11. INTRODUCTION

1.1 Membership

Chairman:Prof. Fred SternIowa Institute of Hydraulic Research,UNITED STATES OF AMERICA

Secretary:Dr. Hoyte C. RavenMaritime Research Institute Netherlands,NETHERLANDS

Members:Dr. Ulderico BulgarelliInstituto Nazionale per Studi ed Esperienzedi Architettura Navale, ITALY

Mr. Lars T. GustafssonSSPA Maritime Consulting AB, SWEDEN

Dr. Moustafa Abdel MaksoudSchiffbau-Versuchsanstalt Potsdam GmbH,GERMANY

Prof. Luis Perez-RojasEscuela Tcnica Superior de Ingenieros Na-vales, SPAIN

Prof. Toshio SuzukiOsaka University, JAPAN

Prof. Lian-di ZhouChina Ship Scientific Research Center,CHINA

1.2 Meetings

The committee met 5 times:April 1997, Rome, ItalyNovember 1997, Potsdam, GermanyMay 1998, Osaka, JapanAugust 1998, Iowa, USANovember 1998, Madrid, Spain

1.3 Tasks and Report Structure

Below we list the tasks given to the 22ndResistance Committee (RC), and indicate howthese have been carried out.

Review the state of the art, comment on thepotential impact of new developments of theITTC, and identify the need for researchand development for resistance and flow.Monitor and follow the development of newexperimental techniques and extrapolationmethods.

Prepare an up-to-date bibliography of rele-vant technical papers and reports.

Monitor the development of CFD methods.

State-of-the-art reviews are given regardingResistance and Flow Physics (Section 2),Trends in Experimental Techniques (Section 3),and Trends in Computational Fluid Dynamics(CFD) (Section 4). Section 7 (Prognosis forTowing Tank Work) reviews trends in shipdesign and operation, and impacts of these andof the developments described in the precedingsections, on the future of our profession and theoperation of towing tanks.

The Resistance Commitee

Final Report andRecommendations to the 22nd ITTC

2The reviews focus on the last three years,except for topics not covered in recent RC re-ports which cover a longer time period.

The RC was unable to comprehensively re-view development of extrapolation methods, atask previously carried out by the PerformanceCommittee. Some comments on extrapolationof viscous resistance are, however, included inSection 2.

Review the ITTC recommended procedures,benchmark data, and test cases for valida-tion and uncertainty analyses and update asrequired. Pass the information to the Qual-ity Systems group for publication in 1999.

Identify the requirements for new proce-dures, benchmark data, validation, uncer-tainty analyses and stimulate the necessaryresearch for their preparation.

Review ASME and ITTC recommendationson quality assurance and uncertaintyanalyses. Derive procedures for imple-menting guidelines for typical ITTC ex-periments in the field of resistance and flow.

Updated procedures for experimental un-certainty analysis methodology and guidelinesfor towing-tank experiments are described inSection 5, and illustrated with an example for atowing-tank resistance test based on collabora-tive work by most RC institutes. This effortdemonstrates the procedures and providedsome improvements. The resulting proceduresare included in the Quality Manual (QM) andrecommended for adoption by the 22nd ITTC.

Work on the development of proceduresand methodology for verification and validationof CFD simulations with an example are sum-marized in Section 6. The resulting proceduresare included in the QM and are recommendedfor interim adoption by the 22nd ITTC.

Available benchmark data for CFD valida-tion for resistance and propulsion is evaluatedin Section 6.5. The resulting procedure is in-cluded in the QM and recommended for adop-tion by the 22nd ITTC.

The RC has cooperated closely with theQuality Systems Group in reviewing and edit-ing other procedures to be included in the QMbased on previous RC recommendations.

Continue to encourage and monitor CFDvalidation including liaison with other or-ganizations such as ASME.

All members were active in their respectiveregional professional organizations. In particu-lar, close liaison was maintained with EuropeanThematic Network on CFD and ASME activiti-es concerning verification and validation ofCFD simulations.

2. RESISTANCE AND FLOW PHYSICS

The flow around a ship hull displays a largevariety of physical phenomena, many of whichare relevant for resistance and propulsivepower. The RC restricts itself to physics of in-terest for a ship in steady motion in still water,including the effect of the propulsor on the hullflow.

Response to a questionnaire distributed bythe 21st RC indicated some flow phenomenathat were expected to be relevant for future shipdesigns and would require attention from aphysical point of view, viz. bow-wave breaking,bilge vortices, and separated flows. However,many more phenomena are of interest, such as:Reynolds number (Rn) effects and scaling,boundary layer and wake, stern flow, turbu-lence, vortex flow and separation, Froude num-ber (Fn) effects, wave breaking, bow flow, tran-som flow, propeller-hull interaction, wave-boundary layer and wake interaction, etc. Thissection will discuss several of these challenges,recent ideas, and developments.

2.1 Waves

In the field of ship waves, there has beenrecent interest in the physics of breaking waves,the detailed phenomena at the ship bow, shipwaves in restricted water, and wave-wash ef-fects. These topics are discussed below.

Breaking Waves. Breaking wave phe-nomena are widely recognized to be of impor-tance in ship hydrodynamics. Breaking wavesdissipate wave energy and affect resistance.Subsequent spray formation and air entrain-ment can be important for ship wake signatures.Under the safety point of view, breaking oceanwaves interacting with ships are of main im-portance for ship capsizing. Although shipwave breaking phenomena are associated

3mainly with bow flows, they may occur any-where in the ship wave pattern, and in particu-lar play an important role for transom sterns.

Baba (1969) discussed a component of shipresistance generated by the breaking of waves,especially at the bow of full ships. Based onsimilarity with a shallow water hydraulic jump,he supposed this resistance component to fol-low Fn law of similitude, like wave resistance.He also pointed out that this component can becaught by wake survey method and correspondsto the head losses found near the free-surfaceand outside the usual frictional wake belt.

In recent experiments for a VLCC model,Van et al. (1998a,b) noted that low momentumfluid accumulated near the free-surface at theoutside of the wake. Also in this line, Kanai etal. (1996) showed through numerical simula-tions using Reynolds-averaged Navier-Stokes(RANS) codes, that the energy deficit generat-ed near the bow is convected downstream anddistributed near the free-surface. At the aft partof the ship, the loss due to wave breaking ismingled with the losses due to viscous effects,and apparently has an influence on the forma-tion of the wake.

There have been several more fundamentalstudies of the physics of wave breaking. Anexcellent review of the current knowledge isgiven by Longuet-Higgins (1996). In particular,starting from the experimental observations ofDuncan et al. (1994), the role of surface tensionin characterizing the breaking wave field up towavelengths of 2 meters is discussed. Althoughthis is not necessarily of quantitative concernfor full-scale ships, it has to be taken carefullyinto account when interpreting model-scaleexperiments. At full scale, viscous dissipationis of primary importance.

Duncan (1983) made systematic measure-ments of breaking wave phenomena by towinga submerged hydrofoil in the laboratory. In hispicture of the flow, a large part of the pressuredrag on the hydrofoil, which is due to thepresence of the free-surface, appears as mo-mentum loss in the turbulent surface wake.This corroborated Babas assumption.

Like Baba, Dabiri & Gharib (1997) alsosuggested that wave breaking phenomena canbe modeled as a hydraulic jump where Fn isbased on the thickness of the free-surface jet

and on the velocity of the free-surface jet justprior to breaking.

Also based on Duncan's experiments,Cointe & Tulin (1994) derived a physical andmathematical model for steady spilling break-ers. They suppose the breaker itself to be anessentially stagnant eddy, sitting on the forwardface of the breaking wave. It is held in place bya balance between the weight of the breakingvolume of fluid and the turbulent shear stressesacting on the streamline that separates thebreaker and the underlying flow. Sadovnikov &Trincas (1998) consider that viscous processesshould be taken into account, since energy dis-sipation plays a leading role in spilling breakers.They combine a model of a steady spillingbreaker with a numerical technique based onfully non-linear potential theory, which implic-itly includes viscous effects. They demonstratethat the hydrostatic model by Cointe & Tulin(1994) is a particular case of their proposedmodel. In their opinion, the model should beimproved on the basis of new experimentaldata concerning the shape of the spillingbreaker and the density of aerated water inside.

Obviously, the modeling of wave breakingphenomena is still incomplete. Also on the on-set or inception of wave breaking there seemsto be incomplete understanding. There is exten-sive literature on breaking of ocean waves, butperhaps not all of their properties carry over toship waves. It is known that the onset of aspilling breaker is connected with the near-surface vorticity as well as the dynamic char-acteristics of the near-surface shear layer. Dab-iri & Gharib (1996) pointed out that the vortic-ity injection due to the free-surface decelerationis dominant over the gravity-generated vorticityflux. Miller et al. (1998) found that thepresence of free-surface drift layers reduces themaximum non-breaking wave height and thatthis wave height correlates with the surface-drift velocity.

A somewhat separate problem occurs incalculations of ship wave patterns or oceanwaves. If no modeling of breaking and the con-sequent dissipation is included, one at leastwants to be able to continue the computation,and to approximately represent the effect ofwave breaking on trailing wave amplitudes.This requires both a criterion for the occurrenceof breaking, and a model for its dissipation.Recently, Subramani et al. (1998a,b) have pro-posed a curvature-based criterion using the fact

4that when waves break, they attain a profilewith a sharp crest of infinite curvature. Ales-sandrini & Delhommeau (1998) proposed avariation in order to take into account non-symmetrical free-surface flows.

