Experimental and Numerical Investigation of the Flow around a Ship model at Various Froude Numbers

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NATIONAL TECHNICAL UNIVERSITY OF ATHENS

DEPARTMENT OF NAVAL ARCHITECTURE AND MARINE ENGINEERING

Experimeñtal and Numerical Investigation of the Flow

around a Ship model at Various Froude Numbers

by

Dimitrios A. Garofailidis..

Submitted in Fulfilment of the Requirements for the degree of Doctor of Engineering in Naval Architecture and Marine Engineering

Advisory Committee

G. Tzabiras, Assoc. Professor, N.T.U.A., Thesis Supervisor. T. Loukakis, Professor, N.T.U.A.

G. Politis, Assist. Professor, N.T.U.A.

Examination Committee

T. Loukakis, A. Papanikolaou, V. Papazoglou, G. Athanassoulis, G.. Tzabiras, G. Grigoropoulos, G. Politis, Professor, N.T.U.A. Professor, N.T.U.A. Professor, N.T.U.A. Assoc. Professor, N.T.U.A.

Assoc. Professor, N.T.U.A. (Thesis Supervisor)

Assist. Professor, N.T.U.A. Assist. Professor, N.T.U.A.

DedAeate4 wits o'e.

Acknowledgements

I would like to thank from this point all these people who helped andsupported me

in my effòrts the last seven years. First, theMembers of the Steering Committee of this

thesis,

George Tzabi ras (Assoc. Professor, N. T. U.A. ) who discretelysupervised my work all these

years, leavIng me the freedom to do whatever I felt like and who recognised me the

privilege oflearningfrom my own mistakes. It was his work and dedication to the science that inspired and encouraged me during a long period of my life, about

thirteen years now.

Theodore Loukakis ( Professor, N.T.U.A. ) who from his position as

Director of the

Labo ratoryfor Ship & Marine Hydrodynamics eased my work both by offering me his long experience in the area of experimentation and by giving me the opportunity

to occupy the towing tank for untold periods. Without his funding support, the

construction of all the dedicated measuring devices would not be possible. Even at the moment of writing these lines, his contribution is vividly expressed by the

thorough revision of the initial manuscripts.

Gerasimos Politis (Assist. Professor, N.T.U.A. ) who in many occasions eased my life with

his experience and advices with respect to more theoretical aspects of the

Hydrodynaiñics. Also, it was he who in times of disagreement with my computer had just the perfect idea to solve every problem.

and theñ the rest of the examination committee,

Gregory Grigoropoulos (Assist Professor, N. T. U.A. ) who as superintendent of the towing

tank facilities in the Laboratory for Ship & Marinà Hydrodynamics managed to

arrange the other obligations so that the installations were free for the time

required to do each set of measurements.

Apostolos Papanikolaou (Professor, N.T. U.A.),

Vasilios Papazoglou (Professor, N.T. U.A. ) and

Gerasimos Athanassoulis (Assoc. Professor, N. T. U.A. ) who honoured me by participating this examination committee.

I wish also to express my thanks to the techniciansof the towing tanl for sharing my thoughts and efforts andfor giving their best to construct the varióus devices. Michael Nouflos was the one who had the patience to assist me even late in the night, whenever the

work required so. Dionysios Synetos performed always more than expecte4 when the details of the electronic parts of each experiment weredesigned and manufactured.. His

kiiowiedge came in some cases to rescue me from things that were beyond my insight to the

behaviour of the sensors used throughout the experimental work Fotios Kasapis was

always willing to operate the carriage taking one concern out

of my mind. George

Margaronis concentrated all his experience and talent to manufacture the prototype of the

model and the Five-Hole Pitot supporting construction. To these persons I feel much

obligeL because they offered me experiences that can not be found in any textbook

Many thanks should also be addressed to all the members of the faculty in the Department, for their friendliness that made mefeel N. T. U.A. as my second home these years.

I cañnòt forgèt my good friend Yiannis Ventikos (.Post-doctoral Researcher,

Georgia Tech, Altanda, Ph.D. Naval Architect N.T. U.A. ) with whom I spend many years together, having an almost parallel route..

Katerina Prifti (Ph.D. Candidate, Naval Architect, N.T.U.A.)for her special way to drop away all concerns with just a few words.

Aikaterini Georgiou, who supported me with discreetnessduring the hard time of the manuscripts final revieWs. ;. .

I cannot list the names of all these students and colleagues who, while working in the same building, were always willing to help .me in various small, but important, things that! could not perform alone. J shall rememberfor ever the feelings that generated in my hart when in the loneliness of the towing tank, somet mes late in the night or very early in the morning, one of them appeared asking whether it was anything that he or she could do

forme.

It is, however, beyond any dispute that this work would never have been completed without the support of the two Maries in my life, the one of them being my mother, who were the re for me day and night. This work cannot be considered but as the result of their

love. .

PART I Measurements and Numerical Simulations

CONTENTS

Acknowledgments

Contents

Prologue

Introduction

Introduction References

Chapter 1 : Resistance, parallel sinkage and runrnng trim measurements

General

i

Description 7 Instrumentation 11 Calibration 12 Experimental Uncertainty 13 Corrections 14

Presentation of Resistance, parallel sinkage and running trim measurements 16

Trip wire, eO.8 mm. 16

Trip wire, eO.5 mm. 17

Cylindrical studs 18

Total resistance coefficient compariaoñ 19

Conclusions 21

Chapter 2a Wave Profile Measurements

General

i

Description 3

Experimental Uncertainty 8

Presentation of the Wave Profile Measurements 9

Conclusions 13

References 14

Chapter 2b: Local Wave Measurements

General 1

Description 2

Experimental Uncertainty 8

Presentation of the Local Wave Measurements 8

Conclusions 12,

References 13

Chapter 2c: Global Wave Measurements

General

i

Description 2

Calibration 5

Experimental Uncertainty 5

Presentation of Global Wave Measurements 7

Conclusions 12

References 14

Chapter 2d: Free Surface formation

General

i

Description

i

Results 5

Chapter 3 Flow Field

Measurèments

General i

Description 2

Calibration 3

Eperimenta1 Uncertainty 8

Presentation of Field Measurements 10

Conclusions 14

References 15

Chapter 4 Pressure Field on the Hull

General

i

Description i

Calibration 5

Experimental Uncertainty 5

Presentation of Hull Pressure Measurements 6

Effects of the turbulence stimulator 9

Effects of the external tubing 11

Conclusions 12

References 14

Chapter 5 Numerical simulations

General

i

Description 3 Grids 3 Governing equations 7 Boundary conditions 9 Solution procedure 12

Preséntation of the Numerical Simulations 13

Grid independence tests 13

compnsonbeten field measurements and mimerical results

16

Comparison of surface pressures on the hull 27

Comparison of integrated results 31

Conclusions 39

References 41

References

PART II: Uncertainty

Analysis for the Measurements

CONTENTS

Appendix O: (Preface tO thè Appendices)

An mtroduction to error analysis

General

Errors 2

Uncertainty Anal'sis Basics 5

Literature review of importance in the area 9

Conclusions 14

References 17

Appendix I : Resistance, Trim and Sinkage Uncertainty Analysis

General i

Uncertainty estimates, deduced fromrepeated experiment 2 Proposed by the I.T.T.C. Resistance Uncertainty Analysis 6

