Local Scour Mechanism of Offshore Wind Power Pile Foundation Based on CFD-DEM

Abstract

The local scour around offshore pile foundations often seriously affects the normal operation of offshore wind power. The most widely used numerical simulation method in the study of local scour is the Euler two-fluid model (TFM). However, the contact effect between sediment particles is neglected in this model. Thus, the momentum and energy transfer between sediment particles and the fluid is not realistically reflected, which limits its significance in revealing the mesoscopic mechanism of local scour. Therefore, the computational fluid dynamics-discrete element method (CFD-DEM) numerical model was applied in this study, which fully considers the contact between solid particles and momentum transfer between two phases. The model was first verified by experimental data of a local scour test under clear water scour. Then, the mechanism of local scour was further discussed from macro and micro perspectives. The results showed that CFD-DEM could be effectively used to study the local scour around a pile foundation. The local scour was comprehensively affected by flow velocity, gravity, fluid force, drag force, and interaction between particles, etc. Although the maximum average drag force happened in the area about 90° from the direction of incoming flow, the maximum scour depth always occurred at about 45°. Corresponding findings and conclusions can be used for future reference when designing and protecting the offshore wind power pile.

1. Introduction

As one of the important initiatives of renewable energy development and utilisation, offshore wind power has been an indispensable part of China’s strategic science and technology industry; it is an emerging industry and important for marine economic development. Therefore, developing and deploying offshore wind power technology is critical for maximizing on the commanding heights of new energy technology. Nevertheless, hydrodynamic characteristics such as the horseshoe vortex, circumferential vortex, and wake vortex around wind power pile foundations easily cause different degrees of local scour of the seabed around the pile, posing a serious threat to the foundation’s safety and stability throughout the life cycle of the offshore wind power pile. Hence, the mechanism of the local scours around the wind power pile foundation need to be studied.

The main methods used to study local scours around a pile foundation are flume experiments [1,2] and numerical simulations [3,4]. The flume scour experiment is usually performed in a glass flume with sand beds and pile foundations. Meanwhile, a certain scale hydraulic circulation system needs to be equipped to provide a hydrodynamic force. The most important scour data, such as flow field characteristics, scour pit elevation, and scour time history, are obtained via acoustic doppler velocity (ADV) ultrasonic current metre, 3D topographic scanner, geographic information system (GIS) sensor, and other monitoring equipment. Melville [5] had previously performed a series of studies on influencing factors of the local scours around the pile, scour depth time history, and the evolution of scour pit morphology via flume experiment, laying the foundation for a follow-up study on local scour mechanisms. The influence of different hydraulic conditions [6,7,8], pile foundation form [9,10,11], and pile foundation layout [12,13,14] on the scour mechanism has been further considered by scholars through flume scour experiments due to the complexity of practical ocean engineering problems. A flume experiment is the most effective means to study local scour. Nevertheless, the experimental costs are often high because of the experimental and data monitoring equipment. Moreover, capturing the motion information of individual sediment particles during data monitoring is challenging. This makes the experimental study of the scour mechanism difficult at the particle level.

With the development of computer science and technology, a numerical simulation based on computational fluid dynamics (CFD) was gradually applied to fluid mechanics, which was favoured by scholars because of its low cost and easy operation. Generally, researchers study local scour by the Euler two-fluid model (TFM), which treats both fluid and sediment as continuous phases and respectively controls the movement of fluids and sediments by the Navier–Stokes (N–S) equation and sediment transport formula [15,16]. The evolution of scour pit morphology can be realised with the sand slide model [17,18,19]. However, the sediment transport formula is an empirical formula based on the sediment concentration and results of the sediment scour test. Although it can accurately predict the scour depth under certain working conditions, it cannot explain the real interactions between sediment particles during local scour. The essence of local scour is the complex movement of sediment particles around piles under the action of flow field drag. Thus, the local scour model under the Euler–Eulerian framework cannot accurately reflect the momentum and energy transfer between sediment particles and fluid, and has limited significance in revealing the mesoscopic mechanism of local scour and proposing scour control measures.

The computational fluid dynamics-discrete element method (CFD-DEM) is a method for solving fluid–structure interaction problems at the particle scale, based on the Euler–Lagrange computing framework [20], and requires no complex constitutive relations between stress and strain tensors of discrete particles under different flow conditions. Therefore, it applies to many flow systems [21]. Unlike TFM, CFD-DEM in the Euler–Lagrange framework treats the solid phase as a discrete phase, considers solid particle interactions, and uses Lagrangian particle tracking to capture the force state, motion trajectory, and other information of sediment particles, which is critical for understanding the mesoscopic mechanism of local scour [22]. The CFD-DEM method has been widely applied to the field of deep-sea mineral pipeline transportation [23,24], submarine pipeline scours [25,26,27], fluidised-bed [28,29], and other fields of particle multiphase flow. However, its application in the local scour of pile foundations is still limited.

