Passive control of flow structures around a circular cylinder by using screen

Journal of Fluids and Structures 33 (2012) 229–242

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Passive control of flow structures around a circular cylinder by using screen Vedat Oruc- n Department of Mechanical Engineering, Dicle University, 21280 Diyarbakır, Turkey

a r t i c l e i n f o

abstract

Article history: Received 16 June 2011 Accepted 18 May 2012 Available online 20 June 2012

The results of PIV measurements are presented in this paper for the water flow downstream of a circular cylinder surrounded with a screen (meshed outer control element) which had a streamlined shape. The diameter of cylinder, D was 50 mm and the Reynolds number based on the cylinder diameter was 5200. The characteristic length of the control element, L was tested for different cases so that the values of L/D were 2, 2.4, 2.8 and 3.2 in the experiments. It was noted that a forced reattachment of the shear layers separated from the cylinder was achieved by setting up the screen around the cylinder. As a consequence, the formation of vortical flow pattern was suppressed and turbulence statistics of the flow such as the intensity of turbulence, Reynolds shear stress, and turbulent kinetic energy were drastically diminished in comparison to the bare cylinder case. It was also found that the variable parameter of L/D did not dominantly influence the characteristics of the distribution of turbulence statistics along streamwise and transverse directions, however, the turbulence level decreased slightly for a smaller case of L/D. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Flow over cylinder Ka´rma´n vortex street Passive control of flow PIV technique Suppression of vortex shedding Turbulence statistics

1. Introduction Flow over a bluff body leads to separation of boundary layer and vigorous flow oscillations in the wake region downstream of the body. Some illustrative examples can be considered as the flow past an automobile, a submarine, an airplane, a bridge support, a chimney, a tower, a cable or an offshore structure, etc. A circular cylinder is the most common and good representative of a 2-D bluff body because of its geometrical simplicity. Williamson (1996) presented an excellent review on the vortex dynamics in the cylinder wake. The flow becomes unstable as the shear layer vortices which are shed alternatively from both the top and bottom surfaces of a cylinder interact with one another and constitutes a ´rma ´n vortex street which generates an oscillating regular vortex pattern. Such a vortical pattern in the wake is known as Ka flow with a specific frequency depending on the flow Reynolds number, Re. The investigators have been continuously investigating vortex shedding and near-wake flow structure since Roshko (1955) first measured Ka´rma´n vortex shedding period downstream of a bluff body. The vortical flow structure around the body has been widely determined by using particle image velocimetry (PIV) technique. The undesired strong structural vibrations, substantial increase in the average lift and drag fluctuations, enhanced mixing, acoustic noise, excess energy losses as well as other flow induced problems develop frequently (particularly when frequency of the vortices corresponds to one of the structure’s resonant frequencies) as a result of the periodic vortex shedding over a wide range of Re. It is obvious that the vigorous suppression of vortex shedding is highly significant in n

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0889-9746/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfluidstructs.2012.05.002

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Nomenclature

u0

D hw L Re t TKE U w x y

v0

diameter of the cylinder height of water length of control element Reynolds number time normalized turbulent kinetic energy average free stream velocity width of the control element streamwise distance transverse distance

u02 =U 2 v02 =U 2 u0 v0 =U 2 u0rms =U v0rms

o

fluctuating velocity component in streamwise direction fluctuating velocity component in transverse direction time-averaged streamwise Reynolds normal stress time-averaged transverse Reynolds normal stress time-averaged Reynolds shear stress intensity of turbulence in streamwise direction intensity of turbulence in transverse direction time-averaged vorticity

