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Journal of Fluids Engineering | Volume 131 | Issue 5 | Technical Brief
Technical Briefs

Inviscid Flow Past Two Cylinders

[+] Author and Article Information
R. S. Alassar, M. A. El-Gebeily

Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

J. Fluids Eng 131(5), 054501 (Apr 16, 2009) (6 pages) doi:10.1115/1.3114678 History: Received April 02, 2008; Revised March 11, 2009; Published April 16, 2009
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References
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Citing Articles

A simple solution of the problem of inviscid flow past two circular cylinders is presented. The two cylinders may be of different diameters and located at any distance from each other. The solutions of the two main cases, namely, when the flow is perpendicular to the center-to-center line and when the flow is parallel to it (tandem cylinders), lead to a solution of the problem when the flow is in an arbitrary direction.
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Copyright © 2009 by American Society of Mechanical Engineers
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References

1
Alassar, R. S., Badr, H. M., and Allayla, R., 2000, “Viscous Flow Over a Sphere With Fluctuations in the Free-Stream Velocity,” Comput. Mech., 26 (5), pp. 409–418.  [CrossRef]
2
Badr, H. M., 1994, “Oscillating Inviscid Flow Over Elliptic Cylinders With Flat Plates and Circular Cylinders as Special Cases,” Ocean Eng., 21 (1), pp. 105–113.  [CrossRef]
3
Alassar, R. S., and Badr, H. M., 1999, “Oscillating Flow Over Oblate Spheroids,” Acta Mech.  [CrossRef], 137 (3–4), pp. 237–254.
4
Alassar, R. S., and Badr, H. M., 1999, “Oscillating Viscous Flow Over Prolate Spheroids,” Trans. Can. Soc. Mech. Eng., 23 (1A), pp. 83–93.
5
Alassar, R. S., and Badr, H. M., 1997, “Analytical Solution of Oscillating Inviscid Flow Over Oblate Spheroids With Spheres and Flat Disks as Special Cases,” Ocean Eng., 24 (3), pp. 217–225.  [CrossRef]
6
Hicks, W. M., 1880, “On the Motion of Two Spheres in a Fluid,” Philos. Trans. R. Soc. London, 171 , pp. 455–492.  [CrossRef]
7
Basset, A. B., 1886, “On the Motion of Two Spheres in a Liquid, and Allied Problems,” Proc. London Math. Soc., s1–18 , pp. 369–378.  [CrossRef]
8
Herman, R. A., 1887, “On the Motion of Two Spheres in Fluid and Allied Problems,” Q. J. Math., 22 , pp. 204–231.
9
Lamb, H., 1932, "Hydrodynamics", 6th ed., Cambridge University Press, Cambridge, UK, Chap. 6.
10
Rouse, H., 1976, "Advanced Mechanics of Fluids", Krieger Publishing Company, Malabar, FL, Chap. 3.
11
Bentwich, M., 1978, “Exact Solution for 2-Sphere Problem in Axisymmetrical Potential Flow,” ASME Trans. J. Appl. Mech., 45 , pp. 463–468.
12
Sun, R., and Chwang, A. T., 2001, “Hydrodynamic Interaction Between a Slightly Distorted Sphere and a Fixed Sphere,” Theor. Comput. Fluid Dyn.  [CrossRef], 15 , pp. 11–22.
13
Bjerknes, V. F. K., 1906, "Fields of Force", Columbia University Press, New York.
14
Lagally, M., 1929, “The Frictionless Current in the Outer Areas of Double Circuits,” Z. Angew. Math. Mech., 9 , pp. 299–305.  [CrossRef]
15
LagallyM., 1931, “The Frictionless Flow in the Region Around Two Circles,” N.A.C.A. Technical Memorandum No. 626.
16
Wang, Q. X., 2004, “Interaction of Two Circular Cylinders in Inviscid Flow,” Phys. Fluids  [CrossRef], 16 (12), pp. 4412–4425.
17
Crowdy, D. G., Surana, A., and Yick, K. -Y., 2007, “The Irrotational Motion Generated by Two Planar Stirrers in Inviscid Fluid,” Phys. Fluids  [CrossRef], 19 , p. 018103.
18
Crowdy, D. G., 2006, “Analytical Solution for Uniform Potential Flow Past Multiple Cylinders,” Eur. J. Mech. B/Fluids, 25 , pp. 459–470.  [CrossRef]

Figures

Grahic Jump Location
+Boundary conditions
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Boundary conditions
Figure 2

Boundary conditions

Grahic Jump Location
+The problem configuration
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The problem configuration
Figure 1

The problem configuration

Grahic Jump Location
+Boundary conditions for tandem cylinders
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Boundary conditions for tandem cylinders
Figure 5

Boundary conditions for tandem cylinders

Grahic Jump Location
+Streamline patterns for the case r1=4, r2=1, and H=6
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Streamline patterns for the case r1=4, r2=1, and H=6
Figure 6

Streamline patterns for the case r1=4, r2=1, and H=6

Grahic Jump Location
+The pressure distribution around the right cylinder for the case r2=1, H=6
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The pressure distribution around the right cylinder for the case r2=1, H=6
Figure 7

The pressure distribution around the right cylinder for the case r2=1, H=6

Grahic Jump Location
+Streamline patterns for the case r1=1, r2=4, H=7, and δ=π/4
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Streamline patterns for the case r1=1, r2=4, H=7, and δ=π/4
Figure 8

Streamline patterns for the case r1=1, r2=4, H=7, and δ=π/4

Grahic Jump Location
+Streamline patterns for the case r1=1, r2=2, and H=4
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Streamline patterns for the case r1=1, r2=2, and H=4
Figure 3

Streamline patterns for the case r1=1, r2=2, and H=4

Grahic Jump Location
+The pressure distribution around the right cylinder for the case r1=1, r2=1
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The pressure distribution around the right cylinder for the case r1=1, r2=1
Figure 4

The pressure distribution around the right cylinder for the case r1=1, r2=1

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