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Investigation of flow characteristics around a sphere placed in a boundary layer over a flat plate
Experimental Thermal and Fluid Science 44 (2013) 62–74
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Investigation of flow characteristics around a sphere placed in a boundary layer over a flat plate Muammer Ozgoren a,⇑, Abdulkerim Okbaz a, Sercan Dogan a, Besir Sahin b, Huseyin Akilli b a b
Selcuk University, Engineering and Architecture Faculty, Mechanical Engineering Department, Konya 42079, Turkey Cukurova University, Engineering and Architecture Faculty, Mechanical Engineering Department, Adana 01330, Turkey
a r t i c l e
i n f o
Article history: Received 10 April 2012 Received in revised form 27 May 2012 Accepted 28 May 2012 Available online 6 June 2012 Keywords: Boundary layer Flow visualization Reattachment Sphere PIV Turbulence Vorticity Wake
a b s t r a c t Flow characteristics around a sphere located over a smooth flat plate were experimentally investigated using dye visualization and PIV technique. The sphere was embedded in a turbulent boundary layer with a thickness of 63 mm which was larger than the sphere diameter of D = 42.5 mm. Instantaneous and time-averaged flow patterns in the wake region of the sphere were examined from the point of flow physics for different sphere locations in the range of 0 6 G/D 6 1.5 where G was the space between the bottom point of the sphere and the flat plate surface. Reynolds numbers with a range of 2500 6 Re 6 10000 based on the free-stream velocity while the velocity distributions over the plate surface are the developed turbulent boundary layer condition attained by using a tripwire. Distributions of velocity fluctuations, patterns of sectional streamlines, vorticity contours, velocity fields, turbulent kinetic energy and corresponding Reynolds stress correlations are obtained using PIV data. It was found that a jet-like flow stimulated the flow entrainment between the core and wake regions as a function of the sphere locations. The gap ratio has a strong influence on the flow structure of the wake-boundary layer interaction and the variation of the reattachment location of the separated flow from the plate surface. The time-averaged flow patterns yield asymmetric structures downstream of the sphere due to the effect of the boundary layer flow distribution. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Flow around a sphere has many engineering applications in single and two phase flows such as nuclear and thermal power plants, towed sonar, swimming bodies in the water, pneumatic and hydraulic conveying, chemical and food processing, conveying of sediments in the river, rain drops, submarine research vehicles, combustion systems and sport balls. The wake of a sphere in uniform unbounded flow condition has been studied extensively for several years because of its complex flow features and practical applications. In the nature and engineering applications surfaces of most structures are exposed to non-uniform incoming boundary layer flow due to the proximity of a wall. The spherical structure finds application in not only gas tanks, but also in artistic structures and some types of vehicles [1]. The presence of boundary layer flow over the plane wall introduces significant complications into the wake of the sphere due to non-uniform velocity profile, gap flow between the bottom section of the sphere and plate surface and also occurrence of the vorticity field in the boundary layer region. When a sphere is immersed close to the wall, vortex ⇑ Corresponding author. Tel.: +90 555 45170, +90 332 223 2764 (office); fax: +90 332 2410635. E-mail addresses: [email protected], [email protected] (M. Ozgoren). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.05.014
shedding changes noticeably due to the influence of a non-uniform velocity profile which is formed as a result of boundary layer flow developed over the plane wall. This results in asymmetry in the strength of vortex shedding from upper and lower sides of the sphere and changes the direction of the mean force acting over the body away from the plane wall. The interaction between the turbulent wake of the sphere and the plane boundary layer is influenced by several factors such as approaching boundary layer thickness, free-stream disturbances, Reynolds number and gap flow between the sphere and plane wall. Therefore, a well-understanding of this kind of flows has crucial importance to choose or develop suitable flow control methods. There are few studies around a sphere located in a boundary layer at intermediate Reynolds number. Tsutsui [1] performed a study related to interaction of boundary layer and a sphere in the wind tunnel to investigate flow around a sphere placed at various heights above a plane turbulent boundary layer at the Reynolds number 8.3 104 based on the sphere diameter. Okamoto [2] investigated the flow field of a sphere in contact with a plane and examined the wake structure and the aerodynamic force on the sphere. On the other hand, some of the studies for incoming uniform conditions were done experimentally and numerically. For example, Ozgoren et al. [3] performed an experimental investigation of flow structures downstream of a circular cylinder and
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sphere immersed in a free-stream flow for Re = 5000 and 10000 using qualitative and quantitative flow visualization techniques. They stated that the concentration of small scale vortices is more dominant in the wake of the sphere than that of the cylinder. Hassanzadeh et al. [4] carried out a numerical investigation of flow structures around a sphere at Re = 5000. As a preliminary study, Ozgoren et al. [5] investigated the flow-structure interaction of separated shear flow between the sphere wake and a flat plate and then they applied a passive flow control with a 2 mm o-ring located on the sphere surface at 55° with reference to the stagnation point at Re = 5000. They pointed out that the wake flow structure becomes symmetrical at smaller gap ratios and reattachment point on the flat plate surface occurs earlier. Jang and Lee [6] reported the vortical flow structures of the sphere wake in the streamwise plane at Re = 11000 in order to demonstrate flow structures and turbulence statistics. Leweke et al. [7] presented experimental visualization of flow structure in the wake of a sphere at Re = 320 and they observed periodic shedding of counter rotating of vortex filaments. Taneda [8] presented the wake configuration of a sphere and Sakamoto and Haniu [9] investigated the vortex shedding from spheres in a uniform flow. Achenbach [10] visualized the vortical structure of the sphere wake at Re = 1000 using dye and measured skin friction to investigate flow-separation angles in the range of Re = 105–106. Drag force around a stationary smooth sphere placed in a boundary layer type gradient flow for Reynolds numbers in the range of 3.62 103 6 Re 6 6.45 104 was examined [11]. A series of experiments varying particle size, particle density, particle loading and the Reynolds number for particle-turbulence interaction in wall turbulent flows was conducted [12]. Moradian et al. [13] investigated experimentally the effects of free-stream turbulence intensity and integral length scale as free-stream turbulent parameters on the drag coefficient of a sphere in a closed circuit wind tunnel for Re = 22000– 80000. They confirmed that the drag coefficient is decreased with increasing turbulence intensity. Also, Tyagi et al. [14] studied the effect of free-stream turbulence on the sphere wake and they found that the vortex shedding process downstream of the sphere was reduced when large organized motions were suppressed by the free-stream turbulence. Boundary layer interaction of two dimensional bluff body presents similar flow characteristics for the case of touching the wall surface. For example, a comprehensive review of Simpson [15] for cylinder reports several physical features of junction flows around bluff bodies such that, horseshoe vortices form in all types of bluff bodies’ junction causing high rate of turbulent intensities, pressure fluctuations, circulatory motions and heat transfer rate around the bases of bluff bodies. Akoz et al. [16] experimentally investigated the characteristics of two
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dimensional turbulent flow around a horizontal wall mounted circular cylinder in the range of 1000 6 Re 6 7000 based on the cylinder diameter. They reveal the mechanisms of vortical flow structure which mostly responsible for scour and burial process. In the heat transfer field, a sphere was available for the heat transfer enhancement on a plane, which was studied [17]. Prediction of flow and heat transfer around a body mounted on a surface is very important in relation to many of heat exchangers and fluid machineries [18–21]. Vortex shedding due to the scouring process causes additional unsteady forces such as lift and drag acting on the sphere. Consequently, the sphere becomes unstable and damages may occur on it. In order to prevent these problems, the flow structure around a sphere placed over the wall should be investigated, in detail. In the present study, interaction of flow-structure between the separated shear flow emanating from periphery of the sphere and a flat plate is investigated using dye visualization and PIV technique for 2500 6 Re 6 10000. The sphere locations from the flat plate surface vary in the range of 0 6 G/D 6 1.5 to evaluate both the gap flow and boundary layer effects. 2. Experimental method and setup Experiments were performed in a large-scale open water channel with a test section length of 8000 mm and a width of 1000 mm at the Department of Mechanical Engineering at Cukurova University, Turkey. To perform the present experimental study, the test section made from 15 mm thick transparent Plexiglas sheet, which had a total height of 750 mm, was filled with water to a level of only 450 mm. Before reaching the test chamber, the water was pumped into a settling chamber and passed through a honeycomb section and a two-to-one channel contraction. An overview of the experimental system of the sphere is shown in Fig 1. The freestream turbulence intensity of the flow is less than 0.5% in the range of the present Reynolds numbers, Re ¼ ðU 1 DÞ=v ; based on the sphere diameter. Here, v and D are kinematics viscosity and the diameter of the sphere, respectively. U1 is the free-stream velocity in the range of 59–236 mm/s. The sphere with a diameter of 42.5 mm was made of Plexiglas so that the laser light easily propagates through the sphere. The sphere surface was highly polished to avoid the effects of surface roughness. To fix the sphere in the water channel, a circular bar with a 5 mm diameter was connected to the sphere from the back surface of the sphere at the measurement plane in order to avoid support’s effects while images were taken at the equator cross-section of the sphere. The disturbing effect of the support bar on the laser sheet location of the measurement plane that was observed by dye injection was
Fig. 1. Schematic view of the experimental setup of PIV system, laser illumination for a sphere located in a boundary layer.
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negligible in the consideration of support diameter with respect to the sphere diameter. The solid blockage ratio of the sphere including support was 1.3%. p The ffiffiffiffiffiffiffiffiFroude number based on the water depth hw was Fr ¼ U 1 = ghw = 0.03–0.12 depending on the freestream velocity, which was subcritical flow region owing to the Froude number less than 1.0. A flat plate with dimensions of 2000 mm 980mm 10mm having sharp leading edge is located over the bottom surface of the water channel. The hydrodynamically developed boundary layer was obtained by a tripping wire of diameter 5 mm placed 80 mm downstream of the leading edge of the flat plate. The gap between the lower point of the sphere and the surface of the flat plate was changed from 0 to 63.75 mm and normalized with the sphere diameter designated as G/D. In the absence of the sphere, the time-averaged distribution of the streamwise velocity along the vertical line at the sphere location is seen in Fig. 2. The sphere was positioned at a distance of 1400 mm from the leading edge of the plate in order to allow development of a fully turbulent boundary layer. It was determined in the absence of the sphere that the resulting hydrodynamically developed boundary layer thickness is d = 63 mm at the center of the sphere location for Re = 5000. The nominal thickness of the boundary layer d was estimated from the velocity profile using the definition of one percent defect of the free-stream velocity. The ratios of the displacement d⁄ and momentum h thicknesses relative to the boundary layer thickness were found to be d⁄/ d = 0.18 and h/d = 0.13, respectively. The boundary layer shape factor H = d⁄/h is 1.42 which is very close to the well known range of 1.2 < H < 1.4 for fully developed turbulent flow. The Reynolds number ranges from 2500 to 10000, the results show that the ensemble-averaged velocity profiles exhibited shape factor variation of H = 1.4–1.5. Comparison of the experimental results with power law expression of u/U1 = (y/d)1/n for n = 7 is in good agreement as indicated in Fig 2. Nd:YAG laser was used to generate a laser sheet that was perpendicular to the axis of the sphere and the symmetry axis (i.e. equator of the sphere) was passed through them. A CCD camera having a resolution of 1600 1186 pixels was used to record the images. The laser sheet was generated from a dual pulsed Nd:YAG system, having the maximum output of 120 mJ per pulse, which had time delays Dt = 1.0–1.7 ms for the present experiments. The suspended seeding particles with a diameter of 10 lm in the flow were silver metallic coated hollow spheres. The illuminating laser sheet thickness in the flow field was approximately 1.5 mm. As shown in Fig. 1, the laser was mounted in a fixed position beneath the water tank while the camera was the right angle to the laser sheet. The high-image-density criterion was satisfied by ensuring
Fig. 2. Velocity distribution for a developed turbulent boundary layer with the effect of a tripwire over a sharp-edged flat plate at Re = 5000 and comparison of the experimental results with power law expression of u/U1 =(y/d)1/n for n = 7.
that a minimum of approximately 20–30 particles was contained within the interrogation area. Dantec Flow Grabber digital PIV software employing the cross-correlation algorithm was used to compute the raw displacement vector field from the particle image data. An interrogation window of 32 32 pixels in the image was selected and converted to grid size approximately 1.44 1.44 mm2 for the sphere (0.034D 0.034D). The overall fields of physical view had 7227 (99 73) velocity vectors for whole taken images. During the interrogation process, an overlap of 50% was employed in order to satisfy the Nyquist criterion. Patterns of instantaneous particle images with a total of 700 images consisting of two separate 350 images in a continuous series were taken at the rate of 15 Hz to calculate the time-averaged patterns of the flow structure. The vorticity value at each grid point was calculated from the circulation around the eight neighboring points.
