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E-raamat: Theory of Lift: Introductory Computational Aerodynamics in MATLAB/Octave

Series edited by (University of Liverpool, UK), Series edited by (BAE Systems, UK), Series edited by (MIT), Series edited by (Parker Aerospace Group, USA), (University of Sydney)
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  • Sari: Aerospace Series
  • Ilmumisaeg: 22-May-2012
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118346280
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Theory of Lift: Introductory Computational Aerodynamics in MATLAB/OctaveSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Aerospace Series
  • Ilmumisaeg: 22-May-2012
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118346280
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"Accessible introduction to aerodynamics using a unique computational approach based on widely available MATLAB software tools. Based on the author's years of experience teaching aerodynamics to students, he has developed an approach combining the use ofwidely available MATLAB commercial code (also compatible with Octave GNU open source code) with clear narrative explanations of the concepts that simplifies the understanding of aerodynamics without sacrificing the mathematical underpinnings or leaving the reader overwhelmed with complex formulas. The ability of the reader to download and run the code examples makes this an ideal self-learning tool, as well as a valuable course text.The choice of compatible MATLAB/Octave code ensures anyone can run the examples - either using open-source GNU Octave software as many consultancies and small firms do, or using the MATLAB commercial application (including the student edition) which is used widely in industry and is almost ubiquitous in academia. The code hasbeen carefully compiled and checked for compatibility with both applications"--Provided by publisher.

"Provides a clear introduction to aerodynamics based on a line and panel methods"--Provided by publisher.



Starting from a basic knowledge of mathematics and mechanics gained in standard foundation classes, Theory of Lift: Introductory Computational Aerodynamics in MATLAB/Octave takes the reader conceptually through from the fundamental mechanics of lift to the stage of actually being able to make practical calculations and predictions of the coefficient of lift for realistic wing profile and planform geometries.

The classical framework and methods of aerodynamics are covered in detail and the reader is shown how they may be used to develop simple yet powerful MATLAB or Octave programs that accurately predict and visualise the dynamics of real wing shapes, using lumped vortex, panel, and vortex lattice methods.

This book contains all the mathematical development and formulae required in standard incompressible aerodynamics as well as dozens of small but complete working programs which can be put to use immediately using either the popular MATLAB or free Octave computional modelling packages.

Key features:

  • Synthesizes the classical foundations of aerodynamics with hands-on computation, emphasizing interactivity and visualization.
  • Includes complete source code for all programs, all listings having been tested for compatibility with both MATLAB and Octave.
  • Companion website (www.wiley.com/go/mcbain) hosting codes and solutions.

Theory of Lift: Introductory Computational Aerodynamics in MATLAB/Octave is an introductory text for graduate and senior undergraduate students on aeronautical and aerospace engineering courses and also forms a valuable reference for engineers and designers.

Arvustused

This book is a very useful digest of key points from the literature, carefully structured and presented with helpful pointers as to how the successive aerodynamical models can be implemented in the now so readily available interactive matrix computation systems.  (Aeronautical Journal, 1 August 2013)