Bow Flow. There have been some recentdetailed studies of local flow phenomena at thebow of ships. For sufficiently fine bows, a thinsplash is created on the side of the hull, whichrises and eventually falls, and oblique wavesappear moving away on either side. A detailednumerical study of this phenomenon was madeby Tulin & Wu (1996), using a non-linear two-dimensional plus time (2D+T) approach. Thisconfirmed the strongly nonlinear nature of thenear-bow flow. Explanations were presentedfor certain differences between the Kelvin pat-tern and a typical ship wave pattern, in whichthe crests of the divergent bow waves tend tobe straight and have an inclination decreasingwith increasing Fn.

The sheet of water rising along a fine shipbow, and the resulting spray formation, mayaffect the wave pattern and the electromagneticscattering properties (radar signatures). Therehave been some recent detailed studies of thesephenomena. Stern et al. (1996b) reinvestigatedthe bow flow of the Series 60 CB=0.6 shipmodel using both experiments and CFD. Thedata indicated a thin film and beads at the bow,which with distance from the bow underwenttransition from steady laminar to unsteady tur-bulent flow and merged with the downstreambow wave with increasing wake width and de-creasing free-surface disturbances. The beadflow appears vortical and suggests significantviscous and surface tension effects.

Dong et al. (1997a) studied, through parti-cle image velocimetry (PIV) measurements andfree-surface visualisation, the flow around aship model, focused on the flow within the liq-uid sheet forming around the bow. They de-monstrated that the formation of the bow waveand the thin liquid sheet on the body, upstreamof the point at which the bow wave separatesfrom the model, involved considerable vorticityproduction. Considerable energy loss occurredin the forward face of the wave, especially nearthe toe.

Dai et al. (1996, 1998) made an experi-mental study of turbulent primary break-up ofplane turbulent free jets, as a model of the sepa-rated portion of the bow sheet. Sarpkaya &

Merrill (1998), through experimental investi-gation of the ligament and drop formation atthe free-surface of liquid wall jets flowing oversmooth and sand-roughened plates, suggestedthat smoother bow surfaces with suitable cur-vatures may help to alleviate the spray problem.

In computations of bow flows it is often as-sumed that the free-surface is single-valued andair entrainment is not accounted for. To cir-cumvent this problem, Dommermuth et al.(1998) propose a LES formulation with a level-set approach, which permits the simulation ofturbulent free-surface flows and the modelingof air entrainment.

Restricted Water Effects. Restricted wateraffects not only the wave resistance but also theviscous resistance. The latter effect can ariseeven at low Fn, when insignificant wave mak-ing occurs, due to the change in pressure andvelocity field around the hull associated withproximity of the seabed.

Not many studies on restricted water effectshave been published in recent years. Chen &Sharma (1994) found by numerical computa-tion, and verified experimentally, that the waveresistance of a ship moving at supercriticalspeed in a channel can be reduced significantlyby shifting its track from the channel centrelineto a certain speed-dependent location near oneof the channel sidewalls. Intuitively, since wavedispersion is weaker in shallow water, the inter-ference between waves arising from differentorigins becomes more effective than in deepwater, especially at supercritical speeds. Morerecently, Chen & Sharma (1997) showed thatthe wave resistance acting on a slender body ina channel becomes zero for a suitable combi-nation of body speed, channel depth and widthif the afterbody geometry is adapted to an arbi-trary forebody.

Another significant aspect of waves gener-ated by fast ships in shallow water is their non-linearity. A ship moving in a shallow channelnear the critical speed can shed solitary waves,which run ahead of the ship, travel a bit fasterthan it, and cause oscillations of the ship. Jiang& Sharma (1997) made numerical simulationsof this. Jiang (1998) focuses his study on thenumerical implementation of the Boussinesqequations. These equations combine the non-linear and dispersive effects of shallow waterwaves.

5Wave Wash. The effects of waves generat-ed by ships, are of increasing concern. Primereason is the continuing introduction of fastferry services, supposed to lead to larger waveeffects than conventional ships. In particular inScandinavia, detailed studies of various aspectsof fast ferry operation, including wash, havebeen carried out recently (Kofoed-Hansen,1996; Forsman, 1996).

The occurrence of detrimental effects ofship waves (e.g. damage to moored vessels orconstruction, danger to swimmers, coastal orbank erosion) depends on various aspects of thewave system and the local situation. Thismakes it impossible to indicate a single crite-rion governing the occurrence or absence ofwash effects. The more serious wash problemspredominantly had to do with coastal or bankerosion and danger to swimmers, caused bywave patterns generated in the open sea or inconfined waters (Kofoed-Hansen, 1996; Ko-foed-Hansen & Mikkelson,1997).

In restricted water, important factors are thecritical speed effects and wave reflections. Aprime factor in many wash problems is the am-plification of ship waves while they proceedfrom deep into shallow water. This amplifica-tion is determined by the ratio of wavelength towater depth. Therefore it may be much strongerfor the long waves generated by a fast ferry,than for the shorter ones of a conventional shiprunning at perhaps half the speed. Conse-quently, fast ferry waves, while perhaps hardlyvisible in deep water, have occasionally beenfound to cause violent wave impacts on thecoast and energetic plunging breakers onbeaches; while waves from conventional ships,perhaps having a larger amplitude in deep wa-ter, undergo a much smaller amplification andmay reach the coast as spilling breakers (Ko-foed-Hansen, 1996). Raven et al. (1998) showmodel test data for a ship wave pattern in achannel with a sloping bank, and in one casefound a threefold increase of wave amplitude atthe bank compared to a channel with a rectan-gular section. Besides, there may be effects ofwave focusing due to a variable waterway crosssection.

2.2 Viscous Flow

In this subsection we address some of thephysics connected with viscous flows; in par-ticular, turbulence, with emphasis on the effects

of the free-surface on it, flow around append-ages, and stern and wake flows. Some remarksare made on scaling and the possible Rn depen-dence of form factors.

Turbulence. There are some measured dataavailable of distributions of turbulence quanti-ties around ship hulls. One recent set is foundin Suzuki et al. (1998a), who measured the tur-bulence in the flow around two ship models, bya triple-sensor hot wire in a wind tunnel. Afterstudying the turbulent kinetic energy balancethey found that a local equilibrium is not satis-fied in a stern flow field: production and dissi-pation of turbulence energy were not equal.

An important but rarely addressed aspectfor viscous ship flows is surface roughnesseffects. The principal effect of roughness is achange in the velocity and turbulence distribu-tion near the surface. Patel (1998) shows thatrecent applications of the k- turbulence modelmimic the known effects of roughness ratherwell, and may be employed in complex flows,but there remains a need to make fresh ap-proaches to this old problem.

An additional complication for ship flows isthe modification of turbulence by the free-surface. This can be considered as one of thesources of error in CFD simulations comparedto full scale data of surface-ship wakes (Hyman,1998). There is quite little investigation in theliterature on the effects of a free-surface onturbulence. A few of the recent numerical andexperimental studies are mentioned by Sreed-har & Stern (1998a). These studies indicate thatthe inter-component transfer and the overallincrease in kinetic energy near the free-surfaceis due to the anisotropic nature of the dissipa-tion tensor and an overall decrease in dissipa-tion rate near the free-surface. Sreedhar & Stern(1998b) indicate that the effect of the free-surface on turbulence is similar to that of thewall in some aspects, especially in the behaviorof normal Reynolds stresses. The turbulent ed-dies are flattened near the surface, with the sur-face-normal fluctuations suppressed and theother two components of velocity fluctuationsgaining energy. Unlike the wall region, there isnegligible shear and turbulence production nearthe free-surface.

This anisotropy of normal stresses is gener-ally known to be a cause of secondary flows. Inthis regard, Longo et al. (1998), in an experi-mental study for a surface-piercing flat plate,

6report the thickening of the boundary layer andwake near the free-surface and the existence oftwo regions of high streamwise vorticity ofopposite sign near the juncture region. Hyman(1998) indicates that the free-surface/turbulence interaction model does forceanisotropy at the free-surface and leads to en-hanced spreading.

At a more fundamental modeling level, it isknown that coherent structures play an impor-tant role in wall turbulence (Robinson, 1991).A very important type of structure is low-speedstreaks (Blackwelder & Kaplan, 1976). Theseprobably come from the transition process andgenerate internal high-shear layer. Breakdownof the flow is possible when the shear reaches acertain threshold, leading to a turbulent burst,(Kim et al., 1971). It is now evident that wallturbulence is non-homogeneous and non-isotropic. The nearly periodic process of burstgeneration, the presence of low-speed streaksand the no-slip condition at the wall determinea complex flow that accurate models for cal-culations of averaged quantities in numericalcodes are very difficult to make, even for sim-ple body shapes, (Speziale, 1994). Nevertheless,the use of turbulence models will be unavoid-able for many more years, for flows at high Rnaround bodies with complex geometry.

Stern and Wake Flows. The viscous flowin the stern of a ship hull is characterized by athick boundary layer, viscous-inviscid interac-tion, highly skewed flow, complex turbulentflow field, near wake and propeller action, andoften a pair of longitudinal vortices. The latterare created where the flow passes over a regionwith large girthwise variations of the wall pres-sure field, causing near-wall flow convergenceand open separation. The longitudinal vorticesmay pass through the propeller disk and cause adistortion of the inflow to the propeller.

While the vortices in principle lead to anincreased resistance, the flow distortion is oftenused to advantage for equalizing the wake field.V-shaped sterns generally induce weaker sternbilge vortices and lower viscous resistance; U-shaped sterns result in generation of strongervortices but may thus make the propeller inflowmore uniform. The designer must find the bestcompromise.