various engineering applications; thereby many experimental investigations were carried out to control vortex shedding when fluid flows over a bluff body (Gad-el-Hak and Bushnell, 1991). The methods for the suppression of vortex shedding downstream of a circular cylinder or a 2-D bluff body can be classified into two main groups as passive and active control techniques. Some typical examples for the former are splitter plates (Cruz et al., 2005; Farhadi et al., 2010; Gu et al., 2012), setting up a small cylinder near the main cylinder (Dalton et al., 2001; Kuo and Chen, 2009; Strykowski and Sreenivasan, 1990; Thiria et al., 2009), modification in the trailing edge geometry (Xu et al., 2010) and base bleed (Fu and Rockwell, 2005a). These papers clarify that flow structure can be passively controlled by altering the surface configuration or attaching additive devices to the bluff body which is tested. The various passive control devices were comprehensively discussed by Zdravkovich (1997). For the latter, heating the cylinder (Lecordier et al., 1991), rotary oscillation of the cylinder at an appropriate frequency (Lee and Lee, 2008; Naim et al., 2007), acoustics excitations (Blevins, 1985), and control of the electromagnetic force (Kim and Lee, 2001) can be remarked as the sample investigations. The passive control methods (Lam et al., 2010; Zhou et al., 2011) are still developed since there is no external energy input and no feedback sensor; furthermore they are easier to carry out than the active control methods which require actuation as well as sensing. However, many studies on the active control methods were also performed for improving efficiency of the control. Kahraman et al. (2002) stated that a strip of surface elements can significantly retard and attenuate the large-scale vortex formation process. They suggested that the small-height control elements may be placed on the bed at a suitable point in the near wake region for achieving the desired flow control. Igarashi (1978) observed that, in comparison to the case of a plain cylinder, the region of vortex formation noticeably displaced downstream with the presence of a slit cut along the span of the cylinder. Base bleed can markedly change the vortex formation process from a bluff body with a blunt trailing edge (Bearman, 1967; Wood, 1964). The flow downstream of a circular cylinder in shallow water was passively controlled by a splitter plate which was located at various streamwise locations in the wake region (Akilli et al., 2005). The length of splitter plate was equal to the cylinder diameter, D. It was noticed that the splitter plate significantly suppressed the vortex shedding for the gap, which was the distance between base of the cylinder and leading edge of the plate, changed from 0 to 1.75D. Their measurements showed that the effect of the plate was negligible when the splitter plate was located at a distance of 2D from the cylinder base. Subsequently, the control of vortex shedding around a circular cylinder by splitter plates of different lengths attached on the cylinder base was investigated in shallow water flow (Akilli et al., 2008). They demonstrated that the length of the splitter plate has a remarkable effect on the flow structure. The flow characteristics in the near-wake seriously changed up to the case of splitter plate length was equal to the cylinder diameter, but flow characteristics were affected insignificantly for greater plate lengths. The splitter plate can thus be considered as a favorable passive control method for suppressing the vortex shedding behind a cylinder. Lim and Lee (2003) experimentally investigated the flow structure around a circular cylinder with U-grooved surfaces. They noted that the U-shaped grooves decrease the drag coefficient by 18.6%, compared with that of plain cylinder. The longitudinal grooves shifted the position of vortices toward the cylinder and reduced the vortex formation region in comparison to the plain cylinder. Xu et al. (2010) expressed that due to the passive control of the flow past a wavy cylinder, the mean drag coefficient of the wavy cylinder was much smaller than that of the circular cylinder and the drag reduction up to 26% was determined. The fluctuating force coefficients were also diminished to be nearly zero. It was concluded that the vortical structures near the base region of the wavy cylinder were less strong than those of the circular cylinder. The results of their study presented physical insight into the understanding of the mechanisms for the passive control of the flow over a wavy surface. Thiria et al. (2009) experimentally investigated the passive drag control of a turbulent wake by a small secondary cylinder placed behind a 2-D bluff body with a blunt trailing edge. Mean pressure and PIV measurements were accomplished in the wake. The presence of the control cylinder caused the pressure inside and bubble recirculation length to increase. It was also shown by referring to the phase averaging of the vorticity field that the circulation of the

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large-scale structures was not significantly influenced. The results of their study pointed out that the drag was reduced up to 17.5% due to the smaller cylinder placed behind the bluff body. It seems that the presence of secondary cylinder is useful in terms of the passive drag control around a bluff body. The findings of aforementioned papers clearly reveal that vortex shedding behind a bluff body can successively be suppressed by a proper passive control method. As a result drag and fluctuating forces acting on the body, turbulence intensity as well as Reynolds stresses measured in the near wake can be reduced significantly by controlling of the flow. Therefore, it was aimed in the present work to carry out an experimental research directed for passively controlling flow around a circular cylinder vertically placed in uniform flow of water. The novelty of the study is the utilization of a screen (meshed controlling element), which has the streamlined shape, surrounding the cylinder. The velocity fields of near-wake downstream of the circular cylinder were determined by using PIV measurement technique. The turbulence statistics obtained from the velocity field measurements downstream of the cylinder were analyzed in detail.

2. Experimental set-up and data acquisition system Experimental measurements were accomplished in a circulating water channel which has the dimensions of 8000 mm  1000 mm  750 mm at Fluid Mechanics Laboratory of Mechanical Engineering Department of C - ukurova University. The PIV technique was used to get velocity vector fields downstream of a vertical cylinder which had a diameter, D of 50 mm. The side view of the experimental set-up, the cylinder-control element combination, the laser sheet’s location and the top view of the CCD camera are shown in Fig. 1(a). The depth of the water in the channel was 600 mm. The experiments were carried out above a platform with the length of 2300 mm. The distance from the leading edge of the platform to the cylinder was 1800 mm so that fully-developed boundary layer was established during the experiments. The water height, hw was 25 mm which corresponded to the distance from free surface to the base of the platform as depicted in Fig. 1(a). In this case shallow flow, whereby the diameter or width of the body is considerably larger than the fluid depth, condition was provided (Fu and Rockwell, 2005a). The ratio of the cylinder diameter to the

Fig. 1. (a) Side view of the experimental set-up including the configuration of the laser sheet and CCD camera. (b) The top view of the control element and the enclosed circular cylinder.

