UNCLASSIFIED

Defense Technical Information CenterCompilation Part Notice

ADP023922TITLE: Resistance Predictions for a High-Speed Sealift Trimaran

DISTRIBUTION: Approved for public release; distribution is unlimited.

This paper is part of the following report:TITLE: International Conference on Numerical Ship Hydrodynamics [9th]held in Ann Arbor, Michigan, on August 5-8, 2007To order the complete compilation report, use: ADA495720The component part is provided here to allow users access to individually authored sectionsf proceedings, annals, symposia, etc. However, the component should be considered within

[he context of the overall compilation report and not as a stand-alone technical report.

The following component part numbers comprise the compilation report:ADP023882 thru ADP023941

UNCLASSIFIED

Ninth International Conference on Numerical Ship HydrodynamicsAnn Arbor, Michigan, August 5-8, 2007

Resistance Predictions for aHigh-Speed Sealift Trimaran

K.J. Maki 1 , L.J. Doctors 2, S.H. Rhee', W.M. Wilson4 , R.F. Beck 1 , A.W. Troesch1

(1University of Michigan, 2The University of New South Wales,'Seoul National University, 4Naval Surface Warfare Center)

Abstract 1 Introduction

The purpose of this work is to compare the capa- 1.1 Backgroundbility of two different numerical techniques for pre-dicting the calm-water resistance of a high-speedsealift trimaran. The vessel is representative of a The trimaran vessel has been under considerationfuture advanced naval design that must be able to for many years now. However, it is only in re-travel long distances with heavy payloads, but is cent years that the concept has been subjected toconstrained geometrically in order to operate in aus- high-level technical scrutiny. The reader is referredtere ports upon arrival. It has a relatively shallow to books by Dubrovsky and Lyakhovitsky (2001)draft and has an extendable centerhull that pos- and Dubrovsky (2004), where the general advan-sesses a wave-piercing bow. This particular design tages and disadvantages are explained. Other pub-has hulls that are of essentially equal dimensions. lications of a design or descriptive nature include

those of Summers and Eddison (1995), PattisonFor comparison of the codes, a series of large- and Zhang (1995), van Griethuysen, Bucknall, and

scale model tests was conducted for six different Zhang (2001). In these papers, the principal inter-configurations of the three hulls (variations of over- est has been in the application of the concept toall vessel beam and length). A thin-ship theory is naval vessels, so that the emphasis has been placedshown to be effective in predicting resistance. Re- on matters of layout and operability, rather than de-sults for both the absolute value and the relative tails of resistance and structural strength. The pre-change in resistance due to change in the hull con- cise categorization of vessel type is often difficult;figuration, together with the computational efficacy an interesting example of a hybrid form, namely aof the method demonstrate utility for the designer. small-waterplane-area trimaran, was described byThe complex effect on the resistance due to the Lamb (2004). A recent example of a successful civilproximity of the three hulls is addressed in a first- application of the trimaran is that detailed by Arm-principle manner to enhance the prediction from the strong (2004). In the development of that vessel,thin-ship theory. effort was invested in determining the optimal geo-

metric configuration to minimize both overall resis-The commercial computational fluid dynamics tance and motions in a seaway.

code FLUENT is shown to more accurately predictthe resistance when the calculations are performed A fundamental question, which must be asked,with the body fixed at the experimental sinkage and relates to the potential resistance advantage of atrim. The temporal expense associated with com- trimaran over more traditional hullforms, such asputational fluid dynamics is reduced in this study monohulls and catamarans. Over three decades ago,by using very simple computational grids. Also, the Narita (1976) examined this problem, using a multi-solution convergence is enhanced by using polyhe- body extension to the hallmark linearized theory ofdral finite volumes which improve cell skewness. Michell (1898) for a monohull. This matter was also

studied in depth by Doctors (1999), who compared timum is through a search technique that is codedboth the wave resistance and the total resistance of in order to avoid local false optimums.vessels possessing between one and six subhulls.

It is necessary to test theoretical predictionOne is strongly interested in minimizing wave methods against experiments. This is most conve-

resistance if the concern is about the wave genera- niently achieved at model scale in a towing tank.tion, such as for river-based ferries, when bank ero- Examples of such effort is characterized by thesion must be avoided. In this case, increasing the papers by Scrace (2000), Kennell (2004), Mizine,number of subhulls is generally favorable, although Amromin, Crook, Day and Korpus (2004), Colic-there is little additional reduction in wave genera- chio, Colagrossi, Lugni and Faltinsen (2005), andtion after two or three subhulls depending on the Degiuli, Werner and Zotti (2005). In general, itspeed range of interest. If there is a primary con- can be stated that current methods based on thecern to minimize total resistance, it is found that Michell (1898) theory or computational fluid dy-the increase in wetted surface area is a major draw- namics (CFD) provide useful results. Nevertheless,back of a vessel with many subhulls. Indeed, if a the predictions are often not as accurate as thosetrimaran is to compete on this basis, it is vital to for catamarans. It is believed that this is due tokeep to a minimum the size of the sidehulls. In such the possible strong flow interferences between thecircumstances, the sidehulls may be referred to as sidehulls and the centerhull, which can create anoutriggers, adverse effect (that is, a large increase) on the fric-

tional form factor. We will specifically refer to thisIn this current research, we also principally point again later in this paper.

wish to investigate the resistance characteristics oftrimarans, because the application is to sealift ves-sels, in which the operational range is to be max-imized. Thus, there is a need to minimize the to- 1.2 Current Worktal resistance. Clearly, the most obvious idea is toconsider different longitudinal positions (the stag- In the current work, we describe an exhaustive in-ger) and different lateral positions (the spacing) vestigation into the resistance for a candidate high-of the sidehulls. In this regard, one can refer to speed sealift trimaran. The purpose of the effortthe work of Wood (1988), Wilson and Hsu (1992), was twofold: to consider a suitable trimaran designGale, Hall and Hartley (1996), Ackers, Michael, Tre- and to test our available computational tools.dennick, Landen, Miller III, Sodowsky and Hadler(1997), Battistin, Danielli and Zotti (2000), Doc- The software developed by Doctors (1999) andtors and Scrace (2003), Day, Clelland and Nixon Doctors and Scrace (2003), based on extensions to(2003), Begovic, Bove, Bruzzone, Caldarella, Cas- the Michell (1898) theory, represented one focus ofsella, Ferrando, Tincani and Zotti (2005), and Ya- the computational work. Computations were per-sukawa (2005). A common theme is that the side- formed in a "blind fashion", in that the experimen-hulls should be located aft in order to reduce the tal results for the resistance were not initially maderesistance. Obviously, the precise answer must de- available to those persons performing the calcula-pend on the relative displacements of the centerhull

and he ideull aswel as he ntededopeatinal tions. Of course, the opportunity was later providedand the sidehull, as well as the intended operational to learn from the comparisons of theory and exper-Froude number. iment and, consequently, to improve the software.

