Influence of Six-Degree-of-Freedom Motion of a Large Marine Data Buoy on Wind Speed Monitoring Accuracy

Abstract

In order to quantitatively analyze the data measurement accuracy of ocean buoys under normal and extreme sea conditions, in this study, we simulated the six-degree-of-freedom motion response of self-designed ocean buoys under different sea conditions based on a separated vortex simulation and the fluid volume method and analyzed the impact of the unsteady motion of buoys on data measurement. The results indicate that under normal sea conditions, the deviation between the numerical method used in this paper and the experimental results is less than 10%. The heaving motion of a buoy is most sensitive to changes in wave conditions. The fluctuation intensity of buoy motion is modulated by the height and wavelength of waves. When the wave height and wavelength are similar to the overall geometric size of a buoy, the wave characteristics of the buoy’s heave, yaw, and pitch motion are significant. In addition, under extreme sea conditions, the movement of the buoy can also cause a deviation in the measured velocity in the transverse flow direction, but the overall deviation is less than 10%. In extreme sea conditions, the wind speed measurement results should be corrected to improve the measurement accuracy of a buoy.

1. Introduction

The stability and reliability of large oceanographic data buoys in complex sea conditions make them the main buoys used in China’s marine data buoy network. These large oceanographic data buoys need to have strong adaptability in various environments, especially in relation to the aspects of buoy stability, settle ability, wave following, structural strength, anchorage tensile and breaking strength, size, and attitude, as well as vibration and shock resistance in their electronic systems [1].

At sea, buoys are affected by wind, waves, and currents and will inevitably experience surge, roll, heave, and wind displacement, which will affect the data collection ability of equipment on the buoy. Harsh natural environments will cause a buoy to move violently and may even lead to overturning [2]. In particular, they have a great impact on the accuracy of wind-speed-monitoring results, because when a buoy is moving, the measured wind speed may be the coupling result of the actual wind speed and the moving speed of the buoy, resulting in a certain error between the measured result and the actual wind speed [3,4].

The superior performance of large ocean data buoys is mainly manifested in their hydrodynamic characteristics, structural characteristics, and monitoring performance. Monitoring performance is closely related to hydrodynamic characteristics and structural characteristics, which directly affect the accuracy of buoy-based monitoring of ocean data [5]. Wang et al. [6] calculated the shock force, additional mass force, and wave damping coefficients of disc buoys with diameters of 3 m and 10 m using the three-dimensional potential flow theory and calculated the heave motion of free buoys using the single-degree-of-freedom motion equation. The heave motion of two mooring buoys and the influence of mooring on the heave motion of buoys were discussed. Sun Qi et al. [2] used AQWA to study the hydrodynamic characteristics of an all-titanium 6 m ocean data buoy, calculated the rolling and heave hydrodynamic characteristics of the buoy in the intended ocean environment, and verified that the designed all-titanium Marine data buoy met the design requirements. Fan et al. [7] carried out a numerical simulation and experimental research on a disc-shaped ocean data buoy with a diameter of 10 m and applied a spectral analysis method to make a short-term prediction of its motion response under extreme sea conditions, providing a reference for the preliminary design of 10 m buoy. Amaechi et al. [8] established an OrcaFlex coupling model of an underwater CALM buoy system based on a Lazy-S configuration and studied the motion of a square buoy (SB) and a cylindrical buoy (CB). The results showed that surge, heave motion, response amplitude operators (RAOs), radiation damping, additional mass, geometry, and the skirts of the buoys all affect their hydrodynamic characteristics.

