Philippe Lafon

Stochastic Approach to Noise Modeling for Free Turbulent Flows

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.

Application of a κ‐ε turbulence model to the prediction of noise for simple and coaxial free jets

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 ...

Computation of noise generation and propagation for free and confined turbulent flows

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.

Numerical study of self-induced transonic flow oscillations behind a sudden duct enlargement

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.

Reliable reduced-order models for time-dependent linearized Euler equations

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.

Computation of Acoustic Propagation in Two-Dimensional Sheared Ducted Flows

Most aeroacoustic noise-prediction methods rely on an acoustic analogy featuring a propagation equation associated with source terms. These models were mainly applied to computation of acoustic far fields radiated by simple free flows like jets. The assumption is made in many formulations that the radiated acoustic field is not perturbed by the shear flow giving rise to the noise sources. These acoustic analogies thus do not provide a full description of acoustic/flow interactions. The Lilley equation was introduced to account, to a certain extent, for mean shear effects on propagation. More recently, this problem has been treated by making use of the linearized Euler equations, which are more flexible and more adequate for numerical simulations. As several types of modes are supported by the Euler equations, problems linked to their coupling have to be considered. It is then necessary to investigate acoustic field computations in complex flows. Our aim in the present article is to validate the wave operator associated with linearized Euler equations. Numerical tests deal with propagation in two-dimensional sheared ducted flows. Results are compared with other solutions deduced from analytical developments and direct numerical simulations. This study shows that the linearized Euler operator may be used to account for mean effects on wave propagation in the presence of sheared ducted flows. Processes that are specifically considered are 1) convection effects on axial disturbances, 2) refraction effects on oblique wave generation, and 3) source radiation effects on propagation in sheared flows.

Computation of Aeroacoustic Phenomena in Subsonic and Transonic Ducted Flows

A sonic flow in a plane duct passing an abrupt increase in cross-section is numerically studied by solving the 3-D compressible Navier-Stokes equations. Different flow patterns are likely to appear in such configuration. For a very low downstream pressure, the flow is entirely supersonic. For higher pressures, unstable flow patterns emerge. One of these patterns features a normal shock, that oscillates due to a self-exciting mechanism. As the duct is open at the outflow, aeroacoustic coupling occurs when the shock oscillations get in resonance with the longitudinal acoustic modes of the duct. The main flow features are well captured by the present numerical simulations but no coupling with longitudinal duct modes is found. The governing equations are solved using high-order methods based on central finite differences. To damp out spurious oscillations supported by central differences selective filtering and a well established non-linear shock-capturing term are used. A highorder overset grid approach is implemented in order to tackle with complex geometries.

A high-order algorithm for compressible LES in CAA applications

A high-order finite-difference algorithm is proposed in the aim of LES and CAA applications. The subgrid scale dissipation is performed by the explicit high-order numerical filter used for numerical stability purpose. A shock-capturing non-linear filter is also implemented to deal with compressible discontinuous flows. In order to tackle complex geometries, an overset-grid approach is used. High-order interpolations make it possible to ensure the communication between overlapping domains. The whole algorithm is first validated on canonical flow problems to illustrate both its properties for shock-capturing as well as for accurate wave propagation. Then, the influence of the multi-domain approach on the high-order spatial accuracy is assessed. Afterwards, the algorithm is extended to dynamic mesh applications with overlapping grids. Finally, two industrial cases are presented to highlight the potential of the proposed algorithm.

Computation of noise generation by turbulence in internal flows

Stochastic modelling techniques are currently used to deal with various problems in turbulence. These methods are explored in this article with as objective the computation of the solution of aeroacoustic noise problems. The principle may be described as follows. The mean flow field is first deduced from a RANS calculation associated with a turbulence closure scheme like the k — e model. Next, a space-time turbulent field is synthetized stochastically, providing the local turbulent fluctuations and the associated noise sources. The radiated sound field is then calculated numerically. The present article is structured around the three following points. The aeroacoustic calculation is presented in the first part. The stochastic model of turbulence is described in the second part. The last section is devoted to computational methods and to numerical results related to noise generation by diaphragms placed in ducted flows. Three-dimensional numerical results are compared with experimental data in terms of acoustic levels. Results of calculations are in good agreement with predictions.

Sound vs. Pseudo-sound Contributions to the Wind Noise

We develop in this paper an analytical solution for the sound transmitted into a rigid rectangular cavity by a flexible plate loaded by the turbulent boundary layer of a grazing external flow. This simplified geometry aims to represent the vibro-acoustic response of a car front door window excited by the turbulent air flow that forms along the exterior surface of the vehicle. The modal expansion method is used to describe the plate displacement as well as the acoustic pressure in the cavity. The fluid loading is simulated using a direct noise computation code in the wake of a car rear view mirror. This code solves the full compressible three dimensional Navier-Stokes equations with highly accurate space and time algorithms and is able to capture the low amplitude acoustic part of the wall pressure fluctuations. The advantage of the modal approach is that the structural modes of the plate are represented in the wavenumbers’ space as an array of dots. It is thus possible using a wavenumber diagram to separate the plate modes which are spatially coupled to the propagative acoustic component from the modes which are spatially coupled to the aerodynamic convected component of the wall pressure fluctuations. Although the acoustic component is of small magnitude compared to the convected component of the fluid loading, it is shown that its contribution to the interior sound pressure level is crucial above the acoustic critical frequency of the plate.