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

LC record available at https://lccn.loc.gov/

Cover Design: Wiley

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v

To My Family

They make everything worthwhile!

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vii

Contents

Preface xxxi

Acknowledgments xxxv

About the Companion Website xxxvii

1 Ship Hydrodynamics 

. Calm Water Hydrodynamics 

. Ship Hydrodynamics and Ship Design 

. Available Tools 

2 Ship Resistance 

. Total Resistance 

. Phenomenological Subdivision 

. Practical Subdivision 

.. Froude’s hypothesis 

.. ITTC’s method 

. Physical Subdivision 

.. Body forces 

.. Surface forces 

. Major Resistance Components 

3 Fluid and Flow Properties 

. A Word on Notation 

. Fluid Properties 

.. Properties of water 

.. Properties of air 

.. Acceleration of free fall 

. Modeling and Visualizing Flow 

. Pressure 

4 Fluid Mechanics and Calculus 

. Substantial Derivative 

. Nabla Operator and Its Applications 

.. Gradient 

.. Divergence 

.. Rotation 

.. Laplace operator 

5 Continuity Equation 

. Mathematical Models of Flow 

. Infinitesimal Fluid Element Fixed in Space 

List of Figures

List of Tables xxvii

xvii

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viii Contents

. Finite Control Volume Fixed in Space 

. Infinitesimal Element Moving With the Fluid 

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

. Summary 

6 Navier-Stokes Equations 

. Momentum 

. Conservation of Momentum 

.. 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 

.. 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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Contents ix

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 

. Momentum 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 

. Effect of Form 

. Estimating Frictional Resistance 

14 Inviscid Flow 

. Euler Equations for Incompressible Flow 

. Bernoulli Equation 

. Rotation, Vorticity, and Circulation 

15 Potential Flow 

. Velocity Potential 

. Circulation and Velocity Potential 

. Laplace Equation 

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

16 Basic Solutions of the Laplace Equation 

. Uniform Parallel Flow 

. Sources and Sinks 

. Vortex 

. Combinations of Singularities 

.. Rankine oval 

.. Dipole 

. Singularity Distributions 

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 

. Added Mass 

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18 Viscous Pressure Resistance 

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

. Flow Separation 

19 Waves and Ship Wave Patterns 

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

. Fundamental Observations 

. Kelvin Wave Pattern 

20 Wave Theory 

. Overview 

. 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 

. Dispersion Relation 

. Deep Water Approximation 

23 Wave Properties 

. Linear Wave Theory Results 

. Wave Number 

. Water Particle Velocity and Acceleration 

. Dynamic Pressure 

. Water Particle Motions 

24 Wave Energy and Wave Propagation 

. Wave Propagation 

. Wave Energy 

.. 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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Contents xi

. Panel Methods 

26 Ship Model Testing 

. Testing Facilities 

.. Towing tank 

.. Cavitation tunnel 

. Ship and Propeller Models 

.. Turbulence generation 

.. Loading condition 

.. Propeller models 

. Model Basins 

27 Dimensional Analysis 

. Purpose of Dimensional Analysis 

. Buckingham ��-Theorem 

. Dimensional Analysis of Ship Resistance 

28 Laws of Similitude 

. Similarities 

.. Geometric similarity 

.. Kinematic similarity 

.. Dynamic similarity 

.. Summary 

. 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 �� 

. Wave Resistance Coefficient ���� 

. Skin Friction Correction Force ���� 

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 

. Historical Development 

. Guldhammer and Harvald’s Method 

.. Applicability 

.. Required input 

.. Resistance estimate 

. Extended Resistance Estimate Example 

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

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xii Contents

.. 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 

. Wake Fraction 

. 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 

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

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Contents xiii

. Ideal Angle of Attack 

. Parabolic Mean Line 

40 Lifting Wings 

. Effects of Limited Wingspan 

. Free and Bound Vorticity 

. Biot–Savart Law 

. Lifting Line Theory 

41 Open Water Test 

. Test Conditions 

. Propeller Models 

. Test Procedure 

. Data Reduction 

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 

. Summary 

. Solving the Intersection Problem 

. Example 

45 Cavitation 

. Cavitation Phenomenon 

. Cavitation Inception 

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

. Detrimental Effects of Cavitation 

46 Cavitation Prevention 

. Design Measures 

. Keller’s Formula 

. Burrill’s Cavitation Chart 

. Other Design Measures 

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

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xiv Contents

47 Propeller Series Data 

. Wageningen B-Series 

. 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  

. Design Charts 

. Computational Tools 

49 Hull–Propeller Matching Examples 

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

.. Design constant 

.. Initial expanded area ratio 

.. First iteration 

.. Cavitation check for first iteration 

.. Second iteration 

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

. Optimum Diameter Problem 

.. Design constant 

.. Initial expanded area ratio 

.. First iteration 

.. Cavitation check for first iteration 

.. Second iteration 

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

.. Attainable speed check 

50 Holtrop and Mennen’s Method 

. Overview of the Method 

.. Applicability 

.. Required input 

. Procedure 

.. Resistance components 

.. Total resistance 

.. Hull–propeller interaction parameters 

. Example 

.. Completion of input parameters 

.. Resistance estimate 

.. Powering estimate 

51 Hollenbach’s Method 

. Overview of the method 

.. Applicability 

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

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Contents xv

.. Required input 

. Resistance Estimate 

.. 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 

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

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xvii

List of Figures

. 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 ���� and wave resistance coefficient

���� 

. Viscosity of the fluid has significant effect on the flow within the boundary

layer around a ship hull 

. Results of a paint flow test. Photos courtesy of Dr. Alfred Kracht, Versuch￾sanstalt für Wasserbau und Schiffbau (VWS), Berlin, Germany 

. Resistance coefficients and resistance for a container ship as functions of

the Froude number (velocity) 

. Comparison of absolute and relative size of resistance components for

three different displacement type vessels at design speed. The data are

taken from Larsson and Raven (, pages ,) 

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

. The pressure force d��

��

acting on a small

surface 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 the

way 

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

. The distance ����

traveled 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 �� of a finite volume �� fixed in space 

. Flow through a contraction nozzle 

. Momentum flux in ��-direction through the surface of an infinitesimal,

fixed fluid element d�� 