Understanding Aerodynamics E-Book

Doug McLean

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Aerospace Series (PEP)
• Sprache: Englisch

Seitenzahl: 1197

Veröffentlichungsjahr: 2012

Beschreibung

Much-needed, fresh approach that brings a greater insight into the physical understanding of aerodynamics

Based on the author’s decades of industrial experience with Boeing, this book helps students and practicing engineers to gain a greater physical understanding of aerodynamics. Relying on clear physical arguments and examples, Mclean provides a much-needed, fresh approach to this sometimes contentious subject without shying away from addressing "real" aerodynamic situations as opposed to the oversimplified ones frequently used for mathematical convenience. Motivated by the belief that engineering practice is enhanced in the long run by a robust understanding of the basics as well as real cause-and-effect relationships that lie behind the theory, he provides intuitive physical interpretations and explanations, debunking commonly-held misconceptions and misinterpretations, and building upon the contrasts provided by wrong explanations to strengthen understanding of the right ones.

• Provides a refreshing view of aerodynamics that is based on the author’s decades of industrial experience yet is always tied to basic fundamentals.
• Provides intuitive physical interpretations and explanations, debunking commonly-held misconceptions and misinterpretations
• Offers new insights to some familiar topics, for example, what the Biot-Savart law really means and why it causes so much confusion, what “Reynolds number” and “incompressible flow” really mean, and a real physical explanation for how an airfoil produces lift.
• Addresses "real" aerodynamic situations as opposed to the oversimplified ones frequently used for mathematical convenience, and omits mathematical details whenever the physical understanding can be conveyed without them.

