Numerical Analysis of Flow-Induced Transverse Vibration of a Cylinder with Cubic Non-Linear Stiffness at High Reynolds Numbers

Numerical calculations were performed to study the vortex-induced vibration (VIV) of a circular cylinder, which was elastically supported by springs of linear and cubic terms. These simulations were conducted at high Reynolds numbers ranging from 4200 to 42,000. To simulate the cylinder's motion and the associated aerodynamic forces, Computational Fluid Dynamics were employed in conjunction with dynamic mesh capabilities. The numerical method was initially verified by testing it with various grid resolutions and time steps, and subsequently, it was validated using experimental data. The response of cubic nonlinearities was investigated using insights gained from a conventional linear vortex-induced vibration (VIV) system. This 2D study revealed that both the amplitude and frequency of vibrations are contingent on the flow velocity. The highest output was achieved within the frequency lock-in region, where internal resonance occurs. In the case of a hardening spring, the beating response was observed from the lower end of the initial branch to the upper end of the initial branch. The response displacement amplitude obtained for the linear spring case was 27 mm, whereas in the cubic nonlinear case, the value was 31.8 mm. More importantly, the results indicate that the inclusion of nonlinear springs can substantially extend the range of wind velocities in which significant energy extraction through vortex-induced vibration (VIV) is achievable.