Effect of the Pore Distribution of Fishing Tanks on Hydrodynamic Characteristics Under the Wave Action

Abstract

A perforated aquaculture vessel represents an environmentally sustainable approach to fish farming, leveraging seawater circulation to optimize water quality and enhance fish health and growth. The perforations on the side of the fish tank significantly influence its hydrodynamic characteristics. This study investigated the influence of pore parameters on the perforated fishing tank with various pore designs, such as the asymmetric distribution of the opening in depth, windward, and leeward directions. A numerical study was conducted using STAR-CCM+ to analyze the perforated tank under beam wave conditions. This study aimed to analyze the effects of pore location, opening ratio, and asymmetric distribution on the hydrodynamic performance and flow characteristics within aquaculture tanks. The results demonstrated that an asymmetric pore distribution on the windward and leeward sides of the vessel had a notable impact on the roll motion and the flow velocity in the vicinity of the pores. The findings also indicated that the effects of pore distribution were more significant than those of opening ratio, especially regarding asymmetry. The results revealed that higher flow velocities occurred under a smaller opening ratio. Modifying pore structure parameters on the windward and leeward sides can alter the local flow field.

1. Introduction

In recent years, with the increasing scarcity of fishery resources in nearshore waters and the environmental pollution issues faced by human industry activities, marine aquaculture is gradually expanding from coastal areas to the deep sea. Compared with nearshore fish aquaculture, offshore aquaculture has several advantages: (i) better water quality and more favorable natural ocean environmental conditions; (ii) more stable temperature, oxygen, and salinity conditions, increasing fish production; (iii) reduced interference with other human activities in coastal areas [1,2]. Offshore aquaculture is evolving quickly to satisfy the growing demand for high-quality fish protein [3].

Therefore, new technological advancements are needed to address these challenges. Fish farming systems can be classified as open aquaculture systems (such as sea cages), semi-enclosed systems, and closed systems depending on the permeability of the enclosure [4]. Open aquaculture systems are the most widely used and researched [5,6,7,8,9,10,11,12,13].

Mobile aquaculture vessels are uniquely characterized by their high flexibility, environmental friendliness, and outstanding productivity [14]. Compared with a closed aquaculture vessel, a perforated mobile fishing vessel is a type of semi-enclosed system, which is perforated in the vessel side to allow free exchange of water and nutrients. Perforated aquaculture vessels are usually converted from second-hand bulk carriers. This innovative design addresses the growing issue of aging vessels in the maritime industry by repurposing decommissioned ships, thereby reducing costs, enhancing operational efficiency, and minimizing energy consumption and emissions.

Zhang et al. [15] used the boundary element method (BEM) to study the hydrodynamic response under various filling scenarios and based on the Navier–Stokes equation to evaluate the fluid viscosity and nonlinear effect influence the flow inside and outside the compartments. Based on porous theory and potential flow theory, Li et al. [16] developed a BEM model to evaluate an improved fish vessel with perforated side walls. The aim was to study the wave loads, hydrodynamic coefficients, and motion responses of the improved fishing vessel under the wave action. Taking into account variable incident angles and incoming current velocities’ action, Xue et al. [17,18] focused on the flow field characteristic of perforated culture tanks aboard aquaculture vessels. Their research also evaluates the suitability of the flow field for fish welfare. Cui et al. [19,20] used mathematical and statistical methods to analyze the uniformity of velocity distribution and the efficiency of water exchange, and established a method for assessing the fishability of the water environment in the hold of the aquaculture vessel. Their study shows that the roll motion can accelerate the velocity to shorten the water exchange time. Wang et al. [21] investigated the hydrodynamic and nonlinear interactions of the “Deep Blue 1” submerged steel frame offshore fish farm with regular waves. The effects of regular wave parameters, net, and structural variations on the kinematic response and mooring line force of the fish farm system were investigated. All of the aforementioned studies on perforated fishing vessels focus on the hydrodynamic characteristics under the action of currents or waves. However, relatively few studies have analyzed the effect of the pore distribution on aquaculture tanks’ hydrodynamic characteristics and motion responses.

