Method for simulating sediment erosion around offshore wind turbine foundation by ISPH combined with modified k-epsilon turbulence model

Abstract

This invention discloses a method for simulating sediment erosion around offshore wind turbine foundations using an ISPH-modified k-ε turbulence model. The method includes the following steps: establishing an ISPH discretization algorithm for solving the ensemble-averaged mass conservation equation and momentum conservation equation; modifying the standard k-ε turbulence model; and calculating the turbulent eddy viscosity ν in the Reynolds stress tensor expression. t This invention introduces the critical initiation theory on slopes to modify and extend the traditional two-dimensional sediment initiation model, establishing a three-dimensional sediment initiation model. A local scour experimental flume model for a single pile foundation of an offshore wind turbine is established, along with a corresponding ISPH numerical flume model. The experimental and numerical flume models respectively simulate the sediment scour process around the cylinder, and the numerical simulation results are compared, verified, and analyzed with the experimental results. This method can effectively simulate the sediment erosion process around a single pile foundation of an offshore wind turbine, with short computation time and meeting the needs of practical engineering.

Description

Technical Field

[0001] This invention belongs to the field of local scour technology around offshore wind turbine foundations, and particularly relates to a method for simulating sediment erosion around offshore wind turbine foundations using an ISPH combined with a modified k-ε turbulence model. Background Technology

[0002] Wind energy, as a clean, pollution-free, and renewable energy source, has received widespread attention and vigorous promotion from the international community. Offshore wind power, superior to onshore wind power in terms of stability, power generation, environmental impact, and grid connection convenience, is increasingly valued and applied. The Global Wind Energy Council's "Global Offshore Wind Report 2023" shows that by the end of 2022, the global installed capacity of offshore wind power reached 64.3 million kilowatts, of which Europe accounted for 30 million kilowatts. In 2022, the global newly installed offshore wind power capacity reached 8.8 million kilowatts, continuing to lead the growth of the global offshore wind power market. As of June 30, 2023, China's installed capacity of offshore wind power has maintained its leading position globally for many consecutive years, achieving more than 5 million kilowatts of new installed capacity in 2022, further consolidating China's dominant position in the global offshore wind power market. Despite the promising market prospects for offshore wind power, offshore wind power still faces many problems and challenges. The most significant challenge lies in the lack of mature wind turbine foundation technology, which is a crucial component of offshore wind turbines. Depending on factors such as water depth and load, various types of offshore wind turbine foundations have emerged, including large-diameter monopile foundations, gravity structural foundations, tripod foundations, jacket foundations, and suction bucket foundations. The most widely used is the large-diameter monopile foundation; in Europe, over 81.5% of offshore wind turbine foundations are monopile foundations. Furthermore, the monopile foundation is recommended by DNV standards, the most widely used standard in the offshore wind power development industry, as the optimal foundation type for near-shore wind turbines in water depths below 30m. Since most of my country's wind turbines are located in shallow near-shore waters, monopile foundations are even more suitable.

[0003] In marine environments, wind turbine monopile foundations can be approximated as pile structures. The presence of these pile structures alters the original flow field characteristics, particularly in the area surrounding the structure, potentially creating strong vortex effects and hydrodynamic disturbances. These factors exacerbate localized scouring. The deepening of scour pits means a reduction in the burial depth of the piles originally anchored to the seabed. This can lead to decreased pile stability and changes in the horizontal loads borne by the piles, such as increased eccentricity, posing a potential threat to the structural safety of the entire wind turbine. In recent years, localized scouring around offshore wind turbine foundations has become a critical challenge in marine engineering and offshore power generation. For offshore wind turbines, the stability of the foundation determines the safety of the entire turbine. In the ocean, wind turbines are subjected to the coupled effects of horizontal loads such as wind, waves, and currents. Simultaneously, under the influence of waves and currents, the monopile foundation is also subject to localized scouring, forming scour pits at the bottom of the piles. This prevents the seabed from providing sufficient support for the turbine, creating safety hazards and potentially leading to turbine instability and failure, resulting in major safety accidents. Therefore, revealing the local scour process and sediment movement patterns around the monopile foundation of offshore wind turbines has become a key issue in the field of marine engineering. At the same time, studying the local scour characteristics and maximum scour depth around the wind turbine foundation has become a top priority in wind turbine construction.

