Flow past a rotating circular cylinder 1 4

FLOW PAST A ROTATING CIRCULAR CYLINDER DUONG THI THU LINH NATIONAL UNIVERSITY OF SINGAPORE 2011 FLOW PAST A ROTATING CIRCULAR CYLINDER DUONG THI THU LINH (B. Eng (Hons.), M.Sc.) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINERRING NATIONAL UNIVERSITY OF SINGAPORE 2011 Acknowledgement Acknowledgement First and foremost, I would like to express my deepest appreciation to my supervisors, Associate Professor Luo Siao Chung and Professor Chew Yong Tian, for their valuable guidance and advice throughout this project. I would like to send my deep gratitude to them for being patient and supportive whenever I need their instruction and advice. They not only guide me with their valuable suggestions, but also teach me a lot in doing research. Being their student has been a great honour for me. I would like to thank all the staffs in the Fluid Mechanics Laboratory, namely Mr. Yap Chin Seng, Mr. Tan Kim Wah, Ms. Iris Chew, Ms. Lee Cheng Fong, Mr. James Ng, Mr. Looi Siew Wah for their help in my experiments. Special appreciation goes to Mr. Yap Ching Seng and Mr. Tan Kim Wah for their help in fabrication of my experimental test rig and advice in the set up design since my first day at NUS. I would like to thank Professor Lim Tee Tai for his advice in using the facilities in the Fluid Mechanics Laboratory. I would like to thank Dr. Lua Kim Boon for his help in guiding me with PIV measurement techniques. I would also like to thank Dr. Cui Yong Dong for his advice in hot-film measurement techniques. I would like to thank the National University of Singapore for offering me the post graduate research scholarship. Finally, I would like to thank my family members for their love and support. My deepest gratitude goes to my husband, Khang, and my son, Bon, for their continuous support and encouragement throughout my project. I Table of Contents Table of Contents Acknowledgement I Table of Contents II Summary IV List of Tables V List of Figures VI List of Symbols XIII Chapter Introduction 1.1 Background 1.2 Objectives and Scopes of the Project 1.3 Outline of the Thesis Chapter Introduction 1.1 Background 1.2 Objectives and Scopes of the Project 1.3 Outline of the Thesis Chapter Literature reviews 2.1 Flow past a stationary circular cylinder 2.1.1 Different regimes of flow past a stationary circular cylinder 2.1.2 Relationship of Strouhal number and Reynolds number 19 2.2 Flow past a Rotating circular cylinder 24 2.2.1 Vortex shedding structure 25 2.2.2 Vortex shedding frequency 38 2.2.3 Aerodynamics forces 40 Chapter The Experimental set-up and Techniques 43 3.1 Water channel 43 3.2 Experimental setup and techniques 44 3.2.1 Dye flow visualization 47 3.2.2 Particle tracking flow visualization (PTFV) 50 3.2.3 Hot-film measurement 53 3.2.4 PIV measurement 54 3.2.5 Force measurement 59 II Table of Contents Chapter Flow visualization and hot-film measurement 65 4.1 Flow past a stationary circular cylinder 67 4.1.1 Flow structure 67 4.1.2 Vortex spacing 72 4.1.3 Separation angle 74 4.1.4 St-Re relationship 75 4.2 Flow past a rotating circular cylinder 78 4.2.1 Case of <   2.3 78 4.2.2 Case of 2.3 <   91 4.3 Concluding remarks 97 Chapter PIV Measurement 5.1 Stationary cylinder 99 101 5.1.1 Flow structure in the surrounding of the cylinder surface 101 5.1.2 Flow structure in the spanwise direction of the stationary cylinder 111 5.2 Rotating cylinder 114 5.2.1 Flow structure in the surrounding region of the cylinder surface 115 5.2.2 Flow structure in the spanwise direction of the cylinder 154 5.3 Concluding remarks 165 Chapter Force Measurement 167 6.1 Measurement of lift and drag force 167 6.2 Lift coefficient 168 6.3 Drag coefficient 174 6.4 Lift to Drag ratio 175 6.5 Concluding remarks 177 Chapter Conclusion and Recommendation 178 7.1 Conclusion 178 7.2 Recommendation 183 List of References 194 III Table of Contents Summary Among various types of flow past a bluff body, flow over a circular cylinder is one of the most fundamental