Leseprobe

Table of Contents

Aerospace Series List

Title Page

Copyright

Foreword

Series Preface

Preface

List of Symbols

Greek Symbols

Subscripts

Greek Subscripts

Superscripts

Acronyms and Abbreviations

Chapter 1: Introduction to the Conceptual Landscape

Chapter 2: From Elementary Particles to Aerodynamic Flows

Chapter 3: Continuum Fluid Mechanics and the Navier-Stokes Equations

3.1 The Continuum Formulation and Its Range of Validity

3.2 Mathematical Formalism

3.3 Kinematics: Streamlines, Streaklines, Timelines, and Vorticity

3.4 The Equations of Motion and their Physical Meaning

3.5 Cause and Effect, and the Problem of Prediction

3.6 The Effects of Viscosity

3.7 Turbulence, Reynolds Averaging, and Turbulence Modeling

3.8 Important Dynamical Relationships

3.9 Dynamic Similarity

3.10 “Incompressible” Flow and Potential Flow

3.11 Compressible Flow and Shocks

Chapter 4: Boundary Layers

4.1 Physical Aspects of Boundary-Layer Flows

4.2 Boundary-Layer Theory

4.3 Flat-Plate Boundary Layers and Other Simplified Cases

4.4 Transition and Turbulence

4.5 Control and Prevention of Flow Separation

4.6 Heat Transfer and Compressibility

4.7 Effects of Surface Roughness

Chapter 5: General Features of Flows around Bodies

5.1 The Obstacle Effect

5.2 Basic Topology of Flow Attachment and Separation

5.3 Wakes

5.4 Integrated Forces: Lift and Drag

Chapter 6: Drag and Propulsion

6.1 Basic Physics and Flowfield Manifestations of Drag and Thrust

6.2 Drag Estimation

6.3 Drag Reduction

Chapter 7: Lift and Airfoils in 2D at Subsonic Speeds

7.1 Mathematical Prediction of Lift in 2D

7.2 Lift in Terms of Circulation and Bound Vorticity

7.3 Physical Explanations of Lift in 2D

7.4 Airfoils

Chapter 8: Lift and Wings in 3D at Subsonic Speeds

8.1 The Flowfield around a 3D Wing

8.2 Distribution of Lift on a 3D Wing

8.3 Induced Drag

8.4 Wingtip Devices

8.5 Manifestations of Lift in the Atmosphere at Large

8.6 Effects of Wing Sweep

Chapter 9: Theoretical Idealizations Revisited

9.1 Approximations Grouped According to how the Equations were Modified

9.2 Some Tools of MFD (Mental Fluid Dynamics)

Chapter 10: Modeling Aerodynamic Flows in Computational Fluid Dynamics

10.1 Basic Definitions

10.2 The Major Classes of CFD Codes and Their Applications

10.3 Basic Characteristics of Numerical Solution Schemes

10.4 Physical Modeling in CFD

10.5 CFD Validation?

10.6 Integrated Forces and the Components of Drag

10.7 Solution Visualization

10.8 Things a User Should Know about a CFD Code before Running it

References

Index

Aerospace Series List

Introduction to UAV Systems, 4

th

Edition

Fahlstrom and Gleason

August 2012

Theory of Lift: Introductory Computational Aerodynamics with MATLAB and Octave

McBain

August 2012

Sense and Avoid in UAS: Research and Applications

Angelov

April 2012

Morphing Aerospace Vehicles and Structures

Valasek

April 2012

Gas Turbine Propulsion Systems

MacIsaac and Langton

July 2011

Basic Helicopter Aerodynamics, 3

rd

Edition

Seddon and Newman

July 2011

Advanced Control of Aircraft, Spacecraft and Rockets

Tewari

July 2011

Cooperative Path Planning of Unmanned Aerial Vehicles

Tsourdos et al

November 2010

Principles of Flight for Pilots

Swatton

October 2010

Air Travel and Health: A Systems Perspective

Seabridge et al

September 2010

Design and Analysis of Composite

Kassapoglou

September 2010

Structures: With applications to aerospace Structures

Unmanned Aircraft Systems: UAVS Design, Development and Deployment

Austin

April 2010

Introduction to Antenna Placement & Installations

Macnamara

April 2010

Principles of Flight Simulation

Allerton

October 2009

Aircraft Fuel Systems

Langton et al

May 2009

The Global Airline Industry

Belobaba

April 2009

Computational Modelling and Simulation of Aircraft and the Environment: Volume 1 - Platform Kinematics and Synthetic Environment

Diston

April 2009

Handbook of Space Technology

Ley, Wittmann Hallmann

April 2009

Aircraft Performance Theory and Practice for Pilots

Swatton

August 2008

Surrogate Modelling in Engineering Design: A Practical Guide

Forrester, Sobester, Keane

August 2008

Aircraft Systems, 3

rd

Edition

Moir & Seabridge

March 2008

Introduction to Aircraft Aeroelasticity And Loads

Wright & Cooper

December 2007

Stability and Control of Aircraft Systems

Langton

September 2006

Military Avionics Systems

Moir & Seabridge

February 2006

Design and Development of Aircraft Systems

Moir & Seabridge

June 2004

Aircraft Loading and Structural Layout

Howe

May 2004

Aircraft Display Systems

Jukes

December 2003

Civil Avionics Systems

Moir & Seabridge

December 2002

This edition first published 2013

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Library of Congress Cataloging-in-Publication Data

McLean, Doug (Doug J.)

Understanding aerodynamics : arguing from the real physics / Doug McLean.

pages cm

Includes bibliographical references and index.

ISBN 978-1-119-96751-4 (hardback)

1. Aerodynamics. I. Title.

TL570.M3823 2013

629.132′–dc23

2012032706

A catalogue record for this book is available from the British Library

Print ISBN: 978-1-119-96751-4

Foreword

The job of the aeronautical engineer has changed dramatically in recent years and will continue to change. Advanced computational tools have revolutionized design processes for all types of flight vehicles and have made it possible to achieve levels of design technology previously unheard of. And as performance targets have become more demanding, the individual engineer's role in the design process has become increasingly specialized.

In this new environment, design work depends heavily on voluminous numerical computations. The computer handles much of the drudgery, but it can't do the thinking. It is now more important than ever for a practicing engineer to bring to the task a strong physical intuition, solidly based in the physics. In this book, Doug McLean provides a valuable supplement to the many existing books on aerodynamic theory, patiently exploring what it all means from a physical point of view. Students and experienced engineers alike will surely profit from following the thought-provoking arguments and discussions presented here.

John J. TracyChief Technology OfficerThe Boeing CompanySeptember 2012

Series Preface

The field of aerospace is wide ranging and multi-disciplinary, covering a large variety of products, disciplines and domains, not merely in engineering but in many related supporting activities. These combine to enable the aerospace industry to produce exciting and technologically advanced vehicles. The wealth of knowledge and experience that has been gained by expert practitioners in the various aerospace fields needs to be passed onto others working in the industry, including those just entering from University.

