Heimann_justus CFD Based Optimization of the Wave-making Characteristics of Ship Hulls

Justus Heimann

CFD Based Optimization of theWave-Making Characteristics of Ship Hulls


vorgelegt vonDiplom-IngenieurJustus Heimann

aus Berlin

von der Fakultt V Verkehrs- und Maschinensystemeder Technischen Universitt Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften Dr.-Ing.

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr.-Ing. Klaus BrieBerichter: Prof. Dr.-Ing. Gnther F. ClaussBerichter: Prof. Dr.-Ing. Gerhard JensenBerichter: Prof. Dr.-Ing. Lothar Birk

Tag der wissenschaftlichen Aussprache: 2. Mrz 2005

Berlin 2005D 83


Dipl.-Ing. Justus Heimann

Approved by theFaculty of Mechanical Engineering and Transport Systems

of the Technical University Berlinin partial fulfillment of the requirements of the degree of

Doktor der Ingenieurwissenschaften Dr.-Ing.

Doctoral committee:

Prof. Dr.-Ing. Klaus Brie (Chair) Technical University BerlinProf. Dr.-Ing. Gnther F. Clauss Technical University BerlinProf. Dr.-Ing. Gerhard Jensen Technical University Hamburg-HarburgProf. Dr.-Ing. Lothar Birk University of New Orleans

Day of the oral examination: 2nd March 2005

Berlin 2005D 83

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ISBN 3-89820-445-6 Dissertation, Technische Universitt Berlin, 2005

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Preface

Several years ago when I was an enthusiastic regatta sailor the foundation for the present researchwork was laid. Many times during the races occurred the challenging question how to improve myown performance and that of my Laser dinghy very likely, I wasnt the only one!My tactical and sailing skills improved over the years. So I refined techniques like roll tacking andjibing, sailing close-hauled and upright on upwind courses, steering through waves with minimal speedloss, reducing the wetted hull surface on downwind courses or speeding up in planning conditions. Buthow to improve the hull hydrodynamics? Since the Laser dinghy is the ultimate one design there is noroom left for hull modifications. Nevertheless, my friends and I did or at least we thought we did our best to optimize the hull hydrodynamics, mostly within the rules. For instance we polished theunderwater hull with sandpaper to generate a micro air cushion, we shaped the leading and trailingedges of the centreboard to increase the lift-drag ratio and we fitted a little (invisible) flapper tothe transom edge to improve the planning performance. However, all this hydrodynamic fine tuningremained rather a matter of faith than of measurable benefit.Nowadays, after several years of study and research think I have come a bit closer to the answer of howto improve the hull hydrodynamics measurably at least the size of the dinghies has improved a lot.

The present research work was undertaken at the Division of Naval Architecture and Ocean Engineer-ing of the Technical University Berlin. Preparation and finalization of the thesis were undertaken at thepremises and with the generous support of FRIENDSHIP SYSTEMS GmbH. For a long educationalperiod I was supervised by Prof. Dr.-Ing. Dr. h.c. Horst Nowacki in whose team I had the pleasure towork as a research and teaching scientist from 1995 to 2000 in the field of ship geometric modelling,numerical hydrodynamics and optimization. I wish to express my sincere thanks to Prof. Nowacki forhis valuable advice, inspiration, criticism and support and his companionship of the present work.I like to express my sincere thanks to Prof. Dr.-Ing. Gnther F. Clauss for guiding my first scientificsteps and for his commitment in the doctoral examination to become thesis supervisor. I am very grate-ful to Prof. Dr.-Ing. Gerhard Jensen and Prof. Dr.-Ing. Lothar Birk for taking interest in my work andfor being thesis supervisors. Furthermore, I would like to thank Prof. Dr.-Ing. Klaus Brie for chairingthe doctoral examination.I would like to say thank you to Prof. Dr. Carl-Erik Janson from Chalmers University of Technology andFLOWTECH Int. AB, Gteborg, Sweden, for his continuous support, many fruitful discussions and forcustomizing the CFD system SHIPFLOW according to my needs. Many thanks goes to Prof. Dr. LarsLarsson and the whole FLOWTECH team for kindly making available the SHIPFLOW system.Very special thanks I owe to my friend Dr.-Ing. Stefan Harries for being an excellent colleague formany years and for his invaluable support and encouragement in finalizing this work.A nice and valuable time I spent with my friends and colleagues, particularly Claus Abt, FraukeBaumgrtel, zgr Baskaya, Dr.-Ing. Carl-Uwe Bttner, Jrn Hinnenthal, Dr.-Ing. Karsten Hochkirch,Dr.-Ing. Katja Jacobsen, Bernd L. Kther, Bernhard Krger, Dr.-Ing. Yeon-Seung Lee, Prof. Dr.-Ing. Detlef Schulze and, last but not least, Dr.-Ing. Geir Westgaard.Thanks for being close friends in every respect to Dr. Uwe Laude, Stephan Meyer and Suse Pfeiffer.

I wish to express my deep gratitude to my parents Prof. Ingrid and Prof. Gerhard Heimann and to mybrother Felix Heimann. Finally, without the love, the steadfast support, endless patience and continuouspushing of the woman I love, Antje Kmmerer, this work would not have come to its happy end.

Justus Heimann Potsdam, March 2005

J. Heimann CFD Based Optimization of the Wave-Making Characteristics of Ship Hulls 3

Abstract

Ship optimization based on computer simulations has become a decisive factor in the development ofnew, economically efficient and environmentally friendly ship hull forms. An important task at an earlydesign stage is the optimization of the wave-making characteristics of the ship hull since for fast ships aconsiderable resistance component stems from the steady ship wave system. Moreover, the ship wavescause adverse effects in the far field as the wash hits the shore line or other vessels.

A novel hull form optimization approach has been developed and implemented. It builds on a CFD(Computational Fluid Dynamics) based evaluation of the nonlinear ship wave pattern, on realization ofthe cause and effect relation of hull variations and their impact on wave formation, which is accessedby a perturbation approach, and on wave cut analysis (WCA). WCA yields an excellent assessmentof the wave-making characteristics of a hull form in terms of its free wave spectrum and the waveassociated pattern resistance. These features are highly integrated and controlled by a fully automatedoptimization scheme. The scheme is specific in the way it tackles the optimization problem:

The hull adaptation is driven directly by hydrodynamics, avoiding prerequisites to the shaperepresentation and to the hull modification method.

Wave cut analysis yields the objective function of optimization in terms of the free wave spectrumand the wave pattern resistance. This considerably improves the system identification allowinga focused optimization.

The hull optimization is carried out directly for the effective wetted hull portion of the advancingship including the effects of dynamic trim and sinkage and wave formation along the hull.

The optimization process is established in terms of an iterative marching scheme of successivesub-optimization loops. In each loop a region of the solution space is mapped to a simplifiedconvex quadratic image which merely possesses a single minimum determined by the activeconstraints. This enables a straightforward solution procedure and a simultaneous treatment ofa large number of locally acting optimization variables, introducing much freedom to the hullvariation.

All aspects of the proposed optimization approach are presented. Applications of the optimizationscheme to practical ship hull forms show the following:

The wave-making characteristics can be considerably improved with a tangible reduction of thewave (pattern) resistance.

Hull variations are driven by the optimization to the expected optimum hull shapes with the hullgeometry fully self-adjusting according to the optimization requirements.

Optimal interferences of local wave trains are enforced both in amplitude and phase which resultsin a beneficial cancelation of the wave trains.

The specific fingerprints of locally confined hull variations (e.g., at the bulbous bow) can beeffectively traced in the wave spectrum and in the wave pattern resistance to allow a focusedminimization of particular adverse wave components.

The system identification can be significantly improved by utilizing additional information interms of the wave spectrum and the distribution of the wave pattern resistance over the wavesrange.

4 J. Heimann CFD Based Optimization of the Wave-Making Characteristics of Ship Hulls

Kurzfassung

Die Entwicklung konomisch und kologisch effizienter Schiffe erfordert im groem Mae den Ein-satz moderner, rechnergesttzter Verfahren. Eine ausschlaggebende Rolle hierbei spielt die auf Com-putersimulationen basierende hydrodynamische Optimierung des Schiffsrumpfes, die in einem frhenEntwurfsstadium erfolgen sollte. Ein erheblicher Teil des Rumpfwiderstandes und damit des Leistungs-bedarfs wird bei schnellen Schiffen durch Energieverluste infolge der Ausbildung des stationrenSchiffswellensystems verursacht. Zudem gefhrden Schiffswellen Kstenschutzmanahmen, Uferbe-bauungen, die Ufervegetation, Hafenanlagen und andere Schiffe sowie Badende.