Preface xvii
Series Preface xxiii
PART ONE PLANE IDEAL AERODYNAMICS
1 Preliminary Notions
3(22)
1.1 Aerodynamic Force and Moment
3(2)
1.1.1 Motion of the Frame of Reference
3(1)
1.1.2 Orientation of the System of Coordinates
4(1)
1.1.3 Components of the Aerodynamic Force
4(1)
1.1.4 Formulation of the Aerodynamic Problem
4(1)
1.2 Aircraft Geometry
5(3)
1.2.1 Wing Section Geometry
6(1)
1.2.2 Wing Geometry
7(1)
1.3 Velocity
8(1)
1.4 Properties of Air
8(5)
1.4.1 Equation of State: Compressibility and the Speed of Sound
8(2)
1.4.2 Rheology: Viscosity
10(2)
1.4.3 The International Standard Atmosphere
12(1)
1.4.4 Computing Air Properties
12(1)
1.5 Dimensional Theory
13(5)
1.5.1 Alternative methods
16(1)
1.5.2 Example: Using Octave to Solve a Linear System
16(2)
1.6 Example: NACA Report No. 502
18(1)
1.7 Exercises
19(3)
1.8 Further Reading
22(1)
References
22(3)
2 Plane Ideal Flow
25(22)
2.1 Material Properties: The Perfect Fluid
25(1)
2.2 Conservation of Mass
26(1)
2.2.1 Governing Equations: Conservation Laws
26(1)
2.3 The Continuity Equation
26(1)
2.4 Mechanics: The Euler Equations
27(3)
2.4.1 Rate of Change of Momentum
27(1)
2.4.2 Forces Acting on a Fluid Particle
28(1)
2.4.3 The Euler Equations
29(1)
2.4.4 Accounting for Conservative External Forces
29(1)
2.5 Consequences of the Governing Equations
30(5)
2.5.1 The Aerodynamic Force
30(3)
2.5.2 Bernoulli's Equation
33(1)
2.5.3 Circulation, Vorticity, and Irrotational Flow
33(2)
2.5.4 Plane Ideal Flows
35(1)
2.6 The Complex Velocity
35(6)
2.6.1 Review of Complex Variables
35(3)
2.6.2 Analytic Functions and Plane Ideal Flow
38(2)
2.6.3 Example: the Polar Angle Is Nowhere Analytic
40(1)
2.7 The Complex Potential
41(1)
2.8 Exercises
42(2)
2.9 Further Reading
44(1)
References
45(2)
3 Circulation and Lift
47(20)
3.1 Powers of z
47(6)
3.1.1 Divergence and Vorticity in Polar Coordinates
48(1)
3.1.2 Complex Potentials
48(1)
3.1.3 Drawing Complex Velocity Fields with Octave
49(1)
3.1.4 Example: k = 1, Corner Flow
50(1)
3.1.5 Example: k = 0, Uniform Stream
51(1)
3.1.6 Example: k = -1, Source
51(1)
3.1.7 Example: k = -2, Doublet
52(1)
3.2 Multiplication by a Complex Constant
53(1)
3.2.1 Example: w = const., Uniform Stream with Arbitrary Direction
53(1)
3.2.2 Example: w = i/z, Vortex
54(1)
3.2.3 Example: Polar Components
54(1)
3.3 Linear Combinations of Complex Velocities
54(2)
3.3.1 Example: Circular Obstacle in a Stream
54(2)
3.4 Transforming the Whole Velocity Field
56(1)
3.4.1 Translating the Whole Velocity Field
56(1)
3.4.2 Example: Doublet as the Sum of a Source and Sink
56(1)
3.4.3 Rotating the Whole Velocity Field
56(1)
3.5 Circulation and Outflow
57(4)
3.5.1 Curve-integrals in Plane Ideal Flow
57(1)
3.5.2 Example: Numerical Line-integrals for Circulation and Outflow
58(1)
3.5.3 Closed Circuits
59(1)
3.5.4 Example: Powers of z and Circles around the Origin
60(1)
3.6 More on the Scalar Potential and Stream Function
61(1)
3.6.1 The Scalar Potential and Irrotational Flow
61(1)
3.6.2 The Stream Function and Divergence-free Flow
62(1)
3.7 Lift
62(2)
3.7.1 Blasius's Theorem
62(1)