In this study, a new numerical model of local scour was developed using the CFD software Fluent and the discrete element software EDEM; the unsteady Reynolds mean N–S equation and the standard k-epsilon (k-ε) turbulence model [30] were used to simulate the flow in the hydrodynamic model; the Hertz–Mindlin no-slip model [31] was used to describe the contact effects between sediment particles in DEM; and the interphase momentum transfer between water and sand was characterised by the Gidaspow drag model [32]. First, the validity of the model was verified by flow velocity distribution, scour hole shape evolution, and scour time history of the local scour test under the conditions of clear water scour. Second, the macro scour mechanism of different areas around the pile was revealed from the aspects of local scour depth, average sediment drag, movement speed, and upstream sediment transport. Third, based on Lagrangian particle tracking, the movement track and stress state of sediment particles were obtained, and the meso erosion mechanism of particle size in the scouring process was studied. Finally, by comparing the contribution of local hydrodynamic action and sediment contact action to local scour, the influence of both on the sediment erosion mechanism was further analyzed. Corresponding findings and conclusions can be used as a reference for designing and protecting the offshore wind power pile.

2. Numerical Model

2.1. CFD Model

The motion control equations for fluids include the continuity equation and momentum conservation equation. The expressions are shown in Equation (1):

$$\left\{\begin{array}{l}\frac{\partial }{\partial t}\left({\alpha }_f{\rho }_f\right)+\nabla \cdot \left({\alpha }_f{\rho }_f{u}_f\right)=0\hfill \\ \frac{\partial }{\partial t}\left({\alpha }_f{\rho }_f{u}_f\right)+\nabla \cdot \left({\alpha }_f{\rho }_f{u}_f{u}_f\right)=-{\alpha }_f\nabla p+\nabla \cdot \left({\alpha }_f{\mathbf{\tau }}_f\right)+{\alpha }_f{\rho }_{f}g-f\hfill \end{array}\right.$$

(1)

where ${\alpha }_f$ is the volume fraction of the fluid, ${\rho }_f$ is the fluid density, t is time, ${\mathbf{u}}_f$ is the instantaneous velocity of the fluid, p is the hydrostatic pressure, g is the gravitational acceleration, ${\mathbf{\tau }}_f$ is the fluid stress tensor, ${\mathbf{\tau }}_f$ = (μ + ${\mu }_t$)[▽${\mathbf{u}}_f$ + ▽${\mathbf{u}}_f^{\mathbf{T}}$], μ is the hydrodynamic viscosity coefficient, μ_t is the vorticity coefficient, and f is the momentum transferred by the fluid contained in the unit volume grid to all particles in the grid cell by buoyancy and drag.

The turbulence model adopts the standard k-ε model [30], in which turbulent kinetic energy and turbulent dissipation rate are used to solve the vorticity coefficient in Boussinesq’s vorticity hypothesis. The expression is shown in Equation (2):

$${\mu }_t={\rho }_f{C}_{\mu }\frac{k^2}{\epsilon }$$

(2)

where k and ε are turbulent kinetic energy and turbulent dissipation rate, respectively. The transport equations are shown in Equation (3):

$$\left\{\begin{array}{l}\frac{\partial }{\partial t}\left({\alpha }_f{\rho }_{f}k\right)+\nabla \cdot \left({\alpha }_f{\rho }_{f}k{u}_f\right)=\nabla \cdot \left({\alpha }_f{\xi }_k\nabla k\right)+{\alpha }_f{P}_k-{\alpha }_f{\rho }_f\epsilon \\ \frac{\partial }{\partial t}\left({\alpha }_f{\rho }_f\epsilon \right)+\nabla \cdot \left({\alpha }_f{\rho }_f\epsilon u_f\right)=\nabla \cdot \left({\alpha }_f{\xi }_{\epsilon }\nabla \epsilon \right)+{\alpha }_f{C}_1{P}_k\frac{\epsilon }{k}-{\alpha }_f{\rho }_f{C}_2\frac{{\epsilon }^2}{k}\end{array}\right.$$

(3)

where ξ_k = μ + ${\mu }_t$ /${\sigma }_k$, ξ_ε = μ + ${\mu }_t$ /${\sigma }_{\epsilon }$, ${\sigma }_k$ and ${\sigma }_{\epsilon }$ are the Prandtl number corresponding to turbulent kinetic energy and turbulent kinetic energy dissipation rate and are valued at 1.0 and 1.3, respectively; C_μ, C₁, and C₂ are empirical constants and are valued at 0.09, 1.44, and 1.92, respectively; P_k is the generic term of turbulent kinetic energy caused by the time-mean velocity gradient; and P_k = ${\mu }_t$▽${\mathbf{u}}_f$·[▽${\mathbf{u}}_f$ + ▽${\mathbf{u}}_f^{\mathrm{T}}$].