[0004] To assess the safety of wind turbine foundations, accurate prediction of sediment erosion processes and scour depths around the foundations is crucial. Previous physical model experiments and field observations have struggled to accurately capture the sediment erosion process. Furthermore, grid-based models suffer from significant numerical dissipation when dealing with complex free surface deformations, such as water drop during tsunami surges, due to the need to solve convection terms in the equations. In recent years, with the rapid development of computer technology, numerical simulation has gained importance due to its low cost, adaptability to various fluids and complex terrains, and high flexibility. The Incompressible Smoothed Particle Hydrodynamics (ISPH) method offers significant advantages in handling complex free surfaces and water-sediment interfaces. While numerous studies have investigated the numerical simulation of localized scour of offshore wind turbine monopile foundations, research using the ISPH method in conjunction with sediment initiation models and modified turbulence models to simulate localized scour of monopile foundations is scarce. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a method for simulating sediment erosion around offshore wind turbine foundations. Based on the ISPH method combined with a sediment initiation model and a modified k-ε turbulence model, this method studies the three-dimensional local scouring problem of a monopile foundation cylinder. It can effectively simulate the sediment erosion process around the monopile foundation cylinder of an offshore wind turbine, aiming to reveal the laws governing the sediment erosion process around the wind turbine foundation and provide safety guidance for the safe design and installation of wind turbines.

[0006] This invention is implemented as follows: a method for simulating sediment erosion around offshore wind turbine foundations using ISPH combined with a modified k-ε turbulence model. The method utilizes ISPH combined with a sediment initiation model and a modified k-ε turbulence model to simulate the flow field characteristics and local scour process around the offshore wind turbine foundations. The method includes the following steps:

[0007] S1. Establish the ISPH discretization algorithm for solving the average mass conservation equation and momentum conservation equation (i.e., NS equation) of the fluid dynamics ensemble. The NS equation is expressed as follows:

[0008]

[0009]

[0010] In the formula, ρ0 is the fluid density, t is time, u is the ensemble average velocity, g is the gravitational acceleration, ν0 is the kinematic viscosity, and p is the pressure. Let Reynolds stress tensor be the stress tensor.

[0011] S2, Modify the standard k-ε turbulence model and calculate the turbulent eddy viscosity ν in the Reynolds stress tensor expression. t ;

[0012] S3 introduces the critical sediment initiation criterion on the slope, modifies and extends the traditional two-dimensional sediment initiation model, and establishes a three-dimensional sediment initiation model.

[0013] S4. Establish a physical model of the test water tank for scour of a single pile foundation of an offshore wind turbine.

[0014] S5, Establish the corresponding ISPH numerical flume model;

[0015] S6. The experimental water tank model and the numerical water tank model respectively simulate the characteristics of the sediment scouring process around the cylinder. The numerical simulation results are compared with the experimental results for verification and analysis.

[0016] Furthermore, in step S2, a turbulent kinetic energy k is defined at each particle i. i and energy dissipation rate ε i For turbulence in the ocean, the standard k-ε turbulence closure model has the following form:

[0017]

[0018] In the formula, σ k =1.0, σ ε =1.3, C ε1 =1.44, C ε2 =1.92, where P represents the generation term of turbulent kinetic energy, t is time, and the viscosity ν of the turbulent eddy current is... t Make corrections:

[0019]

[0020] In the formula, To correct the dissipation rate, we take λ3 = 0.1. in Represents the deformation rate tensor. This represents the rotational rate tensor of the ensemble-mean flow field. The subscript 'initial' indicates the time-averaged and depth-averaged values ​​within the first wave cycle in the potential flow region. Let p be the value of the rotational rate tensor. 0initial =1.24s -2 p Ωinitial =1.18×10 -8 s -2 C μ C1 and C2 are empirical constants, and in this model, C μ =0.09, C1=1.33, C2=1.92.

[0021] Furthermore, S3 modifies and extends the traditional two-dimensional sediment initiation model, and the extended equation is:

[0022]

[0023] In the formula, Let α be the ratio of the critical shear stress of the slope sediment to the critical shear stress of the horizontal plane, α be the angle between the S-plane and the S' plane on the yz plane, β be the angle between the S-plane and the S' plane on the xz plane, φ be the angle of repose of the sediment, and η be 0.85. This ratio represents the ratio of the calculated shear stress of the bedrock particles to the critical shear stress of the horizontal sediment obtained from the Shields curve. It is then assumed that the bed particles have reached the critical initiation state, will transform into turbid water particles, and will participate in the calculation of the Navier-Stokes equations, τ bi Calculation of shear stress in sediment:

[0024]

[0025] In the formula, κ is the Karman coefficient, taken as 0.4, D is the diameter of the particle, and u bi Let i be the tangential velocity component of particle i.

