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Investigation on the effectiveness of helical strakes in suppressing VIV of flexible riser
Applied Ocean Research 44 (2014) 82–91
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Investigation on the effectiveness of helical strakes in suppressing VIV of flexible riser Lee Kee Quena , * , Aminudin Abua , Naomi Katob , Pauziah Muhamada , Asnizah Sahekhainia , Hanida Abdullaha a b
Intelligent Dynamic and System I-kohza, Malaysian-Japan International Institute of Technology, Universiti Teknologi Malaysia, Malaysia Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, Japan
a r t i c l e
i n f o
Article history: Received 8 August 2013 Received in revised form 24 October 2013 Accepted 23 November 2013 Keywords: Vortex-induced vibration Helical strakes Flexible cylinder Suppression
a b s t r a c t The effectiveness of the strakes in suppressing the vortex-induced vibration (VIV) of a long flexible cylinder is investigated by varying the pitch (p) and height (h) of the strakes. Measurements of cross-flow (CF) vibration amplitude, in-line (IL) and CF frequency responses, and hydrodynamic forces are presented for low mass flexible cylinders with helical strakes. Cylinders with aspect ratio of 162 were applied with constant pretension to restrict the vibration in IL and CF directions. Six cases with about 180 runs were executed under subcritical Reynolds number (Re = 0.144 to 1.384 ) of uniform flow. Calculation on the laminar boundary layer thickness around a circular cylinder was performed as a benchmark in deciding the height of strakes. Present study shows that at certain strakes’ height which is larger than the laminar boundary layer thickness, significant VIV mitigation is found. However, the suppression effectiveness of helical strakes on flexible cylinder is less notable compared to a rigid cylinder. The change on pitch of strakes affects the occurrence of lock-in region and prevents the frequency to switch into higher mode. On the other hand, increase on the height of strakes narrows the lock-in region and plays the most major role in suppressing the vibration of a cylinder. The hydrodynamics forces indicate an unexpected phenomenon where the bare cylinder possesses higher force coefficients compared to cylinders with helical strakes. However, large drag penalty is still found in a particular case at higher reduced velocity. The most effective configuration of strakes in terms of the dynamic responses is p = 10D and h = 0.15D model. However, model of p = 10D and h = 0.10D performs better in reducing the hydrodynamic forces. c 2014 Elsevier Ltd. All rights reserved.
1. Introduction Interaction between fluids and riser, which associates with vortexinduced vibrations (VIV), is subjected to substantial research in both industries and academic field during the past few decades due to the high demand in exploring hydrocarbon resources [1–3]. The VIV can be explained as the vibration motion excited by vortices of external fluid flow interacting with the structure. When the shedding frequency of the vortices formed behind the structure synchronizes with the natural frequency of the structure, lock-in is induced and it is usually accompanied by significant vibration. If the riser vibrates under synchronization for a long period, it might considerably reduce the fatigue life of riser, and consequently cause detrimental effects. In addition, as the exploration of the hydrocarbon resources has been moved into deeper water, longer riser with higher aspect ratio is increasingly required, which leads to the high risk of VIV. Numbers of attempts to understand the phenomenon of VIV of long riser are found in the literature. Xue et al. [4], for example, developed a simplified
* Corresponding author. Tel.: +60 126877052. E-mail address: [email protected] (L.K. Quen).
c 2014 Elsevier Ltd. All rights reserved. 0141-1187/$ - see front matter http://dx.doi.org/10.1016/j.apor.2013.11.006
empirical model to investigate the influence of current flow, diameter and length towards the fatigue damage of a top-tensioned riser, and found that added mass and reduced velocity are the significant variables that affect the response frequency of VIV. Sanaati and Kato [5] varied the pre-tension and stiffness of a flexible cylinder to obtain its dynamic responses, and revealed that high pre-tension leads to high hydrodynamic lift forces. Modarres-Sadeghi et al. [6], who analysed the chaotic responses of long riser, discovered that long riser possesses high possibility of experiencing simultaneous excitation of several modes. In order to reduce the VIV of riser, various suppression devices are introduced. In general, they can be classified into (i) surface protrusions type where the cylinder surface is modified [7–9] and (ii) near-wake stabilizers type where obstacle is positioned in the near wake of cylinder [10–12]. Among these devices, helical strake, which is under the first category, is one of the most common devices implemented in riser application. Although some experimental researches discuss the effectiveness of the strakes [13–15], the available results are limited to short rigid cylinder, which is defined as a cylinder that is inflexibly mounted and the allowable motion is in cross flow (CF) direction only. The performance of flexible cylinder that can withstand both cross-flow and in-line movements, especially with high
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Table 1 Model parameters. Outer diameter (D) Inner diameter (d) Length (L) Pre-tension (T) Bending stiffness (EI) Spring stiffness (ks ) Cylinder axial stiffness (EA/L) Cylinder air weight Total weight including internal water (m) Mass ratio (m* =4m/ρπ D2 ) (Structural + viscous) damping ratio (z) Applied strakes’ height (h) Applied strakes’ pitch (p) Number of helix Flow speed (U) Subcritical Reynolds number range (Re)
18 mm 13 mm 2.92 m 147 N 9.0 Nm2 6.5 N/mm 100 N/mm 1.64 N/m 2.97 N/m
Fig. 1. Flexible cylinder with three-start helical strakes.
1.17 0.028 0.05D, 0.10D, 0.15D 5D, 10D, 15D 3-start helical 0.1–1.0 m/s 1380–13,800
Fig. 2. Position of pairs of strain gauges on a square cross-sectioned rod.
aspect ratio and low mass ratio is still scarce. To the knowledge of the authors, detailed discussion on the hydrodynamic forces of a long flexible cylinder based on different configuration of strakes is still inaccessible. Therefore, in the present study, we aim to focus on the effectiveness and force responses of helical strakes on a long flexible cylinder in uniform cross-flow. Parameters of vibration amplitude, frequency responses as well as hydrodynamic forces are of interest. In the following sections, the experimental details and the parameters are discussed and these are then followed by a brief conclusion. 2. Experimental details [17] The experiment was conducted in the towing tank of the Department of Naval Architecture and Ocean Engineering of Osaka University. The experiment basin is 100 m × 7.8 m × 4.35 m in length, width and depth, respectively. The cylinder models were horizontally installed, and were submerged in water with 0.35 m from the still-water level in order to avoid the influence of free surface on the response of cylinders. The cylinders were towed by the carriage to generate the specified uniform flow from 0.1 m/s to 1 m/s, as shown in Table 1 with interval of 0.03 m/s, providing the subcritical Reynolds number range from 1380 to 13,800. Because of the limited size of the towing tank and operational characteristic of the towing carriage, the cylinders can only be examined in the sub-critical range of Reynolds number. However, the findings can be directly applied to real world riser at much higher Reynolds numbers as the increase of Reynolds number does not affect the performance of helical strakes. This is due to the fact that the separation points of the flow remain the same for various Reynolds number [27]. In addition, it was proved that the drag coefficient of a cylinder with strakes was practically unchanged over sub-critical, critical and post-critical flow condition, as cited by Simantiras and Willis [21]. More description of the experimental facility can be referred to [16]. A poly vinyl chloride (PVC) cylinder was chosen as riser model as it offers high flexibility with low bending-dependence. Universal joints were used to pin the both ends of cylinder in order to allow the bend of cylinder in IL and CF directions, but constrained in torsion. One of the cylinder ends was allowed no translational movement, while the other end was free to move in axial direction. At the sliding end (movable end), a constant pre-tension of 147 N was applied to provide a tension-dominated cylinder model. More details about the setting of cylinder and the pre-tension can be referred to [17]. The helical strakes were made of rubber and were designed to have three-start helical, as illustrated in Fig. 1. The height of strakes was designed by considering the laminar boundary layer thickness of a circular cylinder. Based on Pohlausen’s
approximation on a circular cylinder [18], the thickness of the boundary layer, y can be estimated by:
VL =
y R
u∞ R v
(1)
where VL is the boundary-layer velocities, R, u∞ and ν denote radius of cylinder, velocity and kinematic viscosity, respectively. Since the Pohlausen’s approximation is based on the assumption that the ambient flow has no separation while strong interaction is actually observed between the ambient flow and separation in real condition, large angle of separation point, 103.14◦ is chosen in present study. The calculation shows that the boundary layer thickness is about 0.06D, where D is the outer diameter of cylinder. In general, height of 0.05– 0.2D is accepted as optimal in the industries. Based on this statement and by considering the laminar boundary layer thickness, three configurations of heights, 0.05D, 0.10D and 0.15D were selected in the present study to investigate the influence of the height of strakes in suppressing the VIV of flexible cylinder. The specification of the cylinder and the strakes are listed in Table 1. The vibration amplitude in CF direction was measured using underwater CCD camera. The camera was installed at the centre of the cylinder, with location of approximately 20D (diameter) downstream and above of the cylinder in order to avoid the wake interference. The video data recorded by the camera were sampled at 30 Hz. Only the responses at the centre of the cylinder were recorded. Before running the experiment, calibration on camera within allowable motions was conducted in three-dimensions. The analyses of video data recorded by the above and downstream camera were done simultaneously by using PcMAG, a motion tracking commercial software. To identify the strain bending moment in IL and CF directions, two half-bridge strain gauges were installed on a square cross-section rod in each direction at a specified distance, d of 3 cm, which result in a total of eight strain gauges of four stations for measurements, as shown in Fig. 2. The sampling rate of bending was 200 Hz, which was adequate to obtain accurate measurement. Since unsolicited noises were generated during the experiment, the analogue measured data had to be prepossessed by applying low-pass filter of 100 Hz cut-off frequency, before converting it to digital data. A total of 180 runs based on six cases were measured for bare cylinder and all configurations of strakes. The combinations of the strakes arrangement are: pitch p = 10D height h = 0.05D; p = 10D h = 0.10D; p = 10D h = 0.15D; p = 5D h = 0.10D and p = 15D h = 0.10D. The duration to collect measurements starting from still water was 75 s, but the analysis was only based on the data after speeded to a
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Table 2 Natural frequencies of cylinders with various configurations of strakes.