2.2. DEM Model

The translation and rotation of particles are controlled by Newton’s Second Law of Motion. The motion control equations for individual particles are shown in Equation (4):

$$\left\{\begin{array}{l}{m}_p\frac{d{u}_p}{dt}=m_{p}g+{\displaystyle \sum F_N}+{\displaystyle \sum F_T}+F\hfill \\ I_p\frac{\partial {\omega }_p}{\partial t}=M_p\hfill \end{array}\right.$$

(4)

where m_p is particle mass, u_p is the velocity of particles, F is the fluid force on particles (see Section 2.3 for details), I_p is the moment of inertia, ${\mathsf{\omega }}_p$ is the rotational angular velocity of particles, M_p is the total torque on particles, and F_N and F_T are the normal and tangential contact forces on particles from particles and geometry. The contact between particles and particles and geometry is described by the Hertz–Mindlin no-slip model [31]. As shown in Figure 1, using the collision between two particles as an example, this model comprises spring and damper. The spring exerts a repulsive force that pushes the particles away, with only the elastic part of the collision being considered. The damper produces viscous damping, considering the energy dissipation during particle collisions.

The contact forces include contact force amplitude and damping force. The normal contact force amplitude ${\mathbf{F}}_N^e$ and tangential contact force amplitude ${\mathbf{F}}_T^e$ are the function of normal overlap ${\delta }_N$ and tangential overlap ${\delta }_T$, respectively, and mainly consider the elastic response during collision. The expressions are shown in Equation (5):

$$\left\{\begin{array}{l}{F}_N^e=\frac{2}{3}{S}_N{\delta }_N\cdot n\hfill \\ F_T^e=-\min \left\{S_T{\delta }_T,{\mu }_s\left|F_N^e\right|\right\}\cdot t\hfill \end{array}\right.$$

(5)

Normal damping force ${\mathbf{F}}_N^d$ and tangential damping force ${\mathbf{F}}_T^d$ consider energy dissipation during collision, which are expressed in Equation (6):

$$\left\{\begin{array}{l}{F}_N^d=-2\sqrt{\frac{5}{6}}\frac{\ln e}{\sqrt{{\ln }^{2}e+{\pi }^2}}\sqrt{S_N{m}^{*}}\cdot v_N^{rel}\hfill \\ F_T^d=-2\sqrt{\frac{5}{6}}\frac{\ln e}{\sqrt{{\ln }^{2}e+{\pi }^2}}\sqrt{S_T{m}^{*}}\cdot v_T^{rel}\hfill \end{array}\right..$$

(6)

where S_N and S_T are the normal stiffness and tangential stiffness of particles, respectively; E^*, G^*, R^*, and m^* are the equivalent Young’s modulus, shear modulus, radius, and mass of particles, respectively. The expressions are shown in Equations (7)–(12):

$$S_N=2E^{*}\sqrt{R^{*}{\delta }_N}$$

(7)

$$S_T=8G^{*}\sqrt{R^{*}{\delta }_N}$$

(8)

$$E^{*}={\left[\frac{\left(1-{\nu }_i^2\right)}{E_i}+\frac{\left(1-{\nu }_j^2\right)}{E_j}\right]}^{-1}$$

(9)

$$G^{*}={\left[\frac{2\left(2-{\nu }_i\right)\left(1+{\nu }_i\right)}{E_i}+\frac{2\left(2-{\nu }_j\right)\left(1+{\nu }_j\right)}{E_j}\right]}^{-1}$$

(10)

$$R^{*}={\left(\frac{1}{R_i}+\frac{1}{R_j}\right)}^{-1}$$

(11)

$$m^{*}={\left(\frac{1}{m_i}+\frac{1}{m_j}\right)}^{-1}$$

(12)

In Equations (7)–(12), n and t are the normal and tangential unit vectors of contact points, respectively; E_i, $v_i$, R_i, $m_i$ and E_j, $v_j$, R_j, $m_j$ are the Young’s modulus, Poisson’s ratio, radius, and mass of two contact particles, respectively; e is the collision recovery coefficient; ${\mathbf{v}}_N^{rel}$ and ${\mathbf{v}}_T^{rel}$ are the normal and tangential components of relative velocity, respectively; and ${\mu }_s$ represents sliding friction coefficients.

The rolling friction of particles is considered by applying a reverse torque τ on the contact surface between particles, and the expression is shown in Equation (13):

$$\mathsf{\tau }=-{\mu }_r{F}_N^{e}R$$

(13)

where ${\mu }_r$ represents rolling friction coefficients and R is the distance from the contact point to the centre of mass.

