Numerical Research on the Infl uence of Interceptor Flaps on the Planing Hydrodynamic Performance Numeričko istraživanje utjecaja zakrilaca krmenog praga na hidrodinamičke performanse glisiranja

The trim tab and interceptor have been utilized to optimize the running trim and motion control of planing boats at varying speeds in calm water. Increasing the height of the interceptor can create excessive drag and bow-down trim. The eff ectiveness of the interceptor can be increased by integrating it with a horizontal fl ap. This research focuses on the impact of the infl uence caused by interceptor fl aps on the pressure distribution and fl uid fl ows around the vessel. To simulate trim and sinkage measurement, the environment was modeled in the two-degree of freedom condition. Variation of integrated interceptor fl aps has been analyzed with Finite Volume Method (FVM) based on RANS (Reynolds-Averaged Navier-Stokes) equation using overset mesh. The turbulent K-ε and VOF (Volume of Fluid) models are used to model the water and air phases. The grid convergence study is performed to establish the parallel solver’s grid independence. To confi rm the accuracy of the test in the bare hull condition, the numerical approach was tested experimentally. The result of drag, trim, and sinkage was calculated and it has been proved that the added fl aps into interceptors are very useful in drag reduction and trim control. The percentage of interceptor height is directly proportional to the resulting lift force. Higher lift force can more eff ectively improve trim and reduce drag. Overall, this study shows an improvement in ship performance when using an interceptor and interceptor fl ap. One of the model confi gurations in the study has been shown to reduce drag by up to 33.3% at Froude number 1.45 when compared to ships without an interceptor.


INTRODUCTION / Uvod
Changes in speed signifi cantly aff ect the performance of fast boats.Dynamic instability causes various negative impacts on boat safety.To address this issue, an automatic control policy often employs active actuators such as fl aps and interceptors to maintain a pre-calculated 'optimal' dynamic trim angle for minimum drag.The interceptor is able to move vertically due to a system controlled by a hydraulic mechanical engine [1].The interceptor can control the trim so that it can reduce the ship's drag with good fl exibility.The eff ect of the layout and blade height of the interceptor was illustrated using numerical simulation [2].The interceptor can reduce drag by as much as 57% at a Froude number of 0.87 near the chine position [3].Mansoori and Fernandes proved that the interceptor was able to improve ship behavior by controlling the porpoising eff ect [4].The interceptor can reduce resistance up to 15% for monohull vessels and 12% for catamaran vessels [5].Unfortunately, by applied interceptor in high Froude number caused a decisive moment and increase total drag.
On the other hand, the interceptor has the disadvantage on producing excessive pressure, resulting in bow-down trim on the ship.These conditions have the potential to increase ship resistance and are dangerous for ship safety.In calm water, Mansoori and Fernandes investigated interceptors using the CFD method.The study explains that interceptors can cause negative trim at certain speeds [6].Other studies also state that interceptors can create excessive pressure, causing bow-down trim [4].
The stern fl ap is a device that can reduce drag while reducing trim angle.The working principle of the stern fl ap is almost the same as the interceptor.A stern fl ap is a plate that extends at an angle from the transom to the ship's buttock plane.It modifi es ship operating trim, reduces propulsion resistance, and improves maximum speed.Important stern fl ap design considerations include chord length, fl ap angle referred to the hull bottom, and fl ap span across the transom.The stern fl ap is believed to be able to control the trim and create the ideal pressure.Several studies on stern fl aps have been carried out.The stern fl ap can reduce drag up to 5.53% using the CFD approach [7].Five stern fl ap models were subjected to experimental studies to determine the optimal geometric characteristics.The most optimal design can reduce resistance by up to 8.2%.Experimental studies show stern fl aps can reduce drag by up to 7.2% [8].Research conducted by Ghadimi showed that the stern fl ap was able to reduce EHP in the propulsion system [9].However, interceptors can reduce pitch and sinkage motions in calm water and regular head waves compared to the hull without an interceptor [10].Another device called the bulbous bow was investigated with experimental and numerical results indicate that a decrease in the total resistance up to 7% [11].
Tsai and Hwang conducted an experimental study to analyze the performance of stern fl aps, interceptors, and their combination in calm water conditions [12].Other studies also compared interceptors, stern fl aps, and their combination with numerical simulation methods [13].It is assumed that the interceptor fl ap can be used with better eff ectiveness because the height of the interceptor can be controlled so that it can improve the wake formed.Changes in the dimensions of the fl aps can aff ect the fl uid fl ow around the stern.The combination of interceptor and stern fl ap can present a new phenomenon, so research on this subject continues to be developed.The properties of the fl uid fl ow, wave pattern, and pressure distribution for the interceptor fl ap combination with a 12-degree fl ap angle have not been recorded.It is essential to comprehend what occurs during the installation of an interceptor fl ap and how fl uid fl ows near the interceptor fl ap at the transom.It directs the designers to enhance the conduct of boats with interceptor fl ap installations.
The development of science followed by computational technology has an impact on increasing research based on numerical simulations.The application of genetic algorithm used in ship design is the primary step [14].The most commonly used CFD methods for planing hull are Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM).Yousefi et al showed that the experimental method and CFD resulted in a fairly good accuracy in analyzing the ship's planing hull.Numerical simulations using the fi nite volume method are often used to predict hydrodynamic performance on planing hull ships [15].Until now, the FVM method has become one of the most popular methods used in numerical simulations [16].Research shows that FVM is the most widely used choice for predicting ship planing hull performance in terms of accuracy [17].The results of the experimental analysis and CFD can be said to have conformity with each other by reviewing the pressure distribution, wave contour, and ship resistance coeffi cient [18] and also estimating the energy effi ciency design index from the data of ship resistance [19].The Reynolds-Averaged Navier-Stokes (RANS) formulation is a mathematical model for solving fl uid fl ow equations.It was created to simulate turbulence's eff ects on fl uid fl ows.Turbulence is a phenomenon in fl uid fl ows that occurs when the fl ow becomes unpredictable.It is distinguished by small-scale, high-frequency fl uctuations in fl ow variables such as velocity, pressure, and temperature.The RANS formulation averages out these fl uctuations over time to obtain a time-averaged fl ow description.This time-averaged description can be used to predict fl ow mean behavior, such as mean velocity and pressure distribution.
The selection of ship speed and dimensions has nothing to do with developing the RANS formulation.However, when using the RANS formulation to simulate the fl ow around a ship, selecting an appropriate simulation speed and scale is critical.It is crucial to select a simulation that accurately captures the eff ects of the ship's size and speed on the fl ow behavior around it.This study uses a turbulence model with a standard k epsilon to describe turbulence in the fl ow.
The novelty of this research is to analyze the combination of interceptor and stern fl ap on the performance of ship planing hull.This study represents the results of CFD by comparing the drag, sinkage, and trim values of the experiment Park et al [20].Validation is carried out by RANS confi guration and solving turbulence problems based on ITTC recommendations [21].This study combines interceptor and fl ap to achieve a broader speed range for reduced drag and practical trim optimization.Changes in the length of the fl ap to the length of the interceptor were observed to form a wave pattern at the stern of the ship.