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width of the test section was 5% which expresses the geometric blockage of the cylinder. The flow of the water in the channel was supplied through a pump operated by a variable-speed electric motor. The depth-averaged flow velocity, U in the channel was 103.5 mm/s which corresponds to the Reynolds number of 5200 based on the cylinder diameter. For this Re the flow around the circular cylinder was fully developed and laminar as well as the turbulence intensity was about 0.5%. Fig. 1(b) shows the schematic representation of the inner circular cylinder and outer screen which has a width, w of 80 mm at the center (therefore, w/D ¼ 1.6 throughout the present investigation). The axial length L in Fig. 1(b), which describes the distance from the leading edge to the trailing edge of the control element, had four values expressed in nondimensional form as L/D ¼ 2, 2.4, 2.8 and 3.2 in order to see its contribution to the flow control. The outer element (screen) was made of thin steel wire meshes. The porosity of the outer element was 0.5 which defines the ratio of open area due to the meshes on the screen to the whole outer surface area of the screen. The coordinate system is also represented in Fig. 1(b) and the circular cylinder base (downstream) is the reference position, i.e. x ¼ 0 and y ¼ 0 according to this sketch. It should also be remarked that the center points of the outer control element and the circular cylinder were coincided in the experiments. The experimental measurements were carried out and processed with the PIV system and software installed on a computer. The illumination in the test section was performed through an intense laser light sheet from a pair of doublepulsed Nd:YAG laser units. The maximum energy output of each laser unit was 120 mJ at 532 nm wavelength. The laser sheet was parallel to the surface of the platform in the channel and it was emitted to the mid-height of hw as shown in Fig. 1(a). The time interval between pulses was 1.5 ms and the thickness of the laser sheet illuminating the measuring plane was nearly 2 mm through out the experiments. The values of time interval and the laser sheet thickness were selected to achieve the maximum amount of particles in the interrogation window. The image capturing was achieved with an eight-bit cross-correlation charge-coupled device (CCD) camera which had a resolution of 1600 pixels  1200 pixels. The total number of velocity vector was 7227 (99  73) acquired instantaneously with a rate of 15 frames per second. The geometric size of the overall view field was 160 mm  120 mm. In the image processing, 32  32 rectangular interrogation pixels were selected as well as an overlap of 50%. The water was seeded by hollow glass sphere particles which had a diameter and density of 12 mm and 1100 kg/m3, respectively. In each experiment, 350 instantaneous images of the flow were captured and recorded to the computer. There were maximum 2% spurious velocity vectors in the measurements and they were eliminated by means of the local median-filter technique. They were replaced between surrounding vectors by applying bilinear least squares fit technique. Moreover, the Gaussian smoothing technique was utilized to avoid dramatic changes in the velocity vector field. As a consequence of the mentioned refinements, the uncertainty in the measured velocity relative to U was about 2%. Finally, the instantaneous and mean vorticity maps (vorticity value at each grid point was calculated from the circulation around eight neighboring points) and turbulence statistics such as Reynolds stresses were determined as a result of post-processing operation. 3. Results and discussion 3.1. Interpretation of the experimental data by referring to the contours of flow field The experimental result with the flow over the circular cylinder was initially obtained for making a comparison with the case when the control element (screen) was present outside the cylinder. Then the experiments were repeated by utilizing the screen shown in Fig. 1(b) to suppress the vortical flow structure downstream of the cylinder. The timeaveraged streamline topology is shown in Fig. 2 for the bare cylinder case. First of all, it is obvious from Fig. 2 that the near wake region is almost symmetrical. It can be clearly observed that two focus points emerge in the close region of the cylinder and the saddle point develops at approximately x/D ¼ 1.1 which may also be considered as the vortex formation length. The time-averaged contours of vorticity o, and normalized Reynolds shear stress, u0 v0 =U 2 are demonstrated in Fig. 3 for the bare cylinder as well as presence of the outer control element cases (2 rL/D r3.2). The black and gray lines in the plots of Fig. 3 correspond to the counterclockwise (positive) and clockwise (negative) contours, respectively. The incremental value in o distribution is 2 s  1 for the bare cylinder case. It can be deduced from the vorticity distribution of bare cylinder case that the higher vorticity values occur at the shear layers as a result of robust fluctuations in transverse direction. The positive and negative vorticity contours are evidently symmetrical and they seem to be merged in the near wake. The interactions of synchronized vortex shedding from upper and lower sides of the cylinder causes the formation of Ka´rma´n vortex street at approximately x ¼ D, which can also be regarded as vortex formation region (Lam et al., 2004). The shear layers can also be noticed from the distribution of u0 v0 =U 2 where a double-peak pattern is present in the shear layer of the wake region. The positive and negative peak magnitudes of u0 v0 =U 2 have been determined as 0.102 and 0.106, respectively, by giving the information that the interval between two successive contours is 0.01 for the bare cylinder case. These maximum values then start to decrease steadily along the downstream direction. In addition to the pronounced u0 v0 =U 2 concentrations in the shear layers, a weaker Reynolds shear stress distribution also emerges at the vicinity of the cylinder base as a consequence of fluid flow from free stream into that region. The time-averaged vorticity and Reynolds shear stress contours for the flow downstream of control element located around the circular cylinder are also presented in Fig. 3 with different L/D cases. It is emphasized that the incremental values of o and u0 v0 =U 2 contours are 1 s  1 and

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Fig. 2. Time-averaged streamline pattern for the bare cylinder.

