Hydrodynamic Performance of Cubic Artificial Reefs During Deployment Process Based on Smoothed Particle Hydrodynamics

Abstract

Currently, research on the hydrodynamic characteristics of artificial reef deployment still faces challenges such as insufficient environmental coupling, but accurate simulation of the deployment process holds significant engineering importance for optimizing deployment efficiency and ensuring reef stability. This study employs the Smoothed Particle Hydrodynamics (SPH) method to establish a 3D numerical model, focusing on the influence of key parameters—inflow velocity and water entry angle—on the hydrodynamic characteristics of cubic artificial reef deployment. The results indicate that under flow velocities of 0.4–0.5 m/s, pressure fluctuations are relatively minor, with peak pressure gradients below 15 kPa/m, exhibiting a gradual trend, while particle concentration remains high, and drag gradually increases. At flow velocities of 0.6–0.8 m/s, the maximum pressure at the bottom reaches up to 35 kPa, with low-pressure areas at the tail dropping to −10 kPa; particle concentration decreases compared to conditions at 0.4–0.5 m/s; settling time extends from 8.4 s to 12 s, representing a 42% increase. Under different water entry angles, drag varies nonlinearly with the angle, reaching its maximum at 20° and its minimum at 25°, with a reduction of approximately 47% compared to the maximum. The anti-sliding safety factor and anti-overturning safety factor are used to assess the stability of the cubic reef placed on the seabed. Across different inflow velocities, the anti-sliding safety factor of the cubic artificial reef significantly exceeds 1.2, whereas the anti-overturning safety factor is below 1.2 at 0.4 m/s but exceeds 1.2 at velocities of 0.5 m/s and above, indicating that the reef maintains stability under the majority of these flow conditions. Our findings provide a scientific basis for the deployment process, site selection, and geometric design of cubic artificial reefs, offering valuable insights for the precise deployment and structural optimization of artificial reefs in marine ranching construction.

1. Introduction

Artificial reefs (ARs) are marine structures deliberately deployed to restore marine ecosystems, enhance fishery resources, optimize marine ecological functions, or mitigate coastal erosion. By modifying local flow field structures, ARs generate upwelling currents, vortices, and low-velocity zones, thereby promoting plankton aggregation, improving benthic habitats, and providing shelter for fish populations [1,2,3]. However, the ecological effectiveness of ARs is intrinsically linked to their hydrodynamic characteristics, which directly determine reef stability, flow field effects, and ecological performance post-deployment. Improper deployment methods may induce flow disturbances, sediment accumulation, or even structural failure. After the failure of fish reefs, the original shelter for fish to avoid predators no longer exists, which may lead to an increase in predation risk. Fish lose their habitat, especially for benthic fish and small fish, which may result in an increase in mortality in open waters lacking shelter [4]. Consequently, investigating the hydrodynamic behavior during AR deployment and optimizing deployment strategies carry significant scientific and engineering implications.

At present, numerical simulation studies on the deployment process of artificial reefs are relatively limited, but this process shares many similarities with the phenomenon of structural water entry. Concurrently, the 2-D boundary element method has been employed to study the water entry of horizontal cylinders [5]. Numerical simulations of the vertical water entry process of horizontal cylinders have also been conducted using the CIP (Constrained Interpolation Profile) method [6]. Furthermore, studies have utilized the VOF (Volume of Fluid) multiphase flow model to analyze the hydrodynamic characteristics and supercavitation evolution of revolving bodies under different water entry velocities [7].

Regarding the study of hydrodynamic performance of artificial reefs, traditional approaches primarily include theoretical analysis, physical model experiments, and numerical simulation experiments, mostly based on Computational Fluid Dynamics (CFD) methods. Compared to other research methods, numerical simulation applies fundamental principles of fluid dynamics combined with computer simulation technology, setting boundary conditions, meshing, and controlling function parameters within the computational domain to analyze in detail the variations in physical properties such as flow velocity, pressure, and temperature in the simulated flow field. It offers advantages like low computational cost and operational convenience, enabling the simulation of more complex and detailed processes. For instance, existing studies have constructed a TLP-type modular floating structural system to simulate hydrodynamic interactions and mechanical coupling effects between structures [8]; applied numerical simulation methods to analyze the hydrodynamic morphological evolution processes in artificial reef areas [9]; conducted numerical simulations on the free-fall process of torpedo anchors in water [10]; or employed full-process simulations to analyze artificial reef deployment, revealing the mechanical response patterns of the reef at different stages [11]. Furthermore, numerical simulations have been utilized to investigate flow field characteristics near artificial reefs under wave action [12], as well as to simulate the dynamic process of free-falling gravity-installed anchors in water [13]. These studies effectively demonstrate the advantages of numerical simulation in terms of low cost and detailed process simulation. However, the quality of the mesh to some extent affects the accuracy of numerical simulation results.

A comparative analysis reveals that the Smoothed Particle Hydrodynamics (SPH) method not only eliminates the need for mesh generation when solving problems but also offers advantages in handling issues such as free-surface deformation. As a Lagrangian meshless particle method [14,15,16], SPH combines the strengths of Lagrangian methods in describing material interfaces while avoiding the distortion problems associated with mesh deformation in grid-based methods. SPH has also demonstrated unique advantages in simulating structural water entry problems [17,18,19]. For example, existing studies have utilized the SPH method to simulate water entry processes under different flow velocities, analyzing the evolution of the free surface, velocity and pressure distributions, and the forces and motion responses of the object [20]. Additionally, a simplified water exit model has been proposed and validated, demonstrating that a linearized model incorporating nonlinear correction terms can effectively predict hydrodynamic loads [21]. Regarding wedge water entry, multiple typical test cases have been established to compare pressure predictions with theoretical analysis and experimental data for validation [22]. Concurrently, a multiphase SPH model has been employed to simulate cavity evolution during wedge water entry [23]. Other studies have simulated the water entry process and characteristics of capsule structures, investigating the influence of vertical velocity, mass, and pitch angle on peak impact loads [24]. Algorithm accuracy has been validated through buoyant cylinder water entry cases, further examining the effects of different velocities and directions [25]. Furthermore, 2D and 3D numerical simulations of bow-flare section water entry have been conducted to validate the model, while systematically analyzing the influence of roll angle on such water entry processes [26].

