Optimization of the Propulsive Efficiency of a Fast Catamaran

Journal of Marine Science and Engineering

Article Optimization of the Propulsive Efﬁciency of a Fast Catamaran

Yan Xing-Kaeding 1,* and Apostolos Papanikolaou 2,*

1 Hamburg Ship Model Basin (HSVA), D-22305 Hamburg, Germany 2 National Technical University of Athens (NTUA), 15773 Athens, Greece * Correspondence: [email protected] (Y.X.-K.); [email protected] (A.P.)

Abstract: The present study deals with the local optimization of the stern area and of the propulsive efficiency of a battery-driven, fast catamaran vessel. The adopted approach considers a parametric model for the catamaran’s innovative transom stern and a QCM (Quasi-Continuous Method) body- force model for the effect of the fitted propellers. Hydrodynamic calculations were performed by the CFD code FreSCO+, which also enabled a deep analysis of the incurring unique propulsive phenomena. Numerical results of achieved high propulsive efficiency were verified by model experiments at the Hamburgische Schiffbau Versuchsanstalt (HSVA), proving the feasibility of the concept.

Keywords: propulsive efﬁciency; wake and thrust deduction; hull efﬁciency; tunneled transom; fast catamaran; hydrodynamic ship design; parametric design; multi-objective optimization; model experiments

1. Introduction Citation: Xing-Kaeding, Y.; Papanikolaou, A. Optimization of the The design and hydrodynamics of fast catamarans (and of multi-hull vessels in gen- Propulsive Efficiency of a Fast eral) has been a favorite subject of scientific research and of innovative naval architectural Catamaran. J. Mar. Sci. Eng. 2021, 9, engineering for many decades [1]. The complex hydrodynamics both in calm water and 492. https://doi.org/10.3390/ in waves are related to both the generated waves at higher speeds and to the interaction jmse9050492 between the buoyant demihulls carrying the ship’s superstructure. The generally adopted slenderness of the demihulls eases, to a certain degree, the numerical modeling of the Academic Editor: Carlo Francesco associated physical phenomena, enabling the application of simplified slender body or thin Mario Bertorello ship theory methods [2]. It is well established that the demihull interaction effects, which have, in general, a negative effect on calm water resistance. It is less well established that Received: 7 April 2021 under certain conditions related to the optimization of the lengthwise distribution of the Accepted: 28 April 2021 catamaran’s displacement and speed of advance, the interaction effect on resistance may Published: 1 May 2021 be positive, thus reducing the sum of the demihulls single hull resistance [2]. In any case, the interaction effects in general decrease with the increase in the demihulls’ separation dis- Publisher’s Note: MDPI stays neutral tance, at the expense of an increased structural weight of the catamaran due to the increase with regard to jurisdictional claims in in weight of the unsupported deck structure. Even more, the increase of the separation published maps and institutional affil- distance leads to a drastic increase in the waterplane’s transverse moment of inertia and iations. of the catamaran’s transverse metacentric height; thus, decreasing its natural roll period, resulting in large transverse and vertical accelerations and unpleasant seakeeping comfort for people onboard and cargo. To enable high speeds for any type of vessel (and even more of catamarans) operating Copyright: © 2021 by the authors. around and beyond a Froude number of 0.50, it is essential to conduct a hydrodynamic Licensee MDPI, Basel, Switzerland. optimization of the ship’s hull form and its propulsive devices for the least power and This article is an open access article of the overall design for the least structural and lightship weight. While we deal, in the distributed under the terms and present paper, only with the calm water hydrodynamic optimization, it may be of interest to conditions of the Creative Commons study additional works on the optimization of the overall design of twin-hull vessels [3,4] Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ and on the analysis of their seakeeping and wave-induced motions and loads [5]. 4.0/).

J. Mar. Sci. Eng. 2021, 9, 492. https://doi.org/10.3390/jmse9050492 https://www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2021, 9, 492 2 of 14

The optimization of a catamaran’s main dimensions and its hull form for the least resistance needs to account for its basic constituents, namely the wave and viscous resistance, while considering that a catamaran’s wetted surface (and at least the frictional component of the viscous resistance) will be inherently larger than that of a monohull of equal displacement, in view of the demihull’s double inside surface. Thus, the main effort is to reduce the catamaran’s wave resistance, while the associated wave wash will be also of importance when the catamaran is operating in coastal areas [6]. The reduction of the catamaran’s (and that of multihulls, in general) wave resistance is well established and is associated with the slenderness of the demihulls and their least separation distance to avoid undesired negative interaction effects on the wave resistance value, whereas a variety of methods were employed for the determination of wave resistance. These methods range from simplified thin and slender body theory methods [7,8], to 3D Boundary Element (BEM) and traveling source panel methods [2] and advanced CFD methods [9]. Regarding the employed optimization methods, they range from Lagrange multiplier methods (in relation to thin ship theory approaches to the wave resistance) [7] to parametric modeling and genetic algorithm optimization methods [4,10]. While the optimization of the catamaran’s hull form for least resistance is well established, this is not so with its propulsive efficiency that requires the proper account of the hull–propeller–shaft–rudder interaction that will be the focus of the present paper and is inspired and supported by the EU funded project TrAM [11]. The aim of the TrAM project is to develop battery-driven zero emission fast passenger vessels for coastal areas and inland waterways. The innovations of the project are in the introduced marine batteries and associated technology, in the design and in the manufactur- ing, namely the application and development of modular methods in the marine industry. An essential constraint for the success of the project is that the developed electric-powered vessels should be fast transport vehicles and competitive in terms of offered services to conventional vessels, have a very low environmental footprint and sustainable life-cycle cost. In the frame of the project, in-depth numerical and experimental research was carried out on the hydrodynamic optimization of a battery-driven catamaran’s hull form and its propulsion system, minimizing the power requirements and energy consumption, which are essential for a battery-driven marine vehicle. A review of the unique problems related to the design of battery-driven fast catamarans is given in [10]. The present paper deals with the unique propulsive efficiency of a fast, battery-driven catamaran, the so-called Stavanger demonstrator of the TrAM project. It includes the analysis of all contributing propulsive factors (transom stern tunnel, wake and thrust deduction factors, and open water propeller efficiency), as determined by an advanced CFD solver (FreSCo+,[12]) and verified by model experiments at HSVA.

