2. Bore Impingement on a Vertical Cylinder
The flow around the obstacles is described here. Both velocity and surface data are used in combinations with video footage. The main focus is the bore generated using h1 = 250 mm, where h1 is the initial water impoundment depth behind the gate, and the column is placed in the initial water depth h0 = 20 mm.
Figure 2.1 shows a series of photographs captured by a high-speed camera at 100 frames per second of the upstream side of the circular column. Each photo is marked with the elapsed time since the gate opening. Figure 2.1a shows the splash-up on the upstream side of the column just after the bore has arrived. After the initial impact, there forms a compact surface roller right upstream of the column (Fig. 2.1b). This heap of water around the column quickly flattens out both in the upstream direction and towards the sides of the tank (Fig.2.1c). When the wave coming off the column reaches the sidewalls (Fig. 2.1d), a wave forms over the whole width at the upstream edge of the column (Fig. 2.1e) which then starts to propagate upstream (Figs. 2.1f–h). A smaller wave can be seen moving at an angle from the sidewalls.
Figure 2.1. Views of the flow around the circular column from upstream for h1 = 250 mm.
Figure 2.2 shows the temporal variation of the water surface upstream of the circular column; the surface profiles are captured with the laser-induced fluorescent technique by illuminating the vertical longitudinal plane along the centerline of the column. It shows the bore propagating towards the column and then impinging it. In this graph the front edge of the column is at x = 0, z is measured upward from the bottom of the tank and t = 0 when the gate starts to open. After the initial splash-up that exceeds z = 250 mm, the water level at the upstream edge of the column remains constant, approximately 170 mm. The smooth water surface away from the impinging disturbance during t = 3.5 to 4.9 s is at about h2 = 90 mm but with a small-but-adverse water-surface gradient, i.e. gradual increase in water depth toward the complex flow disturbance (i.e. surface roller) in front of the cylinder. Throughout the process, the surface roller formation is confined to the area extending about 100 mm upstream of the column.
Figure 2.2 also exhibits the significant wave in the duration of t = 5 and 7.5 s: its peak is clearly seen at x = -300 mm at t = 6.6 s. This is the influence of the reflected wave from the sidewall that was observed in Figs. 2.1 f –h (t = 5.36 – 6.38 s). This is only the first one of two prominent waves propagating upstream. The second wave is more gradual and can be seen at x = -300 mm at t = 8.9 s. The second wave appears to be affected by additional reflections occurring in the tank. These waves – presumably induced by the flow blockage similar to the chocking phenomenon described in a steady open-channel flow – are caused by the insufficient breadth of the laboratory tank together with the flow condition that is very close to “critical” in the laboratory coordinate system: as shown in Table 1. Hence a small disturbance can trigger the chocking phenomenon that causes the upstream flow condition being subcritical: F2 < 1.0.
Figure 2.2. Evolution of the water-surface profile in the vertical plane at the centerline upstream of the circular column for h1 = 250 mm. The upper sketch depicts a plan view of the vertical laser sheet relative to the circular cylinder.
Figure 2.3 shows the temporal variation of the water surface upstream of the circular column with expanded detail near the time of initial impingement of the bore on the column. At t = 3.06 s the arriving bore is first seen. The bore surface at the toe is quite irregular as can be expected from the overturning and air entrainment at the bore face. At t = 3.23 s the water hits the structure and begins to climb up the front face. As the bore continues to impinge on the column, both the water level on the column and the depth of flow upstream increase. The runup on the column surface reaches a maximum of 270 mm at t = 3.5 s and begins to break, sending the broken volume of water back upstream. This blocked heap of water reaches x = -100 mm at t = 3.8 s.
Figure 2.3. Evolution of the water-surface profile in the vertical plane at the centerline upstream of the circular column for h1 = 250 mm. Expanded view near the initial impact.