Configuration of strakes No strakes (bare cylinder) 3 strakes pattern, p = 5D, h = 0.10D p = 10D, h = 0.10D p = 15D, h = 0.10D p = 10D, h = 0.05D p = 10D, h = 0.15D
Mass (kg)
Natural frequency, Fn (measured/analytical value)
0.484
2.91/2.92
0.588
2.80/2.82
0.595 0.544 0.559 0.636
2.78/2.82 2.89/2.86 2.76/2.85 2.67/2.78
constant value. 10 min breaks were taken between each run in order to avoid the flow transient effects. Free decay test was conducted before starting the experiment for bare cylinder as well as cylinders with strakes in order to obtain the natural frequencies by imposing an initial displacement on the cylinder and then released it. Since the mass of the cylinder with strakes are different due to the additional mass of the strakes, the natural frequency of each cylinder is slightly different from each other, as shown in Table 2. The natural frequency of cylinder in water can also be identified by using the analytical method as shown below: 2 2 n 2 T EI n π + ≈ f n n = 1, 2, 3, . . . (2) 2 2 mL 2 mL 4 where T and L are the tension and length of cylinder respectively, EI is the bending stiffness and m is the mass per unit length (include addedmass, ma where the added-mass coefficient is assumed to be 1). Table 2 shows that the measured natural frequencies are in consistency with the analytical values. 3. Results and discussion 3.1. Vibration amplitude responses In the following section, the responses of bare cylinder of present study are included as a basis of comparison. Fig. 3 indicates the vibration amplitude ratio of bare cylinder and cylinder with different pitch and height of strakes versus the reduced velocity. The amplitude ratio is calculated by using standard deviation of the time series of displacement and divided by the diameter of cylinder (A* = Astd /D) while the reduced velocity is defined as Vr = u/fn D. A well-known amplitude trend for a bare cylinder with low mass-damping ratio; the initial, upper, lower and desynchronization branches with two obvious peaks can be easily seen in the figure. By applying the strakes on bare cylinder, the characteristics of amplitude branches with two obvious peaks have been altered into only one significant peak by eliminating the lower branch in the lock-in region. Fig. 3a shows no remarkable reduction on the amplitude ratio as the pitch of strakes increases, with maximum amplitude ratio range of 0.2–0.3. This can be understood by the effect that the amplitude of vibration can only be suppressed if the formation of the regular vortices behind the pipe is disrupted by the change of boundary layers separation, which results in the shrinking of separated vortex region [19] and prevent the interaction of shear layers [13]. By changing the pitch of strakes, it only alters the coverage of the strakes of cylinder surface which gains less effect on the separation of boundary layers. There is an optimum angle of strakes that is able to reduce the amplitude responses of a cylinder and suppress the occurrence of higher mode frequency based on the condition of the cylinder. In general, the optimal pitch of strakes used in industries is about p = 5D. Recent study by Simantiras and Willis [20] suggested that p = 15D is as effective as p = 5D for a rigid cylinder. However, for a long flexible cylinder with low mass ratio, p = 10D is apparently more effective in
Fig. 3. (a) Amplitude response of cylinder with different pitch of strakes and (b) amplitude response of cylinder with different height of strakes.
suppressing the vibration amplitude based on Fig. 3a as the amplitude of p = 10D model is smaller than p = 15D model. Fig. 3b shows that strake with p = 10D h = 0.15D has successfully suppressed the vibration of the cylinder to around 0.1 of amplitude ratio, which is about 72% reduction of the amplitude. In comparison with a rigid cylinder, however, the effectiveness of strakes on a flexible cylinder is less, as up to 90% of the amplitude can be suppressed for a rigid cylinder with the same strakes configurations [14]. The least amplitude suppression is found in p = 10D h = 0.05D model, with reduction of 46% of amplitude. From the theoretical calculation (1), it is found that the boundary layer thickness for a cylinder is around 0.06D. We can suppose that strakes with h = 0.10D are sufficient to disrupt the flow boundary layer and significantly reduce the amplitude of vibration. However, Fig. 3b shows that only 58% of amplitude reduction is achieved for p = 10D h = 0.10D model. At higher velocity, all types of strakes are able to suppress the cylinder vibration to 0.1 of amplitude ratio. Offshore structures, especially for those which experience high flow current, lock-in condition is undesirable but unavoidable. Therefore, it is essential to discover an effective tool to minimize the vibration within this critical region. As a whole, the lock-in bandwidth reduces considerably as the strakes are installed. Fig. 3a indicates that increasing the pitch of strakes delays the occurrence of lock-in phenomena but slightly increases the lock-in bandwidth. On the other hand, the synchronization is obviously suppressed with a narrower lock-in bandwidth as the height of strakes increases, as shown in Fig. 3b. This result suggests that the height of strakes delays the separation of boundary layer which indirectly postponed the interaction between the shear layers that were generated behind the cylinder. This finding is in agreement as proposed by Zhou et al. [13] who suggested that strakes produced shear layers that interacting far from the cylinder. Besides, larger height of strakes widens the shear layers which prevent the interaction between them, similar as reported by Korkischko and Meneghini [7]. Therefore, the formation of regular vortices can be evaded and the VIV of cylinder can be suppressed. Based on the aforementioned descriptions, it can be concluded that
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the change of height of strakes contributes in suppressing the VIV amplitude and lock-in region more than the change of pitch of strakes. 3.2. Frequency responses For the purpose of comparison, the frequency responses of IL and CF directions for strakes with different heights and pitches are analysed in this section. Only the dominant frequency is considered in each case by using Fast Fourier Transform (FFT) based on the time series of hydrodynamic forces data. The IL-to-CF frequency ratio is presented as well to identify the relationship between the IL and CF responses. Fig. 4a, which displays the IL frequency ratio of cylinder with different strakes’ pitch configurations, indicates that all of the strakes configurations are able to suppress high mode frequency into a lower value during the lock-in region. Fig. 4b, on the other hand, indicates the CF frequency ratio of cylinders with different pitch of strakes at low velocity is similar because the high frequency mode in lock-in region is suppressed in all of the cases. The increase of the pitch slightly delays the CF frequency mode from entering into lock-in region. In general, the distribution of the strakes along the cylinder is highly correlated to the angle of flow attack towards the cylinder surface. According to Blumberg et al. [25], the angle of flow attack affects the responses of the cylinder and there is an optimum angle (pitch) in reducing the responses of the cylinder. In the present study, the frequency responses of p = 10D h = 0.10D strakes possesses the narrowest lock-in region (4.6 < Vr < 10.6) based on Fig. 4. Besides, p = 10D h = 0.10D model is able to keep lower IL frequency values while the rest switch between high and low mode dominant IL frequencies at higher reduced velocity. These observations designate that p = 10D h = 0.10D model has the optimum angle of attack and hence performs better in suppressing the high frequency modes. On the other hand, the larger the height of strakes as displayed in Fig. 5a is, the higher the effectiveness of strakes in suppressing the high mode IL frequency of cylinder is. At higher reduced velocity, the IL frequency of p = 10D h = 0.05D strakes is unable to be suppressed while p = 10D h = 0.10D and p = 10D h = 0.15D strakes are able to maintain the IL frequency ratio to less than 2.5 throughout the velocity range. Fig. 5a and b indicates that the IL and CF frequency ratio of p = 10D h = 0.15D model is scattered around 1. The reason for the phenomena is that the p = 10D h = 0.15D model is randomly vibrates without synchronizing with the natural frequency of cylinder. Therefore, it is able to eliminate the lock-in region and is capable to inhibit the occurrence of higher mode and secondary lock-in at high speed. These phenomena are unable to be achieved by the other configurations. As a result, p = 10D h = 0.15D model possesses remarkable ability in suppressing CF responses. Although p = 10D h = 0.10D model is unable to remove the lock-in phenomena based on Fig. 5b, it reduces the values of high mode IL frequencies. No significant reduction of CF frequency is found also for p = 10D h = 0.05D model. In fact, higher CF mode, which is even larger than the bare cylinder, is discovered in p = 10D h = 0.05D model at higher reduced velocity. This proves that the height of strakes should be greater than the boundary layers thickness (0.06D) in order to disrupt the vortices formation and prevent severe vibration from the cylinder. For the low reduced velocity range from 2 to 6, which belongs to the initial and upper branches of the vibration amplitude, the IL-to-CF ratio of bare cylinder varies significantly, where it increases rapidly from 1 to 4 and then fluctuates slightly at 3 before decreasing to 2, as shown in Fig. 4c. The varying of IL-to-CF ratio indicates the formation of irregular and unstable vortices in the near wake of cylinder. After passing the maximum vibration amplitude (Fig 3a), the IL-to-CF ratio decreases and maintains at 2 throughout the velocity range, denoting the creation of regular vortices. It is a well-known fact that the IL frequency response should be twice of CF frequency response for a bare cylinder. However, the condition changes as the strakes are applied
