Verification and validation of calculations of the viscous flow around KVLCC2M in oblique motion

Date Author Address

March 2005 SI. Toxopeus

Deift University of Technology

Ship Hydromechanics Laboratory

Mekéiweg 2, 26282 CD Deift

TU De Ift

Deift University of Technology

Page lof 1/1

Verification and' validation of calculationsof the

viscous flow around KVLCC2M in oblique motion.

by

S.L. Toxopeus

Report No. 1425-P

2005

5th Osaka Colloquium "On Advanced Research on Ship Viscous Flow and Hull Form Design by EFDand.CFD Approaches, Osaka Prefecture Institute, Osaka, Japan

Pre-Prints

5th

Osaka Colloquium

On Advanced Research on Ship Viscous Flow

and Hull Form Design

by EFD and CFD Approaches

WI

_-OC'O5

1ÎvOw2ca'CoUoqMLv-.n'

Pre-Prints

5th

Osaka Colloquium

On Advanced Research on Ship Viscous Flow

and hull Form Design

by EFD and CFD Approaches

Osaka Prefecture University, March 14-15, 2005

Organized by

5th

_{Osaka Colloquium Organizing Committee}

Supported by

The Kansai Society of Naval Architects, Japan

The Society of Navat Architects of Japan

The West Japan Society of Naval Architects, Japan

The National Maritime Research Institute, Center for CFD Research

mIR- Hydroscience and Engineering

Italian Ship Model Basin (INSEAN)

Table of Contents

On the Influence of Grid Topology on the Accuracy of Ship Viscous Flow Calculations

L Eça,MHoekctra

Simulation of the Flow around Complex Hull Geometries by an Overlapping Grid Approach

R Muscari,A DiMasclo

Recent Progress in Unstructured Navier-Stokes Solver for Ship Flows

A Vorticity-Velocity Formulation for Numerical Simulations of Viscous Flows around Impulsive

Started Bodies

Seung-Jae Lee, Kwang-Soo Kim, Jung-Chun Suh

...- ...27

Computation o Viscous Flows around a Two-Dimensional Oscillating Airfoil Using a Finite Volume

Method for the Solution of the Incompressible RANS Equations

Pyung-Kuk Lee, Hyoung-Tae Kim ...-

...37

Numerical Analysis of Mass Conservation Property of the L2 Least-Squares Finite Element

Methods for Stokes Equations

Shin-.Jye Liang, Yìh-Jena Jan

- ... ... ...43

Microbubbles A Large Scale Model Experiment and a New Full Scale

Experiment-Y Kodama, T Takahashi, M Makino, T Hori, H Kawashima, T Ueda, T Suzuki, Experiment-Y Tod

KYamashita

..., 55

The Proposal of a New Friction Line

T Katsui, If A.sai, Y Himeno, Y Tahara

... -61

Free-Surface RANSE Simulations 1t Moving Bodies with Adaptive Mesh Refinement

A.. Leroyer A. Hay, P Queu:ey, M. Visonneau .-69

RANSE with Free Surface Computations around Fixed and Free DTMB 5415 Model, in Still Water

and in Waves

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

79

Vorticai and Thrbulent Structures and Instabilities in Unsteady Free-Surface Wave Induced

Separation

M Kandasaniy, T Xing. R. Vilson, F Stern ...89

Slamming Experiments on a Ship Model: Forced Motion Tests on Calm Water

J-M Rousset, B Pettinotti, O Quillard, J-L Toula,astel, P Fer,ant

103

Determination of Optimum Hull of Ice Ship Going

Jaswar...- -

-- 109

CFD-Based Multi-Objective Optimization of a Surface Combatant

Y Tahara, D. Peri, E F Campana, F Stern ...117

A Comparison of Global Optimization Methods with Application to Ship Design

CFD Prediction of the Flow around a Submarine.Manoeuvring in Open and Confined Water

R Broglia, A. Di Mascio, F Mandolesi

...145

RANS Computation of Turbulent Free Surface Flow around a Self-Propelled LNC Carrier

Jin Kim, Il-Ryong Par1c Kwang.Soo Kirn, Suak-Ho Van

...155

Experiments and Numerical Modelling of the Flow around the KVLCC2 Huilform at an Angle of

Yaw

Ri Pattenden, SR.. Turnock M. Bissuel, C Pashias

.. ...-1b3

Verification and Validation of Calculations of the Viscous Flow around KVLCC2M in Oblique

Motion

S. L Toxopeus

LES Simulation of the Flow Field around the KVLCC2 Model Hull.

U Svennberg. R Bensow ...-

- - 181

Numerrical Simulations of Flows around Submarine under Full Surface and

Submerged

Conditions.

