Experimental study on flow past a rotationally oscillating cylinder

A series of experiments was carried out to study the flow behaviour behind a rotationally oscillating cylinder at a low Reynolds number (Re=300) placed in a recirculation water channel. A stepper motor was used to rotate the cylinder clockwise- and- counterclockwise about its longitudinal axis at selected frequencies. The particle image velocimetry (PIV) technique was used to capture the flow field behind a rotationally oscillating cylinder. Instantaneous and timeaveraged flow fields such as the vorticity contours, streamline topologies and velocity distributions were analyzed. The effects of four rotation angle and frequency ratios Fr (Fr=fn/fv, the ratio of the forcing frequency fn to the natural vortex shedding frequency fv) on the wake in the lee of a rotationally oscillating cylinder were also examined. The significant wake modification was observed when the cylinder undergoes clockwise-and-counterclockwise motion with amplitude of π, especially in the range of 0.6≤Fr≤1.0.


Introduction
The phenomenon of the vortex-induced vibration (VIV) of circular cylinders has been widely investigated in the theoretical aspect and offshore and ocean engineering applications, such as mooring lines, cables and risers, which is highly undesirable due to the increasing risk of the fatigue failure in engineering structures (Williamson and Roshko, 1988;Khalak and Williamson, 1996;Sarpkaya, 2004;Gabbai and Benaroya, 2005;Chaplin et al., 2005;Williamson and Govardhan, 2008). It is well known that the alternating vortex shedding from a circular cylinder gives rise to periodic changes in the pressure distribution on the cylinder surface, especially for the multi-cylinders, the dynamic responses of the VIV are found to be more complicated than those of a single cylinder, and the displacement or oscillation amplitude could be enhanced under some arrangements (Gohel et al., 2013;Wang et al., 2013Wang et al., , 2014Wang et al., , 2015. Therefore understanding how to control or suppress the vortex shedding and the resultant VIV is of considerable practical interest. Reduction of the VIV can be achieved with either active Re = U 0 D/υ or passive flow control. In the case of active flow control, the structure is either rotated or set in oscillatory motion as in Taneda (1978), Coutanceau and Ménard (1985), Massons et al. (1989), Filler et al. (1991 and Stansby and Rainey (2001). Tokumaru and Dimotakis (1991) observed four distinct flow modes depending on the forcing condition, and noted a significant reduction of the VIV at high forcing frequency with a high Reynolds number Re=1.5×10 4 (where , D is the cylinder diameter, U 0 is the free-stream velocity and υ is the kinematic viscosity). Similar behavior has also been documented by Thiria et al. (2006) using the laser induced fluorescence (LIF) and particle image velocimetry (PIV) technique at a low Reynolds number Re=150, for which the structure of the shed vortex and fluctuations of drag coefficients were found to be strongly affected by the forcing parameters, such as the forcing amplitude and the ratio of forced and natural frequencies of the vortex shedding. The effects of forcing parameters on the modification of the near-wake behind the rotational cylinder have also been investigated from the experiments performed in a closed-return type subsonic wind tun-nel at Re=4140 by Lee andLee (2006, 2008). According to the forcing frequency ratio F r , (defined as the ratio of the forcing frequency f n to the natural vortex shedding frequency f v ), three well-defined flow regimes -non-lock-on, transition and lock-on regimes were observed. Nazarinia et al. (2009Nazarinia et al. ( , 2012 extended the study of the purely rotational oscillation case and investigated the flow behavior behind a circular cylinder undergoing the combined translational and rotational oscillation. They found that both V r (the ratio between the translational and rotational velocities) and F r have significant effects on the synchronization of the nearwake vortex structures. Sellappan and Pottebaum (2014) investigated the effect of the rotary forcing on the vortex shedding and heat transfer in rotationally oscillating cylinders using the digital particle image velocimetry. The results indicate that the effects of rotary forcing frequency and amplitude on the heat-transfer rate were found to be quite profound under certain forcing conditions.
To our best knowledge, most of the reported experimental studies were focused on the flow around a rotational oscillating cylinder at high Reynolds numbers Re≥2000 (Tokumaru and Dimotakis, 1991;Fujisawa et al., 2001Fujisawa et al., , 2005Saad et al., 2007) or low Reynolds numbers Re≤185 (Thiria et al., 2006;Kumar et al., 2013). Only very few reported experimental studies were carried out to investigate the flow behaviour behind a cylinder undergoing periodic clockwise-and-counterclockwise rotation at Re=300. For instance, Taneda (1978) investigated how the wake of the two-dimensional flow past a circular cylinder can be substantially modified by high values of the control parameters for 30≤Re≤300. The experimental work by Taneda (1978) was focused on the investigation of the relationship between Reynolds number, critical forcing frequency and angular amplitude. Wu et al. (1989) investigated the effect of control parameters on a cylinder at Re=300, and they found that the control parameters strongly affected the fluid forces act-ing on the cylinder. It was realized after examining the existing literature that there are several questions which have either not been asked or only partially answered for this problem, such as what kind of flow patterns will appear when the cylinder is under a clockwise-and-counterclockwise rotation at Re=300? How will the rotational frequency ratio be affected by the flow pattern and structures? These questions are still unanswered fully today, and no attempt was made using the PIV technique to capture the flow fields in the lee of a cylinder under a clockwise-and-counterclockwise rotation at Re=300.

