Effects of a Bulbous Bow Shape on Added Resistance Acting on the Hull of a Ship in Regular Head Wave

Journal of Marine Science and Engineering

Article Effects of a Bulbous Bow Shape on Added Resistance Acting on the Hull of a Ship in Regular Head Wave

Trung-Kien Le 1,* , Ngo Van He 2,* , Ngo Van Hien 2,* and Ngoc-Tam Bui 1,3,*

1 School of Mechanical Engineering (SME), Hanoi University of Science and Technology (HUST), No.1 Dai Co Viet, Hanoi 10000, Vietnam 2 School of Transportation Engineering (STE), Hanoi University of Science and Technology (HUST), No.1 Dai Co Viet, Hanoi 10000, Vietnam 3 College of Systems Engineering and Science (CSES), Shibaura Institute of Technology (SIT), Tokyo 135-8548, Japan * Correspondence: [email protected] (T.-K.L.); [email protected] (N.V.H.); [email protected] (N.V.H.); [email protected] (N.-T.B.)

Abstract: In this study, the effect of bow shape on resistance acting on a hull in regular head waves was investigated by applying a commercial Computational Fluid Dynamics (CFD) code. For this purpose, the hydrodynamic performance as well as the resistance of ships with blunt and bulbous bows were simulated. By analyzing the obtained CFD simulation results, the effects of the bow shape on the hydrodynamic performance and resistance of the ships were found. A new bulbous bow shape with drastically reduced added resistance acting on the hull in waves is proposed. Finally, the obtained CFD results for the hydrodynamic performance of ships are presented.

Keywords: resistance; CFD; regular head waves; hull; bulbous bow; hydrodynamic

Citation: Le, T.-K.; He, N.V.; Hien, N.V.; Bui, N.-T. Effects of a Bulbous Bow Shape on Added Resistance 1. Introduction Acting on the Hull of a Ship in Regular Head Wave. J. Mar. Sci. Eng. A bulbous bow is a long-established solution for reducing the added resistance acting 2021, 9, 559. https://doi.org/ on ships by using the bulbous bow’s wave-generating effect. The study of reducing added 10.3390/jmse9060559 waves’ resistance as well as reducing the total resistance of ships so as to reduce fuel consumption is still an important topic in the marine transportation field. For ships with Academic Editor: Nikos Themelis huge hulls and blunt bows, the resistance from added waves acting on the hull accounts for a large percentage of the total resistance in conditions of both calm water and waves. Received: 18 April 2021 Therefore, many researchers around the world have given importance to the study of Accepted: 20 May 2021 reducing added waves’ resistance acting on ships’ hulls. Published: 21 May 2021 In recent years, a large number of published papers have examined the topics of reduced added waves’ resistance on ships, optimal hydrodynamic hull shapes, the effects Publisher’s Note: MDPI stays neutral of bow and stern shapes on added waves’ resistance, and the optimal hull shape in wave with regard to jurisdictional claims in conditions, etc. We offer a comprehensive literature review below. published maps and institutional affil- There are many published papers on applying a commercial Computational Fluid iations. Dynamics (CFD) code to investigate ship hydrodynamic performance. CFD has been a useful and popular tool for solving problems of the hydrodynamic performance of ships with high accuracy. By applying CFD, various hull forms with small resistances have been proposed [1–16]. Copyright: © 2021 by the authors. The Non Ballast Water Ship (NBS) model has been known since 2010, when it was de- Licensee MDPI, Basel, Switzerland. veloped at the laboratory of Prof. Ikeda at Osaka Prefecture University (OPU). Tatsumi et al. This article is an open access article (2010) presented a study on the development of a new energy-saving NBS tanker with distributed under the terms and multiple podded propulsors. The ship was developed with a round and streamlined hull conditions of the Creative Commons to drastically reduce viscous resistance and multiple podded propulsors moving up and Attribution (CC BY) license (https:// down to keep the propellers deep enough in the water. Using an experimental model in creativecommons.org/licenses/by/ the towing tank at OPU for several hull forms, their results confirmed that the resistance 4.0/).

J. Mar. Sci. Eng. 2021, 9, 559. https://doi.org/10.3390/jmse9060559 https://www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2021, 9, 559 2 of 16

