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Dispersion in a curved tube during oscillatory flow

Published online by Cambridge University Press:  26 April 2006

M. K. Sharp ,
R. D. Kamm ,
A. H. Shapiro ,
E. Kimmel  and
G. E. Karniadakis
M. K. Sharp
Affiliation:
Fluid Mechanics Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Departments of Civil and Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA.
R. D. Kamm
Affiliation:
Fluid Mechanics Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
A. H. Shapiro
Affiliation:
Fluid Mechanics Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
E. Kimmel
Affiliation:
Fluid Mechanics Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Agriculture Engineering Department, Technion, Haifa 32000, Israel.
G. E. Karniadakis
Affiliation:
Fluid Mechanics Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA.
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Abstract

The effect of curvature on longitudinal dispersion in an axially uniform toroidal tube during oscillatory flow is investigated. The regimes of dispersion and the rate of longitudinal transport are estimated by order-of-magnitude arguments. Experiments are reported for the range, 0.66 < Dn2/α4 < 2.4, 5.4 < α < 26, Sc = 0.68, where Dn is the Dean number, α is the Womersley number and Sc is the Schmidt number. For β2 = α2Sc > 30, curvature causes a sharp increase in the effective diffusivity, relative to that for a straight tube, by a factor of about 6 at Dn2/α4 ≈ 2. The results from two numerical simulation methods are also presented. One, a Monte Carlo simulation (0.01 < Dn < 10, 0.01 < α < 0.32, Sc = 104), predicts the spread of a bolus in quasi-steady flow. The other, a spectral-element method (1 < Dn < 1000, 1 < α < 100, Sc = 0.68), is used to find the dispersion in unsteady oscillatory flow subjected to a constant longitudinal concentration gradient. Two mechanisms are identified by which axial transport is modified by curvature. First, the enhanced lateral transport due to secondary flow decreases axial transport by a factor of up to 5 for low β2 and increases axial transport by an even greater amount for high β2. Second, axial transport is enhanced owing to a form of resonance when the secondary flow circulation time is equal to the cycle period.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 537 - 563
Copyright
© 1991 Cambridge University Press

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