Im Rahmen der Arbeit wurde ein neuartiger Optimierungsansatz entwickelt und implementiert, dersich auf die Wellenbildungseigenschaften von Schiffsrmpfen konzentriert. Das Verfahren beruht aufder rechnergesttzten Simulation des nichtlinearen, stationren Schiffswellenfeldes, auf der Betrach-tung des Ursache-Wirkungs-Zusammenhanges von Rumpfvariationen und deren Auswirkung auf dieWellenbildung sowie auf der Wellenschnittmethodik, die ein ntzliches Instrument fr die Bewertungder Wellenbildungseigenschaften von Rumpfgeometrien in Form von freien Wellenspektren sowie desWellen(bild)widerstands liefert. Diese Bausteine wurden zu einem voll automatischen Optimierungs-system integriert. Das Problem der Wellenwiderstandsminimierung wird hierbei auf eine spezielle Wei-se angegangen:

Rumpfformadaptionen werden direkt ber Strmungsgren gesteuert, unabhngig von einerspeziellen Geometriedarstellung sowie einem speziellen Verfahren zur Geometrievariation.

Mit Hilfe der Wellenschnittmethodik lsst sich eine aussagekrftige Zielfunktion in Form vonfreien Wellenspektren und des Wellen(bild)widerstands ber den Einzelwellenkomponenten de-finieren, was eine erheblich verbesserte Systemidentifikation und damit eine zielgerichtete Opti-mierung ermglicht.

Die Optimierung erfolgt direkt fr den benetzten Rumpf unterhalb der Wellenkontur des fahren-den Schiffes in seiner dynamischen Schwimmlage.

Der Optimierungsprozess baut auf aufeinander folgenden Sub-Optimierungsschleifen, in denenjeweils ein Ausschnitt des Lsungsraums vereinfacht auf einen konvex, quadratischen Raumabgebildet wird, von dem man wei, dass er ein einziges Minimum aufweist, das von den aktivenNebenbedingungen bestimmt wird. Dadurch wird das Lsungsverfahren beschleunigt und dieVerwendung einer groen Zahl von Optimierungsvariablen mit jeweils lokalem Einflussbereichermglicht. Dies generiert ein substantielles Ma an Freiheit fr die Formvariation.

Die vorliegende Arbeit stellt alle Aspekte des Optimierungsansatzes ausfhrlich dar. Die Anwendungdes Verfahrens auf praxisnahe Rumpfformen weist folgendes nach:

Die Wellenbildung lsst sich deutlich verringern. Dies ist mit einer erheblichen Reduktion desWellen(bild)widerstand verbunden.

Rumpfgeometrievariationen sind entsprechend den Erfordernissen der Optimierung so einstell-bar, dass sich erwartete optimale Geometrienderungen ergeben. Freiheiten der Rumpfvariationknnen dort in das System eingebracht werden, wo im spezifischen Entwurfszusammenhangnoch Freirume vorliegen.

Optimale berlagerungen verschiedener Einzelwellensysteme in Amplitude und Phase entlangdes Rumpfes stellen sich so ein, dass die Einzelwellensysteme sich gegenseitig auslschen.


Der Fingerabdruck lokal begrenzter Rumpfvariationen (z.B. im Bugwulstbereich) lsst sich pr-zise bis in die Wellenspektren und bis zum Wellen(bild)widerstand verfolgen, was eine zielge-richtete Minimierung besonders schdlicher Wellenanteile ermglicht.

Mit den Wellenspektren und der Verteilung des Wellen(bild)widerstands ber den Einzelwel-lenkomponenten werden wertvolle Informationen bereit gestellt, die eine erheblich verbesserteSystemidentifikation und damit eine zielgerichtete Optimierung erlauben.


Contents

1 Introduction 9

2 Hydrodynamic optimization approach 112.1 Motivation and goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Cause and effect chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Process flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Hydrodynamic analysis 193.1 CFD simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.1 Boundary value problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.1.2 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.3 Numerical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.4 The CFD system SHIPFLOW . . . . . . . . . . . . . . . . . . . . . . . . . . 263.1.5 Application aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Wave cut analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Boundary value problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2.2 Longitudinal wave cut analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.3 Truncation correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2.4 Application aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Sensitivity analysis 434.1 Design variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Perturbation approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2.1 Perturbation of the discretized boundary value problem . . . . . . . . . . . . . 454.2.2 Perturbation magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3 Panel relocation scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.3.1 Joint relocation of hull panels . . . . . . . . . . . . . . . . . . . . . . . . . . 564.3.2 Relocation range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.4 Process flow of sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.5 Impact on hull form and main form parameters . . . . . . . . . . . . . . . . . . . . . 714.6 Impact on wave elevation and flow quantities . . . . . . . . . . . . . . . . . . . . . . 794.7 Impact on free wave spectra and wave pattern resistance . . . . . . . . . . . . . . . . 844.8 Evaluation of gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5 Improvement of the wave-making characteristics 955.1 Constrained minimization problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965.2 Optimization functional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.2.1 Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105


Contents

5.2.2 Penalty functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.3 Solution scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.4 Hull form adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6 Applications 1176.1 Introductory comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176.2 Wigley hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.3 FantaRoRo ferry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7 Conclusion 1617.1 Main achievements and contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 1617.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

7.2.1 Improvement and validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1627.2.2 Coupling to high level geometric modelling and variation schemes . . . . . . . 1637.2.3 Coupling to seakeeping optimization methods . . . . . . . . . . . . . . . . . . 164

Lists 165Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179Symbols, Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181


1 Introduction

In recent time ship optimization based on computer simulations has become a decisive factor in thedevelopment of new, economically efficient and environmentally friendly ship hull forms. An impor-tant task at an early design stage is the optimization of the hydrodynamic properties of the ship hull.For instance, the reduction of the power consumption of a medium-sized ferry typical of fast short-seashipping by 1% already reduces the annual fuel costs by about $50.000 and the annual greenhouse gasemissions by about 350 t.

A considerable resistance component stems from the steady ship wave system even when sailing inrelatively calm water. Fast displacement type ships consume 50% and above of their installed powerto overcome the wave resistance. The waves generated also cause adverse effects in the far field as thewash hits the shore line or other vessels. It therefore is mandatory to reduce wave-making as much aspossible.

In order to do so early in the design process a novel hull form optimization approach has been developedand implemented. The optimization process is fully automated requiring no user interaction, however,permitting it. The steady wave system of a ship moving through otherwise calm water is approximatedby means of CFD (Computational Fluid Dynamics) simulation applying the state of the art nonlinearfree surface Rankine panel module of the SHIPFLOW system. The proposed optimization methodaims at an improvement of the wave-making characteristics, i.e., the minimization of the energy lossesassociated with the wave formation along the hull. A valuable measure of the energy losses is attainedby wave cut analysis (WCA) which allows to determine the free wave spectrum and the wave patternresistance. Wave cut analysis yields the wave pattern resistance while by convention an integrationof the longitudinal pressure components over the hull provides the wave resistance.

The present optimization approach substantially differs from other approaches to wave resistance min-imization in the way it tackles this objective. The substantial differences are:

Hull variations are driven directly by hydrodynamics, i.e., the hull shape is controlled via aselected flow quantity along the hull surface. Neither, are prerequisites to the hull geometryrepresentation and its characteristic features nor to the hull variation method imposed. The op-timization variables are flow related, constituting a link between the hull geometry and theirhydrodynamic properties.

The objective function of optimization is directly related to the steady ship wave systems interms of the free wave spectrum and the wave pattern resistance as determined by a longitudinalwave cut analysis. This improves the system identification by tracing hull variations up to theirrespective fingerprints in the wave spectral distribution and in the wave pattern resistance. Thus,waves can be influenced and reduced more systematically and with higher control.

The hull optimization is carried out for the effective floating position of the advancing shipincluding trim and sinkage. Variations are directly applied to the wetted hull portion under (andslightly above) the actual wavy free surface level.


1 Introduction

The optimization process is established in terms of an iterative marching scheme of successivesub-optimization loops which built on top of each other. In each sub-optimization the boundaryvalue problem is accessed by a linear perturbation approach around the current base point yield-ing a convex quadratic image of the solution space in a trust-region, a sub-optimization spacearound the current base point. This simplified image of the solution space is known to possess asingle minimum determined by the active constraints. Thus, fast and straightforward evaluationof the gradients of the objective function and the constraints is enabled, allowing a simultaneoustreatment of numerous, locally acting optimization variables which introduces great freedom tothe hull variation.

This particular optimization concept was conceived to pursue the following goals:

Optimization of the wave-making characteristics, i.e., tangible reduction of the wave patternresistance of the hull at its dynamic floating position.

Self-adjusting hull geometry variation, driven directly and solely by the hydrodynamic optimiza-tion.

