Figure 1.
Geometrical parameters of a helical graft.
Figure 2.
Helical tubes with different helical pitches (H/R0) and radii of curvatures (Rc/R0).
Table 1.
Representative experimental parameters of helical tubes at Re = 814.
Figure 3.
Schematic diagrams of the experimental set-up.
(a) Flow circuit system, (b) PIV velocity field measurement system, (c) schematic of the stenosis model.
Figure 4.
Computational grid and block arrangement.
Figure 5.
Comparison of PIV and CFD results data at the outlet of a helical tube (H/R0 = 8, Rc/R0 = 1.0).
(a) Axial velocity distribution and (b) normal-direction vorticity contours and corresponding streamlines.
Figure 6.
Comparison of normal-direction peak vorticity magnitude at the outlet of the helical tubes obtained from PIV and CFD.
Rc/R0 are fixed to 1.0. The error bars indicate 95% confidence limits. The helical graft of H/R0 = 4 was omitted for the clarity of the figure because its data overlaps with the others.
Figure 7.
Normal-direction vorticity field contours at the outlet of the helical tubes for a range of helical curvatures and pitches.
The results obtained by (a) CFD and (b) PIV are compared at Re = 814.
Figure 8.
Variations of swirling intensity (S) for a range of helical curvatures and pitches at Re of (a) 814, (b) 609, (c) 410 and (d) 213.
Figure 9.
Effect of Re on the variation of swirling intensity (S) at H/R0 = 8.
Figure 10.
Variations of swirling intensity (S) with respect to Gn*.
(a) Effect of Re on swirling intensity variation, (b) a linear regression curve (S = 0.0004×Gn*–0.0075, R2 = 0.834) and 95% confidence and prediction bands.
Figure 11.
Helicity variations at the outlet surface with respect to Gn*.
Figure 12.
The effect of swirling flow on the length of flow reattachment (L/D) and WSS at the post-stenosis.
(a) Velocity contours and streamlines at the post-stenosis. Poiseuille and swirling inlet flows are generated by the straight and helical tubes (Rc/R0 = 0.6, H/R0 = 4) at Re = 814. (b) distribution of normalized WSS at the post-steonsis. WSS was normalized by the WSS that would exist in Poiseuille flow in a conduit at the same Re. The error bars indicate 95% confidence limits and only half of them are shown for clarity. (c) variations of L/D with respect to S, (d) variations of L/D with respect to Gn*. Mean standard deviations of L/D = 0.39.
Figure 13.
The effect of axial velocity skewness on reattachment length.
Figure 14.
The effect of pulsatile swirling flow on flow structure at the post-stenosis. (
a) Pulsatile waveforms of the normalized velocity at the stenosis apex. The maximum Re, mean Re and Womersley number (α) of the flow are 860, 212 and 9.69, respectively. (b) Phase-averaged velocity waveform. Velocity contours and streamlines are shown at (c) t/T = 0.15, (d) t/T = 0.25, (e) t/T = 0.39, (f) t/T = 0.55, (g) t/T = 0.75, (h) t/T = 0.90. The Poiseuille flow (upper) and swirling flow (lower) are generated by the straight and helical tubes (Rc/R0 = 0.6, H/R0 = 4).
Figure 15.
The effect of pulsatile swirling flow on the flow reattachment (L/D) and OSI at the post-stenosis.
(a) Variations of flow reattachment (L/D) obtained from phase-averaged velocity fields, (b) OSI distribution at the post-stenosis. The Poiseuille flow (upper) and swirling flow (lower) are generated by the straight and helical tubes (Rc/R0 = 0.6, H/R0 = 4).
Figure 16.
Variations of the effective torsion (β·η) curve for various helical curvatures and pitches.
(a) Effect of helical pitch on β·η, (b) prediction of maximum β·η for a range of helical curvatures.