Classification of Pulsating Flow Patterns in Curved Pipes

Abstract

The fully developed periodic laminar flow of incompressible Newtonian fluids through a pipe of circular cross section, which is coiled in a circle, was simulated numerically. The flow patterns are characterized by three parameters: the Womersley number Wo, the Dean number De, and the amplitude ratio beta. The effect of these parameters on the flow was studied in the range 2.19 < or = Wo < or = 50.00, 15.07 < or = De < or = 265.49 and 0.50 < or = beta < or = 2.00, with the curvature ratio delta fixed to be 0.05. The way the secondary flow evolved with increasing Womersley number and Dean number is explained. The secondary flow patterns are classified into three main groups: the viscosity-dominated type, the inertia-dominated type, and the convection-dominated type. It was found that when the amplitude ratio of the volumetric flow rate is equal to 1.0, four to six vortices of the secondary flow appear at high Dean numbers, and the Lyne-type flow patterns disappear at beta > or = 0.50.

Aspects of Fluid Dynamics Applied to the Larger Arteries

“…Chang & Tarbell (1985) demonstrated the existence of many multiple vortices and complex induced #ow patterns. These authors and others (Tada et al, 1996;Weston et al, 1998) showed that the direction of secondary #ow can reverse during a cycle. Bodies oscillating in a #uid may also excite steady secondary #ow components (Stuart, 1966) which Seed & Wood (1970) found to distort calibrations intended for an arterial hot-"lm probe.…”

Pulsatile Flow Patterns and Wall Shear Stresses in Arch of a Turn-Around Tube With/Without Stenosis

“…4(b)) to two counter-rotating vortices centered at two "focuses" at t *  0.187 (Fig. 4(d)) due to the effect of centrifugal force [1,2,6]. Terms in Fig.…”

“…Most of the results of the analytical and numerical analyses revealed interesting secondary flow in the cross section of the curved section [1][2][3][4][5][6]. Tada et al [1] studied periodic laminar flow in a curved pipe through numerical simulation, and demonstrated secondary flow evolution with increasing Womersley parameters (, square of  represents a measure of the ratio of the unsteady local acceleration to the viscous retarding force) and Dean numbers (De, represents the ratio of the centrifugal to viscous forces) [9].…”

“…Tada et al [1] studied periodic laminar flow in a curved pipe through numerical simulation, and demonstrated secondary flow evolution with increasing Womersley parameters (, square of  represents a measure of the ratio of the unsteady local acceleration to the viscous retarding force) and Dean numbers (De, represents the ratio of the centrifugal to viscous forces) [9]. Lyne [2] had shown earlier, that in the case of oscillatory flow the maximum axial velocity shifted towards the center of curvature of the tube and that the maximum wall shear stresses occurred at the wall of the inner curve.…”

“…It is well known that the unsteady flow through curved pipes plays an important role in several biotechnical and industrial applications, such as the blood flow in vessels and the disordered flow in chemical plants [1]. The flow pulsatility in conjunction with the curved geometry results in a fairly complex three-dimensional flow structure: Hence such conditions have generated much fluid mechanics research interest.…”