Fundamentals of Ship Hydrodynamics

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.

List of Figures xvii

List of Tables xxvii

Preface xxxi

Acknowledgments xxxv

About the Companion Website xxxvii

1 Ship Hydrodynamics 1

1.1 Calm Water Hydrodynamics 1

1.2 Ship Hydrodynamics and Ship Design 6

1.3 Available Tools 7

2 Ship Resistance 10

2.1 Total Resistance 10

2.2 Phenomenological Subdivision 11

2.3 Practical Subdivision 12

2.3.1 Froude's hypothesis 14

2.3.2 ITTC's method 15

2.4 Physical Subdivision 17

2.4.1 Body forces 18

2.4.2 Surface forces 18

2.5 Major Resistance Components 20

3 Fluid and Flow Properties 26

3.1 A Word on Notation 26

3.2 Fluid Properties 29

3.2.1 Properties of water 29

3.2.2 Properties of air 31

3.2.3 Acceleration of free fall 32

3.3 Modeling and Visualizing Flow 32

3.4 Pressure 35

4 Fluid Mechanics and Calculus 41

4.1 Substantial Derivative 41

4.2 Nabla Operator and Its Applications 44

4.2.1 Gradient 44

4.2.2 Divergence 45

4.2.3 Rotation 47

4.2.4 Laplace operator 48

5 Continuity Equation 50

5.1 Mathematical Models of Flow 50

5.2 Infinitesimal Fluid Element Fixed in Space 51

5.3 Finite Control Volume Fixed in Space 54

5.4 Infinitesimal Element Moving With the Fluid 55

5.5 Finite Control Volume Moving With the Fluid 55

5.6 Summary 56

6 Navier-Stokes Equations 59

6.1 Momentum 59

6.2 Conservation of Momentum 60

6.2.1 Time rate of change of momentum 60

6.2.2 Momentum flux over boundary 60

6.2.3 External forces 63

6.2.4 Conservation of momentum equations 65

6.3 Stokes' Hypothesis 66

6.4 Navier-Stokes Equations for a Newtonian Fluid 67

7 Special Cases of the Navier-Stokes Equations 71

7.1 Incompressible Fluid of Constant Temperature 71

7.2 Dimensionless Navier-Stokes Equations 75

8 Reynolds Averaged Navier-Stokes Equations (RANSE) 82

8.1 Mean and Turbulent Velocity 82

8.2 Time Averaged Continuity Equation 84

8.3 Time Averaged Navier-Stokes Equations 87

8.4 Reynolds Stresses and Turbulence Modeling 89

9 Application of the Conservation Principles 94

9.1 Body in a Wind Tunnel 94

9.2 Submerged Vessel in an Unbounded Fluid 99

9.2.1 Conservation of mass 100

9.2.2 Conservation of momentum 102

10 Boundary Layer Theory 106

10.1 Boundary Layer 106

10.1.1 Boundary layer thickness 107

10.1.2 Laminar and turbulent flow 108

10.1.3 Flow separation 110

10.2 Simplifying Assumptions 111

10.3 Boundary Layer Equations 115

11 Wall Shear Stress in the Boundary L Wall Shear Stress in the Boundary Layer 118

11.1 Control Volume Selection 118

11.2 Conservation of Mass in the Boundary Layer 119

11.3 Conservation of Momentum in the Boundary Layer 121

11.3.1 Momentum flux over boundary of control volume 122

11.3.2 Surface forces acting on control volume 124

11.3.3 Displacement thickness 130

11.3.4 Momentum thickness 131

11.4 Wall Shear Stress

12 Boundary Layer of a Flat Plate 132

12.1 Boundary Layer Equations for a Flat Plate 132

12.2 Dimensionless Velocity Profiles 134

12.3 Boundary Layer Thickness 136

12.4 Wall Shear Stress 140

12.5 Displacement Thickness 141

12.6 Momentum Thickness 142

12.7 Friction Force and Coefficients 143

13 Frictional Resistance 146

13.1 Turbulent Boundary Layers 146

13.2 Shear Stress in Turbulent Flow 152

13.3 Friction Coefficients for Turbulent Flow 153

13.4 Model-Ship Correlation Lines 155

13.5 Effect of Surface Roughness 157

13.6 Effect of Form 160

13.7 Estimating Frictional Resistance 161

14 Inviscid Flow 165

14.1 Euler Equations for Incompressible Flow 165

14.2 Bernoulli Equation 166

14.3 Rotation, Vorticity, and Circulation 171

15 Potential Flow 177

15.1 Velocity Potential 177

15.2 Circulation and Velocity Potential 182

15.3 Laplace Equation 184

15.4 Bernoulli Equation for Potential Flow 187

16 Basic Solutions of the Laplace Equation 191

16.1 Uniform Parallel Flow 191

16.2 Sources and Sinks 192

16.3 Vortex 196

16.4 Combinations of Singularities 198

16.4.1 Rankine oval 198

16.4.2 Dipole 202

16.5 Singularity Distributions 204

17 Ideal Flow Around A Long Cylinder 207

17.1 Boundary Value Problem 207

17.1.1 Moving cylinder in fluid at rest 208

17.1.2 Cylinder at rest in parallel flow 210

