Fundamentals of ship hydrodynamics  fluid mechnics, ship resistance and propulsion

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Fundamentals of Ship Hydrodynamics

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Fundamentals of Ship Hydrodynamics

Fluid Mechanics, Ship Resistance and Propulsion

Lothar Birk School of Naval Architecture and Marine Engineering The University of New Orleans

New Orleans, LA United States

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Library of Congress Cataloging-in-Publication Data Names: Birk, Lothar, - author.

Title: Fundamentals of ship hydrodynamics : fluid mechanics, ship resistance and propulsion / Lothar Birk, University of New Orleans.

Description: Hoboken, NJ : John Wiley & Sons, Ltd, [] | Includes bibliographical references and index.

Identifiers: LCCN | ISBN  (hardcover) | ISBN  (epub) Subjects: LCSH: Ships–Hydrodynamics.

Classification: LCC VM B  | DDC ./–dc

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Cover Design: Wiley Cover Image: © zennie / Getty Images Set in pt Warnock Pro Regular by Lothar Birk

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. Ship Hydrodynamics and Ship Design 

. Major Resistance Components 

3 Fluid and Flow Properties 

. Fluid Properties 

.. Properties of water 

.. Properties of air 

.. Acceleration of free fall 

. Modeling and Visualizing Flow 

. Mathematical Models of Flow 

. Infinitesimal Fluid Element Fixed in Space 

List of Figures List of Tables xxvii

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. Finite Control Volume Fixed in Space 

. Infinitesimal Element Moving With the Fluid 

. Finite Control Volume Moving With the Fluid 

6 Navier-Stokes Equations 

.. Time rate of change of momentum 

.. Momentum flux over boundary 

.. External forces 

.. Conservation of momentum equations 

. Stokes’ Hypothesis 

. Navier-Stokes Equations for a Newtonian Fluid 

7 Special Cases of the Navier-Stokes Equations 

. Incompressible Fluid of Constant Temperature 

. Dimensionless Navier-Stokes Equations 

8 Reynolds Averaged Navier-Stokes Equations (RANSE) 

. Mean and Turbulent Velocity 

. Time Averaged Continuity Equation 

. Time Averaged Navier-Stokes Equations 

. Reynolds Stresses and Turbulence Modeling 

9 Application of the Conservation Principles 

. Body in a Wind Tunnel 

. Submerged Vessel in an Unbounded Fluid 

.. Conservation of mass 

.. Conservation of momentum 

10 Boundary Layer Theory 

.. Boundary layer thickness 

.. Laminar and turbulent flow 

.. Flow separation 

. Simplifying Assumptions 

. Boundary Layer Equations 

11 Wall Shear Stress in the Boundary Layer 

. Control Volume Selection 

. Conservation of Mass in the Boundary Layer 

. Conservation of Momentum in the Boundary Layer 

.. Momentum flux over boundary of control volume 

.. Surface forces acting on control volume 

.. Displacement thickness 

.. Momentum thickness 

. Wall Shear Stress 

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12 Boundary Layer of a Flat Plate 

. Boundary Layer Equations for a Flat Plate 

. Dimensionless Velocity Profiles 

. Boundary Layer Thickness 

. Wall Shear Stress 

. Displacement Thickness 

. Friction Force and Coefficients 

13 Frictional Resistance 

. Turbulent Boundary Layers 

. Shear Stress in Turbulent Flow 

. Friction Coefficients for Turbulent Flow 

. Model–Ship Correlation Lines 

. Effect of Surface Roughness 

. Bernoulli Equation for Potential Flow 

16 Basic Solutions of the Laplace Equation 

. Uniform Parallel Flow 

. Sources and Sinks 

17 Ideal Flow Around A Long Cylinder 

. Boundary Value Problem 

.. Moving cylinder in fluid at rest 

.. Cylinder at rest in parallel flow 

. Solution and Velocity Potential 

. Velocity and Pressure Field 

.. Velocity field 

.. Pressure field 

. D’Alembert’s Paradox 

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18 Viscous Pressure Resistance 

. Displacement Effect of Boundary Layer 

19 Waves and Ship Wave Patterns 

. Wave Length, Period, and Height 

. Fundamental Observations 

. Kelvin Wave Pattern 

20 Wave Theory 

. Mathematical Model for Long-crested Waves 

.. Ocean bottom boundary condition 

.. Free surface boundary conditions 

.. Far field condition 

.. Nonlinear boundary value problem 

. Linearized Boundary Value Problem 

21 Linearization of Free Surface Boundary Conditions 

. Perturbation Approach 

. Kinematic Free Surface Condition 

. Dynamic Free Surface Condition 

. Linearized Free Surface Conditions for Waves 

22 Linear Wave Theory 

. Solution of Linear Boundary Value Problem 

. Far Field Condition Revisited 

. Water Particle Motions 

24 Wave Energy and Wave Propagation 

.. Kinetic wave energy 

.. Potential wave energy 

.. Total wave energy density 

. Energy Transport and Group Velocity 

25 Ship Wave Resistance 

. Physics of Wave Resistance 

. Wave Superposition 

. Michell’s Integral 

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. Partial Dynamic Similarity 

.. Hypothetical case: full dynamic similarity 

.. Real world: partial dynamic similarity 

.. Froude’s hypothesis revisited 

29 Resistance Test 

. Test Procedure 

. Reduction of Resistance Test Data 

. Form Factor 𝑘 

. Wave Resistance Coefficient 𝐶 𝑊 

. Skin Friction Correction Force 𝐹 𝐷 

30 Full Scale Resistance Prediction 

. Model Test Results 

. Corrections and Additional Resistance Components 

. Total Resistance and Effective Power 

. Example Resistance Prediction 

31 Resistance Estimates – Guldhammer and Harvald’s Method 

. Extended Resistance Estimate Example 

.. Completion of input parameters 

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.. Range of speeds 

.. Residuary resistance coefficient 

.. Frictional resistance coefficient 

.. Additional resistance coefficients 

.. Total resistance coefficient 

.. Total resistance and effective power 

32 Introduction to Ship Propulsion 

. Propulsion Task 

. Propulsion Systems 

.. Marine propeller 

.. Water jet propulsion 

.. Voith Schneider propeller (VSP) 