2. The Propulsive Efficiency Optimization Problem 2.1. The Approach Assuming that the catamaran’s main dimensions and hull form have been optimized for least total resistance in the frame of a global optimization procedure, as elaborated in [9], it remains to optimize the stern area of the hull for the least propulsive power for the catamaran to achieve the specified service speed. This optimization includes the shaping of the transom stern, the propeller sizing/design and the inclination of the shaft lines (including their brackets). The herein applied optimization approach consists of the parametric modeling of the ensuing stern hull geometry, in which a propeller of maximum diameter is fitted and the inclination of the shaft line is introduced through a maximum inclination angle constraint. The computational method applied is a coupled RANS-BEM method. Though the propeller can, nowadays, be geometrically modeled by RANS codes through Sliding Interface (SI) or overlapping grid methods, a more practical and efficient approach, applied herein, is to simulate the propeller effect through a 3D body-force model, as this allows the quick evaluation of a large number of design variants. The body forces are obtained in this study J. Mar. Sci. Eng. 2021, 9, 492 3 of 14

from a Propeller Vortex Lattice Method (QCM), which is coupled in an iterative manner to the RANS method to enable numerical self-propulsion simulations. More details of these methods are explained below.

2.2. RANSE Method The HSVA in-house code FreSCo+ is a finite volume fluid flow solver, which is the result of a joint development between the Institute of Fluid Dynamics and Ship Theory (FDS) of the Hamburg University of Technology (TUHH) and the Hamburg Ship Model Basin (HSVA). Emphasis is thereby placed on an important element of maritime problems, namely the prediction of the free surface flow around ships, which is expressed in the name FreSCo, standing for Free Surface Computation. The computational method in ‘FreSCo+’ is based on a finite-volume method and allows both structured-grid and unstructured-grid discretization. FreSCo+’s mathematical model is essentially the Reynolds-averaged Navier-Stokes (RANS) equations, supplemented with a series of turbulence models based on the eddy viscosity concept and a treatment of multi- phase flows using the volume-of-fluid approach. The FreSCo+ code solves the incompressible, unsteady Navier-Stokes equations (RANSE). The transport equations are discretized with the cell-centered finite volume method. Using a face-based approach, the method is applied to fully unstructured grids using arbitrary polyhedral cells or hanging nodes. The governing equations are solved in a segregated manner, utilizing a volume- specific pressure correction scheme to satisfy the continuity equation, [13]. To avoid an odd–even decoupling of pressure and velocity, a third-order pressure smoothing is employed along a route outlined in [14]. The solution is iterated to convergence using a SIMPLE-type pressure-correction scheme. The fully implicit algorithm is second order accurate in space and time. The approximation of the integrals is based on the mid-point rule. Diffusion terms are approximated using second-order central differences, whereas advective fluxes are approximated based on blends between high-order upwind-biased schemes (e.g., QUICK), first order upwind and second order central differences schemes. The latter are applied in scalar form by means of a deferred-correction approach. The method is applied to fully unstructured grids using arbitrary polyhedral cells or hanging nodes. In addition, features such as sliding interface or overlapping grid techniques have been implemented into the code [12]. Various turbulence-closure models are available for application, such as k-ε (Standard, RNG, Chen), k-ω (Standard, BSL, SST), Menter’s One Equation model and the Spalart-Allmaras turbulence model. In this paper, the k-ω SST model has been mainly used.

2.3. Propeller Vortex Lattice Method QCM The method implemented in the “QCM” code is a vortex lattice method (VLM). The blades of the propeller are reduced to lifting surfaces, which account for camber and angle of attack. The lifting surfaces are built up by section mean lines. The thickness effect is accounted for by prescribed source densities on the lifting surfaces. To calculate the load distribution on a lifting surface, a system of rectilinear vortices is introduced. This system is further divided into ‘bound’ vortices in span-wise direction and ‘shed’ vortices in chord-wise direction. This procedure can be considered a special type of a Boundary Element Method. The solution technique follows the standard procedure of boundary element methods in hydrodynamics: the prescribed normal component of the inflow velocity has to be compensated by the downwash due to the vortex system. Demanding this kinematic condition for a set of control points, one gets a system of linear equations. From this system, the strength of every rectilinear bound vortex is calculated. The system of vortices of known strength is now sufficient to derive the pressure and the forces on the blade surfaces. The typical vortex structure in the propeller wake in QCM is illustrated in Figure1. More details on the method can be found in [15,16]. QCM can be used to compute the propeller flow under both steady and unsteady inflow conditions. The drawback of the method is that the flow is considered potential J. Mar. Sci. Eng. 2021, 9, 492 4 of 15

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flow and the modeling of the propeller hub is critical. Viscous effects on the drag of the propeller blades are treated in QCM via empirical corrections based on the 2D profile viscous resistance. Good results can be obtained at the propeller design point. In the case of large oblique inflow angles to the propeller, however, larger errors are expected since J. Mar. Sci. Eng. 2021, 9, 492 4 of 15 the free vortex transport direction in the propeller wake is aligned with the propeller shaft without consideration of the actual inflow direction.

Figure 1. Vortex structure in the propeller wake in QCM for a typical propeller in a homogeneous inflow.

QCM can be used to compute the propeller flow under both steady and unsteady inflow conditions. The drawback of the method is that the flow is considered potential flow and the modeling of the propeller hub is critical. Viscous effects on the drag of the propeller blades are treated in QCM via empirical corrections based on the 2D profile viscous resistance. Good results can be obtained at the propeller design point. In the case of large oblique inflow angles to the propeller, however, larger errors are expected since the free vortex transport direction in the propeller wake is aligned with the propeller shaft FigureFigurewithout 1. 1.VortexVortex consideration structure structure in in ofthe the the propeller actual wakewakeinflow in in QCM direction.QCM for for a typicala typical propeller propeller in ain homogeneous a homogeneous inflow. inflow. 2.4.2.4. Numerical Numerical Self-Propulsion Self-Propulsion Using Using RANS-QCM RANS-QCM Coupling Coupling QCMTheThe can present present be used local local to stern sterncompute form form optimizationthe optimization propeller studies,flow studies, under aiming aiming both at atsteady very very high andhigh propulsiveunsteady propulsive efﬁciency, have been conducted using the RANS-QCM coupling approach of HSVA to inflowefficiency, conditions. have Thebeen drawback conducted of using the method the RANS-QCM is that the couplingflow is considered approach ofpotential HSVA to perform the numerical self-propulsion test. To this end, the code FreSCo+ is coupled with flowperform and the the modeling numerical of self-propulsionthe propeller hub test. is Tocritical. this end, Viscous the code effects FreSCo on the+ is drag coupled of the with QCM in an iterative manner as shown in Figure2. propellerQCM in blades an iterative are treated manner in QCM as shown via empirical in Figure corrections 2. based on the 2D profile viscous resistance. Good results can be obtained at the propeller design point. In the case of large oblique inflow angles to the propeller, however, larger errors are expected since the free vortex transport direction in the propeller wake is aligned with the propeller shaft without consideration of the actual inflow direction.

