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Research Papers: Fundamental Issues and Canonical Flows

# Numerical Study of Two-Dimensional Circular Cylinders in Tandem at Moderate Reynolds Numbers

[+] Author and Article Information
Ali Vakil

e-mail: alivakil@interchange.ubc.ca

Sheldon I. Green

e-mail: green@mech.ubc.ca
Department of Mechanical Engineering,
University of British Columbia,

1Corresponding author.

2Present address: Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, BC, V6T 1Z4, Canada.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 3, 2012; final manuscript received Mach 15, 2013; published online May 17, 2013. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 135(7), 071204 (May 17, 2013) (9 pages) Paper No: FE-12-1106; doi: 10.1115/1.4024045 History: Received March 03, 2012; Revised March 15, 2013

## Abstract

Computer simulations of the flow around a pair of two-dimensional, tandem circular cylinders in a flow, for Reynolds numbers in the range 1–40, are described. Cylinder surface-to-surface separations in the range $0.1 (D = cylinder diameter) were considered. The computed wake of a single cylinder at these low to moderate Reynolds numbers was in surprisingly good agreement with the laminar wake approximation, and a simple theory is presented to explain this agreement. With tandem cylinders, the drag on the downstream cylinder is a monotonic function of the cylinder separation. The laminar wake approximation can be used to explain reasonably well the variation in drag. The drag on the upstream cylinder is also a monotonic function of separation distance provided that the Reynolds number is less than about 10. For Reynolds numbers between 10 and 40, the upstream cylinder drag first decreases as separation increases up to a few diameters and then increases monotonically with separation distance.

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## Figures

Fig. 1

The geometry of the problem

Fig. 2

(a) Computational domain indicating the inlet, outlet, and slip walls. (b) A Close-up view of the hybrid mesh around the cylinders. For clarity, not all mesh elements are shown.

Fig. 3

Drag coefficient versus number of mesh volumes for s/D=10, for Re=5, and Re=40

Fig. 4

Developing flow in the wake of a cylinder at Re=40 at several distances downstream of the cylinder

Fig. 5

The developed defect-velocity profile of the laminar wake approximation and those obtained from numerical simulations at 5 < ReD < 40

Fig. 6

The developing velocity profile downstream of a single cylinder at Re=10 and x/D=10. (a) Normalized x-velocity and (b) normalized y-velocity.

Fig. 7

Steady flow around two equal cylinders arranged in tandem at different Reynolds numbers and different spacings

Fig. 8

Downstream separation bubble length versus gap spacing at Re=20

Fig. 9

Upstream separation bubble length versus gap spacing at Re=20

Fig. 10

Normalized drag coefficient of the downstream cylinder versus gap spacing with Re as a parameter

Fig. 12

Normalized drag coefficient of the upstream cylinder versus gap spacing with Re as a parameter

Fig. 11

Comparison of the downstream cylinder drag, in Newtons per meter, between full simulations and the local wake velocity approximation, at representative pulp fiber conditions (Re = 40; D = 40 μm; U∞=1 m/s; μ/ρ=10-6 m2/s)

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