The Aerospace Series aims to be a practical and topical series of books aimed at engineering professionals, operators, users and allied professions such as commercial and legal executives in the aerospace industry, and also engineers in academia. The range of topics is intended to be wide ranging, covering design and development, manufacture, operation and support of aircraft as well as topics such as infrastructure operations and developments in research and technology. The intention is to provide a source of relevant information that will be of interest and benefit to all those people working in aerospace.

Aerodynamics is the fundamental enabling science that underpins the world-wide aerospace industry—without the ability to generate lift from airflow passing over wings, helicopter rotors and other lifting surfaces, it would not be possible to fly heavier-than-air vehicles as efficiently as is taken for granted nowadays. Much of the development of today's highly efficient aircraft is due to the ability to accurately model aerodynamic flows using sophisticated computational codes and thus design high-performance wings; however, a thorough understanding and insight of the aerodynamic flows is vital for engineers to comprehend these designs.

This book, Understanding Aerodynamics, has the objective of providing a physical understanding of aerodynamics, with an emphasis on how and why particular flow patterns around bodies occur, and what relation these flows have to the underlying physical laws. It is a welcome addition to the Wiley Aerospace Series. Unlike most aerodynamics textbooks, there is a refreshing lack of detailed mathematical analysis, and the reader is encouraged instead to consider the overall picture. As well as consideration of classical topics—continuum fluid mechanics, boundary layers, lift, drag and the flow around wings, etc.—there is also a very useful coverage of modelling aerodynamic flows using Computational Fluid Dynamics (CFD).

Peter Belobaba, Jonathan Cooper, Roy Langton and Allan Seabridge

Preface

This book is intended to help students and practicing engineers to gain a greater physical understanding of aerodynamics. It is not a handbook on how to do aerodynamics, but is motivated instead by the assumption that engineering practice is enhanced in the long run by a robust understanding of the basics.

A real understanding of aerodynamics must go beyond mastering the mathematical formalism of the theories and come to grips with the physical cause-and-effect relationships that the theories represent. In addition to the math, which applies most directly at the local level, intuitive physical interpretations and explanations are required if we are to understand what happens at the flowfield level. Developing this physical side of our understanding is surprisingly difficult, however. It requires navigating a conceptual landscape littered with potential pitfalls, and an acceptable path is to be found only through recognition and rejection of multiple faulty paths. It is really a process of argumentation, thus the “arguing” in the title. This kind of argumentation is underemphasized in other books, in which the path is often made to appear straighter and simpler than it really is. This book explores a broader swath of the conceptual landscape, including some of the false paths that have led to errors in the past, with the hope that it will leave the reader less likely to fall victim to misconceptions.

We'll encounter several instances of serious misinterpretations of mathematical theory that are in wide circulation and of erroneous physical explanations that have found their way into our folklore. In any case where a misconception has been widely enough propagated, the “right” explanation would not be complete without the debunking of the “wrong” one. I have tried to do this kind of debunking wherever it seemed appropriate and have not hesitated to say so when I think something is wrong. This is part of what makes aerodynamics so much fun. It's one of those little perversities of human nature that coming up with a good explanation is much more satisfying when you know there are people out there who have got it wrong. But debunking bad explanations serves a pedagogical purpose as well, because the contrast provided by the wrong explanation can strengthen understanding of the right one.

This effort devoted to basic physical rigor and avoiding errors comes at a cost. We'll spend more time on some topics than some will likely think necessary. I realize some parts of the discussion are long and are not easy, but I hope most readers will find it worth the effort.

We are now well into what I would call the computational era in aerodynamics, made possible by the ever-advancing capabilities of computers. In the 1960s, we began to calculate practical numerical solutions to linear equations for inviscid flows in 3D. In the 1970s, it became economical to compute solutions to nonlinear equations for inviscid transonic flows in 3D and to include viscous effects through boundary-layer theory and viscous/inviscid coupling. By the 1990s, we were routinely calculating solutions to the Reynolds-averaged Navier-Stokes (RANS) equations for full airplane configurations. These computational fluid dynamics (CFD) capabilities have revolutionized aerodynamics analysis and design and have made possible dramatic improvements in design technology. CFD is now such a vital part of our discipline that this book would not be complete if it did not address it in some way. While this is not a book about CFD methods or about how to use CFD, there are conceptual aspects of CFD that are relevant to our focus, and these are considered in chapter 10.