This obviously requires that location andstrength of the vortices (at full scale) can bepredicted and influenced. This explains the

large current interest in the computational pre-diction of longitudinal vortices in a ships wake.With standard turbulence models, currentRANS solvers generally are unable to reliablypredict the strength and location of the longitu-dinal vortices, the local axial velocity deficit inthe vortex core, and the "hook shape" in theisolines for axial velocity. The longitudinalvortex strength at the propeller position is oftenunderestimated by present codes; a near-wallnon-isotropic turbulence model seems neededto do better (Deng & Visonneau, 1997).

Appendages. A variety of appendages maybe present on ship hulls, and these involvesome particular physics. For high-speed shipsto maintain stability and speed in a rough sea,some means of controlling the ship motions arenecessary. Among various devices, fins havebeen recognized as very effective. Lee et al.(1998) found that the free-surface effect on thelift characteristics of fins attached to a body issignificant when the submergence depth is lessthan three times the chord length. The domi-nant cause is the change in the flow incidenceangle to the fins induced by the free-surfacedeformation caused by the strut. Masuko(1998) studied the effects of stern fins compu-tationally. Stern fins interrupt the downwardflow of bilge vortices and the pressure abovethe fins increases. This pressure increase causesa reduction of resistance.

It is known that adoption of stators locatedin front of the propeller can result in a reduc-tion of rotational energy losses, so that propul-sion efficiency can be increased. In addition, anon-axisymmetric upstream stator can alter theinflow to the propeller in such a way that un-steady forces and cavitation can be reduced.Recently Shen (1997), for an appended body ofrevolution, considered such a guide vanecomposed of 4 radially placed foils.

The flow at the junction of an appendageand a hull can be very complex. The hullboundary layer flow encounters an obstruction,often nearly perpendicular to the upstream flow.This results in both a non-recoverable loss ofenergy (drag) and a spatially varying flow fieldcharacterised by the so-called horseshoe vortexsystem shed around the obstacle. This structureis of interest since an excessive level of noiseor vibration may have its origin in the genera-tion of additional turbulence in the core of thehorseshoe vortex. Through calculations, Deng& Visonneau (1998) showed the strong turbu-

7lence anisotropy associated with the develop-ment of this horseshoe vortex.

More studies about appendages would beneeded in order to understand fully the flowaround them and their influence on the flowaround the ship hull.

Scale Effects and Form Factor. The flowaround a model differs from the flow aroundthe equivalent full-scale vessel due to the Rndifference. In general, for increasing Rn theflow features become more compact and com-pressed, and boundary layers and shear layersget thinner relative to the length of the vessel.However, other changes in the viscous flowmay occur that are harder to foresee.

While scale effects have different aspects,here we shall only address the scale effect on"form factor." The form factor tries to ap-proximate the influence of three dimensionalityon viscous resistance, as a function of Rn. Alt-hough in principle it may vary with Rn as wellas Fn, in the ITTC (1987) the use of a Rn-independent 1+K was recommended for routinework.

In ITTC (1996a), the RC concluded that thevariation of the form factor with Rn depends onthe distribution of resistance between frictionand pressure. For a typical ship hull, the pres-sure component seemed to dominate and there-fore the form factor would increase with in-creasing Rn. Nevertheless, the Powering Per-formance Committee at the same ITTC (1996b)concluded that the variation of form factor withscale might be within the level of uncertaintywith which the form factor can be estimated.

Grigson (1996) reanalysed the resistancetests of the Lucy Ashton and Victory geosims.Using the ITTC 1957 Correlation Line, he hadgot a marked scale effect, with a form factorlarger at full-scale, in discord with what shouldbe expected from the physics of the flow. Therelative displacement thickness of the boundarylayer decreases with scale, relatively the flowbecomes less full as scale increases. Never-theless, any scale effect on the form factor isvery small and if anything, the form factor issmaller at full scale than for the model when afairly accurate friction law is used as the authorprovides. He is demanding a new CorrelationLine.

Bruzzone et al. (1997) presented the resultsfrom various geosim tests, highlighting theinfluence of Rn and Fn and of the hull form onthe form factor but not with an unambiguousconclusion about scale effects. The values ofthe form factor sometimes increased and some-times decreased with scale. They propose toestablish a minimum dimension of the modeland for the large-scale models to make a cor-rection for blockage effects. Furthermore, it isnecessary also to establish type, dimension, andposition on the model of the turbulence stimu-lators.

Garofallidis (1996) also pointed out thatturbulence stimulation is of primary importancefor the correlation, and raised questions aboutthe applicability of the form-factor method formodels 3 to 4 metres long. Kasahara & Masuda(1998), for different models of the DAIOHship, found that the measured form factor in-creases as Rn increases for models longer than7 m, but decreases up to this length.

With the present developments in CFD,trends of the form factor in principle could becomputed, particularly the Rn-dependence.However, there are difficulties associated withthis, such as doubts on the validity of turbu-lence models and the lack of validation data forvery high Rn.

2.3 Wave/Viscous Interaction

Interaction between the wave making andviscous flow is conventionally disregarded inmodel test extrapolation and in computationalprediction. Such interaction comes in manyforms, such as effects of the inviscid pressurefield upon the viscous flow, the effect of themodified (wavy) streamline pattern along thehull, the free-surface boundary conditions inthe viscous-flow region, the effect of the free-surface on turbulence, and the differentgeometry of the wetted hull surface if wavesare taken into account.

The first phenomenon mentioned above, theeffect via the pressure field, is easily under-stood from considering the inviscid pressuredistribution on the hull. It is common to obser-ve that the pressure variations along a ship hullare drastically larger in the flow with free-surface, than in a double-body flow. This may,e.g., cause a much steeper pressure rise fromthe aft shoulder towards the stern, in viscous

8flow possibly leading to local-flow separationnear the waterline. This separation may occurin a certain Fn range only, and may be supposedto lead to a rather drastic and sudden change ofthe viscous resistance and stern flow at a cer-tain speed; raising many questions on thevalidity of resistance extrapolation techniques.

Choi & Stern (1993) showed that the free-surface boundary conditions in the viscous flowhave an important influence in regions of largevelocity gradients and wave slopes, includingsignificant free-surface vorticity flux and com-plex momentum and vorticity transport in alayer close to the free-surface.

Wave-Induced Separation. The separationsolely due to free-surface wave-induced effectsinvolves the complexities of free-surface de-formations, vorticity, and turbulence in addi-tion to the already formidable subject of three-dimensional (3D) boundary-layer separation.This phenomenon was first identified by Chow(1967) and has been studied by various authors.Recently, Zhang & Stern (1996) studied wave-induced separation for a surface-piercingNACA 0024 foil. The separation patterns werefound to be Fn-dependent. The free-surface ismainly a sink of vorticity. A part of the vortic-ity generated at the body surface fluxes up intothe free-surface and the rest goes to the wake.Using video cameras above the surface Po-gozelski et al. (1997) observed that the reversedflow appeared only at Fn exceeding 0.30.

Connected to the complicated physics, thestudy of Zhang & Stern (1996) mentions sever-al difficulties in modeling that need to be ad-dressed in order to predict such flows. It is de-sired to evaluate the performance of turbulencemodels for prediction of free-surface inducedseparated flows, and the approximation usedfor the free-surface boundary conditions, and toobtain time-accurate unsteady solutions.

Stern and Wake Flows. While in Section2.2 stern and wake flows already have beenconsidered from a viscous flow point of view,here the wave/viscous interaction is discussed.One aspect of this is the viscous effect on thestern wave system. Neglecting this, the sternwaves are over predicted due to the neglect ofthe displacement effect of the hull boundarylayer and due to the neglect of the viscousdamping of the generated waves (Larsson,1997b, Raven, 1998). This effect is considera-

bly larger for bluff ships, where the stern wavessometimes almost disappear.

For transom sterns, various flow regimesmay occur. One is a flow with a clean free-surface separation from the edge of the transom,which is typical of higher speeds and lowertransom immersions. In other conditions anarea with highly turbulent and often unsteadyflow behind the transom face may occur. In thetransition from one regime to the other, wavebreaking and wave/viscous interaction play adominant role, but a precise model seems to belacking and at present it is hard to predictwhich regime will occur in which speed range(Raven, 1998). It is noted that, since the sameregimes occur just as well for transoms that areabove the design waterline, a transom depth Fnis not a useful parameter in this regard.

Van et al. (1998b) made an experimentalinvestigation on two models, a 3600TEU con-tainer ship and a 300K VLCC that can be con-sidered as two types of modern practical hullforms. For the container ship the wave eleva-tion near the stern was observed to be flatterdue to the transom effects, although the tran-som stern of this ship (located above the designwaterline) was not entirely cleared. In this casethe so-called dry transom modelling is notentirely appropriate for accurate simulation. Inthe case of the VLCC, the designed waterlinewas located above the transom edge, and therewas apparently no transom effect; but the localflow measurements revealed that the flow angleseems to have an abrupt change of directiondue to the transom, and possibly flow reversal.

2.4 Propeller-Hull Interaction

The presence of the propeller affects theflow both by inducing a swirling effect and bylocally accelerating the flow. On the one hand,this helps to stabilize the boundary layer andprevents separation ahead of the propeller(Turnock and Molland, 1998), on the otherhand the propeller may also induce separation,in particular on the hull above the propeller.

