Research on the influence of helical strakes on dynamic response of floating wind turbine platform

The stability of platform structure is the paramount guarantee of the safe operation of the offshore floating wind turbine. The NREL 5MW floating wind turbine is established based on the OC3-Hywind Spar Buoy platform with the supplement of helical strakes for the purpose to analyze the impact of helical strakes on the dynamic response of the floating wind turbine Spar platform. The dynamic response of floating wind turbine Spar platform under wind, wave and current loading from the impact of number, height and pitch ratio of the helical strakes is analysed by the radiation and diffraction theory, the finite element method and orthogonal design method. The result reveals that the helical strakes can effectively inhibit the dynamic response of the platform but enlarge the wave exciting force; the best parameter combination is two pieces of helical strakes with the height of 15%D (D is the diameter of the platform) and the pitch ratio of 5; the height of the helical strake and its pitch ratio have significant influence on pitch response.


Introduction
The demand for renewable energy has increased steadily in recent years in response to the shortage of traditional energy as well as the environmental pollution. Among the available renewable energy resources, wind energy is considered to be one of the most promising forms of energy. Compared with the onshore wind energy, the offshore wind energy is optimized due to its high speed, small shear and saving of resources (Pantaleo et al., 2005). The usable offshore wind energy in China is three times the onshore one, with 7.5×10 9 kW coastal power reserve and even more at the ocean scale . It is the definite tendency of future wind farms to be offshore, deep-sea and advanced to floating type (Kim et al., 2014). Pursuant to the limitation of technology and budget, the current offshore wind turbines mostly adopt the fixed base and the location is normally within 30 meters shallow sea area (Musial et al., 2004). For better wind resources in the deep sea area with more than 60 meter depth, the floating type platform shall be adopted through the economic analysis. Obviously, the stability of platform structure is the fundamental guarantee of the safe operation for the offshore floating wind turbine. The form and characteristics are the major parts of the design of offshore wind turbine.
The floating wind turbine platform can be categorized as per its method to set up stability, namely Spar platform, TLP (Tension Leg Platform), and Barge platform (Butterfield et al., 2007). Their stability comes from the ballast restoring moment, the pulling force of the mooring line system, and the water plane moment. It is more of a combination of the three in actual instance. A Spar platform focuses on deep-sea oil and gas production, manufacturing and processing, being one of the most important approaches to the oil and gas exploration (Zhu et al., 2013). FLOAT was first developed by the UK Department of Trade and Industry in 1991 as a Spar type offshore floating wind turbine, and other prototypes were also developed according to different water depths (Tong et al., 1993). The demonstration running showed that Spar platform has good stability under wind and wave loading and convenience of building, Spar platform is benefited from its small water-line profile and low gravity center which reduce its dynamic response to rough wave (Wang et al., 2008). Nevertheless, the Spar platform is exposed to large vortex-excited force arising out of the flow around and its auto-periodical fallout, the motion of which leads to the fatigue of anchor chains and tubes, reduces its fatigue life and increases the total structural damping. Therefore, a few institutions have been studying the Spar platform stability and come out with some resolutions. Rho et al. (2002Rho et al. ( , 2003 carried out model test and numerical simulation for heave and coupled pitch of the typical Spar platform, and analysed the impact of helical strake and mooring on the structural motion amplitude. Van Dijk et al. (2003a, 2003b analyzed the response characteristics of a Truss Spar under the impact of vortex-induced motions with uniform flow, followed by the mooring system under the impact of the platform's vortex-induced motions. Koo et al. (2004) factored in the mooring effect and conducted numerical simulation on the heave and pitch coupled motion of the Spar platform in regular waves by the advanced Mathieu formula. It is found that the mooring lines would increase the pitch damp and change the inherent frequency of the structural pitch, which would stabilize the platform. Wang et al. (2011) studied on the coupling motion response of the Spar platform and the mooring line, which results in the conclusion that the increase of the line stiffness and initial tension would also stabilize the platform from its surge, while the heave and pitch are not affected. Shen et al. (2012) simulated the heave movement of a Truss Spar platform in random wave and found that the platform tends to have great heave movement when the wave period is close to the heave period of the platform. The heave movement coincides with the significant wave height. Hao et al. (2012) focused on the inhibition of the helical strakes on the periodical tailing vortex shedding with the column structure by using CFD numerical calculation and the particle image velocimetry system. The destruction of the eddy structure by the helical strake increases if the thread height increases.
In this sense, the movement of a floating wind turbine Spar platform under the accumulated oceanic impact of wind, wave and current is complicated. The type of platform, the mooring line system and the dynamic environment would all influence its dynamic response. At current stage, both domestic and global analysis of the floating Spar platform are based on the offshore oil platform but are very rare on the floating wind turbine. The modern wind turbine is the largest rotating machinery that human beings have ever built. It is distinguished from the developed offshore oil platform as of its great aerodynamic force generated from the continuous rotating wheel, its induction on the hydrodynamic loading, the loading change during starting process, and the overall dynamic instability due to the change of propeller and brake. Hence the modelling methods, boundary conditions and even the analytic result of the same phenomena are all different from those of the offshore oil platform.
The helical strakes can interrupt the spatial relative length of the vortex by altering the radial inflow separation angle, so that the vortex strength is weakened and eventually the vortex-induced motion is reduced. The particulars of different helical strakes would result in various reduction of the vortex-induced motion. As such the preferable selection of helical strakes set is crucial to the floating wind turbine Spar platform. In this paper, the impact on the dynamic response of the floating wind turbine Spar platform from the various particular sets of helical strakes is analyzed by numerical simulation based on orthogonal theory. Coupled with the previous experience on the study of offshore oil platform, the analysis uses the method of applying helical strakes to the peripheral column of the platform together with the mooring system in the hope to provide theoretical feasibility preference for the optimized design and improvement of safety for the offshore wind turbine platform.

