Journal of Fluid Mechanics

Papers

Steady inlet flow in stenotic geometries: convective and absolute instabilities

M. D. GRIFFITHa1a2 c1, T. LEWEKEa2, M. C. THOMPSONa1 and K. HOURIGANa1

a1 Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering & Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia

a2 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

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.

(Received October 15 2007)

(Revised September 01 2008)

Correspondence:

c1 Email address for correspondence: martin.griffith@eng.monash.edu.au

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