acting on the new ship was reduced by up to 44.8% of the total resistance with ballast, and up to 17.5% at full load [17]. The original hull form with a blunt bow shape was proposed at first. The experimental model test demonstrated that, at a low Froude number of less than 0.16, the resistance acting on the original ship was significantly higher because of the possibly increase in wave resistance [18,19]. Tomita et al. (2011) and Tasumi et al. (2011) presented a study on developing a new bulbous bow for the original NBS model with reduced added resistance at the hull, achieved using an experimental model in a towing tank. The ships with the new bow shape could reduce the total resistance in calm water by up to 11%. Additionally, the model could reduce the added waves’ resistance in moderated short waves by up to 25%; the waves’ height (Hw) was 0.02 m and the waves’ length per ship length (λ/Lpp) was less than 0.6 for the 2 m long model tested in the towing tank [18,19]. In other research on the development of a new bow form for the NBS performed at Ikeda’s laboratory at the OPU, a commercial CFD code was applied to optimize the bow shape. The ship resistance, both in calm water and in wave conditions, was the object of the optimization process for designed parameters such as the volume of the bow shape, the height of the volume at the center of the bow, the angle of the bow’s bottom, and the length of the bow. Analysis of the results showed that the optimal bulbous bow shape could reduce the total resistance of the hull form by up to 15% in calm water and by up to 18% in regular head wave conditions (Hw = 0.02 m; λ/Lpp < 0.6) [2–4,20–22]. Luo et al. (2016) presented a study on the optimal design of the lines of a bulbous bow shape using applied parametric modeling and CFD computation. In the study, the lines of the ship’s bow were optimized by using an optimal platform at the hull shape design stage using automatic progress. Additionally, the Rankine source panel method was applied to evaluate the added waves’ resistance acting on the hull of a Ro-Ro ship. The results showed that added wave resistance was clearly reduced and the wave bow profile became gentle in the ship design with optimized lines of the bulbous bow [23]. Others studies also used the Rankine source panel method; for example, Lu et al. (2016) presented a study of an innovative method for the optimization of the hydrodynamic performance of a bulbous bow while considering different conditions [24]. Zhang et al. (2017) presented research on the optimal bulbous bow shape based on the newly improved PSO algorithm. In the study, the total resistance of the ship in calm water was defined as the objective function, and the overset generated mesh method was applied to meshing. The volume of fluid method, together with the Reynolds Averaged Navier–Stokes (RANS) equation, was applied to evaluate the resistance acting on the hull [25]. Lee et al. (2019) presented research on the effects of bow form on ship resistance in both calm water and wave conditions for the 66,000 DWT bulker carrier. In the study, a computational tool was used to clearly find the cause of reduced resistance acting on the ship hull in both calm water and wave conditions for the sharp bow shape in comparison to the blunt bow shape of the 66,000 DWT bulker carriers. The unsteady flow with two phases method, the RANS equations, and the turbulent viscous k-ε model were applied to a realizable model. The results showed good agreement between the CFD and experimental towing tank results. The pressure viscous resistance of the ship in calm water and wave conditions with the sharp bow shape could be reduced by up to 8.9% and 12.7%, respectively, in formed head waves compared with those of the hull with a blunt bow shape [26]. Other published papers reported on the hydrodynamics and resistant hull forms of different hulls of ships studied using experimental measurements at towing tanks and CFD computation. Begovic et al. (2014) presented a result of a model towing tank test on seakeeping assessment of a ship with a warped planning hull series [27]. Casalone et al. (2020) presented a study on unsteady RANS computational fluid dynamic simulations of sailboats and compared their results with the resistance results of the full scale experiment [12]. Feng et al. (2020) presented a study on the numerical computation of resistance acting on the hull of a KCS ship at different depth conditions for a scale computed model and the full J. Mar. Sci. Eng. 2021, 9, 559 3 of 16

scale model [13]. Ngo (2017) presented a study on a newly developed reduced concept for river ships in calm water [28]. Kahramano˘gluet al. (2020) presented a study on a numerical simulation used to predict the component vertical responses of planning ships under wave conditions [14]. Sun et al. (2020) studied numerical computation used to investigate ship resistance and ship motion stability for a high-speed planning trimaran [15]. Other similar J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 3 of 18 studies include [11,16,29]. In this study, a commercial CFD tools named ANSYS-Fluent v.15.0 has been applied to investigate the effect of a bulbous bow shape on ship resistance, both in calm water and onin the regular hull headof a KCS waves ship conditions. at different The dept originalh conditions hull form for a of scale the NBScomputed with a model blunt bowand theform, full which scale wasmodel developed [13]. Ngo by (2017) Prof. Ikedapresented at Osaka a study Prefecture on a newly University, developed was usedreduced as a conceptreference for ship river model. ships Byin calm using water the CFD, [28]. theKahramano hydrodynamicğlu et al. performance (2020) presented and resistance a study onacting a numerical on the hulls simulation with and used without to predict a bulbous the component bow shape vertical were simulated responses to of determine planning shipsthe effect under of wave the bulbous conditions bow [14]. shape. Sun From et al. the (2020) obtained studied results, numerical a new computation hull shape with used a tobulbous investigate bow ship and reducedresistance added and ship resistance motion has stability been clearlyfor a high-speed identiﬁed planning in this study. trimaran [15].2. The Other Reference similar Modelstudiesand include Simulating [11,16,29]. Domain In this study, a commercial CFD tools named ANSYS-Fluent v.15.0 has been applied 2.1. The Reference Model Used for Simulation to investigate the effect of a bulbous bow shape on ship resistance, both in calm water and in regularIn this head research, waves the conditions. original hullThe formoriginal of thehull NBS form was of the used NBS as awith reference a blunt model bow form,to validate which the was CFD developed results andby Prof. investigate Ikeda at the Osaka effect Prefecture of bow shape University, on the was added used waves’ as a referenceresistance ship of the model. ship. TheBy using original the NBS CFD, was the developed hydrodynamic at the laboratoryperformance of Professorand resistance Ikeda of OPU in 2010. The ship was designed with a blunt bow shape and round cross section acting on the hulls with and without a bulbous bow shape were simulated to determine to reduce viscous resistance in calm water [2,3,17,19–21]. The principal dimensions of the the effect of the bulbous bow shape. From the obtained results, a new hull shape with a original NBS are shown in Table1. The designed original NBS hull shape is shown in bulbous bow and reduced added resistance has been clearly identified in this study. Figure1. 2. The Reference Model and Simulating Domain Table 1. Principal dimensions of the original NBS. 2.1. The Reference Model Used for Simulation In thisNo. research, the original Description hull form of the NBS was Value used as a reference Unit model to validate the1 CFD results Length and investigate of the ship, Lthepp effect of bow2.000 shape on the added waves’ m resistance of2 the ship. The Depthoriginal of theNBS ship, was H developed at the 0.181 laboratory of Professor m Ikeda of OPU in3 2010. The ship Breadth was designed of the ship, with B a blunt bow 0.359 shape and round cross m section 4 Draft of the ship, d 0.131 m to reduce5 viscous resistance Displacement in calm of thewater ship, [2 D,3,17,19–21]. 0.06504 The principal dimensions ton of the original NBS6 are shown Wetted in Table surface 1. The area, desi Sgned original 0.921 NBS hull shape ism shown2 in Figure 1.7 Block coefﬁcient, Cb 0.691 -

Figure 1. Original NBS developed by Professor Ikeda of OPU in Japan [2,3,17]. Figure 1. Original NBS developed by Professor Ikeda of OPU in Japan [2,3,17].

Table 1. Principal dimensions of the original NBS.