N Zhang, H C. Sheng, H Z. Yao, Q. X Gao

191

The Undulatory Structure of the Euler-Lamb and Na'vier Stokes Equations and the Implication of

This Structure In the Lubrication Theory and the CFD Numericál Method

A.. Va.silèscu, M Vasilescu .

VERIFICATION AND VALIDATION OF CALCULATIONS OF THE

VISCOUS FLOW AROUND KVLCC2M IN OBLIQUE MOTION

S.L. Toxopeus

Maritime Research Institute, Netherlands / Deift University of Technology

ABSTRACT

Viscous-flow calculatiOns have been condúcted for the KVLCC2M hull form in oblique motion. Several

different drift angles were considered inthis study. For one drift angle1 a detailed grid-dependency study was carried out in order to obtain theuncertainty in theresults. lt is observed that in order to arrive at reliable results, special attention must be paid to the gridding of the computational domain To validate the results a comparison with integral as well as field variables available from measurements is made The paper addresses the methods

used and a detailed discussion about the accuracy of the results is presented. Very encouraging results are obtained, but the relatively high level of uncertainty 'in the evaluation of the pressure components requires

further attention.

INTRODUCTION

Table I: Main particulars of KVLCC2M

Before results of viscous-flow calculations can be

used practically in design studies, the uncertainty and

accuracy of the results for similar cases should be

known. Otherwise, conclusiOns based on erroneous

results might be drawn, resulting in sub-optimal

designs. Therefore, demonstration of the capabilities of viscous-flowsolvers fora wide range of ship types

is required.

During the Tokyo CFD Workshop 2005, participants were invited to conduct calculations for a full-block tanker hull' form, the KVLCC2M, in steady

manoeuvring motión. As part of the work for this'

workshop, an extensive series of viscous-flow

calcUlations has been condúcted for the KVLCC2M hull form in oblique motion: Drift angles ranging up to 12° were considered in this' study. Forthe 12° drift

angle case, a detailed grid-dependency study was conducted in order to obtain the uncertainty in the

results. Additionally, the results have 'been' compared to experimental data from Nt'4R1 for'validation.

PARTICULARS OF THE SHIP AND

TEST CONDITIONS

The hull form under consideration is the' KVLCC2M. The particulars of this' hull form are presented below, taken from' the website of the Tokyo CFD Workshop

2005' (www.nmri.go.ip/cfdlcfdws05):

The measurements were carried out with the model 'restrained from moving in any direction relative to the carriage Bilge keels, rudder and propeller were

not present during the model tests and were therefore not modelled in the calculations.

The calculations were conducted with an undisturbed water surface, i.e. neglecting the generation of waves.

The 'Reynolds number in the calculàtions was

3.945x106, corresponding toa tbll scale ship speed:of

15:5 knots.

NUMERICAL PROCEDURES

Coordinate system'

The origin of the right-handed system' ofaxes used in

this study is located at the intersection of the water

plane, rnidshipand centre-plane, withx directedaft, y

to starboard and z vertically upward. Note that all coordinates given in this

paper are made

non-dimensional with unless otherwise specified. All velocities are made' non-dimensionál with the

Designation Model sca1e(1:64:4) Full scale

Length 497m 320.0 m

Beam B 0.9008 m ,, 58.0in

Draught T 0.323'! m 20.9 m

BlockcoefficientCa 0.81 ' 0.81

undisturbed velocity U. The forces and moments,

presented in this paper are given relative to the origin

of the coordinate axes, but in a right-handed system

with the longitudinal force directed forward positive

and the transverse force positive when directed to

starboard.

A positive drift angle corresponds to the flow

comingfrom port side.

Flow solver

The càlcùlätions presented; in this paper were performed with the MARiN in-house flow solver

PARNASSOS, see. Hoekstra 'and Eça [1] and

Hoekstra [2].

This solver is

based

ofl a

finite-difference discretisatiòn of the Reynolds-averaged

contiñuity and momentum equations with

fully-collocatedvariables anddiscretisation. The equations

are solved

with a

coupled procedure, retaining the continuity equatión in its original form. The goverhing equations are integrated doWn to thewall,

i.e ño wall-flinctionsare used.

In PARNASSOS several eddy-viscosity turbulence

models are available.

In a

numerical calculation of the flòw around a ship, the turbulence model

selection

is not

only based on the quality of the

pEedictións, butalso on the numerical robustnessand the ability to converge the.solution, i.e. reduce the.

iterativeerror to thedesiredvalue.

Theoneequation model proposed by Menter ['3] is

the most commonly used turbulence model

in

PARNASSOS. This model leads to a remarkably

robust method and allows convergence of the

solutionto machine accuracy inmany cases.

The Spalart correctioñ to. account for the effects of

stream-wise vorticity, described in Dacles-Mariani et

al. [4],

is adopted in the turbulence model. No

attempts have been made to add special features' for

modelling transition So the basis turbulence model acts asthe transition model aswell.