problems and is probably the most studied one. Unlike the flow over a stationary cylinder where the flow structure depends only on the Reynolds number, the flow past a rotating circular cylinder is dependent on both the Reynolds number and the speed ratio (α), which is defined as the ratio of the cylinder surface tangential velocity to the free-stream velocity. Although many investigations of the flow around a rotating circular cylinder have been conducted, a lot of uncertain issues remain. Further, most of the previous works are two-dimensional numerical studies and there are very few experimental studies. The present study is mainly experimental. The experiments will be conducted in four parts, including qualitative flow visualization, hot-film measurement, particle image velocimetry (PIV) measurement and force measurement. Dye flow visualization provides a visual understanding of the flow structures. In addition, the particle tracking flow visualization (PTFV) method is also used to study the flow at some high speed ratio and Reynolds numbers cases when dye visualization fails due to dispersion. Hot-film measurement detects the vortex shedding frequency of the cylinder. PIV measurement gives a good quantitative analysis of velocity and vorticity flow field. Finally, a load cell attached to the experimental set up measures directly the aerodynamic forces exerting on the cylinder. IV List of Tables List of Tables Table 2.1 Different ranges of flow past a smooth surface circular cylinder (regenerated in  Niemann and Holscher (1990)).  . 13 Table 2.2 Values of constants in the St‐Re formula.   20 Table 2.3 Summary of previous studies on vortex shedding of flow past a rotating circular  cylinder.   37 Table 2.4 Estimation of forces on rotating cylinder.   42 Table 4.1. Wake geometric parameters at Re = 141; 296 and 592.  . 73 Table 5.1 Spanwise instability wavelengths for stationary cylinder.  . 111 V List of Figures List of Figures Figure 2.1 Regimes of flow past a circular cylinder (Houghton and Carpenter (2003)).   8 Figure 2.2 Wake structure behind a circular cylinder (Ahlborn et al (2002)).   10 Figure 2.3 Karman vortex street at Re=140 (taken by Sadatoshi Taneda, regenerated in Van Dyke  (1982)).  . 11 Figure 2.4 Definition of recirculating bubble length (Silva (2003)).  . 11 Figure 2.5 Recirculating bubble length versus Re (Silva (2003)).  . 12 Figure 2.6 St‐Re relationship (Williamson (1988)).   14 Figure 2.7 Symmetry of mode A and mode B (Williamson (1996)).  . 15 Figure 2.8 Lengthening of formation region in mode B regime (Williamson (1996)).  . 16 Figure 2.9 Drag coefficient and Strouhal number versus Re in different flow regimes for rough  and smooth surface cylinder (Niemann and Holscher (1990)).  . 19 Figure 2.10 St‐Re relationship (Roshko (1954)).  . 21 Figure 2.11 Comparison between traditional form and new form of St‐Re relationship fitting onto  the numerical data of Henderson (1997) (Williamson and Brown (1998)).  . 23 Figure 2.12 Using 2 formulae of new St‐Re relationship ( St  A  B  ) to fit in the  Re experimental data of Williamson (1988) (Williamson and Brown (1998)).  . 23 Figure 2.13 St‐Re relationship (Bearman (1969)   24 Figure 2.14 Base pressure coefficient versus Reynolds number (Bearman (1969)).  . 24 Figure 2.15 Vortex shedding from a rotating cylinder at Re=200 (taken from computational result  reported in Mittal and Kumar(2002) with counter clockwise rotation and flow from left to right).    26 Figure 2.16 Vortex shedding from a rotating cylinder at Re=9000 (Dol et al. (2008)  with counter  clockwise rotation and flow from left to right).  . 26 Figure 2.17 Instantaneous streamlines at Re = 100, α = 0.5 (Chou (2000)).   28 Figure 2.18 Vorticity field of rotating cylinder at Re = 200 (Elakoury et al. (2008)).   29 Figure 2.19 Vorticity field of rotating cylinder at Re = 200 and different  (Mittal and Kumar  (2003)).  . 29 VI List of Figures Figure 2.20 Instantaneous streamlines at Re = 1000, α = 6 at (a) t = 1, (b) t = 3, (c) t = 5 and (d) t =  10 (Chew et al. (1995)).   