Turbulent Natural Convection in Horizontal Coaxial Cylindrical Enclosures: LES and RANS Models

1. Turbulence, Heat and Mass Transfer 5 Dubrovnik, Sept 25-29, 2006 K. Hanjalić, Y. Nagano and S. Jakirlic (Editors) 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)

2. Industrial Relevance: Advanced Gas Cooled Reactor (AGCR) • - 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

3. Industrial Pb Simplification to 2D Case (axially homogeneous) RANS pre-study with imposed heat flux-T relation => Realistic simplification and comparable toRa=2.381010 Single cyl. heat sink Homogeneous 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  109) • Case 1- Natural convection in annular cavity (Ra=1.8109) • Case 2- Annular cavity single coaxial cylinder (Ra=2.381010) • Case 3- Annular cavity with 3 coaxial cylinders (Ra=2.381010) • 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 D=2 cell Vol. or Cs =0,08 for D= cell Vol.) + Van Driest damping, maximum t/=1.7 for lower Ra case. • PrtSGS= 0.4 or 0.9 • Coarse grid: 8020035 = 560,000 cells • + local refinement (fine grid) = 795,000 cells • RANS: k-e 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, Bishop89 Centred Diff. for V CD of Mars for T

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

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

9. Comparison with 2 eqn models Velocity magnitude Temperature T.k.e Ra =1.18109 Ro/Ri = 3.36

10. Intermittency and transition (Ra=1.8109) Iso-values of temperature Monitor point SGS visc/Molecular visc.<1.7 on coarse grid time

11. Case 2: Higher Ra=2.381010 , and 3 cylinder case Intantaneous T Levels More turbulence activity CASE-2: Ra=2.3810E+10 CASE-3: Ra=2.3810E+10 NB: inner cylinder now cooled (upside down / case 1)

12. Comparison to Low-Re RANS models predictions Streamlines Temperature distribution RANS models show less stratified flow in upper part (plume overshoot) Ra =2.381010 Ro/Ri = 3.37

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1010 Ro/Ri = 3.37 Combined cold plumes effect Less visible with k-e

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

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

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

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

20. Conclusions • Single cylinder case, • Ra = 2 109too low, (intermittency, transition) • Ra = 2 1010 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: • q2- 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.