Research object / Predmet istraživanja
The main dimensions of the planing hull, interceptor, and stern fl ap can be seen in Table 1. Figure 1 shows the design of the Planing Hull and Interceptor Flap.The dimensions of the modifi ed interceptor fl ap can be seen in Table 2.This study uses the Aragon 2 ship which has been analyzed experimentally by Park et al [20].Experimental testing refers to the commercial HUMPHREE X300 interceptor.The X300 interceptor is the initial design that will be tested using a numerical approach.The interceptor fl aps were combined according to the comparison shown in Table 2.According to Mansoori and Fernandes' study, the angle of the stern fl ap used in each model was 120 degrees [22].The combination confi guration of the interceptor and stern fl ap in this study can be seen in Figure 2. The scale and size of the interceptor were selected based on experimental tests conducted by Park et al [20].

Solver settings / Postavke solvera
The discrete control volumes are created by dividing the domain into discrete grid volumes using the fi nite volume approach.The area between our geometrical margins is fi lled was the Reynolds stress term; was the source term.
It is crucial to give the organized elements in the generated grid surrounding the body, particularly when there is a free surface in the simulation region, as the simulation of the free surface is highly dependent on the grid quality.To accurately imitate the waves, the grid surrounding the free surface must be of high quality.The number of elements is a crucial determinant in the quality of grid generation.The accuracy of numerical computation is created by high-quality mesh density, time step, and extra running time.Grid independence is used to prove that the mesh confi guration is correct and that the mesh has no signifi cant impact on the calculation results.
The output of this study is shear drag and pressure drag [24].Shear drag is the tangential vector component of the total surface frictional resistance of the ship against fl uids.While pressure drag is normal resistance or drags due to pressure which consists of wave and viscous pressure.Mathematically it can be formulated as follows: (2) Where: is static pressure is the area vector is normal pressure is the node vector or fl uid volume is the stress tensor.This research referred to the Savitsky method to calculate lift force that infl uences the running state of planing hull, as follows [25]: (5) Where: Cl is Lift coeffi cient L is Lift force of the ship is fl uid density V is velocity of the ship S is projected are of the plates on the free surface C L interceptor is the coeffi cient of lift force interceptor C L lap is the coeffi cient lift force fl ap B is the breadth of the ship l lap is the lift force fl ap l interceptor is the lift force interceptor The increase in the lift force, drags, and trim with fl ap defl ection is readily found by subtracting the force and moment for fl ap defl ection.A hydrodynamic phenomenon known as the Stern Flap Eff ect occurs when a fl ap is attached to the aft end of a ship's hull.This fl ap covers a fi xed area of the ship's surface and improves the vessel's performance.The lift force due to the fl ap is: (6) Where L lap is the length of the chord of fl ap.
Furthermore, the interceptor lift coeffi cient is equal to: Shear stress is the frictional force of the ship's surface against the fl uid.In the case of a planing hull ship by reviewing the performance of fast boats including drag, sinkage, and trim, some of the ITTC recommendations followed in this study are: 1.The size of the computational domain 2. Mesh density 3. Convergence 4. Time step 5. Grid on the ship wall (y+)

