Calculation of hydrodynamic manoeuvring coefficients using viscous-flow calculations

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Date Author Address

October 2006 Toxopeus, Serge

Deift University of Technology

Ship Hydromechanics Laboratory Mekelweg 2, 26282 CD Deift

Calculation of hydrodynamic manoeuvring

Coefficients using vlscous4low calculations

by Toxopeus, Serge

Report No. 1498-P 2006

PUblication: 7th International Conference on

Hydrodynamics, 6th October 2006, Ischla, Italy, ISBN:88-901174-9-4

TU De Ift

Deift University of Technology

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i

Conference Proceedings

7th INTERNATIONAL

_{CONFERENCE ON HYDRODYNAMICS}

4th_{- 6}_{th October 2006} Ischia - ITALY eynote Lectures ist of Authors ist of Papers echnical Session rganization omepage

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file://X:\html\preface.htm 2006-10-25

PREFACE _{Page 1 of 1}

PREFACE

This ICHD 2006 is the seventh International Conference on Hydrodynamics. The first one was held in

Wuxi, China, in 1994. Since then four Conferences have taken place approximately biannually in

_Hong

Kong, Seoul, Yokohama and Taiwan. After these five successful Symposia, the sixth ICHD 2004

was

moved for the first time out of the Asian Region to Perth, Australia. The ICHD 2006 is the first

one the

Conference takes place in Europe. We would like to remember now our friend, lost to soon. Maurizio

Landrini who stron 1 believed in the .ossibility to host the conference in Europe.

The main goal of ICHD Conferences is to promote exchange of knowledge and

discussions among

researchers, designers and engineers in various branches of hydrodynamics. Themes of this

Conference

include Naval Architecture and Ocean Engineering, Coastal Engineering, Environmental, Hydraulics _and

Water Resources, Computational Fluid Dynamic and Experimental Techniques, Fundamental Research in Hydrodynamic and Industrial Fluid.

The ICHD provides an opportunity for people, working in these fields, to present and discuss theoretical _and

experimental researches, and to consider practical applications of research activities.

It is our strong belief that works in the fields discussed in the Conference will be beneficial to solve practical engineering problems, and to promote our understanding both of sea resources protection and conservation and of coastal environments.

The ICHD 2006 is co-hosted by the Department of Naval Architecture and Marine Engineering of

_the

University "Federico II" of Naples and by II'ISEAN (the Italian Ship Model Basin).

The ICUD 2006 Proceedings contain four keynote lectures, on top of the papers to be presented at the

Conference.

Proposal for about 150 works were received from 20 countries and almost 100

_{were accepted for}

presentatioñ.

We strongly hope that the high quality of the selected works will guarantee a success comparable to that of the previous editions.

Based on the information available to the Organising Committee, this Conference will be attended by _over

110 delegates from around the world.

We, as the ICHD Organising Committee, would like to thank all the members of the International Scientific Committee for their devotion towards the success of the ICHD 2006 Conference.

It is also almost impossible for us to find a proper expression, to express our sincere gratitude to Mr.

Pasquale Cioffi of the ICI-ID Secretariat, for the time and the efforts devoted, during the past two years, in the Conference preparation.

We have done our utmost to create the proper atmosphere for an interesting and enjoyable Symposium. We wish everyone a nice stay in Ischia!

VAdm.Giano Pisi

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'Coastal Engineering

Computational Fluid Dynamics and Experimental Techniques

LIU Xiao-long Prediction of Steady and Unsteady

Performance of Ducted Propellers With Stators by Potential Based Panel' Method

A Numerical Study on Wave-Mud Interaction

Nurnencal Study on Resistance of ShipChengsheng Wu Moving in Shallow Water

MinGu

Calculation of Hydrodynamic Manoeuvring Càefficients Using Viscous-Flow Calculàtions

Ng Chiu-On

Zhang Dao'Hua

Toxopeus Serge

Ma Zheng Theoretical and Experimental' Study on

the Free Surface Air-Entrainment Chen Hongxun Vortex

Schbol of'Naval Architecture, Ocean and

,WANG Guo-qiang, 'Civil Engineering, Shanghai Jiao Tong China

University, Shanghai'

Development and 'Demonstration of'

Simulation Based Design for Parachute Tahara Y Aerodynamic Design

Urneda, S.

