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Journal of Biomechanical Engineering | Volume 128 | Issue 1 | TECHNICAL PAPERS
TECHNICAL PAPERS: Fluids/Heat/Transport

Pulsatile Flow and Mass Transport Over an Array of Cylinders: Gas Transfer in a Cardiac-Driven Artificial Lung

[+] Author and Article Information
Kit Yan Chan, Hideki Fujioka, James B. Grotberg

Department of Biomedical Engineering, The University of Michigan, Ann Arbor, Michigan 48109

Robert H. Bartlett, Ronald B. Hirschl

Department of Surgery, The University of Michigan Medical School, Ann Arbor, Michigan 48109

J Biomech Eng 128(1), 85-96 (Sep 14, 2005) (12 pages) doi:10.1115/1.2133761 History: Received May 04, 2005; Revised September 14, 2005
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The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.
Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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+Artificial lung device (reproduced with permission from Michigan Critical Care Consultant Inc., Ann Arbor, MI)
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Artificial lung device (reproduced with permission from Michigan Critical Care Consultant Inc., Ann Arbor, MI)
Figure 1

Artificial lung device (reproduced with permission from Michigan Critical Care Consultant Inc., Ann Arbor, MI)

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+Fiber arrangement. The unit cell is marked by the dashed lines
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Fiber arrangement. The unit cell is marked by the dashed lines
Figure 2

Fiber arrangement. The unit cell is marked by the dashed lines

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+Example of unit cells
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Example of unit cells
Figure 3

Example of unit cells

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+Two functional forms of pulsatile input U(t)
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Two functional forms of pulsatile input U(t)
Figure 4

Two functional forms of pulsatile input U(t)

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+Gas concentration computational domain and boundary conditions. Dash rectangle represents the computational domain.
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Gas concentration computational domain and boundary conditions. Dash rectangle represents the computational domain.
Figure 5

Gas concentration computational domain and boundary conditions. Dash rectangle represents the computational domain.

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+Sample grid
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Sample grid
Figure 6

Sample grid

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+Plot of time-averaged Sherwood number and gas concentration vs fiber layer number. (Square array: α=1; Re=10; A=0.5; ε=0.8036.)
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Plot of time-averaged Sherwood number and gas concentration vs fiber layer number. (Square array: α=1; Re=10; A=0.5; ε=0.8036.)
Figure 7

Plot of time-averaged Sherwood number and gas concentration vs fiber layer number. (Square array: α=1; Re=10; A=0.5; ε=0.8036.)

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+Concentration profile and instantaneous streamlines: squared array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).
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Concentration profile and instantaneous streamlines: squared array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).
Figure 8

Concentration profile and instantaneous streamlines: squared array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).

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+Concentration profile and instantaneous streamlines: staggered array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).
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Concentration profile and instantaneous streamlines: staggered array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).
Figure 9

Concentration profile and instantaneous streamlines: staggered array. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous streamlines pattern. (a) t=14cycle; (b) t=34cycle; (c) U(t) (α=1; Re=10; A=0.5; ε=0.8036).

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+(a) α influence on the surface-average Sherwood number time cycle. (b) α influence on ΔP∕L time cycle (Re=10; A=0.5; ε=0.8036).
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(a) α influence on the surface-average Sherwood number time cycle. (b) α influence on ΔP∕L time cycle (Re=10; A=0.5; ε=0.8036).
Figure 10

(a) α influence on the surface-average Sherwood number time cycle. (b) α influence on ΔP∕L time cycle (Re=10; A=0.5; ε=0.8036).

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+Concentration profile and instantaneous streamlines. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous stream lines pattern. (a) t=0cycle; (b) t=12cycle; (c) U(t) (α=2; Re=10; A=0.5; ε=0.8036).
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Concentration profile and instantaneous streamlines. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous stream lines pattern. (a) t=0cycle; (b) t=12cycle; (c) U(t) (α=2; Re=10; A=0.5; ε=0.8036).
Figure 11

Concentration profile and instantaneous streamlines. The upper plot indicates the concentration contours lines and the lower plot shows the instantaneous stream lines pattern. (a) t=0cycle; (b) t=12cycle; (c) U(t) (α=2; Re=10; A=0.5; ε=0.8036).

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+(a) A influence on the surface-average Sherwood number time cycle. (b) A influence on the ΔP∕L time cycle (α=1; Re=10; ε=0.8036).
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(a) A influence on the surface-average Sherwood number time cycle. (b) A influence on the ΔP∕L time cycle (α=1; Re=10; ε=0.8036).
Figure 12

(a) A influence on the surface-average Sherwood number time cycle. (b) A influence on the ΔP∕L time cycle (α=1; Re=10; ε=0.8036).

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+(a) Re influence on the surface-average Sherwood number time cycle. (b) Re influence on the ΔP∕L time cycle (α=1; A=0.5; ε=0.8036).
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(a) Re influence on the surface-average Sherwood number time cycle. (b) Re influence on the ΔP∕L time cycle (α=1; A=0.5; ε=0.8036).
Figure 13

(a) Re influence on the surface-average Sherwood number time cycle. (b) Re influence on the ΔP∕L time cycle (α=1; A=0.5; ε=0.8036).

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+(a) ε influence on the surface-average Sherwood number time cycle. (b) ε influence on ΔP∕L time cycle (α=1; Re=10; A=0.5).
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(a) ε influence on the surface-average Sherwood number time cycle. (b) ε influence on ΔP∕L time cycle (α=1; Re=10; A=0.5).
Figure 14

(a) ε influence on the surface-average Sherwood number time cycle. (b) ε influence on ΔP∕L time cycle (α=1; Re=10; A=0.5).

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+Streamline patterns of staggered array with different ε(t=14cycle). (a) ε=0.4973; (b) ε=0.8036.
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Streamline patterns of staggered array with different ε(t=14cycle). (a) ε=0.4973; (b) ε=0.8036.
Figure 15

Streamline patterns of staggered array with different ε(t=14cycle). (a) ε=0.4973; (b) ε=0.8036.

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+Concentration profile and instantaneous stream lines with cardiac U(t): squared array. (a) t=14cycle; (b) t=11∕20cycle; (c) U(t).
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Concentration profile and instantaneous stream lines with cardiac U(t): squared array. (a) t=14cycle; (b) t=11∕20cycle; (c) U(t).
Figure 16

Concentration profile and instantaneous stream lines with cardiac U(t): squared array. (a) t=14cycle; (b) t=11∕20cycle; (c) U(t).

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+Concentration profile and instantaneous stream lines with cardiac U(t): staggered array. t=14cycle; (b) t=11∕20cycle; (c) U(t).
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Concentration profile and instantaneous stream lines with cardiac U(t): staggered array. t=14cycle; (b) t=11∕20cycle; (c) U(t).
Figure 17

Concentration profile and instantaneous stream lines with cardiac U(t): staggered array. t=14cycle; (b) t=11∕20cycle; (c) U(t).

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+The log-log plot of space-average Sherwood vs Reynolds number. The solid symbols represent actual data; the solid line is the least-square fit. (Re=10, ε=0.4986).
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The log-log plot of space-average Sherwood vs Reynolds number. The solid symbols represent actual data; the solid line is the least-square fit. (Re=10, ε=0.4986).
Figure 18

The log-log plot of space-average Sherwood vs Reynolds number. The solid symbols represent actual data; the solid line is the least-square fit. (Re=10, ε=0.4986).

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