Comparison of Different Configurations of Two Spheres at Re=5000 in a Uniform Flow

Transcription

1 Comparison of Different Configurations of Two Spheres at Re=5000 in a Uniform Flow Muammer Ozgoren 1,*, Sercan Dogan 1, Eyub Canli 1, Huseyin Akilli 2, Besir Sahin 2 1: Department of Mechanical Engineering, Faculty of Engineering, University of Selcuk, Konya, Turkey 2: Department of Mechanical Engineering, Faculty of Engineering and Architecture, University of Cukurova, Adana, Turkey * correspondent author: mozgoren@selcuk.edu.tr Abstract In this study, flow characteristics past a sphere and dual spheres in side-by-side, staggered at an angle of 30 o and in-lined arrangements were experimentally investigated. The experiments were conducted employing a Particle Image Velocimetry (PIV) system and Rhodamine 6G dye method in a water channel at Re=5000. A peculiar geometry of sphere/spheres orients the instantaneous flow characteristics around sphere/spheres to be profoundly three dimensional as well as unsteady in the wake region. It was demonstrated that all of the arrangements developed a very chaotic structure in the wake region. In addition, time-averaged flow patterns such as streamline topology, velocity components, rms velocities in x and y directions were fairly symmetrical with respect to the sphere equator line. Dual sphere experiments were performed with three altered gap ratios (G/D) of spheres, for example, G/D=1.0, 1.5 and 2.0. Here, G is the length between the focal points of the spheres and D is the sphere diameter. In comparison to a sphere case, at G/D=1.0, appearances of wake of dual spheres are identical to a single sphere case but the wake expands to a larger size. A jet flow at G/D=1.5 occurs between the spheres for three different arrangements. For G/D=2.0, the wake for each sphere becomes a separated region and the effect of jet like flow disappears more or less completely. The results obtained in this study can be a fruitful source for developing and validation of new codes both in scientific and commercial manner. 1. Introduction A vast variety of solutions for flow problems have been developed in the fundamental fluid dynamics research area. These basic researches include theoretical approaches, experimental observations and advanced numerical simulations using advanced computational facilities. Results and interpretations are often presented having various variable and dimensionless numbers. For instance, most frequently used flow variables are velocity and pressure, in some cases, to interpret vortex induced vibrations, flow induced forces. In this senses, accurate measurement of velocities in the separated flow domain vitally important to interpret vortex induced vibrations, flow induced forces and turbulent statistics. Digital Particle Image Velocimetry (PIV) is one of the most commonly used experimental methods in present time to study e unsteady flow problems. Various experimental research methods have their own advantages and disadvantages. This flow measuring technique is capable of capturing instantaneous velocity vectors in a certain flow domain with an acceptable sensitivity. Distributions of velocity components and turbulence statistics over the flow field and vorticity can be derived from these instantaneous velocity data as determined in the present work. Pinar et al. (2013) have reported the behavior of flow past a single and two sphere located side-by-side using the PIV technique to report the effect of G/D ratios on the downstream wake and jet like flow occurring in between side-by-side spheres. Flow characteristics of cylinder and sphere have been compared by Ozgoren et al. (2011) in the free-stream flow at Re=5000 and employing PIV. They have concluded that it was quite hard to distinguish two dimensional time-averaged wake patterns of cylinder and sphere. As known that flows downstream of circular cylinders in the free-stream are two dimensional, but, it is three dimensional in the case of sphere due to its geometry. This difference indicated that the flow at the rare of sphere is more disordered comparing to the flow a single cylinder in the free-stream. Similarly, flow around a single sphere for Re=11000 was also studied experimentally by Jang and Lee (2008). This method of - 1 -

