Research on Course-Changing Performance of a Large Ship with Spoiler Fins

Abstract

The poor maneuverability inherent to large ships is a non-negligible problem that restricts the development of the shipping industry, as large ships can only cruise at an excessively conservative speed when they encounter complicated traffic conditions; nevertheless, ship collision accidents still occasionally occur. In the present study, the novel concept of spoiler fins for modern large ships is proposed. In order to assess their effectiveness in enhancing ship maneuverability, a KRISO container ship (KCS) was selected to carry a pair of spoiler fins, after which a simplified simulation approach for saving the calculation resource was designed for ship collision avoidance conditions, and a full-scale numerical model, including the ship hull, fin, and fluid field domain, was established. Transient-state hydrodynamic forces were calculated during collision avoidance maneuvers using the CFD method; the pressure and velocity contours around the ship were demonstrated; and the ship motion trajectories under different initial ship speeds were simulated and predicted through the adoption of overset mesh and 6-DOF dynamic mesh techniques. Eventually, the improved course-changing performance, dependent on the spoiler fins, was validated.

1. Introduction

The poor maneuverability inherent to large ships is a non-negligible problem that restricts the development of the shipping industry, as large ships can only cruise at an excessively conservative speed when they encounter complicated traffic conditions; for example, a large cargo ship should generally navigate at a low speed, under 5 kn, in a port or some other restricted water, such as a narrow channel. Nevertheless, ship collision accidents still occasionally occur, as shown in Figure 1. Screw propellers, rudders, and side thrusters are the most conventional, uncomplicated, and reliable devices with which to manipulate a ship, but the mass inertia of a large ship is so enormous that its motion state is very difficult to change when relying only upon a screw propeller or rudder. Even if thrusters are equipped, they can only take effect under a very low ship speed. Thus, maintaining a slow speed is the first requirement to ensure navigation safety; however, this is very inefficient, and a large number of underway hours are wasted to dodge only a negligible probability of ship collision. Moreover, as intelligent ships are developed, the poor maneuverability of large ships raises the difficulty and costs of realizing precise ship manipulation during autonomous navigations, and the motion response produced by the computer’s steering or engine orders causes a large time delay to be monitored with sensors and fed back to the control system, a problem that potentially strongly disturbs the control logic of the ship.

Inspired by the spoilers on airplanes and sport cars (shown in Figure 2), which are both designed to help the vehicles brake rapidly, the novel concept of spoiler fins for modern large ships is proposed in the present study. Firstly, the concept is very different from the existing fin stabilizers on ships, which are designed to reduce the rolling motion of a ship when it navigates through waves by producing a hydrodynamic lift force on the spread fin when the water flows around it; however, its structural strength is always limited, and it cannot form a strong enough resistance force to be treated as ship-braking equipment, whereas the spoiler fins acquire enough strength and resistance at the expense of more steel and broadside area. Secondly, the concept is also different from that of spoilers on planes or cars. When a large cruising ship is suddenly faced with an obstacle dead ahead, the captain will try their best to not only brake the ship but also change its heading and course angles as soon as possible, as only reducing speed will fail to stop such a heavy ship in time. The stopping stroke of a large ship weighing tens of thousands of tons usually reaches several nautical miles, but the density of traffic on the sea is much lower than that of road traffic, and adequately utilizing the course-changing performance of a ship is a more advisable measure for collision avoidance. Therefore, it is not enough to only discuss how much of a braking effect spoiler fins can provide when a ship travels in a straight line; instead, this procedure involves both braking and course changing.

Hydrodynamic force and moment are the sources of ship resistance and motion manipulation, so estimating the ship performance enhancement brought about by the spoiler fins using a hydrodynamic calculation, taking the new ship appendages into account, is necessary. Due to the indispensability of water viscosity when discussing a water flow problem around a ship, the field of computational fluid dynamics (CFD) and some representative solving tools have emerged and grown rapidly in recent decades. In past years, scholars have always focused on the navigating resistance of ships, including under different conditions, such as calm water, waves, drafts, and trims, and although few opinions have been proposed to enhance ship maneuverability depending on the types of ship appendages, these studies provided mature calculation methods for solving the problems of ship resistance. Simonsen et al. [1] investigated the KCS container ship in calm water and regular head seas using EFD and CFD, with the CFD study conducted using CFDSHIP-IOWA and STAR-CCM+, as well as the technologies of overset mesh and dynamic mesh. Islam et al. [2] provided some of the resistance and maneuverability characteristics of a MOERI KCS in calm water using a CFD solver based on the Reynolds-averaged Navier–Stokes method; overset structured mesh, including inner mesh and outer mesh, was used to conduct these simulations. Huang and Duan [3] performed a maneuvering simulation for a 1:45.7 model of KVLCC2 using Star-CCM+, and the VOF technique was adopted to capture the free surface of water. Yu et al. [4] organized verification and validation of the total resistance for a KCS model utilizing RANS and VOF. Wang and Wan [5] performed a CFD study of the ship-stopping maneuver via the overset grid technique, using the CFD solver naoe-FOAM-SJTU and a KVLCC1 model. Omweri et al. [6] proposed a rudder-attached thrust fin for a merchant ship, believing it can produce additional thrust for a ship; similar to the present study, CFD and RANS methods were used to predict the performance of the thrust fin, and the dynamic overset mesh and hole cutting process were applied to the numerical model. Sakamoto et al. [7] developed a viscous CFD estimation of rudder-related parameters in an MMG model for a ship with a flap rudder, another type of ship appendage; an overset structured mesh was applied to conduct CFD simulations, and then new parameters were concluded from the CFD results to update the MMG model; nevertheless, no concepts about spoiler or braking fins have been raised. Moreover, Ebrahimi et al. [8] investigated the effects of water and air fluids on the behavior of a planning catamaran using experimental and numerical methods. The fluid volume model was applied to simulate two-phase flow, and the SST $k-\omega$ turbulence model was used. Wang and Wan [9] reviewed the recent progress in CFD techniques for numerical solutions of typical complex viscous flows in ship and ocean engineering, discussing typical techniques, including VOF for a sharp interface, dynamic overset grid, high-efficiency Cartesian grid, GPU acceleration, and fluid–structure coupling. Martic et al. [10] studied the effects of the prismatic coefficient, longitudinal position of the center of buoyancy, and other parameters on added resistance for the KCS under different sea conditions, the calculations for which were differently performed using the 3D panel method instead of CFD methods. Han and Yang [11] conducted self-propulsion calculations on the KCS at a model scale, for which the overset grid method and VOF method were both used. Jin et al. [12] adopted a 3-DOF MMG model to predict the vessel’s trajectories under different sea conditions, and turning circle and zig-zag tests were solved using overset grids. There are still many other ship maneuvering investigations using the CFD method or model tests [13,14,15], and, in addition to spoiler fins, there are some other new-style ship appendages for which patents have been introduced in recent years [16,17,18,19,20].