0.002, respectively, when the cylinder is enclosed by the mentioned control element. The distributions of o and u0 v0 =U 2 describe that positive and negative layers are almost symmetrical about the cylinder center. Especially, o and u0 v0 =U 2 contours specify that the outer screen has a definite effect on the flow field since the interference of the shear layers has been suppressed by flowing of fluid from the meshes of screen into the wake region in the form of a jet. In fact, the results presented in Fig. 3 are qualitatively in good agreement with those obtained by Fu and Rockwell (2005a). Consequently, when the outer control element is present, the vorticity contours precisely elongate without any interaction as well as the double peak pattern does not occur in u0 v0 =U 2 distribution by contrast to the bare cylinder case. The u0 v0 =U 2 contours dramatically loose their concentration for the case of 2rL/D r3.2. Therefore, when the flow was controlled with the mentioned element, the peak magnitude of u0 v0 =U 2 was noted to be 0.01 which corresponds to only 10% that of bare cylinder case. The next issue with Fig. 3 is related to the ratio of L/D which, in the covered range, seems not to be so effective on o and u0 v0 =U 2 distributions. The behavior observed in the contours is nearly the same as expressed for any L/D ratio. It is clearly seen in the investigations by Fu and Rockwell (2005a,b) that shallow flow past a vertical cylinder leads to a horseshoe (necklace) vortex system formation about the upstream surface of the cylinder. They found that the flow structure was three-dimensional and unsteady in vicinity of the bed as a result of the presence of these horseshoe vortices. Besides, coherent vortical patterns developed earlier in the separating shear layers as the amplitude of the undulations in the horseshoe system increased. The horseshoe vortex structure eventually moved further downstream exterior to the shear layer. The growth of vortical structures in the separating shear layer downstream of the cylinder cannot be considered independent of the horseshoe vortex system (Fu and Rockwell, 2005b). Therefore, the process of the vortex origination in the near wake of the cylinder completely includes vorticity due to both the horseshoe vortices emanating from the upstream base of the cylinder and the vortex shedding from the cylinder. It is certain by paying attention to the aforementioned information that a horseshoe vortex system has already developed about the fore region of the cylinder in the present study. The horseshoe vortices have significantly influenced the downstream flow structure. Namely, the vortical flow pattern in Fig. 3 encompasses vorticity not only from the separating shear layer but also from the vorticity layers related to the horseshoe vortex about the fore part of the cylinder. Although the formation process and flow structure of the upstream horseshoe vortex system are outside scope of this investigation, the certain effect of horseshoe vortices on the unstable flow field downstream of the cylinder has presumably been suppressed partly by using outer screen element. It can further be said that if the horseshoe (necklace) vortex system had not developed about the upstream surface of the cylinder, the concentration of the contours would have been much weaker for the bare cylinder as well as controlled flow cases in Fig. 3. The vorticity distributions at an arbitrary instant (t ¼ 10 s) are demonstrated in Fig. 4 to check whether the instantaneous flow structure supports the time-averaged results given in Fig. 3. The negative (clockwise) and positive (counterclockwise) vortices are described with the gray and black contours, respectively, while the incremental value is 5 s  1 throughout the plots in Fig. 4. The vorticity layer of the bare cylinder case is a good sample of Ka´rma´n vortex pattern due to the evident amalgamation of the contours just after the cylinder. On the other hand the considerable elongation of the contours is remarkable if the outer control element has been located around the cylinder. It can be stated as a result that not only mean flow pattern but also instantaneous flow structure obviously verifies the control of flow which yields

234

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Fig. 3. Time averaged vorticity and Reynolds shear stress contours for various cases.

with the desired suppression of vortex shedding. Further, it is remarked in reference to Fig. 4 that there seem to be so many small-scale vortices which should primarily be related to the Kelvin–Helmholtz instability along the shear layers prior to the formation of large-scale vortices. Kelvin–Helmholtz instability occurs when the boundary layer which develops on the cylinder surface separates (Bloor, 1964; Prasad and Williamson, 1997). Afterwards, these small-scale

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1.2 0.8

y/D

0.4

bare cylinder

0

-0.4 -0.8 -1.2 -0.2 0.2 1.2

0.6

1.0

1.4

1.8

2.2

2.6

0.8

y/D

0.4

L/D=2

0

-0.4 -0.8 -1.2 0.1

1.1

2.1

3.1

1.2 0.8

y/D

0.4

L/D=2.4

0

-0.4 -0.8 -1.2 0.4

1.4

2.4

3.4

1.2 0.8

y/D

0.4

L/D=2.8

0

-0.4 -0.8 -1.2 0.6

1.6

2.6

3.6

1.2 0.8

y/D

0.4

L/D=3.2

0 -0.4 -0.8 -1.2 0.8

1.8

2.8

3.8

x/D Fig. 4. The instantaneous vorticity contours for various experimental cases at t ¼ 10 s.

vortices feed into the large-scale vortices. Since the main aim is to suppress the formation of large-scale vortex system (Ka´rma´n vortex street) downstream of the cylinder, the presence of small-scale vortices is not focused in this investigation. The vortical structures are closely associated with the streamwise and transverse Reynolds normal stresses which are defined by the normalized average terms as u02 =U 2 and v02 =U 2 , respectively. Furthermore, the vortex dynamics and the evaluation of turbulence mixing are connected directly with the turbulent kinetic energy, TKE which can be computed (Lim and Lee, 2003) in non-dimensional form as TKE ¼ 0:75ðu02 =U 2 þ v02 =U 2 Þ:

