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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Aerospace Series (PEP)
- Sprache: Englisch
Optimal aircraft design is impossible without a parametric representation of the geometry of the airframe. We need a mathematical model equipped with a set of controls, or design variables, which generates different candidate airframe shapes in response to changes in the values of these variables. This model's objectives are to be flexible and concise, and capable of yielding a wide range of shapes with a minimum number of design variables. Moreover, the process of converting these variables into aircraft geometries must be robust. Alas, flexibility, conciseness and robustness can seldom be achieved simultaneously. Aircraft Aerodynamic Design: Geometry and Optimization addresses this problem by navigating the subtle trade-offs between the competing objectives of geometry parameterization. It beginswith the fundamentals of geometry-centred aircraft design, followed by a review of the building blocks of computational geometries, the curve and surface formulations at the heart of aircraft geometry. The authors then cover a range of legacy formulations in the build-up towards a discussion of the most flexible shape models used in aerodynamic design (with a focus on lift generating surfaces). The book takes a practical approach and includes MATLAB®, Python and Rhinoceros® code, as well as 'real-life' example case studies. Key features: * Covers effective geometry parameterization within the context of design optimization * Demonstrates how geometry parameterization is an important element of modern aircraft design * Includes code and case studies which enable the reader to apply each theoretical concept either as an aid to understanding or as a building block of their own geometry model * Accompanied by a website hosting codes Aircraft Aerodynamic Design: Geometry and Optimization is a practical guide for researchers and practitioners in the aerospace industry, and a reference for graduate and undergraduate students in aircraft design and multidisciplinary design optimization.
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Veröffentlichungsjahr: 2014
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AIRCRAFT AERODYNAMIC DESIGN
GEOMETRY AND OPTIMIZATION
András Sóbester and Alexander I J Forrester
Faculty of Engineering and the Environment, University of Southampton, UK
This edition first published 2015 © 2015 John Wiley & Sons, Ltd
Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
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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.
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Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book's use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.
Library of Congress Cataloging-in-Publication Data
Sóbester, András. Aircraft aerodynamic design: geometry and optimization/András Sóbester, Alexander Forrester. pages cm – (Aerospace series) Includes bibliographical references and index. ISBN 978-0-470-66257-1 (hardback) 1. Airframes. 2. Aerodynamics. I. Forrester, Alexander I J. II. Title. TL671.6.S58 2014 629.134′1–dc23
2014026821
A catalogue record for this book is available from the British Library.