Conclusions 19

22

Appendix lia : Wave Profile Measurement Uncertainty Analysis

General i

Wave Profile Measurement Uncertainty Analysis

i

Conclusions 8

Appendix lIb: Local Wave Measurement Uncertainty Analysis

General I

Local Wave Measurement Uncertainty Analysis 2

Conclusions 9

References 9

Appendix lic : Global Wave Measurement Uncertainty Analysis

General i

Global Wave Measurement Uncertainty Analysis i

COnclusions

io

References 11

Appendix III: Flow Field Measurement Uncertainty Analysis

General

i

Flow Field Measurement Uncertainty Analysis 2

Errors during the calibration of the Five-Hole Pitòt probe 8

Errors during measurements with the Five-Hole Pitot probe 16

Conclusions 26

References 28

Appendix 1V: Hull Pressure Field Measurement Uncertainty Analysis

General

i

Hull Pressure Field Measurement Uncertainty Analysis

i

Conclusions 12

Prologue

Prologue

Almost six years of continuous effort were necessary for the completion of the work

that is presented in these volumes. Although my teacher, G. Tzabiras, guided my early research steps in the area of numerical hydrodynamics,

the lack of documented and

consistent databases with experimental results made me turn hito the problems of the towing tank

Most of the work that is found in this volume deals with several aspeèts of

experimental methods that áre practised in a tOWing tank. The decision to develop ali thé instrumentation necessary to perform a various types of measuréments, that cover almost every field in the ñaval hydrodynamics, was täken for two reasons. First, to develop some experience with méasurements that by no means can be characterised as trivial. Resistance, sinkag

and trim measurements are an every-day task in the towing tank as well as

seakeepthg experiments, bût with respect to free surface, wake and hull pressures the previous experience was sparse. All the specialised instrumentation that was needed for

these measurements was manufactured in the machinery store of Our laboratory, giving us

the chance tO obtain some constructing experience too. After designing a series of

measurements and completmg the relevant mstruments, numerous tests were performed to

check their ability to provide with accurate réadings of the parameter they were made to

measure. In many cases some adjustments had tO be done to improve the performance of the experiment. These adjustments considered not only changes in the design of the devices

used, but alsO mödifications of the procedures and methods that were adopted.

Unfortunately, inseveräl cases the magnitude of the error was not obvious before the entire set of the specific experiment was completed dictating in some cases the repetition of a part.

A question that was generated during the progress of the thesis, was the degree of accuràcy the meásurements weré taken with. From this simple question a whole new area of rósearch raised in front of us. Quality assurance. After thesé years, my small experience says that it is not very difficult to take a measurement, with respect to a single number. The

difficUlt part, is to take the correct number or, at least, to know how much error this

incorporates with a confidence level. The improvements were often a result of empirical error assessment, as a feeling was developed about what would "work 0k" and what would

2

Prologue

not be of much help. With the time and the growing experience it became easier to

comprehend the discussions about the error analysis in the small number of relevant

publications that were spread over a wide area of Journals, Symposiums or Conferences. It was a big surprise, however, when I realised that the towing tank research community

ascertainted the error not in a regular basis. According to each authors' judgement, a

detailed analysis or just a declaration about his intuition could be found, but in most of the

cases not even a single word was given on the subject. Expressions of the style "the

accuracy is estimated to be within..." seemed suddenly to be the standard in almost every work, including the most important ones in the area, while the discussion on the subject

expanded over less than one single page. However, the time is close that this is going to be a story of the past, as most of the professional institutions (such as the ASME or the ITTC) become more sensitive in the issue of error estimation. A very serious contribution to this

direction was given by the Panel on Validation Procedures, during the 19thITTC. An excellent review of the subject is presented and the first proposals are made towards the

development of a universally accepted code for the analysis of measurement uncertainty.

Also, the issue of CFD validation was addressed in some extent. One conclusion can be

drawn from the work of this Panel. As the development of computer technology together with the evolution in the theory of incompressible viscous flow make feasible the usage of

numerical tools for the optimisation of the hull, less but more detailed and accurate

measurements are required.

During the previous decade, an animosity was established between the people who

work in the towing tank and those who work with numerical tools, as it was the belief of the latter that they c uld soon improve their codes in such a degree that the towing tank

would be useless. Today their ambitions seem illusive. At present, the CFD methodologies need the measurements to guide their development and to validate their results. More and more researchers find the two methodologies to have a complementaryrole in the design of new hulls and become more acquainted with their capabilities and their limitations.

However, experiments in the towing tank have an unrecoverable problem. Scaling effects.

As the flow around the models that are used in the towing tanks presents extensive areas of laminar behaviour, which does not appear around the ship, the extrapolation of the

measurements to the real problem scale with mathematically consistent methods is

impossible. Semi-empirical methods were created to provide the Naval Architect with some estimate, but the accuracy of the prediction is always uncertain. CFD tools do can help in this area, as they can simulate the flow around the model as fully turbulent. Moreover, they

have the ability to give a prediction at the full-scale, however this requires significant

Prologue 3

It is not simple to solve the full problem of the translating ship at constant speed and at calm sea. As the body floats, the change of the pressure field overits hull causes changes

in its position also. So, sinkage andtrim can be observed, that vary with the shape of the

hull and the speed. The problem becomes more complicated under the presence of the wave system that is generated on the free surface of the surrounding water, asit interacts with the pressure field and the wake behind the hull. A numerical solver would first have to predict

the flow around the hull under a planar free surface, then calculate the newequilibrium

position based on the newly calculated pressure field, estimate the wave system and redo the job, unii! convergence of all parameters is achieved. Today, no such code is known.

It is the feeling of the research team in N.T.U.A. that there is a long way until some

definite improvements in this direction appear. Before coñfldence in the numerical

piedictions is established, a better understanding onthe mechanisms of turbulence has to be devóloped and special models adapted to the problems of the Naval Hydrodynamics

should be created. In this Work, a new

method is proposed towards a more accurate

prediction of the full-scale problem. The method is based on both measurements and solution of the Navier-Stokes equations, getting benefit from the advantages the two methods separately present. More specifically, the dynamic position of the translating model is measured in the towingtank, together with the shape of the free surface around it at the design speed. This information serves as input to the numericalscheme, which takes Over to calculate the viscous flowunder the measured free, surface and around the

model at the correct sinkage and trim, providing the details of the flow.

Under the

assumption that the shape of the free surface will not change significantly at full scale,

calculations can also be done forthe real ship also. Naturally, the increase of the Reynolds

numberrequires that the resolution used for the flow domain will be significantly higher,

but this is expected not to be a problem

in the near future. Many advantages can be

recognised in the màthod. As the dynamic position òf the hull is a-priori known, no

iterations are required for this purpose. Furthermore, the shape of the free surface has not to be calcúlated, which is today an additional source of uncertainties.

Two parts are distinguishable in this thesis. First, each experiment is presented separately, with its description, the associated problems, änd the results. Only a short comment on the issue of the uncertainty analysis is to b found in each of thesechapters.

Judging from the extent of the uncertainty analyses in their complete form, it was decided

that they are gathered at the

end of the thesis, thus forming a series of appendices. A

description of the proposed method is found after the experiments, to be followed by a short epilogue which summarises the. experience obtained in this work.

Chapter 1,

contains the description of the resistance, sinkage and trim

measurements.

A very interesting discussion on the issue of stimulating turbulence is found in this chapter,

presenting a case study that was performed during these measurements. Three different turbulence stimulators of two types (trip wire and cylindrical studs ) were tested for their

effects on the measured total resistance curve.