In recent work, for a target structure with a size of hundreds of meters, such as a large ship, floating platform, or offshore wind turbine, many researchers have performed CFD calculations in a scale ratio because the fluid domain can be solved more easily in a small dimension, the results of which can then be converted into the full scale according to a similarity principle. This procedure is quite similar to that of a scaled model test in a water tank, but in numerical terms; however, there is a critical problem in data conversion with this method, called the scale effect, which causes inaccurate conversion. Sometimes, a small-scale model system cannot be designed to absolutely satisfy several similarity criteria with the full-scale system at the same time. For example, only Froude number similarity is satisfied in a ship resistance or maneuverability test; thus, the small-scale CFD simulation is not always a perfect solution. Moreover, in some references, only a scaled CFD model was simulated to obtain conclusions without a model-to-reality conversion, even if the scaled numerical model had been validated through performing scaled model tests in a water tank. Strictly speaking, it is difficult to exclude the influence of the scale effect on the analysis procedure. Full-scale simulations are still valuable if the computing resource is rich enough and the cost can also be accepted. Islam, Rahaman, Akimoto, and Islam [2] compared the EFD and CFD results for KCS, but the mesh used in the simulation was non-dimensional; actually, the Froude and Reynolds numbers used to make the comparison indicate that the data are from a scaled model test, and the CFD data were also obtained in the scale of the model test, but the real-ship resistance and resistance coefficient will be different from those of the model. Islam and Guedes Soares [21] predicted the resistance of a KRISO container ship at three different Froude numbers and drafts using RANS simulations, with the CFD and EFD tests in the study all performed in a model scale. Moreover, there are some other studies in which the scale effect was probably ignored in order to balance the calculation cost [1,5,6]; thus, if a new simulation method can be designed to simplify the calculation and reduce the threshold of costs to a lower level, the practicality of the full-scale simulation will significantly improve.

In order to address disturbed ship motion with spoiler fins directly, calculating the hydrodynamic force formed on the wet surfaces of the hull and fin in real time and solving the transient acceleration, velocity, and position of the ship through motion law in real time are both necessary. Dynamic mesh is applied to address the problem that a rigid body moves relative to its adjacent fluid domain. If the relative motion is known and defined, the surface mesh of the rigid body is an active dynamic mesh; if the relative motion is subject to the resultant fluid dynamic force summed from the body surfaces, it is a passive dynamic mesh that should be set as a 6-DOF (degree of freedom) mesh. This operation means that the body motion will be updated in every time step, according to the theorem of motion of the mass center. Additionally, because the motion is unpredictable before the CFD simulation, the best choice to ensure the mesh around the rigid body has enough density is to use overset mesh; regardless of where the body moves, the overset mesh can provide an adjacent dense mesh region following the movement of the body surfaces. Therefore, the amount of dense mesh in the near field and that of sparse mesh in the far field can be balanced well at different time steps.

Nevertheless, when the techniques of overset mesh and 6-DOF dynamic mesh are both adopted to predict a rigid body’s motion in a flow field, the calculation resources, such as CPUs, internal memory, and hard disks, are terribly occupied; worse, it is very difficult to achieve numerical iteration convergence if a too-large time step is chosen. Thus, the time cost to complete a motion simulation is considerably immense. Traditionally, when a ship maneuvering test is numerically simulated through the application of a CFD calculation, the far field domain is set as absolutely static and extensive enough to contain the entire range of ship movement. For a simulation in the full scale of a large ship’s length, hundreds of meters or a few nautical miles, it is possible to consume several weeks to obtain a prediction of only a few seconds; in order to avoid these conditions, a reasonable CFD simulation method is necessary for simplification of the fluid domain to be solved, and then to reduce the number of mesh elements.

In the current study, the novel concept of spoiler fins for modern large ships is proposed. In order to assess their effectiveness in enhancing ship maneuverability, a KRISO container ship (KCS) is selected to carry a pair of spoiler fins. Subsequently, a simplified simulation approach for saving the calculation resource is designed for ship collision avoidance conditions, and a full-scale numerical model, including the ship hull, fin, and fluid field domain, is established. Transient-state hydrodynamic forces are calculated during collision avoidance maneuvers using the CFD method, and the pressure and velocity contours around the ship are demonstrated. Furthermore, the ship motion trajectories under different initial ship speeds are simulated and predicted through the adoption of an overset mesh and 6-DOF dynamic mesh techniques. Eventually, the improved course-changing performance, dependent on the spoiler fins, is validated. Additionally, the proposed simulation method is proven to have practical applications in solving continuous ship manipulations in full scale.

2. KRISO Container Ship (KCS)

The KRISO container ship is designed by KRISO (now MOERI) in Korea; it is a typical modern container ship with a bulbous bow, a length of 230 m, and a full load displacement of 53,000 t. Thus far, many research institutions have investigated its hydrodynamic performance using EFD (experimental fluid dynamics) and CFD, including SIMMAN (Workshop on Verification and Validation of Ship Maneuvering Simulation Methods) and NMRI (National Maritime Research Institute). Thus, it is particularly suitable to be remodeled and validated in the current numerical analysis. An accurate naked hull is important to obtaining the high-fidelity effect of the spoiler fins and, due to the higher design speed, container ships are more suitable to carry the spoiler fins proposed in the present study than other types of large cargo ships, as the higher ship speed causes stronger demands on braking and course changing in emergency situations. The parameters of the hull are summarized in

Table 1. Parameters of the hull and spoiler fins.

