FLOW CHARACTERISTICS AROUND A CIRCULAR CYLINDER NEAR A PLANE BOUNDARY

ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA FLOW CHARACTERISTICS AROUND A CIRCULAR CYLINDER NEAR A PLANE BOUNDARY Chang Lin*, Wei-Jung Lin*, Sing-Shing Lin** *Department of Civil Engineering, National Chung Hsing University Tauchung 402, Taiwan E-mail: clin@mail.ce.nchu.edu.tw **Gen-Yeh Engineering Consultants Inc., Taiwan Keywords: vortex shedding, circular cylinder, boundary layer, gap ratio, Strouhal number Abstract The flow characteristics around a circular cylinder placed near a plane boundary was investigated experimentally at R e = 780. Flow visualization technique was used to reveal the flow pattern with and without the influence of plane boundary layer. Particle image velocimetry (PIV) and fiber laser Doppler velocimetry (FLDV) were conducted in the measurements with boundary layer effect for different gap ratios from 4.0 to 0. Vortex shedding frequency was increased while G/D decreased from 3.0 to 0.6 and turned to be decreased as G/D was smaller than 0.6; where G is the gap distance between cylinder and plane boundary and D is the cylinder diameter. Detail results of time-averaged properties such as the gap flow and the formation lengths behind the cylinder illustrated the differences of the wake structure at different gap ratios. 1 Introduction There have been many researches of flow around a circular cylinder placed near a plane boundary, because of the interesting fluid flow phenomena and practical importance in various engineering applications (such as the design of pipelines, submarine cables, stacks, and bridge piers). Many previous investigations on the vortex shedding frequency behind a isolated cylinder have been reported (e.g., Blevins [1], Lin and Hsieh [2], Lin etc. [3]). In Blevins study, Strouhal number, S t ( = D f / U 0, where f is the vortex shedding frequency behind the cylinder, and U 0 is the free-stream velocity), is in the range from 0.20 to 0.22 at different Reynolds numbers, R e ( = D U 0 /ν, whereνis the kinematic viscosity of water). The same result of the S t with R e = 400 ~ 12000 is also included in Lin and Hsieh [2]. For the circular cylinder near a plane, it is expected that the vortex shedding was influenced by Reynolds number (R e ), the thickness of plane boundary (δ), and the gap ratio (G/D). Experiments and numerical methods were both conducted in this issue (e.g., Bearman and Zdravkovich [4], Muraoka and Tashiro [5], Taniguchi and Miyakoshi [6], Lei et al. [7]). There is a good agreement in previous studies, for the Reynolds numbers that shedding vortex appeared behind the cylinder, the flow phenomena in the wake could be classified into three regions by: (i) the far region where the flow and shedding characteristics are similar to the isolated cylinder case; (ii) the region for which the vortex shedding is influenced by a plane boundary; (iii) periodic shedding frequencies suppressed as gap ratio is smaller than the critical gap height. Bearman and Zdravkovich [4], Taniguchi and Miyakoshi [6] found the behavior with vortex shedding suppressed at the critical gap height (G/D) cr = 0.3. Most of the previous studies concentrated on the relationship between vortex shedding frequency and gap ratio, indicating that the vortex shedding was influenced by the boundary layer of the plane and suppressed at the critical gap ratios. However, the studies on the differences of flow phenomena around a 1

