1. Introduction
Offshore wind power is recognized globally as a key source of clean, renewable energy due to its inherent cleanliness, abundant reserves, and ease of conversion [
1]. Types of foundations for offshore wind turbines include gravity foundations, monopile foundations, pile group foundations, jacket foundations, and floating foundations [
2]. Among these different foundation types, jacket foundations have gained widespread application in recent years due to their high structural strength, light weight, and ease of transportation and installation [
3].
According to a study by Satari et al. [
4], the installation of jacket foundations significantly affects the surrounding flow field, often resulting in local scour around the foundation. Yuan et al. [
5] indicated that this scour can lead to uneven settlement, compromising the overall stability of the structure and the safe operation of the wind turbine. Additionally, based on the study by Zhu et al. [
6], the complex truss structure of the upper part of the jacket foundation further complicates the development of local scour compared to simpler foundation types. Due to the different scour characteristics between monopile and jacket foundations, existing scour protection measures or countermeasures for monopile foundations may require improvement or adjustment before being applied to jacket foundations [
7,
8]. Therefore, studying the flow field around jacket foundations is crucial for understanding local scour, improving engineering design, and enhancing scour protection measures. This ensures safe operation and facilitates maintenance.
Over the past few decades, researchers have conducted extensive physical experiments and numerical simulations to study the flow characteristics around complex foundations for offshore wind turbines. Breusers and Raudkivi [
9] found that, compared to monopile foundations, the key factors influencing scour around pile groups are the spacing between the piles and their arrangement. Currently, jacket foundations are increasingly adopted in offshore wind farms (OWFs) worldwide, yet research on the flow and local scour characteristics around such foundations remains limited. Moreover, the flow field and scour characteristics around jacket foundations under wave and current actions are not fully understood. Lian et al. [
10] developed a three-dimensional numerical model to investigate the scour characteristics around large-diameter multi-pile foundations in deep water. They optimized the mesh partitioning and discussed the effects of jacket height, pile diameter, and pile spacing on the flow field and scour depth. Their study revealed that, as the height of the jacket piles increases, the scour depth first increases to a peak value and then decreases. The scour depths around the front row of piles decrease with an increase in the pile diameter, while they increase with an increase in the pile diameter around the rear row of piles. Jiang et al. [
11] investigated the scour around jacket foundations on the cohesive seabed. Their experiments demonstrated that the scour depth around the foundation increases with larger pile diameters and higher wave–current velocities but decreases with greater water depth. They found a nearly linear relationship between the ratio of wave–current velocity to the critical initiation velocity of sediment and the maximum scour depth. Additionally, they observed that the maximum scour depth increases with both the ratio of wavelength to water depth and the increases in Froude and Reynolds numbers. Li et al. [
12] systematically analyzed the effects of wave and current actions on the local scour depth and range around a jacket foundation for a wind farm project. Welzel et al. [
13] simulated the scour problem around jacket foundations when waves and current flow directions were perpendicular. Their experiments revealed rapid scour depth development around the piles of the foundation due to the compression and intensified flow. They also found that scour under combined wave and current action is more severe than under steady flow conditions. Recently, Chen et al. [
14] conducted a flume experiment to investigate scour characteristics around jacket foundations under different hydrodynamic conditions. The findings revealed that due to the resistance effect of the truss structure and flow disturbance at the piles, the scour extent around jacket foundations is less significant compared to monopile foundations under the same hydrodynamic conditions.
However, the above experimental studies mainly focus on the scour problem around jacket foundations, particularly focusing on the scour process and equilibrium scour depth around the foundation. Few studies have simulated the flow field around jacket foundations, and there is a lack of comprehensive analysis regarding flow characteristics around these structures and their influence on the local scour process. To better understand the flow characteristics around the jacket foundation during the initial and equilibrium stages of the scour process, flow fields around jacket foundations on flat-bed and equilibrium scour bathymetry were analyzed. This study employed the OpenFOAM platform and used the LES method to simulate the flow field around the jacket foundation under constant flow. A physical experiment was conducted in a current flume, and the experimental results were used for numerical modeling and validation. The close agreement between experimental and numerical results indicates that the LES model accurately reflects the flow patterns around the jacket foundation. Subsequently, the characteristics of the time-averaged flow field, turbulence field, instantaneous flow field, AKE, and bed shear stress were studied numerically. Their influence on the local scour around the foundation was analyzed and discussed to further explain the local scour mechanism around jacket foundations.