2.4. Numerical Self-Propulsion Using RANS-QCM Coupling The present local stern form optimization studies, aiming at very high propulsive efficiency, have been conducted using the RANS-QCM coupling approach of HSVA to perform the numerical self-propulsion test. To this end, the code FreSCo+ is coupled with QCM in an iterative manner as shown in Figure 2.

Figure 2. Numerical self-propulsion test scheme by FreSCo+ and QCM. Figure 2. Numerical self-propulsion test scheme by FreSCo+ and QCM.

AtAt the the start start of of the the simulation, simulation, a nominala nominal wake wake distribution distribution is extractedis extracted on on the the propeller propel- planeler plane from from the convergedthe converged RANS RANS solution solution without without the the propeller propeller effect. effect. This This velocity velocity distributiondistribution and and an an estimated estimated turning turning rate rate are are used used as inputsas inputs for thefor QCMthe QCM code code to compute to com- thepute forces the forces on the on propeller the propeller blades blades (thrust (thrust and torque). and torque). The hydrodynamic The hydrodynamic forces forces of the of propellerthe propeller areconverted are converted in the in the form form of 3Dof 3D body body forces forces (source (source terms) terms) assigned assigned to to cells, cells, whichwhich represent represent the the propeller propeller disk. disk. The The turning turning rate rate in in QCM QCM is is iteratively iteratively adjusted adjusted until until thethe propeller propeller thrust thrust requiredrequired toto overcomeovercome the ship resistance resistance (in (in self-propulsion self-propulsion mode) mode) is isobtained. obtained. Figure 2.TheThe Numerical resulting resulting self-propulsion distribution distribution test of of the schemethe body body by forces FreSCoforces is + isand used used QCM. as as an an input input to to the the next next RANS RANS calculationcalculation loop. loop. TheThe RANSRANS computationcomputation isis continuedcontinued inin the the next next iteration iteration cycle cycle and and a a newnewAt total thetotal start velocity velocity of the ﬁeld field simulation, is is created. created. a nominal The The propeller-induced prope wakeller-induced distribution velocities velocities is extracted of of the the on previous previous the propel- cycle, cycle, lerwhich plane are from an the output converged of the QCMRANS code, solution are subtractedwithout the from propeller the total effect. velocity This ﬁeld.velocity The distributionresulting effective and an estimated wake distribution turning israte used are asused input as ininputs the subsequent for the QCM QCM code calculation. to com- puteThe the iteration forces ison repeated the propeller until blades the equilibrium (thrust and between torque). the The resistance hydrodynamic of the shipforces under of the propeller are converted in the form of 3D body forces (source terms) assigned to cells, which represent the propeller disk. The turning rate in QCM is iteratively adjusted until the propeller thrust required to overcome the ship resistance (in self-propulsion mode) is obtained. The resulting distribution of the body forces is used as an input to the next RANS calculation loop. The RANS computation is continued in the next iteration cycle and a new total velocity field is created. The propeller-induced velocities of the previous cycle,

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the self-propulsion condition and the propeller thrust is reached. Normally, around 10–15 loops are needed to reach the equilibrium. Since the QCM computation is very fast, the computational time due to QCM is almost negligible compared to the required RANS simulation time. More details of this method can be found in [17].

2.5. Local Optimization Studies The conducted global optimization [9] refers to the determination of the main dimensions and of the integrated hull form characteristics minimizing the calm water resistance, while the local hull form optimization takes into account not only the calm water resistance, but also the propulsive speed–power performance. Thus, the local hull form optimization study has focused on the optimization of the stern tunnel area and of the propulsive efficiency. The stern hull form area was mathematically captured by six local form parameters, such as transom and tunnel width, height of centerline/chine at tunnel and transom positions. In addition, four parameters were incorporated related to the main propeller characteristics, such as propeller diameter, position and shaft inclination [9]. The in- volved ten local optimization variables are listed in Table1. The parametric model for the stern hull form and propulsive arrangement is illustrated in Figure3. In the present study case, the propeller, its shaft and brackets, as well as the rudder, were specified by the propeller manufacturer, thus their characteristics were not a subject of this study; however, their interaction with the catamaran’s hull form was fully considered in the transom stern optimization. There are, in total, eight constraints related to the propeller, shaft brackets and electric motor installation and class specification requirements (see Table2). These constraints have a certain impact on the design space exploration and have been implemented before the design optimization procedure starts, which allows the evaluation of valid designs only and makes the whole procedure more efficient. The applied optimization procedure and the details of the design variables and constraints are elaborated in [9].

Table 1. Local optimization variables.

CLZ_ATS0 Z coordinate of the centerline at transom CLZ_ATX1_7m Z coordinate of the centerline at tunnel CHINEDZ_ATS0 Z coordinate of the chine relative to centerline at transom CHINEZ_AST2 Z coordinate of the chine relative to Centerline at tunnel CHINEY_ATS0 Transom width deﬁnition CHINEY_ATS2 Tunnel width deﬁnition D_Propeller Propeller diameter X_Propeller X coordinate of the propeller position Z_Propeller Z coordinate of the propeller position Beta_Propeller Propeller inclination angle

The identified best design with respect to the required delivered power (DHP) was found to be about 6% lower than the baseline design. It was further fine-tuned to minimize the risk of air suction by ensuring that no air enters into the propeller tunnel during opera- tion. Additionally, the hull pressure fluctuations and amplitudes have been assessed by use of a vortex-lattice code with respect to the cavitation risk, which will not be elaborated in this paper [18]. Figure4 compares the computed pressure coefficient Cp distribution in the resistance mode (without propeller action) and in the self-propulsion mode (with the acting propeller). As can be observed, a slight change in the pressure field can be detected on the tunnel surface in front of the propeller once the propeller is activated; at the same time, a slightly lower pressure is visible on the tunnel surface behind the propeller, which leads to a small thrust deduction factor. J. Mar. Sci. Eng. 2021, 9, 492 6 of 14 J. Mar. Sci. Eng. 2021, 9, 492 6 of 15

