fulltext

J Mar Sci Technol (2003) 8:76–87DOI 10.1007/s00773-003-0156-4

PIV velocity field measurements of flow around a KRISO 3600TEUcontainer ship model

Sang-Joon Lee, Min-Seok Koh, and Choung-Mook Lee

Department of Mechanical Engineering, Pohang University of Science and Technology, San31, Hyoja-dong, Nam-ku, Pohang 790-784, Korea

Abstract The main purpose of this investigation was to dem-onstrate a useful application of the particle image velocimetry(PIV) method to analyze the complex flow characteristicsaround a ship. For a sample illustration, the KRISO 3600TEUcontainer ship model was chosen. The flow structure in thestern and near-wake region of the model has been investi-gated experimentally in a circulating water channel. Instanta-neous velocity fields measured by the PIV velocity fieldmeasurement technique have been ensemble-averaged to givedetails of flow structures such as the spatial distributions of thelocal mean velocity, vorticity, and turbulent kinetic energy.The free-stream velocity was fixed at Uo = 0.6 m/s, and thecorresponding Reynolds number based on the length betweenperpendiculars was about 9.0 ¥ 105. The container ship modelshows a complicated three-dimensional flow structure in thestern and near-wake regions. The PIV results clearly revealedthe formation of large-scale bilge vortices in the stern regionand their effect on the flow in the near-wake. The resultsshown here provide valuable information for hull form designand the validation of viscous ship flow codes and of turbulencemodels.

Key words Ship wake · PIV · Longitudinal vortex

1 Introduction

The flow around a ship is very complex, and an accurateanalysis is important for modern ship design. For abetter understanding of the flow around a modern ship,it is necessary to obtain reliable experimental data.

Several numerical and experimental studies havebeen carried out to investigate the flow around rela-tively simple and idealized hull forms. Larsson1 and

Hoffman2 measured the flow structure of turbulentboundary layers on ship hulls. Löfdahl3 measured themean velocities and Reynolds stresses in the stern re-gion of an SSPA 720 liner. Knaack et al.4 measuredturbulence data for an HSVA tanker in the stern andnear-wake regions. For a Wigley hull form, Patel andSarda5 carried out a wind-tunnel test using a double-decker model, in which they measured pressure, meanvelocities, and Reynolds stresses in the region frommidship to almost a ship-length downstream. However,since the hull forms used in these previous studies weresomewhat simple and idealized,6,7 the flow structures aredifferent from those of modern hull forms.

Recently, there has been noticeable progress in nu-merical analysis by predicting the details of ship sternand wake flows. For example, the Gothenburg 2000Workshop on computational fluid dynamics (CFD) inship hydrodynamics dealt with three different ship mod-els.8 In addition, several workshops on numerical simu-lation have been organized to assess the accuracy ofnumerical models and predictions, and to identify re-search areas in need of further study. To develop reli-able numerical methods and a better understanding ofthe flow around a real ship, it is necessary to accumulatereliable experimental bench-mark data on practical hullforms of modern ships.

Most previous experimental studies on ship hydrody-namics have been carried out in a towing tank. Re-cently, Kim et al.9 measured flows around moderncommercial ship models. However, it was difficult to getturbulence statistics from the towing tank experiment.In order to investigate the turbulent structure of flowaround modern ship shapes, Lee et al.10 carried outwind-tunnel experiments for a double-decker KRISO3600TEU container ship model.

In this investigation, the flow characteristics over thestern and near-wake regions of a modern container hullform have been investigated experimentally using theparticle image velocimetry (PIV) method. The main

Address correspondence to: S.-J. Lee(e-mail: [email protected])Received: December 25, 2001 / Accepted: May 12, 2003

77S.-J. Lee et al.: Flow around a container ship model

objective of this study was to investigate the flow char-acteristics around a container ship model in detail, andaccumulate experimental data for validating numericalpredictions. The spatial distributions of the mean veloc-ity, turbulent kinetic energy, and vorticity at severaltransverse sections and longitudinal stations are pre-sented, and relevant discussions are made.

2 Experimental apparatus and method

2.1 Ship model

The experiments were carried out in a circulating waterchannel (CWC) with a test section of 1.0W ¥ 1.0H ¥ 4.5L.The maximum speed of the circulating water channelwas about 2.2m/s, and the surface-flow accelerator wasoperated to provide a uniform flow at the CWC test-section.

