NF Krasnov Fundamentals of Theory. Aerodynamics of an Airfoil and a Wing Mir Publishers Moscow

512 Pages·2002·17.38 MB·English

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N. F. Krasnov
Fundamentals of Theory.
Aerodynamics of an
Airfoil and a Wing
Translated from the Russian by
G. Leib
Mir Publishers Moscow
First published 1985
Revised from the 1980 Russian edition
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Preface
Aerodynamics is the theoretical foundation of aeronautical, rocket, space,
and artillery engineering and the cornerstone of the aerodynamic design of
modern craft. The fundamentals of aerodynamics are used in studying the exter
nal flow over various bodies or the motion of air (a gas) inside various objects.
Engineering success in the fields of aviation, artillery, rocketry, space flight,
motor vehicle transport, and so on, i.e. fields that pertain to the flow of air
or a gas in some form or other, depends on a firm knowledge of aerodynamics.
The present textbook, in addition to the general laws of flow of a fluid,
treats the application of aerodynamics, chiefly in rocketry and modern high
,peed aviation. The book consists of two parts, each forming a separate vol ume.
fhe first of them concerns the fundamental concepts and definitions of aero
dynamics and the theory of flow over an airfoil and a wing, including an un
steady flow (Chapters 1-9), while the second describes the aerodynamic design
of craft and their individual parts (Chapters 10-15). The two parts are designed
for use in a two-semester course of aerodynamics, although the first part can be
used independently by those interested in individual problems of theoretical
aerodynamics.
A sound theoretical background is important to the study of any subject
because creative solutions of practical problems, scientific research, and dis
coveries are impossible without it. Students should therefore devote special
attention to the first five chapters, which deal with the fundamental concepts
and definitions of aerodynamics, the kinematics of a fluid, the fundamentals of
fluid dynamics, the theory of shocks, and the method of characteristics used
widely in investigating superO'onic flows. Chapters 6 and 7, which relate to the
now over airfoils, are also important to a fundamental understanding of the
subject. These chapters contain a fairly complete discussion of the general
theory of now of a gas in two-dimensional space (the theory of two-dimensional
flow). The information on the supersonic steady flow over a wing in Chapter 8
relates directly to these materials. The aerodynamic design of most modern craft
is based on studies of such flow.
One of the most topical areas of mOllern aerodynamic research is the study
of optimal aerodynamic confIgurations of craft and their separate (isolated)
parts (the fuselage, wing, empennage). Therefore, a small section (6.5\ that
defmes a flIlite-span wing with the most advantageous planform in an incompres
sible flow has been included here. This section presents important practical
and methodological information on the conversion of the aerodynamic coeffic
ients of a wing from one aspect ratio to another.
The study of non-stationary gas flows is a rather well developed field of
modern theoretical and practical aerodynamics. The results of this study are
widely used in calculating the effect of aerodynamic forces and moments on
6 Preface
craft whose motion is generally characterized by non-uniformity, and the nou
stationary aerodynamic characteristics thus calculated are used in the dynamics
of craft when studying their flight stability. Chapter 9 concerns the general
relations of the aerodynamic coefficients in unsteady flow. Aerodynamic deriv
atives (stability derivatives) are analysed, as is the concept of dynamic stability.
Unsteady flow over a wing is also considered. The most important section of
this chapter is devoted to numerical methods of calculating the stability deriv
atives of a lifting surface of arbitrary planform, generally with a curved leading
edge (i.e. with variable sweep along the span). Both exact and approximate
methods of determining the non-stationary aerodynamic characteristics of a
wing are given.
A special place in the book is devoted to the most important theoretical
and applied problems of high-speed aerodynamics, including the thermodynamic
and kinetic parameters of dissociating gases, the equations of motion and energy,
and the theory of shocks and its relation to the physicochemical properties of
gases at Iitigh temperatures. Considerable attention is givl~n to shock waves
(shocks), which are a manifestation of the specific properties of supersonic flows.
The concept of the thickness of a shock is discussed, and the book includes graphs
of the functions characterizing changes in the parameters of a gas as it passes
through a shock.
Naturally, a tElxtbook cannot reflect the entire diversity of problems facing
the science of aerodynamics. I have tried to provide the scientific information
for specialists in the field of aeronautic and rocket engine€ring. This inform
ation, if mastered in its entirety, should be sufficient for young specialists to
cope independently with other practical aerodynamic problems that may appear.