School of Naval Architecture, Ocean and

Civil Engineering, Shanghai Jiao Tong China

University, Shanghai

Department of Mechanical Engineering, The University of Hong Kong, PökfUIarn

Road,, Hông Kong

Department ofMechanical' Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

China Ship Scientific Research Center, Wuxi, Jiangsu 214082

Maritime Research Institute Netherlands (MARIN), Wageningen, The Netherlands DeIft University of Technology, DeIft

China Ship Scientific Research Center, Shanghai'

Shanghai Institute of Applied 'Mathematics

'and Mechahics, Shanghai University, China

Shanghai

Osaka Prefecture University, Department ofMarine, System Engineering;

Kanazawa University; Kanazawa

China China' China China The Netherlands China Japan Japan

file;//X:\html\Technical session\Computational FluId Dynamics and Experimental Technique 2006-FO-25

Fundamental Research

Naval Architecture and Ocean Engineering

_{Hydrodjnamics and'}

'Industrial Fluids

Computational Fluid'

Dynamics and

Experimental Techniques

Marine Structures and

Environmental Hydraulic and Water Resources

Eiigineering

Shanghai Institute of Applied Mathematics

Li 'Halfen g and Mechanics,, Shanghai, University; ' China

(5)

Naval Architecture and Ocean Eng _{Page 2 of 5}

file:/IX:\html\Technical session\Computational Fluid Dynamics and Experimental Technique... 2006-10-25

Numerical Simulations of Unsteady Bubble Motions in Water

Yuhi M. Kanazawa University, Kanazawa Japan

Air-Isukioka K. Kawasaki Plant Systems, Ltd.,Tokyo Japan Ishida H. Kanazawa University, Kanazawa Japan Colicchio G. INSEAN, Italian Ship Model Basin, Roma Italy

An Experimental and Numerical Faltinsen O.M.

Centre for Ship and Ocean Structures,

NTNU, Trondheim

Noa

Investigation of the Flip-Through Phenomenon

Colagrossi A. INSEAN, Italian Ship Model Basin, Roma Italy

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Numerical Simulation of Wave Breaking near Ship Bow at Different Ship Speeds

Study on Ship Motions' Mechanism Analysis Based on Chaos Theory

Research on Pressure Distribution of Inside Wall of a Moon Pool in Uniform Fluid Condition

VIRTUE - The Virtual Tank Utility in Europe Extending the Scope and Capabilities of Maritime CFD

Ship Maneuvers Simulation Using Free-Surface RANS solver

Lee Seung-Hee Kim NamChul Lee Young-Gill Quanming Miao Ming Cu Salman Sadiq YAO Xiong-liang Dai Wei Kang Zhuang Marzi Jochen

Dept. of Naval Arch. & Ocean Eng., Inha South

University, Incheon _Korea

Jungseok Research Institute of

South

International Logistics and Trade, Inha

Korea

University, Incheon

Dept. of Naval Arch. & Ocean Eng., Inha South

University, Incheon _Korea

China Ship Scientific Research Center,

China

Wuxi 214082

China

Wuxi 214082

School of Shipbuilding Engineering, Harbiri

China

Engineering University, Harbin 150001 School of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001 School of Shipbuilding Engineering, Harbin

China Engineering University, Harbin 150001

Hamburgische Schiffbau Versuchsanstalt

-HSVA, D-22305 Hamburg, Bramfelder Str. 184 phone +49 40 69203-236, fax i-49 40 69203-345, marzi@hsva.de

China

School of Shipbuilding Engineering, Harbin

China

Engineering University, Harbin 150001

Germany

Raven Hoyte C. MARIN, Wageningen Netherlands Extending the Benefit of CFD Tools in

Ship Design and Performance van der Ploeg _{MARIN, Wageningen} _Netherlands Auke

Prediction

Eça Luis Instituto Superior Técnico, Lisbon Portugal Drouet A. Bassin d'essais des carènes, DGA France

Guillerm P.-E. _{Bassin d'essais des carènes, OCA} _France Alessandrini B. Ecole Centrale de Nantes France Perdon P. _{Bassin d'essais des carènes, DGA} _France Jacquin E. _{Bassin d'essais des carènes, DGA} _France Validation of Slender-Body Method for Maritime Research Institute Netherlands

file://X:\html\Technical session\Computational Fluid Dynamics and Experimental Technique... 2006-10-25

Brocchini M. DIAM, University of Genova- Genova Italy

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Prediction of Linear Manoeuvring Coefficients Using Experiments and Viscous-Flow Calculations

Naval and Offshore Applications of an

Efficient Potential / RANSE Solution Alessandrini B. Scheme for Wave I Body Interactions

CFD-Based Design of International One Metre Radio-Controlled Yacht

Hybrid RANS and Potential Based Numerical Simulation of Self-Propulsion Test for a Practical Ship

Toxopeus Serge Luquet R. Ducrozet G. Gentaz L. Ferrant P. Harries Stefan Wu Zichao VIRTUE: Integrating CFD Ship Design Marzi Jochen

Duffy Alex Petz Christoph Schneider A. Amone A. Kim J. Kim K.S. Kim G.D. Van S.H. Park l.R. ZHAO Feng

