Numerical Investigations On Low-Re Flow Around And Vortex Induced Vibration Of A Dual-step Circular Cylinder

The mechanics characteristic and vibration response of variable cross-section structure such as the riser with buoyancy module under the action of complex currents is very complicated,but there are few related studies.This makes the design of the marine riser with buoyancy module too conservative and wasteful.Therefore,flow past a stationary dual-step cylinder under the uniform and shear flow conditions,as well as the freely vibrating dual-step cylinder in the uniform flow condition are numerically simulated utilizing the iterative and high precision immersed boundary method in this paper.The effects of the variation of the diameter ratio?D/d?,shear rate???and other parameters on the wake of the dual-step cylinder and the complex changes of the wake vortex topology are explored.A pair of streamwise vortices,i.e.,the center vortex,existed at the center of large cylinder in the near wake are found and defined in the flow around the dual-step cylinder under uniform flow condition.The N-S?D/d=2.00?mode,the transitional?D/d=1.43?and L-S?D/d=1.19?mode occur successively as the decreasing of diameter ratio.In the N-S mode,N-cell is dominant at the downstream of large cylinder,with a lower frequency compared to that of the uniform cylinder at the same Re.In the transitional,the vortex wake of the large cylinder alternates between L-and N-cell,and the corresponding frequency also varies.In the L-S mode,affected by the combine frequency originating from the wake interaction between the large and small cylinders,although the large cylinder wake is L-cell,its frequency fluctuates with time.The characteristics of the vortex wake in different cases were studied in detail,and the half-loop,double-half-loop and triple-half-loop connections,as well as the rule of vortex shedding and phase adjustment were observed and analyzed.Focused on the vortex-induced vibration of the dual-step cylinder under the uniform flow,it can be concluded that when the diameter ratio is relatively large?D/d=2.00?,the flow velocity will change over a long period of time,while the smaller diameter ratio will not.The vibration characteristics of the cylindrical structure are explored,it is found that the larger diameter ratio?D/d=2.00?causes the presence of lower beat frequency in the streamwise vibration,while there is only regular single frequency vibration during the smaller diameter ratio cases?D/d=1.43 and 1.19?.In the vortex wake of VIV cases,L-and S-cell will form the direct connection and the“X”connection at the diameter ration of D/d=2.00,and the same time,there is no half-loop connections between two S-cells with different sign.Moreover,the shedding process of S-cell is no longer locked in a fixed frequency and vortex intensity,and the phenomenon of irregular vortex shedding occurs.The essential reason is that the shedding frequency of the small cylinder vortex and the structural vibration frequency are not synchronized.In the flow around the dual-step cylinder under the shear flow condition,as the shear rate???increases,the flow and fluctuation energy downstream of the large cylinder gradually migrate to the high speed region,but a similar distribution to the uniform flow can still be observed.When Re<300?i.e.,there is no natural transition of three-dimensional wake?,distinct vortex cells(i.e.,S_low-,S_high-,L₁-and L₂-cell)appear in the wake of the dual-step cylinder in the shear flow.When Re>300,there are many streamwise vortices in the near wake,which are the outcome of the naturnal transition from two-dimensional to three-dimensional,causing the poor spanwise coherence.Therefore,the wake becomes very chaotic,and no obvious cells occur.