Procedure for Uflcertainty estimation

The uncertainty, U, of any integral or local' flow

quantity4) is estimated; with a procedure based on a

least squares root version from Eça 'and Hoekstra [81

of the Grid Convergence Index (Gd), proposed by

Roache [9.] Two basic error estimators are involved

in the present procedure for uncertainty estimation:

the extrapolation togrid cell size zero'performed with

Richardson extrapolation, &i; and the maximum

difference'betweenthe data points availabk,AM

Ignoring the round-off and iterative errors, the error

estimation 6nn obtained by Richardson extrapolation

is defined as: = 4)o 'ahi'. In this definition,4),

is the numerical solution of any local or integral

.scalar quantity on a given grid i, 410 is the estimated

exact solution, a is

a constant, h, identifies the representative relative grid cell size (or relative step

size) and p is the observed order of accuracy. The

relative step size h1 is calculated using (n1 -I )/(n1- I),

withni the number of nodes in stream-wisedirection for the finest grid, and n1 the number of nodes 'in

stream-wise direction for grid i. The typical relative step sizeof i refers thereforeto the finest grid.

Based on

experience with several variants of

uncertainty estimation procedures and on the

outcome of the Workshop on CFD Uncertainty

Analysis, see Eça and Hoekstra [1'OJ, the following options Were adopted 'in thepresent calculations:

Determine the observed order of accuracy, p,

from' the available data.

s _{For 0.95 <p <205, U0 is estimated with the GCI}

and thestandarddeviatioñU of the fit:

U0 =1.25 Ö +U0.

FOr O <p <095, the sameerror estimate is made

but

is then compared with

the

value of

AM, multipliedby afactor ofsafety of1.25,so that U$

is obtained from:

U0=min( I.25 8RE+

U, 1.25

AM)

For p

2.05,

a' new error estimate ô

is

calculated 'in the least squares root sense with

p=2. The uncertainty then follows from:

U0 =max(1.25 5m + Ufl,, 1.25AM).

If monotonic convergence is not observed,

U0 =3 AM.

Based on the uncertainty analysis, it is assumed 'that

the numerical solution 4)o for zero step size will be

boundwith 95% confidence by the interval: 4 -U0 <

4) <4 +

Computational domain and grid topolOgy

Several grid topologies have, been used for the

calculation of the flow around the KVLCC2M double model [5]. The results presented in thispaperwereall obtained on structured grids with H-O topology, with

extra grid clustering close to the bow and propeller

plane.

For the zero-driftcase a single-block calculation was

domain was decomposed into effectively two blocks. The six boundaries of the computational domain are the following: the inlëtboundary isa transverse plane

located upstream of the forward perpendicular, the outlet boundary is a transverse plane downstream of

the aft perpendicular; the external boundary is a

circular or elliptical cylinder; the remaining

boundaries are the ship surface, the symmetry plane

of the ship or coinciding block boundaries and the

undisturbed water surface.

The flow around the hull at non-zero duft angles has

no port-starboard 'symmetry and the computational domain must be extended to cover the port side as well. Furthermore, a larger domain is required in order to incorporate the drift angle. On each side of

the domain the grid consists of an inner block and an outer block, see Figure 1. The inner block is the same for all yaw angles and the outer block can deform to

allow for the drift angle of the ship. Therefore grids for various drift angles can be made efficiently. Use is made of an in-house grid generator, see Eçaet.al.

[6].

Figure 1': Inner'and outer blocks (coarsened)at 12° driftangle..

The inner block is generated with a number of cells similar to the grids as sed by Eça and Hoekstra [5] for thezero-drift case.

Based on early calculations by Toxopeus [7] grid clustering at the propeller plane and the bow of the

ship was applied to resolve the gradients of the flow at these locations moreaccurately.

To incorporate the drift angle of the ship, the inner block is rotated around the vertical z-axis over the

desired yaw angle. Then the outer block is generated around the inner block. The cell stretéhing used in the innerblock isautomatically applied to the:oüter block

as well. lt was decided to have matching interfaces

between the blocks so that the inner and outer blocks

coUld be merged. The size of the outer blocks is

chosen such that the rotated inner block can smoothly

be incorporated in the outer grids. This means that increasing drift angles will result iñ wider domains The size of the domain is basedon the useofa.solver for potential flow to calculate the velocities in the

inflOw and' external planes.

Before starting the

calculations, the separate blocks are merged into one

block for the port side of the ship and another block

for'the starboard' side of the ship.