Linear wave theory predicts an exponential decay in the dynamic pressure exerted by water particles with increasing depth below the surface. The flow of water in the culture tank is one of the important factors for fish survival. Therefore, this study focuses on hydrodynamic characteristics and motion responses under various conditions, including different porosities and pore distributions. Particular attention is paid to an asymmetric pore distribution in different locations. The aim is to clarify the influence of the asymmetric pore distribution in depth, as well as windward and leeward sides.

The aim of the present study is to detail the influence of the asymmetric pore distribution, as well as to provide some suggestions for the design of aquaculture tanks.

In order to provide the analysis of the influence of asymmetric pore distribution, the structure of this paper is as follows: Section 2 presents the mathematical model. This section focuses on the mathematical models, including the governing equations, turbulence model, and VOF (volume of fluid) method. Section 3 details the parameter settings of the established numerical model, such as the numerical model and perforated tank setup. Building on this, Section 4 presents the model validation by comparing its results with physical model test data, demonstrating the reliability and accuracy of the developed model. The reliability of the model is also validated in Section 4 through grid convergence and comparative analysis with an experimental model. Section 5 discusses the results of the numerical analysis. Specifically, it presents the numerical results regarding the effects of various opening ratios and pore distributions on motion responses, mooring line forces, and flow field characteristics such as velocity vectors. Section 6 summarizes the key conclusions from the results.

In conclusion, the research in this paper focused on the effects of pore parameters of perforated fishing tanks on the hydrodynamic characteristics under wave action. The innovative aspects of this study are as follows:

(1)

The influence of the opening ratio on the motion response and mooring line forces was analyzed. The opening ratio was defined as the percentage of the pore area divided by the side area. Different perforation areas had distinct effects on the motion response and mooring line forces.

(2)

The effect of the asymmetric pore distribution in different locations was investigated. The findings also indicated that the effects of pore distribution were greater than those of the opening ratio. The results demonstrated that an asymmetric pore distribution in the windward and leeward sides of the vessel had an impact on the roll motion and the flow velocity near the pores. It is beneficial for enhancing the water circulation in the aquaculture tank.

2. The Mathematical Model

2.1. The Definition of the Problem

This study employed computational fluid dynamics (CFD) to investigate wave interactions with a moored, perforated floating fishing tank. CFD is a cost-effective and flexible alternative to physical experiments, providing detailed insights into complex flow fields, which are crucial for modern marine structure design. Specifically, the Star-CCM+ software (version 2020.1.0, provided by Siemens Digital Industries Software, Plano, TX, USA) was employed to conduct the numerical simulations. These simulations were performed on a workstation equipped with an Intel Xeon Gold 6248R CPU (GenuineIntel (Santa Clara, CA, USA) 2.50 GHz, 20 cores), utilizing parallel processing.

Considering the limited computational resources, a floating tank with diverse perforation configurations was employed. The geometric parameters are illustrated in Figure 1. This approach imposes lower demands on memory and computing power, enabling the research to be carried out within the constraints of the existing hardware facilities. The primary objective of this study was to investigate the influence of perforations on hydrodynamic characteristics. The tank structure facilitates a more concentrated and efficient analysis. Therefore, the numerical model of the perforated fishing vessel was simplified into a tank structure, with dimensions of 0.48 m × 0.696 m × 0.30 m, a hull thickness specified as 0.01 m, and a draft of 0.20 m.

2.2. Governing Equations

For incompressible flow in Cartesian coordinates, the mass continuity equation is as follows:

$${\displaystyle \frac{\partial \rho }{\partial \mathrm{t}}}+{\displaystyle \frac{\partial (\rho \overline{u_i})}{\partial x_i}}=0$$

(1)

and the momentum equations are as follows:

$${\displaystyle \frac{\partial (\rho \overline{u_i})}{\partial t}}+{\displaystyle \frac{\partial (\rho \overline{u_i}\overline{u_j})}{\partial x_j}}=-{\displaystyle \frac{\partial \overline{p}}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}[\mu ({\displaystyle \frac{\partial \overline{u_i}}{\partial x_j}}+{\displaystyle \frac{\partial \overline{u_j}}{\partial x_i}})-\rho \overline{u_i^{\prime }{u}_j^{\prime }}]$$

(2)

where $\overline{u_i}$ is the mean fluid velocity vector, $\overline{u_i^{\prime }{u}_j^{\prime }}$ is the turbulent stress tensor, t is the time, ρ indicates the fluid density, $\overline{p}$ is the mean pressure, and μ is the fluid dynamic viscosity.

