developing the integral solution of the Helmholtz equation in terms of the cross-spectral densities of turbulent quantities. It is shown that agreement of a statistical source, such as would be obtained by the above-mentioned wavepacket models, in averaged amplitudes and phases in the near field is not a sufficient condition for exact agreement of the far-field sound. The sufficient condition is that, in addition to the amplitudes and phases, the statistical source should also match the coherence function of the flow fluctuations. This is exemplified in a model problem, where we show that the effect of coherence decay on sound radiation is more prominent for subsonic convection velocities, and its neglect leads to discrepancies of more than an order of magnitude in the far-field sound. For supersonic flows errors are reduced for the peak noise direction, but for other angles the coherence decay is also seen to have a significant effect. Coherence decay in the model source is seen to lead to similar decays in the coherence of two points in the far acoustic field, these decays being significantly faster for higher Mach numbers. The limitations of linear wavepacket models are illustrated with another simplified problem, showing that superposition of time-periodic solutions can lead to a correlation decay between two points. However, the coherence between any pair of points in such models remains unity, and cannot thus represent the behaviour observed in turbulent flows.

We present a numerical method to compute acoustic scattering by finite poroelastic plates. A boundary element method is applied to solve the Helmholtz equation subjected to boundary conditions related to the vibration of the plate. This analysis is performed by rewriting the boundary conditions in terms of the vibration modes of the plate, which allows an iterative solution of the problem. A parametric study is carried out for a two-dimensional acoustic problem of scattering by a point quadrupole by poroelastic plates with infinite span but finite chord, with a clamped leading edge and a free trailing edge. It is shown that both elasticity and porosity tend to decrease the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce the strength of acoustic scattering when excited near resonance by an acoustic source. However, finite- plate effects become significant for low Helmholtz numbers, where elasticity is shown to produce lower sound reductions compared to the rigid case, and in some cases an increase of the scattered sound. Porosity, on the other hand, is shown to become more effective in reducing the radiated sound for low Helmholtz numbers. Poroelastic plates have the combined beneficial effects of elasticity and porosity, and are shown to be effective in reducing the scattered sound for a broader range of Helmholtz numbers.

It has been shown recently that the near-field of subsonic turbulent jets is composed largely of wavepackets produced by the linear interaction of the perturbing velocity field with the steady base flow. However, computation of the far-field sound from such wavepacket models inevitably lead to an error of more than an order of magnitude despite a close statistical agreement near the jet axis. Recent work (Cavalieri and Agarwal, "Coherence decay and its impact on sound radiation by wavepackets", Journal of Fluid Mechanics, Vol. 748, 2014) suggests that this discrepancy may be caused by the mismatch between the perfect coherence in linear wavepacket models and the decaying coherence in experimental flow fluctuations. We investigate whether this is the case for wavepacket sound radiation in two axisym- metric turbulent jets of Mach number 0.4 and 0.6 using a Linearized Euler Equation (LEE) solver. The objective is to impose the coherence function of flow fluctuations found in experiments on near-field structures, generated using LEE with a fluctuating inflow boundary condition. This is achieved with a boundary value formulation on a cylindrical surface which encloses the jet and using the linear wave equation to project the near-field pressure on the surface to the far-field. This technique is adapted to extrapolate the two-point cross spectral density (CSD) to the far-field. The effect of multiplying the CSD on the cylindrical surface with a coherence contour envelope obtained from experiments is tested prior to projecting the results to the far-field. We observe that matching the near-field coherence profile in this manner yields far-field sound pressure levels that show good agreement with experimental results. An investigation of the CSD on the cylindrical surface reveals that the effect of the coherence envelope is to spread the hydrodynamic component of the linear wavepacket source on to acoustic wavenumbers resulting in a more efficient acoustic source. These results suggest that the decaying coherence profile observed in experiments is the missing link in relating the far-field sound to near-field fluctuations in turbulent jets. This paves the way for the development of a jet noise model which is linear in all aspects, except the coherence profile where all of the non-linearity is confined.