Among these problems, not reflected in the book, are magnetogasdynamic invest
igations, the application of the method of characteristics to three-dimensional
gas flows, and experimental aerodynamics. I will be happy if study of this text
book leads students to a more comprehensive, independent investigation ot
modern aerodynamics.
The book is the result of my experience teaching courses in aerodynamics
at the N.E. Bauman Higher Engineering College in l\[oscow, USSR. Intended
for college and junior-college students, it will also be a useful aid to specialists
in research institutions, design departments. and industrial enterprises.
All physical quantities are given according to the International System of
Units (SI).
In preparing the third Russian edition of the book, which the present English
edition has been translated from, I took account of readers' remarks and of the
valuable suggestions made by the reviewer, professor A.I\!. Mkhiteryan, to whom
I express my profound gratitude.
Nikolai F. Krasnov
Contents
Preface 5
Introduction 13
Chapter 1 25
Basic Information 1.1. Forces Acting on a Moving Body 25
Surface Force 25
from Aerodynamics
Property of Pressures in an Ideal Fluid 26
Influence of Viscosity on the Flow
of a Fluid 28
1.2. Resultant Force Action 36
Components of Aerodynamic Forces
and Moments 36
Conversion of Aerodynamic Forces
and '\[oments from One Coordinate
System to Another 40
1.3. Determination of Aerodynamic For
ces and Moments According to the
Known Distribution of the Pressure
and Shear Stress. Aerodynamic Coef-
ficients 41
Aerodynamic Forces and Moments and
Their Coefficients 41
1.4. Static Equilibrium and Static Stab-
ility 52
Concept of Equilibrium and Stability 52
Static Longitudinal Stability 53
Static Lateral Stability 57
1.5. Features of Gas Flow at High Speeds 58
Compressibility of a Gas 58
Heating of a Gas 59
State of Air at High Temperatures 65
Chapter 2 2.1. Approaches to the Kinematic Invest
r igation of a Fluid 71
Kinematics of a Fluid Lagrangian Approach 71
Eulerian Approach 72
Streamlines and Pathlines 73
'.2. Analysis of Fluid Particle Motion 74
2.3. Vortex-Free Motion of a Fluid 79
8 Contents
2.4. Continuity Equation 80
General Form of the Equation 80
Cartesian Coordinate System 81
Curvilinear Coordinate System 82
Continuity Equation of Gas Flow
along a Curved Surface 86
Flow Rate Equation 88
2.5. Stream Function 89
2.6. Vortex Lines 90
2.7. Velocity Circulation 91
Concept 91
Stokes Theorem 92
Vortex-Induced Velocities~ 94
2.8. Complex Potential 96
2.9. Kinds of Fluid Flows 97
Parallel Flow 98
Two-Dimensional Point Source and
Sink 98
Three-Dimensional Source and Sink 100
Doublet 100
Circulation Flow (Vortex) 103
Chapter 3 3.1. Equations of Motion of a Viscous
Fluid 106
Fundamentals
Cartesian Coordinates 106
of Fluid Dynamics Vector Form of the Equations of
Motion 113
Curvilinear Coordinates 114
Cylindrical Coordinates 116
Spherical Coordinates 118
Equations of Two-Dimensional Flow
of a Gas Near a Curved Surface 120
3.2. Equations of Energy and Diffusion
of a Gas 121
Diffusion Equation 121
Energy Equation 124
3.3. System of Equations of Gas Dyna-
mics. Initial and Boundary Con-
ditions 129
3.4. Integrals of Motion for an Ideal Fluid 134
3.5. Aerodynamic Similarity 138
Concept of Similarity 138
Similarity Criteria Taking Account
of the Viscosity and Heat Con-
duction 141
3.6. Isentropic Gas Flows 149
Configuration of Gas let 149
Flow Velocity 150
Pressure, Density, and Temperature 152
Flow of a Gas from a Reservoir 154
Chapter 4 4.1. Physical Nature of Shock Wave For-
mation 159
Shock Wave Theory 4.2. General Equations for a Shock 162
Oblique Shock 163
Normal Shock 168