Model of the floating wind turbine
The floating wind turbine contains three parts: the wind turbine, the floating platform, and the mooring system. In this paper, it is chosen as OC3-Hywind Spar Buoy (Jonkman, 2009;Jonkman and Matha, 2009) for the platform and NREL 5MW (Robertson and Jonkman, 2011) for the wind turbine. The model in Fig. 1 is based on the particulars of NREL 5MW wind turbine and OC3-Hywind Spar Buoy. The main body is the slim buoy with certain draft attached with three catenary cables.
With reference to the experience of offshore oil platform, remodelling is done with helical strakes attaching to the Spar platform column for the purpose of convenience to compare with normal Spar platform by the same criterion. Fig. 2 shows the modelling diagram of Spar platform with helical strakes attaching. Mooring system and upper wind turbine are left out to better display the helical strakes.
to simplify the calculation while maintaining the generality.
3.1 Wind load (Nielsen et al., 2006) In consideration of the feasibility of the research, it is assumed that the wind-induced thrust at the top of the tower can be estimated based on the thrust coefficient applied to the overall area swept by the rotor. As the simplified wind turbine model is used in the present simulations, the rotor thrust force is obtained based on the thrust force coefficient. The thrust force F T on the turbine is given as: where C T is axial thrust coefficient, ρ a is the air density, A is the area that the wheel of a normal operating turbine would cover, and v is the wind speed. Actually, the thrust coefficient varies with the relative wind speed and control strategy, but it is used as a constant based on the 5MW baseline wind turbine rotor thrust vs. wind speed, the selected rotor thrust coefficient is 0.78 (Zhao et al., 2012).
The rotor thrust force under different wind speeds is shown in Fig. 3. (Jeon et al., 2013) This paper uses the radiation and diffraction theory to solve the wave loading of the floating platform. With the effect of wave, the velocity potential of the defined wave is:

Wave load
The potential function is considered to be from the following factors: the radiation wave potentials from six de-grees, the incident wave potential, and the diffraction wave potential. Hence the potential function can be further displayed as: where is the incident wave potential, is the diffraction wave potential, is the radiation wave potential from the motion of the floating object in the degree of j, is the displacement of the floating object under unit amplitude in the degree of j, and ω is the circular frequency of incident wave.
Based on the linearized Bernoulli equation, the first order linear water pressure gradient is solved by the speed potential: According to the water pressure distribution, the integration of water pressure on the wet surface of the floating object would result in the wave loading. By accumulating the regular wave with different amplitudes, wavelengths, and directions, the wave loading of irregular wave can be obtained.
The second order excitation force that a floating object would receive in the wave includes the mean wave drift force, sum frequency force, and different frequency force. Under the impact of single regular wave, the second order wave force would only be the mean wave drift force. It is the continuous regular wave impedance, smaller than the first order wave force by magnitude scale, but will create large horizontal motion by resonance condition. There are far field method, near field method, and approximate method for calculation. By the far field method, it is feasible to obtain the components from surge, sway and yaw, which significantly increases the accuracy of drift forces of surge and sway. However, the yaw drift force has slow convergence and can only result in one total force. By the near field method, the pressure is integrated directly in the wet surface of the floating object. With sufficient nodes, all six degrees components can be available and thus can be applied to the calculation of wave drift force for any shape of floating objects. The disadvantage is the complexity of the formula. The formulas for average drift force and moment by the near field method are as follows:  is the wet surface of the floating object; X is the movement of the surface of the floating object; is the weight of the floating object; I S is the inertia moment matrix of the floating object; R is the rotation moment of the floating object; and X g is the acceleration vector of the gravity of the floating object.
3.3 Current load (Wang, 2010) Vortex will occur at both sides of the platform when the current comes across the Spar platform. Each pair of vortex with opposing lifting force will constitute the alternating force vertical to the current direction, namely the vortex-induced lifting force. The lifting force on the main body of the platform is: As for marine engineering structure, the vortex and its release will also create drag force in the downstream direction against the column: where U is the current speed; C 1 and C d are the lifting coefficient and drag coefficient, respectively; D is the diameter of the platform; and ω v is the vortex-induced frequency.