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The spatial distributions of u02 =U 2 , v02 =U 2 and TKE are depicted in Fig. 5. The contours for the bare cylinder case are concentrated apparently in the near wake. The increments from a contour to the next one in the represented plots of Fig. 5 are 0.02 and 0.005 for the bare cylinder and 2rL/D r3.2 cases, respectively. These numerical values clearly imply that the concentration of the contours weakens on controlling the flow. The peak magnitude of TKE for the bare cylinder case was equal to 0.278 while it was noted to be 0.037 for L/D ¼ 2.4 case. Therefore, it is obvious by comparing with the bare cylinder case that the TKE concentration is nearly 7.5 times smaller due to the presence of outer control element. It can be stated that such a worthy decrease in TKE is absolutely connected to the reduction of the drag force exerted on the circular cylinder (e.g., Lim and Lee, 2003). It should also be emphasized at this point that although the contours for 2 r L/D r 3.2 cases are very similar to each other, but there is a difference between them, namely the peak magnitudes of TKE for L/D ¼ 2, 2.8 and 3.2 cases were found as 0.035, 0.054 and 0.074, respectively. Therefore, it presumably seems that the lower peak value of TKE can be obtained as a result of a smaller L/D case. The next important issue noted from Fig. 5 is the analogy among u02 =U 2 , v02 =U 2 and TKE contours such that the distributions of TKE is similar to that of v02 =U 2 for the bare cylinder case. There is a single-peak pattern in both plots in contrary to contours of u02 =U 2 where a peak-and-peak pattern is evident. In fact, such behavior can also be seen in the study of Feng and Wang (2010). However, when the cylinder is confined by outer control element (2 rL/D r3.2 cases in Fig. 5), TKE and u02 =U 2 contours are strongly similar. The reason of such an interesting physical phenomenon will be discussed later. Furthermore, in contrary to the bare cylinder case, the evident concentrations in u02 =U 2 , v02 =U 2 and TKE contours do not occur when the outer control element is used. 3.2. The streamwise and transverse distributions of turbulence statistics at a specified location in the measurement region The variations of turbulence statistics are discussed in this section. The distribution of parameters along streamwise direction was examined at a fixed y/D, besides their variations with transverse direction were obtained at a constant x/D value. The considered parameters are intensity of turbulences, u0rms =U, v0rms =U which are the root mean square of fluctuating components, normalized Reynolds shear stress, u0 v0 =U 2 and normalized turbulent kinetic energy, TKE. First of all the streamwise distributions of the turbulence statistics at y/D ¼ 0.5 for different L/D values as well as bare cylinder case are presented in Fig. 6. The selected location of y/D ¼ 0.5 corresponds to the upper boundary (shear layer region) of the inside circular cylinder where the rigorous vortex shedding is prominent. It is also recalled that x/D ¼ 0 seen in Fig. 6 coincides with the base of the cylinder. The turbulence level in the vicinity of the circular cylinder base is increased by the formation of vortical flow structure. In other words, the turbulence intensities u0rms U and v0rms U in Fig. 6 increase rapidly (Nakamura and Igarashi, 2007) in the region of vortex formation which corresponds to the location of nearly x/D ¼ 1. It is seen that initially u0 rms/U ¼ 0.19 and v0rms =U ¼ 0:15 at the base of the cylinder. The peak value for both u0rms =U and v0rms =U in the shear layer is approximately 0.4 and they start to decrease beyond the position of x/D ¼ 1, but the behavior is too different for the mentioned parameters. The reduction in u0rms =U is more distinct based on the peak magnitude such that the values of u0rms =U and v0rms =U at x/D ¼ 3, which is the limit of field view in the PIV experiment for bare cylinder case, are roughly 0.18 and 0.32, respectively. Furthermore, it seems that u0rms =U proceeds to decrease markedly while v0rms =U slightly diminishes for x/D 4 3. This situation expresses that transverse fluctuations are predominant in the vortical flow structure and their effects continues to be drastic through a long axial distance downstream of the cylinder. Meanwhile, the Reynolds shear stress, u0 v0 =U 2 , which has a magnitude of  0.005 at x/D ¼ 0, for the bare cylinder case in Fig. 6 markedly decreases in the vortex formation region to the value of 0.1 then it increases to about  0.02 at x/D ¼ 3. It should be emphasized that since the plots in Fig. 6 corresponds to the location of y/D ¼ 0.5, where vortices shed in clockwise direction above the symmetry line, the values in the distribution of u0 v0 =U 2 are negative as previously observed in Fig. 3. The normalized turbulent kinetic energy, TKE for the bare cylinder case in Fig. 6 also abruptly increases in the region of vortex formation. The value of TKE at x/D ¼ 1 is noted to be 0.25 which corresponds to approximately six times of TKE measured at the base of the cylinder, eventually it is nearly 0.09 at x/D ¼ 3. The significance of using the control element for diminishing the effect of vortex shedding downstream of the cylinder is conspicuous in Fig. 6. The behavior of turbulence statistics for the case of 2rL/D r3.2 is fairly different in comparison to the bare cylinder case. The fluctuating velocity distributions are almost similar to those obtained by Nakamura and Igarashi (2007). The values of u0rms =U, v0rms =U, u0 v0 =U 2 and TKE along streamwise direction are considerably diminished because of suppression of Ka´rma´n vortex street formation (for example, TKE is almost equal to 0.01 regardless of L/D). If the flow is controlled by the outer control elements, the distributions of turbulence statistics illustrate that any peak value as in the trend of bare cylinder case does not occur along flow direction (this behavior has already been supported by consulting to Fig. 3). It is further remarkable that u0 v0 =U 2 is nearly negligible downstream of the cylinder surrounded with the control element. The distributions of u0rms =U and v0rms =U show that the maximum intensity of turbulence for any L/D is 5% in the range of 0.5 o x/D o 3 and there is a mild increase in these parameters for x/D 4 3 such that it is about 10% at x/D ¼ 4. Moreover, the effect L/D can be more clearly discussed by the plots of u0rms =U and v0rms =U rather than that of u0 v0 =U 2 and TKE in Fig. 6. It can be asserted by observing mentioned distributions that greater L/D case results in a somewhat higher intensity of turbulence for x/D 43 especially. This interpretation may be confirmed by the distinct behavior of L/D ¼ 3.2 case from which maximum turbulence intensity is noted in contrast to the remaining smaller L/D cases providing the lowest value of u0rms =U or v’rms/U.