[0026] Furthermore, the experimental water tank model described in step S4 has a total length of 35m, a width of 7m, and a depth of 1.6m. A 9m long area is set in the center of the water tank as a scouring test area, which is pre-filled with a layer of experimental fine sand with a depth of 0.60m. A cylindrical model with a diameter of 0.6m is set in the center of the test area. An inflow area is set on the left side of the experimental water tank, and an outflow area is set on the right side to maintain water level balance. There are no fewer than 5 experimental groups, with an experimental water depth of 0.3m and an average flow velocity of 0.157~0.216m / s.

[0027] Furthermore, in step S5, to improve computational efficiency and facilitate observation of key areas, the computational domain of the numerical flume model is set to a length of 5.45m, which is 9 times the diameter of the cylindrical model, and a width of 5m, which is 8.3 times the diameter of the cylindrical model; the particle diameter in the numerical model is set to 0.02m; an inflow region is set on the left side of the model, and a uniform flow velocity is applied according to actual experimental data to simulate the inflow of upstream water; an outflow region is set on the right side of the model to keep the water level relatively constant throughout the model; along the longitudinal section of the cylinder in the direction of water flow, a series of numerical velocity measurement points are set according to different water depths to collect velocity data at the corresponding locations during the simulation.

[0028] Furthermore, step S6 verifies and analyzes the flow field distribution characteristics around the cylinder, including velocity distribution, vortex structure, and turbulent kinetic energy distribution; then, it verifies and analyzes the characteristics of the sediment scouring process around the cylinder.

[0029] The beneficial effects of this invention are:

[0030] (1) Compared with the existing technology, by using ISPH and combining the sediment initiation erosion model and the modified k-ε turbulence model, a three-dimensional numerical flume was established to simulate the flow field around the offshore wind turbine foundation under unidirectional water flow. The numerical simulation results were compared with the experimental results to verify the accuracy of the flow field calculation.

[0031] (2) The numerical model results are in good agreement with the experimental data. The established numerical flume can effectively simulate the flow field around the wind turbine monopile foundation and can accurately reflect the flow field distribution characteristics around the wind turbine monopile foundation. The downward flow in front of the monopile, the streamline contraction on both sides of the monopile and the tail vortex behind the monopile are all well simulated, which verifies the accuracy and applicability of the numerical model of the present invention.

[0032] (3) Based on the physical model test results of the scouring around the cylinder, the method of the present invention can well simulate the erosion process of mud and sand around the monopile foundation of offshore wind turbine, which can meet the needs of actual engineering.

[0033] The present invention will be further explained in detail below with reference to the accompanying drawings and specific implementation methods. Attached Figure Description

[0034] Figure 1 3D slope diagram;

[0035] Figure 2 A diagram showing the angular relationship between local and global coordinates;

[0036] Figure 3 Schematic diagram of the experimental water tank layout;

[0037] Figure 4 Numerical model settings;

[0038] Figure 5 Horizontal velocity diagrams at different depths of the cross-section;

[0039] Figure 6 Numerical model water depth variation at x = 1.5m;

[0040] Figure 7 Graph showing velocity variation trends at different water depths;

[0041] Figure 8 Vortex diagram around a cylinder;

[0042] Figure 9 Streamline diagram around a cylinder;

[0043] Figure 10 Diagram illustrating the formation process of a horseshoe vortex;

[0044] Figure 11 Turbulent kinetic energy distribution cloud map;

[0045] Figure 12 Plan view of the sediment erosion process;

[0046] Figure 13 Longitudinal profile of the sediment erosion process;

[0047] Figure 14 Comparison of experimental and simulation results of scour depth in front of a cylinder;

[0048] Figure 15 Comparison of experimental and simulation results of scour depth behind a cylinder;

[0049] Figure 16 Comparison of experimental and simulation results of lateral scour depth of a cylinder; Detailed Implementation

[0050] This invention discloses a method for simulating sediment erosion around offshore wind turbine foundations using ISPH combined with a modified k-ε turbulence model. The method utilizes ISPH, combined with a sediment initiation model and a modified k-ε turbulence model, to simulate the flow field characteristics and local scouring process around the cylindrical foundation of an offshore wind turbine. Incompressible Smoothed Particle Hydrodynamics (ISPH) discretizes a continuous fluid domain into a series of particles with a certain mass. These particles represent a portion of the fluid and carry various physical properties of the fluid, such as density, velocity, and pressure, and move according to the Navier-Stokes equations.

