Experimental Study of Flow Structures around Side-by-Side Spheres

Article pubs.acs.org/IECR

Experimental Study of Flow Structures around Side-by-Side Spheres Engin Pinar,† Besir Sahin,*,† Muammer Ozgoren,‡ and Huseyin Akilli† †

Mechanical Engineering Department, Faculty of Engineering and Architecture, Cukurova University, Adana, Turkey Mechanical Engineering Department, Faculty of Engineering, Selcuk University, Konya, Turkey

‡

ABSTRACT: The flow characteristics of a single and the two side-by-side spheres immersed in a uniform flow for Re = 5 × 103 are studied qualitatively and quantitatively employing dye visualization and a particle image velocimetry. The current study focuses on the analysis of the flow behavior using instantaneous and time-mean flow data in plan-view and cross-sectional planes. Flow features and distributions of velocity vectors, V*, at the critical locations; patterns of velocity fluctuations, u* and v*; contours of sectional streamlines, ⟨ψ⟩; patterns of vorticity, ω*; and correlations of Reynolds stress, ⟨v′w′/U∞2⟩ are interpreted. The gap ratios between two side-by-side spheres varying within the range of 1.0 ≤ G/D ≤ 2.50 influence the instability of flow structures substantially. 104. Their experimental results demonstrated that dimensions of wake regions, the peak values of turbulence statistics, and locations of singular and double points varied as a function of bluff bodies’ geometries. They stated that small scale vortices were more effective over the sphere wake compared to the case of the cylinder. However, at Re, for example, Re = 5 × 103, due to the lack of data under various conditions, further investigations are needed to report the variations of flow structures around the two side-by-side sphere arrangements.

1. INTRODUCTION Flow characteristics at the rear of a single sphere or multiple spheres are encountered frequently in various chemical and industrial applications. Typical spherical-body flows have various chemical engineering applications as mentioned in the open literature. Most particles in fluids have spherical shapes. It is obvious that gravitational, hydrodynamic, and intermolecular forces have to be taken into account during particle-fluid interactions. Drag coefficient, CD; pressure distributions, CP; separation points around the sphere surface; and most importantly characteristics of wake regions are sensitive to fluid properties and other particle interactions. In this respect, Achenbach1 experimentally observed the flow around a sphere with a smooth surface in detail for Reynolds numbers, Re, between 5 × 104 and 6 × 104. He reported that the flow separation point occurred at a point during the transition from the laminar boundary layer to the turbulent boundary layer further downstream and reported a high rate of dependency of the coefficient of drag, CD, on Reynolds numbers, Re. But, having the surface of a sphere with roughness develops earlier conversion of the laminar boundary layer into a turbulent boundary layer, leading to a lower critical Reynolds number, Rec, where the point of separation moves further downstream on the sphere surface, and hence the coefficient of drag, CD, decreases to a minimum value as reported by Achenbach.2 In order to be successful in controlling the flow of a bluff body such as sphere, it is essential to understand the physical behavior of the flow of a bluff body. The flow characteristics of the sphere wake region play an important role in computing the steady/unsteady forces implemented on the bluff body. Most of the experimental research involving flows around a sphere/ spheres was performed employing dye visualization and the point-wise measurement technique. But a few experimental works have been performed using the PIV technique. This velocity measuring method provides quantitative information such as instantaneous velocity distributions in the field of the separated flow region. Ozgoren et al.3 conducted experiments to visualize the flow behaviors qualitatively and quantitatively in the rear of a sphere and a circular cylinder submerged in a uniform flow having Reynolds numbers Re = 5 × 103 and 1 × © 2013 American Chemical Society

2. PREVIOUS WORK A large number of investigations were performed on the flow dynamics of a sphere/spheres for a wide range of Reynolds numbers, and hence large amounts of data for the vortex shedding frequency, f; coefficient of pressure, CP; coefficient of drag, CD; and coefficient of lift, CL, have been accumulated. In the present work, qualitative and quantitative experimental observations of wake flow structures at the rear of the two sideby-side spheres were taken into consideration. In this respect, Lee4 studied the variations of the drag force, FD, of the test sphere at Re = 104 influenced by the existence of the neighboring spheres. For two and three spheres with various combinations, Tsuji et al.5 performed visualization and force measuring experiments. It was reported that as the gap ratio between spheres is reduced in the lateral direction, the drag force, FD, rises, but this rising of drag force, FD, disappears beyond a gap spacing of 2 sphere diameters. Kim and Durbin6 reported that the separating shear layers with small-scale and large-scale instabilities in the wake flow region downstream of a sphere cause the two frequency modes. Kim et al.7 studied the 3-D flow of two identical spheres submerged in a uniform flow and kept them fixed relative to each other for low Reynolds numbers, such as Re = 50, 100, and 150. Their results indicated that two spheres repel each other when the gap distance is one sphere diameter, but spheres deficiently attract each other at an Received: Revised: Accepted: Published: 14492

July 17, 2013 September 14, 2013 September 16, 2013 September 16, 2013 dx.doi.org/10.1021/ie4022732 | Ind. Eng. Chem. Res. 2013, 52, 14492−14503

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Figure 1. Schematic view of the experimental system for side view and plan view with cross-sectional measuring planes for end-view and definition of parameters for a two side-by-side spheres arrangement.

