Helical Flow Around Arterial Bends for Varying Body Mass

[+] Author and Article Information
L. Zabielski, A. J. Mestel

Department of Mathematics, Imperial College of Science, Technology and Medicine, 180 Queen’s Gate, SW7 2BZ London, United Kingdom

J Biomech Eng 122(2), 135-142 (Oct 28, 1999) (8 pages) doi:10.1115/1.429635 History: Received January 14, 1999; Revised October 28, 1999
Copyright © 2000 by ASME
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A helical pipe of radius a, pitch 2πa=2π/ε, and radius of curvature b=2.5a, appropriate for the aortic arch 9
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(a) Measured velocity profile from Parker 15, and (b) pressure gradient px(t) inferred from Eq. (15). Velocity is to be scaled with α−1Rsν/a.
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Flow patterns inside a helical bend with ε=1, b=2.5, at various stages of the cardiac cycle as indicated on the far left. Flow conditions correspond to the aortic arch of a 20 kg dog. The inside of the bend is to the left. The middle column portrays contours of the down-pipe velocity ν. The left column shows the streamlines of the cross-pipe flow Ψ, and contours of the down-pipe vorticity ξ are drawn in the right-hand column. The boundary layers on the top and bottom separate near the inside of the bend and complex structures with regions of back flow are thrown into the mainstream.
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Flow just after separation inside a planar (toroidal) bend with ε=100, b=2.5, and mass 3 kg (rabbit). From left to right: Ψ, ν, and ξ. The boundary layers on the top and bottom collide and separate symmetrically near the inner bend on the left, leading to strong shear in the core.
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Separated flow inside a stretched helical bend ε=0.5, b=2.5, for a mass of 60 kg (man)
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Computed flux, Q, with ε=1, b=2.5, for a dog of mass 20 kg
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A typical time dependence, σ̃H(t), of the down-pipe component of the wall shear rate inside a helical bend ε=1, b=2.5, and mass 20 kg
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Spatial distribution w(x) of the down-pipe shear in nondimensional units to be multiplied by σ̄H(t) [s−1]. For a helical bend ε=1, b=2.5: ––– dog, mass 20 kg; –⋅ – rat, mass 0.6 kg. For a helical bend ε=0.5, b=2.5a: —— man, mass 50 kg. x measures angle around the pipe cross section starting from the outer bend toward the top of the pipe.
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Wall shear on the boundary of a helical bend ε=1, b=2.5. flow conditions corresponding to the canine aortic arch with mass 20 kg. The direction and magnitude of the total shear stress are shown from two angles at the indicated times. The pipe is viewed from on top (left) and from the bottom (right).




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