Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-20T08:35:25.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Steady inlet flow in stenotic geometries: convective and absolute instabilities

Published online by Cambridge University Press:  10 December 2008

M. D. GRIFFITH ,
T. LEWEKE ,
M. C. THOMPSON  and
K. HOURIGAN
M. D. GRIFFITH*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering & Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), CNRS/Universités Aix-Marseille, 49 rue Frédéric Joliot-Curie, BP 146, F-13384 Marseille Cedex 13, France
T. LEWEKE
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), CNRS/Universités Aix-Marseille, 49 rue Frédéric Joliot-Curie, BP 146, F-13384 Marseille Cedex 13, France
M. C. THOMPSON
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering & Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia
K. HOURIGAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering & Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Steady inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted flows, in terms of the total blockage. The Reynolds number is varied between 50 and 2500 and the stenosis degree by area between 0.20 and 0.95. Numerically, a spectral-element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. At low Reynolds numbers, the flow is steady and characterized by a jet flow emanating from the contraction, surrounded by an axisymmetric recirculation zone. The effect of a variation in blockage size on the onset and mode of instability is investigated. Linear stability analysis is performed on the simulated axisymmetric base flows, in addition to an analysis of the instability, seemingly convective in nature, observed in the experimental flows. This transition at higher Reynolds numbers to a time-dependent state, characterized by unsteadiness downstream of the blockage, is studied in conjunction with an investigation of the response of steady lower Reynolds number flows to periodic forcing.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 616 , 10 December 2008 , pp. 111 - 133
Copyright
Copyright © Cambridge University Press 2008

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

Ahmed, S. A. 1998 An experimental investigation of pulsatile flow through a smooth constriction. Expl Therm. Fluid Sci. 17, 309–318.CrossRefGoogle Scholar
Ahmed, S. A. & Giddens, D. P. 1983 a Flow disturbance measurements through a constricted tube at moderate Reynolds numbers. J. Biomech. 16, 955–963.CrossRefGoogle ScholarPubMed
Ahmed, S. A. & Giddens, D. P. 1983 b Velocity measurements in steady flow through axisymmetric stenoses at moderate Reynolds numbers. J. Biomech. 16, 505–516.CrossRefGoogle ScholarPubMed
Ahmed, S. A. & Giddens, D. P. 1984 Pulsatile poststenotic flow studies with laser doppler anemometry. J. Biomech. 17, 695–705.CrossRefGoogle ScholarPubMed
Blackburn, H. M. & Sherwin, S. J. 2007 Instability modes and transition of pulsatile stenotic flow: pulse–period dependence. J. Fluid Mech. 573, 57–88.CrossRefGoogle Scholar
Cassanova, R. A. & Giddens, D. P. 1978 Disorder distal to modified stenoses in steady and pulsatile flow. J. Biomech. 11, 441–453.CrossRefGoogle Scholar
Deplano, V. & Siouffi, M. 1999 Experimental and numerical study of pulsatile flows through stenosis: wall shear stress analysis. J. Biomech. 32, 1081–1090.CrossRefGoogle ScholarPubMed
Drikakis, D. 1997 Bifurcation phenomena in incompressible sudden expansion flows. Phys. Fluids 9, 76–87.CrossRefGoogle Scholar
Durst, F. & Unsal, B. 2006 Forced laminar-to-turbulent transition of pipe flows. J. Fluid Mech. 560, 449–464.CrossRefGoogle Scholar
Griffith, M. D. 2007 The stability and behaviour of flows in stenotic geometries. PhD thesis, Department of Mechanical & Aerospace Engineering, Monash University, Melbourne, Australia.Google Scholar
Griffith, M. D., Thompson, M. C., Leweke, T., Hourigan, K. & Anderson, W. P. 2007 Wake behaviour and instability of flow through a partially blocked channel. J. Fluid Mech. 582, 319–340.CrossRefGoogle Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods of the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–443.CrossRefGoogle Scholar
Ku, D. N. 1997 Blood flow in arteries. Annu. Rev. Fluid Mech. 29, 399–434.CrossRefGoogle Scholar
Long, Q., Xu, X. Y., Ramnarine, K. V. & Hoskins, P. 2001 Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis. J. Biomech. 34, 1229–1242.CrossRefGoogle ScholarPubMed
Mallinger, F. & Drikakis, D. 2002 Instability in three-dimensional, unsteady, stenotic flows. Intl J. Heat Fluid Flow 23, 657–663.CrossRefGoogle Scholar
Marquillie, M. & Ehrenstein, U. 2003 On the onset of nonlinear oscillations in a separating boundary-layer flow. J. Fluid Mech. 490, 169–188.CrossRefGoogle Scholar
Ohja, M., Cobbold, R. S. C., Johnston, K. W. & Hummel, R. L. 1989 Pulsatile flow through constricted tubes: an experimental investigation using photochromic tracer methods. J. Fluid Mech. 203, 173–197.Google Scholar
Sheard, G. S., Thompson, M. C. & Hourigan, K. 2003 From spheres to circular cylinders: classification of bluff ring transitions and structure of bluff ring wake. J. Fluid Mech. 492, 147–180.CrossRefGoogle Scholar
Sherwin, S. J. & Blackburn, H. M. 2005 Three-dimensional instabilities of steady and pulsatile axisymmetric stenotic flows. J. Fluid Mech. 533, 297–327.CrossRefGoogle Scholar
Stroud, J. S., Berger, S. A. & Saloner, D. 2000 Influence of stenosis morphology in flow through severely stenotic vessels: Implications for plaque rupture. J. Biomech. 33, 443–455.CrossRefGoogle ScholarPubMed
Stroud, J. S., Berger, S. A. & Saloner, D. 2002 Numerical analysis of flow through a severely stenotic carotid artery bifurcation. J. Biomech. Engng 124, 9–19.CrossRefGoogle ScholarPubMed
Taneda, S. 1956 Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers. J. Phys. Soc. Japan 11, 302–307.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K. & Sheridan, J. 1996 Three-dimensional instabilities in the wake of a circular cylinder. Expl Therm. Fluid Sci. 12, 190–196.CrossRefGoogle Scholar
Thompson, M. C., Leweke, T. & Provansal, M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15, 575–585.CrossRefGoogle Scholar
Varghese, S. S., Frankel, S. H. & Fischer, P. F. 2007 a Direct numerical simulation of stenotic flows. Part 1. Steady flow. J. Fluid Mech. 582, 253–280.CrossRefGoogle Scholar
Varghese, S. S., Frankel, S. H. & Fischer, P. F. 2007 b Direct numerical simulation of stenotic flows. Part 2. Pulsatile flow. J. Fluid Mech. 582, 281–318.CrossRefGoogle Scholar
White, F. M. 1999 Fluid Mechanics (4th ed.). McGraw-Hill.Google Scholar
Wootton, D. M. & Ku, D. N. 1999 Fluid mechanics of vascular systems, diseases, and thrombosis. Annu. Rev. Biomed. Engng 1, 299–329.CrossRefGoogle ScholarPubMed