Chapter 2 deals with the measurement of the shape of the free water surface around the modeL As this task required the application of three different methods that could each cover a different part of the surface, the chapter is divided in three sub-chapters. The details

of each method are presented in them, and discussions on the quality of the data and the

associated problems are also given. A fourth sub-chapter deals with the issue of

concentrating and processing the results from the three measurement areas. The relevant uncertainty analyses were also divided in three appendices, to prevent any confusions

because of the similarities that exist and are found in Appendix ¡Ja, lib and Hc.

Wake measurements, taken at the bow and the stem area at various Froude numbers are presented in Chapter 3. The purpose of these measurements was to obtain data for CFD

codes validation purposes and for further improvements guidance. A very interesting

uncertainty analysis for this experiment is found in Appendix 1H. For these measurements

a Five-Hole Pitot tube was used. The particular uncertainty analysis presents unusual difficulties, since the procedure of measuring with such a device involves two distinct experiments, that of calibration and the measurements. Final estimates for error have to

account for its from one experiment to the other, apart the local error sources.

Measurements for the hull surface pressure are presented. in Chapter 4. As before, the discussion on the uncertainty analysis is found in Appendix IV An effort in the direction

of covering areas of very low hull thickness was made during these experiments, using tappings that hàd to cross completely the hull and be partly exposed to the flow on the

opposite side of the model. How much the flow field and the measurements were affected by the presence of these taps with their tubing, is also discussed. Interesting results on the applicability of such methods, when no other choice is available, are given.

Finally, the details of the numerical method are presented in Chapter 5. Since the initial numerical scheme and the code itself were not developed during this thesis, but

represent the efforts of my supervisor for over fIfteen years, extensive reference is made to

previous publications that describe the work, its advantages, quality of results and

possibilities to predict accurately the flow around arbitrary 3D bodies. Details are given in

Prologue

this work on the modifications and the extensions that were necessitated to include the

predetermined water free surface.The teSúlts are còiipared withthe measurements taken in this work and important conclusions are derived that maydirect further improvements,

In the epilogue, a general discussion on the experience that wasobtained by the

author is given, along with proposals for future work in both the areasof measurements and numerics.

The practice of putting the references after each chapter or appendixis adopted in

this work, which may be seen as

peculiar to many readers. It was preferred over the

concentrated references at the end of the text book to enable the separate useof each part. As every chapter describes a completely independent experiment, it is easy to separate the woìk in this way and obtain a series of specialised 'user manuals', hatI hope will be of use to the future engineerswho will choose the way ofmeasuring.

Introduction

Introduction

Among the many problems that a naval architect has to solve during thedesign of a ship, is the accurate prediction of its propulsive requirements.This is a crucial point in the preliminary design stage as, inmost cases, the speed of the ship is a contractual obligation

accepted by the shipyard.

The shape of the hull has to fulfill two

conttadictive

requirements. Its ability to carry agiven amount of cargo is of primary importance, but it must also present goodhydrodynamic characteristics to have as low as possible running costs. The problem is more complicated than it sounds and it can be divided into three distinct components.First theresistance of the bare hull has to be predicted with a degree of accuracy. The second problemis the performance of the propulsor. The third problem is the interaction between

the hull and the propulsion system. It is obvious that the

propulsor changes significantly the flow field at the stern, thus affecting the thrust and

torque requirements. 1f the complete problem could besolved, then the efficiency of the machinery systems could be also maximized. Unfortunately, there are so manydifficulties in the prediction of the hydrodynamic part of the problem, that theengineer is obliged to use semi-empirical methods. Evidently, the first of the aforementioned problems that has to be solved is the prediction of the resistance in calm water atsteady forward speed [1.1].

Why does a floating-body experience resistance when it moves

in nature ? Its

motion is associated with a continuous loss of energy, which is spent to maintain several other phenomena that appear around the translating hull. Some examples, arethe tûrbulent nature of the flow at high Reynolds numbers, which is the case ofthe ship, the generation

of the wave pattern on the free surface of the water ( which may presentalso breaking

waves) and the complicated flow phenomena that are due to the shape and the irregularities

of the surface ( e.g. flow separation and appendage effects). The natureof many of the

aforementioned problems is still not fully understood. When the self-propulsion ( unsteady action of the propeller) is added to the problem, it is easily seen that significantdifficulties appear in formulating the problem mathematically or solvingit numerically [1.2 1. This is the reason why, till today, predictions that use data from model scaleexperiments dominate. However, even these predictions are not absolutely accurate, due to thenonlinear scaling

effect problems. To understand these problems better, we can

follow the classical

approximation of the dimensional analysis, which can be found in almost every book that

deals with naval hydrodynamics and will not be replicated here ( more details may for

example be found in [¡.1 ]).

Applying dimensional analysis and introducing certain

2

Introduction

simplifications, it is deduced that the total resistance force can be expressed in the following

way:

R =

c7(FnRn).(!pV2S)

where R is the total resistance force, p the density of the water, V the speed of the ship and

S the wetted surface of the hull under the water line. The notation c 1(Fn,Rn) is the total

resistance coefficient and is assumed here to be a function of two parameters. These are the non-dimensional Froude and Reynolds numbers respectively, defined

_as:

V

Fn =

-V

where g is the gravitational acceleration, L a characteristic length of the ship and y the

kinematic viscosity of the water.

Obviously, when the total resistance coefficient is known the resistance force can be calculated, and vice versa. Unfortunately, in naval architecture it is impossible to predict

exactly the CT value, either analytically or by carrying out experiments at model scale. According.to the laws of similitude,the two non-dimensinnal parameters (Fn and Rn ) must

have the same value between the experiment and the real problem in order for the

corresponding flows to be dynamically sinii1m. Practically this is impossible to be achieved, as it is well.known.

As a result of the aforementioned difficulties, towing tak engineers try to apply a. number of assumptions for the extrapolation of the total resistance coefficient, measured

at model scale, to the real ship. Today two methods are widely used, the one proposed by William Froude in 1868 [1.12] and then several variations of the form factor method. [1.28, 29 J.

According to Froude's method a total resistance coefficient is assumed that can be

decomposed in the form:

c7(Fn,Rn) =

cR(Fn)+cF(Rn) . . (1.4.)

where CR is the residual resistancê coefficient, a fûnction of the Froude number and CFthe frictional resistance coefficient, depending upon the Reynolds number. Frictional resistance

Introduction

T.T.C.at full scale.

coefficients were initially calculated using data from experiments with planks.During the

International Towing Tank Committee in Ì957, it was proposed to use the "I.T.T.C'57

correlation line" instead, in order to include secondaiy effects of the Reynolds number to

CR. It is alsoassumed that the residual resistance coefficient includes all other resistance sources, sch as theform and the wavemaking components. Froude's hypothesis, is based on observations of the wave pattern around models of the same form but of different sizes

(geosims) and is expressed his "Lawof Comparison ", stating that the residual resistance

coefficient could be assumed to have the same value between model and ship.Practically,

the total resistancé coefficient is measured in the towing tank at the speed

which is

calculated when the Fraude number between the two scales is kept the same. Then, the frictional resistance coefficient is taken from the I.T.T.C.'57 correlation line and their

subtraction gives the residual resistance coefficient. This cRvalue is added to theCFof the

full-scale Reynolds number predicting the ship's c It isrecognised, that the method of

Froude overestimates in general the ship resistance, as the increase of the Reynoldsnumber at full scale affects the stern pressure field so that the full scale C Rappçarslower.