Nevertheless, the major effect of the pro-peller on the flow upstream on the hull is theasymmetric acceleration of the flow, whichleads to different pressure reductions on theport and starboard sides for a single screw ship.The cause is the interaction of the upward

9component of the wake field and the directionof rotation of the propeller.

Abdel-Maksoud et al. (1998a-c) point outthe problems in the interaction between theflow around the stern of the ship and the flowinduced by the propeller: the necessity to in-clude viscous forces and turbulence effects; thecomplexity of the geometry and the resultingeffort to discretise the problem; the interactionbetween the rotating propeller and the station-ary ship; and the inherently unsteady nature ofthe problem. The results of their computationsshowed the strong influence of the propeller onthe flow region, especially on the pressure field.

2.5 Conclusions

Numerous studies have been conductedconcerning ship resistance and flow physics.However, physical understanding of many de-tailed aspects of ship resistance remains in-complete since most studies are phenome-nological and fail to provide useful models.Limited study has been devoted to the impor-tant topic of scaling/extrapolation methods.More work is needed on wave breaking, turbu-lence, roughness effects, and viscous flow/free-surface interaction.

3. TRENDS IN EXPERIMENTAL TECH-NIQUES

3.1 Introduction

Trends in experimental techniques over thelast ten years of relevance to towing-tanktesting are summarized. Techniques are consid-ered which are useful both for routine testingfor design and evaluation as well as for morecomplex testing at model and full scale forphysical understanding and CFD validation.Experimental techniques are divided into twocategories: current and developing techniques.Current techniques refers to those alreadywidely used, whereas developing techniquesrefers to those not widely used or from otherfields which likely have near-term applicabilityto towing tanks. For many developing tech-niques, further developments are required, e.g.,in extending a technique from physical tomodel or full scale testing. For each category, asub division is made with regard to the scale of

the experiment, i.e., physical-, model-, or full-scale testing.

Physical-scale experiments are directed atproviding data for documenting a particularphysical phenomenon such as effects of pres-sure gradients on flow separation, effects ofroughness on turbulent boundary layers andwakes, effects of turbulence and pressure gra-dients on corner vortices, etc. Such experimentsare conducted using specialized/idealized ge-ometry, which may not resemble a ship's hullbut may represent a local portion of it, e.g.,appendage/hull juncture and flat plate with animposed pressure gradient. Both time-mean andunsteady data are procured and used for physi-cal understanding, model development, andCFD validation.

Model-scale experiments are directed atproviding data for design and evaluation andfor documenting particular physical phenomenasuch as boundary-layer and wake, vortex flowand separation, propeller-hull interaction, etc.Such experiments are conducted using scaledmodel ships, e.g., cargo/container, combatant,and tanker hull forms. The intention is to repli-cate full-scale conditions; however, lack ofsimilitude and environmental conditions im-pose significant limitations. Both time-meanand unsteady data are procured and used fordesign and evaluation, physical understanding,model development, and CFD validation.

Full-scale experiments are directed atproviding data for sea trials, design andevaluation, and for documenting particularphysical phenomena such as Rn scale effects,turbulence, cavitation, etc. Such experimentsare extremely difficult and subject to variableenvironmental conditions. Both time-mean andunsteady data are procured and used for seatrials, design and evaluation, physical under-standing, model development, and CFD vali-dation.

These categories and divisions will changeeven in the near future as advancements aremade, e.g., developing techniques for physicalscale will be used for model scale and devel-oping techniques for model scale (e.g. flowmeasurements and flow observations) will beused for full scale.

3.2 Current Techniques

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Physical Scale. Physical-scale tests are notusually conducted in towing tanks.

Model Scale. Current techniques formodel-scale tests were identified through aquestionnaire distributed to RC and severalJapanese ITTC members. The techniques aresummarized in Table 1 and include measure-ment systems for forces (and moments), car-riage/model speed, water temperature, motion(sinkage and trim), flow visualization, surfacepressure, nominal wake, wave profiles, andwave elevations. Additionally, in some cases,wind tunnel tests are done using double models.Current techniques are conveniently discussedwith regard to routine and non-routine tests.

Routine tests include forces, carriage/modelspeed, water temperature, sinkage and trim,flow visualization, wave profile, wave eleva-tions, and nominal wake at the propeller plane.For force/moment measurements, most towingtanks use load cells and only a few are still us-ing the counter-weight method. Measuredforces are converted to digital format and aver-aged by computer programs (e.g., Longo &Stern, 1996). Model velocity is measured bytwo different methods. One is to measure ve-locity relative to the ground (carriage speed)using a speed circuit; the other is to measurethe velocity relative to the water using a currentmeter. Conventional mercury and semi-conductive thermometers are used to measurewater temperature. Sinkage and trim are meas-ured using potentiometers or ultra-sonic heightmeters. The measurements are taken at twopoints near the forward and after perpendicu-lars and converted to sinkage and trim. Flowvisualization is performed using surface ordepth tufts mounted to the hull surface. A tuftgrid is also used to observe rotational flow atthe propeller plane. Paint on the hull surface ordye injection is also used for flow visualization.Surface pressures are measured at select loca-tions using pressure taps and differential pres-sure transducers. Wave profiles along the hullare measured by photo or CCD camera. Servo-mechanism and finger wave probes are used tomeasure transverse wave elevations. Capaci-tance and resistance type wave probes are usedto measure longitudinal wave elevations (cuts).Longitudinal wave cuts are used for deriving

wave pattern resistance, CFD validation, etc. Inthe former case, the probe position is important.Each towing tank has its own standard for pro-be position and data acquisition time. Nominalwake is usually measured using Prandtl-tube or5-hole pitot probe rakes and differential pres-sure transducers.

Non-routine tests include the same variablesas for routine testing, but with considerablylarger mapping of the flow through dense datalocations. Examples include surface pressure(Toda et al., 1990), wave elevations (Toda et al.,1992, Ikehata et al., 1998), and detailed meanvelocity and pressure measurements using 5-hole pitot probes (Longo & Stern, 1996). Othernon-routine tests are mean velocities and Rey-nolds stress measurements using double modelsin wind tunnels and triple hot wire sensor ane-mometer (Hyun & Patel, 1991a,b, Suzuki et al.,1997, 1998a-c). In these cases, six componentsof the Reynolds stress are measured, togetherwith the three mean velocity components. Thedata are mainly used to validate CFD predic-tions.

Full Scale. Routine tests for full-scale shipsare measurement of propeller torque, propellershaft revolution, and the velocity relative toground and water. Sea conditions as waveheight (observations) and relative wind velocityare also measured. Baba & Ikeda (1991) im-proved the Togino type torque meter for full-scale ships using a one line CCD sensor.

Non-routine tests are thrust and towingforce measurement, wake measurements by 5-hole Pitot tube or laser Doppler velocimetry(LDV) systems, cavitation observation, andmeasurement of pressure fluctuations aroundthe propeller. Shaft thrust force was measuredfor the icebreaker SOYA (Uto & Narita, 1998)using direct measurement of propeller shaftcompressive strain. Torque coupling effectscaused by misalignment of the gauges wereevaluated by Suzukis method (Suzuki et al.,1992). Towing force measurements were per-formed using a patrol boat (Hara et al., 1994) inthe case of a rescue operation in a rough seastate.

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Table 1. Current techniques for towing tank testing of resistance and flow.

Type of test Equipment CommentsForce Load cell + filter

Counterweight Balance

Measured forces are for example: resistance and trans-verse forces at FP and AP or at rudder; lift and dragforces measured on model advancing with drift angle; 6-component forces at constrained hull; unsteady meas-urements of resistance, pitching moment and heave andforces at fixed model conditions.

The resistance force or added resistance in waves is bal-anced by weights.

Velocity Current meter

Wheel + pulse counter

Velocity relative to the water typically measured at 0.5L1.0L in front of model at half of mean model draft.

Velocity of the carriage relative to the ground (rail).Temperature Mercury thermometer

Resistive thermometerQuartz thermometer

Temperature is typically measured as mean temperatureover the measured distance at half of mean draft ofmodel or at one/several fixed depths at fixed locations inthe tank. Occasionally combined with artificial mixing oftank water.

Motion(sink-age/trim)

PotentiometerUltrasonic distance me-ter

Vertical displacements are measured in generic positionsfore and aft of the model where after sinkage and trim arecalculated.

Flow visu-alization

Wet paint

Tufts on hull or grid

Paint applied in stripes on hull, which becomes flowlines when model is towed or self-propelled through wa-ter.

Tufts applied to hull (grid) with needles or with thin tape.Documented by video and observations.

Hull pres-sure

Pressure tap + DPT (DPT = Differentiated Pressure Transducer)

Wake Prandtl tube rake + DPT

5-hole pitot probe rake +DPT

Small propeller typevelocimeter

Normally measured in the propeller plane (typically atthe intersection between r/R=0.7 and the generator line)for every 5-15 degrees, or with smaller intervals if neces-sary. Sometimes measured in a rectangular mesh.

Wave eleva-tion at hullside

Visual observationsfrom photo or video

Professional cameraSpray paint

Model is marked with stations and waterlines where afterwave height along hull side is estimated from photos orvideo.Video and photographs of free-surface turbulence andwave breakingWave profile obtained by moving the camera step by stepfrom bow to stern.

Wave eleva-tion at free-surface

Resistance probeCapacitance probe

Longitudinal cuts at different distances from hull side.Wave heights also measured at non-fixed locations e.g.stern wave measurements.

