Numerical Investigations Of Nonlinear Dynamics Of Rotatable Circular Cylinder With Splitter Plate Subject To Steady Flow

Based on the method of using rotatable splitter plate to suppress vortex-induced vibration behind a circular cylinder,numerical results of nonlinear dynamics of a circular cylinder with splitter plate subject to steady flow are presented in this paper,including the phase dynamics of the forced rotation and nonlinear dynamic responses of the freely rotatable assembly,based on the results of the forced oscillation model,a coupled wake oscillator model is also set up to predict the rotation of the structure in steady flow.Firstly,as for the forced rotation of the structure,phase dynamics,characteristics of the flow field,vortex shedding pattern are discussed according to the numerical results with different forced amplitude and frequency.Besides,the boundary(Arnold Tongue)between synchronization and de-synchronization is also given,according to the phase difference between the fluid force and structural motion.Three types of phase dynamics are discussed in this paper,including phase locking,phase trapping and phase slipping.The numerical results also show that the phase dynamics of the forced rotation is related to the flow field of the fluid-structure interaction system.Secondly,a coupled wake oscillator model is set up based on the forced rotation of the structure.In this part,A Van der Pol equation is used to describe the characteristics of the fluid.According to the results of forced rotation model,parameters of Van der Pol equation are determined.Then,the Van der Pol wake oscillator model is used to predict the rotation of the structure in steady flow.The numerical results of the prediction are also given,including torque and rotary angle.Thirdly,the rotary oscillation of the structure in this work is modelled by a Duffing oscillator with both linear and nonlinear restoring force,denoted by dimensional k and ?,respectively.Numerical simulations were carried out for various reduced velocities Ur?[9 to 15] and ??[0 to 20] at a relatively low Reynolds number.Our previous investigations of a purely linear oscillator(i.e.,?=0)show that the equilibrium position of the rotary oscillation is not parallel to the free stream as the reduced velocity exceeds a critical value,that is,bifurcation occurs.The present numerical studies suggest that,for a specific reduced velocity Ur,the increase in the nonlinear stiffness ? can eliminate the undesirable bifurcation.The numerical results also suggest that both odd and even-number lift frequency components appear for bifurcate cases,while only odd-number lift frequencies are observed for non-bifurcate cases.The dynamic mode decompositions for the wake flow corresponding to each lift frequency are presented.