The Effect of Hull Form Parameters on the Hydrodynamic Performance of a Bulk Carrier

Journal of Marine Science and Engineering

Article The Effect of Hull Form Parameters on the Hydrodynamic Performance of a Bulk Carrier

Rui Deng 1,2, Shigang Wang 1,2, Yuxiao Hu 1,2, Yuquan Wang 1,2 and Tiecheng Wu 1,2,*

1 School of Marine Engineering and Technology, Sun Yat-sen University, Zhuhai 519000, China; [email protected] (R.D.); [email protected] (S.W.); [email protected] (Y.H.); [email protected] (Y.W.) 2 Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China * Correspondence: [email protected]; Tel.: +86-187-4514-7797

Abstract: In this study, the effect of joint optimization of the principal dimensions and hull form on the hydrodynamic performance of a bulk carrier was studied. In the ﬁrst part of the joint optimization process, fast principal-dimension optimization of the origin parent ship considering the integrated performance of ship resistance, seakeeping, and maneuverability, as well as their relationships with the principal dimensions were analyzed in detail based on the ship resistance, seakeeping qualities, and maneuverability empirical methods of Holtrop and Mennen, Bales, and K and T indices, respectively. A new parent ship was chosen from 496 sets of hulls after comprehensive consideration. In the remaining part, a further hull form optimization was performed on the new parent ship according to the minimum wave-making resistance. The obtained results demonstrate

that: (a) For the case in which the principal dimension of the original parent-type ship is different from that of the owner’s target ship, within the bounds of the relevant constraints from the owner, an

Citation: Deng, R.; Wang, S.; Hu, Y.; excellent parent ship can be obtained by principal-dimension optimization; (b) the joint optimization Wang, Y.; Wu, T. The Effect of Hull method considering the principal dimension and hull form optimization can further explore the Form Parameters on the optimization space and provide a better hull. Hydrodynamic Performance of a Bulk Carrier. J. Mar. Sci. Eng. 2021, 9, Keywords: principal-dimension optimization; ship resistance; seakeeping; maneuverability; Holtrop 373. https://doi.org/10.3390/ and Mennen’s empirical methods; towing tank test jmse9040373

Academic Editor: Kostas A. Belibassakis 1. Introduction To reduce maritime greenhouse gas (GHG) emissions to reach the International Mar- Received: 13 March 2021 itime Organization (IMO) 2050 target, new energy-efﬁcient ships are urgently needed. Accepted: 30 March 2021 Published: 1 April 2021 Although these energy-efﬁcient designs have a higher newbuild cost, the savings on fuel consumption and, in turn, the cost, tend to be considerably larger than the additional

Publisher’s Note: MDPI stays neutral newbuild cost [1–4]. with regard to jurisdictional claims in Among the various aspects of ship performance, hull form optimization has long published maps and institutional affil- focused on minimizing ship resistance. For certain hull forms, hull form optimization iations. can reduce resistance. Sariöz [5] presented an optimization approach to be used in the preliminary design stage to create a high-quality ship hull form geometry. Hong et al. [6] developed a self-blending method to modify and optimize a bulbous bow. The shape of the bulbous bow of a fishing vessel was optimized, and the resistance was reduced by 2%. Rotteveel et al. [7] analyzed the optimization of propulsion power for various Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. water depths using a parametric inland ship stern shape. Cerka et al. [8] presented a This article is an open access article numerical simulation of hull form optimization of a multi-purpose catamaran-type research distributed under the terms and vessel based on the method of successive approximations. Deng et al. [9] used nonlinear conditions of the Creative Commons programming and genetic algorithms to optimize the hull form and achieved promising Attribution (CC BY) license (https:// results. Cheng et al. [10] used a new hull surface automatic modification method based creativecommons.org/licenses/by/ on Delaunay triangulation to perform hull form optimization, which can significantly 4.0/). improve the optimization efficiency. Hou [11] presented the hull form optimization design

J. Mar. Sci. Eng. 2021, 9, 373. https://doi.org/10.3390/jmse9040373 https://www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2021, 9, 373 2 of 16

method for minimum Energy Efficiency Operation Index (EEOI), and four case studies were conducted to verify the feasibility and superiority of the novel approach. Zheng et al. [12] took numerical functions and the surface combatant model DTMB 5415 as the research objectives for knowledge extraction by combining the partial correlation analysis and self- organizing map (SOM) based on optimization data. Kim et al. [13] studied an efficient and effective hull surface modification technique for the Computational Fluid Dynamics (CFD)- based hull form optimization. Numerical results obtained in this study have shown that the present hull surface modification technique can produce smooth hull forms with reduced drag effectively and efficiently in the CFD-based hull form optimization. Feng et al. [14] performed an experimental and numerical study of multidisciplinary design optimization to improve the resistance performance and wake field quality of a vessel. Lin et al. [15] set up an automatic design optimization of a small waterplane area twin-hull (SWATH) that provides accurate flow prediction and is integrated into the optimization module. They obtained lower resistance than the original hull, which shows the effectiveness of the optimization. Seok et al. [16] applied the design of experiments and CFD to improve the bow shape of a tanker hull. The results show that the added resistance of the improved hull form is reduced by 52%. Priftis et al. [17] applied a holistic optimization design approach to study the parametric design and multi-objective optimization of ships under uncertainty. Papanikolaou et al. [18] performed a numerical and experimental optimization study on a fast, zero-emission catamaran. Jeong et al. [19] proposed two methods for comparing the mesh deformation method for hull form optimization. Various bow shapes of the Japan Bulk Carrier were applied to validate the applicability of the methods. The proposed mesh deformation method was efficient and effective for CFD-based hull form optimization. However, in general, hull form optimization does not result in significant changes to the original hull form, and the corresponding effect on the resistance reduction becomes increasingly limited with the improvement in the hull form. Compared with hull form optimization, the principal dimensions of the hull can have a more significant impact on the hydrodynamic performance of the ship; however, they are usually determined by the usage requirements, parent ship dimensions, and other constraints in the initial stage of ship design, following which the modification of the principal dimensions is seldom considered. Therefore, few researchers have conducted studies on resistance reduction based on principal-dimension optimization. Zhang et al. [20] used regression analysis to study the sensitivity of the resistance to the principal dimension of the hull form; the principal dimension parameters with the most significant effects on the total resistance were identified, and the ship resistance was significantly reduced by changing the principal dimensions. Pechenyuk [21] proposed a wave-based optimization method for hull form design, which changes the displacement volume distribution by varying the principal dimensions and thus optimizes the transverse and scattered waves induced. The optimized design of the hull provided the best displacement volume distribution, and the resistance was reduced by 8.9% compared with that of the parent ship. Lindstad et al. [1,4,22–24] studied how hull forms can be made more energy efficient for realistic sea conditions by modifying the main ratios among beam, draught, and length to reduce the block coefficients while keeping the cargo-carrying capacity unchanged. In addition to resistance optimization, Ouahsine et al. [25,26] proposed a numerical method based on c the combination of a mathematical model of nonlinear transient ship maneuvering motion in the horizontal plane and mathematical programming techniques; this method was validated by the turning circle and zigzag maneuvers based on experimental data of sea trials of the 190,000 dwt oil tanker. Subsequently, they developed a numerical model to predict ship maneuvering in a confined waterway using a nonlinear model with optimization techniques to identify the hydrodynamic coefficients accurately. Some studies have been performed for hull form and principal-dimension optimization of ships. Few scholars have conducted relevant research on the joint optimization of principal dimensions and hull form of ships considering the integrated performance of ship resistance, seakeeping, and maneuverability. Thus, there are still some important J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 3 of 16