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to it. The IL-to-CF ratio of all configurations of cylinder with strakes (Figs. 4c and 5c) is one throughout the synchronization (4.5 < Vr < 11). This demonstrates that the strakes are able to suppress the high mode vibration during lock-in where both IL and CF responses are in the same frequency. At higher speed, however, only p = 10D h = 0.10D and p = 10D h = 0.15D models are able to remain this ratio. The low IL-to-CF frequency ratio indicates the cylinders are in low vibration mode with less vibration intensity which is generated by the vortices. This can be proved by referring to their power spectral density (PSD) in IL and CF directions, as shown in Fig. 6 where significant peak with substantial PSD values are found for a bare cylinder and p = 10D h = 0.05D model. In contrast, p = 10D h = 0.10D model shows far smaller PSD value while no peak is observed in p = 10D h = 0.15D model. The trajectory of bare cylinder, which is obtained by taking the IL and CF displacement at the centre of the cylinder simultaneously, shows a classical eight-shape trajectory as a result of IL-to-CF frequency ratio of 2. The application of strakes, which leads to the ILto-CF frequency ratio of 1, indicates the suppression of eight-shape trajectory into crescent (Fig. 7b) or circular trajectories (Fig. 7c–f). Among these strakes, p = 10D h = 0.15D model displays the smallest oscillation in IL as well as CF directions. The capability of p = 10D h = 0.15D model in controlling the low IL-to-CF frequency ratio throughout various speeds and displaying insignificant motion trajectory proves that it is the most effective strakes configuration in suppressing the frequencies of the cylinder. Based on the frequency and amplitude responses (Figs. 3–5), it can be seen that the flexible cylinders with strakes are still experiencing lock-in phenomena, except for p = 10D h = 0.15D model, which is in contrast with the rigid cylinder [13]. It may be due to the low mass ratio of the cylinder and the flexible end condition of cylinder which complicates the interaction between the cylinder and fluids. Similar condition was also reported by Bearman and Brankovic´ [26], where for a cylinder with strakes, 2S and 2P mode of shedding were identified at reduced velocity of 4.92 and 6.3, respectively. They also suggested that the behaviour of a low mass ratio of cylinder with strakes is similar to a bare cylinder, but with smaller amplitudes. 3.3. Hydrodynamic forces Hydrodynamic forces are some of the important parameters that need to be considered in evaluating the performance of suppression devices. It is commonly weighed in terms of mean drag coefficient (Cdmean ), fluctuating drag coefficient (Cdfluct ) and fluctuating lift coefficient (Clfluct ). The Cdmean and the fluctuating terms of Cdfluct and Clfluct can be obtained by taking the mean and standard deviation of the force data which are then divided by the length of the cylinder that were exposed to constant velocity, as expressed in Eqs. (3)–(5) respectively. C d mean =
F d mean 1/2ρ U 2 LD
(3)
C d fluct =
F d std 1/2ρ U 2 LD
(4)
C l fluct =
F l std 1/2ρ U 2 LD
(5)
Fd mean , Fd std and Fl std denote the mean drag force, standard deviation drag force and standard deviation lift force, respectively, which are decomposed from the total forces. The ρ , U, L and D represent the density, the flow velocity, the length of cylinder, and the diameter of cylinder, respectively. In the analysis, the drag of 0.1m/s is discarded due to the large initial forces that lead to the enormous drag coefficients.
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Fig. 4. Frequency ratio of cylinder with different pitch of strakes: (a) IL frequency ratio, (b) CF frequency ratio and (c) IL-to-CF frequency ratio.
Table 3 Average mean drag coefficient of cylinders with various strakes configurations. Strakes configuration
C d mean
Bare p = 10D,h = 0.05D p = 10D, h = 0.10D p = 10D,h = 0.15D p = 5D,h = 0.10D p = 15D,h = 0.10D
2.654 2.079 1.604 1.656 1.629 1.881
3.3.1. Drag force coefficient (Cd mean ) The Cd mean of the bare cylinder in present study are in good agreement with the experimental data of Sanaati and Kato [5], where a very similar trend is found, but with slightly higher values of Cd mean . The average Cd mean of the bare cylinder throughout the entire velocity range of the present study is 2.654 (Table 3), which is larger than those of short rigid cylinder that undergoing force and free motions. The same condition was also reported by Vandiver [22] where the Cd mean of a flexible rope excessed three under uniform flow during lock-in condition. This may be due to the end condition of the flexible cylinder where instead of fixing both end of cylinder, the movement of cylinder is unconstrained in IL and CF direction. Therefore, large amplification of VIV with higher drag forces is generated. Fig. 8a indicates the values of Cdmean of all pitch configurations
of strakes and bare cylinder is at the highest in the lock-in region (4.5 < Vr < 11), which is in good agreement with [22,23]. However, as the reduced velocity increases, the value of Cd mean remains at a high value, which is in contrast with the result reported by Huera-Huarte and Bearman [23] where the drag reduces to a lower value that is similar to a stationary cylinder. The values Cd mean of different pitches are lower than the bare cylinder in the lock-in region, in particular, the strakes of p = 5D h = 0.10D has the smallest fluctuation. As the condition moves from lock-in to lock-out (Vr > 11), the values Cd mean of strakes with different pitches tend to remain constant at higher reduced velocity. This designates that the Cd mean is not affected by the changes of speed in the lock-out region. Based on Fig. 8a and b, only p = 10D, h = 0.05D model experiences drag penalty where it encounters higher Cd mean than the bare cylinder. Other configurations are able to reduce the drag forces to lower values. This finding is different from the well-known fact that installation of helical strakes induces large drag penalty on the cylinder [24]. Besides, it is also found that the Cd mean values of flexible cylinders with strakes after the lock-out region are close to the rigid cylinder with strakes [14]. This condition suggests that after applying the strakes, the force responses of a flexible cylinder are altered to be similar to a rigid cylinder with strakes after the synchronization region. Another interesting phenomenon is that although the Cd mean of p = 10D h = 0.15D model is smaller than the bare cylinder in the lock-in region, it is amplified significantly starting from Vr = 13.1–13.9 and Vr
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Fig. 5. Frequency ratio of cylinder with different height of strakes: (a) IL frequency ratio, (b) CF frequency ratio and (c) IL-to-CF frequency ratio.
= 15.2–16. Similar conditions are found in Cd fluct and Cl fluct as well for the same strake configuration (Figs. 11a and 12a). In order to explain this phenomena in detail, the power spectral density (PSD) of p = 10D h = 0.15D strakes model in CF and IL directions are presented in Fig. 9 along with p = 10D h = 0.10D strakes for comparison. Based on Fig. 9a and b, it can be seen that the IL and CF frequencies of p = 10D h = 0.15D strakes are broad-banded, instead of in narrow region with significant peak (Fig. 9c and d). The reason that the strakes of p = 10D h = 0.15D to be so unique is that the large height of strakes changes the separation point of the cylinder significantly based on the position of strakes, results in the variation of the vortex pattern of the cylinder. On the contrary, the separation of strakes with smaller height (h = 0.05D, 0.10D) may be controlled by the bare region of cylinder and hence retain partially the correlated wake pattern of bare cylinder, as reported by Constantimides and Oakley [21]. This phenomenon can be proved as well by observing Fig. 10a where the inline force of p = 10D h = 0.15D is fluctuated intermittently, instead of in cyclic form (Fig. 10b). This designates that the installation of p = 10D h = 0.15D strakes has eliminated the coherent vortex structures, and results in the broad-banded frequencies with large hydrodynamic forces. Extensive study on the flow visualization should be conducted in order to verify this situation. By comparing the Cd mean among the 3-helical strakes configurations in Table 3, it is found that p = 10D h = 0.10D strakes possess the lowest value. Therefore, the most effective strake in term of drag
forces is p = 10D h = 0.10D model.
