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BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications Milano, Italy, July, 20-24 2008 FLOW AROUND WALL-MOUNTED CYLINDERS WITH DIFFERENT GEOMETRIES: EXPERIMENT AND SIMULATION Stefan Becker, Irfan Ali and Thomas Uffinger Institute of Fluid Mechanics University of Erlangen-Nuremberg, Cauerstr. 4, 91058 Erlangen, Germany e-mail: [email protected] Keywords: LDA-measurements, CFD, turbulence models, unsteady flow. Abstract. The flow field around cylindrical structures such as pantographs of trains, highrise buildings, car antennas, beams, fences and supports in internal and external flows is very complex. Topic of the present work is the investigation of the flow around simplified wallmounted cylindrical geometries. The aim is to get detailed information about the flow structures and phenomena around such cylinders. In combination with acoustic inquiries which have been carried out at the institute the process of aeroacoustic sound generation is meant to be understood more detailed. From a variety of cylinder geometries investigated acoustically three were chosen for the studies of the flow field – a square cylinder, a cylinder with an elliptical afterbody and a cylinder with a wedge in front of it. The investigations are mainly focused on an approach velocity U∞ of 10 m/s. Experimental and numerical methods are complementary used. Measurements were carried out with a laser Doppler anemometer. For each geometry a highresolution grid which consists of several planes is used. For the numerical investigations two different approaches were applied. The computations were carried out as large eddy simulations (LES) and also as scale adaptive simulations (SAS). 1 Stefan Becker, Irfan Ali and Thomas Uffinger 1 INTRODUCTION Studies of the flow around simplified ground bound cylinders are a major contribution to understand the fundamental basics of bluff body aerodynamics. Currently, interests are also focused on the radiated sound field of such geometries. Cylindrical geometries are present in many engineering applications such as the pantographs of trains, high-rise buildings, car antennas, beams, fences and supports in internal and external flows. Therefore, the flow around cylindrical objects has been the subject of a large number of research activities. The selected geometries are based on previous investigations of the flow induced sound field. The results show that drag reduction does not correspond automatically with the flow induced sound for the different wall mounted cylinder geometries [1]. To get a better physical understanding about these phenomena very extensive investigations of the basic flow and turbulence field were done by using experimental and numerical methods. Based on the acoustic part of the objective, the work was focused on the unsteady flow field and the turbulence quantities. A direct comparison between both methods shows a dependency on the different turbulence modeling in the simulations. Necessary accuracy of the simulations with respect to flow induced sound prediction will be discussed. The setup investigated in this work is shown in Fig. (1). A rigid square cylinder with edge length D is mounted vertically on a flat wall. The cylinder has a constant aspect ratio (L/D) of 6. The flow over a finite-length cylinder is strongly three-dimensional due to the interaction of the tip vortex with the Kármán vortex shedding and the horseshoe vortex. The resulting flow field strongly depends on the aspect ratio and the ratio between cylinder length L and the boundary layer thickness [2], [3], [4]. When the aspect ratio exceeds 5 (smooth geometries), periodic spanwise vortex shedding occurs over almost the whole span except very close to the wall. Additional separation occurs from the top of the cylinder, but the flow region behind the cylinder is dominated from the spanwise vortex shedding. The general flow structure for this case is depicted in Fig. (2). Figure 1: Basic setup: Wall mounted square cylinder in cross-flow Figure 2: Flow structure behind a square prism with aspect ratio L/D > 5 [3] The nature and the thickness of the boundary layer in relation to the cylinder length influences the flow field. On approaching the cylinder, the boundary layer separates due to the adverse pressure gradient inducing vortices which are being stretched around the cylinder forming a horseshoe vortex. The Strouhal number St related to the spanwise vortex shedding frequency increases with increase of the ratio between cylinder length and boundary layer thickness. 2 Stefan Becker, Irfan Ali and Thomas Uffinger Different shapes are used as fore- or afterbodies on the square cylinder and their influence on the flow field is studied. Starting from the basic square cylinder geometries with an additional elliptical forebody (outer dimensions 20 x 30 mm), an elliptical afterbody with the same dimensions and a three-edged wedge (dimensions 20 x 10 mm) are tested. The square cylinder itself has a edge length of D = 20 mm and a length of L = 120 mm. 2 EXPERIMENTAL INVESTIGATIONS The measurements of the flow field were carried out in the aerodynamic wind tunnel of the institute using a two-component laser Doppler anemometer. Here, the square cylinder is not placed on the floor of the tunnel. Instead, it is mounted in the center of a plate (thickness 12 mm) which is located about 0.5 m above the tunnel floor and extends 1 m in the streamwise direction and 0.6 m in the lateral direction (Fig. (3)). At the leading edge of the plate an NACA 0001 profile is attached. Thereby a thinner boundary layer compared with the cylinder length can be obtained. The leading edge of the plate is located 0.5 m downstream of the exit cross-section of the wind tunnel. The aerodynamic wind tunnel is also of closed return type. The nozzle exit cross-section has a