Some studies have been performed for hull form and principal-dimension optimiza- J. Mar. Sci. Eng. 2021, 9, 373 tion of ships. Few scholars have conducted relevant research on the joint optimization3 of 16of principal dimensions and hull form of ships considering the integrated performance of ship resistance, seakeeping, and maneuverability. Thus, there are still some important aspects that need to be investigated further regarding this topic, such as the accuracy and aspectsapplicability that need of empirical to be investigated methods for further the rapid regarding prediction this topic, of ship such resistance, as the accuracy seakeeping, and applicabilityand maneuverability; of empirical accuracy methods correction for the of rapid empirical prediction methods of shipfor given resistance, ship types; seakeep- and ing,relationships and maneuverability; of resistance, accuracy seakeeping, correction and maneuverability of empirical methods performance for given with ship the types; prin- and relationships of resistance, seakeeping, and maneuverability performance with the cipal dimensions. principal dimensions. In this study, the effect of joint optimization of the principal dimensions and hull In this study, the effect of joint optimization of the principal dimensions and hull form form on the hydrodynamic performance of a bulk carrier (origin parent ship) is studied on the hydrodynamic performance of a bulk carrier (origin parent ship) is studied based on based on empirical methods and towing tank tests, considering the integrated perfor- empirical methods and towing tank tests, considering the integrated performance of ship mance of ship resistance, seakeeping, and maneuverability. First, empirical methods of resistance, seakeeping, and maneuverability. First, empirical methods of ship resistance, ship resistance, seakeeping, and maneuverability are introduced, and then the accuracy seakeeping, and maneuverability are introduced, and then the accuracy correction of the correction of the resistance empirical method based on CFD for the given ship is studied. resistance empirical method based on CFD for the given ship is studied. Second, the Second, the resistance, seakeeping, and maneuverability of 496 sets of hulls with different resistance, seakeeping, and maneuverability of 496 sets of hulls with different principal principal dimensions are calculated using the modified empirical methods, and the rela- dimensions are calculated using the modified empirical methods, and the relationships of tionships of resistance, seakeeping, and maneuverability of the hull with the principal di- resistance, seakeeping, and maneuverability of the hull with the principal dimensions are analyzedmensions in are detail. analyzed Thereafter, in detail. a new Thereafter, parent ship a new with parent L = 136.0 ship m andwith B L = = 18.38 136.0 m m is and chosen B = through18.38 m theis chosen systematic through analysis the ofsystematic principal-dimension analysis of principal optimization.-dimension Finally, optimization. further hull formFinally, optimization further hull and form verification optimization based and on verification the new parent based ship on bythe the new towing parent tank ship test by arethe presented.towing tank The test remainder are presented. of this The paper remainder is organized of this as paper follows. is organized Section1 discussesas follows. theSection literature 1 discusses review the of literature the form review and principal-dimensionof the form and principal optimization-dimension of optimization ships. The geometricof ships. Themodel geometric and offset model point and information offset point of the information parent ship of are the described parent inshipSection are de-2 . InscribedSection in3 Section, the ship 2. In resistance, Section 3, the seakeeping ship resistance, qualities, seakeeping and maneuverability qualities, and maneuver- empirical methodsability empirical of Holtrop methods and Mennen, of Holtrop Bales, and and Mennen, K and T Bales, indices and are K described, and T indices respectively. are de- Thescribed, accuracy respectively. correction The of accuracy Holtropand correction Mennen’s of Holtrop empirical and method Mennen’s based empirical on CFD method for the givenbased ship on CFD type for is studied the given in detail.ship type Section is studied4 presents in detail. the relationships Section 4 presents between the resistance, relation- seakeeping,ships between and resistance, maneuverability seakeeping, performance and maneuverability with the principal performance dimensions. with theSection princi-5 describespal dimensions. the optimization Section 5 describes procedure. the Further optimization hull foam procedure. optimization Further and hull verification foam opti- basedmization on theand selectedverification new based parent on ship the selected are discussed new parent in Section ship6 are. Section discussed7 provides in Section a summary6. Section of7 provides this study. a summary of this study.

2.2. GeometricGeometric ModelModel andand InformationInformation ofof thethe ParentParent ShipShip InIn thisthis study,study, a bulk carrier carrier was was treated treated as as the the origin origin parent parent ship, ship, with with a length a length of 132 of 132m, width +m, width of 18.2 of m, 18.2 and m, draft and draftof 5.9 ofm, 5.9 block m, blockcoefficient coefﬁcient of 0.6025, of 0.6025, displacement displacement of 8806.6 of 8806.6t, and t,designed and designed speed speedof 19 kn. of 19The kn. 3- Thedimensional 3-dimensional geometric geometric model model and the and offset the offsetpoints pointsused for used calculation for calculation are shown are shown in Figure in Figure 1. 1.

FigureFigure 1.1.Geometric Geometric model model and and offset offset points points of of the the parent parent ship: ship: (a ()a Side) Side view view of of the the geometric geometric model model of the parent ship; (b) top and side views of the offset points of the parent ship; (c) front of the parent ship; (b) top and side views of the offset points of the parent ship; (c) front and stern and stern views of the geometric model of the parent ship; (d) front and stern views of the offset views of the geometric model of the parent ship; (d) front and stern views of the offset points of the points of the parent ship. parent ship.

The required offsets were extracted and calculated by the software GAMBIT which is a registered trademark of Fluent, Inc (now owned by ANSYS Inc, Canonsburg, PA, USA) (Figure1). The stations were set every 0.2 m for the bow, every 1.0 m for the hull, and every J. Mar. Sci. Eng. 2021, 9, 373 4 of 16

0.5 m for the stern, such that the underwater part of the hull was divided into 161 stations from the bow apex to the stern. A total of 70 offset points were obtained for each station line, and the maximum distance between the offset points was approximately 0.14 m. A total of 13,651 offset points were obtained from the waterline, and the maximum distance between the offset points was approximately 0.44 m. This yielded a total of 24,921 offset points to ensure that the hull geometric information was accurately captured.

3. Methodology Owing to the large Reynolds numbers of full-scale ships, the numerical calculation of their viscous wake fields based on the CFD method requires many cells and specific turbulence models, 2-phase flow models, and degree of freedom motion models, leading to a high threshold of numerical skills and long computation time. Therefore, this method is not applicable for the comparison of multiple schemes in the preliminary design stage. In contrast, existing empirical methods based on regression analysis of model tests and trial data of many ships have good usability and are less time-consuming. Although the calculation accuracy for a particular hull form is limited, it can accurately reflect the changes in the hydrodynamic performance of the ship as the principal dimension changes. Therefore, in this study, the empirical methods of Holtrop and Mennen, Bales, and K and T exponents were used in principal-dimension optimization to calculate the resistance, seakeeping, and maneuverability of a series of hull forms.