3.3.2. Fluctuating drag coefficient (Cd fluct ) Based on Fig. 11a, it is noticed that the maximum Cd fluct of bare cylinder occurs at Vr = 3.25, which is around 73% of the Cd mean at the first IL lock-in region. As entering the CF lock-in region (Vr = 4.5), another peak of the Cd fluct of bare cylinder is found. After the lock-in region, the Cd fluct then reduces gradually as the reduced velocity increases, until it reaches a constant value. The Cd fluct slightly increases again starting from Vr = 13 where secondary CF lock-in occurs. This shows that the Cd fluct of bare cylinder is highly influenced by the frequency synchronization. The Cd fluct reduces notably as the strakes are applied to the cylinder, where the larger the strakes’ height becomes, the more reduction of Cd fluct is achieved. The maximum fluctuating drag is around 47%, 23% and 124% of the mean value of bare cylinder, for p = 10D h = 0.05D, p = 10D h = 0.10D and p = 10D h = 0.15D models, respectively. The changes of pitch configurations, on the other hand, indicate less influence on the Cd fluct (Fig. 11b). The maximum fluctuating drag is around 25%, 23% and 23% of mean drag value of bare cylinder for p = 5D h = 0.10D, p = 10D h = 0.10D and p = 15D h = 0.10D models, respectively. All configurations of strakes are able to abolish the large fluctuating drag in the first IL lock-in. However, minor peaks are still found in CF lock-in, except for p = 10D h = 0.15D model.
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Fig. 8. (a) Mean drag coefficient of cylinder with different pitch of strakes and (b) mean drag coefficient of cylinder with different height of strakes.
Fig. 6. The power spectral density of cylinders with different strakes configurations at V = 0.7 m/s (Vr ≈ 14): (a) bare cylinder, (b) p = 10D, h = 0.05D, (c) p = 10D, h = 0.10D and (d) p = 10D, h = 0.15D.
3.3.3. Fluctuating lift coefficient (Cl fluct ) By applying the strakes, the Cl fluct peaks reduce significantly and become broad-banded. This is in contrast to the bare cylinder which has a sharp and narrow peak. Based on Fig. 12a, it is obvious that increase of the height of strakes decreases the Cl fluct of cylinder by 3%, 72% and 92% in the lock-in region for p = 10D h = 0.05D, p = 10D h = 0.10D and p = 10D h = 0.15D models, respectively. The reduction of Cl fluct is mainly due to the disruption of regular shedding of vortices. Korkischko and Meneghini [7] indicated that the oscillating wake was absent in the wake of cylinder with strakes, as there was no interaction between the shear layers. Without the oscillating wake and regular asymmetry vortices, the lift force can be reduced significantly. The increase of the pitch of strakes in Fig. 12b delays the occurrence of Cl fluct peak. Besides, the maximum Cl fluct is found during the synchronization region. These circumstances are very similar to the vibration amplitude of a cylinder. This shows that the lift force components are able to describe the CF displacement of the cylinder in lock-in region. The peak reduction of strakes in the lock-in region are 45%, 72% and 70% for p = 5D h = 0.10D, p = 10D h = 0.10D and p = 15D h = 0.10D models, respectively. At the higher reduced velocity, p = 10D h = 0.10D model is able to keep the Cl fluct in a smaller value, while the Cl fluct of p = 15D h = 0.10D model has the tendency to increase from Vr = 18 onwards. 4. Conclusion
Fig. 7. Trajectory of cylinder with different strakes configurations, from 40 s to 41 s, at V = 0.4 m/s (Vr ≈ 7.9): (a) bare cylinder, (b) p = 10D h = 0.05D, (c) p = 10D h = 0.10D, (d) p = 10D h = 0.15D, (e) p = 5D h = 0.10D and (f) p = 15D h = 0.10D.
The present study investigated the effectiveness of helical strakes in suppressing the VIV of long flexible cylinder with low mass ratio. The results presented in the preceding sections show that although the change of pitch of strakes contribute less in reducing the amplitude of vibration, a higher pitch of strakes delays the occurrence of lock-in. The model with the pitch of 10D is also found to be able to prevent the jump of frequency into higher mode. Besides, it can be concluded that the higher the strakes’ height becomes, the more effective the strakes are in suppressing VIV of a flexible cylinder. Present results show that p = 10D h = 0.05D model
L.K. Quen et al. / Applied Ocean Research 44 (2014) 82–91
Fig. 9. The PSD of strakes with p = 10D h = 0.15D in (a) CF and (b) IL directions, strakes with p = 10D h = 0.10D in (c) CF and (d) IL directions.
Fig. 10. Time series of inline force of (a) p = 10D h = 0.15D strakes and (b) p = 10D h = 0.10D strakes at v = 0.77 m/s (Vr ≈ 15.8).
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with 72% of amplitude reduction. In short, the effect of the height of strakes is more significant than the pitch of strakes in reducing the VIV of a cylinder. However, compared to a rigid cylinder, the suppression effectiveness of strakes on a flexible cylinder is less. In the hydrodynamic forces analysis of long flexible cylinder, it is surprising to find that the Cd mean of cylinder with strakes is lower than bare cylinder, which is different from the previous study of rigid cylinder [14]. However, the flexible cylinders with strakes of the present study behave similarly to the rigid cylinder with strakes at higher reduced velocities. In contrast to the amplitude of cylinder, the most effective configuration of strakes in term of hydrodynamic forces is p = 10D h = 0.10D model. Acknowledgements The authors are grateful to Department of Naval Architecture and Ocean Engineering, Osaka University for providing the towing tank and facilities for the experiment. In addition, special thanks to the lab members in Kato Laboratory, under the Department of Naval Architecture and Ocean Engineering, Osaka University for their kindly help in succeeding the experiment. References
Fig. 11. (a) Fluctuating drag coefficient of cylinder with different height of strakes and (b) fluctuating drag coefficient of cylinder with different pitch of strakes.
Fig. 12. (a) Fluctuating lift coefficient of cylinder with different height of strakes and (b) fluctuating lift coefficient of cylinder with different pitch of strakes.
fails to reduce the large amplitude and frequency response. p = 10D h = 0.10D model, on the other hand, is capable to inhibit the occurrence of high mode frequency at higher velocity with 58.9% of the amplitude reduction. The most effective strakes configuration by considering the suppression of amplitude and frequency is p = 10D h = 0.15D model,
[1] Vandiver JK. Dimensionless parameters important to the prediction of vortexinduced vibration of long, flexible cylinders in ocean currents. Journal of Fluids and Structures 1993;7:423–55. [2] Chaplin JR, Bearman PW, Cheng Y, Fontaine E, Graham JMR, Herfjord K. Blind predictions of laboratory measurements of vortex-induced vibrations of a tension riser. Journal of Fluids and Structures 2005;21:24–40. [3] Song J-n, Lu L, Teng B, Park H-i, Tang G-q, Wu H. Laboratory tests of vortexinduced vibrations of a long flexible riser pipe subjected to uniform flow. Ocean Engineering 2011;38:1308–22. [4] Xue H, Guo J, Tang W, Zhang S. Characteristic analysis of VIV-induced fatigue damage of top tensioned risers based on simplified model. Journal of Offshore Mechanics and Arctic Engineering 2011;133, 021314-1. [5] Sanaati B, kato N. A study on the effects of axial stiffness and pre-tension on VIV dynamics of a flexible cylinder in uniform cross-flow. Applied Ocean Research 2012;37:198–210. [6] Modarres-Sadeghi Y, Chasparis F, Triantafyllou MS, Tognarelli M, Beynet P. Chaotic response is a generic feature of vortex-induced vibrations of flexible risers. Journal of Sound and Vibration 2011;330:2565–79. [7] Korkischko I, Meneghini JR. Experimental investigation of flow-induced vibration on isolated and tandem circular cylinders fitted with strakes. Journal of Fluids and Structures 2010;26:611–25. [8] Huang S. VIV suppression of a two-degree-of-freedom circular cylinder and drag reduction of a fixed circular cylinder by the use of helical grooves. Journal of Fluids and Structures 2011;27:1124–33. [9] Wu H, Sun DP, Lu L, Teng B, Tang GQ, Song JN. Experimental investigation on the suppression of vortex-induced vibration of long flexible riser by multiple control rods. Journal of Fluids and Structures 2012;30:115–32. [10] Assi GRS, Bearman PW, Kitney N, Tognarelli MA. Suppression of wake-induced vibration of tandem cylinders with free-to-rotate control plates. Journal of Fluids and Structures 2010;26:1045–57. [11] Zhu H, Lin Y, Jia Q, Yang X. Simulations of suppressive effect of VIV on marine riser with splitter plates. Computer Science and Information Technology 2010;6:337–41. [12] Allen DW, Lee L, Henning DL. Fairings versus helical strakes for suppression of vortex-induced vibration: technical comparisons. In: Offshore technology conference, OTC 19373. 2008. [13] Zhou T, SF Mohd. Razali, Hao Z, Cheng L. On the study of vortex-induced vibration of a cylinder with helical strakes. Journal of Fluids and Structures 2011;27:903– 17. [14] Boubenider R, Alptunaer K, Fourchy P, de Wilde JJ. Effectiveness of polyethylene helical strakes in suppressing VIV response after sustaining high roller load deformation during S-lay installation. In: Offshore technology conference, OTC 19289. 2008. [15] Bearman P, Brankovic´ M. Experimental studies of passive control of vortexinduced vibration. European Journal of Mechanics-B/Fluids 2004;23:9–15. [16] B Sanaati. An experimental study on the VIV hydrodynamics of pre-tensioned flexible cylinders with single and multiple configurations. PhD thesis, Osaka University, Japan, 2012. [17] Sanaati B, Kato N. Vortex-induced vibration (VIV) dynamics of a tensioned flexible cylinder subjected to uniform cross-flow. Journal of Marine Science and Technology 2012. http://dx.doi.org/10.1007/s00773-012-0204-z. [18] Schlichting H. Boundary-layer theory. 6th ed. McGraw Hill Book Company; 1968. [19] Kato N. A study on separated flows behind bluff bodies by inviscid vortex models (2nd report). Journal of the Society of Naval Architects of Japan 1982;151:15–22.