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3.3 Developing Techniques

Physical Scale. Many developing tech-niques have application to towing tanks, alt-hough as already noted in many cases furtherdevelopments are required in extending a tech-nique from physical to model or full scale test-ing. The following discussions focus on severaldeveloping techniques, which hold promise forapplications in towing tanks, i.e., PIV, LDV,deformation measurements, shear-stress meas-urements, pressure measurements, and com-bined experiments and CFD.

PIV. 3D velocity measurements by imageprocessing techniques have rapidly progressedin the last ten years; in particular the PIV tech-niques discussed below. In most commonmethods for measuring fluid flow velocities,the fluid is seeded with particles or markers,where after the flow field easily can be tracedand imaged. In the absence of particles, flowshave also been tagged with lines or grids usinglaser induced photochemical reactions or laserinduced fluorescence.

Barnhart et al. (1995), Slepicka & Cha(1997), and Fabry (1998) measured 3D velocityfields by using a holographic method. The 3Dparticle positions in the water channel are fro-zen in two holographic pictures with a smalldifference in time. The reproduced particle im-ages are detected as two-dimensional move-ments in the screen. In the case of 3D motions,the screen was moved to focus the particle im-ages. Adrian et al. (1997) and Gaydon et al.(1997) investigated the use of stereoscopicphotographs and thus analysed the 3D particlemotions. Kawakatsu et al. (1991) also used thestereoscopic photograph method but analysed itby a particle image correlation method. Koba-yashi et al. (1995) measured 3D positions andtemperature simultaneously by the use of a mi-cro-capsulated liquid crystal particle. Kawasue& Ishimatsu (1996) introduced a very interest-ing method to measure 3D positions of particleimages. They rotated the camera images andfound that the diameters of circled images wererelated to the axial distance from the camera toparticles.

Raffel et al. (1995) applied a dual lasersheet technique to measure 3D velocity com-ponents, and succeeded to measure the 3D ve-locity fields around simple models in waterchannels. Post et al. (1994) developed a two-colour laser sheet method and measured the

behaviour of high shear layer. Nishio (1995)proposed a statistical approach to measure thetime-mean velocity. The frequency of imagescattering was measured and a statistical ap-proach was applied. Okuno (1995) applied aspatio-temporal method to measure the velocityin a separated flow, and also applied thismethod to measure the movement of an oil filmon a ship model surface. Okuno & Sakamoto(1990) applied Fourier transformation to theimage picture and found the direction of mo-tion and the distance of the particles.

Error analysis for PIV has been performedand compared with theoretical calculations.Wei et al. (1995) discussed the effects of vorti-ces and shear layers. Lourenco and Krothapalli(1995) discussed the accuracy of detecting themaximum auto-correlation point. Peysson &Guazzelli (1998) and Oschwald et al. (1995)analysed that if the light sheet plane is out offocus from the focal plane of the camera, theposition in the image plane is not a linear func-tion of the position in the light-sheet plane.They also pointed out the systematic errors inPIV for a rotating mirror method. Thomas et al.(1993) studied the response of particles to alarge velocity gradient field by measuring 3Dparticle velocities in a shock wave using PIVand 3-component LDV.

LDV. Compton & Eaton (1996) succeededto measure the viscous sublayer in the turbulentboundary layer by high resolution LDV using asmall mirror in the flow. The measurementpoint closest to the wall surface was at abouty+=5. The results showed good agreement withvelocities and 6 components of Reynoldsstresses measured by pressure probe or X-typehot wire anemometry.

Deformation Measurements. Many papersfocus on the correlation of two successive sca-lar images for the purpose of measuring imagedfluid motions. A methodology for direct meas-urement of velocity and velocity gradient fieldwas developed by Tokumaru & Dimotakis(1995). They used a temporal spatial methodand introduced the velocity and velocity gradi-ent as unknown parameters in an optimisationprocess. Su & Dahm (1996) propose a ScalarImaging Velocimetry (SIV) technique for fullyresolved four-dimensional (x, y, z, t) vectorvelocity field measurements in turbulent flows.SIV technique is one of the temporal spatialmethods applicable to inner turbulent shear

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flow. They succeed to measure the unsteadyvelocity field in a 3D volume.

Laser excited fluorescence was studied byHill & Klewicki (1996). They dealt with theLIPA (Laser Induced Photochemical Ane-mometry) and measured velocity and stream-wise vorticity distributions in the inner layer.This method entails the use of a laser and alight sensitive chemical. Two types of photo-chemical can be used: photochromic or phos-phorescent chemicals. The paper by Hill &Klewicki (1996) proves that this technique is avaluable measurement tool for understandingturbulence because of the high frequency re-sponse of the luminescent fluid. Gendrich &Koochesfahni (1996) present a spatial imagecorrelation technique for estimating the dis-placement vector of the tagged regions with amuch higher level of accuracy then had previ-ously been achieved.

Shear-Stress Measurements. Various tech-niques for measuring shear stress on a wallhave been developed, e.g. Preston tubes, float-ing elements, or laser based systems. The latterdo not have probe disadvantages like mixedsensitivity, individual calibration, direct electri-cal contact, fragility of the sensors, etc. Theseadvantages of laser systems are proven by theholographic fan fringe sensor, which Millerd etal. (1996) used to measure velocity gradients(shear stress and skin friction) inside theboundary layer. The dual-cylindrical wave(DCW) system, studied by Naqwi (1993), pro-duces an optical measuring volume by two in-terfering cylindrical waves from a laser. Thissystem is a variation of LDV, and its applica-tion to shear-stress measurements in turbulentboundary layers and particle sizing are devel-oped in some studies.

Shear stress near the wall is determined bythe local velocity gradient immediately adja-cent to the wall. Nepomuceno & Lueptow(1997) measured it using a hot film wall shear-stress probe, mounted upstream of a hearing aidmicrophone for wall pressure measurementsand a hot wire velocity probe. The shear stressprobe was calibrated against a Preston probe.

Preston probes cannot be used to measurewall friction in a ship model bow region due tothe thin boundary layer. Ito & Oyanagi (1992)and Matsumura et al. (1995) proposed a non-contact measurement method using an oil film.The principle is that the oil dot or oil film on

the model surface spreads at a rate proportionalto the wall shear stress. The movements aredetected by an image processing technique.Further investigations were proposed to findthe precise relation between the oil dot velocityand the local skin friction. If successful thelocal skin friction of any type of body surfacecould easily be measured. Another idea, devel-oped by Wang (1993), was to select a materialin which the fluid shear force can be transferred,but the movement of fluid is extremely re-stricted. A sintered metal using small spherescan meet these requirements. A sensor is there-after used to measure a pressure difference in-dicating the wall shear stress.

Some other systems using laser light orfloating elements have also been developed.Lubrication theory relates the local skin frictionforce to the thinning of an oil film placed onthe test surface. Mateer & Monson (1996) de-veloped a laser interferometer skin-friction(LISF) technique. They measured the thicknessof the oil film on a wing model by laser inter-ferometer and calculated the skin friction dis-tributions. They got good agreement with CFDresults for both shear stress and pressure distri-bution. Liu & Sullivan (1998) used a lumines-cence intensity method. Luminescent moleculesare dispersed in an oil film and the luminescentlight is proportional to the thickness of the oilfilm. Three kinds of NACA wings were used inmeasurements, showing good agreement withCFD predictions.

Micro-electro mechanical systems (MEMS)based sensors were applied to measure theshear stress on a two-dimensional airfoil (Na-gaoka et al. 1997). A micro-electro hot filmsensor (0.2mm*0.2mm) on a small silicon wa-fer determined the separation region on the foil.The force acting on the large eddy break up(LEBU) devices was measured using a friction-al force balance to clarify the reduction of fric-tional force by LEBU (Lynn et al., 1995).

Pressure Measurements. Pressure sensitivepaint (PSP) seems to be a valuable techniquefor measuring surface-pressure distribution inwind tunnel models. PSP contains a componentthat is luminescent when excited by an appro-priate light source. The luminescence of thepaint varies as a function of the partial pressureof oxygen, which is proportional to the staticpressure of air at the coated surface. This en-ables measurement of essentially continuousproperty distributions. The limitation is only

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the resolution of the imaging equipment. Mor-ris et al. (1993) applied this technique for awing-body model and McLachlan et al. (1993)for a 2D NACA-0012 wing. The results werecompared with pressure-tap measurements andshowed good agreement. The brightness of apressure-sensitive paint is a function of pres-sure, temperature, photo degradation, illumina-tion intensity, and coating thickness. Bell &McLachlan (1996) point out the importance ofthe model alignment and propose a projectiveequation of photo grammetry to relate model toimage coordinates. Experiments performed byWoodmansee & Dutton (1998) confirm that thePSP are temperature sensitive, so a tempera-ture-correction data reduction method shouldbe used to obtain quantitatively accurate sur-face-pressure measurements.

Studies of wall-pressure fluctuation weremotivated by an interest in hydro-acousticproperties of smooth surfaces with irregulargeometry. Horne & Handler (1991) propose amethodology to cancel the contaminating noisein the measurement of turbulent wall pressurefluctuations using the signals from two flushmounted wall pressure transducers, directedtransverse to the mean flow. Corrected resultsshow good behaviour in the low frequencyrange.

Instead of traditional plug-in probes,Nitsche et al. (1989) used miniature pressuretransducers or piezoelectric foils. The piezoe-lectric effect of polarised plastic foils is used toregister time-dependent pressure or shear loads.Lfdehl et al. (1994) use very small siliconbased sensors manufactured using microelec-tronic technology, to measure wall pressure inturbulent flows. High frequency pressure fluc-tuations can be captured by the very small sizeof the transducers.