2.3. Water–Sand Interaction Model

This model mainly describes the interaction between fluid and particles. For the large-diameter sediment studied here, the drag and buoyancy of the particles is much greater than lift forces [33,34]. Therefore, the influence of buoyancy and resistance on particle motion is mainly considered in the local scour model of this paper. The expressions are shown in Equations (14) and (15):

$$f=f_b+f_d$$

(14)

$$F={\omega }_i\cdot V_{cell}\cdot f$$

(15)

where f_b and f_d are the momentum transfer of fluid contained in a unit volume grid to all particles in the grid cell due to buoyancy and drag, respectively; V_cell is the grid cell volume; and ${\omega }_i$ is the interphase force distribution coefficient of the ith particle in the grid cell.

Buoyancy is caused by the pressure difference between upper and lower surfaces of particles, and the magnitude of the buoyancy depends on the interphase density difference. The expression is shown in Equation (16):

$$f_b={\alpha }_p\left({\rho }_p-{\rho }_f\right)\cdot g$$

(16)

where α_p is the volume fraction of particles and ρ_p is particle density.

When there is relative motion between fluid and particles, the fluid is affected by resistance to flow on the particle’s surface, which in turn is affected by the drag exerted by the fluid. There is continuous momentum transfer during the interaction between the particles and fluid, and this momentum transfer is described by the Gidaspow drag model [32]. The expression is shown in Equation (17):

$$f_d=K_{fp}\left(u_f-u_p\right)$$

(17)

where K_fp is the fluid–particle momentum exchange coefficient used to characterise the transfer of particle momentum by the fluid. The expressions are shown in Equation (18):

$$K_{fp}=\left\{\begin{array}{l}\frac{3}{4}{C}_D\frac{{\alpha }_f{\alpha }_p{\rho }_f\left|u_f-u_p\right|}{d_p}{\alpha }_f^{-2.65},\hspace{1em}{\alpha }_f>0.8\\ 150\frac{\mu {\alpha }_p^2}{{\alpha }_f{d}_p^2}+1.75\frac{{\rho }_f{\alpha }_p\left|u_f-u_p\right|}{d_p},\hspace{1em}{\alpha }_f\le 0.8\end{array}\right.$$

(18)

where d_p is particle size and C_D is the drag coefficient. The expression is shown in Equation (19):

$$C_D=\frac{24}{{\alpha }_{f}R{e}_p}\left[1+0.15{\left({\alpha }_f{\mathrm{Re}}_p\right)}^{0.687}\right]$$

(19)

where Re_p is the relative Reynolds number of particles. The expression is shown in Equation (20):

$$R{e}_p=\frac{{\alpha }_f{\rho }_f{d}_p\left|u_f-u_p\right|}{\mu }$$

(20)

3. Establishment of Local Scour Model

3.1. Geometric Model and Grid Partition

The CFD software Fluent and discrete element software EDEM were used to create the CFD-DEM numerical model in this study. As shown in Figure 2, the local scour model comprises fluid domains, the sediment seabed, and circular pile foundations. The seabed model is a porous media domain (Figure 3) filled with 300,000 discrete particles generated by EDEM. The porosity of the seabed model ranges from 0.4–0.5, which is close to actual seabed porosity [17,35,36]. The filling process occurs before scour. A relatively even distribution of particles should be ensured during filling. Furthermore, there should be full contact and collision between particles. When particle velocity in the seabed approaches 0, it indicates that the seabed deposition has been relatively stable. Meanwhile, the seabed should be of sufficient size in the incoming vertical direction to reduce the effects of the seabed sidewall on the flow field around the flow.

The fluid grid size must strictly be larger than the particle size for the unresolved CFD-DEM coupling model [37]. This is to prevent the appearance of an unreal particle volume fraction in a fluid grid, which would affect the drag calculations and the stability of iterations. Therefore, the model was divided into 2 × 10⁵ hexahedral grid cells (Figure 4). The grid was relatively dense near the sediment domain around piles and relatively sparse elsewhere. The grid size was between 12–18 mm, which is much greater than the particle size in the whole model.

3.2. Setting of Simulation Parameters

3.2.1. EDEM Parameters

During local scour, the effects of the interaction between sediment particles on the scour mechanism are important. The motion state and trajectory of particles around piles are determined by friction and momentum transfer between particles, determining the size and depth of the scour pit. The collision and contact between sediment particles are described by the Hertz–Mindlin no-slip model. The collision recovery coefficient describes the kinetic energy transfer after a collision between sediment particles. The kinetic energy transfer after a collision between sediment particles is characterised by the collision recovery coefficient. The collision recovery coefficient in this model was set to 0.45, according to an experiment of Wang et al. [38]. The static friction coefficient corresponded to the tangent value of the friction angle of sediment particles; the corresponding natural angle of repose of sediments was 33°. The sediment particles had small rolling friction in the water, and the rolling friction coefficient was set to 0.01. The sediment particle density was set to 2670 kg/m³. The Poisson’s ratio was 0.35. The shear modulus was 5 MPa. As the simulation time of discrete elements was significantly affected by particle size and quantity, sediment particle size was set to 5 mm to improve simulation efficiency. The EDEM simulation time step was set to 5 × 10⁻⁵ s. Meanwhile, the interval for data saving was set to 0.05 s to accurately track the motion of individual sediment particles.

