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New data and review of the spanwise coherence length is provided for flows over cylinders of different cross-sections: circular of diameter d, and rectangular of sectional aspect ratios (breadth (b) to height (d) ratio AR = b/d) of 1, 2 and 3. In the present measurements, the body has both d and spanwise length of 70d fixed, and the Reynolds number (based on d) range 6000–27,000 is covered. Two-point data are obtained from two hot-wire probes, one fixed in the symmetry plane and the other moving on the corresponding spanwise axis. Their position in a cross plane are deduced from preliminary measurement of the mean flow with a single probe, allowing fair comparisons between the different geometries and the introduction of uncertainty bars on coherence length values. At all tested regimes, a very good agreement is noticed between velocity-based and pressure-based coherence experimental data. Coherence length definitions are revisited, and the aeroacoustically consistent, integral length definition is selected, allowing fair synthesis of literature data into a single chart and empirical functions. Definitions for coherence decay models (e.g. Gaussian or Laplacian) are also adapted so that coherence length and coherence integral shall be equivalent. This preliminary work on coherence data and its spanwise integration enables transparent regressions and model selection. Generally, the Gaussian model is relevant for the lift peak, while the coherence exhibits a Laplacian decay at harmonics. On average, at peak Strouhal number, the coherence length for the circular and square cylinders is of 5d while it is of the order of 15d for the rectangular sections. It is concluded that the flow over those latter geometries is still a two-dimensional dynamics at the tone frequency. These values are almost preserved over the tested Reynolds number range. Coherence length value at harmonics is extensively documented. Spanwise coherence length is also discussed as an ingredient of acoustic efficiency.

The tonal noise generated by the flow over elongated cylinders is measured using microphones in the anechoic wind tunnel BETI of Institut Pprime. The effect of the length to diameter ratio of the cylinder is assessed by varying the diameter from 6 mm to 20 mm within the constant width (750mm), open jet, test section. The velocity is varied from 10 to 40 m/s, leading to a Reynolds number range of about 4,000 ­ 53,000. A proper normalization is needed to obtain a good collapse of experimental data from nearly 10 studies on the same evolution in 3 steps: for very short cylinders, the tone level does not depend on the length; for semi-long cylinders, it follows the fourth power of the length to diameter ratio; for very long cylinder, the length's influence vanishes in the form of a sound level asymptote. This sigmoidal evolution is noticed for both the circular section and the square section cylinders, and questions the classical modelling of the aeroacoustic process using compact, coherent segments of cylinder associated with a coherence length to account for spanwise phase loss. Literature data from numerical simulation or experiment using end-plates are included in the analysis too.

The Reynolds number for the onset of flow unsteadiness is determined for several canonical geometries (triangles, rectangles, ellipses and lozenges) at different sectional breadth ( L ) to height ( d ) ratios (aspect ratio AR = L ∕ d ), for more than 70 shapes. The flow is modeled using a direct Navier–Stokes incompressible two-dimensional solver and the shape is defined by an Immersed Boundary Method. The employed procedure takes the fluctuation of the velocity in the wake as the criterion to define the unsteadiness and a binary search to find the transition. This procedure yields critical Reynolds number Re c values in agreement with available data in the literature. When AR approaches zero, the five shapes lead to almost the same value of 31, which corresponds to Re c for a flat plate normal to the flow. It is then found that Re c grows exponentially with the aspect ratio, the influence of the cross section shape being accounted for by a single regression parameter. For all aspect ratios, the ellipse exhibits the highest Re c , and the front-pointing triangle the lowest, the three other geometries laying in between those two. The physics of the influence of cross-section shape on Re c is analyzed, considering its link with recirculation length in particular. An exploitation of the results is outlined for the analysis of recent aeroacoustic shape optimizations at fixed Re = 150 , through correlation between the lift fluctuation at this regime with the distance to the onset of unsteadiness it corresponds to.