I believe that although we now rely on CFD for much of our quantitative work, it is vitally important for a practicing engineer to have a sound understanding of the underlying physics and to be familiar with the old simplified theories that our predecessors so ingeniously developed. These things not only provide us with valuable ways of thinking about our problems, they also can help us to be more effective users of CFD.

The unusual scope of the book is deliberate. The book is not intended to be a handbook. Nor is it intended as a substitute for the standard textbooks and other sources on aerodynamic theory, as I have omitted the mathematical details whenever the physical understanding I seek to promote can be conveyed without them. This applies especially to the discussion of the basic physics in the early chapters. Those looking for rigorous derivations of the mathematical details will have to look elsewhere. Also, exhaustive scope is not a practical goal. So, for the details on many of the topics treated here, and for any treatment at all of the many topics neglected here, the reader will have to consult other sources. This book is also not intended as an introduction to the subject. Though it would not be impossible for someone with no prior exposure to follow the development given here, some experience with the subject will make it much easier. And while I assume no prior knowledge of the subject, I do assume a higher level of technical sophistication than is often assumed in undergraduate-level texts.

An understanding of the physical basics is more secure if it includes an appreciation of the “big picture,” the logical structure of the body of knowledge and the collection of concepts we call aerodynamics. I have tried to at least touch on all of the topics that are so basic that the overall framework could not stand without them. I also devote more attention than most aerodynamics textbooks to the relationships between the parts, to how it all “fits together.” Beyond that, several considerations have guided my choice of topics and the kinds of treatment I've given them. One is my own familiarity and experience. Another is my observation of some common knowledge gaps, things that don't seem to be covered well in the usual aero engineering education. But we'll also spend a good part of our time on some of the very familiar things that we tend to take for granted. Our understanding of these things is never so good that it can't benefit from taking a fresh look. We'll put a different spin on some familiar topics, for example, what the Biot-Savart law really means and why it causes so much confusion, what “Reynolds number” and “incompressible flow” really mean, and a real physical explanation for how an airfoil produces lift.

As we'll see in chapter 1, the subject matter of aerodynamics consists of physical principles, conceptual models, mathematical theories, and descriptions and physical explanations of flow phenomena. Some of this subject matter has direct practical applications, and some doesn't. We'll spend considerable time on some topics that have no apparent practical import, for example, physical explanations of things for which we have perfectly good quantitative theories and esoterica such as how lift is felt in the atmosphere at large. We'll do these things because they provide general fluid-mechanics insight and because they serve to expand our appreciation of the cognitive dimension of the subject, the processes by which we think about aerodynamic phenomena and the practical problems that arise from them. They also help us to see how mistaken thinking can arise and how to avoid it. The medical profession in recent years has begun to pay more attention to the cognitive dimension of their discipline, studying how doctors think, in an effort to improve the accuracy of their diagnoses and to avoid mistakes. Doing some of the same would be good for us as well.

Aerodynamics as a subject encompasses a wide variety of flow situations that in turn involve a multitude of detailed flow phenomena. The subject is correspondingly multifaceted, with a rich web of interconnections among the phenomena themselves and the conceptual models that have been developed to represent them. Such a subject has a logical structure of course, but it is not well suited to exposition in a single linear narrative, and there is therefore no ideal solution to the problem of organizing it so that it flows completely naturally as a single string of words. The organization I have chosen is based not on the historical development or on a progression from “easy” concepts to “advanced,” but on a general conceptual progression, from the basic physics, to the flow phenomena, and finally to the conceptual models. I have tried to organize the material so that it can be read straight through and understood without the need to skip forward. I have also tried to provide direct references whenever I think referring back to previous chapters would be helpful and to alert the reader when further discussion of a topic is being deferred until later.

The general flow of the book is as follows. First, we take an overview of the conceptual landscape in chapter 1. Then we consider the basic physics as embodied in the NS equations in chapters 2 and 3. We turn to the phenomenological aspects of general flows in boundary layers and around bodies in chapters 10 and 5. We then enter the more specific realm of aerodynamic forces and their manifestations in flowfields to deal with drag in chapter 6 and lift generation, airfoils, and wings in chapters 7 and 8. All of this sets the stage for a bit of a regression into theory, with discussions of theoretical approximations and CFD in chapters 9 and 10.

