Investigating Fluid Flow Phenomena behind Intersecting and Tapered Cylinders using submerged Stereoscopic PIV Chittiappa Muthanna 1, Jan Visscher 2, Bjørnar Pettersen 3 1: Offshore Hydrodynamics, MARINTEK, Trondheim, Norway: email:chittiappa.muthanna@marintek.sintef.no 2: Dept. of Marine Technology, NTNU, Trondheim, Norway: email: jan.h.visscher@ntnu.no 3: Dept. of Marine Technology, NTNU, Trondheim, Norway: email: bjornar@ntnu.no Abstract Particle Image Velocimetry (PIV) has been successfully utilized in a towing tank facility to measure the fluid field behind a grid of intersecting cylinders, and behind a tapered cylinder. The study was also performed to ascertain the feasibility and applicability of using the Stereoscopic PIV technique in towing tanks, as the setup is now submerged underwater thereby limiting access to the optics once the measurement program is underway, as well as introducing complications to seeding and calibration methods. The primary challenges encountered were ensuring accurate alignment of the optics once the system is submerged, successfully seeding the area of interest in such large volumes of water, and calibrating the system accurately underwater. Results from the PIV measurement on the grid of intersecting cylinders showed the interaction of the vertical and horizontal wakes shed by the cylinders, and correctly measured that the strength of the vortical structures increased with Reynolds numbers. The results from the tapered cylinder tests showed that the PIV system was able to capture the vortex dislocations present in the vortex sheet behind the cylinder. Overall, the measurements have shown that while performing stereoscopic PIV measurements in towing tank facilities is complex, it is nonetheless feasible and applicable to studying turbulent flow phenomena in such facilities. Consequently, the results from the PIV tests will be incorporated into concurrent numerically calculated results of these two test cases ongoing at the Department of Marine Technology at NTNU. This joint approach of numerical and experimental studies highlights the benefit of applying the PIV technique in the ongoing study of marine hydrodynamics at MARINTEK and NTNU. 1. Introduction When studying fluid flow phenomena, particularly time evolving flows, it is desirable to obtain whole field time varying measurements. Particle Image Velocimetry (PIV) is a whole field measurement technique that is able to measure time varying fluid flows, and is thus ideally suited to studying time evolving flows, Raffel et al. (1998), such as those found behind marine structures such as aquaculture cages, pipelines and risers, and the wakes and flow around ship hulls and bluff bodies. The aim of the present study is to develop a submerged Stereoscopic PIV system that can be used in towing tank facilities to measure these time varying flows. Measurements made in traditional towing tanks have mainly concentrated on point based techniques that are robust enough to use i.e. hot film sensors, pitot-probes, and visualisations using video recordings. The use of optical based techniques has proved difficult to accomplish due to the complications that arise with the presence of open water that is found in towing tanks. It goes without saying that PIV has traditionally been a very complicated and time consuming technique that involves accurate adjustments of the optics involved. Extrapolating this technique to be used in towing tanks presents considerable challenges in designing and operating a system that is to be used underwater. The PIV experiments described here were used to study the flow behind a grid of intersecting cylinders, and tapered circular cylinders. The two topics studied have very interesting features particular to them, and have been well documented and studied previously. Not only do the studies enable us to evaluate the feasibility of using PIV in a towing tank environment, the addition of PIV measurements to the previous studies provides a new insight into the nature and behavior of these - 1 -
two types of flow. The primary motivation towards studying the flow around intersecting cylinders was influenced by the aquaculture industry, where a simple representation of intersecting cylinders could represent parts of fish aquaculture cages. The cages are situated in open water and are subjected to currents, and thus the vortex shedding behind the individual cage elements would influence the position and structural integrity of the structure, Fredriksson et al. (2005). The flow around intersecting cylinders has been studied in great detail previously Osaka et al. (1983), Zdravkovich (1983, 1985), Fox and Toy (1990), Fox (1991, 1992), Shirakashi et al. (1994). These studies mainly concentrated on a single cruciform