30 Figure 2.21 Four vortices captured at Re = 100,  = 4.96 (Yildirim et al. (2007)).  . 33 Figure 2.22 Four vortices captured at Re = 100,  = 5.1 (Yildirim et al. (2007)).  . 34 Figure 2.23 Instability diagram of the rotating cylinder (regenerated from Elakoury et al. (2008)).    35 Figure 2.24 Instability diagram of the rotating cylinder (Stojkovic et al. (2003)).  . 35 Figure 2.25 St vs. α at different Re (regenerated from Kang et al. (1999)).  . 38 Figure 2.26 St at different speed ratios in (a), Mittal and Kumar (2003) and (b), Elakoury et al  (2007).   39 Figure 2.27 St at different speed ratios in the 2nd vortex shedding regime (Stojkovic et al. (2003)).    39 Figure 2.28 Lift coefficient versus α at Re = 200 (Mittal and Kumar (2003)).   41 Figure 3.1 The water channel.   44 Figure 3.2 The water channel’s test section (the flow is from left to right in this picture).   44 Figure 3.3 Gear and belt mechanism.   46 Figure 3.4 Cylinder end sits in the base plate in the test section (flow is from left to right).   46 Figure 3.5 Summary of different experimental methods.   47 Figure 3.6 Dye flow visualization (flow is from left to right).  . 48 Figure 3.7 Dye flow visualization set up installed above the water channel.   49 Figure 3.8 Air‐tight junction connecting cylinder and dye reservoir.  . 49 Figure 3.9 Overall dye flow visualization set up (flow from left to right).  . 50 Figure 3.10 Overall PTFV set up (flow from left to right).   52 Figure 3.11 Laser beam emitted from Suwtech LDC‐2500 to water channel flow.  . 53 Figure 3.12 Chain of component connections in CTA setup (from Dantec hot‐wire anemometer  user guide).  . 53 Figure 3.13 Setup for Hot film measurement.  . 54 Figure 3.14 PIV measurement principle (taken from Dantec PIV system document).   55 Figure 3.15 Setup for PIV measurement in streamwise plane.   56 VII List of Figures Figure 3.16 Setup for PIV measurement in spanwise plane . 56 Figure 3.17 Camera view in streamwise PIV setup.  . 57 Figure 3.18 Sketch of laser light direction and the shadow region.  . 57 Figure 3.19 Replacement of shadow region in counter‐clockwise rotating cylinder to get whole  field data.   58 Figure 3.20 Load cell and measurement resolution and range (taken from “ATI product  specification”).   59 Figure 3.21 Electronic hardware outline (taken from “ATI F/T DAQ installation and operation  manual”).   60 Figure 3.22 Force measurement setup.  . 62 Figure 3.23 Setup sitting on a testing table.  . 63 Figure 3.24 Force measurement setup sitting on the load cell.  . 63 Figure 3.25 Load cell supporting set up through supporting plate 2 and fixed to supporting plate  3 on the top of the water channel.   64 Figure 4.1 Definition sketch of flow past a rotating circular cylinder, free stream velocity and the  cylinder rotation are shown in their positive direction.  . 66 Figure 4.2 Cartesian coordinates and vertical mid‐plane.   66 Figure 4.3 Evolution of dye pattern in one cycle of vortex shedding at Re = 141 (stationary  cylinder).  . 67 Figure 4.4 Karman vortex street (stationary cylinder). a) at Re = 140 (Van Dyke 1982); b) at Re =  141 (present study).  . 68 Figure 4.5 Evolution of dye pattern in one cycle of vortex shedding at Re = 296 (stationary  cylinder).  . 68 Figure 4.6 Evolution of dye pattern in one cycle of vortex shedding at Re = 592 (stationary  cylinder).  . 69 Figure 4.7 Vortex shedding at a) Re = 110, b) Re = 206, and c) Re = 1067 (stationary cylinder, flow  from left to right).  . 70 Figure 4.8 Spanwise vortex shedding at Re = 226 (stationary cylinder, time sequence from 1‐6).    71 Figure 4.9 Spanwise vortex shedding at Re = 319 (stationary cylinder, time sequence from 1‐6).    71 Figure 4.10 Spanwise vortex shedding at Re = 455 (stationary cylinder).  . 