EdF meeting 18 May 2009

Review of all the work done under the framework of

Code_Saturneby

S. Rolfo

School of Mechanical, Aerospace & Civil Engineering (MACE)

The University of Manchester

Manchester, M60 1QD

www.CFDtm.org

Summary

Use of unstructured meshes in Code_Saturne: Taylor Green vortices Laminar Channel flow

Developments: Hybrid RANS/LES Calculation of statistics: store of gradients (need only

feedback)

Refined LES of flow in fuel rod bundle arranged into a triangular array

Sodium Fast Reactors (SFR) fuel bundles.

Energy conservation: Taylor-Green vortices test case.

)22cos()2cos(4

1

)sin()cos(

)cos()sin(

1

212

211

kxkxp

kxkxu

kxkxu

20

20

ij j

jL2

jj

φ (x) φ (x)

err =φ (x)

Taylor-Green vortices test case: mesh generation.

Resolution: 60 x 60

Time step: 0.01 => CFLmax < 0.2

RR=ABAC

Effects of different Refinements Ratio (RR)

Effects of different Refinements Ratio (RR)

Refinements 1-2 optimization.

Map of 1-2 optimization

Example of optimization.

P1 P3

In terms of energy conservation the tilting is not producing the best results.The best results are obtained keeping the interface flat. Moving the position of the interface does not affect to much the results.

Results optimization

Global error on U and dU/dx for different meshes

Error conformal mesh

Error RR=0.97 mesh

Error RR=0.75 mesh

Error RR=0.50 mesh (base)

Error RR=0.50 mesh (“optimal” P3)

Error Hybrid mesh poly+hexa

Laminar channel flow poly mesh

Test of laminar flow at Ret=501. Mesh for Ret=395

1. N cells: 6390002. N Faces: 36600003. Different type of optimization, no big improvements (no reducing

of warping, skewing angle, etc)4. Interface prism/poly @ y+~100=>interface @ y=0.18

2. Mesh for Ret=10201. N cells: 35000002. N Faces: 205000003. Interface prism/poly @ y+=100=>interface @ y=0.1

In both the cases relatively big oscillation of V, W, P were found. Moreover the maximum velocity at the centre line was 20 or less.

(Ret=50 => Umax=25). This means a difficulty of the mesh to converge.

Laminar channel flow mesh 395 ( History)

Laminar channel flow mesh 395 (Profile)

Laminar channel flow mesh 1020 ( History)

Laminar channel flow mesh 1020 (Profile)

Rod Bundle arranged in a triangular array

Geometrical configuration: P/D = 1.06 Big computational

domain (7 mil cells)

Thermal Hydraulic regime Re=5994

Heat transfer (qw=60 W/m2)

New cases to run Re=5994 with imbalance

in the temperature Re=12000 (mesh ready

with 14 mil cells) Possible Higher P/D

Mean quantities

<U> <T>

Re stresses

<uu>

<vv>

<ww>

<uv>

<uw>

<vw>

Temperature

<θθ> <uθ>

<wθ><vθ>

Imbalance of temperature

28

SFR fuel assembly: Case presentation Flow parameters:• P/D = 1.1 • Re = 11000 (Bulk vel = 1 m/s)• Working fluid liquid sodium

• = 847 kg/m3• µ = 2.55 10-4 Kg/m/s• Pr = 5 10-3

SFR test case

SFR rod bundle

Future near work Calculation of the complete geometry with 271 pins (mesh ready, but

problem with some warp faces). Literature review on experimental paper of the same geometry with

different numbers of fuel elements.

Future work Extension of the 6 pin mesh in order to perform low Reynolds

calculations. Extension of the case to different number of pins and comparison of the

results with the available experiments Refined calculations: LES?!!

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

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 width

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

RANS-LES Results

Gradient calculation.

Gradient calculation and store in PROPCE Now available only for the velocity and version 1.4.0 Addition of pressure and temperature really straight forward Possible use to compute budgets , but extension in order to include

second order derivatives is necessary => huge number of properties will be stored

Need a feedback about the implementation in order to carry out the addition of all the others term.