Hull Parameters	Unit	Magnitude
Length between perpendiculars	m	230.0
Maximum beam of waterline	m	32.2
Depth	m	19.0
Draft	m	10.8
Displacement volume	m3	52,030
Ship mass	kg	53,330,750
Moment of inertia	kg·m2	1.763 × 1011
Service speed	kn	24.0
Service speed	m/s	12.35
Froude number (Fn) at service speed	-	0.260
Moment of Inertia (KZZ/LPP)	-	0.25
Spoiler Fin Parameters	Unit	Magnitude
Thickness	mm	30
Projected area in normal direction	m2	66.31
Maximum spreading angle	°	30

, which was obtained from the T2015 Workshop (Workshop on CFD in Ship Hydrodynamics, hold by NMRI) [22]. The geometry of the KCS modeled in the present study is shown in Figure 3.

3. Spoiler Fins

Drawing on the designs of airplane and sports car spoilers, the proposed spoiler fin was arranged on each side of the ship hull with bilateral symmetry. Due to the ship’s plump parallel middle body, the fins were deployed at the midship, with a small offset toward the stern, thereby allowing the fins to be absolutely retracted to lean fully against the original hull shape when the ship navigates normally; it is also easy to find a cabin in which to place fin actuator devices, e.g., hydraulic pumps and telescopic brace rods. When spreading the fins to brake the ship, the action center of the additional resistance will fall back to the ship’s center of gravity, so its kinetic stability can be maintained well. In terms of the actual navigation situation, the captain can choose to spread both or one of the fins at different angles in order to brake or change the course to different degrees. The configuration and dimensions of the spoiler fins are illustrated in Figure 4. Both the retracted and spread fins on the hull are demonstrated in Figure 5.

4. Numerical Model

Numerical simulation is mainly applied to quantitatively study the ship performance enhancement caused by appending spoiler fins. A CFD model is necessary for considering the viscosity and turbulence of water, two matters that are of great concern with regard to correctly handling the flow resistance problem around a ship. Subsequently, the drag forces on the different parts of the ship will directly affect how the ship moves in water. In order to validate the simulation results, some resistance calculations for the ship’s hull and spoiler fins were completed using the same modeling and calculation settings before the ship’s course-changing motion predictions were carried out. Finally, the acquired hull resistance values fit well with the model test results published by T2015 Workshop and SIMMAN 2008. Directed against the specific course-changing prediction of the ship, a new style of simulation method was presented and the CFD model was generated in full scale.

4.1. Assumptions

To simplify the hydrodynamic and motion problems, the following assumptions are introduced into the current study:

• The simulations are only performed under calm sea conditions, and the air resistance on the superstructures is disregarded;
• The free surface effect of water is neglected to avoid solving a multiphase flow with water and air, and the model stacking method is used to set the water surface as a symmetric boundary;
• The heave, roll, and pitch motions are limited, and only 3-DOF in-plane motions are considered;
• The structural strength and stiffness of the spoiler fins and their actuating device are supposed to be strong enough to avoid material damage or large deformations under the hydrodynamic loads;
• Only the effect of the spoiler fin is taken into account, and the rudder effect on course changing is not considered;
• The fin is spread very slowly so that the transient-state response during the action can be ignored, and the obstacle that the ship needs to avoid is stationary on the sea.

4.2. Flow Fundamental Equations and Turbulence Model

The hydrodynamic force on a ship invariably comes from a surface integration of pressure distribution on all of its wet surfaces. In the fluid field around a ship, the velocity and pressure at each coordinate should be satisfied with the flow fundamental equations and boundary conditions of time and space. Previous studies have shown, in the scale of a real ship, that the water flowing around the hull is generally in a turbulent state; based on this situation, Reynolds-averaged Navier–Stokes (RANS) equations are applied to solve the fluid field. The conservation equations for mass and momentum obtained with a time average are shown in Equation (1) and Equation (2), respectively.

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

(1)

where $\rho$ is the fluid density, $t$ is the time variable, $x_i$ is the coordinate component, and $u_i$ is the velocity component. The equation is valid for homogeneous, incompressible flows. The mass conservation equation is also called the continuity equation. For viscous, incompressible flows (e.g., the water in the present problem), the momentum conservation equations can be written as follows.

$$\begin{array}{l}{\displaystyle \frac{\partial }{\partial t}}(\rho u_i)+{\displaystyle \frac{\partial }{\partial x_j}}(\rho u_i{u}_j)=-{\displaystyle \frac{\partial p}{\partial x_i}}\\ +{\displaystyle \frac{\partial }{\partial x_j}}[\mu ({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}-{\displaystyle \frac{2}{3}}{\delta }_{ij}{\displaystyle \frac{\partial u_l}{\partial x_l}})]+{\displaystyle \frac{\partial }{\partial x_j}}(-\rho \overline{u_i^{\prime }{u}_j^{\prime }})\end{array}$$

(2)

where $p$ is static pressure, and $\mu$ indicates the molecular viscosity of the fluid. ${\delta }_{ij}$ is the component of a unit tensor, $\overline{u_i^{\prime }}$ and $\overline{u_j^{\prime }}$ are the averaged fluctuating velocities, and $-\rho \overline{u_i^{\prime }{u}_j^{\prime }}$ is the term of Reynolds stresses. Furthermore, a standard $k$-$\epsilon$ turbulence model was adopted to simulate the turbulence flow. The transport equations for the model are expressed in Equation (3) [23].

$$\left\{\begin{array}{l}{\displaystyle \frac{\partial }{\partial t}}(\rho k)+{\displaystyle \frac{\partial }{\partial x_i}}(\rho k{u}_i)\\ \hspace{1em}={\displaystyle \frac{\partial }{\partial x_j}}[(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}){\displaystyle \frac{\partial k}{\partial x_j}}]+G_k+G_b-\rho \epsilon \\ \hspace{1em}\\ {\displaystyle \frac{\partial }{\partial t}}(\rho \epsilon )+{\displaystyle \frac{\partial }{\partial x_i}}(\rho \epsilon u_i)\\ \hspace{1em}={\displaystyle \frac{\partial }{\partial x_j}}[(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}){\displaystyle \frac{\partial \epsilon }{\partial x_j}}]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}(G_k+C_{3\epsilon }{G}_b)-C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}\end{array}\right.$$

(3)

where $k$ is the turbulence kinetic energy, $\epsilon$ is the dissipation rate, $x_i$ is the position component in the $i$-th direction, $x_j$ is the position component in the $j$-th direction, $u_i$ is the velocity component in the $i$-th direction, ${\mu }_t$ is the turbulent (or eddy) viscosity. ${\sigma }_k$ and ${\sigma }_{\epsilon }$ are the turbulent Prandtl numbers for $k$ and $\epsilon$, $G_k$ represents the generation of turbulence kinetic energy due to the mean velocity gradients, and $G_b$ represents the generation of turbulence kinetic energy due to buoyancy. $C_{1\epsilon }$, $C_{2\epsilon }$, and $C_{3\epsilon }$ are model constants.