Figure 2.4 shows a series of 8 photographs – captured by the high-speed camera – of the wake of the large circular column for the case of h1 = 250 mm. In Fig. 2.4a the front of the bore has passed the column. Most of the water shoots straight downstream, whereas only a small portion bends around the column and moves towards the centerline (Fig. 2.4b). The bore front has traveled about two diameters downstream before the two sides meet in the wake (Fig. 2.4c). Figure 2.4d shows the wake during the impact of the two swerving fronts. They originally flow past each other (Fig. 2.4e) but soon so called rooster tail forms at the junction of the opposite flows as can be seen in Fig. 2.4f. The rooster tail is unsteady and oscillates around the centerline (Figs. 2.4g and h).
Figure 2.4. View of flow around the circular column from downstream for h1 = 250 mm
Figure 2.5 shows the velocity fields at t = 3.886 s measured at z = 15 and 35 mm above the floor, respectively, by DPIV. The flow field presented in each figure is a montage of 9 DPIV panels (each panel is indicated with dotted lines): each panel has a 160 x 160 mm DPIV capture area, and the montage was made by the time-synchronized experiments. In spite of the nine-times repeated experiments of the transient and highly turbulent flow, the constructed montage appears very coherent as a whole, which demonstrates the excellent repeatability of the experiments. A slight positive velocity v (towards the sidewall) can be seen between the column and the wall in both figures. This corresponds the disturbance caused by the initial impact on the cylinder that generates a heap of water around the column then expands towards the sides of the tank (see Fig. 2.1c). The direction of v is negative (away from the sidewall in the figures) further downstream, showing the effects of the wall. Where positive and negative values of v converge behind the cylinder, the water surface is forced up forming what is termed a rooster tail because of its arcing narrow shape. The rooster tail is forming in the wake and is now a little to the left of the centerline. Figure 2.5b shows the velocity field at the same time as Fig. 2.5a, but 20 mm higher in the flow, i.e. z = 35 mm above the floor. The three-dimensional character of the wake is evident when the two figures are compared to each other. At different elevations in the flow, the velocity deviations from the downstream direction are significantly different at points with the same relative location with respect to the column. At the upstream side near the cylinder, the horizontal velocity is higher closer to the bottom. At the higher elevation, more of the fluid is swaying upwards as part of the buildup upstream of the column. Downstream of the column, the width of the separation area is greater higher up in the flow than near the bottom. Consequently the upward flow component is anticipated there that forms the rooster tail.
Figure 2.5. Horizontal velocity fields around the circular column at t = 3.886 sec and at a) z = 15 mm and b) z = 35 mm for h1 = 250 mm.
Figure 2.6 shows the temporal variation of the water-surface profiles at two different transverse cross-sections in the wake of the large circular column. Again, the water-surface profiles are captured with the laser-induced fluorescent technique by illuminating the vertical transverse plane at the location indicated in the figures. The centerline of the tank is at y = 0 and the sidewall at y = -305 mm. The water level is highest near the centerline. This rise represents the rooster tail that forms in the wake. It oscillates around the centerline (y = 0), with an oscillation period of about 1.0–1.5 s. From x = 350 to 470 mm, the rooster tail becomes lower and wider. At x = 350 mm, the water level at the sidewall rises to 107 mm right after the bore first passes, but establishes at about (76 ± 3) mm, so that is an overshoot of about 40 %. The same kind of behavior can still be seen at x = 470 mm, where the initial peak is 93 mm but the flow stays at about (60 ± 3) mm after that. Here the overshoot is 55 %. As we discussed, this overshoot is caused by the disturbance (shock) generated at the initial impact of the bore front onto the cylinder: by the initial impact, the pulse of swift wave propagates downstream as well as the gradual choking build-up upstream as discussed in Figs. 2.1 and 2.2.
Figure 2.6. Time history of surface data in the wake of the circular column at a) x = 350 mm, and b) x = 470 mm. The upper sketch in each figure depicts a plan view of the laser sheet location relative to the cylinder.