doi:10.1016/j.jfluidstructs.2006.09.002
Copyright © 2006 Elsevier Ltd All rights reserved.
Features of flow-induced forces deduced from wavelet analysis
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X.Q. Wanga, 
, 
, R.M.C. Soa, b and W.-C. Xiec
aDepartment of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, PR China
bIndustrial Center,The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, PR China
cDepartment of Civil Engineering, University of Waterloo, Waterloo, Ont., Canada
Received 22 December 2005;
accepted 11 September 2006.
Available online 28 November 2006.
Abstract
In the present study, the effect of Reynolds number (Re) on flow interference between two side-by-side stationary cylinders and the associated flow-induced forces are investigated using finite element method and wavelet analysis. The pitch ratio chosen is T/D=1.7, where T is the separation distance measured between cylinder centers and D is the diameter, and Re, based on the free-stream velocity and the diameter of the cylinder, is varied within the laminar flow regime, i.e., 60<Re<200. The method of continuous wavelet transform is used to analyze time-variant features of flow-induced forces in the time–frequency domain. Flow patterns in the form of vorticity plots are presented to demonstrate the underlying physics. It is found that flow interference initially occurs in the inner vortices shed from the two cylinders, and extends to the outer vortices with increasing Re. The flow behind two cylinders undergoes three regimes: Regime I—unbiased gap flow, Regime II—stable biased gap flow, and Regime III—unstable gap flow. Flow-induced forces show significant variations when the flow transits from one regime to another. In particular, during the transition from Regimes II to III, the forces not only increase by amplitude, but also change their nature from deterministic to random, and show some nonstationary features. This is shown to be caused by the amalgamation of inner and outer vortices behind the two cylinders when the flow interference extends from inner vortices to outer vortices. Whenever possible, the present results are compared with experimental measurements and theoretical predictions. The numerical simulations are consistent with these other results.
Keywords: Two side-by-side cylinders; Flow-induced forces; Reynolds number effect; Wavelet analysis
Fig. 1. Computational domain and the mesh used in the numerical simulation.
Fig. 2. Plots of mean and root-mean-square values of the lift and drag coefficients versus Re. When the root-mean-square values are time-variant (at Re=105 and 200), their minimum, mean, and maximum values are plotted.
Fig. 3. Time histories of the lift and drag coefficients: (a) Re=70; and (b) Re=80.
Fig. 4. CWT spectrograms of the lift and drag coefficients: (a) lift at Re=70; (b) lift at Re=80; (c) drag at Re=70; and (d) drag at Re=80.
Fig. 5. Zoomed view of CWT spectrograms and selected instantaneous CWT spectra at Re=70: (a) lift; and (b) drag.
Fig. 6. Vorticity plots at selected times at Re=70: (a) t=314; (b) t=326; and (c) t=334.
Fig. 7. A typical vorticity plot and the corresponding instantaneous CWT spectra of the force coefficients at Re=80 and at t=300: (a) vorticity plot; (b) instantaneous CWT lift spectrum; and (c) instantaneous CWT drag spectrum.
Fig. 8. Time histories of the lift and drag coefficients: (a) Re=100 and (b) Re=105.
Fig. 9. CWT spectrograms of the lift and drag coefficients: (a) lift at Re=100; (b) lift at Re=105; (c) drag at Re=100; and (d) drag at Re=105.
Fig. 10. Typical vorticity plots and the corresponding instantaneous CWT spectra of the force coefficients at Re=100 and at t=622 and 661: (a) vorticity plots; (b) instantaneous CWT lift spectra; and (c) instantaneous CWT drag spectra.
Fig. 11. Vorticity plots corresponding to the low-amplitude parts of the time histories and the corresponding instantaneous CWT spectra of force coefficients at Re=105: (a) t=400; and (b) t=750.
Fig. 12. Instantaneous CWT spectra of the force coefficients and the corresponding flow pattern at Re=105: (a) t=368; and (b) t=680.
Fig. 13. Time histories of the force coefficients and the corresponding CWT spectrograms at Re=200: (a) lift; (b) drag; (c) CWT lift spectrogram; and (d) CWT drag spectrogram.
Fig. 14. Typical vorticity plot and the corresponding instantaneous CWT spectra of the force coefficients at Re=200 and t=680.
Table 1.
Statistics of lift and drag coefficients for all Re investigated
Nonstationary behavior is found in this regime, thus the statistics given here are only representative mean values. See text for details.
Corresponding author. Tel.: +852 27664502; fax: +852 23654703.
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