4.3. Simulation Method

In the present study, the course-changing performance of the ship is emphasized rather than the turning performance in a whole circle. The former focuses on the initial phase of ship turning, and the response speeds of decelerating and course changing are the main indicators to be researched. For a collision problem, the prediction duration after the point of applying the turning maneuver will be long enough if, at the end of the simulation, the ship entirely avoids a head-on obstacle and there is no longer a collision risk, thereby significantly reducing the size and number of time steps in the transient-state simulation.

Inspired by the concepts of infinity pools and flow boarding, a 6-DOF dynamic mesh for the ship and its near field was embedded in a forward-moving background mesh of the far field. The near field was set over the far field, thus creating an overset mesh. Due to equivalent relative motion, the water in the background mesh was set to flow from the ship’s bow to stern. The water flow velocity was selected as the ship’s initial speed in straight sailing. Originally, it was necessary to leave a big enough space in the far field for the ship to complete the stopping stroke. Now, on the other hand, only a much smaller downstream space is required, as the ship will gradually move backward relative to the stationary background, and the mesh’s motion velocity is just a difference value between the flow velocity and the real-time ship speed, which further increases the value, incrementally, from zero; therefore, the fluid domain dimensions have been compressed effectively using this method. Finally, the motion procedure was converted into a static water environment in terms of Galilean transformation, whereby, if a current emerges on the sea, it can be taken into account under this method through introducing an initial drift angle for the hull and adding a correction with the current speed into the Galilean transformation; however, a wave or wind is hard to simulate under the proposed fluid domain configuration.

Although a rolling motion will generally occur due to the inertia and centrifugal force of superstructures when a ship turns to port or starboard, only three DOFs were taken into consideration, including the surge, sway, and yaw motions. The mass of the ship and the rotary inertia of yawing were set to the near field dynamic mesh. Only the hydrodynamic pressures on the wet surfaces of the hull and the spoiler fin affect the mesh’s motion, and the remaining volume of mesh simply follows the motion passively. The other three DOFs of the 6-DOF dynamic mesh were permanently locked. To determine the difficulty and costs of solving the calculation, the free surface of water was neglected to avoid building a complicated VOF (Volume of Fluid) model, and a symmetric boundary condition was set to a stationary water surface in terms of the ship model stacking method. At the beginning of the simulation procedure, the near field mesh had to be set as stationary to initialize a steady flow field of a ship sailing straight at different speeds. Once the stationary condition was unlocked, the ship’s hull and spoiler fin started to appear as translations and rotations under hydrodynamic forces and moments. It is assumed that the fin was spread slowly, and the transient hydrodynamic response during the spreading of the fin was ignored in the present research. The overset 6-DOF dynamic mesh used in this study is shown in Figure 6. In order to ensure the convergence and accuracy of solving iterations, denser mesh and the boundary layer mesh were generated around the wet surfaces, including the hull and the fin, especially at the downstream region of the fin, because the fin strongly disturbs the normal flow of water near the ship’s sides. Specifically, the element size of the hull surface is 2.0 m, the element size of the fin surface is 0.2 m, the element size of the far field is 5.0 m, and the element size at the downstream region of the fin is 0.5 m. The CFD analysis procedure is summarized in a sketch diagram, shown in Figure 7.

4.4. Full-Scale CFD Model

To avoid the influence of the scale effect, which probably results in inaccurate simulation results, a full-scale CFD model was generated in a cuboid with a length of 1000 m, a width of 600 m, and a water depth of 100 m. The length of the ship was 230 m, and the distance between the inlet of fluid domain and the center of gravity of the ship was 400 m. The length direction was defined as the X-axis, the width direction was defined as the Y-axis, and the depth direction was defined as the Z-axis. The full-scale fluid domain is demonstrated in Figure 8. In the figure, the X-coordinates at different positions are represented by different colors.

5. CFD Model Validation

Before the course-changing performance of the fin-spread ship was investigated, the simple braking performances of the fin-retracted and fin-spread ships were predicted, as compared with the published data of previous ship model tests. Additionally, a test of mesh independence was completed to prove that the mesh used to analyze the present problem was refined adequately.

5.1. Resistance of the Naked Hull

If the resistance magnitude of the naked hull can be obtained correctly, it can prove the mesh and the model settings are appropriate for solving the hydrodynamic problem of the ship. Going a step further, if the geometry of the model is replaced with the fin-spread hull, while all other settings are kept unchanged, the updated results will also be basically reliable. Thus, a numerical resistance in the full scale was checked for consistency with those obtained from the model tests in a towing tank. The full-scale model and results for the naked hull are exhibited in Figure 9. To simplify the CFD calculations, the model stacking method was used in the same way. Although the wave-making resistance component is difficult to consider using this method, the results are still valuable because the proportion of this component is always relatively low for a large, low-speed merchant ship. In terms of the total resistance coefficient measured from the scaled model tests—published by the T2015 Workshop—the converted resistance of the real ship at 10.0 m/s is about 1000 kN, by using the classic conversion of Froude method or 3-dimension method. This result is very close to the values calculated from the current CFD numerical model. The specific data of resistance conversion between scaled EFD and full-scale CFD are listed in

Table 2. Contrasting resistance values between EFD and CFD.

EFD Data from the Scaled Model [24]		Converted EFD Data into Full Scale		CFD Data from the Full-Scale Model
$L_{ppm}$	7.279 m	$L_{pp}^{\prime }$	230.0 m	$L_{pp}$	230.0 m
$V_m$	1.779 m/s	$V^{\prime }$	10.0 m/s	$V$	10.0 m/s
$F{r}_m$	0.211	$F{r}^{\prime }$	0.211	$Fr$	0.211
$C_{fm}$	2.99 × 10−3	$C_f^{\prime }$	1.42 × 10−3	-	-
$C_{tm}$	3.47 × 10−3	$C_t^{\prime }$	2.19 × 10−3 *	-	-
			2.04 × 10−3 **
$R_{tm}$	52.42 N	$R_t^{\prime }$	1045 kN *	$R_t$	907 kN
			971 kN **

*: Froude method; **: 3-dimension method.

