Secondary flow vortical structures in a ${180}^{\circ }$ elastic curved vessel with torsion under steady and pulsatile inflow conditions

Secondary flow structures in a ${180}^{\circ }$ curved pipe model of an artery are studied using particle image velocimetry. Both steady and pulsatile inflow conditions are investigated. In planar curved pipes with steady flow, multiple (two, four, six) vortices are detected. For pulsatile flow, various pairs of vortices, i.e., Dean, deformed-Dean, Lyne-type, and split-Dean, are present in the cross section of the pipe at ${90}^{\circ }$ into the bend. The effects of nonplanar curvature (torsion) and vessel dilatation on these vortical structures are studied. Torsion distorts the symmetric secondary flows (which exist in planar curvatures) and can result in formation of more complex vortical structures. For example, the split-Dean and Lyne-type vortices with same rotation direction originating from opposite sides of the cross section tend to merge together in pulsatile flow. The vortical structures in elastic vessels with dilatation (0.61%–3.23%) are also investigated and the results are compared with rigid model results. It was found that the secondary flow structures in rigid and elastic models are similar, and hence the local compliance of the vessel does not affect the morphology of secondary flow structures.

Figure 1

Model of curved pipe with torsion. $\mathrm{\Delta }Y$ shows the center to center vertical distance from the planar (no torsion, T-0) condition at the ${90}^{\circ }$ cross section

Figure 2

Schematic of test section, laser sheet location, and camera direction.

Figure 3

Pulsatile carotid artery physiological waveform [45]. PIV data acquired between $t/T=0.16$ and $t/T=0.32.$

Figure 4

In-plane velocity magnitude and velocity vectors at the ${90}^{\circ }$ cross section for $T-0$ (top) and $T-2$ (bottom) for four steady flow Re. For clarity only 1/4 of velocity vectors are displayed.

Figure 5

Plane-normal vorticity and velocity vectors at the ${90}^{\circ }$ cross section for $T-0$ (top) and $T-2$ (bottom) for four steady flow Re. Magnitude smaller than 5% of range are shown in white to show the boundaries between positive and negative.

Figure 6

Negative regions of $d_2$ at the ${90}^{\circ }$ cross section for $T$-0 (top) and $T$-2 (bottom) for four steady flow conditions. The vortices are colored by their rotation directions: clockwise (CW) and counterclockwise (CCW). DD, L, and SD labels denote deformed-Dean, Lyne-type, and split-Dean vortices, respectively. Numbers represent the circulation values $\mathrm{\Gamma }\times {10}^{-4}$ (${\mathrm{m}}^2$/s) for each vortex.

Figure 7

Comparison of in-plane velocity magnitude and velocity vectors at the ${90}^{\circ }$ cross section in planar rigid model (top) and planar elastic model E2 (bottom) for four phases

Figure 8

Comparison of plane-normal vorticity and velocity vectors at the ${90}^{\circ }$ cross section in planar rigid model (top) and planar elastic model E2 (bottom) for four phases. Magnitude smaller than 5% of range shown in white to show the boundaries between positive and negative

Figure 9

In-plane velocity magnitude and velocity vectors at the ${90}^{\circ }$ cross section for elastic models, $T$-0 (left), $T$-1 (middle), and $T$-2 (right) at six phases.

Figure 10

Plane-normal vorticity and velocity vectors at the ${90}^{\circ }$ cross section for elastic models, $T$-0 (left), $T$-1 (middle), and $T$-2 (right) at six phases. Magnitude smaller than 5% of range shown in white to show the boundaries between positive and negative. DD, L, and SD labels denote deformed-Dean, Lyne-type, and split-Dean vortices, respectively.

Figure 11

Negative regions of $d_2$ at the ${90}^{\circ }$ cross section for elastic models, $T$-0 (left), $T$-1 (middle), and $T$-2 (right) at six phases. The vortices are colored by their rotation directions: clockwise (CW) and counterclockwise (CCW). DD, L, and SD labels denote deformed-Dean, Lyne-type, and split-Dean vortices, respectively. Numbers represent the circulation values $\mathrm{\Gamma }\times {10}^{-3}$ (${\mathrm{m}}^2$/s) for each vortex.