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Compressibility Effects on the Return to Compressibility Effects on the Return to

Isotropy of Homogeneous Anisotropic Isotropy of Homogeneous Anisotropic

Turbulence Turbulence

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Solving 3D compressible Navier-Stokes equations

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Spatial derivatives

Inviscid flux : 5th Order WENO (Ponziani et al., 2003) Viscous flux : 6th Order Compact Scheme (Lele, 1992)

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Time advancement

4th order Runge-Kutta algorithm (Jiang and Shu, 1996)

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Parallel implementation

– OpenMP, MPI-like programming

– AMD Opteron 885 Dual-Core Server (8 proc.)

Matthieu Crespo, Stéphane Jamme and Patrick Chassaing

ENSICA, 1 place Emile Blouin 31056 Toulouse Cedex 5,France

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Simulation Parameters

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Turbulence structure

- Tear drop shape for the joint PDF of velocity gradient as for incompressible turbulence.

- Slight influence of the anisotropic state.

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Velocity decomposition

- The return to isotropy phenomenon could be observed only on the solenoidal part of the velocity field as the compressible part remains isotropic

Compressibility control parameters : Anisotropy parameters :

Turbulent Reynolds number : Configuration :

Cubic domain with periodic conditions.

Imposed energy spectrum over initial quantities.

Grid size :

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Shocklets

- PDF of dilatation shows important compression events. ( )

- PDF of local Mach number present supersonic regions.

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Skewness

- Coupled effects of mt and chi - No major influence of the

anisotropic state.

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Initial transient

- Important redistribution of energy for the duration of the initial transient

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Return to isotropy velocity

- A clear influence of compressibility parameters has not been observed.

Return to isotropy velocity Transient

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