Marine Hydrodynamics J. N. Newman foreword by John Grue Marine Hydrodynamics 40th anniversary edition The MIT Press Cambridge, Massachusetts London, England © 2017 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in ITC Stone Serif Std and ITC Stone Sans Std by Toppan Best-set Premedia Limited. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Names: Newman, J. N. (John Nicholas), 1935– author. Title: Marine hydrodynamics / J. N. Newman ; foreword by John Grue. Description: 40th anniversary edition. | Cambridge, MA : The MIT Press, [2017] | Includes bibliographical references and index. Identifiers: LCCN 2017023272 | ISBN 9780262534826 (pbk. : alk. paper) Subjects: LCSH: Ships--Hydrodynamics. | Hydrodynamics. Classification: LCC VM156 .N48 2017 | DDC 623.8/12--dc23 LC record available at https://lccn.loc.gov/2017023272 10 9 8 7 6 5 4 3 2 1 To my family and friends Contents Foreword xi Preface to the 40th Anniversary Edition xvii Preface to the First Edition xix 1 Introduction 1 2 Model Testing 9 2.1 Falling Body in a Vacuum 10 2.2 Pendulum 11 2.3 Water Waves 12 2.4 Drag Force on a Sphere 14 2.5 Viscous Drag on a Flat Plate 17 2.6 Viscous Drag on General Bodies 18 2.7 Hydrofoil Lift and Drag 22 2.8 Screw Propeller 25 2.9 Drag on a Ship Hull 29 2.10 Propeller-Hull Interactions 34 2.11 Unsteady Force on an Accelerating Body 37 2.12 Vortex Shedding 40 2.13 Wave Force on a Stationary Body 41 2.14 Body Motions in Waves 45 2.15 Ship Motions in Waves 48 Problems 50 References 53 3 The Motion of a Viscous Fluid 55 3.1 Description of the Flow 56 3.2 Conservation of Mass and Momentum 58 viii Contents 3.3 The Transport Theorem 59 3.4 The Continuity Equation 61 3.5 Euler's Equations 62 3.6 Stress Relations in a Newtonian Fluid 62 3.7 The Navier-Stokes Equations 65 3.8 Boundary Conditions 66 3.9 Body Forces and Gravity 66 3.10 The Flow between Two Parallel Walls (Plane Couette Flow) 67 3.11 The Flow through a Pipe (Poiseuille Flow) 68 3.12 External Flow Past One Flat Plate 70 3.13 Unsteady Motion of a Flat Plate 72 3.14 Laminar Boundary Layers: Steady Flow Past a Flat Plate 75 3.15 Laminar Boundary Layers: Steady Two-Dimensional Flow 81 3.16 Laminar Boundary Layers: Closing Remarks 88 3.17 Turbulent Flow: General Aspects 88 3.18 Turbulent Boundary Layer on a Flat Plate 91 3.19 The 1/7-Power Approximation 99 3.20 Roughness Effects on Turbulent Boundary Layers 100 3.21 Turbulent Boundary Layers: Closing Remarks 102 Problems 102 References 104 4 The Motion of an Ideal Fluid 107 4.1 Irrotational Flows 108 4.2 The Velocity Potential 110 4.3 Bernoulli's Equations 112 4.4 Boundary Conditions 114 4.5 Simple Potential Flows 116 4.6 The Stream Function 121 4.7 The Complex Potential 123 4.8 Conformal Mapping 125 4.9 Separation of Variables 129 4.10 Fixed Bodies and Moving Bodies 132 4.11 Green's Theorem and Distributions of Singularities 133 4.12 Hydrodynamic Pressure Forces 138 4.13 Force on a Moving Body in an Unbounded Fluid 141 4.14 General Properties of the Added-Mass Coefficients 147 Contents ix 4.15 The Added Mass of Simple Forms 151 4.16 The Body-Mass Force 155 4.17 Force on a Body in a Nonuniform Stream 156 4.18 The Method of Images 160 Problems 161 References 164 5 Lifting Surfaces 167 5.1 Two-Dimensional Hydrofoil Theory 169 5.2 Linearized Two-Dimensional Theory 172 5.3 The Lifting Problem 176 5.4 Simple Foil Shapes 180 5.5 Drag Force on a Two-Dimensional Foil 184 5.6 Two-Dimensional Source and Vortex Distributions 186 5.7 Singular Integral Equations 189 5.8 Three-Dimensional Vortices 197 5.9 Three-Dimensional Planar Lifting Surfaces 200 5.10 Induced Drag 206 5.11 Lifting-Line Theory 210 5.12 Cavity Flows 216 5.13 Symmetric Cavity Flows 218 5.14 Supercavitating Lifting Foils 223 5.15 Unsteady Hydrofoil Theory 229 5.16 Oscillatory Time Dependence 236 5.17 The Sinusoidal Gust Problem 239 5.18 Transient Problems 241 Problems 242 References 244 6 Waves and Wave Effects 247 6.1 Linearized Free-Surface Condition 248 6.2 Plane Progressive Waves 250 6.3 Finite-Depth Effects 253 6.4 Nonlinear Effects 256 6.5 Mass Transport 261 6.6 Superposition of Plane Waves 263 6.7 Group Velocity 268 6.8 Wave Energy 271 x Contents 6.9 Two-Dimensional Ship Waves 277 6.10 Three-Dimensional Ship Waves 282 6.11 The Method of Stationary Phase 286 6.12 Energy Radiation and Wave Resistance 290 6.13 Thin-Ship Theory of Wave Resistance 292 6.14 Wave Pattern Analysis 294 6.15 Body Response in Regular Waves 297 6.16 Hydrostatics 302 6.17 Damping and Added Mass 306 6.18 Wave-Exciting Force and Moment 313 6.19 Motion of Floating Bodies in Regular Waves 319 6.20 Ocean Waves 323 6.21 Motions of Bodies in Irregular Waves 333 Problems 334 References 338 7 Hydrodynamics of Slender Bodies 341 7.1 Slender Body in an Unbounded Fluid 342 7.2 Longitudinal Motion 348 7.3 The Lateral Force 351 7.4 Ship Maneuvering: The Hydrodynamic Forces 357 7.5 Ship Maneuvering: The Equations of Motion 363 7.6 Slender Bodies in Waves 369 7.7 Strip Theory for Ship Motions 374 7.8 Slender