For each grid, the variation in the number of .grid nodes in the streamwise, normal and girth-wise (ne, nq and n) directions is presented in Table 2, which includes also the maximum y value for the cells

adjacent to the h Il, designated y2, that was obtained

during the calculations Note that also a calculation with zero drift angle was conducted in order to be

able to determine the relation between the drift angle and integral or local variables consistently.

Table 2: Number of grid nodes and Y2.

Table 3 presents the sizes. of the computational

domains for the drift case calculations. For increasing drift angles

the computational domain

size is

increased in order to be able to incorporate the inner:

block in theouter deforming mesh.

Table 3: Size of.computational domain.

For a drift angle of 12°, a series of geometrically

similär grids has been generated in order to

investigate the discretisatión error.

The grid coarsening has been conducted 'in all three

directions, 'For some of 'the

grids however, the

distance of the first node to the hull surface has been maintained in order 'to capture the velocity gradients in the boundary 'layer. Table 4 presents'the number of nodes and' y2 values for these grids.

D n n ' nodes Y2 0° 449 ' 81 45 16x106 032 3° ' 449 95 ' 2x45 " 38x106 0:40 60 , 449 95 2x45 38x106 0:55' 9° , 449 95 2x45 38x106 0.69 12° ' 449 95 2x45 38x106 0:80 p inlet ' . outlet ' L width depth 00 _{-0.73 0.92 2x0.18 0.18} 3° -0.74 0.93 2x042 0.36 6° ' -0.75 0.94 2x049 0.36 9° -0.76' , 0.95 2x055 0.36 12° -076 H, 0.95 2x0:61 0.38

Table4: Properties f grids for'uncertainty analysis.

For grid 5, it was unfortunately not possible to

converge the results until the required convergence criterion was reached Therefore the results for this

grid aredropped from further analysis.

Boundary conditions

At the ship surface the no-slip condition is applied

directly and the normal pressure derivative is

assumed to be zero. The undamped eddy viscosity,

the variable in Menter's' one-equation model, vanishes at a no-slipwall.

Symmetry conditions are applied at the undisturbed

water surface and on the ship symmetry plane (for the

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

velocity profiles are obtained from 'a potential flow

solution, which also determines the tangential velocity components and the pressure at the external

boundary. At the

outlet boundary, stream-wise

diffusion is neglected and the stream-wise pressure

derivative is set equal to zero.

For the drift cases, the lift generated by the hull form is modelled in' the potential flow solution by applying a vortex sheet on the symmetry plane of the ship. At

the stern of the ship, the Kutta condition (the flow leaves the trailing edge smoothly) is applied, which

allows the solution of the unknown vortex strengths

on the sheet. Since the only purpose of the potential

flow solution' is to set the boundary conditions' for the

viscous flow solution

at the

inlet and external

boundaries, vortex shedding from the bilges of the

ship is omitted.

RESULTS AND DISCUSSION

Numerical Convergence

In the calculations a reduction of the maximum

difference in pressure between consecutive iterations to 5*1 0 was adopted as the convergence criterion. It is assumed that this is sufficiently small compared to

the discretisation error and therefore the iteration

erroris ignored in the uncertainty analysis.

For all

cases, 'the adopted convergence criterion results in a reduction of the 'difference in the '(totál)

force and moment components between. consecutive

iterations of well below lx.lOE5.

Computing times

All computations except for 6° drift angle have been

conducted on a PC using, a

singlè Pentium 4

processor with 2.4 GI-Iz clock 'cycle frequency and I GB of internal memory. The calculations for 6° drift angle have been conducted on a SGI supercomputer and the computation times for this computer have not been recorded.

The'computing times required for the calculations are presented in Table 5.

Table 5: Computing times.

Uncertainty analysis

In this and following sections, the forces and

moments presented are made non-dimensional using respectively V2pU2LpT and V2pU2L2T, in

accordance with specifications for the Tokyo' CFD'

Workshop 2005. CX' is the longitudinal force, CY the

transverse force, CZ the vertical fòrce, CK the'

heeling moment, CM the pitching moment and' CN

rid 3 fl n,, n h, nodes

yf

1 12° .449 95 2x45 1.00' 3.8xIO 0.80 2 12° 409 87' 2x41 1.10 219x106 0.75 3 12° 361 81 2x37 1.24 212x106 0.62 4 12° 329 74 2x33, 1.37 16x106 0.71 5 12° 297 65 2x29 1.51 ' 11x106 0.94 6 12° 249 65 2x25 1.81 8Ax105 0.78 7° 12° 225 48 2x23 200 SOxlO 1.15 '8" :12° 177 41, 2x19 2.55 2:8x10 1.25 9°" :12° 145 33 2x15 3.11 1.4x10 1.73 10 12° 12'! 33 2x13 3.73 I0x10 132 '11' 12° 113 24 2x12 4.00 65x10 2.17