In this study, the SPH method is applied to investigate the hydrodynamic characteristics of cubic artificial reef deployment, including pressure distribution, vortex structures, drag variation, and stability indices, thereby overcoming the limitations of conventional grid-based methods in handling large free-surface deformations. The research systematically examines the effects of inflow velocity and entry angle on the hydrodynamic performance of cubic reefs, elucidating the complex mechanisms governing drag forces, stability, and flow field interactions. Through multiple numerical simulation cases, optimization strategies for reef deployment and operation are proposed, providing theoretical foundations and technical guidance for precise deployment parameter selection, reef structural optimization, and marine ranch planning.

2. Numerical Methods

2.1. Fluid Governing Equations in SPH Formulation

The SPH method employs particle distributions to represent the computational domain. Under the isothermal conditions adopted in this study (with the energy conservation law excluded), the motion of both fluid and solid phases under gravity can be governed by the mass conservation [15] and momentum conservation equations [27]. The partial differential equations are first converted into integral forms through kernel approximation, then discretized via particle approximation of the kernel functions. The resulting discrete equations are solved to obtain field variables at particle locations. The discretized mass conservation equation is expressed as:

$${\displaystyle \frac{\mathrm{d}{\mathsf{\rho }}_{\mathrm{i}}}{\mathrm{d}\mathrm{t}}}=\sum _{\mathrm{j}=1}^{\mathrm{N}}{\mathrm{m}}_{\mathrm{j}}\overrightarrow{{\mathsf{\nu }}_{\mathrm{i}\mathrm{j}}}\cdot {\displaystyle \frac{\partial {\mathrm{W}}_{\mathrm{i}\mathrm{j}}}{\partial \overrightarrow{{\mathrm{x}}_{\mathrm{i}\mathrm{j}}}}}$$

(1)

In the formula, $\mathsf{\rho }$ is the fluid density (kg/m³), $\mathrm{t}$ is the time (s), ${\mathrm{m}}_{\mathrm{j}}$ is the mass of the particle, $\mathrm{N}$ is the total number of particles $\mathrm{j}$ within the support domain of the particle, ${\mathrm{W}}_{\mathrm{i}\mathrm{j}}$ and is the smooth function of the influence of the particle $\mathrm{j}$ on the particle $\mathrm{i}$.

The expression of the momentum equation is:

$${\displaystyle \frac{d\nu }{dt}}=-{\displaystyle \frac{1}{\rho }}\nabla p+{\displaystyle \frac{\eta }{\rho }}{\nabla }^2\nu +g$$

(2)

In the formula, $\eta$ is the kinematic viscosity coefficient; $p$ is pressure; $\nu$ is the fluid velocity (m/s); and $g$ is gravitational acceleration.

Monaghan [16] proposed an artificial viscosity calculation method applicable to fluid viscosity, discretizing the momentum equation into the SPH particle form as:

$${\displaystyle \frac{d\overrightarrow{{\nu }_i}}{dt}}=-\sum _j^N{m}_j\left({\displaystyle \frac{p_j}{{{\rho }_j}^2}}+{\displaystyle \frac{p_i}{{{\rho }_i}^2}}+{\Pi }_{ij}\right){\overrightarrow{\nabla }}_i{W}_{ij}+\overrightarrow{g}$$

(3)

In the formula, ${\Pi }_{ij}$ is the viscosity term.

The specific form of the viscosity term ${\Pi }_{ij}$ is as follows:

$${\Pi }_{ij}=\left\{\begin{array}{l}{\displaystyle \frac{-\alpha \overline{c_{ij}}{\mu }_{ij}}{{\rho }_{ij}}},\overrightarrow{{\nu }_{ij}}\cdot \overrightarrow{r_{ij}}<0\\ 0,\overrightarrow{{\nu }_{ij}}\cdot \overrightarrow{r_{ij}}>0\end{array}\right.$$

(4)

In the formula, ${\overrightarrow{r}}_{ij}={\overrightarrow{r}}_i-{\overrightarrow{r}}_j,\overrightarrow{{\nu }_{ij}}=\overrightarrow{{\nu }_i}-\overrightarrow{{\nu }_j}$, $\alpha$ is the viscosity coefficient, with a value of 0.01 adopted in this study.

$${\mu }_{ij}={\displaystyle \frac{h\overrightarrow{{\nu }_{ij}}\cdot \overrightarrow{r_{ij}}}{{\overrightarrow{r_{ij}}}^2+{\eta }^2}}$$

(5)

$$\overline{c_{ij}}={\displaystyle \frac{c_i+c_j}{2}}$$

(6)

In the formula, $\overline{c_{ij}}$ represents the average speed of sound, ${\eta }^2=0.01{\mathrm{h}}^2$.

2.2. Boundary Conditions

When employing the SPH numerical method for simulations, boundary conditions must be precisely handled to capture the interactions between the reef structure and the fluid. Accurate boundary treatment enables the simulation of realistic flow conditions on the reef surface and in the surrounding fluid, including critical parameters such as flow velocity, direction, and vortex structures, ensuring that the system can respond rapidly and accurately to interactions between fluid particles and boundary particles.