width of 1.87 m in the horizontal direction and a height of 1.4 m in the vertical direction (contraction ratio 5:1). The turbulence level of this tunnel is 0.12 %. Figure 3: LDA - probe during the measurements Measurements are carried out at U∞ = 10 m/s and U∞ = 30 m/s, resulting in Reynolds numbers ReD of 12.5·104 and 37.6·104 based on the cylinder edge length D. When carrying out measurements at a flow speed of 30 m/s, in both tunnels, a tripping tape is placed near the upstream end of the plate in order to create a well-defined turbulent boundary layer. The flow field of the selected configurations is investigated via LDA. Fig. (4) illustrates the three-dimensional flow field of the three studied geometries. In all cases, the horseshoe vortex system caused by the adverse pressure gradient of the stagnation point can be seen in front of the cylinder. The recirculation zone and the wake behind the cylinder are also typical flow features. The behavior of the flow over the top of the cylinder is rather different for the three cases. For the plain square cylinder, the flow separates at the top leading edge and does not reattach any more. With the elliptical body mounted on the back side of the cylinder, the flow separates at the top leading edge also, but reattaches at the top trailing edge. In the case of the cylinder with a wedge on the front side, no separation on the cylinder top side is evident. The drag coefficient is calculated by the momentum loss based on a comparison of the distribution of the mean velocity in different planes in front of and behind the cylinder geometries. The value of the drag coefficient correlates with the values of the turbulent kinetic energy k, 3 Stefan Becker, Irfan Ali and Thomas Uffinger which is also displayed in Fig. (4). The highest amount of turbulent kinetic energy k and the largest drag coefficient cD are observed for the flow around the unmodified cylinder. The lowest values for both the turbulent kinetic energy and the drag coefficient are found for the cylinder with the wedge in front of it. At the same time, the configuration with the wedge is the most silent one. However, this does not mean that a reduction in the turbulent kinetic energy or the drag coefficient automatically causes a reduction in the sound generated by the geometry, since the configuration with an elliptical afterbody also shows a reduction in the turbulent kinetic energy and the drag coefficient in comparison with the unmodified square cylinder, but a rise in the sound pressure level. To understand this physical phenomenon, one has to look in more detail at the measured flow fields, which is done in the following. Figure 4: Flow visualization, velocity distribution and turbulent kinetic energy for a) unmodified cylinder, b) cylinder with elliptically afterbody and c) cylinder with wedge in front (U∞ = 10 m/s) 4 Stefan Becker, Irfan Ali and Thomas Uffinger For the interpretation of the velocity fields, just one y-z plane at a distance of 2 D behind the back side of the unmodified cylinder and the center plane (x-z) is used. Fig. (5) displays the distribution of the mean velocity in the mentioned y-z plane for the unmodified cylinder. The velocity vectors in the center plane for the same geometry are shown in Fig. (6). The velocity distribution is symmetrical in the y-z plane. Vortex cores are obtained due to the periodic flow separation at the leading edges of the cylinder which forms a vortex street behind it. The influence of the flow over the top of the cylinder is strong, as Fig. (6) shows. Fluctuations of the U and V components of the velocity are of about the same level and larger than fluctuations of the third component W. Figure 5: Mean velocity of the unmodified cylinder at U∞ = 10 m/s in the y-z plane Figure 6: Vector plot and streamlines for the unmodified cylinder at U∞ = 10 m/s (center plane) The velocity field for the flow around the cylinder with an elliptical afterbody is displayed in Fig. (7) and Fig. (8). Overall turbulence is reduced compared with the unmodified square cylinder (Fig. (4)). The distribution of the velocity is also symmetrical in the y-z plane. However, due to the afterbody and the resulting reattachment of the roof vortex, the influence of the flow over the top of the cylinder on the recirculation area is much smaller and the vortex street behind the cylinder can develop almost undisturbed. The velocity fluctuations are dominated by the U component whereas the fluctuations of the V and W components are lower and of about the same level. The velocity field of the third investigated geometry (wedge in front of the cylinder) is shown in Fig. (9) and (10). In this case, the flow field is no longer symmetrical in the y-z plane (both mean and fluctuating field). Responsible for this flow characteristic is the sharp edge of the wedge. This edge produces an instability point in front of the cylinder. Usually, the oncoming flow in the wind tunnel experiments cannot be perfectly homogeneous and symmetrical with respect to the center plane. Therefore, small disturbances or inhomogeneities at the instability point or line cause non-uniform incoherent vortex formations. Furthermore, no flow separation occurs at the upper leading edges of the wedge. A roof vortex of slightly smaller size than in the case of the unmodified cylinder is present in the wake of the cylinder nevertheless. Turbulence levels found downstream of the cylinder are the lowest of all three geometries. The fluctuations of all velocity components are of about the same magnitude. 