3.2.2. Fluent Parameters

The transient calculation was enabled in Fluent, and fluid control equations were discretised using the finite volume method. The SIMPLE algorithm was used, which is based on pressure–velocity coupling and uses a first-order upwind difference approach. The inlet and outlet boundary of the fluid domain were set to velocity inlet and pressure outlet, respectively. The average inlet velocity was 0.92 m/s. The direction was perpendicular to the inlet boundary. Turbulence intensity was set to 5%. The outlet was set to the pressure boundary. The pressure was set to the standard atmospheric pressure. The side and top surfaces were set to the symmetric boundary, and the rest of the boundary was set to the solid wall without slipping. The turbulence model was a standard k–ε model, and the wall model was a standard wall function. The drag model was the Gidaspow drag model. During coupling, the Fluent time step needed to be an integer multiple of the EDEM time step to ensure data transmission stability and simulation iteration. Therefore, the Fluent time step in this model was 100 times the EDEM time step, i.e., 5 × 10⁻³ s. There were 10,000 simulation time steps lasting a total of 50 s. The maximum number of iterations for each time step was set to 500 to meet the convergence requirements for the absolute residual needing to be less than 10⁻³.

3.3. Fluent-EDEM Coupling

Fluent 2020R2 completed the calculation of flow field information within the domain during the fluid–structure interaction process. The particle information in the sediment domain was updated by EDEM. The information transfer between the two domains was completed by the interface programme. The interface program was a user-defined code imported into Fluent, which was used to calculate the interphase force, particle volume fraction, and transfer the information of particles and fluids. The fundamental process was as follows: the iteration in step n began after the iterative convergence in step n − 1. Fluent obtained the particle position information and momentum transmission of the particle to the fluid. First, the flow field calculation in step n was performed. The convergence of flow field calculations and the force of the flow field on particles were then transmitted to EDEM through the interface programme. Afterward, EDEM began to calculate equations of particle motion and update particle positions. Finally, this information was returned to Fluent through the coupling interface, along with the interphase force. This concluded the iteration in step n.

4. Analysis and Discussion

This model was verified via a unidirectional scour experiment of Xu [39], and the specific working conditions are shown in

Table 1. Comparison of scour conditions.

Parameter	V1D3 Test [39]	CFD-DEM
Pile foundation diameter D (m)	0.1	0.1
Average flow velocity V (m/s)	0.286	0.92
Water depth h (m)	0.4	0.4
Median sediment particle size d50 (mm)	0.29	5
Natural angle of repose of sediments (°)	33	33
Shields number θ	0.035	0.048
Critical Shields number θcr	0.038	0.052
θ/θcr	0.92	0.92

. Although the simulation sediment particle size was larger than that of the test sediment, undistorted effects could be simulated by synchronously increasing the velocity of water in the simulation to ensure the consistency of dimensionless Shields number in the CFD-DEM simulation and Xu’s experiment. The dimensionless Shields number is defined as the ratio of Shields number θ to critical Shields number θ_cr [40], and the expressions are shown in Equations (21) and (22):

$$\theta =\frac{{\tau }_s}{{\rho }_{f}g\left(s-1\right)d_{50}}$$

(21)

$${\theta }_{cr}=\frac{0.3}{1+1.2D_{*}}+0.055\left[1-\exp \left(-0.02D_{*}\right)\right]$$

(22)

where τ_s is the shear force of water flow near the bed surface; s is the ratio of sediment particle density to water density; d₅₀ is the median particle size of sediment; and D^* is the dimensionless diameter. The expressions of τ_s and D^* are shown in Equations (23) and (24):

$${\tau }_s={\rho }_f{\left[\frac{\kappa }{\ln \left(d_{50}/12h\right)+1}\right]}^2{V}^2$$

(23)

$$D^{*}=d_{50}{\left[\left(\frac{{\rho }_p}{{\rho }_f}-1\right)g/{\nu }^2\right]}^{\frac{1}{3}}$$

(24)

where κ is the Carmen coefficient and is valued at 0.4; h is the depth of water; V is the average velocity of water flow along the depth of the water; and ν is the kinematic viscosity of water.

4.1. CFD-DEM Model Verification

4.1.1. Velocity Distribution

Figure 5 shows the variation of the average velocity of flow upstream of the pile foundation with the depth of flow. The coordinate Z is a vertical coordinate, which represents the flow depth. The average flow velocity in the simulation and test was normalised by respective critical starting flow velocities V_c to facilitate the comparison of simulation and test results. As shown in Figure 5, the dimensionless flow velocity distribution in the simulation conforms to the logarithmic velocity distribution law, which is consistent with the experiment data from Xu [39].

