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The present work is dedicated to turbulence synthesis tailored to lateral periodic boundary conditions for direct noise computations through compressible large eddy simulations. Synthetic turbulence can be essential for aeroacoustic applications when computing airfoil turbulent inflow noise or for accurately capturing the behavior of boundary layers. This behavior determines both trailing edge noise and complex flow structures such as laminar separation bubbles. For airfoil simulation purposes, spanwise periodic boundary conditions are usually considered. If synthetic perturbations are injected without observing the periodicity rule, strong spurious pressure waves are emitted and pollute the entire computational domain. In this work, the random Fourier modes method for turbulence generation is adapted in order to respect the spanwise periodicity constraint right at the computational domain inlet. This approach does not affect the turbulence properties such as the spectral shape and the turbulent kinetic energy decay. Since the emphasis is put on the generation and convection of the turbulence, only the turbulence convection region between the inlet and the airfoil is considered in this paper, without the airfoil. Two geometrical configurations are tested: the first one is a simple box with a constant mesh size, and the second one concentrates the fine cells on the area in front of the airfoil. In the second configuration, the computational cost is reduced by up to 25%, but more spurious noise is present because of interpolation areas between different grids using the Chimera method. Finally, the results’ reproducibility is assessed using different turbulence realizations.

International audience; The interaction of inflow turbulence with an airfoil is significant for low Reynolds number applications, as it generates leading edge noise, but also strongly modifies the airfoil boundary layer properties and thus the produced noise. Inflow turbulence impact still demands to be better understood and is also a numerical challenge. Large Eddy Simulations are here carried out with both incompressible and compressible solvers. The Synthetic Eddy Method and the Random Fourier Modes method, used to generate synthetic turbulence, are studied in this work. In order to eventually perform airfoil simulations, the second method is modified to take into account spanwise periodic boundary conditions, to reduce spurious noise level in compressible simulations. First, properties of the methods are studied with a spatially decaying turbulence academic case. Even if the decay is not well represented, the methods show satisfactory properties in terms of isotropy, homogeneity and one-dimensional spectra. Furthermore, spurious noise levels are reduced thanks to the modified method. Preliminary airfoil simulations are then carried out with inflow turbulence for flow validation in presence of a laminar separation bubble. The drag coefficient is in very good agreement with experimental results. However, there are some discrepancies between simulations and experiments on the lift coefficient, which is extremely sensitive to perturbations. These discrepancies are attributed to a lack of experimental turbulence characteristic information, such as isotropy or integral length scale and to too short simulations at high angles of attack.

International audience; Natural grounds can exhibit small scale geometric irregularities, compared to the acoustic wavelength, known as ground roughness. This roughness has a noticeable effect on sound pressure levels and produces a surface wave. In the context of prediction methods improvement for outdoor sound propagation, using an effective impedance appears to be an useful approach to model the effects of surface roughness. Two time-domain numerical methods are considered: finite difference schemes (FDTD), and the transmission line modeling (TLM) method. An effective impedance model for random ground roughness defined by a roughness spectrum, called the SPM model, is exposed. The efficiency of this model for taking into account the mean effects of random roughness on sound pressure levels and for modeling the roughness-induced surface wave is shown, by comparing with results of TLM simulations of propagation above random rough grounds. The direct implementation of the SPM model as a boundary condition in both TLM and FDTD methods is then studied. This approach allows the modeling of ground roughness effects in numerical methods without having to mesh finely the ground roughness profile, allowing easier and faster computations, and more accurate predictions for future impact studies in environmental acoustics.

Development of optimal reduced-order models for linearized Euler equations is investigated. Recent methods based on proper orthogonal decomposition (POD), applicable for high-order systems, are presented and compared. Particular attention is paid to the link between the choice of the projection and the efficiency of the reduced model. A stabilizing projection is introduced to induce a stable reduced-order model at finite time even if the energy of the physical model is growing. The proposed method is particularly well adapted for time-dependent hyperbolic systems and intrinsically skew-symmetric models. This paper also provides a common methodology to reliably reduce very large nonsymmetric physical problems.

