Calculation of the Flow around the KVLCC2M Tanker

Date Author Mdress

March 2005 S.L. Toxopeus

Deift UnÍversity of Technology Ship Hydromechanics Laboratory

Mekelweg 2, 26282 CD Deift

TU Deift

DeIftUniversltyot Technology

Calculation of the Flow around the KVLCC2M

Tanker.

by

S.L. Toxopeus

Report No. 1426-P

2005

CFD Workshop "CFDWSO5, National Maritime

Research Institute, Tokyo, Japan, march 9-11,2005

PREPR INTS of

CFD WORKSHOP TOKYO 2005

Editor TAKANORI BINO

March 9-11, 2005

National Maritime Research Institute

Tokyo, Japan

CONTENTS

Part A: lest Cases and Huh! Data

A I. Test Cases

A2. Hull Data

Part B: Computational Methods

Bi. Acronyms and Code Names

Original Questionnaire

Summary of Replies to the Questionnaire

Part C: COmputed Results

CL Global Qúantities,All Test Cases

C2 Local Quantities (Test Case I)

C2.1 Local Quantities (Test Case 1.1)

C2.2 Local Quantities (Test Case 1.2)

C23 Local Quantities (Test Case 1.3)

C2.4 Local Quantities (Test Case 1.4)

Local quantities (Test Case 2)

Local quantities (Test Case 3)

Local quantities (Test Case 4)

Local quantities (Test Case 5)

Part D,: Papers

Luquet, R., Jacquin E., Alessandrini, B. and Guillerm, RE.:

RANSE with Free Surface Computationsaround Fixed and Free

DTMB 5415 Model, in Still Waterand in Waves

Broglia,R., Muscari, R. and Di Mascio, A.:

Computations of Free Surface Turbulent Flows Around Ship Hulls

by a RANS Solver

Rhee, S.H. and Skinner, C:

Unstnctured Grid Based Navier-Stokes Solver for Free-Surface Flow

around Surface Ships

Ptteñden, Ri., Turnock, S.R. and Pashias,C.:

Obli4ue Ship Flow Predictiòns Using Identification of Vortex Centres

to Control Mesh AdaptatiOn

Hsu, K.L., Chen Y.L, Chau,

Chien, HP. and Kouh,J.S.:

Ship Flow ComputatiOn of DTMB 5415

Chien, H.P., Kouh, J.S., Chau, S.W, Hsu KiL; and Chen Y.J.:

Ship FlOw Computation of KVLCC2M

Östman, A.:

Computation of Free-Surface Viscous Flow Around the DTMB 54 F5

and KCS Hull Forms

Deng,G.B. , Guilmineau, E., Queutey, P. and Visonneau, M.:

Ship Flow Sinuilations with the ISIS CFDCode

Chao, K. K.-Y.::

Numeric Propulsion Simulátion for the KCS Container Ship

Wilson, R., Carrica,P. and Stern, F.:

RANS Simulation of a Container Ship Using a Single-Phase Level Set Method

with Overset Grids

Carrica,RM.,, Wilson, R.V. and Stern, F:

Linear and Nonlinear Response of Forward Speed Diffìaction

fora Surface COmbatant

Simonsen, C.D and Stern, F.:

RANS Simulation of the Flow around the KVLCC2 Tanker

Regnström, B., Broberg, L.,Östberg, M., Bathfield, N. and Larsson, L.

Drag Prediction forthe KVLCC2M Hull

Gorski, J.J. and COleman, R. M.:

Computations oftheKVLCC2M Tanker under Yawed Conditions

Miller, R., Gorski, J., Wilson, R. and Cárrica, P.:

RANS Simulation of a Naval Combatant Usinga Single-Phase

Level Set Method with Overset Grids

Bull, P.W.:

Verification and Validation of KVLCC2M Tanker Flow

Lübke, LO.:

Numerical Simulation of the Flow. aroundrthe PropelledKCS

Cura Hochbaum,A. and Pierzynski, M.:

Flow Simulation for a Combatant in Head Waves

Kim, J. Park. 1.-R. and Van, S.-H.:

RANS Computations for KRISO'Container Ship and VLCC Tanker

using, the WAVIS code

Tahara, Y., Wilson,R., and Carrica,P.:

Comparison of Free-Surface Capttiring and Tracking Approaches in Application to Modern Container Ship and. Prognosis for Extension

to Self-Propulsion Simulator

Chou, SK, Chin,

Chang, F.N. and Wu, CH.:

Computations of Flow around Ships with Free Surface or Obliqued

Towing Angle

Starke, B. van der Ploeg, A. and Raven, H.:

Free-surface Viscous Flow Computations for KCS and 5415 Models

Using the PARNASSOS Code

Eça, L., Hoekstra, M. and Toxopeus, S.L.:

Calculation of the Flow around the KVLCC2M Tanker

Suzuki, K., Hirakawa, R., OjimaA. and Kamemoto, K.:

Calculation of Viscous Flow around Ship Models by Means of

Advanced Vortex Method

Hirata, N. and Kobayashi, H.:

Ship Flow Computations for KVLCC2M

Hino, T. and Sato, Y.:

Ship Flow Computations by Unstructured Navier-Stokes SolverSURF

Kume,K., Hasegawa, J., Tsukada, Y., Fujisawa, J., Fukasawa, R. and Hinatsu, M.:,

Measurements of Hydrodynamic Forces, Surface Pressure and Wake for

Obliquely Towed KVLCC2M ModeL and Uncertainty Analysis

SUMMARY

The flow around the double-body KVLCC2M tanker is:computed ingrids with H-O topology. First the zero-driftangle case is considered Two turbülence models are used: Menter'sone-equationmodel and Kok's

ver-sion ofthek - wmodel A thorough uncertainty anal-ysis based on solutions on 8 grids of various density

is carried out. In the second part of the paper the flow predictions for drift angles 3, 6, 9 and 12 degrees are discussed; Encouraging, results are obtained, but the relatively high level of uncertainty in theiprersure drag evaluation requires further attention.

INTRODUCTION

The calculations for the, KVLCC2M tanker hull

form were performed with the flow solver

PAR-NASSOS (Hoekstra & Eça, 1998), which is based on a finite-difference discretisationof the Reynolds-averaged continuity and momentum equations with fully-collocated variables and discretisation. The equations are solvedwith a coupledprocedure,

retain-ing the continuity equation in its original form.

In PARNASSOS several eddy-viscosity

turbu-lence models are available. In a numerical calculation of a ship stern flow, the turbuléncemodel selection is

not only based on the quality ofthe predictions, but

alsoon the numerical robustnessandthe ability to

con-verge the solution, ie. reduce.the iterativeerror tothe desiredvalue.

Mostapplied in PARNASSOSis theone-equation

model proposed by Menter (1997), which leads to a

remarkably robust method andallows convergeüceof the solütion to machine accuracy in almost any case. However, several validation studies have shown that

the predictions of the flow field: in the bilge vOrtex region are not as good as the ones obtained with the k - w model. Therefore, we have also

perfomiedcal-culations for the zero-drift case using the TNT version

of the kw model:(Kok, 1999). The main advantage

of the TNT version when compared with the popular BSL ànd SST versions (Menter, 1994) is the absence of references to the distance to the Wall. The calcula-tions for thedrift cases were conductedusing Menter's turbulence model only.

Calculation. of the Flow around the KVLCC2M Tanker

L; Eça1, M. Hoekstra2 and S.L. Toxopeus2

Instituto Superior Técnico, Portugal

2 Maritime Research

Institute, Netherlands

Deift University of Technology, Netherlands

The Spalart correction to account for the effects

ofstreamwise vorticity, described in Dacles-Marianiet aL (1994), is adopted in both turbulence models. No

attempts have been made to add special features for modelling transition. So the basis turbUlence model acts as the transition model as welL The Reynolds

number is equal to 3945 x 106.

Ail computations

were performed using dimensionless quantities with

LppandU as the reference length and velocityscales.

COMPUTATIONALDOMAIN ANDGRID TOPOLOGY

All calculations described in this papér were

con-ducted for theünappendedthtill form.