In the boundary configuration, the flow inlet is set as a uniform incoming flow along the positive X-axis with a specified velocity of U = 0.6 m/s. To achieve this condition, four layers of inlet ghost particles are pre-defined at the upstream end of the flow domain. At each time step, these ghost particles are “injected” into the computational domain at the fixed inlet velocity U, becoming new fluid particles. Simultaneously, a corresponding number of particles are removed from the downstream region of the computational domain to maintain the conservation of the total particle number in the system. This method physically simulates a steady inflow process of mass and momentum. Similarly, the outlet is configured with four particle layers as a fully developed free outflow boundary to minimize flow reflection and overcome constraints imposed by the system’s physical scale. The bottom and both side walls are set as no-slip boundaries, which are implemented by arranging multiple layers of stationary ghost particles at these walls. When fluid particles approach the walls, they interact with these stationary ghost particles. Through the solutions of the continuity and momentum equations, the wall ghost particles exert a repulsive force and a viscous dissipative force on the fluid particles, thereby enforcing the no-slip condition that “the fluid velocity is zero at the wall.” This configuration accurately simulates the adhesion effect of real fluids on solid walls, which is crucial for modeling boundary layer development and flow structures near the walls. The top boundary is designated as a free surface to simulate the realistic free liquid surface in marine environments.

2.3. Sliding Resistance Safety Factor and Overturning Resistance Safety Factor

To evaluate the stability of cubic artificial reefs when deployed on seabeds with varying flow velocities, the hydrodynamic forces acting on the reef can be analyzed to calculate both the sliding resistance safety factor ${\mathrm{S}}_1$ and overturning resistance safety factor ${\mathrm{S}}_2$ for stability assessment. The formulations for equations are expressed as follows:

$${\mathrm{S}}_1={\displaystyle \frac{\mathrm{W}\mu \left(1-\mathsf{\rho }/\mathsf{\sigma }\right)}{{\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$$

(7)

$${\mathrm{S}}_2={\displaystyle \frac{\mathrm{W}\left(1-\mathsf{\rho }/\mathsf{\sigma }\right){\mathrm{l}}_{\mathrm{W}}}{{\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathrm{h}}_0}}$$

(8)

In the formula, ρ is the density of the fluid (kg/m³); $\mathrm{W}$ is the weight of the reef. The static friction coefficient $\mu$ between the reef and the seabed contact surface is taken as 0.6 in this paper. ${\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum fluid force (N); $\mathsf{\sigma }$ is the unit density of the reef material (kg/m³); ${\mathrm{l}}_{\mathrm{W}}$ is the horizontal distance from the center of rotation of the flip to the center of gravity (m); ${\mathrm{h}}_0$ is the height of the point of action of the fluid resultant force acting on the reef (m).

3. Establishment of 3D Numerical Model for Cubic Artificial Reef Deployment

This study employed the 3D Computer-Aided Design (CAD) software SOLIDWORKS (2019) to complete the geometric modeling of the cubic artificial reef, providing an accurate geometric model and structural foundation for subsequent SPH-based computational analysis. The numerical model of the reef has a side length of 2.0 m and a panel thickness of 0.15 m. A flow-guiding plate is positioned at the center of the model, with a thickness of 0.11 m and a central opening side length of 0.50 m (Figure 1). Upon completion of the model construction, it was exported in STL format [28]. This format discretizes the object surface through a series of irregular triangular facets, ensuring geometric accuracy of the physical model and providing the necessary geometric input for particle-boundary interaction calculations. The model was then imported into DualSPHysics, an open-source CFD solver developed based on the SPH method. The code, written in C++ and CUDA, enables efficient large-scale particle simulations through GPU parallel computing, facilitating the subsequent numerical simulations.

The computational domain is configured with dimensions of length A = 12.00 m, width B = 10.00 m, and height C = 14.00 m (Figure 1). The cubic artificial reef is positioned at the exact center of the top boundary of the computational domain, with distances of 5.00 m to both front and rear boundaries, and 6.00 m to both left and right boundaries. This configuration ensures the reef is centrally located within the flow field while providing sufficient surrounding space to accurately simulate flow field effects during and after reef deployment.

4. Model Validation

This study assumes a deployment method where the artificial reef is released with an initial velocity of zero, positioned close to the sea surface, and allowed to descend freely under its own weight. After release, the vertical loading on the reef is analyzed. During its free fall from the sea surface, the reef is subjected to gravitational force (W), buoyancy (F_b), and hydrodynamic drag (F_d). As the reef descends over a certain distance, the influence of gravity causes the hydrodynamic drag to increase correspondingly until a state of equilibrium is reached—where the gravitational force equals the sum of buoyancy and drag. At this point, the reef attains a constant velocity, referred to in this study as the terminal velocity [29].

Based on previous research [29], the terminal velocity of an artificial reef upon reaching the seabed can be calculated using the following formula:

$${\mathrm{u}}_{\mathrm{c}}=\sqrt{{\displaystyle \frac{2\mathrm{g}\mathsf{\nu }}{{\mathrm{C}}_{\mathrm{d}}\mathrm{A}}}\left({\displaystyle \frac{\mathsf{\sigma }}{\mathsf{\rho }}}-1\right)}$$

(9)

$$C_D={\displaystyle \frac{2F_D}{\rho U^{2}A}}$$

(10)

In the formula: $\mathrm{g}$ is the gravitational acceleration, $\mathsf{\nu }$ is the volume of the artificial reef (m³), $\mathrm{A}$ is the projected area of the reef obstructing the water flow (m²), $\mathsf{\sigma }$ is the density of the artificial reef, $\mathsf{\rho }$ is the density of seawater, ${\mathrm{C}}_{\mathrm{d}}$ is the drag coefficient of the reef, $F_D$ is the total drag force acting on the reef (N), and $U$ is the inflow velocity (m/s).

Based on previous research, the relevant parameters calculated by the reef theory are shown in

Table 1. Parameters for theoretical calculation of reef structure.