3.1. Holtrop and Mennen’s Empirical Methods of Ship Resistance At present, there are many empirical formula methods for resistance, such as Ayre’s method, Lap–Keller’s method, and Holtrop and Mennen’s method. Ayre and Lap–Keller’s methods are based on the statistical data of ship types of the 1940s and 1950s. Thus, obvious errors arise from new types of ships in the estimation after the late 1980s. In the early 1980s, Holtrop and Mennen developed a resistance prediction method based on regression analysis of model tests and trial data of Marine Research Institute Netherlands (MARIN), the model basin in Wageningen, The Netherlands [27–31]. Holtrop and Mennen’s method was arguably the most popular method for estimating the resistance and horsepower of displacement-type ships. It was based on the regression analysis of a vast range of model tests and trial data, which provided wide applicability [32]. Holtrop and Mennen’s method deﬁnes the total resistance as:

RT = RF + RP + RW, (1)

where RT is the total resistance, and RF, RP, and RW represent the frictional, pressure, and wave resistances, respectively. The friction resistance is corrected by introducing the form factor k, which affects the estimation of the residuary resistance, and the pressure resistance is included in the friction resistance. The frictional resistance RF is computed on the basis of the international towing tank conference (ITTC) 1957 model–ship correlation line coefﬁcient CF as the resistance of a ﬂat plate with wetted surface S:

RF(1 + k) = RF + RP, (2)

2 2 RF = 1/2CFρV S, CF = 0.075/(log Re − 2) , (3)

To estimate the wave resistance RW, Holtrop deﬁnes RW as the range of Froude numbers into 3 sections:

 d −2 c c c ρg∇ · em1 Fr +m4 cos (λFr ) if Fr ≤ 0.4  1 2 5 R = (20Fr−8) . (4) W RW (0.4)+ 3 [RW (0.55) − RW (0.4)] if 0.4 0.55

In Equations (2)–(4), ρ is the density of sea (fresh) water, V is the velocity of the ship, ∇ is the volumetric displacement, and Re and Fr are the Reynolds and Froude numbers, J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 5 of 16

d 2 m14 Fr mcos Fr   c c c g e if Fr  0.4  1 2 5  (20Fr  8) RWWWW R(0.4)+ R (0.55)  R (0.4) if 0.4< Fr  0.55 . (4)  3 d 2  m34 Fr mcos Fr  J. Mar. Sci. Eng. 2021, 9, 373  c17 c 2 c 5  g e if Fr  0.55 5 of 16 In Equations (2)–(4), ρ is the density of sea (fresh) water, V is the velocity of the ship,  is the volumetric displacement, and Re and Fr are the Reynolds and Froude numbers, respectively. Furthermore, Furthermore, c1c,1 c, 2c, 2c,5,c c517, ,c 17d,, λd, ,mλ1, m31,, andm3, m and4 arem 4coefficientsare coefficients for the for wave the resistancewave resistance computation computation in Equation in Equation (4), and (4), the and detailed the detailed description, description, definition, definition, and andcal- culationcalculation equations equations of the of the above above coefficient coefficientss can can be befound found in references in references [27 [–2732–].32 ]. For the the empirical empirical formula formula methods methods proposed proposed in the in ship the resistance ship resistance evaluation evaluation method methodsection, section, the methods the methods should should be first be compared first compared to determine to determine the one the to one be to applied. be applied. The Theresistance resistance of 3 of types 3 types of shipsof ships [33 []33 (25,000] (25,000 t tanker,t tanker, 82,000 82,000 t t bulk bulk carrier, carrier, andand 900900 TEU container ship) was predicted by the empirical formula methods and compared with the experimental data, as shown in Figure2 2..

(a) (b)

(c)

Figure 2. Comparison between the results of the Ayre’s,Ayre’s, Lap–Keller’s,Lap–Keller’s, Holtrop and Mennen’s methods and experimental data. ( a) 25,000 t tanker; (b) 82,000 t bulk carrier; (c)) 900900 TEUTEU containercontainer ship.ship.

From the comparison of the results in Figure 2 2,, itit cancan bebe observedobserved thatthat thethe calculationcalculation results of various empiricalempirical formula methods can basically maintain the tendency as the experimental results and can reﬂectreflect the resistance characteristics ofof thethe ship.ship. Owing to the different applicability of each method, the errors errors for different different ship types types are are also also different; different; Ayre and Lap–Keller’s methods have better accuracy at low speeds and gradually become misaligned as the speed increases. These methods are based on the statistical data of ship types in the 1940s and the 1950s, and the resistance estimation errors for emerging ship types are relatively large. Although the Holtrop and Mennen’s method has certain errors, it is generally better than the other two methods. In chronological order, this method was also the latest resistance empirical formula method, which has certain credibility for the estimation of modern ship types. Therefore, in terms of resistance prediction, the J. Mar. Sci. Eng. 2021, 9, 373 6 of 16

Holtrop and Mennen’s method can be recommended as a credible method for estimating the resistance of the target ship.

3.2. Brief Description of Bales’s Empirical Method for Ship Seakeeping Performance Bales calculated the seakeeping properties of 20 destroyers, used 6 geometric characteristics CWF, CWA, Td/L, C/L, CVPF, and CVPA as variables for regression analysis, and established the relationship between the seakeeping rank factor R and geometric characteristics. The seakeeping prediction model proposed by N.K. Bales [34,35] was adopted by the ship design department of the US Navy and was later promoted and can be used in a variety of ship types. The rank factor R is deﬁned as follows:

∧ T C R = 8.422 + 45.104C + 10.078C − 378.465 d + 1.273 − 23.501C − 15.875C (5) WF WA L L VPF VPA

∧ where R is the estimated value of R; C is the distance from Station 0 to the cut-up point; Td and L are the draft and length between the perpendiculars of the ship; CWF and CWA represent the water-plane coefficients forward and aft of amidships, respectively; and CVPF and CVPA are the vertical prismatic coefficients forward and aft of amidships, respectively. The rank factor R indicates the degree of seakeeping performance: A larger value indicates better performance. The detailed description, definition, and calculation equations of the above coefficients can be found in references [34,35].

3.3. Brief Description of K and T Indices Empirical Methods for Ship Maneuverability Nomoto [36,37] studied the problem of ship maneuverability from the viewpoint of control engineering based on the linear equation of ship maneuverability motion and regarded the various maneuvering motions caused by changing the rudder angle as the response of the output maneuvering motion to the input rudder angle. In addition, a second- order maneuvering motion equation was derived, which was also called K. Nomoto’s model. The exponents K and T of K. Nomoto’s model can define the maneuverability of the ship, which has a clear physical meaning. The K index reflects the turning ability of the ship and is called the turning ability index; the T index represents the ship’s rapid response to the rudder and navigation stability and is called the turning lag index. K and T are collectively referred to as the ship’s maneuverability index. Ships with good maneuverability should have a large positive K value and a small positive T value. Zhang et al. [38,39], based on the research of Hong [40] and Yao [41] by increasing the number and types of statistical ships, and considering the influence of nonlinear factors between the data vol- umes, used the parameters of 59 ships as samples, established the quaternion second-order polynomial regression mathematical model, and obtained a statistical regression formula. The results of this formula were compared with the Z-shaped experimental results of the ship, which were not in the statistical samples, to verify the validity of the equation. The estimation formulae for K and T are defined as follows: ∧ L LTd 2 L B K = 47.875 − 2.64 + 0.004 + 66.589Cb − 112.702Cb + 3.826Cb − 0.393Cb , (6) B AR B Td

∧ LTd L LTd L 2 T = 26.464 + 0.408Cb − 0.033 − 79.114Cb + 0.757 + 46.129Cb . (7) AR B AR B ∧ ∧ where K and T are the estimated values of K and T, respectively; Td, B, and L are the draft, breadth, and length between the perpendiculars of the ship, and Cb and AR represent the block coefﬁcient and rudder area, respectively. The maneuverability index P is deﬁned as P = K/T, in which a larger P-value indicates better ship maneuverability. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 7 of 16

 LTddLL LT 2 TCCC26.464  0.408b  0.033  79.114 b  0.757 +46.129 b . (7) ABABRR

  where K and T are the estimated values of K and T, respectively; Td, B, and L are the draft, breadth, and length between the perpendiculars of the ship, and Cb and AR represent J. Mar. Sci. Eng. 2021, 9, 373 the block coefficient and rudder area, respectively. The maneuverability index P is defined7 of 16 as P = K/T, in which a larger P-value indicates better ship maneuverability.