Bodies in Shallow Water 388 Problems 397 References 399 Appendix: Units of Measurement and Physical Constants 403 Notes 405 Index 409 Foreword F o r e w o r d John Grue © Massachusetts Institute of TechnologyAll Rights Reserved I became acquainted with this book in 1980 while completing my master’s degree in mechanics at the University of Oslo. After the North Sea oil boom of the 1970s, it was apparent that there was a need for improved higher education and research related to the oil industry. The University of Oslo developed a curriculum in marine hydrodynamics, and interest in the field grew rapidly as students signed up for the program. I was one of them. The course in marine hydrodynamics was offered for the first time dur- ing the 1980–1981 academic year, and has been lectured approximately once a year since its inception. J. N. Newman’s textbook felt like a gift to our cohort and to our professor, Enok Palm. The entire book comprised a new curriculum with the exception of chapter 3, as viscous flow was cov- ered in other courses. Like us, Palm was new to the subject, so the course was taught as a seminar. I was assigned the duty of giving lectures based on the book because our professor believed that having the youngest (and presumably the least experienced) student give the lectures would slow the pace of the course. I presented two hours of lectures each week for the entire academic year. During the lectures, Palm conducted a detailed examination of all statements and deductions I wrote on the blackboard, and I fielded questions from my classmates as well. By the end of the spring term, I knew the book by heart. The following year, the entire research division of Det Norske Veritas (now DNV GL) attended the course. This time, Enok Palm lectured the course himself. “I just can’t ask a master’s student to teach such an important course to the scientific leaders of Veritas,” he told me. I was given the duty of leading the exercises instead. Reading this book—a real classic—has been the most defining experi- ence of my scientific career. I use it frequently in my teaching and scientific xii Foreword work. This text is a continuous font of inspiration for a master’s or PhD project. How does one define marine hydrodynamics? First, it’s important to understand the meaning of offshore engineering. Put simply, offshore engineering deals with the design, construction, and safety considerations, including insurance, of both stationary and moving structures at sea. Regarding the first question, marine hydrodynamics defines the theoretical framework of offshore engineering. Marine hydrodynamics is an extensive subject as it treats the hydrodynamics in relation to all conceivable geom- etries exposed to the forces in the ocean environment. This includes the forces from the waves as well as those acting on lifting surfaces, either in water or in air. Sailors, rowers, canoeists, and kayakers are all faced with the same challenges: how does one reduce wave or frictional resistance, and optimize sail, rudder shape, or paddle motion? These are all examples of marine hydrodynamics. Calculating extreme loads and thereby ensur- ing the survival of structures exposed to extreme conditions—such as the record high Draupner wave, detected in the North Sea on New Year’s Day 1995 with a crest height of more than 18 meters, a wave height of more than 25 meters, and a wavelength slightly exceeding 200 meters—is the ultimate goal. (Note that the design waves of the platforms in the North Sea are stronger than the Draupner wave.) Stationary bodies are either fixed to the seafloor or floating on the sur- face with a stiff or slack mooring maintaining their position. There is a variety of such bodies, including all kinds of ships, barges, offshore plat- forms in transit from one position to another, and other objects towed by ships. Offshore wind turbines are more recently studied geometries. In most cases these are organized in large wind farms that are mounted on the seafloor as at Horns Rev 1 and 2 in Danish waters, and at Dudgeon on the coast of the United Kingdom. Hywind, developed by the Norwegian oil and gas company Statoil, is an offshore wind turbine prototype that floats on a spar buoy. The current target wing span of these geometries is twice that of an Airbus A380! Other geometries in offshore engineer- ing include cages for aquaculture, which may be either closed or open. Making them larger and sufficiently strong enough to be placed in harsh ocean environments is a new development in the fish farming industry. New development of coastal infrastructure would require road crossings of fjords. Proposed bridges would be supported by floating, moored pontoons; John Grue xiii submerged floating tunnels are another alternative. Wave power devices are another example of structures where the subject of marine hydrody- namics is relevant, and where the design of successful structures must be based on this subject. This textbook is