Parameter Nomenclature	Value
Cubic artificial reef length ($l$)	2 m
Cubic artificial reef volume ($v$)	1.05 m3
Cubic artificial reef frontal area ($A$)	4 m2
Cubic artificial reef drag coefficient ($C_d$)	2.2
Cubic artificial reef density ($\sigma$)	2295 kg/m3
Seawater density ($\rho$)	1030 kg/m3

.

Based on the established model for the deployment process of the cubic artificial reef, Figure 2 illustrates the variation of velocity over time during the settling process. As shown after water entry, the vertical settling velocity of the reef increases rapidly and gradually approaches a constant terminal velocity after approximately t = 7 s. The establishment of this terminal velocity indicates that the gravitational force, buoyancy, and fluid drag acting on the reef have reached a dynamic equilibrium. This steady low-speed motion state significantly reduces the impact force of the reef on the seabed while simultaneously providing surrounding fish with sustained and predictable flow field signals, thereby increasing the time and likelihood for effective evasion.

As shown in

Table 2. Comparison between numerical simulation results and theoretical formula calculations.

Parameter	Value	Absolute Error	Error Rate
Theoretical terminal velocity	1.69 m/s	0.21	12.4%
Simulated terminal velocity	1.48 m/s

, the variation curve of velocity over time during the reef settlement process is monitored (Figure 2). The time-averaged value after reaching a stable fluctuating state is taken as the terminal velocity obtained from numerical simulation, which is 1.48 m/s. Using Equation (9), the theoretical terminal velocity for the cubic artificial reef studied in this paper to reach the seabed is calculated as 1.69 m/s. The difference between the two values is 0.21, with an error rate (error value/theoretical value) of 12.4%, which falls within an acceptable range. This comparative result indicates that the current SPH model can reasonably predict the terminal state of reef settlement, demonstrating the validity of the numerical model for the cubic artificial reef deployment process established in this study.

5. Research Results

5.1. Hydrodynamic Effects During Cubic Artificial Reef Deployment

Building upon the validated numerical model, a full-scale artificial reef model was established to simulate the 3D deployment process of cubic reefs. With the inflow velocity set to 0 m/s, the numerical simulations investigated the impact of cubic reef deployment on marine environments.

Figure 3 illustrates the dynamic evolution of particle distribution in the surrounding flow field at different moments during the deployment of the cubic artificial reef. As clearly observed in the figure, the reef generates a disturbance effect on the sea surface during the initial water-entry phase: at 1 s, slight particle disturbances begin to appear around the reef. By 4 s, the particle distribution around the reef has undergone significant changes, forming more complex vortex structures, which indicate strong disturbance to the surrounding environment. At 10 s, the changes in particle distribution reach their peak. At this moment, the vortex structures around the reef become even more intricate, and the motion trajectories of particles exhibit greater variability. As the reef continues to sink, distinct stratification emerges in the surrounding flow field: particles in the upper water layer gradually disperse outward due to the reef’s descent, leading to a decrease in particle density in the surrounding flow field; in the middle water layer, a pronounced vortex structure forms behind the reef, resulting from the wake effect generated during sinking, with particles in the vortex region showing a spiral distribution and relatively lower density; in the lower water layer, particle motion is primarily influenced by pressure changes induced by the reef’s descent, resulting in a more uniform particle distribution. From an ecological perspective, the vortex structures and complex particle motion generated during the initial water entry of the artificial reef can induce intense local water vibrations. This transient stimulus is likely to startle nearby fish, leading to short-term avoidance behavior. However, such disturbances are notably transient and spatially confined. As the reef approaches the final stage of its descent, the flow field structure gradually transitions toward a “steady state”. The relatively uniform flow field in the lower layers facilitates sediment settlement. These stable flow field structures constitute key physical habitat features that fish will rely on for resting, foraging, or evading predators in the future [4].

As observed in Figure 4, the velocity variations in the flow field surrounding the cubic artificial reef during deployment exhibit distinct dynamic characteristics. At 1 s, the flow velocity around the reef gradually decreases, indicating that kinetic energy begins to dissipate during sinking, and the disturbance effect on the surrounding flow field weakens. During this stage, vortex structures gradually form behind the reef, leading to noticeable gradient changes in velocity distribution. By 4 s, the velocity further decreases to approximately 0.2 m/s, signifying a significant reduction in the kinetic energy of the sinking reef and a gradual stabilization of the flow field. At this point, the reef’s influence range on the surrounding water narrows, velocity distribution becomes more uniform, and vortex structures stabilize. It is noteworthy that during the early deployment phase (t = 1 s to 4 s), high velocity values are observed in the flow field near the inlet and outlet regions. This is primarily due to the transient adjustment effect resulting from the model’s initiation from a static initial state, combined with the global flow response induced by the reef’s water-entry impact within the finite computational domain. This phenomenon is characteristic of the numerical simulation capturing the initial high-disturbance phase. At 10 s, the flow velocity around the reef approaches 0 m/s, indicating that the sinking process has essentially concluded and the flow field has reached a steady state. At this stage, fluid motion around the reef is predominantly governed by the equilibrium between gravity and buoyancy, with velocity distribution stabilizing and flow field disturbances nearly diminishing.

5.2. Influence of Flow Velocity on the Deployment Process of Cubic Artificial Reefs

Previous studies indicate that the flow velocity in deployment areas of cubic artificial reefs typically ranges from 0.2 to 0.85 m/s, with velocities between 0.4 and 0.8 m/s being the most prevalent. To investigate the effect of inflow velocity on the deployment performance of cubic artificial reefs, this section examines five flow velocities: 0.4 m/s, 0.5 m/s, 0.6 m/s, 0.7 m/s, and 0.8 m/s. Through numerical simulations of the reef deployment process under these varying flow conditions, we analyze the impacts of flow velocity on reef stability, flow field distribution, and pressure variations.