A container model, with a length (LPP) between twoperpendiculars of 1.5m, a breadth (B) of 0.21m, a draft(T) of 0.07m, and a block coefficient (CB) of 0.65, wasmade of fiberglass-reinforced plastics (FRP) to a 1/153scale of the KRISO 3600TEU container ship (hereaftercalled the KCS). The principal dimensions of the ex-perimental model are given in Table 1. Figure 1 repre-sents the body plan of the KCS prototype. Figure 2shows photographs of the front, rear, and side views ofthe KCS model. When the ship model was installed inthe CWC, the blockage ratio, defined as the ratio of theprojection area of the KCS model to the CWC cross-sectional area, was about 1.47%. Therefore, no velocitycorrection was made since the blockage effect can beneglected.11 The free-stream velocity was fixed at Uo =0.6m/s, and the corresponding Reynolds number basedon the model length (LPP = 1.5 m) was about Re = 9.0 ¥105.

2.2 PIV velocity-field measurement system

The PIV velocity-field measurement system consists ofan Nd :YAG laser, a CCD camera, a frame-grabber, a

delay generator, and an IBM PC, as shown in Fig. 3. TheNd:YAG laser has two heads, which were speciallydesigned for PIV measurement. Its maximum energyoutput is larger than 25mJ per pulse, and the maximumpulse repetition rate of each laser is 20Hz. Since thelaser pulse has a short pulse-width of about 7ns, thehighly turbulent flow motions can be frozen in a clearparticle image. The Kodak 2K ¥ 2K CCD camera cancapture digital particle images at a frame rate of 4 f.p.s.(frames per second). A delay generator was used tosynchronize the Nd: YAG laser and the 2K ¥ 2K CCDcamera. The time-interval Dt between two laser pulseswas controlled by the delay generator.

Figure 4 shows the timing diagram for synchronizingthe CCD camera and the pulsed Nd: Yag laser. Thesynchronizing circuit plays an important role in captur-ing clear particle images for velocity-field measure-ments. When a laser sheet is formed in the flow, someparticles move in and out of the laser light sheet duringthe time-interval Dt. Therefore, it is important to adjustthe thickness of the laser light sheet appropriately, andto make the time-interval as short as possible. However,

Table 1. Principal dimensions of the prototype and model ofthe KRISO 3600TEU container ship

Parameters Full-scale CWC model

LPP 230.0 1.5B 32.2 0.21D 23.0 0.15T 10.8 0.07CB 0.65Re — 9 ¥ 105

CWC, circulating water channel

Fig. 1. Body plan of the KRISO 3600TEU container ship

Fig. 2. a Front, b rear, and c side views of the KRISO3600TEU container ship model

a b

c

78 S.-J. Lee et al.: Flow around a container ship model

the time-interval Dt depends mainly on the maximumparticle displacement in the interrogation window. Thethickness of the laser light sheet used for velocity-fieldmeasurements in the transverse sections was 3 mm.

Velocity fields of flow around the KCS model weremeasured using a 2-frame cross-correlation PIV tech-nique. Figure 5 shows the coordinate system andmeasurement planes used in this study. The positivedirections of coordinates X, Y, Z were the downstreamdirection from the bow to the stern, from thewaterplane toward the keel, and from the center-planetoward the starboard side, respectively. The measure-ment planes were divided into three regions: six trans-verse sections (stations 0, 0.35, 1, 2, 4, 6) in the sternregion, three transverse sections (stations -0.5767, -1,-3) in the near-wake region, and five longitudinalplanes (Z/(B/2) = 0, 0.1, 0.2, 0.4, 0.6) in the near-wake

region. These PIV velocity field measurement sec-tions were defined by Cartesian coordinates, not byboundary-layer coordinates.