When I started writing I had something less ambitious in mind, something more on the scale of a booklet with a collection of helpful ways of looking at aerodynamic phenomena and a catalog of common misconceptions and how to avoid them. As the project progressed, it became clear that effective explanations required more background than I had anticipated, and the book gradually grew more comprehensive. The first draft in something close to the final form was completed in late 2008 and was reviewed by several Boeing colleagues (acknowledged below). Their feedback was incorporated into a second draft that was used in a 20-week after-hours class for Boeing engineers in 2009. Feedback from class participants and others led to significant revisions for the final draft. As it turned out, the general argumentative approach I've taken to the subject extended to the writing process itself. Many sections saw multiple and substantial rewrites as my thinking evolved.

I gratefully acknowledge the help of many people in getting me through this long process. First, my wife, Theresa, who put up with the many, many weekends that I spent in front of our home computer. Then The Boeing Company, which allowed me to spend considerable company time on the project, Boeing editors, Andrea Jarvela, Lisa Fusch Krause, and Charlene Scammon, who turned my raw Word files and graphics into a presentable draft and helped me take that draft through several revisions, and Boeing graphics artist John Jolley, who redrew nearly half the graphics. Finally, the friends and colleagues without whose help the book would have been much poorer. Mark Drela (MIT), Lian Ng, Ben Rider, Philippe Spalart, and Venkat Venkatakrishnan provided very detailed feedback and suggestions for improvement. Steve Allmaras and Mitch Murray made special CFD calculations just for the book. My former Boeing colleague Guenter Brune wrote the excellent 1983 Boeing report on flow topology that introduced me to the topic and served as the basis of much of Section 5.2.3. Another former Boeing colleague, Pete Sullivan, did the CFD calculations plotted in Section 6.1.5. And many others contributed feedback on various drafts of the manuscript: Anders Andersson, John D. Anderson (University of Maryland), Byram Bays-Muchmore, Bob Breidenthal (University of Washington), Julie Brightwell, Tad Calkins, Dave Caughey (Cornell University), Tony Craig, Jeffrey Crouch, Peg Curtin, Bruce Detert, Scott Eberhardt, Winfried Feifel, David Fritz, Arvel Gentry, Mark Goldhammer, Elisabeth Gren, Rob Hoffenberg, Paul Johnson, Wen-Huei Jou, T. J. Kao, Edward Kim, Alex Krynytsky, Brenda Kulfan, Louie LeGrand, Adam Malachowski, Adam Malone, Tom Matoi, Mark Maughmer (Penn State University), the late John McMasters, Kevin Mejia, Robin Melvin, Greg Miller, Deepak Om, Ben Paul, Tim Purcell, Steve Ray, Matt Smith, John Sullivan (Purdue University), Mary Sutanto, Ed Tinoco, David Van Cleve, Paul Vijgen, Dave Witkowski, Conrad Youngren (New York Maritime College), and Jong Yu.

Thanks also to the copyright owners who kindly gave permission to use the many graphics I borrowed from elsewhere. They are acknowledged individually in the figure titles.

Doug McLean, April 2012.

List of Symbols

Many of the symbols listed below have different meanings in different contexts, as indicated when multiple definitions are given. When an example of usage (a figure or equation) is listed, it is not necessarily the only example.

English Symbols

Greek Symbols

Subscripts

1

In the boundary-layer x direction (

equation 4.2.15

)

Denotes conditions upstream of a cascade (

figure 7.4.23 (b)

)

Denotes conditions upstream of the shock on a transonic airfoil (

figure 7.4.31

)

2

Denotes conditions downstream of a cascade (

figure 7.4.23 (b)

)

Denotes conditions downstream of the shock on a transonic airfoil (

figure 7.4.31

)

3

In the boundary-layer z direction (

equation 4.2.15

)

b

Of the boundary-layer coordinate system (

figure 4.2.2

)

c

Pertaining to a vortex core (

figure 8.3.3

)

Cross-flow component (

figure 4.1.7

)