[0051] The method steps include:

[0052] S1. Establish the ISPH discretization algorithm for solving the average mass conservation equation and momentum conservation equation (i.e., NS equation) of the fluid dynamics ensemble. The NS equation is expressed as follows:

[0053]

[0054] In the formula, ρ0 is the fluid density, t is time, u is the ensemble average velocity, g is the gravitational acceleration, ν0 is the kinematic viscosity, and p is the pressure. Let be the Reynolds stress tensor.

[0055] S2, Modify the standard k-ε turbulence model and calculate the turbulent eddy viscosity ν in the Reynolds stress tensor expression. t .

[0056] In the ISPH method, a turbulent kinetic energy k is defined at each particle i. i and energy dissipation rate ε i For turbulence in the ocean, the k-ε turbulence closure model has the following form:

[0057]

[0058] In the formula, σ k =1.0, σ ε =1.3, C ε1 =1.44, C ε2 =1.92, where P represents the generation term of turbulent kinetic energy, t is time, and the viscosity ν of the turbulent eddy current is... t Make corrections:

[0059]

[0060] In the formula, To correct the dissipation rate, we take λ3 = 0. in Represents the deformation rate tensor. This represents the rotational rate tensor of the ensemble-mean flow field. The subscript 'initial' indicates the time-averaged and depth-averaged values ​​within the first wave cycle in the potential flow region. Let p be the value of the rotational rate tensor. 0initial =1.24s -2 p Ωinitial =1.18×10 -8 s -2 C μ C1 and C2 are empirical constants, and in this model, C μ =0.09, C1=1.33, C2=1.92.

[0061] S3 introduces a critical sediment initiation criterion on slopes to modify and extend the traditional two-dimensional sediment initiation model, establishing a three-dimensional sediment initiation model. In this three-dimensional model, especially on sloping terrain, the influence of gravity on sediment leads to significant differences in the initiation shear stress between the positive slope (along the direction of water flow) and the negative slope (against the direction of water flow). On the positive slope, sediment is more easily washed away by the water flow, resulting in a relatively small initiation shear stress; while on the negative slope, due to the effect of gravity against the water flow, a larger shear stress is required for sediment to be initiated. To address this issue, a critical sediment initiation theory on slopes is introduced into the three-dimensional sediment initiation model, modifying and extending the traditional two-dimensional model.

[0062] Under normal circumstances, the critical shear stress τ of horizontal sediment is... c The calculation method is as follows: calculate parameters The values ​​are: d is the actual sediment particle size, ν is the viscosity, and γ is the viscosity. s γ and τ are the unit weights of sediment and water, respectively. In the Shields curve, τ * Find the corresponding value on the line where τ = 0.1; draw a line with a slope of 2 through this point that intersects the curve, and the ordinate of the intersection point is the critical Shields number τ. *c Then substitute it into equation τ *c =τ c / (γ s -γ)d, the critical starting shear stress τ can be obtained. c .

[0063] To accurately simulate the movement and erosion process of sediment on sloping terrain, an approximate plane (representing the slope surface S') is first fitted to the set of neighboring particles within the smooth radius of each particle on the substrate surface using the least squares method. Figure 1 Let S' be the local coordinate system of any particle on the slope surface. The angular relationship between the local coordinates and the global coordinates is as follows: Figure 2 As shown. The extended equation for the sloping terrain is:

[0064]

[0065] In the formula, Let α be the ratio of the critical shear stress of the slope sediment to the critical shear stress of the horizontal plane, α be the angle between the S-plane and the S' plane on the yz plane, β be the angle between the S-plane and the S' plane on the xz plane, φ be the angle of repose of the sediment, and η be 0.85. This ratio represents the ratio of the calculated shear stress of the bedrock particles to the critical shear stress of the horizontal sediment obtained from the Shields curve. It is then assumed that the bed particles have reached the critical initiation state, will transform into turbid water particles, and will participate in the calculation of the Navier-Stokes equations, τ bi Calculation of shear stress in sediment:

[0066]

[0067] In the formula, κ is the Karman coefficient, taken as 0.4, D is the diameter of the particle, and u bi Let i be the tangential velocity component of particle i.