L.K. Quen et al. / Applied Ocean Research 44 (2014) 82–91 [20] Simantiras P, Willis N. Investigation on vortex-induced oscillations and helical strakes effectiveness at very high incidence angles. In: The ninth international offshore and polar engineering conference, ISOPE-99 Brest. 1999. [21] Constantimides Y, Oakley OH. Numerical prediction of bare and straked cylinder VIV. In: 25th international conference on offshore mechanics and arctic engineering, OMAE 2006-92334. 2006. [22] Vandiver JK. Drag coefficients of long flexible cylinders. In: Offshore technology conference, Texas, USA. 1983. [23] Huera-Huarte FJ, Bearman PW. Wake structures and vortex-induced vibrations of a long flexible cylinder. Part 2. Drag coefficients and vortex modes. Journal of Fluids and Structures 2009;25:991–1006. [24] Recommended Practice DNV-RP-F204; October 2010. http://www.dnv.com.
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[25] Blumberg M, Tellier E, Deka D, Zhou T. Experimental evaluation of vortex induced vibration response of straked pipes in tandem arrangements. In: 31th international conference on ocean, offshore and arctic engineering, OMAE2012. 2012, paper no. 83772. [26] Bearman P, Brankovic´ M. Experimental studies of passive control of vortexinduced vibration. European Journal of Mechanics-B/Fluids 2004;23:9–15. [27] Korkischko I, Meneghini JR, Gioria RS, Jabardo PJ, Casaprima E, Franciss R. An experimental investigation of the flow around straked cylinders. In: 26th international conference on offshore mechanics and arctic engineering, OMAE200729057. 2007.
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Applied Ocean Research journal homepage: www.elsevier.com/locate/apor
Investigation on the effectiveness of helical strakes in suppressing VIV of flexible riser Lee Kee Quena , * , Aminudin Abua , Naomi Katob , Pauziah Muhamada , Asnizah Sahekhainia , Hanida Abdullaha a b
Intelligent Dynamic and System I-kohza, Malaysian-Japan International Institute of Technology, Universiti Teknologi Malaysia, Malaysia Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, Japan
a r t i c l e
i n f o
Article history: Received 8 August 2013 Received in revised form 24 October 2013 Accepted 23 November 2013 Keywords: Vortex-induced vibration Helical strakes Flexible cylinder Suppression
a b s t r a c t The effectiveness of the strakes in suppressing the vortex-induced vibration (VIV) of a long flexible cylinder is investigated by varying the pitch (p) and height (h) of the strakes. Measurements of cross-flow (CF) vibration amplitude, in-line (IL) and CF frequency responses, and hydrodynamic forces are presented for low mass flexible cylinders with helical strakes. Cylinders with aspect ratio of 162 were applied with constant pretension to restrict the vibration in IL and CF directions. Six cases with about 180 runs were executed under subcritical Reynolds number (Re = 0.144 to 1.384 ) of uniform flow. Calculation on the laminar boundary layer thickness around a circular cylinder was performed as a benchmark in deciding the height of strakes. Present study shows that at certain strakes’ height which is larger than the laminar boundary layer thickness, significant VIV mitigation is found. However, the suppression effectiveness of helical strakes on flexible cylinder is less notable compared to a rigid cylinder. The change on pitch of strakes affects the occurrence of lock-in region and prevents the frequency to switch into higher mode. On the other hand, increase on the height of strakes narrows the lock-in region and plays the most major role in suppressing the vibration of a cylinder. The hydrodynamics forces indicate an unexpected phenomenon where the bare cylinder possesses higher force coefficients compared to cylinders with helical strakes. However, large drag penalty is still found in a particular case at higher reduced velocity. The most effective configuration of strakes in terms of the dynamic responses is p = 10D and h = 0.15D model. However, model of p = 10D and h = 0.10D performs better in reducing the hydrodynamic forces. c 2014 Elsevier Ltd. All rights reserved.
1. Introduction Interaction between fluids and riser, which associates with vortexinduced vibrations (VIV), is subjected to substantial research in both industries and academic field during the past few decades due to the high demand in exploring hydrocarbon resources [1–3]. The VIV can be explained as the vibration motion excited by vortices of external fluid flow interacting with the structure. When the shedding frequency of the vortices formed behind the structure synchronizes with the natural frequency of the structure, lock-in is induced and it is usually accompanied by significant vibration. If the riser vibrates under synchronization for a long period, it might considerably reduce the fatigue life of riser, and consequently cause detrimental effects. In addition, as the exploration of the hydrocarbon resources has been moved into deeper water, longer riser with higher aspect ratio is increasingly required, which leads to the high risk of VIV. Numbers of attempts to understand the phenomenon of VIV of long riser are found in the literature. Xue et al. [4], for example, developed a simplified
* Corresponding author. Tel.: +60 126877052. E-mail address: [email protected] (L.K. Quen).
c 2014 Elsevier Ltd. All rights reserved. 0141-1187/$ - see front matter http://dx.doi.org/10.1016/j.apor.2013.11.006
empirical model to investigate the influence of current flow, diameter and length towards the fatigue damage of a top-tensioned riser, and found that added mass and reduced velocity are the significant variables that affect the response frequency of VIV. Sanaati and Kato [5] varied the pre-tension and stiffness of a flexible cylinder to obtain its dynamic responses, and revealed that high pre-tension leads to high hydrodynamic lift forces. Modarres-Sadeghi et al. [6], who analysed the chaotic responses of long riser, discovered that long riser possesses high possibility of experiencing simultaneous excitation of several modes. In order to reduce the VIV of riser, various suppression devices are introduced. In general, they can be classified into (i) surface protrusions type where the cylinder surface is modified [7–9] and (ii) near-wake stabilizers type where obstacle is positioned in the near wake of cylinder [10–12]. Among these devices, helical strake, which is under the first category, is one of the most common devices implemented in riser application. Although some experimental researches discuss the effectiveness of the strakes [13–15], the available results are limited to short rigid cylinder, which is defined as a cylinder that is inflexibly mounted and the allowable motion is in cross flow (CF) direction only. The performance of flexible cylinder that can withstand both cross-flow and in-line movements, especially with high
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Table 1 Model parameters. Outer diameter (D) Inner diameter (d) Length (L) Pre-tension (T) Bending stiffness (EI) Spring stiffness (ks ) Cylinder axial stiffness (EA/L) Cylinder air weight Total weight including internal water (m) Mass ratio (m* =4m/ρπ D2 ) (Structural + viscous) damping ratio (z) Applied strakes’ height (h) Applied strakes’ pitch (p) Number of helix Flow speed (U) Subcritical Reynolds number range (Re)
18 mm 13 mm 2.92 m 147 N 9.0 Nm2 6.5 N/mm 100 N/mm 1.64 N/m 2.97 N/m
Fig. 1. Flexible cylinder with three-start helical strakes.