Airfoil chord

ch

Chordwise (figures

4.3.11

and

4.3.12

)

cut

Pertaining to a cut through a wake (

figure 6.1.3

)

d

Based on diameter

Drag per unit span

D

Drag

e

At the edge of the boundary layer

f

Friction

i

Incompressible

Induced, as applied to a propeller

j

Pertaining to a blowing jet (

equation 4.5.1

)

K

Kinematic (

equation 4.6.8

)

l

Lift per unit span

L

Based on length L

Lift

local

Denoting the effective local freestream condition for an excrescence

m

Pitching moment per unit span

n

Connectivity of a 2D domain (

equation 5.2.5

)

Direction normal to wake cut (

equation 8.3.10

)

o

Denotes conditions at the start of an airfoil pressure recovery (

equation 7.4.1

)

p

At constant pressure

Propeller

ref

Reference

rms

Root-mean-square

s

Relative to streamwise direction at boundary-layer edge (

figure 4.1.8

)

sep

Denotes conditions at separation (discussion of

figure 7.4.13

)

sp

Spanwise (figures

4.3.11

and

4.3.12

)

sw

From steamwise at boundary-layer edge to the wall (

figure 4.1.8

)

t

Turbulent (

equation 3.7.5

)

Total (or stagnation) (equations

3.8.3

–

6

)

T

Thermal (

equation 4.6.2

)

v

At constant volume

w

At the wall

x

Based on x

∞

At infinite distance, far field

At infinite height from ground (

figure 8.3.12

)

⊥

Perpendicular

perp

Perpendicular to constant-percent-chord lines (

figure 8.6.11

)

||

Parallel

Greek Subscripts

δ*

Based on displacement thickness

μ

Momentum, as in C

μ

(

equation 4.5.1

)

θ

Based on momentum thickness

τ

Friction velocity, in

Superscripts

Acronyms and Abbreviations

1D

One dimensional

2D

Two dimensional

3D

Three dimensional

BC

Boundary condition

BLC

Boundary-layer control

CFD

Computational fluid dynamics

CF

Cross-flow

CPU

Central processing unit

DES

Detached-eddy simulation

DNS

Direct numerical simulation

ESDU

Engineering Sciences Data Unit

GGNS

General geometry Navier-Stokes

HLFC

Hybrid laminar flow control

LES

Large-eddy simulation

LFC

Laminar flow control

LTA

Lighter than air

NACA

National Advisory Committee for Aeronautics

NASA

National Aeronautics and Space Administration

NLF

Natural laminar flow

NS

Navier-Stokes

ODE

Ordinary differential equation

ONERA

Office National d'Etude et Recherches Aérospatiales

PC

Personal computer

PDE

Partial differential equation

RABL

Reynolds-averaged boundary-layer equations

RANS

Reynolds-averaged Navier-Stokes equations

SA

Spalart-Allmaras

SBVG

Sub-boundary-layer vortex generator

SST

Shear Stress Transport

TKE

Turbulence kinetic energy

TS

Tollmien-Schlichting

URANS

Unsteady Reynolds-averaged Navier-Stokes

VG

Vortex generator

WINGOP

 Wing Optimization

Chapter 1

Introduction to the Conceptual Landscape

The objective of this book is to promote a solid physical understanding of aerodynamics. In general, any understanding of physical phenomena requires conceptual models:

It seems that the human mind has first to construct forms independently before we can find them in things. Kepler's marvelous achievement is a particularly fine example of the truth that knowledge cannot spring from experience alone but only from the comparison of the inventions of the intellect with observed fact.

—Albert Einstein on Kepler's discovery that planetary orbits are ellipses

Einstein wasn't an aerodynamicist, but the above quote applies as well to our field as to his. To understand the physical world in the modern scientific sense, or to make the kinds of quantitative calculations needed in engineering practice, requires conceptual models. Even the most comprehensive set of observations or experimental data is largely useless without a conceptual framework to hang it on.

In fluid mechanics and aerodynamics, I see the conceptual framework as consisting of four major components:

1. Basic physical conservation laws expressed as equations and an understanding of the cause-and-effect relationships those laws represent,

2. Phenomenological knowledge of flow patterns that occur in various situations,

3. Theoretical models based on simplifying the basic equations and/or assuming an idealized model for the structure of the flowfield, consistent with the phenomenology of particular flows, and

4. Qualitative physical explanations of flow phenomena that ideally are consistent with the basic physics and make the physical cause-and-effect relationships clear at the flowfield level.

