Wake-Induced Vibrations of a Circular Cylinder behind a Stationary Square Cylinder Using a Semi-Implicit Characteristic-Based Split Scheme

Abstract

This study develops a semi-implicit characteristic-based-split (SI-CBS) finite-element algorithm under the framework of the fractional step method to cope with the vortex-induced vibration (VIV) problem. The authors present a modified linear spring analogy algorithm for successful updating of the grid deformation. They verify the computational code against two benchmark problems. One is the VIV of an elastically mounted cylinder with transverse oscillation at R=150. The other is the transversely wake-induced vibration (WIV) of a circular cylinder by a stationary one. The authors conduct a two-dimensional (2D) numerical investigation on the problem of laminar flow over a two-cylinder system, which consists of a front stationary square cylinder and a rear two-degree-of-freedom (2-DOF) circular cylinder in a tandem arrangement. They find that the Reynolds number and reduced velocities play key roles in the WIVs of the circular cylinder. In addition to the wake patterns 2S, 2P, and P+S, the authors observe a steady-state wake pattern. They observe performances of dual-resonance, which means synchronization in both the in-line and transverse directions. For the X-Y trajectories of the circular cylinder, they obtain figures in the shape of an egg, a figure-8, and a point.