The horseshoe vortex and vortex shedding around a vertical wall-mounted cylinder exposed to waves

Abstract

This study concerns the flow around the base of a vertical, wall-mounted cylinder - a pile - exposed to waves. The study comprises (i) flow visualization of horseshoe-vortex flow in front of and the lee-wake-vortex flow behind the pile and (ii) bed shear stress measurements around the pile conducted in a wave flume, plus supplementary bed shear stress measurements carried out in an oscillatory-flow water tunnel. The Reynolds number range of the flume experiments is ReD = (2-9) x 103 and that of the tunnel experiments is ReD= 103—5 x 104, in which ReD is based on the pile size. Steadycurrent tests were also carried out for reference. The horseshoe-vortex flow (like leewake-vortex flow) is governed primarily by the Keulegan-Carpenter number, KC. The range of KC was from 0 to about 25 in the flume experiments, and from 4 to 120 in the tunnel experiments. The experiments were conducted mainly with circular piles. The results indicate that no horseshoe vortex exists for KC < 6. The size and lifespan of the horseshoe vortex increase with KC. The influence of the cross-sectional shape of the pile on the horseshoe vortex was investigated. The results show that a square pile with 90° orientation produces the largest horseshoe vortex while that with 45° orientation produces the smallest one, the circular-pile result being between the two. The influence of a superimposed current on the horseshoe vortex was also investigated. The range of the current-to-wave-induced-velocity ratio, Uc/Um, was from 0 to about 0.8. The overall effect of the superimposed current is to increase the size and lifespan of the horseshoe vortex. This effect increases with increasing Uc/Um. Regarding the near-bed lee-wake flow, the flow regimes observed for the two-dimensional free-cylinder case exist for the present case, too, but with one exception: in the present case, no transverse vortex street was observed in the so-called single-pair regime. The results show that the bed shear stress beneath the horseshoe vortex and in the lee-wake area is heavily influenced by KC. The amplification of the bed shear stress with respect to its undisturbed value is maximum (O(4)) at the side edges of the pile, in contrast to what occurs in steady currents where the maximum occurs at an angle of about 45° from the upstream edge of the pile with an amplification of O(10).

Numerical Study on Hydrodynamic Force and Wave Induced Vortex Dynamics around Cylindrical Pile

“…It can be seen that when KC is very small, the horseshoe vortex may not even be formed. Instead, for the large KC the flow in each half-period is similar to when steady current, which are in line with Sumer et al results [1]. In addition to Q criterion, the vorticity field is investigated for all cases.…”

“…Four cases of experimental studies of Sumer et al [1] with different wave characteristics are numerically modelled to investigate the influence of KC number on the hydrodynamic forces acting on pile and vortex dynamics around the pile. In all four cases wave tank dimensions were equal to lx= 26.5 m, lz= 0.6 m and h= 0.8 m. Table 1 presents the wave and the pile characteristics.…”

“…Consequently, a great deal of effort is required to investigate the vortex dynamics around the pile. For the large piles, flow does not separate, hence no vortices occur; while, reflection and diffraction occur [1]. It is beyond the scope of this paper to investigate on the large piles.…”

“…For the slender piles the flow field changes significantly with the increase of disturbance around the pile. At upstream of the pile, the horseshoe vortex is formed due to rotation in the incoming flow; the lee side vortices are caused by the rotation in the boundary layer over the surface of the pile [1]. For the intermediate piles, the turbulence around them is more complex.…”

“…Due to the importance of wave-pile interaction, both physical and numerical modeling of the wave-pile interaction has been of great interest in the last decades. Sumer et al [1] carried out vast experiments on flow passing over vertical cylinders as well as the wave induced vortex shedding around vertical cylinders. A range of different KC numbers is used to investigate its influence on different parameters around the pile e.g.…”