Computational Analysis for Estimation of Mooring Force Acting on Various Ships in Busan New Port

Abstract

Recently, smart port systems connected to autonomous ships have attracted increasing interest. Thus, an intelligent port system can automatically berth to create an intelligent port system. To ensure the safety of large ships moored in open coastal terminals, which are often subjected to bad weather such as strong winds, it is necessary to calculate and evaluate their mooring security on a case-by-case basis. In this study, the mooring capacities of the large ships were estimated according to the port and fishing port design criteria of the Ministry of Ocean and Fisheries. Under the wind speed of 14 m/s, the longitudinal and lateral forces acting on the JBC, KCS, and KVLCC ships are 41.2 and 340 kN, 38.7 and 837 kN, and 77.2 and 222 kN, while under the wind speed of 30 m/s, they are 43 and 1674 kN, 132.7 and 4118 kN, and 159.2 and 1091 kN, respectively, for the mooring forces.

1. Introduction

With the rapid development of the global shipping business, there are increasing ports and terminals, and ships tend to be larger; meanwhile, with the improvement of loading and unloading efficiency, frequent mooring operations have become the norm in the shipping industry. The operation of mooring cables by crew and shore workers is the riskiest task in port operations due to hydro-meteorological conditions and frequent changes in the ship draft caused by loading and unloading operations. The statistics regarding mooring accidents and injuries in the maritime industry are concerning and emphasize the need for improved mooring methods.

According to the European Harbor Masters’ Committee (EHMC) [1], 95% of registered mooring injuries are caused by ropes and wires, with 60% occurring during mooring operations. Reports indicate that losses from major accidents exceeded USD 34 million between 1995 and 2016 [2]. These accidents primarily occur during the handling of ropes and wires. Rope and wire breakages account for 53% of the accident rate, while rope and wire slipping or jumping from the end of the drum or bite contribute to 42% of the accident rate. Equipment failure is responsible for 5.0% of these accidents (Figure 1) [3,4,5]. The UK P&I Club states that approximately 1/10 of personal injuries in ports are caused by mooring failures, with separate ropes and wire ropes being the primary cause [6,7,8,9]. The Australian Maritime Safety Authority (AMSA) received 227 mooring-related incident reports between 2011 and 2015, resulting in 51 injuries [10]. The International Maritime Health Association collected 331 mooring reports from 2006 to 2016 [11]. Data from the Transportation Safety Board of Canada (TSB) database reveal that from 2007 to 2017, 24 mooring incidents were reported involving both Canadian and foreign-flag ships, leading to twenty-four injuries, including two serious injuries. Over a seven-year period from 2001 to 2017, other member states of the International Maritime Organization (IMO) investigated 25 marine incidents and 14 very serious marine incidents related to mooring. These incidents resulted in a total of 27 injuries and 13 serious injuries, caused by the buckling or trapping of mooring lines, as well as crews tripping, falling, hitting, or being struck during mooring operations [12]. According to a report by CHIRP Maritime, the numbers of mooring accidents in the years 2018, 2019, 2020, and 2021 were 10, 12, 8, and 13, respectively [13]. Additionally, MACI reported mooring accidents and incidents at rates of 7.14%, 5.26%, and 14.55% from 2019 to 2021 [14].

These statistics underscore the importance of addressing the challenges associated with traditional mooring methods and developing improved techniques in the field of ocean engineering to enhance safety and efficiency in mooring operations. The research on mooring systems has evolved from single-cable monitoring to system monitoring, with that on automatic mooring systems in port terminals being widely emphasized and gradually applied in recent years, and automation technology can be used to ensure the safety of ship operations during mooring instead of the traditional cable method. This area is represented by the results developed by European companies, such as the Shore Tension^® and MoorMaster^TM mooring systems, both of which are already in use as automated mooring solutions (Figure 2). According to the mooring arrangement, automated mooring branched into two types, with and without the cable [16,17]. Jan et al. [18] proposed a shore-based, ship-independent mooring aid that supports master and pilot maneuvering in tight harbor pools and inclement weather by measuring distance and speed to determine precise mooring positions through reference points aligned with dock metrics, thus meeting the challenges of damage that can be caused by too-rapid approaches and steep angles of attack. Chen et al. [19] analyzed and calculated the ship’s heading and normal vector, determined the bow and stern position using feature points, obtained the line segment between the ship and the pier with the help of the area growth method, and applied a visibility analysis to identify the bow and stern. Using 3D LiDAR data, the distance, speed, and approach angle between the bow and stern of the dynamic ship and the quay were analyzed qualitatively and quantitatively, and the berthing situation of the Ro-Ro ship “Ocean Island” in Lushun port was effectively monitored in field experiments, which fully demonstrates the feasibility and effectiveness of this method in the identification of dynamic ships’ targets and safe berthing. Çağatay et al. [20] analyzed the operational strategies, technology applications, renewable energy and alternative fuels, and energy management systems through a systematic literature review to indicate the research directions and research gaps that exist in order to improve the energy efficiency and environmental performance of the ports and terminals, revealing the existence of a great potential for the ports in the field of energy efficiency and providing influential research opportunities for the researchers. Çagatay et al. [21] showed that smart grids can reduce costs and that deploying energy storage systems in port microgrids will result in important cost savings. Overall, ports utilizing renewable energy can realize significant cost savings. Kuzu et al. [3] conducted a comparative analysis of vacuum-based automated, magnetic, and conventional mooring systems involving ropes and windlass, considering operation safety, operating cost, maintenance cost, environmental impact, ease of handling, and system limitations. Their findings suggest that the vacuum-based automated mooring system is more suitable for future applications. Çağatay et al. [22] developed a recoverable robust optimization approach to enhance the performance of container terminals by considering uncertainty parameters in berth and quay crane planning and minimizing costs due to resource efficiency. This study provides a feasible theoretical basis for the future installation of mooring equipment.