.

5.2. Resistance of the Hull with the Fins Spread

In addition to the parameters of calculation—calibrated using model tests—the resistance increment for straight braking after the fins are spread is also discussed, as shown in Figure 10. In addition, a parameter sensitivity analysis regarding different ship speeds and fin spread angles is promoted. The series of resistances are demonstrated in Figure 11, proving that the braking effect provided by the spoiler fins is outstanding, and if the fins are spread entirely, the stopping stroke based on ship inertia is approximately 200 m shorter than that of the origin hull at 2 min after the test begins. The distance increases to 600 m in the following 2 min. As the results also show, the present CFD mesh parameters and model settings have good universality to wide work conditions for the spoiler fins.

5.3. Mesh Independence Test

For the sake of balancing the numerical convergence and the calculation resource occupancy, a greater number of mesh elements does not always mean better performance. Actually, the precision shows very limited improvement after the element number reaches a certain magnitude. Therefore, a mesh independence test was implemented as the mesh was generated in higher and higher density. The total element numbers were 4.41, 4.58, 5.41, 6.05, 8.59, and 10.90 million, from low to high, as shown in Figure 12. As the element number increases, the resistance results gradually converge at 3040 kN. The element number selected to perform the present study was 5.41 million, and the corresponding resistance was 3120 kN. To ensure this calculation was carried out with good efficiency, its precision can be accepted to a certain extent, the convergence procedure of which is plotted in Figure 13.

6. Results and Discussions

The large ships with a single propeller are generally inclined to turn right during an emergency ship stopping even though maintaining a 0° rudder angle because the single propeller is ordinarily designed as right-handed forward rotation (clockwise if observed from stern to bow), and when decelerating and reversing the propeller to brake the ship, a lateral hydrodynamic force toward port (left) will be formed on the propeller, and then the ship will yaw and turn to starboard, which is also why turning starboard is recommended in a head-on situation with two ships, according to the collision regulation. Therefore, in the present research, braking and course-changing procedures of the KCS turning starboard with the help of the starboard fin are predicted and analyzed. In addition, the current study discusses the situation of emergency ship stopping, so only the maximum spreading angle is considered here. To simplify the problem, only different initial straight speeds of the ship are taken into account, and the propeller and rudder effects are neglected in the simulation because they are the original devices to manipulate the ship. During an emergency stopping in tradition, the captain should first try to stop the propeller rotation, and then the rudder effect is limited very much when no accelerated discharge current of the propeller flows around the rudder.

6.1. Forces and Moments of Turning Ship

The hydrodynamic and motion time histories under five initial ship speeds were simulated with the CFD method, including 12.35 (24 kn), 10.0, 7.5, 5.0, and 2.5 m/s. The velocity and pressure contours were plotted once every second for the five time histories. In every contour, the velocity magnitude or static pressure distributed on the water surface and the ship hull were displayed in different colors. Each time history ended at the moment that the lateral displacement of the ship in the Y-direction exceeded 175 m; thus, the lower the initial speed, the longer the corresponding time history. For a high ship speed (actually a high inlet velocity), it was better to select a smaller time step in order to ensure computational stability. Conversely, for a low ship speed, slightly larger time steps can be chosen because it is generally easy to keep a time integration running normally at a low inlet velocity; additionally, selecting a larger time step will reduce the required number of time steps. Moreover, the information contained in the CFD results is abundant; in order to demonstrate these procedures briefly, the contours at the initial speeds of 10.0 m/s and 5.0 m/s have been bypassed here. The other three time histories are also exhibited in different time intervals. Owing to the continuous change in the flow field between different time histories or different snapshots in one time history, the omitted contours can also be inferred to link up the overall simulation. Finally, the calculation and exhibition parameters set to the different time histories are summarized in

Table 3. Parameters set to different time histories.

	12.35 m/s	10.0 m/s	7.5 m/s	5.0 m/s	2.5 m/s
Duration (s)	127.5	152.5	194	278.5	540.5
Time Step (s)	0.25	0.25	0.5	0.5	0.5
Number of Time Steps	511	611	389	558	1082
Number of Exhibitions	6	-	8	-	6
The First Time Point (s) *	5	-	5	-	5
Time Interval of Exhibition (s)	25	-	25	-	100
The Last Time Point (s)	130	-	180	-	505

*: the i-th second after the starboard fin was spread.

. The beginning time (0.0 s) of all of the predicted procedures was recorded at the moment the fin was spread to the maximum angle. The contours at 12.35 m/s, 7.5 m/s, and 2.5 m/s are shown in Figure 14, Figure 15 and Figure 16, respectively. The sequence of pictures is from left to right and top to bottom. The velocity contours are shown in orange on the left in each group, and the global position of the ship in the whole fluid domain can be observed in the velocity contour. The pressure contours are shown in green on the right in each group. For ease of observing the water pressure distribution around the ship in high definition, the pressure contour is zoomed in on the near field of the ship.

In every time history, the fin-spread ship was initially at the origin point (0,0) in the X and Y coordinates. In terms of the principle of relative motion, if the ship keeps still in the fluid domain the entire time, the ship speed in the real situation is the same as the current inlet velocity. Actually, the ship’s speed becomes slower over time because the resistance in the X-direction decelerates the ship, so it looks as if the ship is moving gradually to the downstream fluid domain. Additionally, the unbalanced force on the starboard fin forms a turning ship moment, which turns the hull toward the starboard side. It can be found in the pressure contours that there is an obvious region of high pressure (red color) in front of the spread fin, and there are regions of low pressure (blue color) behind and inside the fin. The force on the fin’s front is backward and larger, while the force on the fin’s back is forward and smaller. As a result, the force on the fin is backward and only present on the starboard side, so the hull begins to turn starboard. When the hull has turned by a heading angle, the hull can be regarded as a hull rudder or an airfoil. On the basis of airfoil theory, a lift force (crossing the incoming flow and forward-to-starboard here) and a drag force (along the incoming flow) both increase as the attack angle of the hull rudder increases; moreover, its force increases more quickly. These two forces comprise centripetal force that causes the ship to move in a clockwise circular motion, also to starboard. It can be seen in pressure contours that the pressure on the port side is generally higher than that on the starboard side when the hull has an angle of attack. If the velocity contours are considered, the water flow through the starboard fin successively experiences phases of speed reduction (yellow color), speed increase (red color), and speed reduction with turbulence development (blue, green, and yellow colors). Furthermore, they do not only reveal the water velocity but also indicate the hull motion. Due to water viscosity, the water that sticks to the hull’s surface is always moving with the hull, so the water velocity as distributed on the hull is actually representative of the instantaneous velocities of different points on the rigid body. At the beginning of the simulations, the colors on the hull were all dark blue, indicating that the hull was still in the current reference frame. Thereafter, the dark blue begins to turn to light blue, which implies that the hull starts to move translationally to the downstream. As the color close to the bow of the ship becomes lighter and lighter, the hull starts to turn starboard. The lower the initial ship speed, the flatter the velocity and the pressure differences.