Combined Experiments and CFD. BothCFD and flow field measurements have exten-sively been used to understand flow fields. Alt-hough CFD easily can estimate the entire flowfield, it inevitably contains numerical errors.Meanwhile, the various field measurementsusually require a lot of labour and also containexperimental errors. Although some experi-mental techniques can measure flow velocitiesat many points simultaneously, it is difficult tomake a dense measurement for a large field.Therefore, some new techniques have beenproposed to understand the whole flow field by

combining various experimental techniques andCFD.

Yamaguchi et al. (1996), Ohwaki et al.(1998), and Sugii et al. (1996a,b, 1997) pro-posed a technique to predict a complete flowfield by combining PIV and CFD. In this tech-nique, velocities at points where no data havebeen measured are calculated by using locallyobtained PIV data as a boundary condition. ThePIV data are corrected simultaneously to reducemeasurement errors using CFD results and fun-damental equations of fluid dynamics. In cor-recting the data, the cost function, which repre-sents the sum of the adjusted amount of ob-served data and the residual of the fundamentalequations, is used; the whole flow field is ob-tained by minimizing the cost function. Thistechnique has been applied to 3D non-isothermal flow fields and flow fields with ro-tation, shear, and expansion.

Dong et al. (1997b) presented an approachto determine the pressure distribution by usingmeasured velocity field data and RANS equa-tion. The approach was tried on an airfoil sec-tion at 8 degrees incidence. The velocity andReynolds stress distribution around the foilwere measured in a cavitation tunnel by LDV.The RANS equation, the Euler equation and theBernoulli equation were employed separately tosolve for the pressure while the velocities andReynolds stresses were considered as knownfrom the measured data. The results were com-pared with the pressure directly measured onthe foil surface, showing good agreement. Ji etal. (1998) tried this approach to determine thepressure distribution on a body of revolutionwith tail fins. For validation, direct pressuremeasurements were carried out.

Model Scale. Developing techniques atmodel scale include applications of some of thedeveloping techniques discussed above by afew towing tanks as well as techniques formodel-scale experiments from other fields. Thefollowing discussions focus on several devel-oping techniques, which hold promise for ap-plications in towing tanks, i.e., shear-stressmeasurements, velocity and turbulence meas-urements, wave-resistance measurements, andwave-pattern measurements.

Shear-Stress Measurements. In order to re-duce turbulent frictional drag, several tech-niques can be used, all requiring the shearstress to be measured. Kato et al. (1990), Fujii

15

et al. (1991), Doi et al. (1991), Takahashi et al.(1997a,b), Watanabe et al. (1997), Larrarte &Kodama (1997), Sato et al. (1997), and Toku-naga et al. (1998) all succeeded to carry outshear stress measurements using similar float-ing element devices.

Velocity and Turbulence Measurements.Turbulence measurements in the boundarylayer on a ship model can be done using hot-wire or hot film anemometers. Mori & Hotta(1988) and Wu & Bose (1992) obtained veloc-ity profiles and boundary layer properties. Inboth cases a hot-film anemometer has beenused, as it seems to be a practical, economicaland accurate tool for towing-tank applicationsduring ship model testing. Wu & Bose (1992)consider this equipment, which also can beused to measure high frequency components ofthe flow as well as the mean velocity compo-nents, as more accurate than Pitot tubes. Alimitation is that it cannot be used in reversingflows.

Kakugawa et al. (1989) applied one-dimensional LDV to measure the velocity fieldaround a ship stern and compared the resultwith 5-hole Pitot tube data. The comparisonshowed good agreement. Eca et al. (1994)measured tip vortices in a cavitation tunnel by3D LDV system. The results were comparedwith CFD results and good agreement was ob-tained. Hoekstra & Aalbers (1996) have madeextensive wake measurements for 8 ship mod-els using 3D LDV. The two-colour backscattersystem permitted simultaneous measurement of3 velocity components in the towing tank, suchthat turbulence intensities and Reynoldsstresses could be determined. Longo et al.(1998) performed measurements of solid/free-surface boundary layer and wake using a towedtwo-component LDV system.

Traditionally, 5-holes Pitot probes havebeen used for measuring 3D aerodynamic flowfields. The development of 4-hole probes hasbrought the advantages of a smaller size, fewermeasurements in calibration and application,and less instrumentation. Improvements of the5-hole Pitot tube are made in the form of a 4-hole pyramid probe, as explained by Main et al.(1996), or a 7-hole probe by Payne et al. (1989).Zilliac (1993) analysed the performance ofseven-hole pressure probes and found themaximum probe onset-flow angle is approxi-mately 70 degrees. Payne et al. (1989) com-pares its suitability and accuracy for delta wing

vortex flow fields with LDV measurements. Itwas found that the seven-hole probe is reason-ably accurate for measurements at location be-fore and after vortex breakdown except near thevortex breakdown region. The major disad-vantage of this probe, however, is its inabilityto measure reversed flows, and its usage islimited in the breakdown region.

Turbulence near the water surface has beenmeasured by image processing (Peirson, 1997,Logory et al. 1996, Kumar & Banerjee, 1998).Shear stress or vorticity distributions close tothe water surface are also obtained with thistechnique giving interesting results. Pogozelskiet al. (1997) and Chang & Liu (1998) measuredwave-breaking phenomena by PIV and foundvortices behind the breaking regions. Kumar etal. (1998) measured upwelling in a channelflow. Hering et al. (1997a,b) measured driftcurrent under the wind-wave interaction.

Wave Resistance. Hirano et al. (1991)measured the pure wave-pattern resistancearound a high-speed craft. They also quantifiedthe spray drag by measuring the spray flux dis-tribution. Their approach was to take out thespray flux, which contaminated the wave pat-tern around the ship, by using a small bucket.

Wave Pattern Measurements. Besides theconventional wave-cut measurements, wavepatterns can be measured using image-processing techniques. Bonmarin et al. (1989)use a slit laser light sheet to measure wind-generated wave characteristics. Zhang & Cok(1994) colour-coded the wave slope by an opti-cal method, and Zhang (1996) integrated theslope to obtain the wave height. Oshima et al.(1994) measured the stern wave pattern ofhigh-speed craft using laser sheet and CCDcamera in a circulating water channel. Theyalso measure the wave pattern of a high-speedcontainer ship in a towing tank (Nisho et al.,1996). Suzuki & Sumino, (1993), Suzuki & He(1997) and Suzuki et al. (1994) measured the2D wave pattern using projected light distribu-tions which are proportional to the free-surfacecurvature. They measured the wave-patternresistance around the Series 60 (CB=0.6) modeland compared it with experimental data.

Full Scale. Use of developing techniques atfull-scale tests is limited.

Velocity Measurements. Kux (1990) andTanibayashi (1990) performed wake measure-

16

ments at the propeller position by LDV. Komu-ra et al. (1991) performed 3D particle trackingvelocimetry (PTV) and LDV measurementssimultaneously. However, the comparison ofdata did not show a good agreement.

Propeller Forces. Kamiirisa et al. (1991)and Uchida et al. (1989) measured propellerblade fluctuating stresses. Uchida et al. (1989)also measured the effects of the propellerblades crossing the free-surface. Ukon et al.(1990) and Ukon et al. (1991) measured thepressure distributions for a conventional and ahighly skewed propeller.

Sea Trials. Takezawa et al. (1994) per-formed sea trials of superconducting electro-magnetohydrodynamic propulsionship Yamato 1. They succeeded to propel acraft by superconducting electromagnetohydro-dynamic propulsive water jet pumps.

3.4 Conclusions

There is an increasing demand for moredetailed model- and full-scale local-flow data,both for design and for CFD calibra-tion/validation. The advent of modern physical-scale LDV, PIV, surface shear stress and pres-sure distribution, and wave-elevation meas-urement systems (instrumentation, data acqui-sition and reduction) holds promise for meetingthis demand. More work is needed on full-scalemeasurements, especially local flow.

4. TRENDS IN COMPUTATIONAL FLUIDDYNAMICS

The development of CFD for marine appli-cations has continued at an increased pace, ashas its use in practical ship design. The fol-lowing sections summarise the trends over thelast 3 years, of relevance to ship resistance andflow. Section 4.1 discusses application of CFDtechniques in ship design practice with regardto status and needs. In Sections 4.2, 4.3 and 4.4,the present state of the art and recent develop-ments in inviscid and viscous flow methodsand CFD-based optimisation are described. Thediscussion will be essentially limited tomethods for steady flow calculations.

4.1 Practical Application of CFD; Status andNeeds

The actual application of CFD methods inship design has always lagged behind the de-velopment of methods, which justifies a sepa-rate discussion. This survey partly updates the21st ITTC Resistance Committee's discussionon "A Naval Architects View", and likewise ispartly based on the committee's own perception,since the general status on applications is noteasily retrieved in the literature.

Inviscid Flow Calculation Methods. MostCFD applications in ship design today concernthe wave pattern and inviscid flow around thehull. The methods used, discussed in Section4.2 below, usually are panel methods imposingeither linearised or nonlinear free-surfaceboundary conditions. The former are easier todeal with for less experienced users, as they donot iterate for the free-surface location. Thenonlinear methods are significantly more accu-rate and complete, but all the same need not beappreciably more time-consuming or less ro-bust.