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u' 2 /U 2

237

v' 2 /U 2

TKE

1.2 0.8 0.4

bare cylinder

0

0.278 -0.4 -0.8 -1.2 -0.2

0.2

0.6

1.0

1.4

1.8

2.2

2.6 -0.2

0.2

0.6

1.0

1.4

1.8

2.2

2.6 -0.2

0.2

0.6

1.0

1.4

1.8

2.2

2.6

1.2 0.8 0.4

0.035

0

L/D=2

-0.4 -0.8 -1.2 0.1

1.1

2.1

3.1

0.1

1.1

2.1

3.1

0.1

1.1

2.1

3.1

1.2 0.8

y/D

0.4

L/D=2.4

0.037

0 -0.4 -0.8 -1.2 0.4

1.4

2.4

3.4

0.4

1.4

2.4

3.4

0.4

1.4

2.4

3.4

1.2 0.8 0.4

L/D=2.8

0.054

0 -0.4 -0.8 -1.2 0.6

1.6

2.6

3.6

0.6

1.6

2.6

3.6

0.6

1.6

2.6

3.6

1.2 0.8 0.4

0.074

0

L/D=3.2

-0.4 -0.8 -1.2 0.8

1.8

2.8

x/D

3.8

0.8

1.8

2.8

x/D

3.8

0.8

1.8

2.8

x/D

Fig. 5. The contours of time-averaged Reynolds normal stresses and turbulent kinetic energy.

3.8

238

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Fig. 6. The distribution of streamwise turbulence statistics at y/D ¼ 0.5.

The distributions of turbulence statistics along the transverse direction at three axial stations x/D of 1.2, 2 and 3 are demonstrated in Fig. 7. It seems from Fig. 6 that the experimental data nearly coincides for the covered L/D cases, namely the results of two test sets L/D ¼ 2.4 and L/D ¼ 2.8 take place in between the experimental data for L/D ¼ 2 and L/D ¼ 3.2 cases. Therefore, for convenience, the results are plotted for L/D ¼ 2 and L/D ¼ 3.2 cases in Fig. 7(a)–(d). The crosssectional distributions of statistical flow properties displayed in Fig. 7 are considerably compatible with those obtained by Fujisawa and Takeda (2003). The variation of streamwise intensity of turbulence, u0rms U with y/D is presented in Fig. 7(a). First of all the behavior of bare cylinder case is discussed, then the effect of outer control element on the variation of

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u0rms =U with y/D is considered. It should be remarked that as the boundary layer separates from the surface of the cylinder, the fluid particles close to there accelerate in flow direction because of vigorous fluctuations during vortex shedding. The enhanced turbulence level in vicinity of upper and lower boundary of the cylinder therefore leads to development of double peaks of u0rms =U in the shear layers in bare cylinder case. Accordingly, it is not surprising that u0rms =U has a smaller magnitude towards the position of y/D ¼ 0 (i.e. the symmetry line downstream of the cylinder) since turbulence effects in streamwise direction will be reduced as moving away from the surface of the cylinder. It is clear by referring to x/D ¼ 1.2 and x/D ¼ 2 cases that the greater magnitudes of u0rms =U occur at approximately y=D ¼ 8 0:5 in the shear layers. However, the maximum values of u0rms =U are observed at about y=D ¼ 8 1 for x/D ¼ 3 case of the bare cylinder. Therefore, the transverse position y/D, where the turbulence level is maximum, shifts outside the boundary of the cylinder for longer distances from the cylinder base (according to Fig. 7(a), the mentioned length can be suggested as x/D Z 3). The shorter streamwise distance downstream of the cylinder x/D leads to higher intensity of turbulence, for instance the maximum values u0rms =U related to the bare cylinder can be determined to be roughly 0.38, 0.28 and 0.23 for x/D cases of 1.2, 2 and 3, respectively (u0rms =U has decreased by about 40% as long as the axial locations of x/D ¼ 1.2 and x/D ¼ 3 are considered). In other words such a trend points out the diminishing of turbulence effects as moving away from the cylinder. It can additionally be referred by comparison to the peak points that u0rms =U is lower outside the boundary of the cylinder for. It is an indisputable fact that, the presence of outer control element leads to substantial reduction in u0rms =U. When the flow is controlled, there is not an appreciable difference between the variations of u0rms =U with y/D for different x/D cases, namely the greatest value of u’rms/U appears in vicinity of y=D ¼ 8 1, which approximately correspond to the upper and lower boundaries outer control element, with a value of about 0.18. The streamwise turbulence level arises with a high rate in the shear layers mostly and therefore the apparent double peaks of u0rms =U for any L/D case emerge near y=D ¼ 8 1

Fig. 7. (a) Variation of u0 rms with y/D at different axial locations. (b) Variation of v0 rms with y/D at different axial locations. (c) Variation of Reynolds shear stress with y/D at different axial locations. (d) Variation of turbulent kinetic energy with y/D at different axial locations.