. Efficiencies in Ship Propulsion 

33 Momentum Theory of the Propeller 

. Thrust, Axial Momentum, and Mass Flow 

. Ideal Efficiency and Thrust Loading Coefficient 

34 Hull–Propeller Interaction 

. Thrust Deduction Fraction 

. Relative Rotative Efficiency 

35 Propeller Geometry 

. Propeller Parts 

. Principal Propeller Characteristics 

. Other Geometric Propeller Characteristics 

36 Lifting Foils 

. Foil Geometry and Flow Patterns 

. Lift and Drag 

. Thin Foil Theory 

.. Thin foil boundary value problem 

.. Thin foil body boundary condition 

.. Decomposition of disturbance potential 

37 Thin Foil Theory – Displacement Flow 

. Boundary Value Problem 

. Pressure Distribution 

. Elliptical Thickness Distribution 

38 Thin Foil Theory – Lifting Flow 

. Lifting Foil Problem 

. Glauert’s Classical Solution 

39 Thin Foil Theory – Lifting Flow Properties 

. Lift Force and Lift Coefficient 

. Moment and Center of Effort 

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. Ideal Angle of Attack 

. Parabolic Mean Line 

40 Lifting Wings 

. Effects of Limited Wingspan 

. Free and Bound Vorticity 

. Lifting Line Theory 

41 Open Water Test 

. Test Conditions 

. Propeller Models 

. Test Procedure 

42 Full Scale Propeller Performance 

. Comparison of Model and Full Scale Propeller Forces 

. ITTC Full Scale Correction Procedure 

43 Propulsion Test 

. Testing Procedure 

. Data Reduction 

. Hull–Propeller Interaction Parameters 

.. Model wake fraction 

.. Thrust deduction fraction 

.. Relative rotative efficiency 

.. Full scale hull–propeller interaction parameters 

. Load Variation Test 

44 ITTC 1978 Performance Prediction Method 

. Summary of Model Tests 

. Full Scale Power Prediction 

. Locations and Types of Cavitation 

. Detrimental Effects of Cavitation 

46 Cavitation Prevention 

. Keller’s Formula 

. Burrill’s Cavitation Chart 

. Other Design Measures 

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. Wageningen B-Series Polynomials 

. Other Propeller Series 

48 Propeller Design Process 

. Design Tasks and Input Preparation 

. Optimum Diameter Selection 

.. Propeller design task  

.. Propeller design task  

. Optimum Rate of Revolution Selection 

.. Propeller design task  

.. Propeller design task  

. Computational Tools 

49 Hull–Propeller Matching Examples 

. Optimum Rate of Revolution Problem 

.. Final selection by interpolation 

.. Final selection by interpolation 

.. Attainable speed check 

50 Holtrop and Mennen’s Method 

. Overview of the Method 

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.. Frictional resistance coefficient 

.. Mean residuary resistance coefficient 

.. Minimum residuary resistance coefficient 

.. Residuary resistance coefficient 

.. Correlation allowance 

.. Appendage resistance 

.. Environmental resistance 

.. Total resistance 

. Hull–Propeller Interaction Parameters 

.. Relative rotative efficiency 

.. Thrust deduction fraction 

.. Wake fraction 

. Resistance and Propulsion Estimate Example 

.. Completion of input parameters 

.. Powering estimate 

Index 

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. Ship sailing in its natural habitat 

. Self-propelled ship sailing in calm water with constant speed 

. Towed bare hull (no propeller or appendages) moving in calm water 

. Comparison of inflow conditions for a propeller operating in behind and

in open water condition 

. Comparison between Froude’s and ITTC’s current method of derivation

for the residuary resistance coefficient 𝐶 𝑅and wave resistance coefficient

. Fresh and seawater properties as a function of temperature 

. The pressure force d𝐹 𝑝acting on a smallsurface element 

. Forces on a small cube in hydrostatic equilibrum 

. Hydrostatic pressure in a water column 

. Pressure distribution around a ship 

. Following a fluid particle and the flow properties it encounters along theway 

. A moving, finite control volume 𝑉 which changes over time 

. The distance 𝑠 𝑛traveled by a surface element in normal direction 

. Four types of mathematical models for fluid flows and the resulting form

of the conservation law 

. Mass flux through the surface of a fluid element 

. Flux through the surface 𝑆 of a finite volume 𝑉 fixed in space 

. Flow through a contraction nozzle 

. Momentum flux in 𝑥-direction through the surface of an infinitesimal, fixed fluid element d𝑉 

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. 𝑥-components of surface and body forces acting on the fixed, infinitesimal

fluid element d𝑉 

. Forces comprising the Navier-Stokes equations for an isotropic Newtonianfluid 

. Mean and actual velocities in steady and unsteady turbulent flow 

. Velocity and turbulence distribution across an air duct 

. Body of revolution in a wind tunnel (simplified) 

. Ellipsoid moving in an unbounded fluid 

. Basic properties of the velocity distribution in the boundary layer 

. Transition from laminar to turbulent flow of the air rising from a burningcandle Reproduced with kind permission by Dr Gary S Settles, Floviz,Inc 

. Flow characteristics of laminar and turbulent boundary layers 

. Development of the boundary layer along a flat surface Note that theouter limit of the boundary layer is not a streamline 

. Development of velocity profile in the boundary layer along a curvedsurface with flow separation 

. Cross section through a finite, fixed control volume 𝑉 in the boundary

layer 

. Surface forces acting on the control volume 

. Definition of displacement thickness 𝛿1and displacement effect on exteriorflow 

. Laminar boundary layer along a flat plate 

. Boundary layer shear stress for laminar flow over a flat plate as

dimension-less position dependent skin friction coefficient 𝐶 𝑓 𝑥 

. Boundary layer thickness 𝛿, displacement thickness 𝛿1, and momentumthickness Θ for laminar flow over a flat plate 

. Features of a turbulent boundary layer over a flat plate (zero pressuregradient) 

. A typical turbulent boundary layer velocity profile depicted in outer andinner scaling 

. Comparing the modified log–wake law with experimental data from lund () (Profile SWF) 

Öster-. Flat plate friction coefficients for smooth surfaces 

. Types of technical surface roughness and their effect on friction 

. Definition of equivalent sand roughness 𝑘 𝑆 

. Flat plate friction coefficient for turbulent flow and its dependency on

Reynolds number and relative surface roughness 𝑘 𝑆 ∕𝐿 

. A fluid element d𝑚 moves from point A to point B along a streamline 

. Determining the flow speed by measuring pressure difference in a tion nozzle 

contrac-. Translation and linear deformation of a fluid element 

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List of Figures xix

. Rotation and angular deformation of a fluid element 

. Definition of circulation Γ 

. Symmetric foil with lifting flow (Γ ≠ 0) and nonlifting flow (Γ = 0) 

. The work spent on moving an object from point A to point B 

. Definition of simply and multiply connected regions 

. Examples of basic potential flows 

. Flow field around a symmetric foil at angle of attack 𝛼 

. Planar uniform flow at angle 𝛼 

. Streamlines (𝜓 = const.) and isolines of velocity potential for a planar source/sink flow 𝑞 𝑇 = (𝜉, 𝜂)is the location of the source 

. Streamlines (𝜓 = const.) and equipotential lines for a planar source/sink flow; the source/sink is located at (𝜉, 𝜂) = (2.5, 1.3) 𝑇 

. Streamlines (𝜓 = const.) and equipotential lines for a planar vortex flow;

the vortex is located at 𝑞 = (2.5, 1.3) 𝑇 

. Superposition of parallel flow and a source/sink pair 

. Flow field for a Rankine oval, a superposition of parallel flow, source, andsink 

. Velocity and pressure distribution along the dividing streamline (Rankine

oval, 𝑈∞= 1.0 m/s, 𝜎 = 2𝜋 m2/s) 