Chang Lin, Wei-Jung Lin, Sing-Shing Lin cylinder approaching the plane with and without plane boundary layer conditions have received little attention to date. Furthermore, a systematic study for the mean or instantaneous full-field velocity maps and the flow characteristics around the cylinder corresponding to different gap ratios still needs to be made clear in order to achieve a better understanding of such a flow. The purpose of the present study is to provide detailed insight of the flow around a circular cylinder near a plane at R e = 780 and G/D changing from 4.0 to 0. By flow visualization technique, the different flow phenomena on the net gap between cylinder and plane under the conditions with and without boundary layer are observed. As involved with the FLDV and PIV systems, the instantaneous velocity fields, the formation lengths, and the characteristics of the deflected gap flow in the wake of circular cylinder for different gap ratios will be addressed in detail to highlight the flow characteristics. 2 Experimental System and Instrumentation 2.1 Water Channel, Test Model, and Flow Visualization Technique Experiments were conducted in a recirculating water flume at the Fluid Mechanics Laboratory of the Department of Civil Engineering, National Chung Hsing University, Taiwan. The internal dimensions of the working section were 305.0 cm long, 50.0 cm wide by 54.0 cm deep. The working section is enclosed by glass windows on both sides and bottom to allow visual and optical studies throughout the flow domain. It was possible to achieve quite stable flow from 3.0 to 40.0 cm/s by employing a speed-control unit with a shaft speed feedback circuit, and by adjusting the opening of a butterfly valve. Three layers of perforated steel plates (which are installed in the upstream settling plenum 222 cm long), one piece of honeycomb 10 cm in length, four meshes with different grid sizes, and a specially designed 3-D contraction 200 cm in length were arranged to remove any large-scale irregularities and to smooth the inlet flows. By means of such a combination, a turbulence intensity of less than 0.8 % at 30.0 cm/s could be achieved at the inlet of the working section. Moreover, the spanwise flow uniformity, defined as the ratio of the uniform flow section outside the side-wall boundary layer to the flume width, was estimated to be 95.0 %. A circular cylinder (D = 13 mm, L = 430 mm) was used for experimental test model at R e = 780. By fixing the cylinder on a carriage, which moved relatively to the still water, the flow condition without boundary layer effect was simulated. The carriage was able to achieve quite stable moving speed from 0.5 to 7.0 cm/s by a control panel to the server motor. Flow visualization was carried out by using particle tracking technique. Aluminium powder were used as the tracking particles. The light source was a 6 W argon-ion laser tube (Coherent Innova 90-4), from which a laser beam was emitted and spread into a fan-shaped light sheet (about 1.5 mm thick) by a cylindrical lens. The light sheet was used to illuminate the motion of the dye tracer on a vertical plane along the longitudinal direction of the water channel, aiming to confirm two-dimensionality of the vortex structure. 2.2 Velocity Measurement Technique Local velocity histories were measured using fiber laser Doppler velocimetry (FLDV). The equipment was a two-component colorburst-based, four-beam fiber-optic system (TSI System 90-3). A 5 W argon-ion laser tube (Coherent Innova 90-4) was used as the light source. The scattered signals captured by the receiving optics of the fiber-optic probe (TSI Model 9832) were transmitted by a fiber cable into the multicolor receiver (TSI Colorlink), where the power for acousto-optic, Bragg cell, frequency shifting and downmixing, and signal amplification were supplied. The amplified Doppler signals were processed by two signal processors and then digitized using an 8-channel PC-based A/D converter. The FLDV system was mainly used to measure the streamwise velocity, u(t). Spectral analysis of the streamwise velocity fluctuation was then used to identify whether the motion of a wake vortex 2

FLOW CHARACTERISTICS AROUND A CIRCULAR CYLINDER NEAR A PLANE BOUNDARY system was periodic or not. The sampling rate was kept at 50 Hz and the sampling duration varied from 85 seconds to several minutes in each run, depending on the oscillation frequency of the vortex system. Several runs were repeated. A high-resolution particle image velocimetry (PIV) system was used to detail the entire velocity field in the wake of a cylinder near a plane. The PIV system included several main components: light source, light sheet optics, digital camera, synchronizer, and computer and acquisition software. The light source for the PIV system included the Continnum Surelite Nd : YAG dual lasers, which contained a crystal harmonic generator to produce the frequency-doubled (532 nm) green light from the original (1064 nm) invisible infrared light. The laser beam had a pulse width of 4~6 ns and a maximum energy output of 200 mj/pulse for the wavelength 532 nm. Each laser beam could be pulsed at a maximum rate of 15 Hz so that 30 frames per second could be obtained for the dual lasers. The laser beam diameter was about 3 mm. The light sheet generation optics consisted of one cylindrical lens with a negative focal length and a spherical lens with a positive focal length. With combinations of these lenses, the laser beam could be expanded into a fan-shaped light sheet about 1 mm thick. The image recording equipment used in this study was a digital cross-correlation camera (TSI Pivcam 10-30) with 1024 1024 pixel resolution and a maximum rate of 30 frames per second. To capture a flow field image with PIV, the laser pulse and digital camera must be synchronously triggered by the TSI Laser Pulse Synchronizer to provide the correct sequence and timing. The computer-controlled synchronizer could easily be used to set up the appropriate pulse separation and pulse duration for the particle images of the flow field through the software. During image capturing, the synchronizer locked in with the frame rate of the digital camera and output the trigger signal to control the Nd : YAG laser pulsing sequence so that the laser pulses were exactly located in the appropriate frames of the digital camera. By employing a frame straddling technique, the time between frames can be reduced as low as a few microseconds. Cross-correlation analysis using TSI Insight NT Analysis Software was then performed on successive frame-pairs to obtain two-dimensional velocity fields at a rate up to 15 frames per second. Using the camera and the cross-correlation techniques, the directional ambiguity in the flow field could be satisfactorily resolved. It should be mentioned here that due to the high power Nd : YAG pulse lasers and abundant neutrally suspended particles in groundwater, no more seeding particles were introduced into the water channel. Under such seeding conditions, high quality particle images could be obtained in each frame for PIV measurements. 2.3 Coordinate Systems The coordinate systems employed for the present study is shown schematically in Fig. 1. The origin is located at the center of the circular cylinder, where x is the streamwise axis with x = 0; y is the vertical (transverse) axis with y = 0; and z is the spanwise axis with z = 0 at the midspan of the cylinder. Fig. 1 Schematic diagrams of the experimental arrangement and coordinate systems. top view; side view. 3