intermediate gap spacing for Re = 50. For a small gap ratio, the flow structures in the wake flow are substantially distinguished because of the occurrence of axisymmetric wake with large separations. Furthermore, Cichocki et al.,8 Dandy and Dwyer,9 Johnson and Patel,10 and Hassanzadeh et al.11 performed numerical predictions for 3-D flows of a single sphere. Leweke et al.12 conducted dye visualization on wake flow characteristics at a rear of sphere for Re = 320. The periodic shedding of counter-rotating of vortex filaments was observed. Sakamoto and Haniu13 and Kiya et al.14 categorized wake patterns of a sphere based on Reynolds numbers, Re, for the range of 300 ≤ Re ≤ 4 × 104. In their works, pulsations of a vortex tube, periodic vortex shedding with asymmetric flow, and also irregular vortex shedding were observed. Arrangements more than a couple of spheres were investigated by Liang et al.15 and Chen and Lu.16 It was reported that the spacing length between spheres influences the drag force, FD; lift force, FL; and vortex shedding patterns. In general, the drag force, FD, increases with a decrease in the gap ratio between the two side-by-side arrangements of spheres for a moderate Reynolds numbers. Chen and Wu17 have experimentally investigated flow structures of an interactive sphere shaped particle for Re ≥ 200 based on the sphere shaped particle diameter using a laser doppler anemometer. The influences of distance between test and secondary particles and dimensions of the secondary particle on the drag force, FD, are

more effective as the secondary particle is located upstream of the test sphere. Folkersma et al.18 used the finite element method to investigate hydrodynamic interactions between spheres. Their main conclusion agreed with the results of Kim at al.,7 that the two spheres are repelled when the separation distance is one sphere diameter between spheres, but attraction between spheres is weak at intermediate separation distances for Re = 50. Schouveiler et al.19 investigated the periodic coupled wakes downstream of the side-by-side spheres submerged in a free stream flow for 200 ≤ Re ≤ 350 numerically and experimentally. They observed distinctly different flow regimes based on the gap ratio between spheres. Jadoon et al.20 have numerically studied force characteristics and the vortex shedding patterns under several sphere arrangements for Re = 300 and 600 having pulsating and steady inflow regimes. The location of the neighboring sphere was varied from 0° to 90° with an increment of 15° for the distance of separation, such as 1.5D and 3D. They recorded that the drag force, FD, is slightly increased in the side-by-side arrangement of spheres. Interactions of spheres are attenuated with an increase in both gap distance and the Reynolds number. Recently, Ozgoren et al.21 have studied flow characteristics of a sphere placed over a smooth flat plate experimentally employing PIV for Re = 5 × 103. The sphere was immersed in a turbulent boundary layer. It was reported that a jet-like flow encouraged the flow mixing between the region of wake and 14493

dx.doi.org/10.1021/ie4022732 | Ind. Eng. Chem. Res. 2013, 52, 14492−14503


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through the flow straightener and a section of contraction. A schematic of test arrangements of spheres is shown in Figure 1. The turbulence intensity of free stream flow was lower than 0.5%. The Reynolds number based on the sphere diameter was taken as Re = 5 × 103 throughout the experiments, Re = (U∞D)/ν. During the measurements, uniform velocity was U∞ = 118 mm/s. The Froude number, Fr, is a good indicator to show the surface distortion in the flow field. In the present experiment, the Froud number, Fr, of the water channel flow was Fr = U∞/(ghw)1/2 = 0.056, which is well below the critical Froud number (Fr < 0.2) for the Reynolds number of Re = 5000. Spheres made of Plexiglas had a diameter of 42.5 mm. To minimize the influence of surface roughness on the flow structures, each sphere surface was polished. Dye ports having 0.7 mm diameters were placed on the periphery of spheres at angles of 0°, 70°, 90°, 110°, 180°, 250°, 270°, and 290° taking the free-stream flow direction as a reference line. The speed of dye mixture was well below the speed of water flow around the sphere. The laser light sheet was placed at a level of 225 mm above the test section of the bed surface, while the water height level, hw, was 450 mm. A steel rod having a 0.5 mm diameter was hooked up to the spheres in order to keep them stationary in the water channel. This rod was connected to a traverse mechanism located above the water channel. A Nd:YAG laser having 120 mJ per pulse, which had a time delay of t = 1.7 ms, was employed to produce a laser light sheet with a thickness of 1.5 mm which was normal to the symmetry axis of the spheres. Hollow plastic spheres with a silver metallic coating having a diameter of 12 μm were used as seeding particles in the flow. A CCD camera with a resolution of 1600 × 1186 pixels was employed to capture images of flow fields. More or less 20−30 seeding particles were provided within the interrogation area to satisfy the high-image-density criterion. To compute the raw velocity vector field obtained from the PIV readings, the crosscorrelation algorithm was applied using Dantec Flow Grabber software. An interrogation window of 32 × 32 pixels was chosen and transferred to a grid of size 1.5 × 1.5 mm2 for the single sphere (0.035D × 0.035D) and 1.06 × 1.06 mm2 (0.024D × 0.024D) for the cross-sectional measuring planes. The overall flow fields for all images have in total 7227 (99 × 73) velocity vectors. Two dimensionless lengths were provided as a gap ratio G/D and length ratio L/D where G is the length between centers of the two spheres for the plan-view experiment and L is the length between measuring planes and the sphere center. The experiments were performed for G/ D = 1.0, 1.25, 1.5, and 0.5 and L/D = 0.5, 0.75, 1.5, and 3.0 for the cross-sectional planes as indicated in Figure 1. A mirror was located in the channel at a point 1000 mm from the rear edge of the sphere having an angle of 45° with reference to the streamwise flow direction. Before performing experiments in plan-view planes, the influence of the mirror on the wake behavior at the rear of the sphere was examined, and it was observed that the mirror had a negligible effect on the wake flow region. An overlap of 50% was employed in order to satisfy the Nyquist criterion during the interrogation process. In total, 350 images of flow field were taken at 15 Hz. Time-mean flow structures were determined from instantaneous images. Spurious velocity vectors in the flow field caused by laser sheet distortions, reflections, and shadows were erased by employing the local median-filter technique and replaced by employing bilinear interpolation between neighboring velocity vectors. Particle image velocimetry (PIV) used in the present work was similar to the work of Sahin et al.30 who reported that