. Creation of a dipole (doublet) by superposition of source and sink 

. Streamlines (𝜓 = const.) and isolines of velocity potential for planar dipole flows Dipole is located at (𝜉, 𝜂) = (2.5, 1.3) 𝑇 

. An infinitely long cylinder moving with speed 𝑈∞in positive 𝑥-direction

in a fluid at rest 

. An infinitely long cylinder at rest in parallel flow 

. Streamlines and velocity field for a cylinder in parallel flow 

. Contours of constant pressure coefficient 𝐶 𝑝 for a cylinder in parallelflow 

. Pressure coefficient 𝐶 𝑝 distribution on the cylinder surface (𝑟 = 𝑅) for a

cylinder in parallel flow 

. The displacement effect of a boundary layer changes the effective hullshape 

. The effect of viscous flow on the pressure distribution 

. Velocity profiles within the boundary layer near a separation point 

. Comparison of pressure and forces acting on a cylinder in inviscid andviscous flow 

. Comparison of turbulent and laminar boundary layer flow around a der 

cylin-. Definition of wave length 𝐿 𝑤 and wave height 𝐻; the vertical scale is

exaggerated 

. Surface elevation of a harmonic, long-crested wave 

. Recording of surface elevation of a harmonic, long-crested wave at a fixed

position (𝑥 = 0) 

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. Spatial extension of surface elevation of a linear, harmonic, long-crested

wave captured at time (𝑡 = 0) 

. A snapshot of the wave elevation in a wave group 

. Kelvin wave pattern in deep water 

. Change of Kelvin wave pattern with increasing velocity on deep water 

. Kelvin wave pattern like cloud formation in the slipstream of AmsterdamIsland in the southern Indian Ocean Photo courtesy of NASA EarthObservatory 

. Wave pattern of a ship at 𝐹𝑟 = 0.26 

. Definition of coordinate system and domain boundaries for wave theory

of long-crested waves 

. Simplified two-dimensional fluid domain for long-crested waves 

. The mathematical free surface model is valid for nonbreaking waves only 

. Simplified two-dimensional fluid domain for long-crested regular waves 

. The hyperbolic sine and cosine functions 

. Wave phase velocity as function of wave number and water depth based

on linear wave theory 

. The positive arm of the hyperbolic tangent function 

. Graphical verification of a solution of the nonlinear dispersion relation 

. Distribution of wave properties over . wavelength at the calm water level

(𝑧 = 0) for a wave with wave period 𝑇 = 10 s 

. Snapshot (𝑡 = 0) of the velocity field for a wave in restricted water depth 

. Amplitude of dynamic pressure over depth 𝑧 

. Photo of water particle trajectories Photo courtesy of Dr Walter L lein, seaice Ltd & Co KG, www.seaice.com 

Kuehn-. Water particle trajectories over one wave period 𝑇 for deep water (left)

and restricted water (right) 

. Propagation of wave profile and the movement of a water particle over onewave period 

. Wave length 𝐿 𝑤 as a function of water depth ℎ for constant wave period

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List of Figures xxi

. Propagation of a group of regular waves over  wave periods 

. Wigley hull at Froude number 𝐹𝑟 = 0.26 showing the connection between

fluid and hull surface pressure and the resulting wave elevation Lightcolors indicate high pressure and high wave elevation Dark colors indicatelow pressure and low values of wave elevation 

. Pronounced humps and hollows in a wave resistance curve Data frommodel tests with Wigley hulls (Bai and McCarthy, ) 

. Wave resistance coefficient of a single submerged sphere; see Equations (.)and (.) 

. Wave pattern and wave profile created by a single submerged sphere at

position 𝑥∕𝐿 = +0.5 (forward) The sphere’s dimensionless speed is the Froude number 𝐹𝑟 = 0.252, which is based on 𝐿 = 10𝐷 

. Wave pattern and wave profile created by a single submerged sphere at

position 𝑥∕𝐿 = −0.5 (aft) The sphere’s dimensionless speed is the Froude number 𝐹𝑟 = 0.252 

. Combined wave pattern and profile of two submerged spheres Froude

number 𝐹𝑟 = 0.252; favorable superposition of waves resulting in low

wave heights 

. Comparison of wave profiles created by submerged spheres at positions

𝑥∕𝐿 = ±0.5 The spheres’ dimensionless speed is the Froude number

𝐹𝑟 = 0.252 

. Wave pattern and wave profile of two submerged spheres Froude number

𝐹𝑟 = 0.282; unfavorable superposition of waves, resulting in high wave

heights 

. Comparison of wave profiles created by submerged spheres at positions

𝑥∕𝐿 = ±0.5 The spheres’ dimensionless speed is Froude number 𝐹𝑟 = 0.282 

. Comparison of wave patterns and wave profiles created by two submerged

spheres for Froude numbers 𝐹𝑟 = 0.252 (upper half, favorable tion) and 𝐹𝑟 = 0.282 (lower half, unfavorable superposition) 

superposi-. Wave resistance coefficient for a system of two submerged spheres;

dis-tance between centers is 𝐿 = 10𝐷, submergence is 𝑠 = 𝐷 

. Wave resistance coefficient for a Wigley hull with length–beam ratio of

𝐿∕𝐵 = 10 and beam–draft ratio of 𝐵∕𝑇 = 1.6 

. Discretization of vessel bow into small panels for wave resistance tation 

compu-. Towing tank of the Hamburg Ship Model Basin, Photo courtesy of burgische Schiffbau-Versuchsanstalt GmbH (HSVA), www.hsva.de 

Ham-. Towing tank at the School of Naval Architecture and Marine Engineering

of the University of New Orleans 

. Schematic view of a towing tank 

. Definition of rail sagitta 𝑠 

. Schematic of a cavitation tunnel without free surface 

. A model is prepared for cutting on the five axis mill Photo courtesy

of Hamburgische Schiffbau-Versuchsanstalt GmbH (HSVA), www.hsva

de 

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. The beginnings of a five bladed propeller model Photo courtesy of burgische Schiffbau-Versuchsanstalt GmbH (HSVA), www.hsva.de 

Ham-. Simplified flow pattern at a propeller blade section Kinematic similarityrequires that the angle of attack remains the same for full scale and modelpropeller blade section 

. Relationship of total static pressures for model and full scale ship 

. Ship model set up for resistance test 

. Measured and derived data in the resistance test 

. Tank cross section area 𝐴 and blockage factor 𝑚 

. Measurements and length definitions for the computation of sinkage andtrim (sinkage and trim are exaggerated) 

. Method of Prohaska to determine the form factor 𝑘 

. Finding the form factor with Prohaska’s method; only data points with

0.1 ≤ 𝐹𝑟 ≤ 0.2 are used 

. Measured mean sinkage and running trim angle of model 

. Measured total resistance of model as function of model speed 

. Resistance coefficients of model 

. Resistance coefficients of full scale ship 

. Full scale total resistance prediction (calm water) 

. Full scale effective power 

. Definition of the midship section and the computational length 𝐿 for

Guld-hammer and Harvald’s resistance estimate (Andersen and GuldGuld-hammer,

) 

. Guidance for the optimum location of 𝐿𝐶𝐵 as a function of Froude number

𝐹𝑟 Here, negative 𝐿𝐶𝐵 values indicate a location aft of midship 

. Resistance coefficients for the Guldhammer and Harvald method ple 

exam-. Total resistance and effective power for the Guldhammer and Harvaldmethod example 

. Charts for standard residuary resistance coefficients 𝐶 𝑅stdafter

Guldham-mer and Harvald () for vessels with length-speed ratio 𝐿∕𝑉1∕3= 6.0.

