Véronique Fortuné

Short note: Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation

In this short note, we show how to use a highly accurate finite-difference scheme to compute second derivatives in the Navier-Stokes equations while ensuring targeted numerical dissipation. This approach, essentially non conservative, is shown to be close to an upwind method and is straightforward to implement with a negligible computational extra cost. The benefit offered by the resulting discrete operator is illustrated for the direct computation of sound in aeroacoustics and in the more general context of large-eddy simulation through connections with hyperviscosity and spectral vanishing viscosity.

An iterative algorithm for computing aeroacoustic integrals with application to the analysis of free shear flow noise

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.

Identifying the dynamics underlying the large-scale and fine-scale jetnoise similarity spectra

This work concerns the development of a diagnostic tool for the analysis of jet noise source mechanisms. The technique comprises three steps: (1) synchronous measurement of pressure and velocity fluctuations (pressure measured in the irrotational nearand farfield regions; velocity measured in the rotational region of the flow); (2) filtering of the near pressure field into radiating and non-radiating components; (3) reconstruction of the velocity fluctuations which are linearly associated with the radiating component of the near pressure field. The technique is here applied to an isothermal, co-axial jet (primary Mach=0.5; secondary Mach=0.25; Re=1,000,000), and we perform a further filtering of the near pressure field so as to extract the space-time structure of the field which radiates to 30 degrees and to 90 degrees (finally, the flow dynamics associated with each of these components is to be estimated). Preliminary results show that: (1) the radiating ‘source’ activity does not occur in the regions of peak turbulence (in agreement with previous numerical results of Freund); and, (2) the shape of the radiating sound spectrum looks to be made up of three main components: a coherent low-frequency component associated with the dynamics at the end of the potential core; a coherent high-frequency component associated with the near-nozzle dynamics; and a more broadband high frequency component which may be associated with ’fine-grained’ turbulence. The ’fine-grained’ component appears to be an order of magnitude less energetic than the two coherent components, and the flatness of the 90◦ spectrum appears to be a result of a superposition of the highfrequency near-nozzle and the low-frequency potential-core dynamics.

Numerical Investigation of the Noise Radiated from Hot Subsonic Turbulent Jets

Experimental studies have highlighted the existence of additional sources of sound due to temperature fluctuations in heated jets, in comparison with unheated jets. Whereas cold jets have been the subject of many numerical investigations, little research has been devoted to the topic of hot jets. Thus, a specific model to investigate the acoustic radiation from these jets based on numerical predictions wing a k-e turbulence closure is attempted. First, a model for the additional source term is suggested, which is a function of mean axial velocity, mean temperature, and turbulent kinetic energy. Next a computation model of acoustic intensity spectrum is developed in which three different contributions appear: The first represents the contribution of the velocity fluctuations in the sound emission, the second that of the temperature fluctuations, and the third a mixed term issuing from the two preceding contributions. Then the model is applied to compute the acoustic radiation of hot jets. Results provided quite a full description of the acoustic features of a hot jet: spectrum shape, radiated acoustic intensity levels, and influence of jet temperature. Finally, the model seemed capable of predicting the trends in noise radiation of turbulent hot jets correctly.

Numerical Study of Mach Number and Thermal Effects on Sound Radiation by a Mixing Layer

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.

Direct Computation of the Sound Radiated by Shear Layers Using Upwind Compact Schemes

It is well known that direct numerical simulation (DNS) of compressible flow and computational aeroacoustics (CAA) require the use of accurate numerical schemes allowing the drastic reduction of dispersive and dissipative errors. Despite this agreement in the DNS/CAA community about the usefulness of highly accurate schemes, there is no consensus about the best combination of numerical techniques to solve the compressible Navier–Stokes equations, even for free-shock flow. An important point in the various approaches lies in the control of spurious oscillations at marginal resolution, these oscillations being linked to the nonlinear nature of the governing equations and to the artificial treatment of boundary conditions. In the literature, the specific care about this numerical artefact is found to differ significantly from one simulator to another. As a first condition, previous authors have shown that the formulation of governing equations can influence the robustness of the computational procedure. For instance, the improvement of conservation properties through relevant term splitting [11,17] has been found to enhance numerical stability. As an additional condition to avoid spurious oscillations, the spatial discretization itself can be adapted via the grid arrangement (staggered schemes, see for instance [3,16]) or the introduction of upwinding in the spatial differentiation [2]. Alternatively, the use of an artificial damping term [19] or a filtering procedure [7,9,10] have allowed some authors to simply use a collocated grid in conjunction with finite central difference schemes of high accuracy [5, 13]. Note that in the context of large eddy simulation (LES), some authors use also an explicit filtering procedure as a subgrid scale modelling [6,14]. To our knowledge, no extensive comparisons between the corresponding numerical

Analysis of acoustic source mechanisms in free shear flows

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.

Analysis of Free-Shear Flow Noise Through a Decomposition of the Lighthill Source Term

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.

Decomposition of the Lighthill source term and analysis of acoustic radiation from mixing layers

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 pred...