Figure 3. Side view of the geometry of parametric model for transom stern optimization. Figure 3. Side view of the geometry of parametric model for transom stern optimization. Table 2. Design constraints defined for the local optimization. Table 2. Design constraints deﬁned for the local optimization. Propeller Tip Clearance Greater than 20% of Diameter of Propeller Propeller Tip ClearanceGreater than certain value Greater to thanguaran 20%tee of the Diameter propeller of shaft, Propeller gearbox and Propeller Shaft Forward End Above the Hull Greater than certainelectric value motor to guarantee installation the propeller shaft, gearbox and PropellerPropeller Shaft Shaft Forward Entry End Above Above the theHull Hull Greater than certain value to electricguarantee motor the installationpropeller shaft, gearbox and Propeller Shaft Entry Above the Hull Greater than certainelectric value motor to guarantee installation the propeller shaft, gearbox and electric motor installation Propeller Shaft Inclination Less than 5° ◦ PropellerZ_max_prop Shaft Inclination Propeller submergence at Less smallest than 5 displacement Z_max_prop Propeller submergence at smallest displacement LWL at Largest Displacement Less than certain value LWL at Largest Displacement Less than certain value HeightHeight ofof ShaftShaft BracketBracket LeadLead Less than Less certain than certain value valueto guarantee to guarantee the propeller the propeller shaft installation shaft installation HeightHeight ofof ShaftShaft BracketBracket TailTail Less than Less certain than certain value valueto guarantee to guarantee the propeller the propeller shaft installation shaft installation J.Longitudinal Mar.Longitudinal Sci. Eng. Position2021, Position9, 492 of Electric of Electric Motor Motor Forward For- EndLessLess than than certain certain value value to guarantee to guarantee the thespace space for forelectric electric motor motor instal- installation7 of 15 ward End lation

The identified best design with respect to the required delivered power (DHP) was found to be about 6% lower than the baseline design. It was further fine-tuned to minimize the risk of air suction by ensuring that no air enters into the propeller tunnel during oper- ation. Additionally, the hull pressure fluctuations and amplitudes have been assessed by use of a vortex-lattice code with respect to the cavitation risk, which will not be elaborated in this paper [18]. Figure 4 compares the computed pressure coefficient Cp distribution in the resistance mode (without propeller action) and in the self-propulsion mode (with the acting propeller). As can be observed, a slight change in the pressure field can be detected on the tunnel surface in front of the propeller once the propeller is activated; at the same time, a slightly lower pressure is visible on the tunnel surface behind the propeller, which leads to a small thrust deduction factor. The propeller-loading simulated herein via a body force method can be observed in Figure 5, together with the streamlines passing through the propeller discs.

FigureFigure 4. 4.Comparison Comparison of of computed computed pressure pressure ﬁeld field in in the the portside portside demihull’s demihull’s stern stern tunnel tunnel region; region; top, top, without without propeller propeller actionaction at at 23 23 knots; knots; and and bottom, bottom, with with propeller propeller action action at at 23 23 knots. knots.

Figure 5. Computed streamlines in the stern tunnels and passing the propellers discs.

3. Experimental Verification and Validation of Numerical Results For the validation of the numerical predictions of the calm water performance of the TrAM Stavanger demonstrator, a prototype of which is presently in the production stage, a large model of 5.34 m in length (scale 1:5.6) was tested in the large towing tank of HSVA (300 m length × 18 m width × 5.6 m depth). The tested large model allowed very precise measurements, while minimizing scale effects. The large width of the towing basin mini- mized wall refection effects on the catamarans wave resistance. The model test results were analyzed by use of HSVA’s Standard Correlation Method, which is in accordance with Froude's method. The demihull models were manufactured out of thin layer wood and were cross-connected by high-strength metal beams. A view of the tested model under way at Froude 0.69 (23 knots full scale speed) and a close-up of a demihull’s stern area with the fitted CP propeller, shaft, brackets and (twisted) rudder is shown in Figure 6.

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Figure 4. Comparison of computedThe propeller-loading pressure field in simulated the portside herein demihull’s via a body forcestern methodtunnel canregi beon; observed top, without in propeller Figure5, together with the streamlines passing through the propeller discs. action at 23 knots; and bottom, with propeller action at 23 knots.

Figure 5. Computed streamlines in the stern tunnels and passing the propellers discs. Figure 5. Computed streamlines in the stern tunnels and passing the propellers discs.

3.3. Experimental Experimental Verification Verification and Validation and Validation of Numerical of ResultsNumerical Results For the validation of the numerical predictions of the calm water performance of the TrAMFor Stavanger the validation demonstrator, of the anumerical prototype of predictions which is presently of the incalm the productionwater performance of the stage,TrAM a large Stavanger model of demonstrator, 5.34 m in length (scalea prototype 1:5.6) was of tested which in theis presently large towing in tank the ofproduction stage, HSVAa large (300 model m length of ×5.3418 mm width in length× 5.6 (scale m depth). 1:5.6) The was tested tested large in model the allowedlarge towing very tank of HSVA precise(300 measurements,m length × 18 while m width minimizing × 5.6 scale m depth). effects. The The large tested width large of the model towing allowed basin very precise minimizedmeasurements, wall refection while effects minimizing on the catamarans scale effects. wave resistance. The large The width model of test the results towing basin mini- were analyzed by use of HSVA’s Standard Correlation Method, which is in accordance withmized Froude’s wall method. refection The effects demihull on models the catamarans were manufactured wave out resistance. of thin layer The wood model test results andwere were analyzed cross-connected by use by high-strengthof HSVA’s metalStandard beams. Correlation A view of the Method, tested model which under is in accordance waywith at Froude Froude's 0.69 (23method. knots full The scale demihull speed) and models a close-up were of a demihull’smanufactured stern area out with of thin layer wood theand fitted were CP propeller,cross-connected shaft, brackets by high-strength and (twisted) rudder metal is shownbeams. in A Figure view6. of the tested model un- 3.1.der Computational way at Froude Setup 0.69 (23 knots full scale speed) and a close-up of a demihull’s stern area withThe the computational fitted CP propeller, domain used shaft, herein brackets for the resistance and (twisted) and propulsion rudder simulation is shown in Figure 6. (both taking into account the free surface effect) extends to 2 Lpp in front of, 5 Lpp behind, 3 Lpp to the side of, and 3 Lpp below the vessel, and is shown in Figure7. A symmetry boundary condition was applied to the symmetry-plane of the catamaran. Local grid refinement was applied to the tunnel, propeller, appendages and free surface region. The generated numerical mesh is shown in Figure8. The total number of used cells counts 5.7 M. Both the computational domain and the mesh generation comply with the HSVA internal best practice guidelines, which are based on a large number of past numerical grid studies. Therefore, no specific grid study was made for this case. To simulate the dynamic trim and sinkage motion of the catamaran, the free-form deformation method was applied to adapt the grid for the ship motion. J. Mar. Sci. Eng. 2021, 9, 492 8 of 14 J. Mar. Sci. Eng. 2021, 9, 492 8 of 15