[0068] S4. Establish a physical model of the experimental water tank for local scour of a monopile foundation of an offshore wind turbine. For example... Figure 3 As shown, the experimental water tank model has a total length of 35m, a width of 7m, and a depth of 1.6m. A 9m long area is set in the center of the water tank as the scouring test zone. The scouring test zone is pre-filled with a layer of fine sand to a depth of 0.60m. A cylindrical model is set in the center of the test zone. An inflow area is set on the left side of the experimental water tank, and an outflow area is set on the right side to maintain water level balance. There are no fewer than 5 experimental groups. The diameter of the cylindrical model is 0.6m, the water depth is 0.3-0.5m, and the average flow velocity is 0.157-0.216m / s.

[0069] Table 1 Experimental group and parameters

[0070]

[0071] S5, establish the corresponding ISPH numerical flume model. For example... Figure 4As shown, to improve computational efficiency and facilitate observation of key areas, the dimensions of the actual experimental area were adaptively adjusted according to the simulation requirements. The initial parameters of the model were as follows: the computational area of ​​the numerical flume model was set to a length of 5.45m, which is 9 times the diameter of the cylindrical model, and the width was set to approximately 5m, which is 8.3 times the diameter of the cylindrical model. The particle diameter in the numerical model was set to 0.02m. An inflow region was set on the left side of the model, and a uniform flow velocity was applied according to the actual experimental data to simulate the inflow of water from the upstream source. An outflow region was configured on the right side of the model to maintain a relatively constant water level throughout the model. A series of numerical velocity measurement points were set along the longitudinal section of the cylinder along the water flow direction, according to different water depths, to collect velocity data at the corresponding locations during the simulation.

[0072] S6. Experimental and numerical flume models were used to simulate the sediment scouring process around the cylinder. Using ISPH combined with a three-dimensional sediment initiation model and a modified k-ε turbulence model, the numerical simulation results were compared with experimental results to verify the accuracy of the flow field calculations and analyze the flow field distribution around the wind turbine monopile foundation. The flow field distribution characteristics around the cylinder were analyzed, including velocity distribution, vortex structure, and turbulent kinetic energy distribution. Finally, the sediment scouring process characteristics around the cylinder were verified and analyzed.

[0073] Specifically, the numerical model verification uses the water depth and average flow velocity of experimental group 1 in the experimental water tank, and the scouring area at the bottom of the model is reduced to a frustum shape, such as... Figure 4 As shown in the red area in (b), an initial water level is preset above the bed surface, such as... Figure 4 As shown in blue in the middle, an inflow area is set on the left side of the model and an outflow area is set on the right side. Based on the experience of multiple debugging, 10 layers of particles are set in both the inflow and outflow areas. The flow velocity adopts a vertical uniform inflow method. There is a sand pit in the central area that can be eroded by sediment, and the depth of the sand pit is 0.6m.

[0074] The model verification is performed on the longitudinal section of the cylinder along the water flow direction. A series of numerical velocity measurement points are set according to different water depths, as shown in Table 2, to record the velocity data at the corresponding locations during the simulation.

[0075] Table 2 Location of Flow Velocity Measurement Points

[0076]

[0077] 1. Flow field verification

[0078] Figure 5The figure shows the horizontal flow velocity at different depths of the cross section. It can be seen from the figure that the water flow velocity is significantly lower near the bottom, and the increase in flow velocity follows a logarithmic change with water depth. The calculated average flow velocity of the cross section is 0.158 m / s, which is close to the average flow velocity of 0.157 m / s required for the experiment. Figure 5 The red dot in the middle Figure 7 The data shows the specific changes in flow velocity.

[0079] Figure 6 , Figure 7 The curves showing the change in water depth and the change in flow velocity over time at different water depths are displayed. Figure 6 The water depth fluctuated significantly in the early and middle stages due to the unstable water flow velocity at the start of the numerical simulation. However, the fluctuations gradually decreased after 5 seconds, and the water depth stabilized after 15 seconds. Furthermore, the water depth remained above 0.3 m after 5 seconds, which is consistent with the water depth required by the experimental data. Figure 7 (a) and (b) show the changes in water flow velocity over time at distances of 0.1 m and 0.2 m from the bottom, respectively. Because Figure 7 In diagram (a), the water flow is relatively close to the bottom, resulting in a relatively low velocity, which matches the actual flow rate. In diagram (b), the velocity fluctuation is relatively large at the beginning, but gradually decreases after 5 seconds, fluctuating around a velocity of u = 0.157 m / s. Although the initial fluctuations in the numerical simulation are relatively large, the overall trend matches the flow velocity conditions required by the experiment. Therefore, this numerical model can simulate a relatively realistic flow field, and the simulated flow field can reproduce the flow field required by the experiment.

