Analysis of Fully Developed Unsteady Viscous Flow in a Curved Elastic Tube Model to Provide Fluid Mechanical Data for Some Circulatory Path-Physiological Situations and Assist Devices

Abstract

The unsteady and steady flow components of pulsatile flow response, to an experimentally monitored representative pressure pulse, are computed to provide fluid mechanical data for the etiology of arteriosclerosis at arterial curvature sites and for the design analysis of some extracorporeal dialysis and oxygenatory systems. The unsteady flow component of pulsatile flow in curved elastic tubes is simulated by the superposition of the first six Fourier components of a derived oscillatory flow solution of a viscous, incompressible fluid through an elastic tube of small curvature. The computer flow patterns, wall shear stress and hoop and axial stresses in the wall, due to unsteady and steady flow components of pulsatile flow response, are compared and their implications are discussed. The results show that the unsteady component yields shear stress of an order of magnitude greater than the steady flow, but the steady flow component has a greater variation in the shear stress distribution over a cross section. The steady and unsteady flow patterns are presented for several values of the tube diameters and curvature parameters typical of major arteries in the human circulatory system. The flow pattern and the stress variations could also prove useful in the design of extracorporeal systems such as dialysis machines and oxygenators.