The Numerical Investigation of Solid–Liquid Two-Phase Flow Characteristics Inside and Outside a Newly Designed 3D Sediment Trap

Abstract

Sediment transport serves as a link for material exchange between land and sea. Using sediment traps, we can observe the capture and transport processes of sediments. Based on the sediment particle size distribution characteristics in Jiaozhou Bay, this paper analyzes the influence of a newly designed 3D sediment trap on the water–sand two-phase flow process inside and outside a trap device during its operation. Meanwhile, under a certain concentration condition, a numerical formula model is researched and proposed to evaluate the impact of the device’s structure, the environmental flow speed, and the particle size on particle capture efficiency. This model is based on the CFD-DPM coupling in Fluent 2021R1 software, and the particle filtration process is solved using a combination of porous media and UDF functions. Finally, by analyzing the distribution of sediment movement in the fluid domain, two concepts, namely the percentage of particles entering the tube and the effective capture rate, are proposed. Suggestions for optimizing the structure of the trap are put forward to achieve optimal capture effects.

1. Introduction

The coastal zone, serving as a buffer and transition area where the ocean and land interact, is the starting point for the transportation of sediments from land to sea [1,2]. This zone encompasses the intertidal zone, the supratidal zone, and the underwater bank slope. Due to its unique dynamic environment and geographical location, the coastal zone possesses many inherent advantages such as a comfortable living environment, abundant natural resources, convenient land and water transportation, and attractive beach tourism resources. This has resulted in nearly two thirds of the world’s largest cities and over sixty percent of the population being distributed in coastal areas [3,4].

However, coastal areas are also susceptible to geological disasters. Landform evolution and disasters caused by land–sea interaction pose a serious threat to economic development and engineering construction in coastal areas. Therefore, the sedimentary dynamic process of the coastal zone system and its response to global changes and high-intensity human activities have become a global research hotspot since the end of the 20th century. In response to this issue, international programs such as the Land–Ocean Interactions in the Coastal Zone (LOICZ) and the Future Earth Coasts (FEC) programs have been proposed [5,6,7].

One of the core processes of coastal sedimentary dynamics is sediment transport. It serves as the nexus of sediment inter-transfer between land and sea, with rivers worldwide discharging up to $1.9\times {10}^{10}$ tons of sediment to the sea each year [8,9]. This plays a direct role in the overall scouring and siltation changes of beaches, as well as in the evolution of localized landform development. Under different sea states, the suspension and transport processes of sediment can vary significantly. Meanwhile, under the same sea state condition, due to variations in environmental factors such as water depth, wave height, different breaking degrees, wave environment, turbulence intensity, and sediment particle size combination, the sediment suspension transport process can show spatial differences [10,11,12,13,14]. By studying the processes of sediment suspension and transportation and accurately capturing sediment particles, we can gain a deeper understanding of the process of sediment transformation from a “source” to a “sink”. This can help us reasonably explain the characteristics of sediment suspension and transportation and the geomorphological evolution of the coastal zone under different sea states and spatial conditions [15,16,17,18,19,20,21,22,23].

For the monitoring of the sediment transport flux, the current technical means are mainly divided into two categories: direct measurements and indirect measurements [24,25,26]. Direct measurements primarily involve multipoint sampling during survey cruises and the deployment of sediment traps to obtain samples. Indirect measurements mainly involve long-term in situ monitoring with acoustic and optical equipment, obtaining flow velocity, turbidity, and other parameters for the conversion and indirect estimation of sediment transport fluxes, or processing watercolor images through satellite remote sensing observations and estimating suspended sediment concentrations on the macroscale.

Sediment traps, serving as a sampling device designed to capture and collect sedimented material in seawater, are primarily utilized for in situ monitoring of sediment fluxes. These traps are categorized into two types: vertical and horizontal [27]. With the progression of research on sediment movement, geomorphological evolution, material transport, and ecological behavior in estuaries, coasts, and offshore areas, the demand for professional and applicable sediment traps has been increasing. There have been an increasing number of studies on the use of sediment traps to collect particles in the ocean (primarily in coastal areas) and in typical lakes abroad [28].

Conventional vertical traps collect particulate matter deposited vertically in a water column, while horizontal ones are used to capture sediment parallel to the bottom boundary layer. Both types of traps have a significant limitation—they ignore the process of sediment transport and only obtain the final deposition result [29].

The existing sediment traps, designed to be placed on a seafloor or lake bed for extended periods, collect sediments settling from above, forming a sequence of sediment deposition. However, these sediment traps are primarily oriented upwards in their design, focusing solely on the natural sedimentation process and overlooking the impact of horizontal sediment transport. Simultaneously, the structure of a laterally opening sediment trap deployed on the shore is simplistic, lacks a sediment flux analysis method that corresponds to the structure, and thus does not possess the capability to capture the process changes of sediment erosion, resuspension, and deposition. Building on previous research, our team developed a novel three-dimensional sediment trap (3D trap). In contrast to traditional vertically opening sediment traps and simplistic laterally opening sediment traps, this trap can be directly applied for the observation of the resuspension and transport processes of sediments. Combined with indirect observation methods such as acoustic and optical methods, this trap enables the in situ, long-term three-dimensional dynamic observation of the oceanic suspended sand transport mechanism. Meanwhile, a multilevel sand transport flux time series analysis method based on the flow velocity and suspended sand concentration was established. Sediment samples at different moments were analyzed through indoor tests to determine their physical and chemical properties.