' Based on;grid! 1 coarsenedby 2x2x2

Based onigrid3, coarsenediby 2x2x2

'°° Based ongrid 5, coarsenedby 2x2x2

Based'ongrid6, coarsenedby 2x2x2

Based'ongrid 1, coarsenedby 4x4x4

Id D nodes ' iterations CPU time

t(s)

t/(nn)

xlÓ5 0° 1.6xlOb _{569 33178} 3.6 3° 38x106 549 130393 6.2 6° 38x106 ' - - -9 3.8x10 1175 266985 5.9 I 12° 38x.106 1885 343179 47 2 12° 2.9x.106 1251 151967 4.2 3 12° 2.2x106 958 98848 4.8 4 12° 1.6*106 1403 85910 3.8 6 12° 8.1xi0 794 38242 6.0 7 12° 5.Ox'i05 644 10543 3.3 8 12° ' 2.8x'I0 360 2238 2.2 9 12° 1.4xI0 329 1061 2.2 10 12° '1.Ox10 330 758. 22 l'I 12° 6.5x10 363 613 2.6

the yawing moment with respect to the origin of the

xyz coordinate system, which is located at station 10.

For a drift angle of 12°, the predicted values of the

friction (index f) and pressure (index p) components as well as the total force and moment coefficients are presented in Table 6 with the estimated uncertainties.

Based on an analysis of the results for each grid, it was decided to use the 6, 7 or 8 finest grids for the uncertainty analysis. The number of grids n5 used

depended on the scatter in the results for the coarsest

grids.

Table 6: Uncertainty analysis, 13=12°.

The absolute uncertainty in the pressure components

is larger than in the friction components. The

uncertainty in the longitudinal friction component is about one-third of the uncertainty in the longitudinal

pressure component. For the

other forces and

moments, the uncertainty in the friction component is

at least one order of magnitude smaller than the

uncertainty in the pressure component. Since most integral forces and moments are dominated by the pressure component, this results in relatively large

uncertainties in the overall forces and moments. In Figure 2 the friction component of the longitudinal force is graphically presented for the different grids. Although scatter exists, the results appear to converge

for a relative step size below 2.5. However, due to

scatter in the pressure component, convergence is not found for the overall longitudinal force coefficient.

0.0138 -0.014 -0.0142 -0.0144 -0.0146 -0.0148 -0015 -0.01 52 -0.0154 -0.0156 -0.01 58 0.074 0.072 0.07: 0.068 0.066 0.064 0.062 0.06 0.058 ° cfd

- p

1.5 - - -U2.1% D D o Quantity n8 U p CX 7 - 1.78x102 12.0% (2) CXf 6 1.57x1W2 1.54x102 2.1% 1.45 CXp 7 - -232x1113 50.0% (3) CY 7 6.67x102 6.43x1W2 5.6% 1.13 CYf 6 l.84x10 1.70x11r 13.4% 1.34 CYp 7 6.45x10 626x1112 4.8% 1.25 CZ 7 3.41x10 3.21x10' 4.7% 0.51 CZf 6 - 1.20x10 13.2% (2) CZp 7 3.39x10' 3.20x1& 4.7% 0.52 CK 7 - -3.07x10 10.3% CKf 6 2.16x10 1.74x10 12.9% 0.44 CKp 8 - 3.24x10 19.7% «) CM 7 3.94xIO2 3.86x102 6.1% (41 CMf 7 1.09x10 i.O8xi0 0.7% 1.71 CMp 7 - 397xIO2 9% (2) CN 7 - 2.53x10 14.8% (21 CNf 7 - -2.94x10 CNp 7 - 2.55x102 14.2% (2)

Oscil atory convergence

(2)

Monotonous divergence

(3)

Oscillatory divergence

0 0.5 I 1.5 2 2.5 3 3.5 4

relative step size

Figure 3: CY convergence with grid refinement,

13=12°.

In Figure 3, the convergence of the side force

coefficient with grid refinement is presented. lt ¡s seen that upon grid refinement, the estimated value

for CY (indicated by cfd) comes closer to the

experimental value (indicated by exp). Considerable

scatter is visible on the data and therefore it is not easy to establish whether data points are located in

the asymptotic range of convergence. This is typical

for this type of calculation, as already observed

previously by e.g. Eça et al. [10] and Hoekstra et al.

[11].

Looking at the yawing moment CN, the maximum

difference between the estimated values for all grids

is 5.1%. Because the difference between the estimated values is relatively small and scatter on the

data is found, monotonous divergence is found and extrapolation to zero step size could not be made.