Based on the above pressure distributions around the wet surfaces of the ship, the specific force and moment in real time were calculated using integrations. The hydrodynamic force and moment time histories are shown in Figure 17 under different initial speeds. The forces in the X-direction are expressed in full curves, the forces in the Y-direction are shown in dotted curves, and the moments of the ship turning around the Z-axis are represented by double-dotted curves. Here, the forward direction of the Y force is set toward the port side of the ship in order to avoid overlapping curves. The forward direction of the X force is set toward the stern. The forward direction of the turning moments is set clockwise (looking down from the top). It can be observed that the Y force on the ship actually pushes it to the port side, rather than starboard, in the first several seconds. Similar to the rudder effect of the ship, when turning the full right rudder on a straight-running ship, the hull first moves to the port side slightly and then turns and moves to starboard. The phenomenon of moving in the opposite direction is called a kick in the turning circle of a ship. When turning the right rudder, the lift force on the rudder occurs toward the port side, as, before the hull begins to rotate starboard, the opposite lateral force pushes the hull to the port side. In our study on the fins, this phenomenon can also be found in the first pressure contour of every time history, as there is obviously a high-pressure area in the front of the spread fin and on the starboard side of the hull, explaining how the opposite force forms. As a result of their global orientation, the directions of the X and Y forces do not rotate, even though the ship has a yawing motion. Firstly, the larger the initial speed is, the higher the order of magnitude of the force or moment. Secondly, the X force moves downward as the Y force rises upward in the first one-third of the duration because, during the period in which the spread fin, originally a bulge on the hull, begins to be hidden gradually behind the hull, the resistance in the X-direction reduces due to the fairing effect of the hull, while the lift force in the Y-direction increases because of the widening attack angle. This phenomenon is slightly different from the ordinary airfoil theory. The attack angle of the hull where the drag force starts to increase again is about 5°, and the moment curves gradually climb upward and then suddenly drop downward. Thus, different from the regular turning circle of the ship, wherein the propeller and rudder can provide a moment of continuous ship turning, the course-changing performance of the fin is mainly concentrated in the early stage of turning. As the ship turns off from its original straight route, the turning effect of the fin begins to fade, and the ship continues to run in a new deflected course, but this effect is still enough to avoid some emergencies. At the end of the moment curves, the values even become negative, preventing the ship from turning, and the tendency to continue turning slows down.

6.2. Real-Time Ship Motions

Under the above-mentioned forces and moments, the fin-spread ship will have planar motions along the water surface. All of the ship’s motions are described on the bases of its center of gravity and heading angle. Due to the boundary conditions of relative motion, the ship’s motion in the fluid domain can be converted into a still-water region through applying Galilean transformation. Because these two systems are both inertial reference systems, the actual position in the X-direction, $X$, after a certain period of time, $t$, should be expressed as $X=V_0\cdot t+X_r$. Here, $X_r$ is the relative X-position in the fluid domain. The actual transverse position and yaw angle are the same as those in the fluid domain. In the field of ship navigation, X indicates the advance of the ship, and Y represents its transfer when the heading angle of the ship has changed by 90°. In the present study, to describe the procedures easily, these concepts have been extended to real-time situations, even though the heading angle could have any value.

The real-time ship positions under different initial speeds are plotted in Figure 18; however, due to the different proportions of the X- and Y-axes, the curves cannot correctly reflect the trajectory shapes in real space, so a graph with the true proportion of the X–Y directions is also shown in Figure 19, even though the curves and data points are not displayed so clearly, as only the first data point is displayed with a label every 10 s. The higher the ship’s speed, the longer the distance the ship will move during the same time interval; thus, there are scattered labeled points on the curve of 12.35 m/s and concentrated ones on the curve of 2.5 m/s. An outline of the fin-spread ship is shown in Figure 19 for ease of understanding of the maximum occupied region of the hull and fin. In the figures, the faster the initial ship speed, the lower the curvature of the trajectory, but the shorter the consumed time at the same level of transfer. Taking an example of a 175 m transfer, the advance at 12.35 m/s is about 180 m longer than that at 2.5 m/s, and it is about 0.78 times the ship’s length. The maximum advance at 12.35 m/s is nearly 1200 m, which corresponds to 0.65 nautical miles and 5.22 times the ship’s length.

The figures of the ship position cannot express the heading angle and ship velocity; thus, in order to contrast these variables, a vector diagram is provided in Figure 20, with five time histories placed side by side in sequence, from 12.35 m/s (left) to 2.5 m/s (right). Similarly, the arrows are also displayed every 10 s, and the real-time states represented by these displayed arrows are treated as sampling points. In the field of ship navigation, the course angle is different from the heading angle; here, due north is set at the top of every figure, the orientation to due north is set as 0°, and a clockwise rotation is positive. If the ship moves on its original straight route the entire time, the heading angle and course angle are both at zero degrees, where the heading angle represents the orientation of the bow of a ship. Because the ship does not always move relative to water in its heading direction—as perhaps the ship is turning or there is crossing wind or a current—the velocity vector at the center of gravity of a ship is not always in the heading direction. The orientation of the velocity vector is called the course angle. The included angle between the heading and course directions is known as the drift angle. In the figure, every sampling point features two arrows where the red arrow represents the real-time heading angle, and the length of the arrow is changeless as time goes by, while the blue arrow indicates the real-time course angle, and the length of the arrow is variable to express different ship velocities. As time goes by, the arrows of a pair of angles separate by a drift angle. In the time span of the present study, the drift angle becomes larger and larger in nearly every time history. The maximum drift angle in different time histories changes from 10.9° to 11.5°, and the slower the initial speed, the larger the maximum drift angle. The course angle is always smaller than the corresponding heading angle. Therefore, even if an obstacle is observed at the front and port side (based on the heading direction) of a ship when it is turning starboard, there will still be a risk of a collision, as the ship’s stern will probably sweep against the obstacle. It can be observed that the length of the velocity arrow (in blue) becomes shorter and shorter, revealing that the ship speed reduces as the course changes. The detailed procedures of speed changing can be obtained from Figure 21, Figure 22, Figure 23, Figure 24 and Figure 25.