Several shipyards have started collectingexperience with these methods. Steps are beingmade to integrate these calculations into thedesign process (Tuxen et al., 1998, Kim et al.,1998c). This involves interfacing with CADsystems, automatic panel generation tools,postprocessing and visualisation programs. Attowing tanks and institutes the use of thesemethods is more advanced and comprehensive.For some of them, inviscid flow calculationshave become a standard component of any shiphull form design project, preceding modeltesting. Accreditation of these tools is a desirednext step.

While often the predicted wave resistance isthe main result on which design variations arecompared or optimised, there is increasingawareness that this is not the best way to ex-ploit these tools. In the first place, the resis-tance value gives no specific indication ofwhich features of the design affect the wavemaking, how the design could be improved, orwhat aspects of the calculation are less reliable.Secondly, the predicted wave resistance may bethe least accurate part of the results. In particu-lar linearised methods may give quite poor re-sistance predictions, due to their basic assump-

17

tions (Raven, 1990). Nonlinear codes at leastprovide positive and more consistent resistanceestimates, but still suffer from numerical inac-curacy in the pressure integration over the hulland sensitivity to modelling details. Improve-ment may be obtained by applying wave patternanalysis to the calculated pattern (Nakos &Sclavounos, 1994, Raven & Prins, 1998).

Even with sufficient numerical accuracy thewave resistance derived from an inviscid flowcode still may be unreliable due to the neglectof viscous effects on wavemaking. While per-fectly justified over most of the hull, this ne-glect may lead to an appreciable overestimationof the stern wave system (and thereby of thewave resistance) for fuller hull forms, for cruis-er stern shapes, and in case of flow separationor dead-water areas aft of a transom (Raven,1998). Corrections for viscous effects shouldimprove this, but are hard to prescribe by sim-ple rules due to the sensitivity to the hull form.

Consequently, wave resistance from invis-cid-flow codes will only be quantitatively accu-rate for rather slender vessels at higher speed, ifpredicted by a nonlinear method and with muchcare for numerical accuracy. For other applica-tions they may still be very useful for rankingdesign variations, but not for modifications thatsignificantly affect the viscous effects on wavemaking, e.g. Janson & Larsson (1996). Pub-lished evidence that the predicted wave resis-tance is always good enough for ranking pur-poses, is rather limited. In any case it is prefer-ably always used in combination with a judge-ment on the predicted wave pattern.

The predicted wave pattern is much morereliable and accurate. Predictions of the fore-body wave making and in particular the bowwave height at the hull are frequently used forassessing designs and ranking variations. Non-linear methods here give significantly morerealistic and comprehensive predictions thanlinear ones. The wave profile along the remain-der of the hull is more easily predicted, andfore- and aft shoulder waves usually are accu-rate also for linearised methods.

The use of predicted stern wave systems ismuch harder, and judgement still plays a sub-stantial role. In any case, linearised methods arenot applicable to the common sterns with atransom above the still water level. Nonlinearmethods perform much better in that regard butstill suffer from the uncertainty whether the

transom will be cleared or wetted by the flow,an intricate viscous effect not modelled. For awetted transom, the stern wave system may bestrongly overestimated. However, some suc-cesses have been shown for more slender ves-sels, for which the trends of the wave patternand resistance with stern shape and transomheight were well predicted (Raven & Valkhof,1995, Raven, 1998). Experiments are desiredfor determining the dependencies and limits ofinviscid methods for stern flows.

Predicted wave patterns may be useful forestimating wash (Hughes, 1997, Raven et al.,1998), provided the wave evolution over largedistances (and ideally other effects such as su-percritical flows or effects of bottom topogra-phy) can be accurately handled, which is achallenge.

Viscous Flow Calculation Methods. Forviscous flow calculation methods, RANSmethods today are dominant. Besides dedicatedcodes for ship flows, also commercial general-purpose RANS solvers are being used. In mostpractical cases free-surface effects are disre-garded, but this may well change soon.

Use of RANS solvers in ship design gener-ally is not yet a routine procedure but is largelylimited to special applications or specific des-ign questions, mainly by towing tanks/institutes.The number of actual design calculations usingviscous flow codes is limited but increasing.Also some large shipyards use viscous flowsolvers on a more or less experimental basis.Reportedly, in the Far East the practical use ofRANS codes at shipyards is more widespread(Larsson, 1997b).

In principle, calculation of the viscous flowaround the hull holds great promise for futureapplications: to support the extrapolation ofmodel tests to full scale; to predict viscous re-sistance at model or full scale; to provide theeffective wake field at full scale and permit anintegrated optimisation of hull and propeller;and to predict the occurrence, extent and risk ofseparation at full scale, e.g. permitting to fixmore precisely the limit of afterbody fullness.However, almost none of these examples hasbeen realised so far and current possibilities aremore limited, although quite helpful.

A major restriction is that most currentsolvers have limited applicability for full scale.The very large velocity gradients at the wall

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require large grid stretching and excessive cellaspect ratios, causing numerical problems formany codes. Wall functions alleviate this butare less accurate. Consequently, almost allpractical use today is for model scale, and pub-lications on full scale viscous flow are rare. Eca& Hoekstra (1996) show accurate full-scalecalculations without wall functions. Bull &Watson (1998) present scale effect studies foran appended submarine using some differentturbulence models.

Besides possible numerical problems, otherissues are turbulence modelling for high Rn,and the difficulty of carrying out experimentalvalidation at full scale. Nevertheless, becauseof the scarceness of other information on scaleeffects, numerically accurate full-scale solu-tions already can be very useful and instructive.

Regarding viscous resistance, substantialprediction errors are still found in the literature.In SRI (1994), results varied enormously be-tween methods, but about half of the predic-tions was within 10% of the data. Larsson et al.(1998) suppose that the prediction may be ac-curate enough for ranking design variations,provided much care is exercised in the genera-tion of the grid, particularly at the hull ends.Precise grid dependence studies are required.Bertram (1998) gives an example of a correctranking of viscous resistance, although themagnitude of the (relatively small) differenceswas overestimated. Kasahara & Masuda (1998)apply a regression-analysis-based correction totheir CFD-predictions, and thus predict formfactors for a variety of ships to within 2 %. Thissuggests a correct ranking, but in absolute val-ue their CFD predictions for resistance oftenare 15 % in error. Therefore, as with inviscidmethods the main benefit is not in predictingjust resistance, but in providing comprehensivethough qualitative flow field information andprediction of trends.

As for the wake field in the propeller plane(with or without propeller effect), the generalstatus is that its details cannot yet be reliablypredicted. For slender ships good predictionsmay be obtained, for more critical cases usuallythe predicted wake contours are too smooth andshow too little influence of longitudinal vor-tices. The circumferentially averaged wake ispredicted better, and the wake fraction aver-aged over the propeller disk can be fairly good,according to limited information (e.g. Kasahara& Masuda, 1998). However, propeller design

cannot fully rely on the wake field predictionsnow (Larsson et al., 1998). Two main causes ofthis are insufficient resolution of flow details,and deficiencies in turbulence modelling. Bothmay be significant in certain cases, but the cur-rent opinion seems to emphasise the lattercause.

Predicted flow fields could also be veryuseful and practical for appendage alignment,design of energy saving devices and twin-gondola stern design. There is a large practicaldemand in this regard, since experimental tech-niques are subject to scale effects. However,calculations are hard due to the complicatedgeometries, and a very high accuracy of theresult is often required. Larsson et al. (1998)state that useful predictions may be made forappendages that are not too close to the pro-peller plane, or for slender transom stern ves-sels. For other cases the flow directions may beexpected to have a similar unreliability as thewake field.

A most useful application for a class ofcases is the prediction of occurrence and typeof flow separation. Shortcomings in the turbu-lence modelling seem of less influence here,and calculations give much more informationthan is obtainable otherwise. Valkhof & Hoek-stra (1998) illustrate the practical benefit ofsuch calculations.

Summarising we believe that the very largepotential of viscous flow calculations is notfully exploited yet in design; partly due to cur-rent limitations such as insufficient wake fieldpredictions and problems for full scale; partlydue to circumstances such as the required timefor grid generation and geometry treatment, orthe experience required for applying themethods successfully to a variety of cases.Therefore, attention is desired for:

improving wake and flow field predictionsaround the stern, by better representation ofturbulence effects, e.g. using tuned eddy-viscosity models, Reynolds stress model(RSM) or even large eddy simulation(LES);

improving numerical accuracy; improving the ease, speed and range of ap-

plication, e.g. via multiblock, unstructured,or adaptive grids;

enhancing the applicability for full scale,and collecting full-scale validation data.

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After this discussion of practical applications ofCFD in ship design, we will now discuss recentadvances in research and development.

4.2 Inviscid Flow Calculation Methods

Introduction. Inviscid models for the steadyflow around a ship hull predict the wave patternand wave resistance, the velocity and pressurefield; and lift effects (hydrofoils, sailing yachts).Usually the Laplace equation for the velocitypotential is solved; in some cases, the Eulerequations, but these mostly are intended as astep towards solving RANS equations withfree-surface, and are discussed in that contextlater. For calculating the steady wave patternone can either solve a transient problem untilthe steady state has been reached, or solve thesteady problem directly. Unlike viscous flowcomputations, virtually all inviscid methods usethe latter approach, which is successful andmore efficient. This requires that a particularcombination of kinematic and dynamic free-surface boundary condition is imposed, ofwhich the Kelvin condition is one example.

Steady Potential Flow Solution Methods.The exact inviscid free-surface boundary con-ditions are nonlinear and must be imposed onan unknown wave surface. Until around 1986the problem was virtually always linearised,and research concentrated on devising suitablelinearisations. Slow-ship linearised methodssuch as Dawson's were dominant, giving fairlyrealistic results at modest computational effort.While linearised codes are being used in in-dustry, during the last few years there is littledevelopment on these, as little further progressseems possible and linearisations are in mostcases not needed anymore.