Yongmao Zhu and Jiarui Zhang completed the innovative design of the device’s structure and proposed a method to analyze the sediment transport flux based on the structure of this 3D sediment trap [30,31]. Liu and Fei established and refined a multilevel sediment transport flux time-series analysis method based on the flow velocity and suspended sand concentration through indoor flume experiments [32]. Using the numerical simulation method of the Fluent program, Cheng Wang explored the influence of the trap tube and screen structures on the original environmental flow field after the device was placed on the seafloor and obtained the corresponding relationship between the flow velocity inside and outside the 3D trap [33].

In this paper, the Eulerian–Lagrangian two-phase flow dynamics model of water and sand inside a transverse sediment trap was established with the Ansys Fluent and the UDF programs written in the C programming language. An analysis of the flow characteristics of the water flow phases inside the trap tube as well as a kinetic study of the sediment particle phases inside the trap tube with a prediction of the capture situation were accomplished. This study also investigated the effects of different particle sizes on the capture efficiency under different flow rate environments and proposed a set of analytical formulas for predicting the particle capture volume inside the 3D trap device. This can aid us in the subsequent work of structural modifications, the evaluation of suitable applications, and the revivification of sediment flux in the “laboratory”.

2. Introduction of 3D Trap and Its Working Principle

2.1. Structural Design of 3D Trap

The primary structure of the three-dimensional (3D) trap is composed of a sediment trapping system, an observation system, a control module, a platform frame, and a sedimentation compensation system. The design of the platform frame is informed by the seabed-based observation platform used for sediment observation. The entire structure is based on a round bottom platform, which facilitates the mounting, disassembly, and maintenance of sampling instruments. The bottom of the base is designed with penetrating pins that can be inserted into the seabed. The symmetrical structure on the upper part of the base ensures the stability of the entire system, thereby meeting the equipment layout observation under different geological conditions. An overall schematic of the 3D trap is shown in Figure 1a.

The specific structure of the capture tube is shown in Figure 1b. A horizontally oriented inlet facing the mixed sea current is provided at the front of the water flow tube. Simultaneously, an inclined sediment screen is provided within the capture tube, which is angled relative to the inlet to provide an environment conducive to sediment deposition. The settling tube is installed beneath the positive screen, sealed at the bottom, with a funnel-shaped opening at the top. It is connected to the water flow tube to collect the sediment particles settled by the filter capture screen.

2.2. Working Principle of the Sediment Trap

Upon the entry of the mixed flow of sediment, driven by the seabed seawater power, into the device, the structural design of the sediment trap catcher allows the sediment screen to intercept the sediment flowing through the water flow channel. Consequently, all sediment particles larger than the screen’s aperture and within the capture interval are retained. These particles are deposited in the settling tube under the effect of the sediment’s own gravity.

The three inlets, each corresponding to a direction of the incoming flow, are stepped in height from the base. This design enables the collection of sediment particles from different layers in that direction. The suspended sediments transported by the current through the traps at different heights and directions can be captured in a three-dimensional manner. A schematic diagram of the working principle is shown in Figure 2.

2.3. Analytical Equations for The Prediction of Particle Capture

The device’s internal flow tube is equipped with a flow meter and a turbidimeter, which continuously collect and record the suspended sediment concentration, $SS{C}_{(d,h,t)}$, and flow velocity, $V_{C(d,h,t)}$, of the water flowing through the flow tube during the observation period. The sediment transport flux of the external ambient flow field can be obtained by inversion. An analytical relationship for sediment transport fluxes based on the flow velocity and suspended sand concentration can be established as follows [33]:

$$Q_{\mathrm{out}}=V_{out}\times SS{C}_{out}$$

(1)

$$V_{out}\propto V_{in}$$

(2)

$$SS{C}_{out}\propto SS{C}_{in}$$

(3)

For equal flow rates and concentrations of sediment transport, the capture quantity obtained by the device will vary due to the differing physical characteristics of the sediment particles themselves, such as particle size and density. Therefore, this study exclusively discusses the correspondence between the benthic current flow rate and capture under constant concentration conditions, considering particle size.

3. Establishment of Computational and Analytical Models and Numerical Simulation of Transverse Traps

3.1. Establishment and Meshing of the 3D Model

3.1.1. Establishment

The three-dimensional modeling software Solidworks 2020 was utilized to construct the assembly in three dimensions and to implement appropriate simplifications. The coordinate origin is designated at the center of the pipe inlet, with the centerline of the horizontal flow channel aligning with the x-axis. The centerline of the vertical pipe flow runs parallel to the y-axis. The filter screen forms a 45° angle with the planes of the upper and lower pipe walls. The specific size structure is illustrated in Figure 3.

3.1.2. Meshing

The software Spaceclaim 2021R1 was employed to finalize the creation and the extraction of the computational domain of the flow field both inside and outside the 3D trap in a 3D virtual undersea environment. Subsequently, the model file was imported into Fluent Meshing to mesh the device’s internal and external flow fields. The computational domain mesh was divided using the unstructured polyhedral–hexahedral technique. The surface and internal meshes of the device were locally encrypted. The generated mesh profile is illustrated in Figure 4.

3.1.3. Independence Verification

Prior to the formal simulation calculation, it is imperative to conduct a mesh-independent validation to enhance solution accuracy and verify the computational model’s validity. This study primarily focuses on the efficiency of particle capture inside the transverse sediment trap. Consequently, the number of particles entering the transverse trap tube’s interior is taken as validation. For the irrelevance validation simulation employing different levels of mesh, the inlet flow velocity is set at 0.6 m/s, the diameter of the incident particles is set at d = 0.1 mm, the particle density is set at $1700{ \mathrm{kg}/\mathrm{m}}^3$, and the particle flow rate is set at $8.9\times {10}^{-3} \mathrm{kg}/\mathrm{s}$.

As shown in

Table 1. Mesh table for different mesh numbers.

