Zhou

Experimental Thermal and Fluid Science 69 (2015) 19–26

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Control of flow past a dimpled circular cylinder Bo Zhou ⇑, Xikun Wang, Wei Guo, Wie Min Gho, Soon Keat Tan Maritime Research Centre, School of Civil and Environmental Engineering, Nanyang Technological University, 639798, Singapore

a r t i c l e

i n f o

Article history: Received 18 September 2014 Received in revised form 30 May 2015 Accepted 27 July 2015 Available online 30 July 2015 Keywords: Flow control Drag reduction Surface roughness Dimpled cylinder

a b s t r a c t In this paper, the flow past a circular cylinder with dimpled surface (the roughness coefficient k/D = 0.05, k is the depth of the dimple hole, and D is the diameter of the cylinder) was investigated. The experiments were conducted in an open water channel and the Reynolds number ranged from 7.43  103 to 1.798  104. Drag and lift forces on the cylinder were measured directly using a load cell. Two types of surface roughness were investigated, i.e., half dimpled and fully dimpled. The study revealed that the cylinder covered with dimples uniformly over the total surface could produce a drag coefficient of about 90% of a smooth cylinder. On the other hand, the force coefficients (drag and lift) of the half dimpled cylinder varied considerably, depending on the orientation of the dimpled surface with respect to the incident flow. The flow field in the wake of the cylinder was measured using particle image velocimetry (PIV) technique, confirming that the dimpled surface could affect the strength of vortex shedding from the cylinder. Ó 2015 Elsevier Inc. All rights reserved.

1. Introduction Effective control of flow separation and wake in the lee of a cylinder and hence the reduction of drag and lift is an important theme in many engineering applications. The mechanism of drag reduction due to surface roughness is thought to be caused by the transition from laminar to turbulent boundary layer. Flow over a rough surface is known to display an early transition to turbulence, which means that a rough cylinder may have a lower drag coefficient than a smooth cylinder at a certain range of Reynolds numbers [3]. Different types of roughness pattern have been considered by previous researchers, for example dimples and grooves [2,3], surface trip wire [9,14], roughness strips [10], dimples [4,12], grooves [8,7,13], helical strakes [18], screened surface [11], and periodic blowing and suction [6], among others. These studies brought to light the fact that hydrodynamic forces on a cylinder could be modified through introduction of pertinent roughness patterns. For example, Bearman and Harvey [4] demonstrated that the dimpled surface can have a substantial effect in reducing drag on the cylinder over Reynolds number range from Re = 2  104 to 3  105 (where Re ¼ DU=v , in which D is the diameter of the cylinder, U is the flow velocity and v is the kinematic viscosity). The dimpled surface was made of twelve equally spaced dimples (k/D = 0.9  102) machined around the circumference of the cylinder. ⇑ Corresponding author. Tel.: +65 97438252; fax: +65 67906620. E-mail address: [email protected] (B. Zhou). http://dx.doi.org/10.1016/j.expthermflusci.2015.07.020 0894-1777/Ó 2015 Elsevier Inc. All rights reserved.

Butt et al. [5] investigated the flow over cylinders with hexagonal dimples (k/D = 1.98  102) in a subsonic wind tunnel over the range Re = 3.14  104–2.77  105. Their results showed that the dimpled cylinder could achieve a drag coefficient of about 0.65 times of a smooth one. However, we are not aware of any reported study on flow past a cylinder with this type of dimpled surface (fully or partially covered dimple patterns). In this study, the characteristics of eight different types of dimpled pattern were investigated. The findings of this paper would serve to produce better understanding of the dynamic forces (drag and lift) on the cylinder with dimpled rough surface. 2. Experimental set-up Comprehensive measurements were conducted in an open channel located at the Maritime Research Centre, Nanyang Technological University to investigate the complex non-linear flow phenomena in the wake of the cylinders. The re-circulating open channel was 6 m long with a rectangular cross section of 0.3 m  0.4 m (width  height). The bottom and the two side walls of the test section were made of glass to facilitate optical access. The streamwise turbulence intensity in the free stream was found to be low such that it was below 2%. Particle Imaging Velocimetry (PIV) technique was used to measure flow around the cylinder with or without dimples. The PIV system had a double cavity Nd:YAG laser light sheet at 532 nm wavelength (Litron model, power  135 mJ per pulse, duration  5 ns). 1050 instantaneous