3.7.2 The Kutta-Joukowsky Theorem
63(1)
3.8 Exercises
64(1)
3.9 Further Reading
65(1)
References
66(1)
4 Conformal Mapping
67(12)
4.1 Composition of Analytic Functions
67(1)
4.2 Mapping with Powers of ξ
68(3)
4.2.1 Example: Square Mapping
68(1)
4.2.2 Conforming Mapping by Contouring the Stream Function
69(1)
4.2.3 Example: Two-thirds Power Mapping
69(1)
4.2.4 Branch Cuts
70(1)
4.2.5 Other Powers
71(1)
4.3 Joukowsky's Transformation
71(4)
4.3.1 Unit Circle from a Straight Line Segment
71(1)
4.3.2 Uniform Flow and Flow over a Circle
72(1)
4.3.3 Thin Flat Plate at Nonzero Incidence
73(1)
4.3.4 Flow over the Thin Flat Plate with Circulation
74(1)
4.3.5 Joukowsky Aerofoils
75(1)
4.4 Exercises
75(3)
4.5 Further Reading
78(1)
References
78(1)
5 Flat Plate Aerodynamics
79(14)
5.1 Plane Ideal Flow over a Thin Flat Plate
79(8)
5.1.1 Stagnation Points
80(1)
5.1.2 The Kutta-Joukowsky Condition
80(1)
5.1.3 Lift on a Thin Flat Plate
81(1)
5.1.4 Surface Speed Distribution
82(1)
5.1.5 Pressure Distribution
83(1)
5.1.6 Distribution of Circulation
84(1)
5.1.7 Thin Flat Plate as Vortex Sheet
85(2)
5.2 Application of Thin Aerofoil Theory to the Flat Plate
87(2)
5.2.1 Thin Aerofoil Theory
87(1)
5.2.2 Vortex Sheet along the Chord
87(1)
5.2.3 Changing the Variable of Integration
88(1)
5.2.4 Glauert's Integral
88(1)
5.2.5 The Kutta-Joukowsky Condition
89(1)
5.2.6 Circulation and Lift
89(1)
5.3 Aerodynamic Moment
89(1)
5.3.1 Centre of Pressure and Aerodynamic Centre
90(1)
5.4 Exercises
90(1)
5.5 Further Reading
91(1)
References
91(2)
6 Thin Wing Sections
93(18)
6.1 Thin Aerofoil Analysis
93(5)
6.1.1 Vortex Sheet along the Camber Line
93(1)
6.1.2 The Boundary Condition
93(1)
6.1.3 Linearization
94(1)
6.1.4 Glauert's Transformation
95(1)
6.1.5 Glauert's Expansion
95(2)
6.1.6 Fourier Cosine Decomposition of the Camber Line Slope
97(1)
6.2 Thin Aerofoil Aerodynamics
98(3)
6.2.1 Circulation and Lift
98(1)
6.2.2 Pitching Moment about the Leading Edge
99(1)
6.2.3 Aerodynamic Centre
100(1)
6.2.4 Summary
101(1)
6.3 Analytical Evaluation of Thin Aerofoil Integrals
101(4)
6.3.1 Example: the NACA Four-digit Wing Sections
104(1)
6.4 Numerical Thin Aerofoil Theory
105(4)
6.5 Exercises
109(1)
6.6 Further Reading
109(1)
References
109(2)
7 Lumped Vortex Elements
111(16)
7.1 The Thin Flat Plate at Arbitrary Incidence, Again
111(3)
7.1.1 Single Vortex
111(1)
7.1.2 The Collocation Point
111(1)
7.1.3 Lumped Vortex Model of the Thin Flat Plate
112(2)
7.2 Using Two Lumped Vortices along the Chord
114(3)
7.2.1 Postprocessing
116(1)
7.3 Generalization to Multiple Lumped Vortex Panels
117(1)
7.3.1 Postprocessing
117(1)
7.4 General Considerations on Discrete Singularity Methods
117(2)
7.5 Lumped Vortex Elements for Thin Aerofoils
119(4)
7.5.1 Panel Chains for Camber Lines
119(2)
7.5.2 Implementation in Octave
121(1)
7.5.3 Comparison with Thin Aerofoil Theory
122(1)
7.6 Disconnected Aerofoils
123(2)
7.6.1 Other Applications
124(1)
7.7 Exercises
125(1)
7.8 Further Reading
125(1)
References
126(1)
8 Panel Methods for Plane Flow
127(16)
8.1 Development of the CUSSSP Program
127(10)
