Analysis of Vortex Shedding Mechanism through PIV Measurement of Flow past a Rotating Circular Cylinder

Transcription

1 Analysis of Vortex Shedding Mechanism through PIV Measurement of Flow past a Rotating Circular Cylinder Linh Duong *, Siao Chung Luo, Yong Tian Chew Department of Mechanical Engineering, National University of Singapore, Singapore * correspondent author: dthulinh@gmail.com Abstract The vortex shedding mechanism of a rotating circular cylinder is investigated experimentally using Particle Image Velocimetry (PIV) method. The experiments were conducted for flow past a circular cylinder with an aspect ratio of 16 in a recirculating water channel at a Reynolds numbers of 110 and 206. The rotational to translational speed ratio α varies from 0 to 3. The PIV measurement was carried out in a cross section plane of the cylinder at the cylinder s mid span (of the immersed part of the cylinder in the water channel). The vortex shedding process is analyzed by studying the time sequence of vorticity contours and streamline patterns in the surrounding field of the cylinder surface and in the wake of the cylinder. The vortex shedding was observed up to α = 3 (up to α = 2 at Re = 1000 in Chew et al. (1995)). In the range of 0 < α < 3, the present result shows that the vortex formation mechanism seems to differ on the upper and lower side of the cylinder. At the lower side (rotation of the cylinder is in the same direction with free stream velocity), the positive anti-clockwise vortex is formed through the growth of a recirculating region, similar to the normal formation process in stationary cylinder, as described in Gerrard (1966). However, at the upper side (rotation of the cylinder is in the opposite direction with free stream velocity), the negative vortex is formed by interaction of shed positive vortex with the shear layer as it is being drawn much closer to the shear layer by the rotation of the cylinder. Through this investigation, it is hoped that understanding of the mechanism of the vortex shedding of a rotating circular cylinder will lead to better understanding of the cylinder s rotation effect on the flow structure around the cylinder. 1. Introduction Flow past a circular cylinder is one of the most fundamental problems among various types of flow over bluff bodies. It has been studied widely because of its relevance to many important practical applications such as offshore engineering and wind load on tall building etc. However, despite the simple geometry of the cylinder, the flow structure is complicated and behaves very differently at different Reynolds numbers. Williamson (1996) suggested that the flow structure behind the cylinder is the combination of three important regions: boundary layer, shear layer and wake. As the flow behaviour is strongly dependent on Reynolds numbers, the flow can be categorized into different ranges of Reynolds numbers. In each range, the flow exhibits some typical characteristics. Within certain ranges, a highly regular vortex shedding takes place which results in an organized vortex wake called von Kármán vortex street. The von Kármán vortex street is characterized with two unstable rows of opposite-signed vortices. Since the finding of the vortex street, many studies have been carried out to investigate the mechanism of the vortex shedding process in the cylinder wake. Gerrard (1966) described a basic mechanism of the vortex shedding in the wake of a circular cylinder in which vortex from one side of the cylinder is fed by circulation from the shear layer and grows until it becomes strong enough to draw the other shear layer across the wake of the cylinder. An opposite-sign vortex is formed and is sufficiently strong to cut off the supply of circulation to the previously mentioned growing vortex. This vortex is then shed downstream. This description implies that fluid is drawn across the wake by the growing vortex on the other side of the cylinder. One part of the mentioned fluid is entrained by the growing vortex, while another part is entrained by the shear layer upstream of the - 1 -

2 vortex and the rest goes into the interior of the formation region. Unlike the flow over a stationary cylinder where the flow structure depends only on the Reynolds number (Re), the flow past a rotating circular cylinder is dependent on both the Reynolds number and rotational to translational speed ratio (α). As a result, flow past a rotating cylinder is more complex than flow past a stationary cylinder. Many studies have been conducted both to investigate the effects of rotating the cylinder as a mean of boundary layer control and to understand the flow structure at different cylinder s rotation rates. Among the many important features of the flow past a rotating circular cylinder, two features have drawn a lot of attention from the fluid mechanics research community. The first feature is that the rotation of the cylinder can control the separation of the boundary layer around the cylinder, hence (under certain circumstances) suppressing the vortex shedding from the cylinder. The second feature is the generation of a lift force on the cylinder and the possibility of form drag reduction while rotating the cylinder. Many studies have been carried out to study these two features and most of them are numerical. The present experimental investigation is carried out to fill in the void of experimental investigation on wake structure associated with flow past a rotating circular cylinder. This study investigates the mechanism of the vortex shedding behind a rotating circular cylinder by PIV measurements. 2. Experiments Experiments were carried out in the water channel in the Fluid Mechanics Laboratory of The National University of Singapore. It is a closed loop water channel with a free surface, and its test section has a cross section of 0.45m (height) by 0.4m (width) and a length of 1.8m. The two side and bottom walls of the channel test section are made of Acrylic glass. Throughout the experiment the room temperature was maintained at 20 o C. In the present investigation the turbulence intensity of the flow is below 1%. The sketch of experimental set up (in Figure 1) shows the arrangement of experimental equipments for the PIV measurement. Illuminated particles Cylinder Flow Laser sheet Captured area Optics Camera Laser - 2 -