Chang Lin, Wei-Jung Lin, Sing-Shing Lin 3 Results and Discussion 3.1 Observation of the flow around cylinder Flow visualization is the most straightforward method to demonstrate the flow around a cylinder as it is positioned near a plane. To understand the effect of the plane, it is helpful to realize the flow patterns for an isolated cylinder or to know the difference between the plane with and without boundary layer first. 3.1.1 Wake behind an isolated circular cylinder Vortex shedding is well known as one of the main characteristics in the near wake of a circular cylinder. As the fluid passes a cylinder, the inward spiraling vorticity from the upside and downside of the cylinder, entrains the adjacent irrotational flow into the alternative shedding vortex. Photo 1 (a, b) present the typical instant flow patterns in the near wake of an isolated circular cylinder for R e = 780. It is observed the formation region at x/d = 2.0 ~ 3.0 and the regular vortices shed from both the upside and downside at the end of this region to form the vortex street downstream the cylinder. 3.1.2 Flow patterns without plane boundary effect The simplest condition of the influences by a plane will be totally neglecting the effect of the plane boundary layer. Photo 2(a ~ c) present the flow patterns in front of the cylinder at G/D = 0.3 ~ 0.1, δ/ D = 0, and R e = 780. It can be easily observed that the stagnant point moves to the bottom as the cylinder is positioned closer to the plane. (c) Photo 1 Two instant flow patterns in the near wake of a cylinder at G/D = and R e = 780. Photo 2 Flow patterns in front of a cylinder in different gap ratios at R e = 780 without plane boundary layer. G/D = 0.3; G/D = 0.2; (c) G/D = 0.1. 4

FLOW CHARACTERISTICS AROUND A CIRCULAR CYLINDER NEAR A PLANE BOUNDARY Photo 3 shows the vortex pattern behind the cylinder without plane boundary effect at G/D = 0.2, and R e = 780. The larger scale vortices are formed on the upside of the cylinder than those are formed on the plane side. The flow pattern in photo 3 is similar to that in photo 3, which is under the condition with boundary effect. In both these two pictures, vortices structures can be observed on the upside behind the cylinder. With the effect of plane boundary layer, no vortex is formed on the plane side downstream. recirculating eddies are formed on the plane upstream the cylinder at small gap ratios, and a larger scale of the eddy is developed at a smaller gap ratio. It is also observed the gap flow between cylinder and plane is constricted by the enlargement of this eddy, and the stagnant point on the cylinder slightly moves to the upside as the gap ratio decreased. (c) Photo 3 Flow patterns in the near wake of a cylinder at R e = 780 with and without plane boundary layer in absolute motion. with boundary layer; without boundary layer. 3.1.3 Flow patterns with plane boundary effect It can be expected that the existence of the plane boundary layer could have some influences as a cylinder moved to the plane. In fact, flow patterns upstream are quite different under the condition with and without boundary layer effect. Photo 4(a ~ d) display the flow patterns upstream the cylinder at different gap ratios for R e = 780, and δ/ D = 1.41. The (d) Photo 4 Flow patterns in front of a cylinder in different gap ratios at R e = 780 with plane boundary layer. G/D = 0.3; G/D = 0.2; (c) G/D = 0.1; (d) G/D = 0. 5