3. Results and discussion Comparison of flow visualization of flow structure with laser illumination of Rhodamine dye injection technique, normalized instantaneous velocity V and vorticity x⁄ around the sphere for 0 6 G/D 6 1.5 at Re = 5000 is shown in Fig 3. Time-averaged flow patterns and their maximum values are given on each image displayed in Figs. 4 and 5, Figs. 6a and 6b. Instantaneous vorticity contours of the wake structure is normalized as x⁄ (i.e., x⁄ = xD/U1). All figure dimensions are normalized with the appearance diameter of the sphere as x/D, y/D and G/D. Layers of positive and negative vortices are displayed with red and blue lines, respectively. The separated and recirculating flows in the near-wake region around the sphere are clearly seen with the help of flow visualization technique in the left column of Fig 3. In the dye visualization, representative images of the small scale vortices are designated by A–G to show evolution and progress of them for all gap ratios. Wavy structure in the wake region occurs due to vortex shedding around the periphery of the sphere and the velocity difference between the wake and free-stream flow as well as gradient flow in the boundary layer. The small-scale Kelvin–Helmholtz instability leads to rapid transition of the separated shear layer, with consequent irregular perturbation of the interfacial layer that leads to entrainment. When the sphere is located on the flat plate at G/ D = 0, the contact point of the sphere and the flat plate blocks the fluid flow resulting in preventing the shedding of vortices from the lower section of the sphere. Thus, clockwise rotating vortices with a helical form shed from the upper section of the downstream of the sphere. For G/D = 0, the flow separates from only upper section of the sphere circumference in the visualization plane and small scale vortices in the wake region are formed around and in the larger vortices with a wavy appearance due to Kelvin Helmholtz instability in the boundary layer region. There is a region of separated flow from the upper section of the sphere and a shear layer with strong vorticity sheds at G/D = 0. For G/D > 0.25, large scale helical vortex shedding that may induce self-excited oscillation in the wake takes place similar to the Karman Vortex Streets two sphere diameters away from the sphere center. The streamwise spacing of successive vorticity peaks in the near wake region of the sphere is smaller than further downstream for all gap ratios. As displayed in PIV images, there are many eddies in the wake region owing to high level effect of the boundary layer and three dimensional flow separation. The flow is three-dimensional, and shedding vortices convey fresh fluid into the sphere wake flow region, magnifying the entrainment thus developing many eddies. These circulatory flows occur disorderly at different locations in the boundary layer causing instabilities. As the flow travels in the downstream direction, the vortices are shed from the upper section of the sphere directly to the inward wake region and the
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Fig. 3. Comparison of flow visualization of flow structure with laser illumination of Rhodamine dye injection technique (column I), normalized instantaneous velocity V (column II) and vorticity x⁄ (column III) around the sphere for 0 6 G/D 6 1.5 at Re = 5000. The minimum and incremental levels of the vorticity x⁄ are taken as |x⁄|min = h|x⁄|imin = ± 2.
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Fig. 4. Comparison of normalized time-averaged velocity components in x and y directions hu⁄i (column I), hv⁄i (column II), time-averaged vorticity hx⁄i (column III) along with vorticity fluctuations hxrms i (column IV) around the sphere for 0 6 G/D 6 1.5 at Re = 5000. The minimum and incremental levels of the flow patterns are taken as |hu⁄i|min = ± 0.1, hDu⁄i = 0.1, |hv⁄i|min = ± 0.05, hDv⁄i = 0.05, |hDx⁄i|min=|hDx⁄i|min = ± 2 and hDxrms imin = ± 0.25.
separated flow reattaches on the flat plate. In the case of G/D = 0.1, the gap flow between the bottom of the sphere and the flat plate highly affects the wake region. It appears that the low-speed
streaks observed near the plane are formed between pairs of longitudinal counter-rotating vortices. This vortices elongated in the direction of flow as clearly seen for the cases of G/D = 0.25 and 0.5.
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Fig. 5. Distributions of time-averaged streamwise velocity fluctuations hurms i (column I), cross-stream velocity fluctuations hv rms i (column II), Reynolds stress correlations hu0 v 0 =U 21 i (column III) and turbulent kinetic energy (TKE) (column IV) around the sphere for 0 6 G/D 6 1.5 at Re = 5000. The minimum and incremental levels of the flow patterns are taken as|hurms i|min = 0.075, hD urms i = 0.025, |hv rms i|min = 0.050, hD v rms i = 0.025.| hu0 v 0 =U 21 i |min = 0.004 and hDu0 v 0 =U 21 i=0.004. Both the minimum and incremental levels of the TKE flow patterns are 0.004.
The instantaneous velocity patterns V and corresponding vorticity fields x⁄ observed in the measuring plane display the small and large-scale waviness and rotate slowly around its axis while trav-
eling in the downstream flow direction. The instantaneous velocity vector distributions, V, indicate that a flow with high magnitude of velocity vectors occurs along the shear layer. The velocity gradients
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Fig. 6a. Variations of the time averaged streamline topology hWi for G/D = 0, 0.1 and 0.25 around the sphere located over a flat plate for the Reynolds number range of 2500 6 Re 6 10,000.
appearing in the shear layer separating from the sphere surface increase with decreasing gap ratio. Well-defined small and largescale swirling patterns of velocity vectors are evident in the wake. Shear layers emanating from the sphere create a complex flow field consisting of a number of vortices that move randomly in time and space. The location of reattachment point is not clearly defined by the instantaneous velocity vectors V, because the point of the reattachment moves forward and backward randomly due to the instability of the vortical flow structure. Through the observation of an animation of instantaneous images, it is seen that small-scale concentrations of vorticity convey the fresh fluid into the wake flow region magnifying the entrainment between the core flow and wake flow regions. The wavy flow structure of the sphere wake in the streamwise plane has also been reported by Ozgoren et al. [3]; Jang and Lee [6]; Sakamoto and Haniu [9]; Yun et al. [22]; Leder and Geropp [23]; Wu and Faeth [24]. The secondary vortices with negative and positive magnitudes are generated due to the fluctuating velocity gradient in the boundary layer and move inwards of the wake. This increases the energy level of reversed flow region in the wake. The flow is extremely unsteady in the boundary layer due to the sphere obstruction and moves in the direction of the main flow towards the sphere downstream and later attaches to the surface of the sphere. The corresponding velocity vector fields also show the large size of separated flow regions. This is a direct consequence of the separated boundary layer and the formation of vorticity in the wake. The sphere located on and over the plate is exposed to the shear flow on the boundary layer which, in turn, creates more powerful vortices in the vicinity of the sphere. Clockwise and counterclockwise small-scale vortices having consistently variation of magnitude and position of the maximum values are alternately formed in an irregular manner with time. The distributions of instantaneous
velocity vectors, also present the rotating flow along the shear layer indicating the existence of Kelvin–Helmholtz’s vortices which occur in an unsteady mode. The animation of 700 images also reveals that the three dimensional unsteady vortical flow structures occupy the surroundings of the sphere over the plate surface. In the case of G/D = 0.1, the gap flow between the bottom of the sphere and the flat plate is clearly seen in the column III of Fig. 3. These vortices have a tendency to move upwards because of the gap effect and lower pressure quantity of the wake. The secondary vortices with negative and positive magnitudes are generated considerably due to the jet flow through the gap and move inwards of the wake for G/D = 0.1 and 0.25 that lead to a strong up wash flow of rear surface of the sphere. As the gap ratio increases to G/ D = 0.25, the effect of gap flow between lower point of the sphere and the flat plate surface is restless. However, the tendency of the flow to move upwards decreases slightly as seen in the PIV results of vorticity contours in Fig. 3. It is clearly seen from dye visualization and the PIV results of vorticity contours that the wake regions of the sphere deflect upward due to gap flow. The positive vortices produced due to gap flow over the flat plate move in the downstream direction and separate from the wall of the flat plate around 0.5D away from the rear surface of the sphere. Layered vorticity patterns in the gap and along its wake may occur due to the sudden velocity variation along the plate surface. Although, for G/ D = 0.50, the gap flow do not form dominantly in comparison with G/D = 0.25 case, the wake region of the sphere still deflects upward direction. The region of this structure is that boundary layer region covers the upper section of the sphere wake with existing of a nonuniform velocity profile. The downstream separation region contains many counter-rotating vortices separated around the sphere. No regular vortex shedding was observed at this configuration.
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Fig. 6b. Variations of the time averaged streamline patterns hWi for G/D = 0.5, 1.0 and 1.5 around the sphere located over a flat plate at Re = 2500, 5000 and 10,000.
However, it is observed that, in the case of turbulent boundary layer, vortex shedding occurs at a gap ratio of G/D = 1.5, which is very similar uniform incoming flow condition. The patterns of vorticity, x⁄ presented in the last column of Fig. 3 repeatedly change in the wake flow region as a function of the gap spacing. A cluster of the negative vorticity is situated in close region of the plate surface for the cases of G/D 6 1.0. Frequency of fluctuating velocity components and corresponding Strouhal numbers were not determined because of insufficient data collecting with the present system and occurrence of chaotic flow structure. Flow patterns of vorticity show distinctly small-scale concentrations embedded in the larger-scale structures. They induce new types of elongated large-scale structures in the near-wake region, thus extending recirculation region for G/D = 0.25 and G/D = 1.0. Flow structures around the sphere for G/D = 1.5 case, shown in the bottom images of Fig. 3, resemble to the flow structure of the single sphere exposed to uniform flow. Large-scale broken vortices form in the wake region as a result of combining small-scale shear-layer vortices that developed along the separating shear layers similar to the results of Ozgoren et al. [3,6,25]. Fig. 4 presents the normalized time-averaged velocity components in x and y directions hu⁄i, hv⁄i, time-averaged vorticity hx⁄i along with vorticity fluctuations hxrms i around the sphere. Distributions of streamwise velocity components, hu⁄i, indicate the locations of free stagnation points which are indicated as black dots in column I of Fig 4. The distributions of transverse and streamwise velocity components, hu⁄i and hv⁄i, also demonstrate that the wake-flow region is energetic. In the wake flow region downstream of the sphere for G/D = 0, a large reverse flow region of hu⁄i is formed. The minimum reverse velocity values hu⁄i, were given
on each image and the location of free stagnation points for 0 6 G/D 6 1.5 are given in Table 1. Contours of cross-stream velocity components hv⁄i in the second column of Fig 4 are formed in a ‘‘switching’’ of the orientation of the positive and negative values of hv⁄i downstream of the sphere. Negative pairs are more dominant owing to the lower velocity magnitudes (i.e. lower pressure) in the boundary layer for G/D = 0. The wake patterns are considerably asymmetrical. A large amplitude of cross-stream velocity hv⁄i might indicate that the developing shear layers which originally separate from the periphery of the sphere entrained a significant mass flow in the base region of the wake. In the third column of Fig 3, the time-averaged vorticity hx⁄i images designated with ‘‘P’’, ‘‘Q’’ and ‘‘R’’ reveal that the detailed instantaneous structure of the small-scale vortices, Kelvin Helmholtz vortices and downstream part of the large scale broken vorticity streets are lost due to the unsteady flow structure and alternating direction of the vortex shedding, which emanates from the sphere periphery in the range of 0 6 G/D 6 1.5. The positive and negative time-averaged vortices are formed in the upper and lower region of the gap designated as ‘‘Q’’ and ‘‘R’’, respectively which have a tendency to move upward direction because of the gap flow effect and the lower pressure prevailing within the wake. For the low gap ratios of G/ D = 0.1, 0.25 and 0.5, owing to the velocity profile of the bounded gap flow between the sphere and the plate surface negative vorticity, ‘‘Q’’, also forms. The concentrated time-averaged vortex clusters of P, Q and R expand along the shear layer in the downstream direction for G/D = 0.1, 0.25 and 0.5. A substantial reduction takes place in the level of the vorticity due to the expansion of core-flow region in streamwise direction. The mixing layer in the downstream region of the flow is dominated by the negative
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Table 1 Locations and magnitudes of flow features at critical points that are displayed in Figs. 4–6a and 6b for Re = 5000. Schematic figure under the table shows the positions of Dx and Dy. Gap ratio