The form factÓr method makes an effort to solve this problem, assuming thatit is

the ratio between the total viscous drag and the nominal frictional resistance ( e.g. the

I.T.T.C. friction limé ) that remains the same at both scales, and not thevalue itself. This is

expressed in the following equation:

.cT =

(l+k)cFJTTc+CR

(1.5)

where k is the form factor coefficient. For the determination of its value it is necessary to conduct resistance measurements at verylow speeds in the towing tank, where the wave

phenomena are assumed to be

negligible ( e.g. Prohaska's method [1.52]).

Then, by

subtracting the (1 + k) CFJTTc value at the speed corresponding to the design Froude

number from the relevant measuredtotal resistance coefficient, a prediction for the c R obtained. Finally, the full scale c..isobtained through (1.5) using the cR and k valuesánd

the correspondingCF,i

In contradiction to the Froude's method, the form

factor methodology

underestimates sometimes the total ship resistance. This has been also verified by numerical experiments [1.54 ]. A basic reason is that there is no physical evidence of the adopted k analogy. Moreover, the estimate ofk is based on experiments at very low Froude numbers. At the corresponding model Reynolds numbers, however, the accurate natureof the flow

is quite uncertain, as both laminar

and turbulent flow regimes exist together

with a

Introduction

become turbulent is veiy limited and, as will be seen in the relevant chapter, there are significant uncertainties at the low speed area [1.32 ]. It is characteristic that, for bypassing

the aforementioned problems, a number of different correction techniques have been

proposed duringthe I.i'.T. Conferences, like theCA factor [ 1.271for the Froüde method or.

the different functiòns for the k which are depending on the shape of the hull. References [1.3 ] through [1.32 ] present the relevant progression of the towing tank procedures.

To overcome the aforementioned problems of extrapolation at full scale, the

development of numerical methods has been cònsidered as a powerful alternative. Besides,

these methods may illuminate the flow mechirnisms that govern complex phenomena.

Initially, thin boundary layer approaches were developed, of integral or differential type,

:for the double hull case. The first dedicated workshop in the area of viscous ship

hydrodynamics was held in 1980, at SSPA in Goteburg, Sweden [1.38 ], in an effort to assess the state of the art m ship boundary layer calculations Results were presented for two well documented cases and the conclusion was that all methods worked well for the

areas of thin boundary layer, but failed near the Stern, where it was thicker. In this area the full Navier-Stokes equations had to be used, that solve simultaneously the velocity and the

pressure fields. . .

During the next ten years, the sigpiflcant growth in computer capacity and

performance enabled the solution of the Navier-Stokes equations in the 3D space, at least at the model scale. A.special workshop on Ship Viscous Flow was hçld in 1990 at Chaitners

University of Technology, in Göteburg, Sweden [1.39]. Substantial improvements _were

presented in the ability to predict the flow around the stern with a high degree of accuracy,

while comparison with experiments revealed the insufficiency of commonly used

turbulence models to predict some local phçnomena. First Tzabiras presented

some

numerical results for the full scale problem in two impressive works [1.53, 54]. In 1995, the magnificent work Of Sotiropoulos and Patel [1.50] showed that, adoptinga Reynolds stress model, quite accurate predictions can be made at model scale, removing essentially the weak points of the two equation models (.e.g. the k-c model ):

Since 1990, several other methods that solve the Navier-Stókes equations predicting also the shape of the free surface appeared [1.40, 1.41, 1.42, 1.43 ]. However, the results

presented until today pertain to simple hull geometries only and require enonnous

computer times and resources for the calculation.

It has to be stressed however, that the aforementioned results address the model

Introduction

procedure as the high aspect ratio meshes influence seriously cónvergence. In addition,the actual geometry of ship forms includes elements that are very difficult to bedesèribed with grids ( e.g. bulbs). There' arc still no clear indications about thebehaviour of the numerical

schemes when applied to "difficult"geometries. Among the unresolved problems, is also

the prediction of the dynamic position of the undergoing vessel, thatis the sinkage and the

trim values when running. This problem is of primary importance for fast ships, astheir

position may change significantly.

In this worlç, an intermediate method is used that combines the advantages of

experimental measurements with the power of numerical calculations, towards the solution

of the resistance problem. Based on Froude's observations about the similitude ofthé

generated wave pattern, it is assumed that the wave system around the translating ship will be almost the same between the model and the full scale. Then, detailed measurements can

be taken in the towing tank to determine the free surface, which is introduced as input to

a viscous flowsolver (it is named Paralos, from the intials of PARabolic ALgorithm On Surface). Therefore, the free surface is treated as an additional boundary of the calculation domain, on which special conditions are applie Many advantages can be recognised in the proposed method. First, the dynamic stability position of the hull can be taken into account, since it is measured during the model tests. Secondly, the method can beapplied to include special shapes.that are used to reduce resistance, e.g. bulbs etc. Third, the proposed method needs a relatively small area around the hull to be covered in a viscous manner,assuming that the potential flow is validoutside thi area; This is a reasonable assumptionsince the viscous effects remain bounded with, the hull, permitting however the usage of areasonable

number of computational nodes

with respect to the capabilities of modern computer

systems. Certainly, the free surface at the, stem area and in the wake will be different for the ship, due to Reynolds scale effecs. In any case however, the proposed methodis expected

to predict total resistance values on the safe side, which is in many cases required to

compensate for other, unpredictable, factors.

A first effort in the same direction has been published already in 1990 [1.511by the

N.T.U.A. research team. The results were of moderate success, revealing the dependency

of the method to the quality of themeasured free surface. Since the advantages that such

a method would offer were

significant, it was decided to repeat the work more

systematically. In this thesis, the first two steps are presented, namely the experimental

work and the model scale calculations at various Froude numbers. Extensive comparisons are made between the measured data and the calculations,revealing the areas' where some

improvements are required in both the experimental methods úsed and the numerical

6

Introduction

Since an important part of the method deals with measurements in the towing tank;

it was decided to conduct also a detailed set of measurements for all the parameters of

interest (i.e. the resistance and dynamic position of the model, the shape of the free surface, the flow field values at the bow and stern areas and, finally, the hull surface_pressures).

Qu1ity assurance became recently a serious issue and a great deal of work is done

in this direction, under the name "Uncertainly Analysis",

_{as it is referenced today. A}

discussion on the problems of the error recognition and evaluation can be found in the Preface to the Appendices. It is very important, when experimental data are used for comparisons, to knQw the degree of accuracy they are measured with. It seems to be a

common secret that there is not such a thing as a perfect measurement, however the error

bounds are often neglected. In many cases, the conclusions drawn from _{discussions that}

include the possible error in the compared values are quite different than when this is not taken into account. A serious effort was made in this thesis, to estimate the possible error

intervals within which lie all measured parameters. The general directions given by the

Panel on Validation Procedures during the 19 thI.T.T.C. were followed. For _{some of the}

experiments no previous efforts could be found in this direction,so new methodologies were developed that are adapted to the towing tank procedures.

The original elements of this thesis are discussed in the Epilogue, together with the areas for further research.

Introduction 7

References

1.1 J. P. Comstock (editor), "Principles on Naval Architecture",S.N.A.M.E, New York,

1967.

1.2 L. Larsson, "CFD as a Tool in Ship Design", Proceedings, CFI) Workshop,Tokyo,

Japan, 1994.

1.3 L. Tursini, "Leonardo da Vinci and the Problems of Navigation and Naval Design", L.N.Ä., 1953.

1.4 G. S. Baker, "Development of Hull Form of Merchant Vessels", N.E.C.!., 1937 - 38.

1.5 F. H. Todd, "The Fundamentals of Ship Model Testing", S.N.A.M.E., 1951.

1.6 M. G. Beaufoy, "Nautical and Hydrauliö Experiments", edited andpublished by H.

Beaufoy, London, 1834.

