Title Details

LOTHAR BIRK has more than two decades of experience teaching ship and offshore hydrodynamics, first at the Technische Universität Berlin and now at the University of New Orleans (UNO). Fascinated by the world of boats and ships, he studied naval architecture at Technische Universität Berlin (TUB) in Germany. After graduation he worked at TUB as a research scientist completing projects and teaching classes related to hydrodynamics and optimization of ship and offshore structures. In 2004, he joined the faculty of the School of Naval Architecture and Marine Engineering at UNO where he teaches classes in ship resistance and propulsion, propeller hydrodynamics, experimental, numerical and offshore hydrodynamics as well as computer aided design and optimization. His passion for teaching has earned him several awards by student organizations.

Contents v

Preface xvii

Acknowledgements xxi

1 Ship Hydrodynamics 1

1.1 Calm Water Hydrodynamics 1

1.2 Ship Hydrodynamics and Ship Design 6

1.3 Available Tools 8

2 Ship Resistance 11

2.1 Total Resistance 11

2.2 Phenomenological Subdivision 12

2.3 Practical Subdivision 14

2.3.1 Froude's hypothesis 15

2.3.2 ITTC's method 17

2.4 Physical Subdivision 18

2.4.1 Body forces 20

2.4.2 Surface forces 20

2.5 Major Resistance Components 22

3 Fluid and Flow Properties 29

3.1 A Word on Notation 29

3.2 Fluid properties 32

3.2.1 Properties of water 33

3.2.2 Properties of air 35

3.2.3 Acceleration of free fall 35

3.3 Modeling and Visualizing Flow 36

3.4 Pressure 38

4 Fluid Mechanics and Calculus 46

4.1 Substantial Derivative 46

4.2 Nabla Operator and its Applications 49

4.2.1 Gradient 50

4.2.2 Divergence 50

4.2.3 Rotation 53

4.2.4 Laplace operator 53

5 Continuity Equation 55

5.1 Mathematical Models of Flow 55

5.2 Infinitesimal Fluid Element Fixed in Space 57

5.3 Finite Control Volume Fixed in Space 59

5.4 Infinitesimal Element Moving with the Fluid 60

5.5 Finite Control Volume Moving with the Fluid 61

5.6 Summary 61

6 Navier-Stokes Equations 64

6.1 Momentum 64

6.2 Conservation of Momentum 65

6.2.1 Time rate of change of momentum 65

6.2.2 Momentum ux over boundary 66

6.2.3 External forces 68

6.2.4 Conservation of momentum equations 70

6.3 Stokes Hypothesis 71

6.4 Navier-Stokes Equations for a Newtonian Fluid 73

7 Special Cases of the Navier-Stokes Equations 77

7.1 Incompressible Fluid of Constant Temperature 77

7.2 Dimensionless Navier-Stokes Equations 82

8 Reynolds Averaged Navier-Stokes Equations (RANSE) 89

8.1 Mean and Turbulent Velocity 89

8.2 Time Averaged Continuity Equation 91

8.3 Time Averaged Navier-Stokes Equations 94

8.4 Reynolds Stresses and Turbulence Modeling 96

9 Application of the Conservation Principles 101

9.1 Body in a Wind Tunnel 101

9.2 Submerged Vessel in an Unbounded Fluid 106

9.2.1 Conservation of mass 108

9.2.2 Conservation of momentum 110

10 Boundary Layer Theory 114

10.1 Boundary Layer 114

10.1.1 Boundary layer thickness 115

10.1.2 Laminar and turbulent ow 116

10.1.3 Flow separation 119

10.2 Simplifying Assumptions 120

10.3 Boundary Layer Equations 124

11 Wall Shear Stress in the Boundary Layer 127

11.1 Control Volume Selection 127

11.2 Conservation of Mass in the Boundary Layer 128