hu⁄i (Dx/D, Dy/D)
hu0 v 0 =U 21 i (Dx/D, Dy/D)
hurms i (Dx/D, Dy/D)
hv rms i (Dx/D, Dy/D)
hWi (Dx/D, Dy/D)
TKE (Dx/D, Dy/D)
G/D = 0
0 (1.98, 0.49) 0.370 (1.05, 0.41) 0 (1.04, 0.32) 0 (1.66, 0.50) 0 (0.56, 0.59) 0.211 (0.58, 0.39) 0.215 (1.05, 0.51) 0.347 (0.80, 0.25)
0.021 (1.63, 0.42) 0.017 (2.06, 0.06) 0.036 (0.97, 0.60) 0.016 (0.86, 0.04)
0.205 (1.56, 0.44)
0.219 (1.82, 0.17)
0.252 (0.9, 0.59)
0.246 (0.97, 0.53) 0.158 (1.30, 0.34)
R1 (2.01, 0.5) F1 (2.22, 0.22) F1 (0.99, 0.20)
0.033 (1.61, 0.45) 0.034 (2.10, 0.07) 0.059 (0.98, 0.57)
0.025 (1.45, 0.48)
0.208 (0.45, 0.43)
0.183 (0.62, 0.07)
S1 (0.56, 0.59) S2 (1.69, 0.59)
0.032 (0.79, 0.13) 0.032 (0.46, 0.44)
0.049 (1.03, 0.52)
0.321 (1.05, 0.55)
0.281 (1.42, 0.30)
0.084 (1.00, 0.54)
0 (1.32, 0.27)
0.023 (1.54, 0)
0.220 (1.36, 0.52)
G/D = 0.5
0.333 (0.86, 0.25) 0 (1.34, 0.29)
0.045 (1.14, 0.54) 0.024 (1.14, 0.24)
0.302 (1.12, 0.60) 0.206 (1.17, 0.22)
0.267 (1.34, 0.26)
G/D = 1.0
0.397 (0.93, 0.26) 0 (1.46, 0.28)
0.053 (1.30, 0.53) 0.022 (1.34, 0.16)
0.309 (1.17, 0.56) 0.192 (1.17, 0.28)
0.300 (1.59, 0.32)
G/D = 1.5
0.415 (0.98, 0.18) 0 (1.52, 0.18)
0.056 (1.36, 0.45) 0.035 (1.66, 0.19)
0.342 (1.08, 0.56) 0.268 (1.26, 0.37)
0.337 (1.73, 0.32)
F1 F2 F3 S1 F1 F2 S1 F1 F2 S1 F1 F2 S1
G/D = 0.1
G/D = 0.25
time-averaged vorticity hx⁄i as seen in Fig 4. In the left column of Fig 4, the time-averaged vorticity fluctuations hxrms i clearly show the unsteady and wavy structure of the wake excitation of the sphere for all cases. Maximum values of the hxrms i take place along the shear layers due to occurrence of high velocity gradient in these sections of the flow. Distributions of time-averaged rms streamwise velocity fluctuations, hurms i, cross-stream velocity fluctuations hv rms i, Reynolds stress correlations hu0 v 0 =U 21 i and turbulent kinetic energy (TKE) around the sphere are given in Fig 5. The distribution of the streamwise velocity fluctuations, hurms i, reveals virtually identical flow structures on the circumference of the sphere. For G/D = 0, only streamwise velocity fluctuations of the upper shear layer are formed whereas two peak points of streamwise velocity fluctuations occur due to the flow separation from the upper and lower shear layers for G/D = 0.1. For G/D = 0.25, the peak magnitude of the streamwise velocity fluctuations hurms i, of the upper shear layer is 0.321, while that of the lower shear layer of the sphere is 0.220, respectively. At the gap ratio of G/D = 1.5, peak magnitudes of the streamwise velocity fluctuations hurms i, are slightly higher than the other positions. The rms streamwise velocity patterns, hurms i, have detectable double peaks at almost equal distances in the upper and lower wake regions of the centerline of the sphere. Their locations and magnitudes are given in Figs. 5 and 6a and 6b along with in Table 1 for validation and comparison purposes. In addition, the difference between the peak values of the hurms i for the upper and lower shedding shear layers of the sphere increases with increasing gap ratio. When the gap ratio G/D is greater than 0.5, the upper shear layer of the spheres become in a larger and longer size due to the exposing of uniform incoming flow condition. The distri-
(0.86, (0.71, (1.38, (1.25, (0.76, (0.67, (1.16, (0.98, (0.73, (1.35, (1.03, (0.83, (1.45,
0.48) 0.26) 0.68) 0.37) 0.45) 0.37) 0.36) 0.49) 0.27) 0.37) 0.46) 0.34) 0.28)
0.027 (1.35, 0.55) 0.072 (1.14, 0.55) 0.037 (1.11, 0.24) 0.081 (1.18, 0.55) 0.037 (1.41, 0.09) 0.088 (1.17,0.55) 0.058 (1.23, 0.39)
butions of the rms of streamwise and transverse velocity fluctuations, hurms i and hv rms i, presented in the first and second columns of Fig. 5 indicate that the peak values of the root mean square of velocity components occur along the shedding shear layers and wake center. The peak magnitude of streamwise velocity fluctuation hurms i is generally greater than that of transverse velocity, hv rms i. The, hv rms i distribution has a peak value at approximately merging point of the shear layer around the sphere for G/D = 1.5. The hv rms i increases rapidly until the peak point and decreases slightly to reach the free-stream flow condition for G/D = 1.5. In the first and second columns of Fig 5, cross comparison of the results reveals the existence of double peaks for hurms i placed in the shear layers while a single peak is observed in hv rms i with a maximum for G/D P 0.25. To reveal the relative effects of G/D ratio on the wake of the sphere and boundary layer interactions, Reynolds stress correlations hu0 v 0 =U 21 i are presented in the third column of Fig 5. In gradient approaching flow condition, Reynolds stress correlations of flow past a sphere are formed asymmetric about the centerline of the sphere wake with negative and positive peak values. This asymmetric distribution of Reynolds stress correlations hu0 v 0 =U 21 i is formed with the effect of boundary layer flow in close proximity of the wall. For G/D = 0, only negative Reynolds stress occurs on the upper shear layer. As the gap ratio is increased to G/D = 0.1, besides the large-scale cluster of the hu0 v 0 =U 21 i having a negative value, there are two additional clusters with positive and negative values located downstream of the sphere base for Re = 5000. This situation occurs as a result of different behaviors of the jet-like flow through the gap. At G/D = 0.1, one of the peak value of Reynolds stress correlations occurs on a location where the jet like flow
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starts to accelerate to maximum streamwise velocity magnitude while the other peak value occurs on a location where the jet-like flow spreads up through the rear surface of the sphere as displayed in Fig 5. Reynolds stress correlations hu0 v 0 =U 21 i point out that there are no small-scale concentrations in the wake region of the sphere due to the very small magnitudes of the oscillations in that region as a result of separation around the periphery of the sphere. On the other hand, distributions of the hu0 v 0 =U 21 i which resemble the same behaviors of the flow stated above for other flow structures do not form symmetrical shape. A cluster and a maximum value of hu0 v 0 =U 21 i occur on the upper section of the sphere and along the shedding shear layer. On the other hand, the Reynolds stress values decrease substantially near the plate surface for G/D = 0.1, 0.25 and 0.5. The magnitude of Reynolds stress correlation hu0 v 0 =U 21 i keeps its strength due to the high rate of entrainment between wake and core flow regions, and then it decays down while the vortical flow travels in the downstream direction. This feature is consistent for all values of the sphere locations. As can be seen in the left column of Fig 5, TKE increases in downstream direction starting from the base of the sphere and reaches its peak value as indicated on each image, and then starts to decrease gradually in the downstream direction. Vortical flow in the wake interacts with the wall so that enhancement of TKE intensities in streamwise direction occurs. Moreover, the distributions of hv rms i show the single peak patterns whereas the TKE and hu0 v 0 =U 21 i contours point out double-peak patterns. For G/D = 0.1 and 0.25, the flow through the gap between the sphere and the plane affects the wake flow so that the TKE has two more peak values near to the wall. However, for larger gap ratios of G/D = 1.0 and 1.50, the effect of gap flow loses completely but the effect of the non-uniform velocity profile of the boundary layer still modifies the TKE of the sphere wake. The magnitudes of the maximum value of Reynolds stress correlations hu0 v 0 =U 21 i and TKE decrease from their peak values to a moderate level at a location further downstream. The peak values and their locations of the TKE for all of the cases are given in Table 1. The deviation in contour distributions of TKE around the sphere with respect to the gap ratio is much larger on the upper section of the sphere than that on the lower section due to the difference of the velocity magnitude. The rate of entrainment due to the high rate of circulatory flow motion of vortical flow structure is extremely high which results in enriching TKE values of the wake flow structures. Velocity distributions around the sphere show alternating high-speed and low speed regions in the boundary layer which results in counter-rotating streamwise vortex pairs. This phenomenon might be responsible for most of the turbulence kinetic energy dispersion and a contributor to the transport of Reynolds stress in Fig 5. Variations of the time averaged streamline patterns hWi for the different positions around the sphere located over a flat plate for the Reynolds number in the range of 2500 6 Re 6 10,000 are displayed in Figs. 6a and 6b. The time-averaged streamline topology for all arrangements in Figs. 6a and 6b is displayed and interpreted in terms of foci, F, and saddle points, S. The junction point of the streamlines separated from the rear surface of the sphere that is called as saddle point and denoted with ‘‘S’’ which shows the merging point of the shear layers emanating from the periphery of the sphere. The reattachment point of the streamlines separated from the upper section of the sphere to flat plate wall is denoted with ‘‘R’’. Locations of foci designated with ‘‘F1, F2 and F3’’ that are rolling in the clockwise and/or in counter clockwise with respect to the central axis of the sphere exhibit well-defined critical points and they indicate the evidence of three-dimensional flow. For the case of the sphere touching the flat plate at G/D = 0, a large circulation region designated as F1 which is entrapped by shear layer separated from the upper section of the sphere forms and covers whole the wake flow region. The separated flow from the
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upper section of the sphere reattaches on the flat plate surface after approximately 2D away from the sphere center downstream direction for 2500 6 Re 6 10,000. A stable focus F1 that is the streamlines spiral inward the center point of the focus is developed close to downstream of the sphere, which agrees well with the results of Tsutsui [1]; Seban and Caldwell [17]. As the jet flow begins to occur, the shedding shear layer from the upper section of the sphere does not reattach and the only focus F1 happens for Re = 2500, 5000 and 7500. Cross-comparison of streamline topology demonstrates the occurrence of focus F1 with a higher and bigger size bubble at G/D = 0 than the other gap ratios for 2500 6 Re 6 10,000. As the gap ratio increases to a value of G/D = 0.1, the modifications of flow patterns realize depending on the Reynolds number. The wake region with foci F1 and F2 are identifiable, and then the two saddle points S1 and S2 are formed just near the plate surface due to the gap flow and reverse flow effects. For Reynolds numbers 2500, 5000, and 7500 cases, a large scale separation bubble that is unstable recirculation having outward rotation is formed. For the case of G/D = 0.1 at Re = 2500, besides the large-scale separation bubble, there is one additional small scale stable recirculation focus, F2. When the Reynolds number is increased to 5000 and 7500, the small-scale recirculation focus, F2, disappears and a new large scale separation bubble, F1, is enhanced until Re = 7500. Moreover, the fluid flow through the small gap turns sharply through the intermediate region between the close region of the rear surface of the sphere and the large separation bubble, and thus the jet flow interacts with the flow separated from the upper section of the sphere for Re = 2500, 5000, and 7500. This interaction affects the vortex shedding characteristics and creates a good mixing of fluid layers causing enhancement in the wake, which is helpful for convective phenomena. That is, the flow pass the sphere could not be shed from the periphery of the sphere due to powerful jet-like flow between the sphere and the flat surface. For the biggest Reynolds number, Re = 10,000, the large scale separation bubble completely disappears and two recirculating regions which are embedded by the shear layers separated from the circumference of the sphere in the measurement plane occur. For G/D = 0.25, as clearly seen in Fig. 6a, two recirculation regions with foci designated with F1 and F2 take place in the wake region of the sphere. But there is a tendency of the wake to move upward and the two recirculation regions become asymmetric about the sphere centerline. The lower recirculation region is wider in length and shorter in weight than the upper one due to the gap flow as a conclusion of the non-uniform velocity profile in the boundary layer. As well known, separation on the surface of the plate occurs due to the streamwise adverse pressure gradient. This is the reason of occurring another small separation bubble on the plate surface in the wake of the sphere for G/D = 0.25. In other words, due to the strong coupling between the boundary layer and the lower shedding shear layer of the sphere, the boundary layer deflects away from the wall forming a small downstream separation bubble, F3, at Re = 2500 and Re = 5000 as shown at the bottom row of Fig. 6a. Thus, a small-sized focus takes place in close region of the sphere wake on the plate surface due to the occurrence of concentrated secondary vortices on the wall and lower pressure in the wake. The focus size, F3, decreases in length with increasing the Reynolds number to a higher value and disappears for Re = 7500 and 10,000. Increasing the gap ratio to a value of G/ D = 0.25, two recirculation regions occur in the wake region of the sphere for all Reynolds numbers as clearly seen in Fig. 6a. But there is a tendency to move upward of the wake of the sphere and the two recirculation regions are asymmetric about the sphere centerline. The upper recirculation region is slightly longer than the lower one in length whereas lower recirculation region is larger than the upper one in circulation shape and size.