We use model problems to explore the mechanisms that underpin jitter and coherence decay-related phenomena, both of which are important for wavepacket sound generation from subsonic jets. The inquiry is motivated by the incapacity of linear models to capture these important dynamic traits explicitly, and the need to understand how to distill a non-linear system down to some simplified form in which they are preserved. We first consider solutions of the non-linear Burgers' equation subject to periodic and stochastic upstream forcing; from these we obtain time-invariant and time-varying base flows about which linearisation is performed. The linearised systems are driven with up- stream conditions similar to the non-linear case and the solutions analysed in terms of jitter and coherence decay; both can be preserved when linearisation is performed about a time-varying base flow. A similar investigation is then undertaken using the Linearised Euler Equations (LEE). Solutions are obtained using a previously studied, experimentally obtained, base flow, on which low-frequency, deterministic and stochastic, time variations are imposed. This intro- duction of time variations in the base flow amounts to a constrained permission of non-linear dynamics and additional, associated, degrees of freedom in what remains a linear model. The axial and radial hydrodynamic structures and radiated sound fields of the resulting wavepackets are compared with those obtained using a steady base flow. It is shown that many of the discrepancies observed between classical linear models (stability theory or LEE for instance) and experiment can be reduced: the wavepackets jitter, their axial coherence decays, the axial evolution of their uctuation energy downstream of the end of the po- tential core shows qualitative agreement with experiment; and, most importantly, sound levels are boosted by many orders of magnitude. © 2012 by P. Jordan.

Using linear stability analyses, a systematic approach is followed to determine modifications to the base flow of a jet that reduce the growth rate and phase speed of disturbances in the Kelvin-Helmholtz instability. This has the potential to reduce the sound radiated from wavepackets in the jet. For the two-dimensional Bickley jet, an adjoint-based sensitivity analysis is used to determine the sensitivity of the eigenvalues of the Orr-Sommerfeld equation to base-flow changes. The growth rate of the disturbances may be reduced by reducing the shearing near the points where the adjoint eigenfunction peaks. When targeting a reduction in the phase speed of the disturbances, the base flow also changes around the peak of the adjoint eigenfunction. It is seen that base-flow changes to reduce growth rate or phase speed at a certain frequency can have adverse effects at higher frequencies. The analysis of the two-dimensional jet is extended and applied to an axisymmetric round jet by solving the linearized Navier-Stokes equation and its adjoint, to determine the stability characteristics and the optimal base-flow changes. For the round jet, as for the 2D jet, the base flow changes around the peak of the axial adjoint eigenfunction, with growth-rate reductions obtained by reducing shearing at this point. Attempts to reduce the growth rate of disturbances are successful over a range of frequencies around the target frequency, but can have adverse effects at high frequencies. Also, upon increasing deviations between the modified velocity profile and the reference, a second mode becomes unstable and dominates the behaviour at high frequencies, leading to high growth rates. Attempts to reduce the phase speed do not have the same adverse high frequency effects, but do cause the growth rate to increase across a range of frequencies.

The dynamics of large scale structures in unforced turbulent jets at subsonic speeds have been related to the generation of the peak noise radiated the aft direction. The utility of instability wavepackets computed by linear stability theory or parabolised stability equations (PSE) have been demonstrated for the modeling of the near-field pressure fluctuations associated with the coherent structures. In this paper, we investigate whether the velocity field corresponding to the wavepackets also represents adequately that of the coherent structures. Previous research showed remarkable agreement in the velocity field up to the end of the potential core, but the agreement is lost gradually downstream. Locally-parallel linear stability theory (LST) of jet velocity profiles is revisited to further study the evolution of the wavepackets and the manner in which PSE models them. An adjoint-based eigenmode decomposition technique is used to project cross-sectional velocity profiles measured using time-resolved particle image velocimetry (PIV) on the Kelvin-Helmholtz eigenmode responsible for the wavepacket amplification. The instability wave thus extracted is then compared, both in amplification and shape, to the PSE wavepacket and to the dominant coherent structures obtained from the proper orthogonal decomposition of the PIV measurements. The comparisons between PSE models and POD-filtered fluctuations define three spatial regions along the streamwise direction that are explained in terms of changes in the LST eigenspectrum.

