passive control of vortical flow structure around a sphere...

6th

International Advanced Technologies Symposium (IATS’11), 16-18 May 2011, Elazığ, Turkey

287

Abstract—Passive control of vortical flow structuret around a

sphere by an o-ring for Re=5,000 was experimentally

investigated. Visualization with Rhodamine dye and particle

image velocimetry technique were performed in order to examine

the flow characteristics such as instantaneous velocity fields,

vorticity contours and time-averaged flow patterns of rms

velocities in x and y directions, velocity fields and Reynolds stress

correlations. O-rings with 2mm and 3mm diameters were located

at the front side of the sphere having 42.5 mm diameter at angles

of 45o, 50o, 55o and 70o to see its suppression effect in terms of dye

experiment. It was found from dye visualization that the

controlled flow structure results of the sphere with 2mm o-ring at

55o was the most effective and here PIV experiments were only

done for the 2mm o-ring. It was obtained from the comparison of

the smooth sphere and sphere with o-ring that the maximum

locations of Reynolds stress correlations, the rms velocities in x

and y directions occurred closer to the sphere base for the sphere

with o-ring case although their magnitudes did not change

considerably. These findings may be interpreted that the drag

coefficient of the sphere with o-ring can be lower than that of the

smooth sphere owing to the suppression effect of the o-ring in the

wake region. Furthermore, the obtained results can be helpful for

developing and validating of numerical predictions as well as

designing purposes.

Keywords—Flow control, Instability, o-ring, PIV, Sphere,

Vorticity, Turbulence, Wake flow

I. INTRODUCTION

phere has many engineering applications in single and two

phase flows such as air pollution, nuclear and thermal

power plants, pneumatic and hydraulic conveying, chemical

and food processing, combustion systems, sport balls and

bomb. Therefore, there are numerous of experimental,

theoretical and numerical studies in the literature concerning

with basic features of the flow structure around a sphere 1-

26. However, fewer studies were found about flow control

around sphere given in the references and cited therein such as

dimpled sphere13-15, roughened sphere 16-18, vented

sphere19, 20, sphere with o-ring and other control

methods21-26. Some of the other related studies on flow

control concerning with the present study can be found in the

literature27-34. However, these investigations concentrated

on the flow characteristics such as for vortex shedding

frequency, pressure coefficient and drag coefficients. It is not

encountered any study in the literature that investigates flow

structure characteristics and their controls with o-ring using

Particle Image Velocimetry (PIV) technique and dye

visualization.

II. EXPERIMENTAL 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

experimental system of the sphere is shown in Fig. 1. Free

stream turbulence intensity of the flow is less than 0.5% in the

range of the present Reynolds numbers, vDURe ,

based on the sphere diameter (D). Here, and D are

kinematics viscosity and diameter of the sphere (D),

respectively. U∞ is free-stream velocity taken as 117.6 mm/s

for Re=5,000. The sphere with a diameter of 42.5 mm was

made of plexiglas so that the laser light propagates easily from

them. In addition, water cell segment of the sphere equator

with a diameter of 38.5mm and a wall thickness of 2.0 mm was

created. To support the sphere in the water channel, a circular

bar with a 5 mm diameter was connected to the sphere from

the top. Disturbance effect of the support bar on the laser sheet

location of the measurement plane that was observed by dye

injection was 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 %.

Sphere models are presented in Figure 2b. The sphere with o-

ring made of solid plexiglas and did not permit to pass the

laser light. The o-rings with 2mm and 3mm diameters were

made of rubber located at the front side of the sphere having

42.5 mm diameter at angles of 45o, 50

o, 55

o and 70

o.

Passive Control of Vortical Flow Structure

around a Sphere by an O-ring

M. Ozgoren1, A. Okbaz

2, S. Dogan

3, A. Kahraman

4, R. Hassanzadeh

5, B. Sahin

6, H. Akıllı

7

1,2,3,4Selcuk

University, Konya, Turkey, [email protected], [email protected],

[email protected], [email protected], 5,6,7

Cukurova University, Adana, Turkey,

[email protected], [email protected], [email protected]

S

mailto:[email protected]



M.Ozgoren, A.Okbaz, , S.Dogan , A.Kahraman, R.Hassanzadeh, B.Sahin, H.Akıllı

288

(a)

(b)

Figure 1: Schematic view of the experimental set up and sphere

models

Nd:YAG laser was used to generate a laser sheet that was

perpendicular to the axis for the sphere and the symmetry axis

(i.e. equator of the sphere) was passed through them. A CCD

camera having a resolution of 1,600 x 1,186 pixels was used to

record the images. The seeding particles with a diameter of 10

µm in the flow were silver metallic coated hollow plastic

spheres. The densities of the particles and water are close

enough so that the distribution of particles in suspension

remains uniform for several hours. The illuminating laser

sheet thickness in the flow field was approximately 1.5 mm.