The automated mooring systems in ports hold a significant role regarding operational reliability and safety enhancement, the minimization of human involvement during berthing, and the elimination of potential errors and risks. Additionally, automated mooring systems improve port operation efficiency and reduce downtime. These systems shorten the mooring time and streamline berth operation procedures, leading to shorter transit times and enhanced terminal operation efficiency and throughput.

The intricate interactions among the ship, dock, and water pose significant challenges due to wind, wave, and current disturbances. Achieving precise control in automated mooring requires a comprehensive understanding of the forces acting on the ship during the process. This study aims to investigate the primary forces involved, including wind, wave, and current forces, considering both the transverse and longitudinal directions. By quantifying these forces under various environmental conditions, valuable insights can be gained to improve the design and optimization of automated mooring systems, ensuring their reliability and effectiveness in challenging operational scenarios.

Andersen [23] studied the influence of the cargo-hold configuration on wind forces on the deck of a 9000 TEU container ship using wind tunnel tests with a 1:450 scale model. Longitudinal and transverse forces, together with yawing moments, were measured. Wang et al. [24] investigated the wind and wave loads regarding the motion characteristics of a 1900 TEU container ship through wind tunnel tests, towing tank experiments, and computational fluid dynamics (CFD) simulations. The results indicated that the combined wind and wave loads resulted in higher resistance than the sum of independent wind and wave loads. Ricci et al. [25] conducted three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations to study the wind forces acting on a large cruise ship docked at the Rotterdam cruise terminal. The study revealed that tall buildings nearby may increase the local surface pressure on the ship, reducing horizontal forces but increasing vertical uplift forces. In smaller ships, tall buildings nearby may increase both horizontal and vertical forces. Zhou et al. [26] investigated the impact of wind and currents on the dynamic behavior of ships in ports and waterways by analyzing automatic identification system data, meteorological data, and hydrological data from the Port of Rotterdam. The results demonstrated variations in the influence of wind and currents on the ground speed, yaw angle, and drift angle for different-sized ships. Kobayashi et al. [27] performed a grid sensitivity analysis on the superstructure of a ship using their in-house solver and overset grid technology with the Japan Bulk Carrier (JBC) model. The study revealed that steady-state CFD analysis reliably estimates the wind forces and moments on the superstructure of different ship models in wind tunnel tests, showing good agreement with measurement data and outperforming regression formulas in certain cases. Martić et al. [28] conducted a study on the influence of the prismatic coefficient, the longitudinal position of the center of buoyancy, the trim, the pitch radius of gyration, and the ship speed on the added resistance in waves for the KCS ship under regular head waves and different sea conditions using the 3D panel method based on the Kelvin-type Green function. The research findings provide insights into how variations in ship characteristics affect the added resistance in waves. Sasa et al. [29] proposed a novel algorithm to simulate the sliding anchor and grounding situations under wave and wind conditions, comparing the results of dynamically computed anchor chain forces with those from the catenary method. Their aimed to provide valuable insights for improving port planning related to anchorage. Lee et al. [30] conducted a failure analysis on a ship that experienced anchor failure in a port, revealing that wave drift forces could lead to the failure of mooring systems. They suggested new mooring system designs considering wave loads for port planning. Lin et al. [31] conducted a resistance and propulsion performance analysis on a 25 m ship model in actual wind, wave, and current flow environments. Additionally, corresponding correction methods were developed to ascertain the performance under actual sea conditions. The study also evaluated the impact of an energy-saving device (ESD) on the ship’s performance in actual sea conditions. Farkas et al. [32] investigated the resistance and propulsion characteristics of a handy-size bulk carrier through full-scale numerical and experimental evaluations. They detailed the analysis result, verified the numerical results, and compared the different turbulence models provided, along with the pros and cons of the extrapolation methods discussion. The study emphasized the significance of viscous flow based CFD in enhancing the reliability of extrapolation methods and reducing the increment of the resistance coefficient. It also highlighted the advantages of assessing ship hydrodynamic characteristics using full-scale evaluations.