(MARIN), Wageningen, The Netherlands

The

DeIfl University of Technology, DeIft

Netherlands Hamburgische Sâhiffbau-Versuchsanstalt

GmbH, HSVA, Hamburg Lermany

Technische Universit"at Hamburg-Harburg,

Germany TUHH, Hamburg

Technische Universitat Hamburg-Harburg,

Germany

TUHH, Hamburg

Technische Universit at Hamburg-Harburg,

TUHH, Hamburg Germany

Laboratoire de Mécanique des Fluides I EHGO UMR CNRS 6598 Ecole Centrale de Nantes, Nantes,

Laboratoire de Mécanique des Fluides I EHGO UMR CNRS 6598 Ecole Centrale de Nantes, Nantes

Laboratoire de Mécanique des Fluides / EHGO UMR CNRS 6598 Ecole Centrale de Nantes, Nantes

FRIENDSHIP SYSTEMS GmbH, CAD Centre, DMEM, University of Strathclyde

HSVA

CAD Centre, DMEM, University of Strathclyde

ZIB

"Sergio Stecco" Department of Energy Engineering, University of Florence "Sergio Stecco" Department of Energy Engineering, University of Florence Maritime & Ocean Engineering Research Institute (MOERI) / KORDI

Maritime & Ocean Engineering Research Institute (MOERI) I KORDI

Maritime & Ocean Engineering Research Institute (MOERI) / KORDI

Maritime & Ocean Engineering Research Institute (MOERI) I KORDI

China Ship Scientific Research Center, Wuxi, Jiangsu France France France France France Germany Uk Germany Uk Germany Italy Italy Korea Korea Korea Korea Korea China

file://X:\html\Technical session\Computational Fluid Dynamics and Experimental Technique... 2006-10-25

Naval Architecture and Ocean Eng _{Page 4 of 5}

1-lafermann D.

RANS-Based Flow Analysis for Schmode D. Propellers and its Benefits

Vorhölter H. Rung T.

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China

CHANG Yu

Practical Application of CFD in Wake Wuxi, Jiangsu Simulation of a Hull Model with Various

Appendages _{China Ship Scientific Research Center,}

ZHANG Zhi-rong

Wuxi, Jiangsu China

Department of Marine Technology,

Yousef-nejad R. Amirkabir University of Technology (AUT), Iran

Numerical Hydrodynamic Analysis of Tehran,

Planing Hull Surface _{Department of Marine Technology,}

Ghassemi H. Amirkabir University of Technology (AUT), Iran

Tehran

Fujii Akihiko Mitsui Engineering & Shipbuilding Co.,

Ltd., Tokyo Japan

Study on Interaction between Ship Hull Yamasaki Etsuo

Akishima Laboratory (Mitsui Zosen) Inc.,

Tokyo Japan

and Propeller using RANS Method with VLM

Taketani Tadashi Akishima Laboratory (Mitsui Zosen) Inc.,

Tokyo Japan

Kimura Koyu Akishima Laboratory (Mitsui Zosen) Inc.,

Tokyo Japan

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Calculation of hydrodynamic manoeuvring coefficients using

viscous-flow calculations

Serge Toxopeus

Maritime Research institute Netherlands ('MARIN,), Wageningen, The Netherlands Delfi University of Technology, Delfi. The Netherlands

ABSTRACT: In the present paper, the work conducted by the author regarding implementation

and improvement of efficient calculation of hydrodynamic coefficients within the manoeuvring

work package of VIRTUE is presented The improvements are mamly realised using variation of grid topology and density In the paper, a mathematical model for the bare hull forces and moments based on the viscous-flow calculation will be given Comparisons with experimental

data obtained withm the project shows that using accurate viscous flow calculations, a

considerable improvement in the prediction of the forces and moments on the ship compared to

conventiònal empiric methods can be obtained.

I INTRODUCTION

Ship-owners and shipyards increasingly require accurate predictions of the manoeuvrability of

ships in order to

_{verif' compliance with manoeuvring criteria. To improve computer}

predictions, one of the aims in the European integrated project VIRTUE is therefore_{to derive} hydrodynamic manocuvring coefficients from viscous-flow calculations in order to be able to predict the manoeuvrability of ships more accurately than conventional empiric manoeuvring predictions. The derived coefficients are implemented in fast-time manoeuvring simulation

programs and used to predict selected manoeuvres. This method provides an alternative to

conducting fast-time simulations using empirical mathematical manoeuvring models on the one hand and conducting direct simulation of manoeuvres using viscous-flow solvers coupled with body motion equations in the time domain on the other. Although the first method provides results very quickly, the accuracy and resolution of design details are often insufficient for designers. The second method using directsimulation is expected to provideaccurate results but

at impractically long computation times. Therefore the method using hydrodynarnic coefficients derived from viscous-flow calculations in fast-time simulations is at the moment an attractive

solutiOn ta the designer.