Several grid topologies have been tested for the

calculation of the flow aroundthe KVLCC2M double model (Eça & Hoekstra, 2005). Theresúlts presented in this paper wereall obtained onstructuredgrids with H-O topology with someextra grid clusteringcloseto

the propeller plane. For the zero-drift case, a single-block calculation was conducted while for the

non-zerodrificase the domain wasdecomposed into

effec-tively two blocks. The six boundariesofthecomputa

tional domain are the following: the iñlet boundary is

ax = constant plane located upstream of the forward

perpendicúlar;theoútlet boundary is also a transverse plane downstream of the aft perpendicular; the exter-nal boundary isa circular or elliptical cylinder; the re-maining boundariesarethe ship surface, thesymmetiy

planeoftheship and the undisturbedwater surface;

Zero-drift case

Forthe zero-drift case, the inlet boundary was located at 0.25Lppupstreamoftheforward perpendicular. Thé outlet boundary was located at 0.25Lpp downstream

of the aft perpendicular. The radius ofthe cylinder

defining the external boundary was 0.1 8Lpp. Eight geometrically similar gilds have been gen-erated with in-house codes (Eça, Hoekstra & Windt, 2002)for theestimation of the discretisation error. The

variation in the number of grid nodes in the stream-wise, n, normal, n0 and girthstream-wise, nc directions is

Figure 1: Gridat botiñdariesofthecomputational

do-main.

presented in Table 1, which includes also the maxi-mumy obtained at the firstgrid nodeaway from the waIl(y) with Menter's one-equationmodeL Figure 1 givesan impression ofthe(coarsened) point

distribu-tion on the boundaries of the computadistribu-tional domain.

Table 1: Number of gridnodesand y at the first grid node away from thewall.

Non-zero drift cases

The flow around the hull at non-zero drift angles has no port-starboard symmetry and the computational do-main must be extended'to cover the port side as well. Furthermore, alarger dowainisrequiredin order to in-corporate the drift angle. On each side of the dOmain

thegridconsiststof an inner block andan outer block, see Figure 2. The innerblock is the same for all yaw anglesandthe outer blockcan deform toallow forthe

drift angle of the ship Therefore grids for various drift

anglescanbe madeefficiently.

The inner block is generated with a number of

cells similarto the grids as usedfor the zero-drift case.

Based on early calculations (Toxopeus, 2004),. grid clustering at the propeller plane and the bow of the

ship was applied to resolve thegradients of the flow at these locations more accurately.

To incorporate the drift angle of the ship, the in-nerbiock is rotated around the vertical zaxis over the desired yaw angle. Then the outer block is generated

aroundthe innerbiock. Thecell stretching used in the

inner block is automatically appliethto the outer block

as well. lt wasdecidedto have

matchinginterfacesbe-tween the blocks sothattheinner and Outer blocks can be merged. The sizeof the outer blocks is chosen such that the rotated inner block can smoothly be

incorpo-rated in the outer grids This means that increasing drift angles will result in wider domains. The sizeof thedomainisbasedonthe assumption that a solverfor

potential flow isUsedto calculate thevelocities in the inflow and external planes. Before starting the

calcu-lations, theseparateblocks are mergedinto one block forthe portside of the ship andanother block for the

starboard side of the ship.

Figure 2:

Inner and outer blocks (coarsened) at

120 drift angle.

The number ofnodes in the gridsused for the drift casesarepresentedin Table 2, Which includes also the

maximum y+ value for the cells adjacent to the hull

that was obtained during the calculátions. A positive

drift angle ß correspondsto:theflowcomingfrom port

side. Note thatalsora calculation withzero drift angle

was conducted with a grid similar to the grids used

for non-zero drift in order to be able to determine the

relation between the drift angle and integral or local

variablesconsistently.

Table 2: Number of grid nodes andy for drift cases.

Table 3 presents the sizes of the computational domains for the drift case calculations. For

increas-ing drift angles, the computational domain size is

in-creased in order to be able to incorporate the inner

block in theouter deforming mesh. Grid n

n,jn

4-01

561 113

57 24

02

481 97 49 0i27 G3 441 89 45 0.26 G4 401 81 41

30

G5 361 73 37

034

G6 321 65 33 0.37 G7 281 57 29

046

G8 241 49 25 0.59

ß

n n nodes y24 0° 449 81 45 1.6 x 106 0.32 30 _{449 95 2 x 45}

_{3.8x 106 40}

6° 449 95 2 x 45 38 X 106 0.55 90

_{449 952x45 38x106}

₀₆₉

12° 449 95 2 x 45 3.8 X 106 0.80

Table 3:. Size of'computationaî domain for drift cases.