Concerted reduction of particular adverse wave components. Improvement of the system identification, i.e., correlation of cause and effect of local hull varia-

tions and their respective fingerprints in the wave spectrum and in the wave pattern resistance.

All aspects of the proposed optimization approach are presented. Chapter 2 introduces the optimizationapproach and outlines the process flow. Chapter 3 elaborates the hydrodynamic analysis in terms ofCFD simulation of the nonlinear free surface flow and it represents the wave cut analysis techniqueas applied to the computed wave pattern. Chapter 4 substantiates the particular choice of flow relatedoptimization variables. A perturbation approach is derived to access the boundary value problem ina straightforward manner. The impact of variations on the hull form, on the flow field, the free sur-face wave elevation and finally the free wave spectrum and the wave pattern resistance is presented.The compilation of gradients matrices for the objective function and the constraints is discussed. InChapter 5 the constrained minimization problem is introduced, the optimization functional is set-up,the necessary conditions for a minimum are applied, and the solution by an iterative weighting schemeis outlined. The chapter closes with a discussion of the hull form adaptation scheme. In chapter 6the capabilities of the present optimization approach are illustrated by means of one academic and onepractical ship optimization application. The former refers to the standard Wigley hull, the latter to astate of the art twin screw ferry featuring a bulbous bow and tunnelled transom stern. Finally, in chap-ter 7 the main achievements and contributions of the present work are summarized and an outlook tofurther research work is given.


2 Hydrodynamic optimization approach

The basic ideas underlying the presented hydrodynamic ship hull optimization approach areoutlined. The pursued goals are stated. The optimization concept and the process flow isdescribed.

Over the last decade ship optimization based on computer simulations has become an indispensablefactor in the development of new hull forms. Optimization applications comprise all engineering tasksinvolved in the design and construction process of a ship. However, an important task at an early designstage is the optimization of the hydrodynamic properties of the ship hull. In this respect the reductionof the ship resistance and, hence, the power consumption pays off economically for the shipownerand/or the operator in terms of savings of operating costs. An additional benefit is less environmentalimpact due to reduced emissions of exhaust-gas and noise, less wastage of fossil fuel and a protectionof the shore lines as a consequence of a reduction of the waves emitted by the ship.

A considerable resistance component stems from the steady ship wave system. This effect amplifies 1as the ship speed increases. Fast displacement type ships consume 50% and above of their installedpower to overcome the wave resistance. It therefore is mandatory to reduce wave-making as muchas possible. In order to do so early in the design process a focused hull form optimization approachhas been developed and implemented in terms of a MATHEMATICA (Wolfram (2003)) based opti-mization environment. It controls the optimization process flow, it comprises a sensitivity analysis, theoptimization kernel and a longitudinal wave cut analysis (WCA) scheme, and it establishes the connec-tion to the CFD (Computational Fluid Dynamics) system SHIPFLOW. The entire optimization processis fully automated. Nevertheless, user interaction is supported if need be.

2.1 Motivation and goals

An extensively studied field of ship hydrodynamics is the determination of the wave pattern and thewave resistance of a ship moving with constant speed through otherwise calm water. This is explainedby the importance of the wave flow for the design of the entire ship hull. Hence, hydrodynamic ship hulloptimization has been challenging for numerous researchers since decades. A comprehensive compila-tion of literature on geometric ship hull modelling and CFD based hull optimization since the outgoing19th century until the state of the art in 1998 is given by Harries (1998). The reader is referred to thispublication for additional references. Milestones in the development of wave resistance optimizationmethods are in chronological order: 2 Michell (1898), Taylor (1915), Weinblum et al. (1957), Inui(1962), Pien and Moore (1963), Lin et al. (1963), Wigley (1963) (the collected papers of Sir Thomas1 This holds true for displacement type ships; planning or semi-planning hulls experience a resistance reduction after transi-

tion to the planning condition.2 this list neither claims to be complete nor representative



Method Flow Objective Evaluation of Free Constraintsanalysis function objective function variables (N)

Experimental EFD Residuary Froudes hypothesis Distinctive Form parameters,study resistance, (k-factor method), hull features max. dimensions,

wave height wave probes testing (N 101) stability...Interactive / CFD Wave Hull pressure Hull shape - dito -Automatic inviscid (pattern) integration, wave parametersoptimization resistance pattern analysis (N 102)Present CFD Wave Wave pattern Flow related - dito -automatic inviscid pattern analysis quantities (at dynamicoptimization resistance (wave spectrum) (N > 103) floating position)

Tab. 2.1: Wave resistance optimization techniques.

Havelock on hydrodynamics), Sharma (1966), Kracht (1978), Hsiung (1981), Janson and Larsson(1996), Nowacki (1997), Sding (1997), and Harries (1998).Due to the availability of fast and reliable CFD codes, in particular free surface Rankine panel codes,advanced CASHD (Computer Aided Ship Hull Design) tools for the geometric hull modelling anda wide range of suitable optimization methods, hydrodynamic ship hull optimization has becomea rapidly developing field of both research and practical application. Tools range from fully auto-matic implementations over semi-interactive environments to highly interactive optimization processes.The latter are still favoured by many shipyards and model basins and often involve EFD (Experi-mental Fluid Dynamics). Recent CFD based wave resistance optimizations are reported, e.g. byBaskaya (1997), Hirayama et al. (1998), Huan and Huang (1998), Huang et al. (1998), Harries and Abt(1999), Birk and Harries (2000), Harries et al. (2001), Hendrix et al. (2001), Percival et al. (2001),Peri et al. (2001), Sding (2001a), Tuck et al. (2002), Birk and Harries (2003), Heimann and Harries(2003), Maisonneuve et al. (2003), Valdenazzi et al. (2003), Valorani et al. (2003), and Grigoropoulos(2004).The formation of waves generated by a ship moving with constant speed through unrestricted calmwater is determined by its hull shape and speed. 3 The design speed, normally, is fixed very early bythe prospective shipowner and/or the operator. A fleet, service and/or route optimization might havebeen conducted to determine an appropriate service speed. Hence, a minimum requirement to shipdesign is that the ship reaches the demanded service speed. However, more critical is the requirementof an optimal hydrodynamic performance at (or around) the service speed. In terms of resistance andpower consumption the latter requirement is accomplished solely by a favourable hull design.

The present optimization approach aims at an improvement of the wave-making characteristics, i.e.,the minimization of the energy losses associated with the wave formation along the hull which can bemeasured in terms of the free wave spectrum and the wave pattern resistance. This improves the systemidentification by tracing hull variations up to their respective fingerprints in the spectral distributionand in the wave pattern resistance. Hull variations are driven directly by hydrodynamics, i.e., the hullshape is controlled via a selected flow quantity along the hull. The motivation of addressing the waveresistance problem by an optimization approach which focuses on wave cut analysis and, hence, on the3 disregarding the influence of different loading conditions


2.2 Cause and effect chain

free wave spectrum and the wave pattern resistance may be best given by citation of selected historicalreferences:

"[...] The above important equation [editorially: integral equation for the wave pattern resistance de-termined from the free wave spectrum] not only gives a method of calculating wave-making resistancebut also clearly indicates that the wave-making resistance can be reduced only by reducing the ampli-tude of each individual elementary wave. Hence, the main effort of our research work in this field is toderive a method of reducing these amplitudes. [...]"Pien and Moore (1963)"[...] Since the free-wave spectrum suffices to describe the dominant part of the entire wave field,we can approximately predict the wave flow in a major part of the fluid, once we have measured itat a few places. Further, it should be noted that within the linearized approach [...] the free-wavespectrum is a linear function of the generating source distribution whereas the wave resistance is not.Hence we can predict the wave-making properties of certain linear combinations of systems which havebeen analyzed individually. For example, if we only know the wave resistance of a certain hull form,we cannot estimate rationally the wave-resistance of a catamaran, consisting of a pair of such hulls.However, if we know the free-wave spectrum of the single hull, we can reasonably predict the waveresistance of any parallel configuration of two or more such hulls in the horizontal plane. Evidently,this principle has potential applications to design work. [...]"Sharma in Eggers et al. (1967)"[...] The use of the wave-resistance integral [editorially: integral equation for the wave pattern re-sistance determined from the free wave spectrum] with experimental measurements of the amplitudefunction A() to determine the total wave resistance provides a direct measurement of the wave re-sistance without recourse to Froudes hypothesis. This approach is known as wave pattern analysis.A significant feature of this technique is that the measured quantity A() is linear in the ships dis-turbance, as compared to the quadratic wave resistance. By relating changes in the wave amplitudeto changes in hull form, a linear optimization of the hull shape can be achieved more directly than ispossible by studying the effects of shape on the total wave resistance. [...]"Newman (1977)The present optimization approach substantially differs from other approaches to wave resistance min-imization in the way it tackles this objective. Table 2.1 gives an outline of the present optimizationapproach in comparison to EFD and other CFD based wave resistance optimization techniques. Dif-ferences to related methods comprise the

Objective function: Wave pattern resistance (free wave spectrum)Evaluation of the objective function: Wave pattern analysis of the computed ship wave patternFree variables: Flow related quantities along the hull surface (N > 103)Scope: Optimization of confined hull regions or the entire hull in its dynamic floating position

2.2 Cause and effect chain

The cause and effect chain from the variation of an optimization variable up to its impact in the wavespectrum and the wave pattern resistance is, in its proper sense, of complicated and nonlinear nature.