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flow fields were obtained for each case at the frequency of 15 Hz. More details of the open channel could be found in Wang and Tan [17] and Zhou et al. [19]. The test circular cylinders were made of initially smooth, solid perspex rod with a constant diameter of D = 40 mm. Dimple patterns were later milled on the cylindrical surface as roughness elements. The design picture of the dimpled cylinders is shown in Fig. 1. Model A corresponded to the cylinder with one half of its exterior surface covered with dimples. Model B was fully covered with dimples. The dimples were laid out in checker fashion with two dimple densities, i.e., sparse and dense with 16 and 32 dimples along the circumference, respectively. The diameter (d) and depth (k) of the dimples were 4 mm (d/D = 0.1D) and 2 mm (k/D = 0.05), respectively. The center-to-center spanwise distance between dimples was 8 mm (0.2D). Fig. 1 shows detailed dimensions of the dimpled cylinders. The test cylinders in the experiment are shown in Fig. 2. The length of the cylinders was 400 mm, leading to an aspect ratio length-to-diameter of 10. This aspect ratio was considered large enough to ensure a 2D flow in the near wake of the cylinder

[16]. The coordinates x, y and z denote the streamwise, transverse and spanwise directions, respectively. In the present test, the free-stream velocity (Ue) was set as 0.18, 0.29, 0.37 and 0.45 m/s, corresponding to Re = 7.43  103, 1.179  104, 1.479  104 and 1.798  104, respectively. This Re range is quite common used for engineering applications, such as offshore or in-land structures. The lists of test cases are shown in Table 1. A platform was used to affix the test cylinder at its top end, as shown in Fig. 3. A piezoelectric three-axis load cell (Kistler model) was mounted on the platform, and was used to measure the integral lift and drag forces on the cylinder. In this way, the dynamic drag (FD) and lift (FL) forces acting on the cylinder could be measured directly. The mean and root-mean-square (r.m.s.) values of the drag coefficient CD (¼ F D =0:5qU 2e A, where q is fluid density and A is the projected frontal area) and lift coefficient CL (¼ F L =0:5qU 2e A) were deduced from the measurements, which are the main load parameters for engineering applications. Through a number of repeated experiments on the smooth cylinder, the uncertainty in the mean drag coefficient was found to be within 1%.

Fig. 1. Schematics of the cross-sectional and side views of the dimple cylinders (dimensions are in mm).

B. Zhou et al. / Experimental Thermal and Fluid Science 69 (2015) 19–26

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Fig. 2. Photographs of the test cylinder(s) with (a) different types of roughness elements (dimples) (b) sparse checker dimple pattern (c) dense checker dimple pattern.

Table 1 The covered test cases. No.

Test case description

Remark

1

Sketch

Smooth

Smooth

2

Dimple full

DF

3

Dense Dimple full

DDF

4

Dimple Half Forward

DHF

5

Dimple Half Side

DHS

6

Dimple Half Backward

DHB

7

Dense Dimple Half Forward

DDHF

8

Dense Dimple Half Side

DDHS

9

Dense Dimple Half Backward

DDHB

Fig. 3. Photograph of the experimental set-up (side view).

the reported values in the subcritical regime [15]. As observed in Fig. 4, the value of C D for the dimpled cylinders is generally lower 3. Results and discussion

than that of the smooth cylinder. It could be seen that the C D value for the case of ‘‘dimple half backward’’ (DHB) case is higher than

3.1. Force coefficients

those of ‘‘dimple half forward’’ (DHF) case. The C D value of the DHF cylinder appeared to depict the lowest value. On the other

The time series of the instantaneous lift (C L ) and drag (C D ) coefficients for the smooth and dimpled cylinders at Re = 1.798  104 are presented in Fig. 4. It is noted that in each case both C L and C D have achieved the ‘‘steady state’’, as reflected in the signals oscillate about a mean value (C D and C L ). For the smooth cylinder, the mean drag coefficient, C D , is about 1.1, which agrees well with

hand, the value of C L for each case is constant at C L  0, suggesting good flow symmetry about the cylinder axis. The amplitude of the lift fluctuation is significantly larger than that of the drag, reflecting the pressure fluctuations due to the periodic vortex shedding from the two sides of the cylinder. Here, the Fast Fourier Transforms (FFT) method is used to analyze the spectral characteristics of the measured C L time series. Fig. 5

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Fig. 4. Time history of the instantaneous lift and drag coefficients for the smooth and dimpled cylinders at Re = 1.798  104.

