Introductory Aerodynamics and Hydrodynamics of Wings and Bodies: A Software-Based Approach

259 Pages·1997·11.83 MB·English

by  Frederick O. Smetana

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Introductory Aerodynamics and
Hydrodynamics of Wings and Bodies:
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62 A Software-Based Approach
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g | Frederick O. Smetana
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a. Raleigh, North Carolina
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nl EDUCATION SERIES
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Do J. S. Przemieniecki
Series Editor-in-Chief
Air Force Institute of Technology
Wright-Patterson Air Force Base, Ohio
Published by
American Insitute of Aeronautics and Astronautics, Inc.
1801 Alexander Bell Drive, Reston, VA 20191
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n- American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
nsi
o
c Library of Congress Cataloging-in-Publication Data
Wis
of Smetana, Frederick O., 1928-
v
ni Introductory aerodynamics and hydrodynamics of wings and bodies :
U
y a software-based approach / Frederick O. Smetana.
d b p. cm. - (AIAA education series)
de Includes bibliographical references and index.
a
nlo ISBN 1-56347-242-2 (alk. paper)
w 1. Aerodynamics-Data processing. 2. Hydrodynamics-Data
o
D processing. I. Title. II. Series.
TL573.S5723 1997
629.132/3—dc21 97-11859
CIP
Copyright (c) 1997 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Printed in the United States. No part of this publication may be reproduced, distributed, or transmitted,
in any form or by any means, or stored in a database or retrieval system, without the prior written
permission of the publisher.
Data and information appearing in this book are for informational purposes only. AIAA is not re-
sponsible for any injury or damage resulting from use or reliance, nor does AIAA warrant that use or
reliance will be free from privately owned rights.
3
1 Leb wohl, du kiihnes, herrliches kind!
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4/4. —Wotan's farewell to his daughter
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25 Brtinnhilde from Act III of
10. Die Walkiire by Richard Wagner
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Table of
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xiii
3
11 Acknowledgment........................................ xvii
2
6
8
4.
4/ Chapter 1. The Atmosphere and the Ocean . . . . . . . . . . . . . . . . . . . .. 1
1
25 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1
0.
OI: 1 1.2 Relation of Pressure and Altitude . . . . . . . . . . . . . . . . . . . . . . . .. 1
D 1.2.1 In the Ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2
org | 1.2.2 In the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2
aa. 1.3 Density-Altitude Relationship . . . . . . . . . . . . . . . . . . . . . . . . . .. 4
ai
arc. 1.4 Density-Temperature Relationship in Water . . . . . . . . . . . . . . . . .. 4
p:// 1.5 Definition of Altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5
htt
2 | 1.6 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5
1
0 1.6.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6
2
30, 1.6.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7
ber Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8
m
e
pt
Se Chapter 2. Elementary Flow Functions . . . . . . . . . . . . . . . . . . . . . .. 11
n
n o 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
o
dis 2.2 Potential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
a
M 2.3 Conditions for Irrotationality . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
n-
nsi 2.4 Laplace's Partial Differential Equation and the Stream Function ... 15
o
Wisc 2.5 Euler's Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
of 2.6 Bernoulli's Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
niv 2.7 Elementary Solutions of Laplace's Equation . . . . . . . . . . . . . . . .. 20
U
y 2.7.1 Uniform Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20
b
d 2.7.2 Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20
e
d
oa 2.7.3 S i n k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20
nl
w 2.7.4 Vortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22
o
D
2.8 Superposition of Elementary Flow Functions . . . . . . . . . . . . . . .. 22
2.8.1 Source in a Uniform Stream . . . . . . . . . . . . . . . . . . . . .. 22
2.8.2 Separated Source and Sink . . . . . . . . . . . . . . . . . . . . . .. 22
2.8.3 Separated Source and Sink in a Uniform Stream:
Rankine Oval . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
2.8.4 Coincident Source and Sink: Doublet ................ 23
2.8.5 Doublet in a Uniform Stream . . . . . . . . . . . . . . . . . . . . .. 23
2.8.6 Sink and Vortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
2.8.7 Vortex and Uniform Flow . . . . . . . . . . . . . . . . . . . . . . .. 26
VII
2.8.8 Counter-Rotating Vortices . . . . . . . . . . . . . . . . . . . . . . .. 28
2.8.9 Circular Cylinder with Circulation in a Uniform Stream ... 28
2.9 Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30
2.9.1 Magnus Effect................................ 31
2.10 Relationship of Stream Function and Potential Function . . . . . . . .. 32
2.11 Stream Function Generation Software . . . . . . . . . . . . . . . . . . . .. 33
2.12 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35