Chang Lin, Wei-Jung Lin, Sing-Shing Lin Photo 5 Two instant flow patterns in the near wake of a cylinder at G/D = 1.0 and Re = 780. Photo 5(a, b) show the two instants of regular vortex shedding behind cylinder at G/D = 1.0. The corresponding instant velocity fields are shown in Fig. 2 with the same flow condition in photo 5. It can be seen that the gap flow slightly deflected to the cylinder side and the separation occurred on the plane, which formed a low-speed recirculation region downstream the plane. It can also be observed the interaction between the vortex street and this low-speed recirculation region along the plane. Photo 6(a ~ c) demonstrate the flow patterns downstream the cylinder as gap ratios equaling 0.2, 0.1, and 0. For G/D = 0.2, photo 6 shows the gap flow rolled up and formed the formation region behind the cylinder. It is noticeable that although the differences in magnitude between the vortices from upside and downside of the formation region, the vortices still shed regularly. (c) Fig. 2 Two instant velocity fields corresponding to the flow condition of photo 4. Photo 6 Flow patterns in the wake of a cylinder near a plane boundary in different gap ratios at Re = 780. G/D = 0.2; G/D = 0.1; (c) G/D = 0. 6

FLOW CHARACTERISTICS AROUND A CIRCULAR CYLINDER NEAR A PLANE BOUNDARY Photo 6 and 6(c) present the flow pattern at G/D = 0.1 and 0, respectively. The wake flow seemed similar in these two pictures although in photo 6 the gap flow still rolled up, no vortex shedding but the large scale recirculation region on the plane is formed downstream the cylinder. It should be noted that the eddy structure formed and moved downstream in the border between the uniform flow field and the large scale recirculation region at x/d = 4.0 ~ 6.0, y/d = 0.5 ~ 1.5. (c) Fig. 3 Time-averaged velocity fields for different gap ratios. G/D = 1.0; G/D = 0.2; (c) G/D = 0.1; (d) G/D = 0. 3.2 Wake characteristics To achieve better understanding of the features at different gap ratios, the wake characteristics of the cylinder are investigated by the measurements of PIV for R e = 780 and δ/ D = 1.41. 3.2.1 Time-averaged velocity fields The data in Fig. 3(a ~ d) show the detailed results of time-averaged velocity fields which measured by PIV for about 50 vortex shedding cycles. It is observed that the gap flow rolled up behind the cylinder deflecting the formation region to the upside slightly and the interaction between vortex street and the low-speed region along the plane in Fig. 3(a, b). As the gap ratios decreased down to 0.1 and 0, a large recirculation region is formed behind the cylinder in Fig. 3(c, d). Although the gap flow still rolled up and separated from the plane at G/D = 0.1, it is too weak to form the regular vortices. 3.2.2 Closure point of formation region As the fluid passes a circular cylinder, the inward spiraling vorticity from the upside and downside of the cylinder, entrains the adjacent irrotational flow into the vortex in the formation region. With analyzing the data measured by PIV, the location of the mean closure point could be picked out precisely. (d) Fig. 4 Positions of the closure points for different gap ratios at R e = 780, δ/ D = 1.41. 7

Chang Lin, Wei-Jung Lin, Sing-Shing Lin Fig. 4 presents the influence of a plane on closure point locations. It is observed that as G/D 3.0, the location of the closure point is equally to the isolated cylinder condition which occurred right behind the centerline of the cylinder. As the cylinder is moved toward a plane, the closure point position is moved to the upside downstream the centerline of the cylinder, indicating the effect of gap flow deflection. 3.2.3 Separation point on the plane and the gap flow At the small gap ratios, the gap flow would deflect to the upside and the low-speed region would be formed downstream along the plane. The position where gap flow rolled up can be defined as the separation point on the plane. This point would be moved within a small range as the gap flow interacting with the formation region in the period of vortex shedding. Fig. 5 shows the range of the separation points on the plane at various gap ratios. As the cylinder moved closer to a plane, the separation point is moved to the upstream along the plane, which indicating the deflection of the gap flow. For gap ratios smaller than G/D 0.3, the positions of the separation point abruptly moved downstream the plane. As the weak gap flow shown in photo 6 for G/D = 0.1, the separation points occurred back close to the cylinder at x s /D = 0.85 ~ 0.91. The positions of the maximum timeaveraged velocity vector of the gap flow are analyzed to determine the mean axial line. Fig. 6 presents the result of the nonlinear fitting curve and experimental data of the gap flow at different gap ratios. The regression equation can be expressed as: (y m /D)/(G/D) 0.15 =0.059[(x m /D)/(G/D) 0.45 ] 2 +0.0398(x m /D)/(G/D) 0.45-0.846 (R 2 = 0.9246) Fig. 6 Regression curve of the gap flow at different gap ratios for R e = 780, δ/ D = 1.41. Fig. 5 Range of the separation points on the plane at various gap ratios for R e = 780, δ/ D = 1.41. Fig. 7 Strouhal number versus gap ratio at R e = 780. 3.3 Strouhal number The characteristic of vortex shedding frequency is presented by the Strouhal number, S t. Fig. 7 shows the gap ratio effect on the Strouhal number for different boundary layer thicknesses (δ/d = 1.41, 1.22, 0.86) at R e = 780. 8