72 VIII Chapter Flow visualization and hot-film measurement the near-surface fluid region, resulting in the delay of boundary separation which can be seen by the displacement of the separation point in the cylinder rotation direction. On the other side of the cylinder, the increase in relative motion between the moving surface and the free stream flow shifts the separation point further upstream. This upstream movement increases with α. a) b) c) d) Figure 4.21 Flow separation (close up view) at Re = 164 and a) α = 0, b) α = 0.6, c) α = 1.2, and d) α = 2.5. b. Particle image flow visualization (PTFV) The vortex shedding is also observed (as seen in the wavy form of the cylinder wake) in PTFV experiment for Re = 110 (Figure 4.22), Re = 206 (Figure 4.23) and Re = 1067 (Figure 4.24). The PTFV flow images show the wavy form of the cylinder wake in stead of the vortex form (as observed by dye flow visualization) because the camera was fixed with the ground. In order to capture the vortex images, it’s better to have the camera travelling with the flow. The results show that the vortex street is still observed at Re = 110, Re = 206 and Re = 1067 up to  = 2. However, the wavy form of flow trace at Re = 206 is more “straighten” than that at Re = 110, and at Re = 1067 is more “straighten” than that at Re = 206. This shows that at the same , the cylinder wake becomes narrower at higher Re. 83 Chapter Flow visualization and hot-film measurement The results also show that the cylinder wake is deflected in one side of the cylinder towards the rotation direction of the cylinder. a) b) c) Figure 4.22 Vortex shedding at Re = 110 and a)  = 1, b)  = 1.5, c)  = 2.0 (flow from left to right, anti-clockwise rotation). a) b) c) Figure 4.23 Vortex shedding at Re = 206 and a)  = 1, b)  = 1.5, c)  = 2.0 (flow from left to right, anti-clockwise rotation). 84 Chapter Flow visualization and hot-film measurement a) b) c) Figure 4.24 Vortex shedding at Re = 1067 and a)  = 1, b)  = 1.5, c)  = (flow from left to right, anti-clockwise rotation). c. Vortex spacing and separation angle Based on the dye flow visualization results at Re = 141, the time averaged vortex spacing (Figure 4.25) and separation angle (Figure 4.26) are estimated at different speed ratios, based on the methods described in section 4.1.2 and 4.1.3, respectively. The data are calculated based on around 40 visualization images. 85 Chapter Flow visualization and hot-film measurement 2.5 a/D, b/D, a'/D, b'/D a'/D b'/D a/D 1.5 b/D b'/a' b/a 0.5  0 0.5 1.5  Figure 4.25 Vortex spacing at Re = 141 and <  < 2. The plot of vortex spacing shows an increase in longitudinal vortex spacing a/D with increasing . The lateral spacing b/D initially decreases slightly with  until  of around 0.8, and thereafter shows a slight increases with . However, the vortex spacing ratio changes little, showing little if any  dependence. In general, as  increases, the vortex street is stretched both streamwise and laterally, resulting in the above-reported fairly constant b/a ratio of around 0.4. s (deg.) 150 100 50   0 -50 0.5 1.5 upper side U s,u  s,l lower side -100 -150 Figure 4.26 Separation angle at different speed ratios, Re = 141. 86 Chapter Flow visualization and hot-film measurement Figure 4.26 shows the separation angle on the upper and lower sides of the cylinder. When  increases, the separation angle on the upper side (s,u) of the cylinder decreases, the lower side separation angle (s,l) exhibits some kind of periodic-like variation which shows the same value of s,l at  and (+1). The upper and lower separation points move along the rotation direction of the cylinder (anti-clockwise) when  increases. The surface on the lower side of the cylinder moves in the same direction with the flow (left to right) when the cylinder rotates in anti-clockwise direction. On the upper side of the cylinder, the separation therefore occurs earlier than that on the lower side. The separation point on the upper side is then moved further upstream which results in the decrease in the upper separation angle with increasing . The trend of s,l is somewhat less intuitive and requires further investigation. The increase in  also results in an increase in wake inclination angle  (Figure 4.27). This is related to the shift of flow separation angles on both sides of the cylinder. A plot of  versus  is shown in Figure 4.27. 