2.3. Free Surface Modeling

A key challenge of the present study in predicting the hydrodynamic response of moored floating structures under wave action is multiphase flow, where accurate free-surface capturing is fundamentally critical. To effectively track this constantly changing air–water interface, the water–air flows were solved by employing the volume of fluid (VOF) method with the fraction of volume α. When α = 1, the computational cell is completely occupied by the water phase; conversely, when α = 0, the cell is filled with air. In the present study, α = 0.5 was used to track the wave surface.

$$\rho ={\rho }_{\mathrm{w}}\alpha +{\rho }_a(1-\alpha )$$

(3)

$$\mu ={\mu }_{\mathrm{w}}\alpha +{\mu }_a(1-\alpha )$$

(4)

Here, ρ represents the average density of the fluid domain, ρ_a is the density of the air, and ρ_w is the density of the water.

For cells adjacent to the water–air interface, the value of α ranges between 0 and 1. The gradient of α serves as a critical parameter for determining the normal direction of the interface. After obtaining the α values and their corresponding gradients for all computational cells, the approximate position of the free surface within each cell can be determined. This process enables precise surface tracking in multiphase flow simulations, facilitating a detailed analysis of the interface dynamics. Once Equations (1) and (2) were solved, α was updated based on the transport equation.

$${\displaystyle \frac{\partial \alpha }{\partial t}}+\nabla ·(u\alpha )+\nabla ·[\alpha (1-\alpha )u_r]=0$$

(5)

The compression term ∇ [α(1 − α)u_r], in which u_r denotes the compression velocity vector, was introduced by Weller et al. (1998) [22] to mitigate numerical diffusion.

2.4. Turbulence Model

According to the perforated vessel ship hydrodynamic flow characteristic, in the present study, the realizable k-ε model was utilized to describe the turbulence [17,18,23].

This particular turbulent model has demonstrated good performance in accurately predicting the dispersion of round jets from nozzles thanks to its incorporation of fluctuating vorticity dynamics within the turbulent energy dissipation rate equation (Gorle et al., 2020 [24]). The conservation equations for k and its dissipation rate ε can be expressed as follows:

$$\begin{array}{l}{\displaystyle \frac{\partial (\rho k)}{\partial t}}+{\displaystyle \frac{\partial }{\partial {\chi }_j}}(\rho k{v}_j)={\displaystyle \frac{\partial }{\partial {\chi }_j}}[(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}){\displaystyle \frac{\partial k}{\partial {\chi }_j}}]+{\mathrm{G}}_k+{\mathrm{G}}_{\mathrm{b}}-\rho \epsilon +S_{\mathrm{k}}\\ {\displaystyle \frac{\partial (\rho \epsilon )}{\partial t}}+{\displaystyle \frac{\partial }{\partial {\chi }_j}}(\rho \epsilon v_j)={\displaystyle \frac{\partial }{\partial {\chi }_j}}[(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}){\displaystyle \frac{\partial \epsilon }{\partial {\chi }_j}}]+\rho C_1{S}_{\epsilon }-{\displaystyle \frac{\rho C_2{\epsilon }^2}{k+\sqrt{v\epsilon }}}+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}{C}_{3\epsilon }{\mathrm{G}}_{\mathrm{b}}+S_{\epsilon }\end{array}$$