The values have been computed and redrawn based on the regressionformula provided by Andersen and Guldhammer () 

. Charts for standard residuary resistance coefficients 𝐶 𝑅stdafter

Guldham-mer and Harvald () for vessels with length-speed ratio 𝐿∕𝑉1∕3= 6.5.

The values have been computed and redrawn based on the regressionformula provided by Andersen and Guldhammer () 

. Forces acting on ship without and with propulsion system 

. A five-bladed fixed pitch propeller with a Schneekluth nozzle to improvepropeller inflow 

. Schematic of a water jet 

. The propulsion system with transmission powers and efficiencies 

. Fixed control volume around an idealized propeller (actuator disk) 

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List of Figures xxiii

. Velocity and pressure distribution according to momentum theory 

. Ideal efficiency (jet efficiency) of propulsor momentum theory as a function

of thrust loading coefficient 

. Example of a nominal wake field of a single propeller ship with moderateblock coefficient 

. Example of a nominal wake field of a single propeller ship with high blockcoefficient 

. Major contributions to the nominal wake fraction 

. Frictional wake for twin screw vessels 

. Effect of propeller on pressure and velocity distribution at the stern 

. Parts of a propeller Shown is a right-handed, fixed pitch propeller withfour blades 

. Definition of propeller diameter 𝐷, blade radius 𝑅, hub radius 𝑟 ℎ, and disk

area 𝐴0 

. Hydrofoil section within a propeller blade 

. Pitch angle variation for a propeller with constant pitch 𝑃 

. Helical paths for propeller with constant pitch 𝑃 

. Relationship between pitch 𝑃 and pitch angle 𝜙 

. Helical paths for propeller with variable pitch 𝑃 

. Basic geometric properties of a lifting hydrofoil 

. The expanded blade for a Wageningen B-Series propeller with four blades

and 𝐴 𝐸 ∕𝐴0= 0.85 Drawing is based on data from Oosterveld and van

Oossanen () 

. Definition of the expanded area 𝐴 𝐸 ∕𝑍of a propeller blade 

. Two examples of expanded area ratios 𝐴 𝐸 ∕𝐴0 = 0.55on the left and

𝐴 𝐸 ∕𝐴0= 0.85on the right 

. Side elevation of a propeller blade and definition of propeller rake 𝑖 𝐺 (𝑥) and rake angle 𝜃 

. Definition of propeller skew-back and skew angle 𝜃 𝑠 

. Cupping of a propeller blade 

. Definition of foil geometry 

. Flow pattern and pressure distribution for a D foil section at angle of

attack 𝛼 

. Foil in stalled flow condition 

. Complete vortex system of the foil section 

. Forces acting on the foil section at angle of attack 𝛼 

. Typical lift–drag curves for a thin, cambered foil 

. Setup of boundary value problem for a thin foil operating at angle of

attack 𝛼 

. Definition of normal vectors for upper and lower foil surface 

. The boundary value problem of a symmetric thin foil with finite thicknessand zero angle of attack 

. The inverse tangent function 

. The source strength distribution 𝜎(𝜉) as a function of the slope d𝑡∕d𝑥 of

the foil surface 

Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page xxii — #

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xxiv List of Figures

. Comparison of thin foil theory and conformal mapping (exact) pressurecoefficient for an elliptical foil with thickness to chord length ratio of

. The effect of leading edge suction for a thin plate at angle of attack 𝛼 

. Section lift coefficient 𝐶 𝑙of thin, symmetric foil sections and a thin,

cam-bered foil section with zero lift angle 𝛼0= −4degree 

. Definition of the moment 𝑀 𝑧created by the pressure force acting on athin foil 

. Pressure distribution for a flat plate at  degrees angle of attack 

. A prescribed pressure distribution resulting in the NACA 𝑎 = 0.8 mean

line 

. Pressure distribution on a wing of finite span 𝑠 

. Simplest model of the vortex system of a wing 

. Cross section through the velocity field of the wing tip vortices revealingdownwash and updraft 

. A model of a wing with varying bound circulation Γ𝑏 (𝜂)and the resultingfree vortex sheet 

. Actual shape and roll up of trailing vortex sheet 

. Velocity vectors on upper and lower wing surfaces 

. Velocity vectors on upper and lower wing surface and mean velocity

𝑓 and its effect 

. Establishing a connection between bound and free vorticity by integrationover the boundary of a simply connected region 

. The velocity induced by an element of a vortex filament 

. The velocity induced by a straight vortex filament 

. The effect of downwash on the angle of attack 

. Induced drag caused by the downwash 

. Simplified velocities triangle for an unrolled propeller blade section at

radius 𝑥 = 0.75 (induced velocities have been ignored) 

. Open water test of model propeller with propeller boat in towing tank 

. Open water test of model propeller in a circulating water tunnel / cavitationtunnel 

. Typical propeller open water diagram 

Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page xxiii — #

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List of Figures xxv

. Fluid forces acting on a propeller blade section at model scale 

. Comparison of model scale and full scale forces acting on a propeller bladesection 

. Comparison of measured open water characteristics and predicted fullscale propeller performance 

. Setup of model for propulsion test with single skin friction correction force(continental method) 

. The relative difference of resistance for model and full scale vessel 

. Self propulsion point of model propeller under the assumption of thrustidentity 

. Self propulsion point of model propeller under the assumption of torqueidentity 

. Setup of model for propulsion test with load variation (British method) 

. Typical results of a load variation test (British method) 

. Matching propeller thrust 𝐾 𝑇𝑆 𝑂with the thrust requirement of the shipassuming thrust identity 

. Setup for solving the intersection problem with discrete open water data 

. Simplified phase diagram of fresh water 

. Flow around a cavitating foil section and the associated pressure tion for back (upper) and face (lower) side 

distribu-. Locations and common types of cavitation 

. Open water test of five-bladed model propeller in a cavitation tunnel; tipvortex and bubble cavitation 

. Open water test of five-bladed model propeller in a cavitation tunnel;

propeller blades completely covered in sheet cavitation 

. Loss of thrust and efficiency due to cavitation 

. Life of cavitation bubble 

. Limits for the propeller loading coefficient as a function of cavitation ber and acceptable level of cavitation After Burrill and Emerson (),however, the curves represent the regression equations from Table .

num-

. Usage of the Burrill chart 

. Open water chart for a Wageningen B-Series propeller with 𝑍 = 4 and

𝐴 𝐸 ∕𝐴0= 0.85 derived from 𝐾 𝑇 and 𝐾 𝑄polynomials Equations (.) and(.) 