Model of the mooring line system
The mooring system of the Spar platform floating wind turbine adopts the catenary modeling, the restoring force is applied on the fairlead point, and the catenary modeling is shown in Fig. 4.
When the cable is completely lifted without any touch with the sea bottom, the formulas are: where x F and z F are the coordinates of the fairlead; H F and V F are the restoring forces of the cable at the fairlead (both vertical and horizontal); C B is the friction coefficient between the cable and sea bottom; EA is the tensile stiffness of the cable; w is the gravity of unit length cable in water; L is the length of cable without tension; and L B is the length of the cable which touches the sea bottom, . When the mooring line parameter and the fairlead coordinate are known, both the vertical and horizontal restoring forces of the mooring line at the fairlead will be available through the catenary formula, and thus the restoring moment of the cable is also available. The experiment of Jason (2009) has proven the accuracy of this modeling.

Motion equation and response freedom
According to Newton Second Law, the motion equations of the floating wind turbine platform under the impact of wind, wave and current loading are: x andθ where m and J are the total weight and inertia moment of the floating wind turbine, respectively; are the linear/ angular accelerations of the translation and rotation of the platform; are aerodynamic force, wave force, current force, and systematic restoring force, respectively; are their corresponding moments, of which the restoring force (moment) is provided by catenary cables.
The motion of the floating wind turbine platform under external loading in six degrees includes the translation along x-, y-and z-axis and the rotation along various axes. Translation includes surge, sway and heave, the size of which is presented by length unit. Rotation includes roll, pitch and yaw, the strength is presented by angle unit. The motion of the Spar platform in six degrees is shown in Fig. 5.
The response of the floating platform under the impact of wave is an irregular random process. The irregular wave can be considered as the accumulation of numerous simple cosine waves with different amplitudes, frequencies and initial phrases which spread with different directions of the x axis. With the superposition principle, the various statistics of structural response can be derived by the spectrum ana- lysis method. The response of the platform to the wave can be written as: where S y (ω) is the response spectrum, H(ω) is the frequency response function (RAO), and S x (ω) is the wave spectrum density function.

