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, 4th Edition Theory of Lift: Introductory Computational Aerodynamics with MATLAB and Octave Sense and Avoid in UAS: Research and Applications Morphing Aerospace Vehicles and Structures Gas Turbine Propulsion Systems Basic Helicopter Aerodynamics, 3rd Edition Advanced Control of Aircraft, Spacecraft and Rockets Cooperative Path Planning of Unmanned Aerial Vehicles Principles of Flight for Pilots Air Travel and Health: A Systems Perspective Design and Analysis of Composite Structures: With applications to aerospace Structures Unmanned Aircraft Systems: UAVS Design, Development and Deployment Introduction to Antenna Placement & Installations Principles of Flight Simulation Fahlstrom and Gleason McBain August 2012 August 2012 April 2012 April 2012 July 2011 Angelov Valasek MacIsaac and Langton Seddon and New- July 2011 man Tewari July 2011 Tsourdos et al November 2010 Swatton October 2010 Seabridge et al September 2010 Kassapoglou September 2010 Austin Macnamara Allerton April 2010 April 2010 October 2009 May 2009 April 2009 April 2009 Aircraft Fuel Systems The Global Airline Industry Computational Modelling and Simulation of Aircraft and the Environment: Volume - Platform Kinematics and Synthetic Environment Handbook of Space Technology Langton et al Belobaba Diston Aircraft Performance Theory and Practice for Pilots August 2008 Forrester, Sobe- August ster, Keane 2008 Moir & SeabridgeMarch 2008 Wright & Cooper December 2007 Langton September 2006 Moir & SeabridgeFebruary 2006 Moir & SeabridgeJune 2004 Howe May 2004 Jukes December 2003 Surrogate Modelling in Engineering Design: A Practical Guide Aircraft Systems, 3rd Edition Introduction to Aircraft Aeroelasticity And Loads Stability and Control of Aircraft Systems Military Avionics Systems Design and Development of Aircraft Systems Aircraft Loading and Structural Layout Aircraft Display Systems Ley, Wittmann Hallmann Swatton April 2009 Civil Avionics Systems Moir & SeabridgeDecember 2002 This edition first published 2013 © 2013 Boeing All rights reserved Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books Designations used by companies to distinguish their products are often claimed as trademarks All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners The publisher is not associated with any product or vendor mentioned in this book This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold on the understanding that the publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional should be sought 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) 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 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 Tracy Chief Technology Officer The Boeing Company September 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 Defect, velocity: boundary layer wake Deformation of a fluid element Density Detached shock Detached-eddy simulation (DES) Diffuser Dimensionless parameters Direct numerical simulation (DNS) Discontinuity: in body slope or curvature shock (idealized) vortex sheet (idealized) Discretization Displacement effect Displacement thickness Dissipation, turbulent Dissipation, viscous Disturbance amplitude Disturbance frequency Disturbance, small Divergence, flow Drag crisis of a sphere polar prediction reduction, laminar flow reduction, turbulent rise, transonic Drag categories: base excrescence induced interference inviscid “interference" parasite pressure profile shock skin friction slot surface roughness viscous Dumping velocity, trailing edge Dynamic pressure Dynamic similarity Eddy viscosity Eigenvalues (laminar stability theory) Elementary particles Elevator Elliptic equations Elliptic spanload Emmons spot Empirical drag correlations Endplate Energy: conservation of internal Engine inlet Enstrophy Enthalpy, total Equation of state Equations of motion Equilibrium turbulent boundary layer Equivalent sand-grain roughness Euler equations Eulerian formulation Excrescence drag magnification factor Exhaust nozzle Explicit finite difference method Fallacy: 2D biplane lift reduction as loss of “efficiency" base drag and Hoerner's jet pump boundary-layer displacement surface as effective wall constant pressure in boundary layer dependence of induced drag on aspect ratio expectation of high accuracy from turbulence modeling explanations of 2D airfoil lift induction integrated downward momentum in Trefftz plane inviscid “interference" drag laminar sublayer one-way causation pressure drag or thrust on a portion of a body reducing pressure drag surface streamlines as indicators of flow direction tinkering with vorticity zero Cf as universal signature of separation Farfield boundary conditions Favorable pressure gradient: effect on transition effect on velocity profile First law of thermodynamics Flap Krueger slotted Flat-plate boundary layer Flow tangency boundary condition Flow visualization: by streaklines by timelines Fluctuating part Fluid, definition of Form factor, profile-drag Free-stream boundary condition Frequency, disturbance Friction velocity Fuel mass Full-potential equations Fully developed duct flow Fully rough wall Fuselage