3 Figure 1. Sketch of experimental set up for PIV measurement. A Litron laser system and a Dantec PIV2100 processor system were used to measure the flow field. Spherical glass particles 10 microns in diameter were chosen as seeding particles. A Kodak ES1.0 Digital CCD Camera located with line of view approximately perpendicular to the laser plane was used to capture the flow images. The laser light illuminated the X-Y plane which is parallel to the flow direction (x-direction) and perpendicular to the cylinder axis. The camera focused on a captured area of 46.2mm x 46.2mm (= 2.9D x 2.9D, where D is the cylinder diameter) for a close view of the cylinder wake, and an area of around 136mm x 136mm (= 8.5D x 8.5D) as shown in Figure 2. For each case of speed ratio and Reynolds number, 450 sets of data were collected. A Dantec Flow Manager software was used for data post-processing to obtain streamline and vorticity fields of the flow. A stainless steel cylinder was installed vertically in the water channel test-section. The cylinder is of 0.016m in diameter and 0.7m in length (but only a 0.4m long portion is immersed in the water in the test section). The immersed part of the cylinder has an aspect ratio of 25. The cylinder was rotated by a motor via a belt. The entire cylinder rotation mechanism was installed above the water surface. The positive flow velocity is from left to right and positive cylinder rotation direction is counter-clockwise (Figure 2). ω ω U D D θ 2.9D U D 1.5D θ 8.5D 1.45D 4.25D 2.9D 8.5D a) Camera view in the close field of the cylinder. b) Camera view in the large field of the cylinder. Figure 2. Flow area captured by camera. 3. Results The instantaneous streamline patterns around the cylinder at Re = 110 and α = 0, 1 and 2 are shown in Figure 3 (a), (b) and (c) respectively. The blank space (in white colour with no streamline pattern) below the cylinder is the shadow region where the laser light is blocked by the cylinder. It can be seen when the vortex on one side of the cylinder is being shed, the vortex on the other side of the cylinder is generated and grows. The rotation of the cylinder adds more asymmetric on the vortex shedding structure. The position of positive and negative vortices varies with different speed ratio. The streamline patterns at time step (t) and (t + 3T/5) for the case of stationary cylinder (Figure 3 (a)) seems to be the image of each other through x-axis. At α = 1 and 2 (Figure 3 (b), (c)), the cylinder rotation has altered the symmetric of the streamline around the cylinder. Therefore, after half a vortex shedding cycle, the streamline patterns at time step (t + 3T/5) does not reflect the - 3 -

4 image of those at time step (t), unlike that can be seen at α = 0. t t+ T/5 t+ 2T/5 t+ 3T/5 t+ 4T/5 t+ T a) Re = 110 α =

5 t t+ T/5 t+ 2T/5 t+ 3T/5 t+ 4T/5 t+ T b) Re = 110 α = 1. t t+ T/5 t+ 2T/5 t+ 3T/5 t+ 4T/5 t+ T c) Re = 110 α =