4.3. Shock in the Flow of a Gas with
Contents 9>
Constant Specific Heats 109
System of Equations 169"
Formulas for Calculating the Param-
eters of a Gas Behind a Shock 170
Oblique Shock Angle 176
4.4. Hodograph 179
4.5. A Normal Shock in the Flow of a
Gas with Constant Specific Heats 184
4.6. A Shock at Hypersonic Velocities
and Constant Specific Heats of a Gas 186
4.7. A Shock in a Flow of a Gas with Vary-
ing Specific Heats and with Dissocia-
tion and Ionization 188
4.8. Relaxation Phenomena 193
Non-Equilibrium Flows 193
Equilibrium Processes 195
Relaxation Effects in Shock Waves 196
Chapter 5 5.1. Equations for the Velocity Potential
and Stream Function 2(10
Method 5.2. The Cauchy Problem 205
of Characteristics 5.3. Characteristics 209
Com pa tibili ty Conui tions 209
Determination of Characteristics 209
Orthogonali ty of Characteristics 213
Transformation of the Equations for
Characteristics in a Hodograph 214
Equations for Characteristics in a
Hodograph for Particular Cases of
Gas Flow 219
5.4. Outline of Solution of Gas-Dynamic
Problems According to the !\Iethod of
Characteristics 222
5.5. Application of the .'IIethod of Charac
teristics to the Solution of the Prob
lem on Shaping the :'\Jozzles of Super-
sonic Wind Tunnels 230
Chapter 6 6.1. Thin Airfoil in all Incompressible
Flow 234
Airfoil and 6.2. Transverse Flo\\' over a Thin Plate 240
Finite-Span Wing 6.3. Thin Plate at an ,\ngle of Attack 243
in an Incompressible 6.4. Finite-Span Wing in an Incompres-
sible Flow 249
Flow
6.5. Wing with Optimal Planform 258
Conversion of Coefficients clJ and ex,i
from One \Ving Aspect Ratio to
Another 258
Chapter 7 7.1. Subsonic Flow over a Thin .. \ irioil 264
Linearization of the Equation for
An Airfoil in a the Velocity Potential 264
Compressible Flow Relation Between the Parameters of
a Compressible and Incompres:-ible
Fluid Flow over a Thin Airfoil 266
7.2. Khristianovich .'Ilethod 269
Content of the !\Iethod 269
10 Contents
Conversion of the Pressure Coefficient
for an Incompressible Fluid to the
Number Moo> 0 271
Conversion of the Pressure Coefficient
from M001 > 0 to M002 > 0 272
Determina tion of the Cri tical Num-
ber M 273
Aerodynamic Coefficients 274
7.3. Flow at Supercritical Velocity over
an Airfoil (Moo> M oo,cr) 274
7.4. Supersonic Flow of a Gas with Con-
stant Specific Heats over a Thin Plate 278
7.5. Parameters of a Supersonic Flow over
an Airfoil with an Arbitrary Con
figuration 285
Use of the Method of Characteristics 285
Hypersonic Flow over a Thin Airfoil 291
Nearly Uniform Flow over a Thin
Airfoil 293
Aerodynamic Forces and Their
Coefficients 293
7.6. Sideslipping Wing Airfoil 29g,
Definition of a Sideslipping Wing 299
Aerodynamic Characteristics of a
Sideslipping Wing Airfoil 301
Suction Force 3(5
Chapter 8 8.1. Linearized Theory of Supersonic Flow
over a Finite-Span Wing 308
A Wing in Linearization of the Equation for the
a Supersonic Flow Potential Function 308
Boundarv Conditions 310
Components of the Total Values of
the Veloci ty Potentials and Aero-
dynamic Coefficients 313
Features of Supersonic Flow over
Wings 315
8.2. :Method of Sources 317
8.3. Wing wi th a Symmetric Airfoil and
Triangular Planform (a = 0, c = 0) 321
Ya
Flow over a Wing Panel with a Sub-
sonic Leading Edge 321
Triangular Wing Symmetric about
the x-Axis with Subsonic Leading
Edges 326
Semi-Infinite Wing with a Supersonk
Edge 328
Triangular Wing Symmetric about the
x-Axis with Supersonic Leading Edges 330
8.4. Flow over a Tetragonal Symmetrie
Airfoil Wing with Subsonic Edges
at a Zero Angle of IAttack 331
8.5. Flow over a Tetragonal Symmetrie
Airfoil Wing with Edges~of Different
Kinds
(Subsonic and Supersonic) 343