Many scholars have previously studied the mooring forces of ships; however, the combined effects of wind, waves, and currents have not been considered. This research aimed to calculate the mooring forces on three types of ships commonly operated in ports: cargo ships, container ships, and oil tankers. The results obtained from this study can be adopted to estimate the mooring forces for these three types of ships, thus enhancing the safety of ships under mooring conditions. Numerical simulations for wind resistance were performed using the unsteady Reynolds-averaged Navier–Stokes solver in STAR CCM+. The simulations investigated the variation of resistance on ships under different wind directions and uniform wind velocities while considering the design draught of the ship. In addition, under moored conditions, the port and fishing port design criteria were utilized to calculate the maximum current force acting on the ship within the harbor. Furthermore, ANSYS AQWA software was employed to calculate the maximum wave force on the ship during a three-hour period under irregular wave conditions. The combination of these calculations provided a more accurate estimation of the mooring forces experienced by ships in moored conditions.

2. Numerical Setup

2.1. Target Ship

The JBC (Japan Bulk Carrier) is a capsize bulk carrier equipped with a stern duct as an ESD. The National Maritime Research Institute (NMRI), Yokohama National University, and the Ship Building Research Centre of Japan (SRC) were jointly involved in the design of a ship hull, a duct, and a rudder. Towing tank experiments were planned at NMRI, SRC, and Osaka University, which included resistance tests, self-propulsion tests, and PIV measurements of stern flow fields. The KCS was conceived to provide data for the explication of both the flow physics and CFD validation for a modern container ship with a bulbous bow. The Korea Research Institute for Ships and Ocean Engineering (KRISO) performed towing tank experiments to obtain the resistance, mean flow data, and free surface waves. The KRISO 300 K Very Large Crude Carrier (KVLCC) is a specific type of VLCC ship developed by the KRISO designed for large volumes of crude oil across long distances (Figure 3,

Table 1. Main dimensions of ship models analyzed in the study [33].

Main Particulars		JBC	KCS	KVLCC
Length Overall (LOA)	m	291.3	232.5	325.5
Length Between Perpendicular (LBP)	m	280	230	320
Breadth (B)	m	45	32.2	58
Mean Draft (Fully loaded condition)	m	25	19	30
Transverse Projected Area	m2	964	839	1085
Lateral Projected Area	m2	3364	4975	2665
Displacement (Fully loaded condition)	m3	178,370	52,030	312,738
Block Coefficient (Cb)		0.86	0.65	0.81
GM (Fully loaded condition)	m	5.32	0.62	0.65

).

2.2. Ocean Environmental Condition

The target ship will be moored at the Busan New Port, Republic of Korea, as shown in Figure 4. The mooring force acting on the ship in the port is affected by various environmental disturbances. In general, ports are designed to minimize disturbances to the environment. However, wind loads are inevitably generated. To reduce the loads caused by waves, tidal barriers and breakwaters (including offshore breakwaters) are installed around the harbor, resulting in the size of the waves being proportional to the height of the sea level. Thus, the wave size in the harbor decreased significantly. The JBC, KCS, and KVLCC ships are large ships that can also be moored in the harbor when a typhoon occurs. The wind speeds of 14 and 30 m/s were considered in the mooring forces calculation of the ship’s moored condition. In Korea, a work alert is issued when the wind speed reaches 14 m/s at sea, and during a typhoon, the wind speed can reach 30 m/s. In addition, the water depth at Busan New Port is approximately 17 m, and the maximum tidal current of 1 m/s is listed in the available information [34]. As shown in Figure 4, on the left and right sides of the outer periphery of the harbor, breakwaters have been installed to ensure the smoothness of the water surface within the port. Due to the ship’s angle with the port when it is moored, the current velocity and direction were set at 2 knots and 30 degrees, respectively (Figure 5).

The wave height is 1 m where the wave direction is established at 30 degrees, according to the port and fishing port design criteria and the information on Busan New Port [34]. Due to the breakwater at the harbor entrance, there are no long waves within the port, and the wave height is not very high. Based on the data from the Busan New Port, the wave period is 3.5 s, and the wave height is 0.5 m.