Combined Mesh Number	401,408	708,827	1,579,809	2,158,510	3,446,393
Number of entry particles	7031	9705	10,622	10,746	10,724
Rate of change (%)	−33.81	−8.63	As benchmark	+1.17	+0.96

, we employ the model with 1,579,809 combined meshes as the standard computational mesh. When the number of combined meshes is less than 401,408, the computational accuracy significantly decreases with a rate of change of -33.81%. When the number of combined meshes increases to 708,627, the rate of change is -8.63%. Upon further increasing the number of meshes from 1,579,809 to 3,446,393, the rates of change in the number of particles which enter the inlet tube fluctuate within 1%, which can be considered to satisfy the error range condition.

Therefore, 1,579,809 combined meshes are optimal, considering both the computational cost and the computation’s accuracy.

3.2. Numerical Simulation Method

3.2.1. Selection of Multiphase Flow Models

This paper conducts a numerical simulation to investigate the particle capture efficiency of a submarine lateral sediment trap. The simulation employs computational fluid dynamics with Ansys Fluent 2021R1, using a sandy water stream as the working medium. This medium comprises a liquid phase (water) and a solid phase (sediment particles), constituting a standard fluid–particle two-phase flow.

For the simulation and computation of a fluid–particle two-phase flow, two traditional research methods exist:

(1)

The Eulerian–Eulerian method, which treats the solid particle phase as a proposed fluid. It considers that the particles and the fluid are two continuous phases co-existing and interpenetrating with each other, dealt with under the Euler coordinate system, i.e., two-fluid modeling (TFM).

(2)

The Eulerian–Lagrangian method, which treats the fluid as a continuous medium and the granular phase as a discrete system. It deals with the motion of the continuous phase in the Euler coordinate system and the motion of the discrete phase in the Lagrange coordinate system, i.e., a discrete particle model (DPM).

Either of these research methods has its own application scenarios and should be selected in conjunction with the actual situation. Typically, solid–phase sediment particles in seawater are small in content, mass, and size. Therefore, the interaction forces between particles are considered small and negligible from a macroscopic perspective [34,35,36].

The two-way coupling between the continuous phase and the granular phase is addressed, i.e., using a non-stoichiometric particle tracking method under transient computational conditions. This method combines the concept of particle “Parcel” in Ansys Fluent with the particle orbital model (DPM) that comes with Fluent for the simulation. It treats the particle parcel, which is formed by the aggregation of multiple particles, as the smallest unit of the study. Even so, this numerical simulation approach still has certain limitations and uncertainties: it restricts the particle concentration to less than 10% and does not consider the actual volume of the particles.

3.2.2. Parameter Idealization Assumptions

To facilitate the numerical simulation calculations, the following assumptions are made in the simulation process:

(1)

The continuous phase (liquid phase) is an incompressible fluid, and the particle phase is a discrete system. The physical properties of the two phases are constants, and there is no phase transition phenomenon.

(2)

The effect of temperature is ignored, and heat transfer in the two-phase flow is neglected.

(3)

The particle phase consists of spherical and uniformly dense sediment particles, with particle fragmentation being ignored.

(4)

Smooth walls are assumed, and the effect of wall roughness on the flow field is neglected.

(5)

It is assumed that the liquid and particle phases at the inlet of the fluid domain are uniformly distributed.

These assumptions are made to simplify the computational process while still providing a reasonable approximation of the physical system.

3.3. Mathematical Characterization Models of Fluids

3.3.1. Turbulence Model

The flow characteristics of submarine currents are notably complex, exhibiting typical turbulent motions accompanied by stochasticity and diffusivity. The primary engineering practice for studying turbulence problems is non-direct numerical simulation. In this study, we adopt the RNG k–ε turbulence model, which offers higher accuracy in the calculation of flow fields with large velocity gradients. The equations for the turbulent kinetic energy (k) and the turbulent dissipation rate (ε) are provided below [37]:

$$\frac{\partial (\rho k)}{\partial t}+\frac{\partial (\rho k{\mu }_i)}{\partial x_i}=\frac{\partial }{\partial x_j}[(\mu +{\mu }_t)\frac{\partial k}{\partial x_j}]+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(4)

$$\frac{\partial (\rho \epsilon )}{\partial t}+\frac{\partial (\rho \epsilon {\mu }_i)}{\partial x_i}=\frac{\partial }{\partial x_j}[(\mu +{\mu }_t)\frac{\partial \epsilon }{\partial x_j}]+C_{1\epsilon }\frac{\epsilon }{k}(G_k+C_{3\epsilon }{G}_b)-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}+S_{\epsilon }$$

(5)

where $x_i,x_j$ are the position coordinates in the i and j directions, respectively; $\rho$ indicates the fluid density (${\mathrm{kg}/\mathrm{m}}^3$); $t$ is the time (s); $\mu$ indicates the hydrodynamic viscosity ($\mathrm{P}\mathrm{a}\cdot \mathrm{s}$); $S_k,S_{\epsilon }$ indicate the user-defined source terms; $G_k$ indicates the stress source term generated by the velocity gradient; $G_b$ indicates the stress source term generated by the buoyancy; $Y_M$ indicates the fluctuation expansion term in compressible turbulence; and

$$G_k={\mu }_t(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i})\frac{\partial u_i}{\partial x_j},G_b=\beta g_i\frac{{\mu }_t}{p{r}_t}\frac{\partial T}{\partial x_i},Y_M=2\rho \epsilon M_{\mathrm{t}}^2$$

where $p{r}_t=0.85$ is the turbulent Prandtl number; $\beta$ is the coefficient of thermal expansion; and $M_t$ is the turbulent Mach number.