35 (deg.) 30 25 20 15 10  0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.2 Figure 4.27 Inclination angle  versus . The difference angle and the total angle as defined in Figure 4.28 of the two separation points on the cylinder surface vary in a wavy form (Figure 4.28). This shows 87 Chapter Flow visualization and hot-film measurement that sometimes the two separation points on the cylinder move closer, but sometimes they move away from each other. 300 angle (deg.) 250 200 |s,u| - |s,l | difference angle |s,u| + |s,l | total angle 150 100 50  0 0.5 1.5 Figure 4.28 Difference and total angle of the separation angle on two sides of the cylinder at Re =141. From the visualized pictures in Figure 4.18 (Re = 141) and Figure 4.19 (Re = 226), it is observed that at  = 2.3 a regular vortex street no longer exists. This is an important result as it supports similar findings reported earlier via two-dimensional numerical approach such as: Chew et al. (1995) (two-dimensional viscous incompressible hybrid vortex scheme, critical value of  is around at Re = 1000), Kang et al. (1999) (critical value of  is around 1.4, 1.8, and 1.9 for Re = 60, 100, and 160, respectively), Stojkovic et al. (2003) (critical value of  is around 1.9 at Re = 100, critical value of  is reported to be increased with Re), Mittal and Kumar ( 2003) (critical value of  is 1.9 at Re = 200), Elakoury et al. (2007) (critical value of  is 2.5 at Re=300). Because only discrete  values were investigated in the present work, the critical  magnitude at which the vortex shedding ceases is estimated to be between 2.1 and 2.3. This is slightly different from the value of reported by Chew et al. (1995) and 1.91 by Mittal and Kumar (2003). The difference in critical  observed is likely to be related to the difference in flow 88 Chapter Flow visualization and hot-film measurement conditions like two-dimensional versus three-dimensional flow and the presence of cylinder end conditions in the present experimental study, etc. d. Spanwise flow structure The flow structure in spanwise plane is observed at α = 1.4 and 1.6 for Re = 319 (Figure 4.29) and at α = 1.8 for Re = 455 (Figure 4.30). The vortex shedding for nonrotating circular cylinder at these Reynolds numbers is reported to be in mode B regime by Williamson (1996). The spanwise flow structure supports the shedding of regular vortices in mode B configuration at these flow conditions. Regular columns of vortex (A, B and C as seen in Figure 4.29 and Figure 4.30) are shed downstream. U D A Ω B D B A C C a) α = 1.4. D Ω A B D A C B C U b) α = 1.6. Figure 4.29 Spanwise vortex shedding at Re = 319 and a) α = 1.4, b) α = 1.6 (time sequence from left to right). Vortices are marked at A, B, C positions. 89 Chapter Flow visualization and hot-film measurement A B C A D Ω B C D U Figure 4.30 Spanwise vortex shedding at Re = 455 and α = 1.8 (time sequence from left to right). Vortices are marked at A, B, C positions. However, the dye trace was so diffused towards the two ends of the cylinder that only one pair of vortices are observed in the spanwise direction. More study of the spanwise flow structure will be discussed in PIV measurement. Figure 4.31 shows that in the Re range of up to about 1000, the trend of St-Re curve is rather similar at different speed ratio. The Strouhal number increases with Re in the lower Re part of the Re range investigated, and from Reynolds number of 600 up to 1000, the Strouhal number seems to approach some sort of an asymptotic magnitude, which is higher for larger speed ratio. The St-α relationship shown in Figure 4.32 shows that Strouhal number increases with increasing speed ratio. The likely reason for this is because the rotation of the cylinder draws the vortex from lower part of cylinder closer to the shear layer from upper part of the cylinder, resulting in earlier interaction and hence higher frequency of vortex shedding. This shows that changing the speed ratio can influence the frequency at which the vortices are shed. 90 Chapter Flow visualization and hot-film measurement 0.3 St  0.25  0.2  0.15 Re 0.1 200 400 600 800 1000 1200 Figure 4.31 St-Re relationship at different speed ratio. 