Avancées en Modélisation de la

Turbulence

SFEN ST 6

CFD pour conception & sureté des réacteurs,

Chatou, le 29 Avril 2009

D. Laurence & F. Archambeau, MFEE

2

What is new in Turbulent Modelling? …. Computers work more so modellers can sit

back •  Osborne Reynolds (1895): RANS “Re Averaged Navier Stokes” => exact expression for the production of stresses (&fluxes),

•  Joseph Valentin Boussinesq (1897) Eddy Viscosity

•  Ludwig Prandtl (1925): mixing length

•  Andrei Komogorov (1942): energy cascade production – dissipation scales separation

• LES Joseph Smagorinsky (1964): 1980-1990 Stanford CTR, Kim, Moin, Moser, Ferziger, Piomelli …

• k-eps : Jones & Launder (1972), Launder & Sharma (1974),

• Re Stress Transport: Launder, Reece, Rodi (1975), Speziale Sarkar Gatsky(1991)

• 2000 – 2009 , lower cost HPC => LES for everyone and everything ?

1 43 2 3

0andt

kL

3

LES preamble: Only Large Scales Matter (most of the time)LES preamble: Only Large Scales Matter (most of the time)

Large Scales & Human activity

Drag, mixing, heat transfer, chem. reactions …

Large Scales dictate physics

Generated by/scale with obstacle

Impose dissipation rate

Exceptions: noise, combustion, 2-phase flows

…and NEAR WALLs !

4

LES => great, colourful results … IF .. the mesh is such that large scales are well captured (which means ... solution is already known ?)

LES => great, colourful results … IF .. the mesh is such that large scales are well captured (which means ... solution is already known ?)

5

Channel Flow LES on structured gridat Re*=395 (Re*=y+ at centre )From N. Jarrin 2006 www.cfdtm.org

% error on friction

Under-Resolved Channel LES

Coarse-mesh LES is more dangerous than coarse RANS !

6

Detached Eddy Simulation (DES)Scale Adaptive Simulation (SAS)

- LES limitation: too strongly dependent on mesh, unreliable for true “predictions”- Hybrid RANS-LES methods developed in EU AEROSPACE project DESIDER 2004-2007.- Validation limited to aerodynamics, seems premature for Reactor thermal hydraulics !

“SAS-SST model formulation dos not involve the grid spacing, it avoids the undefined model regimes of DES. In case of overly coarse grids, the model reverts back to the underlying RANS formulation. Fig. 5.2: The SST-SAS model can represent the true nature of the flow, by allowing a break-down of the turbulent structures into a spectrum (down to the grid limit)”

From “Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications” OECD NEA workgroup on CFD in reactor studies www.nea.fr/html/nsd/csni/cfd.htm

7

Flow ventilation of room with release of passive scalar

From Dr S. Gant. 'Challenges in validation of unsteady modeling approaches (DES/SAS/URANS)‘ presented at: http://cfd.mace.manchester.ac.uk/Main/KnooWorkshop To appear http://www.hse.gov.uk/ and J Flow, Turbulence and Combustion

DES error

SAS error

RANS error

8

Kolmogorov lengthscale

Taylor microscale

Turbulent energy scale:

First 3 are only “models” but can be obtained from “good” RANS models(*)

“True” Taylor and Integral scale are only given by2 point correlations, i.e. curvature and integral, e.g.:

More work needed to extract “true” scales from DNS or expt. and test predictions from recent advanced RANS models

(*) e.g. SST model in a simple channel flow will dramatically underestimate k near wall by a factor 2-3, and over-estimate lenghscale at centre by a factor 2!

13 4

2

2

1

1

2f

u

u

x

23k

Lturb

11 11 111 0

1, , ,

0, ,L x t R e r x t dr

R x t

Better RANS models to predict Length scales

9

Channel flow LES with “Taylor scale” mesh, N total = 0.44 Million , Re = 395

U U

y/h y+

y+

10

Unstructured meshing strategy for LESUnstructured meshing strategy for LES

a)

Possible FV near-wall refinements: a) dichotomy, b) non-conforming, c) & d) polyhedral & zoom.

Lenghtscale predicted by PRECURSOR RANS, then L= (k**3/2)/eps

11

Conclusions Conclusions Can we design next gen. nuclear power plants using LES/DES ?

Errors can be much larger than in RANS Beware vast majority of LES are “post-dictions”, or “explanations”how many failed LES were never published ?

Mesh influence is tremendousLES quality criteria progressing (see Q-LES workshops B. Guerts et al.) but trial and error most expensive with LES

Use “good” RANS model as precursor for LES feasibility study and mesh generation (but more user practice and control and over meshing software is needed)

Progress in RANS-LES coupling (google ANR STURM4)

RANS models are progressing quietly but surely (elliptic blending, algebraic structure based models… ), but no time to present…

Beyond “cold / aerodynamic” flows “good” RANS models will still be major engineering tool for complex physics (2 phases flows, near wall effects, heat transfer, combustion, natural convection) which need more than just eddy viscosity predictions (time-scales, lenghtscales, anisotropy…)

12

- LES community very activeon this topic- First idea (DES) reduce viscosity when turbulent scale > cells- Bad transition region (kink)where RANS viscosity is reduced but resolved structures are still too weak

Current solution is to OVERLAP RANS and LES

Zonal modelling / RANS-LES coupling

Re Cells395 40x30x30 59 39 26 158590 40x40x30 88 59 32 184

1100 50x50x40 140 88 46 2662000 50x50x40 256 160 83 4854000 64x80x64 400 200 99 574

Dx+ Dz+y+ @ f=0.5

y+ @ f=0.99

Uribe, J., Jarrin, N., Prosser, R., Laurence, D. 2009 "Two velocities hybrid RANS-LES of a trailing edge flow". J. Flow, Turbulence and Combustion.

Zonal RANS-LES coupling, Uribe model

Integral length scales in channel flow

Turbulent energy scale is easy RANS “model” but does not represent true (2 point correlation) integral scale for channel flow

23k

Lturb

streaks1- x : streamwise 2- y : wall normal 3 – z : spanwise Solid: stream-wise separation

Dashed: span-wise separationAddad, Y.,Gaitonde, U., Laurence, D., Rolfo, S. Optimal unstructured meshing for large eddy simulations, ERCOFTAC Series, Springer, Quality and Reliability of Large-Eddy Simulations. Meyers, Geurts & Sagaut, (Eds.), Vol. 12, pp. 93-103.

15

0.3

0.5

0.7

0.9

1.1

1.3

1.5

0.01 0.1 1 10

Bo

Nu

/Nu

0

Launder & Sharma Model (CONVERT)Cotton & Ismael Model (CONVERT)Suga Non-Linear Eddy Viscosity Model (CONVERT)Lien-Chen-Leschziner k-eps Model (STAR-CD)k-omega-SST Model (STAR-CD)Lien & Durbin v2f Model (STAR-CD)k-omega-SST Model (Code_Saturne)Manchester v2f Model (Code_Saturne)Large Eddy Simulation (STAR-CD)DNS - You et al (2003)

Near wall RANS model developments – heated pipe

buoyancy aidingbuoyancy aiding