3.4. Accuracy Correction of Holtrop and Mennen’s Empirical Method Based on CFD for the 3.4. Accuracy Correction of Holtrop and Mennen’s Empirical Method Based on CFD for the Given ShipGiven Type Ship Type InIn the the principal-dimension principal-dimension optimization optimization part, part, the the resistance resistance performance performance was was the the mostmost importantimportant aspectaspect ofof thethe hydrodynamichydrodynamic performance,performance, followedfollowed byby seakeepingseakeeping andand maneuverability.maneuverability. Accuracy correction was only performedperformed forfor thethe empiricalempirical methodmethod ofof resistance.resistance. BecauseBecause thethe shipship usedused inin thethe establishmentestablishment ofof HoltropHoltrop andand Mennen’sMennen’s empiricalempirical methodmethod was somewhat somewhat different different from from the the one one used used in inthis this study, study, and and as described as described in Sec- in Sectiontion 3.1, 3.1 directly, directly using using this thismethod method to calculate to calculate the resistance the resistance of a ship of awill ship result will in result certain in certainpotential potential errors. Therefore, errors. Therefore, it was necessary it was necessary to improve to improvethe accuracy the accuracyof Holtrop of and Holtrop Men- andnen’s Mennen’s empirical empirical method methodaccording according to the ship to theused ship in usedthis study. in this In study. the process In the process of correc- of correctiontion for the for empirical the empirical method method of resistance, of resistance, the toolbox the toolbox commercial commercial CFD software CFD software STAR STARCCM+ CCM+ was used was to used calculate to calculate the total the totalresistance resistance of the of parent the parent ship shipat speeds at speeds of 9, of 11, 9, 11,13, 13,15, 15,17, 17,19, 19, 21, 21, and and 23 23 kn, kn, and and the the detailed detailed experience experience and and description of thethe numericalnumerical calculationcalculation strategy can can be be found found in in our our previous previous research research [42 [,4243,].43 The]. The total total resistance resistance was wascomposed composed of friction of friction and and residual residual resistances. resistances. Because Because the the frictional frictional resistance resistance in the the HoltropHoltrop and Mennen’s method method was was calculated calculated using using the the ITTC ITTC-1957-1957 formula, formula, it can it can be as- be assumedsumed that that the the frictional frictional resistance resistance was was correct correct after after considerable considerable experience, experience, and and the the er- errorror of of the the method method only only comes comes from from the the residual residual resistance. resistance. Subsequently, Subsequently, the the residual residual re- resistancesistance was was separated separated from from the the numerical numerical results, results, and and the the residual residual resistance calculatedcalculated byby HoltropHoltrop waswas compared.compared. The ratio of thethe twotwo partsparts waswas usedused toto establishestablish aa correctioncorrection coefficientcoefficient relatedrelated toto thethe FrFr number,number, andand thenthen thethe residualresidual resistanceresistance termterm ofof HoltropHoltrop andand Mennen’sMennen’s empirical empirical method method was was corrected. corrected. Finally, Finally, principal-dimension principal-dimension optimization optimization was performedwas performed based based on the on modified the modified method method with with acceptable acceptable accuracy. accuracy. AA comparisoncomparison betweenbetween the predictionprediction resultsresults ofof thethe originaloriginal andand modifiedmodified HoltropHoltrop andand Mennen’sMennen’s methodmethod andand thethe CFDCFD resultsresults ofof thethe full-scalefull-scale shipship isis presentedpresented inin FigureFigure3 .3.

FigureFigure 3. ComparisonComparison between between the the results results of ofthe the original original and and modified modiﬁed Holtrop Holtrop and andMennen’s Mennen’s method and the CFD data. method and the CFD data.

AsAs indicatedindicated byby FigureFigure3 3,, the the modified modified Holtrop Holtrop and and Mennen’s Mennen’s method method demonstrates demonstrates goodgood agreementagreement withwith thethe CFDCFD results,results, betterbetter pertinence,pertinence, andand accuracy.accuracy. Thus,Thus, itit cancan bebe adopted as a reliable approach for subsequent research. Although the correction coefficient for Holtrop and Mennen’s empirical formula in this study is only suitable for the parent ship and is not applicable to all the ships, the correction strategy employed can be implemented for specific ship types and has universal applicability.

4. Relationships of Resistance, Seakeeping, and Maneuverability Performance with the Principal Dimensions The variation of the principal dimensions in the study was constrained to within ±15% and +15% of the original ship length, beam: The length varied between 112.2 m ≤ L ≤ 151.8 m, with one length selected every 1% of the baseline length (132 m), for a total of 31 lengths; J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 8 of 16

adopted as a reliable approach for subsequent research. Although the correction coefficient for Holtrop and Mennen’s empirical formula in this study is only suitable for the parent ship and is not applicable to all the ships, the correction strategy employed can be implemented for specific ship types and has universal applicability.

4. Relationships of Resistance, Seakeeping, and Maneuverability Performance with the Principal Dimensions J. Mar. Sci. Eng. 2021, 9, 373 8 of 16 The variation of the principal dimensions in the study was constrained to within ±15% and +15% of the original ship length, beam: The length varied between 112.2 m ≤ L ≤ 151.8 m, with one length selected every 1% of the baseline length (132 m), for a total of the31 lengths; ship beam the ship varied beam within varied the within range the of 18.20 range m of≤ 18.20B ≤ m20.93 ≤ B ≤ m, 20.93 with m, one with ship one beam ship selectedbeam selecte everyd every 1% of 1% the of baseline the baseline ship beamship beam (18.20 (18.2 m),0 for m), a totalfor a oftotal 15 of ship 15 beams.ship beams. The ship’sThe ship’s length length and and beam beam were were considered considered as as the the main main variables, variables, and and the the draftdraft waswas considered as aa secondarysecondary variable.variable. The draft waswas determineddetermined afterafter selectingselecting differentdifferent shipship lengthslengths and beams, while keeping the displacement constant at 8600 t, yieldingyielding a totaltotal ofof 496 sets of hulls with different principal dimensions. Among them, the change in principal dimensions met the regulations and owner requirements, andand thethe generalgeneral arrangementarrangement ofof the ship.ship. The relationshipsrelationships of thethe totaltotal hullhull resistance,resistance, seakeeping,seakeeping, andand maneuverabilitymaneuverability with thethe lengthlength andand beambeam atat thethe designdesign speedspeed (19(19 kn)kn) areare shownshown inin FigureFigure4 4..

(a) (b)

(c)

FigureFigure 4.4. Relationships of various hydrodynamic performancesperformances withwith thethe principalprincipal dimensions:dimensions: ((aa)) shipship resistance;resistance; ((bb)) rankrank factorfactor RR ofof seakeepingseakeeping performance;performance; ((cc)) maneuverabilitymaneuverability indexindexP P( (PP= = KK//TT).).