In the proposed method the whole chain is simplified, i.e., linearized by linear perturbation of theboundary value problem around its actual state. The boundary value problem is that of potential the-ory dealing with the nonlinear free surface conditions. By application of the perturbation approachthe nonlinear relations are transferred to explicit equations depending in a linear and straightforwardmanner on the optimization variables.

As a consequence, the whole cause and effect chain starting with the variation of the optimizationvariables, resulting in a hull form variation, affecting the flow quantities like the free surface velocitiesand the wave formation, and finally bringing about a variation of the free wave spectrum and the wavepattern resistance, as the latter determined by longitudinal wave cut analysis, can be consistently traced.This opens the track to an improved system identification and optimization since hull variations can beexplicitly traced all the way to their respective fingerprints in the spectral distribution and in the wavepattern resistance. In the present scheme the cause and effect relations can be simply represented bysensitivity terms or gradients.

2.3 Process flow

The optimization process flow is shown in figure 2.1. A full sub-optimization task is performed byprocessing the flow chart once from the initial quality assessment down to the improvement assessment.Normally, a series of sub-optimization tasks is conducted by progressively reentering the loop.

The flow simulations are conducted by means of the nonlinear free surface potential flow module ofthe CFD system SHIPFLOW. SHIPFLOW is a Rankine panel solver requiring a panelization of thehull and the free surface. On the basis of the waves computed with SHIPFLOW a detailed performanceassessment is carried out in terms of the free wave spectrum and the wave pattern resistance. A longi-tudinal wave cut analysis utilizing a novel implementation of the longitudinal wave cut method in thecode SWASH, see chapter 3, is undertaken.

Within the optimization environment five stages are highly integrated setting up a complete sub-optimization task:

Initial quality assessment Initialization Sensitivity analysis Hull improvement Improvement assessment

Initial quality assessment

The optimization process commences with the initial 4 quality assessment. At this stage the processcontrol parameters and the hull geometry enter the process. Control parameters concern the globalprocess flow, the perturbation and sensitivity analysis, the free surface flow simulation, the wave cutanalysis and the set-up and solution of the minimization problem. The hull geometry is given in terms4 or an intermediate quality assessment when the process progresses


2.3 Process flow

Freesurfaceflowsimulation(CFD)

Performanceassessment(WCA)Detailedshapeevaluation

Systematichullperturbationanalysis

Systematicvariationofdesignvariables

(flowquantityrelated)

Impactonhullform(inverseperturb.solution)

(Re-)Initializationofoptimizationtask

(variables, constr.,bounds)

Impactonflowfield(waveelevat.,flowquant.)

Impactonwaveenergydistribution

(freewavespectrum, RWP)

Transfermatrices

Parent/interimhullform

Controlparameterset(processflow)

Evaluationofgradients(MoM,constraints,bounds)Gradientsmatrices

Minimizationofobjectivefunctionimplyingconstraints

(iterativescheme)

Generationofimprovedhullform&

predictionofgains/changes


Performanceassessment(WCA)

Detailedshapeevaluation&furtherprocessing

Improvedhullform

Modificationofcontrolparameterset

(Restart)

Stop

Initi

alqu

ality

asse

ssm

ent

Initi

aliza

tion

Sensi

tivity

anal

ysis

Hull

impr

ovem

ent

Impr

ove

men

t ass

essm

ent

Automaticadaptationof

optimizationtask


Performanceassessment(WCA)Detailedshapeevaluation

Systematichullperturbationanalysis

Systematicvariationofdesignvariables

(flowquantityrelated)

Impactonhullform(inverseperturb.solution)

(Re-)Initializationofoptimizationtask

(variables, constr.,bounds)

Impactonflowfield(waveelevat.,flowquant.)

Impactonwaveenergydistribution

(freewavespectrum, RWP)

Transfermatrices

Parent/interimhullform

Controlparameterset(processflow)

Evaluationofgradients(MoM,constraints,bounds)Gradientsmatrices

Minimizationofobjectivefunctionimplyingconstraints

(iterativescheme)

Generationofimprovedhullform&

predictionofgains/changes


Performanceassessment(WCA)

Detailedshapeevaluation&furtherprocessing

Improvedhullform

Modificationofcontrolparameterset

(Restart)

Stop

Initi

alqu

ality

asse

ssm

ent

Initi

aliza

tion

Sensi

tivity

anal

ysis

Hull

impr

ovem

ent

Impr

ove

men

t ass

essm

ent

Automaticadaptationof

optimizationtask

Fig. 2.1: Optimization process flow.



of an offset or panel input point mesh. The offset geometry is used to perform an initial nonlinearfree surface CFD computation with free trim and sinkage which is forced to firm convergence. Thecomputed free surface elevations and the panel mesh geometry are then passed to a longitudinal wavecut method which provides the wave spectrum and the wave pattern resistance. 5 Details are given inchapter 3. The flow solution from SHIPFLOW along with the wave spectrum and the wave patternresistance from the wave cut analysis using SWASH serve as the base point (base solution) for thesub-optimization task.

Initialization

At the second stage the optimization variables (flow related quantities in terms of the hull panel sourcedensities) are set according to the control parameters. The constraints (bounds) are determined. Asystematic hull perturbation analysis is conducted which correlates the optimization variables, the (dis-cretized) hull geometry, the flow velocities, the wave formation, the wave spectrum and the wavepattern resistance. This yields transfer matrices which serve as the basic instrument for the sensitivityanalysis. Details are given in chapter 4.

Sensitivity analysis

Once the transfer matrices are assembled the systematic variation of the optimization variables (i.e., thehull panel source densities) starts. The variation of a single optimization variable has an impact on thehull form, on the flow field, on the wave formation and, finally, on the free wave spectrum and the wavepattern resistance. All these influences are determined within the present environment for all variables(by parallel solving) and are compiled in terms of gradients matrices for the objective function and theconstraints (bounds). Details are given in chapter 4.

Hull improvement

The gradients matrices are directly utilized by the hull improvement instance. The optimum theminimum of the objective function or measure of merit (MoM) is determined within the limits ofthe sub-optimization task. The governing linear equation system is repeatedly solved for the seekedoptimization variables in terms of an iteration scheme which is used to isolate the active from thepassive constraints. Finally, an improved hull form is derived applying the gradients matrices. The hullform is obtained in terms of a relocated hull panel input point mesh which possesses the same topologyas the initial mesh. Details are given in chapter 5.

Improvement assessment

The final stage of the sub-optimization task serves as the base point (base solution) for the successivesub-optimization loop. The improved hull geometry is sent again to SHIPFLOW to compute the fullynonlinear free surface flow. The longitudinal wave cut method then provides the wave spectrum andthe wave pattern resistance.

5 The evaluation of the free surface elevations and their bidirectional interpolation which yields the longitudinal wave cut isperformed outside SHIPFLOW by the wave cut method.


2.3 Process flow

The optimization process is terminated by three alternative stopping criteria. Details are given insection 6.1. If none of the stopping criteria apply the optimization enters the next sub-optimizationloop. The optimization process is fully automated requiring no user interaction. However, the usermay manually interrupt the process at certain points. This allows, for instance, to restart from anyprevious solution with a modified or adapted set of control parameters.

Formally, each sub-optimization task is composed of a prediction and a correction step. The predictionstep, essentially, comprises the optimization kernel, i.e., the initialization, the sensitivity analysis andthe hull improvement stage. In the correction step the predicted improvements are assessed by a fullflow and wave cut analysis. Here, the predicted optimization results are corrected for nonlinearities, forthe new dynamic floating position and for effects caused by the reconstruction of a coherent hull sur-face. The solution of the correction step then serves as the base point (base solution) for the subsequentsub-optimization task.


3 Hydrodynamic analysis

The hydrodynamic flow analysis comprises the evaluation of the nonlinear free surface waveflow by a CFD simulation and the analysis of the energy components contained within thewave pattern. The first task is accomplished by the free surface potential flow module XPANof the CFD system SHIPFLOW. The second task is performed by longitudinal wave cut analy-sis utilizing a new tool called SWASH, developed by the author. The potential theory basedCFD simulation as well as the wave cut analysis method are presented in this chapter.