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For the higher gap ratios G/D P 0.25, the two foci F1 and F2 in the recirculation wake region happen and they are asymmetric about the centerline of the sphere. For larger gap ratios of G/ D = 0.5, 1.0 and 1.5, the effect of gap flow becomes weaker dramatically but the effect of the non-uniform velocity profile of the boundary layer still modifies the flow structure of the sphere for Reynolds numbers in the range of 2500 6 Re 6 10,000. It is observed that asymmetry of streamline topology hWi decreases in the wake region for G/D = 1.5 at Re = 10,000 as seen in Fig. 6b. Patterns of sectional streamlines hWi clearly identify that as the Reynolds number increases, the saddle point, S1 moves slightly towards the rear surface of the sphere as seen in the left column of Fig. 6b. A separation bubble decreasing in size with increasing the Reynolds number has also been identified using oil film visualization and dye visualization [3,8,26]. At G/D = 1.5, the recirculation lengths of the shear layers become almost equal to each other similar to a sphere wake in uniform incoming condition. Distributions of time-averaged streamwise velocity component hu⁄i and streamwise velocity fluctuations hurms i along the vertical lines designated as ‘‘K, L, M, N and O’’ in the left column images of Figs. 4 and 5 downstream of the sphere at gap ratios of G/ D = 0, 0.1 and 0.25, top row for Re = 5000 and bottom row for Re = 10,000 are given in Fig. 7a–7c. Here, solid line represents the boundary layer velocity profile over a flat plate in the absence of the sphere as shown in Fig 2. The streamwise velocity component, hu⁄i, at different locations, L/D, on the vertical center of the sphere and in wake region is shown in Fig. 7a. The negative horizontal
Fig. 7c. Variation of Reynolds stress correlations hu0 v 0 =U 21 i along the vertical line displayed in the third column of Fig. 5 at 0.83D away from the rear surface of the sphere for 0 6 G/D 6 1.5 at Re = 5000.
velocity components in the separation regions downstream of the sphere are clearly seen from the velocity distributions. The negative velocity component decreases with increasing Reynolds numbers. Velocity profile of the boundary layer enhances the turbulence of the wake because of the gap flow and high level of vortex shedding. For G/D = 0, distributions of the hu⁄i from station ‘‘L’’
Fig. 7a. Distributions of time averaged streamwise velocity component hu⁄i along the vertical lines designated ‘‘K, L, M, N and O’’ in the left column images of Fig. 4 downstream of the sphere at gap ratio values of G/D = 0, 0.1 and 0.25, top row for Re = 5000 and bottom row for Re = 10,000. Continuous line represents the boundary layer velocity profile over a flat plate in the absence of the sphere as shown in Fig. 2.
Fig. 7b. Distributions of time-averaged streamwise velocity fluctuations hurms i along the vertical lines designated ‘‘K, L, M, N and O’’ in the left column images of Fig. 5 downstream of the sphere at gap ratio values of G/D = 0, 0.1 and 0.25, top row for Re = 5000 and bottom row for Re = 10,000.
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to ‘‘N’’ involve the negative reversed flow while the station ‘‘O’’ located approximately on the reattachment point comprises of positive magnitudes for Re = 5000 and 10,000. Variations of the negative velocities are smaller for Re = 10,000 than Re = 5000. The velocity distribution for G/D = 0.1 at station ‘‘M’’ is negative till y/D ffi 0.5 for Re = 5000 whereas it becomes positive due to the different behavior of the gap flow for Re = 10,000. The peak values of the jet flow for G/D = 0.25 at stations ‘‘K, L and M’’ reach to higher and they become smaller at stations ‘‘N and O’’ than the velocity profile of the boundary layer without the sphere for both Reynolds numbers. A global view on the asymmetry in the intensity of the timeaveraged streamwise velocity fluctuations, hurms i, show a thinning of the lower shear layer and a thickening of the upper shear layer due to the influence of boundary layer flow over the flat plate as seen from cross-comparison of Re = 5000 and Re = 10,000 in Fig. 7b. For G/D = 0, streamwise velocity fluctuations of the upper shear layer are formed a higher magnitude for both Reynolds numbers. For G/D = 0.10, the jet-like flow through the gap between the sphere and flat plate becomes effective on the streamwise velocity fluctuation patterns of the sphere wake. As clearly seen in Fig 7b, the jet-like flow has different behaviors resulting in different influences on the sphere wake depending on the Reynolds number. For G/D = 0.25, three peak points of streamwise velocity fluctuations occur at stations ‘‘L, M and O’’ for both Reynolds numbers. Two of them occur along the upper and lower shear layers of the sphere wake region and the third one occurs as a result of boundary layer separation from the flat plate wall due to the acceleration of the jet-like flow through the gap. However, the strength of the streamwise velocity fluctuations of the upper and lower shear layers is still different owing to interaction of shedding shear layers and boundary layer flow, but the difference is lower for Re = 10,000 case than Re = 5000. Fig. 7c displays variation of Reynolds stress correlations hu0 v 0 =U 21 i along the vertical line displayed in the third column of Fig 5 at 0.83D away from the rear surface of the sphere base for 0 6 G/D 6 1.5 at Re = 5000. The gap between the bottom point of the sphere and the plate surface varied from 0 to 63.75 mm. For G/D = 0, only negative Reynolds stress hu0 v 0 =U 21 i occur on the upper shear layer for the sphere. At G/D = 0.1 and 0.25, the distributions of hu0 v 0 =U 21 i become asymmetric about the sphere centerline with negative Reynolds stress in the upper shear layer and low levels of positive Reynolds stress in the lower shear layer. As the gap ratio increases further, variation of Reynolds stress correlations hu0 v 0 =U 21 i becomes larger due to the reducing effect of the boundary layer flow. There are more than one peak variation owing to the sphere placed totally in the boundary layer flow for gap ratio values of G/D = 0, 0.1 and 0.25. 4. Conclusions In this experimental study, the effect of plane boundary layer flow on the wake flow characteristics of the sphere has been investigated in open water channel for 2500 6 Re 6 10,000. The following results are obtained; The results of the flow visualization conducted demonstrate clearly a significant change of the wake structure at different gap ratios for the sphere. The flow patterns show that the effects of the flow interference caused by the boundary layer are severe when the gap ratios are small. The rate of entrainment due to the high rate of circulatory flow motion of vortical flow structure is extremely high which results in causing unstable wake flow structures. The non-uniform velocity profile of the boundary layer flow causes a difference in the strength of the separated shear layers from the periphery of the sphere forming asymmetry in the wake
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region. It was found that instantaneous flow patterns may change their direction from positive to negative close to the plate surface which can result in variation of the drag and lift forces of the sphere. Viewing all of the instantaneous vorticity clusters, it is observed that magnitudes of the instantaneous vortices, x⁄, decay downstream direction in the wake region. Experimental results have shown that the interaction between the sphere wake and turbulent boundary layer depending on the gap ratio significantly changes the flow structure. For the smallest gap ratio G/D = 0.1, the jet-like flow through the small gap turns the wake sharply into the intermediate region between the rear of the sphere and the large separation bubble, and then it interacts with the fluid separated from the upper side of the sphere. This interaction affects the vortex shedding characteristics and creates a good flow mixing resulting in enhancement of heat transfer phenomena. For G/D = 0.1, the direction of the wake region of the sphere is deflected to upward from the flat plate while surrounding to the rear surface of the sphere. It is demonstrated that the gap flow occurring between the sphere bottom section and the flat plate surface has very high scouring effect until G/D = 0.50 and then a distinguishable asymmetrical flow structure of the wake region keeps up to G/D = 1.0. It is observed from the streamline topology that when the Reynolds number increases to Re = 5000, the size of the downstream separation bubble rapidly decreases and disappears at Re = 7500. It is confirmed that the presence of the gap flow causes a jet flow and tends to suppress the reattachment in the boundary layer. Occurrence of foci in the wake represents the three-dimensionality of the flow structure. Clusters of vortices occur on the near plate surface where a larger velocity gradient exists. The rate of entrainment through the gap, due to the high rate of the circulatory motion of vortical flow structures, is extremely high, which causes the wake-flow structures to fluctuate further. It is seen that the gap ratios between the sphere and the boundary layer vary in the range of 0 6 G/D 6 1.5 influencing the instability of the vortical flow structure, significantly. For the gap ratios until G/D = 0.5, the separated flow from the bottom section of the sphere is strongly affected by the gap flow and the flow separation around the bottom section of the sphere is delayed. It is demonstrated that the wall affects the sphere wake at small gap spacing, constrains the flow passing through the gap, and restricts the vortex shedding from the sphere, especially in the lower section of the sphere. Regular vortex shedding occurs in the near wake when the gap ratio is greater than G/D = 1.0. Viewing of all images together shows that concentrated vortices gradually enlarge and weaken while the flow proceeds further downstream in the wake depending on the sphere location over the plate. Distributions of vortices and corresponding streamlines also indicate that mixing of the wake and core flow regions are expanded along the shear layers throughout the flow field due to the circulatory flow motion in the measuring plane. The present flow field and point-wise results given in Table 1 and Figs. 3 and 7a–7c can be useful for development, assessment and validation of numerical studies.
Acknowledgments The authors would like to acknowledge the funding of The Scientific and Technological Research Council of Turkey (TUBITAK) under Contract No. 109R028, Scientific Research Projects Office of Cukurova University Contract No. AAP20025, Selcuk University’s Scientific Research Project Office and DPT Project Contract No. 2009K12180.
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References [1] T. Tsutsui, Flow around a sphere in a plane turbulent boundary layer, Journal of Wind Engineering and Industrial Aerodynamics 96 (2008) 779–792. [2] S. Okamoto, Turbulent shear flow behind a sphere placed on a plane boundary, Turbulent Shear Flow 2 (1980) 246–256. [3] M. Ozgoren, E. Pinar, B. Sahin, H. Akilli, Comparison of flow structures in the downstream region of a cylinder and sphere, International Journal of Heat Fluid Flow 32 (6) (2011) 1138–1146. [4] R. Hassanzadeh, B. Sahin, M. Ozgoren, Numerical Investigation of flow structures around a sphere, International Journal of Computational Fluid Dynamics 25 (10) (2011) 535–545. [5] M. Ozgoren, A.Okbaz, S. Dogan, B. Sahin, H. Akilli, Turbulent shear Flow downstream of a sphere with and without an o-ring located over a plane boundary, Experimental Fluid Mechanics Conference, vol. 22–25 (November), Liberec, Czech Republic, 2011b, pp. 847–862. [6] Y.IIJ. Jang, S.J. Lee, PIV analysis of near-wake behind a sphere at a subcritical Reynolds number, Experimental in Fluids 44 (6) (2008) 905–914. [7] T. Leweke, M. Provansal, D. Ormie‘res, R. Lebescond, Vortex dynamics in the wake of a sphere, Physics of Fluids 11 (9) (1999) 12. [8] S. Taneda, Visual observations of the flow past a sphere at Reynolds numbers between 104 and 106, Journal of Fluid Mechanics 85 (1) (1978) 187–192. [9] H. Sakamoto, H. Haniu, A study on vortex shedding from spheres in a uniform flow, Journal of Fluids Engineering 112 (1990) 386–392. [10] E. Achenbach, Vortex shedding from spheres, Journal of Fluid Mechanics 62 (2) (1974) 209–221. [11] P.C. Patnaik, N. Vittal, P.K. Pande, Drag coefficient of a stationary sphere in gradient flow, Journal of Hydraulic Research 30 (3) (1992) 389–402. [12] M. Rashidi, G. Hetstroni, S. Banerjee, Particle–turbulence interaction in a boundary layer, International Journal of Multiphase Flows 16 (6) (1990) 935– 949. [13] N. Moradian, S.-K.D. Ting, S. Cheng, The effects of free-stream turbulence on the drag coefficient of a sphere, Experimental Thermal and Fluid Science 33 (2009) 460–471.