As shown in Figure4, while the displacement was kept constant, the resistance monotonically increased with the hull beam and monotonically decreased with increasing ship length. The seakeeping index rapidly increased with ship length and slightly increased with increasing hull beam, which may be resulted from a decrease in the draft. The

maneuverability index exhibited opposite change tendencies: as the ship length increased, the maneuverability index ﬁrst increased and then decreased, whereas as the ship beam increased, the maneuverability index ﬁrst decreased and then increased. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 9 of 16

As shown in Figure 4, while the displacement was kept constant, the resistance monotonically increased with the hull beam and monotonically decreased with increasing ship length. The seakeeping index rapidly increased with ship length and slightly increased with increasing hull beam, which may be resulted from a decrease in the draft. The maneuverability index exhibited opposite change tendencies: as the ship length increased, J. Mar. Sci. Eng. 2021, 9, 373 9 of 16 the maneuverability index first increased and then decreased, whereas as the ship beam increased, the maneuverability index first decreased and then increased.

5. Optimization5. Procedure Optimization Procedure 5.1. Rough Selection5.1. Rough from Large Selection Amounts from Largeof Data Amounts of Data A rough selectionA rough from large selection amounts from of large data amounts set of performance of data set is of discussed performance in this is discussed in subsection. Thethis schematic subsection. diagram The schematicof the optimization diagram ofprocess the optimization is shown in processFigure 5. is First shown in Figure5 . of all, we establishedFirst of 496 all, sets we establishedof hulls with 496 different sets of principal hulls with dimensions different principal based on dimensions the based original parenton ship, the originalwith the parent variation ship, interval with the of variationthe principal interval dimension of the principal as the con- dimension as the straint condition.constraint The variation condition. interval The of variation the principal interval dimension of the principal was described dimension in detail was described in in Section 4. Secondldetail iny, the Section hull4 resistance,. Secondly, seakeeping, the hull resistance, and maneuverability seakeeping, and indices maneuverability were indices calculated for 496were selected calculated sets forof principal 496 selected dimensions sets of principal using resistance, dimensions seakeeping using resistance, qual- seakeeping ities, and maneuverabilityqualities, and empirical maneuverability methods empiricalof Holtrop methods and Mennen, of Holtrop Bales, and and Mennen, K and Bales, and K T indices, respectively.and T indices, In addition, respectively. we got a In data addition, set of ship we performance. got a data set Thirdly, of ship performance.a rough Thirdly, selection from alarge rough amounts selection of fromdata was large carried amounts out of based data on was constraints carried out and based selection on constraints and conditions. Theselection constraints conditions. and selection The constraintsconditions were and selectionas follows: conditions (a) The resistan were asce follows:of (a) The the hulls shouldresistance be smaller of than the hulls that of should the parent be smaller ship at than the thatdesign of thespeed parent (19 kn); ship (b) at the the design speed change ranges(19 of seakeeping kn); (b) the changeand maneuverability ranges of seakeeping are within and 21% maneuverability and 9%, respectively. are within 21% and 9%, Finally, we gotrespectively. five sets of hulls Finally, through we got the ﬁve rough sets ofselection. hulls through the rough selection.

Figure 5. Schematic diagram of rough selection from large amounts of data in the optimization Figure 5. Schematic diagram of rough selection from large amounts of data in the optimization process. process. The performance parameters for the ﬁve sets of principal dimensions and the parent The performanceship at a parameters speed of 19 for kn the are five presented sets of inprincipal Table1. dimensions and the parent ship at a speed of 19 kn are presented in Table 1. Table 1. Performance parameters for the different principal dimensions and parent ship at 19 kn. Table 1. Performance parameters for the different principal dimensions and parent ship at 19 kn. 2 NO. L (m) B (m) T (m) CB CP CWP S (m ) RT (KN) Seakeeping (R) Maneuverability (P) B P WP 2 NO. L (m)1 B (m) T 141.2 (m) 18.38C C 5.555 C 0.6027 S (m 0.6158) RT 0.7089 (KN) Seakeeping 2838 345.1 (R) Maneuverability 13.90 (P) 0.9051 1 141.22 18.38 5.555 139.9 0.6027 18.38 0.6158 5.608 0.7089 0.6025 2838 0.6514 345.1 0.7114 282213.90347.9 13.620.9051 0.9173 2 139.9 18.38 5.608 0.6025 0.6514 0.7114 2822 347.9 13.62 0.9173 3 138.6 18.38 5.661 0.6025 0.6507 0.7596 2806 350.9 13.32 0.9291 3 138.6 18.38 5.661 0.6025 0.6507 0.7596 2806 350.9 13.32 0.9291 4 137.3 18.38 5.715 0.6025 0.6502 0.7161 2790 354.2 13.03 0.9406 4 137.3 18.38 5.715 0.6025 0.6502 0.7161 2790 354.2 13.03 0.9406 5 136.0 18.38 5.771 0.6023 0.6496 0.7814 2774 357.7 12.72 0.9518 5 136.0 18.38 5.771 0.6023 0.6496 0.7814 2774 357.7 12.72 0.9518 Original parent ship 132.0 18.20 6.003 0.6025 0.6256 0.7724 2723 368.1 11.57 0.9851 Original parent ship 132.0 18.20 6.003 0.6025 0.6256 0.7724 2723 368.1 11.57 0.9851

As indicated inAs Table indicated 1, the inhulls Table of1 the, the five hulls selected of the principal ﬁve selected-dimension principal-dimension combina- combina- tions had a lowertions resistance had a lower in the resistance 16–20 kn in speed the 16–20 range kn and speed also range larger and seakeeping also larger and seakeeping and maneuverability indices. This indicates that the vessels of these ﬁve principal-dimension combinations had better seakeeping and maneuverability.

5.2. Effect Analysis of Principal-Dimension for the Selected Five Sets of Hulls To analyze the effects of principal-dimension optimization on the resistance, seakeeping, and maneuverability, the resistance of the ﬁve hull forms and the parent ship within the speed range of 4–25 kn were analyzed, and the results are shown in Figure6. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 10 of 16

maneuverability indices. This indicates that the vessels of these five principal-dimension combinations had better seakeeping and maneuverability.

5.2. Effect Analysis of Principal-Dimension for the Selected Five Sets of Hulls To analyze the effects of principal-dimension optimization on the resistance, seakeeping, and maneuverability, the resistance of the five hull forms and the parent ship within the speed range of 4–25 kn were analyzed, and the results are shown in Figure 6. As shown in Figure 6, when the speed was lower than 17.5 kn, the effect of principal- dimension optimization was insignificant, and the resistance of the optimized hull form was not significantly lower than that of the parent ship. When the speed was higher than 17.5 kn, the effect of the principal-dimension optimization was more significant, and the resistance of the hull forms after the principal dimensions were changed was significantly lower than that of the parent ship. Furthermore, the resistance is decreased when the ship length is increased, mainly because wave-making resistance can be reduced by increasing the ship length at high speed. Additionally, the ship beams were identical for the five hull forms, with good resistance performance. This implies that for the hull form adopted in this study, if the displacement remains adopted and the principal dimensions are altered to reduce the resistance at high speed, an optimal value can be obtained for the ship beam. In addition, it is helpful to increase the ship length and reduce the draft for resistance reduction at high speed. For the selection of one hull form from the five sets of principal- dimension combinations, if the key consideration is the resistance at the design speed (19 kn), the principal dimensions of the hull form with the minimum resistance are L = 141.24 J. Mar. Sci. Eng. 2021, 9, 373 10 of 16 m and B = 18.38 m, indicating a 6.7% reduction in resistance, 18.4% improvement in seakeeping, and 8% reduction in maneuverability compared with the parent ship.