Figure 5 illustrates the velocity contours and locally magnified particle distribution diagrams of the surrounding flow field at different time points (0.5 s, 1 s, 2 s, and 10 s) during the artificial reef deployment process under an inflow velocity of 0.6 m/s. According to the particle distribution contours, as the deployment time progresses, the particle distribution gradually transitions from dense to sparse. During the initial deployment phase (0.5 s and 1 s), the impact force generated by the reef’s water entry causes significant fluid disturbance, resulting in densely concentrated particles, particularly in the immediate vicinity and lower region of the reef. As time elapses (2 s and 10 s), the reef stabilizes progressively, fluid disturbances diminish, and the particle distribution becomes more uniform with expanding sparse regions. This observation demonstrates that the reef deployment induces substantial flow field disturbances initially, but the flow field gradually regains stability as the reef stabilizes.

In the flow field velocity contours around the reef structure, during the initial deployment stage (0.5 s and 1 s) when the artificial reef enters the water, the velocity distribution in the surrounding water exhibits significant heterogeneity. Particularly in the area beneath and behind the reef, the velocity gradient is pronounced, forming distinct vortex and recirculation zones. As time progresses (2 s and 10 s), the velocity distribution gradually becomes more uniform, with reduced spatial extents of vortex and backflow regions and progressively diminishing velocity gradients. This demonstrates that the reef deployment initially exerts considerable influence on the velocity distribution of the surrounding flow field, but as the reef stabilizes, the flow field velocity gradually recovers to a more uniform state.

Figure 6 presents the pressure contour plots at different time instants (0.5 s, 1 s, 1.5 s, 2 s, and 2.5 s) during the initial deployment stage of the artificial reef under varying inflow velocities of 0.4 m/s, 0.5 m/s, 0.6 m/s, 0.7 m/s, and 0.8 m/s. The pressure distributions exhibit significant variations with increasing inflow velocity. At lower velocities (0.4 m/s and 0.5 m/s), relatively uniform pressure distributions are observed with minor pressure fluctuations and gradual pressure gradients during reef submersion. As the inflow velocity increases to 0.6 m/s, 0.7 m/s, and 0.8 m/s, pronounced pressure fluctuations emerge, particularly beneath and behind the reef, where steeper pressure gradients form distinct high- vs. low-pressure zones. This demonstrates that higher inflow velocities intensify pressure disturbances in the surrounding water during deployment. Temporally, the initial deployment phase (0.5 s and 1 s) shows substantial pressure fluctuations, with rapid pressure elevation forming conspicuous high-pressure zones upon water entry. The presence of this high-pressure zone serves as a critical indicator for evaluating the structure’s transient impact load and potential risk of local cavitation. The occurrence of such cavitation is a highly unsteady process, leading to intense fluctuations in lift, drag, and moments acting on the reef. These irregular impact loads may disrupt the attitude stability of the reef during descent, alter the flow field morphology and pressure distribution around the reef, potentially exacerbating energy dissipation. The modified flow field due to cavitation may also compromise the ability of the reef to form anticipated ecologically beneficial flow structures—such as upwelling and lee vortex zones—once it stabilizes. Concurrently, the low-pressure zone formed behind the reef signifies the instantaneous generation of flow separation and initial vortex structures. This visually reflects the rapid conversion of water-entry impact kinetic energy into fluid vortex energy (i.e., flow structures), representing a core phase of energy dissipation and flow field reconstruction during the deployment process.

Over time (1.5 s, 2 s, and 2.5 s), the pressure distribution progressively stabilizes, providing a quantitative reference for determining the end of the primary dynamic loads on the hoisting system and assessing whether subsequent operations—such as fine-tuning the attitude or releasing the reef—can proceed. The extent of both the high- and low-pressure zones gradually diminishes, and the pressure gradient weakens progressively. This indicates that the pressure disturbance exerted on the surrounding water by the reef is most pronounced during the initial deployment phase, but as the reef stabilizes, the pressure distribution gradually returns to equilibrium. This trend toward stabilization reflects the sustained hydrodynamic forces (drag and lift) acting on the reef during the later stages of its descent, influencing its settling trajectory and final seating attitude, and thus serves as a key reference link for predicting the deployment endpoint position.

Figure 7 illustrates the particle distribution in the surrounding flow field at the final moment of the cubic artificial reef deployment under different inflow velocities (0.4, 0.6, and 0.8 m/s). By comparing particle distributions across varying flow velocities, significant effects of velocity on particle diffusion behavior can be observed. Under lower flow velocity conditions (e.g., 0.4 m/s), particles tend to accumulate more readily around the reef, forming localized regions of higher concentration. This phenomenon may be attributed to reduced flow disturbance at lower velocities, allowing particles to deposit more stably near the reef. However, as the inflow velocity increases (e.g., 0.6 m/s and 0.8 m/s), the distribution range of particles expands significantly. Higher flow velocities enhance the kinetic energy of the water, causing particles to be dispersed more rapidly and distributed over a wider area. Under lower flow velocities, a relatively stable flow field helps minimize disturbances to the settlement of sessile organism larvae and may create stable low-pressure zones on the leeward side of the reef, providing a food source for benthic organisms. Under higher flow velocities, more developed vortex and wake structures, while potentially increasing local disturbances, can significantly enhance water mixing and material transport. This not only supplies filter-feeding organisms with more abundant food and oxygen but also attracts, fish aggregation through the formation of complex flow fields [1,2,3,4].

Table 3. The time required for the deployment of square artificial reefs to the seabed at different inflow velocities.

