Flow Patterns and Wall Shear Rates in a Series of Symmetric Bifurcations

Abstract

<p> This study investigates the flow patterns and wall shear rate distributions downstream from a series of three glass model symmetric bifurcations, typical of the blood vessels in man. The models have a single included angle of 75° and total output to input flow area ratios of 0.75, 1.02 and 1.29, covering the physiological range. The Reynolds numbers studied (based on parent tube) were 400, 800 and 1200 in steady flow.</p> <p> Local fluid velocities were obtained at a number of axial positions along the bifurcation daughter tube via a neutrally buoyant tracer particle technique utilizing cine photography. This provided sufficient information to determine the three velocity components for each particle. The tangential and radial components were in general less than 6% of the mean axial velocity. In the case of the axial components, an analytical representation of the velocity in polar coordinates was obtained. This analytical function permits evaluation of wall shear rate distribution.</p> <p> The velocity pro£iles were found to be symmetric with respect to the plane of the bifurcation. At two diameters downstream from the carina the velocity profiles in the plane of the bifurcation showed a high peak near the inside wall of the branch. With distance downstream the peak was convected tangentially evening out the profile towards an axially symmetric mountain plateau with a dished top.</p> <p> Wall shear rate as a function of θ at constant axial position was represented by displaced cosine function. The highest shear rates always occurred on the inside wall of the daughter tube and the lowest on the outside wall. In general, the largest deviation from developed shear rates occurred close to the carina.</p> <p> The largest positive deviation in wall shear rate from developed values was found in the small area ratio bifurcation and the lowest wall shear rate value was found in the large area ratio bifurcation (a = 1.29) indicating possible flow separation near the carina. The biological implications of the shear rate information generated are discussed.</p>