(a) (b)

Figure 6. Comparison ofof the the total total resistance resistance and and resistance resistance reduction reduction rates rates before before and and after after principal-dimension principal-dimension optimization: optimi- (zation:a) total (a resistance;) total resistance; (b) resistance (b) resistance reduction reduction rates. rates.

BasedAs shown on the in comparison Figure6, when of the the resistance speed was performance lower than 17.5 before kn, and the after effect the of principal-principal- dimensiondimension optimization,optimization wasthe insignificant, seakeeping and and maneuverability the resistance of of the the optimized five selected hull form hull formswas not within significantly the range lower of 16– than20 kn that were of further the parent compared, ship. Whenand the the results speed are was shown higher in Figurethan 17.5 7. When kn, the the effect shipof beam the principal-dimensionwas fixed, the seakeeping optimization gradually was increased more significant, with the increasingand the resistance ship length, ofthe and hull the seakeeping forms after index the principal was maximized dimensions when were ship changedlength was was L =significantly 141.2 m, indicating lower than that that increasing of the parent the ship ship. length Furthermore, and reducing the resistancethe draft can is decreased improve thewhen seakeeping the ship length underis the increased, same displacement mainly because (see wave-makingFigure 7a). As resistance shown in can Figure be reduced 7b, the maneuverabilityby increasing the exhibited ship length the at opposite high speed. tendency Additionally, when increasing the ship beams ship length were identical within the for speedthe five range hull forms,of interest. with When good resistancethe speed performance.was less than This17 kn, implies the maneuverability that for the hull index form wasadopted increased in this with study, the if ship the displacement length, indicating remains better adopted maneuverability; and the principal when dimensions the speed wasare alteredhigher tothan reduce 17 kn, the the resistance maneuverability at high speed, index anwas optimal decreased value with can ship be obtained length. Hence, for the ship beam. In addition, it is helpful to increase the ship length and reduce the draft for resistance reduction at high speed. For the selection of one hull form from the five sets of principal-dimension combinations, if the key consideration is the resistance at the design speed (19 kn), the principal dimensions of the hull form with the minimum resistance are L = 141.24 m and B = 18.38 m, indicating a 6.7% reduction in resistance, 18.4% improvement in seakeeping, and 8% reduction in maneuverability compared with the parent ship. Based on the comparison of the resistance performance before and after the principal- dimension optimization, the seakeeping and maneuverability of the five selected hull forms within the range of 16–20 kn were further compared, and the results are shown in Figure7. When the ship beam was fixed, the seakeeping gradually increased with the increasing ship length, and the seakeeping index was maximized when ship length was L = 141.2 m, indicating that increasing the ship length and reducing the draft can improve the seakeeping under the same displacement (see Figure7a). As shown in Figure7b, the maneuverability exhibited the opposite tendency when increasing ship length within the speed range of interest. When the speed was less than 17 kn, the maneuverability index was increased with the ship length, indicating better maneuverability; when the speed was higher than 17 kn, the maneuverability index was decreased with ship length. Hence, the maneuverability did not vary monotonically with ship length over a wider speed range, and increasing the ship length at high speed did not benefit the maneuverability of the examined hull form. The variation of the maneuverability with respect to the ship beam was more significant when the ship beam was smaller than 17 m. For the hull with L = 141.2 m and B = 18.38 m, the maneuverability was good at a low speed but poor at high speed. The hull with L = 136.0 m and B = 18.38 m yielded the best maneuverability at high speed, and the maneuverability was improved by 5.16% when the speed was 19 kn compared with the case of the hull with L = 141.2 m and B = 18.38 m. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 11 of 16

the maneuverability did not vary monotonically with ship length over a wider speed range, and increasing the ship length at high speed did not benefit the maneuverability of the examined hull form. The variation of the maneuverability with respect to the ship beam was more significant when the ship beam was smaller than 17 m. For the hull with L = 141.2 m and B = 18.38 m, the maneuverability was good at a low speed but poor at high speed. The hull with L = 136.0 m and B = 18.38 m yielded the best maneuverability at J. Mar. Sci. Eng. 2021, 9, 373 11 of 16 high speed, and the maneuverability was improved by 5.16% when the speed was 19 kn compared with the case of the hull with L = 141.2 m and B = 18.38 m.

(a) (b)

FigureFigure 7. 7. VariationVariation of of seakeeping seakeeping and and maneuverability maneuverability with with the the principal principal dimensions: dimensions: ( (aa)) Seakeeping; Seakeeping; (b (b) )maneuverability. maneuverability.

5.3. Further Selection from the Five Sets of Principal-Dimension Combinations 5.3. FurtherA further Selection selection from from the Five the Sets five of sets Principal-Dimension of principal-dimension Combinations combinations is dis- cussedA in further this subsection. selection from According the five setsto the of law principal-dimension of actual ship manufacturing combinations cost, is discussed the in- creasein this of subsection. ship length According under the to same the law conditions of actual will ship directly manufacturing lead to the cost, increase the increase in shipof buildingship length cost. under In the the further same conditionsselection process, will directly in addition lead to to the considering increase in the shipbuilding ship’s resistance,cost. In seakeeping, the further and selection maneuverability process, in performance, addition to considering it also comprehensively the ship’s resistance, consid- ersseakeeping, the additional and construction maneuverability costs performance, caused by the itincrease also comprehensively in the length of the considers ship. the additionalBy comprehensively construction costs considering caused by the the ship’s increase length, in the resistance, length of seakeeping, the ship. and maneuverability,By comprehensively we have established considering a comprehensive the ship’s length, optimization resistance, seakeeping,index, and the and compre- maneu- hensiveverability, optimization we have established index Z is adefined comprehensive as follows: optimization index, and the comprehensive optimization index Z is defined as follows: LLRRPPRti  Rt0   Z  2.5i0   0.8 i 0  0.8 i 0 (8) Li − L0L|Rti − RtRt0| Ri − RR0 P Pi − P0 Z = −2.5 +0 0+ 0.8 0+ 0.8 0 (8) L0 Rt0 R0 P0 Note: Compared with the parent ship, the five ship types have negative effects on the relativeNote: comprehensive Compared with optimization the parent indexes ship, the of fiveship ship length types and have maneuverability, negative effects and on “−” the shouldrelative be comprehensive added, and the optimization weights of indexeslength, resistance of ship length seakeeping, and maneuverability, and maneuverability and “−” areshould 2.5, 1, be 0.8, added, and 0.8, and respectively the weights. of length, resistance seakeeping, and maneuverability are 2.5,Where 1, 0.8, Li, andRti, 0.8,Ri, and respectively. Pi are the length, resistance, rank factor of seakeeping perfor- Where L , Rt , R , and P are the length, resistance, rank factor of seakeeping performance and maneuverabilityi i i indexi of the selected five sets of hulls, and L0, Rt0, R0, and P0 aremance the andlength, maneuverability resistance, rank index factor of theof selectedseakeeping five performances sets of hulls, andandL maneuverability0, Rt0, R0, and P0 indexare the of length,the parent resistance, ship, respectively. rank factor The of seakeeping calculation performances results of the and comprehensive maneuverability in- index of the parent ship, respectively. The calculation results of the comprehensive index dex of the selected five sets of hulls are shown in Table 2. of the selected five sets of hulls are shown in Table2.