2.3. Governing Equation for Simulations

2.3.1. Viscous Fluid Solver

In the commercial software package STAR-CCM+, a mathematical model based on the Reynolds-averaged Navier–Stokes (RANS) equations is used. These equations are derived from the laws of conservation of mass and momentum. For the incompressible, non-stationary case, the equations are as follows:

$$\frac{\partial \overline{u_i}}{\partial x_i}=0$$

(1)

$$\rho \overline{u_j}\frac{\partial \overline{u_i}}{\partial x_j}=\rho \overline{f_i}+\frac{\partial }{\partial x_j}\left[-\overline{p}{\delta }_{ij}+\mu \left(\frac{\partial \overline{u_i}}{\partial x_j}+\frac{\partial \overline{u_j}}{\partial x_i}\right)-\rho \overline{{u^{\prime }}_i{u^{\prime }}_j}\right]$$

(2)

where μ is the viscosity modulus of the fluid, P is the static pressure, $-\rho \overline{{u^{\prime }}_i{u^{\prime }}_j}$ is the Reynold stress, and $\overline{f_i}$ is the force of the object per unit volume.

The RANS turbulence model is based on the modeling of the Reynolds stress transport equation (RST). The stress tensor is modeled as a function of the mean flow. The model used in this study belongs to the class of eddy-viscosity models, which use the concept of the turbulent eddy-viscosity coefficient μ_t to model the stress tensor. According to the Boussinesq hypothesis, the RST is modeled as follows [35]:

$$-\overline{\rho {u^{\prime }}_i{u^{\prime }}_j}=u_t(\frac{\partial \overline{u_i}}{\partial x_j}+\frac{\partial \overline{u_j}}{\partial x_i})-\frac{2}{3}\rho k{\delta }_i{}_j$$

(3)

where u_t and k represent turbulent viscosity and turbulent kinetic energy, respectively, while the symbol δ_ij denotes the Kronecker delta. All the turbulence models employed in the present study are based on the Boussinesq hypothesis. The realizable k-ε (RKE) turbulence model is a two-equation model that solves the transport equations for the turbulent kinetic energy k and turbulent dissipation rate ε. The eddy viscosity in this model is described by the following equation [35]:

$$u_t=\rho C_{\mu }\frac{k^2}{\epsilon }$$

(4)

where C_μ is a model coefficient. The k and ε transport equations are as follows:

$$\frac{\partial }{\partial t}(\rho k)+\frac{\partial }{\partial x_i}(\rho k\overline{u_i})=\frac{{\partial }^{2}k}{\partial x_i^2}(\mu +\frac{{\mu }_t}{{\sigma }_k})+f_c{G}_k+G_b-{\gamma }_M-\rho (\epsilon -{\epsilon }_0)+S_k$$

(5)

$$\begin{array}{l}\frac{\partial }{\partial t}(\rho \epsilon )+\frac{\partial }{\partial x_i}(\rho \epsilon \overline{u_i})=\frac{{\partial }^2\epsilon }{\partial x_i^2}(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }})+\\ \frac{1}{T_e}{C}_{\epsilon 1}(f_{c}Sk+C_{\epsilon 3}{G}_b)-C_{\epsilon 2}{f}_2\rho (\frac{\epsilon }{T_e}-\frac{{\epsilon }_0}{T_0})+S_{\epsilon }\end{array}$$

(6)

where σ_k and σ_ε are turbulent Schmidt numbers; f_c is the curvature correction factor, G_k is the turbulence generation term; G_b is the buoyancy generation term; ε₀ is the ambient turbulence value that counteracts the turbulence attenuation; γ_M is the expansion dissipation; Cε₁, Cε₂, and Cε₃ are the model correlation coefficients; S is the modulus of the mean strain tensor; and S_k and Sε are the user-defined source terms.

2.3.2. Calculation of the Current Force

According to fluid dynamics, fluid pressure consists of two parts: frictional resistance and pressure resistance. Frictional resistance is predominant in the bow direction of the ship. For lateral flow, pressure drag is predominant. However, it is very difficult to strictly distinguish between frictional and pressure resistance and perform calculations. According to [36] (7), the fluid pressure caused by the tidal flow can be calculated as

$$R_f={\rho }_{w}g\lambda \{1+0.0043(15-t)\}S{V}^{1.825}$$

(7)

Rf: fluid Pressure (kN).

Ρ_w: specific gravity of seawater (1.03 ton/m³).

T: temperature (15 °C).

S: flooded surface area (m²).

V: flow velocity (m/s).

λ: coefficients (0.14).

2.3.3. Calculation of the Wave Force

For the hydrodynamic analysis of a ship under regular waves based on three-dimensional potential flow theory, the following conditions must be satisfied: the water is an ideal and incompressible fluid with no rotation, and the waves are small-amplitude waves. The velocity potential function should satisfy the following conditions [37]:

Control equation:

$${\nabla }^2\varphi =0$$

(8)

Free-surface boundary condition:

$$-{\omega }^2\varphi +g\frac{\partial \varphi }{\partial z}=0,z=0$$

(9)

Seabed boundary condition:

$$\frac{\partial \varphi }{\partial n}=0,z=-h$$

(10)

Free-surface motion condition after linearization:

$$\frac{\partial \xi }{\partial t}-\frac{\partial \varphi }{\partial z}=0$$

(11)

Free-surface dynamic condition after linearization:

$$\frac{\partial \varphi }{\partial t}+g\xi =0$$

(12)

In general, the above conditions are solved using the Green function method, which establishes the integral equation between the velocity potential and the Green function. When solving the integral equation, the boundary element method is employed to discretize the object surface into a certain number of units. Subsequently, the strength at the center of each unit (referred to as the source point) is calculated under the boundary conditions, and the velocity potential at each node is obtained based on the pulse source distribution.

