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A partnership between Institute of Mathematical Modeling, Moscow, and INRIA

**Involved researchers:**

Tatyana K.Kozubskaya, IMM,

Ilya Abalakin, IMM,

Bruno Koobus, u. of Montpellier and INRIA

**Industrial adviser:**

Michel Mallet, Dassault-Aviation

The collaboration concentrates on numerical investigation of unsteady turbulent flows and simulation of acoustic noise created by turbulence.

The investigations are planned in order to examine a class of k-epsilon like turbulence models for the simulation of flows with quasi-periodic structures and its use for the modeling of acoustic phenomena.

Although k-epsilon models are widely used for academic and industrial calculations, many questions remain open concerning with their use in more complex situations than the single prediction of mean steady flows. In some case, the model is not able to provide a steady flow, and in fact, the user wishes some information concerning some unsteady structures. In some other case, methods for exploiting the output of the model have to be designed in order to get information about acoustic events related to turbulence.

The work aims to contribute to the prediction and to prepare the control of macroscopically unsteady turbulent flows. The prediction of these flows is today one of the most important problem in aerodynamics. For most turbulent flow of industrial interest, the prediction of a mean flow is not sufficient, and some of the structures have to be depicted.

A lot of work concentrate on introducing adhoc turbulent viscosity models, for obtaining large structures (LES techniques relying on Smagorinsky viscosities), or organized structures (Organized Eddy Simulation -OES- relying on Boussinesq closure viscosities). Our option is to concentrate on examining improvements of the OES class of models. It will rely on different types of averaging, and on closures of k-epsilon type. One rather original point of view will consists in extracting a steady mean flow from an unsteady one in order to propose a new definition of the closure terms. Indeed, viscosity source terms should be decoupled from unsteady local velocity gradients, and turbulent energy from the predicted quasi-periodic component should not be accounted for in the filter applied other modes of the spectrum. Global turbulent viscosity is thus decreased, and one purpose of the study is to examine the impact of that decreasing on the prediction of quasi-periodic structures.

This investigation will take benefit from concurrent progress in steady of $k-\varepsilon$ modeling, in particular from several strategy aiming at producing lower levels of turbulent viscosity. We shall consider the following ideas:

- the adaptation of a wall law involving buffer zone modelling,

- the adaptation of a viscosity limiter inspired from the Shear Stress Transport model of Menter, relying on the Bradshaw law,

- the introduction of laminar regions (vanishing turbulent viscosity) and (depending on time) of a transition rustic model to adapt to the $k-\varepsilon$ one.

The work is to be carried out on the basis of standard academic test cases (wake after square and circular cylinders, etc.) and on several 2D geometries of industrial interest, to be specified in connection with Dassault Aviation (single airfoil, multi-body high-lift airfoils).

The goal of this part is the development of numerical technique for the prediction of acoustic flow field on the base of the information about flow characteristics obtained at the stage of turbulent flow simulation including steady mean flow components and quasi-periodic structures.

The work is intended to the elaboration of the model for the simulation of distributed acoustic noise sources as possible with a wide applicability area. This model has to consider various factors (for instance, 'turbulence-turbulence', 'turbulence-acoustics'interactions, refraction) influencing the noise generation process. The impact different type sources is aimed to be analysed.

To predict the fields of turbulent disturbances, stochastic models are often used. One of this work aims is an attempt to develop more deterministic model. This could be provided, in particular, by the determination of flow characteristic frequencies with the help of a specially prearranged numerical experiment consisting in the flow exposure to white noise irradiation from artificial sources. The advantages of this numerical technique are to be investigated.

To reach the above goals, adequate numerical algorithms are required. This is especially needed if taking into account the presence of strongly nonlinear source terms in the linearized Navier-Stokes equations and a small scale of acoustic disturbances in comparison with mean steady and quasi-periodic components. That's why a considerable attention is to be paid to the selection of a set of advanced numerical tools best suited to the prediction of 2D CAA problems both with the use of structured (rectangular) and unstructured (triangular) meshes. The corresponding compatible codes are to be written.

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Unstable and unsteady aerodynamics : compared information from different numerical models
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The behavior of two near-wall models for k-epsilon prediction of stall
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A Half-Stochastic Model for Noise Simulation in Free Turbulent Flows, AIAA paper 2001-2258
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Computational Study of Mathematical Models for Noise DNS, AIAA2002-2585
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**Other references**:

Abalakin, I. and Dervieux, A., ``A new MUSCL high-order method for CAA applying on triangulations `` INRIA Techn. Report, to appear

Alexandrov, A.V. and Kozubskaya, T.K., ``Simulation of Acoustic Noise Propagation through Supersonic Viscous Compressible Gas Flow'', Matemeticheskoe Modelirovanie (Mathematical Modeling), 1999, v.11, No 12, p.3--15 (in Russian).

Alexandrov, A.V., Chetverushkin, B.N. and Kozubskaya, T.K., ``Numerical Investigation of Viscous Compressible Gas Flows by Means of Flow Field Exposure to Acoustic Radiation'', Parallel CFD 2000 Conference (Trondheim, Norway, May 22-25, 2000).

Kozubskaya, T.K., ``A Way of Acoustic Noise Modeling for Turbulent Gas Flows'', ECCOMAS 2000 Conference (Barcelona, Spain, September, 2000), CD-ROM Proceedings.

Abalakin, I.V. and Kozubskaya, T.K., ``To Noise Prediction for Turbulent Flows'', The 5th French-Russian-Fnnish Workshop (Jyvaskyla, Finland, June, 2000).

Alexandrov A.V., Chetverushkin, B.N. and Kozubskaya, T.K., ``Noise Prediction for Shear Layers'', Parallel CFD 2001 Conference (Egmond on Zee, Netherlands, May, 2001), to appear.

Bobkov, V.G., Abalakin, I.V. and Kozubskaya, T.K.,
``A Half-Stokhastic Model for Noise Simulation in Free Turbulent Flows'',
AIAA paper, to appear.