2 velocity measurement can obtain quantitative information. For example, it is possible to measure instantaneous velocity readings over the flow domain of separated flow region (Ozgoren, 2013). There are many investigations in the open literature related to sphere/spheres arrangements and some of them are stated here. The flow characteristics past the sphere in the streamwise plane at the subcritical Reynolds number, Re=1.1x10 4 have been studies experimentally by Jang and Lee (2008) in order to identify evolving vorticity, the length recirculation and turbulence statistics. Instabilities of wake and shear-layers which are the key elements in reveling the flow characteristics in the sphere wake studied by Yun et al. (2006) using large eddy simulations for Re=3,7x10 2 and Re=1x10 4. Patterns of sphere wake Classifications in relation to the Strouhal number, St for 300 Re 4 x10 4 have been done by Kiya et al. (2001), Sakamoto and Haniu (1990). The periodic emanating of counter rotating of vortex filaments have been demonstrated by Leweke et al. (1999) in terms of visualization of flow behavior in the sphere wake for Re=320. A drag of sphere and its wake varying Reynolds numbers from Re=8000 to Re=16000 have been investigated experimentally by Tsuji et al. (1991) for periodically pulsating flow. It has been reported that intensity of turbulence in the wake is weaker with the time of acceleration than deceleration. Kim and Durbin (1988) have stated that the detached shear-layers with the small-scale instability and wake with the high rate of instability cause two modes with different frequency in turbulent wake at a rear of sphere. Achenbach (1972, 1974) observed the unsteady behaviors of a sphere wake at Re=1,000 employing dye visualization and measured skin friction to determine flow detachment angles for Reynolds numbers, from Re = 10 5 to Re=10 6. There are several numerical studies available for 3-D flows over a sphere in the literature some of which are; Cichocki et al. (1988), Dandy and Dwyer (1990), Johnson and Patel (1990), Tomboulides et al. (1991), Kim et al. (1993), and Hassanzadeh et al. (2011, 2013 ). Influences of positioning a second sphere at a periphery of a reference sphere at a defined angle which is based on the direction of main flow have been studied by Tsuji et al. (1982, 1991 and 2003), Liang et al. (1996), Chen and Wu (2000) and Prahl et al. (2007), Jadoon et al. (2010), Pinar et al. (2013), Ozgoren (2013). The drag applied on a pair of interacting in-lined particles for Reynolds numbers based on particle diameter varying from 20 to 130 have been examined by Zhu et al. (1994). Preliminary studies were performed by Ozgoren et al. (2007) for the in-lined two spheres and Ozgoren et al. (2009) for the staggered two spheres. They stated that the effect of the first particle on the drag of the second particle is considerably higher than that of the second particle on the first particle. The periodic pair of wakes at the rear of two spheres oriented side-by-side in a free-stream for Re with the range of 200 Re 350 have been investigated experimentally as well as numerically by Schouveiler et al. (2004) Flow structures of an interactive sphere for the Re based on particle diameter less than 200 have been studied by Chen and Wu (2000). The size of the sphere periphery and effects of distance between particles on the drag are further influential when the secondary sphere is placed in the forward side of the reference sphere. For the low Reynolds number, Folkersma et al. (2000) studied the flow interactions between spheres numerically employing a finite element method. Kim et al. (1993) investigated the 3-D flow past the two dual spheres kept stationary perpendicular to the free-stream flow direction, for Reynolds numbers of 50, 100, 150. It was realized that the coefficient drag C D, and gradually levels off to the value for an isolated sphere. The relation between drag forces and the presence of the neighboring spheres at Re=10 4 was reported by Lee (1979). In the study of Jadoon et al. (2010), two spheres were investigated in respect of their position changing in angle between the spheres incrementally in the range of 0 o -90 o by arranging increment steps to 15 o for separation distances 1.5 and 3 times the diameter of the spheres. Separation distance and the Reynolds number decrease the effect of the interactions when their values are increased. Spheres in tandem formation was reported by Prahl et al. (2009) after a numerical investigation for Re=300. The distance between spheres were changed between 1.5 to 12 sphere diameters and inlet condition was set to steady and pulsating conditions respectively. In this study, lift and drag fluctuations were found to be bigger in magnitude comparing to the single sphere since the flow is unsteady. On the experimental side, Ozgoren et al. (2011) presented PIV and dye visualization results of a measurement plane located rear side of a sphere and a cylinder according to the flow direction for 5000 and Reynolds numbers. They showed that positional arrangements and geometries of blunt bodies act as an independent variable effecting the turbulence characteristics and wake regions. Ozgoren et al. (2013) also performed a study for a sphere located over a flat plate at 5000 Reynolds number, with the help of a PIV system. After flow was tripped at the leading edge of the flat plate, a turbulent boundary layer was obtained and sphere was placed in that - 2 -