No. Description Value Unit 1 Length of the ship, Lpp 2.000 m 2 Depth of the ship, H 0.181 m 3 Breadth of the ship, B 0.359 m 4 Draft of the ship, d 0.131 m 5 Displacement of the ship, D 0.06504 ton

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2.2. Simulating Domain and Setup Boundary Conditons In the CFD computation, the steps of the simulation include designing the computation domain, generating a mesh, and setting up the computed conditions, all of which must be conducted as per the user guideline documents, which have been published as the International Towing Tank Conference (ITTC) manual for applying the CFD code [30–35] and previous publications [2–4,8,9,20,21,28,30,32,35–39]. In this study, the computed fluid domain has been limited to 6.5, 0.55, and 0.75 L instead of 13 m length, 1.1 m breadth, and 1.5 m height. Meshing the simulated domain in the structured H-grid was generated in 2.63 million grids. The turbulent viscous model k-ω, applied to unsteady flow and the Volume of Fluid (VOF) multiphase model, were used. The inlet and outlet of the computed domain were set up with a velocity inlet and a pressure outlet. In the CFD simulation, the simulated domain should be designed to be large enough for the problem. However, the limited dimensions of the simulated domain affect the size of the mesh, as well as affecting the hardware and the running time. The effects of the limited dimensions of the computed domain on the CFD results will become small if the computed domain is large enough. Therefore, we must design an optimal computed domain and set up appropriate boundary conditions. In this study, the time step was set up to be 0.005 s, and the running time included 6000 time steps. Figure2 shows the simulated domain and the generated mesh in the H-grid structure used for the computation. In the CFD computation, the effects of the mesh of the computed domain on the CFD results have been reported in many previous papers [2,3,13–15,30,35,39]. Moreover, in the computation of ship resistance in waves, the height and size of the mesh at the free surface of the computed domain determine the accuracy of the incident wave profile. Therefore, we must make an appropriated mesh for the computed domain. In this study, we independently generated results regarding the resistance acting on the hull of the mesh in the computational domain in CFD. Conditions of both calm water and waves have been simulated in different scenarios; at the Froude number of 0.163, the wave height is 0.02 m and wave length is 0.8 m. Table2 lists details of the mesh of the computed domain and the computed ship resistance coefficients in the different computed cases. Figure3 shows the curves of the mesh effect on the computed ship resistance coefficients in calm water and in regular head waves. Figure3 shows the results of the different resistance coefficients ( ∆CT) in the different computed cases listed in Table2. The results show that the differences among the computed resistance coefficients in calm water were smaller than those of the ship in wave conditions. The difference between the computed results was less than 10% when the value of y+ was less than 1.057, as shown. In calm water, when the mesh number was over 1.488 million instead of a y+ value below 1.592, the resistance coefficient was the same for all computed cases. In regular wave conditions, the different resistance coefficients were close when the y+ value was below 0.872, as shown.

Table 2. Details of the mesh and the CFD results of ship resistance coefﬁcients.

Total Minimum Maximum Minimum Maximum C C No. y+ Elements Face Area, m2 Face Area, m2 Volume, m3 Volume, m3 T(0) T(W) (×10−2) (×10−2) (×106) (×10−8) (×10−4) (×10−6) (×10−2) 1 7.221 0.783 1.5226 12.2256 2.6854 3.2564 0.4921 0.5679 2 5.772 0.868 1.2256 9.6255 2.3566 2.9265 0.5010 0.5810 3 3.616 1.057 1.0500 8.0123 2.0952 2.7326 0.5124 0.6133 4 1.592 1.488 0.2840 2.9620 1.1325 0.9958 0.5176 0.6325 5 1.328 1.822 0.0126 2.8423 0.0562 0.9965 0.5181 0.6384 6 0.872 2.368 0.1193 2.2821 0.3752 1.0921 0.5189 0.6429 7 0.582 3.286 0.0295 2.0123 0.1265 1.2446 0.5201 0.6468 8 0.363 5.682 0.0156 1.9852 0.0625 1.1955 0.5198 0.6479 9 0.221 7.524 0.0184 2.9621 0.0326 0.6955 0.5204 0.6489 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 4 of 18

6 Wetted surface area, S 0.921 m2 7 Block coefficient, Cb 0.691 -

2.2. Simulating Domain and Setup Boundary Conditons In the CFD computation, the steps of the simulation include designing the computation domain, generating a mesh, and setting up the computed conditions, all of which must be conducted as per the user guideline documents, which have been published as the International Towing Tank Conference (ITTC) manual for applying the CFD code [30– 35] and previous publications [2–4,8,9,20,21,28,30,32,35–39]. In this study, the computed fluid domain has been limited to 6.5, 0.55, and 0.75 L instead of 13 m length, 1.1 m breadth, and 1.5 m height. Meshing the simulated domain in the structured H-grid was generated in 2.63 million grids. The turbulent viscous model k-ω, applied to unsteady flow and the Volume of Fluid (VOF) multiphase model, were used. The inlet and outlet of the computed domain were set up with a velocity inlet and a pressure outlet. In the CFD simulation, the simulated domain should be designed to be large enough for the problem. How- ever, the limited dimensions of the simulated domain affect the size of the mesh, as well as affecting the hardware and the running time. The effects of the limited dimensions of the computed domain on the CFD results will become small if the computed domain is large enough. Therefore, we must design an optimal computed domain and set up appropriate boundary conditions. In this study, the time step was set up to be 0.005 s, and the J. Mar. Sci. Eng. 2021, 9, 559 running time included 6000 time steps. Figure 2 shows the simulated domain and the5 of 16 generated mesh in the H-grid structure used for the computation.

(a)

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(b)

(c) J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 6 of 18 FigureFigure 2. 2. SimulatedSimulated domain domain and and structured structured mesh. mesh. (a) (Mesha) Mesh of simulated of simulated domain; domain; (b) mesh (b) mesh at sev- at several eral cross sections in the simulated domain; (c) mesh in the hull surface of the model. cross sections in the simulated domain; (c) mesh in the hull surface of the model. In the CFD computation, the effects of the mesh of the computed domain on the CFD results have been reported in many previous papers [2,3,13–15,30,35,39]. Moreover, in the computation of ship resistance in waves, the height and size of the mesh at the free surface of the computed domain determine the accuracy of the incident wave profile. Therefore, we must make an appropriated mesh for the computed domain. In this study, we independently generated results regarding the resistance acting on the hull of the mesh in the computational domain in CFD. Conditions of both calm water and waves have been simulated in different scenarios; at the Froude number of 0.163, the wave height is 0.02 m and wave length is 0.8 m. Table 2 lists details of the mesh of the computed domain and the computed ship resistance coefficients in the different computed cases. Figure 3 shows the curves of the mesh effect on the computed ship resistance coefficients in calm water and in regular head waves.