	Inflow Velocity/m·s−1
	0.4	0.5	0.6	0.7	0.8
Time/s	8.4	9.2	10.8	11.6	12.0

documents the temporal evolution of reef settlement, demonstrating progressive time elongation with increasing velocity. At 0.4 m/s and 0.5 m/s, complete seafloor contact occurs at 8.4 s vs. 9.2 s, respectively, whereas higher velocities (0.6–0.8 m/s) require extended durations (10.8 s, 11.6 s, vs. 12.0 s), representing a 42% increase. Notably, interim measurements at 10 s reveal remaining distances of 0.958 m, 1.246 m, vs. 1.825 m respectively, quantitatively substantiating the retarding effect of flow velocity on settlement dynamics. These findings systematically demonstrate dual velocity-dependent mechanisms: delayed settling chronology and potential incomplete seafloor attainment under high-flow conditions. The intense impact under high flow velocities significantly amplifies disturbances in the flow field around the artificial reef, adversely affecting its long-term durability. Furthermore, the substantial extension of settling time implies that in stronger currents, the horizontal drift distance of the reef from water entry to stable seabed settlement increases considerably. This corroborates the practice in actual reef deployment operations of prioritizing sea areas with lower flow velocities to mitigate environmental disturbances and avoid the adverse effects of higher flow velocities on reef settlement. From an engineering perspective focused on ensuring deployment accuracy, this validates the practice of prioritizing sea areas with low velocities in actual artificial reef deployment operations, while avoiding regions with faster velocities to minimize the impact of current on reef settlement. However, from the standpoint of the reef’s long-term ecological functionality, moderate ambient flow velocities are crucial for maintaining effective water exchange and forming complex flow field structures that attract fish. Therefore, during site selection and planning, it is advisable to choose locations that can provide suitable long-term flow conditions while meeting deployment requirements.

Table 4. The anti-slip safety coefficient and anti-overturning safety coefficient at the final moment of deployment of square artificial reefs under different incoming flow velocities.

Flow Velocity (m/s)	0.4	0.5	0.6	0.7	0.8
Drag (N)	675	879	953	1060	1256
Anti-slip safety coefficient S1	1.95	1.50	1.38	1.24	1.05
Anti-overturning safety S2	1.13	1.47	1.59	1.77	2.09

presents the hydrodynamic drag forces acting on the cubic artificial reef at the final deployment stage under different inflow velocities (0.4 m/s, 0.5 m/s, 0.6 m/s, 0.7 m/s, vs. 0.8 m/s). The results demonstrate a pronounced increasing trend in drag force with progressively higher inflow velocities, indicating a significant positive correlation between the drag force and inflow velocity. This observed trend primarily stems from enhanced impact forces and frictional effects on the reef surface caused by greater flow velocities. According to fundamental fluid dynamics principles, increased flow velocity substantially elevates the kinetic energy of the water flow, thereby generating larger pressure differentials and shear stresses on the reef surface, which ultimately manifest as markedly higher drag forces.

The results indicate that under different inflow velocities, the anti-sliding safety factor S₁ of the cubic artificial reef is greater than 1.2. However, under the high-flow velocity condition of 0.8 m/s, the value falls below 1.2, indicating that the stability of the reef is compromised under high flow velocities. The anti-overturning safety factor is below 1.2 at a velocity of 0.4 m/s, but exceeds 1.2 at velocities of 0.5 m/s and higher. This demonstrates that the reef maintains a stable state under the majority of the aforementioned flow velocity conditions.

5.3. Effect of Entry Angle on Cubic Artificial Reef Deployment

The reef entry angle refers to the inclination angle between the artificial reef and the sea surface during deployment (as illustrated in Figure 8). To investigate the influence of entry angle on the deployment process, this section examines seven entry angles (0°, 5°, 10°, 15°, 20°, 25°, and 30°) under a constant inflow velocity of 0.6 m/s through numerical simulations. By varying the entry angle, the study analyzes the pressure distribution, velocity variations, and motion trajectories of the reef during water entry under different inclination conditions.

Figure 9 illustrates the pressure variations in the surrounding flow field at different initial moments (0.5 s, 1 s, 1.5 s, 2 s, and 2.5 s) during the deployment of the cubic artificial reef at various water entry angles. As shown in the figure, the pressure distribution of the cubic artificial reef exhibits significant variation patterns during the initial deployment phase across different water entry angles. The results demonstrate distinct pressure distribution patterns during the initial deployment phase across different entry angles. At 0.5 s, all configurations exhibit relatively high pressure values, particularly in the water-entry contact regions where pressure concentrations and non-uniform distributions are observed, indicating significant impact forces and consequent localized pressure spikes during the initial water entry. As time progresses to 1 s and 1.5 s, the pressure magnitudes decrease while their spatial distribution expands, reflecting the gradual attenuation of impact effects and pressure diffusion into the surrounding water. Comparative analysis reveals notable differences among various entry angles—smaller entry angles (e.g., 5°and 10°) maintain higher pressure concentrations at the reef’s leading edge, whereas larger entry angles (e.g., 25° and 30°) demonstrate more uniform pressure distributions. By 2 s and 2.5 s, further pressure reduction and homogenization occur, suggesting the dissipation of impact effects and flow field stabilization. While pressure distribution differences between angles diminish at this stage, smaller entry angles still exhibit localized pressure concentrations, contrasting with the smoother pressure transitions observed for larger entry angles.

Figure 10 presents the velocity distributions in the flow field surrounding the cubic artificial reef at the final moment of deployment with varying entry angles (5°, 10°, 15°, 20°, 25°, and 30°). The results clearly demonstrate a nonlinear trend in velocity variations around the reef structure with increasing entry angles, characterized by an initial velocity increase followed by a decrease after reaching a peak value, and subsequently another rise. This pattern likely stems from the complex interplay between hydrodynamic forces acting on the reef during water entry and its geometric configuration.

Of particular significance is the observed increase in flow velocity above the reef with larger entry angles, which becomes particularly pronounced at higher angles (e.g., 30°) This phenomenon may be attributed to enhanced flow disturbances caused by the reef’s more aggressive water entry at steeper angles, resulting in stronger velocity gradients in the upper water column. These findings provide critical scientific insights for optimizing reef deployment angles to enhance ecological effectiveness, while establishing a fundamental basis for future investigations into flow field characteristics under different entry conditions and their environmental impacts.