J. Mar. Sci. Eng. 2021, 9, 492 9 of 15 Figure 6. Stavanger demonstrator model at Froude number 0.69 (up) and close-up of its stern area (down) with fitted Figure 6. Stavanger demonstrator model at Froude number 0.69 (up) and close-up of its stern area (down) with ﬁtted propellers, shafts, brackets and rudders. propellers, shafts, brackets and rudders. 3.1. Computational Setup The computational domain used herein for the resistance and propulsion simulation (both taking into account the free surface effect) extends to 2 Lpp in front of, 5 Lpp behind, 3 Lpp to the side of, and 3 Lpp below the vessel, and is shown in Figure 7. A symmetry boundary condition was applied to the symmetry-plane of the catamaran. Local grid refinement was applied to the tunnel, propeller, appendages and free surface region. The generated numerical mesh is shown in Figure 8. The total number of used cells counts 5.7 M. Both the computational domain and the mesh generation comply with the HSVA internal best practice guidelines, which are based on a large number of past numerical grid studies. Therefore, no specific grid study was made for this case. To simulate the dynamic trim and sinkage motion of the catamaran, the free-form

deformation method was applied to adapt the grid for the ship motion. Figure 7. Computational domain ofFigure FreSCo+ 7. Computational and 5.7 M mesh domain used of FreSCo+for the resistance and 5.7 M meshand propulsion used for the resistancesimulation and. propulsion simulation.

Figure 8. Generated mesh for the demihull with local refinements (cross sectional, lateral and bottom-up views).

3.2. Discussion of Results The predicted full-scale values obtained by CFD simulations could be very well con- firmed by the physical test campaigns. The numerically predicted resistance and propulsion power in full scale were well verified by the model experiments, with an error margin of 3% on average (see Figure 9).

Figure 9. Comparison on calm water resistance (left) and delivered power (right) per displacement between model tests and full scale CFD for the Stavanger Demonstrator.

The predicted dynamic trim and sinkage by full scale CFD also show good agreement with the model experiments (see Figure 10). The observed stern-down trim of about one degree at the planned service speed of 23 knots is moderate, while the associated dynamic sinkage at the same speed is practically zero.

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Figure 7. J.Computational Mar. Sci. Eng. 2021 domain, 9, 492 of FreSCo+ and 5.7 M mesh used for the resistance and propulsion simulation. 9 of 14

Figure 7. Computational domain of FreSCo+ and 5.7 M mesh used for the resistance and propulsion simulation.

Figure 8. Generated mesh for the demihull with local refinements (cross sectional, lateral and bottom-up views). Figure 8. GeneratedFigure 8. Generated mesh for mesh the demihull for the demihull with local with reﬁnements local refinements (cross (cross sectional, sectional, lateral lateral and and bottom-up bottom-up views). views).

3.2. Discussion of3.2. Results Discussion3.2. Discussion of Results of Results The predicted Thefull-scale predictedThe values predicted full-scale obtained full-scale values by values CFD obtained obtained simulations by by CFDCFD couldsimulations simulations be very could could well be very be con- very well con- well firmed by the physical test campaigns. The numerically predicted resistance and propul- firmed by the physicalconﬁrmed test by campaigns. the physical The test numerically campaigns. predicted The numerically resistance predicted and propul- resistance and propulsionsion power power in full full scale scale were were well well verified veriﬁed by the by model the model experiments, experiments, with an with erroran margin error sion power in full scaleof were 3% on well average verified (see Figure by the 9). model experiments, with an error margin margin of 3% on average (see Figure9). of 3% on average (see Figure 9).

Figure 9. Comparison on calm water resistance (left) and delivered power (right) per displacement between model tests and full scale CFD for the Stavanger Demonstrator.

The predicted dynamic trim and sinkage by full scale CFD also show good agreement Figure 9. FigureComparison 9. Comparison on calm water onwith resistancecalm the water model (left resistance )experiments and delivered (left (see) and power Figure delivered (right 10). )The per power observed displacement (right stern-down) per between displace- trim model of about tests one and full scalement CFD between for the model Stavanger testsdegree Demonstrator. and fullat the sc plannedale CFD service for the speed Stavanger of 23 knot Demonstrators is moderate,. while the associated dynamic sinkage at the same speed is practically zero. The predicted dynamicThe predicted trim dynamic and sinkage trim andby full sinkage scale by CFD full scalealso show CFD also good show agreement good agreement with the modelwith experiments the model (see experiments Figure 10). (see The Figure observed 10). The stern-down observed stern-down trim of about trim of one about one J. Mar. Sci. Eng. 2021degree, 9, 492 at the planneddegree atservice the planned speed service of 23 knot speeds is of moderate, 23 knots is moderate,while the whileassociated the associated dynamic dynamic 10 of 15

sinkage at the samesinkage speed at the is same practically speed is zero. practically zero.

Figure 10. Comparison of dynamic trim (left) and sinkage (right) between model tests and full scale CFD for the Stavanger Figure 10. Comparison of dynamic trim (left) and sinkage (right) between model tests and full scale CFD for the Stavanger Demon- Demonstrator. strator. A remarkable result of the conducted model tests was the achieved very high propulsive efficiency. Notably, the high propulsive efficiency is not only achieved for the design condition, but also kept for off-design conditions (see Table 3).

Table 3. Experimentally measured hull and propulsive efficiencies at trial condition BF 0 for the design and off-design displacements of the Stavanger demonstrator (full scale). V: speed in knots; Fn: Froude number; ηD: propulsive efficiency.

V Fn ηD at Δ1 ηD at Δ2 ηD at Δ3 [KTS] [-] [-] [-] [-] 13.00 0.39 0.736 0.742 0.733 15.00 0.45 0.728 0.731 0.723 17.00 0.51 0.738 0.739 0.731 19.00 0.57 0.751 0.753 0.748 21.00 0.63 0.768 0.769 0.767 23.00 0.69 0.781 0.784 0.783 25.00 0.75 0.793 0.795 0.793 27.00 0.81 0.800 0.802 0.798

We will be discussing in the following section the contributing factors to this high propulsive efficiency. The propeller open-water efficiency of the model tested is shown in Figure 11. It reaches an efficiency of about 80% at a speed advance ratio J of about 1.40.