main flow depending on the gap ratio between the sphere and the plate surface. The gap ratios have substantial influence on the interaction of the wake boundary layer as well as the point of flow detachment from the plate surface. Asymmetric flow characteristics of the sphere are evident because of the boundary-layer flow patterns. Kishore22,23 conducted numerical studies on the flow characteristics around two and three spheroid particles in the tandem arrangement for Reynolds numbers within the range of 1 ≤ Re ≤ 100. He concluded that the flow structures and drag coefficients, CD, were substantially affected by the particle Reynolds number, the particle aspect ratio, and the length between particles. Hassanzadeh et al.24 numerically investigated the influence of free-surface flow on the wake flow of a sphere applying the large eddy simulation model, to demonstrate the rate of free-surface flow influence on the wake of the sphere that was positioned close to the free surface. Ozgoren25 conducted experiments to investigate vortical flow structures past a three sphere arrangement in an equilateral-triangular combination at Re = 5 × 103. It was determined that the variation of separation distance of spheres alters the vortical flow parameters. Hassanzadeh et al.26 reported that the large eddy simulation of flow around the two side-by-side spheres predicted that the rate of interaction between the wakes of a couple of spheres placed side-by-side is strongly influenced by the separation distance between spheres. This rate of wake interaction influences the coefficient of pressure, CP; coefficient of drag, CD; coefficient of lift, CL; and turbulent statistics of spheres. Drag behaviors of a spherical particle or bubble in the shear-thinning and shear-thickening fluids were part of numerical studies by Dhole et al.,27 Rajasekhar and Kishore,28 and Kishore et al.29 They found that the drag behavior of spherical shaped bluff bodies were changed as a function of the power-law index for all values of Reynolds numbers. As reported in recent years, several numerical works with improved turbulence models and point-wise measuring experiments have been performed to study flow around a single sphere or side-by-side spheres. But, the numerical works have difficulties in approving their predictions in the present subject, for example, flow separation angle, wake length, and statistics of turbulence, because of the lack of comparative experimental results for Re = 5 × 103 in which the drag coefficient, CD, is almost constant while flow characteristics change randomly. In addition, the point-wise measuring experimental techniques present difficulty when conducting a quantitative observation in a separated flow or unsteady flow regions. This implies that for validation of CFD models and results, there are wide ranges of demands for reliable experimental results. The variation of the wake in end-view planes for the two side-by-side spheres has not been examined by the PIV technique yet. The aim of this work is to reveal the vortical flow characteristics relevant to the patterns of shear layers as well as wake instabilities and then compare the flow characteristics of the single sphere and two spheres arranged side-by-side with dye observation and PIV readings at Re = 5 × 103.

3. EXPERIMENTAL ARRANGEMENTS Experimental works were conducted in a water channel having an 800 cm length of test section, 100 cm width, and 75 cm height. Transparent Plexiglas sheets with a thickness of 15 mm were used to construct the test section. Water was pumped through multistage filters in order to break up large scale vortices to convey the water into a large reservoir passing 14494



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Figure 2. Comparison of flow visualization of flow structure with laser illumination of rhodamine dye injection technique in wake region around a single sphere and two side-by-side spheres with different gap ratios at Re = 5 × 103.

varies depending on the gap ratio where the rolling-up vortex starts locally in the free-stream flow direction, which was also observed by Sakamoto and Haniu,13 Yun et al.,33 and Ozgoren et al.3 For G/D = 1.25 and 1.50, shown in Figure 2c, d, and g, almost symmetrical flow behavior occurs in the wakes at the rear of spheres. Here, the gap ratio was normalized by the sphere diameter. The jet-like flow occurs between spheres and then extends as far as the merging point of the shear layers. Interactions between the wake regions of spheres get weaker and the influence of the jet-like flow on the wake decreases while the gap ratio, G/D, between spheres increases. As shown in Figure 2g, outer shear layers around wake flow regions merge at a location with a distance of 3D from the central points of spheres. As reported by Yun et al.,33 the mechanism which is responsible for this wavy shaped large-scale vortical flow is associated with the temporal evolution of vortices along the shear layers. Flow structures around each sphere for the G/D = 2.0 case, shown in Figure 2h and i, resemble the flow structure of the single sphere as shown in Figure 2e. A sudden coalescence of small-scale vortices creates large scale vortices in the area of shear layers, as demonstrated by Ozgoren et al.3 and Ozgoren.34 However, wake regions of the two side-by-side spheres interact with each other, occasionally. The flow patterns coupled, as in phase or antiphase mode, as shown in Figure 2h and I for G/D = 2.0. 4.2. Instantaneous Flow Patterns. Representative normalized instantaneous velocity vector fields V* = V/U∞, in x and y directions, velocity components u* = u/U∞ and v* = v/U∞, and vorticity contours ωZ* = ωzD/U∞ of the wake structures made dimensionless by free-stream velocity component U∞ are illustrated in Figure 3. Streamwise velocity component u* = u/U∞ has negative contours immediately downstream of the sphere(s), while those of v* = v/U∞ have negative and positive contours. Also, these contours exhibit

the uncertainty value in the instantaneous velocity magnitudes was lower than ±2%.