The left correlation coefficients are empirical:

$$C_{1\epsilon }=1.44,C_{2\epsilon }=1.92,C_{3\epsilon }=C_{2\epsilon }-\frac{C_{\mu }\rho {\eta }^3(1-\frac{\eta }{{\eta }_0})}{1+\beta {\eta }^3},C_{\mu }=0.0845,{\eta }_0=4.377$$

3.3.2. Continuous Phase (Liquid Phase) Control Equations

• Mass conservation equation:

$$\frac{\partial \rho }{\partial t}+\frac{\partial (\rho u_j)}{\partial x_j}=0$$

(6)

• Conservation of momentum equation:

$$\frac{\partial (\rho u_i)}{\partial t}+\frac{\partial (\rho u_i{u}_j)}{\partial x_j}=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}[\mu (\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i})]+\rho g+F_i$$

(7)

where $x_i,x_j$ are the position coordinates in the i and j directions, respectively; $u_i,u_j$ indicate the instantaneous velocity of the fluid (m/s); $\rho$ indicates the fluid density (${\mathrm{kg}/\mathrm{m}}^3$); $t$ is the time (s); $\mu$ indicates the hydrodynamic viscosity ($\mathrm{P}\mathrm{a}\cdot \mathrm{s}$); and $F_i$ indicates the interaction force between a continuous phase and a discrete phase ($\mathrm{N}$) [38].

3.3.3. Discrete Phase (Granular Phase) Control Equations

The equations of motion for the particle phase are derived by solving the momentum equations of the particles within the Lagrangian framework, thereby determining their trajectories. The motion of the particles is bifurcated into translations and rotations, with the momentum equations being governed by Newton’s second law. This approach ensures a comprehensive understanding of the particle dynamics [38].

$${\mathrm{m}}_d\frac{d{U}_a}{dt}=\sum F$$

(8)

$$I_{\mathrm{a}}\frac{d{\Omega }_a}{dt}=\sum T$$

(9)

where $U_a (\mathrm{m}/\mathrm{s})$ and ${\Omega }_a (\mathrm{m}/\mathrm{s})$ represent the translational and rotational velocities of particle $a$, respectively; $\sum F (\mathrm{N})$ represents the combined external force on particle $a$; and $\sum T (\mathrm{N}\cdot \mathrm{m})$ represents the combined external moment acting on particle $a$.

3.4. Setting of Parameters Related to Finite Element Simulation

3.4.1. Filter Screen Structure

The utilization of Ansys Fluent’s inherent Porous Media Model to address fluid dynamics problems involving screen structures has increasingly become the preferred choice for many researchers [39,40,41,42]. The screen’s obstructive effect on the fluid is characterized by introducing a porous medium momentum source term, $S_i$, in the momentum control equation. This term models the viscous and inertial losses caused by the volume pressure drop, as demonstrated subsequently in Equation (10):

$$S_{\mathrm{i}}=-{\displaystyle \sum _{j=1}^3{C}_{1ij}}{\mu }_g{v}_j+\frac{1}{2}{\displaystyle \sum _{j=1}^3{C}_{2ij}}{\rho }_g\left|v\right|v_j$$

(10)

where $C_1$ is the viscous drag coefficient and $C_2$ is the inertial drag coefficient. Assuming that the filter screen structure used is a uniformly isotropic porous media structure, the viscous drag coefficient and the inertial drag coefficient are calculated as follows:

$$C_1=\frac{150(1-\epsilon {)}^2}{D^2{\epsilon }^2}$$

(11)

$$q=\frac{1}{D}$$

(12)

$$C_2=\frac{3.5(1-\epsilon )}{D{\epsilon }^2}$$

(13)

In Equations (11)–(13), $D$ denotes the aperture of the screen within the trap, $q$ signifies the permeability, and $\epsilon$ represents the porosity of the screen. The porosity percentage, $\epsilon$, of a screen is indicative of the ratio of the screen’s pore area to the total area of the screen’s surface.

$$\epsilon =\frac{D^2}{{(D+d_s)}^2}\times 100\%$$

(14)

where $d_{\mathrm{s}}$ refers to the diameter of the sieve line. The values of the remaining key parameters are presented in

Table 2. Main parameters of standard screen with 100 meshes.

Mesh Number	D/(mm)	Screen Thickness/(mm)	Screen Wire Diameter/(mm)	ε/%	q/(m2)	C1/(m−2)	C2/(m−2)
100	0.150	2	0.063	50	$7.50\times {10}^{-10}$	1.33 × 1010	93,333.33

.

A User-Defined Functions (UDF) program was developed to facilitate the implementation of particle–wall conditions, specifically to intercept particles of varying sizes at the filter’s front end and to enumerate the particle count within each localized region of the flow field. The UDF employed encompasses three primary DEFINE macros [43]:

(1)

The DEFINE_ADJUST macro, executed once upon the completion of each iteration step, is utilized to integrate parameters within a specified computational domain. This integration yields the counts of distinct particles, which are subsequently transferred and stored in the User-Defined Memory (UDM).

(2)

The DEFINE_EXECUTE_AT_END macro, also executed once after each iteration step, employs the SUM function. This function accumulates the particle count computed at each step by the DEFINE_ADJUST macro and subsequently displays this value on the console.

(3)

The DEFINE_DPM_BC macro is employed to specify the particle–wall conditions. Particles smaller than the standard 100-mesh screen aperture (D = 0.15 mm) are permitted to pass directly through the screen’s front plane, while particles larger than the screen’s aperture are rebounded. This action is schematically depicted in Figure 5.