Most publications now concern solution ofthe fully nonlinear free-surface potential flowproblem. Taking into account the nonlineareffects improves the predictions much morethan was expected before, and in other casesthan was assumed. Bow wave height and di-verging bow wave system, severely underesti-mated by linearised methods, can now be quitewell predicted. In Raven (1997) the differencesbetween wave patterns found with linear andnonlinear methods are analysed and explained.Principal effects are due to imposing the free-surface boundary condition on the actual watersurface instead of the still water plane, and dueto the refraction of the ship's wave system by

the velocity field around the hull. In addition,nonlinear methods include a more completerepresentation of several hull form features,dynamic trim and sinkage, and the flow off a(dry) transom stern.

These methods seem mature now, and sev-eral development lines have converged to fairlysimilar solutions. Some references are Jensen(1988), Jensen et al. (1989), Raven (1993),Raven (1996), Kim et al. (1994), Janson (1997),and Hughes (1997). In Raven (1998) the mainfeatures of the leading methods are comparedand capabilities and limitations of this flowmodel are outlined.

The nonlinear problem is solved iteratively.Most methods start from an undisturbed free-surface and uniform flow, and obtain a con-verged result in O(10) iterations in practice.Each step solves a linearised problem that isfairly similar to that in Dawson's method.While the basic set-up is rather straightforward,care is needed for numerical details in order tocome to a convergent and stable procedure.

Within each iteration the Laplace equationfor the potential, subject to hull and free-surface boundary conditions, is solved, usuallyby a Boundary Integral or Panel method, eitherin Green's identity or in source distributionform. Remarkably, the leading nonlinearmethods now all use raised singularities ordesingularisation, i.e. sources located at adistance above the wave surface. This uncon-ventional approach was first proposed by Xia(1986) and Jensen et al. (1986) for the waveresistance problem; and by Schultz et al. (1990)for unsteady free-surface problems. Raised sin-gularity methods owe their popularity in thisapplication to some favourable properties. Us-ing the theoretical analysis method proposed bySclavounos & Nakos (1988), Raven (1992,1996) analyses the stability, numerical disper-sion and damping and concludes that raised-panel methods substantially reduce the numeri-cal dispersion and can eliminate point-to-pointoscillations. Janson (1997) extends this analy-sis to higher-order raised panels and finds thatthese give no significant increase in accuracycompared to first order.

The "radiation condition" that excludes anysteady waves upstream of the disturbance, re-quires a particular treatment. There are twopopular ways of imposing this. One is, usingupwind difference schemes in the implementa-

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tion of the free-surface boundary condition, adevice introduced by Dawson (1977). This in-troduces some numerical damping, which,however, can be minimised by a suitable choiceof the scheme, Raven (1998). The alternativeway to satisfy the radiation condition is, shift-ing the free-surface collocation points forwardover one panel length relative to the panels, atechnique proposed by Jensen et al. (1986) andJensen (1987). This permits to use analyticaldifferentiation of panel inductions instead of adifference scheme, which is theoretically moreaccurate and free of numerical damping; alt-hough Janson (1997) found little advantage inpractice.

While the multiple iterations could requirean order of magnitude more computational ef-fort than previous linearised methods, the dif-ference has largely disappeared due to bettermatrix solvers. The combined free-surfaceboundary condition together with a source-onlyformulation leads to a rather poorly conditionedsystem of equations, in the past solved byGaussian elimination, requiring O (N3) opera-tions for N panels. Today, several methods usean iterative matrix solver with proper precon-ditioning, reducing the effort to O (N2) andsaving much calculation time. The fastestmethods now solve a fully nonlinear problemwith e.g. 4000 panels in half an hour on a PC.

There have been various proposals forfurther speedup. Soeding (1996) proposes amultigrid type approach for a panel method,and a panel clustering technique that combinesthe effect of several remote panels, reducingstorage and computational time. More ad-vanced are "multipole acceleration" techniques(Korsmeyer et al., 1993) that approximate bothfar and local potential fields in spherical har-monics, permitting a reduction of the computa-tional effort for the entire method to O(N). In asimple example, for 5000 singularities the CPUtime was reduced by a factor of 5 (Scorpio etal., 1996). An alternative, perhaps more easilyapplied to common steady wave pattern calcu-lation methods, is the "Precorrected FFT tech-nique" (Korsmeyer et al., 1996). Application ofall these techniques to the problems consideredhere is just starting, and substantial further im-provement seems possible. However, the pri-mary benefit of these techniques will be forradiation/diffraction or wave propagationproblems, where far larger panel numbers arerequired.

Unsteady Potential Flow Solution Methods.Most unsteady potential flow methods are pri-marily meant for truly unsteady applications(seakeeping etc.), but some can be used to cal-culate the evolution of the wave pattern until asteady solution of the nonlinear problem hasbeen found. All methods use the kinematicfree-surface boundary condition to find an up-dated wave surface, and the dynamic conditionto find a new potential at that surface. Ratherfew methods in this class permit a substantialforward speed. A noteworthy development isthat of Beck et al. (1993), Scorpio et al. (1996),Subramani et al. (1998b), an unsteady desin-gularised point source method. For somesteady wavemaking problems they get goodagreement with the data (Ratcliffe, 1998).However, for steady applications this approachis less efficient, requiring two orders of mag-nitude more CPU time than a steady nonlinearpanel code.

Transom Sterns. There is continued interestin the flow off a transom stern, most researchaddressing the immersed transom sterns usedfor high-speed ships, rather than the transomsabove the still waterline that are common formerchant vessels. Inviscid flow approximationsonly apply to a flow regime in which the tran-som is dry and the water surface detaches fromthe transom edge. There needs to be no diffi-culty in computing such a smooth transom flowas long as a potential flow solution exists.However, in a range of cases the transom willactually be wetted and the potential flow solu-tion is locally unrealistic, but the calculationsdo not indicate this (Raven, 1998).

For dry-transom cases a particular treatmentof the free-surface detachment from the tran-som edge is required. A variety of methods andphysical models has been proposed, mostly forlinearised methods. The fundamental inconsis-tency of a transom flow model with most line-arisation assumptions often has caused diffi-culties. Doctors & Day (1997) assume a shapeof the hollow of the water surface aft of thetransom, described by a few empirical parame-ters; and include this hollow as an extension ofthe hull in a Michell theory program. Telste &Reed (1993) model the flow off an immersedtransom stern in a Neumann-Kelvin method,and propose a modified linearisation relative toa cylindrical surface extending aft from thetransom edge. Wang et al. (1996) compare aKelvin source and Rankine source method, anda method proposed by Tulin & Hsu (1986)

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valid asymptotically for very high speed. Forthe former two methods the treatment of thetransom flow is not discussed. Results shown,for the wave resistance of a single hull form,are inconclusive.

In a nonlinear method the treatment of theflow off a transom stern is much more obvious.The free-surface boundary conditions are im-posed on the actual wave surface, and the mod-elling just needs to make sure that this wavesurface has the proper behaviour at the transomedge. Raven (1993, 1996) argues that physi-cally no vorticity is involved, and points out theanalogy with free-streamline theory. While theflow off the hull is tangential, the curvature ofthe streamlines at the transom edge may tend toinfinity (although this seems to have little effectin practice). Comparison with dedicated ex-periments (Raven & Valkhof, 1995, Raven,1998) shows that for a dry transom the correcttrend of stern wave height and shape with tran-som immersion is predicted; but that somesystematic deviations occur due to the neglectof viscous effects.

Subramani et al. (1998b) apply a 2D versionof their time-dependent nonlinear desingul-arised code to a semi-infinite body with tran-som. The calculations reproduce the two possi-ble flow regimes, one with a stagnation point atthe transom face, another with a smooth flowoff the transom edge; and agree very well withanalytical results for the trailing wave steepness.

Simplified Methods. There have been somerecent proposals for simplified treatments, in-tended to give a clearer view of the physics orto permit solution of problems that cannot bedealt with by complete nonlinear codes.

Noblesse et al. (1996) consider the Neu-mann-Kelvin problem, or the correspondingproblem of radiation with forward speed in thefrequency domain. They extend the Kochintheory to simplify the numerical evaluation ofthe velocity field induced by a distribution ofKelvin singularities on the hull surface. Theyderive an explicit form for the wavy velocityfield away from the hull, in terms of a velocitydistribution on a matching surface found frome.g. a nonlinear inviscid or viscous flow calcu-lation for the near field; thus enabling apromising composite approach.

In the "2D+T" approximation for slenderships, the steady 3D velocity field is consideredas a 2D field in cross-sectional planes, evolving

in time. This approximation disregards trans-verse waves and upstream influences (via thepressure field). However, the 2D fully non-linear problems in crossplanes can be solvedwith very high resolution, and it is easier toinclude overturning wave crests. Tulin & Wu(1996) use this to study the origin and behav-iour of diverging bow waves, producing physi-cally plausible bow wave breaking. A compari-son with a fully nonlinear 3D result showsqualitative agreement for the wave patternshape.

4.3 Viscous Flow Calculation Methods

There has been much recent activity in de-velopment of viscous flow calculation methodsfor maritime applications. In virtually all casesthis concerned solution methods of the RANSequations. This subsection reviews some of themain trends and achievements, addressing gridgeneration; numerical algorithms; free-surfacetreatment; turbulence; and unsteady flow c