The influence of the filter shape on the effective scale separation and the numerical accuracy of large-eddy simulations based on relaxation filtering (LES-RF) is investigated. The simulation of the turbulent flow development of a high-Reynolds number low-subsonic compressible mixing layer is performed using the LES-RF procedure, for discrete filters of order 2–10. A reference solution is first obtained using high-order numerical algorithms and shows a good agreement with experimental data found in the literature. Discrete filters of order 2, 4, 6, 8 and 10 are then considered to study the influence of the filter shape on numerical results. The 2nd-order scheme turns out to be too dissipative and prevents the emergence of unsteady motions within the mixing layer. For higher order schemes, from 4th- to 10th-order, the flow solutions are turbulent but exhibit mean flows and turbulent intensities depending on the filter. The investigation of the one-dimensional kinetic energy spectra then shows that the 4th-order filter may still be too dissipative whereas large scales remain unaffected using the 6th-, 8th- and 10th-order filters. A further study of the kinetic energy spectra nonetheless demonstrates that the effective spatial bandwidth of the LES increases with the order of the filtering scheme. Simulations using the 6th-, 8th- and 10th-order filters, with mesh sizes chosen to provide the same effective LES cut-off wavenumber, are performed and yield similar results. It is hence found that the value of the effective LES cut-off wavenumber, rather than to the filter shape itself, is mainly responsible for the discrepancies between the flow statistics obtained using different filters. One may conclude that filter shape independence is consequently achieved in the present LES of a mixing layer.

International audience; A sonic flow in a plane duct passing an abrupt increase in cross section is studied using compressible large-eddy simulations. Different flow patterns are likely to appear in this configuration according to the ratio between the downstream ambient pressure and the upstream reservoir pressure. For low pressure ratios, the flow is entirely supersonic in the channel and a steady symmetrical shock pattern is observed. For higher pressure ratios, the flow can be attached to one side of the channel with a jet-like shock cell structure, or can be characterized by strong oscillations of a single normal shock located near the sudden expansion, known as base-pressure oscillations in literature. A hysteresis phenomenon is found experimentally and the state reached by the transonic flow depends on the path followed by the pressure ratio. Moreover, a coupling of these base-pressure oscillations with the quarter-wavelength resonance of the duct can occur. All these regimes are numerically investigated and the results are favorably compared to available experimental data. A case of frequency locking of this self-excited mechanism is also reproduced, in agreement with a modeling of the resonator. The governing equations are solved using high-order central finite differences combined with an overset grid approach. The large-eddy simulations are based on a relaxation filtering and a nonlinear shock-capturing scheme is also implemented for shock waves.

A direct computation of the noise radiated by a turbulent flow in a duct obstructed by a diaphragm is performed by compressible large-eddy simulation. For the low Mach number configuration considered, a two-step hybrid method could be less expensive, but would fail at characterizing sound-flow interactions. The application of direct calculation is thus challenging but gives both the acoustic and aerodynamic fields in the same computation in order to shed light on the noise generation mechanisms. Acoustic energy is produced and dissipated in the asymmetric jet-type flow issuing from the diaphragm. A low-frequency radiation is correlated with the breakdown of the coherent jet-column structures as the plane jet reattaches the upper wall. The Kelvin–Helmholtz vortices in the shear layers of the jet constitute the primary instabilities but do not radiate sound. On the contrary, this vorticity shedding seems to dissipate waves propagating upstream by enforcing the unsteady Kutta condition.

High levels of vibrations have been observed on the last row blades of a low pressure steam turbine for nominal operating conditions. A self-excited phenomenon known as flutter is suspected to be the cause of the vibrations for non-stall transonic conditions. The non-homogeneous distribution of vibratory levels on the row is attributed to mistuning effects. They are beyond the scope of our study. A time-dependent ALE formulation of Euler equations is derived on a quasi-3D domain and coupled with a one-degree-of-freedom structural model. The work-by-cycle (WBC) method is performed in order to analyse the stability of the vibrating blades in the surrounding flowfield, for a perfectly tuned assembly. On the top part of the blades, the flow is transonic and fully attached. It is shown that, for these operating conditions, the cascade aeroelastic behaviour is linear. By using the influence coefficient method, an instability region is exhibited. The effects of the flowfield on the vibrating blades are discussed. They are expressed in terms of added damping and stiffness in order to be used as the input data of a structural mistuning analysis.Copyright © 2005 by ASME

International audience; Acoustic radiation of shock free supersonic jets is modified in comparison with subsonic jet noise because of Mach wave emission. Intense noise is radiated when turbulent structures are convected supersonically relative to the ambient sound speed. Using the framework of Lighthill's equation, Ffowcs Williams and Maidanik developed an approximation of Lighthill's term for a supersonically convected acoustic source in a turbulent shear layer. From this result, a model can be deduced for axisymmetric jets. One then shows that the local knowledge of the mean flow and a characteristic time of turbulence in the source volume may be used to calculate the spectral directivity of Mach wave noise. As a consequence of this local formulation of the acoustic source term, the noise model contains a single unknown multiplicative constant. It also requires a calculation of the mean flow which may be carried out with a k − e compressible turbulence model. Two cold jet cases at M = 1·7 and M = 2·0 and a hot jet at M = 2·0 and Tj /T0 = 2·5 are analyzed. Comparisons with available experimental data and Tam's calculations based on an alternative description in terms of instability waves travelling at the convection speed show a good agreement between calculations and measurements.