configuration. The flow downstream of a single cruciform configuration is characterized by a large cross shaped wake downstream of the intersection, with the wakes then becoming more two dimensional as you move away from the center. An aquaculture cage consists of many such elements, and thus a grid of intersecting cylinders was chosen so as to replicate the effects of these multiple elements. The flow behind the intersections thus is highly turbulent with a combination of horizontal and vertical wakes from the cylinders. Similarly, in order to evaluate the capabilities of the PIV system, the flow downstream of a tapered cylinder was studied. A tapered cylinder is characterized by a linearly changing diameter along the span, which is described by the taper ratio, defined as RT=L/(d2-d1), with d1 and d2 being the diameter of the smaller and the larger end, respectively and L being the length of the cylinder. Tapered cylinders are a good representation of numerous marine structures, such as oil derrick legs, and bridge pontoons. Identical to the flow behind straight cylinders, the Reynolds number (Re=dU/ν, based on the cylinder diameter d) is the governing flow parameter, while the Strouhal number (St=fs d/u, where fs is the vortex shedding frequency) identifies the dimensionless shedding frequency. Since the Strouhal number is generally nearly constant at a given Reynolds number in a specific experiment, a spanwise varying diameter forces a variation in vortex shedding frequency. The tendency of the spanwise vortices to form persistent structures leads to the unique features of this flow, i.e. oblique vortex shedding and periodic vortex dislocations. These flow structures are difficult to measure and predict as they are very random and highly time dependent in nature as shown in Narasimhamurthy (2006), Hsiao and Chang (1998), Piccirillo and Van Atta (1993). Also, as the exact position of these dislocations are not known along the span of the cylinder, a full field, time varying measurement technique such as PIV could provide us with the capability of measuring and documenting these flow features. To perform such a measurement in a towing tank is not ideal, but given the complexity of such a measurement, it does provide an interesting challenge to the equipment being used. The present paper reports PIV measurements of these two fluid flow cases, and is primarily concerned with the applicability and feasibility of using a submerged PIV system in a towing tank environment. The results are just part of a more extensive test program that involves more experimental studies, as well as a complementary computational fluid dynamic study being performed by the Marine-CFD group at NTNU in Trondheim, Norway. 2. Apparatus and Instrumentation 2.1 Towing Tank Facility The Marine Cybernetics towing tank facility (MCLab) at the Department of Marine Technology at NTNU in Trondheim, Norway was used for these experiments. The facility is a 40m long towing tank (X) with a width of 6.45m (Y), and has a maximum water depth of 1.5m (Z). The carriage is towed in the X-direction, and has a maximum velocity of approximately 0.8m/s, and has been tested at speeds as low as 0.01 m/s. Models are mounted to a 4 DOF traverse system (X, Y, Z, and rotation about the Y (vertical) axis). 2.2 Experimental Models - 2 -
Intersecting Cylinder studies For the intersecting cylinder studies, a grid of 32mm diameter cylinders was fabricated. The grid consisted of a 5x5 configuration of cylinders (shown in Fig. 1), with a center to center spacing of 150mm to give a solidity of 0.38. The grid was towed at two different speeds, 0.1 m/s, and 0.2 m/s, which corresponds to a Reynolds number based on the diameter of a cylinder of 3200 and 6400 respectively. The tests were done at as low as possible Reynolds numbers to be able to complement numerical simulation studies being carried out concurrently. Fig. 1 Photograph of the grid of (5x5) intersecting cylinders Tapered Cylinder Studies Two cylinder models (A1, B1) of the same length L =600mm with different diameters and aspect ratios a (based on the mean diameter, a = l: d m ) were used (see Table 1). The taper ratio R T was fixed to 75:1 to match with existing results, Picchirillo (1993) and Hsiao (1998). Additionally, both cylinders were tested with another endplate mounted in the center of the span, leading to models A2 and B2 to check for the aspect ratio influence. Furthermore, a straight cylinder model (S) was tested for comparison and check for end effects. All models were equipped with thin circular endplates (D = 3d 2 ) to eliminate disturbances caused by free ends, an effect which has been reported by several authors. Table 1 Details of the different types of cylinders used for the Tapered Cylinder Studies, R m is Reynolds number based on the mean diameter dm Taper min max Model d ratio 1 d m d 2 l a = l:d m Re m Re m [-] [mm] [mm] [mm] [mm] [-] [-] [-] A1 42 46 50 600 13:1 2.3 103 18.4 103 B1 19 23 27 600 26:1 1.15 103 9.2 103 75:1 A2 46 48 50 300 6.25:1 2.4 103 19.2 103 B2 23 25 27 300 13:1 1.25 103 10 103 S 23 23 23 600 26:1 1.15 103 9.2 103-3 -