The fields of view for the transverse sections in thestern and near-wake regions were 140 ¥ 140mm2 and150 ¥ 150mm2, respectively. The longitudinal sectionsin the wake region consisted of two consecutive cross-sections of 120 ¥ 120 mm2. A region of about 10 mmoverlapped between the two measurement sections.The interrogation window was fixed at 48 ¥ 48 pixels2 insize. A total of 400 instantaneous velocity fields weremeasured at each measurement plane. They wereensemble-averaged to get the spatial mean velocityfield. The fluctuating-velocity vector fields were ob-tained by subtracting the mean velocity field from theinstantaneous velocity vector fields. All the fluctuatingvelocity vector fields were statistically averaged to getthe spatial distributions of the turbulence statistics,including turbulent kinetic energy.

The stream-wise component of vorticity in the trans-verse section was calculated using the followingequation:

w∂∂

∂∂x

i j i j i j i jwy

vz

w w

y

v v

z= -

ÊËÁ

ˆ¯̃

ª-

--Ê

ËÁˆ

¯̃+ - + -1

212 2 2

1 1 1 1. . . .

D D (1)

Here, the central difference numerical scheme wasused, and Dy, Dz indicate the grid dimensions.

The turbulent kinetic energy k in the longitudinalsections was calculated from the following two-dimensional approximation:

k u v w u v= + +( ) ª +( )- - - - -12

34

2 2 2 2 2r r (2)

This assumption uses the concept of isotropic flow struc-ture. Therefore, the real turbulent kinetic energy will bea little different from this result.

Fig. 3. Schematic diagram of the PIV experimental set-up andsystem

Fig. 4. Timing diagram of synchronization for the PIVvelocity-field measurements

X

Y

ZLongitudinal sections of the wake region

Transverse sections ofthe wake region

Transverse sections of the stern region

(Station 0, 0.35, 1, 2, 4, 6) (Z/(B/2)=0, 0.1, 0.2, 0.4, 0.6)

(Station -0.5767, -1, -3)

Fig. 5. Velocity-field measurement sections and coordinatesystem

79S.-J. Lee et al.: Flow around a container ship model

A plane mirror of 300 ¥ 300mm was located at X =0.67 LPP to illuminate the thin laser light sheet for mea-suring velocity fields in longitudinal sections. It was alsoused to capture particle images for the transverse sec-tion measurements.

3 Results and discussion

3.1 Flow characteristics in the stern region

3.1.1 Mean velocityThe mean velocity field was obtained by ensemble-averaging 400 instantaneous velocity fields. The in-plane coordinates Y and Z in the transverse sections arenondimensionalized by draft (T) and half-beam (B/2),respectively. Figure 6 shows the spatial distributions ofthe mean velocities V and W non-dimensionalized bythe free-stream velocity Uo at six down-stream locations.In order to show the flow direction clearly, the cross-flow streamlines are depicted on the mean velocityfields. The right-hand sides show the equivelocity con-tours of cross-flow defined as the square root of meanvelocities V and W.

At station 6, the cross-flow is weak at the turn of thebilge, and nearly zero in the region near the waterline(Y = 0). However, a clockwise (looking toward the bow)vortex is formed at the bottom of the ship hull. A largevelocity gradient caused by the cross-flow is locally dis-tributed at the corner of the bilge. At station 4, a littledown-stream from station 6, the flow converges abovethe lower bilge. However, the clock-wise vortex at thebottom of station 6 has disappeared owing to the inclin-ing contour of the cross section. As the flow goes down-stream, the area of dominant cross-flow expands aroundthe concave hull surface at a depth of (0.6 < Y/T < 1.0).At station 2, the cross-sectional area was drasticallyreduced and has a concave hull shape. As shown in Fig.6c, the speed of cross-flow is increased and the flowmoves toward the concave hull surface.

According to wind-tunnel tests12 which were con-ducted for a double-decker KCS model in the speed-regime of Re = 3.3 ¥ 106 the maximum magnitude ofcross flow is about 20% of the free-stream velocity atstation 2.0. The flow pattern and cross-flow size shownin Fig. 6c are in good qualitative agreement with thewind-tunnel results. Since the present PIV measure-ments were confined to two-dimensional planes, onlythe in-line two-velocity components could be measured,i.e., the main-stream component U was not measured inthe transverse sections. In the region 0 < Y/T < 0.2 nearthe free-surface at station 2, there is a region havinga large W velocity component whose magnitude in-creased to 70% of that at station 4.0.

