The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 29, Taipei, Taiwan THREE DIMENSIONAL STRUCTURES OF FLOW BEHIND A SQUARE PRISM Hiromasa Kawai 1, Yasuo Okuda 2 and Masamiki Ohashi 3 1 Professor, Disaster Prevention Research Institute, Kyoto University Gokasyo, Uji, Kyoto 611-11, Japan, kawai@dpri2.mbox.media.kyoto-u.ac.jp 2 Chief Research Engineer, Building Research Institute Tachihara 1, Tsukuba, Ibaraki, 35-82, Japan, y_okuda@kenken.go.jp 3Senior Research Engineer, National Institute for Land and Infrastructure Management Tachihara 1, Tshukuba, Ibaraki, 35-82, Japan, ohashi-m92j7@nilim.go.jp ABSTRACT Three dimensional structures of steady and unsteady flows behind a square prism with aspect ratio of 2.7 in a smooth flow, are investigated by PIV technique synchronizing with velocity measurement by a hot wire anemometer. It was seen that an arch-type vortex is formed behind the prism. A stagnation point is observed in the wake at a location of 1.75D behind the prism and.3h above the floor, where D is width and H is height of the prism. Therefore flow over the prism does not attach on the floor but runs away some distance above the floor. When separated shear layers are rolled up to form Karman vortex in a wake, the arch-type vortex is still keeping its form in the formation region though the vortex line is twisted very much. As the vortex is growing and moving downstream, the vortex line is stretched in a stream-wise direction near the tip of the vortex which does not move and locates stationary just behind the prism at any instant. KEYWORDS: WAKE, PIV, KARMAN VORTEX, 3D PRISM, ARCH-TYPE VORTEX Introduction Flow structures behind various buildings have been investigated as CFD and PIV techniques have been developing and using widely. However, as three dimensional flows around buildings are very complicated, detail of the flow structure is still not so clear. Particularly, an interaction between a flow over a top of a building and vortices formed by separated shear layers from side faces is still uncertain until now. Three dimensional flow structures behind a square prism in smooth flow are discussed in the paper based on results of flow measurements by PIV technique synchronized with velocity measurement. According to the investigation, vortex lines of vortices from the both sides of the prism connect to that of a vortex formed by the flow over the top of the prism to organize an arch- type vortex in a wake. The arch-type vortex is clearly seen not only in an ensemble averaged mean flow but also is still keeping during Karman vortex formation in unsteady flow. When Karman vortex is glowing and moving in the formation region, the vortex line of the arch-type vortex is stretched to the stream wise direction near the tip of the vortex, but the position of the tip does not move and locates just behind the prism at any instant. Experimental arrangements Wind tunnel experiments were carried out at a wind tunnel of Building Research Institute, Japan. In order to avoid an effect of naturally developing boundary layer on the tunnel floor, a temporally floor was set at 3cm above the tunnel floor. A square prism of
which section is 5mm x 5mm and height is 135mm was set at a position of 8cm from the windward edge of the temporally floor. Figure 1 shows profiles of mean velocity and turbulence intensity at the position of the prism. Effect of a boundary layer developed on the temporally floor is observed up to 4mm above the floor. The flow is uniform and the turbulence intensity is below 1% beyond 4mm. Mean wind velocity is 3m/s in the experiment. z/h, Height.8.7.5.3.1.8 1 1.2 U/Uz/H=.7, Mean velocity Two dimensional PIV measurements were carried out in 17 horizontal sections of which height is 1mm to 17mm every 1mm interval, and 17 vertical sections from the center line of the prism to ±4mm every 5mm interval. In the measurements, instanttaneous velocity vectors at 63 x 63 points were calculated from two images, which are taken by a highspeed video camera 5msec interval. 58 sets of the images are taken for 3Hz rate in a run. In order to investigate an unsteady flow pattern during Karman vortex is been forming, velocity fluctuation was measured at a position of 15mm apart from the windward corner of the prism by a hot-wire anemometer synchronizing with the PIV measurement as is shown in Figure 2. Each set of the images is sampled conditionally based on the velocity signal, and then is ensemble averaged..8.7.5.3.1.5.1.15 Iz, Turbulence intensity Figure 1 Profiles of mean velocity and turbulence intensity Laser sheet X z/h, Height Figure 2 Experimental arrangement Y Hot wire z=65mm 15mm D=5mm Structure of time averaged flow Figure 3 shows patterns of ensemble averaged mean stream lines for the typical horizontal sections. A pair of vortices and a divided point of stream lines are observed when z/h is.74~.96. When z/h is 1.4, effect of the vortices is still observed just behind the prism, but is not so obvious when z/h is 1.11. A flow just above the top face of the prism at z/h=1.11 shows very an attractive pattern of stream lines. Flow coming from upwind is drawn into the face at a center of