Boo et al. [9] designed a moored buoy system suitable for Wave Energy Conversion (WEC) platforms and performed numerical simulations under a sea state period of 1 in 50 years. The results showed that the analyzed ocean data buoy had a significant dynamic response under extreme sea conditions, which has a certain influence on its monitoring value. Odijie et al. [10] studied the structural stability of a double-column semi-submersible platform and found that the flow angle has a relatively large influence on the stress distribution with the change in wave amplitude. Sun et al. [11] studied the dynamic response characteristics of the CALM system in an extreme environment through numerical simulation and found that the main swell has the greatest impact on the pitch of a buoy. They also found that the motion characteristics of a buoy are reflected in the resonance phenomena with respect to the main swell, sway, heave, and pitch and that the dynamic characteristics of the CALM system are closely related to the peak frequency of the main swell. Gerrit et al. [12] simulated the error and uncertainty of 6-DOF platform motion on LiDAR measurements, and the results showed that buoy movements had a significant impact on the monitoring accuracy of wind detection radar, among which tilt movement was the most important. Cool GA [13] et al. studied the influence of wave period, wave number, and wave height on the reconstruction accuracy of radar wind speed measurement. The results revealed that wave parameters do not have a significant influence on the average 10 min wind speed value, while wave height, wave period, and wave number affect the accuracy of turbulence intensity measurement. By studying ships and NOMAD weather buoys, Taylor et al. [14] explored the wind fluctuation and vector and scalar wind differences of the wind speed sensors of buoys under the influence of waves, and the results showed that the wind speed monitoring accuracy of the buoys would exhibit a large error in the detection results under the action of waves.

To sum up, there have been a number of studies on the hydrodynamic characteristics of buoys, and some scholars have studied the accuracy of the wind speed monitoring of buoys through numerical simulations and experiments.

Table 1. Summary of operating conditions, research objects, and research content in relation to the buoys used in the literature.

Ref.	Conditions	Object	Content
[2]	Wave	Heave Pitch	Heave and pitch motion response.
[6]	Wave	Heave	Heave motion response.
[7]	Wave	Heave Pitch	Heave and roll motion response.
[8]	Wave	Heave	The influence of buoy geometry on motion response.
[9]	Wave	Heave Pitch Surge Sway Roll	Evaluation of buoy motion, mooring tension, and other design parameters.
[10]	Wave	Heave Pitch Roll	Hydrodynamic response and interaction stress distribution of semi-submersible platform column.
[11]	Wave Wind Swell Current	Heave Pitch Surge Sway	The influence of survival and operation conditions on buoy performance.
[12]	Wave Wind	Rotate Tilt Move	Influence of platform 6-DOF motion on measurement error and uncertainty of LiDAR.
[13]	Wave Wind	Wind speed reconstruction accuracy	Effect of wave height, period, and wave number on wind speed reconstruction accuracy.
[14]	Wave Wind	Vector/Scalar wind differences wind fluctuations wave sensor	The effects of buoy motion on vector and scalar wind difference, wind speed fluctuation, and wave-monitoring accuracy.

lists the existing studies on the hydrodynamic characteristics and monitoring accuracy of buoys as well as the operating conditions, research objects, and research content of the buoys used in the research. It can be clearly seen in Table 1 that the study of the hydrodynamic characteristics of buoys mainly focuses on the heave and pitch response characteristics under wave conditions and the six-degree-of-freedom response of buoys under other natural conditions. However, only the analysis of motion characteristics under these conditions is focused on, and the influence of these dynamic responses on wind speed measurement under these conditions is not studied. The existing research on the wind speed measurement of buoys mainly focuses on the error correction and modeling of wind speed measurement under certain wave parameters, but there is a relative lack of research on the motion response behavior of buoys acting together with wind and waves under various actual sea state levels and the specific relationship between these responses and wind speed monitoring accuracy. Given the lack of research in this area, in this study, we aimed to consider different sea conditions on the open sea, for which we used the commercial software STAR-CCM+ 2206 (17.04.007-R8) to conduct numerical simulation research on the six-degree-of-freedom motion and wind speed monitoring of a large, disc-shaped ocean data buoy with a diameter of 10 m under the combined action of wind and waves. On the basis of verifying the accuracy of the numerical simulation scheme, we analyzed the dynamic response rules of heave, pitch, and roll of marine data buoys under different wind and wave conditions, and we provide an in-depth discussion of the influence of these motion responses on the accuracy of wind speed monitoring.