Calculation conditions and process procedure
The environmental parameters are set as follows: (1) The wave spectrum is P-M, the significant wave height is 6 m, and the wave circle is 8.5 s.
(2) The wind speed spectrum is chosen as Ochi & Shin spectrum, the wind speed is 11.4 m/s, and the reference point is the hub center.
(3) The current speed is 1.2 m/s. (4) Wind, waves and currents are directly inflowing into the wind turbine with the worst case scenario of upwind wheel direction.
Since wind, waves and currents are inflowing with -180°, the analysis will focus on the response of surge, heave and pitch. In order to meet the statistical characteristics, the set-ting for irregular wave and turbulence wind are 2000 s for emulation time, 0.02 s for time step and total 105 operating point parameters.
The main procedures are as follows, and the flow chart of the simulation procedure is shown in Fig. 6.
(1) Resolve the dynamic response of the floating platform under no wind operation. Translate the velocity fluctuation of the floating platform motion into the velocity fluctuation of the wind flow at the rotor. Use the superposition of such with the inflow wind speed as the relative wind speed. Use the blade element momentum theory and the variations to resolve the wind loading. Apply the time-domain wind loading into the floating platform motion equation. Documents prove the effectiveness of this coupling modeling (Ye, 2012).
(2) Use the radiation and diffraction theory to resolve the first order wave force on the floating platform. Use the near field method to resolve the second order average drift force. The simulation is carried out by the commercial FEM software ANSYS AQWA.
(3) Use the fluid mechanics calculation software Fluent to simulate the vortex-induced loading of the floating platform under the sea current effect below sea level. Apply k-ε turbulent model to consider it as incompressible flow because the inflow speed is relatively low and no heat transfer is involved. Use SIMPLE algorithm to couple pressure and velocity inlet, the outlet boundary condition is pressure outlet. The pressure is hydrostatic pressure. No slip condition is set as the surface wall boundary. Grid independent verification is carried out and the final grid quantity is about 1.5 million. All numerical examples are carried out on the work station of 32 cores and 64GB of memory. Unstructural grids are applied in the whole area. The grid distribution of the calculation region and the surface grid of the platform are shown in Figs. 7 and 8. Apply the vortex-induced lifting force and the dragging resistance force into the floating platform motion equation.  DING Qin-wei, LI Chun China Ocean Eng., 2017, Vol. 31, No. 2, P. 131-140 135 7.1 Dynamic response in frequency domain It is mainly focused on the comparison of the normal Spar platform and those with the attachment of helical strakes in terms of the frequency response function (RAO) and the wave exciting force. The change of RAO of the platform and the wave exciting force as per the frequency of the wave are shown in Figs. 9 and 10. Fig. 9 shows that the platform responses on the surge, heave and pitch are all centralized in the low frequency stage due to the large scale structure of the platform and its natural period, which would incur resonance easily with the low frequency stage wave. The helical strakes would substantially reduce the RAO between the platform's heave and pitch degree of freedom. It has little restraint for the RAO of surge and no impact to change the RAO platform as the wave frequency changes. Fig. 10 shows that the wave exciting forces to the platform are significantly enlarged in the surge, heave and pitch directions with the attachment of helical strakes. Nevertheless, the force of wave does not change according to the change of the wave frequency in that the helical strakes can only change the attaching weight and damping by changing the current field. Hence the wave force does not change along with the change of the wave frequency. The reason why the wave exciting force increases when the platform is attached with helical strakes is that the wet surface of the platform attached with helical strakes is bigger than that of the normal platform, the wave exciting force is the result of dynamic pressure effect of pressure field, so the wave exciting force will increase when the wet surface of platform increases.
The average drift force on the platform is calculated by the near field method. Fig. 11 is the amplitude-frequency curve of the average drift force on the platform. As the two types of platforms have the similar size, their average drift force on various degrees of freedom are quite the same. Hence it is only the normal Spar platform that is analyzed as the wave frequency changes. For the convenience of analysis, we will only adopt the positive value of all average drift force without consideration of direction.
According to Fig. 11, compared with the first-order wave force on the platform, the second-order wave is much smaller in terms of magnitude. The drift force is not affected by the incident angle of the wave in the heave direc-    tion. In the surge and pitch wave, the second-order drift is 0 when the wave frequency is below 1.0 rad/s, whereas when the wave frequency is above 1.0 rad/s, the second-order drift increases when the wave frequency increases, and decreases when the angle between the incident and vertical increases.

Optimal combination of helical strakes
As per the result of the frequency-domain analysis, the helical strakes which are attached to the platform function well can optimize the dynamic response of the platform. The different sets of parameters of the helical strakes may result differently in optimizing the dynamic response of the platform. In this sense, the optimal combination of the helical strakes is crucial to the floating wind turbine. However, there are quite many design parameters of the helical strakes, including the number of strakes, the pitch ratio, the height of strakes, and the coverage. All the parameters interact with each other which would make a complete imitation huge and inapplicable in reality.
Orthogonal design is a reasonable and scientific method of mathematical statistics which effectively results from experiment (Mao et al., 2004). The representative experimental elements are selected based on the so called "orthogonal table". The experiment is arranged scientifically and the results are combined for comparison and statistically analyzed so that the optimal set of factors and levels is thus defined. Therefore, this paper will adopt the orthogonal design method for the study of optimal parameters for the helical strakes.
(1) The coverage of strakes: documentation suggests that the bigger the coverage, the better control of vortex-induced motions would be (Frank et al., 2004). Hence this paper sets the coverage at 100%.
(2) The number of helical strakes: documentation suggests that there is not much difference if the number is three or four. Two pieces would, however, result in better effect (Rolf and Halvor, 2006). Hence this paper sets the number of helical strakes at one, two and three.
(3) The height of strakes: the general height that Spar platform nowadays adopts is 5%D-15%D. As per experience, too low height would affect inhibition of the vortexinduced motions negatively; too high height would require better structural strength. Hence this paper adopts the height of low, medium and high in 5%D-15%D to cover the general range while distinguish each other at 5%D, 10%D and 15%D.
(4) Pitch ratio: documentation suggests that the inhibition of the vortex-induced motions would perform the best when the pitch ratio is set as 5 (Lin, 2008). Anything larger than 5 will generate negative effect, thus this paper takes three levels: 3, 5 and 7.
The levels and parameters are shown in Table 1, in which A is the number of helical strakes, B is the height, and C is the pitch ratio.
The choice of orthogonal table is the paramount consideration of orthogonal design. It can normally be done as follows.
(1) This paper focuses on three levels and three parameters and gives consideration to the interaction among various parameters. Therefore, the orthogonal table should have at least 10 columns, i.e. A, B and C for each column, with A×B, A×C, and B×C for two columns respectively, plus one additional column for random error.
(2) There are 6 degrees of freedom for all three parameters and three levels A, B and C. There are 12 degrees of freedom for three interacting effect of A×B, A×C, and B×C. Taking the erroneous degree of freedom into consideration, the total number of degrees of freedom could be as many as twenty. Hence the L27(3) orthogonal table will meet the minimum requirement for this paper. The thread design is shown in Table 2.
Based on the environmental parameters, the example calculation can run repeatedly for 27 times. The key motions affecting the floating wind turbine are surge and pitch, and the extent of the pitch motion response can directly re-   -wei, LI Chun China Ocean Eng., 2017, Vol. 31, No. 2, P. 131-140 137 flect the extent of overturn of the floating wind turbine. Owing to the limit of this paper, only the statistics for the pitch motion is given here, and the results are shown in Table 3 (the maximum time domain pitch RAO).