8.1.1 The Singularity Elements
127(2)
8.1.2 Discretizing the Geometry
129(2)
8.1.3 The Influence Matrix
131(1)
8.1.4 The Right-hand Side
132(2)
8.1.5 Solving the Linear System
134(1)
8.1.6 Postprocessing
135(2)
8.2 Exercises
137(2)
8.2.1 Projects
138(1)
8.3 Further Reading
139(1)
References
139(1)
8.4 Conclusion to Part I: The Origin of Lift
139(4)
PART TWO THREE-DIMENSIONAL IDEAL AERODYNAMICS
9 Finite Wings and Three-Dimensional Flow
143(14)
9.1 Wings of Finite Span
143(2)
9.1.1 Empirical Effect of Finite Span on Lift
143(1)
9.1.2 Finite Wings and Three-dimensional Flow
143(2)
9.2 Three-Dimensional Flow
145(1)
9.2.1 Three-dimensional Cartesian Coordinate System
145(1)
9.2.2 Three-dimensional Governing Equations
145(1)
9.3 Vector Notation and Identities
145(4)
9.3.1 Addition and Scalar Multiplication of Vectors
145(1)
9.3.2 Products of Vectors
146(1)
9.3.3 Vector Derivatives
147(1)
9.3.4 Integral Theorems for Vector Derivatives
148(1)
9.4 The Equations Governing Three-Dimensional Flow
149(1)
9.4.1 Conservation of Mass and the Continuity Equation
149(1)
9.4.2 Newton's Law and Euler's Equation
149(1)
9.5 Circulation
150(4)
9.5.1 Definition of Circulation in Three Dimensions
150(1)
9.5.2 The Persistence of Circulation
151(1)
9.5.3 Circulation and Vorticity
151(2)
9.5.4 Rotational Form of Euler's Equation
153(1)
9.5.5 Steady Irrotational Motion
153(1)
9.6 Exercises
154(1)
9.7 Further Reading
155(1)
References
155(2)
10 Vorticity and Vortices
157(12)
10.1 Streamlines, Stream Tubes, and Stream Filaments
157(2)
10.1.1 Streamlines
157(1)
10.1.2 Stream Tubes and Stream Filaments
158(1)
10.2 Vortex Lines, Vortex Tubes, and Vortex Filaments
159(1)
10.2.1 Strength of Vortex Tubes and Filaments
159(1)
10.2.2 Kinematic Properties of Vortex Tubes
159(1)
10.3 Helmholtz's Theorems
159(1)
10.3.1 `Vortex Tubes Move with the Flow'
159(1)
10.3.2 `The Strength of a Vortex Tube is Constant'
160(1)
10.4 Line Vortices
160(1)
10.4.1 The Two-dimensional Vortex
160(1)
10.4.2 Arbitrarily Oriented Rectilinear Vortex Filaments
160(1)
10.5 Segmented Vortex Filaments
161(5)
10.5.1 The Biot-Savart Law
161(1)
10.5.2 Rectilinear Vortex Filaments
162(2)
10.5.3 Finite Rectilinear Vortex Filaments
164(1)
10.5.4 Infinite Straight Line Vortices
164(1)
10.5.5 Semi-infinite Straight Line Vortex
164(1)
10.5.6 Truncating Infinite Vortex Segments
165(1)
10.5.7 Implementing Line Vortices in Octave
165(1)
10.6 Exercises
166(1)
10.7 Further Reading
167(1)
References
167(2)
11 Lifting Line Theory
169(16)
11.1 Basic Assumptions of Lifting Line Theory
169(1)
11.2 The Lifting Line, Horseshoe Vortices, and the Wake
169(4)
11.2.1 Deductions from Vortex Theorems
169(1)
11.2.2 Deductions from the Wing Pressure Distribution
170(1)
11.2.3 The Lifting Line Model of Air Flow
170(1)
11.2.4 Horseshoe Vortex
170(1)
11.2.5 Continuous Trailing Vortex Sheet
171(1)
11.2.6 The Form of the Wake
172(1)
11.3 The Effect of Downwash
173(1)
11.3.1 Effect on the Angle of Incidence: Induced Incidence
173(1)
11.3.2 Effect on the Aerodynamic Force: Induced Drag
174(1)
11.4 The Lifting Line Equation
