Numerical simulation of Helium dispersion in a semi-confined airfilled
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1 Numerical simulation of Helium dispersion in a semi-confined airfilled cavity 1. Huong Lan TRAN (UPMC, LIMSI-CNRS, CEA-Saclay) 2. Anne SERGENT (LIMSI-CNRS, UPMC) 3. Gilles BERNARD-MICHEL (CEA-Saclay) 4. Patrick LE QUÉRÉ (LIMSI-CNRS) ICHS Brussels, September 9-11,
2 Outline 1. Introduction 2. Configuration 3. Physical modeling 4. Numerical methods and validation 5. Results 2
3 1. Introduction 3
4 Cariteau et al. (Int J Hydrogen Energ, 2012) Experiments Theoretical models Baines and Turner (JFM, 1969), Worster and Huppert (JFM, 1983), Cleaver et al. (J. Hazard. Mater., 1994) : parabolic profile of concentration Linear profile Entrainment coefficient? 4
5 Benchmark of helium-air dispersion (CEA) : evaluate numerical codes Comparison of numerical results and experimental data : large discrepancies in low injection case! Helium vol. frac. Experimental results : agree with theoretical model Bernard-Michel et al. (Technical Report, 2012), Cariteau et al. (Int J Hydrogen Energ, 2012) time 5
6 Present study Objective Develop a 2D numerical tool to simulate the mixing and dispersion a binary mixture of helium and air in a cavity Method Use DNS with axisymmetric hypothesis Validate the results with an incompressible test case of Rogers & Morris, Phys. Fluids, 2009 Compare numerical results with the model of Worster & Huppert, JFM, 1983 Compare numerical results with other numerical and experimental data 6
7 2. Configuration 7
8 Experimental vs. Numerical o T=20 C, P = 1 atm Ambient fluid : air, injected fluid : helium GAMELAN : 3D rectangular parallelepiped [Num] : 2D axisymmetric Top view Side view 8
9 Physical parameters of 5 cases Physical properties of air and helium 4 cases of smaller cavities Grashof Volume Richardson Schmidt = ( ) Injection Reynolds = ( ) 9
10 3. Physical modeling 10
11 + Equations for a binary mixture at constant temperature and pressure + Laws for the variation with : helium mass fraction, : mixture density : mass-averaged velocity,,, 11
12 Boundary conditions 12
13 4. Numerical methods and validation 13
14 Numerical methods Time discretization : Semi-implicit, 2nd order Spatial discretization : finite volume, staggered grid, 2nd order Non-uniform grid with 322x642 nodes for the full cavity Time to simulate 275 s (physical time) for the full cavity : hours (CPU time) 14
15 2D cavity : comparison with theory t=6 t=8 t=10 t=12 Horizontal profile of w z change of variables x Centerline profile of w
16 5. Results of round plumes with axisymmetric assumption 16
17 time Volume fraction fields Cavity 1/10 Cavity 2/5 Cavity 3/5 Cavity 1/5 Cavity 1 17
18 Volume fraction profile : Worster and Huppert's model During the descend of the first front (Worster and Huppert, JFM, 1983) Source buoyancy flux : Cross-sectional area : Entrainment coefficient : 18
19 Volume fraction profile : comparison with Worster and Huppert's model Cavity 1/10 Cavity 1/5 Cavity 2/5 Cavity 3/5 19
20 Volume fraction : comparison with finite element results for cavity 3/5 at 5 points on axis Same axisymmetric assumption at 5 points off axis 20
21 Comparison for the full cavity 115 s 275 s CEA laminar, JCR laminar, NCSRD laminar : no turbulence model CEA LES 2D : LES with axisymmetric hypothesis NCSRD RNG, NCSRD, AL : model JCR SST : model 21 Data taken from Bernard-Michel (Proceedings ICHS, 2013)
22 Conclusions and perspectives Develop a numerical tool to simulate the dispersion and mixing of helium injected in an air-filled cavity with axisymmetric hypothesis Validate the 2D plane case with theory Five cavities with the same aspect ratio have been investigated Obtain close agreement with finite element results with the same axisymmetric assumption The numerical results do not agree with either Worster and Huppert's model or experimental data ---> The need to perform full 3D computations 22
23 References [1] M. G. Worster and H. E. Huppert (1983) Time-dependent density profiles in a filling box. J. Fluid Mech. 132 [2] B. Cariteau and I. Tkatschenko (2012) Experimental study of the concentration build-up regimes in an enclosure without ventilation. International Journal of Hydrogen Energy 37 [3] W. D. Baines and J. S. Turner (1969) Turbulent buoyant convection from a source in confined region. J. Fluid Mech. 37(1) [4] R. P. Cleaver and M. R. Marshall and P. F. Linden (1994) The build-up of concentration within a single enclosed volume following a release of natural gas. J. Hazard. Mater [5] M. C. Rogers and S. W. Morris (2009). Natural versus forced convection in laminar starting plumes. Physics of Fluids, 21. [6] G. Bernard-Michel, J. Trochon, E. Vyazmina and O. Gentilhomme (2012) Resultat du benchmark ventilation sur 3 essais gamelan dans le cadre du projet anr dimitrhy. Technical Report DEN/DANS/DM2S/STMF/LIEFT/RT/12/020/A., CEA Saclay DEN/DANS/DM2S/STMF/LIEFT. [7] G. Bernard-Michel (2013). CFD benchmark based on experiments of heliume dispersion in a 1 m3 enclosure-intercomparisons for plumes and buoyant jets. Proceedings of ICHS
24 Vorticity fields Cavity 3/5, t=4, 10, 20, 46, 93, 139 and
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