Table 2. Details of the mesh and the CFD results of ship resistance coefficients.

Total Ele- Minimum Face Maximum Face Minimum Vol- Maximum Vol- CT(0) CT(W) No. y+ ments Area, m2 (×10−8) Area, m2 (×10−4) ume, m3 (×10−6) ume, m3 (×10−2) (×10−2) (×10−2) (×106) 1 7.221 0.783 1.5226 12.2256 2.6854 3.2564 0.4921 0.5679 2 5.772 0.868 1.2256 9.6255 2.3566 2.9265 0.5010 0.5810 3 3.616 1.057 1.0500 8.0123 2.0952 2.7326 0.5124 0.6133 Figure 3. EffectEffect of of mesh mesh number number on on CFD CFD results results of of tota totall resistance resistance coefficient coefﬁcient of ofthe the ship ship in calm in calm 4 1.592 1.488 0.2840 2.9620 1.1325 0.9958 0.5176 0.6325 water and inin regularregular headhead waveswaves atat FFn = 0.163, H w == 0.02 0.02 m, m, and and λλ/L/Lpp = 0.4.= 0.4. 5 1.328 1.822 0.0126 2.8423 n 0.0562 w 0.9965 pp 0.5181 0.6384

6 0.872 2.368 0.1193Figure 3 shows the 2.2821 results of the 0.3752different resistance 1.0921 coefficients 0.5189 (ΔCT ) in0.6429 the different 7 0.582 3.286 computed 0.0295 cases listed 2.0123 in Table 2. The 0.1265 resu lts show that 1.2446 the differences 0.5201 among0.6468 the com- 8 0.363 5.682 puted 0.0156 resistance coefficients 1.9852 in calm 0.0625water were smaller 1.1955 than those 0.5198 of the ship0.6479 in wave 9 0.221 7.524 conditions. 0.0184 The difference 2.9621 between the 0.0326 comp uted results 0.6955 was less 0.5204 than 10%0.6489 when the value of y+ was less than 1.057, as shown. In calm water, when the mesh number was over 1.488 million instead of a y+ value below 1.592, the resistance coefficient was the same for all computed cases. In regular wave conditions, the different resistance coefficients were close when the y+ value was below 0.872, as shown.

2.3. Validation of the Used CFD In this research, we performed a comparison between the CFD results and the obtained experimental data of the model test at the towing tank at OPU. The original NBS model with a length of 2 m was used for computation, and the experiment investigated the hydrodynamic performance as well as the hull resistance, both in calm water conditions and in regular head waves. Figures 4 and 5 show the results of the comparison regarding the resistance acting on the model in the CFD simulation and the experiment at the towing tank [2,3,17–19].

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2.3. Validation of the Used CFD In this research, we performed a comparison between the CFD results and the obtained experimental data of the model test at the towing tank at OPU. The original NBS model with a length of 2 m was used for computation, and the experiment investigated the hydrodynamic performance as well as the hull resistance, both in calm water conditions J. Mar. Sci. Eng. 2021, 9, x FOR PEER andREVIEW in regular head waves. Figures4 and5 show the results of the comparison regarding 7 of 18 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 7 of 18 the resistance acting on the model in the CFD simulation and the experiment at the towing tank [2,3,17–19].

FigureFigure 4. 4.Comparison Comparison between between the CFDthe CFD results results and experimental and experi datamental of resistance data of resistance acting on the acting on the shipship in in calm calm water. water.

Figure 5. Validation of CFD results of the total resistance coefﬁcients of the ship in regular head and Figure 5. Validation of CFD results of the total resistance coefficientscoefficients ofof thethe shipship inin regularregular headhead shortand short waves, waves, Hw = 0.02 Hw m, = F0.02n = 0.163.m, Fn = 0.163. and short waves, Hw = 0.02 m, Fn = 0.163.

Figures 4 and 5 show a comparison between the CFD results of the total ship resistance coefficients and the experimental data,, bothboth inin calmcalm waterwater conditionsconditions andand inin reg-regular head and short waves. The total ship resistance coefficients in calm water, CT(0), and ular head and short waves. The total ship resistance coefficients in calm water, CT(0), and the total ship resistance coefficients in regular head and short waves, CT(W), are defined by the total ship resistance coefficients in regular head and short waves, CT(W), are defined by the following equation: R C = R C = (1) 0.5ρSV where: CT is the total resistance coefficient; CT is the total resistance coefficient; RT is the total resistance acting on the hull, N; RT is the total resistance acting on the hull, N; 2 S is the wetted surface area, m2;; ρ 3 ρ isis thethe waterwater density,density, kg/mkg/m3;; V is the velocity of the ship, m/s.

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Figures4 and5 show a comparison between the CFD results of the total ship resistance coefficients and the experimental data, both in calm water conditions and in regular head and short waves. The total ship resistance coefficients in calm water, CT(0), and the total ship resistance coefficients in regular head and short waves, CT(W), are defined by the following equation: RT CT = (1) 0.5ρSV2 where:

CT is the total resistance coefﬁcient; RT is the total resistance acting on the hull, N; S is the wetted surface area, m2; ρ is the water density, kg/m3; V is the velocity of the ship, m/s. The results presented in Figures4 and5 show a comparison between the total ship resistance coefﬁcients computed by the CFD and experimental data of the towing tank model test. The agreement between the computed results and the experimental results is fairly good, as shown. In calm water conditions, the difference between the CFD results and the experimental results is less than 6% in the range of the Froude number from 0.08 to 0.18, as shown in Figure4. Figure5 shows a good agreement between the CFD results and the experimental data of the total ship resistance in waves, where the incident waves are short and regular head waves, the λ/Lpp is less than 0.6, and the wave height, Hw, is 0.02 m for the 2 m length of the model at the Froude number of 0.163. The obtained results demonstrate the usefulness of applying CFD to compute the resistance and hydrodynamic performance of ships.