1.7 H. P. Rumble, discussion on paper, "The Admiralty Experiment Works, Haslar",by

R. W. L. Gáwn, I.N.A., 1955.

1.8 W. Froude, "Observations and Suggestions on the Subject of Determining by

Experiment the Resistance of Ships", The papers of William Froude, 1810 - 1879, I.N.A., 1955.

1.9 "A description of the U.S. Experimental Model Basin", E.M.B. Report No. 118,

1925.

1.10 E. Buckingham, "Módel Experiments and the Forms of Empirical Equations",

A.S.M.E., 1915.

1.11 P. W. Bridgman, "Dimensional Analysis", 1922.

1.12 Memorandum to Mr. E. J.Reed, Chief Constructor of the Navy, dated December

Introduction

1.13 Frederic Reech, "Cours de Méchanique", 1852. First announced in 1832, see E. G. Barrillon, N.E.C.!., Vol. 45, 1928 - 1929.

1.14 Osborne Reynolds, "Philosophical Transactions of The Royal Society", London,

England, 1883.

1.15 W. Froude, "Experiments on Surface Friction", British Association Reports, 1872 and 1874.

1.16

T. E. Stanton, J. R. Pannell, "Similarity of Motion in Relation to the Surface

Friction of Fluids", Transactions of The Royal Society, London, England, Series A,

Vol.214.

1.17 G. S. Baker1 "Notes on Model Experiments", N.E.C.I., Vol. 32, 1915 - 1916.

1.18 H. Blasius, "Grenzschichten in Flilssigkeiten mit kleiner Reibung", Zeitschrift !1)r Mathematik und Physik, Band p. 1, 1908.

1.19 L. Prandtl, "Ergebnisse der Aerodynamischen Versuchsanstalt zu Götingen", Vol.

3, T. Von Karman, "Über laminare und turbulente Reibung", Abhandiungen aus

dem Aerodynamischen Institut, Aachen, Vol. 1.

1.20 F. Gebers, "Das Ähnlichkeitsgesetz bei im Wasser geradling fortbewegter Platten", Schiffbau, Vol. 22, 19[9.

1.21 B. I. ..Tideman, "Results of Resistance Tests with Ship Módeis", Memorial van de Marine II. Afdeéling 9e Aflevering, 1876 - 1880.

1.22 D. W. Taylor, "The Speed and Power of Ships", second Èevision, (a list of the

frictional coefficients is given in Table V, p.34), 1943.

1.23

K. E. Schoenherr, "Resistance of Flat Surfaces Moving Through a Fluid",

S.N.A.M.E., 1932.

1.24 G. Kempf, "Results Obtained in Measuring Frictional Resistance", I.N.A., 1929.

1.25 S.N.A.M.E. Bulletin 1-2, "Uniform Procedure for the Calculation of Frictional

Introduction

1.26

S.N.A.M.E. Bülletin 1-25, "Tables of Coefficients for ATTC

Model-Ship

Correlation and of Kinematic Viscosity and Density of Fresh and SaltWater", 1964.

1.27 Proceedings of the 10th I.T.T.C., London, England, 1963; published by National

Physical Laboratory, England.

1.28 G. Hughes, "Frictional Resistance of Smooth Plane Surfaces in Turbulent Flow",

I.N.A., 1952.

1.29 G. Hughes, "Friction and Form Resistance in Turbulent Flow and a Proposed

Formulation for Use in Model and Ship Correlation", I.N.A., 1954.

1.30 J. F. Allan, J. F. C. Conn, "Effect of Laminer Flow on Ship Models", I.N.A., 1949.

1.31 Aeronautical Research Council, R&M 858, 1922-23.

1.32 G. Hughes, J F Allan,"Turbulence Stimulation on Ship Models", SNAME, 1951.

1.33

J. L. Hess, A. M. O.

Smith, "Calculation of Non-Lifting Potential Flow about

Arbitrary Three-Dimensional Bodies", Douglas Aircraft Company Report No.

ES40622, Long Beach, 1962.

1.34

L. Larsson (ed.),

"SSPA-ITTC Workshop on Ship Boundary Layers", SSPA

Publication No. 91, Göteborg, Sweden, 1981.

1.35 C. W. Dawson, "A Practical Computer Method for Solving Ship Wave Problems",

2 InternatiOnal Conference on Numerical Ship Hydrodynamics, Berkeley, 1977.

1.36 S. J. Kline, M. V. Morkovin, G. Sovran, D. J. Cockrell, "Computationof Turbulent

Boundary Layers - 1968 AFOSR-IFP-Staflford Conference", Pioceedings,Stanford University, 1968.

¡.37 K. J. Bai, J. H. McCarthy (editors), "Proceedings of the Workshop on Ship Wave Resistance Computations", DTNSRDC, Bethesda, U.S., 1979.

1.38 F. Noblesse, J. H. McCarthy (editors), "Proceedings of the Second DTNSRDC

Workshop on Ship Wave Resistance Computations", DTNSRDC, Bethesda, U.S.,

10 Introduction

1.39 L. Larsson, Y. C. Pate!, G. Dyne (editors), "Ship Viscous Flow. Proceedings of thè 1990 Workshop", FLOWTECH International Report No.2, 1991.

1.40 _{"Proceedings of the CFD Workshop Tokyo 1994", 22 - 24 March 1994, Tokyo,}

Japan.

1.41 Y. Tahara, F. Stern, "A Large-Domain Approach for Calculating Ship _Boundary Layers and Wakes for Nonzero Froude Number", CFD Workshop, Tokyo, Vol.!,

pp. 45 - 55, Tokyo, 1994.

1.42 _{J. Farmer, L. Martinelli, A. Jameson, "Multigrid Solutions of the Euler and} Navier-Stokes Equations for a Series 60 Cb = 0.6 Ship Hull for Froude Numbers 0.160, 0.220 and 0.3 16 ( Program 1: Navier-Stokes Formulation )", CFD Workshop,

Tokyo, Vol. 1, pp. 56 - 75, Tokyo, 1994.

1.43 B. Alessandrini, G. Deihommeau, "Numerical Calculation of Three-Dimensional

Viscous Free Surface Flow around a Series 60 CB

0.6 Ship Model", CFD

Workshop, Tokyo, Vol. '1, pp. 95 - 104, Tokyo, 1994.

1.44 _{B. Baldwin, H. Lomax, "Thin-Layer Approximation and Algebraic Model for}

Separated Turbulent Flows", AIAA Paper, Wo. 78-257, 1978.

1.45.

S. J. Kline, B. J. Cantwell, G. M. Liley, "1980-81 AFOSR-HTTM-Stanford

Conference on Complex Turbulent Flows", Proceedings, VoL 1

- 3, Stanford

University, 1982.

1.46 _{P. Bradshaw, B. E. Launder, J. L. Lumley, "Collaborate Testing of Turbulence}

models", to appear in the J. Of Fluids Engineering.

1.47

W. T. Lindenmuth, T. J. Ratcliffe, A. M. Reed, "Comparative Accuracy of

Numerical Kelvin Wave Code Predictions

'Wake-Off", Technical Report

DTRC/SHD-1260-Ø1, David:Taylor Research Center, 1988.