BOUNDARY CONDITIONS

At the ship surface the no-slip condition is applied di-rectly and the normal pressure derivative is assumed to be zero. The undamped eddyviscosity, the variable in Menter's one-equationmodel, vanishes at a no-slip

wall. With thepresentformúlation' of thek - amodel

Kok and Spekreijse,:2000), alltthe turbulent quantities

are zero at asolidwall.

Symmetry conditions are applied at the

undis-tUrbed Watersürface and on the ship symmetry plane

(for the zero-drift condition). At the inlet boundary,

the velocityprofiles areobtained from apotential flow solution, which also determines the tangential velocity

components and the pressure at the external bound-aiy. At the outlet boundary, streamwise diffusion is

neglected and the stresmwisepressure!derivative isset

equalto zero.

For the drift cases, the lift generated by the hull

form is modelled in theipotential flow solution by

ap-plying a vortex sheet on the symmetry plane of the

ship. At the stem of the ship, the Kutta condition (the flow leaves the trailing edge smoothly) is

ap-plied, which allows thesolution of the unknown

vor-tex strengths on the sheet. Since the only purpose of

the potential flow solutión is to set the boundary

con-ditions for the viscous flow solution at the inlet and

external boundaries, vortex shedding from thethilge of the ship is omitted.

UNCERTAINTY ESTIMATION

We only deal with the discretisation error, assuming

the iterativeandIround-off errors to be negligible. The uncertainty, LI0, of any integral or local floW quantity is estimated witha procedure based on a least squares root version (Eça and Hoekstra, 2002) of the Grid

Con-vergence Index (Gd), proposed by Roache (1998).

Two basic error estimators are involvedin the present

procedure for uncertainty estimation: the

extrapola-tion to grid cell size zerO performed with Richardson extrapolation, ERE, and the maximum difference be-tween the data pointsavailable,AM.

We have collected some experience with several variants of uncertainty estimation procedures (Eça and

Hoekstra, 2004). In the present calculations we have adopted the following options:

o Determine the observed order of accuracy, p,

from the available data.

o For 0:95 p < 2.05, U0 is estimated with the

GCI andthe standard dèviationUj,, of the fit:

=

l'.25ô +U111.

o For 0<p< 095,thesame error estimate is made

but is then compared with the value of AM mut tiplied by a factor of safety of 1.25, so that U0 is obtained from:

Lío =min(l.25+Uf,,L25AM).

o Forp

2.05, =max( I .255k + Uf,,,! .25AM),

where 5F is also calculated in the least squares root sensewith p

=

2.

If monotonicconvergence is not observed, U0

=

3AM.

RESULTS 'FOR ZERO DRW1'

Numerical Convergence

In 'the' present calculations we have adopted as con-vergence criterion the redUction of the maximum dif-ference betweenconsecutive iterationsofthethree ve-locity componentsand of the pressure to 10 12, which is equivalent tomachine accuracy.

200

400 600

Iteration

800

Figure 3: Convergence history on 281 x 57 x 29 grid.

Unfortunately, we were notable to satisI'this cri-teria for the 8 grids With the TNT k - wirnodel. IO the

grids GI, G3 and G5 the convergence stagnates at a

level that does not allow to neglect the iterativeerror andso we have dropped the results obtained inthese 3

grids. The convergencehistories obtained for theG7

grid with the two turbulencemodels are illustrated in

Figure 1 /3 inlet [Lpp]: outlet [Lpp] width H Lpp] depth ELppJ 0°

_-073

092

H 0.18

18

3° -0.74 0.93 0.42 0.36 6° -0.75 0.94 H 0.49 0.36 90 _{-0.76 0.95} 0.55 0.36 120 _{-0.76 0.95}

_06l

_0:38

ResistanceCOefficients

Thepredicted values of total.resistance, C, friction re-sistance,'Cp, and pressure resistance; Cp, arepresented

in Table 4 with the estimated uncertainties. These force components have, been madè non-dimensional

using pU2Sowith S0, the wettedsurfaceat rest.