In the present paper, the work conducted by MARiN regarding implementation and

improvement of efficient calculation of hydrodynamic coefficients Within the manoeuvring

work package of VIRTUE is presented Based on earlier and present work, see e;g. Eça

Hoekstra and Toxopeus (2005), the improvements were mainly realised using variation of grid

topology and density Furthermore, improvements were obtained by comparing results of

calculations for corresponding test cases from diffèrent partners within the VIRTUE project. As a first .step, hydrodynamic coefficients for the bare hull are calculated. In future work within VIRTUE, alsocoeflicients forthe appended hull and rudder force coefficients wilÏbe derived.

For each obtained coefficient, a sensitivity study is conducted in order to determine its

relative importance on the manoeuvring behaviour of the ship. The work will show that using accurate viscous-flow calculations, a considerable improvement in the prediction of the forces and moments on the shipcompared to conventional empiric methods is Obtained.

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Table I: Non-dimensional main particulars, HTC

The measurements were carried out with the model restrained from moving in any direction relativeto the, carriage. Bilge keels, rudder and propellerwere 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 ofwaves.

Unless otherwise indicated, the Reynolds number in the calculations was 6.29x 106,

corresponding to a full scale ship speed of IO knots.

3 NUMERICAL 'PROCEDURES

3.1 Flow solver, turbulencemodel'and computational domain

All' calculations were performed with theMARINin-house flow solver PARNASSOS, which is based on a finite-difference discretisation of the Reynolds-averaged continuity and momentum equations, using fully-collocated variables and discretisation. The equations are solved with a

coupled procedure, retaining the continúity equation in its original form. The governing equations are integrated down to the wall, i.e. no wall-functions are used. More detailed

information about 'the solver can' be found in Hoekstra'(l 999) or Raven, Van der Ploeg and Eça

(2006).

For the calculations the one-equation turbulence model, proposed by Menter (1997'). The Spalart correction(see 'Dacles-MarianietaL (1995))ófthestream-wise vorticity is included.

The results presented in this paper were all Obtained onstructured grids with H-O topology, with grid clustering near the bow and propeller plane. Appendages and freesurface deformation

were not modelled. More details regarding the computational' domain, the implementation of_a drift angle in the calculations and the applied boundary conditions can be found' in Toxopeus

(2005).

3.2 Coordinate system and non-dimensionalisatioÁ

The origin of the right-handed system ofaxes used in this study is located at theiiitersection of the waterplane, midship and' centre-plane, with x directed aft, y to starboard and z vertically upward; The forces and moments presented in this paper are given relative to the' origin of the

coordinate axes, but m a right-handed system with the longitudinal force directed forward

positive, and the transverse force positive'when directed to starboard.

A positive drift angle 3corresponds to the flow coming fromport side (i.e. Darctan(-v/u)). All forces and moments are presented non-dimensionally. The longitudinal _{force X and}

transverse force Y are made non-dimensional using 4PV,L,,T, the vertical force using

+pV,L,,,B, the heelmg moment K by 4pV,L,,T2, the pitch moment M by 4pV,L,,,,2B and the yaw momént N by

3.3 'Uncertainty analysis

For the uncertainty analysis, the procedure earlier applied to the KVLCC2M is _{used, see}

Toxopeus (2005). The background of this procedure is given in Eçaand Hoekstra(2004).

Description Symbol Magnitude Description Symbol Magnitude Block coefficient Cb 0.650 Length/beam ratio LPJB 5.582 Midship section coefficient Cm 0983 Length/draught ratio L/T 14.922

Prismatic coefficient Waterplane coefficient C,, C 0662 0.822 Beam/draughtratio B/T 2.673

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In all calculations a reduction of the maximum difference in non-dimensional pressure

between consecutive iterations to 5x 105was adopted as the convergence criterion. It is assumed that this is sufficiently small compared to the discretisation error and therefore the iteration error is ignored in the uncertainty analysis. In general, the adopted convergence criterion results in a reduction of the difference in the (total), force and moment components between consecutive iterations of well below I xl 0.

4 HYDRODYNAMIC COEFFICIENTS FOR STEADY DRIFT MOTION 4.1 Influence of discretisation error

Using the HTC hull form, a series of geometrically similar grids has been generated fora drift

angle of 10°, in order to investigate the discretisation error. The grid coarsening has been

conducted in all three directions For each grid, the variatiOn in the number of grid nodes in the

stream-wise, normal and girth-wise (n _{nq and nC) directions is presented in Table 2 which} includes also the maximum y value for the cells adjacent to the hull, designated y2, that was obtained during thecalculations.

For grid 5, the results were not converged until the adopted _{convergence criterion and}

therefore the results for this grid are dropped frOm further analysis.