The analysis of drag forces acting on the artificial reef reveals a trend that initially increases and subsequently decreases with increasing entry angle. Specifically, the drag force reaches its peak value of 4120 N at a 20°entry angle, indicating the most significant hydrodynamic interaction and strongest fluid structure effects at this configuration. When the entry angle increases to 25°, the drag force decreases to approximately 2180 N, representing a 47% reduction from the maximum value. This reduction likely results from altered flow-reef interaction patterns at higher entry angles, leading to more favorable hydrodynamic conditions. Specific angles may alter the location of flow separation points, vortex shedding patterns, and the effective flow-facing area, thereby significantly influencing pressure distribution and the composition of frictional drag. This non-monotonic variation in drag reveals that the angle between the reef and the flow is not simply “the larger the better” or “the smaller the better.” Instead, there exists a “critical angle,” which corresponds to a complex equilibrium relationship among flow separation, pressure distribution, and the drag experienced by the reef. This provides new insights for research aimed at optimizing reef attitude control and reducing environmental disturbances during the deployment process.

All cubic reefs successfully reached and stabilized on the seabed by the final deployment stage. Stability assessment was conducted using the previously defined evaluation metrics—anti-sliding safety factor and anti-overturning safety factor—with quantitative results presented in

Table 5. The anti-slip safety coefficient and anti-overturning safety coefficient at the final moment of deployment of square artificial reefs with different angle of entry.

Angle of Entry (°)	5	10	15	20	25	30
Drag (N)	3410	3740	3930	4120	2180	3240
Anti-slip safety coefficient S1	3.86	3.52	3.35	3.20	6.04	4.06
Anti-overturning safety S2	6.44	5.87	5.58	5.33	10.07	6.77

. The data demonstrate that both safety factors exceed 1.2 across all tested entry angles, confirming the reef’s capability to maintain stable positioning and effectively withstand seabed current-induced sliding forces and overturning moments throughout the investigated angular range.

6. Discussion

This study employs the SPH method to conduct high-fidelity simulations of the hydrodynamic effects and flow field characteristics during the deployment process of cubic artificial reefs, aiming to optimize their deployment efficiency. The results indicate that incoming flow velocity and water entry angle are two key parameters influencing the hydrodynamic response of the reef during deployment. Under flow velocities of 0.4–0.5 m/s, pressure fluctuations are relatively small, with peak pressure gradients below 15 kPa/m, and drag shows a steadily increasing trend. When the flow velocity increases to 0.6–0.8 m/s, the maximum pressure at the bottom of the reef can reach 35 kPa, a significant low-pressure zone appears behind it, drag increases notably, and the settling time extends by approximately 42%. When adjusting the water entry angle, the drag exhibits a nonlinear variation, peaking at 20° and reaching its minimum at 25°, representing a reduction of about 47% compared to the peak value. Under different inflow velocities, the anti-sliding safety factor of the cubic artificial reef is significantly greater than 1.2, while the anti-overturning safety factor is below 1.2 at a velocity of 0.4 m/s, but exceeds 1.2 at velocities of 0.5 m/s and above. This indicates that the reef maintains a stable state under the majority of the aforementioned flow velocity conditions. These findings reveal several core challenges in the practical deployment engineering of artificial reefs (AR), providing a basis and new perspectives for optimizing deployment strategies.

Previous research on the hydrodynamic performance of artificial reefs has predominantly utilized mesh-based CFD methods, focusing on steady-state flow field analyses, such as the vortex structures around reefs and the formation of upwelling currents [30]. Numerical simulation, applying fundamental principles of fluid dynamics, offers advantages like low computational cost and operational convenience, enabling the simulation of more complex and detailed processes. Li [5] proposed a TLP-type modular floating structural system, simulating hydrodynamic interactions and mechanical coupling effects between objects. Wang et al. [10] used numerical simulation methods to model hydrodynamic morphological processes in the Yangmeikeng artificial reef area. Cui [12] analyzed the entire deployment process of artificial reefs, obtaining the mechanical response patterns at different deployment stages. These studies effectively demonstrate the advantages of numerical simulation in terms of low cost and detailed process simulation. However, when simulating problems like reef deployment that involve severe free-surface deformation, transient impacts, and multiphase flow, grid-based methods often face challenges like mesh distortion and insufficient computational stability. In contrast, the innovation of this study lies in introducing the meshless SPH method to capture complex fluid structure interaction phenomena under transient and deforming conditions during deployment. It analyzes the reef’s water entry impact, intense pressure fluctuations, and flow field stratification behavior during settling. These dynamic details are often simplified or difficult to accurately describe in traditional steady-state CFD simulations. The SPH method, being mesh-free, has inherent advantages in handling free-surface deformation and moving boundaries, thereby more realistically reflecting the complexity of fluid structure interactions and further expanding the application scope of SPH in the field of ocean engineering.

6.1. Flow Velocity Control: Balancing Environmental Disturbance and Structural Integrity

The results confirm that increased flow velocity significantly enhances pressure fluctuations and flow field disturbances around the reef and delays the time for the reef to settle to the seabed. The high speed and strong pressure fluctuations during the initial water entry phase reflect the transfer of the reef’s kinetic energy to the surrounding fluid, consistent with the fundamental physical mechanism of water entry impact. The flow field stratification phenomenon observed during the settling process stems from the continuous fluid displacement caused by the reef’s descent and the combined action of gravity-buoyancy balance. This finding aligns with the classical fluid dynamics principle that drag is proportional to the square of velocity and underscores the importance of fully considering current conditions in actual deployment operations. During the high-speed water entry or just before touchdown of the artificial reef, cavitation bubbles may form near its edges due to extreme low pressure. The strong impact pressure under high flow velocities approaches or may exceed the local compressive strength limit of the reef material, especially at locations with manufacturing defects or internal pre-stress, increasing the risk of micro-crack initiation before touchdown and affecting its long-term durability. The significant extension of settling time implies that in strong currents, the horizontal drift distance of the reef from water entry to stable seating increases substantially. Excessive horizontal drift may not only cause the final landing position of the reef to deviate from the intended location but also lead to instability upon settling, potentially triggering sliding or overturning of the reef. This not only increases the uncertainty of deployment positioning, potentially causing the reef to deviate from the pre-set ecological restoration site, but also necessitates longer tracking and adjustment times for the operation vessel, thereby raising operational costs and risks.