3. Effect of Bulbous Bow on the Hydrodynamic Performance of the Ship 3.1. Model of the NBS with the Newly Proposed Bow Shape In this study, a new bow shape was proposed for the NBS to reduce the added resistance of the hull form. The original ship has a blunt bow shape, whereas the new hull has a developed bow shape; the two ships have the same principal dimensions and stern shapes and only differ in their bow shapes. By using the CFD, the ships were computed and the obtained CFD results were compared so as to ﬁnd out the effects of bow shape on the ships’ hydrodynamic performance. Figure6 shows the models of a new hull with a bulbous bow shape used for the computation; detailed principal dimensions of the model are listed in Table3.

Table 3. Principal dimensions of the bulbous bow model.

No. Description Value Unit

1 Length of the ship, Lpp 2.120 m 2 Depth of the ship, H 0.181 m 3 Breadth of the ship, B 0.359 m 4 Draft of the ship, d 0.131 m 5 Displacement of the ship, D 0.0661 ton 6 Wetted surface area, S 0.965 m2 7 Block coefﬁcient, Cb 0.678 -

3.2. Effect of Bow Shape on Pressure Distribution of the Ships in Calm Water In this section, the CFD results of the pressure distributions around the ships in calm water are shown. Figures7 and8 show comparison of pressure distribution around the hull at the free surface of the computed domain of the ships, at the Froude number of 0.163 in calm water conditions. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 8 of 18

The results presented in Figures 4 and 5 show a comparison between the total ship resistance coefficients computed by the CFD and experimental data of the towing tank model test. The agreement between the computed results and the experimental results is fairly good, as shown. In calm water conditions, the difference between the CFD results and the experimental results is less than 6% in the range of the Froude number from 0.08 to 0.18, as shown in Figure 4. Figure 5 shows a good agreement between the CFD results and the experimental data of the total ship resistance in waves, where the incident waves are short and regular head waves, the λ/Lpp is less than 0.6, and the wave height, Hw, is 0.02 m for the 2 m length of the model at the Froude number of 0.163. The obtained results demonstrate the usefulness of applying CFD to compute the resistance and hydrodynamic performance of ships.

3. Effect of Bulbous Bow on the Hydrodynamic Performance of the Ship 3.1. Model of the NBS with the Newly Proposed Bow Shape In this study, a new bow shape was proposed for the NBS to reduce the added resistance of the hull form. The original ship has a blunt bow shape, whereas the new hull has a developed bow shape; the two ships have the same principal dimensions and stern shapes and only differ in their bow shapes. By using the CFD, the ships were computed and the obtained CFD results were compared so as to find out the effects of bow shape on J. Mar. Sci. Eng. 2021, 9, 559 the ships’ hydrodynamic performance. 8 of 16 Figure 6 shows the models of a new hull with a bulbous bow shape used for the computation; detailed principal dimensions of the model are listed in Table 3.

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Figure 6. Models of NBS with a bulbous bow used for simulation. (a) Haft frontal body plan of the new bulbous bow model; (b) new proposed( amodel) used for CFD computation.

Table 3. Principal dimensions of the bulbous bow model.

No. Description Value Unit 1 Length of the ship, Lpp 2.120 m 2 Depth of the ship, H 0.181 m 3 Breadth of the ship, B 0.359 m 4 Draft of the ship, d 0.131 m 5 Displacement of the ship, D 0.0661 ton 6 Wetted surface area, S 0.965 m2 7 Block coefficient, Cb 0.678 -

3.2. Effect of Bow Shape on Pressure Distribution of the Ships in Calm Water

In this section, the CFD results of the(b) pressure distributions around the ships in calm water are shown. Figures 7 and 8 show comparison of pressure distribution around the hullFigure at the 6. Models free surface of NBS of withthe computed a bulbous domain bow used of forthe simulation. ships, at the (a Froude) Haft frontal number body of 0.163 plan of the innew calm bulbous waterbow conditions. model; (b) new proposed model used for CFD computation.

(a)

(b)

n FigureFigure 7. 7. SimulatedSimulated wave wave pattern pattern at atthe the free free surface surface of ofthe the ships ships at atF F =n 0.163= 0.163 in incalm calm water water condi- conditions. tions.(a) The (a) NBSThe NBS with with a blunt a blunt bow bow shape; shape; (b) ( theb) the new new hull hull with with a newlya newly developed developed bow bow shape. shape.

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(a)

(b)

Figure 8. 8. CFDCFD results results of ofdynamic dynamic pressure pressure distribution distribution over over the surface the surface of the of ship’s the ship’shulls at hulls at n Fn=0.163= 0.163 in in calm calm water water conditions. conditions. (a ()a Side) Side view; view; (b ()b frontal) frontal and and aft aft view. view.

In FigureFigure7 7,, the the red red and and yellow yellow regions regions indicate indicate that that the the generated generated waves waves are high, are high, and andthe bluethe blue region region indicates indicates deep deep waves waves made made by the by shipthe ship running running in calm in calm water water conditions. condi- Thetions. results The results clearly clearly show show waves waves of reduced of reduced height height and depthand depth in the in regionthe region around around the thefrontal frontal hull hull of theof the ship ship with with the the developed developed bulbous bulbous bow bow shape. shape. FigureFigure8 8shows shows the the dynamic pressure distributiondistribution over over the the surface surface of of the the hull hull at at the the Froude Froude number number of of 0.163 0.163 in incalm calm water water conditions. conditions. Analyzing thethe dynamicdynamic pressurepressure distribution, distribution as, as shown shown in in Figure Figure8, the8, the red red and and yellow yel- lowregions regions indicate indicate high high dynamic dynamic pressure pressure and theand blue the regionblue region indicates indicates a lower a lower dynamic dy- pressurenamic pressure region overregion the over surface the surface of the ship’s of the hulls. ship’s The hulls. results The show results drastically show drastically reduced reducedhigh dynamic high dynamic pressure regionspressure over regions the surface over th ofe thesurface ship’s of hullthe ship’s with a hull bulbous with bow a bulbous shape. Thebow effectsshape. of The the effects bow shape of the on bow the shape pressure on distributionthe pressure over distribution the surface over of thethe ship’ssurface hull of thecould ship’s be evaluated. hull couldThe be evaluated. effects of the The bulbous effects of bow the shape bulbous on thebow pressure shape on distribution the pressure of distributionthe ships may of bethe evaluated ships may by be a comparisonevaluated by between a comparison the ship between resistance the in ship the resistance two cases inof the two computation cases of the with computation and without with a bulbous and without bow shape. a bulbous bow shape.