Fig. 2a Schematic of the models used d1 is the left end and d2 the right end Fig. 2b Photograph of B1 cylinder mounted in the towing tank 2.3 PIV Instrumentation The PIV instrumentation used is a commercial system purchased from Dantec Dynamics. While the optical and laser hardware are standard PIV components, the manner in which the system is used is not typical of PIV setups. What is unorthodox about the studies performed was that the PIV system was submerged underwater in towing tanks in order to perform the measurements. The optical system is mounted to the towing tank carriage and cameras and lightsheet optics are all submerged in specially designed torpedo shaped housings placed downstream of the models being tested. This setup thus introduces a number of challenges and complications to performing PIV measurements. Two different stereoscopic PIV setups are possible with the actual hardware, and have been tested in the studies presented here. The differences between the two systems lie in the type of cameras (CCD against CMOS sensor) being used, and thus the associated hardware. Details of the PIV hardware are given below - Cameras o 2 Dantec Dynamics Flowsense Cameras. 1600x1186 pixel image sensor CCD 10 Hz Maximum Acquisition Rate at full resolution 15 Hz Acquisition Rate achievable at reduced vertical resolutions. Total number of images that can be acquired is limited by the acquisition hardware. o 2 Dantec Dynamics Nanosense Cameras. 1260x1024 pixel image sensor CMOS 100 Hz Maximum Acquisition Rate (laser limited) at full resolution 4 GB of Internal Memory Approx 1000 image pairs can be acquired (memory limited) - Laser o Litron Lasers NANO-L-50-100 PIV dual cavity laser. >50mJ per pulse at frequencies up to 100Hz. - Data Acquisition Hardware o Dantec Dynamics FlowMap, and TimeResolved Units. - PIV Software o Commercial Dantec Dynamics FlowManager Software In addition to the PIV hardware, the underwater configuration also has two distinct setups, depending on the field of view desired for the measurements. One setup has separate housing for - 4 -
the cameras and laser, and is used for larger fields of view, and lower image acquisition rates. The second setup has a single torpedo housing that carries both the cameras and laser, and has a smaller field of view, but is capable of obtaining images at higher acquisition rates. These two setups are described in more detail below, and shown in Fig. 3 Separate housings/larger field of view PIV configuration, Fig. 3a. The configuration consists of two CCD cameras (Dantec Flowsense MkII) mounted in individual underwater housings close to the side walls of the towing tank, thus being approx. 5 m apart. The laser periscope was mounted in the center of the tank, emitting a vertically oriented light sheet of approx. 3 mm thickness. Depending of the lens used, fields of view of up to 45x45cm can be realized. Full format images (1600x1186 pixels) were taken at rates between 3 and 10 Hz. The maximum stable acquisition rate was 14 Hz with a reduced image height (1600x900 pixels). The system allows the laser flash rate to be a multiple of the acquisition rate in order to operate the laser in the optimal range between 60 and 100 Hz. A Dantec Flowmap System Hub unit was used as synchronization source and as image buffer memory. Single runs could contain up to 1100 stereoscopic double-frames at full resolution. The main advantage of this configuration is that larger fields of view are realized, but at the expense of less light available to the cameras. Torpedo housing PIV configuration, Fig. 3b. In the second variation, the optical system was brought closer to the measurement section in order to have a higher light budget for the cameras. Thus the fields of view are reduced (to about 40x35cm) but due to the increase in the light available from the laser, we can use either the less light-sensitive, but faster CMOS cameras (Dantec Nanosense) or the CCD Flowsense cameras. When using the CMOS Nanosense cameras, the acquisition rate was set between 40 and 80 Hz. Both cameras have internal buffer memories of 4 GB, which allows series of 1000 doubleframes at full resolution. The image height could be reduced to obtain longer series. However, the Dantec FlowManager faced database instabilities when one run contained more than 1600 images. The timing and synchronization signals are controlled by Dantec s TR (Time resolved) PIV