1.17 0.028 0.05D, 0.10D, 0.15D 5D, 10D, 15D 3-start helical 0.1–1.0 m/s 1380–13,800
Fig. 2. Position of pairs of strain gauges on a square cross-sectioned rod.
aspect ratio and low mass ratio is still scarce. To the knowledge of the authors, detailed discussion on the hydrodynamic forces of a long flexible cylinder based on different configuration of strakes is still inaccessible. Therefore, in the present study, we aim to focus on the effectiveness and force responses of helical strakes on a long flexible cylinder in uniform cross-flow. Parameters of vibration amplitude, frequency responses as well as hydrodynamic forces are of interest. In the following sections, the experimental details and the parameters are discussed and these are then followed by a brief conclusion. 2. Experimental details [17] The experiment was conducted in the towing tank of the Department of Naval Architecture and Ocean Engineering of Osaka University. The experiment basin is 100 m × 7.8 m × 4.35 m in length, width and depth, respectively. The cylinder models were horizontally installed, and were submerged in water with 0.35 m from the still-water level in order to avoid the influence of free surface on the response of cylinders. The cylinders were towed by the carriage to generate the specified uniform flow from 0.1 m/s to 1 m/s, as shown in Table 1 with interval of 0.03 m/s, providing the subcritical Reynolds number range from 1380 to 13,800. Because of the limited size of the towing tank and operational characteristic of the towing carriage, the cylinders can only be examined in the sub-critical range of Reynolds number. However, the findings can be directly applied to real world riser at much higher Reynolds numbers as the increase of Reynolds number does not affect the performance of helical strakes. This is due to the fact that the separation points of the flow remain the same for various Reynolds number [27]. In addition, it was proved that the drag coefficient of a cylinder with strakes was practically unchanged over sub-critical, critical and post-critical flow condition, as cited by Simantiras and Willis [21]. More description of the experimental facility can be referred to [16]. A poly vinyl chloride (PVC) cylinder was chosen as riser model as it offers high flexibility with low bending-dependence. Universal joints were used to pin the both ends of cylinder in order to allow the bend of cylinder in IL and CF directions, but constrained in torsion. One of the cylinder ends was allowed no translational movement, while the other end was free to move in axial direction. At the sliding end (movable end), a constant pre-tension of 147 N was applied to provide a tension-dominated cylinder model. More details about the setting of cylinder and the pre-tension can be referred to [17]. The helical strakes were made of rubber and were designed to have three-start helical, as illustrated in Fig. 1. The height of strakes was designed by considering the laminar boundary layer thickness of a circular cylinder. Based on Pohlausen’s
approximation on a circular cylinder [18], the thickness of the boundary layer, y can be estimated by:
VL =
y R
u∞ R v
(1)
where VL is the boundary-layer velocities, R, u∞ and ν denote radius of cylinder, velocity and kinematic viscosity, respectively. Since the Pohlausen’s approximation is based on the assumption that the ambient flow has no separation while strong interaction is actually observed between the ambient flow and separation in real condition, large angle of separation point, 103.14◦ is chosen in present study. The calculation shows that the boundary layer thickness is about 0.06D, where D is the outer diameter of cylinder. In general, height of 0.05– 0.2D is accepted as optimal in the industries. Based on this statement and by considering the laminar boundary layer thickness, three configurations of heights, 0.05D, 0.10D and 0.15D were selected in the present study to investigate the influence of the height of strakes in suppressing the VIV of flexible cylinder. The specification of the cylinder and the strakes are listed in Table 1. The vibration amplitude in CF direction was measured using underwater CCD camera. The camera was installed at the centre of the cylinder, with location of approximately 20D (diameter) downstream and above of the cylinder in order to avoid the wake interference. The video data recorded by the camera were sampled at 30 Hz. Only the responses at the centre of the cylinder were recorded. Before running the experiment, calibration on camera within allowable motions was conducted in three-dimensions. The analyses of video data recorded by the above and downstream camera were done simultaneously by using PcMAG, a motion tracking commercial software. To identify the strain bending moment in IL and CF directions, two half-bridge strain gauges were installed on a square cross-section rod in each direction at a specified distance, d of 3 cm, which result in a total of eight strain gauges of four stations for measurements, as shown in Fig. 2. The sampling rate of bending was 200 Hz, which was adequate to obtain accurate measurement. Since unsolicited noises were generated during the experiment, the analogue measured data had to be prepossessed by applying low-pass filter of 100 Hz cut-off frequency, before converting it to digital data. A total of 180 runs based on six cases were measured for bare cylinder and all configurations of strakes. The combinations of the strakes arrangement are: pitch p = 10D height h = 0.05D; p = 10D h = 0.10D; p = 10D h = 0.15D; p = 5D h = 0.10D and p = 15D h = 0.10D. The duration to collect measurements starting from still water was 75 s, but the analysis was only based on the data after speeded to a
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Table 2 Natural frequencies of cylinders with various configurations of strakes.
Configuration of strakes No strakes (bare cylinder) 3 strakes pattern, p = 5D, h = 0.10D p = 10D, h = 0.10D p = 15D, h = 0.10D p = 10D, h = 0.05D p = 10D, h = 0.15D
Mass (kg)
Natural frequency, Fn (measured/analytical value)
0.484
2.91/2.92
0.588
2.80/2.82
0.595 0.544 0.559 0.636
2.78/2.82 2.89/2.86 2.76/2.85 2.67/2.78
constant value. 10 min breaks were taken between each run in order to avoid the flow transient effects. Free decay test was conducted before starting the experiment for bare cylinder as well as cylinders with strakes in order to obtain the natural frequencies by imposing an initial displacement on the cylinder and then released it. Since the mass of the cylinder with strakes are different due to the additional mass of the strakes, the natural frequency of each cylinder is slightly different from each other, as shown in Table 2. The natural frequency of cylinder in water can also be identified by using the analytical method as shown below: 2 2 n 2 T EI n π + ≈ f n n = 1, 2, 3, . . . (2) 2 2 mL 2 mL 4 where T and L are the tension and length of cylinder respectively, EI is the bending stiffness and m is the mass per unit length (include addedmass, ma where the added-mass coefficient is assumed to be 1). Table 2 shows that the measured natural frequencies are in consistency with the analytical values. 3. Results and discussion 3.1. Vibration amplitude responses In the following section, the responses of bare cylinder of present study are included as a basis of comparison. Fig. 3 indicates the vibration amplitude ratio of bare cylinder and cylinder with different pitch and height of strakes versus the reduced velocity. The amplitude ratio is calculated by using standard deviation of the time series of displacement and divided by the diameter of cylinder (A* = Astd /D) while the reduced velocity is defined as Vr = u/fn D. A well-known amplitude trend for a bare cylinder with low mass-damping ratio; the initial, upper, lower and desynchronization branches with two obvious peaks can be easily seen in the figure. By applying the strakes on bare cylinder, the characteristics of amplitude branches with two obvious peaks have been altered into only one significant peak by eliminating the lower branch in the lock-in region. Fig. 3a shows no remarkable reduction on the amplitude ratio as the pitch of strakes increases, with maximum amplitude ratio range of 0.2–0.3. This can be understood by the effect that the amplitude of vibration can only be suppressed if the formation of the regular vortices behind the pipe is disrupted by the change of boundary layers separation, which results in the shrinking of separated vortex region [19] and prevent the interaction of shear layers [13]. By changing the pitch of strakes, it only alters the coverage of the strakes of cylinder surface which gains less effect on the separation of boundary layers. There is an optimum angle of strakes that is able to reduce the amplitude responses of a cylinder and suppress the occurrence of higher mode frequency based on the condition of the cylinder. In general, the optimal pitch of strakes used in industries is about p = 5D. Recent study by Simantiras and Willis [20] suggested that p = 15D is as effective as p = 5D for a rigid cylinder. However, for a long flexible cylinder with low mass ratio, p = 10D is apparently more effective in
Fig. 3. (a) Amplitude response of cylinder with different pitch of strakes and (b) amplitude response of cylinder with different height of strakes.