2. Flume Experiment and Methodology
To obtain the equilibrium scour hole topography around jacket foundations under steady flow, physical model tests were conducted.
Figure 1 shows the experimental flume used in this study, which is 50 m long, 1 m wide, and 1.5 m high. A 2.5 m long, 1 m wide, and 0.3 m deep sand recess was designed at the middle section of the flume, 24 m from the flume inlet. The model was positioned at the center of the sand recess, with 0.34 m from the pile to the flume wall. A concrete slope with a degree of 1:10 and a height of 0.3 meters was placed 14 m from the flume inlet to ensure smooth water flow transition. An acoustic Doppler velocimetry (ADV) was deployed to measure the velocity distributions at various locations within the flume. After the experiments were completed, the output data from the ADV were filtered using WinADV software, V2.024,the United States [
15]. Data with low correlation (minimum COR < 70) were removed.
Figure 2 shows the schematic diagram of the jacket foundation model, and
Table 1 lists the dimensions of the model components. The pile diameter (
D) was 0.04 m, the spacing between piles was 0.24 m, and the water depth above the artificial deck was 0.3 m.
Once the scour reached equilibrium, the flume was slowly drained, and the topography of the equilibrium scour hole was scanned for numerical modeling. Approximately 150 photos of the sand bed around the jacket foundation model were taken from different angles and levels after each test. These photos were then used to establish a three-dimensional numerical model. For ease of scanning, the jacket foundation could be disassembled into an upper truss structure and piles. In this study, the clear spacing between the piles of the jacket foundation was six times the pile diameter, with the equivalent diameter-to-flume width ratio being 8%, which essentially negates the influence of boundary effects [
16].
Figure 3a shows the particle size distribution of the sand used in the experiment. The sand used in the experiment had a median particle size (
d50) of 0.25 mm, a geometric standard deviation of 1.49, a measured void ratio of 0.47, and a relative weight of 2.65. Based on previous studies, the critical sediment initiation velocity in the experiment was calculated to be 0.231 m/s [
17]. The average flow velocity, which was 0.9 times this critical velocity, was used in this study to ensure a clear water scour condition. Only clear-scour conditions were considered in this study, and no sand was involved in the water motion. The equilibrium scour topography obtained from the experiment is shown in
Figure 3b.
3. Numerical Model and Computational Details
3.1. Numerical Modeling Method
The numerical model in this study employs LES. To filter out small-scale fluctuations, an additional stress term is introduced in the Navier–Stokes equations to dissipate the small-scale vortices and prevent excessive turbulent kinetic energy. After filtering, the three-dimensional Navier–Stokes equations for LES are as follows:
where
xi represents the Cartesian coordinates (
i = 1, 2, 3 correspond to the
x,
y,
z directions, respectively);
t denotes time in seconds;
is the fluid density in kg/m
3;
is the filtered velocity vector in m/s; and
is the filtered pressure in Pascals (Pa). Let
, which is termed the subgrid-scale (SGS) stress. This term is an unsolved term in the equations. Therefore, the above equations can be transformed into the following form:
Equation (3) is similar to the Reynolds-averaged Navier–Stokes (RANS) equation, where an unclosed subgrid-scale (SGS) stress term appears. This term cannot be directly calculated and requires simulation using an eddy-viscosity approach. Based on the concept of eddy viscosity, this study employs the dynamic one-equation eddy-viscosity model (DOEE) to solve the governing equations [
18].
3.2. Numerical Modeling Conditions
The origin of the coordinate system in the numerical model is set at the center of the jacket foundation at the original bed level. The
x-axis is aligned with the flow direction, the
y-axis is transverse to the flume, and the
z-axis is vertical. As shown in
Figure 4a, the computational domain has a length (
L) of 2.5 m, a width (
B) of 1 m (equal to the width of the flume), and a height of 0.3 m, which corresponds to the water depth (
h). The diameter of the jacket foundation piles is
D, and the gaps between the piles are 7
D.
Given the complexity of the jacket structure, this study employed non-uniform hexahedral unstructured grids. To accurately capture various vortex structures, the mesh near the jacket foundation was locally refined using density boxes. Additionally, to simulate the flow details near the wall and the bed shear stress, the mesh near the bed surface was divided into boundary layers. Since the LES model is sensitive to grid scale, the dimensionless distance y+ in the normal direction near the wall should be less than 1.5. After estimation and verification, the thickness of the first layer of the grid near the piles and the bottom surface was set to 0.1 mm. A total of 6,000,000 cells were used.