(6)

where G_k and G_b represent the generation of turbulent kinetic energy by average velocity gradients and buoyancy, respectively. S_k and S_ε are the user-defined source terms; in this paper, S_k and S_ε were set to 0. According to the Launder and experiment value [25,26], C_1ε = 1.44, C_2ε = 1.9, C_t = 1.0, σ_k = 1.0, σ_ε = 1.2, and C_μ = 0.09. In addition, ${\mu }_t=\rho C_{\mu }{\displaystyle \frac{k^2}{\epsilon }}$, $\eta ={\displaystyle \frac{k\sqrt{2S_{\mathrm{ij}}{S}_{\mathrm{ij}}}}{\epsilon }}$, $S_{\mathrm{ij}}={\displaystyle \frac{1}{2}}({\displaystyle \frac{{\partial \upsilon }_j}{\partial {\mathrm{x}}_i}}+{\displaystyle \frac{{\partial \upsilon }_i}{\partial \mathrm{x}j}})$, and $C_1=\max [0.43,{\displaystyle \frac{\eta }{\eta +5}}]$.

To clarify the solution procedure of the integrated model, we generated a flowchart of the complete modeling process [27], shown in Figure 2.

3. Numerical Simulation Setup

3.1. Numerical Model Setup

Hydrodynamic coefficients play a crucial role in determining floating tanks’ hydrodynamic performance characteristics, such as motion response and tension force. Therefore, a numerical model was established to simulate the interaction between the waves and the moored perforated tank. To analyze the influence of the openings on these factors, the focus was placed on the sway, heave, and roll of the floating tank, as well as the tension forces on the windward and leeward surfaces when facing the waves. The main parameters are shown in Figure 1 and Figure 3.

For the accuracy of the numerical simulation results, grid refinement was carried out near the free surface. A total of five layers of refined grids were implemented to more accurately simulate the waves, thereby ensuring the accuracy of the simulation results. The entire numerical simulation time was set at 25 wave periods, with a total duration of 26.25 s. The time step was T/1050 = 0.001 s, and Δz was selected as 2.6 mm.

To simulate the interaction between the waves and the floating body, nested grids were used in the model with the numerical wave flume setting. Waves propagated along the positive direction of the x-axis. The background grid was mainly divided into three areas: A, B, and C (Figure 4).

The wave forcing function provided in STAR-CCM+ was used for wave damping based on the Euler overlay method (EOM) theory (Kim et al., 2012 [28]; Baquet et al., 2017 [29]). To eliminate the reflection wave from the floating body, the wave forcing function was set in Area A.

The mesh setup used a minimum Δx = L/120 and Δz = H/15 within 1.5 times the wave height to meet the requirements of wave propagation. Area B near the floating body had to be refined to meet the requirements of interpolation accuracy with the floating body grid. The overset grid was implemented to determine the floating body’s motion response under the mooring line constraints. A specialized set of refinement zones was created around the body and inside the perforated side to capture more detailed flow information. In this study, the mesh size at the perforations was locally refined, with a size of approximately dx = 0.00368 m in all cases, as shown in Figure 5. There were three layers: the outer, middle, and inner layers. They had mesh sizes of dx = 0.0105 m, 0.00526 m, and 0.00368 m, respectively.

3.2. The Setup of the Perforated Fishing Tank

According to the definition of the openings in the paper by Tang and Liu [30], the parameter of the opening ratio was introduced for analysis. The opening ratio P is defined as the opening area S_p divided by the total area S_total of the side of the hull below the waterline.

$$P={\displaystyle \frac{S_P}{S_{total}}}$$

(7)

A comprehensive numerical simulation study was carried out on the tank structure with different side opening ratios (P). The motion response characteristics, especially sway, heave, and roll, were systematically examined to clarify the impact of various opening ratios on the hydrodynamic behavior of the tank. Circular openings were chosen as the standard configuration, with a fixed quantity of two perforations. Under the two opening conditions, each perforated plate had a length of 0.228 m and a width of 0.20 m, yielding a maximum achievable opening ratio of 55.8%. As a result, the parametric study covered opening ratios ranging from 0% (impermeable configuration) to 3.125%, 6.25%, 12.5%, 20%, 25%, 40%, and 50%, as shown in

Table 1. Various opening ratios under the same conditions.