17.2 Solution and Velocity Potential 211

17.3 Velocity and Pressure Field 214

17.3.1 Velocity field 215

17.3.2 Pressure field 216

17.4 D’Alembert's Paradox 218

17.5 Added Mass 219

18 Viscous Pressure Resistance 223

18.1 Displacement Effect of Boundary Layer 223

18.2 Flow Separation 226

19 Waves and Ship Wave Patterns 230

19.1 Wave Length, Period, and Height 230

19.2 Fundamental Observations 233

19.3 Kelvin Wave Pattern 235

20 Wave Theory 239

20.1 Overview 239

20.2 Mathematical Model for Long-crested Waves 240

20.2.1 Ocean bottom boundary condition 241

20.2.2 Free surface boundary conditions 242

20.2.3 Far field condition 246

20.2.4 Nonlinear boundary value problem 247

20.3 Linearized Boundary Value Problem 248

21 Linearization of Free Surface Boundary Conditions 250

21.1 Perturbation Approach 250

21.2 Kinematic Free Surface Condition 252

21.3 Dynamic Free Surface Condition 254

21.4 Linearized Free Surface Conditions for Waves 256

22 Linear Wave Theory 259

22.1 Solution of Linear Boundary Value Problem 259

22.2 Far Field Condition Revisited 265

22.3 Dispersion Relation 265

22.4 Deep Water Approximation 267

23 Wave Properties 271

23.1 Linear Wave Theory Results 271

23.2 Wave Number 272

23.3 Water Particle Velocity and Acceleration 275

23.4 Dynamic Pressure 279

23.5 Water Particle Motions 280

24 Wave Energy and Wave Propagation 284

24.1 Wave Propagation 284

24.2 Wave Energy 287

24.2.1 Kinetic wave energy 287

24.2.2 Potential wave energy 290

24.2.3 Total wave energy density 292

24.3 Energy Transport and Group Velocity 293

25 Ship Wave Resistance 299

25.1 Physics of Wave Resistance 299

25.2 Wave Superposition 301

25.3 Michell's Integral 310

25.4 Panel Methods 312

26 Ship Model Testing 316

26.1 Testing Facilities 316

26.1.1 Towing Lank 317

26.1.2 Cavitation tunnel 320

26.2 Ship and Propeller Models 321

26.2.1 Turbulence generation 322

26.2.2 Loading condition 323

26.2.3 Propeller models 324

26.3 Model Basins 324

27 Dimensional Analysis 327

27.1 Purpose of Dimensional Analysis 327

27.2 Buckingham -Theorem 328

27.3 Dimensional Analysis of Ship Resistance 328

28 Laws of Similitude 332

28.1 Similarities 332

28.1.1 Geometric similarity 333

28.1.2 Kinematic similarity 333

28.1.3 Dynamic similarity 334

28.1.4 Summary 340

28.2 Partial Dynamic Similarity 340

28.2.1 Hypothetical case: full dynamic similarity 340

28.2.2 Real world: partial dynamic similarity 342

28.2.3 Froude's hypothesis revisited 343

29 Resistance Test 345

29.1 Test Procedure 345

29.2 Reduction of Resistance Test Data 348

29.3 Form Factor k 351

29.4 Wave Resistance Coefficient Cw 354

29.5 Skin Friction Correction Force FD 355

30 Full Scale Resistance Prediction 357

30.1 Model Test Results 357

30.2 Corrections and Additional Resistance Components 358

30.3 Total Resistance and Effective Power 359

30.4 Example Resistance Prediction 360

31 Resistance Estimates - Guldhammer and Harvald's Method 367

31.1 Historical Development 367

31.2 Guldhammer and Harvald's Method 369

31.2.1 Applicability 369

31.2.2 Required input 369

31.2.3 Resistance estimate 372

31.3 Extended Resistance Estimate Example 378

31.3.1 Completion of input parameters 379

31.3.2 Range of speeds 380

31.3.3 Residuary resistance coefficient 380

31.3.4 Frictional resistance coefficient 383

31.3.5 Additional resistance coefficients 383

31.3.6 Total resistance coefficient 384

31.3.7 Total resistance and effective power 384

32 Introduction to Ship Propulsion 389

32.1 Propulsion Task 389

32.2 Propulsion Systems 391

32.2.1 Marine propeller 391

32.2.2 Water jet propulsion 392

32.2.3 Voith Schneider propeller (VSP) 393

32.3 Efficiencies in Ship Propulsion 394

33 Momentum Theory of the Propeller 398

33.1 Thrust, Axial Momentum, and Mass Flow 398

33.2 Ideal Efficiency and ^rust Loading Coefficient 403

34 Hull-Propeller Interaction 408

34.1 Wake- Fraction 408

34.2 ^rust Deduction Fraction 414

34.3 Relative Rotative Efficiency 417

35 Propeller Geometry 420

35.1 Propeller Parts 420

35.2 Principal Propeller Characteristics 422

35.3 Other Geometric Propeller Characteristics 431

36 Lifting Foils 435