After calculating the radiation and diffraction velocity potential of the structure, the first-order hydrodynamic pressure can be expressed as [37]:

$$p=-\rho \frac{\partial \varphi }{\partial t}$$

(13)

The total wave force is obtained by integrating over the wet surface of the object:

$$F={\displaystyle {\iint }_{S}pndS}$$

(14)

where S is the wet surface of the object; in general, the first-order wave force consists of three components:

$$F=F_H{}_S+F_R+F_{EX}$$

(15)

where F is the first wave force; F_HS is the rigid hydrostatic restoring force; F_R is the radiation force; and F_EX is the first wave excitation force and moment, generated in the interaction of wave incidence and diffraction velocity potential.

To consider the ship’s sailing characteristics, it is necessary to select the wave spectrum suitable for the sea area. The common wave spectra used to evaluate the ship’s sailing performance in irregular waves are the Pearson Moskowitz (P-M) spectrum and the Bretschneider JONSWAP spectrum. In this study, the standard spectrum representing a sufficiently open sea area, i.e., the P-M spectrum, was used according to the load analysis guidelines of the Korean Register of Shipping (KR) and Chapter 5 of Part 3 of the Ship Rules [38].

The P-M spectrum is given by Equation (16) [39] with the peak frequency. Figure 6 shows the relationship between the wave spectrum and wave frequency for a significant wave height of 0.5 m.

$$S_{PM}(\omega )=4{\pi }^3\frac{H_S}{T_z{}^4}\times \frac{1}{{\omega }^5}\times \exp (-\frac{16{\pi }^3}{T_z{}^4}\times \frac{1}{{\omega }^4})$$

(16)

The following relationship exists between T_Z, T₁, and T₀ (17):

$$\begin{array}{l}{T}_0=1.408\times T_Z\\ T_1=1.086\times T_Z\end{array}$$

(17)

where T₁ is the mean wave period and T₀ is the peak period.

3. Numerical Results

3.1. Grid Validation and Verification

Considering the variability in the wind speed and the influence of the hull’s cross-sectional shape on the aerodynamic coefficients, it is crucial to calculate the wind loads acting on a streamlined ship. The wind forces acting on the ship branch into longitudinal forces (X direction) and lateral forces (Y direction) (Figure 7). The force exerted by the wind varies significantly based on the upper water surface area. Specifically, wind from the bow direction affects the frontal projection area of the upper water surface, resulting in relatively small longitudinal forces. Conversely, wind blowing from the lateral direction affects the lateral projection area of the water surface, leading to considerably larger lateral forces. In this study, a uniform wind flow assumption was proposed to obtain relatively conservative results, and calculations were accomplished using equations specified in the “Port and Fishing Port Design Criteria” [36].

$$\begin{array}{l}{R}_X=\frac{1}{2}{\rho }_a{U}^2{A}_r{C}_X\\ R_Y=\frac{1}{2}{\rho }_a{U}^2{A}_L{C}_Y\\ R_M=\frac{1}{2}{\rho }_a{U}^2{A}_L{L}_{pp}{C}_M\end{array}$$

(18)

C_X: wind drag coefficient in the X direction.

C_Y: wind drag coefficient in the Y direction.

C_M: wind moment coefficient at the ship’s centerline.

R_X: the X-directional component of the combined wind load (kN).

R_Y: the Y-directional component of the combined wind load (kN).

R_M: moment of rotation of the ship’s center of gravity for wind loads (kN-m).

ρ_a: air density (1.23 × 10⁻³ ton/m³).

U: wind speed (m/s).

A_r: projected frontal area of the hull on the water surface (m²).

A_L: projected lateral area of the hull on the water surface (m²).

L_PP: length between waterlines (m).

The wind pressure coefficients C_X, C_Y, and C_M for a particular ship are obtained optimally from wind tunnel tests or the hydrographic measurements of a distinct ship. However, such tests need excessive time and resources. Based on the results of wind tunnel tests, wind resistance coefficients can be calculated using equations or CFD to obtain more accurate values.