Experimental setup
The flow experiments were conducted in a recirculating open water channel at the Maritime Research Centre, Nanyang Technological University. The water channel was 6 m long with a rectangular cross-section of 0.3 m×0.4 m (W× H). Both the side walls and the bed of the water channel at the test section were made of glass to allow for laser optical access.
The model used in this experiment was a brass cylinder of the diameter D=30 mm, with a length of L=500 mm. The submerged length of the cylinder was L=300 mm, resulting in an aspect ratio of 10. Fig. 1 shows a schematic sketch of the experimental setup. A stepper motor was used to accomplish the clockwise-and-counterclockwise rotation of the cylinder about its longitudinal axis. The upper end of the cylinder extends out of the free surface of the water in the channel and is attached to the stepper motor. No end plate is used in this experiment, and the clearance between the lower end of the cylinder and the water channel bottom was about 15 mm, half of the cylinder diameter, which can be roughly considered as a two dimensional model, and the bottom effect could be ignored in the present work. The oscillation amplitude and frequency were precisely controlled using a programmable controller. The oscillation motion of the cyl- inder can be presented as follows: where θ is the angular position of the cylinder, θ A is the oscillation amplitude, f n is the forcing frequency, and t is time.
The freestream velocity was 0.01 m/s, and the corresponding Reynolds number , was 300. The experiments were performed at the pre-selected rotational frequency ratios from F r =0 to 2.0 at 0.2 increments. The preset oscillation amplitude was θ A =π. For the validation of the forcing frequency ratio used in the cases of a rotationally oscillating cylinder, the natural vortex shedding frequency f v for a stationary cylinder was also analyzed. Fig. 2 shows the power spectral density function Eu of the streamwise velocity fluctuations u at the downstream location x/D=2, y/D=0.5 for a single stationary cylinder. A significant peak is observed at f v =0.07 Hz, and the corresponding non-dimensional vortex shedding frequency is .
Flow field measurements were performed using a PIV system (LaVision model). Based on a compromise between the requirements of recording a large field of view and resolving detailed flow structures, the viewing area in this experimental study was chosen to be about 130 mm×180 mm downstream of the rotationally oscillating cylinder. A Quantel System double cavity Nd: YAG laser (power ~120 mJ per pulse, duration ~5 ns) was used to illuminate the flow field. The particle images were recorded using a 12-bit charge-coupled device (CCD) camera, which had a resolution of 1.6 K pixels×1.2 K pixels at a frame rate of 15 Hz. In the present study, the flow seeds using the neutrally buoyant hollow glass spheres (Spherocel® 110P8) with the approximate diameter of 10-15 µm as the tracer particles, which offered good traceability and scattering efficiency.
The LaVision Davis software was used for PIV analysis, to process the raw particle images and determine the flow fields. Velocity vectors were determined using the FFT (Fast-Fourier-Transform) method based on cross correlation algorithm with the standard Gaussian sub-pixel fit structured as an iterative multi-grid method. The processing procedure included two passes, starting with a grid size of 64 pixels×64 pixels, stepping down to 32 pixels×32 pixels overlapping by 50%. A set of 7500 vectors was obtained in the viewing area. Then a 3×3 median filter was applied to remove possible outliers in the vector map. The central vector will be replaced with the averaged vector obtained from the neighboring interrogation windows if it deviated by more than 5 times the RMS (root-mean-square) value of the eight surrounding neighbours. For the smoothing process, a 3×3 average filter was chosen to obtain the final vector maps. For each case, a set of 1050 frames of the instantaneous flow fields was acquired (i.e. 70 s recordings). Further details regarding the PIV post-processing can be found in Gao et al. (2010).