. Design task  – Input: open water diagram for Wageningen B-series

pro-pellers with 𝑍 = 4 and 𝐴 𝐸 ∕𝐴0= 0.85 derived from 𝐾 𝑇 and 𝐾 𝑄

polynomi-als (.) and (.) Torque coefficient curves 10𝐾 𝑄are emphasized 

. Design task  – Step : locate self propulsion points ◦ at which the pellers absorb the delivered power specified with the design constant

pro-[𝐾 𝑄 ∕𝐽5]from Equation (.) 

. Design task  – Step : find open water efficiencies × for self propulsionpoints ◦ 

Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page xxiv — #

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xxvi List of Figures

. Design task  – Step : draw auxiliary curve through open water efficiencyvalues 

. Design task  – Result: optimum propeller is defined by maximum ofauxiliary curve 

. Design task  – Result: optimum propeller is defined by maximum ofauxiliary curve 

. Design task  – Result: optimum propeller is defined by maximum ofauxiliary curve 

. Design task  – Result: optimum propeller is defined by maximum ofauxiliary curve 

. Simplified task  propeller design 𝐵 𝑃1-chart for Wageningen B-Series

pro-peller with 𝑍 = 4 and 𝐴 𝐸 ∕𝐴 𝑜 = 0.85 

. Optimum diameter chart for design task  

. Propeller design 𝐵 𝑢2-chart for Wageningen B-series propeller B-

Cal-culated and plotted based on the 𝐾 𝑇 , 𝐾 𝑄polynomials by Oosterveld andvan Oossanen () 

. Propeller design 𝐵 𝑢2-chart for Wageningen B-series propeller B-

Cal-culated and plotted based on the 𝐾 𝑇 , 𝐾 𝑄polynomials by Oosterveld andvan Oossanen () 

. Auxiliary plot to determine the expanded area ratio of the final optimumpropeller 

. Auxiliary plots to determine final optimum propeller characteristics The

⋆mark results of first and second iterations 

. Propeller design 𝐵 𝑝1-chart for Wageningen B-series propeller B-

Cal-culated and plotted based on the 𝐾 𝑇 , 𝐾 𝑄polynomials by Oosterveld andvan Oossanen () 

. Propeller design 𝐵 𝑝1-chart for Wageningen B-series propeller B-

Cal-culated and plotted based on the 𝐾 𝑇 , 𝐾 𝑄polynomials by Oosterveld andvan Oossanen () 

. Auxiliary plot to determine the expanded blade area ratio of the finaloptimum propeller 

. Auxiliary plots to determine final optimum propeller characteristics The

⋆mark results of first and second iterations 

. Auxiliary plot to determine the attainable ship speed 

. Comparison of total resistance estimates for the methods by Hollenbach,Guldhammer and Harvald, and Holtrop and Mennen 

. Comparison of predicted rate of revolution and delivered power for themethods by Hollenbach, Guldhammer and Harvald, and Holtrop andMennen 

Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page xxv — #

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xxvii

List of Tables

. Fresh water properties 

. A selection of model basins around the world, sorted alphabetically cording to their commonly used abbreviations 

ac-. Particulars of full scale vessel and model used in the prediction example



. Testing and full scale environments for resistance prediction 

. Measured total resistance and sinkage of model; blockage correction(Schuster, ), dynamic sinkage, and trim 

. Resistance coefficients for the model (𝑘 = 0.1566) 

. Predicted resistance coefficients for the full scale vessel 

. Full scale resistance 𝑅 𝑇𝑆 and effective power 𝑃 𝐸𝑆 

. Range of parameters suitable for Guldhammer and Harvald’s method 

. Required and optional input parameters for Guldhammer and Harvald’smethod 

. Bulbous bow corrections to the standard residuary resistance coefficient(Andersen and Guldhammer, ) 

. Air resistance coefficients for different types of vessels (Kristensen andLützen, ) 

. Principal dimensions for resistance estimate example 

. Selected ship speeds and resulting Froude and Reynolds number 

. Residuary resistance value computation for the standard hull form 

. Computation of the 𝐿𝐶𝐵-correction for the residuary resistance

coeffi-cient 

. Comparison of old and updated bulbous bow correction to the residuaryresistance coefficient 

. Estimate of residual resistance coefficient 

. Frictional resistance estimate 

. Resistance coefficients computed with Guldhammer and Harvald’s methodusing input from Table . 

. Total resistance and effective power computed with Guldhammer andHarvald’s method using input from Table . 

. The three subtasks of thin foil theory 

. Example results of an open water test conducted in a towing tank 

. Open water characteristics of model propeller (see Table .) 

Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page xxvi — #

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xxviii List of Tables

. Intermediate results for scaling open water characteristics of model peller (see Table .) 

pro-. Predicted open water characteristics of full scale propeller (see Table .) 

. Propeller open water characteristics as a set of discrete data points 

. Example input data for the calculation of the self propulsion point for asingle ship speed 

. Data for required thrust parabola at 𝑣 = 11.472 m/s and 𝐶 𝑆 = 0.43372

and propeller open water thrust coefficient 

. Regression equations for the limiting lines in the Burrill chart (Figure .) 

. Basic characteristics of the propellers in the Wageningen B-Series For

each combination of 𝑍 and 𝐴 𝐸 ∕𝐴0propellers with 𝑃 ∕𝐷 = 0.5, 0.6, 0.8, 1.0, 1.2, and 1.4 have been tested 

. Factors and exponents for thrust coefficient polynomials of WageningenB-Series propellers (Oosterveld and van Oossanen, ) 

. Factors and exponents for torque coefficient polynomials of WageningenB-Series propellers (Oosterveld and van Oossanen, ) 

. Coefficients for the estimate of maximum thickness and chord length ofWageningen B-Series propellers (Kuiper, ) For convenience values

have been added at radii 𝑥 = 0.15, 0.25, and 0.75 by interpolation 

. Factors and exponents for Reynolds number effects on thrust coefficientand torque coefficient of Wageningen B-Series propellers (Oosterveld andvan Oossanen, ) 

. The four basic propeller design tasks 

. Input data to illustrate task : optimum propeller diameter selection based

on delivered power, speed of advance, and rate of revolution 

. Results for the propeller selection task  example 

. Results for the propeller selection task  example 

. Optimum rate of revolution problem – example input data for a containership 

. Optimum diameter problem – example input data for a bulk carrier 

. Resistance estimate for bulk carrier from Table . 

. Required and optional input parameters for Holtrop and Mennen’s method 

. Approximate values for appendage form factors 𝑘 2𝑖according to Holtrop() 

. Coefficients for the wave resistance computation in Equation (.) if

Equa-. Propeller data for powering estimate; see also Table . 