2. Numerical Method

In order to further study the influence of the six-degree-of-freedom movement of large ocean buoys on the wind speed monitoring accuracy of large ocean buoys under the combined action of wind and waves, we used a comprehensive numerical simulation strategy that combines Reynolds mean Navier–Stokes equations, the SST k-ω turbulence model, the Volume of Fluid (VOF) method, and the dynamic Fluid Body Interaction (DFBI) method [15,16,17]. This approach is designed to solve problems involving three-dimensional nonlinear waves in order to calculate the change of the flow field and the position of the free surface around a buoy and the dynamic motion of this object. In our numerical simulation framework, the Reynolds mean Navier–Stokes equation is used to describe the average motion behavior of a fluid, the SST k-ω turbulence model is used to capture the turbulent effects in this fluid, the VOF method is used to track the evolution of the free surface, and the DFBI method is used to determine the fluid-induced dynamic motion of a buoy.

In the VOF method, each cell contains a volume fraction value that represents the proportion of the fluid volume that is occupied by that cell. By solving the momentum equations and the volume fractions of one or more fluids, the movement and changes of interfaces in a multiphase flow can be accurately tracked and described in a simulation. In each control volume, the sum of the volume fractions of all phases is one. For phase q, its equation is [18]

$$\frac{\partial {\alpha }_q}{\partial t}+\frac{\partial (u{\alpha }_q)}{\partial x}+\frac{\partial (v{\alpha }_q)}{\partial y}+\frac{\partial (w{\alpha }_q)}{\partial z}=0$$

where q stands for a fluid phase and denotes the volume fraction of a particular fluid in the grid; for gas–liquid two-phase flow, the liquid phase is denoted when q = 1, the air phase is denoted when q = 0, and the free liquid surface is denoted when q = 0.5.

2.1. Geometric Model and Parameters

In this study, a large ocean-data buoy model with an actual size of 10 m was used as the numerical calculation object. It features a circular truncated conical bottom, a cylindrical middle, a flat platform on top, and additional parts. Focusing on the influence of buoy movement on wind speed monitoring under the combined action of wind and waves, the actual buoy shown in Figure 1b was simplified in modeling by omitting additional components but retaining the main features. In the actual buoy, the wind speed sensor is installed 1.2 m or 1.5 m from the top mounting platform. During the simulation, we reduced these two locations to monitoring points 1.2 m and 1.5 m away from the platform, respectively. Figure 1a shows the simplified geometric model of the buoy and the six-degree-of-freedom motion diagram. Surge, sway, and heave represent the translational motion of the buoy along x, y, and z axes, respectively. The direction along the coordinate axis is positive; roll, pitch, and yaw indicate the rotation of the buoy around the x, y, and z axes as well as clockwise rotation in the positive direction. These six movements constitute the six-degree-of-freedom movement of the buoy. The main design parameters of the buoy are shown in

Table 2. Buoy parameters.

Parameter	Value	Parameter	Value
Diameter (m)	10	Windward area (m2)	23.15
Total height (m)	10.5	Water plane area (m2)	68.96
Model height (m)	2.2	Rotational inertia (t · m2)	31.33
Base cylindrical height (m)	1.2	Base height of center of gravity (m)	1.26
Bottom diameter (m)	6.5	Sensor position 1 (m)	1.2
Draft (m)	0.95	Sensor position 2 (m)	1.5
Tonnage (t)	52	Wind speed range (m/s)	≤80
Beam arch height (m)	0.2	Wave height range (m)	≤12.5

.

Water depths ranging from 60 to 600 m correspond to the medium-depth sea area, for which semi-tensioned mooring is generally adopted [19], and the length ratio of the mooring system is 1:0.9. In this numerical simulation, the water depth reference [7] was set as 68 m, the mooring was half-tensed, the mooring length was 70 m, the catenary model was linear, the mass per unit length was 40.6 kg/m, and the stiffness was 10,000 N/m [6].