International audience; A shape optimization for tonal noise generated aerodynamically at low Mach number is performed for a cylinder with polygonal cross-section. Acoustic quantities are derived from a hybrid analytical formula, with aeroacoustic sources obtained from the incompressible solution of the direct Navier-Stokes equations in 2D at Re = 150; the solid domain is modelled by an Immersed Boundary Method. The optimization is done with the Particle Swarm Optimization (PSO) technique and performed in a cluster where each cost function evaluation is an independent flow simulation. The precision on the 4 main shape parameters is set to 0.001, consistently with the convergence criteria in time, grid and swarm. Optimal shapes for minimum drag and minimum acoustic power are relatively similar. A large range between the optimal shapes is obtained: factor 1.8 for drag and 20 dB for the acoustic power. The reduction of noise is associated with long and bluffer geometries, while the louder flows are associated with highly interacting shear layers obtained with back pointing triangles. The fluctuating lift is the major quantity to control noise at fixed length, while increasing the aspect ratio tends to reduce the noise for globally all geometries. An overall correlation between mean drag and fluctuating suction is also noticed.

International audience; In this work,we propose a cost-effective approach allowing one to evaluate the acoustic field generated by a turbulent jet. A turbulence-resolving simulation of an incompressible turbulent round jet is performed for a Reynolds number equal to 460,000 thanks to the massively parallel high-order flow solver In compact 3d. Then a formulation of Lighthill’s solutionis derived, using an azimuthal Fourier series expansion and a compactness assumption in the radial direction. The formulation then reduces to aline source theory, which is cost-effective to implement and evaluate. The accuracy of the radial compact ness assumption, how ever, depends on the Strouhal number, the Machnumber, the observation elevation angle,and the radial extent of the source. Preliminary results are showing that the proposed method approaches the experimental over all sound pressure level by less than 4 dB for aft emission angles below 50◦.

The acoustic radiation by a laminar flow over a rectangular cylinder at incidence is predicted using a two-step approach. The acoustic pressure is evaluated from the compact source approximation of Curle’s analogy, where the fluctuation of the aerodynamic force is the source quantity. The latter is provided by numerical simulation of the incompressible flow, the presence of the bluff body being modelled via an immersed boundary method. The approach is validated by comparison with a direct noise computation of the aeolian tone produced by the flow over a circular cylinder at Re = 150 and M = 0.2 . Ten values of incidence are considered, from 0 ° to 90 ° for the 2D flow, at Re = 200 , over the rectangular cylinder, whose aspect ratio is 4. The acoustic power is strongly enhanced in comparison with the circular cylinder (by 6– 15 dB ) and with the case without incidence (by 30– 40 dB ). The contribution of the drag dipole is also significantly increased. The relative fluctuations of lift and drag drive the directivity for each case. Depending on the incidence, a block rotation of ± 15 ° is observed on the directivity diagram. This is closely linked to the wake organisation, in particular the position of the stagnation point, and the orientation of the fluctuation of the aerodynamic force, all of these features undergoing a qualitative change at an incidence angle of 40 ° . One of the key results is that the acoustic efficiency increases quadratically with respect to the Mach number and to (rms) fluctuations of lift and drag coefficients, and depends linearly on the Strouhal number.

A shape optimization procedure is presented. It is dedicated to the noise generated by obstacle flows. The cost function is the acoustic power efficiency, which is derived directly from the fluctuations of the aerodynamic force through for a single formula from the hypothesis of tonal noise. The force is estimated from the direct solution of the 2D incompressible, unsteady flow in laminar regime over a convex symmetrical obstacle without incidence. The no-slip condition at the boundary is assured by an Immersed Boundary Method, that allows the use of the same mesh for all the geometries. The shape of the obstacle is defined by 4 Bézier curves, constrained by second-order continuity leading to 4 degrees of freedom: the aspect ratio, the position of the maximum cross section and two curvature parameters (up and downstream). The optimization is performed via a Particle Swarm Optimization (PSO) routine. Several tests are performed increasing complexity so that coefficients of the PSO be adjusted to the present response surface. There is up to 16 dB of difference between the power efficiency of the extrema configurations for a fixed aspect ratio (AR) and 8 dB for constrained surface or perimeter. For an AR of 1.5, the optimal shape leads to 3dB less acoustic power than the ellipse of same AR. The shapes that minimize acoustic power are relatively different from those that minimize the mean drag.