Results and discussions
In this section, the instantaneous and time-averaged flow characteristics in the near wake of a clockwise-andcounterclockwise rotationally oscillating cylinder are discussed. The time-averaged flow field is obtained by averaging all 1050 PIV snapshots. Owing to the shadow cast by the brass cylinder in the laser light sheet, a "blank out" region will appear behind the rotationally oscillating cylinder. Therefore, the flow field on the cylinder surface is limited to be considered in the present study.

Instantaneous flow patterns
The instantaneous vorticity contours behind the rotationally oscillating cylinder at different frequency ratios are shown in Fig. 3, where solid and dashed lines represent positive and negative values, respectively. An incremental value of the vorticity is 0.3. As can be seen in Fig. 3, the shear layer and vortex formations behind the rotationally oscillating cylinder strongly depend on the frequency ratio, and different vortex shedding modes are observed in the investigated frequency ratio range (0≤F r ≤2.0).
To obtain a better understanding of the variation of the flow patterns with F r , the flow field behind a stationary cylinder (F r =0) is presented for comparison. As shown in Fig.  3a and when the cylinder is stationary, two symmetrical vortex streets are observed with some small scale vortices shed in the downstream. When the frequency ratio is equal to 0.2 and 0.4 as shown in Figs. 3b and 3c, respectively, the shear layers separated from the rotationally oscillating cylinder appear to be approximately symmetrical about the wake centerline y/D=0, and a primary single shed vortex is generated in the wake. Compared with that of a stationary cylinder under the same flow condition, the vortex formation length is significantly reduced for the rotationally oscillating cylinder while the scale and strength of the vortex shed in the downstream (around x/D=3.0) appear to be amplified. GAO Yang-yang et al. China Ocean Eng., 2017, Vol. 31, No. 4, P. 495-503 When F r =0.6, as shown in Fig. 3d, the flow pattern behind the rotationally oscillating cylinder behaves differently from those with smaller frequency ratios, where the shear layers separated from both upper and lower sides of the rotationally oscillating cylinder are deflected upwards, producing a skewed or asymmetric flow pattern. A vortex structure with negative vorticity is shed from the upper side of the cylinder and multiple vortex structures with positive vorticity are observed in the downstream wake. A similar deflection phenomenon of shear layers is also observed at F r =0.8 and 1.0. When F r =0.8, the vortex formation length for the deflected shear layers appears to be reduced while the scale of the primary vortex with negative vorticity shed from the rotationally oscillating cylinder is increased. When F r equals to the lock on frequency ratio of 1.0, i.e. when the forcing rotationally oscillating frequency f n synchronizes with the vortex shedding frequency f v , the vortex formation length is further reduced, while the scale and vorticity strength of primary vortex become much larger, and the vortex shedding takes place closer to the cylinder surface.
Furthermore, it is important to consider not only the patterns of the vortex formation associated with the lock-on phenomenon, but also the flow behavior beyond the lock-on region to elucidate the different flow characteristics. As F r increases further and equal to 1.2, i.e. beyond the lock-on region, one observes different vortex shedding mode from that at F r ≤1.0, in which a pair of vortex structures with opposite signs are shed from the rotationally oscillating cylinder. Unlike the cases at F r ≤1.0, the scale of the primary shed vortex now decreases with F r instead. Moreover, the vortex formation length also decreases with F r and the rolling up of shear layers occurs much closer to the cylinder surface and with smaller vorticity strength. Similar flow patterns can also be observed at F r =1.4 and 1.6 as shown in Figs. 3h and 3i, respectively. When F r =1.8 and 2.0, as can be seen in Figs. 3j and 3k, respectively, double-row vortices are observed to shed into the wake. The scale of the shed vortex is smaller, plausibly caused by the diffusion of the vorticity with the increasing frequency ratio.
In summary, it appears that a cylinder in rotation has a strong effect on the near wake formation and the vortex shedding mode. According to the rotationally oscillating frequency ratio, the flow patterns may be grouped into four different categories: a symmetric flow pattern at small fre- quency ratio F r ≤0.4; a single vortex shedding mode at lock-in regime 0.6≤F r ≤1.0, parings of the vortex shedding mode at 1.2≤F r ≤1.6; two rows of vortex wake structures at high frequency ratios 1.8≤F r ≤2.0. Generally the vortex formation length decreases with the increasing rotation frequency ratio. Fig. 4 shows the power spectrum of the streamwise velocity behind a rotationally oscillating cylinder at the downstream location x/D=2.0, y/D=0.5 with different frequency ratios. At a small frequency ratio F r =0.2, a single dominant peak is observed at the forcing rotational oscillation frequency f n ≈0.2f v , with a value of 0.014 Hz, and another smal-ler peak is associated with the vortex shedding frequency f ov =0.043 Hz. When F r increases to 0.4, two peaks are observed in the power spectra, the prominent peak occurs at the oscillation frequency f n ≈0.4f v , and another smaller peak appears at the vortex shedding frequency f ov =0.085 Hz, larger than the natural vortex shedding frequency for a stationary cylinder. With the increase of F r to 0.6 and 0.8, two distinct peaks are observed at the rotational oscillation frequency f n =0.6f v and f n =0.8f v , respectively, while another peak corresponding to the vortex shedding frequency is observed at f ov =0.1 Hz, which is also larger than the natural vortex shedding frequency for the stationary cylinder.