carry-through lift Galilean invariance Genus of a region Goldschmied body Goldstein loading for propeller Goldstein singularity Görtler vortices Green's theorem Grid: CFD convergence resolution Ground effect: on induced drag on lift in 2D on lift in 3D Heat: conduction convective transfer viscous dissipation into Hele-Shaw flow Helmholtz vortex theorems: 1st 2nd 3rd and 4th Hiemenz flow Horseshoe vortex Hybrid laminar-flow control Hydraulically smooth wall Hydrostatic pressure Hyperbolic differential equation Ideal (perfect) gas Implicit finite difference method Incompressible flow Incompressible potential flow Independence principle, swept-wing boundary layer Index of a region Induced drag biplane effect of fuselage effect of tail or canard in ground effect minimum (ideal) polar reduction scaling theory of Spreiter and Sacks theory, momentum balance theory, Trefftz-plane Induced efficiency, propeller Induction: Biot-Savart law fallacy Inlet vortex Inlet, engine Inner layer, turbulent Integral momentum equation Interference drag Intermittency (turbulence) Internal energy Inverse design Inverse mode, boundary layer Inviscid flow: Euler equations full-potential equations incompressible potential flow linearized for small perturbations Irrotationality Isentropic-flow relations Isobar Isotropic eddy viscosity Iterative convergence Jet propulsion Junction (necklace) vortex Kelvin's circulation theorem Kinematic description Kinematics of vorticity Kinetic energy of turbulence Kinetic theory of gasses Krueger flap Kutta condition Kutta-Joukowski theorem Lagrangian formulation Laminar boundary layer Laminar flat-plate boundary layer Laminar flow, natural (NLF) Laminar skin friction Laminar sublayer Laminar-boundary-layer similarity Laminar-flow airfoil Laminar-flow control (LFC) Laminar-flow stability theory Laminar-to-turbulent transition Laplace's equation Large-eddy simulation (LES) Law of the wake Law of the wall Lift Bernoulli fuselage carry-through in ground effectD in ground effectD manifestations in atmosphere maximum: limited by 3D effects limited by viscous effects, multi-element limited by viscous effects, single-element physical explanations reaction Lifting-line theory Lifting-surface theory Linearized airfoil theory Linearized boundary condition Linearized for small perturbations Logarithmic law, turbulent effect of roughness Longer path length Lubrication theory Mach number Mach number, critical Magnification factor, excrescence drag Mapping, conformal Marching solution of boundary-layer equations Mass, conservation of Matched asymptotic expansions, method of Maximum lift: limited by 3D effects limited by viscous effects, multi-element limited by viscous effects, single-element Mean flow Mean free path Meme Minimum (ideal) induced drag Mixing length Models, turbulence Molecular motion Moment of momentum Momentum: area coefficient, jet blowing conservation of integral equation, boundary layer thickness, boundary layer Moody chart Natural laminar flow (NLF) Natural transition Navier-Stokes (NS) equations Neutral-stability curves Newton's laws: second law third law Newton's theory of lift Newtonian fluid Newtonian worldview No-slip condition Nodal-point singularity Nonuniqueness of lift curve Normal pressure gradient Normal-force coefficient (Figure 8.3.7) Normal-shock relations Nozzle, exhaust Oblique shock Obstacle effect One-dimensional flow assumption Origin, region of, as definition of separation Orr-Sommerfeld equation Oseen theory Oswald efficiency factor Oswatitsch shock-drag formula Outer layer, turbulent Overlap layer, turbulent Parabolic differential equation Parallel-flow assumption Parasite drag Perfect (ideal) gas Perturbation, singular Perturbation, small Pinching, streamtube Pitching moment Plane-of-symmetry flow Plausible falsehood, von Karman's Plume, propulsion Potential flow equation potential function sink source vortex (Figure 8.1.8a) Power loading coefficient, propeller (Equation 6.1.20) Prandtl boundary-layer theory Prandtl lifting-line theory Prandtl mixing length Prandtl number Prandtl propeller induced-flow factors Pressure coefficient, canonical drag dynamic footprint on ground gradient: effect on transition effect on velocity profile,-7 role in general momentum balance role in separation recovery static total Pressure-driven cross-flow Profile drag Propeller: actuator-disc theory advance ratio blade-element theory efficiency induced efficiency power loading coefficient (Equation 6.1.20) Prandtl induced-flow factors thrust loading torque coefficient torque Propulsion Ackeret boundary-layer plume Protrusion height (riblets) Pseudo-Lagrangian viewpoint Reaction lift Reattachment Receptivity theory Recovery factor Recovery temperature Recovery, pressure Reflection in a solid surface (Figure 4.1.13) Region-of-origin definition of separation Relaminarization Reversal, flow Reynolds averaging Reynolds number Reynolds stresses Reynolds-averaged Navier-Stokes equations (RANS) Riblets Ring wing Rollup, vortex Roughness Reynolds number Roughness, equivalent sand-grain height Roughness, surface Saddle-point singularity Sailboat analogy for winglets Sand-grain roughness Second law of thermodynamics