3 boundary layer by the authors. As a result, authors proposed that wake and main flow were mixed due to a jet like flow between sphere and the flat plate depending on distance of sphere from the plate surface. There is a considerable effect of the gap ratios which influence the interaction of the sphere wake and the boundary layer. Additionally flow detachment from the surface of the flat plate is also effected. Asymmetric flow characteristics of the sphere are more evident because of the boundary-layer flow patterns. As a representative study for the flow phenomena comprising spheres more than two, Ozgoren (2013) investigated flow around three spheres located at the corners of an equilateral triangle at Reynolds Number 5000 defined to the sphere diameter. In this three sphere case, it was stated that flow characteristics are changed greatly as a function of the distance between spheres. More recently, Pinar et al. (2013) have examined the flow characteristics for two side-by-side spheres when they are located in a uniform flow at Re=5000 by means of qualitative examination (i.e. dye visualization) and quantitative investigation (i.e. PIV). This study is targeting a comparison between the single sphere and arrangements of side-by-side, staggered with 30 o angle and in-lined two spheres in respect of vertical flow structures via PIV and dye visualization which has various applications in fluid dynamics phenomena. 2. Experimental Setup and Instrumentation Experiments were conducted in a water channel with a test section length of 800 cm and a width of 100 cm at the Department of Mechanical Engineering of Cukurova University, Turkey. The PIV system used in this work was extensively described in Ozgoren (2006, 2013). The layout of the spheres in the present experimental work is given in Figure 1, schematically. Camera and laser sheet were located as in Fig.1 for the single sphere, two side by side spheres and 30 o staggered spheres while they were replaced for in-lined two sphere experiments in which the laser was placed under the water channel and the camera was positioned perpendicularly to the channel side wall. When the value of Re number defined according to the sphere diameter was arranged to 5000, turbulence intensity for the free stream was less than 1%. The freestream velocity was 118 mm/s. Sphere diameter was 42.5 mm. The bar used for holding the spheres has a diameter of 5 mm. Connection between the rod and the spheres were made at the upper points of the spheres. The Froude Number was Fr=0.08 for the water channel at these conditions. Dantec Flow Manager was used for the calculation of the vector field. Interrogation area size of 32x32 pixel was selected which corresponds to 0.072Dx0.072D area in the captured image field. For satisfying Nyquist criterion, interrogation area was overlapped with itself at a rate of 50%. Image capturing speed was 15 Hz and total measurement time was seconds for a single layout. A wide open water channel was used for experimentation. With an 8000 mm length, 1000 mm width and 750 mm height, the open water channel was made of Plexiglas material supported by steel frames. The distance between free water flow surface and bottom surface of the channel was kept 450 mm during the tests. With the aid of a bell shape 0.5 contraction ratio collector and a honeycomb, flow regime was reformed prior to the test frame. In order to obtain desired Reynolds numbers defined according to the sphere diameter, required free flow velocity was calculated and then obtained via a frequency controller controlling the speed of the system pump. A 120 mj Nd:YAG PIV laser was operated during the experiments with a time delay value of Δt =1.7 ms. For the measurement plane and domain, laser thickness was set to approximately 1 mm. The laser sheet was located at 225 mm above the bottom surface of the channel. A low speed fine resolution charged coupled device camera was used to record 2D PIV images. Despite the fact that laser power and camera resolution were satisfactory for polymer based seeding material usage, silver coated hollow glass spheres were used instead. Seeding material average diameter was 10 µm and the material was carefully handled in order to avoid moisture which may result in particle diameter increase due to combining effect of moisture