Case	1	2	3	4	5	6	7	8
Opening Ratio	0.0%	3.125%	6.25%	12.5%	20%	25%	40%	50%
Height	0.04 m
Period	1.05 s

and Figure 6.

All simulations were executed under consistent wave conditions: a wave incidence angle of 90°, a wave period of 1.05 s, and a wave height of 0.04 m. The similarity ratio between the prototype and the model in the numerical model was 1:60. The detailed operational parameters are recorded in Table 1 and Figure 6.

To ensure the consistency of parameters under various working conditions, the same volume of water was used inside the compartment with an opening ratio of 0%, so as to keep the draft consistent under all working conditions.

4. Model Validation

4.1. Validation of Tank Model Mesh

To verify the stability and convergence of the grid results, we selected Case 1 of Table 1 for mesh verification. We designed three schemes with different grid quantities, with the total grid quantities being 2.55 million (Case a), 2 million (Case b), and 1.56 million (Case c). The numerical results of the three grids, shown in Figure 7 and Figure 8, were very close and in good agreement regarding the heave motion. However, for the mooring tension in the windward, there were differences in some areas between the calculation results of the 1.56 million grid scheme and those of the 2 million grid and 2.56 million grid schemes.

Considering both the computational effort and efficiency, we ultimately chose the scheme with a 2 million grid quantity (Case b) to carry out subsequent numerical simulation work.

4.2. Validation of Floating Liquid Tank

The numerical model was validated against experimental data of the interaction between the wave and the floating body with an internal liquid tank. Yu et al. [30] carried out a series of experimental studies on a floating liquid tank to study its hydrodynamic performance in two dimensions. The accuracy of the numerical results was verified by comparing the motion response of its tank and the tension of the mooring lines. The specific calculation parameters are shown in Figure 9.

The numerical results of motion response and tension were compared with the experimental results in Figure 10, which shows the time history curves of motion responses and tension.

It can be seen from the time history curve of motion responses and tension that the surge error was 1.2%, the roll error was 3.3%, and the tension error in the windward was 2.8%. The time series curves of wave elevations at two measurement points are shown in Figure 11. The numerical results are consistent with the experimental results, demonstrating the accuracy of the numerical method.

5. Results and Analysis

5.1. Analysis of the Effect of Opening Ratio on the Motion Response and Mooring Tension

A numerical simulation study was conducted on the perforated tank structure with varying side opening ratios (P). A comparative analysis was first performed on motion response characteristics, specifically roll, sway, and heave, to evaluate the hydrodynamic behavior of the perforated structure under different opening ratios. The three-degree-of-freedom (3-DOF) motion response time history curves of the perforated tank are presented in Figure 12. As shown in Figure 12, the perforations are beneficial for reducing the motion response amplitudes, which is conducive to fish farming.

To facilitate quantitative analysis of the aforementioned data, the steady-state segments of motion responses and mooring line tensions were selected, with the specific time range (18 s–23 s) indicated in Figure 13.

As depicted in Figure 13, the heave, roll, and mooring tensions on both the windward and leeward sides display a decreasing tendency as the opening ratios increase. Compared to the configuration with a 50% opening ratio, the closed tank scenario showed a reduction in heave amplitude from 26.7 mm to 19.8 mm (a decrease of approximately 25.8%) and a decline in roll amplitude from 6.19°to 3.56° (a 42.6% reduction). The side openings create additional fluid channels, allowing water to flow more freely around the hull. Higher opening ratios enable more water to enter the compartments per unit time. This leads to an increase in the drag and the total mass of the perforated barge. Larger openings enhance viscous dissipation by generating vortices at the apertures, which significantly increases the damping coefficient for heave motion. It was found that the perforation ratios can enhance the hydrodynamic performance.