This paper details the analysis of the relationship between the near-field pressure fluctuations of an unforced, subsonic free jet (0:4 ≤ M ≤ 0:6) and its low-angle, far-field sound emissions. Azimuthal rings of six microphones recorded pressure fluctuations on a conical surface in the jet near field while an azimuthal ring of three microphones recorded fluctuations in the far field at θ = 20° and R=D = 47:1. Recent measurements have shown close agreement between the velocity fluctuations up to the end of the potential core of the currently studied jet and predictions from the linear Parabolised Stability Equations (PSE), indicating the presence of linear wavepackets in the jet velocity field. Solutions of the Linearised Euler Equations (LEE) reported in the present paper also show good agreement with measurements, and provide a first step toward a time-domain description of the said wavepackets. Though the agreement for PSE in the velocity field breaks down downstream of the potential core, Proper Orthogonal Decomposition (POD) of the current results shows that the wavepackets do persist in this region and are clearly apparent in the near pressure field. Attention is then turned to establishing a relationship between these wavepackets and the radiated sound by comparing simultaneously-obtained measurements of the far-field pressure both directly to the near-field signature as well as to numerical predictions of the far-field emissions available from a recent technique using a tailored Green's function. The direct comparisons are made by correlations between the POD modes and the far-field sound. The first POD mode captures most of the flow energy for the frequency range studied, and the correlation between this mode and the far field is nearly identical to the correlation using the full near-field signal. Higher POD modes also show significant correlation to the far field with a different space{time structure than the first mode. The Green's function predictions are performed both statistically and in the time domain, and though they are shown to be valid for a near-field array with a long axial extent, the experimental limitation of a shorter array (0:5 ≤ x=D ≤ 8:9), which truncates the wavepacket source in the calculations, causes inaccurate predictions for the experimental data. This error is thought to be the result of a spurious source introduced by the truncation that interferes both constructively and destructively with the wavepacket source. A validation problem shows that this error would be smaller for a higher-M jet.

We present a study of subsonic jets, controlled by means of a novel actuator that introduces perturbations via steady fluidic actuation from a rotating centerbody. Preliminary results obtained with this kind of actuator were presented during AIAA conference in Portland in 2011.1 Louder and quieter jets are produced, and these are analysed using time-resolved, stereoscopic particle image velocimetry and a hot-wire anemometer. We place the analysis in the framework of wavepackets and linear stability theory, whence we show that the quieter flows can be understood to result from a meanow deformation that attenuates wavepacket growth rates. The meanow deformation is shown, by a triple decomposition, to be due to the generation of Reynolds stresses associated with incoherent turbulence (rather than coherent structures) which arises when the actuation energises the flow with a frequency-azimuthal wavenumber (ω-m) combination to which the mean flow is stable. When the actuation energises the flow with an ω-m combination to which the mean flow is unstable, the response is dominated by coherent structures, whose rapid growth takes them beyond the linear limit where they undergo quadratic wave interactions and lead, consequently, to a louder flow. © 2013 by Snecma.