1.48 _{J. J. Gorski, R. M. Coleman, H. H. Haussling, "Computation of Incompressible}

Introduction - 11

1.49

J. H. Ferziger, "Simulation and Modelling in

Three-Dimensional Turbulent

Boundary Layers : Status and Prospects", CFD Workshop Tokyo 1994, Vol. 1, pp.

22-33, 1994.

1.50 F. Sotiropoulos, V. C. Patel, "Application of Reynolds-Stress Transport Models to Stem and Wake Flows", Journal of Ship Research, Vol. 39,No. 4, pp. 263 - 283,

Dec. 1995.

1.51 G. D. Tzabiras, T. A. Loukalds, D. A. Garofallidis, "On theNumerical Solution of

the Total Ship Resistance Problem Under a Predetermined Free Surface", O.N.R. Symposium, Ann Arbor, Michignan, U.S.A., 1990.

1.52 G. Dyne, "An experimental investigation of the tanker model "Dyne" in a towing

tank", Chalmers Univ. of Technology, Göteburg, Sweden, CHAJNAVRJ-95/0036,

1995.

1.53 G. Tzabiras, "A Numerical investigation of the Reynolds scale

effects on the

resistance of bodies of revolution", Ship Technology Research, Vol. 39, pp.28 - 44,

1992.

1.54 G. Tzabiras, "Resistance and self-propulsion numerical experiments on two tankers

Chapter 1 1

Resistance, parallel Sinkage

and running Trim

measurements

General

During the design of the series of experiments conducted in this work, it was

considered important to compare some representative results with data provided by other

researchers. A good comparison would introduce a

high degree of confidence when

discussing the observations made here. The most comprehensive and representative test in towing tank practice is that of the total resistance measurement. Resistance values would

aid the selection of the conditions for the detailed measurements to follow. It was also possible, by the instruments on the carriage, to obtain information about the dynamic

position of the model, that is its parallel sinkage and trim values when running.

The experiments were conducted at the

Laboratory for Ship and Marine

Hydrodynamics of the National Technical University of Athens. The towing tank is 100 metres long, 4.60 metres wide, and approximately 3.5 metres deep. It is equipped with a towing carriage and a wave generàtor. A wave absorbing beach is found at the other end. All carriage controls as well as the data acquisition equipment are installed on the carriage.

Detailed uncertainty analysis for the resistance measurements is given, as a

contribution to the increasing demand for well documented experimental error sources, in Appendix I.

A major problem in model testing for resistance is the occurrence of substantial

règions of laminar flow at the bow, which is ñot the case for actual ships. Accounting for

this problem in a satisfactory way is necessary, since the basic modelling theory is

dependent upon simihr flow regimes for the model and the ship. In most cases, the towing

tank practice has adopted the well-known useof turbulence stimulators. Their usage not

only ensures stimulation to turbulence, but it also presents the advantage of stabilizing the boundary layer transition process at a predefined longitudinal position and therefore on drag measurements. Of the many different types of stimulators devised, two have found general acceptance, namely tripwires and studs ( cylindrical or trapezoidal). However, none has dominated over the other, as the opinions of various researchers differ. Klebanoffand Diehi

2

Resistance, parallel sinkage and running trim measurements

[1.4 ], found that wires were not entirely suitable because they introduced large distortion

effects into the 'boundary layer, which did not die out for some considerable distance downstream of the wire. On the other hand, some controversy exists about the size and

spacing of studs [1.5, 6] as no definitive rule exists to help the selection of these

parameters.

For similar with the ship flow regimes to occur on the model, it is necessary that the

effective starting position of the turbulent boundary layer occurs at' the same relative position in both scales. Since the full scale problem, is the ship, where no laminar flow

appears, this position is the leading edge in Our case. In model scale however, due to the

lower Reynolds ñumbers, the boundary layer on the hull commences with a laminar part

ând only at some distance downwards the local Reynolds number raises to values that force the flow to transition to tu±bulent. As known, the skin friction coefficient for, the laminar

flow is less than for the turbulent flow, therefore the existence of areas of laminar flow

results in general to an underestimate of the measured total resistance, and a bad prédiction

for the full scale problem. To solve this problem, the practice of placing some kind of irregularity on the hull which enforces turbulence is adopted. Of course, since the flow

encounters an obstacle, the boundary layer thickness raises suddenly. A turbulence

stimulator of this type is considered as well chosen if the thickness of the boundary layer downstream of it has the same value as if the flow did not present any laminar area at all. Obviously, every type of irregularity on the surface of the model causes an abrupt increase

of the boundary layer thickness. 'The term virtual origin refers to the effective starting

position of the turbulent boundary layer, as this may be estimated from the boundary layer thickness past the stimulatot. If the virtual origin occurs before or after the leading edge, then the boundary layer will be "over" or "under" stimulated, leading to larger or smaller

resistance values respectively for the model when compared with the full-scale ship. Unfortunately, tests that reveal the nature of the flow at an area are quite difficult in the

tank envirónment and can not be performed for every model. It should be noted in addition, that the thickness of the boundary layer greatly depends on the shape of the bow ( entrance

angle, rake, stem radius, existençe of a bulb etc. ). Based upon the idea that a proper

stimulator should compensate the decrease in resistance due to the laminar flow area' With its parasitic drag, the selection of the most suitable turbulence stimulator could be assisted by comparisons of resistance measurements. A rule, expressed by Burns and Murphy [1.5], is that a suitable turbulence stimulator produces higher resistance at low speeds and lower

at high speeds when compared to other devices, this method however has the drawback

'It should be reminded that the values of the frictional coefficient cF reduce in areas of laminar flow.

Chapter 1

that it does not lead always to correct selections with respect to the full scale extrapolations.

Extra difficulties arise from the fact that, even when the perfect turbulence stimulator is selected, it would work correctly only at a specific Reynolds number and a small area

around it, while standard resistance tests include a range of speeds. Therefore, one has to

decide between a stimulatorworking near the design speedand another working properly

at very low Froude numbers, where the necessary resistance recordings for the form factor

method should be taken. At very low speeds, where the phenomenon of stimulator

breakdown appears, the problem becomes more than obvious. The "stimulator breakdown" point, is defined as the Reynolds number at which the total drag curve suddenly decreases, owing to the occurrence of large areas of laminar flow over the model.

Considering the above, Joubert and Matheson expressed the opinion that

[1.7]:

"at the present time thére is no method available wherebythe actual stimulator

shape, size, and position can be calculated for transition tobe completed at a

given position, or for the virtual origin of the turbulent boundaiy layer to be

spec fied"

Furthermore, according to their resUlts, the stud or pin-type stimulators, depending on their

geometry, may not be more effective than wires of the same height, in promoting a

turbulent boundary layer at lower Reynolds numbers. In the case of using studs, the distance between them should also have an effect, as excessive intervening distances are expected

to leave large areas of laminar flow unaffected. Since this innovative work no further

investigations in this direction have been presented, despite the tremendous importance for

the daily tank practice. All model basins tend to use systematically some type of a

turbulence stimulation device, but the selection of the shape, size and positioning is rather based on the experience and the feeling of the experimenters.