[0080] 2. Eddy power verification

[0081] Vorticity is typically used to represent the degree of rotation or rotational speed of a fluid at its location. Under the influence of water flow, there will be a significant structural difference in the flow field before and after a cylinder. Due to the obstruction of the cylinder, vortices will form around it, and the size and direction of these vortices are primarily represented by vorticity.

[0082]

[0083] In the formula, the two terms on the right side represent the partial derivatives of the velocity u in the x direction with respect to the y direction and the partial derivatives of the velocity v in the y direction with respect to the x direction, respectively.

[0084] Figure 8This diagram shows the vorticity field around the cylinder. Red particles represent positive vorticity, and blue particles represent negative vorticity. Behind the cylinder, the presence of the cylinder alters the fluid flow path, forcing the water to converge towards the inner side behind the cylinder. This process is accompanied by a loss of kinetic energy and a decrease in velocity. After passing the cylinder, the water's kinetic energy is insufficient to maintain its original straight flow, causing it to gradually detach from the cylinder and slowly diffuse. Simultaneously, water continuously replenishes the area behind the cylinder, filling the "blank" region created by the cylinder's obstruction, thus forming a wake vortex. Furthermore, because the water velocity distribution is inconsistent in the vertical direction, the development of the wake vortex also varies vertically, resulting in a phenomenon where the bottom layer of the wake vortex is smaller than the top layer. Figure 8 As shown in the cloud diagram of the vorticity around the cylinder, it causes the axis of the wake vortex to bend backward.

[0085] Figure 9 These are streamline diagrams at different times, illustrating the process of vortex formation and dissipation. It can be seen that as the fluid flows around the cylinder, vortices initially form near the cylinder's side. As the fluid flows further downstream, these initially formed vortices develop backward along the cylinder's surface, forming a distinct wake structure behind the cylinder. The wake behind the cylinder undergoes a series of development stages: starting with small-scale vortices, it gradually increases in size with increasing distance from the cylinder. During this process, vortices may merge and break up, forming a series of vortex structures of different scales. Ultimately, the larger vortices gradually weaken and disappear due to internal friction and turbulent dissipation. While they dissipate, new vortices are generated as water continuously replenishes the space behind the cylinder.

[0086] Figure 10 The formation process of a horseshoe vortex is shown in the figure. It is clearly visible that there is a downward water flow in front of the cylinder. The flow velocity direction changes in the bottom region in front of the cylinder, forming a horseshoe vortex. It is the presence of this horseshoe vortex that causes strong fluid disturbance and high shear stress in the region in front of the obstacle. The formation of the horseshoe vortex demonstrates that this numerical simulation can effectively simulate the vortex structure of the flow field and accurately reproduce the real flow field characteristics required by the experimental conditions. This provides an analytical basis for subsequent simulations of sediment erosion.

[0087] 3. Turbulent kinetic energy verification

[0088] Turbulence generally refers to the irregular and disordered motion of a fluid during flow due to various factors. In turbulence, the trajectories of fluid particles are exceptionally complex, and physical quantities such as velocity and pressure vary dramatically and randomly in space and time. Generally, a Reynolds number Re > 4000 is considered to indicate that the fluid is in a turbulent state. Turbulent phenomena involve the interaction between large-scale flow structures and small-scale eddies; the energy transfer process from large to small scales is extremely complex, requiring analysis of turbulent kinetic energy. This embodiment uses the aforementioned modified k-ε turbulence model for numerical calculations of turbulence.

[0089] Figure 11 This is a cloud map showing the distribution of turbulent kinetic energy. The trend of turbulent kinetic energy variation is consistent with that of vorticity in the region in front of the cylinder; that is, as the water flow develops, vorticity and turbulent kinetic energy initially increase, and then decrease as the backflow zone develops and the fluid continues to flow. Behind the cylinder, the distribution of turbulent kinetic energy is mainly affected by the shedding of the wake vortex. When the fluid bypasses the cylinder, a series of vortex structures form behind it. These vortices generate strong turbulence and high turbulent kinetic energy during their continuous development, breakup, and reorganization. Therefore, the turbulent kinetic energy region behind the cylinder usually exhibits strong turbulence, and due to the instability and periodic shedding of the wake vortex, the turbulent kinetic energy in this region is typically high, resulting in a more significant impact on phenomena such as bed scouring. As the water flow develops, due to the shedding of the wake vortex, the turbulent kinetic energy behind the cylinder gradually moves closer to the cylinder, such as... Figure 11 The figures (e) and (f) are shown in the diagram.