11.3 Conservation of Momentum in the Boundary Layer 130

11.3.1 Momentum ux over boundary of control volume 131

11.3.2 Surface forces acting on control volume 134

11.3.3 Displacement thickness 140

11.3.4 Momentum thickness 141

11.4 Wall Shear Stress 141

12 Boundary Layer of a Flat Plate 143

12.1 Boundary Layer Equations for a Flat Plate 143

12.2 Dimensionless Velocity Profiles 145

12.3 Boundary Layer Thickness 147

12.4 Wall Shear Stress 151

12.5 Displacement Thickness 153

12.6 Momentum Thickness 153

12.7 Friction Force and Coefficients 154

13 Frictional Resistance 157

13.1 Turbulent Boundary Layers 157

13.2 Shear Stress in Turbulent Flow 164

13.3 Friction Coefficients for Turbulent Flow 165

13.4 Model Ship Correlation Lines 166

13.5 Effect of Surface Roughness 169

13.6 Effect of Form 173

13.7 Estimating Frictional Resistance 173

14 Inviscid Flow 178

14.1 Euler Equations for Incompressible Flow 178

14.2 Bernoulli Equation 179

14.3 Rotation, Vorticity, and Circulation 185

15 Potential Flow 191

15.1 Velocity Potential 191

15.2 Circulation and Velocity Potential 196

15.3 Laplace Equation 199

15.4 Bernoulli Equation for Potential Flow 202

16 Basic Solutions of the Laplace Equation 206

16.1 Uniform Parallel Flow 206

16.2 Sources and Sinks 207

16.3 Vortex 211

16.4 Combinations of Singularities 213

16.4.1 Rankine oval 213

16.4.2 Dipole 218

16.5 Singularity Distributions 221

17 Ideal Flow Around A Long Cylinder 223

17.1 Boundary Value Problem 223

17.1.1 Moving cylinder in uid at rest 224

17.1.2 Cylinder at rest in parallel ow 226

17.2 Solution and Velocity Potential 228

17.3 Velocity and Pressure Field 231

17.3.1 Velocity field 231

17.3.2 Pressure field 233

17.4 D'Alembert's Paradox 234

17.5 Added Mass 236

18 Viscous Pressure Resistance 240

18.1 Displacement Effect of Boundary Layer 240

18.2 Flow Separation 243

19 Waves and Ship Wave Patterns 248

19.1 Wave Length, Period, and Height 248

19.2 Fundamental Observations 251

19.3 Kelvin Wave Pattern 253

20 Wave Theory 258

20.1 Overview 258

20.2 Mathematical Model for Long Crested Waves 259

20.2.1 Ocean bottom boundary condition 261

20.2.2 Free surface boundary conditions 261

20.2.3 Far field condition 266

20.2.4 Nonlinear boundary value problem 266

20.3 Linearized Boundary Value Problem 267

21 Linearization of Free Surface Boundary Conditions 270

21.1 Perturbation Approach 270

21.2 Kinematic Free Surface Condition 272

21.3 Dynamic Free Surface Condition 274

21.4 Linearized Free Surface Conditions for Waves 276

22 Linear Wave Theory 279

22.1 Solution of Linear Boundary Value Problem 279

22.2 Far Field Condition Revisited 285

22.3 Dispersion Relation 286

22.4 Deep Water Approximation 288

23 Wave Properties 292

23.1 Linear Wave Theory Results 292

23.2 Wave number 293

23.3 Water Particle Velocity and Acceleration 296

23.4 Dynamic Pressure 301

23.5 Water Particle Motions 302

24 Wave Energy and Wave Propagation 306

24.1 Wave Propagation 306

24.2 Wave Energy 309

24.2.1 Kinetic wave energy 310

24.2.2 Potential wave energy 313

24.3 Energy Transport and Group Velocity 315

25 Ship Wave Resistance 322

25.1 Physics of Wave Resistance 322

25.2 Wave Superposition 324

25.3 Michell's Integral 333

25.4 Panel Methods 336

26 Ship Model Testing 340