The boundary conditions of the computational domain were set as follows: The inlet boundary was specified as a velocity inlet, with the upstream measured flow velocity varying with water depth, as shown in
Figure 4b. The outlet boundary used a free outflow condition. A slip boundary was employed for the water surface boundary in the modeling. The jacket foundation structure and the sidewalls were set with no-slip conditions. It should be highlighted that in the flume experiment, the bed sand is movable to allow the development of a scour hole around the foundation. However, this study aimed to investigate the flow field characteristics around the jacket foundation on both flat-bed and equilibrium scour bathymetry using numerical modeling. Therefore, the bed sands for both the flat-bed and equilibrium scour bathymetry were set to be immovable in the numerical model. The bed was set with a no-slip condition and included a rough wall boundary condition, with an equivalent sand roughness height of
ks = 2.5
d50.
This study utilized the OpenFOAM platform, V9, the United Kingdom, to develop a large time-step transient incompressible flow solver, pimpleFoam, for solving the numerical model. This solver utilized the PIMPLE algorithm to couple the pressure–velocity equations. Throughout the solution process, second-order accurate finite difference schemes were applied to address time, gradients, pressure terms, and convective terms. Discretization was managed using the geometric algebraic multigrid (GAMG) matrix solver for all discretized components. To ensure closure of the governing equations during computation, a dynamic k equation (DKE) subgrid-scale stress model was integrated. The time step ∆t was set in an adjustable mode to stabilize the calculations in the LES framework, with the maximum Courant number maxCo = 1.0. Initial computations began with a time step of 0.002 s.
3.3. Model Verification
Figure 5 shows the distribution of y
+ around the jacket foundation on flat-bed and equilibrium scour bathymetry, respectively. It can be observed that
y+ values are all less than 1.5, indicating that the first-layer boundary layer mesh thickness used in this study meets the accuracy requirements of LES.
Furthermore, as shown in
Figure 6, the characteristic cross-section (
y/
D = 3.5) was selected for velocity verification. Velocity profiles of horizontal flow were compared between experimental results and numerical simulations at
x/
D = −8.5, −6.5, −5.5, −5, −4.5, −2.5, −2, −1.5, and −0.5. The results are shown in
Figure 7, where profiles (a) to (e) depict velocity profiles on the upstream side of the foundation, indicating close agreement between experimental and numerical results with errors within 5%. Profiles (f) to (i) show the velocity between the front and rear piles of the jacket foundation, where slight differences up to 10% are observed due to the complex vortex structures behind the piles. Overall, the results demonstrate that the LES model established effectively reflects the flow patterns around the jacket foundation.
5. Conclusions
This study investigated the numerical simulation results of the flow field around jacket foundations under steady flow conditions on flat-bed and equilibrium scour bathymetry during the scour process. The vortex system, AKE, the time-averaged flow field, turbulence characteristics, instantaneous flow field, and bed shear stress in flat-bed and equilibrium scour conditions were analyzed. The main conclusions are as follows:
1. Numerical modeling shows that the flow velocity and the extent of downflow on the upstream side of the rear piles are significantly reduced due to the shielding effect of the front row piles and the obstruction and energy dissipation effects of the upper truss structure.
2. The vortex system structure at the rear piles of the jacket foundation is similar to that of the front piles, but the scale of the vortices at the rear piles is approximately half of those at the front pile.
3. The AKE of the flow upstream of the rear piles decreases significantly from 0.60 to 0.54, with reductions of 18.9% in the flat-bed state and 28.0% in the equilibrium state. This indicates more energy dissipation in the equilibrium state and results in less significant scour at the rear piles over time. In contrast, the AKE of the flow upstream of the front piles remains nearly constant, showing that the front piles are less affected by the scour process.
4. The turbulence intensity and the area of high turbulence intensity between the front and rear piles are significantly greater under equilibrium conditions than those under flat-bed conditions. This indicates that intense turbulence and energy dissipation occur between the piles, reducing the kinetic energy of the flow passing through the rear piles.
5. The maximum bed shear stress around the jacket foundation occurs at the 60° position on both sides of the piles, where scour initiates at the foundation. The rear piles experience reduced shear stress magnitude and extent due to the shielding effect of the front piles.