[0090] 4. Verification of the erosion process

[0091] Using the aforementioned three-dimensional sediment initiation model, the sediment erosion process around the cylindrical foundation was verified using experimental group 1 of the experimental water tank as an example. Figure 12 This illustrates the specific process of sediment erosion around the cylinder. (For example...) Figure 12 As shown in Figure (a) at t=1.0s, the sediment erosion process of the cylinder begins at both sides of the cylinder due to the streamline contraction effect, where the water velocity is higher than at other locations. The erosion then gradually spreads forward from both sides of the cylinder, exhibiting a roughly butterfly-shaped symmetrical distribution on both sides until it converges at t=4.0s in front of the cylinder, where it begins to develop together. Simultaneously, at t=4.0s and t=5.0s, the erosion behind the cylinder is minimal due to the cylinder's shielding effect. At t=5.0s, the maximum sediment erosion occurs at the lateral front of both sides of the cylinder.

[0092] like Figure 13The longitudinal profile of the sediment erosion process shown in the diagram illustrates that the erosion process deepens over time. However, at t=4.0s and t=5.0s, the scour depth in front of the cylinder is greater than that behind the cylinder. This is because the cylinder's shielding effect creates a downward water flow in front of the cylinder, which leads to the formation of horseshoe vortices and promotes the formation of scour pits.

[0093] Comparing the numerical simulation results with the experimental scour topographic maps reveals a good agreement between the two results. Both simulations show that scour initially occurs on both sides of the cylinder and then gradually progresses to the front of the cylinder. Therefore, this model can effectively simulate the scour process around the cylinder.

[0094] Taking experimental group 2 of the aforementioned experimental water tank as the research object, numerical simulation results of the scouring depth in front, behind, and side of the cylinder over time were obtained and compared with experimental measurement data, such as... Figures 14-16 As shown in the figure, the numerical simulation of sediment erosion progresses rapidly. In the simulation results, the sediment erosion process reaches its maximum erosion depth and reaches equilibrium within only 6 seconds, while the experimental results show that it takes approximately 10,000 seconds to reach the same erosion depth. Therefore, applying numerical simulation can significantly save time. Meanwhile, in... Figures 14-16 It can be observed that when the scouring time is only one-third of the time required to reach equilibrium, the scouring depth is approximately half of the maximum scouring depth. As scouring continues, the scouring pit continues to develop, and when the scouring time reaches 70% of the time required to reach equilibrium, scouring is essentially complete. However, as the scouring process continues, the change in scouring depth becomes smaller and smaller, gradually approaching a stable state. Therefore, regardless of whether the scouring is in front of, behind, or to the side of the cylinder, the maximum scouring depth obtained from the numerical simulation shows good consistency with the actual experimental results, and the difference between the two is within an acceptable range, demonstrating that the numerical simulation method can effectively reproduce the sediment erosion process.

[0095] This invention utilizes the ISPH method, combined with a modified k-ε turbulence model, to simulate sediment erosion around offshore wind turbine foundations. The method effectively simulates the sediment erosion process around the monopile cylinder of an offshore wind turbine, and analyzes the formation process of scour pits and their impact on the vorticity field. ISPH numerical simulations reveal that the scour process begins on both sides of the cylinder and spreads forward. In the early stage of scour, the streamline contraction on both sides of the cylinder, leading to increased flow velocity, is the main cause of scour pit formation. During the development stage, the scour pit's development is primarily influenced by the combined effects of the horseshoe vortex in front of the cylinder and the streamline contraction on both sides. In the equilibrium stage, the influence of the horseshoe vortex and streamline contraction on the scour pit weakens, but the area behind the cylinder remains affected by the wake vortex, causing the scour pit behind the cylinder to continue developing.

[0096] It should be noted that the above embodiments are for illustrative purposes only and are not intended to limit the invention. It should be pointed out that those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention; therefore, all improvements and modifications made without departing from the scope of the invention are also within the protection scope of the invention.

Claims

1. A method for simulating sediment erosion around offshore wind turbine foundations using an ISPH combined with a modified k-ε turbulence model, characterized in that, The method described above utilizes the ISPH model, combined with a sediment initiation model and a modified k-ε turbulence model, to experimentally simulate the flow field characteristics and local scouring process around offshore wind turbine foundations. The modified k-ε turbulence model is based on the turbulent eddy viscosity ν in the standard k-ε turbulence model. t The corrected turbulent eddy viscosity ν is then determined. t for: In the formula, To correct the dissipation rate, we take λ3 = 0.