system, and does not use the system hub as with the CCD cameras. The camera housings were combined with the laser periscope to one, torpedo-shaped body, which is supposed to be towed in longitudinal direction. However, to obtain the desired measurement plane in the cylinder axis, it was mounted transversally to the flow. While producing undesired drag forces, this setup still proved to work without vibrations or have disturbing influence on the test region for towing speeds up to 0.4 m/s. Fig. 3a Separate housing configuration of the PIV equipment in the MCLab. The laser light sheet can be seen in the middle, with one of the cameras mounted on the long cylinder on the right of the photo Fig. 3b Torpedo configuration of the PIV equipment in the MCLab. The torpedo can be seen underwater in downstream of the intersecting cylinder grid - 5 -
2.4 Calibration Calibration of the PIV system was carried out by inserting a calibration target into the field of view of the cameras. Due to the fact that the cameras and optics are submerged, dry land alignment of the optics, mirrors and camera mounts have to be done before the system is submerged. This adds to the complexity of the experiments, as any slight misalignment results in either the cameras having to be removed, or the water drained from the tank and the optics adjusted. 2.5 Seeding Another issue that had to be addressed when performing PIV measurements in towing tanks was seeding. As the majority of PIV measurements are done in closed circulating water tunnels or channels, the amount of seeding required is not that great. However, when using PIV in towing tanks, seeding has to be inserted upstream of the models between measurement runs so as not to disturb the oncoming flow during runs. Due to the size and volume of the towing tank, in addition to disturbances caused due to the presence of equipment in the water, the seeding has the tendency to disperse. Thus, large amounts of seeding are required, which leads to the requirement that seeding has to be relatively affordable. Simple polyamide spheres were used, with the seeding having a nominal diameter of either 50 microns (when using the torpedo housing) or 100 microns when using the single camera housing configuration. 3. Results and Discussion A novel PIV setup to be used in towing tank facilities was used to make measurements of some well defined fluid flow phenomena in order to ascertain the feasibility of using such a system. The system is unorthodox when compared to traditional PIV systems in that the optical system is submerged underwater, and thus making fine adjustments difficult once the test program is underway. Coupled with the difficulty in seeding the flow, obtaining reliable PIV results presents quite a challenge. It should be stressed that due to the large amount of out-of-plane fluid flow present in such flows, and the difficulty in seeding the flow, obtaining a good PIV measurement using the submerged setup proved to be rather time consuming and difficult. The results presented here are merely an indication that such types of PIV measurements are possible, and that the technique of using PIV in towing tanks is continuously being developed and improved. 3.1 Intersecting Cylinder Studies The results presented here for the intersecting cylinder studies were performed at two Reynolds numbers, 3200 and 6400 based on the cylinder diameter. Velocity maps were taken at a rate of 10Hz, for a total of 20s to give 200 velocity maps per run. This is not a large number of maps from which to obtain statistical data, but due to the fact that we had seeding issues, and towing tank limitations for these first experiments with the underwater setup, it was deemed acceptable in order to observe the flow features behind intersecting cylinders. The model grid was mounted onto the carriage, and positioned such that the edge of the central vertical cylinder was just visible in the field of view of the camera images. The axis system used to present the results is shown in Fig. 4, where positive x is against the towing direction, positive y is upwards, and z completes the right handed co-ordinate system. The system is aligned such that the lightsheet corresponds to one value in the z-direction, and the W velocity corresponds to the velocity perpendicular to the lightsheet. In order to obtain the varying spanwise locations of the velocity maps i.e. different z axis planes, the model was moved using the carriage traverse, thus, the PIV system field of view is fixed, and the model is moved around. - 6 -