36.1 Foil Geometry and Flow Patterns 435

36.2 Lift and Drag 438

36.3 Thin Foil Theory 440

36.3.1 Thin foil boundary value problem 441

36.3.2 Thin foil body boundary condition 442

36.3.3 Decomposition of disturbance potential 445

37 Thin Foil Theory – Displacement Flow 447

37.1 Boundary Value Problem 447

37.2 Pressure Distribution 452

37.3 Elliptical Thickness Distribution 454

38 Thin Foil Theory – Lifting Flow 459

38.1 Lifting Foil Problem 459

38.2 Glauert ’s Classical Solution 463

39 Thin Foil Theory – Lifting Flow Properties 469

39.1 Lift Force and Lift Coefficient 469

39.2 Moment and Center of Effort 474

39.3 Ideal Angle of Attack 478

39.4 Parabolic Mean Line 480

40 Lifting Wings 484

40.1 Effects of Limited Wingspan 484

40.2 Free and Bound Vorticity 488

40.3 Biot-Savart Law 493

40.4 Lifting Line Theory 497

41 Open Water Test 500

41.1 Test Conditions 500

41.2 Propeller Models 503

41.3 Test Procedure 504

41.4 Data Reduction 506

42 Full Scale Propeller Performance 509

42.1 Comparison of Model and Full Scale Propeller Forces 509

42.2 ITTC Full Scale Correction Procedure 511

43 Propulsion Test 516

43.1 Testing Procedure 516

43.2 Data Reduction 519

43.3 Hull-Propeller Interaction Parameters 520

43.3.1 Model wake- fraction 521

43.3.2 Thrust deduction fraction 522

43.3.3 Relative rotative efficiency 523

43.3.4 Full scale hull-propeller interaction parameters 523

43.4 Load Variation Test 525

44 ITTC 1978 Performance Prediction Method 530

44.1 Summary of Model Tests 530

44.2 Full Scale Power Prediction 531

44.3 Summary 534

44.4 Solving the Intersection Problem 535

44.5 Example 537

45 Cavitation 541

45.1 Cavitation Phenomenon 541

45.2 Cavitation Inception 543

45.3 Locations and Types of Cavitation 546

45.4 Detrimental Effects of Cavitation 548

46 Cavitation Prevention 552

46.1 Design Measures 552

46.2 Keller's Formula 553

46.3 Burrill's Cavitation Chart 554

46.4 Other Design Measures 557

47 Propeller Series Data 560

47.1 Wageningen B-Series 560

47.2 Wageningen B-Series Polynomials 561

47.3 Other Propeller Series 565

48 Propeller Design Process 569

48.1 Design Tasks and Input Preparation 569

48.2 Optimum Diameter Selection 571

48.2.1 Propeller design task 1 572

48.2.2 Propeller design task 2 577

48.3 Optimum Rate of Revolution Selection 579

48.3.1 Propeller design task 3 579

48.3.2 Propeller design task 4 581

48.4 Design Charts 581

48.5 Computational Tools 585

49 Hull-Propeller Matching Examples 587

49.1 Optimum Rate of Revolution Problem 587

49.1.1 Design constant 588

49.1.2 Initial expanded area ratio 589

49.1.3 First iteration 590

49.1.4 Cavitation check for first iteration 593

49.1.5 Second iteration 594

49.1.6 Final selection by interpolation 596

49.2 Optimum Diameter Problem 598

49.2.1 Design constant 599

49.2.2 Initial expanded area ratio 600

49.2.3 First iteration 601

49.2.4 Cavitation check for first iteration 604

49.2.5 Second iteration 605

49.2.6 Final selection by interpolation 607

49.2.7 Attainable speed check 608

50 Holtrop and Mennen's Method 611

50.1 Overview of the Method 611

50.1.1 Applicability 611

50.1.2 Required input 612

50.2 Procedure 614

50.2.1 Resistance components 615

50.2.2 Total resistance 621

50.2.3 Hull-propeller interaction parameters 621

50.3 Example 623

50.3.1 Completion of input parameters 623

50.3.2 Resistance estimate 623

50.3.3 Powering estimate 625

51 Hollenbach's Method 628

51.1 Overview of the method 628

51.1.1 Applicability 629

51.1.2 Required input 629

51.2 Resistance Estimate 631

51.2.1 Frictional resistance coefficient 632

51.2.2 Mean residuary resistance coefficient 632

51.2.3 Minimum residuary resistance coefficient 635

51.2.4 Residuary resistance coefficient 637

51.2.5 Correlation allowance 637

51.2.6 Appendage resistance 637

51.2.7 Environmental resistance 638

51.2.8 Total resistance 638

51.3 Hull-Propeller Interaction Parameters 639

51.3.1 Relative rotative efficiency 639

51.3.2 Thrust deduction fraction 640

51.3.3 Wake fraction 640

51.4 Resistance and Propulsion Estimate Example 642

51.4.1 Completion of input parameters 642

51.4.2 Powering estimate 643

Index 651