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3.3. Effect of Bulbous Bow Shape on Ship Pressure under Regular Head Waves Conditons 3.3. Effect of Bulbous Bow Shape on Ship Pressure under Regular Head Waves Conditons In this study, the NBS ship with and without a bulbous bow shape was simulated In this study, the NBS ship with and without a bulbous bow shape was simulated underunder wave wave conditions. conditions. The The incidence incidence of of waves waves at at the the regular regular head head and and the the short short waves waves with Hw=0.02 m and a ratio of λ/Lpp was less than 0.6. Figure 9 shows the CFD results of with Hw = 0.02 m and a ratio of λ/Lpp was less than 0.6. Figure9 shows the CFD results of wave patterns at the free surface of the simulated domain under wave conditions at wave patterns at the free surface of the simulated domain under wave conditions at λ/Lpp λ=/L 0.4,pp=0.4, with with the the Froude Froude number number of 0.163. of 0.163.

(a)

(b)

Figure 9. Simulated wave patterns at the free surface of the ships at Fn = 0.163 with regular head Figure 9. Simulated wave patterns at the free surface of the ships at Fn = 0.163 with regular head waves.waves. (a (a) )The The original original model; model; ( (bb)) the the new new model model with with a a bulbous bulbous bow. bow.

TheThe results, results, as seen inin FigureFigure9 ,9, show show a wavea wave pattern pattern at theat the free free surface surface of the of simulatedthe simu- lateddomain domain when when the ships the ships run under run under wave conditionswave conditions with a with wave a heightwave ofheight 0.02 mof and0.02 them andratio theλ/L ratiopp = λ 0.4/Lpp for = the0.4 2for m the long 2 model,m long at model, the Froude at the number Froude of number 0.163. In of the 0.163. results, In the the results,high and the deep high waves and deep around waves the ships’around bows the areships’ different bows withare different and without with the and developed without thebulbous developed bow. Figurebulbous 10 bow. shows Figure a comparison 10 shows of a thecomparison dynamic of pressure the dynamic distribution pressure over dis- the tributionsurface of over the the ship’s surface hulls of under the ship’s wave hulls conditions. under wave conditions. Analyzing the CFD results of dynamic pressure, as shown in the Figure 10, the bow wave made by the original hull without the bulbous bow is clearly higher than that of the bulbous bow model. The high dynamic pressure area region (red and yellow regions) and low dynamic pressure area regions (blue regions) acting over the hull surface of the bulbous bow model are drastically reduced. The results demonstrate that the new bulbous bow shape may reduce ship resistance under wave conditions.

J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 12 of 18 J. Mar. Sci. Eng. 2021, 9, 559 11 of 16

(a)

(b)

FigureFigure 10. 10. SimulatedSimulated dynamic dynamic pressure pressure distribution distribution over over the the surface surface ofof the the ship’s ship’s hulls hulls in inregular regular head and short waves, Hw = 0.02 m and the ratio λ/Lpp = 0.4, at Fn = 0.163. (a) Side view; (b) frontal head and short waves, Hw = 0.02 m and the ratio λ/Lpp = 0.4, at Fn = 0.163. (a) Side view; (b) frontal andand aft aft view. view.

4. ReducedAnalyzing Ship the Resistance CFD results of dynamic pressure, as shown in the Figure 10, the bow wave4.1. Ship made Resistance by the original in Calm hull Water without the bulbous bow is clearly higher than that of the bulbousIn thisbow study, model. resistance The high acting dynamic on thepressure hulls area of the region NBS in(red calm and water yellow was regions) computed and lowby the dynamic CFD.By pressure comparison area regions of the ship (blue resistance regions) betweenacting over the the two hull ships, surface one withof the a bulb- blunt ousbow bow and model one with are a drastically bulbous bow reduced. shape, The the effectresults of demonstrate the bow shape that on the the new resistance bulbous of bowthe NBSshape in may calm reduce water conditionsship resistance has beenunder found. wave Theconditions. detailed computed results of ship resistance for the 2 m-long models in calm water conditions are listed in Tables4 and5. Figure 11 shows a comparison of the total resistance coefﬁcients of the two ships in calm water conditions.

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Table 4. Resistance acting on the original model in calm water.

Resistance (N) Resistance Coefﬁcients

Fn RP RF RT CP CF CT 0.080 0.0324 0.3020 0.3343 0.00056 0.00523 0.00579 0.120 0.1122 0.5869 0.6991 0.00086 0.00452 0.00538 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW0.140 0.1742 0.7535 0.9276 0.00098 0.00426 0.0052413 of 18 0.163 0.2705 0.9706 1.2411 0.00112 0.00402 0.00514 0.180 0.3699 1.1526 1.5225 0.00126 0.00394 0.00521

4. Reduced Ship Resistance Table 5. Resistance acting on the bulbous bow model in calm water. 4.1. Ship Resistance in Calm Water In this study,Resistance resistance (N) acting on the hulls of the Resistance NBS in calm Coefﬁcients water was computed by theF nCFD. By comparisonRP of theRF ship resistRanceT betweenCP the two ships,CF one withC aT blunt bow0.080 and one with 0.0169 a bulbous 0.3189bow shape, 0.3357the effect of 0.00028the bow shape 0.00532 on the resistance 0.00560 of the NBS0.120 in calm 0.0430water conditions 0.6422 has been 0.6852 found. The 0.00032 detailed computed 0.00476 results 0.00508 of ship resistance0.140 for the 0.0672 2 m-long models 0.8388 in calm 0.9060 water conditions 0.00037 are listed 0.00456 in Tables 0.00493 4 and 5. Figure0.163 11 shows 0.0996a comparison 1.1268 of the total 1.2264 resistance coefficients 0.00040 of 0.00450 the two ships 0.00489 in calm 0.180 0.1304 1.3618 1.4922 0.00043 0.00448 0.00491 water conditions.