By way of introduction, let's take a brief look at what these components encompass, the kinds of difficulties they entail, and how they relate to each other.

The fundamental physical conservation laws relevant to aerodynamic flows can be expressed in a variety of ways, but are most often applied in the form of partial-differential equations that must be satisfied everywhere in the flowfield and that represent the local physics very accurately. By solving these basic equations, we can in principle predict any flow of interest, though in practice we must always accept some compromise in the physical accuracy of predictions for reasons we'll come to understand in Chapter 3.

The equations themselves define local physical balances that the flow must obey, but they don't predict what will happen in an overall flowfield unless we solve them, either by brute force numerically or by introducing simplified models. There is a wide gulf in complexity between the relatively simple physical balances that the equations represent and the richness of the phenomena that typically show up in actual flows. The raw physical laws thus provide no direct predictions and little insight into actual flowfields. Solutions to the equations provide predictions, but they are not always easy to obtain, and they are limited in the insight they can provide as well. Even the most accurate solution, while it can tell us what happens in a flow, usually provides us with little understanding as to how it happens or why.

Phenomenological knowledge of what happens in various flow situations is a necessary ingredient if we are to go beyond the limited understanding available from the raw physical laws and from solutions to the equations. Here I am referring not just to descriptions of flowfields, but to the recognition of common flow patterns and the physical processes they represent. The phenomenological component of our conceptual framework provides essential ingredients to our simplified theoretical models (component 3) and our qualitative physical explanations (component 4).

Simplified theoretical models appeared early in the history of our discipline and still play an important role. Until fairly recently, solving the “full” equations for any but the simplest flow situations was simply not feasible. To make any progress at all in understanding and predicting the kinds of flow that are of interest in aerodynamics, the pioneers in our field had to develop an array of different simplified theoretical models applicable to different idealized flow situations, generally based on phenomenological knowledge of the flow structure. Though the levels of physical fidelity of these models varied greatly, even well into the second half of the twentieth century they provided the only practical means for obtaining quantitative predictions. The simplified models not only brought computational tractability and accessible predictions but also provided valuable ways of “thinking about the problem,” powerful mental shortcuts that enable us to make mental predictions of what will happen, predictions that are not directly available from the basic physics. They also aid understanding to some extent, but not always in terms of direct physical cause and effect.

So the simplified theoretical models ease computation and provide some degree of insight, but they also have a downside: They involve varying levels of mathematical abstraction. The problem with mathematical abstraction is that, although it can greatly simplify complicated phenomena and make some global relationships clearer, it can also obscure some of the underlying physics. For example, basic physical cause-and-effect relationships are often not clear at all from the abstracted models, and some outright misinterpretations of the mathematics have become widespread, as we'll see. Thus some diligence is required on our part to avoid misinterpretations and to keep the real physics clearly in view, while taking advantage of the insights and shortcuts that the simplified models provide.

We've looked at the roles of formal theories (components 1 and 3) and flow phenomenology (component 2), and it is clear that the combination, so far, falls short of providing us with a completely satisfying physical understanding. Physical cause-and-effect at the local level is clear from the basic physics, but at the flowfield level it is not. Thus to be sure we really understand the physics at all levels, we should also seek qualitative physical explanations that make the cause-and-effect relationships clear at the flowfield level. This is component 4 of my proposed framework.

Qualitative physical explanations, however, pose some surprisingly difficult problems of their own. We've already alluded to one of the main reasons such explanations might be difficult, and that is the wide gulf in complexity between the relatively simple physical balances that the raw physical laws enforce at the local level and the richness of possible flow patterns at the global level. Another is that the basic equations define implicit relationships between flow variables, not one-way cause-and-effect relationships. Because of these difficulties, misconceptions have often arisen, and many of the physical explanations that have been put forward over the years have flaws ranging from subtle to fatal. Explanations aimed at the layman are especially prone to this, but professionals in the field have also been responsible for errors. Given this history, we must all learn to be on the lookout for errors in our physical explanations. If this book helps you to become more vigilant, I'll consider it a success.