SeparationD Separation, boundary-layer Separation, shock-induced Shape factor, boundary-layer Shear layer: idealized as vortex sheet in inviscid CFD solutions physical (Figure 3.3.8b) Shear stress laminar turbulent Shear-driven cross-flow Shock: bow capturing detached discontinuity (idealized) drag fitting normal oblique Oswatitsch drag formula unsteady Shock/boundary-layer interaction Similarity: dynamic parameter, laminar boundary layer parameter, turbulent boundary layer solutions, boundary-layer Simple fluid Simple sweep theory angle of attack flow directions force coefficient formulas Mach number Sin-series spanloads Singular perturbation problem Singularity: Goldstein nodal point saddle point Sink, potential-flow Skin friction drag effect on momentum balance laminar reduction, turbulent surface lines turbulent use in empirical drag correlations Slat Slip velocity: apparent, in turbulent flow molecular Slope discontinuity Slot drag Slot effect Slotted flap Small disturbance Small perturbation Source, potential-flow Spalart-Allmaras turbulence model Span-efficiency factor Spanload: basic and additional sin-series Spatial field grid convergence resolution Specific heat Speed of sound Sphere drag Spoiler Squire-Young formula Stability theory (laminar-flow) Stability, numerical Stagnation conditions temperature Stall, airfoil Static pressure Stator Steady flow Stokes flow Stokes's theorem Streaklines Stream function Streamline coordinates Streamline curvature Streamline topology Streamline Streamlined body Streamtube: definition pinching Stress tensor Sublayer, “laminar” or viscous Suction, boundary-layer separation control by Suction, laminar flow control (LFC) Supercritical airfoil Surface roughness Surface streamlines Surface tension Sweep theory, simple angle of attack flow directions force coefficient formulas Mach number Swept wing attachment-line boundary layer boundary layer independence principle inboard tailoring infinite-span boundary-layer theory laminar-to-turbulent transition related to a 2D airfoil separation criterion shock/boundary-layer interaction turbulent attachment line turbulent boundary layer vortex generator installation Swirl (in propeller flows) Taper, effect on wing boundary layer Temperature, recovery Temperature, total Thermal boundary condition Thermal boundary layer Thermal conduction Thermodynamic equilibrium Thin-layer Navier-Stokes equations Three-dimensional boundary layers equations displacement thickness on swept and tapered wings separation turbulent prediction velocity profiles Three-dimensional wings Thrust loading, propeller Time-averaging: of molecular motion of turbulent motion Timelines Tip vortices Tollmien-Schlichting waves Topology, streamline Torque coefficient Total enthalpy Total pressure Total temperature Trailing-edge dumping-velocity elevation Transition to turbulence Transonic airfoil Transpiration to represent displacement effect Transport properties Transverse curvature, effect on axisymmetric boundary layer Traveling wave disturbance Trefftz plane integrated downward momentum in integrated pressure in theory Trip, boundary layer Triple-deck theory Turbine blade Turbofan and turbojet Turbulence: coherent structures eddy viscosity intermittency kinetic energy mixing length modeling Reynolds averaging of Turbulent boundary layer inner layer outer layer overlap layer shear stress similarity skin friction viscous sublayer Turbulent dissipation Turbulent shear stress Turning vane Unsteady blowing (separation control) Validation, CFD Van Driest damping factor Velocity defect: boundary layer wake Velocity potential Velocity profile, boundary-layer 3D, in arbitrary coordinate system approaching separation effect of shape on growth in adverse pressure gradient initial shape factor turbulent with similarity Vertical momentum in atmosphere Viscosity Viscous dissipation Viscous drag Viscous sublayer Viscous/inviscid interaction methods Visualization: of CFD solutions of flow, by streaklines of flow, by timelines von Karman constant von Karman momentum integral equation von Karman plausible falsehood von Karman vortex street Vortex: decay and collapse filament generators generators, sub-boundary-layer induction fallacy line rollup shedding wake sheets from wings sheet stretching unsteady wake shedding wake myths wake of a wing wake reconnection Vortices, tip Vorticity Biot-Savart law bound, of a lifting airfoil or wing budget of a boundary layer equation (creation, convection, diffusion, stretching) interaction with a boundary kinematics of relation to circulation (Stokes's theorem) stretching Wake: law of the momentum area reversal viscous vortex Wall jet Wall, law of the Water-faucet demonstration Wave number Wedge flows Wing structural weight Winggrid tip device Winglet Wingtip device Wingtip vortex Zierep singularity ... 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 97 8-1 -1 1 9-9 675 1-4 ... 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. .. violate the no-through-flow condition at the boundary if the filament were not normal to the boundary Further, if the boundary is a stationary solid surface at which the no-slip condition applies, the