The specific matter of optimization of the con- The second focus of the work was based on afiguration of the trimaran is closely linked to the Reynolds- Averaged Navier-Stokes (RANS) compu-previous comments. This topic has been investi- tational fluid dynamics (CFD) approach using thegated by a number of researchers, including Suzuki commercially available software FLUENT. The ii-and Ikehata (1993), Yang, Soto, L6hner and No- tial intentions were to perform the computations inblesse (2002), Yang, Noblesse and L6hner (2002), a "blind fashion", as in the Doctors results; how-Degiuli, Werner and Doliner (2003), and Brizzolara, ever, difficulties were encountered in dynamicallyBruzzone, and Tincani (2005). When studied in a predicting the sinkage and trim of the model as parttheoretical or computational sense, it must be un- of the computations. Therefore, several fixed modelderstood that the problem is nonlinear. That is, the conditions were simulated, using the experimentallyonly reliable approach to determining the global op- measured sinkage and trim for the model. It is not

Table 1, for the loading cases where the draft is setat 6.510 m.

2.2 Advantages of Concept

It is well known that a resistance-optimal conven-tional trimaran is one in which the sidehulls possessa very small displacement compared to that of thecenterhull. However, in the present application, it

(a) Pictorial of Configuration 6 is intended that the trimaran will be operated inessentially two different (and diverse) modes.

In the cruising mode, the sidehulls are to be7staggered rearward by up to 50% of the length of

the subhulls. In this configuration, the great over-all length of the vessel renders it somewhat simi-lar to a slender monohull from a resistance point ofview. Thus, its resistance qualities are expected tobe good. In the arrival or departure mode, the cen-terhull can be retracted so that it is aligned with thesidehulls. While the resistance is certain to be un-

Figure 1: Vessel Geometry reasonably high in this configuration, it will permitthe vessel to be docked in an austere port.

yet clear what the limiting factor is for predicting This vessel was designed by Dr R. Scher, ofthe sinkage and trim of the model. Previous in- Alion Science and Technology, in Alexandria, Vir-vestigations by some of the authors have success- ginia. The designing of this vessel formed part of thefully computed ship model behaviors for pitch and project Architectural Concepts and Hydrodynamicheave in the presence of incident waves (Sasanapuri, Technologies for High Speed Sealift to Austere Ports:Shirodkar, Wilson, Kadam, and Rhee, 2007), and Subtopic B: Computational Approach and Hydrody-further studies are planned to include the dynamic namic Tools, supported by the US Office of Navalmotion of the model as part of the computations. Research, under the supervision of Project Manager

Dr. L. Patrick Purtell.

2 Design of Candidate3 Towing-Tank Tests

2.1 Geometry3.1 Physical Description of Model

The vessel chosen for our investigation is a trimaran,in which the sidehulls and the centerhull are essen- The bare-hull model resistance tests were conductedtially equal in length, beam, draft, and displace- at the Maritime Research Institute Netherlandsment. The vessel is depicted in Figure 1, where the MARIN. Three individual hulls were constructedperspective view of the extended vessel can be seen out of wood, with a scale factor of 1:34, and con-along with the body plans of the side and center nected together using aluminum beams which al-hulls. lowed for easy reconfiguration. Figure 2 shows an

image of the model in Configuration 4.Both the centerhull and the sidehulls possess

a transom stern, which would permit the installa- The model was attached to the carriage andtion of suitable waterjets. The principal geometric towed with a vertical heave staff and gimbal so thatand hydrostatic data for the subhulls are listed in the model was free to heave and pitch. The longi-

Table 1: Nominal Particulars of HSSL ALT SubhullsCenter- Side-

Item Symbol Units hull hullhull hullDisplacement mass A t 5827 5964Waterline length L m 168.1 168.6Waterline beam B m 10.03 10.04Draft T m 6.510 6.510Waterplane-area coefficient Cwp 0.7770 0.8091Maximum section coefficient CA1 0.7860 0.7863Block coefficient CB 0.5174 0.5279Prismatic coefficient Cp 0.6583 0.6714Slenderness coefficient L/V 1/ 3 9.424 9.375

I (a) Configuration 1

Figure 2: Image of model in Configuration 4 -

tudinal location of the tow point corresponded to (b) Configuration 2the longitudinal center of buoyancy of the trimaran(which varied depending on the stagger of the side-hulls).

3.2 Test Configurations (c) Configuration 3

The towing-tank model was operated in six differ-ent loading configurations, as listed in Table 2 andviewed in Figure 3. Essentially, this consisted of (d) Configuration 4three different staggers of the sidehulls and two dif-ferent offsets 82/2 of the centerplane of the sidehullsfrom the centerplane of the centerhull. During theplanning phase of the experiments, we had intended (e) Configuration 5that the draft should be identical for all test con-figurations. Unfortunately, the freeboard proved tobe too small for the reduced dimensions for Config-uration 4 and Configuration 5; as a result, an exces- ..sive amount of spray impacted on the bridging crossstructure connecting the three subhulls. This defi- (f) Configuration 6ciency in the design of the trimaran could easily becorrected in any planned extension to the project. Figure 3: Bottom View of the 6 Hull Configurations

