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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[biomedical, fluid dynamics] Dimensionless number used to scale the dominant features in a pulsatileflow. The Womersley number is defined as the ratio of changing inertial forces resulting from the localized acceleration in each period of the pulsatile motion with respect to the viscous forces, where r is the radius of the conduit (blood vessel, pipe, etc.), ω is the angular velocity due to changes in pressure gradient of the fluid in motion that is directly related to the frequency (ν) of the oscillation (ω = 2πν), ρ the fluid density, and η the viscosity. In this approximation the elastic behavior of the wall is considered to be negligible.
Blood Flow Mechanics
Published in Michel R. Labrosse, Cardiovascular Mechanics, 2018
The Womersley number α is a dimensionless parameter used to characterize a cyclical flow. () α=Rωρμ,
In-vitro particle image velocimetry assessment of the endovascular haemodynamic features distal of stent-grafts that are associated with development of limb occlusion
Published in Journal of the Royal Society of New Zealand, 2021
Sina G. Yazdi, Paul D. Docherty, Adib Khanafer, Mark Jermy, Natalia Kabaliuk, Patrick H. Geoghegan, Petra Williamson
A circulatory mimicking loop was developed to drive the working fluid through the phantom. The fluid circuit consisted of electromagnetic flowmeter, flow straightener (150 mm long honeycomb pipe), piston pump, header tank and reservoir (Figure 3). The IFC 300 (KROHNE Ltd, UK) flowmeter was a non-intrusive device that did not disturb flow. A bespoke reciprocating piston pump was utilised to generate a physiological pulsatile flow waveform. The pump incorporated a high resolution stepper motor (200 steps per revolution), ball screw, piston and cylinder. The piston rod was connected to a ball screw supported by bearings at the free and motorised ends. The stepper motor was controlled using a Labview programme via a National Instruments 9401 digital module and 9172 CompactDAQ chassis using feedback control. The reciprocating piston pump was utilised to generate a physiological pulsatile flow waveform. The increased dimensions of the phantom allowed greater relative precision in the fabrication of the phantom wall thickness, and thus more uniform compliance. However, this change necessitated Reynolds and Womersley Number matching to ensure that the experiment retained physiological relevance. Reynolds number (Re) is a dimensionless parameter which defines the ratio of the inertial forces to viscous forces (Equation 2). Womersley number (α) is a dimensionless parameter in biofluid mechanics which express the frequency of the ratio of the pulsation frequency to viscosity (Equation 3) where V is the mean velocity, D is the inlet diameter and ν is the kinematic viscosity. where r is the internal lumen radius and ω is the angular frequency.
Effect of asymmetry on the flow behavior in an idealized arterial bifurcation
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2020
Mahesh Nagargoje, Raghvendra Gupta
The flow in the arterial network is pulsatile. The hemodynamics for pulsatile flow has been studied in the literature (Zarins et al. 1983; Ku et al. 1985; Perktold and Resch 1990; Perktold et al. 1991; Qamar et al. 2012, 2017) and can have a significant effect on the hemodynamics. This section discusses the effect of pulsatile flow on hemodynamics for a geometry having asymmetric bifurcation angle for the case of α = 15° and β = 60°. The Womersley number which represents the ratio of transient inertial and viscous effects and is an important parameter for pulsatile flow, is 15.6 for the flow conditions simulated. Figure 19 shows the velocity profile in the mother tube (20 mm from the inlet) at different time instants in a periodic cycle. It may be noted that the velocity profile is not parabolic in the channel. The profile is almost flat in the middle and has gradients near the wall. This is in accordance with the Womersley solution for the high value of the Womersley number (Womersley 1955). The profile is slightly asymmetric with the higher velocity towards the daughter tube having a higher angle. The profiles of x-component of velocity in the daughter vessel (α = 15°) are shown in Figure 20 at two locations S = 1d (a) and S = 8d (b) from the point of bifurcation. There is a clear difference between the steady and unsteady flow for the conditions simulated. While there is backflow near the bifurcation (S = 1d), no backflow is observed near the outlet of daughter tube (at S = 8d) during the entire cycle. Figure 21 shows the x-velocity component for the daughter vessel (β = 60°). There is a clear difference between the velocity profiles in the two daughter tubes. The velocity profile is flatter at the exit in the daughter tube having angle 60°. There exists a negative velocity near the walls on both the sides, which is not present in α = 15° case. Figure 22 shows secondary vortices superimposed on x-velocity contours at different time instants in the two daughter tubes at a distance of d from the point of bifurcation. The fraction of backflow (area covered by negative velocity) is more for the daughter tube having a higher angle in comparison with that for the daughter tube having a lower angle. The recirculation is more at the end of systole for the daughter tube having angle α = 15°.