6.2. Optimization of Water Entry Angle: Active Attitude Control to Reduce Deployment Drag and Environmental Disturbance

On the other hand, the influence of water entry angle on hydrodynamic response exhibits curvilinear characteristics: drag is maximum at 20° and minimum at 25°. Specific angles may alter the flow separation point location, vortex shedding mode, and effective flow-facing area, thereby significantly affecting pressure distribution and the composition of frictional drag. The observed increase in flow velocity above the reef at a 30° water entry angle in Figure 10 indicates that a steeper entry attitude intensifies disturbances and energy transfer in the upper water layer. This non-monotonic variation in drag reveals that the angle between the reef and the flow is not simply “the larger the better” or “the smaller the better.” Instead, there exists a “critical angle,” reflecting a complex balance among flow separation, pressure distribution, and the drag experienced by the reef. This provides new insights for research aimed at optimizing reef attitude control and reducing environmental disturbance during deployment.

Although this study has achieved certain results regarding the deployment process and hydrodynamic performance of cubic artificial reefs, several limitations remain. Future research could be conducted in the following directions: (1) Model Simplification and Parameter Setting: The current study simplifies reef geometry and flow field conditions. Future work could consider more complex reef configurations and multi-factor coupled flow field conditions to enhance model accuracy and applicability. (2) Reef Deployment in Complex Marine Environments: This study primarily focuses on single flow velocities and simple flow field conditions. Subsequent research could further investigate reef deployment processes under complex marine environments involving waves, tides, and storms to comprehensively assess their stability and ecological benefits. (3) Optimization and Expansion of the SPH Method: The SPH method shows significant advantages in simulating large free-surface deformation problems. Future efforts could improve computational efficiency and accuracy through algorithm optimization and apply the method to a broader range of ocean engineering problems, such as collisions of marine structures and wave-structure interactions.

This study successfully extends the application of the SPH method from traditional problems like ship water entry and anchor dropping to the dynamic deployment of ecological engineering structures. It provides a new research framework for understanding transient, large-deformation fluid structure interaction problems, offering certain engineering guidance value. We recommend that in actual reef deployment operations, priority be given to sea areas with flow velocities below 0.5 m/s to reduce pressure fluctuations and environmental disturbances. Future work could further investigate the hydrodynamic characteristics of different reef configurations during deployment to better achieve the synergy between engineering optimization and ecological objectives.

7. Conclusions

Based on the Smoothed Particle Hydrodynamics (SPH) method, this study systematically conducts numerical simulations to investigate the hydrodynamic performance and flow field effects during the deployment process of a cubic artificial reef. By constructing a full-scale 3D numerical model, the flow field variations, pressure and velocity distributions, and drag changes of the reef under different deployment conditions are simulated. The results indicate that the SPH method demonstrates significant advantages in handling large free-surface deformation problems, enabling precise capture of complex flow field variations during reef deployment, particularly the impact effects during the initial water entry phase and the flow field stratification phenomena during the sinking process. The main findings are summarized as follows:

(1)

Flow field variations during artificial reef deployment: The deployment of the cubic artificial reef induces significant disturbance effects on the surrounding flow field. Particularly during the initial deployment stage, the impact force generated as the reef enters the water causes intense water disturbance, leading to the formation of distinct vortex and recirculation zones. Furthermore, during the sinking process, flow field stratification phenomena are observed.

(2)

Influence of inflow velocity on artificial reef deployment performance: At inflow velocities of 0.4 m/s, the pressure distribution is relatively uniform, with minor pressure fluctuations generated during reef water entry and a gradual pressure gradient. As the inflow velocity increases (0.6 m/sand 0.8 m/s), the pressure fluctuations induced during water entry progressively intensify, forming distinct high- and low-pressure zones. Under lower flow velocity conditions (e.g., 0.4 m/s), localized regions of high particle concentration are observed. In contrast, with increasing inflow velocity (e.g., 0.6 m/s and 0.8 m/s), the particle concentration relatively decreases.

(3)

Influence of water entry angle on artificial reef deployment performance: As the water entry angle increases, the drag force acting on the artificial reef exhibits a trend of initial increase followed by a decrease. The drag reaches its maximum at a water entry angle of 20°, while it is minimized at an angle of 25°. Across different water entry angles, both the anti-sliding and anti-overturning safety factors of the reef exceed 1.2, indicating that the reef maintains favorable stability within this range of angles.

This study successfully extends the application of the SPH method from traditional problems like ship water entry and anchor dropping to the dynamic deployment of artificial reefs, offering certain engineering guidance value. It is recommended that in practical artificial reef deployment operations, priority be given to sea areas with low flow velocities to minimize severe environmental disturbances and transient impacts on fish during the deployment process. Concurrently, during site selection, preference should be given to locations that can provide stable, moderate flow velocities over the long term, ensuring the sustained high ecological performance of the artificial reef in the future. Moreover, humped the non-monotonic variation in drag reveals that the angle between the reef and the flow is not simply “the larger the better” or “the smaller the better.” Instead, there exists a “critical angle,” which corresponds to a complex equilibrium relationship among flow separation, pressure distribution, and the drag experienced by the reef. This provides new insights for research aimed at optimizing reef attitude control and reducing environmental disturbances during the deployment process.