4.1.2. Scour Pit Morphology

Figure 6 shows a three-dimensional (3D) view of the scour pit at the equilibrium stage. The water flows in the X direction, and the colour of the particles represents different scour depths. According to this figure, symmetrical scour pits were formed around the pile foundation, and the maximum scours depth was near the pile foundation upstream ± 45° and was approximately 85 mm, close to the balanced scour depth obtained by the experiment.

Figure 7 and Figure 8 show the development process and elevation evolution of scour pits around piles during scouring. According to these figures, the scour first occurred in small areas in front of and on the sides of piles. Many sediments were continuously transported to areas behind piles to form deposition. The scour characteristics at this stage were mainly manifested as the rapid increase in longitudinal scour depth and preliminary formation of scour pit around piles. Afterward, the scour gradually slowed down and scour pits gradually spread perpendicular to the flow direction. The closer the sediment came to the surface of the pile foundation, the more severe the erosion caused by the water flow. With the continuous increase in scouring range, the deposit area behind piles gradually moved downstream, and the sediment height in this area continuously decreased. Consequently, scour pits behind piles were gradually connected, and the depth and range of scour pits were unchanged. The development of local scour tended to be stable.

Figure 9 shows the morphological evolution of the scour pit in front of piles during scouring. The sediment particles rolled by the horseshoe vortex in front of the piles breached the original static equilibrium and started to move under the influence of local hydrodynamic forces. Some sediment was confined to the scour pit in front of the pile by a horseshoe vortex, whereas the remaining sediment was carried downstream by the surrounding water by sliding or jumping. At a certain moment during scouring, the slope of the scour pit may become greater than the underwater angle of repose of sediment. In this case, the side slope of the scour pit becomes unstable, driven by gravity until the slope of the scour pit is smaller than or equivalent to the underwater angle of repose of sediment. As expected, the slope of the scour pit (31°) when scour reached the equilibrium stage was close to the natural angle of repose of sediments set in the model.

4.1.3. Time History

Figure 10 shows the time history of local scours around piles. The ordinate is the maximum scour depth around piles obtained by extracting the Z coordinate of particles at the lowest seabed position around piles. The abscissa is the scour time normalised by the scour equilibrium time t_e. As shown in the figure, the scour rate continually decreased throughout the scour and corresponded to the three stages of local scours around the piles: initial stage of scouring (Stage I), intermediate stage of scouring (Stage II), and equilibrium stage of scouring (Stage III). The scour is the fastest at Stage I, and high-speed scour carries off a large amount of sediment around piles in a short amount of time. Although the scour at Stage II is not as fast as that in Stage I, it can still expand the range of scour pits and increase the scour depth. When the flow field in the scour pit is insufficient to carry off the sediment, the scour rate is close to 0. In this scenario, the depth of scour pits around piles does not significantly change any longer and tends to be stable.

In this section, we used experiment data from Xu [39] to verify the CFD-DEM model. On the premise that the pile diameter D, flow depth h, sediment repose angle, dimensionless Shields number θ/θ_cr, and other parameters were consistent, we compared the distribution of dimensionless flow velocity in the test and simulation, and the data showed that they were basically consistent. On this basis, we compared the shapes of scour holes. The data showed that the maximum depth of scour holes was close to the test, and the dip angle of scour holes was basically the same as the angle of repose of sediment particles, which was consistent with previous research results [41]. Finally, we compared the scouring time history curve, and the error between simulation and test was less than 10%, and the scale effect of sediment particles may cause the difference. Nonetheless, this is usually inevitable. If the particle size is set to a value that is too small, the number of particles considerably increase. The resulting computation will be much larger and a greater challenge for computer hardware. Meanwhile, rather than accurately predicting the eventual consequences of local scour, the CFD-DEM local scour model was mainly used to analyse the motion and force characteristics of sediment in the scour field from a mesoscopic perspective. Therefore, the differences between the simulation and test are acceptable, proving the reliability of the application of the proposed model to the study of the local scour process.

4.2. Macro Scour in Areas around Piles

To study the local scour process at different positions around piles, as shown in Figure 11, three prismatic areas close to the pile side were selected for analysis in this study, with the centre of the pile foundation section as the centre, and with an angle of 0, 45, and 90°, respectively. Figure 12 shows the development process of maximum scour depth, at different positions around piles with the scour time. From the beginning of the scour to Stage III, the scour depth at 45° around the pile was greater than that at 0° in front of the pile and 90° on the pile side. At stage I, the scour rate around the pile was relatively high, and the scour depth quickly increased. At this moment, the scour depth at 0 and 45° around the pile were equivalent, but the scour depth at 90° on the pile side was relatively smaller. As time went on, the scour rate in front of the pile significantly decreased until the scour reached an equilibrium, where the order of the scour depth was: S_45° > S_90° > S_0°.