6.3. Emergency Collision Avoidance

It is assumed that a stationary obstacle is suddenly seen directly ahead by the captain or other crew of the ship when the ship is moving straight in a calm sea. Here, the obstacle can be regarded as a point on the water surface. In this situation, the captain immediately spreads the starboard spoiler fin to execute emergency collision avoidance. Hence, the criterion of a collision occurring should be selected as the obstacle distance to the center of gravity of the ship at 0.0 s is less than a certain threshold value. More widely, if the obstacle is detected ahead and slightly toward the port or slightly farther on the starboard side, the collision will never happen, as long as the obstacle position at 0.0 s does not fall into the stern boundary trajectory of the ship. The stern boundary trajectory shows the outermost margin of the fin-spread ship during its turn to starboard. Specifically, due to the drift angle of the turning ship, the boundary curve forms as the port-side tip of the stern transom plate sweeps through the space above the water surface, a condition which is shown in Figure 26. The horizontal coordinates of the tip point are (−121.0, −16.1), fixed on the hull. The spatial location of the point can be obtained using axis transformation and the Euler rotation matrix as the ship moves along the water surface. The right side of this trajectory can be regarded as the hull sweeping range, illustrated in Figure 21, Figure 22, Figure 23, Figure 24 and Figure 25 under different initial speeds, where the time histories of ship velocity and yaw rate are also shown. The parameters extracted from the figures are listed in

Table 4. Parameters of collision avoidance under different speeds.

	12.35 m/s	10.0 m/s	7.5 m/s	5.0 m/s	2.5 m/s
Threshold Distance (m)	874.80	845.78	797.51	758.96	725.00
Threshold Distance (nautical mile)	0.47	0.46	0.43	0.41	0.39
Remaining Time to Collision (s)	60.96	72.38	90.07	127.39	241.20
Remaining Time to Sweep Over (s)	115	133.75	163.5	226	418.5
Maximum Kick (m)	−21.54	−21.87	−22.29	−22.74	−23.25

. The threshold distance can be measured from the intersection point between the trajectory curve and the original straight route line to the starting point. The threshold distances are from 0.39 to 0.47 nautical miles, and the difference is about 150 m (0.65 times of ship length). Generally, the distance range of visibility on the sea corresponds to a bad visibility level under fog or moderate snow. Therefore, the course-changing performance provided by the fin is handsome. The Remaining Time to Collision indicates that a ship collision would be inevitable if no measures are taken. The Remaining Time to Sweep Over indicates that the stern of the ship would simply sweep over the obstacle and successfully avoid a collision if the fin is spread and the engine is stopped immediately. The maximum kicks were also found under different speed conditions, suggesting that the lower the ship’s speed, the larger the kick.

The ship’s speed in Figure 21, Figure 22, Figure 23, Figure 24 and Figure 25 refers to the magnitude of the resultant velocity on the horizon. At an initial speed of 12.35 m/s, the final speed is 7.24 m/s, and there is a decrease of 41.4%. At 10.0 m/s, the final speed reduces to 5.85 m/s, a decrease of 41.5%. At 7.5 m/s, the final speed becomes 4.42 m/s, a decrease of 41.1%. At 5.0 m/s, the final speed reduces to 2.93 m/s, a decrease of 41.4%. Under 2.5 m/s, the final speed is 1.44 m/s, a decrease of 42.4%. It can be concluded that the speed decrease will be a near-constant ratio if the error in numerical calculation has been eliminated. Due to the constant ratio, the faster the ship runs initially, the larger the final decrease. The curves of the yaw rate are similar S shapes. The yaw rate rises slowly at the beginning, and then it starts to increase more quickly, and finally, it shows a very small decrease after the peak value. It can be inferred that the yaw rate will steadily decrease after the peak value, showing a tendency to slow down the ship-turning motion. From the initial speeds of 12.35 m/s to 2.5 m/s, the peak values of the yaw rate are 0.71°/s, 0.58°/s, 0.44°/s, 0.30°/s, and 0.15°/s respectively. In summary, the faster the ship runs initially, the larger the final peaked yaw rate.

6.4. Course-Changing Performance Enhancement

In this study, the course-changing performance was only evaluated for the fin-spread hull, but the function of the rudder was neglected due to the extensive number of already-existing numerical calculations. Although a fully spread spoiler fin can induce an apparent course change on its own, under emergency conditions, the fin effect added to the original rudder effect is the best choice to avoid a ship collision. Thus, the fin provides an extra performance enhancement to the rudder. Based on the original turning circle of the KCS, the enhancement can be estimated quantitatively by contrasting the aforementioned motion histories with the initial phase of the turning circle. Here, some previous studies of the KCS turning circle are introduced at rudder angles of ±35°, at its design speed of 24 kn (12.35 m/s) [25]. x indicates the advance of the ship, and y represents the transfer of it. The blue full curve on the right side of the chart shows that, when the advance is 600 m, the transfer is about 100 m, and when the advance is 800 m, the transfer is about 250 m. Therefore, the transfer is slightly less than 175 m when the advance is 700 m. As mentioned previously, when the fin-spread hull has a transfer of 175 m, its advance is 1200 m. If the advance of the fin-spread hull approaches 1400 m, the fin effect is 50% of the rudder effect; however, the actual value is only 1200 m, so the fin effect is equivalent to 58.3% of the rudder effect. Furthermore, when superposing these two effects of course changing, it can be estimated that their combined effects would reduce the advance further to 442 m, which is by more than another ship’s length.