suppressing the vibration amplitude based on Fig. 3a as the amplitude of p = 10D model is smaller than p = 15D model. Fig. 3b shows that strake with p = 10D h = 0.15D has successfully suppressed the vibration of the cylinder to around 0.1 of amplitude ratio, which is about 72% reduction of the amplitude. In comparison with a rigid cylinder, however, the effectiveness of strakes on a flexible cylinder is less, as up to 90% of the amplitude can be suppressed for a rigid cylinder with the same strakes configurations [14]. The least amplitude suppression is found in p = 10D h = 0.05D model, with reduction of 46% of amplitude. From the theoretical calculation (1), it is found that the boundary layer thickness for a cylinder is around 0.06D. We can suppose that strakes with h = 0.10D are sufficient to disrupt the flow boundary layer and significantly reduce the amplitude of vibration. However, Fig. 3b shows that only 58% of amplitude reduction is achieved for p = 10D h = 0.10D model. At higher velocity, all types of strakes are able to suppress the cylinder vibration to 0.1 of amplitude ratio. Offshore structures, especially for those which experience high flow current, lock-in condition is undesirable but unavoidable. Therefore, it is essential to discover an effective tool to minimize the vibration within this critical region. As a whole, the lock-in bandwidth reduces considerably as the strakes are installed. Fig. 3a indicates that increasing the pitch of strakes delays the occurrence of lock-in phenomena but slightly increases the lock-in bandwidth. On the other hand, the synchronization is obviously suppressed with a narrower lock-in bandwidth as the height of strakes increases, as shown in Fig. 3b. This result suggests that the height of strakes delays the separation of boundary layer which indirectly postponed the interaction between the shear layers that were generated behind the cylinder. This finding is in agreement as proposed by Zhou et al. [13] who suggested that strakes produced shear layers that interacting far from the cylinder. Besides, larger height of strakes widens the shear layers which prevent the interaction between them, similar as reported by Korkischko and Meneghini [7]. Therefore, the formation of regular vortices can be evaded and the VIV of cylinder can be suppressed. Based on the aforementioned descriptions, it can be concluded that
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the change of height of strakes contributes in suppressing the VIV amplitude and lock-in region more than the change of pitch of strakes. 3.2. Frequency responses For the purpose of comparison, the frequency responses of IL and CF directions for strakes with different heights and pitches are analysed in this section. Only the dominant frequency is considered in each case by using Fast Fourier Transform (FFT) based on the time series of hydrodynamic forces data. The IL-to-CF frequency ratio is presented as well to identify the relationship between the IL and CF responses. Fig. 4a, which displays the IL frequency ratio of cylinder with different strakes’ pitch configurations, indicates that all of the strakes configurations are able to suppress high mode frequency into a lower value during the lock-in region. Fig. 4b, on the other hand, indicates the CF frequency ratio of cylinders with different pitch of strakes at low velocity is similar because the high frequency mode in lock-in region is suppressed in all of the cases. The increase of the pitch slightly delays the CF frequency mode from entering into lock-in region. In general, the distribution of the strakes along the cylinder is highly correlated to the angle of flow attack towards the cylinder surface. According to Blumberg et al. [25], the angle of flow attack affects the responses of the cylinder and there is an optimum angle (pitch) in reducing the responses of the cylinder. In the present study, the frequency responses of p = 10D h = 0.10D strakes possesses the narrowest lock-in region (4.6 < Vr < 10.6) based on Fig. 4. Besides, p = 10D h = 0.10D model is able to keep lower IL frequency values while the rest switch between high and low mode dominant IL frequencies at higher reduced velocity. These observations designate that p = 10D h = 0.10D model has the optimum angle of attack and hence performs better in suppressing the high frequency modes. On the other hand, the larger the height of strakes as displayed in Fig. 5a is, the higher the effectiveness of strakes in suppressing the high mode IL frequency of cylinder is. At higher reduced velocity, the IL frequency of p = 10D h = 0.05D strakes is unable to be suppressed while p = 10D h = 0.10D and p = 10D h = 0.15D strakes are able to maintain the IL frequency ratio to less than 2.5 throughout the velocity range. Fig. 5a and b indicates that the IL and CF frequency ratio of p = 10D h = 0.15D model is scattered around 1. The reason for the phenomena is that the p = 10D h = 0.15D model is randomly vibrates without synchronizing with the natural frequency of cylinder. Therefore, it is able to eliminate the lock-in region and is capable to inhibit the occurrence of higher mode and secondary lock-in at high speed. These phenomena are unable to be achieved by the other configurations. As a result, p = 10D h = 0.15D model possesses remarkable ability in suppressing CF responses. Although p = 10D h = 0.10D model is unable to remove the lock-in phenomena based on Fig. 5b, it reduces the values of high mode IL frequencies. No significant reduction of CF frequency is found also for p = 10D h = 0.05D model. In fact, higher CF mode, which is even larger than the bare cylinder, is discovered in p = 10D h = 0.05D model at higher reduced velocity. This proves that the height of strakes should be greater than the boundary layers thickness (0.06D) in order to disrupt the vortices formation and prevent severe vibration from the cylinder. For the low reduced velocity range from 2 to 6, which belongs to the initial and upper branches of the vibration amplitude, the IL-to-CF ratio of bare cylinder varies significantly, where it increases rapidly from 1 to 4 and then fluctuates slightly at 3 before decreasing to 2, as shown in Fig. 4c. The varying of IL-to-CF ratio indicates the formation of irregular and unstable vortices in the near wake of cylinder. After passing the maximum vibration amplitude (Fig 3a), the IL-to-CF ratio decreases and maintains at 2 throughout the velocity range, denoting the creation of regular vortices. It is a well-known fact that the IL frequency response should be twice of CF frequency response for a bare cylinder. However, the condition changes as the strakes are applied
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to it. The IL-to-CF ratio of all configurations of cylinder with strakes (Figs. 4c and 5c) is one throughout the synchronization (4.5 < Vr < 11). This demonstrates that the strakes are able to suppress the high mode vibration during lock-in where both IL and CF responses are in the same frequency. At higher speed, however, only p = 10D h = 0.10D and p = 10D h = 0.15D models are able to remain this ratio. The low IL-to-CF frequency ratio indicates the cylinders are in low vibration mode with less vibration intensity which is generated by the vortices. This can be proved by referring to their power spectral density (PSD) in IL and CF directions, as shown in Fig. 6 where significant peak with substantial PSD values are found for a bare cylinder and p = 10D h = 0.05D model. In contrast, p = 10D h = 0.10D model shows far smaller PSD value while no peak is observed in p = 10D h = 0.15D model. The trajectory of bare cylinder, which is obtained by taking the IL and CF displacement at the centre of the cylinder simultaneously, shows a classical eight-shape trajectory as a result of IL-to-CF frequency ratio of 2. The application of strakes, which leads to the ILto-CF frequency ratio of 1, indicates the suppression of eight-shape trajectory into crescent (Fig. 7b) or circular trajectories (Fig. 7c–f). Among these strakes, p = 10D h = 0.15D model displays the smallest oscillation in IL as well as CF directions. The capability of p = 10D h = 0.15D model in controlling the low IL-to-CF frequency ratio throughout various speeds and displaying insignificant motion trajectory proves that it is the most effective strakes configuration in suppressing the frequencies of the cylinder. Based on the frequency and amplitude responses (Figs. 3–5), it can be seen that the flexible cylinders with strakes are still experiencing lock-in phenomena, except for p = 10D h = 0.15D model, which is in contrast with the rigid cylinder [13]. It may be due to the low mass ratio of the cylinder and the flexible end condition of cylinder which complicates the interaction between the cylinder and fluids. Similar condition was also reported by Bearman and Brankovic´ [26], where for a cylinder with strakes, 2S and 2P mode of shedding were identified at reduced velocity of 4.92 and 6.3, respectively. They also suggested that the behaviour of a low mass ratio of cylinder with strakes is similar to a bare cylinder, but with smaller amplitudes. 3.3. Hydrodynamic forces Hydrodynamic forces are some of the important parameters that need to be considered in evaluating the performance of suppression devices. It is commonly weighed in terms of mean drag coefficient (Cdmean ), fluctuating drag coefficient (Cdfluct ) and fluctuating lift coefficient (Clfluct ). The Cdmean and the fluctuating terms of Cdfluct and Clfluct can be obtained by taking the mean and standard deviation of the force data which are then divided by the length of the cylinder that were exposed to constant velocity, as expressed in Eqs. (3)–(5) respectively. C d mean =
F d mean 1/2ρ U 2 LD
(3)
C d fluct =
F d std 1/2ρ U 2 LD
(4)
C l fluct =
F l std 1/2ρ U 2 LD
(5)
Fd mean , Fd std and Fl std denote the mean drag force, standard deviation drag force and standard deviation lift force, respectively, which are decomposed from the total forces. The ρ , U, L and D represent the density, the flow velocity, the length of cylinder, and the diameter of cylinder, respectively. In the analysis, the drag of 0.1m/s is discarded due to the large initial forces that lead to the enormous drag coefficients.
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Fig. 4. Frequency ratio of cylinder with different pitch of strakes: (a) IL frequency ratio, (b) CF frequency ratio and (c) IL-to-CF frequency ratio.
Table 3 Average mean drag coefficient of cylinders with various strakes configurations. Strakes configuration
C d mean
Bare p = 10D,h = 0.05D p = 10D, h = 0.10D p = 10D,h = 0.15D p = 5D,h = 0.10D p = 15D,h = 0.10D
2.654 2.079 1.604 1.656 1.629 1.881
3.3.1. Drag force coefficient (Cd mean ) The Cd mean of the bare cylinder in present study are in good agreement with the experimental data of Sanaati and Kato [5], where a very similar trend is found, but with slightly higher values of Cd mean . The average Cd mean of the bare cylinder throughout the entire velocity range of the present study is 2.654 (Table 3), which is larger than those of short rigid cylinder that undergoing force and free motions. The same condition was also reported by Vandiver [22] where the Cd mean of a flexible rope excessed three under uniform flow during lock-in condition. This may be due to the end condition of the flexible cylinder where instead of fixing both end of cylinder, the movement of cylinder is unconstrained in IL and CF direction. Therefore, large amplification of VIV with higher drag forces is generated. Fig. 8a indicates the values of Cdmean of all pitch configurations
of strakes and bare cylinder is at the highest in the lock-in region (4.5 < Vr < 11), which is in good agreement with [22,23]. However, as the reduced velocity increases, the value of Cd mean remains at a high value, which is in contrast with the result reported by Huera-Huarte and Bearman [23] where the drag reduces to a lower value that is similar to a stationary cylinder. The values Cd mean of different pitches are lower than the bare cylinder in the lock-in region, in particular, the strakes of p = 5D h = 0.10D has the smallest fluctuation. As the condition moves from lock-in to lock-out (Vr > 11), the values Cd mean of strakes with different pitches tend to remain constant at higher reduced velocity. This designates that the Cd mean is not affected by the changes of speed in the lock-out region. Based on Fig. 8a and b, only p = 10D, h = 0.05D model experiences drag penalty where it encounters higher Cd mean than the bare cylinder. Other configurations are able to reduce the drag forces to lower values. This finding is different from the well-known fact that installation of helical strakes induces large drag penalty on the cylinder [24]. Besides, it is also found that the Cd mean values of flexible cylinders with strakes after the lock-out region are close to the rigid cylinder with strakes [14]. This condition suggests that after applying the strakes, the force responses of a flexible cylinder are altered to be similar to a rigid cylinder with strakes after the synchronization region. Another interesting phenomenon is that although the Cd mean of p = 10D h = 0.15D model is smaller than the bare cylinder in the lock-in region, it is amplified significantly starting from Vr = 13.1–13.9 and Vr
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Fig. 5. Frequency ratio of cylinder with different height of strakes: (a) IL frequency ratio, (b) CF frequency ratio and (c) IL-to-CF frequency ratio.