4. EXPERIMENTAL RESULTS AND DISCUSSIONS 4.1. Qualitative Flow Demonstration with the Rhodamine Dye Technique. Visualization of instantaneous flow fields downstream of a sphere and the two side-by-side spheres at Re = 5 × 103 using laser light with the Rhodamine dye is presented in Figure 2. Selected images of instantaneous velocity vectors, taken from the time sequence of images, are shown in Figure 3. Small-scale vortices in the wake region of spheres caused by the Kelvin Helmholtz instability are presented in both Figures 2 and 3 qualitatively and quantitatively. The flow patterns presented in Figure 2a and e demonstrate the detachment laminar boundary layer on the sphere surface at a location θ = 85° ± 5° having the free-stream flow direction as a reference line. Along the boundary of the wake and free-stream flow regions, many vortex-ring shaped protrusions are developed, indicating the shear-layer instability also reported by Jang and Lee,31 Pinar,32 and Ozgoren et al.3 In the two sideby-side sphere arrangement, the fluid conveying through the area between spheres accelerates in the downstream direction causing jet-like flow and a low pressure region for 1.25 ≤ G/D ≤ 2.5. Shear layers emanating from the shoulders of the single sphere merge at a location more or less two sphere diameters (2D) downstream from the central point of the sphere. Shearlayer instabilities and irregularities in the flow are retained further downstream, creating vortices on a small scale, as shown in Figure 2e. The circulatory flow region at the rear of the two side-by-side spheres has a lower velocity value compared to the case of a single sphere as seen in Figure 3. The separating shear layer persists in moving farther downstream in order to develop a cylindrical vortex sheet that surrounds the wake region, and its instability causing 3-D flow and vortical flow characteristics 14495



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Figure 3. Comparison of normalized instantaneous velocity fields V*, velocity components in x and y directions u* and v*, and instantaneous vortices ω* for a single sphere and two side-by-side spheres for 1.0 ≤ G/D ≤ 2.5. The minimum and incremental levels of the flow patterns are taken as |ωz*|min = ±2, Δωz* = 1.5, |u*|min = ±0.1, Δu* = 0.1, |v*|min = ±0.1, and Δv* = 0.1. Vertical arrow designated on sphere for G/D = 1.0 indicates the magnitude of free-stream velocity as a reference velocity.

highly fluctuated flow structures due to the rapid changes of unsteady flow. Concentrated vorticity layers, ω*, are shed from the shoulders of spheres as positive vortices, anticlockwise, symbolized by solid lines and as negative vortices, clockwise, designed by a dashed lines. The vorticties, ω*, are developed from the boundary-layer detachment occurring all around the periphery of spheres. These vortices move inward due to the lower pressures occurring within the wake. Shear layers have a tendency to break up into small concentrations of vorticity, ω*, demonstrating the existence of Kelvin−Helmholtz (KH) instabilities. A low level of instantaneous velocity vectors, V*, at the rear of the sphere(s) causes small-scale secondary vortices as shown in the fourth row of Figure 3. Vorticity peaks occur successively due to the shedding vortices, as demonstrated in the animation of instantaneous vorticity images in the cinema sequence. These shedding vortices magnify the flow mixing processes between the main stream and wake by conveying fluid from the main stream into the wake.

Instantaneous velocity patterns, V*, and corresponding vorticity fields, ω*, observed in the measuring plane display the large-scale waviness and rotate slowly around its central axis while moving further downstream, as explained by Sakamoto and Haniu,13 Wu and Faeth,35 and Yun et al.33 The vortex shedding frequency was determined using a power spectrum analysis of u* in the wake. The dominant frequency, f, of vortex shedding is determined using power spectra of the PIV measurements taken at certain points over the shear layers. A well-defined vortex shedding frequency, f, for one sphere is 0.49 Hz and the related Strouhal number St = f D/U∞ = 0.177. This value of Strouhal number agrees well with the data of Sakamoto and Haniu,13 Jang and Lee,31 Ozgoren et al.,3 and Hassanzadeh et al.11 When the distance between the two side-by-side spheres is taken as G/D = 2.5, the flow characteristic becomes very similar to the case of a single sphere, and the shedding frequency, f, and Strouhal number, St, of each sphere is found as f = 0.55 Hz and St = 0.195, respectively. 14496



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Figure 4. Comparison of time-averaged streamline patterns ⟨ψ⟩, rms streamwise velocity fluctuations ⟨urms*⟩, cross-stream velocity fluctuations ⟨vrms*⟩, and Reynolds stress correlations ⟨u′v′/U∞2⟩ for a single sphere and two side-by-side spheres for 1.0 ≤ G/D ≤ 2.5. The minimum and incremental levels of the flow patterns are taken as |⟨urms*⟩|min = 0.02, ⟨urms*⟩ ≥ 0.02, |⟨vrms*⟩|min = 0.02, ⟨vrms*⟩ ≥ 0.02, |⟨u′v′/U∞2⟩|min = 0.04, and ⟨u′v′/U∞2⟩ ≥ 0.04.

interact with each other. The time-mean flow data obtained from 350 images of instantaneous velocity, V*, field and related patterns of sectional streamlines, ⟨ψ⟩, are shown in the first row of Figure 4. Foci, F, and saddle points, S, presented in terms of the time-mean counters of sectional streamlines, ⟨ψ⟩, indicate that the time-mean wake flow structures are nearly identical with reference to the centerline for all gap ratios, G/D. Saddle point, S, indicates the shear layers merging point. Foci symbolized as F1 and F2 rotating clockwise and counterclockwise demonstrate well-defined critical points. Large-scale foci, F1 and F2, dominate the wake region of the sphere(s), agreeing well with the data of Jang and Lee,31 Ozgoren et al.,3 and Ozgoren et al.21 The dimensionless wake lengths (L/D) between the sphere center and the saddle point S are 1.68D and 1.96D for the single sphere and G/D = 1.0 cases, respectively. For G/D > 1.0, under the jet-like flow effect developed in between spheres, the symmetrical wake flow structure of spheres deteriorates. Namely, larger foci F1 and F2 are