26.1 Testing Facilities 340

26.1.1 Towing tank 341

26.1.2 Cavitation tunnel 344

26.2 Ship and Propeller Models 345

26.2.1 Turbulence generation 347

26.2.2 Loading condition 347

26.2.3 Propeller models 348

26.3 Model Basins 348

27 Dimensional Analysis 352

27.1 Purpose of Dimensional Analysis 352

27.2 Buckingham _-Theorem 353

27.3 Dimensional Analysis of Ship Resistance 353

28 Laws of Similitude 357

28.1 Similarities 357

28.1.1 Geometric similarity 358

28.1.2 Kinematic similarity 358

28.1.3 Dynamic similarity 360

28.1.4 Summary 365

28.2 Partial Dynamic Similarity 366

28.2.1 Hypothetical case: full dynamic similarity 366

28.2.2 Real world: partial dynamic similarity 368

28.2.3 Froude's hypothesis revisited 368

29 Resistance Test 371

29.1 Test Procedure 371

29.2 Reduction of Resistance Test Data 374

29.3 Form Factor k 377

29.4 Wave Resistance Coefficient CW 380

29.5 Skin Friction Correction Force FD 381

30 Full Scale Resistance Prediction 383

30.1 Model Test Results 383

30.2 Corrections and Additional Resistance Components 384

30.3 Total Resistance and Effective Power 385

30.4 Example Resistance Prediction 386

31 Resistance Estimates – Guldhammer and Harvald’s Method 394

31.1 Historical Development 394

31.2 Guldhammer and Harvald's Method 396

31.2.1 Applicability 396

31.2.2 Required input 397

31.2.3 Resistance estimate 399

31.3 Extended Resistance Estimate Example 406

31.3.1 Completion of input parameters 406

31.3.2 Range of speeds 408

31.3.3 Residuary resistance coefficient 409

31.3.4 Frictional resistance coefficient 412

31.3.5 Additional resistance coefficient 412

31.3.6 Total resistance coefficient412

31.3.7 Total resistance and effective power 413

32 Introduction to Ship Propulsion 418

32.1 Propulsion Task 418

32.2 Propulsion Systems 420

32.2.1 Marine propeller 420

32.2.2 Water jet propulsion 422

32.2.3 Voith Schneider propeller (VSP) 422

32.3 Efficiencies in Ship Propulsion . 423

33 Momentum Theory of the Propeller 428

33.1 Thrust, Axial Momentum, and Mass Flow 428

33.2 Ideal Efficiency and Thrust Loading Coefficient434

34 Hull-Propeller Interaction 438

34.1 Wake Fraction 438

34.2 Thrust Deduction Fraction 444

34.3 Relative Rotative Efficiency 447

35 Propeller Geometry 451

35.1 Propeller Parts 451

35.2 Principal Propeller Characteristics 453

35.3 Other Geometric Propeller Characteristics 463

36 Lifting Foils 468

36.1 Foil Geometry and Flow Patterns 468

36.2 Lift and Drag 471

36.3 Thin Foil Theory 474

36.3.1 Thin foil boundary value problem 474

36.3.2 Thin foil body boundary condition 476

36.3.3 Decomposition of disturbance potential 479

37 Thin Foil Theory – Displacement Flow 481

37.1 Boundary Value Problem 482

37.2 Pressure Distribution 487

37.3 Elliptical Thickness Distribution 489

38 Thin Foil Theory – Lifting Flow 494

38.1 Lifting Foil Problem 494

38.2 Glauert's Classical Solution 498

39 Thin Foil Theory – Lifting Flow Properties 504

39.1 Lift Force and Lift Coefficient. 504

39.2 Moment and Center of Effort 510

39.3 Ideal Angle of Attack 513

39.4 Parabolic Mean Line 516

40 Lifting Wings 520

40.1 Effects of Limited Wingspan 520

40.2 Free and Bound Vorticity 524

40.3 Biot{Savart Law 530

40.4 Lifting Line Theory 534

41 Open Water Test 538

