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Materials Performance Centre Seminars, 12/09/2006

Application of Large Eddy Simulation

to thermal-hydraulics

in the Nuclear Power Generation Industry.

Dominique.Laurence@manchester.ac.ukSchool of Mech, Aero & Civil Eng.

Fluids AIG / CFD group

Dominique.Laurence@edf.frEDF R&D Chatou

Contributions: Y. Addad, I. Afgan, S. Benhamadouche, S. Berrouk, N Jarrin C. Moulinec, T. Pasutto,

The

Uni

vers

ity

of M

anch

este

r

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Osborne Reynolds 1868, became a professor of engineering at Owens College (now University of Manchester)

Reynolds tank, G. Begg building

Low speed jet

Higher speed jet

Turbulence, Reynold Number Re = UD/visc.

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Kolmogorov Energy Cascade

2 212

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Assume : ( ) sin( ) 2 /

. sin( )cos( ) sin(2 )

thus energy transfer from 2 / to 2 2 /( )

i i i i

i i i i i i i

i i i i

u x u k x k L

duu u k k x k x u k k xdx

k L k L

Андре́5й Никола́5е́вич Колмого5ров

Moscow State Uni. 1939

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Solve the standard (Navier Stokes) flow equation on a very fine mesh- All scales are resolved on that mesh (down to Kolmogorov scale)- No model needed- Results considered as valid as experimental data- Enormous computer resources, for even modest speed-domain size (Reynolds number)

Sergio Hoyas and Javier Jimenez, (2006) "Scaling of velocity fluctuations in turbulent channels up to Re_tau = 2000", Phys. of Fluids, vol 18,

Direct Numerical Simulation (DNS)

Nx=6144, Ny=633, Nz=4608 points = 17,921,212,416 cells

6 Million processor hours on 2048 processors,

Barcelona Supercomputing Center

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Luckily, only Large Scales matter (most of the time)

Large Scales & Human activity• Drag, mixing, heat transfer, • Large Scales dictate flow physics• Generated by/scale with obstacle• Impose dissipation rate

Exceptions: noise, combustion,

Weather forecast (we are the small scales !)

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Large Eddy Simulation = Filtering

1( , ) ( , ') '

2

t T

t Tu x t u x t t dt

T

drrxGtrutxuV

)(),(),(

CFD codes naturally induce filter = 2 dx

Space Filter

Time Filter

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DHIT: Decay of Hom. Iso. Turb.

MANDATORY test case for first time LES !

Reveals numerical dissipation, stability,

G rid

S ta tio n4 2

S ta tio n9 8

U = 1 0 m s0

-1

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• Direct Numerical Simulation (DNS) databases <=> Experiments

= “Costly” Fluid Dyn., exceptional, limited to zoom effect,

- 100% accurate, back to 1st principles, NO modelling hypothesis

• Large Eddy Simulation (LES)= “Colourful” Fluid Dyn., much detail,

fluctuations, spectra,- Applicable Eng. problems, at some cost- Almost as reliable as DNS, but know-how

required, not well established

• Reynolds Averaged (RANS)= “Conventional” Fluid Dyn., used daily in

Eng., only mean values (B&W)- Economical, full reactor or sub-component

design (parametric) possible- Problem: wide range of models to choose

from, - needs improvement & validation for new

range of applications (high temperature, buoyancy, conjugate heat

transfer, )

Future : Coupling of RANS and LES, using DNS for insight & validation

3 Levels of CFD approaches to turbulent flow

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Industrial LES applications to reactor thermal hydraulics

LES is mostly about numerical methods

Grid able to capture most turbulent scales Easier in Power Industry (confined, non-streamlined geometry) Local/embedded grid refinement, polyhedral scales

Boundary conditions Walls => quasi DNS (wall functions not ideal) Some real periodic geometry. pb. in Power Gen (tube bundles) Synthetic inlet turbulence

Target values Order of Mag. (within 10%), not 0.01 on Cd Thermal mixing & loading, spectra, vibrations….

Need Fast Unstructured FV Solver

EDF code Saturne & Star-CD very similar

High Accuracy Numerical Scheme No numerical dissipation

( Central differencing, Second order in time) Avoid any mesh distortion

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LES at EDF: Thermal stresses in T junction

Configuration studied : Thot = 168°C , Tcold = 41°CFlow rate = 1000 m3/h, ratio 20%

- Experimental mock-up (both thermalhydraulics and thermal fatigue mechanical aspects)

- models and numerical tools to gain a better understanding.

Length of the numerical simulation : 11 seconds

QhotQcold

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EDFElectricitéde FranceFluid results

Instantaneous fluid temperature field (Code_Saturne)

(Peniguel et al. ASME-PVP Cleveland 2003)Shortcut to aaPVP_anim.mpg.lnk

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Solid and fluid meshes

Solid mesh : 958 975 nodeswidth of the first solid element : 100 microns

Fluid mesh: 401 472 cells

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EDFElectricitéde FranceSolid temperature fluctuations

Instantaneous fluid temperature Instantaneous solid temperature

Time (s)

Instantaneous solid temperature field (Syrthes)(location C12)

C12

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Location CEX1

- On site meas

-L.E.S.

- Mock-up

CEX1

Frequency (Hz)

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T Junction, stratified case

Fluid temperature and flow structure

Recirculation zone

C12

Temperature In the symmetry plane (case 1)

Temperature near the wall (case 1)

VH = 3,37 m/s

TH = 204°C

VC = 0,77 m/s

TC = 41°C

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Analysis of the results

Attenuation of the fluctuations by the wall thermal inertia

( Ring C12 – 50 °)

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Mesh too coarse for Re=1 Milliontemperatures (ring C12) fluid: probe located at 10° probe located at 50°

Solid:

underestimation of the fluctations (especially at 10°) limitation of the wall function approach ?