This paper deals with, the application of the SNGR ( Stochastic Noise Generation and Radiation) model to compute turbulent mixing noise generated in a duct obstructed by a diaphragm. Two problems must be solved in the framework of an acoustic analogy. First, a wave operator must be derived for sound waves travelling in any mean flow. In the SNGR model, the system of linearized Euler equations is used. An expression of the source term is then deduced from the conservation laws of motion, and can be simplified with classical assumptions of aeroacoustics in the case of subsonic mixing noise. Secondly, the knowledge of the turbulence velocity field is required to compute this source term. In the SNGR model, the spacetime turbulence velocity field is generated by a sum of random Fourier modes. Finally, the radiated acoustic field is calculated numerically by solving the inhomogeneous propagation system. The method is applied in this paper to the case of a two-dimensional duct obstructed by a diaphragm. Numerical results are compared with available experimental ones. Computed noise levels closely match experimental ones and follow the expected U* law.

A numerical solution of a κ‐e turbulence model is used to provide local and statistical properties throughout simple and coaxial round jets. These are inserted into predictive formulas for jet noise based on Lighthill’s theory: Ribner’s formalism postulates locally isotropic turbulence superposed on mean flow; Goldstein and Rosenbaum’s formalism generalizes this to accommodate the more realistic assumption of axisymmetry. Numerical jet noise predictions via the Ribner/κ‐e model (designated Ra) and the Goldstein/κ‐e model (designated Ga), and some variants, are compared with experiment. Only a single empirical factor is used. The Ga model, with its threefold longer axial scale, shows closer agreement with experiment than the Ra model. The predictive capacity of the Ga model is demonstrated by further calculations for coaxial jets. The results confirm the experimental observation of a minimum of acoustic radiation when the outer flow has 0.4 the velocity of the inner flow. An advantage of the κ‐e method is ...

A new approach to noise modeling for free turbulent flows is presented. The equations governing the sound field are obtained in two steps. The first step consists of treating the mean and turbulent components of the flow while the acoustic perturbations are neglected. In the second step, a set of equations is derived for the acoustic variables. On the left-hand side of this system, one finds the linearized Euler equations, whereas the right-hand side exhibits source terms related to the turbulent fluctuations and their interactions with the mean flow. These terms are modeled using a stochastic description of the three-dimensional turbulent motion. This is achieved by synthesizing the velocity field at each point in space and for all times with a collection of discrete Fourier modes. The synthesized field posesses the suitable one- and two-point statistical moments and a reasonable temporal power spectral density. The linearized Euler equations including a stochastic description of noise sources are solved numerically with a scheme based on a fractional step treatment. Each one-dimensional problem is solved with a weak formulation. A set of calculations are carried out for a simple freejet. Comparisons between calculations and experiments indicate that a spatial filtering of the source terms is required to obtain the expected level in the far field. Realistic pressure signals, power spectral densities, and sound field patterns are obtained. It is indicated that the stochastic noise generation and radiation (SNGR) approach may be applied to more complex flows because the numerical codes used to calculate the mean flowfield and the wave propagation are not specific of jet configurations. The limitations of the present model lie in the statistical properties of the synthetic turbulent field and in the use of an axisymmetric modeling of the acoustic propagation.