There are two conditions that must be satisfied by the turbulence stimulation devices in order to have the desired effects. First, their geometrical properties should be selected in such away that steady turbulence is stimulated. For the case of the trip wires, as the flow may be considered equivalent to the one around an infinite cylinder, this criterion leads to a lower limit in the Reynolds number equal to 400. For lower Reynolds numbers the flow

is laminar. Second, their height should not be greater than the thickness of the boundary

layer atthe location they are positioned. If this is the case, then they present high parasitic drag, leadingto overestimation of the resistance force. Combination of these two conditions

results in a range of geometrical values that can beselected for the stimulation devices,

4

Resistance, parallel sinkage and running trim measurements

however, the aim of calculating the thickness of the boundary layer at the bow area is not a straightforward procedure. Extensive theoretical and experimental work may be found in the literature for a related problem, i.e. the velocity distribution in the boundary layer along a flat plate. H. Blasius was the first who constructed an ordinary differential equation that describes the problem [1.18 ]. Other researchers presented later several methods to solve

the equation [1.19, 20, 21]. Increased accuracy, however, was obtained with the solution

presented by L. Howarth [1.23], who gave also numerical values for the parameters of the equations in tabular form [1.24, p. 139 ]. Measurements to test this theory were carried out

first by Burgers [1.25 ], Zijnen [1.26] and Hansen [1.27 ]. Particularly careful and

comprehensive measurements were reported later by Nikuradse [1.28 ]. According to his findings the Blasius solution was verified, but the formation of the boundary layer is greatly influenced by the shape of the leading edge as well as by the very small pressure gradient which may exist in the external flow. Considering these observations in ship model testing,

one should expect significantly lower boundary layer thicknesses than the one resulting

from Blasius' equation, since the geometry of the bow introduces a steep adverse pressure gradient in the external flow field. The application of the two conditions in the case of the present experiments, results to the formation of Table 1.1.

Table 1.1 :Operational range for trip wires according to the Blasius' equation

From Table 1.1 it is obvious that, if the difference of the experimental setup is neglected

(Blasius expressed his theory basing on flat plate results with no pressure gradient at the leading edge ), the selection of the wire diameters should be made between the values of

0.8 to 1.0 when the testing speed range is considered ( 0.5 - 1.914 m/sec). Thp wtre thickness

[mm] Em]

Lower speed limit [m/secl (critical Rn condition)

Upper speed limit [rn/see] (Boundary layer thickness)

0.5 0.020 1.1217 6.8219 0.6 0.024 0.8862 4.7374 0.7 0.028 0.7272 3.4806 0.8 0.032 0.6129 2.6648 0.9 0.035 0.5280 2.1055 1.0 0.040 0.462 1 1.7055

Longitudinal position at 76.4mm downstream of the stem (xtL = 0.05).

5

Chapter 1

Recognising the importance of the proper turbulence stimulation in tank model

testing, Joubert and Matheson conducted a series of tests in the wing tunnel on aship model

with its mirror image, monitoring

the flow on the hull [1.7 ]. In their

work, several dimensions of various types of turbulence stimulators were tested, and results were

presented showing the virtual origin position. The model used was the Lucy Ashton, having

a length of 2.743 metres ( 9 ft ) and the turbulence

stimulators were positioned 5%

downstream the model length from the leading edge. As in the present workthe model had a length of 3.048 metres (10 ft), the aforementioned resultscould be used with a relatively

high degree of confidence. For the preliminary selection of the trip wire thickness, two

Froude numbers were selected, one low ( Fn = 0.09,0.5 m/sec), and one close to theservice

speed of the particular hull (Fn =0.315 or 1.722 ni/sec ). To estimate the location of the

virtual origin from figure 13 in thework of Joubert and Matheson [1.7 lit is necessary to calculate the Reynolds number. Assuming fresh water temperature of 15°C (which gives

a fluid kinematic viscosity of y = 1.13902* 106m2/sec) and a model length at waterline

equal to L = 3.099 m, the followingtable may be filled:

Table 1.2 : Relative position of virtualorigin for various trip wire diameters.

From Table 1.2 is concluded that a wire diameter of 0.02" (0.5 mm ) would position the virtual origin of the turbulence boundary layer approximately at the leading edge ofthe model at higher speeds. A thicker wire - 0.035" (0.8 mm) in diameter - would shift the position to 91.44 mm ( 3.6" ) upstream of the leading edge. Considering now the low Froude numbers, the trends remain in favour for the thinner wire, which is assumed to

position the virtual origin of the turbulent boundary layer closer to the model leading edge.

To investigate the trends it was considered as useful to test with both diameters used by

Joubert and Matheson. No efforts for interpolation were made towards accomplishing an exact positioning of the virtual origin, as the complexity of the case does notallow for such an attempt in a meaningful way. Furthermore, although thethicker wire is presented in the work of Joubert and Matheson as inferior in its efficiency for the specific test case, itwould

Model speed

[m/sec]

Reynolds number Distance of virtual ongm from the model's leading edge

non-dim dimensional øO 02O wire eO 035" wire 0.500 1.360*106 1.340*105 [ft] +63.5 mm +76.20mm 1.722 4.685*106

4.609*10S[ft]

-10.16 mm -91.44 mm Note : Positive distances downstream of stem.

Resistance, parallel sinkage and running trim measurements

be useful to provide some further confirmation of these findings that prove the Blasius

equation to be improper for use in the towing tank enviroúment.

In this work resistance tests with cylindrical studs and trip wires of two thicknesses were made, to obtain extensive data for comparison with results from other institutes [1.8,

9, 10, 11] and the I.T.T.C.'s Cooperative Experimental Program mean values [1.12 ]. It

should be noted, that the results reported by the

18thI.T.T.C. Flow and Resistance

Committee are fôr the full scale problem. An effort tu downscale the total resistance at

model from these data was not made, as this would introduce unpredictable errors, therefore

in the sequel comparisons are not made at model and full scale with the same models. In

Table 1.3 data are given for the various models and the corresponding tank particulars. The

most representative data àre given by the Cooperative Experimental Program (C.E.P.)

coordinated by the International Towing Tank Committee ( I.T.T.C. ) which lasted from the

1 6'-to the i

Conferences. Several observations were made from the results för this

program, as will be discussed in the following paragraphs. In that program of experiments,

contributions from 29 4ifferent institutions were gathered. Among the very first

observations was the çlifferences caused by the various lengths of the used models, which spanned from 1.8 m to 10M m. To enable more rational future comparisons, the data base was split in two major categories, according to the model length, setting as threshold the

value of 4.0 m. This length divided the datá base at aboút the middle (13 models were

shorter than 40 m and 16 models longer). The measurements taken in the present work will be compared in the sequel with the I, T C small models mean line, but other comparisons will be also given. It aliould be noted that at model scale data were available from the IOwa Institute fOr Hydraulic Research and Osaka Univershy. Data for the mean sinkage and the running trim taken frOm the database of the I.'T.T.C. could be used with less reservations, as nó extrapolatioñ procedure was involved.

Chapter 1

Table 1.3 : Definition of comparison database

Description

The ship model chosen for thisseries of experiments follows the Series 60, CB=

0.60, lines based on the original methodical series by Todd [1.1] and has an L/B ratio

equal to 7.5. The lines-plan of the model, shown in Figure 1.1, conformed to the standard offsets without any alteration for a stern tube.

Two geometrically identical models were constructed, a wooden and one of Glass fibre Reinforced Plastic ( G.R.P. ). The latter was constructed to be used for hull pressure measurements, as the larger thickness of the wooden model prohibited access to major areas

of interest.