0.25 St Re = 174 0.2 Re = 161  0.15 0.5 1.5 2.5 Figure 4.32 St-α relationship at different Re. In the next part, the flow behind cylinder at higher speed ratio when the vortex street disappears will be considered. 4.2.2 Case of 2.3 <   a. Dye flow visualization 91 Chapter Flow visualization and hot-film measurement The flow pictures of flow past the cylinder in the range of 2.3 <  < at Re = 141 and Re = 222 are presented in Figure 4.33 and Figure 4.34, respectively. a) b) c) d) e) f) Figure 4.33 Cylinder wake at different speed ratio at Re = 141 and α of a) 2.6; b) 2.9; c) 3.2; d) 4; e) 4.5; and f) 5. a) c) b) d) 92 Chapter Flow visualization and hot-film measurement f) e) Figure 4.34 Cylinder wake at different speed ratio at Re = 222.  = a) 2.6; b) 2.9; c) 3.2; d) 3.5; e) 4; and f) 4.5. a) b) c) d) Figure 4.35 Close field of the flow at Re = 226 and α of a): 2.5, b): 3, c): and d): 5. In the previous section, regular vortex shedding appears to vanish when  reaches the value 2.3. When  reaches the value of 2.6, the von Karman type of vortex street has vanished. Even when the vortex street has vanished, the dye trace in the cylinder wake is inclined more in the rotation direction as  increases, showing the effect of rotation on the cylinder wake. If we take a closer look at the near surface field of the cylinder (Figure 4.36), we notice that at α above αcrit (i.e., α > 2.3), the wake appears to become narrower and slanted and this could result in a decrease in the pressure drag as well as an increase in the lift force. On the side where the cylinder surface moves in the same direction with 93 Chapter Flow visualization and hot-film measurement free stream flow, the separation appears to be suppressed at high value of α (α = in Figure 4.36) as a large additional momentum is injected into the close-wall flow field to overcome the effects of the adverse pressure gradient. Prandtl (1925), in his experiment, also noted that flow separation on one side of the rotating cylinder is completely eliminated when the rotational speed is high. a) b) c) Figure 4.36 Flow separation at Re = 114 and α of a): 2.6, 3.2 and 4. As vortex shedding is caused by the instability of the separated shear layers, one may wonder if the suppression of vortex shedding makes the flow in the wake of cylinder somewhat more stable. More studies need to be carried out to answer this question. A trace of dye is observed to go downstream from the cylinder. However, the abovementioned trace line is not straight but wavy, and is biased towards the cylinder rotation direction. b. Particle image flow visualization The results of PTFV experiment at Re = 110, α = and 4.5 (Figure 4.37) and Re = 1067, α = and 4.5 (Figure 4.38) show that the vortex shedding has completely disappeared at high speed ratio (α > 2.3). 94 Chapter Flow visualization and hot-film measurement a) α = 3. b) α = 4.5. Figure 4.37 Wake structure at Re = 110, a) α = and b) α = 4.5. The effect of the cylinder rotation on the cylinder wake still can be observed by the deflection of the wake towards the cylinder rotation direction at high speed ratio. a) α = 3. 95 Chapter Flow visualization and hot-film measurement a) α = 4.5. Figure 4.38 Wake structure at Re = 1067, a) α = and b) α = 4.5. There is an important issue which was reported in Mittal and Kumar (2003), Stojkovic et al (2002. 