2.2. Calculation Condition Settings

In order to further study the wind speed monitoring accuracy of the wind speed sensor fixed on the buoy under different combined wind and wave conditions in the South China Sea, with reference to the open sea wind and wave levels [20], the average wave height and average period under six different sea state levels were selected as the numerical wave parameters, and the average wind speed was taken as the numerical input reference wind speed. The wave height ranges from 0.67 m to 10.97 m, and the wind speed ranges from 6.7 m/s to 22.6 m/s. These six operating conditions cover various wind and wave levels in the South China Sea. In the study of the relationship between the buoy motion characteristics and wind speed monitoring accuracy under the combined action of representative average wave height and average wind speed under each selected wave class, it is helpful to optimize the design and stability analysis of large-scale ocean data buoys and further improve the accuracy, accuracy, and reliability of wind speed monitoring. The selected simulation conditions are shown in

Table 3. Simulation conditions.

Case	Wind Velocity (m/s)	Wave Height (m)	T (s)	Wave Length (m)
Case 1	6.7	0.67	3.9	23.93
Case 2	9.4	1.31	5.4	45.89
Case 3	12.3	2.50	7.0	77.29
Case 4	15.5	4.45	8.7	119.62
Case 5	19	7.01	10.5	172.58
Case 6	22.6	10.97	12.5	236.73

.

2.3. Computational Domain Parameters and Boundary Conditions

The calculation domain of a cuboid shape was set, and the center of gravity coordinate point of the buoy was taken as the origin of the whole calculation domain, where the positive direction of the x axis is consistent with the direction of wind speed and wave speed and the z-axis is vertical with respect to the free surface in the upward direction. The whole calculation domain is composed of a background domain and an overlapping domain. The background domain defines the working area and wave suppression area and determines the calculation domain size according to the buoy diameter and wavelength. As shown in Figure 2, the total length of the background domain is 2L_max + 16D, and the width is 20D. The height is 136 m, and the water depth reference [7] was set to 68 m. The length, width, and height of the overlapping area are 0.7D × 0.7D × 1.5D. The entrance is 6D away from the center of gravity of the buoy, and the area from the origin along the positive direction x to 10D away from the center of gravity of the buoy is the movement area of the buoy, and the two areas together constitute the working area of the buoy. The distance between the exit and the center of gravity of the buoy is 2L_max + 10D. The area 2L_max away from the exit was set as the wave suppression area. The calculation domain and the wave suppression area together form the background domain. Here, L_max represents the maximum wavelength of the simulated condition, and D represents the diameter of the buoy.

With reference to the calculation domain settings [21], combined with the characteristics of this numerical simulation of wind and wave association and the type of wave dissipation, the boundary conditions of the background domain and overlapping domain were set, as shown in

Table 4. Boundary conditions.

No	Boundary Name	Boundary Condition
1	Inlet	Velocity inlet
2	Outlet	Pressure outlet
3	Top	Velocity inlet
4	Bottom	Non-slip wall
5	Side	Symmetry plane
6	Buoy surface	Non-slip wall
7	Overlap surface	Overlapping grid

.

2.4. Numerical Wave Pool

The boundary numerical wave generation method applied using STAR-CCM+ software was adopted for the establishment of the numerical wave pool. The boundary numerical wave generation method combines computational fluid mechanics and wave theory. By applying specific numerical waveforms on the boundary of the numerical wave pool, waves of different types and characteristics can be simulated, with low cost and slow wave attenuation [22]. The wave pattern of the fifth-order wave in the VOF wave model was selected to simulate the wave [23], and the fifth-order wave model was adopted to further enhance the complexity and accuracy of the generated waves so as to better simulate waves under real sea conditions and provide more accurate data for our research. Figure 3 shows a schematic diagram of the numerical wave pool and boundary conditions used in this study.

Waves were generated in a numerical wave pool in a fifth-order wave model at the velocity inlet and propagated in the x direction toward the pressure outlet. In order to reduce the reflection of waves at the boundary and more accurately simulate the interaction between waves and structures, damping wave dissipation was introduced [24]. The damped wave dissipation model provided by STAR-CCM+ was adopted to eliminate the waves. The length of the wave dissipation region is usually one to two times the constant wave wavelength [25,26]. A 2L_max wave dissipation distance was set at the exit, and the wave dissipation distance on both sides was 100 m. In addition, in order to increase the wave elimination effect, grid-damping technology was used in the density area 2L_max away from the exit in the free surface density area [27]. The wave damping effect is shown in Figure 4. During the wave propagation process, the wave height becomes increasingly greater due to wave absorption. The lower it is, the greater the degree to which wave reflection is significantly reduced.

