3D Visualization of the Exact Womersley Velocity Profile

Abstract

The three-dimensional (3D) visualization of Womersley flow can provide important physiological and physical insights into the Biofluid dynamics of the blood flow through an artery, which is of great significance in the understanding and treatment of vascular diseases, like heart attack and stroke.  In this paper, our goal is to visualize the unsteady velocity profile of the exact Womersley solution obtained in a circular channel due to varying pressure gradients at the inlet and outlet that change with time. In contrast to a steady flow of parabolic nature, the analytical solution of unsteady flow obtained using Bessel functions has complex dynamics.  Using a fictitious method, we developed a circular cylinder from a rectangular parallelepiped to better conceptualize these flow patterns with 3D graphics and animation.  We trust this work would be a primer to better understand blood flow due to time-dependent aortic and ventricular pressure differences which have direct implications in clinical practice.