Research Papers: Fundamental Issues and Canonical Flows

Development of Three-Dimensional Streamline
Image Velocimetry Using Superimposed Delaunay Triangulation and Geometrical Fitting

[+] Author and Article Information
Elishai Ezra, Eliezer Keinan

Grass Center for Bioengineering,
The Hebrew University of Jerusalem,
Edmond J. Safra Campus,
Jerusalem 91904, Israel

Alex Liberzon

School of Mechanical Engineering,
Tel-Aviv University,
Tel-Aviv 69978, Israel

Yaakov Nahmias

Department of Cell and Developmental Biology,
Grass Center for Bioengineering,
The Hebrew University of Jerusalem,
Edmond J. Safra Campus,
Jerusalem 91904, Israel
e-mail: ynahmias@cs.huji.ac.il

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 26, 2015; final manuscript received August 30, 2015; published online October 23, 2015. Assoc. Editor: Prashanta Dutta.

J. Fluids Eng 138(1), 011205 (Oct 23, 2015) (7 pages) Paper No: FE-15-1208; doi: 10.1115/1.4031611 History: Received March 26, 2015; Revised August 30, 2015

Flow behavior in complex three-dimensional (3D) microscale domains is the key in the development of microcirculatory pathologies and the design of 3D microfluidics. While numerical simulations are common practice for the derivation of velocity fields in such domains, they are limited to known geometries. Current experimental methods such as micron-scale particle tracing comprise of intricate algorithmic approaches for the accurate tracing of numerous particles in a dense moving liquid suspension and are fundamentally limited in resolution to the finite size of the interrogated steps. Here, we introduce 3D streamlines image velocimetry (3D-SIV), a method to derive fluid velocity fields in arbitrary resolution for fully developed laminar flow in 3D geometries. Our approach utilizes 3D geometrical fitting and superimposed Delaunay triangulation to reconstruct streamtubes and to trace their volumetric changes. Our algorithm has applications in out-of-plane velocimetries, which we demonstrate in a 3D dilated curved geometry and in an ascending aorta. The 3D-SIV can be applied for high-resolution derivation of velocity fields in microcirculatory pathologies and to 3D microfluidic circuits, extending the potential of out-of-plane velocimetries to complex geometries and arbitrary resolution.

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Fig. 3

Delaunay triangles and lifting algorithm for triangulation

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Fig. 2

Streamtubes reconstruction from acquired particle locations across the field of study using 3D fitting and Delaunay triangulation: (a) 3D fitting of a projected streamline, (b) multiple 3D-fitted streamlines, (c) geometrical fitting, (d) cross-sectional plane, (e) 2D cross-sectional streamlines, (f) circumcircles matching and optimization, and (g) triangulated cross section

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Fig. 1

Visual examination of flow field features

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Fig. 4

Superimposed triangulation of ten experiments for dense definition of streamtubes: (a) single measurements, (b) superimposed measurements, and (c) sensitivity analysis

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Fig. 5

Derivation of a relative velocity field by tracking centroid migration path of each streamtube along the geometry: (a) centroids migration across two sections, (b) area across eight cross sections, (c) relative velocities: inlet to outlet, (d) 3D arrows velocity field, and (e) cross-sectional velocity arrows field

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Fig. 7

The 3D-SIV for an experimental model of hemodynamics in an ascending aorta: (a) aorta model, (b) experimentally derived particles' locations, (c) streamlines fitting to particles' trajectories with triangular cross section, and (d) x–z view, x–y view; velocity at width = 80 mm and 40 mm



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