A probe was set at the entrance of the numerical wave pool and 0.5D in front of the buoy to monitor the wave height at this position. The wave heights of the two monitoring points were analyzed to evaluate the accuracy and reliability of the numerical wave pool simulation in the buoy movement area. This helped us to assess the suitability of the boundary conditions, and it also optimizes the setup of the wave generator for a more realistic and reliable wave simulation. Figure 5 shows wave height timing diagrams of five periods at the case 1 and case 4 monitoring points. It can be seen that the numerical wave pool has good accuracy and reliability.

2.5. Grid Discretization

This simulation study used overlapping grid technology. During mesh generation, surface reconstruction settings and a cutting volume grid generator were used in the background domain. In order to save computing time and resources, a sparse grid was used everywhere except for the free-surface encryption area. The height of the free-surface encryption area is 1.25 times the height of each wave, and the length and width are the same as the length and width of the background domain. An isotropic mesh was used in the sparse area of the background domain, and an anisotropic mesh was used in the free-surface encryption area. The mesh height of the free-surface encryption area in the working area = 1/20 h (h is the wave height of each case), and the mesh aspect ratio is 1:4. Mesh damping technology was used in the free surface encryption region in the wave dissipation region to increase the mesh length and cause greater numerical dissipation. Surface reconstruction, a cutting body mesh generator, and a prismatic layer generator were employed in the overlap domain. An isotropic mesh was used in the overlap domain, and the mesh size of the overlap domain is consistent with the maximum wave height of the simulated condition. In order to ensure the effective propagation of waves in the overlap domain, an anisotropic free surface encryption area was set near the free surface of the overlap domain, and the mesh size ratio is consistent with that of the free surface encryption area of the background domain. A prismatic layer [28] was generated around the body surface, and five layers were selected, with a total thickness of 0.03 m and a growth rate of 1.1. In order to ensure the accuracy of flow field simulation around the buoy, the encryption area shown in Figure 6a was set. The encryption area adopts various same-sex encryption schemes, and the grid height ratio of the outermost grid, the encryption area, and the overlapping area of the entire computing domain is 8:4:2:1. The following figures show the result of grid division.

2.6. Solving Settings

The six-degree-of-freedom solver, implicit unsteady solver, and second-order time discrete scheme were employed. The time step was determined according to the following formula [28]:

$$t_{step}=\frac{T}{2.4n}$$

Above, T is the wave period, and n is the number of grids within one wavelength of a free-surface encryption region.

In numerical simulation calculation, the maximum number of iterations allowed in each time step has a significant impact on the calculation result, but too many iterations will not only consume more computing resources but also fail to improve calculation accuracy. Figure 7 shows the independence curves of the maximum number of iterations of case 1 and case 4 in the numerical simulation calculation of the buoy. It can be seen that the maximum number of iterations is preferably 20.

2.7. Numerical Validation

In order to make simulation results more convincing, the accuracy and effectiveness of a numerical simulation scheme should be checked and compared with existing research results. The authors of [7] conducted a numerical simulation and experiments on the motion performance of a 10 m diameter large disc buoy with respect to a first-order regular wave. During the verification calculation, the geometric parameters of the buoy model were consistent with those in the literature. The grid division scheme was adopted to simulate the buoy’s heave motion in response to a first-order wave, and the simulation results were compared with the experimental data in the literature (shown in Figure 8). It can be seen from the figure that the numerical simulation results are in good agreement with the experiment, and the deviation between the simulation results and the experimental values is basically less than 5%, which shows that the numerical simulation scheme has high reliability and accuracy.