ISBN: 9780470662571
CONTENTS
Series Preface
Preface
Chapter 1: Prologue
Note
Chapter 2: Geometry Parameterization: Philosophy and Practice
2.1 A Sense of Scale
2.2 Parametric Geometries
2.3 What Makes a Good Parametric Geometry: Three Criteria
2.4 A Parametric Fuselage: A Case Study in the Trade-Offs of Geometry Optimization
2.5 A General Observation on the Nature of Fixed-Wing Aircraft Geometry Modelling
2.6 Necessary Flexibility
2.7 The Place of a Parametric Geometry in the Design Process
Notes
Chapter 3: Curves
3.1 Conics and Bézier Curves
3.2 Bézier Splines
3.3 Ferguson’s Spline
3.4 B-Splines
3.5 Knots
3.6 Nonuniform Rational Basis Splines
3.7 Implementation in Rhino
3.8 Curves for Optimization
Notes
Chapter 4: Surfaces
4.1 Lofted, Translated and Coons Surfaces
4.2 Bézier Surfaces
4.3 B-Spline and Nonuniform Rational Basis Spline Surfaces
4.4 Free-Form Deformation
4.5 Implementation in Rhino
4.6 Surfaces for Optimization
Notes
Chapter 5: Aerofoil Engineering: Fundamentals
5.1 Definitions, Conventions, Taxonomy, Description
5.2 A ‘Non-Taxonomy’ of Aerofoils
5.3 Legacy versus Custom-Designed Aerofoils
5.4 Using Legacy Aerofoil Definitions
5.5 Handling Legacy Aerofoils: A Practical Primer
5.6 Aerofoil Families versus Parametric Aerofoils
Notes
Chapter 6: Families of Legacy Aerofoils
6.1 The NACA Four-Digit Section
6.2 The NACA Five-Digit Section
6.3 The NACA SC Families
Notes
Chapter 7: Aerofoil Parameterization
7.1 Complex Transforms
7.2 Can a Pair of Ferguson Splines Represent an Aerofoil?
7.3 Kulfan’s Class- and Shape-Function Transformation
7.4 Other Formulations: Past, Present and Future
Notes
Chapter 8: Planform Parameterization
8.1 The Aspect Ratio
8.2 The Taper Ratio
8.3 Sweep
8.4 Wing Area
8.5 Planform Definition
Notes
Chapter 9: Three-Dimensional Wing Synthesis
9.1 Fundamental Variables
9.2 Coordinate Systems
9.3 The Synthesis of a Nondimensional Wing
9.4 Wing Geometry Scaling. A Case Study: Design of a Commuter Airliner Wing
9.5 Indirect Wing Geometry Scaling
Notes
Chapter 10: Design Sensitivities
10.1 Analytical and Finite-Difference Sensitivities
10.2 Algorithmic Differentiation
10.3 Example: Differentiating an Aerofoil from Control Points to Lift Coefficient
10.4 Example Inverse Design
Notes
Chapter 11: Basic Aerofoil Analysis: A Worked Example
11.1 Creating the
.dat
and
.in
files using Python
11.2 Running XFOIL from Python
Chapter 12: Human-Powered Aircraft Wing Design: A Case Study in Aerodynamic Shape Optimization
12.1 Constraints
12.2 Planform Design
12.3 Aerofoil Section Design
12.4 Optimization
12.5 Improving the Design
Notes
Chapter 13: Epilogue: Challenging Topological Prejudice
References
Index
End User License Agreement
List of Tables
Chapter 7
Table 7.1
Table 7.2
Chapter 8
Table 8.1
Table 8.2
Table 8.3
Chapter 9
Table 9.1
Table 9.2
Chapter 10
Table 10.1
Table 10.2
Chapter 12
Table 12.1
Table 12.2
Table 12.3
Guide
Cover
Table of Contents
Preface
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Series Preface
The field of aerospace is multi-disciplinary and wide ranging, 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, topical and relevant series of books aimed at people working in the aerospace industry, including engineering professionals and operators, allied professions such commercial and legal executives, 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.
Aerodynamics is the fundamental science that underpins the world-wide aerospace industry and enables much of the design and development of today's highly efficient aircraft. Much effort is devoted to the design of new aircraft in order to determine the wing and tail surface geometry that gives the optimum aerodynamic performance.
This book, Aircraft Aerodynamic Design: Geometry and Optimization, covers a range of different aspects of geometry parameterization that is relevant for aircraft lifting surface design. The emphasis is on the efficient construction of an aircraft geometry which can then be coupled to any flow solver and optimization package; however, most of the concepts can be applied to any engineering product. Starting with the underlying principles of geometric parameterization, the reader is taken through the fundamentals of 2D aerofoil optimization onto 3D wing synthesis and the computation of design sensitivities.The most important concepts are illustrated using a basic aerofoil analysis and a human powered wing design. All of the key ideas throughout the book are demonstrated using computer codes, making it easy for the readers to develop their own applications. The book provides a welcome addition to the Wiley Aerospace Series and complements other books on aerodynamic modelling and conceptual aircraft design.
Peter Belobaba, Jonathan Cooper and Allan Seabridge
Preface
In July 1978 the Journal of Aircraft published a paper titled ‘Wing design by numerical optimization’. The authors, Raymond Hicks of the NASA Ames Research Center and Preston Henne of the Douglas Aircraft Company, had identified a set of functions with ‘aerofoil-like’ shapes, which, when added to a baseline aerofoil in various linear combinations, generated other ‘sensible’ aerofoil shapes.
