3D Effects on Vortex-Shedding Flow and Hydrodynamic Coefficients of A Vertically Oscillating Cylinder with A Bottom-Attached Disk

Vortex-shedding flow induced by the vertical oscillation of a cylinder with bottom-attached disks of different diameter ratio Dd/Dc and thickness ratio td/Dc is studied by a 3D （three-dimensional） numerical model developed in this paper, and compared with the results obtained through 2D （two-dimensional） numerical model. The high-order upwind scheme is applied to stabilize the computation, and convergence is accelerated by the multi-grid method. Qualitative and quantitative analyses of the differences between the 2D and 3D simulation results reveal the 3D effect on the flow field characteristics and hydrodynamic coefficients of the vertically oscillating cylinder with a bottom-attached disk. The 3D effect on the fluid field is mainly reflected in the significance of three vortex-shedding patterns： ωx has a greater effect on the flow fields around the sharp edges relative to the vortices generated in the 2D simulation. In the slice along the axial orientation, the vortex effect of ωy along the radial axis is smaller than that of ωx along the circumferential direction, indicating the radial effect on the velocity more pronounced than the circumferential effect around the sharp edges of the disk. The rotational interaction ωz of the fluid in the horizontal plane during the heave motion is insignificant. Based on the 2D and 3D simulation results, the turning points that separate the increasing regimes of the added mass coefficient and damping ratio are identified. The dependence of the turning point on the diameter ratio Dd/Dc and thickness ratio td/Dc are discussed in detail.

NUMERICAL SIMULATIONS OF THE VORTEX-SHEDDING IN FLOWS AROUND RECTANGULAR CYLINDERS

Flows around rectangular cylinders with a series of width-to-height ratios are calculated by means of the Improved Finite Analytic Method (IFAM) and the formation, development and shedding of vortices from the cylinders are simulated successfully. According to these results of time-dependent processes the physical phenomena in the flows are investigated in detail, and the discontinuity of Strouhal number is explained in the case of the width-to-height ratio equal to 3.0. The numer- ical solutions here show good agreement with the experimental results. In addition, based on several hundreds of the calculated flow patterns a moving picture is made by the computer image processing technology and recorded on a video tape, and then the vivid pictures of the physical process of vortex-shedding can be replayed later and analysed in detail.

Effect of perforation on flow past a conic cylinder at Re =100: wavy vortex and sign laws

In order to find the intrinsic physical mechanism of the original Kármán vortex wavily distorted across the span due to the introduction of three-dimensional (3-D) geometric disturbances,a flow past a peak-perforated conic shroud is numerically simulated at a Reynolds number of 100.Based on previous work by Meiburg and Lasheras (1988),the streamwise and vertical interactions with spanwise vortices are introduced and analyzed.Then vortex-shedding patterns in the near wake for different flow regimes are reinspected and illustrated from the view of these two interactions.Generally,in regime Ⅰ,spanwise vortices are a little distorted due to the weak interaction.Then in regime Ⅱ,spanwise vortices,even though curved obviously,are still shed synchronously with moderate streamwise and vertical interactions.But in regime Ⅲ,violently wavy spanwise vortices in some vortex-shedding patterns,typically an Ω-type vortex,are mainly attributed to the strong vertical interactions,while other cases,such as multiple vortex-shedding patterns in sub-regime Ⅲ-D,are resulted from complex streamwise and vertical interactions.A special phenomenon,spacial distribution of streamwise and vertical components of vorticity with specific signs in the near wake,is analyzed based on two models of streamwise and vertical vortices in explaining physical reasons of top and bottom shear layers wavily varied across the span.Then these two models and above two interactions are unified.Finally two sign laws are summarized:the first sign law for streamwise and vertical components of vorticity is positive in the upper shear layer,but negative in the lower shear layer,while the second sign law for three vorticity components is always negative in the wake.

AN EXPERIMENTAL STUDY OF FLUCTUATING LIFT ON A SQUARE-SECTION CYLINDER OSCILLATING TRANSVERSELY IN A UNIFORM STREAM

Experiments on a square section cylinder fixed and forced to oscillate transversely in a uni- form stream were conducted in a water tank.The Reynolds numberof the experiments is in the range of 3·10~3 tO 10~4,the amplitude to side length ratio A/D is up to 0.7 and the range of reduced velocity is 4.5<Vr<12.This study aims at investigating the lock-in phenomenon,the fluctuating lift and the phase shift between fluctuating lift and displacement of the oscillating cylinder.The problems on the aeroelastic insta. bility relating to present experimental results have been discussed.The flow visualization clearly shows that there are drastic changes of vortex-shedding from cylinder at the resonance point and the upper end of the lock-in range.The results of the flow visualization give better understanding of the physical mechanism of the phase shift.

Computations of unsteady transonic flow over airfoil at low Reynolds number

Transonic flow over a thin airfoil at low Reynolds number was studied numerically by directly solving two-dimensional full Navier-Stokes equations through 5th order weighted essentially non-oscillatory(WENO) scheme without using any turbulence model.A series of distinguished unsteady phenomena for a thin 2-D transonic airfoil flow were presented.Due to continuous adverse pressure gradient in the subsonic flow downstream of the sonic line,the unsteady separated boundary layer with main vortex and secondary vortex was developed at the rear of the airfoil.At the trailing edge,the vortex-shedding was characterized by periodical connection of the main vortex and secondary vortex on the other side of the airfoil.The unsteady separation and vortex-shedding occurred with the same period.On the airfoil surface,the average pulse pressure related to the unsteady supersonic region was obviously smaller than that related to the vortex-shedding at the trailing edge.With the attack angle increasing from 0°to 2°,the frequency of vortex-shedding decreases about 4.2%.At last,the turbulence intensity and many second-order statistics in the wake region were investigated.