As shown in Fig. 1, the camera was mounted in a fixed

position beneath the water tank. 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 32x32 pixels in the image was

selected and converted to grid size approximately 1.44x1.44

mm2 for the single sphere (0.034Dx0.034D). The overall fields

of physical view were for both spheres, yielding to 7,227

(99x73) 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 350 images for a sequential

series were taken at the rate of 15 Hz, thereby spanning 23.27

sec. Averaged patterns of the flow structure were calculated

using the set of the instantaneous 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

of t =1.0-1.7 ms for the present experiments. Inappropriate

displacement vectors caused by shadows, reflections, or laser

sheet distortions in the flow field replaced by using bilinear

interpolation between surrounding vectors in the post-

processing step. This algorithm included magnification factor

and image captured rate in order to calculate velocities from

the valid vectors. The field was then smoothed by a Gaussian

weighted averaging technique. To minimize distortion of the

velocity field, a smoothing parameter of 1.3 was chosen. After

having vector field, the vorticity patterns of the wake flow

were determined from the velocity field using a finite

difference scheme with an in-house software.

III. RESULTS AND DISCUSSION

Figures 2a-c show typical dye visualization images of

instantaneous flow fields around a smooth sphere and a sphere

with 2 mm and 3mm o-ring for 5,000 in which dye ports with

0.7mm diameter are located on equator of the sphere at angle

values with respect to the flow direction as 0o, 70

o,90

o, 110

o,

180o, 290

o, 270

o and 250

o. All dimensions in figures are

normalized with the sphere diameter designated as x/D and

y/D. Dye visualization representative images are presented to

show evolution and progress of the small scale vortices

designated by A, B, C, D, E, F and G. The separated and

recirculating flows in the near-wake region of the sphere with

the help of visualization technique are clearly seen for the

sphere with laser illumination using the Rhodamine dye

injection technique. Small scale vortices around the wake

region are formed around larger vortices with a wavy

appearance due to Kelvin Helmholtz instability. Formation of

the spiral vortices begins to occur in the very close region of

the sphere. As the flow travels in the downstream direction, the

domain of the vortices increase around the bluff body. Then

these vortices are shed from the periphery of the sphere

directly to the inward wake region. The large eddies are

formed at a regular frequency and they produce pressure

disturbances in the flow. The flow patterns in Figs. 2a and 2b

show that the laminar boundary layer separates at around

=85o±5

o for Re=5000, where is measured from the front

stagnation point. Shedding shear layer becomes unstable due

to the Kelvin-Helmholtz instability caused by the large

velocity difference at the interface between the free-stream

flow and sphere wake flow regions. Thereafter, the laminar

shear layer turns into a powerful turbulent flow structure.

Several vortex-ring shaped protrusions appear as an indication

of the shear-layer instability along the borders between the

wake and free stream regions, as also observed by Jang and

Lee 4.

It is seen that the near wake circulating region is large and

the wake generates a progressive wave motion. Weaker and

Passive Control of Vortical Flow Structure around a Sphere by an O-ring

289

small-scale vortices occur around the primary vortices. In the

case of the sphere with o-ring, the energy level of the flow

increases due to the instability causing by o-ring and then free

shear layer emanating from the separated flow region around

the sphere has a less tendency to travel in the near wake region

of the sphere than the smooth sphere case. On occasion, the

shedding vortices have taken place at both side of the central

axis of sphere symmetrically and simultaneously. These small

size vortices rotate about their axis and move on in a wavy

form in the wake region for both sphere cases as seen in all

images in Fig 2. Shear layers emanating from the both side of

the sphere merge at a location approximately two sphere

diameter (2D) length from the central point of the sphere and

instability rises after this point as seen in Fig 2a. In the

comparison of both cases, it is observed that the sphere with o-

ring induces earlier occurrence of the high level turbulence

flow structure in the wake region and hence the organized

wavy structure of the Kelvin-Helmholtz vortices is deformed.