F igure 3 Computational domain and boundary condition Slika 3. Računska domena i rubni uvjet
Figure 3 shows the visualization of the boundary conditions and the computational domain.The computational domain and overset box dimensions use three-dimensional Cartesian coordinates.To reduce computation time, the symmetry plane is modeled to divide the ship along its longitudinal axis, and only a portion of the ship is analyzed.Boundary conditions are set as follows: V elocity inlet is present on top and side of the background.The outlet is on the aft side of the vessel and is defi ned as the pressure outlet.The bottom area describes a noslip wall condition.The longitudinal area of the ship is called the symmetry plane.The symmetry boundary condition defi nes a mirror face/surface.It should only be used if the physical object or geometry of the developed solution and the expected fl ow fi eld pattern are mirrored along that surface.It indicates that no wave refl ection will occur.To avoid the interaction between the refl ected wave and the background domain.The fl uid domain was discretized using a hexahedral unstructured mesh type with local refi nements at the regions of special interest and where a more precise resolution of the fl ow was needed.The detail of refi nement was shown in Figure 4.
(10) Where M is the mass and I is the moment of inertia of the ship.The time step is defi ned by involving the CFL (Courant Fredrich Lewy) number which involves the fl ow velocity and the overall length of the ship as well as the complexity of the turbulence model.The time step used is in the range of 0.008 as described in Figure 6 Finer meshes with more minor elements typically produce more accurate results.Finer meshes, on the other hand, take longer to solve.However, there comes the point where the mesh is refi ned enough to capture the results accurately.
In CFD simulations, Y+ is a parameter used to determine the type of boundary layer near a solid surface.The Y+ wall function is used to predict the thickness of the fi rst layer of the mesh near the wall, reducing results inaccuracy.Y+ is expressed in dimensionless units.ITTC recommends y+ value of 30< y+ < 100.Lotfi et al apply y+ value of 50< y+ < 150 for stepped planing vessels [27].Avci et al suggest y+ be in the range of 45-60 [28].
This study applies the range of y+ value is 35-70, as shown in Figure 7.The prediction of friction on the bottom of the ship will be greatly infl uenced by the size of the y+ value.Therefore, the study of the value of y+ becomes one of the most important things to do to achieve the most suitable wall distance.The thickness of the prism layer is one of the techniques used to enhance the accuracy of boundary layer prediction on the ship' s hull.

Grid independence study / Analiza neovisnosti mreže
This study uses fi ve variations of the mesh quantity with a total of 0.52; 0.66;0.87;1.24and 1.47 million cells.The grid study was conducted on Froude number 1.072.Figure 8 shows the results of the analysis of each grid independence study.The fi ve variations of the grid have given a fairly good convergence

