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Vortex, potential forces and phase dynamics of freely vibrating circular, square, and diamond shaped cylinders at a low Reynolds number

At a Glance

Section titled ā€œAt a Glanceā€
MetadataDetails
Publication Date2025-08-01
JournalPhysics of Fluids
AuthorsHimalaya Sarkar, Subhankar Sen

Abstract

Section titled ā€œAbstractā€

Lighthillā€™s [ā€œFundamentals concerning wave loading on offshore structures,ā€ J. Fluid Mech. 173, 667-681 (1986)] decomposition of total lift force, Cl of an oscillator into potential lift, Cpt, and vortex lift, Cvt, and consequent vortex phase, Ļ•vt, and total phase, Ļ• [Govardhan, R. and Williamson, C. H. K., ā€œModes of vortex formation and frequency response of a freely vibrating cylinder,ā€ J. Fluid Mech. 420, 85-130 (2000)] convincingly predict inter-branch transitions and switches in wake modes. For flow-induced transverse-only vibrations of circular, square, and diamond cylinders at a Reynolds number of 100, we determine Cpt and Cvt from equation of oscillator motion and also theoretically by assuming a harmonically varying response. During synchronization, work done by anti-phase Cpt and Cvt tends to balance each other and forms a mechanism to self-limit the response. Discontinuous jump in Ļ•vt marks transition to lower branch of response. This jump does not always alter the wake mode; mode switching involves appearance of a third harmonic in power spectra of Cvt and Cl as for the circular (Karman mode or 2S ā†’ C(2S) or coalesced 2S) and diamond (CNW(2S) ā†’ asymmetric P + S) cylinders admitting high stationary vortex-shedding frequency. Insensitivity of wake mode of a square cylinder to jump in Ļ•vt is established from sustenance of 2S mode around the jump. During jump in Ļ•, anti-phase Cvt and Cpt become comparable in magnitude leading to least fluctuating lift. The maximum fluctuating Cpt of diamond and circular cylinders is about 2.5 times and even higher, respectively, than that of its square counterpart. Cvt and Cpt carry no correspondence with pressure and viscous lifts. Unlike the fluctuating pressure and viscous lifts, fluctuating Cvt and Cpt undergo a crossover at the location of transition to lower branch.

Tech Support

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Original Source

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References

Section titled ā€œReferencesā€
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