Table.4: Predicted resistance coefficients and theires-timateduncertainties (a=k-w,.b=Menter). 3.68 3.64 3.6,

k

C.)

35

O.8 3.52 3.48o 1.6

12

0.4 p 4.l.p=2 o k-w U- 0.072 p-0.8 .0 Mentez h/h11.5 o k-w U- 0.344 p-O.4' .0 Meiner 0.5' 1.5. 2

25

h/b1

Figure4: Convergence of the friction and pressure re-sistance'with grid refinement.

RESULTS FOR DRIVf ANGLES 'In both cases, the uncertainty of Cp is clearly

larger thanthe one of CF. The esti'mateduncertainties

are much larger for thek co modebthan forMenter's

one-equation model. As illustratedin Figure 4, theob-served order of accuracy is below I' for the 'solutions

obtainedwith the k wmodel,,whereas the p obtained with Menter'staodel1 is4.7for CF' and 2 forCp.

'The fit to Cpptotted in Figure 4 is'made'with,p2.

2.5

Velodty field at the'pròpeller'plane

Theselection of the turbulence model has a significant effectonìtheprediction of the velocity field at the

pro-peller ;plane The isolines of axial velocity obtained

with thetWo turbulence models and the transverse ve-locity fields are.plottedinfigure 5.

0.2U '02 .04 '004 'O" 'tOO 404 yL

Figure 5: Velocity field

at the propeller plane

(top:axial velocity,bottom: transverse velOcity).

There is a more pronounced 'hook shape' in the k - w solütion 'than in .the prediction with Menter's

model. There are alsodifferences' in the bilge vortex, specially inthe lower, part closetothe symmetry plane.

Figure6: Uncertainty intheaxial'velocity fieldàt he

propeller plane..

An interesting result is the uncertainty of the ax-ial velocity field prediction at the propeller plane The values of U.áre below00i 'for. most ofthe field. How-ever, atthebilge vortex region the maximum values of

U reach levels above 0l with 'the k w predictions

exhibiting the largest values of uncertainty

Numerical Convergence

In the calcúlatioñs of the drift.cases a reduction of the maximum difference in pressure between consecutive

iterations' to 5 x l05wasadoptedas the convergence

criterion. 1nthesecases' there.is noattempt toestimate

the discretisationerror. Therefore, thereis no need to

reduce the'iterative error tomachineaccuracy.

C -ic Cp Cp

x'103' x103 xl 0 xl'03 Xl0 XIO

a 4.454 0.416 3578 0.072 0.876 0.344

IntegraFCoefficlents

In this section, the forces and moments presented are

madenon-dimensional using respectively pU2LppT

and pU2L,T, in accordancewith specificationsfor

the CFD Workshop 2005. Table 5 presents the results

of thecalculatiòns for each drift anglè ¡3 as well as a

comparison between the calculated variables and the

measured ones. CX is the longitudinal force, CI' the

transverseforce and C'N the yawingmomeñt with' re-spect to theorigin of the xyzcoordinatesystem, which

is located at station 10.

The results for zero drift angle. are comparable to the results as presented in

Table 4 (C =4.19 x io-i, CF = 3.50 x i- and

Cp = 068x l0-).

Table5: Integral variables.

Except maybe for the results for 3° drift angle,

the. predictions obtained by the' calculations are very promising. In almost all cases the prediction.is within 10% from themeasurements. Noteworthy is the con-.sistent underprediction of the transverse force, while

both the longitudinal force and yawing moment are

predicted quite accurately. Figure 7 presents the

yaw-ing moment as a function ofthe drift angle More

results can be found in the proceedings of the CFD

Workshop 2005.

Compared to the results presented for earlier cal-culations for the KV:LCC2M ata drift angle, see

lOx-opeus (2004), the grid refinement at the bow and

stern has improved the prediction of the longitudinal force The earlier calculations were conducted with

an equidistant grid with 251 nodes in longitudinal

di-rection along the hull surface. For the present calcu-lations, the grid was non-equidistant with 342 nodes along thèhuil surface. The improvement in the pre

diction is mainly caused by the change in the

predic-tion .of the pressure component CXì, siñce the fric-tion component CXF is practically equal for the two

z

C., 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000 -0005 -0.0103 _{o 3} 6 beta .9 12

Figure 7: Yawing moment against drift anglà.