[14] H. Tyagi, R. Liu, S.-K.D. Ting, C.R. Johnston, Measurement of wake properties of a sphere in freestream turbulence, Experimental Thermal and Fluid Science 30 (2006) 587–604. [15] R.L. Simpson, Junction flows, Annual Review of Fluid Mechanics 33 (2001) 415–443. [16] M.S. Akoz, B. Sahin, H. Akilli, Flow characteristic of the horizontal cylinder placed on the plane boundary, Flow Measurement and Instrumentation 21 (2010) 476–487. [17] R.A. Seban, G.L. Caldwell, The effect of a spherical protuberance on the local heat transfer to a turbulent boundary layer, Transaction of ASME Journal of Heat Transfer 1 (1968) 408–412. [18] R.J. Goldstein, J. Karni, The effect of a wall boundary layer on local mass from a cylinder in cross-flow, Transaction of ASME, Journal of Heat Transfer 106 (1984) 260–267. [19] E.M. Fisher, P.A. Eibeck, The influence of a horseshoe vortex on local convective heat transfer, Transaction of ASME, Journal of Heat Transfer 112 (1990) 329– 335. [20] M.K. Chyu, V. Natarajan, Local heat/mass transfer distributions on the surface of a wall-mounted cube, Transaction of ASME, Journal of Heat Transfer 113 (1991) 851–857. [21] G. Hetsroni, C.-F. Li, A. Mosyak, I. Tiselj, Heat transfer and thermal pattern around a sphere in a turbulent boundary layer, International Journal of Multiphase Flows 27 (2001) 1127–1150. [22] G. Yun, D. Kim, H. Choi, Vortical structures behind a sphere at subcritical Reynolds numbers, Physics of Fluids 18 (1) (2006) 015102. [23] A. Leder, D. Geropp, The unsteady flow structure in the wake of the sphere, Laser Anemometry Advances and Applications (1993) 119–126. [24] J.S. Wu, G.M. Faeth, Sphere wakes in still surroundings at intermediate Reynolds numbers, AIAA Journal 3 (8) (1993) 1448–1455. [25] M. Ozgoren, Flow structure in the downstream of square and circular cylinders, Flow Measurement and Instrumentation 17 (2006) 225–235. [26] G.K. Suryanarayana, A. Prabhu, Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere, Experiments in Fluids 29 (6) (2000) 582–591.
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Investigation of flow characteristics around a sphere placed in a boundary layer over a flat plate Muammer Ozgoren a,⇑, Abdulkerim Okbaz a, Sercan Dogan a, Besir Sahin b, Huseyin Akilli b a b
Selcuk University, Engineering and Architecture Faculty, Mechanical Engineering Department, Konya 42079, Turkey Cukurova University, Engineering and Architecture Faculty, Mechanical Engineering Department, Adana 01330, Turkey
a r t i c l e
i n f o
Article history: Received 10 April 2012 Received in revised form 27 May 2012 Accepted 28 May 2012 Available online 6 June 2012 Keywords: Boundary layer Flow visualization Reattachment Sphere PIV Turbulence Vorticity Wake
a b s t r a c t Flow characteristics around a sphere located over a smooth flat plate were experimentally investigated using dye visualization and PIV technique. The sphere was embedded in a turbulent boundary layer with a thickness of 63 mm which was larger than the sphere diameter of D = 42.5 mm. Instantaneous and time-averaged flow patterns in the wake region of the sphere were examined from the point of flow physics for different sphere locations in the range of 0 6 G/D 6 1.5 where G was the space between the bottom point of the sphere and the flat plate surface. Reynolds numbers with a range of 2500 6 Re 6 10000 based on the free-stream velocity while the velocity distributions over the plate surface are the developed turbulent boundary layer condition attained by using a tripwire. Distributions of velocity fluctuations, patterns of sectional streamlines, vorticity contours, velocity fields, turbulent kinetic energy and corresponding Reynolds stress correlations are obtained using PIV data. It was found that a jet-like flow stimulated the flow entrainment between the core and wake regions as a function of the sphere locations. The gap ratio has a strong influence on the flow structure of the wake-boundary layer interaction and the variation of the reattachment location of the separated flow from the plate surface. The time-averaged flow patterns yield asymmetric structures downstream of the sphere due to the effect of the boundary layer flow distribution. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Flow around a sphere has many engineering applications in single and two phase flows such as nuclear and thermal power plants, towed sonar, swimming bodies in the water, pneumatic and hydraulic conveying, chemical and food processing, conveying of sediments in the river, rain drops, submarine research vehicles, combustion systems and sport balls. The wake of a sphere in uniform unbounded flow condition has been studied extensively for several years because of its complex flow features and practical applications. In the nature and engineering applications surfaces of most structures are exposed to non-uniform incoming boundary layer flow due to the proximity of a wall. The spherical structure finds application in not only gas tanks, but also in artistic structures and some types of vehicles [1]. The presence of boundary layer flow over the plane wall introduces significant complications into the wake of the sphere due to non-uniform velocity profile, gap flow between the bottom section of the sphere and plate surface and also occurrence of the vorticity field in the boundary layer region. When a sphere is immersed close to the wall, vortex ⇑ Corresponding author. Tel.: +90 555 45170, +90 332 223 2764 (office); fax: +90 332 2410635. E-mail addresses: [email protected], [email protected] (M. Ozgoren). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.05.014
shedding changes noticeably due to the influence of a non-uniform velocity profile which is formed as a result of boundary layer flow developed over the plane wall. This results in asymmetry in the strength of vortex shedding from upper and lower sides of the sphere and changes the direction of the mean force acting over the body away from the plane wall. The interaction between the turbulent wake of the sphere and the plane boundary layer is influenced by several factors such as approaching boundary layer thickness, free-stream disturbances, Reynolds number and gap flow between the sphere and plane wall. Therefore, a well-understanding of this kind of flows has crucial importance to choose or develop suitable flow control methods. There are few studies around a sphere located in a boundary layer at intermediate Reynolds number. Tsutsui [1] performed a study related to interaction of boundary layer and a sphere in the wind tunnel to investigate flow around a sphere placed at various heights above a plane turbulent boundary layer at the Reynolds number 8.3 104 based on the sphere diameter. Okamoto [2] investigated the flow field of a sphere in contact with a plane and examined the wake structure and the aerodynamic force on the sphere. On the other hand, some of the studies for incoming uniform conditions were done experimentally and numerically. For example, Ozgoren et al. [3] performed an experimental investigation of flow structures downstream of a circular cylinder and
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sphere immersed in a free-stream flow for Re = 5000 and 10000 using qualitative and quantitative flow visualization techniques. They stated that the concentration of small scale vortices is more dominant in the wake of the sphere than that of the cylinder. Hassanzadeh et al. [4] carried out a numerical investigation of flow structures around a sphere at Re = 5000. As a preliminary study, Ozgoren et al. [5] investigated the flow-structure interaction of separated shear flow between the sphere wake and a flat plate and then they applied a passive flow control with a 2 mm o-ring located on the sphere surface at 55° with reference to the stagnation point at Re = 5000. They pointed out that the wake flow structure becomes symmetrical at smaller gap ratios and reattachment point on the flat plate surface occurs earlier. Jang and Lee [6] reported the vortical flow structures of the sphere wake in the streamwise plane at Re = 11000 in order to demonstrate flow structures and turbulence statistics. Leweke et al. [7] presented experimental visualization of flow structure in the wake of a sphere at Re = 320 and they observed periodic shedding of counter rotating of vortex filaments. Taneda [8] presented the wake configuration of a sphere and Sakamoto and Haniu [9] investigated the vortex shedding from spheres in a uniform flow. Achenbach [10] visualized the vortical structure of the sphere wake at Re = 1000 using dye and measured skin friction to investigate flow-separation angles in the range of Re = 105–106. Drag force around a stationary smooth sphere placed in a boundary layer type gradient flow for Reynolds numbers in the range of 3.62 103 6 Re 6 6.45 104 was examined [11]. A series of experiments varying particle size, particle density, particle loading and the Reynolds number for particle-turbulence interaction in wall turbulent flows was conducted [12]. Moradian et al. [13] investigated experimentally the effects of free-stream turbulence intensity and integral length scale as free-stream turbulent parameters on the drag coefficient of a sphere in a closed circuit wind tunnel for Re = 22000– 80000. They confirmed that the drag coefficient is decreased with increasing turbulence intensity. Also, Tyagi et al. [14] studied the effect of free-stream turbulence on the sphere wake and they found that the vortex shedding process downstream of the sphere was reduced when large organized motions were suppressed by the free-stream turbulence. Boundary layer interaction of two dimensional bluff body presents similar flow characteristics for the case of touching the wall surface. For example, a comprehensive review of Simpson [15] for cylinder reports several physical features of junction flows around bluff bodies such that, horseshoe vortices form in all types of bluff bodies’ junction causing high rate of turbulent intensities, pressure fluctuations, circulatory motions and heat transfer rate around the bases of bluff bodies. Akoz et al. [16] experimentally investigated the characteristics of two
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dimensional turbulent flow around a horizontal wall mounted circular cylinder in the range of 1000 6 Re 6 7000 based on the cylinder diameter. They reveal the mechanisms of vortical flow structure which mostly responsible for scour and burial process. In the heat transfer field, a sphere was available for the heat transfer enhancement on a plane, which was studied [17]. Prediction of flow and heat transfer around a body mounted on a surface is very important in relation to many of heat exchangers and fluid machineries [18–21]. Vortex shedding due to the scouring process causes additional unsteady forces such as lift and drag acting on the sphere. Consequently, the sphere becomes unstable and damages may occur on it. In order to prevent these problems, the flow structure around a sphere placed over the wall should be investigated, in detail. In the present study, interaction of flow-structure between the separated shear flow emanating from periphery of the sphere and a flat plate is investigated using dye visualization and PIV technique for 2500 6 Re 6 10000. The sphere locations from the flat plate surface vary in the range of 0 6 G/D 6 1.5 to evaluate both the gap flow and boundary layer effects. 2. Experimental method and setup Experiments were performed in a large-scale open water channel with a test section length of 8000 mm and a width of 1000 mm at the Department of Mechanical Engineering at Cukurova University, Turkey. To perform the present experimental study, the test section made from 15 mm thick transparent Plexiglas sheet, which had a total height of 750 mm, was filled with water to a level of only 450 mm. Before reaching the test chamber, the water was pumped into a settling chamber and passed through a honeycomb section and a two-to-one channel contraction. An overview of the experimental system of the sphere is shown in Fig 1. The freestream turbulence intensity of the flow is less than 0.5% in the range of the present Reynolds numbers, Re ¼ ðU 1 DÞ=v ; based on the sphere diameter. Here, v and D are kinematics viscosity and the diameter of the sphere, respectively. U1 is the free-stream velocity in the range of 59–236 mm/s. The sphere with a diameter of 42.5 mm was made of Plexiglas so that the laser light easily propagates through the sphere. The sphere surface was highly polished to avoid the effects of surface roughness. To fix the sphere in the water channel, a circular bar with a 5 mm diameter was connected to the sphere from the back surface of the sphere at the measurement plane in order to avoid support’s effects while images were taken at the equator cross-section of the sphere. The disturbing effect of the support bar on the laser sheet location of the measurement plane that was observed by dye injection was
Fig. 1. Schematic view of the experimental setup of PIV system, laser illumination for a sphere located in a boundary layer.