It is recommended that the wetdeck height,which in the current design is 10.63 m, be increased

by IininmI of 2 in. This is b ed on observ~tionsof the resistance tests and of th sea~keping experinients tht were perforimed on th nodel. (Sea-keeping experiments were also done solely for Con-fiouration 6 and th nodel was selfpropeiled witha. single water jet fitted in ea1ch hull.) Two facto scontributed to the rel tive rise of the free surfac Oibody. Firstl, the eometn of the shorter Coinfinu-ra tions 1, 2, 4 aind 5 places the forward portion ofthe sidehulls in the peak of the dominant- divergingwave of the eenteriull. Secondl, the vess- sinksdownward and trims bow down 'it -. speed of ap-proximately 30 knots. Figures 4 and 5 depict theeffect of firward speed on the running attitude ofthe bod -1-,d thus the freeKo d. Figure 4 siowsin th deep d'tfe Confi-ur a [in 4 ait 30 knots, andthe vanishing freebcard ca be seen. Note that theniodels were tested with the portion of the geonietry from the baseline to the wedeck plane. Figure Fshows how the vessel Ittitude cha.nges at a higherspeed. The bcw'-up trini and rise in the vessel actto increase thE freehcard oil the vessel.

Figure 5: Ininge of niodel underwa, in Configura-Other observations froi the seakeepin exper- tion 1, at a. speed of 44 knots

iments sui-est that a 2 m rise in th wetdeck hioulkbe sufficient to allow cleara nce for the spi y and jet*fw Lter exiting the centerhll. Finally, a rise in the 4 Theoretical Approachwedeck will allw fE 1a~rer free hE rd on the cen-te Lull, which is cirrently lmited by the fact that itmiust retract underne -th the sidehulls for entry into 4.1 Thin-Ship Analysis of aPo t Au er . Transom-Stern Multihull

A computationa1 approach based o the work ofDoctors and Day (1997) was used to prediet the re-sistince o f the I 34-sca-le iodel. PTis a~pproach hasits roots in the linea rized theory of Michell (1898).Ple cUrrent version of the software contains a. nui -ber of enhancements.

Firstl, the prograim can handle any number ofsubhulls tip to six, by employing additi( n- (enter-plarne source distributi ns. The tiaunsverse vekocitiesinduced by one subhull siould be co, rected f bythe use of centerplane dipole (listributions; however,this is ionored for the ske of considerable sinlplifi-cation to the coding of the software.

Figure 4: Ilage of niodel underwa., in the heavyConfiguraition 4 (ba llasted to , Jrift of 6.51 il), at Secondly, in enhanced iodel for the trans, ii-a o speed of 30 knots stern flow has been under development for tel yeirs

now. The current rnodel allows for a realistic hydrody nalic addition to the vessel by inea11s of avirtual extension to the vessel in order to representthe presence of the transoi-stern hollow. This has

been described by Doctors and Beck (2005), Doctors moving at speeds that cause breaking waves. Re-(2006a and 2006b), and Maki, Doctors, Beck, and cent advances in computing technologies and, inTroesch (2006). In this way, the effective hydrody- particular, parallel-processing techniques, have alsonamic length of the subhulls grows with increasing greatly enhanced the ability to perform simulationsvessel speed in a physically realistic manner that has with increased spatial resolution of the flow fieldbeen substantiated by numerous towing-tank exper- and with faster compute times. These improve-iments. ments, along with growing user experience in ap-

plying RANS methods to these types of problems,Thirdly, the transom-stern model includes a are beginning to demonstrate the ability of CFD

procedure for estimating the progressive unwetting methods to impact design and evaluation for ma-or ventilation of the transom. This feature permits rine hydrodynamic problems. A review of applyinga practical estimate of the transom-stern or hydro- RANS techniques to a variety of surface ship con-static drag suffered by such vessels, figurations was given by Gorski (2004). An assess-

ment of different computational tools was given inFourthly, as a special task inspired by the Wilson, Fu, Fullerton, and Gorski (2006).

model experiments to be described here, a furtherprocedure was incorporated in the computer code The commercially available viscous RANS flowin order to take into account the viscous interac- solver FLUENT was used to predict the resistancetion between the subhulls. This simplistic proce- for the 1:34-scale model. The computations focuseddure makes an allowance that the subhulls are in on Configuration 6 (Figure 3(f)) as this was ex-the "shadow" of each other to some degree, as seen pected to be the best performing design configu-in a profile or a side view. This shadow will be great- ration for resistance and seakeeping. The compu-est when the subhulls are abreast of each other and tations were performed using FLUENT V6.3 andwill be particularly strong when they are of similar the parallel computational resources at the Ship En-size. In the present theory, the local gap between gineering and Analysis Technology Center, locatedthe subhulls below the loaded waterplane was com- at the Naval Surface Warfare Center, Carderockputed. From this, an estimate of the increase in lo- Division (NSWCCD) and the Aeronautical Sys-cal water speed was obtained. This increase in speed tems Center (ASC) Major Shared Resource Centerwas applied to the usual formula for frictional resis- (MSRC) High Performance Computing facility.tance, thus leading to an approximate technique fordetermining the frictional form factor. The CFD software uses a cell-centered finite-

volume method and allows a variety of differ-Of course, it is clearly understood that a num- ent computational element (cell) types, including

ber of physical phenomena is neglected here. Ne- quadrilateral, tetrahedral, hexahedral, pyramidal,glected effects include the deformed shape of the prismatic, and hybrid meshes. The latest versionfree surface and the fact that the flow would tend of the software also includes the ability to con-to skirt around the outside of the vessel in cases vert tetrahedral mesh zones into polyhedra, whichwhere the intersubhull gap is very small. However, are constructed from an arbitrary number of sides.we wished to preserve the characteristically simple Computational meshes constructed from polyhedraapproach of the software as well as its fast compu- have several advantages, including reduced compu-tational behavior. tational cell count and greatly improved mesh qual-

ity through reduced cell skewness. Both of theseattributes have a significant positive effect on solu-tion convergence.