This results in a relatively large uncertainty of 14.8%. Figure 4 shows however that the results on the finest

0.5 1 1.5 2 2.5 3 3.5 4

relative step size

Figure 2: CXf convergence with grid refinement,

grids are within 0.5% from the measured value. Even

the result for the coarsest grid is within 3.1% from

the measurement, which is very acceptable.

relative step size

Figure 4: CN convergence with grid refinement,

3= 12°. 1.0 0.8 0.6 0.4 > 0.0 std. 1,1.1.00 - - - . dd:h1.1.10 std: 1,1.1.24 std: 1,1.1.37 cfd:h1.1.81 eep:.I2 0.2 -0.050-0.025 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.2 0.1 -0.1 cfd:l,l.1.80 - - - . std:h1.I.10 cOd: 1,1.1.24 cOd: 111.1.31 dd:h1.1.8l esp: 9.12 -0.2 -0.050-0.025 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0. 75 0.4 0.2 0.0 -0.2 cOd: 1,1.1.00 - - - . dt 1,1.1.10 cOd: ht1.24 std: 1,1.1.37 std: hl1.B1 asp: il.12 -0.4 -0.050-0.025 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 y

Figure 5: Grid dependency for p=12°, WAKE I plane, z=-0.05.

To further veri1' the results, the velocities along a horizontal cut located behind the propeller hub are

compared for several different grid densities. This cut

was located in a plane (designated the WAKE I

plane) perpendicular to the flow at a distance along the longitudinal axis of the ship of 0.48L behind

midship and at a vertical position of z=-0.05. Figure 5

presents the axial, transverse and vertical velocities obtained from the results of grids I through 4 and 6,

together with the experimental results.

In these graphs, it is seen that upon grid refinement

the results in general come increasingly closer to the measurements. Additionally, the differences between two successive grids reduce upon grid refinement.

0.00 -0.05 -0.10 -0.16 -0.20 -0.25 -0.30 -0.35 -0.40 -0.45 -0.50 10 -0.08 -0.06 -0.04 -0.02 0.05 0.00 -0.05 -0.10 e -0.15 -0.20 -0.25 -0.30 -0.301 std: h1.1.00 -. - - - cOd:h1.l.10 cOd: 111.1.24 cOd: 1,1.1.37 e.-p.12 0.00 0.02 y 0.04 0.060.08 0.10

Figure 6: Pressure at hull surface, x-0.4, =l2°.

std: 1,1.1.00 - - - . dd:Id.1.10 cOd: 1,1.1.24 dt 111.1.37 o a.pP12 : lO -0.08 -0.06 -0.04 -0.02 0.00 y 0.02 0.04 0.06 0.08 0.10 Figure 7: Pressure at hull surface, x"0.4, 3°12°. A further investigation is made of the convergence of

the pressure on the hull at two different locations:

x-0.4 and x0.4. For x-0.4 (bow), see Figure 6, it

is seen that only marginal differences exist between the different grids. Except for the location at which

the vortex generated at the bow leaves the hull

(approximately at y=0.012) no significant differences exist. This indicates that for the flow around the bow

the discretisation is sufficiently dense for the grids

selected for the comparison.

For the pressure at the hull surface at x=0.4, see

Figure 7, the differences

are more pronounced.

0.029 0.027 0.022 0.021e 0.028 0.026 0.025 0.024 o o o o 0.023 * exp o cfd - - -U 14.8% 0.5 1 1.5 2 2.5 3 3.5 4

Especially at the position of the separation of the

vortex generated at the stern (at y=O.O1 2) differences

between the successive grids are visible. Also more to the starboard (leeward) side, differences between the coarsest grid in the graph (grid 6, h, = 1.81) and

the. finer grids appear The resülts from grid 6 fail to captüre the strong gradients in the pressure

distribution

Finally, the change in the longitudinal distribution of

the side force upon grid refinement is examined.

Figure 8 shows that once again the results on the

finest grid.approximate the experimental results best.

At the bow and midship region (-0.6 <x <0.2), the.

difference between the solutions at various grid

resolutions is negligible but at the stern (x> 0;2), the

coarser gnds

in

the graph do not follow the

experiiiients . well as the finer .grids Similar to

Figure. 3, this means that the side forces on the

coarser grids are slightly underpredicted compared to the. finergrids. 0.5 0.4 03 0.2 0:1 o exp:3°12 cfd:hIl.00 - - - - cfd:hll.1O cfd hi°1.24 cfd bil.31 cfd hilBl

Validation of integral coefficients

Table 7 presents the results of the calculations for

each drift angle. J3 as well as a comparison between the calculated variables and the measuredones. In the

following sections, only the results found with the

finest grid will bediscüssed for 12° drift angle. Table 7: Integral values

.00253 0.100 0.080, 0.060 0.040 0.020 0.000 .00203 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.0o0 .0.005 00103