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negligible in the consideration of support diameter with respect to the sphere diameter. The solid blockage ratio of the sphere including support was 1.3%. p The ffiffiffiffiffiffiffiffiFroude number based on the water depth hw was Fr ¼ U 1 = ghw = 0.03–0.12 depending on the freestream velocity, which was subcritical flow region owing to the Froude number less than 1.0. A flat plate with dimensions of 2000 mm 980mm 10mm having sharp leading edge is located over the bottom surface of the water channel. The hydrodynamically developed boundary layer was obtained by a tripping wire of diameter 5 mm placed 80 mm downstream of the leading edge of the flat plate. The gap between the lower point of the sphere and the surface of the flat plate was changed from 0 to 63.75 mm and normalized with the sphere diameter designated as G/D. In the absence of the sphere, the time-averaged distribution of the streamwise velocity along the vertical line at the sphere location is seen in Fig. 2. The sphere was positioned at a distance of 1400 mm from the leading edge of the plate in order to allow development of a fully turbulent boundary layer. It was determined in the absence of the sphere that the resulting hydrodynamically developed boundary layer thickness is d = 63 mm at the center of the sphere location for Re = 5000. The nominal thickness of the boundary layer d was estimated from the velocity profile using the definition of one percent defect of the free-stream velocity. The ratios of the displacement d⁄ and momentum h thicknesses relative to the boundary layer thickness were found to be d⁄/ d = 0.18 and h/d = 0.13, respectively. The boundary layer shape factor H = d⁄/h is 1.42 which is very close to the well known range of 1.2 < H < 1.4 for fully developed turbulent flow. The Reynolds number ranges from 2500 to 10000, the results show that the ensemble-averaged velocity profiles exhibited shape factor variation of H = 1.4–1.5. Comparison of the experimental results with power law expression of u/U1 = (y/d)1/n for n = 7 is in good agreement as indicated in Fig 2. Nd:YAG laser was used to generate a laser sheet that was perpendicular to the axis of the sphere and the symmetry axis (i.e. equator of the sphere) was passed through them. A CCD camera having a resolution of 1600 1186 pixels was used to record the images. The laser sheet was generated from a dual pulsed Nd:YAG system, having the maximum output of 120 mJ per pulse, which had time delays Dt = 1.0–1.7 ms for the present experiments. The suspended seeding particles with a diameter of 10 lm in the flow were silver metallic coated hollow spheres. The illuminating laser sheet thickness in the flow field was approximately 1.5 mm. As shown in Fig. 1, the laser was mounted in a fixed position beneath the water tank while the camera was the right angle to the laser sheet. The high-image-density criterion was satisfied by ensuring
Fig. 2. Velocity distribution for a developed turbulent boundary layer with the effect of a tripwire over a sharp-edged flat plate at Re = 5000 and comparison of the experimental results with power law expression of u/U1 =(y/d)1/n for n = 7.
that a minimum of approximately 20–30 particles was contained within the interrogation area. Dantec Flow Grabber digital PIV software employing the cross-correlation algorithm was used to compute the raw displacement vector field from the particle image data. An interrogation window of 32 32 pixels in the image was selected and converted to grid size approximately 1.44 1.44 mm2 for the sphere (0.034D 0.034D). The overall fields of physical view had 7227 (99 73) velocity vectors for whole taken images. During the interrogation process, an overlap of 50% was employed in order to satisfy the Nyquist criterion. Patterns of instantaneous particle images with a total of 700 images consisting of two separate 350 images in a continuous series were taken at the rate of 15 Hz to calculate the time-averaged patterns of the flow structure. The vorticity value at each grid point was calculated from the circulation around the eight neighboring points.
3. Results and discussion Comparison of flow visualization of flow structure with laser illumination of Rhodamine dye injection technique, normalized instantaneous velocity V and vorticity x⁄ around the sphere for 0 6 G/D 6 1.5 at Re = 5000 is shown in Fig 3. Time-averaged flow patterns and their maximum values are given on each image displayed in Figs. 4 and 5, Figs. 6a and 6b. Instantaneous vorticity contours of the wake structure is normalized as x⁄ (i.e., x⁄ = xD/U1). All figure dimensions are normalized with the appearance diameter of the sphere as x/D, y/D and G/D. Layers of positive and negative vortices are displayed with red and blue lines, respectively. The separated and recirculating flows in the near-wake region around the sphere are clearly seen with the help of flow visualization technique in the left column of Fig 3. In the dye visualization, representative images of the small scale vortices are designated by A–G to show evolution and progress of them for all gap ratios. Wavy structure in the wake region occurs due to vortex shedding around the periphery of the sphere and the velocity difference between the wake and free-stream flow as well as gradient flow in the boundary layer. The small-scale Kelvin–Helmholtz instability leads to rapid transition of the separated shear layer, with consequent irregular perturbation of the interfacial layer that leads to entrainment. When the sphere is located on the flat plate at G/ D = 0, the contact point of the sphere and the flat plate blocks the fluid flow resulting in preventing the shedding of vortices from the lower section of the sphere. Thus, clockwise rotating vortices with a helical form shed from the upper section of the downstream of the sphere. For G/D = 0, the flow separates from only upper section of the sphere circumference in the visualization plane and small scale vortices in the wake region are formed around and in the larger vortices with a wavy appearance due to Kelvin Helmholtz instability in the boundary layer region. There is a region of separated flow from the upper section of the sphere and a shear layer with strong vorticity sheds at G/D = 0. For G/D > 0.25, large scale helical vortex shedding that may induce self-excited oscillation in the wake takes place similar to the Karman Vortex Streets two sphere diameters away from the sphere center. The streamwise spacing of successive vorticity peaks in the near wake region of the sphere is smaller than further downstream for all gap ratios. As displayed in PIV images, there are many eddies in the wake region owing to high level effect of the boundary layer and three dimensional flow separation. The flow is three-dimensional, and shedding vortices convey fresh fluid into the sphere wake flow region, magnifying the entrainment thus developing many eddies. These circulatory flows occur disorderly at different locations in the boundary layer causing instabilities. As the flow travels in the downstream direction, the vortices are shed from the upper section of the sphere directly to the inward wake region and the
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Fig. 3. Comparison of flow visualization of flow structure with laser illumination of Rhodamine dye injection technique (column I), normalized instantaneous velocity V (column II) and vorticity x⁄ (column III) around the sphere for 0 6 G/D 6 1.5 at Re = 5000. The minimum and incremental levels of the vorticity x⁄ are taken as |x⁄|min = h|x⁄|imin = ± 2.
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Fig. 4. Comparison of normalized time-averaged velocity components in x and y directions hu⁄i (column I), hv⁄i (column II), time-averaged vorticity hx⁄i (column III) along with vorticity fluctuations hxrms i (column IV) around the sphere for 0 6 G/D 6 1.5 at Re = 5000. The minimum and incremental levels of the flow patterns are taken as |hu⁄i|min = ± 0.1, hDu⁄i = 0.1, |hv⁄i|min = ± 0.05, hDv⁄i = 0.05, |hDx⁄i|min=|hDx⁄i|min = ± 2 and hDxrms imin = ± 0.25.
separated flow reattaches on the flat plate. In the case of G/D = 0.1, the gap flow between the bottom of the sphere and the flat plate highly affects the wake region. It appears that the low-speed
streaks observed near the plane are formed between pairs of longitudinal counter-rotating vortices. This vortices elongated in the direction of flow as clearly seen for the cases of G/D = 0.25 and 0.5.
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Fig. 5. Distributions of time-averaged streamwise velocity fluctuations hurms i (column I), cross-stream velocity fluctuations hv rms i (column II), Reynolds stress correlations hu0 v 0 =U 21 i (column III) and turbulent kinetic energy (TKE) (column IV) around the sphere for 0 6 G/D 6 1.5 at Re = 5000. The minimum and incremental levels of the flow patterns are taken as|hurms i|min = 0.075, hD urms i = 0.025, |hv rms i|min = 0.050, hD v rms i = 0.025.| hu0 v 0 =U 21 i |min = 0.004 and hDu0 v 0 =U 21 i=0.004. Both the minimum and incremental levels of the TKE flow patterns are 0.004.
The instantaneous velocity patterns V and corresponding vorticity fields x⁄ observed in the measuring plane display the small and large-scale waviness and rotate slowly around its axis while trav-
eling in the downstream flow direction. The instantaneous velocity vector distributions, V, indicate that a flow with high magnitude of velocity vectors occurs along the shear layer. The velocity gradients
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Fig. 6a. Variations of the time averaged streamline topology hWi for G/D = 0, 0.1 and 0.25 around the sphere located over a flat plate for the Reynolds number range of 2500 6 Re 6 10,000.
appearing in the shear layer separating from the sphere surface increase with decreasing gap ratio. Well-defined small and largescale swirling patterns of velocity vectors are evident in the wake. Shear layers emanating from the sphere create a complex flow field consisting of a number of vortices that move randomly in time and space. The location of reattachment point is not clearly defined by the instantaneous velocity vectors V, because the point of the reattachment moves forward and backward randomly due to the instability of the vortical flow structure. Through the observation of an animation of instantaneous images, it is seen that small-scale concentrations of vorticity convey the fresh fluid into the wake flow region magnifying the entrainment between the core flow and wake flow regions. The wavy flow structure of the sphere wake in the streamwise plane has also been reported by Ozgoren et al. [3]; Jang and Lee [6]; Sakamoto and Haniu [9]; Yun et al. [22]; Leder and Geropp [23]; Wu and Faeth [24]. The secondary vortices with negative and positive magnitudes are generated due to the fluctuating velocity gradient in the boundary layer and move inwards of the wake. This increases the energy level of reversed flow region in the wake. The flow is extremely unsteady in the boundary layer due to the sphere obstruction and moves in the direction of the main flow towards the sphere downstream and later attaches to the surface of the sphere. The corresponding velocity vector fields also show the large size of separated flow regions. This is a direct consequence of the separated boundary layer and the formation of vorticity in the wake. The sphere located on and over the plate is exposed to the shear flow on the boundary layer which, in turn, creates more powerful vortices in the vicinity of the sphere. Clockwise and counterclockwise small-scale vortices having consistently variation of magnitude and position of the maximum values are alternately formed in an irregular manner with time. The distributions of instantaneous
velocity vectors, also present the rotating flow along the shear layer indicating the existence of Kelvin–Helmholtz’s vortices which occur in an unsteady mode. The animation of 700 images also reveals that the three dimensional unsteady vortical flow structures occupy the surroundings of the sphere over the plate surface. In the case of G/D = 0.1, the gap flow between the bottom of the sphere and the flat plate is clearly seen in the column III of Fig. 3. These vortices have a tendency to move upwards because of the gap effect and lower pressure quantity of the wake. The secondary vortices with negative and positive magnitudes are generated considerably due to the jet flow through the gap and move inwards of the wake for G/D = 0.1 and 0.25 that lead to a strong up wash flow of rear surface of the sphere. As the gap ratio increases to G/ D = 0.25, the effect of gap flow between lower point of the sphere and the flat plate surface is restless. However, the tendency of the flow to move upwards decreases slightly as seen in the PIV results of vorticity contours in Fig. 3. It is clearly seen from dye visualization and the PIV results of vorticity contours that the wake regions of the sphere deflect upward due to gap flow. The positive vortices produced due to gap flow over the flat plate move in the downstream direction and separate from the wall of the flat plate around 0.5D away from the rear surface of the sphere. Layered vorticity patterns in the gap and along its wake may occur due to the sudden velocity variation along the plate surface. Although, for G/ D = 0.50, the gap flow do not form dominantly in comparison with G/D = 0.25 case, the wake region of the sphere still deflects upward direction. The region of this structure is that boundary layer region covers the upper section of the sphere wake with existing of a nonuniform velocity profile. The downstream separation region contains many counter-rotating vortices separated around the sphere. No regular vortex shedding was observed at this configuration.
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Fig. 6b. Variations of the time averaged streamline patterns hWi for G/D = 0.5, 1.0 and 1.5 around the sphere located over a flat plate at Re = 2500, 5000 and 10,000.