Jet noise is analysed using data-processing tools adapted to two particular structural traits of the far field: the strong polar dependence and the temporal intermittency. Proper Orthogonal Decomposition is used to probe the polar structure of the sound field, wavelet transform being used to interrogate the temporal signature. The far field is decomposed, using each of these approaches independently, into a component attributed to 'coherent structures', denoted CS, and a residuum, R. The criteria for the decomposition being different, spatial on one hand and temporal on the other, comparison of the resulting CS components is of considerable interest; both decompositions lead, for instance, to CS components that compare favourably with a wavepacket source Ansatz. Using the two techniques, an analysis methodology is established and applied to data from a Mach 0.9, isothermal jet; a series of metrics are thereby proposed by which to evaluate the data. The methodology and associated metrics are then used to explore the effect of varying Mach number on isothermal and heated jets. The following main results are obtained. Both the unfiltered low-angle sound spectrum and that of the CS component of the isothermal jets are found to scale best with Helmholtz number, indicating that the associated sound source is noncompact. In the heated jet, on the other hand, a Strouhal number scaling is observed, again for both the unfiltered low-angle spectrum and the CS spectrum, suggesting that the associated sources are in this case more compact. Where the intermittency of the farfield signature is concerned it is found that increasing the Mach number of isothermal jets has no discernible impact, whereas in the case of the heated jet this increase is accompanied by a decrease in the intermittency, indicating some kind of associated stabilisation of wavepacket source dynamics. Finally, the unfiltered data is used to perform source imaging, using a wavepacket Ansatz. This allows a more comprehensive eduction of the wavepacket parameters. The trends observed are consistent with known changes in the mean field and with linear stability theory. Finally, the directivity of the wavepackets obtained using the source imaging is compared with those educed from the data using the POD and wavelet filters. Good agreement between all three constitutes a strong evidence supporting the contention that such wavepackets underpin the said, polar and temporal, features of the farfield. © 2013 Elsevier B.V. All rights reserved.

We present a study of subsonic jets, controlled by means of a novel actuator that introduces perturbations via steady fluidic actuation from a rotating centerbody (Kœnig et al. (2011a)). Preliminary results obtained with this kind of actuator were presented during AIAA conference in Portland in 2011 (Kœnig et al. (2011b)). Louder and quieter jets are produced, and these are analysed using time-resolved, stereoscopic particle image velocimetry and a hot-wire anemometer. We place the analysis in the framework of wavepackets and linear stability theory, whence we show that the quieter flows can be understood to result from a mean-flow deformation that attenuates wavepacket growth rates. The mean-flow deformation is shown, by a triple decomposition, to be due to the generation of Reynolds stresses associated with incoherent turbulence (rather than coherent structures) which arises when the actuation energises the flow with a frequency-azimuthal wavenumber (ω-m) combination to which the mean flow is stable. When the actuation energises the flow with an ω-m combination to which the mean flow is unstable, the response is dominated by coherent structures, whose rapid growth takes them beyond the linear limit where they undergo quadratic wave interactions and, consequently, a louder flow.

We study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers m ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10 %, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow-acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers 0.3≤St≤0.9 and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles. © 2013 Cambridge University Press.

Noise source mechanisms are studied for a numerical dataset of a low Reynolds number laminar jet with a Mach 0.9 jet exit velocity (Suponitsky et al., J. Fluid Mech., Vol. 658, 2010) and two experimentally obtained datasets of high Reynolds number, Mach 0.4 and 0.6 turbulent jets (Cavalieri et al., AIAA Vol. 2011-2743, 2012). The objective of the study is to discern the source mechanism, linear or non-linear, by which acoustic radiation is obtained from wave-packets in the context of laminar and turbulent jets. For the laminar jet, it is shown numerically using a Linearized Euler Equation (LEE) solver that the sources of sound stem from a non-linear coupling of hydrodynamic waves. The nonlinear nature of the source mechanism explains why Linear Parabolized Stability Equation (LPSE) formulations are unable to reproduce the relevant near field dynamics at low Reynolds numbers. For the turbulent jets however, experimental evidence indicates that linear wavepackets are likely to be the source mechanism for acoustic radiation. To verify this, a fluctuating boundary condition is incorporated into the LEE solver such that a single frequency hydrodynamic wave is set up. This is used to investigate how the results from linear wavepackets compare with those found from LPSE and experiments. It is found that the power spectral density of the axial velocity fluctuations obtained by LEE shows a close match with those obtained from the LPSE and experiments, and it is also observed that downstream of the potential core, LEE results match more closely with experiments in this regard than do LPSE results. However, although the linear wavepackets formed using a fluctuating boundary condition do radiate sound, a comparison of the far-field directivity results show that the amplitude of the sound produced is significantly lower than those observed in experiments. Based on these results, LEE with a fluctuating boundary condition proves to be more useful in reproducing the near flow field of a turbulent jet but does not appear to be accurate in directly predicting the radiated far-field sound.