4.3. Time-Mean Flow Patterns. The time-mean patterns of sectional streamlines, ⟨ψ⟩; streamwise velocity fluctuations, urms* = ⟨urms/U∞⟩; cross-stream velocity fluctuations, vrms* = ⟨vrms/U∞⟩; and corresponding Reynolds stress correlation, ⟨u′v′/U∞2⟩, are shown in Figure 4 for all cases. The levels of interactions of shear layers and wake flow regions vary based on arrangements of spheres for G/D < 2.5. The wake structures are almost symmetric even for small gap ratios of spheres, for example, G/D = 1.25 and 1.50. It is observed from the animated multiple successive images of instantaneous velocity vectors, ⟨V⟩, and dye visualization that the jet-like flow for the cases of G/D = 1.25 and 1.5 is very prone to being unstable. The acceleration of fluid caused by the nozzle effect for G/D ≤ 1.50 continuously stimulates the generation of vortices caused by the inner sides of shedding shear layers, and thus this jet-like flow delays flow separations on the inner sides of spheres further downstream. On the other hand, for G/D = 2.5 the jetlike flow prevents the inner sides of shedding vortices to 14497



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Figure 5. Variation of the cross-stream velocity fluctuations ⟨vrms*⟩ and Reynolds stress correlations ⟨u′v′/U∞2⟩ at critical points along the horizontal dashed lines indicated in Figure 4.

imum value of ⟨vrms*⟩ increases and reaches a value of 0.36 at 1.97D for G/D = 1.0. Reynolds stress correlations, ⟨u′v′/U∞2⟩, for the two spheres and the gap ratios of 1.0 ≤ G/D ≤ 2.5 are displayed in the bottom images of Figure 4. There are nearly symmetrical flow structures around the sphere(s) and a high level of fluctuations caused by 3-D flow structures in close regions of saddle points S. Reynolds stress correlations, ⟨u′v′/U∞2⟩, are at a minimum along the symmetry axis between negative and positive values of ⟨u′v′/U∞2⟩ due to the symmetrical flow structures and attain their highest values on either side of the wake centerlines for the single sphere case and the two side-by-side spheres with G/ D = 1.0, but this symmetry is altered for G/D greater 1.0. Welldefined patterns of ⟨u′v′/U∞2⟩ produce the maximum Reynolds stress values as a result of velocity fluctuations on the shear layers and close to the saddle points, S. Clusters of ⟨u′v′/U∞2⟩ in the outer regions of wake flow are first developed as a result of the time-dependent nature of vortex shedding. But, clusters of ⟨u′v′/U∞2⟩ in the inner regions of wakes are developed as a result of shading shear layers and the jet-like flow for 1.25 ≤ G/D ≤ 2.5. The magnitude of ⟨u′v′/U∞2⟩ is higher in the inner region of wakes compared to the outer region of wakes because of the jet-like flow which stimulates the velocity fluctuations to a higher level along inner sides of shear layers for G/D = 1.25, 1.5, and 2.5. Variations of ⟨vrms*⟩ and ⟨u′v′/U∞2⟩ for one single sphere and the two side-by-side spheres are presented in Figure 5. Data obtained along the horizontal dashed lines passing through the critical points are indicated in Figure 4. For the

developed in the outer side of the wake zone for G/D = 1.25 and 1.5. The saddle point S2 occurs at locations with distances of 1.37D and 1.41D from the sphere center. An increase of the local Reynolds number, Re, caused by the nozzle effect magnifies the friction drag force, FD, as stated by Chen and Wu.17 For G/D = 1.25 and 1.50, an increase of momentum of the fluid because of the nozzle effect delays the flow detachment and hence increases the friction drag force, FD, but reduces the pressure drag force, FD, which is reported for Re = 200 by Chen and Wu.17 The jet-like flow does not influence the flow behaviors for G/D = 2.5. Because of this reason, the time-mean patterns of sectional streamlines, ⟨ψ⟩, of spheres are identical to each other. Distances of the location of saddle points S1 and S2 are respectively determined as 2.2D and 2.4D for G/D = 2.5. The wake length can also be defined using patterns of ⟨vrms*⟩. As shown in the second and third rows of Figure 4, the maximum ⟨urms*⟩ with two peaks occurs at locations with a distance of approximately 1.35D along shear layers in the single sphere case. But, the maximum ⟨vrms*⟩ with a single peak appears at 1.72D in the wake close to the saddle point, S. The two spheres for G/D = 1.0 reveal double peaks of streamwise velocity fluctuations, ⟨urms*⟩, for each sphere while a single peak is evident in ⟨vrms*⟩ along the wake symmetry axis located at 1.97D. Due to the influence of the jet-like flow through spheres, the maximum value of the fluctuations, ⟨urms*⟩, is measured as 0.37 at 1.09D when the G/D value is taken as G/D = 1.25. The value of ⟨urms*⟩ attenuates when the ratio of G/D increases further. Although the fluctuation level of streamwise velocity component ⟨urms*⟩ decreases, the max14498



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Figure 6. continued

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Figure 6. (a) Comparison of time-averaged flow patterns such as velocity fields ⟨V*⟩, streamwise and cross-stream velocity component contours ⟨v*⟩ and ⟨w*⟩, Reynolds stress correlations ⟨v′w′/U∞2⟩, streamwise velocity fluctuations ⟨wx‑rms*⟩, and spanwise vorticity fluctuations ⟨ωx‑rms*⟩ along with instantaneous vorticity ωx* for the single sphere case at the cross-sectional planes of L/D = 0.5, 0.75, 1.50, and 3.0. The minimum and incremental contour values of the patterns are taken as |⟨v*⟩|min = 0.01, ⟨Δv*⟩ ≥ 0.01, |⟨w*⟩|min = 0.01, ⟨Δw*⟩ ≥ 0.01, |ωx*|min = 1, Δωx* = 1, |⟨ωx*⟩|min = 0.2, ⟨Δωx*⟩ ≥ 0.2, |⟨v′w′/U∞2⟩|min = 0.002, ⟨v′w′/U∞2⟩ = 0.002, |⟨ωx‑rms*⟩|min = 3, and ⟨Δωx‑rms*⟩ ≥ 1. (b) Comparison of timeaveraged flow patterns such as velocity fields ⟨V*⟩, streamwise and cross-stream velocity component contours ⟨v*⟩ and ⟨w*⟩, Reynolds stress correlations ⟨v′w′/U∞2⟩, streamwise velocity fluctuations ⟨wx‑rms*⟩, and spanwise vorticity fluctuations ⟨wx‑rms*⟩ along with instantaneous vorticity ωx* and time-averaged vorticity contours ⟨ωx*⟩ for the two side-by-side spheres at the cross-sectional plane of L/D = 1.5. The minimum and incremental values of the patterns are the same as in part a.