4 3. Results and Discussion Figure 2 shows flow patterns for a single sphere. Vortex evolution in wake region of the sphere present a wavy structure along the free shear layer. This wavy structure known as Kelvin Helmholtz vorticity is occurred due the high velocity gradient and difference between the velocity field rear of the sphere and freestream flow. Instantaneous vorticity involves a scattered velocity vectors and then very large number small scale vortices called as eddy in the wake region. Maximum, minimum and interval values of flow patterns are separately given in all Figures. In Figures 2-5, minimum, maximum and interval values of the contours were instantaneous vortices min = min =2, streamwise velocity component u min = u min = 0.1, vertical velocity component v min = v min =0.1, rms streamwise velocity fluctuations u min =0.075 and u min =0.025, rms vertical velocity fluctuations v min =0.050 and v min = Properties of this unsteady structure affect the variation of drag force, lift force and pressure variation negatively. In order to decrease the fluctuation level and strength, active and/or passive flow control methods can be applied. The streamline patterns for the single sphere reveal that two symmetrical foci, F 1 and F 2, with circulations in opposite directions and a saddle point, S 1. In the wake region downstream of the spheres, the mean flow is almost symmetric with respect to the geometrical symmetry plane and a pair of recirculating regions with similar size is identified. Variation of streamwise velocity component and its rms fluctuations have a symmetrical structure with respect to the sphere centerline. The fluctuation velocities in y direction yield a peak point at the centerline 1.34D away from the rear surface of the sphere. Figures 3, 4 and 5 present the dual sphere arrangement for gap ratio G/D=1.0, G/D=1.5 and G/D=2.0, respectively. The bluff body (i.e. sphere) in the flow stream is affected from the second bluff body with same features placed in the downstream region and thus the flow structure in the wake region for both spheres is dramatically changed. Dye visualization image exerts small scale vortices beginning from the separation on the sphere surfaces for all images. Vortices in the center of the wake for G/D= 1.50 change direction and they are affected with the existence of jet like flow between the spheres and they get higher value in this region as shown in Figures 3-5. For side by side and in-lined two spheres cases at G/D=1.0 in Figs 3 and 4, wake region is similar to the single sphere in Figure 2. The detailed evaluation of the single sphere and side by side two spheres cases were conducted by Ozgoren et al. (2011) and Pinar et al. (2013). On the other, at G/D=1.0 for the 30 o staggered sphere has an inclined wake region as parallel to the arrangement angle. The size of the dual arrangement in length and wide for the side by side and staggered cases forms larger than the single sphere. As the dual spheres are arranged at G/D=1.50, a jet like flow begins to occur between the spheres. The jet like flow has higher velocity than the free stream side of the spheres. As well known, when the velocity increases in a flow domain, the pressure magnitude decreases. The inner side of the spheres, static pressure decrement on the sphere surface causes the less pressure difference between the sphere surface and wake region. The variations phenomena in the pressure retard the flow separation in the inner side of the side by side sphere arrangement. For the staggered and in-lined spheres cases at G/D=1.5, as shown in time-averaged streamline topology flow separation point from the leading sphere delays due to the occurrence of back pressure in the wake region between the spheres. Comparison of normalized timeaveraged velocity components in x and y directions u* and v* indicates the locations of free stagnation points (i.e., the location of saddle points, S) and length of wake region for each case. At G/D=1.0, the reverse flow region occurs resulting in a negative streamwise velocity, u* beginning from the rear surface of the single sphere up to a point with a distance of 1.06D, 1.13D, 0.68D, 1.01D for the single, side by side, in-lined and staggered sphere cases, respectively. Reverse flow indicating dashed contours for u* are smaller for G/D=1.5 comparing with single sphere and G/D=1.0, G/D=2.0 arrangements. There are some curve undulations after the saddle point and contour increment values tend to rise faster. v* contours are given in Figs 3-5, in the second column and after the first encounter of the flow with the sphere surface, a switching of the orientation in the contours is observed noticing that there is a direction change. Cross stream velocity components of the flow are clustered according to their positive and negative values depicting their direction regarding selected coordinate system and their magnitude are in a narrow band to dual two sphere arrangements and combined effect with the wake interactions. Higher v* values pointing out that an important amount of fluid mass might be entrained from the wake region along with the shear layers originating from the periphery of the sphere by means of separation and continuing development. At - 4 -