4.2 Analysis Using RANSThe computational grids for performing the

Computational fluid dynamics codes have demon- CFD calculations employed hexahedral volumes instrated increasing fidelity in recent years in predict- the far-field, boundary-layer prisms on the hullsing the Kelvin wave structure for a variety of ships and polyhedral volumes to connect the boundary-and marine craft. Advancements in computational layer prism caps to the far-field volume. This de-methods for free-surface predictions using level-set composition exploits the advantages of each of theand volume-of-fluid (VOF) techniques have demon- different types of finite-volume cell, while also con-strated marked improvements in the ability to ac- sidering the desire to minimize the difficulty in gridcurately predict flows around surface ships that are generation.

Table 2: Details of Model Experiments

Config- Overall Overall Sidehull Sidehull Draft Displace- Speeduration Length Beam Stagger Offset ment Range

L (m) B (m) r2 (M) 82/2 (m) T (i) A (t) U (kn)1 168.6 56.0 0.0 23.0 6.51 17,756 20-562 210.6 56.0 -42.5 23.0 6.51 17,756 20-603 253.1 56.0 -85.0 23.0 6.51 17,756 20-544 168.2 39.9 0.0 15.0 5.19 12,341 20-545 210.2 39.9 -42.5 15.0 5.19 12,341 20-486 253.1 40.0 -85.0 15.0 6.51 17,756 20-58

Figure 6 shows the surface mesh on the center- ented with z vertically upwards and x downstream.hull and centerplane where each of the three differ- A layer of boundary-layer prisms was generated onent cell types can be seen. Also visible in this Figure each hull. The first cell had a height of 0.001 m andis the thickness over which the free surface is arti- at the speed of 40 kn this resulted in wall y+ valuesficially spread due to numerical discretization. The between 2.0 and 100, with the average value of 39.thickness is seen to be at most three cells, a value The grids used in this work had a total cell count ofthat it not intolerable because even the most ad- approximately 1.6M, composed of 1.34M polyhedravanced and thus complex advection schemes rarely and 265K hexahedra.compress the interface to fewer than two cells.

In the present study, the convective termsThe hexahedral volumes are effective in solv- were discretized using the QUICK scheme (Leonard,

ing both the undisturbed free-surface upstream of 1979). This scheme uses a weighted average of up-the body and the diffracted waves away from the wind and central second-order interpolation meth-body, with a minimum number of finite volumes. ods, which is typically more accurate for structuredThis is contrary to the polyhedra which are better grids aligned with the flow direction. For unstruc-suited for filling volumes of the flow domain that tured meshes, the scheme reverts to the second-are defined by complex geometry but compromise order upwind method. Therefore, this scheme isinterface resolution. very appropriate for the present case, which involves

a hybrid mesh that contains both structured hexa-The polyhedra are touted to reduce the cell hedral elements which are mostly aligned with the

count by up to a factor of five when compared to general flow direction, as well as polyhedra elementsa tetrahedral unstructured grid, but such a large for flexibility in resolving the model geometry andreduction of unknowns must have an impact on the near-body flow. The discretization of the volumeresolution of the flow field. In this application, the fraction equation used a modified version of thepolyhedra were created from a tetrahedral mesh, high-resolution interface capturing (HRIC) methodand as to not excessively reduce the resolution by (Muzaferija, Peric, Sames, and Schellin, 1998). Thelosing too many cells, the original tetrahedral mesh HRIC scheme has been shown to be more accuratewas created with a much greater density. than the QUICK or other second-order discretiza-

tion schemes, and is less computationally expensiveThe division of two separate domains per- than using a complete geometric reconstruction of

mits that one far-field grid be generated and used the interface. The turbulence closure was accom-for all calculations and a new inner domain be plished using a model that is a variant of the k - Logenerated for each simulation that requires the model as described in Wilcox (1998).hull be arranged with a different sinkage andtrim. The outer domain had extents of (X, y, z) G The simulations were performed as fully un-(-20.0, 0.0, -20.5) : (40.0, 20.0, 20.5) in model scale steady in time, marching to an equilibrium solu-units of meter. The inner domain extended from tion. The time advancement was accomplished us-(x, y, z) G (-8.0,0.0, -0.5) : (1.0, .75,0.5). The ing second-order backward differencing, and alge-Cartesian coordinate system is situated at the cen- braic multi-grid methods were used to aid in theterline, transom, calmwater intersection, and ori- solution convergence.

Table 3: Nomenclature

Symbol MeaningU Speed of vesselW Displacement weightf8, Surface-velocity limit factorr2 Stagger of sidehull

82/2 Offset of sidehullA Displacement mass

RE Frictional resistanceRH Hydrostatic resistanceRT Total resistanceRw Wave resistance

(a) Rair Air resistance

ted with the velocity expanded to full scale usingFroude scaling.

We first consider Configuration 1 in Fig-ure 7(a). The wave resistance Rw possesses its typ-ical maximum at the "hump" condition. The hydro-static resistance RH is seen to be relatively small,indicating that little of the transom is immersed inthe water. The frictional resistance RE is estimatedfrom the 1957 ITTC line and is seen to be the majordrag component at the high-speed end of the speed

(b) range, namely at 50 to 60 knots. The simple sumof these components is indicated by the first of the

Figure 6: CFD grid and flow solution. Contours curves for total resistance RT. This predicted re-of volume fraction depict the location of the free- sult may be compared with the experimental datasurface for the 40 knot speed case as represented by the symbols.

It can be seen that this first prediction of the5 Results total resistance, indicated by the symbol f, = 1,

falls short of the experimental resistance. This dis-crepancy increases with speed. It is believed that

5.1 Comparison of Theory and Ex- most of this discrepancy can be traced back toperiment the interactions between the subhulls increasing thefrictional drag, as noted earlier in this paper.