the face. This means than the laser sheet should crosses the separated shear layer at the point. The crossing point moves downward near the side ridges, so the separated shear layer is approaching to the face toward the side ridge. On the other hand, the pattern of the stream line at z/h=1.4 is very complicate, which shows the flow in the separated shear layer. Many singular points exist in the pattern. Figure 4 shows patterns of ensemble averaged mean stream lines for the typical vertical sections. A vortex with a horizontal axis is formed near the top just behind the prism. The dividing stream line for the flow over the top meets the dividing stream line from the floor at z=.3h and x=1.75h in the center section to be a stagnation point in the wake. Therefore, the flow over the top does not attach on the floor. The dividing stream lines are approaching the rear face of the prism when y/d is increasing, which correspond with a cross line of the dividing stream lines in the horizontal section shown in Fig.3 and the vertical sections. When y/d=, the vortex near the top still exists, and the other vortex-like flow pattern is seen near the bottom. When y/d is and.8, flow patterns in the separated shear layer of the side face are observed. The patterns of the stream line are so complicated that it is not so easy to image the flow structure. According to the pattern of the singular lines, the flow may be consisted by three or four cells of the shear z/h=.7 z/h=.3 z/h=.59 z/h=.89 z/h=.96 z/h=1.4 z/h=1.11 Figure 3 Stream lines of mean flow in horizontal sections. y/d= y/d= y/h= y/d= y/d=.8 y/d=1. Figure 4 Stream lines of mean flow in vertical sections.
layer or the shear layer is waving in the vertical direction. Figure 5 shows the vertical profiles of the downstream positions of the vortex center and the dividing stream line crossing point shown in the horizontal section of Fig.3. When z/h is.7 to 2, x/d of the vortex center is.75. The vortex is approaching to the prism when z/h is 2 to.37. When z/h is.37 to.55, the position of the vortex is immovable of which x/d is constant of.55. When z/h is larger.8, the vortex is approaching rapidly to the prism. The position of the crossing point of the divided stream lines is nearly constant of 1.75D when z/h is smaller than.5, then is approaching to the prism. Stream wise position of the vortex is plotted against the lateral position for various heights in z/h, Height.8 Fig.6. The vortex locates inside the projected area of the prism near the bottom and the top, and it locates outside around the central height. According to Fig.6, a line of the vortex center may be spiral. Fig.7 shows velocity vectors in three typical cross sections perpendicular to flow. It can be seen that flow moves upward and diverges outside just behind the prism. 1 Center of vortices Divided point of stream lines.5 1 1.5 2 x/d, Distance from the prizm Figure 5 Stream-wise position of center of vortex and crossing point of dividing stream lines. y/d, Across wind direction 1.8 z/h=.96 z/h=.7 5.5.75 1 x/d, Along wind direction Figure 6 Projective position of center of vortex. x/d=1/12 x/d=7/12 x/d=11/6 x/d=11/6 7/12 1/12 Figure 7 Velocity vectors in cross sections perpendicular to flow. Flow moves downward from the top of the prism when x/d=7/12 where is the center of the vortex. At the wake stagnation point, velocity of the downward flow becomes very strong. Fig.8 shows contour maps of longitudinal vorticity in a section at x/d=11/6 perpendicular to flow and that in stream wise sections at y/d=8/5. Strong vorticity areas with opposite sign are
seen in the perpendicular section outside of the prism. The strong vorticity area is distributed outside the wake region of the prism as is shown in the map of the stream-wise section. Flow structure during Karman vortex formation In order to investigate the three dimensional structure of unsteady flow from 2D PIV measurement, conditional technique has been employed in the analysis. Figure 9 shows a conceptual diagram of the conditional sampling of PIV images. Velocity vector is sampled synchronizing with the hot wire signal at a particular phase of Karman vortex shedding and is ensembleaveraged. Figure 1 which is shown in a next page, x/d=11/6 shows ensemble PIV images averaged stream line patterns in a cycle of the formation and the shedding of Karman vortex. Left figures show those in a horizontal section at z/h=.3. Right figures show those in a vertical section at the center of the prism of y/d=. Rolling up of the separated shear layer begins near a leeward side corner of the prism, then the vortex is growing and moving downstream to the centerline, and sheds into the wake. Each picture is taken for 3Hz interval and the mean velocity is 3m/s, so Strouhal number is.83. As is seen in the stream line pattern in the vertical cross section, the vortex near the top of the prism exists at any instant for the Karman vortex y/d=5/8 Figure 8 Contour maps of longitudinal vorticity in cross section perpendicular to flow and that in stream-wise cross sections. Dark part shows large vorticity region in clock-wise direction. Wind velocity (m/s) 3.4 3.2 3 2.8 2.6 4 45 5 55 6 65 7 75 8 Number of frame Figure 9 Conceptual diagram of the conditional sampling of Across wind direction, y/d.8 - - - -.8 T= T=3/5 T=1/5 T= T=4/5 T=2/5 T=5/5 upper vortex lower vortex T=3/5.8 1 1.2 1.4 Along wind direction, x/d T=1/5 Figure 11 Position of Karman vortex during its formation in a cycle.