3. Result Analysis

3.1. Analysis of Buoy Motion Response

Based on the numerical simulation scheme proposed in Section 2, six working conditions of the analyzed buoy under the combined action of wind and waves were simulated. Figure 9 shows the timing diagram of the 6DOF motion response of the buoy in the six working conditions. It can be seen in the figure that under the combined action of a uniform incoming flow and fifth-order waves, the six-degree-of-freedom response of the buoy tends to be stable after a certain period of time and then maintains a constant amplitude, speed, and frequency. The buoy motion response is closely related to the period and amplitude of the waves. When the wave amplitude and period increase, the response amplitude and speed of the six-degree-of-freedom motion also increase. Figure 10 shows the standard deviation of the six-degree-of-freedom motion response of the buoy under different conditions. The standard deviation reflects the dispersion of the six-degree-of-freedom motion amplitude. It can be seen that under the combined action of wind and waves, the buoy’s movement mainly responds to heave, pitch, and surge, while the response fluctuations of rotation, sway, and roll are smaller.

As wave height and wind speed increase, the amplitudes of yaw, sway, and roll also increase. Their amplitude responses are closely related to the wave period, and the overall response period is consistent with the wave period. As the wave height increases, the heave amplitude of the buoy gradually increases. This is because the higher the wave height, the greater the wave force exerted on the buoy, resulting in a more obvious displacement of the buoy in the vertical direction. Larger waves correspond to faster fluid speeds and corresponding greater heave motion rates. As the wave height increases, the response amplitude of the buoy’s pitch motion also increases, but the rate of pitch motion becomes smaller. At shorter wave periods, the pitch motions become more frequent. As the wave height increases, the amplitude of the swaying motion also increases. Due to the binding effect of the anchor chain, the swaying motion reaches a certain amplitude and then moves back and forth periodically with the waves. For all six working conditions, the more severe the sea state, the greater the response rate of the buoy per unit time, and the greater the impact on the measurement accuracy of the wind speed monitoring point. With the change in the working conditions, the wave height increases from 0.067 times the diameter of the buoy to 1.097 times this diameter, and the wave height gradually approaches the geometric size of the buoy, which makes the impact of wave movement on the buoy more serious. In Case 1~Case 4, the wave height is less than 0.5 times the buoy diameter. In Case 5 and Case 6, the wave height is 0.701 times and 1.097 times the buoy’s direct longitude, respectively, and these values are close to the characteristic diameter of the buoy’s body, indicating that wave height affects the motion characteristics of the buoy. When the height of the wave is close to the overall geometric size of the buoy, the buoy has significant motion fluctuations in terms of heave, surge, yaw, and pitch. However, when the height of the wave is less than the characteristic radius of the buoy, the wave characteristics of its motion are not obvious.

The power spectrum characteristics of buoy motion under six sea conditions are shown in Figure 11. It can be seen from the figure that the buoy’s motion is modulated by the wave motion characteristics. From Case 1 to Case 8, the wave period ranges from 3.9 s to 12.5 s, and the corresponding wave frequency, fc, is reduced from 0.256 Hz to 0.080 Hz. Correspondingly, the 6-DOF motions of the buoy under the six working conditions all exhibit the response characteristics of wave frequency and its multiplier frequency. As the working conditions change, the wave period increases, the wave frequency decreases, the response frequency of the buoy movement advances, and its spectral density increases. It can be concluded that buoy motion and wave motion exhibit a strong coupling effect. The larger the wave wavelength and the greater the wave height, the earlier the frequency response of the buoy motion and the higher its response amplitude.