Table 2: Properties ofgridsfor uncertáinty analysis, HTC,j3=lO°. Comment

basedon grid 1, coarsened by 2x2x2 based on grid:2, coarsened by 2x2x2

basedon,grid3, coarsened. by2x2x2 basedongrid;4, coarsened by 2x2x2

basedongrid2,coarsened'by4x4x4

basedonigrid I, coarsenethby 5x5x5

Table 3: Uncertainty analysis, HTC, l3.10°.

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Monotonous divergence

For a drift angle of 10°,. the predicted values 4 of the friction (subscript. f) and pressure

(subscript p) components as well as .the total force and moment coefficients are presented. in

Table 3 with the estimated uncertainties U Based on an analysis of the results for each grid, it

was decided to use the. eight finest grids for the uncertainty analysis. The number of grids n

used depended on the; scatter in the results. fór the. coarsest grids.

As already found during an uncertainty study for the KVLCC2M hullform, see Toxopeus

(2005), the absolute uncertainty in the pressure components is larger than in the friction

Item 4o _4i U p Item _.410._- _+i

_U

_p

X 140x102 157x102 _141% ₀₉₄ _K 189x102 179x102

_{75% 142}

X1 - -L22xlOE2 50% (2)

K1 1.79x1OE3 I.761O 3.3% 1.97

X,, -5.33x1OE4 3;40x103 111.1% 067 K,, .2.07x,1OE2 I.96xÏ02 70% 1.46

Y 3.76x102 _4Ä2x10:2 18.4%

65

M -1.92x1OE3 -l.25xI0 72.6% 076

Y1 LI8xIOE3 1.I2xlOE3 7.2% .1.80 M1 - 3.Ô3x10 30% (2)

Yp 368x1OE2 4;31xlOE2 19.5% 069 M -2.24x1OE3 l.55xl0 597% 0.75

Z 786x102 8.60x1OE2 2.7% 0.21 N 2.45x102 244x,102 _{3.3% 348} Z1 - 3.40x10' 8.5% (2) N -2.78xI0 -248x10 548% 1.98 Z 7.86xIOE2 8.56x10r2 2.8% 0.22 N,, 2.45x102 244xl02 _{35% 3.45} id _l3 n, n n h, Nodes Y2 1 10 377 95 51x2 1.00 3653130

90

2 10 361 91 49x2 1.04 3219398 086 3 IO 297 77 41x2 1.25 1875258 0.97 4 10 257 65 35x2 1.47 1169350 1.19 5 10 185 48 26x2 2.00 461760 1.48 6 10 177 46 25x2 208 407100 1.51 7 10 145 39 21x2

2i0

237510 1.76 8 10 129 33 18x2 2.94 153252 2.28 9 10 89 .23 13x2 4.17 53222 .3.08 10 10 73 19 11x2 500 30514 4.06

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uncertainty and accuracy of the pressure resistance component is presented.

In Figure 1 the longitudinal force X, transverse force Y and yawing moment N and the non-dimensional de-stabilising arm N/Y are graphically presented for the different grids. The scatter in the results is much smaller than found for the KVLCC2M results. For a relative step size below 3, the results appear to converge. The convergence rate p, however, is found to be small for both X and Y (p=O.9 and 0.6 respectively). Due to the slow convergence, the difference between the extrapolated value₄ _{for zero step-size and the value}

4, is large and hence the uncertainty is relatively large.

Noteworthy is the fact that based on the trends with the current grids, the estimations

(indicated by cfd) for X, Y, N and NA' for increasing numbers of grid nodes do not converge to the experimental values (indicated by exp). This may be caused by either modelling errors or by uncertainties in the experimental values.

-0.013 -0.014 -0-OIS -0.016 -0-OI X -0.018 -0.019 -0.02 -0.021 -0.022 o 0.0255 2 3 4 5 0 0.7 0.65 0.6 . 0.53 z 0.45 0.4 0.35 S O 2 3

rolillve step iIz

4 5

4.2 Influence of Reynolds number

A calculation for 3 100 has been conducted for a full-scale Reynolds number of 7.4x I 0. The grid was geometrically similar to Grid I, except for an increase in the number of grid nodes in wall-normal direction to capture the gradients in the thinner boundary layer at full scale. _With

n= 137, the total number of nodes in this grid was 5.3x 106, with a_y2 _{of 0.56.}

In Figure 2, the calculated axial velocity field at the aft perpendicular for model scale and full scale is compared. Due to the higher Reynolds number, a somewhat thinner boundary layer is present at full scale. However, the structure of the wake does not change drastically.