Figure 11. Propeller open-water efficiency test results.

The variation of the hull, the propeller rotative, and the open-water and the delivered power efficiency with speed are shown in Figure 12, as obtained from model tests and CFD calculations. In the present study, two different post-processing methods were applied in the analysis of the CFD results. The CFD V1 applies the conventional CFD processing procedure, in which the calculated QCM Propeller Blades Force leads to the

J. Mar. Sci. Eng. 2021, 9, 492 10 of 15

J. Mar. Sci. Eng. 2021, 9, 492 10 of 14

A remarkable result of the conducted model tests was the achieved very high propul- Figure 10. Comparison of dynamicsive efﬁciency. trim (left) Notably,and sinkage the (right high) between propulsive model tests efﬁciency and full isscale not CFD only for achievedthe Stavanger for the design Demonstrator. condition, but also kept for off-design conditions (see Table3).

TableA 3. remarkableExperimentally result measured of the conducted hull and model propulsive tests efficiencieswas the achieved at trial very condition high pro- BF 0 for the pulsive efficiency. Notably, the high propulsive efficiency is not only achieved for the de- design and off-design displacements of the Stavanger demonstrator (full scale). V: speed in knots; Fn: sign condition, but also kept for off-design conditions (see Table 3). Froude number; ηD: propulsive efficiency. Table 3. Experimentally measured hull and propulsive efficiencies at trial condition BF 0 for the design and off-design V Fn ηD at ∆1 ηD at ∆2 ηD at ∆3 displacements of the Stavanger demonstrator (full scale). V: speed in knots; Fn: Froude number; ηD: propulsive efficiency. [KTS] [-] [-] [-] [-] Δ Δ Δ V Fn13.00 η0.39D at 1 0.736ηD at 2 0.742ηD at 3 0.733 [KTS] [-]15.00 0.45[-] 0.728 [-] 0.731 [-] 0.723 13.00 0.3917.00 0.51 0.736 0.7380.742 0.7390.733 0.731 15.00 0.45 0.728 0.731 0.723 19.00 0.57 0.751 0.753 0.748 17.00 0.51 0.738 0.739 0.731 21.00 0.63 0.768 0.769 0.767 19.00 0.57 0.751 0.753 0.748 23.00 0.69 0.781 0.784 0.783 21.00 0.63 0.768 0.769 0.767 23.00 0.6925.00 0.750.781 0.7930.784 0.7950.783 0.793 25.00 0.7527.00 0.81 0.793 0.8000.795 0.802 0.793 0.798 27.00 0.81 0.800 0.802 0.798 We will be discussing in the following section the contributing factors to this high propulsiveWe will efficiency. be discussing The propellerin the following open-water section efficiencythe contributing of the factors model to tested this high is shown in Figurepropulsive 11. It efficiency. reaches anThe efficiency propeller open-water of about 80% efficiency at a speed of the advance model tested ratio is J shown of about in 1.40. Figure 11. It reaches an efficiency of about 80% at a speed advance ratio J of about 1.40.

Figure 11. Propeller open-water efficiency test results. Figure 11. Propeller open-water efficiency test results. The variation of the hull, the propeller rotative, and the open-water and the delivered The variation of the hull, the propeller rotative, and the open-water and the delivered power efficiency with speed are shown in Figure 12, as obtained from model tests and powerCFD calculations. efficiency with In the speed present are study, shown two in Figuredifferent 12 post-processing, as obtained from methods model were tests ap- and CFD calculations.plied in the analysis In the of present the CFD study, results. two The different CFD V1 post-processingapplies the conventional methods CFD were pro- applied incessing the analysis procedure, of the in CFDwhich results. the calculated The CFD QCM V1 appliesPropeller the Blades conventional Force leads CFD to processingthe procedure, in which the calculated QCM Propeller Blades Force leads to the propeller thrust and torque; in the second method, CFD V2 considers that the propeller thrust/torque are the sum of the propeller blades’ force (coming from QCM) and the propeller hub force (coming from the RANS computation). It proves that the second method is closer to the model experiment values, as can be seen in Figures 12 and 13, especially in the prediction of the thrust deduction factor. The very high open-water efficiency in view of the fitted propeller with a large diameter and relatively low thrust loading factor is at a speed of over 16 knots, further enhanced by the unique transom stern achieving a relative rotative efficiency (ηR) of over 100% and a total propulsive efficiency (ηD) of close to 80% at 27 knots speed. The optimized unique transom stern with a longitudinal and transverse curvature creates almost perfect inflow conditions for the propeller, as indicated by the very low values of wake and thrust deduction from model tests and CFD results (Figure 13). J. Mar. Sci. Eng. 2021, 9, 492 11 of 15

propeller thrust and torque; in the second method, CFD V2 considers that the propeller J. Mar. Sci. Eng. 2021, 9, 492 11 of 15 thrust/torque are the sum of the propeller blades’ force (coming from QCM) and the propeller hub force (coming from the RANS computation). It proves that the second method is closer to the model experiment values, as can be seen in Figures 12 and 13, especially in thepropeller prediction thrust of andthe thrusttorque; deduction in the second factor. method, CFD V2 considers that the propeller thrust/torqueThe very arehigh the open-water sum of the efficiency propeller in bl viewades’ of force the fitted(coming propeller from QCM) with a and large the diam- pro- pellereter and hub relatively force (coming low thrust from theloading RANS factor computation). is at a speed It proves of over that 16 the knots, second further method en- is closer to the model experiment values, as can be seen in Figures 12 and 13, especially in hanced by the unique transom stern achieving a relative rotative efficiency (ηR) of over the prediction of the thrust deduction factor. 100% and a total propulsive efficiency (ηD) of close to 80% at 27 knots speed. The very high open-water efficiency in view of the fitted propeller with a large diam- J. Mar. Sci. Eng. 2021, 9, 492 eter and relatively low thrust loading factor is at a speed of over 16 knots, further11 ofen- 14 hanced by the unique transom stern achieving a relative rotative efficiency (ηR) of over 100% and a total propulsive efficiency (ηD) of close to 80% at 27 knots speed.