At station 1, the general flow structure is similar tothat at station 2.0. The retarded velocity zone formed in

the upper wake region (0.2 < Y/T < 0.4) expands, andthe cross-flow converges strongly to the concave hullsurface. However, the magnitude of the cross-flow de-creases gradually as the flow goes down stream. Thevertical velocity component of cross flow is nearly zeroin the region 0 < Y/T < 0.2. However, as the flow ap-proaches the hull surface, the flow moves slightly up-ward due to the decrease in the cross-sectional area inthis region. This causes a vortex flow near the waterline.At station 0.35, commonly named the propeller plane,the cross flow was divided into two parts. One was di-rected to the waterline, and the other moved downwardtoward the propeller boss. The latter caused a longitudi-nal vortex rotating counter-clockwise in the regionabove and outward from the propeller boss. The formerenhances the secondary clockwise vortex located nearthe waterline. In particular, the longitudinal vortex lo-cated near the propeller boss can cause serious prob-lems such as cavitation, noise, and vibration. This flowstructure is maintained at station 0.

3.1.2 Vorticity distributionFigure 7 shows vorticity contours at several transversesections in the stern region. The black and white graylevels indicate the clockwise and counter-clockwiserotating vorticities. At station 6, a strong counter-clockwise vortex formed by cross-flow in an elongatedshape from the hull side toward the bilge. The strengthof the vorticity was particularly large at the corner ofthe bilge. It is interesting to note the existence of asmall clockwise vortex at the bottom near the bilge. Itsstrength is rather small, compared with the vorticityaround the bilge corner. At station 4, the strength of theclockwise rotating vortex was increased, and its centerwas located at the lower bilge of the hull. The strengthof the counter-clockwise vortex was decreased, and itscenter was still located near the upper bilge. When go-ing downstream, this vortex moves upward along thehull surface and forms a secondary vortex near thewaterline.

As the cross-sectional area changes largely at station2, a longitudinal vortex of the greatest strength isformed at the bottom bilge. This results from the evolu-tion of the clockwise rotating vortex formed at the bilgecorner of upstream stations, and increases in intensitydue to an abrupt converging flow caused by the reduc-tion of the cross-sectional area of the hull form. Theupper and lower vortices have their maximum strengthat station 2. The location and strength of these twovortices play an important role in determining the nomi-nal wake distribution and the resulting propulsiveefficiency.

As the flow proceeds to consecutive downstream sta-tions, the strength of these two vortices is graduallydecreased. In particular, the main longitudinal vortex at

80 S.-J. Lee et al.: Flow around a container ship model

the propeller plane (station 0.35) is concentratedaround the propeller boss, and its strength near theupper side of the propeller boss is relatively weak. How-ever, this longitudinal vortex may cause some adversepropeller performance. The secondary vortex near thewaterline is very diffusive and its strength has decreasednoticeably. At station 0, the general shape of the vortic-ity distribution is similar to that at station 0.35.

3.2 Transverse sections of near wake

The near-wake formed behind a ship is very importantin the design of high-performance ships. In order tounderstand the wake structure, the mean velocity fieldsand vorticity contours were measured at the three cross-sectional planes in the near-wake region (station-0.5767, station -1, and station -3). Figure 8a shows the

Fig. 6. Mean velocity distributions and equivelocity contoursof cross flow at several transverse stations in the stern region.Left-hand side, mean cross-flow vectors. Right-hand side,

equivelocity contours. a Station 6, b station 4, c station 2, dstation 1, e station 0.35, f station 0

a

b

c

81S.-J. Lee et al.: Flow around a container ship model

mean velocity distribution and vorticity contour at sta-tion -0.5767. As before, the gray levels indicate theclockwise and counter-clockwise rotating vorticity. Twocounter-rotating longitudinal vortices of nearly thesame strength are centered at the location of Z/(B/2) =±0.1. They are symmetric with respect to the wakecenter-plane (Y/T = 0). Another secondary vortex existsnear the waterline at the lateral locations of Z/(B/2) =±0.6. The formation of these secondary vortices is at-

tributed to the flow separation from the hull surfacedue to the rapid reduction of the cross-sectional area.The strength of the main longitudinal vortices separatedfrom the propeller boss is much larger than that of thesecondary vortices near the waterline. At station -1, thestrength of both the longitudinal vortices and the sec-ondary vortices is reduced somewhat compared withthose at station -0.5767. Approaching the station -3,their strength is noticeably reduced to about 40% of