0.025 0.0245 Z 0.024 0.0235 0.023 0.0225 o 2 3

rdadv uIp SIze

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0.02 0.00 0.02 Pl 0.04 0.06 0.08

0.10 Pamasos,HTC.x=O.5OJ.,, 1=1O° Pamassos, HTCIs, x=0.5OL,, fr'lO°

0.10 0.08 0.06 0.04 0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

y

Figure 2: Comparison of axial velocity field for model scale and full scale Reynolds numbers HTC, ¡310° (solid lines: model scale, dotted lines: full scale)

The values of the integral forces and moments for both model scale and full scale are presented in Table 4. In this table, also the relative change when going from model scale to full scale and the uncertainty in the model scale results are given. The changes in X, K and the ratio N/Y are clearly larger than the uncertainties in X, K and N/Y on model scale and therefore it is

concluded that the trends in these components are caused by the change in Reynolds number. For the other components however, the change is smaller than the uncertainty and therefore

conclusions can only be drawn based on physical interpretation.

Theoretically, results for increasing Reynolds numbers are expected to be between results for model-scale Reynolds numbers and potential flow solutions. For a ship at steady drift motion, this means that both the X and Y force components will decrease (paradox of D'Alembert) and the N moment component will approach the so-called Munk moment (which is much larger than

the N moment in viscous flow). Consequently, the de-stabilising arm N/Y will increase.

Considering the values of X, Y, N and N/Y in Table 4, the trends comply with these statements and therefore it is concluded that the full scale values of X, Y, K, N and N/Y are realistic values for the full scale situation.

Table 4: Comparison of integral forces and moments for model scale and full scale, I-fTC, 3=10°

5 1-IYDRODYNAMIC COEFFICIENTS FOR STEADY YAW MOTION 5.1 Implementation of rotational motion

The approach to incorporate rotational motion adopted in PARNASSOS is using a non-inertial reference system. This approach has been used by several authors, see for example section 3.2 in Batchelor (1967) or section 1.15 in Wesseling (2000) and the applications to ships of e.g. Alessandrini & Delhommeau (1998) or Cura Hochbaum (1998). Using this system, the grid is attached to the hull form and rotates with the ship. However, each water particle now should experience centrifugal and coriolis forces due to the rotation of the coordinate system. These forces have to be added to the momentum equation as source terms.

Originally, the momentum equation in PARNASSOS read in a cartesian coordinate system (see equation (2.1) in Hoekstra (1999)):

pu1u1 +p _-i.iu _{-i-p(u:u;) =} ₍₁₎

Condition X Y Z K M N N/Y

model scale (ms) -0.0157 0.0442 0.0860 -0.0179 -0.00125 0.0244 0.551

full scale (fs) -0.009 1 0.0387 0.0871 -0.0201 -0.00152 0.0251 0.648 (fs-ms)/ms -4 1.7% -12.5% 1.3% 12.6% 21.7% 2.9% 17.6%

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with f1 a remaining force tenn per unit volume (e.g. propeller forces), _{the vector of rotation, u}

= (u1, u2, u3)=(u, y, w) the velocity vector and r (X-XR) the radius of rotation with XR the

position of the centre of rotation. In the equation above, the coriolis force is represented by

2pû x u while the centrifugal force is pû x (û x r).

At the outer boundaries, it is assumed that the solution corresponds to a solution for potential flow. Therefore, potential flow calculations _{are used to calculate the velocities at the outer} boundaries and the pressure is obtained from the velocities. Using section 3.5 of Batchelor

(1967), it can be shown that the pressure follows from:

PP,. =((xi)2_I2)

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5.2 Computational grids

In order to maintain the usual definitions of inflow plane, outflow plane, no-slip/symmetiy/jj=1

and off-body plane, the grid needs to adopt a shape facilitating these definitions. This means that the outer boundary (i.e. the off-body plane) should have _{a torus shape. Also the in and} outflow planes have to be rotated to allow for perpendicular in and outflow. Figure 3 provides an example of a grid generated for rotational motion. In this figure, it is seen that the same base grid can be used for all rotation rates or combinations of drift and rotation and the outer blocks

are deformed to suit the computational condition.

Figure 3: Inner and outer blocks (coarsened) for y-O.4

5.3 Influence of discretisation error

For a non-dimensional rotation rate of y=-O.2, a series of geometrically similar grids has been

generated in order to investigate the discretisation error. The grid coarsening has been

conducted in all three directions. Table 5_{presents the number of nodes and Y2 values for these}

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Table 6: Uncertainty analysis, HTC, y =-0.2. O) Oscillatory convergence (2) Monotonous divergence -0.0125 -0.013 -0.0135 -0.014 -0.0145 -0.015 -0.0155

Figure 4: Convergence with grid refinement, HTC, r=-0.2

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 four (grids 3, 4, 6 and

8) finest grids for the uncertainty analysis.