(a) (b)

(c) (d) Figure 12. Full scale propulsive efficiencies as predicted from model tests (left) and CFD (right) for the Stavanger Demon- strator; (a) hull efficiency, (b) propeller rotative efficiency, (c) propeller open water efficiency, (d) total propulsive (hydrodynamic) efficiency (c) (d)

FigureFigure 12 12.. FullFull scale scale propulsive propulsive efficiencies efficienciesThe optimized as as predicted predicted unique from from transom model model tests testsstern (left) (left) with and and a CFDlongitudinal CFD (right) (right) for for and the the Stavanger Stavangertransverse Demon- Demon- curvature strator; (a) hull efficiency, (b) propeller rotative efficiency, (c) propeller open water efficiency, (d) total propulsive (hydro- strator; (a) hull efficiency, (bcreates) propeller almost rotative perfect efficiency, inflow (c) propellerconditions open for water the efficiency,propeller, (d as) total indicated propulsive by (hydrody-the very low dynamic) efficiency namic) efficiency values of wake and thrust deduction from model tests and CFD results (Figure 13). The optimized unique transom stern with a longitudinal and transverse curvature creates almost perfect inflow conditions for the propeller, as indicated by the very low values of wake and thrust deduction from model tests and CFD results (Figure 13).

Figure 13. Taylor wake fraction (left) and thrust deduction factors (right) from model tests and full scale CFD (two analysis methods) for the Stavanger Demonstrator.

The calculated pressure field in the transom stern area, when looking from the bottom and the side, is depicted in Figure 14, showing the small shift of the pressure isolines for the resistance (black isolines) and propulsion (red isolines). This is in line with the observed very small values of the thrust deduction factor that, per definition, represents the augment of the catamaran’s resistance in towing conditions. The reduction of the pressure in the stern area by the propeller action in accelerating the flow in the self-propulsion mode is herein kept at low values as the thrust to propel the ship at a given speed. The computed nominal wake is presented in axial velocity contours and transversal velocity vectors in Figure 15, illustrating and confirming again the minimal wake fraction factor. The nominal axial wake is very homogeneous except for a small region close to 178 degrees, where the wake of the shaft bracket is visible. J. Mar. Sci. Eng. 2021, 9, 492 12 of 15

Figure 13. Taylor wake fraction (left) and thrust deduction factors (right) from model tests and full scale CFD (two analysis methods) for the Stavanger Demonstrator.

The calculated pressure field in the transom stern area, when looking from the bottom and the side, is depicted in Figure 14, showing the small shift of the pressure isolines for the resistance (black isolines) and propulsion (red isolines). This is in line with the observed very small values of the thrust deduction factor that, per definition, represents J. Mar. Sci. Eng. 2021, 9, 492 the augment of the catamaran’s resistance in towing conditions. The reduction of the12 pres- of 14 sure in the stern area by the propeller action in accelerating the flow in the self-propulsion mode is herein kept at low values as the thrust to propel the ship at a given speed.

J. Mar. Sci. Eng. 2021, 9, 492 13 of 15 FigureFigure 14. 14.Isolines Isolines of of computed computed pressure pressure ﬁeld field in in ship’s ship’s stern stern tunnel tunne regionl region for for resistance resistance (black (black isolines) isolines) and and propulsion propulsion (red(red isolines) isolines) condition condition at at 23 23 knots: knots: view view from from bottom bottom (up (up) and) and view view from from side side (down (down). ).

The computed nominal wake is presented in axial velocity contours and transversal velocity vectors in Figure 15, illustrating and confirming again the minimal wake fraction factor. The nominal axial wake is very homogeneous except for a small region close to 178 degrees, where the wake of the shaft bracket is visible.

FigureFigure 15. 15. ComputedComputed nominal nominal axial axial velocity velocity contours contours and and transversal transversal ve velocitylocity vectors vectors at atthe the (port (port side)side) propeller propeller plane plane for for ship ship speed speed at at 23 23 knots knots (view (view from from behind) behind)..

AtAt this this point, point, a a comment is duedue onon thethe notionnotion of of hull hull efficiency, efficiency, commonly commonly used used in thein theassessment assessment of ship’sof ship’s hull–propeller hull–propeller interaction. interaction. Recalling Recalling the definition the definition of the of hull the efficiency hull ef- ficiencyηH = (1 η−H t)/(1= (1 −− t)/(1w), − it w), is evident it is evident that a largethat a value large ofvalue the wakeof the factor wake w factor (typical w (typical for full typefor fullships) type leads ships) to leads high hullto high efficiency hull efficiency values of values well over of well 100%. over This 100%. is, however, This is, however, a deceptive a deceptiveindication indication of the quality of the of aquality ship’s hull–propellerof a ship’s hull–propeller interaction. Ainteraction. large wake A fraction large wake factor fractionwill lead factor to an will inferior leadinflow to an inferior to the propeller inflow to and the to propeller low propeller and to efficiency. low propeller In addition, efficiency.large wake In addition, fraction large factors wake (of fraction full type factors ships) (of are full associated type ships) with are large associated thrust with deduction large thrustfactors deduction and, thus, factors an increased and, thus, augment an increased of the resistanceaugment of that the needs resistance to be that overcome needs to by bethe overcome propeller by thrust. the propeller In the present thrust. study, In the we present detected study, measured we detected (and calculated) measured thrust(and calculated)deduction thrust and wake deduction fraction and factors wake closefraction to zerofactors at certainclose to speedszero at andcertain very speeds high and total verypropulsive high total efficiency propulsive due toefficiency close to idealdue to hull–propeller close to ideal interaction hull–propeller conditions. interaction At speeds conditions. At speeds at or above the design speed, the rotative propulsive efficiency ηR becomes higher than one, and the total propulsive efficiency ηD is even higher than the open water propulsive efficiency ηO. Thus, the traditional hull efficiency factor needs to be always assessed with caution and never separately from the other propulsive efficiency factors. It is noted that similarly low wake and thrust deduction factors are observed for fast twin-screw naval ships of the destroyer type, namely wake fractions between −0.02 and +0.02 for propeller shafts supported by struts and between 0.04 and 0.08 for those supported by brackets. The thrust deduction factors are, in this case, also very small and take similar values [18]. Finally, a systematic variation of a static pre-trim of the vessel delivered valuable information for the arrangement of the ship’s weight distribution in terms of power reduction, suggesting that keeping a moderate stern-down trim of less than 30 cm in full scale would lead to a small power increase or even decrease at higher speeds, while a bow-down trim would only be beneficial at lower speeds as indicated by CFD predictions (Figure 16).

