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Research Papers

Computational Study of the Blood Flow in Three Types of 3D Hollow Fiber Membrane Bundles

[+] Author and Article Information
Zhongjun J. Wu

Artificial Organs Laboratory,
Department of Surgery,
University of Maryland School of Medicine
Baltimore, MD 21201
e-mail: zwu@smail.umaryland.edu

1Corresponding author.

2Current address: Fraser K. H., Department of Bioengineering, Imperial College London, London, UK.

3Current address: Taskin M. E., HeartWare Inc., 14000 NW 57th, Court, Miami Lakes, FL 33014

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received January 11, 2013; final manuscript received October 10, 2013; accepted manuscript posted October 19, 2013; published online November 6, 2013. Assoc. Editor: Dalin Tang.

J Biomech Eng 135(12), 121009 (Nov 06, 2013) (11 pages) Paper No: BIO-13-1014; doi: 10.1115/1.4025717 History: Received January 11, 2013; Revised October 10, 2013; Accepted October 19, 2013

The goal of this study is to develop a computational fluid dynamics (CFD) modeling approach to better estimate the blood flow dynamics in the bundles of the hollow fiber membrane based medical devices (i.e., blood oxygenators, artificial lungs, and hemodialyzers). Three representative types of arrays, square, diagonal, and random with the porosity value of 0.55, were studied. In addition, a 3D array with the same porosity was studied. The flow fields between the individual fibers in these arrays at selected Reynolds numbers (Re) were simulated with CFD modeling. Hemolysis is not significant in the fiber bundles but the platelet activation may be essential. For each type of array, the average wall shear stress is linearly proportional to the Re. For the same Re but different arrays, the average wall shear stress also exhibits a linear dependency on the pressure difference across arrays, while Darcy's law prescribes a power-law relationship, therefore, underestimating the shear stress level. For the same Re, the average wall shear stress of the diagonal array is approximately 3.1, 1.8, and 2.0 times larger than that of the square, random, and 3D arrays, respectively. A coefficient C is suggested to correlate the CFD predicted data with the analytical solution, and C is 1.16, 1.51, and 2.05 for the square, random, and diagonal arrays in this paper, respectively. It is worth noting that C is strongly dependent on the array geometrical properties, whereas it is weakly dependent on the flow field. Additionally, the 3D fiber bundle simulation results show that the three-dimensional effect is not negligible. Specifically, velocity and shear stress distribution can vary significantly along the fiber axial direction.

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Figures

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Fig. 1

Schematic top views of the (a) square, (b) diagonal, (c) random, and (d) 3D arrays. Each array has 216 hollow fibers and the porosity is 0.55. The insert shows the 3D fibers.

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Fig. 2

(a) CFD geometry and (b) mesh illustrations around the fibers for the diagonal array

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Fig. 3

Contours of velocity magnitude (m/s) around fibers at selected cross sections for the (a) square, (b) diagonal, (c) random, and (d–f) 3D arrays when Re is 5.0

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Fig. 4

Flow velocity vectors around selected fibers at a middle cross section for the (a) square, (b) diagonal, and (c) random arrays when Re is 5.0

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Fig. 5

Shear stress contours at the middle plane of the (a) square, (b) diagonal, and (c) random arrays, and wall shear stress contours on the selected fibers for the (d) square, (b) diagonal, and (c) random arrays when Re is 5.0

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Fig. 6

Shear stress contours at the selected cross sections (a) z = 0 mm, (b) z = 0.3 mm, and (c) z = 0.15 mm, and wall shear stress contour on the selected fibers (d) for the 3D array when Re is 5.0

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Fig. 7

Wall shear stress vectors (X- and Y- shear stresses only) at the X-Y plane for the selected fibers for the (a) square, (b) diagonal, and (c) random arrays when Re is 5.0

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Fig. 8

(a) The area-weighted average wall shear stress over individual fibers in a single row along the flow direction when Re is 5.0 and (b) the average wall shear stress over all 216 fibers for different Re

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Fig. 9

Probability density function (PDF) of the global wall shear stress over all 216 fibers when Re is 5.0, for the (a) square, (b) diagonal, (c) random, and (d) 3D arrays

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Fig. 10

Simulated average wall shear stress (black lines) of the square (square symbols), diagonal (diamond symbols), and random (triangular symbols) arrays compared with the analytically solutions (gray lines). The simulation results of the three types of arrays are grouped with the same Re, i.e., Re = 1.0 (dotted lines), Re = 5.0 (dashed lines), Re = 10.0 (solid lines).

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Fig. 11

Probability density function (PDF) of the linear stress accumulation (SA) in the (a) square, (b) diagonal, (c) random and (d) 3D arrays when Re is 5.0

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