5 Stefan Becker, Irfan Ali and Thomas Uffinger Figure 7: Mean velocity of the cylinder with an elliptical afterbody at U∞ = 10 m/s in the y-z plane Figure 8: Vector plot and streamlines for the cylinder with an elliptical aferbody at U∞ = 10 m/s (center plane) It can be summarized that the level of turbulent kinetic energy is not a measure of the radiated sound. Moreover, conclusions cannot be drawn from the drag coefficient. The investigations show that two-dimensional flow structures of a large size, as found in an undisturbed vortex street behind the cylinder geometry, result in higher sound pressure levels. Once the influence of the flow over the top becomes stronger, the vortex street is disturbed and coherent vortex structures become smaller. This effect can be clearly seen if the wedge is added in front of the square cylinder. Then the flow field is highly three-dimensional and smaller vortices are obtained. Furthermore, if the flow field is highly three-dimensional, the fluctuations in all three coordinate directions are of about the same level (configuration with wedge in front of the cylinder). Although the magnitude of the turbulent kinetic energy is nearly equal in the case of the configuration with the elliptical afterbody and the configuration with the wedge in front of the cylinder, the second one is more silent as the fluctuations are isotropic. In the case of the elliptical afterbody, one component of the fluctuations is dominant. Figure 9: Mean velocity of the cylinder with a wedge in front at U∞ = 10 m/s in the y-z plane Figure 10: Vector plot and streamlines for the cylinder with a wedge in front at U∞ = 10 m/s (center plane) 6 Stefan Becker, Irfan Ali and Thomas Uffinger 3 NUMERICAL SIMULATION Two different unsteady fluid fields were computed with the in-house CFD code FASTEST-3D on the one hand and with the commercial CFD code ANSYS-CFX on the other hand. The simulation performed with FASTEST-3D was carried out as a LES (large eddy simulation) using a Smagorinsky model to simulate the transient flow field with a complete resolution of the boundary layer. Simulations were performed on a SGI-ALTIX system with 16 processors using a numerical domain containing approximately 3.1 million volume cells and a time step size of ∆t = 10 µs. For the simulation of the flow using the code ANSYS-CFX a turbulence modeling approach based on SAS (scale adaptive simulation) was employed. The SAS approach allows to use coarser grids than those used in LES computations. Therefore approximately 1.1 million cells were used in this case, which resulted in a shorter computational time and less memory usage. Regarding time discretization, a time step size of ∆t = 20 µs was used in this simulation. The numerical results for the time averaged mean velocity match very well with experimental data in the area of the top vortex above the different cylinder geometries for both the LES and the SAS simulation. The horseshoe vortices in front of the three geometries are also reproduced by the numerical investigations very well. In the wake of the three cylinders either the LES or the SAS matches better with experimental data depending on the location of the comparison. For example, Fig. (11) shows the numerical and the experimental data of the averaged mean component of the velocity in the center plain at two different positions behind the square cylinder (0.5 D and 2 D behind the backside of the cylinder). For both positions some differences between simulations and experiments exist. But the overall agreement is still very satisfactory for both simulation approaches. Figure 11: Comparison of the averaged mean velocity in the centerplane 0.5 (left) and 2 D (right) behind the backside of the square cylinder The magnitude of turbulent kinetic energy is lower than in the experiments for both numerical approaches. The computed flow fields show a strongly unsteady behavior in the wake of the investigated geometries. There is a complex interaction of the top vortex with the developing vortex street behind the cylinders. In addition to the frequency of vortex shedding a much lower fre- 7 Stefan Becker, Irfan Ali and Thomas Uffinger quency is observed. Obviously the vortex shedding shows an unsteady behavior of a much lower frequency than the one of the process of vortex shedding itself. Fig. (12) shows the transient fluid fields obtained from both computations using Q factor analysis. The coherent structures are shown as iso-surface, for the values of λsym = −10000, where λsym is the eigenvalue of the symmetric tensor. The colour of the contour is based on the transient velocity. Figure 12: LES simulation (left) and SAS simulation (right) 4 CONCLUSION The direct comparison between the experimental and numerical results shows a good agreement in the time averaged mean velocities. The calculated turbulent kinetic energy is lower than what we obtained in the experiments. The LES and the SAS approaches provide comparable accuracy, but the SAS simulations need less resources whereas computation speed is higher. A stable vortex frequency cannot be identified for the numerical investigations. In addition, a periodic behavior of the process of vortex shedding is detected. The flow behind the cylinder has a strong unsteady character. The flow field is highly three-dimensional and the top vortex strongly influences the flow behind the different cylinder geometries. These observations match very well with the conclusions drawn from the experimental results. REFERENCES [1] S. Becker, M. Kaltenbacher, I. Ali, C. Hahn, M. Escobar. Aeroacoustic Investigation of the Flow around Cylinder Geometries - a Benchmark Test Case, 13th AIAA/CEAS Aeroacoustics Conference, Rome, AIAA-2006-3511, 2007 [2] H. F. Wang. Flow structure around a finite-length square prism', 15th Australasian Fluid Mechanics Conference, University of Sydney, September 13-17, 2004. [3] H. Sakamoto. Vortex shedding from a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer, J. Fluid Mech., Vol. 126, pp. 147-165, 1983 [4] S. Becker, H. Lienhart, and F. Durst. Flow around three-dimensional obstacles in boundary layers, J. Wind Eng., Vol. 90, pp. 265 --279, 2002. 8