Item _4o _p K -2.49xI0 -2.33xl0 16.3% 5.60 -l.77x1O -1.94x1O 43.9% 2.68 K -2.3Ixl0 -2.14x1OE3 2 1.6% 5.00 M -9.50x IO 11.8% (I) M', M -2.93xItY -l.24xIO 3.6% 8.4% (I) (I) N - 7.22xI0 14.8% (2) N -I.06x1O -1.IlxIO 14.9% 2.24 N - 7.34x lOE3 l4.4% (2) 'C -.3 IO 2 D cId -2.5 _{- - -Ii-83%} -3 -3.5 D -4 2--4.5 -3 -5.5 -6 -6.5 0.21 ri cId 8.5 _{- -IJl4.8%} 0.2 8 0.19 7.5. 0.18 Z 7 0.17 Z 0.16 6.5 0.15 6 _D 0.14 5.5 . 0.13 id y t fl.:; ha Nodes Y2 3 -0.2 297 77 41x2 1.25 1875258 0.97 4 -0.2 257 65 35x2 1.47 ¡169350 1.19 6 -0.2 177 46 25x2 2.08 407100 1.51 8 -0.2 129 33 18x2 2.94 ¡53252 2.28 9 -0.2 89 23 13x2 4.17 53222 3.08 10 -0.2 73 '9 11x2 5.00 30514 4.06 Item 410 41i U p X _l.35x102 1.38x1O2 _7.2% _6.05 X', xp _.l.83xl0 _I.17x102 -2.07x1O 45% 37.6% (I) 5.46 Y -5.98x10 8.3% (I) Yr .2.09x l0 -2.2IxI0 48.5% 2.54 Yp _-5.76xl0 _57%

z

6.16x102 6.06xl02 _1.8% _0.69 Zf 1.62x10 6.4% zp 6.14x102 6.04x102 1.8% 0.71

Table 5: Properties of grids for uncertainty analysis, HTC,_r-O.2.

o ₄

o 2 3 4 5

relative step sIze

Comment

based on grid 2, coarsened by 2x2x2 based on grid 4, coarsened by 2x2x2 based on grid 2, coarsened by 4x4x4 based on grid 1, coarsened by 5x5x5

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fer much between the individual results, but convergence is not always found due to scatter. For

a relative step size below 3, quite consistent results are however found.

6 MATHEMATICAL MODEL

Based on the viscous-flow calculations discussed above, hyckodynamic coefficients for the

forces on the bare hull were derived First the linear _{manoeuvring coefficients for drift and}

rotation were obtained by determination of the slope for

_{zero drift or yaw rate More}

mformation about derivmg linear coefficients is found in Toxopeus (2006), in which also the predicted relation between the forces and moments and the drift angle or yaw rate for the HTC andother ships is given.

Subsequently, non-linear terms were determined to describe the forces for large drift angles or yaw rates. To determine the coefficients Y111' and N111' use was made of calculations for

combined drift and yaw motion. For illustration purposes; the derived coefficients for the transverse force Y and yaw moment N are given below:

Table7Estithatedmanoeuvring coefficients for HIC bare hmll:

With these coefficients, the mathematical model for the bare hull forces amountsto:

='l'uv Icos DI sin f3+Y cosf3 y+ Y,.' sinf3 sin fI +"kr Isinf3 _Y

+ .Jcos f3. sin2

l.sign(sinp)

N1=N,.COsp.Siflf3+N.ICOSpI:.yNsyIyI+NIl.ISiflpI.y

+NuwI.cosf3.sin2f3.sign(sinp)

In Figure 5 a comparison is given of the relation between the trañsverse force and yawing

moment as a fuhctión of the drift angle or non-dimensiónal' yaw rate for the experiments (exp),

viscous-flow calculations (cfd), semi empinc method of SurS im (Sb) (seee g Toxopeus (2006))

and based on the mathematical model presented in equation (4) using the coefficients in Table 7

(cfd fit).

The comparison shows that for drift motion the derived mathematical: model resembles the expenments much better than the semi-empiric method Unfortunately, no experimental data for rotational motion was available at the time of.writing of this paper and thereforeno conclusions

can be drawn regarding the accuracy of the mathematical model forsteady yaw rate.

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Coeffiáient Valúe Coefficient Value

0.183 Na,,' 0.140

Yur' 0.017 Nur' -0.0239

Y,,' 1.118

N'

-0.0378

Y0'

-0.657 0.034

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0.000 -0.100 '. -0.200 -0300 .0.400o -5 lO 15 20 13 25 1'

Figure 5: Comparison between experiments and predicted forces and_{moments, HIC}

7 SENSITIVITY STUDY

In order to determine the influence of estimation

errors in each linear hydrodynamic manoeuvring derivative on the results for standard manoeuvres, a sensitivity study was

conducted. Similar studies have been conducted in the past, see e.g. Lee and Shin (1998). In the present study, a set of fast-time manoeuvres using the mathematical model abovewas conducted

during which one of the coefficients was individually multiplied by_{a factor of 1.1. Zig-zag} manoeuvres were conducted to obtain the first and second overshoot angles (osa) and the initial turning ability (ITA). From turning-circle manoeuvres with 35° steering angle, the advance (AD) and tactical diameter (TD) were obtained.

