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Offshore Technology

# Potential Flow Theory and Numerical Analysis of Forces on Cylinders Induced by Oscillating Disturbances

[+] Author and Article Information
Daniel T. Valentine1

Department of Mechanical and Aeronautical Engineering,  Clarkson University, Potsdam, NY 13699-5725clara@clarkson.edu

Department of Mechanical and Aeronautical Engineering,  Clarkson University, Potsdam, NY 13699-5725

1

Address all correspondence to this author.

J. Offshore Mech. Arct. Eng 134(3), 031301 (Feb 01, 2012) (7 pages) doi:10.1115/1.4005180 History: Received November 10, 2010; Revised June 29, 2011; Published February 01, 2012; Online February 01, 2012

## Abstract

The complete solution of several two-dimensional potential flow problems are reported that deal with the unsteady flow around circular cylinders. Three of the flows considered are induced by an oscillating disturbance near the cylinder. The three elemental disturbances examined are (1) a pulsating source, (2) a pulsating doublet, and (3) a pulsating vortex. The formulas for the force acting on the cylinder due to each of the elemental disturbances were derived by applying the method of images. These results were checked by deriving the equivalent surface distribution of sources to model the cylinder by applying Green’s second identity. The theory helped direct the development of a boundary-integral numerical model described and applied in this paper to solve the unsteady flow around a circular cylinder due to an arbitrarily specified oscillatory disturbance near the cylinder. The numerical method is validated by comparing predictions of the force with the exact solutions. We applied the theory to examine a model problem related to the vortex-shedding force that causes vortex-induced vibration.

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## Figures

Figure 1

The Cartesian and polar coordinate systems used to define the problem of the potential flow around a cylinder induced by a pulsating disturbance located at (x,y)=(xs,0)

Figure 2

The exact solution of the force acting on the cylinder of radius r=1 due to a pulsating source located at (x,y)=(xs,0) with strength m= sin(ωt), and frequency ω=π/20, over the range of dimensionless time 0≤t≤100

Figure 3

Comparison of the force on the cylinder due to an unsteady source with the force on the cylinder due to an unsteady doublet: (a) xs=2 and (b) xs=1.5

Figure 4

The unsteady force acting on a cylinder due to a pulsating vortex at xs=1.5, xs=2, and xs=2.5: (a) the x-component of the force and (b) the y-component of the force

Figure 5

(a) Comparison of numerically determined potential for the case surface distribution of sources with the exact results. (b) Pressure distribution and the force acting on the cylinder modeled by the surface distribution of sources.

Figure 6

The effect of the number of panels required in the boundary-element method to predict the force acting on a cylinder represented by a surface distribution of sources. The cylinder of unit radius is in a steady flow of a unit-strength source at (xs,ys)=(3,0).

Figure 7

Comparison between the numerical predictions of the force due to a pulsating source with the exact solution, in this case xs=1.5

Figure 8

Comparisons between predictions of side force acting on a circular cylinder in way of a fluctuating vortex in a free stream including the effect of finite circulation

Figure 9

Comparisons between predictions of drag force acting on a circular cylinder in way of a fluctuating vortex in a free stream including the effect of finite circulation

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