Fig. 6. Continued

d

e

f

82 S.-J. Lee et al.: Flow around a container ship model

Fig. 7. Vorticity contours in the stern region. a Station 6, b station 4, c station 2, d station 1, e station 0.35, f station 0.0

a

c

e

b

d

f

83S.-J. Lee et al.: Flow around a container ship model

Fig. 8. Mean velocity field (left) and vorticity contours (right) at transverse planes of the near-wake. a Station -0.5767, b station-1, c station -3

a

b

c

84 S.-J. Lee et al.: Flow around a container ship model

that at station -0.5767. With going downstream, thelateral distances between two longitudinal vortices andthe secondary vortices near the waterline increasegradually. The evolution of these vortical structures canbe explained by turbulent diffusion and viscous dissipa-tion. However, the general shape of the vortex structureis maintained over the wake region tested in this study.These flow phenomena represent typical flow character-istics of the near-wake of the KCS hull form.

3.3 Longitudinal planes of near wake

3.3.1 Instantaneous velocity fieldThe wake behind the KCS model has a very compli-cated three-dimensional flow structure. In order to

figure out the three-dimensional flow characteristics,the velocity fields at five longitudinal sections inthe near-wake region were measured using the PIVtechnique. The coordinates X and Y were non-dimensionalized with the length between perpendicu-lars (Lpp) and the draft (T ) of the model.

Figure 9 shows the spatial distributions of the fluctu-ating velocity fields in the axial planes at Z/(B/2) = 0, 0.1,0.2, 0.4. For the purpose of displaying the vortex struc-tures, the mean velocity field was subtracted from theinstantaneous velocity vector fields to establish thefluctuating velocity structures.

At the wake center-plane (Z = 0), the shear flowseparated from the bottom of the ship hull is dominant,and becomes diffusive as the flow goes downstream. The

Fig. 9. Instantaneous velocity fields subtracted by mean velocity in the longitudinal planes of the near-wake region. a Z/(B/2) =0. b Z/(B/2) = 0.1. c Z/(B/2) = 0.2. d Z/(B/2) = 0.4

a

c

b

d

85S.-J. Lee et al.: Flow around a container ship model

center of the main longitudinal vortices which greatlyaffect the wake structure behind the ship model is lo-cated in the longitudinal plane at Z/(B/2) = 0.1, as shownin Fig. 8. At Z/(B/2) = 0.1, the longitudinal vortex iscentered at Y/T = 0.63, and the axial velocity componentis dominant compared with other longitudinal sections.At the height between Y/T = 0.4 and 0.7, the flow showsa wavy pattern along the downstream direction. Thisseems to be related to the spiral motion of the mainlongitudinal vortices, which has a large vorticity in thatregion, as shown in Fig. 8a. When going toward thestarboard, the fluctuating flow motion is largely reduced,and the shear flows and longitudinal vortices decreased.

3.3.2 Stream-wise mean velocity profilesThe mean stream-wise velocity fields were obtained byensemble-averaging 400 instantaneous velocity fields ineach of four longitudinal planes. Figure 10 shows thevariation in the stream-wise mean velocity profiles ex-tracted from the mean velocity field data at five down-stream locations (X/LPP) = 0.01, 0.04, 0.07, 0.1, and 0.13.The wake region behind the ship model is divided intotwo regions: the viscous flow region (0 < Y/T < 1.0) andthe inviscid flow region (Y/T > 1.0). It is of interest thatthe stream-wise velocity profiles at Z/(B/2) = 0 and 0.1are quite different from the others. In the central wakeplane (Z = 0), the magnitude of the stream-wise velocitycomponent is very small at the propeller location of X/LPP = 0.01 and Y/T = 0.63. The stream-wise mean veloc-ity is about 50% of the free-stream velocity. This ismainly attributed to the large velocity deficit of thecenter of the wake behind the bluff-body shape of themodel. In particular, the flow separated from the pro-peller boss has a relatively high speed owing to thelongitudinal vortices. As the flow goes downstream, thestream-wise velocity behind the model recovers gradu-ally to the free stream velocity UO. In the region lower

than Y/T = 0.63, the flow has a larger velocity gradientthan that in the upper region. At the downstream loca-tion of X/LPP = 0.13, the stream-wise velocity at theheight of Y/T = 0.63 is increased to 75% of the free-stream velocity.

