Responses And Mechanism Analysis Of Flow Induced Vibrations Of Square Cylinder

In fluid dynamics,vortices shed from a bluff body is a common physical phenomena.Unsteady separation of fluid flow around a bluff body causes symmetrically vortex shedding,resulting in a repeating pattern of rotating vortices,which is named as a Kármán vortex street.Vortices are formed from the boundary layer of the bluff body,and the pressure distribution around the surface are therefore changed.When the bluff body is elastically mounted,fluctuating forces acting on the bluff body are caused by the swirling vortices,thus leading to vibrations transverse to the fluid flow.The interaction between the bluff body and the fluid flow is called Flow-induced vibrations(FIV).FIV manifests itself in many fields of engineering,such as cables,aircraft airfoils and heat exchanger tube arrays.In traditional engineering,FIV is constantly treated as a destructive problem due to the fatigue damage it may cause to the instruments.A number of research is carried out on control and reducing FIV.however,FIV can also benefit us.With opposite objective efforts of inhibition of FIV,VIVACE(Vortex Induced Vibration for Aquatic Clean Energy)converter is designed by the University of Michigan to harvest kinetic energy from FIV.With the rapid development of ocean engineering,petroleum engineering and wind engineering,FIV has received wild concern.However,the research on FIV of multiple cylinders with square cross-section is still in an exploratory stage.Research of multiple cylinders has great significance on both theory and engineering application.In this paper,FIV of of elastically mounted square cylinders are simulated.2-Dimensional Unsteady Reynolds-Averaged Navier-Stokes equations are achieved using finite volume method with the Spalart-Allmaras one equation turbulence model.The FIV responses of multiple square cylinders with different arrangement are simulated in the present study.The parameters of FIV on the amplitude,frequency,vortex shedding patterns,oscillation forces and body motion in uniform flow are investigated.The mechanisms such as exhibition of FIV and transition between FIV branches are also investigated in this paper.Firstly,the physical model is established for a elastically mounted square cylinder.The oscillator system is simplified as a mass-spring-damping system.In this paper,the FIV of multiple square cylinders with different arrangement are calculated using2-Dimensional Unsteady Reynolds-Averaged Navier-Stokes equations with the Spalart-Allmaras model.GGI(General Grid Interface)and Topological Mesh Changes are used to solve the moving wall boundary condition in FIV.The numerical calculation accuracy is validated in wind tunnel.Experimental results show that the FIV responses of a square cylinder are affected by the mass ratio and the damping ratio of the cylinder.Secondly,the FIV mechanisms of a spring-mounted square cylinder with different attack angle of fluid flow are investigated in the Reynolds number range of1×10~4?Re?1.2×10~5.The attack angle ranges from 0°to 45°,while the direction of oscillation is transverse to the flow.VIV initial branch,VIV upper branch and galloping are clearly observed.Comparing with a circular cylinder,the galloping of a square cylinder is easier to be exhibited.With the increase of the attack angle,the geometric symmetry is lost,which leads to a new FIV branch with a mixed response.The amplitude is higher than the amplitude of the VIV upper branch,while the frequency is half.The equilibrium position offsets from the position at rest.Different wake patterns are observed during several cycles of vibration at higher attack angle.Furthermore,the FIV of two rigid square cylinders,on end linear-springs,in tandem arrangement are investigated.The amplitude of the upstream cylinder increases with the increasing reduced velocity.When 4D?T?6D,the FIV responses of two square cylinders are close.The VIV initial branch,VIV upper branch,transition from VIV to galloping and galloping are observed.When T?3D,the amplitude of the downstream cylinder is obviously lower than the upstream amplitude,while frequency slightly larger than the upstream frequency.Comparing with the FIV of a single square cylinder,the reduced velocity when the FIV of the upstream cylinder exhibited is clearly lower.Finally,the FIV of two rigid square cylinders,on end linear-springs,in side-by-side arrangement are investigated.The amplitude increases continuously with increasing Reynolds number,which reaches a maximum when Re=100,000(U~*water=22.81).The frequency increases rapidly then decreases with increasing Reynolds number,and finally stabilized at the natural frequency.The vortex pattern is accompanied by the FIV branches.