Spectral analysis
When 1.0≤F r ≤1.8, the vortex shedding frequency appears to be synchronized with the rotational oscillation fre- Fig. 4. Power spectrum of streamwise velocity behind a rotationally oscillating cylinder at different frequency ratios. quency, a pronounced peak is observed at the forcing rotational oscillation frequency, consistent with the previous findings showing the lock-on phenomenon (Lee and Lee, 2006). When F r increases to 2.0, two dominant peaks are observed at the oscillation frequency f n =2.0f v and natural vortex shedding frequency f ov =0.07 Hz, respectively. From the power spectrum, it can be seen that for F r <1.0, two dominant peaks are observed at the rotational oscillation frequency and vortex shedding frequency, respectively, except F r =0.2. The vortex shedding frequency appears larger than the natural vortex shedding frequency for a stationary cylinder due to the effect of rotational oscillation. For F r ≥1.0, a dominant peak appears at the forcing rotational oscillation frequency except F r =2.0. 5 shows the non-dimensional time-averaged vorticity contours behind a rotationally oscillating cylinder for a fixed rotation angle of π over a range of frequency ratios F r =0-2.0. The study shows that for each frequency ratio, a pair of "recirculation" contour zones with positive and negative values are formed. They are symmetrical about the wake center line y/D=0, and the vorticity decreases gradually from the maximum at the vortex core, to nearly unity at the outer part of the vortex. It can be seen from Fig. 5 that different time-averaged flow patterns are obtained by varying the frequency ratios. The formation length appears to be suppressed with F r for 0<F r ≤1.0. Thereafter, the formation length is elongated with F r for 1.2≤F r ≤2.0. Compared with a stationary cylinder, a short vortex formation length is observed at F r ≤1.0, where the shortest length is observed at F r =0.6, with the length of 1.0D. In most cases, the time-averaged vorticity contours appear to be elliptical. However at v=1.0, the wake exhibits two vortex structures with sharp edges. As the frequency increases above 1.0, the formation region elongates. The vorticity formation length increases with F r as well, and reaches the maximum value of 3.2D at F r =1.8, similar to that behind a stationary cylinder. The authors noted that the vortex suppression is best exemplified when the frequency of the rotation is near the lock-on frequency which had been identified as 0.6<F r <1.0, as can be seen in Fig. 5.

Effects of rotation frequency on time-averaged flow field
Moreover, compared with a stationary cylinder, the maximum ω * associated with the negative vorticity contours appear to be strengthened when 0<F r ≤1.0 except the case of F r =0.6. In contrary, the maximum ω * at the range of 1.2≤F r <2.0 appears to be lessened. While the maximum ω * associated with the positive vorticity contours seems to be larger than the stationary one. Fig. 6 shows the time-averaged streamline topologies at different values of F r . It can be observed that the rotational oscillation of the cylinder destroys the symmetry of the streamline structures, and significantly affects both the velocity distribution and the trajectories of the eddy cores.