(exp: open circles, cfd: solid line)

different grids, see Table 6 and the results for zero drift angle presented in Table 4. The pressure

com-ponent however decreases considerably for the non-equidistant grid. Thisfinally results in a better predic-tion of the longitudinal force for the non-equidistant

grid.

Tàblà 6: CXcomponents fordifferentgrids.

Also for the transverse force CY the difference in pressure component determines the difference in the

total transverse force, see Table 7. Furthermore, the

friction component is an order of magnitude smaller than the prcssúre component and therefore is almost negligible in the total force. However, when

compar-ing the measurements with the results

forthetwodif-ferent grids it is seen that in this case the finer grid

does not lead tota better prediction. A grid refinement study should'be conducted'to verif' whether sufficient

grid nodesin girth-wisedirectionareapplied.

Table 7: CY components for different grids

Side forcedistributlon

To understand the manoeùvrability Of ships and to

be able to generate reliable generic mathematical ma-noeuvringmodels, the longitudinal distribution of the 15 p

cfd

CX.

xl02 CY x102 CN xlO2 CX x'102 CY xl02 CN x'l02 -1.77 -091 -0.76 -1;80 -1.25 -0.71 00 _{-1.74' 0 0 -1.76 -0.00 -000} 3° -1.77 0.91 0.16 -1.78 1.26 0.61 60 _{-1.79 2.26 1.46 -1.77 2.56 1.39} 90 _{-1.79 4.23 201 -1.73 4.55 1t94} 12° -1.78 6.43 2.53 ' -1.75 7.08 2.54 (3 grid CXp CXF CX x'l02 x102 x102 0° equidistant -0.433 -1.455 -1.889 non-equidistant -0.283 -1.458 -1.741 3° equidistant 0:5l9 -1.457 -1.976 non-equidistant -0.299 - 1.468 - 1.767 /3 ECX ECY CN - -3° -2% -27% 8% 00 _l% -30 _{-1% -28%} 25% 6° 1% -12% 5% 9° 4% -7% 3% 12° 2% -9% -1%

/3 grid CYp CYF CI'

xlO2 xlO2 x102

3° equidistant 0.940 0.049 0.989

sidefòrce is Of interest. Therefore, thepredicted longi-tudinal distribution of the lateral force has been com-pared to the experimental values to determine the

ac-ctiracy ofthepredictions, seeFigure 8.

The comparison shows that although the sideforce according to Table 5 issystematically underpredicted, the predicteddistributionis very close to themeasure-ments and therefore the accuracy of this prediction is

judgedtobe good.

05

0.4 0.3 02 0.1 0 'j oo.o o dV dV o dV dV xp) 6' cId) 6' exp) 12' cfd)12° W;

Figúre8: Side:force distribution.

CONCLUSIONS

At zero drift angle, we have performed calculations with two eddy-viscosity models: the one-equation

model proposed by Menter and the TNT version of

the

k - w

model. Grid refinement studies have been performed with bóthmodels to estimate thenumerical

uncertainty of the predictions. The results show that

the uncertaintyof the pressure resistancecoefiucient is at least one order of magnitude làrger than the uncer-tainty of the friction resistance coefficient. The level of uncertainty of the selectedflow quantities depends

on the turbulence model choice. The

k w

model

leads to higher levels of uncertainty than the Menter model. However,, the comparison of the predicted ve-locity fleldsat thepropeller planeshows a better

agree-ment of the

k - w

predictions with the experimental results.

For the non-zero drift cases, which werealIcon-ducted using Menter's.oneequation model, the com

pliance of the predictedresults With themeasurements

is good and within 10% from the measurements for most cases. Based on a variation of the grid density and grid node spacing it was found howeverthat the

uncertainty in the pressure component of all integral

forces is large. A grid sensitivity study is therefore

recommendèd in orderto verif' the calculated results

0.4 06

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k - w

Turbulence Model", NLRTP-99295, July 1999, National Aerospace Laboratory,

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0.16

-0.4 -0.2 0 0.2