1. in Represents the deformation rate tensor. This represents the rotational rate tensor of the ensemble-mean flow field. The subscript 'initial' indicates the time-averaged and depth-averaged values ​​within the first wave cycle in the potential flow region. Let p be the value of the rotational rate tensor. 0initial =1.24s -2 p Ωinitial =1.18×10 -8 s -2 C μ C1 and C2 are empirical constants, and in this model, C μ =0.09, C1=1.33, C2=1.92; The method steps include: S1. Establish the ISPH discretization algorithm for solving the average mass conservation equation and momentum conservation equation (i.e., NS equation) of the fluid dynamics ensemble. The NS equation is expressed as follows: In the formula, ρ0 is the fluid density, t is time, u is the ensemble average velocity, g is the gravitational acceleration, ν0 is the kinematic viscosity, and p is the pressure. Let Reynolds stress tensor be the stress tensor. S2, Modify the standard k-ε turbulence model and calculate the turbulent eddy viscosity ν in the Reynolds stress tensor expression. t ; S3 introduces the critical sediment initiation criterion on the slope, modifies and extends the traditional two-dimensional sediment initiation model, and establishes a three-dimensional sediment initiation model. S4. Establish a physical model of the test water tank for scour of a single pile foundation of an offshore wind turbine. S5, Establish the corresponding ISPH numerical flume model; S6. The experimental water tank model and the numerical water tank model respectively simulate the characteristics of the sediment scouring process around the cylinder. The numerical simulation results are compared with the experimental results for verification and analysis.

2. The method for simulating sediment erosion around offshore wind turbine foundations using ISPH combined with a modified k-ε turbulence model according to claim 1, characterized in that, The S3 model modifies and extends the traditional two-dimensional sediment initiation model, and the extended equation is as follows: In the formula, Let α be the ratio of the critical shear stress of the slope sediment to the critical shear stress of the horizontal plane, α be the angle between the S plane and the S' plane on the yz plane, β be the angle between the S plane and the S' plane on the xz plane, φ be the angle of repose of the sediment, and η be 0.

85. If the ratio of the calculated shear stress of the bedrock particles to the critical shear stress of the horizontal sediment obtained through the Shields curve is... It is then assumed that the bed particles have reached the critical initiation state, will transform into turbid water particles, and will participate in the calculation of the Navier-Stokes equations, τ b i represents the calculated shear stress in the sediment: In the formula, κ is the Karman coefficient, taken as 0.4, D is the diameter of the particle, and u bi Let i be the tangential velocity component of particle i.

3. The method for simulating sediment erosion around offshore wind turbine foundations using ISPH combined with a modified k-ε turbulence model according to claim 2, characterized in that, The experimental water tank model described in step S4 has a total length of 35m, a width of 7m, and a depth of 1.6m. A 9m long area is set in the center of the water tank as a scouring test area. The scouring test area is pre-filled with a layer of experimental fine sand with a depth of 0.60m. A cylindrical model with a diameter of 0.6m is set in the center of the test area. An inflow area is set on the left side of the experimental water tank and an outflow area is set on the right side to maintain water level balance. There are no less than 5 experimental groups, the experimental water depth is 0.3m, and the average flow velocity is 0.157~0.216m / s.

4. The method for simulating sediment erosion around offshore wind turbine foundations using ISPH combined with a modified k-ε turbulence model according to claim 3, characterized in that, In step S5, to improve computational efficiency and facilitate observation of key areas, the computational area of ​​the numerical flume model is set to a length of 5.45m, which is 9 times the diameter of the cylindrical model, and a width of approximately 5m, which is 8.3 times the diameter of the cylindrical model. The particle diameter in the numerical model is set to 0.02m. An inflow area is set on the left side of the model, and a uniform flow velocity is applied according to actual experimental data to simulate the inflow of upstream water. An outflow area is configured on the right side of the model to maintain a relatively constant water level throughout the model. A series of numerical velocity measurement points are set along the longitudinal section of the cylinder along the water flow direction, according to different water depths, to collect velocity data at the corresponding locations during the simulation.

5. The method for simulating sediment erosion around offshore wind turbine foundations using ISPH combined with a modified k-ε turbulence model according to claim 4, characterized in that, The verification and analysis in step S6 includes velocity distribution, vortex structure, and turbulent kinetic energy distribution; then the characteristics of the sediment scouring process around the cylinder are verified and analyzed.

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