Performance Analysis of Duct Vane Application on Patrol Boats Using Computational Fluid Dynamics

Fast patrol boats are designed for high performance in surveillance and warfare missions. In terms of hull technology development, the fast patrol boat commonly uses a V-type hull with hard chine. A duct vane is an innovation developed to improve the performance of patrol boats by combining the principles of wake-equalizing duct and hydrofoil. The objective of this paper is to investigate the hydrodynamic effect of the application of duct vane on the patrol boat hull design. The investigation was carried out using computational fluid dynamics that was validated using experiment data. The result of the duct vane application can improve the ship speed performance and reduce the total resistance by 40% at Fn 0.6. The results of this study also provide an overview of the influence of the duct vane on the lift force of a hard chine hull-type.

Duct vane; Hydrodynamics; Patrol boat

2.1. Design and the Principal Dimension of the Patrol Boat

A fast patrol boat using a hard-chine hull with a duct vane is designed using linear algebra to determine the meeting points of the plates so that the coordinates are in one flat plane on each plate. The line plan is made into a 3D model using Maxsurf  UK (Maxsurf, n.d.). The ship design employed in this study is a model characterized by main dimensions, including a length overall of 0.75 m, breadth of 0.2 m, height of 0.12 m, and draught of 0.049 m.

Figure 1 Fast patrol boat design with flat plate hull with duct vane

In calculating the need for Hydrofoil on the Duct Vane, the Hydrofoil lift calculation formula is used on the ship by using Equation 1 (Vellinga, 2009). Where L = Lift force (N), A = projected surface area (m²), V = speed (m/s), C_L = coefficient of lift, and F_AR = factor correction for aspect ratio.

Each profile of the hydrofoil section has its own coefficient of displacement depending on the characteristics of the profile shape. After determining the profile used, the next step is to calculate the lift using Equation 1. Through the results of the calculation of the lift from the hydrofoil, the area of the duct vane is obtained, as well as the shape of the hydrofoil used in the duct vane. The profile used for the duct vane is NACA 4412 (AirfoilTools.com, n.d.), and the shape of the hydrofoil used on the duct vane is shown in Figure 2. Detail information of the foil used on the duct vane are Profile NACA 4412, Span 0.2064 m, Chord 0.027821 m, Area 0.0078674 m², F_AR 0.67, CL 0.4 and Lift 19.76 N.

Figure 2 Cross section of NACA 4412 used as hydrofoil

2.2. Simulation Setting and Parameter Inputs

In the simulation geometry settings, the design geometry of the draft ship must be in the form of solid bodies. The design geometry and boundary conditions used as space boundaries in the simulation process are shown in Figure 3. The geometrical model of simulation is based on the practical guidelines for ship CFD applications recommended by ITTC (The International Towing Tank Conference). The dimensions used in this geometric model are the overall length, which is twice the length of the ship model, the height of the inlet and outlet is three times the height of the ship model, the width of the inlet and outlet is three times the width of the ship model.

The simulation has 45778 mesh quality nodes and 199131 elements. The free surface is modeled using the volume of fluid (VoF) method, which involves two phases - water and air. The water conditions are characterized by incompressible flow, as well as steady and multiphase flow. The turbulence model used when water and air fluids are flowing is the k-epsilon standard wall function, which has the simplest turbulence equation. The type of solver chosen is pressure-based because the simulated fluid flow has incompressible flow characteristics. Setting the setup menu in the simulation model includes determining multiphase and turbulence equation models, defining boundary conditions, cell zone conditions, and solution methods.

Figure 3 Boundary conditions on a fast patrol boat simulation

In determining the multiphase model, there are three types of multiphase modeling in Ansys US software (Ansys, 2020), namely Eularian, VoF, and Mixture. VoF modeling of two phases with a special free surface by tracing the grid mesh that has been made. Meanwhile, the mixture is a two-phase model that is commonly used to model a mixture of two or more fluids. In this study, the VOF model was utilized to model the interface between water and air. A surface tension value of 0.072 N/m was assigned to the water-air interface.