The essence of local scour is the movement process of sediment particles under the action of fluid drag. Therefore, the depth of erosion is very much related to the speed and drag force of the particles. Figure 13 and Figure 14 respectively show the statistical results of the average velocity of and average drag on sediment particles. The comparison of the curves in these figures shows that the order of the average drag on and average velocity of particles in the whole scour process is F_drag,90° > F_drag,45° > F_drag,0° and V_average,90° > V_average,45° > V_average,0°, respectively. The reason is that when the flow reaches the pile foundation, it is divided into two symmetrical parts around the pile; meanwhile, the streamline on both sides of the pile gradually shrinks. Moreover, the flow velocity keeps increasing under the action of the favourable pressure gradient until the flow velocity reaches a maximum near 90° on the pile side. In the meantime, the fluid drag on the sediments near 90° on the pile side also reaches a maximum, followed by the values at 45 and 0°. Finally, throughout the scour, the order of sediment transport velocities around the piles is V_{transport,90°} > V_{transport,45°}> V_{transport,0°}.

Throughout the scour, the local scour depth at 90° on the pile side is still slightly smaller than that at 45°. Namely, the local scour velocity around the pile is not exactly equivalent to the escape velocity of the sediments. This is because the scour depth is also affected by another important factor—the upstream sediment runoff, i.e., the content of upstream sediment carried into the scour pit by the flow. The difference between accumulative sediment output and input reflects the variation in local scour depth. Therefore, the accumulative sediment output and input at corresponding positions around the pile were calculated using the number of sediment particles as an indicator. The cumulative sediment output near 90° on the pile side was much higher than that at the other two positions, as seen in Figure 15, which was consistent with the results shown in Figure 13 and Figure 14. Moreover, the input of sediments carried here from upstream was also much higher than that at the other two positions, which highlights the importance of the scour depth at 90° on the pile side being close to or even smaller than that at the 45° position. As the scour was simulated under clear water scour conditions in this study, the effects of upstream sediment input on the scour results were not significant. However, for movable bed scour, the effects of upstream sediment input on local scour should be analysed.

4.3. Mesoscopic Erosion at the Particle Scale

The essence of local scour is the complex movement of sediment particles around piles under the action of flow field drag. Two representative sediment particles were selected in front of the pile foundation for an in-depth analysis of the mechanism of the mesoscopic erosion of sediments at the particle scale under local hydrodynamic action. Their motion trajectory, coordinate time history, and drag time history during scouring were obtained using Lagrangian particle tracking. The three indicators are shown in Figure 16, Figure 17 and Figure 18. Sediment particles were captured by the high-speed turbulent flow around the pile at Point A (A′). Thus, the drag component in all directions began to gradually increase. The drag on sediment particle 1 reached an obvious peak before arriving at 45° on the pile side (Point B). As the changes in motion state had a certain lag with respect to the changes in instantaneous drag, the velocity of this particle did not change in sync with the drag. Instead, it reached a peak at 45° on the pile side (Point B) after a short interval. The particle corresponding to Point C (C′) moved to 90° on the pile side (−90°). As the direction of the water flow here was basically perpendicular to the Y-axis, the drag was mainly distributed in the X and Z directions; the drag component in the Y direction was almost 0. The drag on sediment particles and their components in all directions reached a maximum. Afterward, the order of drag components was F_drag,z > F_drag,x > F_drag,y. In other words, the subsequent scour hydrodynamic force was mainly the drag in Z and X directions.

The analysis of the mesoscopic motion process above shows that the motion state of sediment particles was closely correlated to the drag on them. The local scour effect was mainly affected by the drag in the flow field. Nonetheless, the contact effect between particles cannot be neglected. Figure 19 shows the force diagram of sediment particles during scouring. For the sediment particle j, it was mainly affected by gravity G_p, the force of fluid on sediment F, normal contact force F_Ni, tangential contact force F_Ti between sediment particles, and so on. The force of fluid on sediment is the main factor that induces local scour and decides the degree of erosion on sediment. The tangential contact forces between sediment particles reduce their kinetic energy, inhibiting scour to a great extent. The normal contact force, however, directly determines the tangential contact force. The above-mentioned forces jointly formed an equilibrium force chain system for the sediment particle group and decided the sediment starting state and scour mechanism. When the force of fluid on sediment breaks the original contact force chain between particles, sediments may start to move and cause local hydrodynamic erosion.