41.1 Test Conditions 538

41.2 Propeller Models 542

41.3 Test Procedure 542

41.4 Data Reduction 544

42 Full Scale Propeller Performance 548

42.1 Comparison of Model and Full Scale Propeller Forces . 548

42.2 ITTC Full Scale Correction Procedure 551

43 Propulsion Test 556

43.1 Testing Procedure 556

43.2 Data Reduction 559

43.3 Hull{Propeller Interaction Parameters 560

43.3.1 Model wake fraction 562

43.3.2 Thrust deduction fraction 562

43.3.3 Relative rotative efficiency 563

43.3.4 Full scale wake fraction . 564

43.4 Load Variation Test 566

44 ITTC 1978 Performance Prediction Method 571

44.1 Summary of Model Tests 571

44.2 Full Scale Power Prediction 572

44.3 Summary 575

44.4 Solving the Intersection Problem 576

44.5 Example 579

45 Cavitation 582

45.1 Cavitation Phenomenon 582

45.2 Cavitation Inception 584

45.3 Locations and Types of Cavitation 587

45.4 Detrimental Effects of Cavitation 589

46 Cavitation Prevention 593

46.1 Design Measures 593

46.2 Keller's Formula 594

46.3 Burrill's Cavitation Chart 595

46.4 Other Design Measures 599

47 Propeller Series Data 601

47.1 Wageningen B-Series 601

47.2 Wageningen B-Series Polynomials 602

47.3 Other Propeller Series 607

48 Propeller Design Process 611

48.1 Design Tasks and Input Preparation 611

48.2 Optimum Diameter Selection 614

48.2.1 Propeller design task 1 614

48.2.2 Propeller design task 2 620

48.3 Optimum Rate of Revolution Selection 622

48.3.1 Propeller design task 3 622

48.3.2 Propeller design task 4 624

48.4 Design Charts 625

48.5 Computational Tools 628

49 Hull-Propeller Matching Examples 631

49.1 Optimum Rate of Revolution Problem 631

49.1.1 Design constant 632

49.1.2 Initial expanded area ratio 634

49.1.3 First iteration 634

49.1.4 Cavitation check for first iteration 637

49.1.5 Second iteration 639

49.1.6 Final selection by interpolation 641

49.2 Optimum Diameter Problem 643

49.2.1 Design constant 643

49.2.2 Initial expanded area ratio 645

49.2.3 First iteration 647

49.2.4 Cavitation check for first iteration 650

49.2.5 Second iteration 651

49.2.6 Final selection by interpolation 652

49.2.7 Attainable speed check 654

50 Holtrop and Mennen’s Method 658

50.1 Overview of the Method 658

50.1.1 Applicability 658

50.1.2 Required input 659

50.2 Procedure 661

50.2.1 Resistance components 662

50.2.2 Total resistance 668

50.2.3 Hull{propeller interaction parameters 669

50.3 Example 670

50.3.1 Completion of input parameters 670

50.3.2 Resistance estimate 671

50.3.3 Powering estimate 673

51 Hollenbach’s Method 676

51.1 Overview of the method 676

51.1.1 Applicability 677

51.1.2 Required input 677

51.2 Resistance Estimate 680

51.2.1 Frictional resistance coefficient680

51.2.2 Mean residuary resistance coefficient680

51.2.3 Minimum residuary resistance coefficient685

51.2.4 Residuary resistance coefficient685

51.2.5 Correlation allowance 685

51.2.6 Appendage resistance 686

51.2.7 Environmental resistance 687

51.2.8 Total resistance 687

51.3 Hull{Propeller Interaction Parameters 687

51.3.1 Relative rotative efficiency 688

51.3.2 Thrust deduction fraction 688

51.3.3 Wake fraction 689

51.4 Resistance and Propulsion Estimate Example 691

51.4.1 Completion of input parameters 691

51.4.2 Resistance estimate 692

Index 701