As shown in roll motion, the perforated structure with a 50% opening ratio exhibited a 42.4% reduction in roll amplitude compared to the non-perforated configuration. Mooring tensions on the windward and leeward sides under different opening ratios were systematically observed. When the opening ratio exceeded 20%, the influence of opening size on tension became less pronounced, particularly for the weather-side mooring tension. The underwater openings generated connectivity between windward and leeward sides, enabling cross-flow water exchange through these apertures. This investigation confirms that side openings can effectively mitigate motion responses and mooring tensions, demonstrating beneficial hydrodynamic performance enhancements for perforated vessels. Subsequent analyses, therefore, focused on parametric optimization, including opening arrangement patterns and asymmetric opening distributions, to further explore these hydrodynamic improvements.

5.2. Analysis of Asymmetric Openings Along the Water Depth Direction

According to linear wave theory, wave-induced pressure leads to exponential decay with increasing water depth. To analyze the influence of openings at different locations and the local flow fields, we selected the opening ratio of 12.5% for further study. The reason is that an opening ratio of 12.5% can represent the influence of openings on the motion response of the floating body.

The openings were configured in a two-row arrangement, with six openings symmetrically distributed in each row.One row was positioned adjacent to the waterline, while the other was near the cabin bottom. The design details of the openings were presented in Figure 14 and

Table 2. The arrangement of the asymmetric opening design.

Type	Diameter of the Upper Opening Row	Diameter of the Lower Row	Area of the Upper Opening Row	Area of the Lower Opening Row	The Ratio of the Upper and Lower Opening Row
Case A	22.0 mm	44.0 mm	380 mm2	1521 mm2	1:4.0
Case B	31.2 mm	38.0 mm	765 mm2	1134 mm2	1:1.5
Case C	34.8 mm	34.8 mm	951 mm2	951 mm2	1:1.0
Case D	38.0 mm	31.2 mm	1134 mm2	765 mm2	1.5:1
Case E	44.0 mm	22.0 mm	1521 mm2	380 mm2	4.0:1

.

5.2.1. Motion Response and Mooring Force

Figure 15 shows the motion responses and mooring line tensions under different schemes. Evidently, the opening area exerted an influence on the heave motion. It is observable that diverse distributions on the perforated vessel had a relatively minor impact on the sway and roll motion responses, while they did have some effect on the heave motion response. As the opening area of the waterplane increased, the amplitude of the heave motion decreased correspondingly. Simultaneously, the viscous dissipation of the fluid passing through the openings augmented the heave damping. The rate of change in the roll value was merely 7.63%, and that of the heave value was only 5.20%. Under the same opening area and opening ratio, the openings at different positions along the water depth direction had little influence on the roll and sway motions.

Owing to its position, the overall magnitude of the mooring tension on the leeward side was relatively small, and the opening area had a limited effect on the motion response. Consequently, the change in the mooring chain tension on the leeward side was relatively minor. On the windward side, due to the impact load of the waves, the wave load varied significantly within a short time, and the change rate in the mooring tension reached 18.13%.

5.2.2. Velocity

To further clarify the influence of opening positions on the local flow field, a detailed analysis was conducted on the velocity at key points. The velocity points arrangement is shown in Figure 16. A stable time period of the flow field was selected. Figure 17 shows the velocity vector corresponding to various opening designs. Through systematic examination, it was revealed that the local flow fields of different configurations shared common characteristics. This finding was further validated by consistent outcomes from the motion response analysis. Notably, a strong correlation was observed between the flow velocity and the perforation area. As the area of the upper row openings expanded and the area ratio varied from 1:4 to 4:1, the flow velocity at the openings showed a progressive increase.

5.3. Analysis of Asymmetric Openings in Windward and Leeward Regions

As shown in Figure 18, different opening ratios were set on the windward side and the leeward side. The opening ratios of the wave-facing side and the wave-opposite side were 25% and 12.5%, respectively. As shown in Figure 19, the motion responses, mooring tensions, and local flow velocities at the gauging points under the two asymmetric opening ratios were comparatively analyzed. It can be seen from the figure that under the working condition with an opening ratio of 12.5% on the wave-facing side, the roll motion response was greater, and correspondingly, the mooring chain tension on the wave-facing side was also larger. The velocity points arrangement is shown in Figure 15.