6 Figure 3. Instantaneous streamline pattern in 1 cycle at Re = 110 and a) α = 0, b) α = 1, c) α = 2. With the effect of the cylinder rotation, the positive vortex on the lower side of the cylinder is drawn closer to the shear layer on the upper side of the cylinder as α increases. This gives a better chance for the positive vortex to interact with the shear layer. The fluid entrainment from the shear layer by this interaction can be the source for a new forming negative vortex. A closer look in the near wake of the cylinder at Re = 206 and α = 0 can be seen in a time sequence (in one cycle of vortex shedding) of the streamline patterns in Figure 4. The positive vortex seems to grow large enough in size at time step t. While it is being shed downstream at time step (t + T/7), a negative vortex on the upper side of the cylinder is formed and grows in size at time step (t + 2T/7). This negative vortex keeps growing at time step (t + 3T/7) and a new positive vortex is generated on the lower side of the cylinder while the growing positive vortex is being shed at time step (t + 4T/7). As what can also be observed at Re = 110 and α = 0, after half of the vortex shedding cycle, the streamline patterns at time step (t + 4T/7) reflect the image of those at time step (t). At time step (t + 5T/7), the negative vortex is shed downstream and a new positive vortex is regenerated at time step (t+6t/7) and the vortex shedding process restarts. t t+ T/7 t+ 2T/7 t+ 3T/7 t+ 4T/7 t+ 5T/7 t+ 6T/7 t+ T Figure 4. Instantaneous streamline pattern in 1 cycle at Re = 206, α = 0. To investigate the mechanism of vortex shedding for flow past a rotating cylinder, the instantaneous vorticity contours and streamline patterns during one cycle of vortex shedding (T) are shown in Figure 5 (a)-(i) for Re = 206 and α = 1. In Figure 5 (a), at the first time step (t), the negative (clockwise) vortex starts to shed from the cylinder while the positive vortex has already been shed and is out of the right (downstream) edge of the view area. In Figure 5 (b), the saddle point moves downstream together with the negative vortex while at the same time, the bulging of streamlines begin to appear at θ 0 o position. The negative vortex continues to move downstream in Figure 5 (c) with the disappearance of saddle point, and the bulging of streamline area becomes more distinct. It begins to form a new positive vortex together with a new saddle point at θ 20 o position as shown in Figure 5 (d). In Figure 5 (e), the newly generated positive vortex grows and influences the previously shed negative vortex to become stronger with the appearance of a saddle point. At the same time, it also draws part of the previously shed flow towards the upper side of the cylinder at θ 90 o position. After one more time - 6 -

7 step (at t = t + 6T/9), the previously formed negative vortex is out of the view area. At the same time, the new positive vortex cut off the drawn flow as mentioned previously to become a new negative vortex formed right on the top side of the cylinder surface with a saddle point in Figure 5 (f). In Figure 5 (g), the newly generated negative vortex grows in strength and shed downstream as shown in Figure 5 (h). The new vortex shedding process restarts at the beginning of the next cycle (time step (t + T)). An interesting observation is that the vortex formation mechanism seems to differ on the upper and lower side of the rotating cylinder. At the lower side, the positive vortex is formed through the growth of a recirculating region. However, at the upper side, the negative vortex is formed by interaction of shed positive vortex with the shear layer as it is being drawn much closer to the shear layer by the rotation of the cylinder. This also explains why the streamline pattern of the rotating cylinder after half a cycle does not reflect that at the beginning of the vortex shedding

8 16th Int Symp on Applications of Laser Techniques to Fluid Mechanics (C) vortex core (S) saddle point (S) saddle point (a) t (b) t + T/9 (c) t + 2T/9 Figure 5. Instantaneous vorticity contour and streamline pattern in 1 cycle at Re = 206, α = 1 (continued in next page). -8-

9 16th Int Symp on Applications of Laser Techniques to Fluid Mechanics (d) t + 3T/9 (e) t + 5T/9 (f) t + 6T/9 Figure 5. Instantaneous vorticity contour and streamline pattern in 1 cycle at Re = 206, α = 1 (continued in next page). -9-

10 16th Int Symp on Applications of Laser Techniques to Fluid Mechanics (g) t+7t/9 (h) t + 8T/9 (i) t + T Figure 5. Instantaneous vorticity contour and streamline pattern in 1 cycle at Re = 206, α =

11 4. Conclusion The vortex shedding process of a rotating circular cylinder has been investigated by PIV measurement at Re = 110 and 206 for speed ratio of 0, 1 and 2. The von Kármán vortex street is observed for both stationary and rotating cylinder. Increasing α adds more asymmetric to the wake structure of the cylinder. The vortex formation process on the upper side and lower side of the rotating cylinder shows some difference from that of the stationary cylinder. When rotation is present, the lower-side positive vortex is formed through the growth of a recirculating region while the upper-side negative vortex is formed by interaction of shed positive vortex with the shear layer. 5. References Chew Y T, Cheng M and Luo S C (1995) A numerical study of flow past a rotating circular cylinder using a hybrid vortex scheme. Journal of Fluid Mech. 299: Gerrard J H (1966) The mechanics of the formation region of vortices behind bluff bodies. Journal of Fluid Mech. 25: Williamson C H K (1996) Vortex dynamics in the cylinder wake. Annual review of Fluid Mechanics 28: