Finite-Element Analysis of Transverse Lift on Circular Cylinder in 2D Channel Flow
Publication: Journal of Engineering Mechanics
Volume 124, Issue 10
Abstract
The control volume-based finite-element method was used to investigate the transverse lift on a circular cylinder in a two-dimensional (2D) channel flow. The study was organized in two consecutive steps: (1) Flow past a stationary cylinder; and (2) flow past a freely translating and rotating cylinder. The ratio of the diameter of the cylinder-to-height of the channel was 0.1. The effects contributing to the lift from the fluid inertia, the rotation of the cylinder, and the proximity of the cylinder to the wall of the channel were explored. The results showed that with a stationary cylinder model, the lift was positive everywhere across the channel and pushed the cylinder toward the center of the channel; however, with a freely translating cylinder model, the lift was positive when y0/H was ≲0.15 and negative when y0/H was >0.15. Fluid inertia changed the magnitude of the lift. Rotation of the cylinder increased the lift on a nontranslating cylinder and decreased the lift on a freely translating cylinder. To explain the lift distribution, a particle influence region hypothesis was developed. The results provided an explanation for the inhomogeneous distribution of solid particles across a pipe or channel flow.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Baliga, B. R. (1980). “A control-volume based finite element method for convective heat and mass transfer,” PhD thesis, Univ. of Minnesota, Minneapolis, Minn.
2.
Baliga, B. R., and Patankar, S. V.(1983). “A control volume finite-element method for two-dimensional fluid flow and heat transfer.”Numer. Heat Transfer, 6(3), 245–261.
3.
Bretherton, F. P.(1962). “The motion of rigid particles in a shear flow at low Reynolds number.”J. Fluid Mech., Cambridge, England, 14, 284–304.
4.
Cherukat, P., and McLaughlin, J. B.(1994). “Wall induced lift on a sphere.”Int. J. Multiphase Flow, 16, 899–907.
5.
Cox, R. G.(1965). “The steady motion of a particle of arbitrary shape at small Reynolds numbers.”J. Fluid Mech., Cambridge, England, 23, 625–643.
6.
Cox, R. G., and Brenner, H.(1968). “The lateral migration of solid particles in Poiseuille flow: I. Theory.”Chemical Engrg. Sci., 23, 147–173.
7.
Cox, R. G., and Hsu, S. K.(1977). “The lateral migration of solid particles in a laminar flow near a plane.”Int. J. Multiphase Flow, 3, 201–222.
8.
Drew, D.(1988). “The lift force on a small sphere in the presence of a wall.”Chemical Engrg. Sci., 43, 769–773.
9.
Goldman, A. J., Cox, R. G., and Brenner, H.(1966). “Slow viscous motion of a sphere parallel to a plane wall: I. Motion through a quiescent fluid.”Chemical Engrg. Sci., 22, 637–651.
10.
Goldman, A. J., Cox, R. G., and Brenner, H.(1967). “Slow viscous motion of a sphere parallel to a plane wall: Couette flow.”Chemical Engrg. Sci., 22, 653–660.
11.
Ho, B. P., and Leal, L. G.(1974). “Inertial migration of rigid spheres in two-dimensional unidirectional flow.”J. Fluid Mech., Cambridge, England, 65, 365–400.
12.
Kaplun, S.(1957). “Low Reynolds number flow past a circular cylinder.”J. Math. Mech., 6, 595–603.
13.
Kaplun, S., and Lagerstrom, P. A.(1957). “Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers.”J. Math. Mech., 6, 585–593.
14.
Karnis, A., and Mason, S. G.(1967). “Particle motions in sheared suspensions. XXIII. Wall migration of fluid drops.”J. Colloid Sci., 24, 164.
15.
Lagerstrom, P. A., and Cole, J. D.(1955). “Examples illustrating expansion procedures for the Navier-Stokes equations.”JRMA, 4, 817–882.
16.
Leighton, D., and Acrivos, A.(1985). “The lift on a small sphere touching a plane in the presence of a simple shear flow.”ZAMP, 36, 174–178.
17.
McLaughlin, J. B.(1991). “Inertial migration of a small sphere in linear shear flows.”J. Fluid Mech., Cambridge, England, 224, 261–274.
18.
Oseen, C. W.(1910). “Uber die Stokessche Formel und uber die verwandte Aufgabe in der hydrodynamik.”Ark. f. Mat. Astr. og. Fys., 6, 29.
19.
Patankar, S. V. (1980). Numerical heat transfer and fluid flow. Hemisphere Publishing Corp., Washington, D.C.
20.
Perry, R. H., and Chilton, C. H. (1984). Perry's chemical engineers' handbook, 6th Ed., McGraw-Hill Inc., New York, N.Y.
21.
Proudman, I., and Pearson, J. R.(1957). “Expansion at small Reynolds numbers for the flow past a sphere and a circular cylinder.”J. Fluid Mech., Cambridge, England, 2, 237–262.
22.
Rubinow, S. I., and Keller, J. B.(1961). “The transverse force on a spinning sphere moving in viscous fluid.”J. Fluid Mech., Cambridge, England, 11, 447–459.
23.
Saffman, P. G.(1965). “The lift on a small sphere in a slow shear flow.”J. Fluid Mech., Cambridge, England, 22, 385–400.
24.
Segré, G., and Silberberg, A.(1961). “Behavior of macroscopic rigid spheres in Poiseuille flow—I.”J. Fluid Mech., Cambridge, England, 14, 115–135.
25.
Segré, G., and Silberberg, A.(1962). “Behavior of macroscopic rigid spheres in Poiseuille flow—II.”J. Fluid Mech., Cambridge, England, 14, 136.
26.
Stokes, G. G.(1851). “On the effect of the internal friction of fluids on the motion of pendulums.”Camb. Phil. Trans., 9, 8–106.
27.
Tachibana, M.(1973). “On the behavior of a sphere in the laminar tube flows.”Rheol. Acta, 12, 58–69.
28.
Uijttewaal, W. S. J., Nijhof, E. J., and Heethaar, R. M.(1994). “Lateral migration of blood cells and microspheres in two-dimensional Poiseuille flow: A laser-Doppler study.”J. Biomechanics, 27(1), 35–42.
29.
Vasseur, P., and Cox, R. G.(1976). “The lateral migration of a spherical particle in two-dimensional shear flows.”J. Fluid Mech., Cambridge, England, 78, 385–413.
30.
Whitehead, A. N. (1889). Quart. J. Math., 23, 143.
Information & Authors
Information
Published In
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Oct 1, 1998
Published in print: Oct 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.