7

Tank facility Model length L [ml

Turbulence stimulator Blockage

(AJA1) N.T.U.A. 3.048 T.W., C.S. 0.00465 I.I.H.R. 3.048 C.S. 0.00720 Osaka University 6.000 T.S. 0.00330 C.S.S.R.C. 6.000 N/A 0.00260 I.H.I. 4.000 N/A 0.00220

I.T.T.C. all mean (4.000) (T.S.) (0.00130)

Abbreviations: N.T.U.A. National Technical University of Athens I.I.H.R. Iowa Institute for Hydraulic Research C.S.S.R.C. China Ship Scientific Research Centre

I.H.I. Research Inst. of Ishikawajima-Harima Heavy Industries

I.T.T.C. International Towing Tank Committee

T.W. Trip wire

C.S. Cylindrical Studs T.S. Trapezoidal studs

Resistance, parallel sinkage and running trim measurements

Both models were of identical geometrical characteristics but, due to the different

manufacturing techniques, the accuracy of their surfäces differed. The wooden model was cut using a mechanical model milling machine, which ensured an accuracy of ±0 1mm at

all directions. The polyester coating and the thickness of the paint are included in this estimate. All dimensions were thoroughly exnnined after completion of this model and

were found less than 0.1mm in discrepancy.

The model was painted both at the outer and inner side. Complete coverage of the surface is important when wood is used as construction material for models designed to be tested in water. Wood has the tendency of absorbing water when uncovered, a fact which has undesired effects in its shape and strength, but also in its weight, causing alterations to

the draft. During the entire series of experiments no cracks on the model surface were observed, or any other major change in the quality of the outer hull, because of aging or temperature changes. The condition of the hull was also checked by weighting it. Any

changes from the initial weight value would be a clear indication of absorbed water.

The design water line was drawn around the model using a 0.3 mm permanent

marker. This, enhanced the possibilities of detecting any unpredictable changes in

displacement.

On the G.RP. model some distortion in geometry was found, and more specifically

(percentages were given after division with the Li,):

Table 1.4 : Geometrical distortion of the G.R.P. model.

The length of both models at the design water line was equal to 3.048 m (10 ft). Their principal dimensions and offsets are given in Tables 1.5 and 1.62, respectively. However, during the design of the lines plan of the model, the depth was raised from

2

Tables 1.6 and 1.7 are found after the main text because of their size.

Dimension Deflection [mm] Percentage (%)

Length, at base line -2 0.065

Hogging, at midship section 4 1.333

Beam, at base line O

Chapter 1

9

0.244m to 0.3 m, to avoid entrance of water in the model when towing at high Froude numbers. General hydrostatir datafor the full-scale ship are given in Table 1.7.

Tests were conducted with trip wires having a diameter of 0.8 mm

(0.035") and

0.5mm ( 0.020" ). Also, a row of cylindrical studs of 1.6 nun in height and 3 2 mm in diameter, fitted with 95 mm spacing, was used in an additional set of measurements in order to compare with the results of Stern et al. [1.9 ], who haveused a model with the

same dimensions and this type of stimulator. All threeturbulencestimulation devices were positioned on the model atx/L = 0.05 - that is 5 percent downstream of the leadingedge of the model - on the relevant cross-section contour. The stimulators did notfollow the profile

line at the stem, but this did not

really matter as it is approximately vertical over a

significant part.

The tests for the cases with the trip wires were conducted in close dates, so no

significant differences in the temperature of the tank water ( about 26° C ) existed.This was not the case for the experiments with the studs, since the water temperatureduring this set

of experiments was 12° Celsius, 14°

less than the other two cases. Corrections

for

temperature for the CF curve(I.T.T.C.'57 correlation line) and for the blockage were made to obtain comparable results. In Table 1.8, the summary of the conditions for the three

resistance tests is given.

The model was free to sinkand trim as it was attached to the carriage via a heave

rod - pitch bearing assembly, fixed to the LCB. Thus, measurements ofthe parallel sinkage and running trim were also possible. Results for these values may be convenientlypresented in the form of factors, defined as

follows [1.13, 14]:

Sinkage coefficient: 2

AdF+MA

Fn2 2L

Trim coefficient:

t

2 (1.2)

Fn2

where MF and

4

are the measured draft alterations at the forward and the afterward

ModeL.

Full-scale Ship

3.048 121.920

0.406 16.256

0.977

Table 1.8: Resistance tests

Among the observations made within the C.E.P. was that the towing point plays a significant role in the accuracy of the sinkage and trim measurements [1.12 1. When the towing point was set near the midship, a trim moment was generated which resulted in changes in trim. Vertical displacement of the towing point did not seem to affect the

Table 1.5 : Principal dimensions of the Series 60, CB= 0.60 ship.

[ml 0.163 6.502

Depth _(ml 0.244 9.758

extendedte avoid water entrance) (0.300)

1%

0.600 0.600

m = AJAT :

0.0072 0.0072

Wetted-surface area _[m9 1.579 2515.8

Displaced volume _1ml 0.120 7705.696

Entrance angle _[deg] 70 70

t Wire øO 8mm T Wire eO3mm C Studs

14x3

2mm

mberoÉnà

61 52 65

Ìerature '°Cj

25 26 12 $Leyno2dsNb.

f x10'J

0.9421 6.537 1.808 6.682 0.684 5.119 FrciîdeNo. 0.505 - 0350 0.095 - 0.350 0.050 - 0.3794 7.50 7.50

LeDraft

18.75 18.75 BeamíDrafi 2.50 2.50

lo

Resistance, parallel sinkage and running trim measurements

Parameter

Length _[ml

Chapter 1 11

resulting sinkage, but had a strong influence in the trim values. In general, if the towing

point was set to the centre of buoyancy the results were fouñd to have reducedscattering. It should be noted however, that even this practice provides only anapproximation to the ideal setup. Calculations that include the hull geometry may give easily the coordinates of the centre of buoyancy, but the truly requested point, is the centre of the forces that act on

the model while running. As this includes also the pressure and frictional drag, which

change with speed, it becomes very difficult to have an a-priori estimate for thelocation of

this point, justi!ing the previouscompromise.

Comparisons for the values of parallel sinkage and running trim are made with results from C.S.S.R.C. [1.11 ]and I.H.I. [1.10]. The model at C.S.S.R.C. was towed at

a position other than theCB.The model of I.H.I. was closer in dimensions (

L = 4.0 m) to

the one used in this work and was towed at the c9

Instrumentation

The principal dimensions of the towing tank in the N.T.U.A. Laboratory of Naval Hydrodynamics are 100x4.6x3.5 m, equipped with a carriage that is constructed by Kempf & Remmers. Driven by four electric, electronically controlled motors, it can reach the speed of 5.25 rn/sec. For the purposes of this seflés of experiments, since the speed did notexceed

the value of 2 m/sec, the sampling time could be as high as 20 seconds. The electronic

control of the carriage, although it can be fine-tuned by the user, proved to be very stable and accurate. This is clearly shown by the relevant uncertainty analysis - Appendix I.

An one-component force transducer is used in the dynamometer to perform the

resistance tests. The dynamometer is of type R 47 constructed by Kempf& Remmers, and

is also equipped with transducers for measurement of alteration of trim and draught.

Coupling the model to the carriage by the resistance dynamometer results to prevention

of

surge, yaw and heel. The resistance transducer is designed for a full-scale load of ±20 Kp. This value can be surpassed by up to 30 Kp, when accelerating or decelerating, and up to

50 Kp when strong oscillations occur. The load cell has a sensitivity of approximately

±lmV/V of supply voltage. A range of ±30 degrees is measurable for the trim angle using

a transducer of the typeID 36/45 of Messrs. TWK Elektronik. The extent of measurable

vertical motion amounts to 400mm and is measured with the help of a potentiometer. Only the signal from the load cell is low-filtered on 4 Hz before the data acquisition system.A