International audience; Two assumptions commonly made in predictions based on Lighthill's formalism are investigated: a constant density in the quadrupole expression, and the evaluation of the source quantity from incompressible simulations. Numerical predictions of the acoustic field are conducted in the case of a subsonic spatially evolving two-dimensional mixing layer at Re = 400. Published results of the direct noise computation (DNC) of the flow are use as reference and input for hybrid approaches before the assumptions on density are progressively introduced. Divergence free velocity fields are obtained from an incompressible simulation of the same flow case, exhibiting the same hydrodynamic field as the DNC. Fair comparisons of the hybrid predictions with the reference acoustic field valid both assumptions in the source region for the tested values of the Mach number. However, in the observer region, the inclusion of flow effects in the Lighthill source term is not preserved, which is illustrated through a comparison with the Kirchhoff wave-extrapolation formalism, and with the use of a convected Green function in the integration process.

Mach number and thermal effects on the mechanisms of sound generation and propagation are investigated in spatially evolving two-dimensional isothermal and non-isothermal mixing layers at Mach number ranging from 0.2 to 0.4 and Reynolds number of 400. A characteristic-based formulation is used to solve by direct numerical simulation the compressible Navier-Stokes equations using high-order schemes. The radiated sound is directly computed in a domain that includes both the near-field aerodynamic source region and the far-field sound propagation. In the isothermal mixing layer, Mach number effects may be identified in the acoustic field through an increase of the directivity associated with the non-compactness of the acoustic sources. Baroclinic instability effects may be recognized in the non-isothermal mixing layer, as the presence of counter-rotating vorticity layers, the resulting acoustic sources being found less efficient. An analysis based on the acoustic analogy shows that the directivity increase with the Mach number can be associated with the emergence of density fluctuations of weak amplitude but very efficient in terms of noise generation at shallow angle. This influence, combined with convection and refraction effects, is found to shape the acoustic wavefront pattern depending on the Mach number.

An iterative algorithm is developed for the computation of aeroacoustic integrals in the time domain. It is specially designed for the generation of acoustic images, thus giving access to the wavefront pattern radiated by an unsteady flow when large size source fields are considered. It is based on an iterative selection of source-observer pairs involved in the radiation process at a given time-step. It is written as an advanced-time approach, allowing easy connection with flow simulation tools. Its efficiency is related to the fraction of an observer grid step that a sound-wave covers during one time step. Test computations were performed, showing the CPU-time to be 30 to 50 times smaller than with a classical non-iterative procedure. The algorithm is applied to compute the sound radiated by a spatially evolving mixing-layer flow: it is used to compute and visualize contributions to the acoustic field from the different terms obtained by a decomposition of the Lighthill source term.

International audience; Noise generation by flows is modeled using a pressure wavepacket to excite the acoustic medium via a boundary condition of the homogeneous wave equation. The pressure wavepacket is a generic representation of the flow unsteadiness, and is characterized by a space envelope of pseudo-Gaussian shape and by a subsonic phase velocity. The space modulation yields energy in the supersonic range of the wavenumber spectrum, which is directly responsible for sound radiation and directivity. The influence of the envelope's shape on the noise emission is studied analytically and numerically, using an acoustic efficiency defined as the ratio of the acoustic power generated by the wavepacket to that involved in the modeled flow. The methodology is also extended to the case of acoustic propagation in a uniformly moving medium, broadening possibilities toward practical flows where organized structures play a major role, such as co-flow around cruising jet, cavity, and turbulent boundary layer flows. The results of the acoustic efficiency show significant sound pressure levels, especially for asymmetric wavepackets radiating in a moving medium.