In the longitudinal plane at Z/(B/2) = 0.1, where thecenters of the longitudinal vortices exist, the generalshape of the mean velocity profiles is similar to the caseof Z/(B/2) = 0, but, the magnitude of the mean stream-wise velocity is greater than that at the center plane ofthe wake. As was the case at the center plane (Z/(B/2) =0), the velocity defect is large at the height Y/T = 0.63,since the radial velocity component of the longitudinalvortices is relatively larger than the stream-wise veloc-ity. In the other three longitudinal planes Z/(B/2) = 0.2,0.4, and 0.6, the vortex-free flow is dominant, and thestream-wise mean velocity profiles have nearly the sameshapes.

3.3.3 Turbulent kinetic energyThe fluctuating velocity vector fields were obtained bysubtracting the mean velocity field from the instanta-neous velocity fields. All the fluctuating velocity fieldswere statistically averaged to get the spatial distributionof the turbulent kinetic energy. Figure 11 shows thespatial distributions of turbulent kinetic energy in thelongitudinal planes at Z/(B/2) = 0, 0.1, 0.2, 0.4.

In the center plane (Z = 0), the strong turbulent ki-netic energy is distributed in the lower wake region 0.6< Y/T < 1.0. As the flow goes downstream, the turbulentkinetic energy is gradually decreased due to turbulentdiffusion and the entrainment of shear flow into thewake region.

In the longitudinal plane of Z/(B/2) = 0.1, the turbu-lent kinetic energy is concentrated in the region 0.35 <Y/T < 0.9. This is directly related to the presence of themain longitudinal vortices. In this plane, in which thecenter of the longitudinal vortices passes, the wake flowhas a large turbulent kinetic energy at the height of thepropeller boss (Y/T = 0.63) owing to the strong rota-tional motion of the longitudinal vortex. It was foundthat the turbulent kinetic energy was distributed moredensely in the region lower than Y/T = 0.63 than in theupper region. This may be attributed to the flow interac-tion between the longitudinal vortices and the shearflow separated from the bottom surface of the model.At the outer longitudinal planes of Z/(B/2) = 0.2 and 0.4,the turbulent kinetic energy distributions do not showdistinguishable turbulence production.

Figure 12 represents variations of the turbulent ki-netic energy profiles at several downstream locations infive longitudinal planes. At the downstream location X/LPP = 0.01 in the central wake plane (Z = 0), the turbu-lent kinetic energy has a local maximum value in thelower wake region at Y/T = 0.75. At the same down-

Fig. 10. Variation of the mean stream-wise velocity profiles inthe near-wake region

86 S.-J. Lee et al.: Flow around a container ship model

Fig. 11. Turbulent kinetic energy distributions at four longitudinal planes in the near-wake region. a Z/(B/2) = 0. b Z/(B/2) = 0.1.c Z/(B/2) = 0.2. d Z/(B/2) = 0.4

stream location X/LPP = 0.01 in the next longitudinalplane Z/(B/2) = 0.1, the turbulent kinetic energy has amaximum value at the center of the longitudinal vorti-ces. As the flow goes downstream, the turbulent kineticenergy is decreased slowly by viscous dissipation andturbulent diffusion. The turbulent kinetic energyprofiles in longitudinal planes other than Z/(B/2) = 0and 0.1 have very similar shapes. In the middle plane ofZ/(B/2) = 0.2, the flow seems to be affected by the free-stream velocity, and the wake formed behind the shipmodel is narrow compared with the wake at the center.

4 Concluding remarks

We have described the use of the two-frame PIV veloc-ity field measurement technique to analyze the detailed

flow characteristics in the stern region of a ship model.The KRISO 3600TEU container ship model was experi-mentally investigated in a circulating water channel.The mean velocity field, turbulent kinetic energy, andvorticity contours in the stern and near-wake regionswere measured.