2003) and Elakoury et al. (2008) that a second instability appears in a small range of high α. Within this small range at high α, one sided-vortex shedding was observed at very low frequency. The Strouhal number in this second instability range was reported to be of the order of one tenth the value of the Strouhal number of regular vortex shedding at low α. In the present study, the author did try to verify this second mode of vortex shedding by using dye flow visualization and hot-film measurement, but the author did not observe the reported phenomenon. The dye flow visualization method is not effective at high speed ratio. The PTFV which appears to work better at high speed ratio did not show an evidence for the existence of this reported 2nd instability. In hot-film measurement, the hot-film probe was positioned at different locations in the wake of the cylinder, but the author did not obtain any meaningful regular signal at high speed ratio. This may be a consequence of the three dimensionality of our current experimental conditions. The PIV measurement which was carried out in a wide range of Re (1101067) and speed ratio (0-5) did not show the existence of the 2nd instability either. At high speed ratio, the vorticity contour and streamline plot of PIV data not show any sign of the one-sided vortex shedding as reported in literature. 96 Chapter Flow visualization and hot-film measurement The PTFV experiment was carried out over a very long time period (around 20 times of vortex shedding cycle time for Re = 110) and repeated many times in the α range of 4< α < in order to find out more about the second instability phenomenon that was reported in the literature. However, the author did not observe any one-side vortex shedding at this high range of speed ratio for Re = 110. 206 and 1067. Sometimes, a sign of a “look-alike vortex” was observed to shed from one side of the cylinder, but it does not appear periodically. The author may suggest that it might be due to some 3D “turbulence” appearing in the flow and it is not relevant to the vortex shedding that is considered. 4.3 Concluding remarks In conclusion, the von Karman vortex street is observed at α < 2.3. Above α of 2.3, the vortex shedding disappears. However, even when regular vortex shedding has vanished, a dye trace is still observed and it deflects with increasing α, showing the effect of rotation on the cylinder wake. The existence of the reported second instability phenomenon can not be confirmed in the limit of the present experiment. Numerical study of Chew et al. (1995) reported the observation of a closed streamline around the cylinder surface at high speed ratio when vortex shedding disappears. In the present flow visualization result, the close up view around the cylinder surface in Figure 4.36 shows that there is a closed region of dye accumulated around the cylinder surface. The author believes that there would be some relationship between the present experimental results and the closed streamline reported as no accumulated dye region around the cylinder surface was observed at α < αcrit. When enough dye accumulates in the closed region of the cylinder, the closed boundary of the accumulated dye region appears to break up and releases the dye downstream. This phenomenon occurs intermittently. 97 Chapter Flow visualization and hot-film measurement The St-Re and St-α relationship are obtained by hot-film measurement. Strouhal number measured was found to increase with increasing Re and α. Flow visualization in x-z plane shows mode B instability at low α when vortex shedding takes place. In the next section, results obtained from PIV measurement will be presented and analyzed. 98 [...]... interest, and had been investigated for many years before the rotating cylinder problem began to receive attention In the following, the author will review representative work in flow past both stationary and rotating circular cylinder 2 .1 Flow past a stationary circular cylinder 2 .1. 1 Different regimes of flow past a stationary circular cylinder Flow past a stationary circular cylinder is a classic problem... regime at Re >1. 