5 the gap ration G/D=1.0, time averaged rms velocity in x and y directions, rms streamwise velocity fluctuations < u > have two peak points for the single and the dual sphere cases while rms cross-stream velocity fluctuations < v > has one maximum point. For the gap ratio G/D=1.5 and 2.0, rms streamwise velocity fluctuations < > of each sphere have peak points with different magnitudes due to the more or less jet like flow effect. When compared the gap ratio G/D=1.5 and 2.0, flow structures such as cross-sectional streamline topology, rms streamwise velocity fluctuations < u > and cross-stream velocity fluctuations < v > are closer to the single sphere case for G/D=2.0. For the staggered sphere at G/D=1.5, the reverse flow structure of the wake region owing to the pressure difference between upstream and downstream of the sphere is in the form of complex sine wave. The fluid passing through the gap between the spheres flows spirally in the downstream direction with a pulsating force effect. Because of this effect, symmetrical flow structure in the case of the single sphere is deformed and dynamic forces due to the flow-induced vibration are varied as a function of time more rigorously. Specially, flow separation condition is considerably retarded for the gap ratio G/D=1.5. The modified flow separation, guides the wake region to shrink in size and thus drag forces is fairly reduced. This result indicates that energy consumption during the conveying of spherical bodies pneumatically can be fairly decreased by means of controlling of the arrangement of the spheres. It is observed that the jet like flow through the gap between the spheres for G/D 1.5 is in the pulsated form. However, development of the wake region structure is repeated in a periodic manner. The structure of the turbulent flow, size of the wake region, location of the stagnation point in the downstream region, the position of the peak values of velocity components and vorticity are substantially influenced by the gap variations of the spheres. The obtained results concerning with the near-wake structure of the single sphere and staggered arrangement may provide very essential contribution to the literature from the point of the understanding of sphere wake, wavy flow structure and onset of shear-layer instability. 4. Conclusions For the purpose of revealing vortex and flow characteristics with a comprehensive comparison between some special sphere arrangements and single sphere case, namely spheres side by side, 30 o staggered and in line, experiments were conducted utilizing dye visualization and particle image velocimetry and the results were presented in the present proceeding. Vortex shedding development and the vortical flow characteristics changed by the arrangements of the dual spheres considering the single sphere case. Shear-layer instability caused small and large-scale vortex formations originating from temporal flow events. Quantitative results show that inner shear-layer instabilities at gap distances between G/D=1.0 and G/D=1.5, cause strong wake interactions. The turbulence statistics, the wake size and the formations of critical points, vary with the gap between spheres. At G/D=2.0, effects of sphere arrangements lose their strength. But, the wake regions are still under the influence of the shedding shear layers due to the momentum transfer caused by the jet-like flow occurring through spheres. The influence of jet-like flow on the wake behavior becomes negligible for G/D=2.0 for all three dual spheres. G/D=1.0 arrangement can be regarded as a special case since flow around spheres at this arrangement exhibit flow characteristics similar to a flow around a single bluff body. Cross comparison of the results reveals double peaks for placed in the shear layers while a single peak is observed in with a maximum occurring along the centerline axis that is near to a location coincident with the stagnation point in the downstream of the single sphere case. In the case of the staggered arrangement, vortices shedding from the upstream of the sphere wrap the sphere and retard the flow separation, and then travel in the direction of the main flow along the free shear layers. Flow structures around the spheres usually cause a massive flow separation, unsteady flow, and complicated vortex shedding. During the travelling of these swirls in streamwise direction, the entrainment rate between free flow and wake-flow region gives rise to Kelvin Helmholtz vortices. The presence of the unsteady wavy * rms - 5 -