We turn to Figure 7, whose six parts show the ex- To emphasize this point, one has only to noteperimental and computed results for the abovemen- that the subhulls each possess a maximum localtioned six configurations. The symbols on these beam of approximately 10 m at the waterline. Withplots are listed in Table 3. an overall sidehull-centerplane spacing 82 of 46 m,

this leads to a minimum gap of 13 m. This suggestsThe curves for the resistance components are that the water has been channeled from an initial

all represented in a dimensionless form known as width of 23 m down to 13 m, implying a large in-the specific resistance, namely, the ratio of the re- crease in the local speed of the water over the sur-sistance to the vessel weight. It is important to clar- face of the hull. On the other hand, it should beify that the calculations are all executed at model noted that this effect will be much less on otherscale in order to be directly comparable with the parts of the subhull surface. The current estimatemodel experiments. However, the results are plot- of the velocity increase does take this effect fully

0.12- 0.12-Curve T f A =17760 t Curve T fs r 2 0 m

R/W0 0 0 0 WOm 0 0 0 RT/W s2 30 m 000 -- Rw/W s 2 46 m 0 0.1 - ----

--

- RwW00.08 RH/W 00 0 -. 0 RH /W I

00-RF/W 0.08- R, /T 0--- Rer/IW R~i/lW0

0.06------------ R 7 /W 1 0.06- ----------- Rr/W / ' ---....... RT/W 1.2 /- - -- R /w 12

0.0, -_- R/W - 0.04t o-- RT/W IModel ALT Model = ALT -------

0.02 Scale Model 0.02- Scale = ModelConfiguration 1 A = 12340 t Configuration 4

0- F_ -0' '....... - --- ---

0 10 20 30 40 50 6 0 10 20 30 40 50 6U kn U kn

(a) L = 168.6 m, B = 56.0 m (d) L 168.2 m, B = 39.9 m

0.12- 0.12-Curve f A - 17760 t Curve T fA - 12340 t

0 0 0 0 RT/W r 2 = -42.5 m 0 0 0 RT/W r 2 -- 42.5 m0.1 ------ Rw/W s 2 = 46 m 0.1R W 2 30m

0.08W RHI R /11R/WR0.80

---- i ,W - Rir/w 0< W0.06 ------------ RT/W 1 / < 0.06- ----------- RT/W 1 0 7

.....- RT/W 1.2 -- - RT/W 120.0 _-_- R 1,/W - 0.04 -o- R/W

Model = ALT Model = ALT

0.02- Scale -Model 0.02- Scale = ModelConfiguration 2 Configuration 5

0- 0- TI 0----- r I0 10 20 30 40 50 6 0 10 20 30 40 60 6

U kn U kn

(b) L 21o.6 m, B = 56.0 m (e) L 21o.2 m, B = 39.9 m0.12- 0.12-

Curve f A - 17760 t Curve fs A - 17760 t0 0 0 C RT/W r 2 = -85 m 0 0 0 0 RT/W r 2 = -85 m

0.1 Rw/W s 2 = 46 m 0.1 - -- - Rw/W 2 = 30 m 0

R1/W . R0/W0.08 RF/W 0.08- RF/W o

is, a frictional form factor of 1.0 is employed here.

0.005 Exp. 0 Clearly, the use a larger value of the form factor,CT .10 000@000o such as 1 + k = 1.20, would provide excellent pre-C F -I C -

- dictions for the thin-ship theory code. The results0.004 Cw - - - 0show good agreement by both codes with the experi-

CT [mental data, but more accurate results are provided0.003 CF by the FLUENT RANS code. The average relative

difference between prediction and experiment, when0.002 using the speed range of 20 to 50 knots, is 9.9% and

-1.8% for the thin-ship theory and CFD results re-0.001 , - spectively. When comparing the two computational

I 'methods, we must recall the extra expense of the in-0 creased accuracy. The time required to complete a

0 10 20 30 40 50 60 converged drag result for a single forward speed isUkn approximately 24 to 48 hours using 24 processors

for the RANS method and only about 1 second onFigure 8: Resistance coefficients at model scale, a single processor for the thin-ship theory code.Configuration 6. (o) experiment; (-) thin-ship the-ory with no form factor; (D) FLUENT A sample prediction of free-surface elevation

from the RANS computations for an equivalent for-ward speed of 40 knots is shown in Figures 9. In-

into account in the third theoretical prediction, in- terrogation of the three-dimensional flow solution isdicated by f8 = o. very useful in understanding the resulting Kelvin

wake pattern, as well as the stern wake flows and

It is considered that the prescription explained the interference effects between the center and sidehere overestimates the effect under study, as noted hulls. A closer examination of these figures alsowhen the vessel speed U exceeds 44 knots. Thus, points out how the solution of the wave profiles be-

yet another curve is shown, indicated by f. = 1.2. comes somewhat degraded as the flow informationThe meaning of this is that the coding places an is transmitted across the non-conformal grid inter-

face separating the near-body region from the outerupper linmit on the subhull surface velocity of 1.2n

times the vessel speed. domain. Because the focus of this effort was to ex-amine the ability of the tools to predict the model

The other five parts of Figure 7 pertain to the resistance, this was deemed an acceptable way toother five configurations. On the whole, it is con- relax the mesh resolution requirements, while notfirmed that the surface-velocity limit factor f. = 1.2 significantly impacting the resistance computation,does seem to be a reasonable compromfise for achiev- as evidenced by the results in Figures 7(f) and 8. Ofingssem the be correaionabeten t efor a er- course, if one were interested in accurately predict-in g th e b est c o rrela tio n b etw e en th e o ry a n d ex p e r- n t h w a e b a v o f u h r a ay r m t e h l ,iment. ing the wave behavior further away from the hull,

then commensurate mesh resolution would be re-

Figure 7(f) also shows some calculations based quired. Wilson, Fu, Fullerton, and Gorski (2006)on the FLUENT software. Because computational have shown that increased grid resolution enables atimes are much greater for these very extensive and more accurate prediction of the wave elevation, butdetailed CFD studies, a limited number of com the effect on resistance prediction is still unclear.

puted points only is depicted here. It is indeed mostencouraging to observe the excellent matching be- It is also conjectured that there is perhaps atween the FLUENT data points and the experimen- fundamental physical effect of the sidehull wave in-tal data. terference drag which is being better represented by

the RANS method. The sidehull wave interferenceFigure 8 contains the data of Figure 7(f) re- effect can be seen in Figure 10. As pointed out

plotted non-dimensionally as the resistance coeffi- earlier, this effect increases with increasing forward

cient, CT = RT/(1/2pU2S), at model scale. Thus, speed; hence, the discrepancy between the two com-there is no scaling included in the experimental re- putational methods grows larger at the higher speedsult. The thin-ship theory results are calculated range. We restate that the RANS simulations arewith the surface-velocity limit factor f. = 1.0. That conducted without including the sinkage and trim

prediction as part of the computation, but ratherthe model attitude is fixed based on the experimen-tally measured sinkage and trim. This most likelyprovides a reduction in the error by eliminating thedifference between the predicted and physical modelsinkage and trim that would propagate into errorsin the predicted hull forces.

