Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T07:08:09.287Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 1. Hydrodynamic flow

Published online by Cambridge University Press:  23 March 2011

C. MISTRANGELO
C. MISTRANGELO*
Affiliation:
Karlsruhe Institute of Technology (KIT), IKET, Herrmann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen 76344, Germany
*
†Present address: KIT, Campus North, Postfach 3640, 76021 Karlsruhe, Germany. Email address for correspondence: chiara.mistrangelo@kit.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerical simulations are performed to study three-dimensional hydrodynamic flows in a sudden expansion of rectangular ducts. Separation phenomena are investigated through the analysis of flow topology and streamline patterns. Scaling laws describing the evolution of the reattachment length of the vortical areas that appear behind the cross-section enlargement are derived. The results discussed in this paper are required as a starting point to investigate the effects of an applied homogeneous magnetic field on separation phenomena in a geometry with a sudden expansion.

JFM classification

Waves/Free-surface Flows: Channel flow Mathematical Foundations: Topological fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 120 - 131
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Alleborn, N., Nandakumar, K., Raszillier, H. & Durst, F. 1997 Further contributions on the two-dimensional flow in a sudden expansion. J. Fluid Mech. 330, 169–188.CrossRefGoogle Scholar
Baloch, A., Townsend, P. & Webster, M. F. 1995 On two- and three-dimensional expansion flows. Comput. Fluids 24 (8), 863–882.CrossRefGoogle Scholar
Bühler, L. & Horanyi, S. 2006 Experimental investigations of MHD flows in a sudden expansion. Tech. Rep. FZKA 7245. Forschungszentrum Karlsruhe.Google Scholar
Cherdron, W., Durst, F. & Whitelaw, J. H. 1978 Asymmetric flows and instabilities in symmetric ducts with sudden expansions. J. Fluid Mech. 84 (1), 13–31.CrossRefGoogle Scholar
Chiang, T. P. & Sheu, T. W. H. 1999 A numerical revisit of backward-facing step flow problem. Phys. Fluids 11 (4), 862–874.CrossRefGoogle Scholar
Chiang, T. P., Sheu, T. W. H., Hwang, R. R. & Sau, A. 2001 Spanwise bifurcation in plane-symmetric sudden-expansion flows. Phys. Rev. E 65, 016306 (1–16).CrossRefGoogle ScholarPubMed
Chiang, T. P., Sheu, T. W. H. & Wang, S. K. 2000 Side wall effects on the structure of laminar flow over a plane-symmetric sudden expansion. Comput. Fluids 29 (5), 467–492.CrossRefGoogle Scholar
Délery, J. M. 2001 Robert Legendre and Henri Werlé: Towards the elucidation of three-dimensional separation. Annu. Rev. Fluid Mech. 33, 129–154.CrossRefGoogle Scholar
Drikakis, D. 1997 Bifurcation phenomena in incompressible sudden expansion flows. Phys. Fluids 9 (1), 76–87.CrossRefGoogle Scholar
Durst, F., Mellin, A. & Whitelaw, J. H. 1974 Low Reynolds number flow over a plane symmetric sudden expansion. J. Fluid Mech. 64 (1), 111–128.CrossRefGoogle Scholar
Durst, F., Pereira, J. C. F. & Tropea, C. 1993 The plane symmetric sudden-expansion flow at low Reynolds numbers. J. Fluid Mech. 248, 567–581.CrossRefGoogle Scholar
Fearn, R. M., Mullin, T. & Cliffe, K. A. 1990 Nonlinear flow phenomena in a symmetric sudden expansion. J. Fluid Mech. 211, 595–608.Google Scholar
Haller, G. 2004 Exact theory of unsteady separation for two-dimensional flows. J. Fluid Mech. 512, 257–311.CrossRefGoogle Scholar
Hunt, J. C. R., Abell, C. J., Peterka, J. A. & Woo, H. 1978 Kinematical studies of the flows around free or surface-mounted obstacles: applying topology to flow visualization. J. Fluid Mech. 86, 179–200.CrossRefGoogle Scholar
Legendre, R. 1956 Séparation de l'écoulement laminaire tridimensionnel. La Recherche Aéronautique 54, 3–8.Google Scholar
Lighthill, M. J. 1963 Attachment and separation in three-dimensional flows. In Laminar Boundary Layers (ed. Rosenhead, L.), chap. 2, 2.6, pp. 72–82. Oxford University Press.Google Scholar
Maskell, E. C. 1955 Flow separation in three dimensions. Tech. Rep. 2565. Royal Aircraft Establishment, Farnborough, England.Google Scholar
Mistrangelo, C. 2011 Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 2. Magnetohydrodynamic flow. J. Fluid Mech. doi:10.1017/S0022112011000607.CrossRefGoogle Scholar
Prandtl, L. 1904 Über Flüssigkeitsbewegung bei sehr kleiner Reibung. In Proceedings of the Third International Mathematics Congress, Heidelberg, Germany, pp. 484–491.Google Scholar
Revuelta, A. 2005 On the two-dimensional flow in a sudden expansion with large expansion ratios. Phys. Fluids 17, 028102.CrossRefGoogle Scholar
Schreck, E. & Schäfer, M. 2000 Numerical study of bifurcation in three-dimensional sudden channel expansions. Comput. Fluids 29 (5), 583–593.CrossRefGoogle Scholar
Sobey, I. J. & Drazin, P. G. 1986 Bifurcations of two-dimensional channel flows. J. Fluid Mech. 171, 263–287.CrossRefGoogle Scholar
Surana, A., Grunberg, O. & Haller, G. 2006 Exact theory of three-dimensional flow separation. Part 1. Steady separation. J. Fluid Mech. 564, 57–103.CrossRefGoogle Scholar
Tobak, M. & Peake, D. J. 1982 Topology of three-dimensional separated flows. Annu. Rev. Fluid Mech. 14, 61–85.CrossRefGoogle Scholar
Tylli, N., Kaiktsis, L. & Ineichen, B. 2002 Sidewall effects in flow over a backward-facing step: experiments and numerical simulations. Phys. Fluids 14 (11), 3835–3845.CrossRefGoogle Scholar
Williams, J. C. 1977 Incompressible boundary-layer separation. Annu. Rev. Fluid Mech. 9, 113–144.CrossRefGoogle Scholar
Williams, P. T. & Baker, A. J. 1997 Numerical simulations of laminar flow over a 3D backward-facing step. Intl J. Numer. Meth. Fluids 24, 1159–1183.3.0.CO;2-R>CrossRefGoogle Scholar