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Fig. 7. (continued)

where the shear layers due to the control element are present. Furthermore the behavior is different in comparison to the bare cylinder case that the smallest u0rms =U (about 2%) is measured through the upper and lower boundaries of the cylinder, i.e. the range of  0.5 oy/D o0.5 regardless of x/D. Therefore, it can be justified that the cylinder has not been seriously affected due to such a highly suppressed vortical flow structure in proximity of the cylinder. Meanwhile the distribution in Fig. 7(a) for x/D ¼ 3 related to bare cylinder case approaches to that obtained when flow is controlled. It seems possible thereby that both distributions will overlap and exhibit the same behavior at a proper distance from the cylinder base, in other words the effect of vortices substantially diminishes along y/D (even vortex shedding is not suppressed) as streamwise distance x/D increases step by step. The last subject related to L/D can be stated as the effect of this parameter is not obvious in the range of  0.5 oy/D o0.5, however, there is a scatter of experimental data for y=D Z 8 1 where u0rms =U seems to increase slightly for a grater value of L/D as verified by the three cases in Fig. 7(a). The variation of turbulence intensity in transverse direction v0rms =U with y/D for three different streamwise locations is shown in Fig. 7(b). The distributions for the bare cylinder case are dissimilar to that observed in Fig. 7(a) such that there is only single peak magnitude of v0rms =U which appears exactly at y/D ¼ 0 independent of x/D. The indicated state can be clarified as that the fluid particles from upper and lower boundaries of the cylinder are forced to flow through transverse direction in the course of vortex formation; they strongly amalgamate at the symmetry axis where v0rms =U has a distinct peak thereby. The investigated parameter of v0rms =U is lowest at y/D ¼ 1, subsequently it sharply increases to its peak value y/D ¼ 0 and then decreases again to the lowest value at y/D ¼ 1. The maximum magnitudes of v0rms =U are approximately 0.55, 0.44 and 0.4 concerning the x/D cases of 1.2, 2 and 3, respectively, in Fig. 7(b) for the bare cylinder case. Therefore, the turbulence level in transverse direction v0rms =U (Fig. 7(b), bare cylinder case) is conspicuously higher than that along streamwise direction, u0rms =U (Fig. 7(a)) and the former is a dominant factor in the vigorous vortical flow structure around the cylinder. The distribution relevant to the presence of outer control element is similar to the behavior observed in