Table .8: Error estimates

6 9 12 15

12 15

4 12 .15

0 3 6

beta

Figure9: Integral valuesas a fttnction of drift angle

CX cfd CY CN CX exp CY CN x102 x102 *102 x x102

xi

-1.77 -0.91 0.76 -180 -1.25 -071 -1.74 0' 0 -L76 o.0o F -0.00 3 -1.77 0.91 . 0.76 -1.78 1.26 0.61 6° -1.79 2.26 1.46 -1.77 2.56 1.39 9 -179 4.23 2.01 -1.73 4.55 1.94 12° -1.78 6.43 2.53 -1.75 7.08 2.54 13 t cx 6cY CcN -3° -2% -27% 8% 0° -1% -3° -1% -28% 25% 6° 1% -12% 5% 9° 4% -7% 3% 12° 2% -9% -1% -0.4 -0.2 0 02 0:4 06 X

Figure 8: Side force distribution, °°12°

(bow to the left.of the figure)

From the uncertainty analysis, it is conclUded that a proper choice of the grid density may depend on the purposeof the calculations. A fine grid is required to arrive at accurate results. However, for comparative

purposes a coarser grid solution still cptures all

relevant flòw phenomena. In optimisation studies, a.

coarser grid might. be a good option to compare

different hull forms.

Even between the finest grids, some differences are

still clearly visiblè, in integral variables as well as in local field quantities. Other studies for zero drift, see

Eça and Hoekstra [5],

indicate the possibility to obtain a lower uncertainty when' the grid nodes in

girth-wise direction are stretched to the water plane. This will ;be.examined in furtherstudies.

3 o 6 9 3 o 0.000 -0.005 -0.010 X

u

-0.015 -0.020

Except maybe for the results for 30 drift angle, the

predictions obtained by the calculations are very

promising. In almost all cases the prediction error e (defined by e =ihcfd/exp - 1). is within 10% from the measùrements. Noteworthy is the consistent

underprediction of the transverse force, while both

the longitudinal force and yawiñg moment are

predicted quite accurately. Figure 9 presents. the

longitudinal and transverse forces and the yawing

moment as a function of the drift angle More results

can befoundin Eça et.al. [12] and in theproceedings

of the TòkyoCFD Workshop 2005.

Longitudinal Side force distributioll

To understandthemanoeuvrability of ships and to be able to generate reliable generic mathematical

manoetivring models, the' longitudinal distribution of the' side force is of interest. Therefòre, the predicted longitudinal' distribution of the lateral force has' been compared to the experimental valuesto determine the 'accuracy of the predictions, see Figure 10.

The comparison shows that although the side force

'according to Table 7 is systematically

'underpredicted, the predicted distributions are for both drift angles very close to the measurements. Apparently the physics of the force disfribùtion are captured well by the calculations and therefore the

accuracy of this prediction is judged tobegood. 0.5 0.4 0.3 0.2 0.11 0 o

o..

Figure 10: Side force distribution (bow to the left of the figure)

Comparison of field quantities

Experimental data are' available at a transverse cut

just behindthe propeller hub (in the WAKE I plane at

z=-0!05). The graphs

in Figure 11 provide a

comparison between' the experiments (markers) and

calculations (lines). Except for a small region at the

windward side

(002<y<0

for 3=12°) the calculations follow the measurements closely. Some

discrepancies are seen in the prediction 'of the axial Velocity between 0<y<0.02, but the transverse and vertical velocities in 'this region are matching the

experiments. The velocity profile in this area is

influenced by flow separation from the propeller'hub

and by the vortex shed from the stem, see also

Figure 7. 1.0 0.8 0.6 0.4 > 0.2 0.0 -0.2 -0.4 0O5O -o.o25 .OE 0.8 0.6' 0.4 > 0.2 0.0 -0.2 -0.4' 050 1'.o 0.8 0.6 0.4', > 0.2 0M -02 -0.4 °-.O50 oo25 0.000 0.025 0.050 0.075 oAoo 0. 25

o.óoo 0.025 0.o5o 0.075 o.ioo o:25

-fr'12

0.000 0.025 0.050 0.075 0.00 0:25 y

Figure l'i: Velocity in WAKE 1 plane, z=-0.05

For the present study the experimental dàta of the

wake field in the complete WAKEI plane has kindly been made available by NIVIRI. Figore 12 presents a

comparison of the axial velocity fields between the

experiments (dotted lines) and the calculations (solid' lines) for 00, 6° and 12° driftangle.

This figure shows that in most partsof the plane, the

viscous-flow calculations correspond well with the experiments. Even for 12° drift angle, the strength and position ofthe vortex generated at the starboard

bow (its centre is lòcated at y=0l 1, z=-0.03) is quite accurately captured' by thecalculations.