However, it is observed that, in the case of turbulent boundary layer, vortex shedding occurs at a gap ratio of G/D = 1.5, which is very similar uniform incoming flow condition. The patterns of vorticity, x⁄ presented in the last column of Fig. 3 repeatedly change in the wake flow region as a function of the gap spacing. A cluster of the negative vorticity is situated in close region of the plate surface for the cases of G/D 6 1.0. Frequency of fluctuating velocity components and corresponding Strouhal numbers were not determined because of insufficient data collecting with the present system and occurrence of chaotic flow structure. Flow patterns of vorticity show distinctly small-scale concentrations embedded in the larger-scale structures. They induce new types of elongated large-scale structures in the near-wake region, thus extending recirculation region for G/D = 0.25 and G/D = 1.0. Flow structures around the sphere for G/D = 1.5 case, shown in the bottom images of Fig. 3, resemble to the flow structure of the single sphere exposed to uniform flow. Large-scale broken vortices form in the wake region as a result of combining small-scale shear-layer vortices that developed along the separating shear layers similar to the results of Ozgoren et al. [3,6,25]. Fig. 4 presents the normalized time-averaged velocity components in x and y directions hu⁄i, hv⁄i, time-averaged vorticity hx⁄i along with vorticity fluctuations hxrms i around the sphere. Distributions of streamwise velocity components, hu⁄i, indicate the locations of free stagnation points which are indicated as black dots in column I of Fig 4. The distributions of transverse and streamwise velocity components, hu⁄i and hv⁄i, also demonstrate that the wake-flow region is energetic. In the wake flow region downstream of the sphere for G/D = 0, a large reverse flow region of hu⁄i is formed. The minimum reverse velocity values hu⁄i, were given
on each image and the location of free stagnation points for 0 6 G/D 6 1.5 are given in Table 1. Contours of cross-stream velocity components hv⁄i in the second column of Fig 4 are formed in a ‘‘switching’’ of the orientation of the positive and negative values of hv⁄i downstream of the sphere. Negative pairs are more dominant owing to the lower velocity magnitudes (i.e. lower pressure) in the boundary layer for G/D = 0. The wake patterns are considerably asymmetrical. A large amplitude of cross-stream velocity hv⁄i might indicate that the developing shear layers which originally separate from the periphery of the sphere entrained a significant mass flow in the base region of the wake. In the third column of Fig 3, the time-averaged vorticity hx⁄i images designated with ‘‘P’’, ‘‘Q’’ and ‘‘R’’ reveal that the detailed instantaneous structure of the small-scale vortices, Kelvin Helmholtz vortices and downstream part of the large scale broken vorticity streets are lost due to the unsteady flow structure and alternating direction of the vortex shedding, which emanates from the sphere periphery in the range of 0 6 G/D 6 1.5. The positive and negative time-averaged vortices are formed in the upper and lower region of the gap designated as ‘‘Q’’ and ‘‘R’’, respectively which have a tendency to move upward direction because of the gap flow effect and the lower pressure prevailing within the wake. For the low gap ratios of G/ D = 0.1, 0.25 and 0.5, owing to the velocity profile of the bounded gap flow between the sphere and the plate surface negative vorticity, ‘‘Q’’, also forms. The concentrated time-averaged vortex clusters of P, Q and R expand along the shear layer in the downstream direction for G/D = 0.1, 0.25 and 0.5. A substantial reduction takes place in the level of the vorticity due to the expansion of core-flow region in streamwise direction. The mixing layer in the downstream region of the flow is dominated by the negative
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Table 1 Locations and magnitudes of flow features at critical points that are displayed in Figs. 4–6a and 6b for Re = 5000. Schematic figure under the table shows the positions of Dx and Dy. Gap ratio
hu⁄i (Dx/D, Dy/D)
hu0 v 0 =U 21 i (Dx/D, Dy/D)
hurms i (Dx/D, Dy/D)
hv rms i (Dx/D, Dy/D)
hWi (Dx/D, Dy/D)
TKE (Dx/D, Dy/D)
G/D = 0
0 (1.98, 0.49) 0.370 (1.05, 0.41) 0 (1.04, 0.32) 0 (1.66, 0.50) 0 (0.56, 0.59) 0.211 (0.58, 0.39) 0.215 (1.05, 0.51) 0.347 (0.80, 0.25)
0.021 (1.63, 0.42) 0.017 (2.06, 0.06) 0.036 (0.97, 0.60) 0.016 (0.86, 0.04)
0.205 (1.56, 0.44)
0.219 (1.82, 0.17)
0.252 (0.9, 0.59)
0.246 (0.97, 0.53) 0.158 (1.30, 0.34)
R1 (2.01, 0.5) F1 (2.22, 0.22) F1 (0.99, 0.20)
0.033 (1.61, 0.45) 0.034 (2.10, 0.07) 0.059 (0.98, 0.57)
0.025 (1.45, 0.48)
0.208 (0.45, 0.43)
0.183 (0.62, 0.07)
S1 (0.56, 0.59) S2 (1.69, 0.59)
0.032 (0.79, 0.13) 0.032 (0.46, 0.44)
0.049 (1.03, 0.52)
0.321 (1.05, 0.55)
0.281 (1.42, 0.30)
0.084 (1.00, 0.54)
0 (1.32, 0.27)
0.023 (1.54, 0)
0.220 (1.36, 0.52)
G/D = 0.5
0.333 (0.86, 0.25) 0 (1.34, 0.29)
0.045 (1.14, 0.54) 0.024 (1.14, 0.24)
0.302 (1.12, 0.60) 0.206 (1.17, 0.22)
0.267 (1.34, 0.26)
G/D = 1.0
0.397 (0.93, 0.26) 0 (1.46, 0.28)
0.053 (1.30, 0.53) 0.022 (1.34, 0.16)
0.309 (1.17, 0.56) 0.192 (1.17, 0.28)
0.300 (1.59, 0.32)
G/D = 1.5
0.415 (0.98, 0.18) 0 (1.52, 0.18)
0.056 (1.36, 0.45) 0.035 (1.66, 0.19)
0.342 (1.08, 0.56) 0.268 (1.26, 0.37)
0.337 (1.73, 0.32)
F1 F2 F3 S1 F1 F2 S1 F1 F2 S1 F1 F2 S1
G/D = 0.1
G/D = 0.25
time-averaged vorticity hx⁄i as seen in Fig 4. In the left column of Fig 4, the time-averaged vorticity fluctuations hxrms i clearly show the unsteady and wavy structure of the wake excitation of the sphere for all cases. Maximum values of the hxrms i take place along the shear layers due to occurrence of high velocity gradient in these sections of the flow. Distributions of time-averaged rms streamwise velocity fluctuations, hurms i, cross-stream velocity fluctuations hv rms i, Reynolds stress correlations hu0 v 0 =U 21 i and turbulent kinetic energy (TKE) around the sphere are given in Fig 5. The distribution of the streamwise velocity fluctuations, hurms i, reveals virtually identical flow structures on the circumference of the sphere. For G/D = 0, only streamwise velocity fluctuations of the upper shear layer are formed whereas two peak points of streamwise velocity fluctuations occur due to the flow separation from the upper and lower shear layers for G/D = 0.1. For G/D = 0.25, the peak magnitude of the streamwise velocity fluctuations hurms i, of the upper shear layer is 0.321, while that of the lower shear layer of the sphere is 0.220, respectively. At the gap ratio of G/D = 1.5, peak magnitudes of the streamwise velocity fluctuations hurms i, are slightly higher than the other positions. The rms streamwise velocity patterns, hurms i, have detectable double peaks at almost equal distances in the upper and lower wake regions of the centerline of the sphere. Their locations and magnitudes are given in Figs. 5 and 6a and 6b along with in Table 1 for validation and comparison purposes. In addition, the difference between the peak values of the hurms i for the upper and lower shedding shear layers of the sphere increases with increasing gap ratio. When the gap ratio G/D is greater than 0.5, the upper shear layer of the spheres become in a larger and longer size due to the exposing of uniform incoming flow condition. The distri-
(0.86, (0.71, (1.38, (1.25, (0.76, (0.67, (1.16, (0.98, (0.73, (1.35, (1.03, (0.83, (1.45,
0.48) 0.26) 0.68) 0.37) 0.45) 0.37) 0.36) 0.49) 0.27) 0.37) 0.46) 0.34) 0.28)
0.027 (1.35, 0.55) 0.072 (1.14, 0.55) 0.037 (1.11, 0.24) 0.081 (1.18, 0.55) 0.037 (1.41, 0.09) 0.088 (1.17,0.55) 0.058 (1.23, 0.39)
butions of the rms of streamwise and transverse velocity fluctuations, hurms i and hv rms i, presented in the first and second columns of Fig. 5 indicate that the peak values of the root mean square of velocity components occur along the shedding shear layers and wake center. The peak magnitude of streamwise velocity fluctuation hurms i is generally greater than that of transverse velocity, hv rms i. The, hv rms i distribution has a peak value at approximately merging point of the shear layer around the sphere for G/D = 1.5. The hv rms i increases rapidly until the peak point and decreases slightly to reach the free-stream flow condition for G/D = 1.5. In the first and second columns of Fig 5, cross comparison of the results reveals the existence of double peaks for hurms i placed in the shear layers while a single peak is observed in hv rms i with a maximum for G/D P 0.25. To reveal the relative effects of G/D ratio on the wake of the sphere and boundary layer interactions, Reynolds stress correlations hu0 v 0 =U 21 i are presented in the third column of Fig 5. In gradient approaching flow condition, Reynolds stress correlations of flow past a sphere are formed asymmetric about the centerline of the sphere wake with negative and positive peak values. This asymmetric distribution of Reynolds stress correlations hu0 v 0 =U 21 i is formed with the effect of boundary layer flow in close proximity of the wall. For G/D = 0, only negative Reynolds stress occurs on the upper shear layer. As the gap ratio is increased to G/D = 0.1, besides the large-scale cluster of the hu0 v 0 =U 21 i having a negative value, there are two additional clusters with positive and negative values located downstream of the sphere base for Re = 5000. This situation occurs as a result of different behaviors of the jet-like flow through the gap. At G/D = 0.1, one of the peak value of Reynolds stress correlations occurs on a location where the jet like flow
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starts to accelerate to maximum streamwise velocity magnitude while the other peak value occurs on a location where the jet-like flow spreads up through the rear surface of the sphere as displayed in Fig 5. Reynolds stress correlations hu0 v 0 =U 21 i point out that there are no small-scale concentrations in the wake region of the sphere due to the very small magnitudes of the oscillations in that region as a result of separation around the periphery of the sphere. On the other hand, distributions of the hu0 v 0 =U 21 i which resemble the same behaviors of the flow stated above for other flow structures do not form symmetrical shape. A cluster and a maximum value of hu0 v 0 =U 21 i occur on the upper section of the sphere and along the shedding shear layer. On the other hand, the Reynolds stress values decrease substantially near the plate surface for G/D = 0.1, 0.25 and 0.5. The magnitude of Reynolds stress correlation hu0 v 0 =U 21 i keeps its strength due to the high rate of entrainment between wake and core flow regions, and then it decays down while the vortical flow travels in the downstream direction. This feature is consistent for all values of the sphere locations. As can be seen in the left column of Fig 5, TKE increases in downstream direction starting from the base of the sphere and reaches its peak value as indicated on each image, and then starts to decrease gradually in the downstream direction. Vortical flow in the wake interacts with the wall so that enhancement of TKE intensities in streamwise direction occurs. Moreover, the distributions of hv rms i show the single peak patterns whereas the TKE and hu0 v 0 =U 21 i contours point out double-peak patterns. For G/D = 0.1 and 0.25, the flow through the gap between the sphere and the plane affects the wake flow so that the TKE has two more peak values near to the wall. However, for larger gap ratios of G/D = 1.0 and 1.50, the effect of gap flow loses completely but the effect of the non-uniform velocity profile of the boundary layer still modifies the TKE of the sphere wake. The magnitudes of the maximum value of Reynolds stress correlations hu0 v 0 =U 21 i and TKE decrease from their peak values to a moderate level at a location further downstream. The peak values and their locations of the TKE for all of the cases are given in Table 1. The deviation in contour distributions of TKE around the sphere with respect to the gap ratio is much larger on the upper section of the sphere than that on the lower section due to the difference of the velocity magnitude. The rate of entrainment due to the high rate of circulatory flow motion of vortical flow structure is extremely high which results in enriching TKE values of the wake flow structures. Velocity distributions around the sphere show alternating high-speed and low speed regions in the boundary layer which results in counter-rotating streamwise vortex pairs. This phenomenon might be responsible for most of the turbulence kinetic energy dispersion and a contributor to the transport of Reynolds stress in Fig 5. Variations of the time averaged streamline patterns hWi for the different positions around the sphere located over a flat plate for the Reynolds number in the range of 2500 6 Re 6 10,000 are displayed in Figs. 6a and 6b. The time-averaged streamline topology for all arrangements in Figs. 6a and 6b is displayed and interpreted in terms of foci, F, and saddle points, S. The junction point of the streamlines separated from the rear surface of the sphere that is called as saddle point and denoted with ‘‘S’’ which shows the merging point of the shear layers emanating from the periphery of the sphere. The reattachment point of the streamlines separated from the upper section of the sphere to flat plate wall is denoted with ‘‘R’’. Locations of foci designated with ‘‘F1, F2 and F3’’ that are rolling in the clockwise and/or in counter clockwise with respect to the central axis of the sphere exhibit well-defined critical points and they indicate the evidence of three-dimensional flow. For the case of the sphere touching the flat plate at G/D = 0, a large circulation region designated as F1 which is entrapped by shear layer separated from the upper section of the sphere forms and covers whole the wake flow region. The separated flow from the
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upper section of the sphere reattaches on the flat plate surface after approximately 2D away from the sphere center downstream direction for 2500 6 Re 6 10,000. A stable focus F1 that is the streamlines spiral inward the center point of the focus is developed close to downstream of the sphere, which agrees well with the results of Tsutsui [1]; Seban and Caldwell [17]. As the jet flow begins to occur, the shedding shear layer from the upper section of the sphere does not reattach and the only focus F1 happens for Re = 2500, 5000 and 7500. Cross-comparison of streamline topology demonstrates the occurrence of focus F1 with a higher and bigger size bubble at G/D = 0 than the other gap ratios for 2500 6 Re 6 10,000. As the gap ratio increases to a value of G/D = 0.1, the modifications of flow patterns realize depending on the Reynolds number. The wake region with foci F1 and F2 are identifiable, and then the two saddle points S1 and S2 are formed just near the plate surface due to the gap flow and reverse flow effects. For Reynolds numbers 2500, 5000, and 7500 cases, a large scale separation bubble that is unstable recirculation having outward rotation is formed. For the case of G/D = 0.1 at Re = 2500, besides the large-scale separation bubble, there is one additional small scale stable recirculation focus, F2. When the Reynolds number is increased to 5000 and 7500, the small-scale recirculation focus, F2, disappears and a new large scale separation bubble, F1, is enhanced until Re = 7500. Moreover, the fluid flow through the small gap turns sharply through the intermediate region between the close region of the rear surface of the sphere and the large separation bubble, and thus the jet flow interacts with the flow separated from the upper section of the sphere for Re = 2500, 5000, and 7500. This interaction affects the vortex shedding characteristics and creates a good mixing of fluid layers causing enhancement in the wake, which is helpful for convective phenomena. That is, the flow pass the sphere could not be shed from the periphery of the sphere due to powerful jet-like flow between the sphere and the flat surface. For the biggest Reynolds number, Re = 10,000, the large scale separation bubble completely disappears and two recirculating regions which are embedded by the shear layers separated from the circumference of the sphere in the measurement plane occur. For G/D = 0.25, as clearly seen in Fig. 6a, two recirculation regions with foci designated with F1 and F2 take place in the wake region of the sphere. But there is a tendency of the wake to move upward and the two recirculation regions become asymmetric about the sphere centerline. The lower recirculation region is wider in length and shorter in weight than the upper one due to the gap flow as a conclusion of the non-uniform velocity profile in the boundary layer. As well known, separation on the surface of the plate occurs due to the streamwise adverse pressure gradient. This is the reason of occurring another small separation bubble on the plate surface in the wake of the sphere for G/D = 0.25. In other words, due to the strong coupling between the boundary layer and the lower shedding shear layer of the sphere, the boundary layer deflects away from the wall forming a small downstream separation bubble, F3, at Re = 2500 and Re = 5000 as shown at the bottom row of Fig. 6a. Thus, a small-sized focus takes place in close region of the sphere wake on the plate surface due to the occurrence of concentrated secondary vortices on the wall and lower pressure in the wake. The focus size, F3, decreases in length with increasing the Reynolds number to a higher value and disappears for Re = 7500 and 10,000. Increasing the gap ratio to a value of G/ D = 0.25, two recirculation regions occur in the wake region of the sphere for all Reynolds numbers as clearly seen in Fig. 6a. But there is a tendency to move upward of the wake of the sphere and the two recirculation regions are asymmetric about the sphere centerline. The upper recirculation region is slightly longer than the lower one in length whereas lower recirculation region is larger than the upper one in circulation shape and size.