Time-averaged streamline topologies
Different time-averaged flow structures are also observed behind a rotationally oscillating cylinder as the frequency ratio changes. For a stationary cylinder (F r =0), two closed recirculation zones composed of two eddies symmetrical about the wake centerline y/D=0 are observed. The upper eddy rotates clockwise while the lower one rotates anticlockwise (up-down orientation according to Fig. 6). Even at a small rotationally oscillating frequency ratio F r =0.2, the symmetry of the two recirculation zones has been destroyed. As can be seen in Fig. 6b, the lower eddy is larger, rotates anticlockwise and appears to dominate the flow field in the near wake region. When the frequency ratio increases to 0.4 (see Fig. 6c), the flow structure becomes more asymmetrical, and the clockwise upper eddy vanishes, leaving only a closed anticlockwise eddy at the lower side. A further in-crease of F r to 0.6 and 1.0 brings the flow into the lock-on region, but no closed eddy formation is observed on either side of the rotationally oscillating cylinder.
Beyond the lock-on region, when F r increases to 1.2, two large-scale, approximately symmetrical, eddies appear behind the cylinder in contrast to the case of F r =1.0. At a larger frequency ratio F r =1.4, a larger upper eddy and a smaller lower eddy are observed in the wake. When F r increases to 1.6, the lower anticlockwise eddy appears to dominate the flow field in the near wake region. Further increase of F r to 1.8 and 2.0 makes the increasing the formation of asymmetrical recirculation zones and small scale eddies. It is also observed that the centre of the eddy formation moves closer to the surface of the rotationally oscillating cylinder. GAO Yang-yang et al. China Ocean Eng., 2017, Vol. 31, No. 4, P. 495-503 501 3.5 Mean velocity distribution The mean streamwise velocity and root mean square streamwise velocity distributions behind a rotationally oscillating cylinder at different frequency ratios were extracted from the time-averaged velocity fields. Figs. 7a and 7b depict the lateral distribution of the mean streamwise velocity and root mean square streamwise velocity with the frequency ratio F r at x/D=1.0 behind the rotationally oscillating cylinder, respectively. For each frequency ratio, the mean streamwise velocity distribution is symmetrical about y/D=0.ū /U 0 As shown in Fig. 7a, close to the surface of the rotationally oscillating cylinder, and at x/D=1.0, no apparent difference in the trend of versus the frequency ratio F r can be discerned. As expected, the values of at most of the frequency ratios attained negative values in the recirculation region behind the rotationally oscillating cylinder except those at 0.6≤F r ≤1.0, for which there was no indication of the existence of reverse flow in the lee of the rotationally oscillating cylinder. Take the case of F r =1.0 for example,ū /U 0 the minimum value of at F r =1.0 is found to be positive and much larger than those at other frequency ratios and at the wake centerline y/D=0. It is in accordance with the observation from the time-averaged streamlines topology, where no recirculation zones composed of closed eddy are observed. It can be seen that the shear layer instability is greatly affected by the rotational oscillatory motion of the cylinder, in an agreement with Lee and Lee (2007) and Filler et al. (1991), which they suggested that the shear-layer (secondary) vortices were generated due to the rotational oscillatory motion of the cylinder, and the instability can effectively change the formation length of the mean recirculation and the zone of absolutely unstable wake. Beyond this location, the streamwise mean velocity increases gradually. The streamwise mean velocity at F r =1.0 appears to be larger than those at other frequency ratios along the vertical direction. This observation may be attributed to the acceleration of the fluid adjacent to the cylinder surface as a result of the synchronization of the forced rotational frequency and vortex shedding frequency.
It can be seen in Fig. 7b, and at a location close to the surface of the rotationally oscillating cylinder, that the lateral distribution of the root mean square velocity at low frequency ratios F r ≤1.0 appears distinctly different from those at high frequency ratios 1.0<F r ≤2.0. The root mean square velocity exhibits an approximately M-shaped profile with double-peaks which are symmetrical about the wake centerline y/D=0 for F r ≤1.0; while an irregular distribution of is observed for 1.0<F r ≤2.0. The double peak values for F r ≤1.0 at around y/D=0.5 and -0.5 appear to increase with the frequency ratio, from at F r =0.2 to at F r =1.0. In contrast, for 1.0<F r ≤ 2.0, the value of at the location y/D=-0.5 appears to decrease with F r .

Conclusions
A series of experiments using the PIV technique was performed to investigate the flow past a rotationally oscillat-ing cylinder in a recirculating open water channel. The effect of the forcing frequency ratio on the instantaneous and time-averaged flow fields behind the rotationally oscillating cylinder was analyzed. It was observed that when the cylinder undergoes clockwise-and-counterclockwise rotation with θ A =π, the wake flow behind the rotationally oscillating cylinder is modified significantly, and accompanied by asymmetry of the streamline structures. The change in the flow pattern has significant influence on the velocity distribution and the trajectories of the eddy cores. Compared with the flow pattern in the wake of a stationary cylinder, the size of the vortex formation region behind the rotationally oscillating cylinder is significantly reduced in the vicinity of F r =1.0, whereas it is found to be elongated for F r >1.0. It is noted that the streamlines depicted a pattern very similar to that of ideal flow past a cylinder and without separation at the lock-on frequency ratio F r =1.0. It can be concluded that when the cylinder undergoes clockwise-and-counterclock- wise rotation with θ A =π at F r =0.6, 0.8 and 1.0, the vortex shedding behind the circular cylinder is modified significantly, and would lead to an enhancement of interaction between the large scale vortices.