single sphere case, the maximum ⟨vrms*⟩ occurs in the vicinity of the saddle point S. Similar flow behavior is observed in the two spheres cases, but the maximum value of ⟨vrms*⟩ for two spheres is slightly higher than the single sphere case. For G/D = 2.5, there are two maximum values of ⟨vrms*⟩ close to saddle

points S1 and S2. For G/D = 1.25 and 1.5, there are nearly symmetric distributions of the cross-stream velocity fluctuations, ⟨vrms*⟩. But in the case of G/D = 2.5, shedding vortices influence Reynolds stress correlations, ⟨u′v′/U∞2⟩, causing four peaks with different magnitudes. Variation of ⟨u′v′/U∞2⟩ is 14500



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locations for L/D = 0.5 around the sphere boundary with the magnitudes of 0.04, 0.11, 0.08, and 0.14. The peak values of ⟨wrms*⟩ increase as the flow moves in the downstream direction. At a location L/D = 1.5, cross-stream velocity fluctuations, ⟨wrms*⟩, form quasi-circular rings, and the maximum of ⟨wrms*⟩ with a value of 0.32 occurs at the center of the measuring plane. The flow properties become nearly similar to the free-stream flow properties at L/D = 3.0. In the bottom row (vii) of Figure 6a, vorticity fluctuations, ⟨ωx‑rms*⟩ are given at four different locations. Formation of the timemean clusters of vorticity fluctuations, ⟨ωx‑rms*⟩, is fairly weak in magnitude because of the lower level of velocity and reverse flow effect in the wake. As the fluid moves further downstream, concentrations of vorticity fluctuations, ⟨ωx‑rms*⟩, increase because of merging of the shedding shear layers emanating from the shoulder of the sphere at measuring planes of L/D = 0.5 and 0.75. But, the time-mean vorticity fluctuations, ⟨ωx‑rms*⟩, become weaker at the L/D = 3.0 location, which corresponds to downstream of the saddle point, S, as indicated in plane-view images presented in Figure 4. Figure 6b presents flow data in end-view measuring planes at L/D = 1.5 for the two side-by-side sphere arrangements with the gap ratio in a range of 1.0 ≤ G/D ≤ 1.5. Flow structures on the left-hand-side column of Figure 6b for G/D = 1.0 are similar to the images given in the first column of Figure 6a. Positive and negative flow patterns immediately downstream of the sphere in the wake region interact and merge as they move through their wake region and produce small scale vortices after the merging point of shear layers or location of saddle points, S. The magnitude of interaction between the wake flows of spheres attenuates at L/D = 3.0. Flow structures at the rear of the two side-by-side spheres have an unsteady motion as illustrated in row iv of Figure 6b. As the gap ratio, G/D, between spheres is increased, the flow patterns belonging to each sphere become more symmetric. Figure 7 presents the variation of the maximum streamwise velocity fluctuations, ⟨vrms*⟩; cross-stream velocity fluctuations, ⟨wrms*⟩; corresponding Reynolds shear stress correlations, ⟨v′w′/U∞2⟩; transverse Reynolds normal stress correlations, ⟨v′v′/U∞2⟩; and spanwise Reynolds normal stress correlations, ⟨w′w′/U∞2⟩, at the cross-sectional planes in the range of distance, 0.5 ≤ L/D ≤ 3.5 for a single sphere case. Here, L is