Using linear stability analysis, we determine base-flow modifications to a mixing layer velocity profile that maximise changes in the eigenvalues of Kelvin-Helmholtz instability. This is done by studying both the temporal and spatial stability problems given by the Orr-Sommerfeld equation and its adjoint, leading to an expression for the sensitivity of the eigenvalue to base-flow changes. Two objectives are pursued separately. First, we determine base-flow changes for reduction of growth rates; then, the same procedure is applied so as to obtain lower phase speeds. Both modifications would potentially reduce acoustic radiation by wavepackets. We see that changes in eigenvalues result from appropriate manipulation of the velocity profile near its inflection point. Reductions of growth rate are obtained for velocity profiles with lower shear around the inflection point, and reductions of phase speed result from a shift of the inflection point towards the slower stream. Reductions in the growth rate are obtained in a similar manner for both temporal and spatial instability of a mixing layer; however, although significant reductions of phase speed are obtained for temporal instability, modifying the base flow with this objective is less effective in the spatial problem. A feature observed in all cases is that the modifications of the base flow aimed at changing the Kelvin-Helmholtz mode lead to the appearance of new discrete modes in the eigenspectrum. These modes are stable for small perturbations of the base flow, but can become unstable if the base flow is significantly modified. © 2013 by A. V. G. Cavalieri.

We present experimental results for the acoustic field of jets with Mach numbers between 0.35 and 0.6. An azimuthal ring array of six microphones, whose polar angle,θ, was progressively varied, allows the decomposition of the acoustic pressure into azimuthal Fourier modes. In agreement with past observations, the sound field for low polar angles (measured with respect to the jet axis) is found to be dominated by the axisymmetric mode, particularly at the peak Strouhal number. The axisymmetric mode of the acoustic field can be clearly associated with an axially non-compact source, in the form of a wavepacket: the sound pressure level for peak frequencies is found be superdirective for all Mach numbers considered, with exponential decay as a function of (1-Mc cos θ)2 , where Mc is the Mach number based on the phase velocity Uc of the convected wave. While the mode m= 1 spectrum scales with Strouhal number, suggesting that its energy content is associated with turbulence scales, the axisymmetric mode scales with Helmholtz number-the ratio between source length scale and acoustic wavelength. The axisymmetric radiation has a stronger velocity dependence than the higher-order azimuthal modes, again in agreement with predictions of wavepacket models. We estimate the axial extent of the source of the axisymmetric component of the sound field to be of the order of six to eight jet diameters. This estimate is obtained in two different ways, using, respectively, the directivity shape and the velocity exponent of the sound radiation. The analysis furthermore shows that compressibility plays a significant role in the wavepacket dynamics, even at this low Mach number. Velocity fluctuations on the jet centreline are reduced as the Mach number is increased, an effect that must be accounted for in order to obtain a correct estimation of the velocity dependence of sound radiation. Finally, the higher-order azimuthal modes of the sound field are considered, and a model for the low-angle sound radiation by helical wavepackets is developed. The measured sound for azimuthal modes 1 and 2 at low Strouhal numbers is seen to correspond closely to the predicted directivity shapes. © 2012 Cambridge University Press.