The rebound mechanism employs an empirical formula to assign a rebound recovery coefficient. The empirical coefficients are selected with reference to the literature [44]. In this paper, we adopt the transverse (x-direction) recovery coefficient $e_x=-0.63$, and the vertical (y-direction) recovery coefficient $e_y=0.54$. This implies that after colliding with the front plane of the screen, particles with $d>0.15 \mathrm{mm}$ will have their velocities transformed according to Equation (15):

$$\begin{array}{l}{v}_x^{’}=e_x{v}_x\\ v_y^{’}=e_y{v}_y\\ v_z^{’}=v_z\end{array}$$

(15)

3.4.2. Calculating Domain Boundary Conditions

To minimize the impact of the flow field wall boundaries on the device’s overall capture efficiency and to regulate the total flow time from the inlet to the outlet, the computational domain’s total size in the virtual environment was established as L690 mm × W140 mm × H240 mm, as depicted in Figure 6.

The distance between the collector inlet and the fluid inlet is 500 mm, and the outer surface of the collector is 50 mm from the top of the fluid domain, as shown in Figure 7.

Five types of boundary conditions were implemented: Inlet face 1 was designated as a velocity inlet boundary. Boundary face 2 of the sink was established as a wall boundary. Faces 3, 4, 5, and 6 were designated as internal face boundaries. Outlet face 7 was established as a pressure outlet. Velocity inlet 1 employs a magnitude normal to the boundary, while the remaining surface conditions are set to stationary and no-slip walls.

The time step is set to 0.03 s to simulate an actual flow duration of 30 s. Given that the discrete phase model (DPM) in Fluent does not account for the true volume of the particles, it is unable to accurately consider the actual accumulation of particles in the capture tube. Consequently, the boundary conditions for inlet face 1 and outlet face 2 are set to “escape” to facilitate particle incidence and outflow, while face 4 is set to apply the User-Defined Function (UDF). The boundary condition for face 5 is set to “trap”, implying that the particles are absorbed by surface 5. The remaining faces retain their default settings (reflect). The sample tab is also activated to analyze the motion of incident particles in the flow field at varying flow velocities by studying physical quantities such as the flow velocity, unit mass, etc., of the parcel passing over each monitoring surface.

3.4.3. Solver Settings

The solver is set up as follows: a pressure-based solver, absolute velocity formulation, and transient time calculation model are used. The RNG k–ε turbulence model is selected for the viscous model. The gravitational acceleration is set to $y=-9.81{ \mathrm{m}/\mathrm{s}}^2$. The pressure–velocity coupling is implemented using the coupled algorithm. In the solution method, the gradient calculation uses the least squares cell-based format, the pressure term uses the second-order discretization format, and the momentum term, turbulent kinetic energy, and turbulent dissipation rate use the second-order upwind format. The time-term discretization format is a first-order implicit formula. All other solution control parameters are kept at their default values. The near-wall region of the device is treated with enhanced wall treatment.

3.4.4. Continuous Phase (Liquid Phase) Parameter Settings

The simulation parameters obtained according to the actual working conditions are shown in

Table 3. Simulation parameters of the continuous phase.

Parameters	Values
Working medium	Seawater (10 °C)
Continuous phase density	1030 kg/${\mathrm{m}}^3$
Continuous phase viscosity	0.001308 kg/(m·s)

.

3.4.5. Discrete Phase (Granular Phase) Parameter Settings

The grain size distribution curve of the sediment from Jiaozhou Bay is plotted in Figure 8 according to the actual particle size distribution [45]. Theoretically, during the sediment transport process, a standard 100-mesh screen can capture 10.84% of this soil sample.

This paper uses numerical simulations to investigate the actual capture efficiency of a standard 100-mesh screen for this 10.84% fraction of soil sample particles. A hypothetical solution is set up with equal mass concentrations for each particle size, all at $8.90\times {10}^{-3} \mathrm{kg}/\mathrm{s}$. The hypothetical solution contains five different particle sizes, each accounting for 20% of the total concentration. The total mass flow rate of the particle system is $4.45\times {10}^{-2} \mathrm{kg}/\mathrm{s}$, ensuring that the total concentration is less than 10%. All particles are injected from face 1 using the “Inject Using Face Normal Direction” method. During the actual operation of the 3D trap, it is necessary to capture sediment particles of different sizes under various current velocities and turbidity conditionsIn this paper, numerical simulations are conducted with a constant particle mass concentration in the system. The impact of different flow velocities and particle sizes on the capture efficiency of the 3D trap is analyzed. And the detailed parameter settings for the selected discrete phase used in the simulation are provided in

Table 4. Simulation parameters of the discrete phase.

Particle Material	$\mathbf{Density}/(\mathbf{kg}/{\mathbf{m}}^3)$	Start–Stop Times/(s)	Particle Diameter/(mm)	Mass Flow Rate/(kg/s)
Anthracite	1700	0~1	0.1	0.0089
			0.2
			0.3
			0.4
			0.5

.