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Fig. 7(a) such that vortex shedding is prevented and v’rms/U is (in contrast to bare cylinder case) as low as 2% for the range of  0.5 o y/D o 0.5. The maximum intensity of turbulence near the shear layers originated from the outer control element is about 12% independent of x/D and/or L/D in Fig. 7(b). The variable parameter L/D does not influence decisively the distribution of v0rms =U along y/D. The distribution of Reynolds shear stress u0 v0 =U 2 versus y/D can be inspected in Fig. 7(c). The common characteristic of bare cylinder case regardless of x/D reflects that after formation of vortices, u0 v0 =U 2 is negligible outside the shear layers due to inconsiderable viscous effects in free stream. The counter-clockwise Reynolds shear stress rapidly increases as approaching to the lower boundary of the cylinder, where the degree of fluctuations are very strong, and eventually reaches to its highest value at y/D ¼  0.5. Subsequently it starts to decrease towards the symmetry axis at which the clockwise (negative) and counter-clockwise (positive) Reynolds shear stresses have the same intensity quantitatively. The positive shear stresses are absorbed by the negative ones at y/D ¼ 0 where the condition of u0 v0 =U 2 ¼ 0 inevitably takes place. It should be emphasized at this point that as a result of serious interference between the clockwise and counterclockwise shear stresses for the range of  0.5 o y/D o 0.5, there is a continuous declination in the distribution of u0 v0 =U 2 as long as the specified range is regarded. The reduction in u0 v0 =U 2 continues up to the upper boundary of the cylinder, y/D ¼ 0.5 where the clockwise Reynolds shear stress has a minimum value (the mentioned peaks related to the bare cylinder case have already been verified by the apparent concentrations of u0 v0 =U 2 contours in the shear layers demonstrated in Fig. 3). Finally it starts to increase for y/D 4 0.5 because of effect of negative shear stresses merely and takes again an insignificant value for y/D 4 1 outside the shear layer. It can be stated briefly that the Reynolds shear stress is zero at y/D ¼ 0 and very weak for y/D o 1 as well as y/D 4 1 case while it is so much intensive in the shear layers (at y=D ¼ 80:5) for the bare cylinder case. The longer axial distance causes the effects of u0 v0 =U 2 to be reduced through the transverse direction, for example the peak magnitude of u0 v0 =U 2 for x/D ¼ 3 case is approximately three times less than that determined for x/D ¼ 1.2 case without applying the suggested control method. The Reynolds shear stress distributions for three cases in Fig. 7(c) reveal that when the flow is controlled u0 v0 =U 2 is almost negligible (nearly zero as a result of preventing the interference of upper and lower shear layers downstream of the cylinder) in the range of  0.5 r y/D r 0.5. Nevertheless it is too weak in both ranges of  1.2 o y/D o 0.5 and 0.5 o y/D o 1.2 regardless of both L/D, x/D parameters which do not seem to affect the introduced behavior of the Reynolds shear stress distribution in a remarkable manner. The variation of normalized turbulent kinetic energy, TKE with y/D is shown in Fig. 7(d). The Reynolds stress has a maximum value at the symmetry line as observed from first row of Fig. 5. Therefore, the peak value of TKE which appears at y/D ¼ 0 for the bare cylinder case is noted to be approximately 0.27 for x/D ¼ 1.2 and it decreases with increasing x/D such that TKE ¼ 0.175 and TKE ¼ 0.13 at x/D cases of 2 and 3, respectively. Comparing with the bare cylinder case, the TKE values are reduced strikingly in the range of 0.5 r y/D r 0.5 for the covered L/D cases independent of x/D. The double peaks of TKE downstream of the screen (outer control element) can be easily distinguished and they appear symmetrically in the shear layers of the screen. The value of L/D has an inconsiderable effect on the variation of TKE with y/D, there is almost no difference for the covered L/D cases in Fig. 7(d). It is interesting by comparing the distributions of turbulence statistics along transverse direction that the physical behavior related to distributions of v0rms =U (Fig. 7(b)) and TKE (Fig. 7(d)) for the bare cylinder case are similar. On the other hand when the flow is controlled, one can roughly observe the analogous trends in the experimental data of u0rms =U and TKE shown in Fig. 7(a) and (d), respectively, for any x/D. The behaviors in question has already been determined (Section 3.1) in reference to Fig. 5. The reason of the noticed similarity in the contours of turbulence statistics can be expressed as follows: when fluid flows over the cylinder, boundary (shear) layer separates from the surface of the cylinder. The separated top and bottom shear layers are highly prone to interact with each other. Afterwards, the vortices originate inevitably on merging of shear layers; a well-defined Ka´rma´n vortex structure arises downstream of the cylinder and thus there is a vigorous interference between the fluid particles in both streamwise and particularly transverse directions. This interpretation may be supported quantitatively from Fig. 7(a) and (b) that the maximum amplitudes of u0rms =U and v0rms =U at x/D ¼ 2 are about 0.28 and 0.44, respectively, for the bare cylinder. These magnitudes specify that transverse fluctuations govern the vortical flow structure independent of x/D and that’s why the distribution of TKE is mainly similar to that of v02 =U 2 unless the flow is controlled which has already been recognized by referring to Fig. 5. As far as the presence of outer control element is considered, the fluctuations are robustly suppressed so that formation of vortical flow structure is prevented. As a consequence, the peak values of u0rms =U and v0rms =U both of which appears in the shear layers diminish to be around 0.18 and 0.12, respectively, at x/D ¼ 2 regardless of L/D. It seems in this case that streamwise fluctuations are dominant by comparison to those in transverse direction, namely u0rms =U is primarily effective in the flow field. The behavior in the distributions is thus reversed when the outer control element is present such that contours of TKE in Fig. 5 mostly resembles that of u02 =U 2 . 4. Conclusions The presented study focused on the passive control of flow downstream of a circular cylinder with a diameter D of 50 mm by means of a screen (control element) surrounding the cylinder. The screen was constructed in a streamlined shape as shown in Fig. 1(b) to enhance the suppression rate of the vortex shedding. The variable parameter of the control

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element was the length L as demonstrated in Fig. 1(b) and the investigation was carried out for the different cases of L/D as 2, 2.4, 2.8 and 3.2. The results of measurements with PIV technique have indicated that the existence of control element around the cylinder significantly suppressed the vortex shedding from the outer surface of the cylinder. Consequently, the intensity of turbulence, Reynolds shear stress and turbulent kinetic energy magnitudes were too low not only at the shear layers, but also they were diminished along both transverse and streamwise directions, compared to the bare cylinder case. The parameter of L/D seemed to not affect the distribution of turbulence statistics considerably, nevertheless it was confirmed that the turbulence level was gradually reduced for a smaller L/D case in the experiments. The future studies on passive control of flow around a bluff body may have a meaningful contribution to the literature if the outer control elements in different shapes and/or types are tested.

Acknowledgements The author wishes to acknowledge the support from the national postdoctoral research scholarship program of ¨ _ITAK (The Scientific and Technological Research Council of Turkey). He wishes also to thank the staff in the Energy TUB Division of Mechanical Engineering Department at C - ukurova University for providing the PIV measurement. The contributions by the company of Tesmak for construction of the control elements used in this study are greatly appreciated. References Akilli, H., Sahin, B., Tumen, N.F., 2005. Suppression of vortex shedding of circular cylinder in shallow water by a splitter plate. Flow Measurement and Instrumentation 16, 211–219. Akilli, H., Karakus, C., Akar, A., Sahin, B., Tumen, N.F., 2008. Control of vortex shedding of circular cylinder in shallow water flow using an attached splitter plate. Journal of Fluids Engineering: Transactions of the ASME 130, 041401. Bearman, P.W., 1967. 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