We study the velocity field of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to discern the presence of instability waves in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved, PIV system, the latter being setup so as to measure three components of velocity in cross-stream planes; the field can thereby be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured, synchronously with the PIV acquisition, using a microphone ring array at polar angle, θ = 20° (measured with respect to the downstream jet axis). Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are quite different. The velocity spectrum exhibits a peak at higher azimuthal wavenumber and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown, theoretically, to be due to the radial compactness of the flow. This is confirmed by significant correlations, around 10%, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those previously reported for two-point flow-acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear Parabolised Stability Equations (PSE) (where the experimental mean velocity field is used as the base flow) to ascertain if these modes correspond to linear instability waves. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE results also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence of these unforced jets, the evolution of a certain range of frequencies and azimuthal modes can be modelled as linear instabilities of the mean velocity profile, and that these instabilities are associated with the sound radiated at low polar angles. © 2012 by Peter Jordan.

Experimental velocity measurements of a low-speed jet, performed using time-resolved tomographic PIV, are used to study the dynamics of large-scale structures and their sound radiation. The experimental results show the roll-up of axisymmetric vortices that pair downstream, and subsequently lose their azimuthal coherence. Models of linear instability waves using both steady laminar and mean-field base flows flow are applied. While good agreement can be obtained for the vortex roll-up frequency in the near-nozzle region using the laminar base flow, non-linear effects must be included, via the mean field, in order to capture the downstream evolution of both the fundamental and subharmonic (vortex pairing). The velocity fluctuations for both frequencies have a wave-packet structure with some jitter in the form of modulations of the spatial extent and amplitude of the envelope. The sound radiation is modelled using a jittering wave-packet model, an shows agreement with the exponential directivity shape of Laufer and Yen (J. Fluid Mech. 134, 1983). © 2012 by Peter Jordan.

We present an investigation of the effect of the presence of a flat plate in the vicinity of turbulent, subsonic jet. Experiments have been performed to measure the changes in the velocity field and in the sound radiation for Mach numbers ranging from 0.4 to 0.6, and for distances between the plate and the jet axis ranging from 1 to 2 jet diameters. Results show only very slight changes in the mean flow induced by the plate, and no differences in the velocity fluctuation amplitudes on the jet centerline, suggesting that wave-packet models derived for jets without installation effects may be representative of the installed case, at least for the jet-plate distances considered here. The acoustic results, on the other hand, include a significant increase in the low-frequency sound radiation, and phase opposition between the shielded and unshielded sides of the plate. There is an exponential decay of the scattered sound with increasing jet-plate distance, in agreement with the scattering of evanescent hydrodynamic waves in the jet near field. To model this phenomenon, we calculate sound generation from wave-packet sources using a tailored Green's function that accounts for the presence of a semi-infinite, rigid flat plate. In agreement with the experimental results, the model results present the phase opposition between shielded and unshielded sides, and the scattered sound depends exponentially on the position of the plate; this exponential dependence is related to non-compact effects associated with wavepackets, as compact sources would lead to an algebraic dependence. In addition to providing a simplified model for the installation effect, the results thus further support the contention that low-frequency jet noise sources comprise axially-extended, noncompact, wavepackets. A first quantitative comparison of the model with measurements is performed, and the experimental trends are recovered. © 2012 by peter Jordan.

© Cambridge University Press 2012.This work belongs to the ongoing debate surrounding the mechanism responsible for low-angle sound emission from subsonic jets. The flow, simulated by large eddy simulation (Bogey & Bailly, Comput. Fluids, vol. 35 (10), 2006a, pp. 1344-1358), is a Mach 0.9 jet with Reynolds number, based on the exit diameter, of 4 × 105. A methodology is implemented to educe, explore and model the flow motions associated with low-angle sound radiation. The eduction procedure, which is based on frequency-wavenumber filtering of the sound field and subsequent conditional analysis of the turbulent jet, provides access to space- and time-dependent (hydrodynamic) pressure and velocity fields. Analysis of these shows the low-angle sound emission to be underpinned by dynamics comprising space and time modulation of axially coherent wavepackets: temporally localized energization of wavepackets is observed to be correlated with the generation of high-amplitude acoustic bursts. Quantitative validation is provided by means of a simplified line-source Ansatz (Cavalieri et al. J. Sound Vib., vol. 330, 2011b, pp. 4474-4492). The dynamic nature of the educed field is then assessed using linear stability theory (LST). The educed pressure and velocity fields are found to compare well with LST: the radial structures of these match the corresponding LST eigenfunctions; the axial evolutions of their fluctuation energy are consistent with the LST amplification rates; and the relative amplitudes of the pressure and velocity fluctuations, which are educed independently of one another, are consistent with LST.