An extensively studied field of ship hydrodynamics is the determination of the wave pattern and thewave resistance of a ship moving with constant speed through otherwise calm water. This is explainedby the importance of the wave flow for the design of the entire ship hull. Nowadays, advanced, reliableand fast CFD tools are available for the numerical evaluation of the free surface wave flow. Methodsbased on inviscid potential theory are widespread and are the first choice in practical wave resistancecomputations for a wide range of ship types and flow cases. Moreover, potential flow methods, orrather free surface Rankine panel methods, are extremely useful in the CFD based wave resistanceoptimization, for they are comparatively straightforward in handling, they are fast and they generatereliable results in terms of detailed flow information for a variety of applications.

Most of the CFD codes utilize integral resistance values derived from hull pressure integration. In thisway, however, information is lost on where beneficial and adverse effects originate. A more detailedexamination is attainable on the basis of the spectral distribution of wave energy along the componentsof the steady ship wave system. Hence, the wave pattern evaluated by means of a free surface Rankinepanel method are thoroughly analysed by a longitudinal wave cut analysis. In the present context wavecut analysis is used both in the sense of system identification and to provide the objective function ofoptimization. Wave cut analysis yields the wave pattern resistance RWP while by convention anintegration of the longitudinal pressure components over the hull provides the wave resistance RW .

3.1 CFD simulation

The steady ship wave system is determined by means of a CFD simulation. In the present work thenonlinear free surface Rankine panel module of the SHIPFLOW system is applied, see section 3.1.4.

The boundary value problem of potential theory is solved numerically. Boundary value problems areaddressed by boundary element methods (BEM) which require the discretization of all boundaries ofthe flow domain, here the hull and the wavy free surface. The boundaries are discretized either byfirst order flat or higher order panels. Potential functions are introduced by distributing singularities(usually sources and/or dipoles) along each panel. The boundary conditions on the hull or the wavyfree surface are enforced for each panel at its control point. The solution of the boundary value problemleads to a linear(ized) system of equations for the unknown panel source densities. Once the source



densities are known the velocities and the pressure forces are evaluated. Either linear or nonlinear freesurface conditions are applied. Nonlinear methods have been found superior to linear methods withrespect to predicting the wave amplitudes, the phases and the wave resistance, see Jensen (1988), Raven(1996) and Janson (1997). For a numerical treatment the nonlinear free surface condition is linearizedaround a known base solution. Since the free surface condition is to be applied at the a priori unknownfree surface an iterative solution scheme is used. In the iteration scheme the flow quantities and thefree surface position are updated in an alternating manner. The dynamic floating position is iterativelyupdated by a force and momentum balance.

At present it is not possible to compute the ship resistance by CFD methods, whether viscous or invis-cid, to the same accuracy as in a towing tank test by means of EFD (Experimental Fluid Dynamics).CFD tools still cannot compete with EFD when it comes to power prediction. However, even if CFDcannot provide the absolute power consumption to a high level of accuracy, CFD methods are wellapplicable in comparing different hull shapes or variants in terms of their hydrodynamic performance.This particularly holds true for nonlinear free surface Rankine panel solvers. Compared to EFD, appli-cation of CFD is

fast, relatively inexpensive, not sensitive to measurement uncertainties, reproducible and able to provide detailed flow information.

These properties are especially valuable for CFD based hull optimization. Hence, nonlinear free surfaceRankine panel solvers are frequently used by ship model basins, shipyards and consultants for manualand sometimes semi-automated or even fully automated hull shape improvement.

Solvers that fall in the category of nonlinear free surface Rankine panel methods and which havebeen successfully applied in ship design and optimization are, for instance, KELVIN by Sding(2000), RAPID by MARIN, see Raven (1996) and Raven (2004), SHALLO/-SHALLO by HSVA,see Jensen (1988) and Marzi (2004) and the potential flow module XPAN of the SHIPFLOW systemby FLOWTECH, see section 3.1.4.

3.1.1 Boundary value problem

The boundary value problem of potential free surface flow is thoroughly discussed and documented inthe literature. For instance see Dawson (1977), Ni (1987), Jensen (1988), Jensen et al. (1989), Nowacki(1995), Raven (1996) and Janson (1997) for literature on this topic. In this section only an outline ofthe boundary value problem is given. For a detailed discussion the reader is referred to the givenreferences.

Reference coordinate system and normalization

The flow is described in an Eulerian sense, i.e., the reference coordinate system is fixed to the shiphaving the same speed but does not follow its dynamic trim and sinkage. A right-handed Cartesian


3.1 CFD simulation

system is defined with the origin located at the fore perpendicular in the undisturbed free surface level,x pointing downstream and z pointing upward, see figure 3.2.

All quantities are used in non-dimensional form, normalized by the ship speed |~U| and/or the lengthbetween perpendiculars LPP.

Laplace equation

The governing equation of potential free surface flow is the Laplace equation which is a linear, homo-geneous partial differential equation derived from mass continuity

~2 = 0 . (3.1)

Velocity potential

Assuming an inviscid (ideal) incompressible fluid with irrotational flow, the velocity components canbe determined from the gradient of a scalar potential function

~U = |~U|~ . (3.2)

The total velocity potential comprises the potential of the undisturbed onset flow and the potentialfor the disturbance velocity caused by the ship

= + . (3.3)

The velocity potential has to satisfy the Laplace equation (3.1) and it has to comply with the boundaryconditions.

Kinematic and dynamic hull boundary conditions

For a well posed boundary value problem boundary conditions need to be defined. The kinematic hullboundary condition implies that the flow velocity must have a known component in the hull normaldirection 1

n = F , (3.4)

where, usually F = 0, since no fluid particle is supposed to pass through the surface of a rigid body. Interms of the disturbance potential the kinematic hull boundary condition reads

n =U ~n+ F , (3.5)

where U = ~U/|~U| indicates the unit velocity vector of the undisturbed onset flow. An additionaldynamic hull boundary condition may be imposed, claiming equilibrium between the hydrodynamicand hydrostatic pressure forces on the wetted hull portion and the ships weight distribution. Thisintegral condition primarily determines the dynamic trim and sinkage.1 which is directed into the fluid



Kinematic and dynamic free surface boundary conditions

At the free surface two more boundary conditions are applied, both of which need to be fulfilled at theinitially unknown wavy free surface. The kinematic free surface condition implies that the flow mustbe tangential to the free surface, i.e., no fluid particle is supposed to leave the surface = f (x,y)

x

x +

y

y

z = 0 , (3.6)

where refers to the distance (normalized) of the free surface from the undisturbed initial plane. therefore describes the wave elevation (normalized). The second condition, the dynamic free surfaceboundary condition, states that the static pressure, expressed through Bernoullis equation, must beconstant (atmospheric) at the free surface

F2n

+12

[(x

)2+

(y

)2+

(z

)21]

= 0 . (3.7)

The kinematic (3.6) and dynamic (3.7) free surface boundary conditions are given in normalized form.Fn in (3.7) indicates the Froude number as defined by

Fn =VSgL

.

where VS the ship speed and g the acceleration due to gravity. Here the characteristic length L is takenas the length between perpendiculars LPP.

Linearization of the free surface boundary condition

The free surface problem is nonlinear since the free surface boundary conditions, (3.6) and (3.7), arenonlinear and are to be imposed at the initially unknown free surface. Hence, the flow quantities dependnonlinearly on the location of the free surface. Solution methods for the fully nonlinear free surfaceproblem have been proposed since the 1980s. Present methods linearize the free surface boundaryconditions around a known base solution and solve the problem in an iterative manner. In the iter-ation scheme the flow quantities and the free surface elevation are updated in alternating steps, seesection 3.1.3. A common approach is to linearize the free surface boundary conditions in a first orderTaylor series expansion around the known base solution and to introduce perturbations due to the hulland/or the waves. Thus, higher order contributions are assumed to be small. Reviews of differentlinearizations are presented, e.g., in Newman (1976) and Raven (1996, 1997).The majority of the presently available nonlinear free surface Rankine panel solvers adopt the so calledDawson linearization of the free surface boundary conditions, as originally suggested by Dawson(1977). In Dawsons method the linearization is conducted around the so called double-body flow 2as base solution. The kinematic and dynamic boundary conditions are linearized in a perturbationsense. The perturbation is due to the waves. The free surface boundary conditions, actually, are to besatisfied at the initially unknown free surface. But, so as to allow a direct solution the conditions aretransferred to and solved at the known free surface. Consistency would require to incorporate transferterms to account for this transfer of the boundary conditions. Dawsons linearization is known to be an2 In a double-body flow the water surface is treated as a symmetry plane at which the underwater portion of the hull is

mirrored.