A comparative analysis of velocity measurement data under different opening ratios revealed that the top-layer measuring points on the windward side (A1, A4, A7) exhibited higher flow velocities under smaller porosity ratios (12.5%). Figure 20 shows the velocity vector for Case Ⅰ and Case Ⅱ. The velocity of the measuring points was consistent with the velocity vector. The perforations were positioned exactly at the locations of the first-row measurement points (A1, A4, A7, and A10) and the third-row measurement points (A3, A6, A9, and A12). Consequently, significant differences in flow velocity were observed at these measurement points under two porosity ratios (25% and 12.5%), directly demonstrating the impact of asymmetric perforation on the flow field. The effect of asymmetric perforation was substantial, with the flow velocity variation range for the first-row points reaching 5.8% to 15.8% under different porosity ratios, while that for the third-row points was considerably larger, reaching 6.25% to 81.5%.

This phenomenon agrees with fluid dynamics principles: under identical flow field conditions, reduced opening areas induce more pronounced flow acceleration. Notably, located at the outer edge, points A10, A11, and A12 demonstrate relatively stable velocity characteristics across both porosity conditions due to their position, showing low sensitivity to opening area variations. Velocity data from four non-perforated measuring points (A2, A5, A8, and A11) in the central region confirm that flow patterns in this area remain independent of porosity changes.

Bottom-layer points follow similar trends to their top counterparts, showing progressively increasing flow velocities as the porosity ratio decreases. Modifying pore structure parameters in windward and leeward can alter the local flow field.

This regulatory mechanism holds significant engineering implications for enhancing fluid exchange efficiency within chamber interiors, manifested through three key aspects: (1) modifying pore structure parameters to alter the kinetic energy of the local flow field; (2) establishing directional flow channels to promote internal circulation; and (3) optimizing hydrodynamic load distribution patterns.

6. Summary and Outlook

This study investigated the hydrodynamic characteristics (motion response, mooring tension, and flow velocity) of a perforated tank, focusing on the effects of opening and pore distribution patterns, specifically symmetric versus asymmetric opening designs in terms of depth and location. The parametric study covered opening ratios ranging from 0% (impermeable configuration) to 3.125%, 6.25%, 12.5%, 20%, 25%, 40% and 50%.

(1)

Perforation design generally enhances hydrodynamic performance compared to fully enclosed tanks. At 50% porosity, motion response decreased significantly: heave amplitude reduced from 26.7 mm to 19.8 mm (25.8% reduction), and roll amplitude decreased from 6.19° to 3.56° (42.4% reduction). Mooring tension followed the same trend, indicating that perforation effectively reduces motion response and mooring loads, thereby improving hydrodynamic performance.

(2)

Depth-based perforation distribution exhibits limited influence on motion response. Different vertical configurations minimally affected sway and roll motions (a mere 7.63% difference in roll), with an even smaller impact on the heave (only 5.2% difference). This finding is inconsistent with the initial hypothesis that vertically asymmetric pore distribution would significantly alter the flow field.

(3)

The asymmetric perforation (in windward/leeward sides) exerts a significantly greater influence on motion, internal flow velocity, and water exchange efficiency. Its impact on motion response, internal flow velocity, and water exchange efficiency substantially exceeds that of vertical distribution. Quantitatively, flow velocity variations at first-row measurement points reached 5.8–15.8% across porosity ratios, while third-row points showed a sharp increase to 6.25–81.5%.

(4)

An asymmetric perforation design on the windward and leeward sides effectively regulates local flow velocity and establishes directional flow channel forms. By regulating local velocities to establish directional flow channels, this design achieved 5.8–15.8% velocity differences at top-row points under specific conditions (25% and 12.5% porosity). This configuration simultaneously enhances water exchange efficiency while reducing motion response and mooring tension, representing an effective strategy for hydrodynamic optimization. Adjusting asymmetry levels improves exchange efficiency while ensuring structural stability and reduced mooring loads. This approach challenges the conventional porosity-centric design paradigm, offering novel insights for engineering optimization of tank perforation structures.

The above results were obtained under the beam-sea regular wave conditions. However, actual waves at sea are irregular with variable wave directions, so whether the same pattern exists remains to be analyzed in the next step.