formation and does not move at all. The stream line pattern in the vertical cross section is different little from one instant to the other instant. Circles in the horizontal sections show position of the center of Karman vortex. Figure 11 which is shown in the previous page, shows projected positions of the Karman vortex during a cycle at z/h=.3. The vortex locates outside of the prism when the separated shear layer begins to roll up, and moves very slowly. Then the vortex moves rapidly to the center line of the wake, and sheds into the wake. Figure 12 shows stream line in horizontal sections at various heights at T=/5 which corresponds with the top figures in Figure 1. The vortex at the upper side is formed close to the center line near the floor, and it is away from the center line to the top of the prism. The vortex at the lower side disappears when z/h is larger than.74. Figure 13 shows the stream line in vertical sections at the instant of T=/5. Left and right figures correspond with the upper and the lower sides of the center line of the T=/5 1/5 1/5 2/5 3/5 3/5 4/5 T=/5 5/5 5/5 5/5 wake in the horizontal section of Figure 12. When the separated shear layer begins to roll up at the upper side, the vortex with the horizontal axis can be seen near the top of the prism even at y=d where is outside of the side face of the prism. On the other hand, the vortex with the horizontal axis is becoming to collapse apart from the center line in the lower side, then is separated to two vortices at y=d, and disappears at y=d. Figure 14 shows velocity vectors of three cross sections perpendicular to flow in Karman vortex formation at T=/5. When the separated shear layer rolls up to form the vortex 1/5 2/5 3/5 4/5 Figure 1 Stream lines in horizontal section at z/h=.3 and in vertical section at y/d= during Karman vortex formation in a cycle.
Z/H=. X Y y/d= Y=m Z/H=.3 y/d= y/d=- Z/H=.5 y/d= y/d=- x/d=2 1 1/3 Z/H=.7 y/d= Y/D=- Z/H=.8 y/d=.7 y/d=-.7 Figure 12 Stream line in horizontal sections at various heights at T=/5. Figure 13 Stream line in vertical sections at various transverse positions at T=/5. Right figures show the upper side and left figures show the lower side of Figure 12. x/d=1/3 x/d=1 x/d=2 Figure 14 Velocity vectors of cross sections perpendicular to flow in Karman vortex formation at T=/5. Positions of sections show in Figure 12.
at the left side as is shown in the left figure of Figure 14, flow moves upward outside of the shear layer. On the other hand, flow moves downward from the left side to form vortex like flow at a half height of the right side of the prism in the section near the right side vortex as is shown in the middle figure of Figure 14. When Karman vortex sheds into wake, flow begins to move downward to right from the left side near the top x/d=2 of the prism, and then turns its direction to left as is shown in the middle figure of Figure 14. Figure 15 shows contour maps of longitudinal vorticity in a cross section perpendicular to flow at x/d=2 and stream-wise cross sections at y/d=.7. It can be seen a large clock-wise vorticity area in the perpendicular section. The area corresponds with the position where the down-flow turns from right to left. Conclusions-three dimensional structure of wake According to the results shown in the previous chapters, 3D structures are imaged and their sketch are drawn in Figure 16 and Figure 17. An arch- type vortex is formed behind the prism both in the mean flow and in the unsteady flow during Karman vortex formation and shedding. When the Karman vortex is glowing and moving in the formation region, the vortex line is stretched to the stream-wise direction near the tip of the archtype vortex, but the position of the tip does not move and is located just behind the prism at any instant. References y/d=.7 Figure 15 Contour maps of longitudinal vorticity in perpendicular and stream-wise cross sections. Dark part shows a large vorticity region in clock-wise direction. Figure 16 Schematic diagram of wake of mean flow behind 3D square prism Hunt J. C. R., C. J. Abell, J. A. Petreka, and H. Woo, Kinematical Studies of the Flows around Free or Surface-mounted Obstacles; Applying Topology to Flow Visualization, Journal of Fluid Mechanics, vol.86, part 1, pp.179-2, 1978 Shinji Ito, Yasuo Okuda, Masamiki Ohashi, Yasuhito Sasaki, Tetsuo Matsuyama, Hitomitsu Kikitsu: Synchronous Measurement of Wind Flow and Wind Pressure around a Cubic Model -Instantaneous Reattachment on Surface, Proceedings of 11th International Conference on Wind Engineering (ICWE XI), 25.2 Figure 17 Schematic diagram of wake of unsteady flow during Karman vortex formation behind 3D square prism