3.2. Fluctuation Analysis of Buoy Measurement Results

The buoy moves with the wave, and this 6DOF movement affects the measurement accuracy of the measuring device with respect to the buoy. Figure 12 shows a box diagram of the wind speed (u, v, and w) at the monitoring points of sensor 1 and sensor 2 in the x, y, and z directions in Case 1 to Case 6. When drawing the wind speed monitoring box diagram, in order to clearly reflect the deviation and distribution fluctuation range of the monitoring value relative to the reference wind speed in each working condition, the monitoring data were rendered dimensionless using the reference wind speed. The reference wind speeds corresponding to the uniform inflow under working conditions 1 to 6 were 6.7 m/s, 9.4 m/s, 12.3 m/s, 15.5 m/s, 19 m/s, and 22.6 m/s, respectively. Due to the coupling of wind and wave movement and the six-degree-of-freedom movement of the buoy, there are y direction and z direction wind speeds in the monitoring data of the buoy. As wave height and wind speed increase, the induced velocities in the y and z directions become more pronounced. When the wave heights are 0.067 times and 0.131 times greater, the influence of wave height and 6-DOF motion on wind speed is small. The detected fluctuation range of wind speed is small, and the induced wind speed is almost zero. When the wave is 0.25 times larger than the buoy’s diameter, the variation range of the wind speed at the measuring point begins to increase, and the induced wind speed in the y and z directions also begins to increase. Moreover, the range of variation becomes larger and larger, and the number of abnormal monitoring points also increases, which is closely related to the interaction between waves and wind speed. Especially in case 6, the sea conditions are relatively extreme, the variation range of induced velocity at point y is close to the original wind speed value, and there is also an obvious induced velocity in the z direction. At this time, the velocities in these two directions contribute greatly to the combined velocities of the monitoring points, resulting in a large error component. The buoy wind speed sensors 1 and 2 are located 1.2 m and 1.5 m away from the buoy mounting platform. The motion of the floating body will mainly affect the measurement results in the x direction of the upper measurement point. Therefore, when using buoys to measure speed in extreme sea conditions such as Case 6, the measured X-direction speed must be corrected and calibrated to ensure the accuracy of wind speed measurement.

Waves and wind interact with each other on the sea surface, which results in complex flow fields near the sea surface. When the buoy is in this unstable area, the error in the wind speed monitored at Sensor 1 and Sensor 2 will also become larger. In order to evaluate the wind speed measurement error at Sensor 1 and Sensor 2, we sampled 10 fixed points with an interval of 2 m within the vertical height range of 20 m in front of the buoy. The points start at 6 m above the sea surface and end at an altitude of 26 m. The average value of these ten points was taken as the true value of the ambient wind speed on the sea surface. Figure 13 compares the wind speed and ambient wind speed at Sensor 1 and Sensor 2 in six cases. It can be seen that under the six working conditions, the wind speed measured at these points has good consistency with the ambient wind speed. Even under the more extreme working conditions of Case 6, the wind speed error is less than 10%.

3.3. Flow Field Structure Analysis of the Buoy Movement

The velocity contour near the buoy can visually show the change in buoy motion range. Figure 14 shows the velocity fields of the buoy at different times (t = 10 s, 40 s, 70 s, 100 s, 130 s, and 160 s) under normal sea conditions (Case 1) and extreme sea conditions (Case 8), respectively. In the initial moment stage (t = 10 s), the wave motion is relatively gentle, and the change in buoy motion attitude is small. As time progresses, the wave motion amplitude increases, the buoy motion state is forced by the wave motion, the buoy attitude changes, and the velocity field fluctuation increases. Under normal sea conditions, the motion range of the buoy remains small during the whole period, and the changes in wave motion and the velocity field are gentle. In the extreme sea conditions, the wave motion is violent, the wavelength and wave height are large, the wave period is long, and the geometric size of the wave is equivalent to the geometric size of the buoy, making the buoy have a large motion range and a more severe change in the velocity field. It can also be seen that in Case 6, vorticity caused by waves appears at some moments. Under extreme working conditions, the vorticity caused by the violent movement of the wave surface upstream of the buoy (as shown in the black, dotted area in the figure below) will affect the 6DOF movement of the buoy, thereby increasing the deviation of the speed monitoring value.