shows the computed power spectra for the smooth, ‘‘dimple full’’ (DF), ‘‘dimple half forward’’ (DHF), and ‘‘dimple half backward’’ (DHB). It can be observed that there is always a distinct and definite peak at about Strouhal number St = 0.18 (St ¼ fD=U e , f is the peak frequency), which corresponds to that for periodic vortex shedding from the cylinder [15]. The peak corresponding to the vortex shedding frequency is different over the covered test cases. Normally the peak value of the smooth cylinder is larger than that of the dimpled cylinders at the same Reynolds number. For example, at Re = 1.798  104, the peak value of the smooth cylinder is 0.00512, whereas those of the DF, DHF and DHB cylinders are 0.00126, 0.00124 and 0.0013, respectively. The lower amplitude of the spectral peak for DF, DHF and DHB cases indicates that the strength of vortex shedding becomes weaker due to the presence of dimpled surface. Fig. 6 shows the variation of C D as a function of Re for the smooth and dimpled cylinders. The C D value of the smooth cylinder increases slightly with Re, but is in the neighbourhood of 1.1. In comparison, for the fully dimpled cylinders (DF or DDF), the C D values (about 0.95) are significantly lower than those of the smooth cylinder over the Re range considered. For the half dimpled cylinders, on the other hand, the C D values vary with the orientation of the dimpled surface with respect to the incident flow. When the dimpled surface is located at the lee side of the cylinder, i.e., DDHB or DHB, the C D values are closer to or even higher than that of the smooth cylinder. When the rough surface is orthogonal to the incident flow, i.e., DDHS or DHS, the C D values are less than that of the smooth cylinder, but higher than the fully dimpled case (DF or DDF). In the case when the rough surface faces the incident flow, i.e., DDHF or DHF, the C D values are significantly lower than those of the smooth cylinder, and are close to that for the fully dimpled cylinders (DF or DDF). For example, at Re = 1.798  104, the C D

values for the DHF cylinder are about 14% lower than that of the smooth cylinder. At Re = 1.179  104, the difference in C D value for DDHB and DDHF is about 22%. The lowest value of C D is observed for the DHF cylinder at Re = 7.43  103 with ðC D Þmin  0.9, whereas the largest value of C D is observed for the DDHB cylinder at Re = 1.179  104 with ðC D Þmax  1.3. It could be deduced that the effect of the orientation of the dimpled surface is significant. This discrepancy might be explained as follows. The drag on a smooth cylinder is dominated by the form (or pressure) component, which contributes more than 98% of the total drag, whereas the skin friction (or viscous) component is responsible for the remaining 1–2%, see Achenbach [1,2]. For a rough cylinder, on the other hand, both the form and friction drags are significant and neither components can be neglected, see Sumer and Fredsøe [15]. However, considering the fact that with further increase in Re the total drag coefficient C D of the rough cylinders is lower than that of the smooth counterpart, the form drag of the rough cylinders must have been reduced significantly. One possibility is that the presence of the surface roughness would lead to early transition of the separated boundary layer causing it to achieve a turbulent state and reattach to the body. This might also explain why the orientation of the half dimpled surface has such an effect on the drag force. When the half dimpled surface faces the incident flow, it will help to lead to the early transition of the separated boundary layer. When it faces backward, by contrast, it will not help to reduce the drag force, but increase the friction force. As a consequence, the C D value for the half dimpled cylinder attains the minimum and maximum values when the dimpled surface is orientated upstream and downstream, respectively. For the same dimple design (k/D = 0.05), the numbers of dimples is expected to produce significant impact on the mean drag

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Fig. 5. Power spectra of fluctuating lift coefficient of the cylinder at different Reynolds numbers: (a) Smooth; (b) DF; (c) DHF; and (d) DHB.

coefficient of the cylinder. However, the present experimental results do not confirm this conjecture. For example, the C D value of DDF is lower than that of DF, while the C D value of DDHF is higher than that of DHF. It can be seen from Fig. 4 that the lift force on the cylinder oscillates and appears to be periodic, which is due to periodic vortex shedding from the cylinder. The magnitude of the oscillations can be characterized by their statistical properties such as the root-mean-square (r.m.s.) value. Fig. 7 shows the variation of C 0L (r.m.s. value of the lift coefficient) with Re. It can be seen clearly that the C 0L values are affected considerably by the dimple pattern as well as the orientation of the half dimpled surface with respect to the incident flow. For the higher-Re range (1.179  104 < Re < 1.758  104), C 0L of the DDF cylinder is generally lower than those of other cylinders, and is about 0.2 times of the smooth cylinder. For the lower-Re range (Re = 7.43  103), C 0L of the DHF cylinder is the lowest (about 0.4 times of the smooth cylinder).

Fig. 6. Variation of mean drag coefficient with Re for the smooth and dimpled cylinders.

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clearly show that the effectiveness of dimple patterns in reducing the mean drag and r.m.s. lift coefficients (C D and C 0L ) on the cylinder.

3.2. PIV results

Fig. 7. Variation of r.m.s. lift coefficient with Re for the smooth and dimpled cylinders.

