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Research Papers

Numerical Investigation of Fluid Flow in a Chandler Loop

[+] Author and Article Information
Hisham Touma

Mechanical and Aerospace Engineering,
Polytechnic Institute of New York University,
Brooklyn, NY 11201

Iskender Sahin

Mechanical and Aerospace Engineering,
Polytechnic Institute of New York University,
Brooklyn, NY 11201

Tidimogo Gaamangwe

Systems Design Engineering,
University of Waterloo,
Waterloo, ON, N2L 3G1, Canada

Maud B. Gorbet

Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada

Sean D. Peterson

Mechanical and Mechatronics Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: peterson@mme.uwaterloo.ca

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received October 17, 2013; final manuscript received March 19, 2014; accepted manuscript posted April 2, 2014; published online May 12, 2014. Assoc. Editor: Dalin Tang.

J Biomech Eng 136(7), 071004 (May 12, 2014) (8 pages) Paper No: BIO-13-1494; doi: 10.1115/1.4027330 History: Received October 17, 2013; Revised March 19, 2014; Accepted April 02, 2014

The Chandler loop is an artificial circulatory platform for in vitro hemodynamic experiments. In most experiments, the working fluid is subjected to a strain rate field via rotation of the Chandler loop, which, in turn, induces biochemical responses of the suspended cells. For low rotation rates, the strain rate field can be approximated using laminar flow in a straight tube. However, as the rotation rate increases, the effect of the tube curvature causes significant deviation from the laminar straight tube approximation. In this manuscript, we investigate the flow and associated strain rate field of an incompressible Newtonian fluid in a Chandler loop as a function of the governing nondimensional parameters. Analytical estimates of the strain rate from a perturbation solution for pressure driven steady flow in a curved tube suggest that the strain rate should increase with Dean number, which is proportional to the tangential velocity of the rotating tube, and the radius to radius of curvature ratio of the loop. Parametrically varying the rotation rate, tube geometry, and fill ratio of the loop show that strain rate can actually decrease with Dean number. We show that this is due to the nonlinear relationship between the tube rotation rate and height difference between the two menisci in the rotating tube, which provides the driving pressure gradient. An alternative Dean number is presented to naturally incorporate the fill ratio and collapse the numerical data. Using this modified Dean number, we propose an empirical formula for predicting the average fluid strain rate magnitude that is valid over a much wider parameter range than the more restrictive straight tube-based prediction.

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References

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Figures

Grahic Jump Location
Fig. 1

Coordinate system and variable definitions. (a) XY plane view showing the initial state of the fluid, and (b) tube cross-section.

Grahic Jump Location
Fig. 2

Mass-averaged strain rate in the liquid domain as a function of time for various grid sizes for δ = 0.0125. The various lines represent different grid densities in each case. Grid convergence plots for the other curvature ratios are similar, but excluded here for brevity.

Grahic Jump Location
Fig. 3

Average strain rate magnitude as a function of Dean number and curvature ratio predicted from a perturbation solution of pressure-driven flow through a curved tube.

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Fig. 4

Representative case illustrating volume fraction α in the XY plane (primary torus), with additional resolution at (a) the thin liquid film at the top of the loop, (b) the left meniscus, (c) the right meniscus, and (d) in a cross-section (YZ plane) at the bottom of the loop (with overlaid velocity vectors). De = 24.5, δ = 0.025, κ = 50%.

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Fig. 5

(a) Axial and (b) cross-stream velocity profiles for κ = 70% and δ = 0.025 at various Dean numbers extracted from the YZ plane in the liquid portion of the tube.

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Fig. 6

Representative case illustrating strain rate in the XY plane (primary torus), with additional resolution at (a) the left meniscus, (b) the right meniscus, and (c) in a cross-section (YZ plane) at the bottom of the loop. De = 24.5, δ = 0.025, κ = 50%.

Grahic Jump Location
Fig. 7

Average strain rate magnitude over the liquid domain as a function of Dean number for all cases. Note that from De = 100 to De = 1000 the abscissa scale is logarithmic.

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Fig. 8

Height difference between the two menisci as a function of Dean number for all cases. Note that from De = 100 to De = 1000 the abscissa scale is logarithmic.

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Fig. 9

Rescaled data from Fig. 7 compared with the empirical correlation in Eq. (13)

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