Turbulent fluid flow will tend to occur when a ship passes through the fluid. However, in this case, the flowing fluid is considered a steady flow, and the ship speed is constant so turbulence is predicted to occur, which is not too complicated. Therefore, the K-Epsilon turbulence model is used. In this study, the fluid flow is assumed to be incompressible, viscous, turbulent, and two-phase. Such flow is governed by the incompressible ReynoldAverage Navier Stokes (RANS) equation. The RANS equation has the same general form as the Navier-Stokes equation with velocity and other solutions (Khazaee, Rahmansetayesh, and Hajizadeh, 2019).

The initial state of the geometry and boundary conditions that have been determined will affect the completion of the Navier-Stokes equation and the continuity equation in the simulation process. Boundary conditions are used to model a phenomenon to direct flow in the domain. For flow simulation, boundary conditions are defined as inlet velocity and outlet pressure. There are several different types for certain conditions. In incompressible fluid flow conditions, velocity inlet and outflow are usually used, whereas incompressible fluid flow conditions, mass flow inlet and pressure far-field are used. However, the selection of boundary conditions can be adjusted to a particular problem model.

In the flow simulation that will be carried out, the model ship, which is called the Hard-chine hull is considered as a static object flowing fluid with the speed variations determined in this study. The inlet of the fluid flow is defined as the velocity-inlet, and the exit area is defined as the pressure-outlet. At the inlet side of the fluid flow, a constant velocity in one direction with a turbulence intensity of 0.5% is considered based on wind tunnel experiments where the inlet turbulent intensity is around 0.5% - 1%. The open channel method, particularly suitable for these conditions, is designated as velocity-inlet. Meanwhile, on the exit side, where the fluid flow maintains a constant static pressure, it is deemed appropriate to define it as a pressure outlet, allowing for the distribution of radial equilibrium pressure. In addition, the bottom side, top side, right side and left side of the domain are defined as walls without friction as a symmetry so that they are considered infinitely wide free surfaces.

The following are the settings used for the boundary inlet and outlet. The inlet is defined as a velocity inlet because, in this simulation, the air and water flow from the inlet at a constant velocity. The input speed for the hard-chine hull model without duct vane is 0.8 m/s, 1.2 m/s, 1.6 m/s, 2.0 m/s, 2.4 m/s, 2.8 m/s and 3.2 m/s. As for the hard-chine hull model with duct vane are 1.6 m/s, 1.9 m/s, 2.2 m/s, 2.4 m/s, 2.7 m/s, 2.9 m/s and 3.2 m/s. The speed variation is considered the Froude number for high-speed patrol boats, and the value is higher than 0.5. The intensity and viscosity of the turbulence are given a small value, namely 0.5%. This aims to minimize the turbulent flow that occurs at the inlet to model calm waters. In the multiphase menu, the flowing fluids are defined as water and air. The free surface level setting is adjusted to the modelling of water depth and ship draft, which is 0.049 m (ship draft). Detailed settings at the inlet and outlet are described in Table 1.

Table 1 Detail setting of inlet and outlet of the simulation model

The Solution Method used in this study was determined based on the validation results. In the validation stage, the least square cell-based method is used. According to the validation results, it was found that the arrangement using the least square cell-based method approached the experimental results with an error percentage of around 1.8%. Pressure velocity coupling is an equation derived from the continuity equation to reduce unexpected pressure conditions. Some of the types are Simple, Simplec, Piso, Coupled, and Fractional Step. In this research, the SIMPLE scheme is used because this scheme considers pressure and speed in its calculations (Patankar, 2018). While the second order upwind on momentum, turbulent kinetic energy and turbulent dissipation rate aim to increase the accuracy of the simulation results. The volume fraction is modeled with compressive characteristics to effectively separate the transition between water and air, facilitated by the surface tension of the water-free surface. The Solution Control parameters used in this study were also determined based on the validation results. According to the results of the validation carried out, the parameters used in the Solution Control settings are obtained as shown in Table 1.