The use of the linearised potential model for the analysis of compressible flows is quite widespread, and provides good results for subsonic and supersonic flows. However, the calculation of aerofoils and wings subject to transonic flows requires a non-linear model, such as the transonic small-disturbance (TSD) potential equation. The solution of the problem by a singularity distribution requires singularities over the field, as well as panels on the boundary, characterising the procedure known as field panel method. The present work shows results of calculations of the transonic small-disturbance potential equation for flows without shock waves using the dual reciprocity method (DRM), which permits calculation of integrals only at the boundary of the problem, without the need of field distributions. This approach, compared to the field panel methods, takes considerably less computer time, and shows a significant improvement when compared to results of linear theory without much additional computer time, making this technique adequate to design phases of aircraft. Pressure distribution results show good agreement with other methods found in litterature. The low computational cost of the present method allows us to perform parametric tests and explore the effects of thickness and Mach number on the lift and pitching moment coefficients. A discussion of the physical effect of these parameters on the problem is presented, and the thickness of the aerofoil is shown to increase the lift and change the position of the aerodynamic centre. However, this non-linear effect depends on the precise shape of the thickness distribution.

We apply a filtering procedure, based on a continuous wavelet transform, to acoustic pressure and to the velocity field of an experimental Mach 0.6 jet in order to extract the intermittent bursts in the signals. With an intermittency measure based on this filter, it is possible to quantify the significance of these events in the total acoustic intensity. The acoustic pressure is measured by a ring of six azimuthal microphones, allowing decomposition of the sound field into azimuthal Fourier modes. The wavelet filtering is applied to each azimuthal mode, and the results show that the intermittent bursts occur mostly for the axisymmetric mode and for low polar angles. When high energy thresholds are used for the filtering, so as to retain only the most energetic bursts, more than 80 percent of the intermittent radiation is axisymmetric. © 2011 by P. Jordan. Published by the American Institute of Aeronautics and Astronautics, Inc.

Parabolized stability equation (PSE) models are being developed to predict the evolu- tion of low-frequency, large-scale wavepacket structures and their radiated sound in high- speed turbulent round jets. Linear PSE wavepacket models were previously shown to be in reasonably good agreement with the amplitude envelope and phase measured using a microphone array placed just outside the jet shear layer.1,2 Here we show they also in very good agreement with hot-wire measurements at the jet centerline in the potential core, for a different set of experiments.3 When used as a model source for acoustic analogy, the predicted far field noise radiation is in reasonably good agreement with microphone measurements for aft angles where contributions from large-scale structures dominate the acoustic field. Nonlinear PSE is then employed in order to determine the relative impor- tance of the mode interactions on the wavepackets. A series of nonlinear computations with randomized initial conditions are use in order to obtain bounds for the evolution of the modes in the natural turbulent jet flow. It was found that nonlinearity has a very limited impact on the evolution of the wavepackets for St ≥ 0.3. Finally, the nonlinear mechanism for the generation of a low-frequency mode as the difference-frequency mode4,5 of two forced frequencies is investigated in the scope of the high Reynolds number jets considered in this paper. © 2011 by the author(s).

