Effect of constriction height on flow separation in a two-dimensional channel

Abstract We studied numerically the effect of the constriction height on viscous flow separation past a two-dimensional channel with locally symmetric constrictions. A numerically stable scheme in primitive variables (velocity and pressure) for the solution of two-dimensional incompressible time-dependent Navier–Stokes equations is employed using finite-difference approximation in staggered grid. The wall shear stresses at different heights of the constriction are computed and presented graphically. It is noticed that the maximum stress and the length of the recirculating region associated with two shear layers of the constriction increase with the increase of the area reduction of the constriction. The critical Reynolds number for symmetry breaking bifurcation for the 50%, 60% and 70% area reduction are obtained numerically. The flow field separates after the symmetry breaking bifurcation and the symmetry of the flow depends on the Reynolds number and the height of the constriction.

[1]  Vascular Surgery: Principles and Practice , 2002 .

[2]  M D Deshpande,et al.  Steady laminar flow through modelled vascular stenoses. , 1976, Journal of biomechanics.

[3]  D. F. Young,et al.  Flow through a converging-diverging tube and its implications in occlusive vascular disease. II. Theoretical and experimental results and their implications. , 1970, Journal of biomechanics.

[4]  G. Hutchins,et al.  Correlation between intimal thickness and fluid shear in human arteries. , 1981, Atherosclerosis.

[5]  K. Haldar,et al.  Effects of the shape of stenosis on the resistance to blood flow through an artery. , 1985, Bulletin of mathematical biology.

[6]  D. Ku.  BLOOD FLOW IN ARTERIES , 1997 .

[7]  D W Crawford,et al.  Effect of mild atherosclerosis on flow resistance in a coronary artery casting of man. , 1984, Journal of biomechanical engineering.

[8]  S. A. Ahmed,et al.  Flow disturbance measurements through a constricted tube at moderate Reynolds numbers. , 1983, Journal of biomechanics.

[9]  D. F. Young,et al.  Flow through a converging-diverging tube and its implications in occlusive vascular disease. I. Theoretical development. , 1970, Journal of biomechanics.

[10]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[11]  S Glagov,et al.  The role of fluid mechanics in the localization and detection of atherosclerosis. , 1993, Journal of biomechanical engineering.

[12]  G. C. Layek,et al.  Magnetohydrodynamic Viscous Flow Separation in a Channel With Constrictions , 2003 .

[13]  R. Nerem.  Vascular fluid mechanics, the arterial wall, and atherosclerosis. , 1992, Journal of biomechanical engineering.

[14]  H. Andersson,et al.  Effects of surface irregularities on flow resistance in differently shaped arterial stenoses. , 2000, Journal of biomechanics.

[15]  A. Zeiher,et al.  Effect of stenotic geometry on flow behaviour across stenotic models , 1987, Medical and Biological Engineering and Computing.

[16]  D. F. Young.  Fluid Mechanics of Arterial Stenoses , 1979 .

[17]  Timothy J. Pedley,et al.  The fluid mechanics of large blood vessels , 1980 .