FLUID FORCE ACTING ON A CYLINDRICAL PIER STANDING IN A SCOUR

BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications Milano, Italy, July, 20-24 2008 FLUID FORCE ACTING ON A CYLINDRICAL PIER STANDING IN A SCOUR Takayuki Tsutsui Department of Mechanical Engineering, The National Defense Academy, 1-10-20 Hashirimizu, Yokosuka, Kanagawa 239-8686, Japan E-mail: tsutsui@nda.ac.jp Key Words: Bridge pier, Horseshoe Vortex, Flow Visualization, Pressure Distribution, Scour, Scour Depth, Sand Transfer, Separation, Fluid Force Abstract Scours are often observed at the bottoms of bridge piers in rivers and at poles standing on sand. In this study, a bridge pier was selected for studying a cylindrical structure standing on sand. Local clear water scour around a cylindrical pier was studied in a wind tunnel. The characteristics of fluid flow and fluid force acting on a cylindrical pier standing in a scour were investigated with a pier and five different scour depths (scour depth/pier diameter = 0, 0.5, 0.7, 1.0 and 1.5). The diameter of the pier was 40 mm and the free stream velocity was 16 m/s, making the Reynolds number 4.2 10 4. Flow visualization was carried out using the surface oil-flow pattern and smoke-wire methods. The surface pressure distributions on the pier and scour were measured and the drag coefficient acting on the pier was determined by integrating the surface pressure distribution on the pier. The characteristics of the horseshoe vortex and drag acting on the pier standing on the scour were clarified. The results show that two horseshoe vortices are present near the root of the pier and the drag coefficient has an arc-shaped distribution with a minimum value halfway down the scour depth as the scour continues to grow deeper. At the final scour depth, a stagnant area is formed at the bottom of the scour. 1 INTRODUCTION Local scour is defined as the abrupt decrease in bed elevation near a pier due to the erosion of bed material induced by the local flow structure in the vicinity of the pier. According to previous studies [1, 2], the flow about a pier is dominated by the three vortex systems; a horseshoe vortex system, a wake vortex system and a trailing vortex system. It is well known that the horseshoe vortex system largely dominates the flow field around a pier. The horseshoe vortex surrounding a cylindrical pier has been captured in computation [3]. It was found that two distinct horseshoe vortices influence the scour formation. On the other hand, the creation of local scour at a pier is time dependent [4, 5]; the flow around the pier and the fluid force acting on the pier change with time. This paper will consider the flow mechanism around a pier standing on a local scour, especially the two horseshoes vortices, and the fluid force acting on the pier. 1

Figure 1 shows the distinction in depth between clear water scour and scour with continuous sediment motion. The depth approaches a limit asymptotically with clear water scour, while there are aperiodic oscillations in the scour depth with continuous sediment motion. This study addresses clear water scour. Scour experiments are typically carried out by a flume [4, 5]. But according to previous studies [6, 7], the same scour characteristics can be obtained using a low speed wind tunnel, so the experiments in this study are conducted in a low speed wind tunnel. The increasing tendency of the clear water scour depth with Ut/D from a previous study [4] is shown in Fig. 2. ds in the figure is medium size of a sediment particle 3 4 In general, the front part of the scour depth progresses first for 4 10 Ut / D < 3 10. 4 5 5 In the latter part, 3 10 Ut / D < 2 10, the progress is slow. For 2 10 Ut / D, the scour depth reaches its final depth. 2 EXPERIMENTAL APPARATUS AND METHOD The flow geometry and coordinate system for the experiments are shown in Fig. 3. A cylindrical pier, with diameters D of 40 mm, was made of acrylic resin. Five different depths of scour models were used for this investigation: H/D = 0, 0.5, 0.7, 1.0 and 1.5. All of the scour models were made of acrylic resin. Experiments were performed in a low speed wind tunnel with a 400 mm high, 300 mm wide and 1000 mm long working section. The free stream velocity U was 16 m/s and the Reynolds number Re based on D was 4.2 10 4. The surface pressure on the pier and scour were measured by a multi-tube pressure manometer connected to 0.6 mm diameter pressure taps arranged along a spiral arrangement at ten-degree intervals on the surface of the pier and scour. The pressure measurement system is shown in Fig. 4. The entire pier and scour surface pressure can be determined by rotating the model on its center axis. Visualization of the flow around the pier and scour was performed using the surface oil flow pattern method and the smoke wire method. 3 RESULTS AND DISCUSSION 3.1 Flow Visualization Figure 5 shows the surface oil flow pattern on the cylindrical pier and scour at various depths. The surface of the pier and scour were covered with a black paint to provide the highest possible contrast to the white oil film. (a) clear water scour (b) scour with continuous sediment motion Fig. 1 Time variation of scour depth (1) Fig. 2 Scour depth 2