In this study, a CFD approach was purposed to obtain the wind pressure coefficients, with STAR-CCM+ (Ver. 15.06) as the analysis software. When using STAR-CCM+, we utilized a computer cluster subsisting of six servers, each equipped with an Intel Xeon Gold 6150 CPU featuring 108 cores. Domain boundaries were placed sufficiently far away to avoid their effect on the airflow around the ship. The inlet and outlet boundaries were placed at 3.5 Lpp from the hull, while the top boundary was placed at 0.5 Lpp from the hull. The left- and right-side boundaries were set at 2 Lpp from the hull. The boundary conditions were as follows: Velocity distribution at the inlet boundary; Constant pressure is applied at the outlet boundary; Both side boundaries are symmetric surfaces; Symmetric boundary conditions are applied to the top boundary while the bottom boundary is set as a non-slip wall according to the type of numerical simulation. The reason for setting the non-slip wall boundary condition at the bottom is that a natural boundary layer is formed due to the wind. The velocity distribution is constant, independent of the height since the airflow generated by the ship’s motion does not form a boundary layer. The ship’s surface is defined as a non-slip wall boundary condition. Special attention was paid to the discretization around the wind-loaded region of the ship. The prism layer was carefully created to maintain the non-dimensional wall distance of Y⁺ > 30. The distance between the center of the first cell near the wall and the wall is defined by the following equation [33].

$$y^{+}=0.172(\frac{y}{Lpp}){\mathrm{Re}}^{0.9}$$

(19)

Figure 8 shows the computational domain with the interface mesh enclosing the ship along with the described boundary conditions.

The JBC ship was selected for the calculations during the grid validity verification. As shown in the table, to increase the accuracy of the numerical calculations and reduce the computation time, the convergence speed of the calculations is determined using the CFL (Courant–Friedrichs–Lewy) number. Five cases are selected to verify the influence of mesh partitioning on the simulation drag coefficient to identify the optimal mesh partitioning method. The mesh partitioning methods for the five cases are: high refinement, refinement, conventional, coarsening, and high coarsening (Figure 9). The number of generated grids varies with the change in CFL, as shown in Table 2.

$$CFL=\frac{\delta t}{\delta x}\left|U\right|$$

(20)

δt: time step.

δx: minimum grid size.

|U|: absolute value of velocity.

Figure 9. JBC ship grid with different CFL values.

Figure 9. JBC ship grid with different CFL values.

Table 2. Grid division patterns and quantity (V_wind = 14 m/s).

	Case 1	Case 2	Case 3	Case 4	Case 5
CFL	0.4	1	2	4	8
Number of cells	2.7 × 107	2.1 × 107	1.6 × 107	1.1 × 107	8 × 106

Table 2. Grid division patterns and quantity (V_wind = 14 m/s).

	Case 1	Case 2	Case 3	Case 4	Case 5
CFL	0.4	1	2	4	8
Number of cells	2.7 × 107	2.1 × 107	1.6 × 107	1.1 × 107	8 × 106

When the wind direction at the inlet is set to 180 degrees, the ship is only subjected to drag from the X direction. As shown in Figure 10, the calculated wind resistance coefficient decreases as the CFL value increases. However, when the CFL value is lower than or equals two, the wind resistance coefficient does not change significantly as the CFL value increases. When the CFL value is more than two, the wind resistance coefficient changes drastically as the CFL value increases, so the results cannot be calculated accurately when the CFL value is greater than two. However, at CFL values of less than two, the wind resistance coefficient remains stable while the number of meshes increases exponentially, resulting in a longer computation time. Therefore, in this paper, a CFL value of two was chosen for all grid divisions to ensure accurate and efficient calculation results.

3.2. Estimation of the Wind Force for Various Ships

The detailed configuration of the fine mesh used in the numerical simulations to determine the wind resistance is shown in Figure 11.

3.2.1. Wind Force of JBC Ship

The wind force was separated by the lengthwise and lateral directions of the ship and was dimensionless, as calculated by Equation (7). The X-direction indicates the direction of the wind, 0 degrees indicates that the wind is blowing from the bow, 90 degrees shows that the wind is blowing from the starboard side, and 120 degrees shows that the wind is blowing from the starboard side aft.

The wind resistance of the ship was calculated with a total of seven cases from 0 to 180 degrees with 30-degree intervals. Resulting in the calculations derived to determine the wind resistance coefficients in the X- and Y-directions and the moment coefficients in the Z-direction, respectively, with the same comparison trend as the experimental data of KUME Kenichi [40] (Figure 12 and Figure 13). It was found that the longitudinal and lateral forces are maximum when the wind blows at 150 and 90 degrees, respectively.

Figure 14 shows the moment coefficients at the center of gravity for the JBC ship. The moment coefficients were amplified by a factor of ten due to their small values, of which a maximum value of about −1.3 was observed at approximately 120 degrees. The calculated moment coefficients will be used as input data for future control systems.