It is noteworthy that the initial phase of a ship-turning circle is not fully equivalent to emergency collision avoidance. When a ship steers to form a whole turning circle, the rotation of the engine and propeller will not stop but remain unchanged; of course, the propeller must remain in motion in order to promote a good rudder effect. With regard to the KCS, the rudder is arranged behind the propeller at the stern, as shown in Figure 27, because the propeller can accelerate its discharge current, and the rudder effect under the rudder angle will be significantly enhanced when it subsequently flows through the rudder; however, an inevitable contradiction appears in this situation. If the ship is going to turn for collision avoidance, braking and course changing will both have contributions, in that braking can prolong the response time for the crew and the ship itself, but the propeller should be stopped, while course changing allows the ship to dodge the obstacle in time, but the propeller should be maintained. Even when it reaches the maximum rudder angle, the propeller still provides a propulsive force to prevent the ship from decelerating. Thus, it is not highly efficient to avoid a collision by depending only on the rudder. If the propeller is decelerated and stopped at the beginning, the trajectory is unlikely to form in such a small radius. Even when reversing the propeller, the braking effect will occur, but the rudder effect will worsen and become unstable due to the suction current of the propeller flowing around the rudder. Different from ship turning with the rudder, the spoiler fins can manipulate the ship independently to brake or turn without the propeller or rudder; thus, especially when the ship is running at high speed, the fins’ effect will be superior because of the high-speed flow through them.

Finally, when considering the future of this feature, there are three aspects of the fin that can be optimized to realize better performance. The first is the dimensions of the fin, and the second one is the maximum spreading angle. The larger the fin is, the better braking and course-changing performance the ship will acquire. On the other hand, the larger the angle the fin is spread in, the higher the hydrodynamic loads acted on it will be. Thus, the spreading angle cannot be increased endlessly because of the structural strength of the fin, brace rod, and actuators. Otherwise, the spoiler fins would perhaps become deformed or damaged under high-speed flows. The last aspect is the longitudinal position of the fins on the hull. Theoretically, the closer to the stern the fins are located, the longer the force arm of the ship-turning moment. It is easier for the ship to turn its bow when the same hydrodynamic lateral force is placed only on one fin, but the actual situation is that the structures of the fins still need enough space and strong hull structure in order to remain in place and stable on the ship. Currently, locating the fins at the midship, with a small offset toward the stern, seems to be an ideal choice.

7. Summary and Conclusions

In this study, a novel spoiler fin is proposed and designed for large ships. A case analysis is performed to evaluate the course-changing performance of a fin-spread KCS. To better reflect the real situation, full-scale CFD simulations are conducted through the adoption of overset mesh and 6-DOF dynamic mesh technologies. The real-time motions and trajectories during the initial phase of a ship’s turning circle are predicted under different ship speeds. The velocity and pressure contours around the fin-spread ship are demonstrated, and the curves and vectors are shown in figures to specifically describe the force–motion relationships in these time histories. Finally, the course-changing performance of the proposed fins in emergency collision avoidance is also discussed. Although equipping an existing large ship with spoiler fins will perhaps increase its design, manufacture, and maintenance costs, it is proven in the present study that they can significantly enhance its course-changing and collision avoidance performances, as well as improve the ship’s maneuverability and navigation safety. For combat vessels, spoiler fins can undoubtedly strengthen their survivability. For merchant ships, they can also raise the upper speed limits in ports, anchorage grounds, and narrow channels, raising their shipping efficiency. From the results of our simulations, the following conclusions can be drawn:

(1)

The proposed spoiler fins can provide a significant course-changing effect for an original large ship when only one fin is spread to its maximum. In the ship-turning prediction under a high initial speed of 24 kn design speed, the transfer is 175.43 m when the advance of the ship reaches 1208.77 m, and the transfer–advance ratio reaches 14.5%. Under a very low initial speed of about 5 kn, the transfer is 175.18 m when the advance reaches 1021.46 m, and the transfer–advance ratio becomes 17.15%. The fin effect on a turning ship amounts to 58.3% of the rudder effect. If superposing the fin effect onto the original rudder effect, the course-changing performance of the ship is significantly enhanced so that the advance can be reduced to less than 500 m under the same conditions. Even when only depending on the fins, the course-changing performance of the ship is also adequate to avoid an obstacle dead ahead under the poor visibility of fog or moderate snow.

(2)

According to the additional longitudinal and lateral forces when the spoiler fin is spread, the fin location on the ship is an important factor through which to improve its course-changing performance. On the one hand, the longitudinal force of the fin is mainly used to brake the ship; if the action line of the force is far away from the midline plane of the hull, a turning ship moment forms, but the available ship breadth is always limited. On the other hand, the lateral force of the fin is used to push the hull aside or turn the ship heading; thus, trying to situate the fins as far to the rear of the ship as possible will enlarge the force arm of the ship-turning moment, so as to amplify its course-changing effect, but in an extreme of this placement, when the fin is situated at the stern, its purpose changes to an equivalent rudder. Ultimately, an available location for the fins is also subject to cabin capacity and the structural strength of the hull.

(3)

Under the design speed of 24 kn, the maximum force in the Y-direction reaches 3184 kN, and the maximum moment of ship turning reaches 28,459 kN·m. The maximum force in the X-direction is 4289 kN during the time span of the simulation. Different from the ordinary airfoil theory, when only one of the fins is spread, the drag force first decreases as the attack angle of the hull rises. The attack angle where the drag force starts to rise again is about 5° because the hull can provide a faring effect in front of the fin.

(4)

The proposed simulation method is valid for a large ship in predicting the initial phase of its turning circle. In a study in which the course-changing performance of a ship is emphasized, rather than its turning performance in a whole circle, the new simulation method can save significant calculation resources to reduce research difficulties and costs further. Additionally, this method can be popularized in future studies regarding the manipulation and control of intelligent ships, as greater maneuverability in an intelligent ship usually indicates that the control algorithms of the ship can be designed and executed more easily and safely.

Based on the fundamental assumptions of the current study, the wave-making resistance of the hull could not be solved very exactly. The structural integrity of the spoiler fins will perhaps face challenges under extreme sea states, which can be prevented by using thicker steel plates. In addition, a spread fin can also lead to out-of-plane motions of the hull, e.g., roll and pitch. Nevertheless, these limitations do not significantly change the results and conclusions of the present study. In summary, the study is preliminary, but it may arouse further investigations focusing on the difference between the double-model method and VOF method, the error analysis of the CFD problem, the hydrodynamic coefficients of the fin-retracted or fin-spread hull, the interaction between rudders and spoiler fins, the influences of various sea states and different fin configurations, and the rolling motion if the rudder and the fin are both actuated.