International audience; A prototype device for measuring the volumetric flow-rate by counting vortices has been designed and realized. It consists of a square-section pipe in which are placed a two-dimensional bluff body and a strain gauge force sensor. These two elements are separated from each other, unlike the majority of vortex apparatus currently available. The principle is based on the generation of a separated wake behind the bluff body. The volumetric flow-rate measurement is done by counting vortices using a flat plate placed in the wake and attached to the beam sensor. By optimizing the geometrical arrangement, the search for a significant signal has shown that it was possible to get a quasi-periodic signal, within a good range of flow rates so that its performances are well deduced. The repeatability of the value of the volume of fluid passed for every vortex shed is tested for a given flow and then the accuracy of the measuring device is determined. This quantity is the constant of the device and is called the digital volume (V_p). It has the dimension of a volume and varies with the confinement of the flow and with the Reynolds number. Therefore, a dimensionless quantity is introduced, the reduced digital volume (V_r) that takes into account the average speed in the contracted section downstream of the bluff body. The reduced digital volume is found to be independent of the confinement in a significant range of Reynolds numbers, which gives the device a good accuracy.

A hybrid noise prediction approach is proposed for the study of acoustic emission by laminar flows over 2D bodies of various sections. In a first step, the unsteady incompressible flow is simulated. The presence of the bluff body is modelled through an immersed boundary method. In a second step, the acoustic field is evaluated using Curle’s analogy and the compact source approximation. The validation is provided through the computation of the aelian tone in the flow over the circular cylinder at Re = 150 and M = 0.2. The method is then applied to investigate the influence of the angle of attack of a rectangular cylinder in a 2D flow at Re = 200. Ten values of the incidence are considered from 0 to 90. A change in the vortex street topology around 40 of incidence is exhibited, whose trace on the phase portrait of the aerodynamic force and on the acoustic field is investigated in details.

The objectives of the study are to find a computational method to realize the cavitation flows under a variable rotational motion and develop a turbulence model to describe this phenomenon. We propose an integral model (closure) in the momentum equation and obtain information about the intensity of correlations in the rotational turbulence model. The computational models are as follows. We took the integral of the pressure and moment on the blade balance to the moment of inertia and replaced the variable rotational term with the integral in the momentum equation. We set up the geometry of a pseudo twodimensional centrifugal blade system, and performed four cases of the computations: neither cavitations nor integral form, cavitations and no-integral form, no cavitations with integral form, and cavitations with the integral form. We used the phase field model (PFM) for cavitations and the compressible Navier Stokes equation (MUSCL, third order). We tested the instability of the integration model with the moment of inertia and found the computations were unstable if the no-dimensional moment of inertia was less than 0.3 in (1000rpm, 2000rpm, and 5000rpm). We also found the pressure on the blade relaxed somewhat if we added the integral terms. In cavitation problems without the integral terms, we set the edge of the bubble was located in the middle of the blade passage and the interface was always oscillating. If we added the integral term, the edge of the separation bubble drifted to the trailing edge. The lift was decreased for cavitation conditions, even with a volume ratio of air less than 0.1. We obtained the unsteady rotational terms in the Reynolds stress equation with the integration model. The normalized correlation of the variable rotational term was 0.2 for cavitation flows and 0.25 for no-cavitaion flows. For both cases the variable integral terms should be included in any turbulence modeling. The results infer that the blade made by lighter materials has less moment of inertia and tends to vibrate more easily. The results show that the present computational model can realize the cavitation flows in variable rotation frames.

Sound generations from Ocarina, an Italian musical instrument, are simulated and the density gradient correlations of the flow fields are studied. We successfully generated the sound radiated from the Ocarina with fully open sides and also with one hole in each side of the body. The meshes are taken 100x60x100 (coarse) and 200x120x200 (finer). We compare the pressure patterns to the second and third invariants of the density gradient correlation. This methodology is also applied to the sound radiated by a subsonic mixing-layer, as a comparison. For both flows, it is found that the invariant variables can better extract the characteristics of the fields. The invariant pictures can show the movement of the contraction and expansion of the density well. The results imply that both the fluctuating density gradient correlation and the invariants can be a good index to show the compressibility in low speed aero-acoustics. In addition, the patterns of the invariants are clearer in the finer computations.

An optimized procedure for the computation of acoustic fields given by retarded-time intgrals is provided. It is written in the time-domain and for fixed sources. It is devoted to applications in which there is a large amount of source data. Thus, as many observer points are required to build the acoustic image, the resulting number of source-observer pair may cause an issue in accessing to the source-observer distance, if this quantity can not be stored in a global variable. The algorithm is validated through comparisons with reference data in the case of a simple harmonic source and in the case of the aerodynamic noise generated by the cylinder flow. The implementation of the convected Green function is also presented.

Acoustic radiation from jet flow has been studied extensively by means of theoretical, experimental and numerical approaches over the past decades. Unfortunately, the mechanisms responsible for the production of sound by unbounded turbulence in subsonic flows remain unclear. For advancing our fundamental understanding of these mechanisms, the development of specific analysis tools is needed. Our study is based on a decomposition of the Lighthill source term, which is known to contain all the existing links between the fluid flow and the acoustic field. Ten subterms are written with the help of physically meaningful quantities such as velocity, density, dilatation and vorticity. The methodology is tested through the two‐dimensional compressible mixing layer flow in spatial development, at a Reynolds number of 400 and a Mach number of 0.25. A direct numerical simulation of the flow and its acoustic radiation is performed and used as a reference solution. Acoustic field generated by each source terms is predicted computing the integral solution of Lighthill's equation. Effect of the compressibility on the balance between the contribution of major subterms is of key importance. Directivity and convective effects are identified as well.

A decomposition of the Lighthill source term \(\nabla\cdot(\nabla\cdot(\rho \textbf{u}\otimes\textbf{u}))\) is performed with view to more clearly understanding the mechanisms which underlie the production of flow-induced noise. Observation of source fields and associated radiation patterns leads to 3 main observations: (1) the amplitude of subterms in the source field does not scale with the associated acoustic contributions; (2) balances and destructives interferences are present between subterms; (3) source behaviour associated with convection and sound-flow effects is highlighted.

The behaviour of the immersed boundary method proposed by Goldstein et al. [Goldstein D, Handler R, Sirovich L. Modelling a no-slip boundary condition with an external force field. J Comput Phys 1993;105:354–66] as a second-order damped control system is investigated. The natural frequency and the damping coefficient are introduced as driving parameters of the method. The comparison between the velocity response at forced points in the startup flow over a square cylinder with the theoretical response of a second-order damped oscillator is performed. The role of each parameter appears clearly. At the beginning of the startup flow, the response time depends directly on the natural frequency, and this parameter determines the level of residual velocities achieved in an unsteady flow. The damping coefficient drives the oscillation of the velocity response at the beginning of the startup flow, but has negligible influence during the establishment and in the unsteady flow. At forced points facing no unsteady perturbation from the flow, the zero-velocity set point is reached asymptotically, as usual in second-order damped-systems. Through the simulation of the flow over a blunt flat plat at Re = 1000 , it is observed that the initial thickness of the mixing layer due to the separation at the edge may vary during the simulation because the sharpness of the edge increases as the residual velocities decrease. This insight gained on the behaviour of the response allows a time-step optimisation, which, completed with comparisons to reference literature results, confirms the feedback forcing method a competitive tool for accessing near-wall unsteady flow over sharp-edged bodies.

Specific tools devoted to the study of the source mechanisms related to the dynamic of free shear flows are developed. Our analysis methodology is based on a decomposition of the Lighthill source term into ten sub-terms, in which the velocity, vorticity, dilatation and density fields appear explicitly. This decomposition is applied to the source term involved in a 2D spatially evolving mixing-layer, computed by DNS. The compressible Navier-Stokes equations are solved in a computational domain which includes both aerodynamic and acoustic fields. The numerical code is based on sixth-order accurate compact finite difference schemes and a fourth-order Runge-Kutta time marching, while the characteristic analysis is used to specify non-reflecting boundary conditions. Acoustic results show that only five of the ten sub-terms of the decomposition contribute to the sound field.

The noise generated by the interaction between a gust and an airfoil in a uniform flow is investigated. This problematic is of major industrial interest, regarding fans, turbomachinery, or wind turbine applications. A two‐dimensional symmetric Joukowski‐type airfoil is immersed without incidence in a flow at Mach number 0.5, disturbed by a harmonic gust at 45° of incidence (4th CAA Workshop on Benchmark Problems, 2004). Our methodology is first to perform a high‐order direct resolution of Euler's equations of the disturbed flow over the airfoil and the associated acoustic emission, which is taken as a reference simulation. Second, the near aerodynamic field is simulated with Fluent 6.3 solver based on finite volume method with second‐order schemes. The aerodynamic data thus obtained are used for far field acoustic prediction, based on Ffowcs Williams and Hawkings analogy. Finally, following another hybrid approach, the noise is predicted by using integral formulations with source field from the DNS. The a...

The influence of the shape on the sound emission of cylindrical bluff-bodies is studied. Simulations are performed in two-dimensions (2D) at low-Reynolds number (Re=20-200), with the incompressible direct Navier-Stokes (DNS) solver incompact3D, using the Immersed Boundary Method (IBM) formalism; the acoustic emission is evaluated by a single formula derived from Curle’s equation for compact cylinders. In anechoic wind tunnel, the acoustic signature is measured for about 30 geometries, Re=4,000-53,000; hot-wire measurements of the spanwise flow characteristics are performed for a subset of the tested cylinders. The influence of both the shape of the upstream portion of the geometry and the breadth-to-height ratio (AR) are proved to be major features in terms of both the flow and its acoustic emission in 2D. By reducing the strength of the vortices and pushing them downstream and affecting the mechanics of the von Kármán instability (delaying the transition to unsteadiness), stretched shapes (with higher AR) are generally quieter. From the experiments, it is found that the geometries of biggest AR are the loudest, contraposing the results obtained in 2D. The disparity is justified by a significant increase of the spanwise coherence associated with the larger AR’s, practically fully-phased, thus more acoustically efficient. Globally, it is implied that geometries which have weakly perturbed flow in 2D, marked by a later transition to unsteadiness (larger critical Reynolds number), are also more organized in 3D, high-Reynolds number regimes. The underlying relationship between low and high-Reynolds number transitions must be further investigated.; L’influence de la forme de cylindres longs sur leur rayonnement acoustique en écoulement est étudiée. Des simulations bidimensionnelles (2D) sont réalisées à bas nombre de Reynolds (Re=20-200), à l’aide du code de calcul direct (DNS) incompressible incompact3D au moyen d’une méthode de frontière immergée (IBM). Une formule dérivée de l’équation de Curle pour un cylindre compact permet la quantification de l’émission acoustique en 2D. En soufflerie anéchoïque, la signature acoustique d’une trentaine de géométries est mesurée, Re=4,000-53,000 ; l’anémométrie par fil chaud est utilisée pour la description des propriétés axiales de l’écoulement. L’avant corps et l’allongement (AR) sont les plus importantes propriétés géométriques tant pour l’écoulement que pour le rayonnement acoustique en 2D. Les géométries allongées sont généralement les plus silencieuses car les tourbillons sont moins intenses et repoussés vers l’aval et l’apparition de l’instationnarité est retardée. De leur côté, les résultats expérimentaux montrent que les géométries allongées sont les plus bruyantes, ce qui est à l’opposé des conclusions précédentes. Ceci est justifié par une augmentation significative de la cohérence de l’écoulement en envergure pour les AR les plus longs, presque complètement en phase, donc plus efficace acoustiquement. Globalement, cela implique que les géométries dont l’écoulement 2D est faiblement perturbé, marqué par un déclenchement plus tardif de l’instationnarité (Reynolds critique plus élevé), sont aussi plus organisées en 3D aux Re des mesures. La relation sous-jacente entre les transitions successives vers la turbulence nécessite une étude approfondie.