4. Discussion

From the analysis in the previous section, it can be seen that when the wave height is similar to the size of a buoy, it will significantly affect the movement of the buoy, thereby causing deviations in the measurement results, but the overall deviation is less than 10%. Then, for buoys with other design parameters, when the wave height is close to the size of the buoy, it is also necessary to control the data error of the buoy during measurement. The usual method for this is as follows:

(1)

Use a higher sampling rate and a longer recording length for the buoy measurements, as this can reduce the uncertainty and variability of the estimates;

(2)

Apply a calibration or correction method to the buoy measurements, as this can account for the bias and error introduced by buoy motion, sensor noise, or wave breaking;

(3)

Use a combination of different types of sensors, such as wave gauges, acoustic Doppler current profilers, or satellite altimeters, to cross-validate and complement the buoy measurements.

The stability of a buoy can also be improved by improving the design parameters. In sea conditions with high wave heights, using a buoy with a larger geometric size can effectively improve its stability, but this is only a general recommendation. When designing a buoy, one must conduct detailed numerical simulations and experimental tests on the geometric parameters of the analyzed buoy and adjust its characteristic size, weight distribution, mooring system, etc. A streamlined shape will improve the hydrodynamic characteristics of a buoy. The positioning of sensors also has an impact on buoy measurement results, requiring detailed numerical and test-based analysis before the buoy is manufactured. There are some external factors that may affect buoy motion response and data measurement accuracy, such as tides, marine life, offshore wind farm wake, etc. Tides can cause changes in water depth and salinity that may affect a buoy’s stability and drag. Marine life can become attached to the buoy or its sensors and cause fouling or damage. In recent years, many offshore wind farms have been developed. The wake of wind farms has a highly spiral-like structure. The superposition effect of wakes has a more significant impact on the atmospheric environment [29], which will also affect the movement of buoys. Therefore, it is important to monitor and maintain a buoy regularly and to account for these factors when analyzing the data. Furthermore, in terms of structure, the buoyancy, weight distribution, mooring system, and hydrodynamic characteristics of a buoy need to be considered in the design. These aspects will determine how a buoy responds to different wave frequencies and directions and how it maintains its position in the water. In terms of sensor placement, sensor sampling rate, resolution, calibration, and protection also need to be considered. These aspects will determine the ability of the sensors to capture wave information as well as their reliability and robustness in harsh environments. By optimizing these factors, buoys can provide more accurate and consistent data for wave analysis and forecasting. In future work, we will conduct in-depth research on buoy designs with different structures and buoy motion under various environmental influences.

5. Conclusions

The development of sea-related industries such as offshore wind energy has given rise to higher requirements for the accuracy of offshore wind speed measurement [30]. In order to explore the response behavior of a buoy under different wave conditions and the influence of its movement on wind speed measurement at the monitoring point, in this work, we simulated the six-degree-of-freedom movement of a buoy under six sea conditions based on the IDDES method and overlapping grid technology. We focused on analyzing the motion laws of the buoy under different sea conditions and quantified their motion response characteristics. Under the six sea conditions, the heave and pitch motions of the buoy were sensitive to changes in working conditions. When designing a buoy, extra attention should be paid to its stability in the directions of heave and pitch motions.

This work also quantifies the fluctuation degree of buoy motion in different sea conditions. Under different working conditions, the motion fluctuations in the heave, surge, and pitch directions are more severe, and the motion fluctuations in the sway, roll, and yaw directions are small. Wave height and wavelength affect the movement characteristics of a buoy. By analyzing the power spectrum characteristics of the buoy’s movement, it was found that buoy movement and wave movement show a strong coupling effect. The larger the wave’s wavelength and the greater the wave height, the earlier the frequency response of the buoy movement and the higher the response amplitude. When the wave height and wavelength are similar to the overall geometric size of the buoy, the fluctuation characteristics of its movement in terms of heave, surge, and pitch motion are significant. The stability of buoys in extreme sea conditions was also discussed in detail. As the wave height and wavelength increase, the velocity deviation caused by the velocity of the measuring point will further increase, which will significantly affect the accuracy of the measurement results.

In this work, we also analyzed the effect of buoy motion on the velocity measurements of a measuring device. The results show that the movement of the buoy mainly affects the measurement results in the x direction of the measurement point. Therefore, when using a buoy to measure velocity, the measured velocity in the x direction must be corrected and calibrated to ensure the accuracy of the measurement of the atmospheric incoming velocity.