higher on the inner side of the wake regions than the outer side because the jet-like flow improves the fluid mixing process. Similar trends of ⟨u′v′/U∞2⟩ distributions along the measuring cross section are also obtained for G/D = 1.5. In the G/D = 1.25 case, distributions ⟨u′v′/U∞2⟩ are indicated along line a and line b passing through the region where the jet-like flow effects exist. The variation of ⟨u′v′/U∞2⟩ on the measuring line b indicates that at a region further downstream from the saddle points, S, variations of ⟨u′v′/U∞2⟩ are attenuated. 4.4. Instantaneous and the Time-Mean Flow Contours in the Cross-Sectional Planes for a Single and Two Sideby-Side Spheres. The experiments in the cross-sectional planes were performed to be able to understand physics of three-dimensional flows around sphere/spheres by means of instabilities in shear layers and wake regions. Patterns of the time-mean and instantaneous flow data and turbulence statistics are indicated in Figure 6a and b. The cross-sectional measuring planes are presented with a dashed line on the time-mean patterns of ⟨v*⟩ in the bottom image of Figure 6. The timemean velocity vectors shown in Figure 6a reveal that the separated flow moves from inboard to outboard of the wake region. In other words, velocity vectors are aligned toward the periphery of wake region at L/D = 0.5 and 0.75, whereas at L/ D = 1.5 the separated flow moves from outboard to inboard of the wake region. In other words, velocity vectors are aligned toward the central point of the wake region. The time-mean patterns of cross stream velocity components ⟨v*⟩ and ⟨w*⟩ have two well-defined large clusters with positive and negative values due to the fluid mixing process between the main flow and wake regions. The maximum values of flow data depending on the cross-sectional planes are indicated in Figure 6a. The projection of the sphere that is given in the first column is represented by a dashed line in all images. Structures of a small scale and high level of fluctuating vortices are developed because of the source of Kelvin Helmholtz instabilities. The projection of the sphere that is given on the first row of Figure 6b is represented by dashed line in all images. As seen in Figure 6b, the flow data and turbulent statistics indicate fairly symmetrical patters in end-view planes of the two side-byside spheres. Instantaneous vorticity, ωx*, with L/D indicate that the wake flow structure has similar patterns up to L/D = 3.0. Patterns of instantaneous vorticity in the cross-sectional plane at locations of L/D = 0.50, 0.75, and 3.0 shown in the row iv of Figure 6a and b form well-defined vortices across the shedding shear layers. However, numerical results of Yun et al.33 reported that these vortex rings have the same frequency of the shear layer instability, and the vortex shedding frequency is similar to the large-scale wavy structure frequency in the wake. Similar wake flow structures downstream of the sphere were also reported by Sakamoto and Haniu,13 Leder and Geropp,36 and Jang and Lee.31 The vorticity structures presented in Figure 6a (iv) agree with the numerical and experimental results of Hassanzadeh et al.,11 Yun et al.,33 Jang and Lee,31 and Brü cker.37 Reynolds stress correlations ⟨v′w′/U∞2⟩ are presented in row v of Figure 6a. Interaction of the velocity fluctuations at a location L/D = 1.50 is very strong, causing eddy dissipation. For L/D = 0.75 and 1.5, Reynolds stress correlations, ⟨v′w′/U∞2⟩ form identifiable clusters across the shedding shear layers. These clusters of ⟨v′w′/U∞2⟩ become weaker and less concentrated in the end-view measuring plane at L/D = 3.0. As shown in row vi of Figure 6a, the maximum time-mean cross-stream velocity components, ⟨wrms*⟩ occur with four different peaks situated at almost equally distributed

Figure 7. Variation of the maximum values of the streamwise velocity fluctuations ⟨vrms*⟩, cross-stream velocity fluctuations ⟨wrms*⟩, Reynolds stress correlations ⟨v′w′/U∞2⟩, and vorticity fluctuations ⟨wx‑rms*⟩ at the cross-sectional plane locations of L/D = 0.5, 1.0, 1.50, 2.0, 2.50, 3.0, and 3.5. 14501



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measured from the center of the sphere. All curve trends displayed in Figure 7 increase until L/D = 1.5. All turbulent statistics have a maximum values between L/D = 1.5 and 2.0, and the numerical value of flow characteristics decreases when L/D increases beyond L/D = 2. Finally, the data provided in Figure 7 may be fruitful for the comparison of various numerical studies.

REFERENCES

(1) Achenbach, E. Experiments on the flow past spheres at very high Reynolds numbers. J. Fluid Mech. 1972, 54, 565. (2) Achenbach, E. Vortex shedding from spheres. J. Fluid Mech. 1974, 62 (2), 209−221. (3) Ozgoren, M.; Pinar, E.; Sahin, B.; Akilli, H. Comparison of flow structures in the downstream region of a cylinder and sphere. Int. J. Heat Fluid Flow 2011, 32 (6), 1138−1146. (4) Lee, K. C. Aerodynamic interaction between two spheres at Reynolds numbers around 104. Aeronautical Quarterly 1979, 30, 371− 385. (5) Tsuji, Y.; Morikawan, Y.; Terashima, K. Fluid-dynamic interaction between two spheres. Int. J. Multiphase Flow 1982, 8, 71−82. (6) Kim, H. J.; Durbin, P. A. Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation. Phys. Fluids 1988, 31 (11), 3260−3265. (7) Kim, I.; Elgobashi, S.; Sirignano, W. A. Three-dimensional flow over two spheres placed side by side. J. Fluid Mech. 1993, 246, 465− 488. (8) Cichocki, B.; Felderhof, B. U.; Schmitz, R. Hydrodynamic interactions between two spherical particles. Physicochem. Hydraulics 1988, 10, 383−403. (9) Dandy, D. S.; Dwyer, H. A. A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer. J. Fluid Mech. 1990, 216, 381−410. (10) Johnson, T. A.; Patel, V. C. Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 1990, 378, 19−70. (11) Hassanzadeh, R.; Sahin, B.; Ozgoren, M. Numerical Investigation of flow structures around a sphere. Int. J. Comput. Fluid Dynamics 2011, 25 (10), 535−545. (12) Leweke, T.; Provansal, M.; Ormières, D.; Lebescond, R. Vortex dynamics in the wake of a sphere. Phys. Fluids 1999, 11 (9), 12. (13) Sakamoto, H.; Haniu, H. A study on vortex shedding from spheres in a uniform flow. J. Fluids Eng. 1990, 112, 386−392. (14) Kiya, M.; Ishikawa, H.; Sakamoto, H. Near-wake instabilities and vortex structures of three-dimensional bluff bodies: A review. J. Wind Eng. Ind. Aerodynamics 2001, 89, 1219−1232. (15) Liang, S. C.; Hong, T.; Fan, L. S. Effects of particle arrangements on the drag force of a particle in the intermediate flow regime. Int. J. Multiphase Flow 1996, 22 (2), 285−306. (16) Chen, R. C.; Lu, Y. N. The flow characteristics of an interactive particle at low Reynolds numbers. Int. J. Multiphase Flow 1999, 25, 1645−1655. (17) Chen, R. C.; Wu, J. L. The flow characteristics between two interactive spheres. Chem. Eng. Sci. 2000, 55, 1143−1158. (18) Folkersma, R.; Stein, H. N.; Van de Vosse, F. N. Hydrodynamic interactions between two identical spheres held fixed side by side in a uniform stream directed perpendicular to the line connecting the spheres’ centers. Int. J. Multiphase Flow 2000, 26, 877−887. (19) Schouveiler, L.; Brydon, A.; Leweke, T.; Thompson, M. C. Interactions of the wakes of two spheres placed side by side. Eur. J. Mech., B: Fluids 2004, 23, 137−145. (20) Jadoon, A.; Prahl, L.; Revsted, J. Dynamic interaction of fixed dual spheres for several configurations and inflow conditions. Eur. J. Mech., B: Fluids 2010, 29, 43−52. (21) Ozgoren, M.; Okbaz, A.; Dogan, S.; Sahin, B.; Akilli, H. Investigation of Flow Characteristics around a Sphere Placed in a Boundary-layer over a Flat Plate. Exp. Therm. Fluid Sci. 2013, 44, 62− 74. (22) Kishore, N. Numerical Investigation of Interaction between Spheroid Particles in Tandem Arrangement at Moderate Reynolds Numbers. Ind. Eng. Chem. Res. 2012, 51, 10265−10273. (23) Kishore, N. Flow and Drag Phenomena of Tandem Spheroid Particles at Finite Reynolds Numbers. Ind. Eng. Chem. Res. 2012, 51, 3186−3196. (24) Hassanzadeh, R.; Sahin, B.; Ozgoren, M. Large eddy simulation of free-surface effects on the wake structures downstream of a spherical body. Ocean Eng. 2012, 54, 213−222.