(a)

5.2 Effect of Changes to Configura-tion

We now proceed to Figure 11, in which we comparethe change in total resistance when comparing twodifferent configurations.

Figure 11(a) shows the fractional change inspecific total resistance ART/W between Config-uration 1 and either Configuration 2 or Configura-

(b) tion 3. We can point out two important features.Firstly, the experiments indicate a reduction in spe-

Figure 9: Free-surface contours colored by elevation cific total resistance of 0.029 for the greater sidehullstagger of -85 m at a speed of 40 knots. This rep-resents an impressive saving and it vindicates theunusual and novel nature of our trimaran concept.

This reduction in total resistance would be dif-ferent at prototype scale because of the difference inthe Reynolds number.

Secondly, it is heartening to note that the the-ory predicts the nature of the resistance reductionobserved in the experiments. However, at the de-sign speed of 40 knots, the prediction suggests areduction of only 0.021.

Finally we turn to Figure 11(b), which is aplot of the ratio of the two resistances ART/RT,rather than a difference which was plotted in Fig-ure 11(a). With this form of plot, the relative over-all agreement between theoretical predictions andexperiments is actually more encouraging. From a

Figure 10: Contours of free-surface elevation practical viewpoint, we see that there can be a rel-mapped onto the the free surface. Camera is located ative reduction in total resistance of up to 43%, atbetween the center and starboard hulls, looking aft a speed of 38 knots.

0.02- Model = ALT Curve Data longitudinally and 20 panels vertically. Thus, theScale = Model 0 0 0 0 -42.5 rn Exp CPU time is six of seven orders of magnitude less

0.01 f = 1.2 0 0 0 0 -85 Exp than that required for the CFD computations. Of----------- -42.5 Theory course, the CFD results are considerably more use-

o-8 Theory ful, because they provide data for the complete flow0 G d __ field and would be beneficial to the naval architect

!o.oI 000000000 in many ways.L = 168.1 nm

-0.02 L 2 168.6 m E C c2-Cl Figure 7 has been used to demonstrate theA = 17760 t 0 and effectiveness of employing a frictional form factor

0- fp = 1 + k, which has been calculated through an0 10 20 30 40 50 6 estimate of the increased subhull surface velocities

U kn due to the subhull-proximity effects, as already de-(a) Difference in change in configuration tailed. The method developed so far results in a

0.2- value of fp 1.20. That is, it is suggested that theModel = ALT L, = 168.1 m frictional resistance in such cases of closely spaced

0.1 Scale = Model = 1686 m subhulls is increased by about by 20%. The use off= = 1.2 A = 17760 t0 ---------- .S2 = 46 m- such a factor in Figure 8 would bring the thin-ship

0.i ,. 0 El ------- .. " 1 predictions into nearly perfect alignment with the0-0 0 0o ' 0 0 0 0full CFD computations, without the need for any[] -significant additional CPU time.

0~~ ~ 0 4.0Curve r2

-- o -825 m 1 The CFD results contained in this paper were-0.4- ------ - 42.5 C2 n and calculated with a rudimentary grid generation ap-

-0.5- -85 C3/C1 proach that reduces set-up and solution time. A0 10 20 30 40 50 6 goal of the project which supported this work was to

U kn evaluate the codes for transfer to a shipyard and/or(b) Ratio of change in configuration design office. Often in the application of CFD, the

grid generation is a frustrating hurdle for users toFigure 11: Change in resistance: Configuration 2 overcome, so the approach here is very simple to ef-and Configuration 3 WRT Configuration 1 fect, yet it does not seem to sacrifice accuracy. The

overall domain is divided into near-field and far-fieldregions that are filled with polyhedral and hexahe-

6 Conclusions dral cells respectively.

The polyhedral finite-volume cell that was6.1 Current Work used drastically reduces cell skewness and overall

cell count. The reduced skewness causes the equa-

tion coefficient matrices to be more diagonally dom-

This paper contains the results of calm-water resis- inant, and thus improves solution convergence andtance prediction for a high-speed sealift trimaran. robustness.The two numerical codes that were used are athin-ship theory and the commercial CFD software The accuracy of the CFD results was outstand-FLUENT. ing. The error relative to the experimental values

was on average less than 2% with a maximum of 4%.

It has been demonstrated that the thin-ship We remind the reader that the CFD predictions aredone using the experimental values of sinkage andapproach, as exemplified by the results plotted in deinkFigure 7, Figure 8, and Figure 11, provide remark- trim.ably reasonable estimates of the total resistance, if The reconfigurable catamaran is shown to dra-one simply adds the theoretical wave resistance Rw,the ydrstaic ragRHandtheITT 197 fic- matically reduce its total drag by extending the cell-the hydrostatic drag RH, and the JTTC 1957 fric-tional resistance RF. It should be borne in mind terhull. The experiments dictate a 43% reduction

in tota rua oe cl.Ti euto ssfithat computational times are typically one second tal drag at model scale. This reduction is suf-per speed, using a computational grid of 60 panels cient to encourage further investigation of the con-

cept, namely consideration of the actuation system 7 Acknowledgmentsfor the extending hull and requisite gear, and theimpact on the hydrodynamic performance. Also,during the initial design period, it was unclear which The authors would like to gratefully acknowledgesidehull spacing would be best for low resistance. the support of the US Office of Naval ResearchInterestingly, it was the narrowest Configuration 6 through the High-Speed Sealift (HSSL) Program.that had the lowest drag, though the effect was very The specific project title was detailed in Section 2.1.small. The University of Michigan and The University of

New South Wales (UNSW) provided infrastructuresupport.