This completes our brief tour of the conceptual framework, with emphasis on the major difficulties inherent in the subject matter. My intention in this book is to devote more attention to addressing these difficulties than do the usual aerodynamics texts. Let's look briefly at some of the ways I have tried to do this.

The theoretical parts of our framework (components 1 and 3) ultimately rely on mathematical formulations of one sort or another, which leads to something that, in my own experience at least, has been a pedagogical problem. It is common in treatments of aerodynamic theory for much of the attention to be given to mathematical derivations, as was the case in much of the coursework I was exposed to in school. While it is not a bad thing to master the mathematical formulation, there is a tendency for the meaning of things to get lost in the details. To avoid this pitfall, I have tried to encourage the reader to stand back from the mathematical details and understand “what it all means” in relation to the basic physics. As I see it, this starts with paying attention to the following:

1. Where a particular bit of theory fits in the overall body of physical theory, that is, what physical laws and/or ad hoc flow model it depends on; and

2. How it was derived from the physical laws, that is, the simplifying assumptions that were made;

3. The resulting limitations on the range of applicability and the physical fidelity of the results; and

4. The implications of the results, that is, what the results tell us about the behavior of aerodynamic flows in more general terms.

The brief tour of the physical underpinnings of fluid mechanics in Chapters 2 and 3 is an attempt to set the stage for this kind of thinking.

How computational fluid dynamics (CFD) fits into this picture is an interesting issue. CFD merely provides tools for solving the equations of fluid motion; it does not change the conceptual landscape in any fundamental way. Still, it is so powerful that it has become indispensable to the practice of aeronautical engineering. As important and ubiquitous as CFD has become, however, it is not on a par with the older simplified theories in one significant respect: CFD is not really a conceptual model at the same level; and a CFD solution is rightly viewed as just a simulation of a particular real flow, at some level of fidelity that depends on the equations used and the numerical details. As such, a CFD solution has some of the same limits to its usefulness as does an example of the real flow: In both cases, you can examine the flowfield and see what happened, and, of course, a detailed examination of a flowfield is much easier to carry out in CFD than in the real world. But in both CFD and real-world flowfields, it is difficult to tell much about why something happened or what there is about it that might be applicable to other situations.

Before we proceed further, a bit of perspective is in order: While correct understanding is vitally important, we mustn't overestimate what we can accomplish by applying it. As we'll see, the physical phenomena we deal with in aerodynamics are surprisingly complicated and difficult to pin down as precisely as we would like, and it is wise to approach our task with some humility. We should expect that we will not be able to predict or even measure many things to a level of accuracy that would give us complete confidence. The best we'll be able to do in most cases is to try to minimize our unease by applying the best understanding and the best methods we can bring to bear on the problem. And we can take some comfort in the fact that the aeronautical community, historically speaking, has been able to design and build some very successful aeronautical machinery in spite of the limitations on our ability to quantify everything to our satisfaction.

Chapter 2

From Elementary Particles to Aerodynamic Flows

Step back for a moment to consider the really big picture and ponder how aerodynamics fits into the whole body of modern physical theory. The tour I'm about to take you on will be superficial, but I hope it will help to put some of the later discussions in perspective.

First, consider some of the qualitative features of the phenomena we commonly deal with in aerodynamics. Even in flows around the simplest body shapes, there is a richness of possible global flow patterns that can be daunting to anyone trying to understand them, and most flows have local features that are staggeringly complex. There are complicated patterns in how the flow attaches itself to the surface of the body and separates from it (a, b), and these patterns can be different depending on whether you look at the actual time-dependent flow or the “mean” flow with the time variations averaged out. Even in flows that are otherwise steady, the shear layers that form next to the surface and in the wake are often unsteady (turbulent). This shear-layer turbulence contains flow structures that occur randomly in space and time but also display a surprising degree of organization over a wide range of length and time scales. Examples include vortex streets in wakes and the various instability “waves,” “spots,” “eddies,” “bursts,” and “streaks” in boundary layers. Examples are shown in c–f, and many others can be found in Van Dyke (1982). Such features usually display extreme sensitivity to initial conditions and boundary conditions, so that their apparent randomness is real, for all practical purposes. The “butterfly effect” we've all read about doesn't just apply to the weather; the details of a small eddy in the turbulent boundary layer on the wing of a 747 are just as unpredictable.