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Steady inlet flow in stenotic geometries: convective and absolute instabilities

  • M. D. GRIFFITH (a1) (a2), T. LEWEKE (a2), M. C. THOMPSON (a1) and K. HOURIGAN (a1)

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.

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Ahmed S. A. 1998 An experimental investigation of pulsatile flow through a smooth constriction. Expl Therm. Fluid Sci. 17, 309318.
Ahmed S. A. & Giddens D. P. 1983 a Flow disturbance measurements through a constricted tube at moderate Reynolds numbers. J. Biomech. 16, 955963.
Ahmed S. A. & Giddens D. P. 1983 b Velocity measurements in steady flow through axisymmetric stenoses at moderate Reynolds numbers. J. Biomech. 16, 505516.
Ahmed S. A. & Giddens D. P. 1984 Pulsatile poststenotic flow studies with laser doppler anemometry. J. Biomech. 17, 695705.
Blackburn H. M. & Sherwin S. J. 2007 Instability modes and transition of pulsatile stenotic flow: pulse–period dependence. J. Fluid Mech. 573, 5788.
Cassanova R. A. & Giddens D. P. 1978 Disorder distal to modified stenoses in steady and pulsatile flow. J. Biomech. 11, 441453.
Deplano V. & Siouffi M. 1999 Experimental and numerical study of pulsatile flows through stenosis: wall shear stress analysis. J. Biomech. 32, 10811090.
Drikakis D. 1997 Bifurcation phenomena in incompressible sudden expansion flows. Phys. Fluids 9, 7687.
Durst F. & Unsal B. 2006 Forced laminar-to-turbulent transition of pipe flows. J. Fluid Mech. 560, 449464.
Griffith M. D. 2007 The stability and behaviour of flows in stenotic geometries. PhD thesis, Department of Mechanical & Aerospace Engineering, Monash University, Melbourne, Australia.
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, 319340.
Karniadakis G. E., Israeli M. & Orszag S. A. 1991 High-order splitting methods of the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414443.
Ku D. N. 1997 Blood flow in arteries. Annu. Rev. Fluid Mech. 29, 399434.
Long Q., Xu X. Y., Ramnarine K. V. & Hoskins P. 2001 Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis. J. Biomech. 34, 12291242.
Mallinger F. & Drikakis D. 2002 Instability in three-dimensional, unsteady, stenotic flows. Intl J. Heat Fluid Flow 23, 657663.
Marquillie M. & Ehrenstein U. 2003 On the onset of nonlinear oscillations in a separating boundary-layer flow. J. Fluid Mech. 490, 169188.
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, 173197.
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, 147180.
Sherwin S. J. & Blackburn H. M. 2005 Three-dimensional instabilities of steady and pulsatile axisymmetric stenotic flows. J. Fluid Mech. 533, 297327.
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, 443455.
Stroud J. S., Berger S. A. & Saloner D. 2002 Numerical analysis of flow through a severely stenotic carotid artery bifurcation. J. Biomech. Engng 124, 919.
Taneda S. 1956 Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers. J. Phys. Soc. Japan 11, 302307.
Thompson M. C., Hourigan K. & Sheridan J. 1996 Three-dimensional instabilities in the wake of a circular cylinder. Expl Therm. Fluid Sci. 12, 190196.
Thompson M. C., Leweke T. & Provansal M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15, 575585.
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, 253280.
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, 281318.
White F. M. 1999 Fluid Mechanics (4th ed.). McGraw-Hill.
Wootton D. M. & Ku D. N. 1999 Fluid mechanics of vascular systems, diseases, and thrombosis. Annu. Rev. Biomed. Engng 1, 299329.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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