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For the higher gap ratios G/D P 0.25, the two foci F1 and F2 in the recirculation wake region happen and they are asymmetric about the centerline of the sphere. For larger gap ratios of G/ D = 0.5, 1.0 and 1.5, the effect of gap flow becomes weaker dramatically but the effect of the non-uniform velocity profile of the boundary layer still modifies the flow structure of the sphere for Reynolds numbers in the range of 2500 6 Re 6 10,000. It is observed that asymmetry of streamline topology hWi decreases in the wake region for G/D = 1.5 at Re = 10,000 as seen in Fig. 6b. Patterns of sectional streamlines hWi clearly identify that as the Reynolds number increases, the saddle point, S1 moves slightly towards the rear surface of the sphere as seen in the left column of Fig. 6b. A separation bubble decreasing in size with increasing the Reynolds number has also been identified using oil film visualization and dye visualization [3,8,26]. At G/D = 1.5, the recirculation lengths of the shear layers become almost equal to each other similar to a sphere wake in uniform incoming condition. Distributions of time-averaged streamwise velocity component hu⁄i and streamwise velocity fluctuations hurms i along the vertical lines designated as ‘‘K, L, M, N and O’’ in the left column images of Figs. 4 and 5 downstream of the sphere at gap ratios of G/ D = 0, 0.1 and 0.25, top row for Re = 5000 and bottom row for Re = 10,000 are given in Fig. 7a–7c. Here, solid line represents the boundary layer velocity profile over a flat plate in the absence of the sphere as shown in Fig 2. The streamwise velocity component, hu⁄i, at different locations, L/D, on the vertical center of the sphere and in wake region is shown in Fig. 7a. The negative horizontal
Fig. 7c. Variation of Reynolds stress correlations hu0 v 0 =U 21 i along the vertical line displayed in the third column of Fig. 5 at 0.83D away from the rear surface of the sphere for 0 6 G/D 6 1.5 at Re = 5000.
velocity components in the separation regions downstream of the sphere are clearly seen from the velocity distributions. The negative velocity component decreases with increasing Reynolds numbers. Velocity profile of the boundary layer enhances the turbulence of the wake because of the gap flow and high level of vortex shedding. For G/D = 0, distributions of the hu⁄i from station ‘‘L’’
Fig. 7a. Distributions of time averaged streamwise velocity component hu⁄i along the vertical lines designated ‘‘K, L, M, N and O’’ in the left column images of Fig. 4 downstream of the sphere at gap ratio values of G/D = 0, 0.1 and 0.25, top row for Re = 5000 and bottom row for Re = 10,000. Continuous line represents the boundary layer velocity profile over a flat plate in the absence of the sphere as shown in Fig. 2.
Fig. 7b. Distributions of time-averaged streamwise velocity fluctuations hurms i along the vertical lines designated ‘‘K, L, M, N and O’’ in the left column images of Fig. 5 downstream of the sphere at gap ratio values of G/D = 0, 0.1 and 0.25, top row for Re = 5000 and bottom row for Re = 10,000.
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to ‘‘N’’ involve the negative reversed flow while the station ‘‘O’’ located approximately on the reattachment point comprises of positive magnitudes for Re = 5000 and 10,000. Variations of the negative velocities are smaller for Re = 10,000 than Re = 5000. The velocity distribution for G/D = 0.1 at station ‘‘M’’ is negative till y/D ffi 0.5 for Re = 5000 whereas it becomes positive due to the different behavior of the gap flow for Re = 10,000. The peak values of the jet flow for G/D = 0.25 at stations ‘‘K, L and M’’ reach to higher and they become smaller at stations ‘‘N and O’’ than the velocity profile of the boundary layer without the sphere for both Reynolds numbers. A global view on the asymmetry in the intensity of the timeaveraged streamwise velocity fluctuations, hurms i, show a thinning of the lower shear layer and a thickening of the upper shear layer due to the influence of boundary layer flow over the flat plate as seen from cross-comparison of Re = 5000 and Re = 10,000 in Fig. 7b. For G/D = 0, streamwise velocity fluctuations of the upper shear layer are formed a higher magnitude for both Reynolds numbers. For G/D = 0.10, the jet-like flow through the gap between the sphere and flat plate becomes effective on the streamwise velocity fluctuation patterns of the sphere wake. As clearly seen in Fig 7b, the jet-like flow has different behaviors resulting in different influences on the sphere wake depending on the Reynolds number. For G/D = 0.25, three peak points of streamwise velocity fluctuations occur at stations ‘‘L, M and O’’ for both Reynolds numbers. Two of them occur along the upper and lower shear layers of the sphere wake region and the third one occurs as a result of boundary layer separation from the flat plate wall due to the acceleration of the jet-like flow through the gap. However, the strength of the streamwise velocity fluctuations of the upper and lower shear layers is still different owing to interaction of shedding shear layers and boundary layer flow, but the difference is lower for Re = 10,000 case than Re = 5000. Fig. 7c displays variation of Reynolds stress correlations hu0 v 0 =U 21 i along the vertical line displayed in the third column of Fig 5 at 0.83D away from the rear surface of the sphere base for 0 6 G/D 6 1.5 at Re = 5000. The gap between the bottom point of the sphere and the plate surface varied from 0 to 63.75 mm. For G/D = 0, only negative Reynolds stress hu0 v 0 =U 21 i occur on the upper shear layer for the sphere. At G/D = 0.1 and 0.25, the distributions of hu0 v 0 =U 21 i become asymmetric about the sphere centerline with negative Reynolds stress in the upper shear layer and low levels of positive Reynolds stress in the lower shear layer. As the gap ratio increases further, variation of Reynolds stress correlations hu0 v 0 =U 21 i becomes larger due to the reducing effect of the boundary layer flow. There are more than one peak variation owing to the sphere placed totally in the boundary layer flow for gap ratio values of G/D = 0, 0.1 and 0.25. 4. Conclusions In this experimental study, the effect of plane boundary layer flow on the wake flow characteristics of the sphere has been investigated in open water channel for 2500 6 Re 6 10,000. The following results are obtained; The results of the flow visualization conducted demonstrate clearly a significant change of the wake structure at different gap ratios for the sphere. The flow patterns show that the effects of the flow interference caused by the boundary layer are severe when the gap ratios are small. The rate of entrainment due to the high rate of circulatory flow motion of vortical flow structure is extremely high which results in causing unstable wake flow structures. The non-uniform velocity profile of the boundary layer flow causes a difference in the strength of the separated shear layers from the periphery of the sphere forming asymmetry in the wake
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region. It was found that instantaneous flow patterns may change their direction from positive to negative close to the plate surface which can result in variation of the drag and lift forces of the sphere. Viewing all of the instantaneous vorticity clusters, it is observed that magnitudes of the instantaneous vortices, x⁄, decay downstream direction in the wake region. Experimental results have shown that the interaction between the sphere wake and turbulent boundary layer depending on the gap ratio significantly changes the flow structure. For the smallest gap ratio G/D = 0.1, the jet-like flow through the small gap turns the wake sharply into the intermediate region between the rear of the sphere and the large separation bubble, and then it interacts with the fluid separated from the upper side of the sphere. This interaction affects the vortex shedding characteristics and creates a good flow mixing resulting in enhancement of heat transfer phenomena. For G/D = 0.1, the direction of the wake region of the sphere is deflected to upward from the flat plate while surrounding to the rear surface of the sphere. It is demonstrated that the gap flow occurring between the sphere bottom section and the flat plate surface has very high scouring effect until G/D = 0.50 and then a distinguishable asymmetrical flow structure of the wake region keeps up to G/D = 1.0. It is observed from the streamline topology that when the Reynolds number increases to Re = 5000, the size of the downstream separation bubble rapidly decreases and disappears at Re = 7500. It is confirmed that the presence of the gap flow causes a jet flow and tends to suppress the reattachment in the boundary layer. Occurrence of foci in the wake represents the three-dimensionality of the flow structure. Clusters of vortices occur on the near plate surface where a larger velocity gradient exists. The rate of entrainment through the gap, due to the high rate of the circulatory motion of vortical flow structures, is extremely high, which causes the wake-flow structures to fluctuate further. It is seen that the gap ratios between the sphere and the boundary layer vary in the range of 0 6 G/D 6 1.5 influencing the instability of the vortical flow structure, significantly. For the gap ratios until G/D = 0.5, the separated flow from the bottom section of the sphere is strongly affected by the gap flow and the flow separation around the bottom section of the sphere is delayed. It is demonstrated that the wall affects the sphere wake at small gap spacing, constrains the flow passing through the gap, and restricts the vortex shedding from the sphere, especially in the lower section of the sphere. Regular vortex shedding occurs in the near wake when the gap ratio is greater than G/D = 1.0. Viewing of all images together shows that concentrated vortices gradually enlarge and weaken while the flow proceeds further downstream in the wake depending on the sphere location over the plate. Distributions of vortices and corresponding streamlines also indicate that mixing of the wake and core flow regions are expanded along the shear layers throughout the flow field due to the circulatory flow motion in the measuring plane. The present flow field and point-wise results given in Table 1 and Figs. 3 and 7a–7c can be useful for development, assessment and validation of numerical studies.
Acknowledgments The authors would like to acknowledge the funding of The Scientific and Technological Research Council of Turkey (TUBITAK) under Contract No. 109R028, Scientific Research Projects Office of Cukurova University Contract No. AAP20025, Selcuk University’s Scientific Research Project Office and DPT Project Contract No. 2009K12180.
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