Figure 11. Comparison of the total resistance coefﬁcientscoefficients of the ships.

In the computation, ship resistance was divided into the two components of pressure viscous resistance (R (Rpp) )and and frictional frictional viscous viscous resistance resistance (R (RF),F the), the total total resistance resistance (RT (R) isT )de- is fineddefined following following Equation Equation (1), (1), and and the the total total resistance resistance coefficient coefficient is isdefined defined as asfollows: follows:

CTC=T C= PC+P + C CF F (2)

where: CP is the pressure viscous resistance; CP is the pressure viscous resistance; CF is the frictional viscous resistance coefficient. CF is the frictional viscous resistance coefﬁcient.

TableThe 4. Resistance results of acting the totalon the resistance original model coefﬁcients in calm water. of the ships shown in Tables4 and5 and Figure 11 show that the frictional viscous resistance acting on the bulbous bow model was slightly higherResistance than that(N) of the original model, which Resistance may be Coefficients the result of the larger wettedFn surfaceR areaP of the bulbousRF bow shape. Additionally,RT the pressureCP viscousCF resistanceCT and0.080 the total0.0324 resistance acting0.3020 on the bulbous bow0.3343 model were0.00056 smaller 0.00523 than those 0.00579 of the 0.120 0.1122 0.5869 0.6991 0.00086 0.00452 0.00538 0.140 0.1742 0.7535 0.9276 0.00098 0.00426 0.00524 0.163 0.2705 0.9706 1.2411 0.00112 0.00402 0.00514 0.180 0.3699 1.1526 1.5225 0.00126 0.00394 0.00521

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J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 14 of 18 original model by up to 6%. The reasons for this may arise from the effects of the developed bulbous bow shape.

4.2.Table Ship 5. Resistance Resistance acting under on Wave the bulbous Conditions bow model in calm water. In this study, the effect of the bow shape on ship resistance under conditions of regular head waves wasResistance investigated (N) via comparison with the Resistance other CFD Coefficients results of the two ships withFn and withoutRP the bulbous bow.RF Tables6 and7 listRT the detailedCP ship resistanceCF underCT wave0.080 conditions0.0169 with Hw = 0.020.3189 m for the 2 m-long0.3357 model,0.00028 at the Froude0.00532 number 0.00560 of 0.163.0.120 Figures0.0430 12 and 13 show0.6422 a comparison of the0.6852 computed 0.00032 ship resistance 0.00476 under 0.00508 wave conditions0.140 for0.0672 the two ships. 0.8388 0.9060 0.00037 0.00456 0.00493 0.163 0.0996 1.1268 1.2264 0.00040 0.00450 0.00489 Table0.180 6. Computed0.1304 ship resistance1.3618 of the original model1.4922 under wave0.00043 conditions. 0.00448 0.00491 The resultsResistance of the (N)total resistance coefficients of Resistance the ships Coefﬁcients shown in Tables 4 and 5

andλ Figure/Lpp 11 showRP that the frictionalRF viscouRsT resistance CactingP on theC bulbousF bowC Tmodel was slightly0.3 higher 0.8151 than that 0.9069of the original 1.7220 model, which 0.00253 may be 0.00383the result of 0.00636the larger wetted0.4 surface area 0.7116 of the bulbous 0.9523 bow 1.6638shape. Additionally, 0.00248 the 0.00395 pressure viscous 0.00644 re- sistance0.5 and the 0.7344total resistance 0.9591 acting on the 1.6935 bulbous bow 0.00257 model were 0.00393 smaller than 0.00650 those of the0.6 original model 0.7706 by up to 0.9541 6%. The reasons 1.7248 for this 0.00262 may arise 0.00388from the effects 0.00650 of the developed bulbous bow shape. Table 7. Resistance acting on the bulbous bow model in waves. 4.2. Ship Resistance under Wave Conditions Resistance (N) Resistance Coefﬁcients In this study, the effect of the bow shape on ship resistance under conditions of reg- ularλ head/Lpp waves wasRP investigatedRF via comparisonRT withC theP other CFDCF results of CtheT two ships0.3 with and without 0.3381 the bulbous 1.0466 bow. 1.3847 Tables 6 and 0.00135 7 list the detailed 0.00418 ship 0.00552resistance under0.4 wave conditions 0.3725 with H 1.0291w = 0.02 m for 1.4016 the 2 m-long 0.00149 model, at 0.00411 the Froude number 0.00559 of 0.163.0.5 Figures 12 0.3769 and 13 show 1.0386 a comparison 1.4155 of the computed 0.00150 ship 0.00414resistance under 0.00565 wave 0.6 0.3699 1.0484 1.4183 0.00148 0.00418 0.00566 conditions for the two ships.

Figure 12.12. Added wave resistance coefficients coefﬁcients of the ships ships under under wave wave conditions, conditions, H Hww == 0.02 0.02 m m at at Fnn = 0.163. 0.163. In the research, the added wave resistance under wave conditions is deﬁned as in the following equation: CW = CT(W) − CT(0) (3) where:

CT(0) is the total ship resistance coefﬁcient in calm water conditions;

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CT(W) is the total ship resistance coefﬁcient under wave conditions.

FigureFigure 13. 13. TotalTotal ship resistance coefﬁcientscoefficients underunder thethe conditioncondition ofof regularregular headhead waves,waves, HHww == 0.02 m mat at Fn F=n 0.163.= 0.163.