4. Analysis and Discussion of Simulation Results for Sediment Transport Inside and Outside the 3D Trap Device

4.1. Particle Incipient Motion Conditions

The transportation of sediment in the marine environment primarily relies on the entrainment of water currents. Sediment particles of different sizes are subjected to various forces between the water body and the particles, resulting in changes such as incipient motion, saltation, suspension, settling, and resuspension. The phenomenon of stationary bed sediment transitioning into motion is referred to as sediment incipient motion, and the corresponding critical flow conditions are known as the sediment incipient motion conditions. The incipient flow velocity is often used as a judgment criterion. Correspondingly, the critical flow velocity at which moving sediment transitions into a stationary state is referred to as the stopping flow velocity. Through experiments, it was found by Sha that the stopping flow velocity is approximately four fifths of the incipient flow velocity [46]. Based on experimental data, the equation for the incipient flow velocity can be obtained as:

$$V_H=\frac{4}{5}{V}_f$$

(16)

$$V_f=10.5\frac{g^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$8$}\right.}{(\frac{{\gamma }_s-\gamma }{\gamma })}^{{}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$8$}\right.}}{d}^{{}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$8$}\right.}}}{{\omega }_0^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}{R}^{{}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}}$$

(17)

where $V_H$ is the stop flow velocity of the sediment; $V_f$ is the uplift flow velocity of the sediment; $\gamma$ denotes the unit weight of water, taken as $10.0{ \mathrm{KN}/\mathrm{m}}^3$; d is the sediment particle size (mm); ${\gamma }_s$ refers to the dry unit weight of the sediment, taken as $26.5{ \mathrm{KN}/\mathrm{m}}^3$; R denotes the hydraulic radius of the capture tube (R = 0.03 m); g represents the gravitational acceleration ($g=9.81{ \mathrm{m}/\mathrm{s}}^2$); and ${\omega }_0$ is the settling speed of the sediment particles.

According to the superposition principle of resistance, the equation for the sediment particle settling velocity can be derived as follows [47,48,49]:

$${\omega }_0=\sqrt{{(13.95\frac{v}{d})}^2+1.09\frac{{\gamma }_s-\gamma }{\gamma }gd}-13.95\frac{v}{d}$$

(18)

where v is the dynamic viscosity coefficient of water; at 10 °C, v ≈ $0.01{ \mathrm{cm}/\mathrm{s}}^2$.

According to Equations (17) and (18), to mobilize all particles with a diameter ≤ 0.5 mm, the environmental flow velocity needs to reach 30.72 cm/s. Therefore, to ensure that all particles can be mobilized, the range of the sea current inlet velocity (velocity of face 1) is set to 0.3 m/s–3 m/s, with a set of velocities set every 0.3 m/s, totaling 10 sets of velocity conditions.

4.2. Analysis of the Flow Field within the Fluid Domain

As mentioned in the earlier sections of this paper, the transport of sediment in the marine environment primarily relies on its entrainment by water currents. To understand the real reasons behind the particle capture efficiency, it is essential to analyze the distribution of the flow field inside and outside the 3D trap. Next, we will carry out this task and analyze the flow field situation of a typical cross-section at Z = 0, as shown below in Figure 9.

Figure 9 shows a cloud diagram of the velocity distribution and streamlines at the inlet surface when the flow velocity is 2.7 m/s. The following observations can be made:

(1)

Rapids appear directly above and below the capture tube device, with most of the water flowing around the device from above and below. Only a small portion of the water flow sharply slows down and then flows into the capture tube. Simultaneously, there is a portion of the water flow at the back of the device that flows from the top down, with a relatively low inlet flow velocity.

(2)

Eddies are present at the inlet of the capture tube, the funnel opening on the lower side of the screen, and the outlet of the capture tube. There is a significant difference in the flow velocities inside and outside the capture tube.

(3)

When the inlet flow velocity is 2.7 m/s, the average flow velocity of the upstream channel inside the capture tube is only 0.337 m/s. The flow velocities at the inlet of the tube, the upper wall at the corners of the flow channel, and the left wall are relatively large, approximately 0.584 m/s.

(4)

From the funnel-shaped opening downward, the flow velocity inside the entire settling tube is almost zero. After the particles hit the screen plane, they collide and experience friction, losing a significant amount of kinetic energy. They then gradually sink under the effect of gravity and finally fall to the bottom of the settling tube, resulting in effective capture.

We visualized the above process data and created a plot of the analytical relationship between the rate of velocity inside and outside the capture tube and the inlet velocity as follows in Figure 10:

As can be seen from Figure 10, there is a positive correlation between the rate of velocity inside and outside the capture tube and the inlet velocity.

4.3. Correspondence of the Number of Particles Entering the Tube with Flow Velocity and Particle Diameter

In this paper, the sea current inlet velocity is treated as a single variable. With the particle distribution ratio and mass concentration fixed and other conditions kept constant, the impact of the environmental flow velocity on the particle capture efficiency is investigated. Figure 11 reflects the number of various particles entering the capture tube inlet under different flow velocity conditions (the horizontal axis represents the flow velocity of inlet face 1, and the vertical axis represents the rate relationship between the actual number of particles entering the capture tube and the ideal capture quantity).

As illustrated in Figure 11, with an increase in the inlet surface flow rate, the number of particles entering the capture tube also continuously increases, indicating a positive correlation. However, as the inlet surface flow rate continues to increase, the slope of the curve is continuously decreasing. This suggests that as the inlet flow rate increases, the rate of increase in the number of particles entering the tube is continuously decreasing. Simultaneously, the figure also reveals that, under the same flow rate conditions, the particle size influences the number of particles entering the tube. Within a particle size range of d = 0.1 mm~0.5 mm, there is a positive correlation, i.e., the larger the particle size, the greater the rate of particles entering the tube.

In addition, it can be observed that the curve form of the inner and outer flow speed ratio in Figure 10 is very similar to the rate curve of the number of particles entering the tube in Figure 11. By merging the curves from these two figures, a new curve graph can be obtained, as shown below in Figure 12.

In Figure 12, the five short dashed lines represent the graph depicted in Figure 10, and the orange solid line represents what is shown in Figure 11. The following observations can be made:

(1)

The red short dashed line almost coincides with the orange solid line, indicating that the percentage of particles with d = 0.2 mm entering the tube can be directly considered as determined by the ratio of the flow velocity inside and outside the tube. This also indirectly verifies that the process of sediment transport in the marine environment primarily relies on its entrainment by water currents.