. Holtrop and Mennen resistance and powering estimate example; speedindependent procedural coefficients 

Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page xxvii — #

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List of Tables xxix

. Holtrop and Mennen resistance and powering estimate example; speeddependent procedural coefficients 

. Holtrop and Mennen resistance and powering estimate example; resistancecomponents and total resistance 

. Holtrop and Mennen resistance and powering estimate example; wakefraction and self propulsion point analysis 

. Holtrop and Mennen resistance and powering estimate example; cies, propeller rate of revolution, and delivered power 

efficien-. Recommended limits for principal dimensions and form parameters ofsingle screw vessels on design draft 

. Required and optional input parameters for Hollenbach’s method 

. Coefficients for an estimate of the wetted surface 

. Coefficients for computation of the standard residuary resistance cient in Hollenbach’s method 

coeffi-. Coefficients for correction factors of the standard residuary resistancecoefficient in Hollenbach’s method 

. Factors for lower and upper limit formulas of the range of Froude numbers

in which the 𝐶 𝑅formulas are valid 

. Suggested values for the relative rotative efficiency 𝜂 𝑅, if the propulsionestimate is based on Wageningen B-Series propeller data (Hollenbach,

) 

. Suggested values for the thrust deduction fraction 𝑡 (Hollenbach, ) 

. Suggested values for constant 𝐶 for the hull efficiency of twin screw vessel

models (Hollenbach, ) 

. Residuary resistance coefficients for minimum and mean resistance cases 

. Resistance coefficients for example vessel by Hollenbach’s method 

. Comparison of total calm water resistance estimates 

. Prediction of model and full scale wake fraction 

. Self propulsion point based on mean resistance curve 

. Prediction of rate of revolution and delivered power for trial conditionbased on mean resistance curve 

. Predicted efficiencies based on mean resistance curve 

. Comparison of predicted rate of revolution and delivered power 

Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page xv — #

architec-Over the past  years, I have taught ship resistance and propulsion at three different Identified needs

universities and consistently made the following observations:

• The foundation laid by basic fluid mechanics courses in modern engineeringcurricula is incomplete and does not cover everything essential to courses focused

on ship resistance and propulsion

• A wealth of excellent reference books exists covering all aspects of ship dynamics However, no matter how strongly I recommend one of them, moststudents find them too expensive or too intimidating and do not use them asstudy aids

hydro-• Arguably, most reference books are not organized in a way which lends itself tosupport class work The chapters are designed so broadly that it becomes difficult

to assign specific parts to individual class periods

In many engineering curricula in the United States, basic fluid mechanics is covered in Interior vs.

exterior flow

a single course This is just enough to cover hydrostatics and the basic equations of fluiddynamics but leaves hardly any room for boundary layer theory, potential flow, wavetheory, and foil and wing theory In addition, teaching fluid mechanics courses is oftenthe responsibility of mechanical engineering departments, which naturally concentrate

on pipe flows and turbo machinery rather than exterior flows

Authors of reference books assume more prerequisite knowledge than a typical under- Details vs.

coverage

graduate student of today actually has After all, their target audience are practicingengineers In addition, reference books attempt to be comprehensive and cover a broadrange of topics and tend to omit a lot of detail The gaps may be easily filled by anexpert but often pose a seemingly insurmountable obstacle for students trying to un-derstand the origins of a theory or fathom exactly how a certain method works As aconsequence, I find myself compelled to explain to students what reference books coverwith statements like ‘as one can easily see’ Unfortunately, covering extensive details inclass distracts students from important assumptions and conclusions

Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page xvi — #

• Instead of covering all possible aspects of ship hydrodynamics, a selection oftopics is covered in greater detail Sentences like ‘as one can easily see’ or ‘aftersome manipulations’ are kept to a minimum The detailed coverage allows theteacher to concentrate on important assumptions and conclusions Students willfind and study the details in the associated sections

• Each chapter covers material for one, or sometimes two, class periods, whichshould simplify reading assignments As a consequence, the book is organizedinto an unusually large number of chapters Margin notes are used as an additionalorganizational aid There is a continuous thread throughout the book, but thechapters are relatively independent from each other This should make it easier

to skip some of them, assign them as extra reading, or rearrange their orderaccording to the needs of a specific course

The junior level ship resistance and propulsion course serves a dual purpose in our naval

Content overview architecture and marine engineering curriculum at the University of New Orleans On

one hand, it identifies and explains basic flow patterns around a ship sailing at constantspeed On the other hand, it prepares students to conduct basic ship design tasks likeresistance and powering estimates Starting with basic fluid mechanics and ending withpowering estimates spans a wide arc The only way to keep the page count in check was

to concentrate on the immediate topics at hand rather than venturing into all variationsand alternatives The reader will notice that the book focuses on displacement typemonohulls driven by marine propellers As a consequence, multihulls, planing boats,and other propulsion systems are not covered Fundamental analytical and experimentalmethods are discussed but not computational fluid dynamics

The book is subdivided into  chapters organized into three parts: basic fluid mechanics,

Organization

ship resistance, and propulsion However, the boundaries are blurred as I attempt toconnect basic theory with its application in ship hydrodynamics wherever possible Thefirst chapter specifies the calm water resistance and propulsion problem The secondchapter defines ship resistance and its major components In Chapters  through  wedevelop important equations describing viscous flow around submerged bodies and usethem to assess the frictional resistance of a ship Chapters  through  analyze inviscidflow and combine it with viscous flow theory to explain viscous pressure resistance

Chapters  through  tackle wave theory and wave resistance

Chapters  through  explain the concepts and theories which govern ship modeltesting and the prediction of full scale resistance Chapter  provides a first look atresistance estimates for ship design purposes

Chapter  marks the beginning of the ship propulsion part Basic terminology, sor action, hull–propeller interaction, and propeller geometry are illustrated in Chap-

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Chapters  through  address the problem of cavitation, cavitation avoidance, andhow to select a propeller for a specific ship Finally, Chapters  and  describe indetail two methods to estimate resistance and powering requirements in early designstages

Symbols are typically explained when they are introduced A conscious effort has Nomenclature

been made to use the terminology and symbols according to the Dictionary of dynamicsand the ITTC Symbol and Terminology List maintained and published bythe International Towing Tank Conference (ITTC) Both documents are part of thequality systems manual and can be found on the ITTC’s website at www.ittc.info (ITTC,

Hydro-a,b)

In most cases a Cartesian coordinate system < 𝑥, 𝑦, 𝑧 > is employed with its positive Cartesian

coordinate system

𝑥 -axis pointing forward (in the direction of motion), its 𝑦-axis pointing to port, and its

𝑧-axis pointing upwards

A textbook is always a conglomerate of the combined knowledge and wisdom of all Summary

who have worked in the specific field All the presented work has originally beendeveloped by others and I have made every effort to point the reader to the correctsources My job has been to illustrate and explain everything, and as such the errorsare all mine If you find any errors, please feel free to point them out to me via e-mail atlothar.birk@marine-hydrodynamics.com

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I would like to thank my colleagues Dr Janou Hennig, Dr Alfred Kracht, and Dr WalterKühnlein for providing photos for the book Many thanks also to Dr Settles for hisphoto of the laminar–turbulent transition in the airflow above a candle