Based on the sensitivity study, the results as collected in Figure 6 were obtained. It is clearly

seen that for the HTC inaccuracies in _{have the largest impact on the accuracy of the}

prediction. N is also an important coefficient. Y,,. is the least important linear coefficient for

accurate predictions. Similar conclusions were found by Lee and Shin (1998). This means that

for accurate predictions of the manoeuvrability using coefficients derived from CFD

calculations, accurate predictions of the especially the yawing moment must be made.

Yuv61.1 NUV6 1.1 Yur 1.1 Nur 1.1 Yvv6l.1 Yuuuvv*1i UYlvlrl.1 Nrr' 1.1 NUVV6 1.1

Istosa 2ndosa ITA Istosa AD ID UNIvIr6I.1

10/IO IO/lO 20/20

Figure 6: Change in manoeuvring performance due to 10% change in input variable, HTC, 10 knots

0.000 -0.010 -0.020 -0.030 -0.040 -0.050 -0.060 -0.070 30 0 5 lO IS 13 0.060 0.040 0.020 0.000 -0020 HTC ° Z 0.0)0 -0.010 -0.020 -0.030 -0.040 -0.050 -0.060 -0.070 çfd lii 0.2 0.4 0.6 0.8 0.0000 20 25 30 30% 20% 10% 0% -10%

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large uncertainties of the estimated values. It is concluded that in order to obtain consistent

results, grids with a number of nodes of at least should be used. However, due to slow

convergence upon grid refinement, considerable grid dependency is even found with 4x106

nodes

Using, calculations for varióus drift

angles, rotation rates and combined motion,. a

mathematical model was derived The predicted forces and moments have been compared to

predictions using empirical methods. It is demonstrated that using a mathematical model

derived from viscous-flow calculations; better agreement with the experiments is obtained. Based on a sensitivity study in which the linear manoeuvring coefficients were individually

varied, it is found that the simulations are most sensitive to changes in the derivative.

Therefore accurate prediction of especially the yaw moment as a function of the drift angle is

required.

9 ACKNOWLEDGEMENTS

Part of the Work conducted for this paper has been funded by the Commission of thé EurOpean Commun ities for the Integrated Project VIRTUE under grand 516201 in the 6 Research and

Technological Development Framework Programme (Surface Transport Call).

REFERENCES

Alessandrini, B. and Delhomnau, G. 199& Viscous free surface flow pasta shipin drift and in rotating

motion 22" Symposium on Naval Hydrodynamics pages 49 l-507 August 1998

Batchelor, GK. 1967. An Introduction lo Fluid Mechanics. Cambridge University Press. ISBN O 521

66396 2.

Cura Hochbaum, A. 1998. COmputation ofthe turbulent flow arounda ship model in steady turn and in

steady oblique motion. 22nd Symposium on Naval Hydrodynamics, pages 550-567, Augtist 1.998.

Dacles Mariani J Zilliac G G Chow J S and radshaw P 1995 Numerical/experimental Study of a

Wing Tip Vortex in the NearField' A/AA Journal Vol 33 September 1995 _{pp 15611568}

Eça, L and Hoekstra, M , editors 2004 Workshop on CFD Uncertainty Analysis October 2004

Eça, L, Hoekstra, M. andToxopeus, SL. 2005. "Calculatión of the flow around the KVLCC2M tanker". CFD Workshop Tokyo, March 2005.

Hoekstra, M 1999 Numerical Simulation of Ship Stern Flows with a Space Marching Navier Stokes

Method. PhD thesis, DeIft University of Téchnology, Faculty of Mechanical Engineering and Marine Technology, October 1999.

Lee H Y and Shin S 5 1998 'The Prediction of Ship's Manoeuvring Performance in Initial Design Stage",Practical Design of Shipsand.Mobile Units (PRADS), September, 'l99&

Menter, F.R. 1997. "Eddy Viscosity Transpurt Equations and Their Relation to the k-c Model", Journal of Fluids Eñgineering, VOI. 119, December 1997, pp. 876-884.

Raven, H:C., Ploeg, A. vander, and Eça,.L. 2006. "Extending the benefit of CFDtools in ship désign and performance prediction".7IhInternationalConference on Hydrodynamics, October 2006.

Toxopeus S L 2005 "Verification And Validation Of Calculations Of The Viscous Flow Around KVLCC2M InOblique Motion".5thOsakaColloquium, March2005.

Toxopeus, Sl. 2006. "Validation of slender-body method for prediction of linear manoetwring

coefficients using experiments and viscous-flow calcUlations' 7hhI

Internationdl Conference on

Hydrodynamics, October2006.

Wesseling P 2000 Principles of Computational Fluid Dynamics Springer-Verlag ISBN 3 540 67853 0.