ideal for a masters- or PhD-level course. Students using this book should also have completed courses in introductory mathematics, classical physics, and field theory. Additionally, a course in fluid mechanics provides a foundation to build upon with the material contained herein. Most introductory courses in mathematics have some components of com- plex theory and provide a sufficient background for the more advanced exercises in the book; a full course in complex analysis may help the reader but is not required for a good learning outcome. The highlight of the book is the second half of chapter 6, which intro- duces the subject of wave effects. The primary goal is to calculate the responses of a floating body exposed to incoming waves in the six degrees of freedom: heave, sway, surge, roll, pitch, and yaw. Chapter 6, much like the rest of the book, is self-consistent, with the required background of wave theory—including concepts like superposition, group velocity, mass and energy flux, and third-order Stokes wave theory—given in the first half of the chapter. On the basis of potential theory, the matrix equation of the body responses includes the forces and moments due to added mass, wave damping, hydrostatics, and wave excitation. Perturbation-wise, the wave- body interaction problem is linearized and the forces and motions are mod- eled at each spectral frequency, a common assumption and decomposition that is used in marine hydrodynamics. The method provides a platform for a rich mathematical analysis in which the wave effects and responses are analyzed at the fundamental frequency. The resonance frequencies in the vertical modes of motion where the hydrostatic forces balance the inertia forces are defined. The linear analysis corresponds to the basic calculation method used in offshore engineering. Quadratic and higher-order wave effects may be studied using other texts. The introduction of Morison’s equation—a coefficient-based force for- mulation, particularly suitable for slender geometries—is motivated by the dimensional analysis in chapter 2. It is directly related to the long-wave analysis of the wave effects part of chapter 6. The viscous drag term included in Morison’s equation is not modeled by the potential theory analysis of chapter 6, however. Chapter 2 introduces the concept of added mass—an xiv Foreword inertia effect due to the accelerated mass of the surrounding fluid. It con- tributes in a similar way to the mass of a body in classical mechanics. In chapter 4—also directly related to the wave effects part of chapter 6—the forces and moments on a geometry moving in the six degrees of freedom, in unbounded fluid, are derived on exact form, expressed in terms of the six-by-six added mass matrix. This elegant, exact analysis is directly suit- able as a model of the motion of a remotely operated underwater vehicle (ROV). The ways in which animals swim and fly, airplanes and ski jumpers con- trol their flight, and a yacht sails across the water are the result of flow at thin streamlined bodies. Chapter 5 introduces the fundamentals of the flow and force on a lifting surface. Moreover, it describes the propulsive force created by a wing’s flapping motion. The lift problem of a two-dimensional foil section is analyzed in the beginning of the chapter—a starting point in the training of candidates for the growing wind power industry. The sharp trailing edge of the wing enforces the flow velocity to be finite, imposed mathematically by the Kutta condition, controlling the initial flow separation. The mathematical modeling in this book is represented by partial differ- ential equations (PDEs). The solution methods of field equations in marine hydrodynamics—commonly the Laplace equation—differ fundamentally from the common solution methods of PDEs. The main reason is this: The cause of the motion (the geometry) is local whereas the motion is global (the infinite extension of the wave field). Popular methods for solving partial differential equations are often based on volume methods, either difference methods or variants of the finite element method. The special method of separation of variables employs sets of orthogonal functions particularly fitted to geometries of special shape. However, for floating or submerged large-volume geometries of arbitrary shape, use of integral equa- tions is unsurpassed and is a standard method in marine hydrodynamics. This method is extensively used in the offshore industry. The formulation, in terms of integral equations, is directly related to the scattering and radia- tion problems in theoretical physics, although the wave Green functions differ. The application of multipole expansions including the surface wave effects is an efficient, accurate, and convergent method that has found a lesser application in the industry. Thus, chapter 4 involves solving PDEs for the flow in an unbounded fluid by use of integral equations expressed John Grue xv in terms of source and dipole