Table 2. Comprehensive optimization calculation results of the selected ﬁve sets of hulls.

NO. L (m) B (m) Li−L0 |Rti−Rt0| Ri−R0 Pi−P0 Z L0 Rt0 R0 P0 1 141.2 18.38 0.0697 0.0625 0.2014 −0.0812 −0.01559 2 139.9 18.38 0.0598 0.0549 0.1772 −0.0688 −0.00788 3 138.6 18.38 0.0500 0.0467 0.1513 −0.0568 −0.0027 4 137.3 18.38 0.0402 0.0378 0.1263 −0.0452 0.00218 5 136.0 18.38 0.0303 0.0283 0.0994 −0.0338 0.00503

According to the comparative analysis of the ﬁve optimized hull forms, the hull form with L = 141.2 m and B = 183.38 m exhibited a good ship resistance but also a loss of maneuverability due to the increase in the ship length, which increased the production costs. By comprehensively considering the foregoing factors, it was found that while the J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 12 of 16

Table 2. Comprehensive optimization calculation results of the selected five sets of hulls.

LLi  0 Rti  Rt0 RRi  0 PPi  0 NO. L (m) B (m) Z L0 Rt0 R0 P0 1 141.2 18.38 0.0697 0.0625 0.2014 −0.0812 −0.01559 2 139.9 18.38 0.0598 0.0549 0.1772 −0.0688 −0.00788 3 138.6 18.38 0.0500 0.0467 0.1513 −0.0568 −0.0027 4 137.3 18.38 0.0402 0.0378 0.1263 −0.0452 0.00218 5 136.0 18.38 0.0303 0.0283 0.0994 −0.0338 0.00503

According to the comparative analysis of the five optimized hull forms, the hull form with L = 141.2 m and B = 183.38 m exhibited a good ship resistance but also a loss of ma- J. Mar. Sci. Eng. 2021, 9, 373 neuverability due to the increase in the ship length, which increased the production12 costs. of 16 By comprehensively considering the foregoing factors, it was found that while the displacement was kept constant and only the principal dimensions were changed, five hull forms outperformed the parent ship with regard to the resistance performance, seakeep- displacementing, and maneuverability. was kept constant The andshiponly beam the of principalthese five dimensions hull forms werewas 18.38 changed, m, which five hull was formshigher outperformed than that of thethe parentparent shipship. with This regard is acceptable to the resistance because performance,an increase in seakeeping, the beam is andhelpful maneuverability. for improving The stability. ship beam Both of the these resistance five hull performance forms was 18.38 and m, seakeeping which was were higher im- thanproved that with of the an parent increase ship. in This the islength, acceptable but the because maneuverability an increase exhibited in the beam an isinitial helpful im- forprovement, improving followed stability. by Both deterioration the resistance with performance increasing length. and seakeeping In this study, were only improved the dis- withplacement an increase was kept in the constant. length, butHowever, the maneuverability in practice, an exhibitedexcessive anship initial length improvement, increased the followedlightship by weight deterioration and reduced with increasingits effective length. loading In capacity. this study, Furthermore, only the displacement a long and wasslen- keptder constant.hull requires However, further in strengthening practice, an excessive of the hull ship structure. length increased Therefore, the although lightship the weight main andobjective reduced of itsthis effective study was loading to improve capacity. the Furthermore, resistance performance, a long and slender it was also hull necessary requires furtherto consider strengthening the improvement of the hull of structure.other aspects Therefore, of the performance although the and main the objective practical of value this study was to improve the resistance performance, it was also necessary to consider the of the optimized hull form. According to the calculation results in Table 2, it can be improvement of other aspects of the performance and the practical value of the optimized seen that the No.5 ship hull has the largest comprehensive optimization index Z. hull form. According to the calculation results in Table2, it can be seen that the No.5 ship Therefore, after comprehensive consideration, the optimized hull form (new parent ship) hull has the largest comprehensive optimization index Z. Therefore, after comprehensive with L = 136.0 m and B = 18.38 m was chosen. consideration, the optimized hull form (new parent ship) with L = 136.0 m and B = 18.38 m was chosen. 6. Further Hull Foam Optimization and Verification Based on the Selected New Par- 6.ent Further Ship Hull Foam Optimization and Verification Based on the Selected New ParentAfter Ship the principal dimensions were optimized, further hull form optimization was performedAfter the on principal the new parent dimensions ship (L were = 136.0 optimized, m and B further= 18.38 m) hull according form optimization to the minimum was performedwave-making on the resistance. new parent Several ship (L previous = 136.0 mstudies and B reported = 18.38 m) results according in this to thearea minimum, and thus wave-makingwill not be described resistance. here. Several After previous hull form studies optimization, reported no results significant in this changes area, and were thus made will notto bethe described hull form. here. The Afteroptimized hull form hull optimization,form was compared no significant with the changes new parent were made ship, to as theshown hull form.in Figure The 8 optimized, in which hull the formred dashed was compared line indicates with thethe newbody parent plan lines ship, of as the shown opti- inmized Figure hull8, in form, which and the the red solid dashed black line line indicates indicates the bodythe body plan linesplan ofline the of optimized the new parent hull form,ship. andOn thethis solid basis, black the ship line indicatesmodel of thethe body new planparent line ship of theand new the parentoptimized ship. hull On thisform basis,were thecreated ship modelat a scale of the ratio new of parentλ = 22, ship and and a towing the optimized tank test hull was form performed. were created The main at a scaleparameters ratio of ofλ =the 22, optimized and a towing hull tank ship test in the was model performed. and the The full main scale parameters are presented of the in optimizedTable 3. hull ship in the model and the full scale are presented in Table3.

FigureFigure 8. 8Ship. Ship model model for for towing towing tank tank experiment: experiment: ( a(a)) side side view view of of the the ship ship model model of of the the optimized optimized hull from new parent ship; (b) sketch of the bow; (c) front and stern views of the ship plan line of hull from new parent ship; (b) sketch of the bow; (c) front and stern views of the ship plan line of hulls; (d) sketch of the stern. hulls; (d) sketch of the stern.

Table 3. Main parameters of the optimized hull from the new parent ship.

Parameters Symbols Model Scale Ship Scale Length overall (m) Loa 6.5818 147.80 Length on waterline (m) Lwl 6.1791 136.00 Beam (m) B 0.8354 18.38 Depth (m) D 0.4095 9.00

Figure9 shows the resistance of the hull before and after optimization, including the experimental data, empirical formula data, and resistance reduction. The red line is the experimental data of the new parent ship, the green line is the experimental data of the optimized hull of the new parent ship, and the purple diamond points are the Holtrop and Mennen’s empirical formula (modiﬁed) data. Because the new parent ship was formed J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 13 of 16

Table 3. Main parameters of the optimized hull from the new parent ship.

