Research Papers

A van der Pol–Duffing Oscillator Model of Hydrodynamic Forces on Canonical Structures

[+] Author and Article Information
Imran Akhtar1

Interdisciplinary Center for Applied Mathematics, MC 0531, Virginia Tech, Blacksburg, VA 24061akhtar@vt.edu

Osama A. Marzouk, Ali H. Nayfeh

Department of Engineering Science and Mechanics, MC 0219, Virginia Tech, Blacksburg, VA 24061


Corresponding author.

J. Comput. Nonlinear Dynam 4(4), 041006 (Aug 25, 2009) (9 pages) doi:10.1115/1.3192127 History: Received January 15, 2008; Revised February 12, 2009; Published August 25, 2009

Numerical simulations of the flow past elliptic cylinders with different eccentricities have been performed using a parallel incompressible computational fluid-dynamics (CFD) solver. The pressure is integrated over the surface to compute the lift and drag forces on the cylinders. The numerical results of different cases are then used to develop reduced-order models for the lift and drag coefficients. The lift coefficient is modeled with a generalized van der Pol–Duffing oscillator and the drag coefficient is expressed in terms of the lift coefficient. The parameters in the oscillator model are computed for each elliptic cylinder. The results of the model match the CFD results not only in the time domain but also in the spectral domain.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

(a) Geometry of an elliptic cylinder and (b) “O”-grid distributed among eight processors in the η-direction

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Figure 2

Mean surface CP distribution for (a) Case I and (b) Case II: present (solid) and Mittal and Balachandran (22) (triangle)

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Figure 3

Instantaneous spanwise vorticity contours

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Figure 4

Time histories of the lift (solid) and drag (dashed) coefficients

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Figure 5

Spectral analysis parameters from the CFD simulations

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Figure 6

Comparison between the time histories obtained by the lift model with those obtained with CFD

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Figure 7

Comparison between the time histories obtained by the drag model with those obtained with CFD

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Figure 8

Parameters of the van der Pol–Duffing oscillator and drag models



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