O 02 0.4 06

X

0.00 0.02 N 0.04 0.06 0.08 0.06 0.00 0.02 N 0.04 0.06 0.08 0.06 0.00 0.02 N 0.04 0.06 0.08

CONCLUSIONS

Simulations have been conducted of the viscous flow

around the KVLCC2M hull form at several drift

angles. For 12° drift angle, a grid convergence study was performed to study the uncertainty in the results.

The finest grid used in this study contained 3.8

million points.

It is shown that with the finest grid, no significant

changes in the flow field quantities occur, compared

to the second finest grid. Some integral quantities

however still vary upon grid refinement. It is shown

that differences between solutions on increasingly In the port side area (windward), discrepancies are

found

for the

12° drift case,

however. In the

calculations, the contour lines are straightened while

for the experiments, the contour lines retain their

hook-shape. Also just behind the propeller hub for 0°

drift angle, the hook-shape in the measurements

appears more pronounced than in the calculations.

This can be attributed to the turbulence modelling, as was also observed by Eça et al. [10]. A further study

using a k- turbulence model is proposed.

Overall, it

is concluded that the flow field at the

propeller plane is quite accurately predicted.

I

0.03 0.00 0.03 0.06 0.09 0.12 0.15

0.06 0.03 0.00 0.03 0.08

y

Figure 12: Axial velocity in WAKE1 plane, (solid lines: cfd, dotted lines: exp; top 3=0°, middle 3=6°, bottom 3=12°)

finer meshes tend to decrease. But especially the

pressure components of the forces appear sensitive to the grid refinement. It is concluded that possibly the number of grid nodes in girth-wise direction needs to be increased for improved accuracy.

Detailed comparisons with experimental data show that the main flow features are well predicted even when looking at discrete positions in the flow field. Qualitatively, promising results are obtained. For

practical purposes however, the accuracy of the

results should be improved. For the current

calculations, the predicted yaw moment is close to

the measurements but the

side force is

under-predicted. Reason for these discrepancies might be the neglect of the water surface deformation. Some

aspects of the calculated flow fields can also be

improved by choosing a different turbulence model. Both should be studied in future research.

ACKNOWLEDGEMENT

Part of the work conducted for this paper has been

funded by the Commission

of the

European

Communities for the Integrated Project VIRTUE. This project is

part of the Sixth Research and

Technological Development Framework Programme (Surface Transport Call).

REFERENCES

[I] Hoekstra, M. and Eça, L. "PARNASSOS: An

Efficient Method for Ship Stern Flow

Calculation",

Third Osaka

Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, May 1998, pp. 33 1-357,

Osaka, Japan.

Hoekstra, M. Numerical Simulation of Ship

Stern Flows with a Space-Marching Navier-Stokes Method. PhD thesis, Delft University of

Technology, Faculty of Mechanical Engineering and Marine Technology, October 1999.

Menter,

FR.

"Eddy Viscosity Transport

Equations and Their Relation to the k-s Model",

Journal of Fluids

Engineering, Vol. 119,

December 1997, pp. 876-884.

Dacles-Mariani, J., Zilliac, G.G., Chow, J.S. and Bradshaw, P. "Numerical/experimental Study of

a Wing Tip Vortex in the Near Field", ALlA

Journal, Vol. 33, September 1995, pp.

1561-1568.

0.06

[5] Eça, L., Hoekstra, M. "On the Influence of Grid

Topology on the Accuracy of Ship Viscous

Flow Calculations", 51F1

Osäka Colloquium on

Advanced CFD Applications lo Ship Flow and

Hull Form Design,2005, Osaka; Japan.

[61 Eça, L., Hôekstra; M, Windt, J. "Practical Grid

Generation Tools with Applications to Ship

Hydrodynamics", 8th Internal jonal Conference in Grid Generation in Computational Field Simulations,June2002, Hawaii, USA.

Toxopeus, S.L.. "Validation of Calculations of

the Viscous FloW around a Ship in Oblique

Motion", The First MARJN-NMRI Workshop,

October 2004, pp. 91-99.

Eça, L and Hoekstra, M. "An Evalúation of

Verification Procedures for CFD Applications",

24hl Symposium on Naval Hydrodynamics, July

2002, Fükuoka, Japan.

[91 Roache; Pi.

Verification and Validation in Computational Science. and Engineering,

Hermosa Publishers, 199&

[101 Eça, L. and Hoekstra, M. (editors).Proceedings of the Workshop on CFD Uncertainty Analysis,

Lisbon, October 2004.

Hoekstra, M., Eça, L., Windt, J. and Ràven, H. "Viscous FloW Calculations for KVLCC2 and KCS Models using the PARNASSOS Code".

Gothenburg 2000 Workshop on Numerical Ship Hydrodynamics,,2000.

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

'!Calculation, of the Flow around the KVLCC2M Tanker",GFD Workshop Tokyo,20.05.