3.1 CFD simulation

inconsistent linearization since it neglects these transfer terms. However, practical applications haveshown that Dawsons method performs equally well or even more stable than other more consistentlinearizations, see Raven (1996) and Janson (1997) for a thorough investigation. At convergence theinconsistency of the linearization is no longer relevant.

The free surface elevation and the velocity potential are expanded to first order in Taylor seriesaround the known base solution . The expansions are then introduced to the free surface boundaryconditions neglecting higher order contributions in and or mixed higher order terms. Finally, thelinearized kinematic and dynamic boundary conditions are combined to give a formulation in knownand unknown velocities and their derivatives. The linearization of the free surface boundary conditionsis described in detail by Janson (1997).Once the new velocity potential is determined the free surface elevation is obtained from the lin-earized free surface boundary condition 3

(x,y) = 12

F2n

[1+

(x

)2+

(y

)2+

(z

)22

(x

x +

y

y +

z

z

)], (3.8)

with being the velocity potential of the known base solution.

Radiation and transom conditions

Further to the above conditions a radiation condition is required which implies that the disturbancevelocity due to the presence of the hull vanishes as the distance from the hull r approaches infinity

limr |

~ |= 0 . (3.9)

In the steady state solution a further radiation condition is needed to prevent waves from propagatingupstream of the hull. However, this condition is not formulated explicitly in Rankine panel methods.It is enforced implicitly by the numerical method, for instance by applying an upstream differencingscheme and/or an upstream shift of the free surface collocation (control) points in conjunction with theso called raised panel method. 4

If a ship possesses a transom stern a special transom condition is required to model the flow separationat the transom edge (according to the Kutta condition) and the flow behaviour aft of the transom stern.Further boundary conditions are to be applied in case of restricted waters at the bottom and (if present)at canal-walls. In inviscid flows typically a Neumann condition, i.e., a zero normal flow condition, isapplied at these boundaries.

Singularity distribution

Potential functions are introduced by distributing singularities on the boundaries of the flow domain,essentially the hull and the wavy free surface. 5 The singularities (e.g., sources or dipoles) themselves3 linear(ized) in the new velocity potential 4 In the SHIPFLOW code both an upstream differencing operator is applied longitudinally for the evaluation of the numerical

derivatives and, in addition, the free surface collocation points are shifted upstream relative to the corresponding freesurface panels, see Janson (1997) for details.

5 Unless the wave Green function is applied, known as Havelock singularity, which inherently fulfills the linearized freesurface boundary condition and only requires a singularity distribution on the hull.



already satisfy the Laplace equation (3.1), see e.g. Newman (1977) and Wendt (1996). Usually, sourcesingularities are distributed along the boundaries of the flow domain and are integrated to give thedisturbance potential

=Z Z

SD

qrpq

dS , (3.10)

where q is the source density per unit area at point q on the boundary surface SD and rpq is the distancefrom point q where the source is located to an arbitrary point p where the potential is to be computed.

Introducing (3.10) to the kinematic hull boundary condition (3.5) yields the Fredholm integral equationof the second kind which serves as an explicit relation for the unknown hull source densities. Intro-ducing (3.10) to the combined, linearized free surface condition (if the free surface is present) yieldsadditional relations at the unknown free surface. A simultaneous solution of both relations then yieldsthe seeked a priori unknown source densities on the hull and the free surface.

3.1.2 Discretization

However, a solution of the boundary value problem in closed form for practical ship application casesis infeasible. Hence, the boundary value problem is solved numerically. A numerical solution requiresthe discretization of the boundaries of the flow domain, essentially the hull and a reasonable portion ofthe wavy free surface. Panel methods discretize the boundaries by quadrilateral or triangular panels.

Panel methods for computing the potential flow around arbitrary three dimensional bodies were in-vented by Hess and Smith (1962). They introduced flat quadrilateral panels with a constant singularitydistribution to approximate the boundary value problem. In their notation the flat quadrilateral panelsare generated from so called input points which constitute a coherent point mesh along the hull. Froma topological point of view input points are equivalent to offset points which often are arranged alonghull sections and profile curves and are located directly on the hull surface. However, it is impossibleto connect the input points by flat quadrilateral panels along a curved hull surface without introducinggaps between the panel edges. In the original Hess & Smith method the flat quadrilateral panels aredetermined from the input points so that the panel corner points are at least a close approximation of theguiding input points and that the panel normal direction is a good approximation of the actual surfacenormal. The boundary conditions are enforced for each panel at a panel control point. 6 Later Hess(1972, 1979) extended the method to higher order curved panels with a linear singularity distributionacross the panels and to lifting surfaces.

As a consequence of the discretization of the boundary value problem the integral equations are trans-formed to sum equations, which yield an explicit relation for the unknown panel source densities j:

NFSj=1

j Ai j = Bi i = 1, ,NFS , (3.11)

where Ai j indicates the influence coefficient from panel j to the velocity at panel i, Bi is the inhomoge-neous term at panel i. NFS accounts for the total number of panels, including the hull and free surface6 In the original Hess & Smith method the so called null point is suggested where the panel itself induces no velocity in

its own plane. However, the determination of the null point requires the solution of additional simultaneous nonlinearequations, so, usually, it is simply approximated by the centroid of the panel.


3.1 CFD simulation

panels. The influence coefficients Ai j are determined from the induced velocities 7 Xi j, Yi j, Zi j in therespective directions and, in case of the free surface portion, from the velocities and velocity derivativesof the base solution. Details are given in Janson (1997).The free surface domain is discretized by so called Rankine panels. The linearized boundary conditionis satisfied in a discrete sense at the free surface panel collocation points. Accordingly, the free surfaceelevation is evaluated in a discrete sense with the elevation at collocation point i given by virtue of thelinearized free surface boundary condition (3.8):

i = 12 F2n

[1+ 2x i + 2y i + 2z i2 (x i x i + y i y i + z i z i)

]i = NH +1, ,NFS , (3.12)

with x = /x etc. and NH < i NFS for the free surface panels.

3.1.3 Numerical solution

The numerical solution of the nonlinear free surface boundary value problem is thoroughly describedby Jensen (1988), Raven (1996) and Janson (1997).State of the art CFD systems make use of the so called raised panel method. The free surface panels areraised by a certain 8 distance above the free surface collocation points possibly in conjunction with anupstream collocation point shift, Jensen et al. (1986). In this way the radiation condition is implicitlyenforced and convergence is improved. As a further numerical feature the velocity derivatives at thefree surface are determined along longitudinal panel rows by an upstream differencing scheme andtransversally along rows with constant x by a central difference scheme, as originally suggested byDawson (1977).Equation (3.11) provides a linear system of equations for the unknown hull and free surface panelsource densities. But, since the free surface condition is to be applied at the a priori unknown freesurface an iterative solution scheme is used where (3.11) is solved successively. In each iteration theboundary value problem is linearized with respect to the solution of the previous iteration. The setupis as follows:

1. Compute a base solution, e.g., by adopting a Neumann or a double-body condition 9 at theundisturbed free surface.

2. Use the velocities from the previous step to compute the free surface elevation from the linearizeddynamic free surface condition (3.8) at the undisturbed free surface.

3. Move the free surface panels to the new free surface computed at the previous step.

4. Move the latest known flow solution to the adjusted free surface panelization of the previousstep, without being recomputed.

5. Solve the linearized boundary value problem according to (3.11) at the actual free surface.7 Xi j , Yi j , Zi j are pure geometrical quantities and represent the induced portion from panel j to the velocity at panel i in the

x-, y- and z-direction respectively.8 carefully selected9 Applying the double-body condition yields the Bernoulli wave.



Fig. 3.1: Zonal approach of the CFD system SHIPFLOW (courtesy of FLOWTECH Int. AB.)

6. Apply the solution of the previous step to adjust the free surface elevation according to thelinearized dynamic free surface condition (3.8).

7. Continue with step 3 until convergence.

Firm convergence is requested for the maximum wave change, for the maximum change of the sourcedensities and, if allowed to freely adjust, for the trim and sinkage of the hull in successive iterations.The dynamic floating position is updated via a force and momentum balance at each iteration.

The wave resistance is computed from the converged solution by integration of the longitudinal pres-sure components over the hull. For further details be referred to Janson (1997).