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8 Chapter 3. Airfoils and the Joukowski Transform . . . . . . . . . . . . . .. 43
4.
14/ 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43
5
0.2 3.2 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 44
1
OI: 3.3 Conformal Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46
D
g | 3.4 Mapping the Doublet with Circulation in a Uniform Stream
or to an Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47
a.
aia 3.5 Program JOUKOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51
c.
ar 3.5.1 Program Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
http:// 3.5.2 Program Data Entry . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
2 | 3.5.3 Typical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
1
20 3.6 Closure.......................................... 53
0,
er 3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 54
b
m
e
pt Chapter 4. Drag, Viscosity, and the Boundary Layer . . . . . . . . . . . .. 61
e
S
n 4.1 Inroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
o
on 4.2 Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
adis 4.3 The Boundary-Layer Equations . . . . . . . . . . . . . . . . . . . . . . . .. 63
M
n- 4.4 Boundary Layer and Displacement Thickness . . . . . . . . . . . . . . .. 67
nsi
o 4.5 The Momentum Integral Method . . . . . . . . . . . . . . . . . . . . . . .. 72
c
Wis 4.5.1 Application to Turbulent Boundary Layers . . . . . . . . . . .. 76
v of 4.5.2 Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78
Uni 4.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79
y
d b 4.6.1 Steady Internal Axisymmetric Flow with Viscous
e
ad Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . .. 79
o
wnl 4.6.2 Some Classical Boundary-Layer Solutions . . . . . . . . . . . .. 82
o
D 4.7 Closure.......................................... 86
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86
Chapter 5. Direct Computation of Airfoil Characteristics . . . . . . . . .. 91
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91
5.2 Program Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92
5.2.1 Treatment of Viscous Effects Within the
Inviscid Formulation . . . . . . . . . . . . . . . . . . . . . . . .. 95
5.2.2 Algorithm Limitations . . . . . . . . . . . . . . . . . . . . . . . . .. 96
5.2.3 Tuning Applied to the Program . . . . . . . . . . . . . . . . . . .. 96
VIII
5.3 Program AIRFOIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98
5.3.1 Features of the AIRFOIL Program . . . . . . . . . . . . . . . . .. 98
5.3.2 Program Data Entry . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
5.3.3 Typical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
5.3.4 Significance of Results . . . . . . . . . . . . . . . . . . . . . . . .. 103
5.4 Airfoil Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 115
5.4.1 Long-Range Vehicle........................... 115
5.4.2 High-Level Flight Speed . . . . . . . . . . . . . . . . . . . . . . .. 117
3
211 5.4.3 HighCLm:tt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 118
6
8 5.4.4 Supercavitating Hydrofoils . . . . . . . . . . . . . . . . . . . . .. 118
4.
14/ 5.4.5 Sailplanes.................................. 119
5
0.2 5.4.6 Maneuverable, Medium-Speed Vehicle . . . . . . . . . . . . .. 120
1
OI: 5.4.7 Piston Powered Transport Aircraft . . . . . . . . . . . . . . . .. 120
g | D 5.4.8 General Aviation Vehicle . . . . . . . . . . . . . . . . . . . . . .. 120
or 5.5 Other Approaches to Airfoil Design . . . . . . . . . . . . . . . . . . . .. 120
a.
aia 5.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 121
c.
ar Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 121
p://
2 | htt Chapter 6. The Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 131
01 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 131
2
0, 6.2 Induced Angle of Attack due to a Finite Wingspan and its
3
ber Consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 132
m
pte 6.2.1 Calculation of Induced Angle of Attack. . . . . . . . . . . . .. 133
e
S 6.2.2 Effect of Aspect Ratio and Planform Shape . . . . . . . . . .. 137
n
o
n 6.3 Wing-Fuselage Interaction . . . . . . . . . . . . . . . . . . . . . . . . . .. 142
o
dis 6.4 Characteristics of the Three-Dimensional Wing . . . . . . . . . . . .. 145
a
M
n- 6.5 Curve Fitting Aerodynamic Characteristics: POLYFIT......... 148
nsi 6.5.1 Data Entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 149
o
c
Wis 6.5.2 Typical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 149
of 6.6 Converting Two-Dimensional Data to Three-Dimensional:
v
ni Program F2D3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 152
U
y 6.6.1 Program Data Entry . . . . . . . . . . . . . . . . . . . . . . . . . .. 154
b
d
e 6.6.2 Typical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 157
d
a
nlo 6.7 Other Methods of Analyzing Complete Wings . . . . . . . . . . . . .. 157
w
o 6.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 158
D
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 159
Chapter 7. Characteristics of Bodies at Small Angles of Attack ..... 163
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 163
7.2 Theory Behind Program BODY . . . . . . . . . . . . . . . . . . . . . . .. 166
7.2.1 Basic Hess-Smith Model . . . . . . . . . . . . . . . . . . . . . .. 166
7.2.2 Streamline Determination . . . . . . . . . . . . . . . . . . . . . .. 168
7.2.3 Addition of a Wake Body . . . . . . . . . . . . . . . . . . . . . .. 169
7.3 General Program Description . . . . . . . . . . . . . . . . . . . . . . . . .. 173
IX