In terms of reduction in C 0L , the DHF design appears more effective (within the Re range of the experiments). Figs. 6 and 7

PIV technique was used to measure the near-wake flow structure. Representative snapshots of the instantaneous vector plot for the smooth cylinder and the DH cylinder at Re = 1.798  104 are shown in Fig. 8. In order to better depict the intrinsic flow structure, contours of the spanwise vorticity are also superimposed. Basically, the flow behind the cylinder is characterized as Kárman vortex street. Fig. 8 shows a sequence of three instantaneous flow fields (with an interval of 2/15 s between two consecutive snapshots), which roughly represents a vortex shedding cycle with two shear layers alternately emanated from opposite sides of the cylinder and rolled up into discrete vortices. Obviously, there are appreciable differences between the two types of cylinder in terms of the size of the shed vortices and the interactions between upper and lower rows of vortices. As compared to the smooth cylinder, the vortices shed from the DF cylinder are less organized and the interaction between the vortices is also

Fig. 8. Representative snapshots of the instantaneous vector plot (superimposed with contours of spanwise vorticity) for the smooth and dimpled cylinders at Re = 1.798  104: (a) t = 0 s; (b) t = 2/15 s; and (c) t = 4/15 s.

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 2 of the cylinder at Re = 1.798  104 (a) smooth; (b) DF; (c) DHF; and (d) DHB. Fig. 9. Distributions of the normalized turbulent kinetic energy k=U e

weaker. As a manifestation, the vortices shed from the smooth cylinder have a significant transverse motion and periodically penetrate into the wake centerline, whereas the vortices shed from the DF cylinder move downstream largely horizontally with obviously less interaction. Through ensemble averaging the 1050 instantaneous velocity fields obtained for each case, the turbulence kinetic energy behind smooth and dimpled cylinders were obtained. Fig. 9 shows distri 2 ) at butions of the normalized turbulent kinetic energy (TKE, k=U e

Fig. 10. Amplitude spectra of transverse velocity (v) for the smooth and dimpled cylinders at Re = 1.798  104.

Re = 1.798  104. It could be seen that the TKE contours appear to be symmetric about the wake centerline. On average, the smooth cylinder has larger regions of TKE than the dimpled cylinders. For the case of the smooth and DHB cylinders, the peak values of TKE and contour plot areas are larger. The peak value of the smooth case is 0.247, while those of the DHB, DF and DHF cases are 0.237, 0.197 and 0.198, respectively. The area of contour line 0.2 for the smooth case is larger than that of the DHB case. There is no contour line 0.2 for the DF and DHF cases. For contour line 0.15, it is still a connected zone for the DHF case, while it becomes two small zones for DF case. The lower peak values and smaller sizes for the DF and DHF cases indicate that the interactions between the upper and lower shear layers are weaker as compared to the smooth case (similar conclusion is deduced from Fig. 8). This is also in accordance with the force measurement results that the mean drag coefficient of the smooth and DHB cylinders is much larger than that of the DF and DHF cylinders. The transverse velocity (v) at the point (x, y) = (2D, 0) on the wake centerline is retrieved and spectral analysis of fast Fourier transform (FFT) has been carried out to quantify the periodicity

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and strength of vortex shedding. Fig. 10 shows the amplitude spectra of v for both the smooth and dimpled (DF, DHF and DHB) cylinders at Re = 1.798  104. There is an obvious peaks at about St = 0.18 for the smooth cylinder, which is in good agreement with the literature as well as the results in Fig. 5, implying that the prominent peak in the lift spectra indeed corresponds to the vortex shedding from the cylinder. The peaks of all spectra are all around St = 0.18, indicating that the vortex shedding frequency does not vary much with the change in surface pattern. But the peak value of the smooth cylinder is much higher than the dimpled cylinders. The peak value of the smooth case is 0.144, while those of the DHB, DF and DHF cases are 0.102, 0.064 and 0.065, respectively. These results agree well with the TKE results. The results of the DF and DHF cases shows that dimpled surfaces could reduce the strength of vortex shedding from the cylinders. 4. Conclusions This paper presents the findings of an experimental study on the drag and lift forces and flow characteristics of a circular cylinder with smooth and dimpled surfaces. The results show that the effectiveness of the dimpled surface on the cylinder in reducing the mean drag and r.m.s. lift coefficients (C D and C 0L ). For the half dimpled cylinder, the orientation of the rough surface with respect to the incident flow is significant. The C D value is the lowest when the half dimpled surface is oriented toward the incident flow and is the highest when it is at the lee side of the cylinder. PIV results confirms that the dimpled surfaces could reduce the strength of vortex shedding from the cylinder, as evidenced by the size of the shed vortices and their interactions, velocity spectra, and distributions of the turbulent kinetic energy in the wake of the cylinder. Acknowledgment The funding support from the Singapore National Research Foundation (NRF) through the Competitive Research Programme (CRP, NRF-CRP5-2009-01) on this project is gratefully

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