Ver ifying CFD and experimental results / Provjera CFD-a i eksperimentalnih rezultata
This study compares the results of the drag, sinkage, and trim analysis with 100% interceptor conditions in the close-to-keel position.Research verifi cation by comparing the results of the CFD simulation [3] with the experimental results which can be represented in Figure 10.The graph shows the same pattern between the two research methods.Brizzola and Serra conducted a study to determine the accuracy of CFD.CFD is declared quite accurate if the maximum error tolerance is 10% [29].A nother research reported validation results more than 10% and reasonably well with the other CFD studies performed on the hull [30].The diff erence between numerical and experimental ranges from 3-20% for drag and trim cases.The pressure at the bottom as measured near the hull is markedly diff erent.As shown in Figure 11, the bottom pressure generated by the interceptor crest on the interceptor is distributed on the hull plate in front of the interceptor.The pressure produced by the interceptor fl aps peaks just behind the hinge and is distributed over the interceptor fl ap and hu ll.That produces a higher pressure area than the interceptor alone (100% interceptor).This happens because the height of the interceptor is directly proportional to the resulting pressure.The high-pressure area will be higher due to the dominant interceptor as shown in Figure 12. Figure 14 shows a hydrostatic force that produced only moderately extreme ship movements visible in the displacement mode (Froude number 0.29 to 0.58).The peak position of the drag and trim values was signaled by the ship's increase in speed as it entered the transition mode (Froude number 0.87 to 1.16) of motion.This phenomenon was caused by the predominant hydrodynamic force acting upon the ship.Due to the hydrodynamic forces acting on the ship's bottom, the trim angle grew as the ship's speed did.Because the drag value u nder these circumstances is substantial, the interceptor was advised to be used during the transitional phase or the peak of the trim.It is not advised to use an interceptor during the planing mode period because the excessive moments the interceptor generates could cause a bow-down trim.As a result of changes in speed, the interceptor's eff ects on the ship's trim are a result of the ship's interaction with the interceptor.At Froude number 1.74, the ship's state revealed excessive trim, which resulted in poor ship movement.Due to too many interceptor moments, the ship experienced negative trim (bow-down trim) after the interceptor placement at a speed of 1.74.This interceptor was therefore deemed unsuitable.At Froude number 0.87, the use of an interceptor was advised to enhance the ideal trim value (fi t interceptor).Each variation of the interceptor fl ap produces a fairly equivalent value.S5 produces the highest drag compared to other samples.The S4 produces minimum drag.The average range of using interceptor fl aps to reduce drag is in the Froude number 0.29 to 1.74.The same is shown in the sinkage and trim charts.Because it is not negative, the trim value represents a safe number for all Froude ranges.The most eff ective drag is declared on the S4 with a reduction of 4% when compared to the 100% interceptor.In the case of 100% interceptor produces excessive drag at high speeds (Froude number >1.16).In this case, the interceptor generates a very strong moment, which may result in negative trim.Worse, this strong moment contra trim moment may cause the boat to capsize.Moreover, when S4 does not cause excessive drag or endanger the ship.An interceptor is a device designed to prevent the fl ow of water under the hull.Typically, it is a steel plate with a fl at, simple design.As shown in Figure 11 it modifi es the pressure distribution at the stern by forming a virtual wedge.
In Table 3, it is known that the lift force generated by each research variation is for Froude number 1.45.This research is based on CFD calculations.The greater the percentage of the interceptor height, the greater the lift force value generated.This has implications for the trim and drag moments of the ship.The interceptor is more sensitive than the fl ap.
The interceptor can cut the fl ow vertically, but the fl ap cuts the fl ow with the angle function used so that the eff ect of lift force, trim, and drag is less signifi cant and less sensitive than the interceptor.

CONCLUSIONS / Zaključci
The object of this research is a planing hull ship with a modifi ed interceptor installation.This study expects a reduction in drag and trim improvements that do not cause excessive pressure on the planing hull ship.The innovation of this research is the combination of the interceptor and the stern fl ap, hereinafter referred to as the interceptor fl ap.This study guarantees the accuracy of CFD by verifying the Park et al experiment.To minimize CFD inaccuracies, CFD regulation measures have followed ITTC's suggestions.The verifi cation results show that the diff erence between CFD and experimental values is 3%-20% and has succeeded in showing the same pattern on the drag, sinkage, and trim comparison chart.
The use of interceptor fl aps is proven to improve the performance of the planing hull ship.The lift force generated by each interceptor fl ap confi guration shows a diff erent eff ect on drag and trim.It was reported that a larger percentage of interceptors would result in a higher lift force value.A higher lift force can improve trim and reduce drag more effi ciently.
This study shows a comparison between 100% interceptor and S4 variation resulting in a change in lift force of 0.3% which can have an impact on drag reduction of up to 33.3% and trim improvement of 0.8% at Froude number 1.45.It should be noted that a lift force that is too large will endanger the ship, so the design of the interceptor fl ap is very important in planning to make it easier to predict the lift force or ship resistance.This research is limited to the hull geometry of Aragon 2; however, diff erent hull geometries will produce diff erent performance levels.Nonetheless, this study is a preliminary design for a ship with an interceptor fl ap.

Figure 10 3 . 3 .
Figure11illustrates a comparison of the pressure variations caused by the interceptor fl aps.The pressure at the bottom as measured near the hull is markedly diff erent.As shown in Figure11, the bottom pressure generated by the interceptor crest on the interceptor is distributed on the hull plate in front of the interceptor.The pressure produced by the interceptor fl aps peaks just behind the hinge and is distributed over the interceptor fl ap and hu ll.That produces a higher pressure area than the interceptor alone (100% interceptor).This happens because the height of the interceptor is directly proportional to the resulting pressure.The high-pressure area will be higher due to the dominant interceptor as shown in Figure12.

Table 3 T
he diff erence in the prediction of lift force Tablica 3. Razlika u predviđanju sile uzgona