The mean velocity distributions show the develop-ment of cross-flow, and the evolution of longitudinalvortices. The strength of the longitudinal vortices in theconcave stern region is very large due to the entrain-ment of inviscid fluid into the region. The cross-flowin the propeller plane was divided into two parts. Oneis directed downward and forms longitudinal vorticesaround the propeller boss. The other moves upwardalong the hull surface, with a secondary vortex rotatingnear the waterline.

a

c

b

d

87S.-J. Lee et al.: Flow around a container ship model

The longitudinal vortices formed in the stern regiondominate the flow structure in the near-wake region. Inthe region of the main longitudinal vortices, the meanvelocity defect and the turbulent kinetic energy havelarge values compared with those of the surroundingouter regions. The mean velocity gradient in the lowerwake region below the height of the propeller boss islarger than that in the upper wake region owing to theentrainment of the high-speed free-stream flow.

The flow analysis illustrated in this article, includingthe turbulence statistics, can be used not only to guidehull-form design, but also to validate the CFD codes,and to derive more reliable turbulence modeling usingthe CFD code.

Acknowledgment. This research was supported byNational Research Laboratory (NRL) program of theMinistry of Science and Technology (MOST), Korea.

References

1. Larsson L (1974) Boundary layers of ships. Part III. An experi-mental investigation of the turbulent boundary layer on a shipmodel. SSPA, Göthenburg, Sweden, Report No. 46

2. Hoffman HP (1976) Untersuchung der 3-dimensionalen,turbulenten grenzschicht an einem Schiffsdoppelmodell inwindkanal. Institüt Für Schiffbau Der Universität Hamburg,FRG, Report No. 343

3. Löfdahl L (1982) Measurement of the Reynolds stress tensor inthe thick three-dimensional boundary layer near the stern of amodel ship. SSPA, Göthenburg, Sweden, Rep No. 61

4. Knaack T, Kux J, Wieghardt K (1985) On the structure of the flowfield on ship hulls. Proceedings Osaka International Colloquiumon Ship Viscous Flow, Osaka, Japan, pp 192–208

5. Patel VC, Sarda OP (1990) Mean-flow and turbulence measure-ments in the boundary layer and wake of a ship double model.Exp Fluids 8:319–335

6. ITTC (1987) Report of the Resistance and Flow Committee. Pro-ceedings, 18th International Towing Tank Conference. Kobe,Japan, vol 1, pp 47–95

7. Toda Y, Stern F, Tanaka I, Patel VC (1988) Measurements in thestern and wake flow of a series 60 ship with and without a propel-ler. Iowa Institute of Hydraulic Research, University of Iowa,IIHR Rep No. 326

8. Larsson L, Stern F, Bertram V (2000) Gothenburg 2000: a work-shop on numerical ship hydrodynamics. Gothenburg, Sweden

9. Kim WJ, Van SH, Kim DH (2001) Measurement of flows aroundmodern commercial ship models. Exp Fluids 31:567–578

10. Lee JH, Lee SJ, Van SH (1998) Wind-tunnel test on a double-deck-shaped ship model. Proceedings 3rd International Confer-ence on Hydrodynamics. Seoul, Korea, vol 2, pp 815–820

11. Rae WH, Pope A (1984) Low-speed wind tunnel testing, 2nd edn,New York, Wiley

12. Kim HR, Lee SJ (1999) Experimental study on turbulent struc-ture of flow around KRISO 3600TEU container double-deckmodel. Proceedings of SNAK. Seoul, Korea, vol, 3, pp 8–14

13. Van SH, Kim WJ, Kim HR, Lee SJ (1999) Wind tunnel test onflow characteristics of KRISO 300K VLCC double model. Pro-ceedings of the 4th Japan–Korea Joint Workshop on Marine andShip Hydrodynamics (JAKOM). Fukuoka, Japan, pp 157–164

14. Patel VC (1988) Ship stern and wake flows: status of experimentand theory. Iowa Institute of Hydraulic Research, University ofIowa, IIHR Rep No. 323

15. Sotiropoulos F, Patel VC (1995) Application of Reynolds-stresstransport models to stern and wake flows. J Ship Res 39:263–283

16. Wieghardt K (1982) Kinematics of ship wake flow. 7th DavidTaylor Lecture, David Taylor Naval Ship Research and Develop-ment Center, Bethesda, Rep No. DTNSRDC-81/093

Fig. 12. Variation of the turbulent kinetic-energy profiles inthe near-wake region