Fundamentals of Ship Hydrodynamics: Fluid Mechanics, Ship Resistance and Propulsion Lothar Birk, University of New Orleans, USA Bridging the information gap between fluid mechanics and ship hydrodynamics Fundamentals of Ship Hydrodynamics is designed as a textbook for undergraduate education in ship resistance and propulsion. The book provides connections between basic training in calculus and fluid mechanics and the application of hydrodynamics in daily ship design practice. Based on a foundation in fluid mechanics, the origin, use, and limitations of experimental and computational procedures for resistance and propulsion estimates are explained.

The book is subdivided into sixty chapters, providing background material for individual lectures. The unabridged treatment of equations and the extensive use of figures and examples enable students to study details at their own pace.

Key features:

* Covers the range from basic fluid mechanics to applied ship hydrodynamics.

* Subdivided into 60 succinct chapters.

* In-depth coverage of material enables self-study.

* Around 250 figures and tables.

Fundamentals of Ship Hydrodynamics is essential reading for students and staff of naval architecture, ocean engineering, and applied physics. The book is also useful for practicing naval architects and engineers who wish to brush up on the basics, prepare for a licensing exam, or expand their knowledge.

The book is subdivided into sixty chapters, providing background material for individual lectures. The unabridged treatment of equations and the extensive use of figures and examples enable students to study details at their own pace.

Key features:

* Covers the range from basic fluid mechanics to applied ship hydrodynamics.

* Subdivided into 60 succinct chapters.

* In-depth coverage of material enables self-study.

* Around 250 figures and tables.

Fundamentals of Ship Hydrodynamics is essential reading for students and staff of naval architecture, ocean engineering, and applied physics. The book is also useful for practicing naval architects and engineers who wish to brush up on the basics, prepare for a licensing exam, or expand their knowledge.

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

LOTHAR BIRK has more than two decades of experience teaching ship and offshore hydrodynamics, first at the Technische Universitat Berlin and now at the University of New Orleans (UNO). Fascinated by the world of boats and ships, he studied naval architecture at Technische Universitat 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.