This, as a principle, was not new. After all, the National Advisory Committee for Aeronautics was already experimenting with parametric aerofoils in the 1930s. The formulation described by Hicks and Henne (1978) was a new aerofoil family generated in a novel way – building an aerofoil out of weighted shapes, much like one might build a musical sound from multiple harmonics. But this was not the real novelty; how they proceeded to use it was.
Combining the incipient technology of numerical flow simulation (they used a two-dimensional model) with a simple optimization heuristic and their new parametric geometry they performed an automated computational search for a better aerofoil shape.
Here is the idea that thus began to take shape and commence its ascent along the technology readiness level (TRL) ladder of the aerospace industry. A parametric geometry is placed at the heart of the aircraft design process. The design variables influencing its shape are adjusted in some systematic, iterative way, as dictated by an optimization algorithm. The latter is guided by a design performance metric, resulting from a physics-based simulation run on an instance of the parametric geometry.
The TRL rise was to be a slow one, for two reasons. First, because in a world largely reliant on drawing boards for years to come, this was a disruptive idea that would encounter much resistance in this notoriously risk-averse industry. Second, none of the links in the chain of tools required (numerical flow analysis, computational geometry and efficient optimization techniques) would be really ready for some fast optimization action until well into the 1990s.
There is a maxim known by most practitioners of the art, which states that an optimization algorithm will find the slightest flaws in the analysis code (usually comprising a mesher and a partial differential equation solver) and in the geometry model; that is, it will steer the design process precisely towards their weak areas.
This is not (only) due to Sod’s law – more fundamental effects are at play. Most computational analyses have a domain of ‘safe’ operation, outside of which they will either predict unphysically good or unphysically bad performance. Straying into the latter type of area will thus be a self-limiting deviation, but the former will lure the optimizer into ‘discovering’ amazingly good solutions that do not actually exist in ‘real’ physics. Sometimes these are obvious (what rookie optimization practitioner has not ‘discovered’ aerofoils that generate thrust instead of drag?), but more subtle pitfalls abound, and highlighting these remains a challenge in the path of the ubiquitous use of this technology.
Along similar lines, parametric geometry modelling has its own pitfalls, deceptions and hurdles in the path of effective optimal design, and how to avoid (at least some of) them is the subject of this book.
Some of the principles discussed over the pages that follow can be applied to the geometry of any engineering product, but we focus on those aspects of geometry parameterization that are specific to external aircraft surfaces wetted by airflow. Some of the ideas are therefore linked to aerodynamics, and so we will touch upon the relevant aspects of aircraft aerodynamic design – from an engineering perspective. However, this is not a book on aircraft aerodynamics, and, for that matter, nor will it provide the reader with a recipe on how to design an aeroplane. Instead, it is an exposition of concepts necessary for the construction of aircraft geometry that can exploit the capabilities of an optimization algorithm.
The reader may wish to peruse the text simply to gain a theoretical appreciation of some of the issues of aircraft geometry parameterization, but there is plenty to get started with for the more practically minded too. All key concepts are illustrated with code, which can be run ‘as is’ or can form a building block in the reader’s own code. After lengthy deliberations we selected two software platforms to use for this: Mathworks MATLAB® and Python. Some of the Python code calls methods from the OpenNURBS framework, which can be accessed through Robert McNeel & Associates Rhino, a powerful, yet easy to use, lightweight CAD package. Some of the code is reproduced in the text to help illustrate some of the formulations – in each case we selected one of the platforms mentioned above, but in most cases implementations in the others are available too on the website [www.wiley.com/go/sobester] accompanying the book.
Here is a brief sketch of the structure of this book.
After discussion of the general context of aircraft shape description and parameterization (Prologue), in the following chapter (Geometry Parameterization: Philosophy and Practice) we discuss the place of parametric geometries in aircraft design in general and we start the main threads that will be running through this book: the guiding principles of parametric geometry construction and their impact on the effectiveness of the optimization processes we might build upon them.