6 flow structure contains energetic eddies which increase the turbulence quantities, mass and momentum transfers. For the touching two spheres cases at G/D=1.0, the maximum values of both spheres wake are found to be the smallest due to decreasing velocity fluctuation in a wider wake. Velocity components reveal that the wake-flow region is very energetic in the case of the arrangement of the dual spheres, compared to the single sphere case. This means that the circulating type of flow conveys the fluid in between the core- and wake-flow regions at a high rate. Hence, it can be concluded that the hydrodynamically activated wake-flow region increases the rate of heat transfer. It is demonstrated that the separated shear layers from upstream sphere may interact directly with the spheres located downstream for the in-lined and staggered sphere cases. The present results can be useful for development, assessment and validation of numerical studies. Acknowledgments The Scientific and Technological Research Council of Turkey (TUBITAK) supported this work with Contract No: 109R028. Other institutional supports were made by Experimental Scientific Research Projects Office of Cukurova University (AAP20025) and Government Planning Organization (DPT) with 2009K12180 coded projects. Selcuk University Scientific Research Project Office provided the international conference attendance support for 17th International Symposium on Applications of Laser Techniques to Fluid Mechanics. 5. References Achenbach, E (1972) Experiments on the flow past spheres at very high Reynolds numbers. J. Fluid Mech. 54: Achenbach, E (1974) Vortex shedding from spheres. J. Fluid Mech. 62(2): Chen, RC, Lu, YN (1999) The flow characteristics of an interactive particle at low Reynolds umbers. Int. J. Multiph Flow 25: Chen, RC, Wu, JL (2000) The flow characteristics between two interactive spheres. Chem. Eng. Sci. 55: Cichocki, B, Felderhof, BU, Schmitz, R (1988) Hydrodynamic interactions between two spherical particles. Physico Chem. Hyd 10: Dandy, DS, Dwyer, HA (1990) A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer. J. Fluid Mech. 216: Folkersma, R, Stein HN, Van de Vosse, FN (2000) Hydrodynamic interactions between two identical spheres held fixed side by side in a uniform stream directed perpendicular to the line connecting the spheres centres. Int. J. Multiph Flow 26: Hassanzadeh, R, Sahin, B, Ozgoren, M (2013) Large eddy simulation of flow around two side-by-side spheres, J. of Mech. Sci. & Tech., 27(5): Hassanzadeh, R, Sahin, B, Ozgoren, M (2011) Numerical Investigation of flow structures around a sphere. Int J of Comput Fluid D. 25(10): Jadoon, A, Prahl, L, Revstedt, J (2010) Dynamic interaction of fixed dual spheres for several configurations and inflow conditions, Eur J. Mech B-Fluid 29: Jang YIIJ, Lee SJ (2008) PIV analysis of near-wake behind a sphere at a subcritical Reynolds number. Exp. Fluids. 44(6): Johnson, TA, Patel, VC (1990) Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech 378: Kim, HJ, Durbin, PA (1988) Observations of the frequencies in a sphere wake and of drag increase by - 6 -

7 acoustic excitation. Phys. Fluids. 31(11): Kim, I, Elgobashi, S, Sirignano, WA (1993) Three-dimensional flow over two spheres placed side by side, J. Fluid Mech. 246: Kiya, M, Ishikawa, H, Sakamoto, H (2001) Near-wake instabilities and vortex structures of threedimensional bluff bodies: A review. J. Wind Eng. Ind. Aerod. 89: Lee, KC (1979) Aerodynamic interaction between two spheres at Reynolds numbers around 104. Aeronautical Quarterly. 30: Leweke, T, Provansal, M, Ormie`res, D, Lebescond, R (1999) Vortex dynamics in the wake of a sphere. Phys. Fluid. 11(9), 12. Liang, SC, Hong, T, Fan, LS (1996) Effects of particle arrangements on the drag force of a particle in the intermediate flow regime. Int. J. Multiph Flow 22(2): Ozgoren, M (2013) Flow structures around an equilateral triangle arrangement of three spheres, Int. J. of Mul. Flow, 53: Ozgoren, M (2006) Flow structure in the downstream of square and circular cylinders. Flow Meas. and Instrum. 17: Ozgoren, M, Pinar, E, Sahin, B, Akilli H (2011) Comparison of flow structures in the downstream region of a cylinder and sphere. Int. J. Heat Fluid Flow 32(6): Ozgoren M., Sahin B, Pinar E., (2009), Experimental Investigation of flow structure around two staggered spheres, 17. National Thermal Science and Technology Conference, p , June 2009, Sivas Turkey (in Turkish). Ozgoren M, Sahin B,, Yayla S, Pinar E, Akar M.A, (2007) Experimental Investigation of flow structure around two tandem spheres, 16. National Thermal Science and Technology Conference, p , 30 May-2 June 2007, Kayseri Turkey (in Turkish). Pinar, E, Sahin, B, Ozgoren, M, Akilli, H (2013) Experimental study of flow structures around side by side spheres, Ind. & Eng. Chem. Res. 52: Prahl, L, Hölzer, A, Arlov, D, Revstedt, J, Sommerfeld, M, Fuchs, L (2007) A study of the interaction between two fixed spherical particles. Int. J. Multiph Flow 33: Prahl, L, Jadoon, A, Revstedt, J (2009) Interaction between two spheres placed in tandem arrangement in steady and pulsating flow, Int. J. Multiph Flow 35: Sakamoto, H, Haniu, H (1990) A study on vortex shedding from spheres in a uniform flow. J. Fluids Eng. 112: Schouveiler, L, Brydon, A, Leweke, T, Thompson, MC (2004) Interactions of the wakes of two spheres placed side by side. Eur J. Mech. B-Fluids 23: Tomboulides, AG, Orszag, SA, Karniadakis, GE (1991) Three-dimensional simulation of flow past a sphere. The Proceedings of The First International Offshore and Polar Engineering Conference. Heriot-Watt University, Edinburgh, The United Kingdom, August 1991, Tsuji, T, Narutomi, R, Yokomine, T., Ebara, S., Shimizu, A (2003) Unsteady three dimensional simulation of interactions between flow and two particles. Int. J. Multiphase Flow. 29: Tsuji, Y, Kato N, Tanaka, T (1991) Experiments on the unsteady drag and wake of a sphere, Int. J. Multiph Flow 17: Tsuji, Y, Morikawan, Y, Terashima, K (1982) Fluid-dynamic interaction between two spheres, Int. J. Multiph Flow 8: Wu, JS, Faeth, GM (1993) Sphere wakes in still surroundings at intermediate Reynolds numbers. AIAA J. 3(8): Yun, G, Kim, D, Choi, H (2006) Vortical structures behind a sphere at subcritical Reynolds numbers, Phys Fluids. 18(1): Zhu, C, Liang, SC, Fan, LS (1994) Particle wake effects on the drag force of interactive particle, Int. J. Multiph Flow 20:

8 Flow Laser Sheet TOP VIEW SIDE VIEW CCD Camera Flow PIV image area TOP VIEW Laser sheet ND: YAG Laser a) Single sphere b) Side by side two spheres c)in-lined two spheres d) Staggered two spheres Fig. 1. Schematic view of the experimental system for the staggered two spheres (top two views). Arrangement of sphere models is shown at the bottom four images

9 Fig. 2. Variation of flow structures for a single sphere a)flow visualization with laser illumination of Rhodamine 6G dye injection technique, b) instantaneous velocity field V c) time-averaged velocity components in x direction (streamwise) u*, d) time-averaged velocity components y direction (vertical) v* e) rms streamwise velocity fluctuations < u > f) cross-stream velocity fluctuations < v >. The detailed evaluation of the single sphere was conducted by Ozgoren et al. (2011)

10 Fig. 3. Variation of flow structures for the side by side two spheres a)flow visualization with laser illumination of Rhodamine 6G dye injection technique, b) instantaneous velocity field V c) time-averaged velocity components in x direction (streamwise) u*, d) time-averaged velocity components y direction (vertical) v* e) rms streamwise velocity fluctuations < u > f) cross-stream velocity fluctuations < v >. Left column for G/D=1.0, middle column for G/D=1.5 and right column for G/D=2.0. The detailed evaluation of the side by side two spheres cases was conducted by Pinar et al. (2013). * rms

11 Fig. 4. Variation of flow structures for the in-lined two spheres a)flow visualization with laser illumination of Rhodamine 6G dye injection technique, b) instantaneous velocity field V c) time-averaged velocity components in x direction (streamwise) u*, d) time-averaged velocity components y direction (vertical) v* e) rms streamwise velocity fluctuations < u > f) cross-stream velocity fluctuations < v >. Left column for G/D=1.0, middle column for G/D=1.5 and right column for G/D=

12 Fig. 5. Variation of flow structures for the staggered with 30 o two spheres a)flow visualization with laser illumination of Rhodamine 6G dye injection technique, b) instantaneous velocity field V c) time-averaged velocity components in x direction (streamwise) u*, d) time-averaged velocity components y direction (vertical) v* e) rms streamwise velocity fluctuations < u > f) cross-stream velocity fluctuations < v >. Left column for G/D=1.0, middle column for G/D=1.5 and right column for G/D=2.0. * rms