distributions. In chapter 5, the lifting and flapping problems are modeled by vortex and source distributions. The resulting integral equation becomes a singular Fredholm integral equation of the first kind. The equation is directly invertable—a superior, analytical, and generic method directly transferable to other related formulations and problems. The nonsingular integral equation formulated in section 11 of chapter 4 is a Fredholm equation of the second kind. This formulation is robust and easy to invert. Variants of this equation are widely used in the offshore industry. How do I teach this book? I start with the integral representation of the potential flow at a geometry in unbounded fluid found in section 4.11, and subsequently introduce the forces and moments in an unbounded fluid expressed in terms of the added mass matrix. The first assignment is the calculation of the two-dimensional added mass of a circle, an ellipse, and a square, obtaining the various potentials through integral equations and Python or MATLAB scripting. Problems 4, 6, 13, and 15 are mandatory. I continue with chapter 6. I usually give one lecture on linear wave the- ory and a second lecture on energy flux and group velocity. The wave effects part of the chapter comes next, introducing the decomposition of the dif- fraction and radiation potentials, the latter according to the six modes of motion, the added mass and damping, the exciting forces, and the restoring forces. Sometimes, depending on the student group, I will assign section 6.16 (hydrostatics) separately. The students then derive the mathematical formulas in the chapter for subsequent presentation in class. The theories are reworked by completing problems 10–17 on wave effects. Problems 1–8 cover the fundamentals of wave theory. In chapter 5, my lecture covers the introduction and sections 5.1–5.6, as well as problems 8 and 9. The results are put in context of the dimensional analysis of the foil in section 7 of chapter 2. One of my final lectures covers the dimensional analysis of chapter 2, with highlights including the low-level introduction of the concept of added mass and the coefficient-based force formulation included in Mori- son’s equation. Problem 14 illustrates how the contributions from the inertia term and the drag term depend on the cylinder diameter. Froude’s hypothesis for the drag on a ship hull is one of my favorites; I frequently use the ITTC-line in figure 2.12 to estimate the frictional resistance on ships. I used this curve as well as equation (23) of chapter 2 when advising the xvi Foreword kayaker Eirik Verås Larsen as he prepared for the 2012 London Olympics. His question was how to reduce frictional and wave resistance. I suggested that the only variable to play with was the wet area of the kayak—the por- tion touching the water, which should be minimal. Larsen and his team eventually discovered that he could reduce his weight—which he eventu- ally reduced by 10 percent—and won the gold medal on the K1 1000m event. John Grue University of Oslo March 16, 2017 Preface to the 40th Anniversary Edition Preface to the 40th Anniversary Edition Preface to the 40th Anniversary Edition © Massachusetts Institute of TechnologyAll Rights Reserved The field of marine hydrodynamics has broadened greatly over the past 40 years, with applications to a wide variety of vessels and structures. These include systems for converting energy from the wind, waves, and currents; yachts, high-speed vessels, aquaculture facilities, and various types of submerged vessels; and traditional applications to ships and off- shore platforms. The support for education and research has grown accord- ingly; it is gratifying that the term “marine hydrodynamics” has become ubiquitous for university departments, research laboratories, conferences, and publications. The basic topics of the field are unchanged, corresponding broadly to the chapters of this text. Numerical methods that extend the applications of the theory have been developed. Practicing engineers and naval archi- tects are now making routine use of well-established programs to optimize their designs and predict performance. These programs include Navier– Stokes solvers, which analyze viscous effects including turbulence, and “panel” programs based on boundary-integral equations to solve potential- flow problems including lifting and wave effects. This evolution has been accelerated by the universal access to computers of increasing capacity and convenience. Nevertheless, it is essential to understand the underlying principles covered in this text, and to compare the results of computations with simpler approximations to be confident of their validity. I am grateful to the MIT Press for suggesting this special edition and for making it available economically, both as a paperback and as an open access e-book. I am especially grateful to Professor John Grue for the fore- word, which reflects his long experience using this text.