3.1.4 The CFD system SHIPFLOW

In the present work the CFD simulation of the steady ship wave system is conducted by means of thefree surface Rankine panel module XPAN of the CFD system SHIPFLOW 10, see e.g. Larsson et al.(1989, 1990, 2004a,b), Larsson (1993) and Janson (1997).SHIPFLOW solves the boundary value problem of potential theory numerically. The boundaries of theflow domain, essentially the hull and the wavy free surface, are discretized either by flat or, as in thehigher order method, by bi-parabolic quadrilateral panels. Source singularities 11 are distributed alongeach panel either with a constant source density or, as in the higher order method, with a linear distri-bution of the source density along the panel. The boundary conditions on the hull and the wavy freesurface are for each panel enforced at a control point defined as the centroid of the panel. Raised panelsare utilized at the free surface in conjunction with an upstream collocation point shift. Tangential flowseparation at the edge of a transom stern (if present) is modelled by an additional free surface transomgroup which extents downstream of the transom. So called extra hull panels above the free surface levelmight be used in case of ships with transom sterns or complicated geometries to stabilize the conver-gence history. The solution of the boundary value problem leads to a linear system of equations for theunknown panel source densities. Once the source densities are known, the velocities and the pressureforces are evaluated. SHIPFLOW adopts either a linear or the nonlinear free surface condition. For a10 FLOWTECH Int. AB, Gteborg, Sweden, http://www.flowtech.se11 and dipoles on lifting surfaces and on the wake sheet


3.1 CFD simulation

numerical treatment the nonlinear free surface condition is linearized around a known base solution.Since the free surface condition is to be applied at the a priori unknown free surface contour an itera-tive solution scheme is used. In the iteration scheme the flow quantities, i.e., the source densities andvelocities, and the free surface position are updated in an alternating manner, see section 3.1.3. Thedynamic floating position is iteratively updated by a force and momentum balance.

Prominent features of SHIPFLOW/XPAN are:

Wave resistance from pressure integration over the wetted hull surface

Wave pattern resistance from a transverse wave cut method 12

Linear and nonlinear wave pattern

Longitudinal and transverse wave cuts

Flow velocities

Pressure distribution

Dynamic trim and sinkage

Shallow water effects

Multihull option

Automated mesh generation

Propeller representation by an actuator disk model

Lifting surfaces

Induced resistance and lift

The SHIPFLOW code is specifically designed for steady ship hydrodynamics. In addition to the invis-cid potential free surface flow, SHIPFLOW also offers modules to compute boundary layers, viscousflow effects and drag. The way SHIPFLOW handles these unique problems is by splitting the flowinto three zones, which allows an efficient simulation of the governing flow phenomena. The zonalapproach is outlined in figure 3.1. A full investigation comprises the following three stages which areprocessed successively:

Zone 1 Potential flow calculation. Rankine panel method with linear or nonlinear free surface bound-ary conditions and adjustable dynamic floating position.

Zone 2 Boundary layer calculation. Momentum integral method for laminar and turbulent boundarylayers (computation of transition point).

Zone 3 RANSE calculation. Finite difference based solution of the Reynolds-Average Navier-StokesEquations (RANSE) applying a k- turbulence model on a cylindrical structured grid.

12 SHIPFLOW Release 2.8 or higher



SHIPFLOW is robust in application and extensively validated. It comes with an automated meshgeneration utility, it provides a variety of control mechanism and I/O capabilities to the user, supplyingdetailed results. SHIPFLOW Release 2.8.10 and higher provides additional, specifically customized 13interface capabilities like the I/O of the panel geometry, of selected influence coefficients and certainmechanism for the SHIPFLOW execution control. Moreover, the SHIPFLOW system is widely usedby ship model basins, shipyards and consultants both for hydrodynamic analysis in the preliminarydesign stage and for hull shape improvement.

The SHIPFLOW system was therefore selected for the CFD computations in the present work.

3.1.5 Application aspects

The inherent neglect of the viscosity by potential flow methods implies that wave-viscous interactionscannot be captured. A thorough investigation, both numerically and experimentally, of wave-viscousinteractions including propeller effects is reported by Nowacki and Sharma (1972). Wave-viscous in-teractions occur mainly in the stern region where wave amplitudes tend to be overpredicted by CFD.However, the differences are small for the ship types and speed range particularly addressed by thepresent optimization approach: relatively fast and slender hulls like ferries, RoPax, container vesselsetc.. Potential flow codes also assume the boundary layer to be sufficiently thin. This is a valid assump-tion for the forebody of a displacement ship and for the entire hull of a fast ship where the boundarylayer detaches the transom edge without considerable thickening. CFD validation studies comparingcomputed with measured wave pattern showed the excellent ability of modern nonlinear free surfaceRankine panel methods to model the steady wave systems of the ship types and speed range 14 relevantfor the present work, see e.g. Raven (1996), Janson (1997), Raven and Prins (1998a,b), Nowacki et al.(1999), Heimann (2000), Valdenazzi et al. (2003), Heimann and Harries (2003). Furthermore, Rankinepanel methods proved to be sensitive even to small and locally confined hull form changes.

A well known and extensively studied feature of CFD methods, whether viscous or inviscid, is theirdependence upon the grid or mesh on which the discretized flow equations are solved numerically.This property also applies to Rankine panel methods. Further uncertainties are introduced by theraised panel method. These effects are attributed to numerical dispersion (wavelength error) and inparticular to numerical damping (amplitude error). Within the scope of the SHIPFLOW solver grid-dependence and CFD validation studies were reported, e.g., by Janson (1997), Harries and Schulze(1997), Schulze and Harries (1997) and Lee (2003). Janson (1997) provides a valuable guideline forthe panel mesh generation and the selection of certain control parameters.

Raven (1996) and Janson (1997) report comprehensive studies to the application of the nonlinear versusthe linear free surface conditions. In general, nonlinear free surface Rankine panel codes have beenfound superior in predicting the wave amplitudes, the phases and the wave resistance.

3.2 Wave cut analysis

The steady ship wave system, as determined by means of a CFD simulation, is further assessed by awave cut analysis. In the present scheme the longitudinal wave cut method is applied by means of13 Professor Dr. Carl-Erik Janson, Chalmers University of Technology and FLOWTECH Int. AB, Gteborg, Sweden14 0.2 Fn 0.4 (potentially higher Froude numbers)



x

y

Ex

WCy

SV

longitudinalwavecut

z,z

Q = 0

Q > 0

Fig. 3.2: Schematic sketch of the ship wave system (only one symmetric half is considered).

the MATHEMATICA based tool called SWASH (Ship Waves Analysis Light) developed by the author.SWASH is an implementation of the wave cut method following Sharma (1963, 1966) and Eggers et al.(1967).

Wave cut analysis (WCA) in the sense of system identification has shown to be a powerful toolin CFD based optimization of the wave-making characteristics of ships, e.g. Heimann (2000) andHeimann and Harries (2003). Most of the CFD codes utilize integral resistance values derived frompressure integration. In this way, however, information is lost on where beneficial and adverse effectsoriginate. A more detailed examination is attainable on the basis of the spectral distribution of waveenergy along the components of the steady ship wave system by utilizing the so called free wave spec-trum. This improves the system identification, i.e., the energy loss associated with the transverse anddiverging waves can be studied more clearly. Furthermore, the impact of local hull variations on theindividual components of wave formation can be traced by investigating the changes in the wave spec-trum with respect to the associated hull variations. This then allows a reduction of particular adversewave components. However, the primary aim of the present optimization approach is to minimize thetotal energy losses associated with the wave formation along the hull which can be measured in termsof the wave pattern resistance RWP as determined by the wave cut analysis.

As an additional benefit computed wave pattern and hence wave cut analysis based on them proveto be less sensitive to the flow field discretization than hull pressure integration. This is a tentative



result of related studies concerning that topic, e.g. Janson (1997), Raven and Prins (1998a,b) andHeimann and Harries (2003).

3.2.1 Boundary value problem

The boundary value problem of the steady linear free surface potential flow is thoroughly discussed anddocumented in the literature, see Michell (1898), Lord Kelvin (1906), Wehausen and Laitone (1960),Eggers (1962), Inui (1962), Newman (1963), Wigley (1963) (the collected papers of Sir Thomas Have-lock on hydrodynamics) and Sharma (1965) for a condensed selection of literature on this topic. In thissection only a brief outline of the problem is given. For an introduction see also Newman (1977).

Reference coordinate system and normalization

The flow is described in an Eulerian sense, i.e., the reference coordinate system is fixed to the ship.A right-handed Cartesian system is defined with the origin located at the fore perpendicular in theundisturbed free surface level, x pointing downstream and z pointing upward, see figure 3.2. Infinitewater depth is assumed, i.e., the water depth h is greater than half the fundamental wavelength 0:h > 0/2.All quantities are used in non-dimensional form. Length related measures are normalized by the basicwavenumber

k0 =g

V 2S, (3.13)

where g is the acceleration due to gravity and VS the ship speed. VS is assumed constant. In otherwords: The problem described is of steady-state nature and all dependence on time is blended out.