(2)

Under the assumption of Corollary (1), for a particle size range of d = 0.1 mm~0.5 mm, if the particle size, d, is less than 0.2 mm, the smaller the particle size, the larger the negative deviation between the percentage of particles in the inlet tube and the ratio of the flow velocity inside and outside the capture tube. Conversely, if the particle size, d, is more than 0.2 mm, the larger the particle size, the larger the positive deviation between the percentage of particles in the inlet tube and the ratio of the flow velocity inside and outside the capture tube.

The phenomenon described in Corollary (2) may be attributed to the effects of inertia and longitudinal forces. We know that the smaller the flow velocity, the greater the pressure, according to Bernoulli’s principle [50]:

$$p+\frac{1}{2}\rho v^2+\rho \mathrm{g}h=C$$

(19)

In Equation (19), $p$ represents the pressure at a certain point (Pa), $v$ signifies the flow velocity of the fluid at that point (m/s), $\rho$ represents the density of the fluid (${\mathrm{kg}/\mathrm{m}}^3$), $g$ represents the gravitational acceleration ($g=9.81{ \mathrm{m}/\mathrm{s}}^2$), $h$ represents the height at that point, and C is a certain quantity.

At the front end of inlet face 3, where the water flow rapidly decelerates, the static pressure of the water sharply increases. This creates a pressure difference between the upper and lower surfaces of the particles, providing an upward lift for the particles, as illustrated in Figure 13.

The larger the particle size, the greater the mass of a single particle, and consequently, the greater its inertia. At the occurrence of an up-and-down bypass at the capture tube’s inlet face 3, large particles, due to their own inertia, find it difficult to change their state of motion. As a result, some particles do not follow the water flow in a timely manner to turn and bypass; instead, these particles maintain their original state of motion and enter the capture tube’s inlet face 3. Conversely, for small particles, their low inertia makes it easier for them to pass above the inlet of the capture tube with the high-velocity water flow under the effect of lift.

We perform a function fitting for the inlet flow rate, particle size, and the percentage of particles in the inlet pipe in Matlab. Here, the velocity of inlet face 1, $v_{\mathrm{inlet}}$, and the particle size, $d$, are treated as independent variables, while the rate of particle entry, $r_{entry}$, is considered the dependent variable. This allows us to obtain an analytical equation (Equation (20)) between all three parameters ($r_{entry},v_{inlet},d$). A schematic representation of the function is shown in Figure 14:

$$\begin{array}{c}{r}_{entry}=2.581+2.149v_{inlet}-11.21\mathrm{d}+1.352v_{inlet}{}^2+9.36v_{inlet}\cdot d+47.29d^2\\ -0.341v_{inlet}{}^3-2.211v_{inlet}{}^2\times d+4.82v_{inlet}\times d^2-57.65d^3\\ (0.3 \mathrm{m}/\mathrm{s}\le v_{inlet}\le 3 \mathrm{m}/\mathrm{s},0.1 \mathrm{m}\mathrm{m}\le d\le 0.5 \mathrm{m}\mathrm{m},R^2=0.9927) \end{array}$$

(20)

4.4. The Comparison of Results with Other Similar Studies

In former studies, Wang, C. [33] conducted a simulation in flow fields, s, inside and outside a capture tube to investigate the influence of the capture tube structure, screen pore size, and other factors on the on-site flow field. And then, combined with the sediment kinematics formulas, Wang analyzed the ideal sediment capture efficiency of this device without adding the particle phase.

As is illustrated in Figure 9 and Figure 10, our results correspond to Wang’s. Furthermore, we use the Eulerian–Lagrangian two-phase flow dynamics model to research the two-phase water and sediment characteristics inside and outside the 3D trap with the Ansys Fluent and UDF programs written in the C programming language. Meanwhile, under a certain concentration condition, a numerical formula model was researched and proposed to evaluate the impact of the device’s structure, the environmental flow speed, and the particle size on the particle capture efficiency. The research methods in this paper can provide a theoretical basis for future structural modifications of the capture tube structure and the observation of sediment transport fluxes.

5. Distribution of Particle Locations in the Fluid Domain

Utilizing the transient computational DPM model available in Fluent, we can visualize the positional distribution of the particle packages during the flow and trapping processes. Figure 15 displays the distribution of particles in the fluid domain, both inside and in proximity to the capture tube, at a flow velocity of 1.2 m/s when the flow time T = 3 s.

The simulation effectively achieves our anticipated outcome. After the particles collide with the front surface of the screen, only the particles with d = 0.1 mm can pass through. The other particles of four different sizes, which are larger than the aperture of the screen (D = 0.15 mm), are rebounded and then settle under the effect of gravity. They enter the funnel-shaped opening and eventually fall to the bottom of the capture tube (effective capture). However, some particles, due to the sharp reduction in the flow velocity in the pipe, are subjected to turbulent diffusion and settle immediately after entering the device, accumulating on the inner wall of the front flow channel inside the capture tube (front deposition).

Due to the existence of such a large portion of particles that undergo front deposition, this paper introduces a concept called the effective capture rate, $r_{effective}$. This refers to the rate between the particles that fall into the settling tube and the ideal capture quantity.

Figure 16 shows the correspondence relationship between the specific capture percentage of the four types of particles within the filter capture range and the velocity of inlet face 1.

