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Research Papers: Fundamental Issues and Canonical Flows

Morphology of Secondary Flows in a Curved Pipe With Pulsatile Inflow

[+] Author and Article Information
Michael W. Plesniak

Professor
Fellow ASME
Department of Mechanical
and Aerospace Engineering,
The George Washington University,
Washington, DC 20052
e-mail: plesniak@gwu.edu

Kartik V. Bulusu

Assistant Research Professor
Department of Mechanical
and Aerospace Engineering,
The George Washington University,
Washington, DC 20052
e-mail: bulusu@gwu.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 20, 2016; final manuscript received May 31, 2016; published online July 22, 2016. Assoc. Editor: D. Keith Walters.

J. Fluids Eng 138(10), 101203 (Jul 22, 2016) (18 pages) Paper No: FE-16-1045; doi: 10.1115/1.4033962 History: Received January 20, 2016; Revised May 31, 2016

A multiplicity of secondary flow morphologies is produced in the arterial network due to complexities in geometry (such as curvature, branching, and tortuosity) and pulsatility in the blood flow. In clinical literature, these morphologies have been called “spiral blood flow structures” and have been associated with a protective role toward arterial wall damage in the ascending and abdominal aorta. Persistent secondary flow (vortical) structures as observed experimentally in planar cross sections have been associated with flow instabilities. This study presents the results of two rigorous in vitro experimental investigations of secondary flow structures within a 180-deg bent tube model of curved arteries. First, phase-averaged, two-component, two-dimensional, particle image velocimetry (2C-2D PIV) experiments were performed at the George Washington University. Second, phase-locked, three-component, three-dimensional magnetic resonance velocimetry (3C-3D MRV) measurements were done at the Richard M. Lucas Center at Stanford University. Under physiological (pulsatile) inflow conditions, vortical patterns of a variety of scales, swirl magnitudes (strengths), and morphologies were found. A continuous wavelet transform (CWT) algorithm (pivlet 1.2) was developed for coherent structure detection and applied to out-of-plane vorticity (ω) fields. Qualitative comparisons of coherent secondary flow structures from the PIV and magnetic resonance velocimetry (MRV) data were made. In addition to the qualitative depiction of such planar vortical patterns, a regime map has also been presented. The phase dependence of the secondary flow structures under physiological flow conditions and the concomitant 3D nature of these vortical patterns required the full resolution of the flow field achieved by MRV techniques.

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Figures

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Fig. 1

Experimental setup: 180deg curved tube model for arteries

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Fig. 2

Measurement schematics for PIV and MRV experiments: (a) Computer with matlab-based data acquisition and control programs, (b) National Instruments (USB DAQ NI-6229 BNC-type) data acquisition card, (c) trigger and voltage–time signals generated by the data acquisition card, (d) programmable pump (ISMATEC BVP-Z), and (e) 180-deg curved artery test section

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Fig. 3

MRV and PIV generated flow measurements upstream of the curved tube test section from physiological inflow waveform

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Fig. 4

Special toroidal coordinate system (r,ψ,θ) with radial velocity (vr), poloidal velocity (vψ) and streamwise or toroidal velocity (vθ)

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Fig. 5

MRV velocity encoding convention

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Fig. 6

Bulk velocity of inflow waveforms upstream of the 180-deg curved artery test section; physiological carotid artery-based waveform (-x-), two-frequency waveform (-+-), and three-frequency waveform (-o-). All waveforms have α=4.22, T=4 s.

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Fig. 7

Example of the phasewise behavior of secondary flow structures; from strain-dominated secondary flow during acceleration phase, D-L-W structure morphology during early deceleration phase to deceleration phase-dependent, lower energetic and loss of coherent secondary flow structure morphologies

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Fig. 8

Two harmonic frequency inflow waveforms with characteristic phasewise vortical structures

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Fig. 9

Three harmonic frequency inflow waveforms with characteristic phasewise vortical structures

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Fig. 10

Physiological inflow waveform with characteristic phasewise vortical structures

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Fig. 11

Regime map for multiharmonic, pulsatile flow waveforms

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Fig. 12

Comparison of out-of-plane and streamwise, wavelet-transformed vorticity (ω̃) for PIV and MRV data

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Fig. 13

Axial velocity contours in the 180-deg curved artery model during the systolic acceleration: (a), (b), and (c) show streamwise velocity contours (vθ) and secondary flow structure vorticity (ωθ) at t/T=0.15, t/T=0.175, and t/T=0.2, respectively. (d), (e), and (f) show streamwise velocity contours (vθ) and streamwise velocity vectors with threshold, 0.315 m/s to observe the effect of time-dependent centrifugal forces.

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Fig. 14

Axial velocity contours in the 180-deg curved artery model during the systolic deceleration: (a), (b), and (c) show streamwise velocity contours (vθ) and secondary flow structure vorticity (ωθ) at t/T=0.225, t/T=0.25, and t/T=0.275, respectively. (d)–(f) show streamwise velocity contours (vθ) and streamwise velocity vectors with threshold, 0.315 m/s to observe the effect of time-dependent centrifugal forces.

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Fig. 15

λ2 contour along the axial plane cutting through the deformed Dean-type vortex in the upper half of the 180-deg curved artery model; insets— ωθ−,ω̃θ−contours at the 90deg location, systolic peak time-instance, t/T=0.225, marked on the flow rate waveform

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Fig. 16

λ2 contour along the axial plane cutting through midplane of the 180-deg curved artery model; insets— ωθ−,ω̃θ−contours at the 90deg location, systolic peak time-instance, t/T=0.2, marked on the flow rate waveform

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Fig. 17

λ2 contour along the axial plane cutting through the deformed Dean-type vortex in the lower half of the 180-deg curved artery model; insets— ωθ−,ω̃θ−contours at the 90deg location, systolic peak time-instance, t/T=0.225, marked on the flow rate waveform

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