5x106 The flow separates at S = 14 0o for smooth surface cylinder The associated drag is rather constant and low in magnitude j Trans-critical regime (Re > 5x106) 17 Chapter 2 Literature reviews In this regime, the laminar to turbulent boundary layer transition is shifted upstream and close to stagnation point, and the boundary layers separate as turbulent ones, at an angle lower than S... supercritical (10 6 < Re < 5x106) and transcritical (Re > 5x106) and are tabulated with fair detail in the 12 Chapter 2 Literature reviews following table and described below (reported in Niemann and Holscher (19 90)) for a smooth surface cylinder Table 2 .1 Different ranges of flow past a smooth surface circular cylinder (regenerated in Niemann and Holscher (19 90)) Three-dimensional wake transition regime... speed ratio of the cylinder exceeded a critical value (Jaminet and Van Atta (19 69), Chew et al (19 95)) On the other hand, more recently the 2 Chapter 1 Introduction re-appearance of the vortex street was reported at a certain range of speed ratios beyond the critical value (Mittal and Kumar (2003)) The change of aerodynamics forces at various speed ratios is another important challenge Although many investigations... Figure 4 .11  Defintion of longitudinal and lateral vortex spacing.   73 Figure 4 .12  Variation of wake geometric parameters with Re.    74 Figure 4 .13  Definition of separation angle.   75 Figure 4 . 14  Variation of separation angle with Re (stationary cylinder)  (Dimopoulos and Hanratty  (19 68) ).   75 Figure 4 .15  St‐Re relationship in comparing with universal St‐Re in literature (stationary ... separates is laminar and the vortex wake is highly turbulent until Re of around 3x105 (as shown in Figure 2.1d) As the separation points are on the front half of the cylinder, a large wake is formed and results in a large form drag f Re > 10 5 When Reynolds number is greater than about 10 5, the flow is roughly classified into 4 regimes which are subcritical (Re < 1. 4x105), critical (1. 4x105 < Re < 10 6),... modified by dynamically changing the speed and lateral spacing of generated shear layer during the formation of the circulation region, which can be achieved by streamwise and lateral oscillation of the cylinder Besides, rotating the circular cylinder up to a certain angular speed is another method to control the vortex shedding We will look at rotating circular cylinder in greater details later in section... understanding of the flow field associated with uniform flow past a rotating circular cylinder, and in particular attempts to shed light on some of the un-answered questions Therefore, the main purposes of the project are to qualitatively obtain a general view of the flow structure via visualization and to quantitatively measure the characteristics of the flow which include aerodynamics forces on the cylinder. .. Figure 5.7 Vorticity contour and streamline plots of a stationary cylinder at a)  Re = 11 0, b) Re =  206, c) Re = 3 34,  d) Re = 5 41 and e) Re = 10 67.  10 8 Figure 5.8 Strouhal number (from PIV data) versus Reynolds number for flow past a stationary  cylinder.   10 9 Figure 5.9 Comparison of the current PIV St‐Re data with the author earlier hot‐film  measurement and the data reported in Williamson  (19 92). ... drag coefficient was calculated in three Reynolds numbers (2x105, 3.7x105 and 4x105) and was found to decrease sharply with increasing Reynolds number (CD =1. 14, 0 .45 and 0.23 at the three above-mentioned Re) i Super-critical regime (10 6 < Re < 5x106) The separation bubbles are still observed up to Re of around 1. 5x106 The maximum Strouhal number was 0 .48 in this regime The separation bubbles disappear . 4.1 Flow past a stationary circular cylinder 67 4.1.1 Flow structure 67 4.1.2 Vortex spacing 72 4.1.3 Separation angle 74 4.1.4 St-Re relationship 75 4.2 Flow past a rotating circular cylinder. 2.1.1 Different regimes of flow past a stationary circular cylinder 6 2.1.2 Relationship of Strouhal number and Reynolds number 19 2.2 Flow past a Rotating circular cylinder 24 2.2.1 Vortex. FLOW PAST A ROTATING CIRCULAR CYLINDER DUONG THI THU LINH NATIONAL UNIVERSITY OF SINGAPORE 2011 FLOW PAST A ROTATING CIRCULAR CYLINDER