It is evident that only when the inlet velocity exceeds 2.33 m/s will the front deposition phenomenon completely disappear. The larger the particle size, the more pronounced the effect of front-end sedimentation. For the four specific particle sizes in Figure 16, the effective capture rate formulas within a certain range of sea current speeds can be formulated as Equations (21)–(24):

$$r_{effective,d=0.2}=\left\{\begin{array}{l}12.773-\frac{12.881}{1+{(\frac{v_{inlet}}{1.175})}^{3.281}}, 0.3\le v_{inlet}<1.78\\ r_{entry,d=0.2} , 1.78\le v_{inlet}\le 3\end{array}\right.$$

(21)

$$r_{effective,d=0.3}=\left\{\begin{array}{l}20.916-\frac{21.012}{1+{(\frac{v_{inlet}}{1.827})}^{3.226}}, 0.3\le v_{inlet}<2.07\\ r_{entry,d=0.3} , 2.07\le v_{inlet}\le 3\end{array}\right.$$

(22)

$$r_{effective,d=0.4}=\left\{\begin{array}{l}0,0.3\le v_{inlet}<0.71\\ 20.873-\frac{20.997}{1+{(\frac{v_{inlet}}{1.846})}^{5.261}}, 0.71\le v_{inlet}<2.28\\ r_{entry,d=0.4} , 2.28\le v_{inlet}\le 3\end{array}\right.$$

(23)

$$r_{effective,d=0.5}=\left\{\begin{array}{l}0,0.3\le v_{inlet}<0.97\\ 20.670-\frac{20.951}{1+{(\frac{v_{inlet}}{1.843})}^{6.835}}, 0.97\le v_{inlet}<2.33\\ r_{entry,d=0.5} , 2.33\le v_{inlet}\le 3\end{array}\right.$$

(24)

In addition to the four types of particles mentioned above, we also added particles with a diameter of d = 0.1 mm, which is outside the theoretical capture range. Theoretically, these particles will not be intercepted by the filter net but will pass through it entirely. However, in the experiment conducted by Fei [32], a few particles smaller than the mesh aperture were collected. The simulation results for the 0.1 mm particle size are shown in Figure 17:

It can be seen that when $0.3 \mathrm{m}/\mathrm{s}\le V_{\mathrm{inlet}}\le 1.48 \mathrm{m}/\mathrm{s}$, these kinds of particles will also be effectively captured, and even when $0.3 \mathrm{m}/\mathrm{s}\le V_{\mathrm{inlet}}\le 0.84 \mathrm{m}/\mathrm{s}$, front deposition will occur. The formulas for the effective capture rate, $r_{effective}{}^{\ast }$, and the particle penetration rate, $r_{pass}$, are given in Equations (24) and (25):

$$r_{effective}{}^{\ast }=\left\{\begin{array}{l}1.001e^{-\frac{1}{2}{(\frac{v_{inlet}-0.837}{0.336})}^2}-0.161, 0.3\le v_{inlet}<1.48\\ 0 , 1.48\le v_{inlet}\le 3\end{array}\right.$$

(25)

$$r_{pass}=\left\{\begin{array}{l}12.032-\frac{12.496}{1+{(\frac{v_{inlet}}{1.099})}^{2.406}}, 0.3\le v_{inlet}<1.48\\ r_{entry,d=0.1} , 1.48\le v_{inlet}\le 3\end{array}\right.$$

(26)

Through the above analysis, we can find that in this simulation experiment, the issue of front deposition is quite serious, mainly because the front channel of the filter net is designed to be too long. Within a specified range of environmental flow speed, particles begin to settle immediately after entering the capture tube’s inlet face 3, and not all are deposited in the settling tube, which greatly affects the restoration of the sediment flux. In subsequent device designs, consideration can be given to reducing the distance from the capture tube inlet to the filter net.

6. Conclusions and Prospects

(1)

The CFD-DPM method was used to numerically simulate a water–sand two-phase flow inside and outside the 3D trap, researching the effects of the device’s structure, the environmental flow speed, and the particle diameter on the capture results. It fills a research gap by predicting the capture situation when we use this novel device. We obtained a functional relationship, Equation (20), between the percentage of particles entering the tube, $r_{entry}$, under specific concentration conditions and the environmental flow velocity, $v_{inlet}$, as well as the particle diameter, $d$.

(2)

When the flow speed is less than a specific range, using this capture device to collect particles will result in a large amount of front-end deposition of particles near the front inlet of the capture tube. This is not conducive to our effective capture, greatly limits the effective capture rate, and causes distortion of the restored environmental turbidity. In this paper, we provide formulas for the effective capture efficiency of particles of four different sizes within a theoretical capture range under certain environmental circumstances, as shown in Equations (21)–(24).

The reason for this phenomenon is that the flow speed inside the tube decreases sharply, causing the sediment to settle. Therefore, we can try to correct this problem by changing the structure of the device (such as increasing the mouth area, changing the mouth shape, changing the length of the inlet section, etc.).

(3)

For particles with d = 0.1 mm, which are not within the theoretical capture range, they should all pass through the filter net. However, through simulations, we found that these particles did not all pass through the filter net. When $0.3\le v_{inlet}<1.48 \mathrm{m}/\mathrm{s}$, these particles also appeared in the settling tube. Through an analysis, we obtained Formulas (25) and (26) for the effective capture rate, $r_{effective}{}^{\ast }$, and the penetration rate, $r_{pass}$.

This is because the existence of the filter net causes a large difference in the flow speed field inside and outside the device, and the speed of the internal flow field is too small to carry the particles, causing the particles to settle immediately after entering the tube.

(4)

This paper simulates, discusses, and analyzes the sediment capture efficiency of a newly designed 3D trap device under specific environmental conditions. Its primary focus is on the impact of the environmental flow speed and particle size on the device’s capture efficiency. The research also reveals a significant influence of the device’s structure on the effective capture rate and proposes some improved optimization schemes. The research methods and conclusions of this study can provide a theoretical basis for the subsequent design of sediment capture devices and the observation of sediment transport fluxes.