Fig. 4 Co-ordinate system used to present the intersecting cylinder results, the origin is defined at the intersection of the two central cylinders at the middle of the grid Shown in Fig. 5 are comparisons of one instance of the U velocity field normalized on the towing speed of 0.1 m/s (Re=3200), at the different z-positions away from the center of the grid. Towards the center, i.e. the intersection of two cylinders, you see the large velocity deficit, and proceeding away from the intersection, the wake of the horizontal cylinder becomes more clearly defined. At z=30mm and 60mm away from the center of the grid, the features visible in the flow field are a result of the wake from the vertical cylinder, whereas at z=90mm from the center, the influence of the vertical wake is not seen until further downstream from the grid, and the horizontal wake is more clearly defined at z=90mm. Identifying the vertical wake is easier if we take a look at the out of plane component of the velocity field, the W velocity. (a) 0 mm from intersection center (b) 30 mm from intersection center (c) 60 mm from intersection center (d) 90 mm from intersection center Fig. 5 Normalized U velocity contours behind the grid of intersecting cylinders at different z-planes for Re=3200. The results shown are representative of 1 of 200 velocity maps taken with the PIV system Shown in Fig. 6, are plots of the W velocity component of the flow at one instance during the measurement. Positive contours (red based colors) indicate the flow is coming out of the plane, and negative (blue based colors) indicate the flow is going into the plane. Behind the center of the grid at z=0mm, there are many areas of the flow moving perpendicular to the measurement plane. These areas decrease as you move away from the center, showing up further downstream of the grid. The Reynolds number effect is difficult to see, but what is indicated is that the vertical wake at Re=3200 spreads quicker than that at Re=6400, as visible in the W contours at - 7 -
approximately x=200mm for z=30mm and 60mm, but the effect is reduced downstream at z=90mm for Re=3200 when compared to Re=6400. (a) Re = 3200 (b) Re = 6400 Fig. 6 W-velocity contours behind the grid of intersecting cylinders for the two Reynolds numbers tested at different z planes. While not clearly visible in the figures, the z-planes from top to bottom are z = 0mm, 30mm, 60mm and 90mm Shown in Fig. 7, are the velocity vectors obtained during the measurements. These vectors do show regions of circulating flow indicative of vortices, and also show the influence of the vertical wakes on the downstream development of the horizontal wakes behind the cylinders, with the increased spreading of the wake region at planes closer to the vertical cylinders. From the velocity data, the out of plane component of the vorticity vector can be computed and this is presented in Fig. 8. The two flows are remarkably similar is structure, with the difference being the magnitude of the vorticity being larger for the higher Reynolds number case. - 8 -
(a) Re = 3200 (b) Re = 6400 Fig. 7 Velocity vectors behind the grid of intersecting cylinders for the two Reynolds numbers tested at (from top to bottom) z = 0mm, 30mm, and 60mm (a) Re = 3200 (b) Re = 6400 Fig. 8 Computed z-component of the vorticity vectors behind the grid of intersecting cylinders for the two Reynolds numbers tested at (from top to bottom) z = 30mm, 60mm - 9 -
3.2 Tapered Cylinder Studies The results presented here are taken from experiments with the A1, B1 and S cylinder models at Reynolds numbers between Re m = 1.15 103 and 18.4 103. The co-ordinate system used for the tapered cylinder studies is slightly different from that used in the intersecting cylinder studies, and is shown in Fig. 9 below. Fig. 9 Co-ordinate system used to present the tapered cylinder results The results obtained from tapered models show the characteristic features for this kind of flow, i.e. oblique vortex shedding, vortex dislocations and cellular shedding behavior. It becomes obvious in the distribution of the local Strouhal number, which is defined as St local = f s d local /U where f s is the local shedding frequency, dlocal is the local diameter, and U is the incoming flow velocity, along the cylinder span shown in Fig. 10: Within shedding cells, St local changes linearly, while cell boundaries appear as abrupt jumps. Correspondingly, the straight cylinder shows a flat St local distribution. Fig. 10 Plot of the local Strouhal number distribution along the span of the cylinders Fig. 11a shows the evolving vortices through the cross-flow velocity component sampled along a line parallel to the cylinder axis located 92 mm downstream of cylinder model A1. Repetitive vortex splits are visible which form multiple cells with constant shedding frequencies inside at z/l = 0.6, and t= 2s and again at t=15s. Additionally, a remarkable change in the shedding behavior is recorded: The first half of the record (t<17s) reveals two splits (three cells along the span), while the second half (18<t<30s) shows only one split, located in the middle (two cells). - 10 -