This Ph.D. thesis deals with the metastable two-phase flows typical of accidental transients that could occur in nuclear power plants. Those phenomena are of difficult treatment due to the topological difficulty of the flow, the interphase transfers and the strong coupling between thermodynamic features and mathematical aspects.The methods today in use in industry do not fully describe the complexity of these flows because based on too simple models. In fact, they do not take into account the thermo-chemical disequilibrium between liquid and vapor water. On the other hand, the hyperbolic methods recently proposed in the literature for the simulation of metastable flows can not be used in the industry because based on simple equations of state that are not adequate for industrial calculations.The purpose of this Ph.D. thesis is to develop a new approach that couples the modern hyperbolic methods to accurate equations of state. The final product of this work is a new model for the industrial analysis of metastable two-phase flows that incorporates novel techniques for the calculation of interfacial transfers and of steam-water properties. Moreover, it is computationally affordable for its use in industrial configurations.The methods developed in this thesis have been sistematically verified against exact solutions and validated using experimental data of the literature.; Cette thèse de doctorat s’intéresse aux écoulements diphasiques métastables typiques de certains transitoires accidentels qui pourraient intervenir dans les centrales nucléaires. Ces phénomènes sont difficiles à traiter en raison de la complexité topologique de l’écoulement, des transferts entre phases et du couplage fort entre les caractéristiques thermodynamiques et les aspects mathématiques.Les méthodes aujourd’hui en usage dans l’industrie ne décrivent pas complétement la complexité de ces écoulements car elles s’appuient sur des modèles trop simples. En fait ces méthodes ne prennent pas en compte le déséquilibre thermo-chimique entre l’eau liquide et sa vapeur. Par ailleurs, les méthodes hyperboliques proposées récemment dans la littérature pour la simulation des écoulements métastables ne peuvent pas être appliquées dans l’industrie car elles utilisent des lois d’état simples qui ne sont pas adaptées pour les calculs industriels.Le but de cette thèse est de développer une nouvelle approche qui couple les méthodes hyperboliques modernes à des équations d’état précises. Le produit final de ce travail est un nouveau modèle pour l’analyse industrielle des écoulements diphasiques métastables qui associe de nouvelles techniques pour le calcul des transferts interfaciaux et des propriétés de l’eau et de sa vapeur. De plus, cette approche est d’un coût abordable pour les configurations industrielles.Les méthodes développées dans cette thèse ont été systématiquement vérifiées avec des solutions exactes et validées en utilisant des données expérimentales de la littérature.

This Ph.D. thesis deals with the metastable two-phase flows typical of accidental transients that could occur in nuclear power plants. Those phenomena are of difficult treatment due to the topological difficulty of the flow, the interphase transfers and the strong coupling between thermodynamic features and mathematical aspects.The methods today in use in industry do not fully describe the complexity of these flows because based on too simple models. In fact, they do not take into account the thermo-chemical disequilibrium between liquid and vapor water. On the other hand, the hyperbolic methods recently proposed in the literature for the simulation of metastable flows can not be used in the industry because based on simple equations of state that are not adequate for industrial calculations.The purpose of this Ph.D. thesis is to develop a new approach that couples the modern hyperbolic methods to accurate equations of state. The final product of this work is a new model for the industrial analysis of metastable two-phase flows that incorporates novel techniques for the calculation of interfacial transfers and of steam-water properties. Moreover, it is computationally affordable for its use in industrial configurations.The methods developed in this thesis have been sistematically verified against exact solutions and validated using experimental data of the literature.; Cette thèse de doctorat s’intéresse aux écoulements diphasiques métastables typiques de certains transitoires accidentels qui pourraient intervenir dans les centrales nucléaires. Ces phénomènes sont difficiles à traiter en raison de la complexité topologique de l’écoulement, des transferts entre phases et du couplage fort entre les caractéristiques thermodynamiques et les aspects mathématiques.Les méthodes aujourd’hui en usage dans l’industrie ne décrivent pas complétement la complexité de ces écoulements car elles s’appuient sur des modèles trop simples. En fait ces méthodes ne prennent pas en compte le déséquilibre thermo-chimique entre l’eau liquide et sa vapeur. Par ailleurs, les méthodes hyperboliques proposées récemment dans la littérature pour la simulation des écoulements métastables ne peuvent pas être appliquées dans l’industrie car elles utilisent des lois d’état simples qui ne sont pas adaptées pour les calculs industriels.Le but de cette thèse est de développer une nouvelle approche qui couple les méthodes hyperboliques modernes à des équations d’état précises. Le produit final de ce travail est un nouveau modèle pour l’analyse industrielle des écoulements diphasiques métastables qui associe de nouvelles techniques pour le calcul des transferts interfaciaux et des propriétés de l’eau et de sa vapeur. De plus, cette approche est d’un coût abordable pour les configurations industrielles.Les méthodes développées dans cette thèse ont été systématiquement vérifiées avec des solutions exactes et validées en utilisant des données expérimentales de la littérature.