| The vortex induced vibration(VIV)of cylindrical structures extensively exists in engineering,studies on this problem are of great importance for both engineering and research fields.VIV is based on flow pasting cylinders,when the flow force acting on a flexible cylinder,vibration occurs,meanwhile the motion of the cylinder changes the status of the fluid in return,the interaction of the structure and the fluid is very complex and the influencing parameters are numerous,including flow velocity,pressure,viscidity,cylinder's mass,damp and stiffness.In this thesis,the author built numerical models to investigate the structure responses and the hydrodynamic features of VIV of a circular cylinder or a group of cylinders,and to analysis the force,flow field and vortex.In this paper,a finite difference method numerical model named CIP-ZJU(Constrained In-terpolation Profile method in Zhejiang University)is developed to study this problem.The govern equations are the Navier-Stocks equations and the mass conservation equations,this model,estab-lished in the Cartesian coordinate system and based on the CIP method,has shown good efficiency and accuracy in solving the N-S equations.In this model,the fluid-structure interaction is treated as a multi phase flow,where the liquid and solid phases are solved simultaneously.The solid body boundary is solved by applying an immersed boundary method.Firstly,the VIV of a singular circular cylinder was tested to ensure the accuracy of this model.The Reynolds Number is set at 100 and the mass ratio is 10.The results showed good agreements with previous papers.The cylinder entered "lock-in region" at reduced velocity Ur = 4-8,large amplitudes were observed and the largest amplitude occurred at Ur = 5.Out of the "lock-in region",the amplitude keeps at a lower level.Phase change were also observed at higher reduce velocities.Then,the VIV of two circular cylinders at tandem arrangements were studied.The flow-structure interaction process is more complex when involving multi cylinders.The different spac-ing ratios and reduced velocities are considered,and the upstream cylinder is set in two conditions,fixed or elastically mounted,while the downstream cylinder is always free to vibrate.The results showed that the amplitudes of the downstream cylinder are larger than a single cylinder.Finally,the VIV of three rigidly coupled cylinders arranged in equilateral triangle shapes.Three gap ratios which are L/D = 2,3 and 4 and three incident angles which are ? = 0°,30°and 60°.The cylinders are rigidly coupled so their relative positions are fixed and they have the same velocity and displacement.The results showed that the the three cylinder system has quite different dynamic response with that of single cylinder.The effect of incident angle is remarkable,when the cylinder group is asymmetry to the horizonal center line,the cylinders will diverge from the initial center.The highlights of this work includes:(1)It is the first time that the CIP method is used on VIV problems,providing reasonable results and a basis for further investigation.(2)Comprehensively studied the VIV of two tandem cylinders at spacing ratio of L/D = 2,4,6 and 8,analyzed the vibration response,the forces on the cylinders and the fluid information,pointed out that the evident interaction between the two cylinders appears at where L/D ? 4.(3)Numerically investigated the VIV of three rigidly coupled cylinders,the effects of incident angle and gap ratio are investigated. |
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