Fig. 3 Flow geometry and coordinate system Fig. 4 measurement system On the pier, the white oil film remains at two points on the front face, which can be attributed to the interaction of the two horseshoes vortices shown in the (d) flow schematic. One horseshoe vortex is large and rotates clockwise, and another is small and rotates counter clockwise. The oil flow pattern on the rear face is remarkable; a sharp separation line is formed above the rear stagnation point. This fact suggests that a strong flow blows from the bottom of the scour up. This characteristic is detailed in Fig. 9. On the scour itself, a circular separation line is observed, which is caused by the large horseshoe vortex. The deeper the scour, the wider the separation area. To consider the system of horseshoe vortices on the scour, the oil flow pattern photographs from Fig. 5 (a) and (c) were enlarged and are shown in Fig. 6. The top of 6 (a) and (b) are photographs, while the bottoms are schematics of the oil flow pattern. The inner 3

circle shows the pier profile in (a) and (b). The flow image is shown in (c). The streak line caused by the horseshoe vortices is distinct in this figure. (a) H/D = 0.7 (Ut/D = 1.8 10 4 ) (b) H/D = 1.0 (Ut/D = 4.5 10 4 ) (c) H/D = 1.5 (Ut/D = 2.7 10 5 ) (d) Flow schematic Fig. 5 Oil flow patterns on the cylindrical pier and scour surface 4

Fig. 7 shows a section of these horseshoe vortices in front of the pier. In the cross section of the horseshoe vortices, a large vortex rotating clockwise and a small one rotating counterclockwise, which is formed corner of the scour bottom and pier root, are observed. In (b), there are several eddies on the scour slope. However, this study does not discuss this fact, but rather focuses on the large and small eddies. In an attempt to look at the growth of the small horseshoe vortex, a flow visualization was carried out using a flume. The photograph and its growth image are shown in Fig. 8, in which a spiral vortex can be observed. (a) H/D = 0.7 (Ut/D = 1.8 10 4 ) (c) flow image (b) H/D = 1.5 (Ut/D = 2.7 10 5 ) Fig. 6 Oil flow patterns on the scour surface (a) H/D = 0.7 (Ut/D = 1.8 10 4 ) (b) H/D = 1.5 (Ut/D = 2.7 10 5 ) Fig.7 Horseshoe vortices in the front of the pier 5

According to the results of the flow visualization, the horseshoe vortex system can be characterized as shown in Fig. 9. Fig. 9 (a) and (b) are rear view photograph of the x = 0 section. Two horseshoe vortices on both sides of the pier can be observed. Fig. 9 (c) shows a two horseshoe vortex image. The inner horseshoe vortex, which is rotating counter clockwise, surrounds the root of the pier and finally rolls up near the rear face of the pier. This vortex is temporarily called the roll-up vortex. This vortex moves the sediment behind the pier. The outer horseshoe vortex, which is rotating clockwise, moves sediment outside of the scour. Aggradation and degradation are caused by these two horseshoe vortices. Fig.8 Flow visualization by using flume and flow image (H/D=0.7, U=10 cm/s, Re=3.5 10 3 Ut/D=1.8 10 4 ) (a) H/D = 0.7 (Ut/D = 1.8 10 4 ) (c) horseshoe vortex system image (b) H/D = 1.5 (Ut/D = 2.7 10 5 ) Fig.9 Horseshoe vortex system 6