2.3. Validation of Simulation Results

Validation at this stage aims to prove that the results of research data from CFD simulations resemble the results of observational data in experimental tests. It is hoped that the results of the CFD simulation in the form of a graph of velocity against total resistance will have a curve that resembles the graph of velocity against total resistance as the result of the experiment. Table 4 and Table 5 provide a comparison of the results and graphs obtained from experimental testing and CFD simulation for the patrol boat. The results for the patrol boat without a duct vane are shown in Figure 4, while the results for the patrol boat with a duct vane can be found in Figure 5. Validation is carried out by comparing the simulation results with the results of experiments that have been carried out previously. The experiments use the same model dimension as the simulations carried out in the experimental basin. Experiments were carried out with towing tests with the same load and speed variations. The accuracy of the experiment was evaluated using uncertainty analysis. Based on the calculation results of the average deviation error. Obtained error validation results of 2.38%. Because the error obtained is below 10%, it is assumed to be in good agreement. The geometry, mesh, and set-up settings can be used to simulate the Hard-chine hull Ship model. Based on the calculation results of the average deviation error. The obtained error validation results of 3.5%. Because the error obtained is below 10%, the geometry, mesh, and set-up settings can be used to simulate a Hard-chine hull model with duct vane (Duct vane).

Comparison of total resistance between CFD simulation and experiments without duct vane

3.1. Comparison of Drag Coefficient

The analysis was carried out to determine the value of the drag coefficient found in Hard-chine hulls without duct vane. The components contained in the total resistance coefficient are the pressure resistance coefficient (Cp), the viscous resistance coefficient (Cv) and the air resistance coefficient (Ca). Figure 6 illustrates the coefficient of viscous resistance, represented by the blue dots, which tends not to experience a significant decrease in the velocity range of 1.6 m/s to 2.2 m/s. In contrast to the coefficient of pressure resistance, which is depicted with red dots, there is a drastic decrease in the velocity range. In this case, it is suspected that the resistance found on Hard-chine hulls without duct vane is dominated by pressure resistance. This is also evidenced by the value of the drag coefficient. In addition, at a velocity range above 3 m/s, the values of the three drag coefficients are getting smaller, and the values of the three are getting closer. This result consistent with the experiment results (Budiyanto et al., 2021).

Figure 7 shows the value of the drag coefficient found on a hard-chine hull with a duct vane (Ductship). The main components contained in the total resistance coefficient (Ct) are the pressure resistance coefficient (Cp), the viscous resistance coefficient (Cv), and the air resistance coefficient (Ca). As can be seen from the graph below, the pressure resistance coefficient (Cp) has the greatest value compared to the viscous resistance coefficient (Cv) and air resistance coefficient (Ca). In Ductship, the increase in velocity does not significantly affect the magnitude of the viscous drag coefficient (Cv). However, the pressure resistance coefficient (Cp) value decreases as the velocity value increases.

In comparing the velocity graph to the total resistance (Rt) and the velocity graph to the total resistance coefficient (Ct), two curves are used, which are the results of the CFD simulation that has been carried out. Figure 8 illustrates the total resistance results for the two model ships. Both curves share a similar shape, indicating that the ship's resistance value increases as the ship's speed rises. The total resistance curve for a flat plate vessel with a duct vane, which is illustrated with a black line, is shown below the total resistance curve for a flat plate vessel without a duct vane of the hard-chine hull, which is colored in red. This proves that the addition of a duct vane on a hard-chine hull can reduce the value of the total resistance on a hard-chine hull. This result is consistence with the previous result (Murdianto, Budiyanto, and Syahrudin, 2020).

Figure 6 Drag coefficient value of hard-chine hull

Figure 7 Drag coefficient value of application of duct vane

Figure 8 Comparison of the total resistance of the application of the duct vane

From the results of the comparison of the total resistance, it can be seen that a hard-chine hull with duct vane has a smaller resistance compared to a hard-chine hull without using duct vane (hard-chine hull). At the Froude number (Fn) of 0.6, there was a 40% reduction in total resistance (RT). Similarly, at Fn 0.8, there was a 38% reduction, at Fn 0.96, a 30% reduction, and at Fn 1.1, a 20% reduction in total resistance. Observing the calculations of total resistance reduction, it becomes evident that the percentage reduction in total resistance tends to decrease with an increase in speed and Froude number. This proves that the use of duct vane on a hard-chine hull has a percentage reduction in the largest total resistance value at the range of range Froude number of 0.6 to 0.8. In addition to the value of the total resistance of the ship, the coefficient value of the total resistance of the ship is also compared to obtaining a multiplier factor that can be used as a reference to ship design.