J. Mar. Sci. Eng. 2021, 9, 492 13 of 14

at or above the design speed, the rotative propulsive efficiency ηR becomes higher than one, and the total propulsive efficiency ηD is even higher than the open water propulsive efficiency ηO. Thus, the traditional hull efficiency factor needs to be always assessed with caution and never separately from the other propulsive efficiency factors. It is noted that similarly low wake and thrust deduction factors are observed for fast twin-screw naval ships of the destroyer type, namely wake fractions between −0.02 and +0.02 for propeller shafts supported by struts and between 0.04 and 0.08 for those supported by brackets. The thrust deduction factors are, in this case, also very small and take similar values [18]. Finally, a systematic variation of a static pre-trim of the vessel delivered valuable information for the arrangement of the ship’s weight distribution in terms of power reduction, suggesting that keeping a moderate stern-down trim of less than 30 cm in full scale would lead to a small power increase or even decrease at higher speeds, while a J. Mar. Sci. Eng. 2021, 9, 492 bow-down trim would only be beneficial at lower speeds as indicated by CFD predictions14 of 15 (Figure 16).

Figure 16. Results of trim variation studies from model tests and CFD. Figure 16. Results of trim variation studies from model tests and CFD. 4.4. Conclusions Conclusions TheThe hydrodynamic hydrodynamic optimization optimization of of fast fast ships ships is is imperative imperative for for the the feasibility feasibility of of the the designdesign concept, concept, even even more more so so if if the the designer designer is is dealing dealing with with the the feasibility feasibility of of a a battery- battery- driven,driven, fast fast catamaran, catamaran, forfor whichwhich the tradeoff tradeoff between between the the required required propulsion propulsion power power for fora certain a certain speed speed and and the the weight weight of the of the energy energy source source provider, provider, namely namely the thebatteries, batteries, is gov- is governingerning the the feasibility feasibility of ofthe the whole whole design design concept. concept. InIn the the present present study, study, we we focused focused on on the the analysis analysis of of the the propulsive propulsive efficiency efficiency of of a a fast, fast, battery-drivenbattery-driven catamaran, catamaran, a a prototype prototype of of which which is is presently presently under under construction construction and and will will startstart operations operations in in 2022 2022 in in Stavanger, Stavanger, Norway. Norway. Next Next to to the the hull hull optimization optimization with with respect respect toto resistance, resistance, it it was was the the achieved achieved high high propulsive propulsive efficiency efficiency of of close close to to 80% 80% that that proved proved thethe feasibility feasibility of of the the concept. concept. This This was was enabled enabled by by the the unique unique transom transom stern stern form form with with longitudinallongitudinal and and transverse transverse curvature, curvature, the the high high open-water open-water propeller propeller efficiency efficiency associated associ- withated the with fitted the largefitted diameter large diameter propeller propeller in the stern’sin the tunnel,stern’s tunnel, the very the low very values low ofvalues wake of andwake thrust and deductionthrust deduction factors factors and the and optimization the optimization of the concurrentof the concurrent hull, propeller, hull, propeller, and shaftand arrangements.shaft arrangements.

AuthorAuthor Contributions: Contributions:Conceptualization, Conceptualization, A.P. A.P. and and Y.X.-K.; Y.X.-K.; methodology, methodology, Y.X.-K.; Y.X.-K.; software, software,Y.X.-K. Y.X.-; validation,K.; validation, Y.X.-K.; Y.X.-K.; formal formal analysis, anal Y.X.-K.ysis, Y.X.-K. and A.P. and investigation, A.P. investigation, A.P. and A.P. Y.X.-K.; and resources, Y.X.-K.; resources,Y.X.-K.; dataY.X.-K.; curation, data Y.X.-K.; curation, writing—original Y.X.-K.; writing—original draft preparation, draft preparation, A.P.; writing—review A.P.; writing—review and editing, A.P. and and edit- Y.X.-K.;ing, A.P. visualization, and Y.X.-K.;Y.X.-K. visualization,; supervision, Y.X.-K.; A.P.; supervision, project administration, A.P.; project administration, Y.X.-K.; funding Y.X.-K.; acquisition, fund- A.P.ing All acquisition, authors have A.P. read All authors and agreed have to read the publishedand agreed version to the published of the manuscript. version of the manuscript. Funding:Funding:The The TrAM TrAM project project has has received received funding funding from from the the European European Union’s Union’s Horizon Horizon 2020 2020 research research andand innovation innovation program program under under grant grant agreement agreement No No 769303. 769303. InstitutionalInstitutional Review Review Board Board Statement: Statement:Not Not applicable. applicable. InformedInformed Consent Consent Statement: Statement:Not Not applicable. applicable. Conflicts of Interest: The authors declare no conflict of interest.

Reference 1. Papanikolaou, A. Review of Advanced Marine Vehicles Concepts. In Proceedings of the 7th International High Speed Marine Vehicles Conference (HSMV05), Naples, Italy, 21–23 September 2005. 2. Papanikolaou, Α.; Kaklis, Ρ.; Koskinas, C.; Spanos, D. Hydrodynamic Optimization of Fast Displacement Catamarans, In Pro- ceedings of the 2lst International Symposium on Naval Hydrodynamics, ONR' 96, Trondheim, Norway, 24–26 June 1996. 3. Papanikolaou, Α.; Zaraphonitis, G.; Androulakakis, Μ. Preliminary Design of a High-Speed SWATH Passenger Car/ Ferry. Mar. Technol. 1991, 28, 129–141. 4. Skoupas, S.; Zaraphonitis, G.; Papanikolaou, A. Parametric Design and Optimisation of High-Speed Ro-Ro Passenger Ships. Ocean Eng. 2019, 189, 106346, doi:10.1016/j.oceaneng.2019.106346. 5. Papanikolaou, Α.; Schellin, T.h. On Estimating Dynamic Wave Loads for Global Strength Analysis of α Catamaran Ferry. In Proceedings of the 7th Congress of the ΙΜΑΜ, Dubrovnik, Croatia, 26–30 April 1995. 6. Zaraphonitis, G.; Papanikolaou, A.; Mourkoyiannis, D. Hull Form Optimization of High-Speed Vessels with Respect to wash and Powering. In Proceedings of the 8th International Marine Design Conference (IMDC), Athens, Greece, 5–8 May 2003.

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Conﬂicts of Interest: The authors declare no conﬂict of interest.

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