Writing a book is a milestone in a professional career It provides time to pause andreflect on how one got to this point It is obvious to me that I had great teachers inhigh school (which is called Gymnasium in Germany) and throughout my studies atTechnische Universität Berlin Thank you, Mr E Jäckle, Mr H Riekert, Professor G.F

Clauss, Professor H Nowacki, and Professor E Wolf, who all sparked my curiosity andinspired my desire to learn more I hope all readers find great teachers and mentorslike I did

Last but not least, I want to thank my children Benjamin and Kathleen, who bothhelped to correct their dad’s basic English, and of course my love and wife Carola, whoencouraged me all the way and patiently endured my prolonged occupation with thisbook project

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xxxvii

About the Companion Website

The companion website for this book is at

www.wiley.com/go/birk/hydrodynamics

The website includes:

• Python scripts

• FiguresScan this QR code to visit the companion website

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1

1 Ship Hydrodynamics

The field of ship hydrodynamics considers the interaction of vessels with surroundingfluids As the prefix ‘hydro’ suggests, we are most concerned with water; however, theair flow around the super structure has to be dealt with as well In this chapter, wenarrow down this broad field and define calm water hydrodynamics as the context ofthis book We will also discuss the role and responsibilities of the naval architect inthe analysis of ship hydrodynamics and – in broad terms – what tools we have at ourdisposal to solve hydrodynamic tasks in ship design

Learning Objectives

At the end of this chapter students will be able to

• review the complexity of the ship propulsion problem

• explain the concepts of calm water, trial, service, and open water condition

• understand the role of ship resistance and propulsion in ship design

• distinguish basic tools to predict and investigate hydrodynamic performance

Boats and ships crossing any body of water have to negotiate the environment presented The real world

by wind, waves, currents, and the boundaries of their domain Figure . shows themajor interactions between ship and environment

• Wind blowing over water creates a seemingly chaotic pattern of waves throughwhich the ship sets its course Wind and waves may come from different directionsrelative to the ship’s path A ship will change the shape of waves in its vicinity

This is called wave diffraction Wind and waves exert forces on the vessel whichvary with time

• Wind and wave forces cause the ship to move This movement creates additionalwaves, similar to the waves created by a stone dropped into a pond This is known

as wave radiation

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2 1 Ship Hydrodynamics

Figure 1.1 Ship sailing in its natural habitat

• Currents may cause the general flow direction to be oblique to the ship’s path

• A ship, even when moving in undisturbed water, creates a well organized wavepattern It appears in a triangular region behind the ship and consists of divergentand transverse waves

• Some of the waves created by the vessel will break A mix of water and air creates

a band of froth along the ship’s path

• Small and large eddies appear next to and behind the ship They are the result

of friction between hull and water A boundary layer forms over the submergedhull surface and merges into a disturbed flow region behind the ship generallyknown as wake

• A rotating propeller will generate its own twisted wake, further complicating theflow patterns

A moving vessel constantly displaces water and air molecules from their original

po-Unsteady flow

sition As stated in Newton’s laws of motion,forces (Latin: actio) must act on themolecules to change magnitude or direction of their velocities In turn, a reaction force(Latin: reactio) is exerted by water and air on the ship Vessels are usually self-propelled,i.e they have some means of propulsion The most common propulsor today is themarine propeller Sails, oars, paddle wheels, and water jets may be applied depending

on purpose, size, and speed of the vessel Propulsors create the force necessary toovercome the reaction force by water and air Although power settings of the engineturning the propeller are kept constant, the speed of a vessel will still vary because

 Sir Isaac Newton (* – †), famous English mathematician, astronomer, and physicist The

* marks the year of birth and the † marks the year of death

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1.1 Calm Water Hydrodynamics 3

Figure 1.2 Self-propelled ship sailing in calm water with constant speed

waves and wind will alter the reaction force In summary, the flow around a ship hull istime dependent and, as a consequence, the flow will be unsteady

In order to reduce the number of variables which influence the flow, it is often worth- Calm water

• Only the waves generated by the ship itself are considered

This is known as calm water condition (Figure .)

A ship trial is conducted before final delivery of a new vessel Performance is measured Trial condition

and compared to the contracted requirements Trials are conducted in deep, openwaters since the vicinity of the sea bottom or shore lines has a negative impact on shipperformance At the time of a trial, the hull is freshly painted and free of any marinegrowth Together with the calm water condition this is referred to as trial condition

The contract between owner and shipbuilder typically specifies a combination of engine Service condition

power and ship speed which has to be attained on the ship’s trial However, the navalarchitect must optimize the vessel for its intended service A ship will encountercurrents, wind, and waves during its voyages Marine fouling over time will increasethe roughness of any hull surface These are the actual service conditions As a result,resistance will be higher in service than at the ship’s trial Additional resistance has to

be considered during selection of engine and propeller, otherwise the ship will not beable to perform as intended

Application of calm water or trial conditions leaves us with a greatly simplified scenariodepicted in Figure . The ship’s velocity is assumed to be constant in direction and

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4 1 Ship Hydrodynamics

Figure 1.3 Towed bare hull (no propeller or appendages) moving in calm water

magnitude 𝑣 𝑠 = const. Then all forces acting on the ship must be in equilibrium

according to Newton’s first law The propulsor provides exactly the force 𝐹 𝑃 necessary

to compensate the force 𝐹 𝑅exerted by water and air on the ship

In ship resistance and propulsion, we are concerned with the steady forward motion Forthat reason the discussion may be restricted in many cases to just the force componentspointing in longitudinal direction

Simulations of the flow around a ship–propulsor system are a challenge even for today’s

Separation of

hull and propeller multiprocessor computers It is also quite difficult to make measurements in this closed

system which, according to Equation (.), has no resultant external force Similarproblems exist in structural analysis In order to reveal shear forces and bendingmoments in a beam, one side of the beam is ‘removed’ to reveal the internal forces Tothat effect, the ship–propulsor system is split into two parts which are treated separately:

• Bare hull: hull without propulsor and usually without any appendages like rudder,

Total resistance

struts, and bilge keels (Figure .) We remove the propulsor, which means thebare hull has to be towed to achieve the desired speed The required tow force is

equal to the ship hull’s total resistance 𝑅 𝑇

• Propulsor: the propulsor is removed from the ship and its properties are

investi-Open water condition gated in undisturbed parallel flow instead of the disturbed flow field generated by

the hull (Figure .) This is known as open water condition

Separation of the hull–propulsor system into its subsystems has advantages which are

Advantages

exploited in experimental studies of ship hydrodynamics:

• forces of water and air on the hull and the force generated by the propulsor arerevealed,

Underlined quantities, like velocity 𝑣, represent vectors See the beginning of Chapter  for details.