= 15.2–16. Similar conditions are found in Cd fluct and Cl fluct as well for the same strake configuration (Figs. 11a and 12a). In order to explain this phenomena in detail, the power spectral density (PSD) of p = 10D h = 0.15D strakes model in CF and IL directions are presented in Fig. 9 along with p = 10D h = 0.10D strakes for comparison. Based on Fig. 9a and b, it can be seen that the IL and CF frequencies of p = 10D h = 0.15D strakes are broad-banded, instead of in narrow region with significant peak (Fig. 9c and d). The reason that the strakes of p = 10D h = 0.15D to be so unique is that the large height of strakes changes the separation point of the cylinder significantly based on the position of strakes, results in the variation of the vortex pattern of the cylinder. On the contrary, the separation of strakes with smaller height (h = 0.05D, 0.10D) may be controlled by the bare region of cylinder and hence retain partially the correlated wake pattern of bare cylinder, as reported by Constantimides and Oakley [21]. This phenomenon can be proved as well by observing Fig. 10a where the inline force of p = 10D h = 0.15D is fluctuated intermittently, instead of in cyclic form (Fig. 10b). This designates that the installation of p = 10D h = 0.15D strakes has eliminated the coherent vortex structures, and results in the broad-banded frequencies with large hydrodynamic forces. Extensive study on the flow visualization should be conducted in order to verify this situation. By comparing the Cd mean among the 3-helical strakes configurations in Table 3, it is found that p = 10D h = 0.10D strakes possess the lowest value. Therefore, the most effective strake in term of drag
forces is p = 10D h = 0.10D model.
3.3.2. Fluctuating drag coefficient (Cd fluct ) Based on Fig. 11a, it is noticed that the maximum Cd fluct of bare cylinder occurs at Vr = 3.25, which is around 73% of the Cd mean at the first IL lock-in region. As entering the CF lock-in region (Vr = 4.5), another peak of the Cd fluct of bare cylinder is found. After the lock-in region, the Cd fluct then reduces gradually as the reduced velocity increases, until it reaches a constant value. The Cd fluct slightly increases again starting from Vr = 13 where secondary CF lock-in occurs. This shows that the Cd fluct of bare cylinder is highly influenced by the frequency synchronization. The Cd fluct reduces notably as the strakes are applied to the cylinder, where the larger the strakes’ height becomes, the more reduction of Cd fluct is achieved. The maximum fluctuating drag is around 47%, 23% and 124% of the mean value of bare cylinder, for p = 10D h = 0.05D, p = 10D h = 0.10D and p = 10D h = 0.15D models, respectively. The changes of pitch configurations, on the other hand, indicate less influence on the Cd fluct (Fig. 11b). The maximum fluctuating drag is around 25%, 23% and 23% of mean drag value of bare cylinder for p = 5D h = 0.10D, p = 10D h = 0.10D and p = 15D h = 0.10D models, respectively. All configurations of strakes are able to abolish the large fluctuating drag in the first IL lock-in. However, minor peaks are still found in CF lock-in, except for p = 10D h = 0.15D model.
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Fig. 8. (a) Mean drag coefficient of cylinder with different pitch of strakes and (b) mean drag coefficient of cylinder with different height of strakes.
Fig. 6. The power spectral density of cylinders with different strakes configurations at V = 0.7 m/s (Vr ≈ 14): (a) bare cylinder, (b) p = 10D, h = 0.05D, (c) p = 10D, h = 0.10D and (d) p = 10D, h = 0.15D.
3.3.3. Fluctuating lift coefficient (Cl fluct ) By applying the strakes, the Cl fluct peaks reduce significantly and become broad-banded. This is in contrast to the bare cylinder which has a sharp and narrow peak. Based on Fig. 12a, it is obvious that increase of the height of strakes decreases the Cl fluct of cylinder by 3%, 72% and 92% in the lock-in region for p = 10D h = 0.05D, p = 10D h = 0.10D and p = 10D h = 0.15D models, respectively. The reduction of Cl fluct is mainly due to the disruption of regular shedding of vortices. Korkischko and Meneghini [7] indicated that the oscillating wake was absent in the wake of cylinder with strakes, as there was no interaction between the shear layers. Without the oscillating wake and regular asymmetry vortices, the lift force can be reduced significantly. The increase of the pitch of strakes in Fig. 12b delays the occurrence of Cl fluct peak. Besides, the maximum Cl fluct is found during the synchronization region. These circumstances are very similar to the vibration amplitude of a cylinder. This shows that the lift force components are able to describe the CF displacement of the cylinder in lock-in region. The peak reduction of strakes in the lock-in region are 45%, 72% and 70% for p = 5D h = 0.10D, p = 10D h = 0.10D and p = 15D h = 0.10D models, respectively. At the higher reduced velocity, p = 10D h = 0.10D model is able to keep the Cl fluct in a smaller value, while the Cl fluct of p = 15D h = 0.10D model has the tendency to increase from Vr = 18 onwards. 4. Conclusion
Fig. 7. Trajectory of cylinder with different strakes configurations, from 40 s to 41 s, at V = 0.4 m/s (Vr ≈ 7.9): (a) bare cylinder, (b) p = 10D h = 0.05D, (c) p = 10D h = 0.10D, (d) p = 10D h = 0.15D, (e) p = 5D h = 0.10D and (f) p = 15D h = 0.10D.
The present study investigated the effectiveness of helical strakes in suppressing the VIV of long flexible cylinder with low mass ratio. The results presented in the preceding sections show that although the change of pitch of strakes contribute less in reducing the amplitude of vibration, a higher pitch of strakes delays the occurrence of lock-in. The model with the pitch of 10D is also found to be able to prevent the jump of frequency into higher mode. Besides, it can be concluded that the higher the strakes’ height becomes, the more effective the strakes are in suppressing VIV of a flexible cylinder. Present results show that p = 10D h = 0.05D model
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Fig. 9. The PSD of strakes with p = 10D h = 0.15D in (a) CF and (b) IL directions, strakes with p = 10D h = 0.10D in (c) CF and (d) IL directions.
Fig. 10. Time series of inline force of (a) p = 10D h = 0.15D strakes and (b) p = 10D h = 0.10D strakes at v = 0.77 m/s (Vr ≈ 15.8).
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with 72% of amplitude reduction. In short, the effect of the height of strakes is more significant than the pitch of strakes in reducing the VIV of a cylinder. However, compared to a rigid cylinder, the suppression effectiveness of strakes on a flexible cylinder is less. In the hydrodynamic forces analysis of long flexible cylinder, it is surprising to find that the Cd mean of cylinder with strakes is lower than bare cylinder, which is different from the previous study of rigid cylinder [14]. However, the flexible cylinders with strakes of the present study behave similarly to the rigid cylinder with strakes at higher reduced velocities. In contrast to the amplitude of cylinder, the most effective configuration of strakes in term of hydrodynamic forces is p = 10D h = 0.10D model. Acknowledgements The authors are grateful to Department of Naval Architecture and Ocean Engineering, Osaka University for providing the towing tank and facilities for the experiment. In addition, special thanks to the lab members in Kato Laboratory, under the Department of Naval Architecture and Ocean Engineering, Osaka University for their kindly help in succeeding the experiment. References
Fig. 11. (a) Fluctuating drag coefficient of cylinder with different height of strakes and (b) fluctuating drag coefficient of cylinder with different pitch of strakes.
Fig. 12. (a) Fluctuating lift coefficient of cylinder with different height of strakes and (b) fluctuating lift coefficient of cylinder with different pitch of strakes.
fails to reduce the large amplitude and frequency response. p = 10D h = 0.10D model, on the other hand, is capable to inhibit the occurrence of high mode frequency at higher velocity with 58.9% of the amplitude reduction. The most effective strakes configuration by considering the suppression of amplitude and frequency is p = 10D h = 0.15D model,
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