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DLES, Ercoftac Workshop, Trieste, 8-10 September 2008

LES of turbulent flow through a heated rod bundle arranged in a

triangular array.

S. Rolfo, J C Uribe and D. Laurence

The University of Manchester, M60 1QD, UKSchool of Mechanical, Aerospace & Civil Engineering.

CFD group

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Summary

Introduction:

• Code_Saturne

• RANS/LES coupling

• Rod Bundle test case

Results:

• Flow pulsations

• Average field

Conclusions

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Code_Saturne

Code developed by EdF and now open source downloadable from:

http://rd.edf.com/code_saturne

Unstructured

Co-located, Finite Volume Formulation

Different turbulent models (both RANS and LES)

Incompressible or expandable flows with or without heat transfer

Different modules: radiative heat transfer, combustion, magneto-hydrodynamics, compressible flows, two-phase flows

Possible coupling with Code_Aster for structural analysis and with Syrthes for thermal analysis.

Parallel code coupling capabilities (awarded the Gold medal on HPCx)

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RANS-LES coupling (1)

The Hybrid RANS-LES method is following a usual LES decomposition in large scale and sub-grid part:

The anisotropic part of the residual stress tensor and residual heat flux can be decomposed following a Schumann decomposition:

Sub- grid viscosity

RANS viscosity computed from the mean velocity field

For the eddy conductivity a simply turbulent Prandtl number analogy is used

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RANS-LES coupling (2)

The merging between the two velocity fields is done through a blending function to obtain a smooth transition

Turbulent RANS length scale computed with a relaxation model based on

Filter widthEmpirical constants computed in order to match the stress profile for channel flow @ Re = 395

Under-resolved standard LES

Hybrid results with meshSize ~ 0.1 mil cell

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Rod Bundle arranged in a triangular array• Experimental work:

I. Secondary flow : Vonka “Measurement of secondary vortices in Rod Bundle” Nuclear Engineering and Design, Volume 106, Issue 2, 2 February 1988, Pages 191-207

II. Flow pulsations: Krauss, Meyer “Experimental investigation of turbulent transport of momentum and energy in a heated rod bundle”, Nuclear Engineering and Design, Volume 180, Issue 3, April 1998, Pages 185-206

• CFD work (URANS):

1. E. Merzari, H. Ninokata, E. Baglietto “Numerical simulation of flows in tight-lattice fuel bundles Nuclear Engineering and Design”, Volume 238, Issue 7, July 2008, Pages 1703-1719 .

2. D. Chang, S. Tavoularis “Simulations of turbulence, heat transfer and mixing across narrow gaps between rod-bundle sub-channels” Nuclear Engineering and Design, Volume 238, Issue 1, January 2008, Pages 109-123

13 @Re 60000.93

112 @Re 39000Gap

f HzfDSt

f HzU

From II

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Rod Bundle: Cases definitionTwo different geometrical configuration

1. P/D = 1.06I. LES @ Re = 6000 Mesh size ~ 1.6 Million cells with Heat transfer.

– 0.75<Δr+<1.06 – 7.5<rΔθ+<11 – 16<Δx+<22.5

II. Hybrid @ Re = 6000 Mesh size ~ 0.35 Million cells with Heat transfer – 0.8<Δr+<1.3 – 15<rΔθ+<20 – 40<Δx+<60

III. Hybrid @ Re = 39000 Mesh size ~ 0.9 Million cells no Heat transfer – 0.8<Δr+<1.2 – 20<rΔθ+<25 – 50<Δx+<70

2. P/D = 1.15 I. LES @ Re = 6000 Mesh size ~ 1.4 Million cells no Heat transfer

– 0.8<Δr+<1.1 – 6.5<rΔθ+<10 – 16<Δx+<22.5

All the domains have a stream-wise length equal to 12 times the hydraulic diameter

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Results: Flow Pulsation in the mid-plane

Hybid @ Re = 6000LES P/D=1.15 @ Re = 6000

LES @ Re = 6000

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Flow Pulsation in the mid-plane

LES

P/D =1.06

LES

P/D =1.06

LES

P/D =1.15

Hybrid

P/D =1.06

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Results: Power spectra angular velocity P/D=1.06

Point A

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Results: Power spectra angular velocity P/D=1.15

Point A

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Results: Power spectra angular velocity P/D=1.06 (Hybrid)

Point A

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Results: Power spectra angular velocity P/D=1.06 (Hybrid @ Re =39000)

Point A

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Results: Average Field (LES P/D = 1.06 Re = 6000)

<U>/Ub

w,m

w,m b

T T

T T

< θ θ ><uθ>

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Results: Reynolds Stress LES P/D=1.06

<uu>

<vv>

<ww>

<uv>

<uw>

<vw>

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Results: Comparison average values LES/Hybrid

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Results: Comparison Re stress LES/Hybrid @ Re=6000

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Conclusions and future work LES

Flow Fluctuations detected, Presence of a second dominant frequency has to be verified with bigger domain.

Hybrid Flow pulsations detected and dominant frequency in according with LES Problem in the near wall region. Possible reason blending function Same problem for the heat transfer

Future work Calibration of the wall function for the Rod Bundle (in progress) Improvement heat transfer with a dynamic turbulent Prandtl number LES computations with bigger cross section to verify the dominant frequencies Improved geometry with addition of wire wrapped around the pin (SFR reactor).

AcknowledgementsAcknowledgements This work was carried out as part of the TSEC programme KNOO and as such we are

grateful to the EPSRC for funding under grant EP/C549465/1.

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Power spectra angular velocity P/D=1.06

Point B

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Reynolds Stress Hybrid P/D=1.06 Re=5800

<uu>

<vv>

<ww>

<uv>

<uw>

<vw>

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Average value Hybrid

LES viscosity

Blending function

RANS viscosity

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Average value Hybrid (Heat transfer

Average temperature

<uT>

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Reynolds Stress Hybrid P/D=1.06 Re=39000

<uu>

<vv>

<ww>

<uv>

<uw>

<vw>