In the validation of grid validity, CFL = 2 is used for grid division. The experimental data of the JBC ship model obtained from KUME Kenichi and the calculation results of the JBC ship in actual dimensions are shown as red and green, respectively, as shown in Figure 12 and Figure 13. Figure 12 shows that the error of the X-direction damping coefficient is larger at 60 and 120 degrees because the CFD model is the result of the actual ship size calculation, and the difference in the area can be ignored because the X-direction force does not have a significant effect on the ship’s mooring state. Figure 13 shows that the CFD results are almost the same as the experimental results. Therefore, it can be verified again that the chosen meshing method is appropriate for the calculations.

Figure 15 shows how the velocity distribution around the ship is extracted at 60-degree intervals, depending on the wind direction, at Z = 10 m. At 0 and 180 degrees, it is difficult to observe the main features of the flow, but at 60 and 120 degrees, a stagnant flow marked in blue can be seen on the face colliding with the wind, and vortex separation in the opposite direction can also be observed. Therefore, it can be inferred that lateral forces will be found to have an important role.

3.2.2. Wind Force of the KCS Ship

The wind resistance of the ship was calculated for a total of seven cases from 0 to 180 degrees and 30-degree intervals, and the results of the calculations were obtained for the wind resistance coefficients in the X- and Y-directions and the moment coefficients in the Z-direction, respectively (Figure 16 and Figure 17). It was found that the longitudinal and lateral forces are maximum when the wind direction is at 150 and 90 degrees, respectively.

Figure 18 shows the moment coefficients at the center of gravity for the JBC ship. The moment coefficients were amplified by a factor of ten due to their small values. The maximum value occurred at approximately 120 degrees, measuring approximately −1.5. The calculated moment coefficients will be used as input data for future control systems.

Figure 19 shows how the velocity distribution around the ship is extracted at 60-degree intervals, depending on the direction of the wind, at the Z = 10 m position. At 0 and 180 degrees, it is difficult to observe the main features of the flow, but at 60 and 120 degrees, a stagnant flow marked in blue can be seen on the face colliding with the wind, and vortex separation in the opposite direction can also be observed. Therefore, it can be inferred that lateral forces will be found to have an important role.

3.2.3. Wind Force of the KVLCC Ship

The wind resistance of the ship was calculated for a total of seven cases from 0 to 180 degrees and 30-degree intervals, and the results of the calculations were obtained for the wind resistance coefficients in the X- and Y-directions and the moment coefficients in the z-direction, respectively (Figure 20 and Figure 21). It was found that the longitudinal and lateral forces are maximum when the wind direction is at 150 and 90 degrees, respectively.

Figure 22 shows the moment coefficients at the center of gravity for the JBC ship. The moment coefficients were amplified by a factor of ten due to their small values. The maximum value occurred at approximately 120 degrees, measuring approximately −1.1. The calculated moment coefficients will be used as input data for future control systems.

Figure 23 shows how the velocity distribution around the ship is extracted at 60-degree intervals, depending on the direction of the wind, at the Z = 10 m position. At 0 and 180 degrees, it is difficult to observe the main features of the flow, but at 60 and 120 degrees, a stagnant flow marked in blue can be seen on the face colliding with the wind, and vortex separation in the opposite direction can also be observed. Therefore, it can be inferred that lateral forces will be found to have an important role.

Based on the calculations, the wind resistance coefficients in the X- and Y-directions of the JBC, KCS, and KVLCC ships were obtained. Considering these coefficients, the maximum wind force in the X- and Y-directions for each ship at wind speeds of 14 m/s and 30 m/s were further calculated as shown in

Table 3. The maximum wind load on the ship in the X Y direction.

		JBC		KCS		KVLCC
	Vwind m/s	RX [KN]	RY [KN]	RX [KN]	RY [KN]	RX [KN]	RY [KN]
Wind force	14	0.5	340	23	838	20	222
	30	2.3	1674	117	4118	102	1091

.

3.3. Estimation of Current Force for Various Ships

Under the full-load condition, the submerged areas of the JBC, KCS, and KVLCC ships are 19,556 m², 9330 m², and 27,320 m², respectively, with a flow speed of 2 knots (1 m/s). In addition, we assume that the fender and port support structure can provide sufficient support, so the lateral (Y-axis direction) force caused by the current is neglected. According to the formula, the current force is calculated as shown in

Table 4. The maximum wind load on the ship in the X Y direction.

		JBC		KCS		KVLCC
	Vcurrent m/s	RX [KN]	RY [KN]	RX [KN]	RY [KN]	RX [KN]	RY [KN]
Current force	1	8.2	-	3.9	-	11.4	-

.

3.4. Estimation of Wave Force for Various Ships

The calculation of wave forces on the ships is performed using the ship hydrodynamic calculation software ANSYS AQWA, and the mapped mesh method is employed within the AQWA Workbench to conduct more refined time-domain simulations for JBC, KCS, and KVLCC. Figure 24 shows the mesh samples of the model simulated by ANSYS AQWA.