This deformation also effects and changes the periodic

occurrence of the Karman vortex streets. Flow around the

sphere is laminar for Re=5,000 while flow in the water channel

is turbulent. As well known that separation point in the laminar

flow occur on the sphere surface at a smaller angle than the

turbulent flow. Drag coefficient for smooth sphere in the

laminar flow is greater than the turbulent flow and drag

coefficient dramatically decreases around Cd=0.07 for

Re2x105 since the increased inertia forces of the flowing

fluid stick the flow around the sphere to retard the separation

phenomena 4. At the lower Reynolds number such as

Re=5,000, in the present study, o-rings are used to simulate

turbulence on the sphere surface. Different o-ring diameters

and location angles are tried as seen in Fig 2. Sphere with

3mm o-ring creates a higher level fluctuations and hence

causing more energized flow structure. Therefore, the wake

region in the downstream of the sphere becomes wider, which

might be the source of the increased drag. After having

observed this flow structures, investigations concentrated on

only the sphere with 2mm and different angles. The vortices

generated by the shear-layer instability travel in the

downstream direction and eventually compose a large-scale

waviness of vortical structures in the wake. These instabilities

and chaotic structure in the flow retain further downstream in

the free stream flow direction having an “S” form like von

Karman vortex streets approximately after a distance of 2.5D

from the central point of the smooth sphere. Even though

small-scale Kelvin Helmholtz’s vortices are clearly shown for

dye visualization results. However, numerous eddies occur due

to the three dimensional and complex flow structure for both

sphere cases with and without 2mm o-ring. The vortices

produced from the flow separation around the periphery of the

sphere have a tendency to move inwards because of the lower

pressures prevailing within the wake.

(a)

(b)

(c)

Figure 2: Comparison of flow visualization of flow structure with

laser illumination of Rhodamine dye injection technique around (a)

the smooth sphere (b) sphere with 2mm o-ring at angles of 45o, 50o,

55o and 70o c) sphere with 3mm o-ring at angles of 45o, 50o, 55o and

70o .


290

Figure 3: Comparison of instantaneous velocity fields V and vorticity

contours * around the smooth sphere (top row) and sphere with

2mm o-ring (bottom rows) for 5,000.

This situation is counter-balanced by the growing wake size,

which shifted the vortex centerline outwards. Regarding the

onset and development of small-scale vortical structures in the

separating shear layer, regions of low-level vorticity

concentration are discernible in the pattern of instantaneous

vorticity for all patterns. The wake region accommodates

velocity vectors with very small magnitude in the downstream

region of the sphere with and without o-ring cases, which is the

source of small-scale secondary vortices, as seen in Fig. 3. The

streamwise distance of successive vorticity peaks in the near

wake region for the sphere with o-ring is larger than that for

the sphere without o-ring case. The flow is three-dimensional,

and shedding vortices convey fresh fluid into the wake flow

region, magnifying the entrainment thus developing many

eddies.

Table 1: Variation of occurrence points of the maximum values for

(a) Reynolds stress correlations (

2Uv'u' , (b) rms velocities

urms/U and (c) vrms/U.

(a)

Sphere L/D

2Uv'u'

Smooth sphere

0.63

0.66

0.031

0.039

Sphere with 2mm o-ring at 45o

0.52

0.45

0.028

0.049


0.45

0.62

0.037

0.049


0.36

0.51

0.029

0.048


0.67

1.12

0.044

0.068

(b)

Sphere L/D <urms> Smooth sphere

0.63

0.54

0.259

0.291


0.52

0.45

0.256

0.307


0.40

0.44

0.266

0.294


0.26

0.58

0.232

0.285


0.46

0.50

0.369

0.356

(c)

Sphere L/D <vrms> Smooth sphere 1.25 0.293

Sphere with 2mm o-ring at 45o 0.73 0.293




Comparison of rms velocities urms/U and vrms/U

around the smooth sphere (top row) and sphere with 2mm o-

ring (bottom rows) for 5,000 is displayed in Fig. 4. The rms

streamwise velocity patterns urms/U have detectable double

peaks at almost equal distances in the upper and lower wake

regions of the centerline for the smooth sphere and sphere with

2 mm o-ring while a single peak is seen in vrms/U with the

maximum occurrence around the symmetry axis for all

spheres. Their locations and magnitudes are given in Table 1

for validation and comparison purposes. The maximum points

of urms/U and vrms/U becomes closer to the sphere

base for the cases of o-ring locations between 45o and 70

o.

