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Hybrid RANS-LES modelling, single code & grid

Juan Uribe - Nicolas Jarrin University of Manchester, PO Box 88, Manchester M60 1QD, UK

IntroductionMain problem with LES is the near wall restictions, where the size of the cell must decrease in all directions. Ways to avoid that:

•Wall functions.

- Bridge the viscous sublayer.

- Not universal.

•RANS in one domain, LES in the other.

- Interface freely prescribed.

- Treatment of the interface is very impor tant. Need to promote turbulence ( synthetic, rescaled ...)

•RANS-LES in the same domain.

- How to couple two different velocity fields?

- Requires smooth transition.

Hybrid model

The problem:

RANS velocity field is statistically averaged. LES field is instantaneousy filtered.-> not the same properties (subgrid/turbulent viscosity/energy)

LES sub-grid model assumes inertial range isotropic motions.

As the wall is approached, mean shear introduces anisotropy → cell size must be reduced. The model must take into account sub-grid contributions to mean shear and isotropic dissipation effects.

Hybrid model The velocity field can be decomposed as follows:

The subgrid stress tensor can be splited into two parts. One with the instantaneous contribution and one with the averaged.

is the subgrid viscosity

is the RANS viscosity, based on the mean velocity

Hybrid model

The blending function fb is needed to avoid double counting of the

stress and to ensure that as the mesh is refined, the RANS contribution diminishes.

The turbulent lenghscale is predicted by an elliptic relaxation model (v2-f) to accurately predict the near-wall anisotropy

is the filter width

Trailing edge flow: Case specifications

Re=2.5 106 based on chord, Re=2760 (lower side) and Re=3380 (upper side) based on the momentum thickness

Only rear-most 38% of domain computed.

Inlet conditions based on RANS calculation of full aerofoil plus synthetic method.

Fine LES used for comparison used 1536 x 96 x 48

Actual grid used for computations: 512 x 64 x 24

Noise prediction important, therefore unsteady resolution required. Two simulations: DES +F1 shield function and Hybrid Model.

Stramwise velocity profiles over the airfoil

Stramwise velocity profiles in the wake

Turbulent fluctuations profiles over the airfoil

Turbulent fluctuations profiles in the wake

DES: RANS(blue) and LES (red)

Hybrid