Numerical Investigation Of Fluid Interaction With Rigid And Flexible Structures Based On CBS Finite Element Model

Bluff body flow are ubiquitous in nature,the force acting on the structure exerted by fluid may lead to flow-induced vibration（FIV）.In general,FIV tends to impacts on marine structures adversely,even results in structure failure.In this paper,by taking cylinder-splitter plate as research object and establishing fluid structure coupling numerical analyzing model altered characteristic based split finite element method,numerical research of vortex-induced vibration and galloping characteristics of flow over bluff-flexible structure under the condition of Reyn-olds number Re=100 are conducted,with the purpose of revealing the regularity of the effect of section shape and rigidity on system FIV.The details are as follows:First of all,numerical model of rigid-flexible structure of bluff-splitter plate are built.In the frame of Arbitrary Lagrangian-Eulerian（ALE）,the fluid-structure interaction solver is de-veloped in which fluid governing equations are solved by utilizing characteristic based split（CBS）finite element method,complex deformation of flexible structure the absolute nodal co-ordinate formulation（ANCF）and mesh deformation the radial basis functions interpolate（RBFI）method.Validation of the solver shows good agreements with solutions to benchmark problems in other literatures.Secondly,numerical research of rotational oscillation of complex system of rounded square cylinder with rigid splitter plate are carried out.The effect of the relative corner radius（R/D=0～0.5）in which R=0.0 and 0.5 illustrates rectangle and circle section respectively,and rotational reduced velocity（U_r=1.0～20.0）on the rotational vibration characteristics of the structure is mainly examined.The results of numerical analysis show that the radius of the corner has a significant effect on the rotational vibration characteristics of the structure:The phenomenon of rotation bifurcation,that is,the equilibrium position of rotational vibration of the structure deviates from the flow direction by a certain angle,is found at some large corner radius.And,the critical reduced velocity increases with increase in corner radius.When R≤0.1D,no bifurcation is found in the range of U_r=1.0～20.0.The setting of the cylinder corner can effectively reduce the amplitude of the rotational vibration of the structure.The maximum amplitude of rotational vibration of the rounded corner structure decreases with the increase in corner radius,which is contrary to frequency variation when corner radius grows.Further,the wake pattern is“2S”under the conditions of all different corner radius.Thirdly,by the purpose of studying fluid interaction with flexible plate with large defor-mation,numerical research on the characteristic of FIV of fixed rounded square cylinder with flexible plate is performed.The influence of corner radius and rigidly of plate on the character-istics of VIV of the flexible plate and flow field is explored under the condition of L=2 D.It is founded that the rigidity of plate and corner radius has a significant effect on the vibration of the plate by performing an analysis of response features of the plate in regions of lock-in and desynchronization.Foremost,in L₁ region,there is litter difference presented in all kinds of data.They share a common increasing trend when Ae increases.The vibration of plate is sym-metry,and generates a force pointing upstream.And the force obtain its maximum value 0.072on the condition of R=0.5D,Ae=5.4×10⁵.Then,in L₂ region,significant distinction arises of amplitude and frequency of the vibration,force coefficient and phase shift to those in region L₁.And the equilibrium position of the vibration of the plate shifts to a random side away from the centerline.In this region,these characteristics divergent according to the difference of cor-ner radius,and Ae=8×10³ is founded to be the critical normalized elastic module where di-vergence occurs when corner radius varies.And the last,in both D₁ and D₂ regions,the ampli-tude of the vibration of the plate and force coefficients are all in its lowest level and the fre-quency of the vibration is the same as that of wake shedding.The wake shedding pattern is“2S”pattern in all typical cases when R=0.0D while“2P”pattern when R=0.2D and R=0.5D.At last,the features of multidimensional fluid-induced vibration of the system of rigid bluff body with flexible splitter plate which is mounted on a spring support,are studied.The impact of rigidity of the plate and the spring support on VIV and galloping of the system are mainly discussed in the section.Solutions show that:When U _s^*=9,the amplitude of the system is small and the phase shift increases with the increase in U _p^*in the region of U _p^*≤10 while the amplitude boosts and the phase shift decreases with the increase in U _p^*in the region of U _p^*≥12.On the condition of relative large U _s^*,galloping is observed in the region of U _p^*≤10.However,it is suppressed when 14≤U _p^*≤18,in which the amplitude and phase shift un-dergo a jump.It seems that there is an optimal rigidity of plate for the system,which avoids severe VIV and suppresses galloping at the same time.The optimal rigidity of plate is founded to be Ae=1.26×10³（U _p^*=10.7）for the system with corner radius R=0.2D and the length of plate L=2D.