3.2. Duct Vane Lift Force Analysis

In the previous discussion it was found that the addition of Duct Vane can reduce the total resistance of Hard-chine hulls. This reduction in total resistance is thought to be due to the lift force exerted by the Duct Vane on the stern of the ship. Duct vane is an additional device at the stern of the ship that utilizes the shape of the hydrofoil to generate lift force at the stern of the ship. Based on research conducted through experimental methods, it is known that the shape of the hard-chine hull model tends to experience trim by stern when sailing at high speed. Trim by stern is the condition of the ship when sailing where the stern draft is greater than the bow draft. The addition of a duct vane at the stern of a hard-chine hull can solve the trim problem with the lift force provided by the hydrofoil. As stated in the discussion chapter on the hydrofoil, the lift force exerted by the hydrofoil is due to the difference in pressure on the hydrofoil cross-section. So at a certain speed, the ship's hull will rise above sea level due to the lift force provided by the hydrofoil (Kandasamy et al., 2011).

The phenomena obtained from the experiments were also proven by the results of the CFD simulations that had been carried out. Figure 9 is the result of a CFD simulation in the form of volume rendering in the form of a pressure contour on the fluid around the simulated model ship. Volume rendering is done when the ship is flowing with fluid at a speed of 1.6 m/s on both ship models. This speed is used because the speed of the model is a speed value that has a significant effect on the difference in resistance. From the results of this volume rendering, it can be seen that the pressure distribution in the fluid around the model ship. Thus, the effect of the addition of Duct Vane on the pressure distribution around the model ship can be analyzed. 

Figure 9 CFD simulation of a pressure contour on the fluid around the stern hull

Figure 10 Fluid flow passes through the stern of the hard-chine hull and duct vane

Figure 10 shows the fluid flow passing through the stern of the hard-chine hull and duct vane. Based on the figure, it can be seen that the flow passing through the stern of a Hard-chine hull without a duct vane has an irregular and inhomogeneous flow direction. It can be seen that several flow lines have different directions. Meanwhile, at the stern of a hard-chine hull with a duct vane, it can be seen that the direction of fluid flow is more homogeneous. The more homogeneous flow is thought to be due to the addition of a Duct Vane at the stern of the hard-chine hull. With a more homogeneous form of fluid flow, the flow separation that occurs at the stern of the ship can be reduced by adding duct vanes to Hard-chine hulls. The shape of the water fluid flow, which is more regular and homogeneous, also affects the value of the pressure resistance and frictional resistance of flat plate vessels. The results of the flow contours show that the addition of a duct vane can reduce the value of the pressure resistance on hard-chine hulls. One of the additional components of pressure resistance is eddy-making resistance. Eddy-making resistance is an obstacle caused by the separation of shapes on the ship, in this case, on the stern of a hard-chine hull where there are fractures that cause the flow to break away and then form eddies. The addition of duct vane makes the flow at the stern of hard-chine hulls more regular, has a homogeneous direction, and fewer eddies occur compared to the hard-chine hull model, where more eddies occur (Harwood et al., 2019).

CFD simulations have been carried out on hard-chine hulls with duct vanes to calculate ship resistance and are validated by experimental test results. The simulation method uses the multiphase volume of fluid equation and k-epsilon as the turbulence equation. Data validation of the simulation results was carried out on experimental results regarding hard-chine hulls with duct vanes. The average deviation error obtained in the validation is around 2-3% for both ship models. From the two simulated ship models, namely hard-chine hulls without duct vanes and hard-chine hulls with duct vanes (ductship), it can be concluded that adding duct vanes to hard-chine hulls can reduce the total drag on hard-chine hulls. The addition of a duct vane on a hard-chine hull can reduce the total resistance of the ship by 40% at Fn 0.6. Suggestions that can be considered for further research development are the collection of experimental data at high speeds to obtain the physical effects due to the lift force from the duct vane. 

    The authors express their gratitude to the Faculty Engineering Universitas Indonesia for the Seed Funding Program 2023 number NKB-2563/UN2.F4.D/PPM.00.00/2023.

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