Nonlinear modeling of combined galloping and vortex-induced vibration of square sections under flow
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ORIGINAL PAPER
Nonlinear modeling of combined galloping and vortex-induced vibration of square sections under flow Peng Han · Pascal Hémon Emmanuel de Langre
· Guang Pan ·
Received: 20 March 2020 / Accepted: 5 November 2020 © Springer Nature B.V. 2020
Abstract In this paper, we propose a model for the transverse oscillation of a square-section cylinder under flow. The fluctuating transverse force due to vortex shedding is represented using a coupled nonlinear wake oscillator, while the unsteady force for galloping caused by the varying incidence angle effects is modelled using the quasi-steady approach. First, we analytically investigate the lift behavior and phase angle variation of the square cylinder under forced vibrations. Comparison with experimental data is used to determine the form of the coupling terms and its values. The present model shows advantages in predicting the phase angle, and it successfully captures the change in sign of the phase. Second, the proposed model is directly applied in predicting free oscillation cases without any tuning. The dynamical behaviors predicted by this model are compared with published experiments under different Scruton numbers, and reasonable agreement can be found. The results indicate that the model can not only be applied in simulating the “pure galloping” and “pure VIV,” but also is able to capture the interactions of VIV and galloping, including combined and separate VIV-galloping motions. P. Han · G. Pan School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China P. Han · P. Hémon · E. de Langre (B) LadHyX, Ecole polytechnique, CNRS, Institut Polytechnique de Paris, 91128 Palaiseau, France e-mail: [email protected]
Keywords Vortex-induced vibration · Galloping · Square cylinder · Reduced order model · Van der Pol
1 Introduction When a deformable body is submitted to flow, it will vibrate and in turn affect the fluid flow. This wellknown phenomenon is called flow-induced vibration (FIV) and may occur in many fields of engineering, such as civil engineering (chimneys and bridges), offshore engineering (risers and pipes), and energy engineering (electrical cables and power lines); it is therefore of practical interest [1]. There are many forms of FIV, but in this paper, we focus on vortex-induced vibration (VIV) and galloping [2]. VIV is a self-limited motion induced by vortex shedding from a bluff body. The most important feature of VIV is “lock-in,” during which both the vortex shedding frequency and the oscillation frequency are locked [3]. For flow velocities outside the lock-in range, the amplitude of motion is small. Studies on VIV are mainly for a circular-shape cylinder, because it could vibrate in pure VIV, away from the influence of other vibrations, such as galloping [1]. In past decades, a large body of experimental studies have been carried out on VIV of a circular cylinder, see reviews by Bearman [3], Williamson and Govardhan [4], and Sarpakaya [5]. Computing VIV has been considered as a chal
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