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Time-dependent laminar incompressible flow through a spherical cavity

Published online by Cambridge University Press:  11 April 2006

N. V. Gillani  and
W. M. Swanson
N. V. Gillani
Affiliation:
Mechanical Engineering Department, Washington University, St Louis, Missouri 63130
W. M. Swanson
Affiliation:
Mechanical Engineering Department, Washington University, St Louis, Missouri 63130
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Abstract

A finite-difference numerical method for the solution of the unsteady flow of a viscous incompressible fluid through axisymmetric circular ducts of variable axial geometry is developed and applied to the flow in a spherical-cavity geometry approximating the human aortic valve. The presence and motion of the valve leaflets are considered only as long as they can be assumed to present negligible impedance to the flow. The numerical solution is based on the vorticity/streamfunction approach, and is carried out for the systolic acceleration phase of the heart beat. A hybrid-mesh design consisting of a fine cell structure in the region close to the solid walls and a coarser grid in the core region is used. An experimental flow-visualization study in an acrylic model of the spherical cavity shows good agreement with the numerical simulation. An early separation of flow occurs at the entrance to the cavity, and an annular eddy grows in the wake until it occupies most of the cavity. The use of the hybrid mesh also makes possible the simulation of fine secondary-flow features in the cavity under peak-flow conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 1 , 5 November 1976 , pp. 99 - 127
Copyright
© 1976 Cambridge University Press

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