We next tackle the fundamental building blocks of all aircraft geometries, first in two dimensions (the chapter titled Curves), then in three (Surfaces). Two-dimensional sections through wings (and other lifting surfaces) are perhaps the most widely known and widely discussed aerodynamic geometry primitive, and we dedicate three chapters to them: a general introduction (Aerofoil Engineering: Fundamentals), a review of some of the key Families of Legacy Aerofoils and, arriving at the concept at the heart of this book, Aerofoil Parameterization.
Another classic two-dimensional view of aerodynamics is tackled in the chapter titled Planform Parameterization, thus completing the discussion of all the primitives needed to build a three-dimensional wing geometry – which we do in the chapter Three-Dimensional Wing Synthesis.
The ultimate point of geometry parameterization is, of course, the optimization of objective functions that measure the performance of the object represented by the geometry. Recent years have seen a strong push towards making this process as efficient as possible, and one of the enablers is the efficient computation of the sensitivities of the objective function with respect to the design variables controlling the shape. A number of ways of achieving this are discussed in the chapter titled Design Sensitivities.
The most important concepts are illustrated via examples throughout the book, but there are two more substantial such examples, which warrant chapters of their own: Basic Aerofoil Analysis: A Worked Example and Human-Powered Aircraft Wing Design: A Case Study in Aerodynamic Shape Optimization.
We then bring matters to a close by looking ahead and discussing the area where geometry parameterization is most acutely in need of further development – this is the chapter titled Epilogue: Challenging Topological Prejudice.
Parametric geometry is a vast subject, and a book dedicated even to one of its subsets – in this case, the parametric geometry of the external shape of fixed-wing aircraft – is unlikely to be comprehensive. We hope that, beyond a discussion of the formulations we felt to be the most important, this book succeeds in setting out the key principles that will enable the reader to ‘discover’, critically evaluate and deploy other formulations not discussed here. Moreover, it should assist in creating new models – essential building blocks of the design tools of the future.
Finally, we would like to acknowledge some of those who helped shape this text through discussions and reviews: Jennifer Forrester, Brenda Kulfan, Andy Keane, Christopher Paulson, James Scanlan, Nigel Taylor, David Toal and Sebastian Walter. We are also indebted to Tom Carter and Eric Willner at Wiley, whose patience and support made the long years of writing this book considerably easier.
Disclaimer: The design methods and examples given in this book and associated software are intended for guidance only and have not been developed to meet any specific design requirements. It remains the responsibility of the designer to independently validate designs arrived at as a result of using this book and associated software. To the fullest extent permitted by applicable law John Wiley & Sons, Ltd. and the authors (i) provide the information in this book and associated software without express or implied warranties that the information is accurate, error free or reliable; (ii) make no and expressly disclaim all warranties as to merchantability, satisfactory quality or fitness for any particular purpose; and accept no responsibility or liability for any loss or damage occasioned to any person or property including loss of income; loss of business profits or contracts; business interruption; loss of the use of money or anticipated savings; loss of information; loss of opportunity, goodwill or reputation; loss of, damage to or corruption of data; or any indirect or consequential loss or damage of any kind howsoever arising, through using the material, instructions, methods or ideas contained herein or acting or refraining from acting as a result of such use.
András Sóbester and Alexander I J Forrester Southampton, UK, 2014
1Prologue
Geometry is the lingua franca of engineering. Any conversation around a nontrivial design problem usually has even the most articulate engineer overcome, within minutes, by the desire to draw, sketch or doodle. Over the centuries the sketching tools have changed. However, Leonardo da Vinci wielded his chalk and pen for the same reason why today’s engineers slide their fingertips along tablet computer screens, deftly creating three-dimensional geometrical models and navigating around them: the functionality and performance of an engineering product depends, to a very large extent, on its shape and size; that is, on its geometry.