FLOW CHARACTERISTICS AROUND A CIRCULAR CYLINDER NEAR A PLANE BOUNDARY It is demonstrated that the Strouhal numbers are almost constant and equal to 0.218 for G/D 3.0, which are consistent with that in Blevins [1] for a isolated circular cylinder without the effect of plane boundary. The Strouhal number increases as the gap ratio is decreased, and a maximum value is observed at G/D = 0.6. As the cylinder is positioned closer to the plane, G/D 0.6, the reduction in the Strouhal number is observed. 4 Conclusion Flow characteristics around a circular cylinder were experimentally investigated for the net gap height to circular cylinder diameter ratios ranging from 4.0 to 0, at the Reynolds number R e = 780. Flow patterns are revealed by visualization technique and velocity fields at different gap ratios. Spectral analyses of laser Doppler measurements have provided the information on the periodic flow character behind the cylinder placed close to a plane. The main results of the paper are summarized as follows: 1. Flow patterns in front of the cylinder are quite different as the cylinder approaching to a plane with and without the plane boundary layer. In the condition with plane boundary layer, the recirculating eddy formed on the plane upstream the cylinder and the front stagnant point on the cylinder moved slightly upside as gap ratios is reduced. Without the effect of plane boundary layer, no recirculating eddy is formed and the front stagnant point moves to the downside as the cylinder placed closer to a plane. 2. As the cylinder is moved form infinity to the plane, the regular vortices shed from both the upside and downside at the end of the formation region could be influenced by the plane. The deflected gap flow suppresses the growth of the downside vortex gradually as the distance between cylinder and plane decreases. However, vortex shedding disappear at very small gap ratios and large scale recirculation region on the plane is formed downstream the cylinder. 3. The gap ratio influences the vortex shedding phenomenon behind the cylinder with plane boundary effect at R e = 780. As a cylinder is positioned closer to a plane, different flow regimes could be identified as follows: For G/D 3.0, vortex shedding frequency is not influenced by the plane. The Strouhal number (S t ) is constant and equals to 0.218 approximately. The vortex shedding frequency increases while the G/D is decreased from 3.0 to 0.6. (c)the shedding frequency decreases as the G/D is smaller than 0.6. Acknowledgments The authors gratefully acknowledge the support of this work by National Science Council, Taiwan, Republic of China, under grants NSC 93-2611-E-005-002. References [1] R. D. Blevins, Flow-induced vibration, Van Nostrand Reinhold, New York, N.Y.,1977. [2] C. Lin, and S.C. Hsieh, Convection velocity of vortex structures in the near wake of a circular cylinder, Journal of Engineering Mechanics, ASCE, Vol. 129, No. 10, pp. 1108-1118, 2003. [3] C. Lin, S. C. Hsieh, M. J. Kao, and H. Y. Hsu, Study on mean velocity characteristics of near-wake flow behind a circular cylinder: application of simultaneous measurement technique by PIV and FLDV, Journal of the Chinese Institute of Civil and Hydraulic Engineering, Vol. 16, No. 1, pp. 80-98, 2004 (in Chinese). [4] P. W. Bearman, and M. M. Zdravkovich, Flow around a circular cylinder near a plane boundary, Journal of Fluid Mechanics, Vol. 89, part 1, pp. 33-47, 1978. [5] K. Muraoka, and S. Tashiro, The effect of the wake from circular cylinder on boundary-layer transition(1 st report, The effect of gap between the cylinder and surface), Journal of the Japan Society of Mechanical Engineers, Series B, Vol. 50, No. 460, pp. 3152-3158, 1985 (in Japanese). 9

Chang Lin, Wei-Jung Lin, Sing-Shing Lin [6] S. Taniguchi, and K. Miyakoshi, Fluctuating fluid forces acting on a circular cylinder and interference with a plane wall, Experiments in Fluids 9, pp. 197-204, 1990. [7] C. Lei, L. Cheng, S.W. Armfield, and K. Kavanagh, Vortex shedding suppression for flow over a circular cylinder near a plane boundary, Ocean Engineering 27, pp. 1109-1127, 2000. 10