3.2 Pressure distribution on the pier and scour Figure 10 shows the pressure coefficient, Cp, distributions on the circumference of the cylindrical pier. These distributions are classified into three types. (a) H/D = 0.7 (Ut/D = 1.8 10 4 ) (b) H/D = 1.0 (Ut/D = 4.5 10 4 ) (c) H/D = 1.5 (Ut/D = 2.7 10 5 ) Fig. 10 Pressure coefficient distribution on the cylindrical pier surface 7

The first is a Cp distribution like a two-dimensional circular cylinder. The case of Z/D = 0.75, 1.0 for H/D = 0.7, 1.0 and 1.5 can be classified as this type. The second is the Cp distribution with an extremely high back pressure. The cases of Z/D =-0.50 ~ 0.25 for H/D = 0.7, Z/D =-0.75 ~ 0 for H/D = 1.0 and Z/D =-0.50 ~ 0 for H/D = 1.5 can be classified as this type. The roll-up vortex affects the back pressure of the pier. The third is the distribution with little change in Cp. The cases of Z/D =-1.25 and -1.0 for H/D =1.5 can be classified as this type. This third type appears in the final depth condition only. The pressure coefficient contours on the scour are presented in Fig. 11. A white circle in the center of the figure represents the pier. The numbers in the figure are the values of Cp. The figures show the pressure change along the whole scour. A positive pressure area around root of the pier increases as the scour progresses. (a) H/D = 0 (Ut/D = 0) (d) H/D = 1.0 (Ut/D = 4.5 10 4 ) (b) H/D = 0.5 (Ut/D = 9 10 3 ) (e) H/D = 1.5 (Ut/D = 2.7 10 5 ) (c) H/D = 0.7 (Ut/D = 1.8 10 4 ) Fig. 11 Pressure coefficient contour on the scour surface 8

Figure 12 presents the pressure coefficient distribution along the centerline of the cylindrical pier and scour. The inside and outside from the outline of the pier indicate negative and positive pressure areas, respectively. The upper and lower side from the ground and scour level indicate negative and positive pressure areas, respectively. (a) H/D = 0 (Ut/D = 0) (b) H/D = 0.5 (Ut/D = 9 10 3 ) (c) H/D = 0.7 (Ut/D = 1.8 10 4 ) (d) H/D = 1.0 (Ut/D = 4.5 10 4 ) (e) H/D = 1.5 (Ut/D = 2.7 10 5 ) Fig. 12 Pressure coefficient distribution of the cylindrical pier and scour surface on the center line 9

Fig.13 Local drag coefficient of the cylindrical pier Fig. 14 Local drag coefficient of the cylindrical pier under the ground level The distribution on the front face of the pier, Cpf, reaches a minimum value between the two stagnation points shown in Fig. 5. On the rear face, the back pressure coefficient, Cpb, reaches a maximum value on the root, which is the rear stagnation point. The value of Cpb decreases as it moves up because of the roll-up vortex. At the root of the pier and the bottom of the scour, the positive pressure area enlarges with the scour depth, because the pier was surrounded with the horseshoe vortices. 3.3 Drag force acting on the pier The local drag coefficient of the cylindrical pier CDz was obtained by integrating the pressure coefficient distribution on the circumference of the cylindrical pier. The local drag coefficient CDz is plotted against Z/D in Fig.13. Every distribution, except H/D = 0, follows the same tendency. That is, the distribution has a maximum value at about Z/D = 0 and a minimum value at Z/D = -0.7 ~ -0.3, which is approximately the middle of the scour depth. Figure 14 shows the change of CDz with scour depth H under the ground. For H/D = 0.5, 0.7 and 1.0, except for H/D = 1.5, CDz has a distribution in an arc with the minimum value at Z/H = 0.5. In the case of H/D = 1.5, which is the final depth of the scour, little drag acts on the pier for Z/H 0. 5. 4 CONCLUSIONS Experimental studies were conducted on the flow and fluid force acting on a cylindrical pier standing on a scour using a low speed wind tunnel. The results showed that two horseshoe vortices, one of which rotates clockwise while the other rotates counter clockwise, primarily dominate the flow around the pier and scour. In the final depth condition, the root of the pier was found to be surrounded with the horseshoe vortices, and a stagnant region formed at the root of the pier. The drag coefficient has an arc-like distribution with a minimum value equal to half the scour depth while the scour continues to grow deeper. 10

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