For the individual sediment particle j in equilibrium, the components of the forces on it in X, Y, and Z directions are expressed in Equation (25):

$$\left\{\begin{array}{l}{F}_{p,x}=F\cdot \cos \langle F, i\rangle +{\displaystyle {\displaystyle \sum }_{i=1}^{n_c}}\left[F_{Ni}\cdot \cos \langle F_{Ni}, i\rangle +F_{Ti}\cdot \cos \langle F_{Ti}, i\rangle \right]\\ F_{p,y}=F\cdot \cos \langle F, j\rangle +{\displaystyle {\displaystyle \sum }_{i=1}^{n_c}}\left[F_{Ni}\cdot \cos \langle F_{Ni}, j\rangle +F_{Ti}\cdot \cos \langle F_{Ti}, j\rangle \right]\\ F_{p,z}=F\cdot \cos \langle F, k\rangle +{\displaystyle {\displaystyle \sum }_{i=1}^{n_c}}\left[F_{Ni}\cdot \cos \langle F_{Ni}, k\rangle +F_{Ti}\cdot \cos \langle F_{Ti}, k\rangle \right]+G_p\end{array}\right.$$

(25)

where F_p,x, F_p,y and F_p,z correspond to the components of the forces on the sediment particle in X, Y, and Z directions, respectively; i, j and k are the unit direction vectors in X, Y, and Z directions, respectively; and n_c is the number of the sediment particles in contact. The critical moving direction vector s = (F_pX, F_pY, F_pZ) of the particle was defined. When the resultant force of particles in this direction exceeds 0, it indicates that the particles are about to be scoured, i.e.,

$$\Vert F\cdot \cos \langle F,s\rangle +{\displaystyle \sum }_{i=1}^{n_c}\left[F_{Ni}\cdot \cos \langle F_{Ni},s\rangle +F_{Ti}\cdot \cos \langle F_{Ti},s\rangle \right]+G_p\cdot \cos \langle G_p,s\rangle \Vert >0$$

(26)

Under general conditions, Equation (26) characterizes the initial scour mechanism of individual sediment particles. The erosion of sediments is mainly determined by local hydrodynamic action and the contact between sediment particles. To further analyse the effects of the two on the sediment erosion mechanism during local scour, Figure 20 compares normal and tangential contact forces and interphase drag time history between sediment particles. It can be concluded from friction law that normal contact forces mainly cause tangential contact force between particles, so that their time history curves show consistent trends. During the movement of sediment particles toward Point A (A′), the contact forces on particles are much greater than the interphase drag; the normal and tangential contact forces fluctuate significantly more than the drag. This indicates that before sediments are captured by the high-speed turbulent flow around the pile, the contact forces between sediments are the source of the driving force for the initial disturbance of sediment particles, whereas the corresponding scour mechanism is mainly decided by the entrainment of activated sediment particle groups. When sediment particles enter the turbulent flow around the pile, the interphase drag therein is greater than the tangential contact force between particles. Therefore, the erosion mechanism at this stage is dominated by local hydrodynamic action.

4.4. Discussion of CFD-DEM

4.4.1. Advantages of CFD-DEM

The CFD-DEM model has great potential in simulating fluid–structure interactions. The interactions between the flow and sediments and between sediments were considered during our simulation. Each particle’s position and force conditions were recorded, and the velocity of the sediment particle was quantified. Previous research methods have had difficulty recording such detailed information. This is the advantage of the CFD-DEM method. From this point of view, the CFD-DEM method is quite suitable for the quantitative analysis of local scour and exploration of the mesoscopic mechanism at the sediment particle level.

4.4.2. Limits of CFD-DEM

However, there are many limitations in the application of the unresolved CFD-DEM method. For instance, the fluid grid size must be larger than the particle size to ensure simulation feasibility. Therefore, some details of the flow field will inevitably be neglected. A resolved CFD-DEM method may solve the problem of the flow field and the fineness of drag, but the calculation rate of the model will be significantly affected. This is undesirable for local scour simulations due to its long calculation cycle and extensive calculations. To sum up, it is still difficult to coordinate the accuracy and computational efficiency of CFD-DEM method under certain conditions. Many problems would be solved by developing improved computer hardware and updating simulation algorithms.

5. Conclusions

Based on the CFD-DEM, a local scour model of the water–sand bidirectional fluid–structure interaction was developed in this study. The model was verified by a local scour test under the condition of clear water scour. Our research suggests that CFD-DEM can be effectively used to study the local scour around pile foundation.

The local scour of three regions around the pile foundation at 0, 45, and 90° was studied. Through comparison, it was found that the scour depth at 45° was greater than that at 90 and 0° when the local scour equilibrium was reached. In the entire scouring process, the average drag force and movement speed of the sediment at 90° were greater than those at 45 and 0°, which led to a greater sediment transport velocity at 90° than at 45 and 0°. The local scour velocity around the pile was not completely equal to the sediment transport velocity, and the cumulative output and input of sediment jointly determined the change in local scour depth.

Contact forces, gravity, and fluid force between sediment particles form the equilibrium force chain system of sediment particles. When the drag force on the sediment destroys the original balance force chain system between particles, large-scale local scour may be caused. Before the sediment particles are captured by the high-speed turbulence around the pile, the contact force between the sediment particles is the power source that causes the particles to be initially disturbed, and the scouring mechanism depends on the entrainment of the initial sediment particles. When the sediment enters the high-speed turbulent flow area around the pile, the scouring mechanism is mainly controlled by local hydrodynamic forces.