Mixing Through Stirring of Steady Flow in Small Amplitude Helical Tubes

Abstract

In this paper we numerically simulate flow in a helical tube for physiological conditions using a co-ordinate mapping of the Navier-Stokes equations. Helical geometries have been proposed for use as bypass grafts, arterial stents and as an idealised model for the out-of-plane curvature of arteries. Small amplitude helical tubes are also currently being investigated for possible application as A-V shunts, where preliminary in vivo tests suggest a possibly lower risk of thrombotic occlusion. In-plane mixing induced by the geometry is hypothesised to be an important mechanism. In this work, we focus mainly on a Reynolds number of 250 and investigate both the flow structure and the in-plane mixing in helical geometries with fixed pitch of 6 tube diameters (D), and centreline helical radius ranging from 0.1D to 0.5D. High-order particle tracking, and an information entropy measure is used to analyse the in-plane mixing. A combination of translational and rotational reference frames are shown to explain the apparent discrepancy between flow field and particle trajectories, whereby particle paths display a pattern characteristic of a double vortex, though the flow field reveals only a single dominant vortex. A radius of 0.25D is found to provide the best trade-off between mixing and pressure loss, with little increase in mixing above R = 0.25D, whereas pressure continues to increase linearly.

Reducing the data: Analysis of the role of vascular geometry on blood flow patterns in curved vessels

“…1(b) were recently studied for potential application as vascular prostheses, since they promote in-plane mixing. 7,23 All the cross-sectional contours are shown normal to the local tangent vector T, with the directions of the local normal N and binormal B vectors as indicated in the figures. The computational errors in the net balance of mass and momentum are similar in Cartesian and local coordinates, and are too small to be observed in the scales of the figures.…”

Computational modelling of the interaction of shock waves with multiple gas-filled bubbles in a liquid

“…Nonetheless, the results clearly illustrate the important role played by arterial curvature in determining AVF hemodynamics, which to our knowledge has been overlooked in all previous studies. Future studies should investigate the impact of non-planar arterial/venous curvature (e.g., helicity 55,56 ) on blood flow and oxygen transport within AVF, as well as the impact of vessel remodelling via IH (or otherwise) on the flow field. …”

Suppressing unsteady flow in arterio-venous fistulae

“…24 Subsequently, the seminal work of Dean identified a critical Dean number beyond which multiple unsteady vortices develop in a planar curved pipe. 25 More recent work, undertaken specifically in the context of vascular fluid mechanics, includes studies of stenotic flows, 26 pulsatile flow in curved pipes, [27][28][29][30] flow in helical pipes, [31][32][33][34] and flow at junctions. [35][36][37] In terms of simulating flow in AVF configurations, there have been a range of previous Computational Fluid Dynamics (CFD) studies, including 1D simulations, [38][39][40] 2D simulations, 41 3D simulations with rigid walls in idealised geometries, [42][43][44][45][46][47] 3D simulations with rigid walls in more realistic geometries, [48][49][50][51][52][53][54][55] and simulations with distensible walls.…”