We present an analysis of the sound eld radiated by jets at different Mach numbers and temperature ratios. The methodology is similar to that developed by Koenig et al.1 in a previous study, where spatial and temporal structures of the sound eld of a Mach 0.9 cold jet are ltered and analysed by means of Proper Orthogonal Decomposition and wavelet transform. Using both the POD and wavelet-ltered signals the acoustic eld is decomposed into two components: a coherent structure (CS) component and a residuum (R). A source imaging procedure is then applied and the results compared with the CS component obtained by the two ltering operations. The main results include the following observations. (1) While the shallow-angle acoustic spectra of isothermal jets scale best with Helmholtz number, those of the heated jets scale better with Strouhal number. This difference suggests that non-compact effects do not play as important a role in the heated jet where downstream radiation is concerned, contrary to what is observed in isothermal jets; this in turn suggests a change in acoustic wavelength associated with the temperature of the jet, implying that source interference occurs in the core of the flows, an idea consistent with an axially-extended wavepacket source. (2) While in the isothermal jets no change in intermittency is observed as the Mach number is varied, when the jet is heated increasing the Mach number engenders a decrease in intermittency in the acoustic eld; we can conjecture from this that high Mach number hot jets comprise lower levels of source jitter (cf. Cavalieri et al.2). (3) The CS acoustic signatures identied by both wavelet and POD ltering present wavepacket superdirectivity. (4) The trends identied by the source imaging, as a function of Mach number for isothermal and heated jets, are consistent both with known changes in the mean flow structure and the results of linear stability theory. © 2011 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc.

This paper presents an analysis of data generated by means of large eddy simulation for a single-stream, isothermal Mach 0.9 jet. The acoustic field is decomposed into Fourier modes in the azimuthal direction, and filtered by means of a continuous wavelet transform in the temporal direction. This allows the identification of temporally localised, high-amplitude events in the radiated sound field for each of the azimuthal modes. Once these events have been localised, the flow field is analysed so as to determine their cause. Results show high-amplitude, intermittent sound radiation for azimuthal modes 0 and 1. The mode-0 radiation, which dominates low-angle emission, is found to result from the temporal modulation of a basic axisymmetric wave-packet structure within the flow. Similar intermittent activity, observed, again within the flow, for azimuthal mode 1 suggests a link between the modes 0 and 1 dynamics. Both the amplitude and spatial extent of the axisymmetric wave-packet are modulated, and the strongest axisymmetric propagative disturbances are found to radiate from the downstream end of the wave-packet at moments when the wave envelope becomes truncated. The observed behaviour is modelled using a line-source wave-packet ansatz which includes parameters that account for the said modulation. Inclusion of these parameters, which allow the wave-packet to jitter in a manner similar to that observed, leads to good quantitative agreement (accurate to within 1.5 dB), at low emission angles, with the acoustic field of the LES. This result is in contrast with results obtained using a time-averaged wave-packet (one which does not jitter), for which a 12 dB error is observed. This result shows that the said modulations are the salient source feature for the low-angle sound emission of the jet considered. Analysis of a longer time series shows the occurrence of several similar high-amplitude bursts in the axisymmetric mode of the acoustic pressure, and a calculation of the radiated sound for this longer time-series, again using the wave-packet ansatz, once again leads to good agreement with the LES (now accurate to within 1 dB). © 2011 Elsevier Ltd.

Steady and unsteady uidic actuators, in the form of secondary control jets injecting from the nozzle lip, aimed at jet noise reduction, are investigated. Three different geometric congurations are tested: non-converging control jets, Open fluidic triangle convergence and Closed fluidic triangle convergence. By means of a triple decomposition of hot-wire data and a scale-separation argument, the low-frequency perturbation (near-nozzle dynam- ics) and jet response (downstream dynamics) of the ow are studied. Comparison of the phase-averaged component of the decomposition with predictions of linear stability theory (LST) suggest that two qualitatively different responses are active: at the main forcing frequency the jet response looks to be non-linear; at two secondary, higher frequencies, LST gives reasonable predictions for the local growth rates and convection velocities. The considerably lower convection velocity of the non-linear component of the ow response suggests that this control mechanism may constitute a useful manner by which to reduce the effciency of wavepacket sound sources associated with coherent structures. © 2011 by the author(s).