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.
A van der Pol–Duffing Oscillator Model of Hydrodynamic Forces on Canonical Structures
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Akhtar, I., Marzouk, O. A., and Nayfeh, A. H. (August 25, 2009). "A van der Pol–Duffing Oscillator Model of Hydrodynamic Forces on Canonical Structures." ASME. J. Comput. Nonlinear Dynam. October 2009; 4(4): 041006. https://doi.org/10.1115/1.3192127
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