The shortest distance between sphere base and the maximum

point of urms/U and vrms/U occurs for the sphere with

2mm o-ring at 55o. It can be explained that more momentum

transfer occurs through the wake region due to the retarded

flow separation and increasing wake pressure. Therefore, it

can be sated that the drag coefficient for the sphere with o-ring

can specially decrease for the sphere with 2mm o-ring at 55o.

Transverse velocity fluctuation vrms/U along the symmetry

axis has a strong effect on the vortex shedding. They increase

until those points given in Table 1 and then they decrease on

both side of the symmetry axis.

Passive Control of Vortical Flow Structure around a Sphere by an O-ring

291

Figure 4: Comparison of rms velocities urms/U and vrms/U

around the smooth sphere (top row) and sphere with 2mm o-ring

(bottom rows) for 5,000.

Comparison of time-averaged velocity <V> (right column)

and Reynolds stress contour correlations

2Uv'u' (left

column) around the smooth sphere and sphere with 2mm o-

ring for 5,000 is displayed in Figure 5. Well-defined Reynolds

stress patterns due to fluctuations along the shear layers

produce the maximum Reynolds stress region very close to the

base of the sphere with 2mm o-ring at 55o

angle. This behavior

of the flow provides the momentum transfer from the free-

stream flow into the wake region due to pressure difference

between the wake and free-stream flow. For the sphere with o-

ring case, peak values of Reynolds stress correlations are not

varied considerably due to less effect of the instability caused

by the o-ring in the subcritical Reynolds number range. It is

shown from dye visualization and PIV experiments that the

disturbance caused by the o-ring located at the front surface of

the sphere with angles 45o, 50o and 55o trigger the boundary layer

and delay the first separation. It grows further along the separated

shear layer and provides high momentum transfer toward the wake

region resulting in the reattachment of the flow and delay the main

separation as also recorded by Jeon et al. [15].

Figure 5: Comparison of time-averaged velocity <V> (right column)

and Reynolds stress contour correlations

2Uv'u' (left column)

around the smooth sphere (top row) and sphere with 2mm o-ring

(bottom rows) for 5,000.

For Re=5000, turbulence characteristics such as

2Uv'u' ,

urms/U and vrms/U reach apeak value given in Table 1

due to strong effects of vortex shedding and then decreases as

vortex pattern decays. Subsequently, the development of the

wake turbulence causes the turbulence properties to increase

again and finally become nearly constant in the far wake

region as stated by Wu and Faeth [23]. Variations of

2Uv'u' , urms/U and vrms/U along the center line of

sphere in wake region, initially exhibit a more rapid increase to

have maximum numerical value in fluctuation of flow for the

sphere with o-ring and later values of

2Uv'u' , urms/U


292

and vrms/U gradually decrease in the flow direction further

downstream.

IV. CONCLUSIONS

The flow structure in the downstream region of a smooth

sphere and sphere with different diameters and locations of the

o-ring for Re=5,000 was investigated using PIV and dye

techniques in a circulating open water channel. It is seen that

the unsteady flow around the sphere is mainly caused by the

wave motion of the wake with alternating fluctuations, which

is associated with the small scale instability of the separating

shear layer. The obtained results demonstrate that the flow

structure in the wake region of the sphere with 2mm o-ring at

55° is significantly modified by passive control application

and hence the distance between the sphere base and the

location of peak values decreases as shown by the

instantaneous and time-averaged flow patterns. Therefore, it

can be stated that the sphere with 2mm o-ring at 55° triggers

the flow from laminar to turbulence in the boundary layer of

sphere at the low Reynolds number such as Re=5,000 which

retards the flow separation on the sphere surface and may

decreases the drag force. The reattachment of the flow on the

sphere surface was associated with the instability of the

separated shear layer, which the strong incoming disturbances

triggering the shear-layer instability came from the boundary

instability as also expressed by Jeon et al. [15]. The reverse

flow region in the wake for the sphere with 2mm o-ring at 55°

is significantly reduced and the motion in that region also

become weak owing to the free stream momentum force. It

should be frankly stated that alignments of the sphere, o-ring

and connection rod induce slightly the occurrence of

asymmetric flow structure.

ACKNOWLEDGMENT

The authors would like to acknowledge the funding of the

Scientific and Technological Research Council of Turkey

(TÜBİTAK) under contract no:109R028, SU BAP Project

No.2004/131 and CU BAP contract No: AAP20025 .

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