The wave pattern resistance RWP is obtained in non-dimensional form by

RWP = RWPk30g , (3.14)

where the bold expression RWP stands for the dimensional resistance component and is the waterdensity.

Dispersion relation, wavelength and wavenumbers

Prior to the further derivations some important quantities should be defined. The dispersion relationfor infinite water depth connects the wavenumber k, the wavelength of the plane progressive wavemoving at an oblique angle with respect to the x-axis and the speed of the steady wave system. Thedispersion relation is given in non-dimensional form (normalized by k0) by

k() = 2pi() = sec2() . (3.15)

From (3.15) the wavelength directly follows as

() = 2pik() (3.16)



and the wavenumber k is defined according to (3.15) in non-dimensional form (normalized by k0) byk() = sec2() . (3.17)

Based on (3.17) the so called longitudinals() = k() cos() = sec() (3.18)

and transverse wavenumber

u() = k() sin() = sec() tan() (3.19)are derived. The component wave direction , the longitudinal s and transverse u wavenumbers aredefined within the integration bounds 15

0 pi/2 , 1 s < , 0 u < ., s and u are fully convertible into one another, and so are the relations based on them. 16

Linearized free surface boundary condition

A non-viscous (ideal) incompressible fluid with irrotational flow is assumed. The kinematic (3.6) anddynamic (3.7) free surface boundary conditions are linearized around the undisturbed free surface levelwith respect to the undisturbed onset flow. Their combination yields the well known Neumann-Kelvinboundary condition which is given in normalized form by

2x2

+z = 0 . (3.20)

Far field velocity potential

A velocity potential which satisfies the Laplace equation (3.1) and the linearized free surface boundarycondition (3.20) can be derived following Havelock (1934a) at a large distance from the disturbance(the ship) as

=pi/2Z

pi/2e(z sec

2()) cos() [AS() cos(sx+ uy)+ AC() sin(sx+ uy)] d , (3.21)

where AS and AC denote the sine (odd) and cosine (even) component, respectively, of the so called freewave spectrum. The velocity potential (3.21) satisfies the linearized boundary condition at the freesurface in the far field of the ship.

For modelling the whole wave system, including the local, bounded waves in the vicinity of the hull,a special form of the velocity potential can be utilized which is made up by another Greens function,as given in Havelock (1932). This inherently satisfies the linearized free surface boundary condition(3.20) in the whole flow domain, see e.g. Eggers et al. (1967) for details.The wave pattern resistance can be determined from the far field waves represented by the velocitypotential (3.21) alone, as shown below.15 for ship wave systems symmetrical to the midships plane16 The lower integration bound of s = 1 conforms by virtue of (3.18) with = 0, i.e., no waves are longer than those

determined by the fundamental wavelength.



3.2.2 Longitudinal wave cut analysis

The present optimization approach aims at the minimization of the wave pattern resistance which isdetermined by a longitudinal wave cut analysis. In case of flows symmetric to the ship center plane, asingle infinitely long wave cut parallel to the ship suffices to perform the whole analysis.

The longitudinal wave cut method is preferred to other wave analysis methods since it is compara-tively fast, relatively robust in application and it has a broad application range. This points are furtherdiscussed in section 3.2.4.

The used notation and axes orientation follows to a large extent Sharma (1963). Complementary ma-terial is selected from Sharma (1966) and Eggers et al. (1967).

Free wave system

Out of the double infinite manifold of all possible plane progressive waves, varying both in wavenum-ber k and in component wave direction , it is only a single infinite set of so called free waves whichcontribute to the wave pattern resistance, see e.g. Eggers et al. (1967). These free waves satisfy con-dition (3.15), i.e., wavenumber and wavelength of each component of the free wave system are deter-mined one-to-one by its wave direction. Furthermore, outside a confined region around the disturbanceby the ship it is the free waves which constitute the wave pattern. Whereas, the local disturbancearising from the presence of the nonfree waves vanish with the square of the reciprocal distance fromthe disturbance.

Assuming a control surface located parallel to the course of the ship at infinite distance 17 to the ship,the free wave system can be derived from the velocity potential (3.21) and from the Neumann-Kelvinlinearization of the dynamic free surface condition. The elevation of the free waves expressed in termsof the component wave direction is given by

(x,y) =pi/2Z

0

[AS() sin(sx+ uy)AC() cos(sx+ uy)] d , (3.22)

or as a function of the longitudinal wavenumber s by

(x,y) =Z

1

[AS() sin(sx+ uy)AC() cos(sx+ uy)] dds ds . (3.23)

After rearranging in terms of s, relation (3.23) results in a form suitable for further treatment

(x,y) =Z

1

{[AS() cos(uy)+ AC() sin(uy)] sin(sx)+

[AS() sin(uy)AC() cos(uy)] cos(sx)} dds ds . (3.24)

17 Here the control surface at y is adopted for practical reasons in order to conform with the SHIPFLOW internalrepresentation; an analogous derivation can be conducted for the control surface at y+, see Sharma (1963).



Relations (3.22) to (3.24) can be interpreted as a superposition of elementary plane progressive wavesof all feasible wave directions and varying wave amplitudes in compliance with the steadiness conditionfor the phase velocity, see relation (3.17) and compare e.g. Havelock (1934b). This results in the wellknown Kelvin wave pattern which is confined in a bisector to the x-axis of 1928 on deep water.The waves follow the ship. The transverse wave component according to the basic wavenumber andthe basic wavelength travels in the ships advance direction, i.e., with = 0. The transverse wavespossess transversally aligned wave crests and are composed of component waves up to = 3516.Larger values of correspond to the so called diverging waves which have shorter wavelength andconverge toward the origin, compare e.g. Newman (1977).

Fourier transformation

The continuous Fourier integral is applied to transform between the free waves and the related freewave spectrum, as it is represented further below. The Fourier transformation is given by

(x,y) = 1pi

Z

1

[S(s) sin(sx)+C(s) cos(sx)] ds , (3.25)

with the Fourier transforms

S(s) =Z

(x,y) sin(sx)dx ,

C(s) =Z

(x,y) cos(sx)dx , (3.26)

where S and C denote the sine (odd) and cosine (even) components, respectively, of the Fourier trans-forms. In terms of the longitudinal wave cut analysis (x,y = const.) in the Fourier transforms (3.26)represents a longitudinal wave cut either determined from a CFD simulation or from wave probe mea-surements in a towing tank. The longitudinal wave cut is given as wave elevations along varyingx-positions for a constant transverse cutting plane or offtrack position y = const..

Free wave spectrum

The Fourier transforms and the components of the free wave spectrum can be correlated by equating(3.25) with the expression for the free wave pattern (3.24) followed by a separation of variables. Byvirtue of the Fourier transforms (3.26) this yields

S(s) =Z

(x,y) sin(sx)dx = pi [AS() cos(uy)+ AC() sin(uy)] dds ,

C(s) =Z

(x,y) cos(sx)dx = pi [AS() sin(uy)AC() cos(uy)] dds . (3.27)



Resolving (3.27) for AS and AC finally results in

AS() =1pi

[S(s) cos(uy)+C(s) sin(uy)] dsd ,

AC() =1pi

[S(s) sin(uy)C(s) cos(uy)] dsd , (3.28)

with AS and AC denoting the sine (odd) and cosine (even) components, respectively, of the free wavespectrum. For the sake of simplicity AS and AC are referred to as free wave spectra from now on.

The notation of the free wave spectra in terms of A suggests a wave amplitude spectrum. Hence,AS and AC are frequently called wave amplitude functions, e.g. Newman (1977). However, this ter-minology is slightly misleading, since AS and AC do not actually have the physical meaning of waveamplitudes. In fact, the free wave spectra are better denoted as wave energy equivalents, i.e., termswhich express the energy losses associated with the formation of the individual components of the freewave system. The wave spectra correlate with the real and imaginary part of the degenerated form ofthe Kochin function. A detailed derivation and review is given by Eggers et al. (1967).The free wave spectra are pure functions of the hull shape and the ship speed assuming infinite wa-ter depth. They yield a direct measure of the wave energy distribution along the components of theship wave system. This is why they are extremely valuable in ship hull optimization. In the presentoptimization scheme the free wave spectra are directly utilized for decision making in terms of the ob-jective function. However, the free wave spectra ought to be applied with some care since the Fouriertransforms and the free wave spectra are not invariant against coordinate transformations, like a shiftof the origin, whereas the integrand of the wave pattern resistance, equations (3.30) and (3.32) below,is invariant against coordinate transformations.

Wave pattern resistance

Formally, the wave pattern resistance is deduced from energy considerations, i.e., the conservation ofmomentum in a control volume which contains the steady ship wave system composed of a super-position of plane progressive waves of all feasible wave direc

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Heimann_justus CFD Based Optimization of the Wave-making Characteristics of Ship Hulls