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Research Papers: Fundamental Issues and Canonical Flows

# Direct Numerical Simulations of the Flow Past a Cylinder Moving With Sinusoidal and Nonsinusoidal Profiles

[+] Author and Article Information
Osama A. Marzouk

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061omarzouk@vt.edu

J. Fluids Eng 131(12), 121201 (Nov 12, 2009) (9 pages) doi:10.1115/1.4000406 History: Received April 23, 2009; Revised September 25, 2009; Published November 12, 2009; Online November 12, 2009

## Abstract

We perform direct numerical simulations of the flow past a circular cylinder undergoing a one-degree-of-freedom transverse oscillation. The displacement follows a sine function raised to an arbitrary integer power ranging from 1 to 8. When the displacement power is above 2, we have multifrequency oscillation, and the number of Fourier components in the oscillation increases with the power, but they are either odd or even multiples of the input (argument) frequency of the displacement function. We study the responses of the nondimensional lift and drag under these different oscillation profiles and the transfer of nondimensional mechanical energy due to the oscillation, and their trends as the power (hence the number of Fourier components in the oscillation) increases. For odd powers, the energy is transferred to the cylinder; whereas for even powers, it is transferred to the flow. A unity power (harmonic oscillation) corresponds to the maximum energy transfer to the cylinder, which can explain the occurrence of this profile in the case when the cylinder is free to oscillate due to the vortex-induced vibration (VIV) phenomenon. The lift exhibits a mean value only with even powers above 2. The results show that the lift is driven to a large extent by the acceleration of the oscillation rather than its velocity. This should be considered when modeling the fluid-structure coupling in reduced-order VIV models.

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## Figures

Figure 1

The mean of friction-nondimensionalized smallest grid step in the radial direction at Re=300 for Π=5 and Ψ=0.15

Figure 2

The Fy displacement trajectory at Re=500 for Π=1 and Ψ=0.25; from our flow model (dashed line) compared with the one in Ref. 27 (solid line) for validation

Figure 3

Illustration of the effect of Π on the normalized displacement over one Ω period

Figure 4

The nondimensional displacement, velocity, and acceleration of the oscillation for odd values of Π=1 and 7 over one Ω period

Figure 5

The nondimensional displacement, velocity, and acceleration of the oscillation for even values of Π=2 and 8 over one Ω period

Figure 6

Amplitudes of the Fourier components in the displacement, velocity, and acceleration of the oscillation for Π=5 and 7

Figure 7

Amplitudes of the Fourier components in the displacement, velocity, and acceleration of the oscillation for Π=4, 6, and 8

Figure 8

Results of analyzed lift and drag, and the energy transfer for odd and even values of Π

Figure 9

Nondimensional lift for odd values of Π over three Ω periods

Figure 10

Nondimensional lift for even values of Π over three Ω periods

Figure 11

Nondimensional drag for odd values of Π=1 and 7 over three Ω periods

Figure 12

Nondimensional drag for even values of Π=2 and 8 over three Ω periods

Figure 13

Amplitudes of the Fourier components in the nondimensional lift for Π=4–8

Figure 14

Amplitude of the Fourier component in the nondimensional lift at Ω for odd and even Π

## Errata

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