However, Hsiao et al. (1998) found three shedding cells for this Reynolds number range on cylinders with slightly smaller aspect ratios (10:1). For comparison, Fig. 11b displays the flow 46mm behind the straight model: Slight obliqueness and spanwise non-uniformities are visible while no vortex dislocations take place. The results obtained so far show the advantage of PIV compared to hot-wire anemometry and encourage further investigation. The focus lies on long time series to reveal possible periodicities in shedding schemes and on high-resolved analysis of single vortex split events. (a) Re m = 18.400, tapered cylinder model A1 (b) Re m = 2.300, straight cylinder model S Fig. 11 Comparison of the time evolution of the normalized cross flow velocity component v/u between a tapered and straight cylinder. 4. Conclusions Particle Image Velocimetry (PIV) measurements have been made in the MCLab towing tank facility at the Department of Marine Technology at NTNU, in Trondheim, Norway. A customized PIV solution manufactured from Dantec Dynamics that is capable of being submerged underwater was successfully utilized to perform measurements on two different types of turbulent flow fields; behind a grid of intersecting cylinders, and behind a tapered cylinder. The results for the intersecting cylinder cases show a highly turbulent flow characterized by the interaction of the wakes from both vertical and horizontal cylinders. The results from the tapered cylinder study showed that the PIV system was able to capture the vortex shedding dislocations that are typically found in these types of flows due to the spanwise variation of the diameter of the cylinder. The study also highlighted the feasibility of utilizing PIV as a measurement technique in towing tanks. Consequently, the results from the PIV tests will be incorporated into concurrent numerically calculated results of these two test cases ongoing at the Department of Marine Technology at NTNU. This joint approach of numerical and experimental studies highlights the benefit of applying the PIV technique in the ongoing study of marine hydrodynamics at MARINTEK and NTNU. However, the studies also showed that performing PIV measurements in towing tanks is complicated, and further steps have to be undertaken to improve the performance, accuracy, and efficiency of the technique in these facilities. - 11 -
5. Acknowledgements The authors would like to thank The Norwegian Research Council and SINTEF Fisheries for their financial support. 6. References Osaka H, Yamada H, Nakamura I, Kumata Y, Kageyama Y (1983) The Structure of a Turbulent Wake behind a Cruciform Circular Cylinder, 1 st Report, The mean velocity field. Bulletin of the JSME 26: 356-363 Osaka H, Nakamura I, Yamada H, Kumata Y, Kageyama Y (1983) The Structure of a Turbulent Wake behind a Cruciform Circular Cylinder, 2 nd Report The streamwise development of turbulent flow field. Bulletin of the JSME 26: 521-528 Zdrakovich M M (1983) Interference between two circular cylinders forming a cross. Journal of Fluid Mechanics 128: 231-246 Zdrakovich M M (1985) Flow around two intersecting cylinders. Journal of Fluids Engineering 107: 507-511. Fox T A, Toy N (1990) Wind effects on structural intersections. Journal of Wind Engineering and Industrial Aerodynamics 34:27-44 Fox T A (1991) Wake characteristics of two circular cylinders arranged perpendicular to each other. Journal of Fluids Engineering 113:45-50 Fox T A (1992) Interference in the wake of two square section cylinders arranged perpendicular to each other. Journal of Wind Engineering and Industrial Aerodynamics 40: 75-92 Piccirillo P S, Van Atta C W (1993) Experimental study of vortex shedding behind linearly tapered cylinders at low Reynolds-numbers. Journal of Fluid Mechanics 246: 163-195 Hsiao F B, Chiang C H (1998) Experimental study of cellular shedding vortices behind a tapered circular cylinder. Experimental Thermal and Fluid Science 17(3): 179-188. Shirakashi M, Bae H M, Sano M, Takahashi T (1994) Characteristics of Periodic Vortex Shedding from two cylinders in Cruciform arrangement. Journal of Fluids and Structures 8: 239-256. Raffel M, Willert C, Kompenhans J (1998) Particle Image Velocimetry, a practical guide corrected 3rd printing. Springer Fredriksson D W, Robinson Swift M, Eroshkin O, Tsukrov I, Irish J D, Celikkol B (2005) Moored fish cage dynamics in waves and currents. IEEE Journal of Ocean Engineering 30(1):28-36 Narasimhamurthy V D, Schwertfirm F, Andersson H I, Pettersen, B (2006) Simulation of unsteady flow past tapered circular cylinders using an immersed boundary method. ECCOMAS CFD06-12 -