Result of range analysis
Range analysis is used to determine the parameters of the number of helical strakes, the pitch ratio, the strake height, and the impact of their interaction on the time domain pitch RAO of the platform. The results are shown in Table 4, in which K a is the total sum of the corresponding column of level a, R is the range of corresponding parameters or their interaction, and the impact on the time domain pitch RAO of the platform from various parameters and their interaction is judged by R.
As per the range ranking result, with the bigger range of interaction column, the inhibition of the platform time domain pitch RAO is the most effective. For a better observation, the relations between the numbers of helical strakes, the height, the pitch ratio and the time domain pitch RAO are illustrated in Fig. 12 with the level of parameters being abscissa and the average pitch RAO being coordinate.
Given by Fig. 12, the Spar platform pitch RAO is at its minimum level with two pieces of helical strakes, the height of 15%D and the pitch ratio of 5.

Result of variance analysis
Since the fact that range analysis cannot distinguish the data fluctuation between the change of strake parameters and the errors, the errors cannot be calculated, and the variance analysis is adopted for data process and analysis of the platform time domain pitch RAO.
The total sum of 27 experimental pitch RAO H is 128.23, and the average E is 4.75. The calculation correction H 2 /27 is 609. The total square of deviance S T is 11.4. The total square deviance is the square deviance of all the data and their average, reflecting the overall fluctuation of data with the degree of freedom f T at 26.
Various parameters deviation quadratic sum S, mean square V and F can be calculated by Eqs. (16), (17) and (18): ; F= where K ij is the sum of calculation result of data in column i and level j. n is the times of calculations; m is the average level of column i, and r is the time of every level with column i. The degree of freedom with single factor is 2 and interaction 4. The result of variance analysis is shown in Table 5. As the mean squares of A×B and A×C are smaller than the erroneous, they are classified as errors during data analysis.
As per the variance analysis result F of various paramet-   ers and their interaction, it is confirmed that the height of strakes and pitch ratio greatly affect the platform time domain pitch RAO. The interaction of height and pitch ratio and the number of helical strakes have certain effect on the pitch RAO.

Conclusions
Based on the radiation and diffraction theories, and the finite element method, two floating wind turbines are established with the supplement of helical strake for the purpose to analyze the impact of helical strake on the dynamic response of the floating wind turbine Spar platform. The dynamic response of the floating wind turbine Spar platform under wind and wave loading from the impact of number, height and pitch ratio of the helical strakes is analyzed by the radiation and diffraction theory, the finite element method, and orthogonal design method. Several conclusions are drawn as follows.
(1) Helical strakes can significantly reduce the motion response of a platform in the heave and pitch, and enlarge the wave exciting force on the platform. However, the helical strakes cannot change the motion response and the change trend of the wave force along with the change of wave frequency.
(2) The Spar platform pitch RAO is at its minimum level with two pieces of helical strakes, the height of 15%D and the pitch ratio of 5.
(3) Pursuant to range analysis and variance analysis, it is given that the height of strakes and pitch ratio greatly affect the Spar platform pitch response. The interaction of height and pitch ratio and the number of helical strakes have certain effect on the pitch RAO.