Parameters Symbols Model Scale Ship Scale Length overall (m) Loa 6.5818 147.80 Length on waterline (m) Lwl 6.1791 136.00 Beam (m) B 0.8354 18.38 Depth (m) D 0.4095 9.00

Figure 9 shows the resistance of the hull before and after optimization, including the J. Mar. Sci. Eng. 2021, 9, 373 experimental data, empirical formula data, and resistance reduction. The red line13 is of the 16 experimental data of the new parent ship, the green line is the experimental data of the optimized hull of the new parent ship, and the purple diamond points are the Holtrop and Mennen’s empirical formula (modified) data. Because the new parent ship was byformed the principal-dimension by the principal-dimension optimization optimization of the original of the original parent ship,parent the ship, new the parent new shippar- hadent ship undergone had undergone a round of a resistanceround of resistance optimization. optimization. Under the Under condition the thatcondition the hull that form the typehull form did not type change did not signiﬁcantly, change significantly, the maximum the maximum resistance reductionresistance of reduction the hull optimizedof the hull fromoptimized the new from parent the new ship wasparent 1.5%. ship In was addition, 1.5%. aIn comparison addition, a between comparison the experimental between the dataexperimental and Holtrop data and and Mennen’s Holtrop empiricaland Mennen’s formula empirical (modiﬁed) formula data of(modified) the new parentdata of ship the showsnew parent that theship accuracy shows that correction the accuracy of the correction empirical of method the empirical based method on CFD based for the on given CFD shipfor the type given is reliable. ship type is reliable.

FigureFigure 9.9. Resistance ofof thethe hullhull beforebefore and and after after optimization, optimization, including including experimental experimental data, data, empirical empiri- formulacal formula data, data, and and resistance resistance reduction. reduction.

FigureFigure 10 shows the the waveform waveform of of the the hull hull in in the the towing towing tank tank before before and and after after optimi- opti- mization,zation, including including the the bow bow wave, wave, shoulder shoulder wave, wave, and and wave wave scars. scars. From From the the waveform waveform in- informationformation of of the the same same viewing viewing angle angle in in Figure Figure 9, it cancan bebe seenseen thatthat thethe optimized optimized ship ship hashas aa smaller wave-makingwave-making range.range. Because thethe length of the waterline remains unchangedunchanged beforebefore andand afterafter thethe optimization,optimization, thethe frictionalfrictional resistanceresistance (1957(1957 ITTCITTC empiricalempirical formula)formula) ofof thethe shipship remainsremains unchanged,unchanged, andand thethe reductionreduction inin thethe resistanceresistance ofof thethe shipship isis mainlymainly reﬂectedreflected inin thethe residualresidual resistanceresistance component,component, includingincluding thethe wave-makingwave-making resistance.resistance. TheThe aboveabove waveformwaveform informationinformation alsoalso providesprovides thisthis evidence.evidence.

J. Mar. Sci. Eng. 2021, 9, 373 14 of 16 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 14 of 16

FigureFigure 10.10. WaveWave formform ofof thethe shipsships underunder differentdifferent speeds:speeds: (a) Wave formform ofof thethe newnew parentparent ship at the speed of 13 kn; (b) wave form of the optimized hull from new parent ship at the speed of 13 the speed of 13 kn; (b) wave form of the optimized hull from new parent ship at the speed of 13 kn; kn; (c) wave form of the new parent ship at the speed of 19 kn; (d) wave form of the optimized (c) wave form of the new parent ship at the speed of 19 kn; (d) wave form of the optimized hull from hull from new parent ship at the speed of 19 kn. new parent ship at the speed of 19 kn.

7.7. ConclusionsConclusions JointJoint optimizationoptimization ofof thethe principalprincipal dimensionsdimensions andand hullhull formform onon thethe hydrodynamichydrodynamic performanceperformance of of a a bulk bulk carrier carrier (origin (origin parent parent ship) ship) considering considering the the integrated integrated performance performance of shipof ship resistance, resistance, seakeeping, seakeeping, and and maneuverability maneuverability was was studied studied based based on empiricalon empirical methods meth- andods towingand towing tank tank tests. tests. The followingThe following conclusions conclusions were were drawn: drawn: 1.1. Holtrop and Mennen’s method isis arguablyarguably thethe mostmost popularpopular methodmethod forfor estimatingestimating the resistance resistance of of displacement-type displacement-type ships. ships. The results obtained obtained by by the the modified modified Holtrop method method based based on on CFD CFD for for the the given given ship ship in the in present the present study study exhibited exhibited good goodagreement agreement with the with CFD the and CFD experimental and experimental data of the data towing of the tank, towing good tank, pertinence good pertinenceaccuracy. accuracy. 2.2. Variations of of the the principal principal dimensions dimensions affected affected ship ship resistance, resistance, seakeeping, seakeeping, and andma- maneuverability.neuverability. Within Within the the requirements requirements of of regulations, regulations, owner’s requirements, and and general arrangement of the ship,ship, principal-dimensionprincipal-dimension optimizationoptimization cancan improveimprove thethe performance of the originaloriginal parent ship andand provideprovide aa newnew parentparent shipship forfor furtherfurther hull form optimization. 3.3. The joint optimizationoptimization methodmethod consideringconsidering thethe principalprincipal dimensiondimension andand hullhull formform optimization can further explore the optimization spacespace andand provideprovide aa betterbetter hull.hull. SomeSome researchresearch limitations in in this this paper: paper: All All the the optimization optimization in this in this paper paper were were per- performedformed conditions conditions of ofcalm calm water, water, without without considering considering the the influence influence of of wind and waves; OptimizationOptimization targetstargets onlyonly focusfocus onon resistance,resistance, seakeeping,seakeeping, andand maneuverability.maneuverability. ThereThere isis nono verificationverification andand attemptattempt toto adoptadopt moremore updatedupdatedempirical empiricalformula formulamethods. methods.

AuthorAuthor Contributions:Contributions: Conceptualization,Conceptualization, R.D. R.D. and and T.W.; T. W.; methodology, methodology, R.D.; R.D.; software, software, R.D.; R.D.; valida- vali- tion,dation, Y.H. Y.H. and and Y.W.; Y.W.; formal formal analysis, analysis, R.D.; R.D.; investigation, investigation, R.D.; R.D.; resources, resources, T.W.; T.W.; data curation, data curation, T.W.; writing—originalT.W.; writing—original draft preparation, draft preparation, S.W., R.D. S.W., and R.D. T.W.; and writing—review T.W.; writing and—review editing, and R.D. editing, and T.W.; R.D visualization,and T.W.; visualization, S.W.; supervision, S.W.; supervision, R.D.; project R.D.; administration, project administration, R.D.; funding R.D.; acquisition, funding R.D. acquisition, and T.W. AllR.D. authors and T. haveW. All read authors and agreedhave read to the and published agreed to version the published of the manuscript. version of the manuscript. Funding:Funding: ThisThis research research was was funded funded by the by Key-Area the Key-Area Research Research and Development and Development Program Program of Guang- of dongGuangdong Province Province (Grant No.(Grant 2020B1111010002); No. 2020B1111010002); National National Natural Natural Science Science Foundation Foundation of China of (Grant China No.(Grant 51679053; No. 51679053; 12002404); 12002404); Opening Openin Fundg forFund State for KeyState Laboratory Key Laboratory of Shipping of Shipping Technology Technology and Security;and Security Guangdong; Guangdong Basic andBasic Applied and Applied Basic ResearchBasic Research Foundation Foundation (2019A1515110721), (2019A1515110721), the China the PostdoctoralChina Postdoctoral Science Science Foundation Foundation (No. 2019M663243);(No. 2019M663243); the Fundamental the Fundamental Research Research Funds Funds for thefor Centralthe Central Universities Universities (No.20lgpy52). (No.20lgpy52). DataData AvailabilityAvailability Statement:Statement:Data Data isis containedcontainedwithin within thethepresent presentarticle. article.

J. Mar. Sci. Eng. 2021, 9, 373 15 of 16

Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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