In ship wave force, the maximum force is generated in the pitch direction, followed by the heave and roll directions. Therefore, in this study, the surge, sway, and yaw directions are assumed to be fixed. Since no long-period waves were present when the ship moored in Busan New Port, a significant wave height of 0.5 m and a wave period of 3.5 s are assumed. The longitudinal wave forces for the JBC, KCS, and KVLCC ships were determined using ANSYS AQWA, as shown in Figure 25. Additionally, the transverse forces induced by waves are neglected because they are assumed to be adequately supported by the fenders and port structures.

3.5. Estimation of Total Mooring Force for Various Ships

When JBC, KCS, and KVLCC ships are at their design draft with a wind speed of 14 m/s and a tidal current of 2 knots, considering a significant wave height of 1 m and a wave period of 3.5 s, the estimated forces that the ships may experience under normal sea conditions are calculated and presented in

Table 5. Total mooring force acting on the ships (V_wind = 14 m/s).

	JBC		KCS		KVLCC
	FX [kN]	FY [kN]	FX [kN]	FY [kN]	FX [kN]	FY [kN]
Wind force	0.5	340	23	838	20	222
Current force	8.2	-	3.9	-	11.4	-
Wave force	32.5		11.8		45.8
Total force	41.2	340	38.7	837	77.2	222

.

When the JBC, KCS, and KVLCC ships are at their design drafts with a wind speed of 30 m/s, a current speed of 2 knots, and significant wave heights of 0.5 m; with wave periods 3.5 s, the estimated forces exerted on the ships under typical sea conditions are presented in

Table 6. Total mooring force acting on the ships (V_wind = 30 m/s).

	JBC		KCS		KVLCC
	FX [kN]	FY [kN]	FX [kN]	FY [kN]	FX [kN]	FY [kN]
Wind force	2.3	1674	117	4188	102	1091
Current force	8.2	-	3.9	-	11.4	-
Wave force	32.5		11.8		45.8
Total force	43	1674	132.7	4188	159.2	1091

.

The results in Table 5 and Table 6 show that the wind force is the primary external force acting on the ship in the moored state. Due to the small projected area in the longitudinal direction and the absence of strong currents or waves, the wind force becomes relatively small. However, in the transverse direction of the ship, the presence of upper structures and other factors results in a larger projected area, leading to a higher wind resistance. When the wind speed is 14 and 30 m/s, the wind resistance accounts for over 90% of the total resistance. Thus, the wind force has the maximum impact on the mooring system when the ship in the moored state. The calculated ships in this paper are the most operated ships in ports, including the JBC, KCS, and KVLCC ships which represent cargo ships, container ships, and oil tankers, respectively. By calculating the values of C_X, C_Y, and C_M for these three types of ships, the forces F_X and F_Y can be estimated. Furthermore, they can be used to determine whether the ship is suitable for operations in the harbor and the number of mooring devices required since a ship in a moored state does not connect to a single mooring device.

4. Conclusions

In this study, an evaluation was conducted to estimate the mooring forces acting on JBC, KCS, and KVLCC for the basic design of an automatic mooring device suitable for large ships in the future. Most mooring forces result from the wind force, while the forces caused by waves and currents are relatively small.

Considering factors such as wind, waves, and currents, the maximum mooring forces required in the longitudinal direction for JBC, KCS, and KVLCC, with a wind speed of 14 m/s, are 41.2, 38.7, and 77.2 kN, respectively, which are relatively small. However, in the transverse direction, due to the influence of upper structures, the maximum mooring forces required are 340, 837, and 222 kN, respectively. Notably, under extremely severe weather conditions with a wind speed of 30 m/s, the maximum mooring forces required in the longitudinal direction for JBC, KCS, and KVLCC are 43, 132.7, and 159.2 kN, respectively, which are relatively small. However, in the transverse direction, due to the influence of upper structures, the maximum mooring forces required are 1674, 4118, and 1091 kN, respectively. Therefore, these factors should be considered in the design of an automatic mooring device. The calculation results provide information on the mooring forces required for the ship in the moored state and the number of mooring devices needed for the operation. By calculating the results for a wind speed of 30 m/s, it can be determined whether the ship can be moored in the port during a typhoon. If the forces acting on the ship exceed the capacity of the mooring system, separation between the mooring system and the ship may occur, leading to significant accidents at the port. In this study, the wind resistance coefficients for the three types of ships that are most operated in the port have been calculated, which could serve as a reference for estimating the forces for other types of ships. This can enhance the safety of ships under mooring conditions.

Furthermore, the calculated mooring forces did not consider the maritime traffic conditions, such as additional force caused by the interaction among navigating ships. Additionally, if long-period waves exist within the port, the possibility of resonance with the ship cannot be excluded. Hence, future studies may require the use of tension calculation methods to analyze the ship’s motion.