1. Turbulent Natural Convection in Horizontal Coaxial Cylindrical Enclosures: LES and RANS Models Yacine Addad, Dominique Laurence, and Mike Rabbitt (U. Manchester, EDF) (British Energy plc) Turbulence, Heat and Mass Transfer 5 Dubrovnik, Sept 25-29, 2006 K. Hanjalić, Y. Nagano and S. Jakirlic (Editors)

2. Industrial Relevance: Advanced Gas Cooled Reactor - Inner tubes carry water-steam in/out - Gap: hot CO2 thermosyphon flow - Real case: 3 to 44 inner tubes, + support plates acting as baffles + water cooling circuit - RANS simulations at BE ltd. with conjugate heat transfer for casing and concrete temperatures - Question to U Man.: validity of RANS for this type of flow (AGCR)

3. Industrial Pb Simplification to 2D Case (axially homogeneous) RANS pre-study with imposed heat flux-T relation => Realistic simplification and comparable to Ra=2.38  10 10 Homogeneous heat sink Single cyl. heat sink

4. Coaxial heated cylinders (2D-homogneous) study LES validation and parametric test cases: Case 0- Natural convection in square cavity (Ra=1.58  10 9 ) Case 1- Natural convection in annular cavity (Ra=1.8  10 9 ) Case 2- Annular cavity single coaxial cylinder (Ra=2.38  10 10 ) Case 3- Annular cavity with 3 coaxial cylinders (Ra=2.38  10 10 ) Case 4- Flow in actual penetration cavity (bulk Re=620,000). Bishop 88, McLeod 89

5. Previous work on Nat. Conv. in coaxial enclosures - With LES, Miki et al. [4] : Smagorinsky constant < “conventional” 0.065 for proper rms T prediction but small effects on mean velocity and temperature - RANS computations : Chakir et al. [5], wall functions Desai et al. [6] and Kumar [7], Rayleigh number, Prandtl number radius ratio. Kenjereš and Hanjalić [8] : three equations k-e-  2 Numerical Methods and Models used here: - STAR-CD 3.26 code (tested by Y.A. in LES mode on number of cases) - Full CD difference scheme for V. - For T: CD or localised blending (Mars) -Smagorinsky Cs =0,04 (with  =2 cell Vol. or Cs =0,08 for  = cell Vol.) + Van Driest damping, maximum t / =1.7 for lower Ra case. Prt SGS = 0.4 or 0.9 - Coarse grid: 80  200  35 = 560,000 cells + local refinement (fine grid) = 795,000 cells RANS: k-  models, Launder Sharma and NL of Lien et al. [12], - k-  model of Wilcox [13], SST k-  model of Menter [14], - Gibson and Launder RSM closure [15] (but simple eddy diffusivity model for heat flux).

6. Coaxial Cylinder Ra=1.8  109 Effect of Prt and convection scheme Mean Temperatures McLeod, Bishop 89 Centred Diff. for V CD of Mars for T

7. - Prt-SGS = 0.9 and Centred seems best (although 0.4 common) - Mars scheme OK except wall value Coaxial Cylinder Ra=1.8  109 Effect of Prt and convection scheme Rms Temperature Fluctuations

8. local refinement Case-1: Grid resolution and Prt effects 00 mean rms Prt=0.9 now overestimates rms temp. But Prt=0.4 still gives very low wall value

9. Velocity magnitude Temperature T.k.e Ra =1.18  10 9 R o /R i = 3.36 Comparison with 2 eqn models

10. Iso-values of temperature Monitor point Intermittency and transition (Ra=1.8  10 9 ) SGS visc/Molecular visc.<1.7 on coarse grid time

11. CASE-3: Ra=2.38  10E+10 CASE-2: Ra=2.38  10E+10 Case 2: Higher Ra=2.38  10 10, and 3 cylinder case Intantaneous T Levels More turbulence activity NB: inner cylinder now cooled (upside down / case 1)

12. Comparison to Low-Re RANS models predictions Ra =2.38  10 10 R o /R i = 3.37 Temperature distribution Streamlines RANS models show less stratified flow in upper part (plume overshoot)

13. Case 1 & 2: Nusselt Number (LES)

14. Case-3: Three coaxial cylinders Hexa and Tetra cells in the centre Total n. cells: 600,000 Star-CD version 3.24 Ra =2.38  10 10 R o /R i = 3.37 Combined cold plumes effect Less visible with k- 

15. New, Finer Polyhedral Mesh for LES Polyhedral cells in the centre, and (2:3) Local refinement near the walls using hexahedral cells Channel & Pipe flow => more accurate Total n. cells: 1.6 million Star-CD version 4.00

16. Mean T Fine Polyhedral Mesh Results (LES) T rms turb. k. e. V. mag. - Less hot plume overshoot - Top: - No mean motion, no turbulence - What causes « mixing » and Rms T between top cylinders?

17. RANS - All RANS show stratification between top cylinders - RSM and k-  too strong hot plume overshoot - LES and k-  do not show combined cold plumes effect Fine Mesh LES/RANS comparison RANS LES

18. Mean Velocity Magnitude RANS LES Fine Mesh LES/RANS comparison With WF, BL plume too thick and dynamic, RSM especially (overshoot)

19. Instantaneous and rms Temperature Instant. Temp. V mag.

20. Conclusions - Single cylinder case, - Ra = 2 10 9 too low, (intermittency, transition) - Ra = 2 10 10 more relevant to ind. case - All RANS models exaggerate outer hot plume overshoot - SST or k-  model might be recommended (but by chance ?) - Three Cylinder case : more complex ! - Dam effect between top cylinder pair - Mixing only apparent, due to gravity waves and dam overtopping - Would require more advanced RANS model:   - equation and RSM Transient-RANS (Kenjeres, Hanjalic) - LES: - Unstructured useful not only for geometry, but also for embedded refinement. - Need to remove uncertainty due to Van Driest and Prt. Issue (Dynamic model) This work was supported by British Energy plc. and partially from the EPSRC-KNOO project.

21. Instantaneous velocity Magnitude Fine Mesh LES/RANS comparison: Turbulent kinetic energy