TableThe 6. Computed results of ship ship resistance resistances of detailedthe original in Tablesmodel 6under and7 wave clearly conditions. show the ship resistance of the two ships under the condition of regular head waves for the 2 m-long model, at Resistance (N) Resistance Coefficients Hw = 0.02 m and Fn = 0.163. The results in Figures 12 and 13 clearly show the effects of the newλ/Lppbow shapeRP on the resistanceRF acting on the shipRT under waveCPconditions. CF The addedCT wave0.3 resistance0.8151 coefﬁcients of0.9069 the new bow model1.7220 have been drastically0.00253 0.00383 reduced 0.00636 by up to 48%0.4 compared0.7116 with those of the0.9523 blunt bow model,1.6638 as shown. 0.00248 Additionally, 0.00395 the total0.00644 ship resistance0.5 of0.7344 the ship with the0.9591 developed bulbous1.6935 bow was0.00257 reduced by0.00393 up to 13%.0.00650 The results0.6 of ship0.7706 resistance were also0.9541 in good agreement1.7248 with the0.00262 obtained 0.00388 CFD results 0.00650 of the pressure distribution and the experimental data, as shown. The proposed bulbous bow Tableshape 7. could Resistance thus beacting a good on the choice bulbous for bow the NBSmodel to in reduce waves. resistance. However, to clearly ﬁnd the full effects of the bulbous bow shape on the resistance Resistance (N) Resistance Coefficients acting on the ship, we need more comparable results regarding the ships running under differentλ/Lpp conditions,RP including ballastRF conditions andRT in differentC waveP conditionsCF atC otherT Froude0.3 numbers.0.3381 In this study,1.0466 we only aimed to1.3847 show an appropriate0.00135 bulbous0.00418 bow0.00552 shape at0.4 the designed0.3725 draft condition1.0291 and designed speed1.4016 under the0.00149 full load 0.00411 condition 0.00559 of the ships0.5 running0.3769 in calm water and1.0386 in regular head1.4155 waves. The0.00150 incident 0.00414 wave considered 0.00565 was0.6 a regular0.3699 head wave with1.0484 a wave height Hw1.4183= 0.02 m and0.00148 ratio of0.00418λ/Lpp < 0.60.00566 at the designed speed of Fn = 0.163; we will examine other conditions in our future work. In the research, the added wave resistance under wave conditions is defined as in the following5. Conclusions equation:

In this study, the hydrodynamic performanceCW = CT(W) − C andT(0) the resistance of the NBS with and(3) without a bulbous bow shape under full load conditions were investigated using the CFD. where:From the obtained results, the effect of bow shape on ship resistance has been shown. CFurthermore,T(0) is the total the ship CFD resistance results coefficient obtained in in this calm study water show conditions; that the new hull form with CaT(W) proposed is the total bulbous ship resistance bow shape coefficient can be applied under towave considerably conditions. reduce the added wave resistanceThe results as well of as ship to reduce resistances fuel consumption.detailed in Tables The main6 and conclusions 7 clearly show of this the study ship arere- sistancesummarized of the as two follows: ships under the condition of regular head waves for the 2 m-long model,• The at obtained Hw = 0.02 CFD m and results Fn for= 0.163. the two The ships, results namely, in Figures the original 12 and NBS 13 clearly hull with show a blunt the effectsbow of the shape new and bow one shape with on a newthe resistance bulbousbow acting shape on the in theship full under load wave condition, conditions. were The addedobtained. wave It wasresistance conﬁrmed coefficients that the CFDof the code new provided bow model us with have good been results drastically regarding reduced by up to 48% compared with those of the blunt bow model, as shown. Additionally, the total ship resistance of the ship with the developed bulbous bow was reduced by up to 13%. The results of ship resistance were also in good agreement with the obtained CFD

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the computed resistance acting on the hull of the ship, both under calm water and in regular head wave conditions. • The proposed bulbous bow shape had effects on the hydrodynamic performance as well as the ship resistance of the NBS in the computed condition. It has been clearly shown that the developed bulbous bow shape affected both the pressure distribution and the wave pattern at the free surface of the ship in the computed domain. Hence, an appropriate bulbous bow shape could be developed to drastically reduce the total resistance in the computed condition. • The effects of the bulbous bow shape on reduced resistance acting on the NBS in calm water reached about 6% in the case of the higher wetted surface area of the bulbous bow model. • The effect of a bulbous bow shape on the resistance acting on the hull under regular head wave conditions with Hw = 0.02 m and the ratio λ/Lpp < 0.6 was investigated. Using the proposed bulbous bow shape, up to 48% of the added wave resistance and 13% of the total resistance acting on the hull of the NBS at the Froude number of 0.163 in the computed wave condition could be reduced.

Author Contributions: Conceptualization, T.-K.L., N.V.H. (Ngo Van He), N.V.H. (Ngo Van Hien) and N.-T.B.; methodology, T.-K.L., N.V.H. (Ngo Van He), N.V.H. (Ngo Van Hien) and N.-T.B.; software, N.V.H. (Ngo Van He) and N.V.H. (Ngo Van Hien); validation, N.V.H. (Ngo Van He), N.V.H. (Ngo Van Hien) and N.-T.B.; writing—original draft preparation, T.-K.L. and N.V.H. (Ngo Van He), N.V.H. (Ngo Van Hien); writing—review and editing T.-K.L., N.V.H. (Ngo Van He), N.V.H. (Ngo Van Hien) and N.-T.B.; supervision, N.V.H. (Ngo Van Hien); project administration, N.V.H. (Ngo Van He). All authors have read and agreed to the published version of the manuscript. Funding: This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the grant number 107.03-2019.302. The authors would like to warmly express their thanks for the support. Acknowledgments: We would be grateful for the cooperation between the Hanoi University of Science and Technology (HUST) and Shibaura Institute of Technology (SIT) in the CFD computation, guidance, and expertise. This work was also supported by the Centennial SIT Action for the 100th anniversary of Shibaura Institute of Technology to enter the top ten Asian Institutes of Technology. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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