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 5Dubrovnik, Sept 25-29, 2006K. Hanjalić, Y. Nagano and S. Jakirlic (Editors)

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)

Industrial Pb Simplification to 2D Case (axially homogeneous)

RANS pre-study with imposed heat flux-T relation

=> Realistic simplification and comparable to Ra=2.381010

Homogeneous heat sink

Single cyl. heat sink

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=1.8109) Case 2- Annular cavity single coaxial cylinder (Ra=2.381010) Case 3- Annular cavity with 3 coaxial cylinders (Ra=2.381010) Case 4- Flow in actual penetration cavity (bulk Re=620,000).

Bishop 88, McLeod 89

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.

PrtSGS= 0.4 or 0.9 - Coarse grid: 8020035 = 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).

Coaxial Cylinder Ra=1.8109 Effect of Prt and convection schemeMean Temperatures

McLeod, Bishop 89

Centred Diff. for VCD of Mars for T

- Prt-SGS = 0.9 and Centred seems best (although 0.4 common)- Mars scheme OK except wall value

Coaxial Cylinder Ra=1.8109 Effect of Prt and convection schemeRms Temperature

Fluctuations

local refinement

Case-1: Grid resolution and Prt effects0

mean

rms

Prt=0.9 now overestimates rms temp.But Prt=0.4 still gives very low wall value

Velocity magnitude Temperature T.k.e

Ra =1.18109

Ro/Ri = 3.36

Comparison with 2 eqn models

Iso-values of temperatureMonitorpoint

Intermittency and transition (Ra=1.8109)

SGS visc/Molecular visc.<1.7on coarse grid

time

CASE-3: Ra=2.3810E+10

CASE-2: Ra=2.3810E+10

Case 2: Higher Ra=2.381010 , and 3 cylinder case

Intantaneous T LevelsMore turbulence activity

NB: inner cylinder now cooled (upside down / case 1)

Comparison to Low-Re RANS models predictions

Ra =2.381010 Ro/Ri = 3.37

Temperature distribution

Streamlines

RANS models show less stratified flow in upper part(plume overshoot)

Case 1 & 2: Nusselt Number (LES)

Case-3: Three coaxial cylinders

• Hexa and Tetra cells in the centre• Total n. cells: 600,000• Star-CD version 3.24

Ra =2.381010 Ro/Ri = 3.37

Combined coldplumes effectLess visible withk-

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

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 » andRms T between top cylinders?

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

Mean Velocity Magnitude

RANS

LES

Fine Mesh LES/RANS comparison

With WF, BL plume too thick and dynamic,RSM especially (overshoot)

Instantaneous and rms Temperature

Instant. Temp.

V mag.

Conclusions

- Single cylinder case, - Ra = 2 109 too 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: - 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.