6.2 Future Work8 References

The authors are encouraged by the quality of theresults from both the thin-ship theory and CFD. ACKERS, B.B., MICHAEL, T.J., TREDENNICK,At the same time, there are issues which will be O.W., LANDEN, H.C., MILLER III, E.R.,valuable to investigate further to expand the utility SODOWSKY, J.P., AND HADLER, J.B.: "An Inves-of these numerical tools for the designer. tigation of the Resistance Characteristics of Pow-

ered Trimaran Side-Hull Configurations", Trans.The thin-ship predictions can be improved by Society of Naval Architects and Marine Engineers,

a more careful study of the frictional form factor, Vol. 105, pp 349-368, Discussion: 369-373 (1997)which is thought to be the main cause of the total ARMSTRONG, N.A.: "Coming Soon to a Port Neardrag estimate being a little low. The reader is re- You: The 126 m Trimaran", The Naval Architect,minded that, in the literature, there is a large body pp Th ember 04)of evidence indicating that for some vessels, the fric- p 66-78 (September 2004)tional form factor might be as high as 1.40 far BATTISTIN, D., DANIELLI, A., AND ZOTTI,exceeding the model value of around 1.20 indicated I.: "Numerical and Experimental Investigationsearlier. on Wave Resistance of Trimaran Configurations",

Proc. International Maritime Association ofAnother point is the estimate of the length of Mediterranean IX Congress (IMAM 2000), Ischia,

the hollow, which is assumed to grow as the speed Italy, Vol. 1, pp A56-A63 (April 2000)increases, following the extensive model tests re- BEGOVIC, E. BOVE, A., BRUZZONE, D., CAL-ported by Doctors (2006a and 2006b). This increase BEOI, ., BOVE, , RUZZOND, MALin effective hydrodynamic length of the vessel low- DARELLA, S., CASSELLA, P.: FERRANDO, M.,ers the predicted wave resistance. Studies of this TINCANI, E., AND ZOTTI, I.: "Co-operative In-

vestigation into Resistance of Different Trimaranmatter are also in the planning stage. Hull Forms and Configurations", Proc. Eighth In-

ternational Conference on Fast Sea TransportationThe CFD calculations are very expensive in (FAST '05), Saint Petersburg, Russia, 8 pp (June

both the need of parallel computational hardwareand the long computational time to arrive at the 2005)converged solution. Any research that aims at ren- BRIZZOLARA, S., BRUZZONE, D., AND TINCANI,dering the solution algorithms more efficient, or re- E.: "Automatic Optimisation of a Trimaran Hullducing the number of unknowns would be valuable. Form", Proc. Eighth International Conference onIt is natural to expect the solution quality to im- Fast Sea Transportation (FAST '05), Saint Peters-prove with increased grid density, though this has burg, Russia, 10 pp (June 2005)not been proven unequivocally for CFD surface-ship COLICCHIO, G., COLAGROSSI, A., LUGNI, C., ANDresistance predictions. With the new polyhedra el- FALTINSEN, O.M. Experimental and Numericalement now emerging in the CFD community, and Investigation of a Trimaran in Calm Water", Proc.the always evolving naval combatant hull forms, a Eig ationa Conern n ast Wa Tron.detailed grid-refinement study is justified as a con- Eighth International Conference on Fast Sea Trans-tinuation of this work, with the optimism that less portation (FAST '05), Saint Petersburg, Russia,rather than more dense and complex grids will be 8 pp (June 2005)required to arrive at useful predictions. DAY, A., CLELLAND, D., NIXON, E.: "Experi-

mental and Numerical Investigation of 'Arrow' Tri- DUBROVSKY, V. AND LYAKHOVITSKY, A.: Multi-marans", Proc. Seventh International Conference Hull Ships, Backbone Publishing Company, Fairon Fast Sea Transportation (FAST '03), Ischia, Lawn, New Jersey, 495+i pp (2001)Italy, Vol. 3, pp D2.23-D2.30 (October 2003) GALE, M.G., HALL, J.H., AND HART-DEGIULI, N., WERNER, A., AND DOLINER, Z.: LEY, K.B.: "Trimaran Resistance Experi-"Determination of Optimum Position of Outrig- ments Effect of Outrigger Position", Reportgers of Trimaran Regarding Minimum Wave Pat- DRA/SS/SSHE/CR96015, Defence Researchtern Resistance", Proc. Seventh International Con- Agency, Farnborough, Hampshire, United King-ference on Fast Sea Transportation (FAST '03), Is- dom, 62+xii pp (August 1996)chia, Italy, Vol. 3, pp D2.15-D2.22 (October 2003) GORSKI, J.: "Evolving Computational Capabil-DEGIULI, N., WERNER, A., AND ZOTTI, I.: ity for Ship Hydrdynamics", Naval Surface War-"An Experimental Investigation into the Resistance fare Center, Carderock Division, HydromechanicsComponents of Trimaran Configurations", Proc. Department Technical Report, NSWCCD-50-TR-Eighth International Conference on Fast Sea Trans- 2004/058 (December 2004)portation (FAST '05), Saint Petersburg, Russia, KENNELL, C.: Model Test Results for a 55 Knot8 pp (June 2005) High Speed Sealift Trimaran", Proc. InternationalDOCTORS, L.J.: "On the Great Trimaran- Conference on Design and Operation of TrimaranCatamaran Debate", Proc. Fifth Interna- Ships, Royal Institution of Naval Architects, Lon-tional Conference on Fast Sea Transportation don, England, pp 195-204 (April 2004)(FAST '99), Seattle, Washington, pp 283-296 LAMB, G.R.: Investigation of a Small-(August-September 1999) LM, GR" "netgto faSal