LES

Exp

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Fluid meshes 1st mesh : ~ 500 000 hexaedric cells y+~ 300 2nd mesh : ~ 1 000 000 hexaedric cells y+~ 170 (first node at 0,38 mm from the wall)

(1 000 000 cell mesh)

FAATER exp. : Meshes

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Outflow region

Jet

x

y

Cold upflow

Trust & Quality-CFD project: hot wall jet (Magnox case)

Buoyancy: none medium highVelocity: high medium low

3-D view (STCL2). A: t1 = 2114 D j /V bjÝsÞ, B: t t2 = t1 + 18. 5D j /V bjÝsÞ.

Addad Y. , D. Laurence and S. Benhamadouche. The Negative Buoyant Wall Jet: LES Results, I.J. Heat and Fluid Flow, 25, 795-808, 2004

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Grid generation (buoyant case)

● Pre- k-eps simulation

● cell Volume near jet inlet (V)1/3=0.002● y+=1

● In mixing region (V)1/3=0.007

● NCELLS=770 000

●StarCD code

IntegralLength scalefrom k-epsilon

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Horizontal Velocity Comparison

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LES DB => Analytic Wall Function development

(from A. Gerasimov)

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Thermal hydraulics of reactors

Study the physics of the flow in the decay heat inlet pen

Examine the LES solution of the code Star-CD for the natural/mixed convection cases.

Validate further the analytical wall functions developed at UMIST by Gerasimov et al.

Mixed convection in co-axial pipes(Y. Addad PhD, M. Rabitt British Energy)

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K-eps pre-study

Streamlines coloured by temperature

Cold Inlet Pipe in vessel => stratification trap

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Coaxial heated cylinder study

• LES validation and parametric test cases: Case1-Natural convection in square cavity (Ra=1.58 109) Case2-Natural convection in annular cavity (Ra=1.8109) Case3- annular cavity single coaxial cylinder (Ra=2.381010) Case4- annular cavity with 3 coaxial cylinders (Ra=2.381010) Case5- Flow in actual penetration cavity (bulk Re=620,000).

Bishop 88, McLeod 89

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CASE-4: Ra=2.3810E+10

CASE-3: Ra=2.3810E+10

Natural Convection in coaxial cylinders

Case 2: Ra=1.810E+9SGS visc/Molecular visc.<1

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3 Cylinders

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Flow through in-line tube bundles

STAR CCM grid

Mean pressure

gradient

Direction is in-lin

e

Large heat exchanger=> Homogeneous conditions

=> Periodic subset considered

Re=45 000, P/D= 1.5

Objectives: Flow induced vibrations in heat exchangers (Lift & Drag coef.)

Staggered: studied 10 years agoCurrent: in line

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In-line tube bundle

I.Afgan@postgrad.manchester.ac.uk, with STAR-CCM

- Fully symmetric conditions, but non-symmetric solutions

- Coanda effect ?

- Star-CCM LES launched to confirm EDF finding(Benhamadouche et al. NURETH 11, Avignon 2005)

Time averaged velocity field =>

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In-line tube bundle P/D=1.5

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

0 45 90 135 180 225 270 315 360

Azimuthal Angle

No

rma

lize

d P

res

su

re

SATURNE

STAR CCM

STAR CCMMean velocity

(Afgan)

EDF Code-SaturneMean velocity

(Benhamadouche)

mean pressure

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-Vortex Method for Inlet

-Polyhedral Cells (670,000)

-Re=57,400

-Y+=2 (Prisms)

-L1=3D; L2=5D

- Smagorinsky Model, Van Driest Damping

LES in a 180° U-Bend Pipe

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U-Bend Pipe Cross Sections: Mean flow

45 degrees

177 degrees

135 degrees

90 degrees

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Research: Reconstructing fluctuations

Real Eddies in Channel flowCost = 5 days computing

Synthetic Eddies in Channel flowCost = 5 seconds computing

Matches all rms values andgiven spectrum

3-D view (STCL2). A: t1 = 2114 D j /V bjÝsÞ, B: t t2 = t1 + 18. 5D j /V bjÝsÞ.

KNOO project:Develop similar technique to

reconstruct temperature fluctuations at solid wall

Link with materials ageing research

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Research: Mesh strategy for LES

a)

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

- Non dissipative Finite Volume Methods

- Optimal meshing strategy for LES

- Quality criteria for LES General but essential issue. Collaboration with:- CD – Adapaco (STAR-CD code)- EDF R&D (Saturne code)- Health & Safety Labs, CFD for Nuclear Reactor licensing ?

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DNS at Re* N Cells

395 10 Million

640 28 Million

720 84 Million

2000 17,921 Million

RANS LES

Under-resolved LESRANS – LES coupling

U

Wall distance

J. Uribe, Manchester

Research: RANS – LES coupling

LES: ~ 0.1 Million cells

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Conclusions – Industrial LES

• LES of Industrial flow• Much more information:

Thermal stresses, fatigue, Acoustics, FIV (vibrations)• Cost-wise accessible when limited to subdomain

(synthetic turbulence for inlet)• Complex geometry possibly easier than smooth channel flow (academic overkill ?)

• Flexible flexibility with professional/commercial software:

• Opens new range of applications for LES• Medium Re number : DNS near wall resolution possible• Greater breakthrough than elaborate SGS models?

• Further developments: • More meshing control (total cell size control from pre-simulation)• High Re : RANS –LES coupling, embedded LES

• Cross-discipline research: Fluids / Structure-Mech/ Materials ?Cracks, Thermal stripping, ageing,

corrosion …