5. CONCLUSIONS The vortex shedding development and the vortical flow characteristics are significantly altered in the arrangements of side-by-side spheres with regard to the single sphere case. The formations of the small and large-scale wavy shaped vortical flow characteristics occur because of the temporal developments of vortices and the shear-layer instability. The PIV results reveal that the turbulence statistics, the wake size and the formations of critical points, vary with regard to the gap ratio, G/D, of spheres. The two side-by-side spheres act as a unique bluff body for G/D = 1.0. At a very small gap ratio, for example, for 1.0 ≤ G/D ≤ 1.5, wakes of spheres interact strongly because of the inner shear-layer instabilities. Interactions between shedding vortices becomes weaker for G/D = 2.5. 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 = 2.5. As observed from dye visualizations, flow behaviors of the two side-by-side spheres exhibit two parallel vortex streets in an antiphase mode traveling in the flow direction without merging together. The shear layers shedding from the periphery of spheres have locally intensified fluctuations in velocity distributions with a higher rate of ⟨v′w′/U∞2⟩ because of the 3-D vorticity interactions. In the cross-sectional measuring planes located between L/D = 0.5 and 3.5, numbers of longitudinal vortices having opposite signs are situated around the sphere periphery and near the center of the flow field. The wake flow structures at the rear of the sphere show an unsteady behavior and shear-layer instabilities. Flow structures for G/D = 1.0 are similar to the single sphere flow patterns in the end-view plane at L/D = 1.5. It is demonstrated that the positive and negative flow patterns immediately after the sphere in the wake interact and merge as they move through their wake region. Furthermore, the present data provide appropriate information to validate numerical models and practical applications.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +90 322 3385763. Fax: +90 322 3386126. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The funding of the Scientific and Technological Research Council of Turkey under contract number 109R028, Cukurova University under contract number AAP20025, and Selcuk University and DPT under contract number 2009K12180 is greatly appreciated. 14502



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(25) Ozgoren, M. Flow structures around an equilateral triangle arrangement of three spheres. Int. J. Multiphase Flow 2013, 53, 54−64. (26) Hassanzadeh, R.; Sahin, B.; Ozgoren, M. Large eddy simulation of flow around two side-by-side spheres. J. Mech. Sci. Technol. 2013, 27 (7), 1−9. (27) Dhole, S. D.; Chhabra, R. P.; Eswaran, V. Drag of a spherical bubble rising in power law fluids at intermediate Reynolds numbers. Ind. Eng. Chem. Res. 2007, 46, 939−946. (28) Rajasekhar, C. R.; Kishore, N. Wall retardation effects on flow and drag phenomena of confined spherical particles in shearthickening fluids. Ind. Eng. Chem. Res. 2012, 51, 16755−16762. (29) Kishore, N.; Nalajala, V. S.; Chhabra Raj, P. Effects of Contamination and Shear-Thinning Fluid Viscosity on Drag Behavior of Spherical Bubbles. Ind. Eng. Chem. Res. 2013, 52, 6049−6056. (30) Sahin, B.; Ozturk, A. N.; Akilli, H. Horseshoe Vortex System in the Vicinity of the Vertical Cylinder Mounted on a Flat Plate. Flow Meas. Instrum. 2007, 18 (2), 57−68. (31) Jang, Y. J.; Lee, S. J. PIV analysis of near-wake behind a sphere at a subcritical Reynolds number. Exp. Fluids 2008, 44 (6), 905−914. (32) Pinar, E. Experimental Investigation of the Flow Structure Around Spheres Placed Side-by-Side; Cukurova University, Institute of Natural and Applied Sciences: Adana, Turkey, 2009. (33) Yun, G.; Kim, D.; Choi, H. Vortical structures behind a sphere at subcritical Reynolds numbers. Phys. Fluids 2006, 18 (1), 015−102. (34) Ozgoren, M. Flow structure in the downstream of square and circular cylinders. Flow Meas. Instrum. 2006, 17, 225−235. (35) Wu, J. S.; Faeth, G. M. Sphere wakes in still surroundings at intermediate Reynolds numbers. AIAA J. 1993, 3 (8), 1448−1455. (36) Leder, A.; Geropp, D. The unsteady flow structure in the wake of the sphere. SPIE 2052 1993, 119−126. (37) Brü cker, C. Spatio-Temporal Reconstruction of Vortex Dynamics In Axisymmetric Wakes. J. Fluids Struct. 2001, 15, 543−554.

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Experimental Study of Flow Structures around Side-by-Side Spheres

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