Waterplane-Area Trimaran High-Speed Hullform",

DOCTORS, L.J.: "Influence of the Transom-Hollow Technical Digest: Technologies for High-SpeedLength on Wave Resistance", Proc. Twenty- Naval Vehicles, Naval Sea Systems Command,First International Workshop on Water Waves and Naval Surface Warfare Center, Carderock Division,Floating Bodies (21 IWWWFB), Loughborough, Bethesda, Maryland, 44 pp (April 2004)England, 4 pp (April 2006) LEONARD, B.P.:"A Stable and Accurate Convec-DOCTORS, L.J.: "A Numerical Study of the Re- tive Modeling Procedure Based on Quadratic Up-sistance of Transom-Stern Monohulls", Proc. Fifth stream Interpolation", Computer Methods in Ap-International Conference on High-Performance Ma- plied Mechanics and Engineering, Vol. 19, pp 59-98rine Vehicles (HIPER '06), Launceston, Tasmania, (1979)pp 1-14 (November 2006) MAKI, K.J., DOCTORS, L.J., BECK, R.F., ANDDOCTORS, L.J. AND BECK, R.F.: "The Separation TROESCH, A.W.: "Transom-Stern Flow for High-of the Flow past a Transom Stern", Proc. First Speed Craft", Australian Journal of Mechanical En-International Conference on Marine Research and gineering, Vol. 3, No. 2, pp 191-199 (2006)Transportation (ICMRT '05), Ischia, Italy, 14 pp MICHELL, J.H.The Wave Resistance of a Ship",(September 2005) Philosophical Magazine, London, Series 5, Vol. 45,DOCTORS, L.J. AND DAY, A.H.: "Resistance Pre- pp 106-123 (1898)diction for Transom-Stern Vessels", Proc. Fourth MIZINE, ., AMROMIN, E., CROOK, L., DAY, W.,International Conference on Fast Sea Transporta- AND KoRPUS, R.: High-Speed Trimaran Drag:tion (FAST '97), Sydney, Australia, Vol. 2, pp 7 Numerical Analysis and Model Tests", J. Ship Re-'750 (July 1997) search, Vol. 48, No. 3, pp 248-259 (September 2004)DOCTORS, L.J. AND SCRACE, R.J.: "The Optimi- MUZAFERIJA, S., PERIC, M., SAMES, P., ANDsation of Trimaran Sidehull Position for MinimumResistance", Proc. Seventh International Confer- SCHELLIN, T.: A Two-Fluid Navier-Stokes Solverence on Fast Sea Transportation (FAST '03), Ischia, Symposium on Naval Hydrodynamics, pp 277-289,Italy, Vol. 1, pp KL.1-KL.12 (October 2003) Washington, DC (1998)DUBROVSKY, V.: Ships with Outriggers, Back- NARITA, S.: Some Research on the Wave Resis-bone Publishing Company, Fair Lawn, New Jersey, tance of a Trimaran", Proc. International Seminar88-Hi pp (2004) on Wave Resistance, Society of Naval Architects of

Japan, Tokyo, Japan, pp 381-388 (February 1976) AND ZHANG, J.W.: "Trimaran Design ChoicesPATTISON, D.R. AND ZHANG, J.W."Trimaran and Variants for Surface Warship Applications",

Archi- Future Surface Warships (Warships 2001), RoyalShis, Tral. Roya pp Inst153,itu o : 1 Institution of Naval Architects, London, England,tects, Vol. 137, pp 143-153, Discussion: 153-i16 1 9p(Jn201(1995) 19 pp (June 2001)

SASANAPURI, B., SHIRODKAR, V., WILSON, YANG, C., NOBLESSE, F., AND L6HNER, R.:"Practical Hydrodynamic Optimization of a Tri-W.M., KADAM, S. AND RHEE, S.H. Virtual mrnTas oit fNvlAciet n

Model Basin for Resistance, Maneuvering, and Sea- maran", Trans. Society of Naval Architects andkeepng a ANSCFDBase Aproah",Twety- Marine Engineers, Vol. 109, pp 185-196 (Decemberkeeping - a RANS CFD Based Approach", Twenty- 2002)Sixth Int. Conf. Offshore Mech. and Arctic Eng.OMAE '07, San Diego, California (June 2007)SCRACE, R.J.: "Model Experiments to Investi-gate the Hydrodynamic Performance of RV Triton", YANG, C., SOTO, 0., L6HNER, R., AND No-Proc. International Symposium on RV 'Triton': BLESSE, F.: "Hydrodynamic Optimization of a Tri-Timaran Demonstrator Project, Royal Institution maran", Ship Technology Research: Schiffstechnik,of Naval Architects, London, England, 10 pp (April Vol. 49, No. 2, pp 70-92 (April 2002)2000) YASUKAWA, H.: "Influence of Outrigger Position onSUMMERS, A.B. AND EDDISON, J.F.P.: "Future the Performances of a High Speed Trimaran (Sec-ASW Frigate Concept Study of a Trimaran Vari- ond Report: Wave-Induced Motions in Head Sea)",ant", Proc. International Maritime Defence 1995 J. Japan Society of Naval Architects and Ocean En-Conference, Spearhead Exhibitions Ltd, London, gineers, Vol. 2, pp 189-195 (December 2005)England, Vol. 1, 59 pp (March 1995)SUZUKI, K. AND IKEHATA, M.: "FundamentalStudy on Optimum Position of Outriggers of Tri-maran from View Point of Wave Making Resis-tance", Proc. Second International Conferenceon Fast Sea Transportation (FAST '93), Societyof Naval Architects of Japan, Yokohama, Japan,Vol. 2, pp 1219-1230 (December 1993)WILCOX, D. C.: Turbulence Modeling for CFD,DCW Industries, Inc., La Canada, California (1998)WILSON, M.B. AND Hsu, C.C.: "Wave Can-cellation Multihull Ship Concept", Proc. High-Performance Marine Vehicle Conference and Ex-hibit (HPMV '92), American Society of Naval En-gineers, Washington, pp MH26-MH36 (June 1992)WILSON, W.M., Fu, T.C., FULLERTON, A., ANDGORSKI, J.:"The Measured and Predicted WaveField of Model 5365: An Evaluation of CurrentCFD Capability", Proc. Twenty-Sixth Symposiumon Naval Hydrodynamics, Rome, Italy (September2006)WOOD, J.E.: "Effect of Increased Outer Hull Set-back on Resistance for the O'Neill Hull Form Rep-resented by DTRC Models 5355-1, -2", David Tay-lor Research Center, Ship Performance Depart-ment, Report DTRC/SHD-1147-02, 20+v pp (Au-gust 1988)VAN GRIETHUYSEN, W.J., BUCKNALL, R.W.G.,