Stenosis severity effects for unbalanced simple-pulsatile bifurcation flow

Abstract

A numerical finite-difference analysis is made of a plane simple-pulsatile flow past a symmetrical bifurcation which contains an asymmetrical smooth-contoured stenosis in the trunk. In essence, such a situation could represent a stenosed common carotid artery immediately upstream from the carotid junction. The flow is unbalanced; two-thirds of it exits or enters through the lower branch. The effect on various flow parameters of the stenosis itself and on changes in its severity is investigated by comparing the results for a severe stenosis, a mild stenosis, and no stenosis. The simple-pulsatile forcing function is specified in terms of an oscillatory and a steady Karman number. To obtain a significant amount of backflow, the oscillatory trunk Karman number is taken as 1000 compared to the steady value of 250. The frequency of oscillation is stipulated by a trunk Stokes number of 10π. The numerical procedures utilize the vorticity-transport version of the Navier-Stokes governing equations. A non-orthogonal coordinate transform allows the calculations to be made in a rectangular grid where the central difference expressions are easily applied. The results are presented in terms of both kinematic and kinetic parameters. The variation in the basic kinematic variables of stream function and vorticity is shown by temporal sequences of contour plots at times of peak flow and during the flow reversal stages as well as by several velocity vector plots. Kinetic results are given in terms of the temporal variation in shear stresses along boundaries. The peak shears are found to occur at the zenith of the stenosis at times of peak flow: the value for the severe stenosis is twice as large as that for the mild stenosis. The midline pressure distribution in the trunk and the centerline pressure distributions in the branches are also included.