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1.1 Calm Water Hydrodynamics 5

(a) Propeller working in a nonuniform flow field

behind the hull (behind condition)

(b) Propeller working in a uniform flow (open water

condition)

Figure 1.4 Comparison of inflow conditions for a propeller operating in behind and in open water condition

• hulls may be investigated without a specific propulsor, and

• propulsor performance may be determined without the influence of a ship’s wake

However, separating hull and propulsor considerably changes the hydrodynamic system Disadvantages

As a consequence, we need to apply corrections to model test and simulation resultsperformed for hull or propulsor alone

• The flow around the ship hull will be different for hulls with a propulsor attachedand for hulls without a propulsor This is especially true for marine propellers

Rotating propellers accelerate fluid already upstream of the propeller Hence,they have a direct impact on the flow around the stern of a vessel

• Propellers, water jets, or paddle wheels do not operate without a ship attached

to them The hull will create a nonuniform flow field called wake in which thepropulsor is working as indicated in Figure .(a) Therefore, the open watercondition with uniform inflow into the propulsor shown in Figure .(b) is anunrealistic, hypothetical case

• When performance is separately determined for hull and propulsor, the questionarises as to how the results are reconciled to make a prediction for the completehull–propeller system

Although one may argue that it would be better to only investigate the complete hull– Hull-propulsor

interaction

propulsor system, it is today’s practice to perform model tests and even calculations forthe separated components Effects of the omitted part on the performance of the otherpart are quantified by additional hydrodynamic characteristics They will be discussed

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The definition of an effective hull shape is a naval architect’s responsibility Hull

geome-Your future job

try significantly impacts the performance of a vessel and must be assessed from earliestdesign stages until completion of the design

In a nutshell, the responsibilities of a naval architect charged with the design andhydrodynamic assessment of a hull include:

• developing a form with minimum powering requirements

• selection and design of an appropriate propulsor of high efficiency

• contributing information about necessary engine power and propulsor tions to the overall ship design

specifica-• ensuring that the vessel behaves well in waves

• ensuring that the vessel is sufficiently course stable and/or maneuverable ing on its mission

depend-In this book, we consider the first three items related to resistance and propulsion incalm water

The main objective in this element of ship design is the development of a ship–propulsor

Objective

combination which provides the most economic and ecological system to fulfill thevessel’s mission Overall size of the ship is usually defined by its purpose and targetroute Ports of call, seaways, and canals may impose further limits Therefore, changes

to displacement and principal dimensions for hydrodynamic reasons will be small Thesame is usually true for the design speed of merchant vessels A vessel will become part

of a transport chain sustaining a more or less well defined flow of goods If the vessel isslower than envisioned, it becomes a bottleneck in the transport chain If it is too fast,

it will become idle awaiting the next batch of goods

Within the design constraints a naval architect composes a hull shape with minimized

Optimization

problem resistance and develops an optimum propulsor for it Even better would be to formally

optimize the hull–propulsor system for overall high efficiency throughout the tional profile A formal optimization is unfortunately often skipped for merchant vessels

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1.3 Available Tools 7

since it requires sophisticated numerical flow simulations and supporting model tests

Steadily increasing and more affordable computational capacities and more robustsimulation methods will eventually integrate formal optimization into day-to-day shipdesign

For a successful ship design, it is very important to accurately predict the power neces- Performance

prediction

sary to achieve the desired cruising or flank speed The machinery for a main propulsor

is usually the most expensive nonmilitary equipment item An oversized engine wastesspace in the ship which could have been used for more (paying) cargo or a smaller(cheaper) ship Operating costs tend to increase with engine size as well If the predictedrating for an engine is larger than necessary, your design will be more expensive andyour customer might order your competitor’s design instead The ship might not reachits design speed if the naval architect happens to underpredict the power requirements

In many cases there is no easy fix, and shipbuilding contracts commit the shipbuilder ordesign agent to paying hefty fines if the contracted speed is not achieved In the worstcase, the customer might refuse to take ownership of the ship, leaving a shipbuilderwith unpaid bills and an unwanted asset

The essential challenge in ship hydrodynamics is to get it right the first time Most Challenges

ships are one of a kind designs with investment cost so high that a prototype cannot

be built and tested before the actual vessel is constructed Small series exist for navalvessels and smaller ships like pleasure craft and work boats Merchant vessel seriesrarely show more than single digit repeats Numbers that are typical for aircraft or carmodels are never reached in shipbuilding This does not imply that engineering of carsand aircraft is easier It just means that the economic risk of engineering failures perunit is bigger for ships In small series, results for the lead ship are exploited in theconstruction of repeat designs Again, only minor changes will occur If the lead vesseldoes not perform as desired, repeats will be unlikely

The difficulty of our fluid dynamics problem is augmented by the fact that reliableinformation about hull shape, resistance, and propulsion is needed early in the design

Except for minor details, the hull shape needs to be settled as soon as possible since itaffects not only resistance and propulsion, but also stability, structure, and functionality

of the vessel This leaves very little time for extensive computational analyses or modeltests for merchant vessels where the early design time is measured in weeks rather thanmonths Naval vessels tend to have longer lead times, but in their case additional andoften changing mission constraints complicate the design problem

A moving ship creates a complex flow field in its vicinity As naval architects we Task

are interested in the physical properties of the flow field like fluid particle velocities,pressure distributions, and their ultimate effects on the performance of a ship Obtainingquantitative descriptions of the flow processes around a ship hull poses a complexexterior flow problem, characterized by:

• complicated three-dimensional geometries,

• two fluids (air and water), and

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underway Changing water pressure along the hull causes it to deviate from its position

at rest In computational fluid dynamics the boundary between air and water is oftencalled free surface Its wavy shape has to be found as part of the solution

About  years of research and advances in engineering sciences have developed a set

of tools which naval architects may employ to make accurate predictions of resistanceand propulsion properties However, ship hydrodynamics is still an active field ofresearch, and improvements to existing methods and new tools for old and new designproblems will be developed for the foreseeable future

In order to obtain the desired data for our ship design, we can perform:

of the design

– We cannot satisfy all required physical scaling laws at the same time fore, model test data have to be extrapolated to full scale This can introducesignificant errors if not done properly Model testing will be discussed later

There-in the book (Chapters – and –)

– Model tests are considered expensive However, they are cheap comparedwith the overall cost of a ship Model tests are usually done just for thefinal design to confirm earlier predictions Modifications might be tested ifproblems arise which invalidate earlier estimates, and the contracted trialspeed might not be reached

• estimates:

Estimates

– Estimates are only acceptable for early design phases

– Available methods are the result of regression analyses of model test dataand ship trial data The methods are quite simple but not always accurate(about ±10%)

– Despite their limited accuracy, estimates are still the method of choice inearly design stages We will discuss current methods in Chapters ,  and



• CFD (computational fluid dynamics) simulations:

Numerical analysis

– CFD simulations are time consuming, especially the grid generation, andactual computation may take several hours or even days to complete

– CFD is not very reliable yet and a lot of experience is needed to produce

a valid grid and to select appropriate boundary conditions and processparameters An expert user can produce results which are as good as amodel test, but the occasional user should apply CFD results with greatcaution