174(4)
11.4.1 Glauert's Solution of the Lifting Line Equation
175(1)
11.4.2 Wing Properties in Terms of Glauert's Expansion
176(2)
11.5 The Elliptic Lift Loading
178(2)
11.5.1 Properties of the Elliptic Lift Loading
179(1)
11.6 Lift-Incidence Relation
180(2)
11.6.1 Linear Lift-Incidence Relation
181(1)
11.7 Realizing the Elliptic Lift Loading
182(1)
11.7.1 Corrections to the Elliptic Loading Approximation
182(1)
11.8 Exercises
182(1)
11.9 Further Reading
183(1)
References
183(2)
12 Nonelliptic Lift Loading
185(8)
12.1 Solving the Lifting Line Equation
185(3)
12.1.1 The Sectional Lift-Incidence Relation
185(1)
12.1.2 Linear Sectional Lift-Incidence Relation
185(1)
12.1.3 Finite Approximation: Truncation and Collocation
185(2)
12.1.4 Computer Implementation
187(1)
12.1.5 Example: a Rectangular Wing
187(1)
12.2 Numerical Convergence
188(1)
12.3 Symmetric Spanwise Loading
189(3)
12.3.1 Example: Exploiting Symmetry
191(1)
12.4 Exercises
192(1)
References
192(1)
13 Lumped Horseshoe Elements
193(16)
13.1 A Single Horseshoe Vortex
193(2)
13.1.1 Induced Incidence of the Lumped Horseshoe Element
195(1)
13.2 Multiple Horseshoes along the Span
195(5)
13.2.1 A Finite-step Lifting Line in Octave
197(3)
13.3 An Improved Discrete Horseshoe Model
200(3)
13.4 Implementing Horseshoe Vortices in Octave
203(3)
13.4.1 Example: Yawed Horseshoe Vortex Coefficients
205(1)
13.5 Exercises
206(1)
13.6 Further Reading
207(1)
References
207(2)
14 The Vortex Lattice Method
209(16)
14.1 Meshing the Mean Lifting Surface of a Wing
209(3)
14.1.1 Plotting the Mesh of a Mean Lifting Surface
210(2)
14.2 A Vortex Lattice Method
212(4)
14.2.1 The Vortex Lattice Equations
213(2)
14.2.2 Unit Normals to the Vortex-lattice
215(1)
14.2.3 Spanwise Symmetry
215(1)
14.2.4 Postprocessing Vortex Lattice Methods
215(1)
14.3 Examples of Vortex Lattice Calculations
216(4)
14.3.1 Campbell's Flat Swept Tapered Wing
216(2)
14.3.2 Bertin's Flat Swept Untapered Wing
218(1)
14.3.3 Spanwise and Chordwise Refinement
219(1)
14.4 Exercises
220(1)
14.5 Further Reading
221(1)
14.5.1 Three-dimensional Panel Methods
222(1)
References
222(3)
PART THREE NONIDEAL FLOW IN AERODYNAMICS
15 Viscous Flow
225(12)
15.1 Cauchy's First Law of Continuum Mechanics
225(2)
15.2 Rheological Constitutive Equations
227(1)
15.2.1 Perfect Fluid
227(1)
15.2.2 Linearly Viscous Fluid
227(1)
15.3 The Navier-Stokes Equations
228(1)
15.4 The No-Slip Condition and the Viscous Boundary Layer
228(1)
15.5 Unidirectional Flows
229(1)
15.5.1 Plane Couette and Poiseuille Flows
229(1)
15.6 A Suddenly Sliding Plate
230(4)
15.6.1 Solution by Similarity Variable
230(3)
15.6.2 The Diffusion of Vorticity
233(1)
15.7 Exercises
234(1)
15.8 Further Reading
234(1)
References
235(2)
16 Boundary Layer Equations
237(14)
16.1 The Boundary Layer over a Flat Plate
237(4)
16.1.1 Scales in the Conservation of Mass
237(1)
16.1.2 Scales in the Streamwise Momentum Equation
238(1)
16.1.3 The Reynolds Number
239(1)
16.1.4 Pressure in the Boundary Layer
239(1)
16.1.5 The Transverse Momentum Balance
239(1)
16.1.6 The Boundary Layer Momentum Equation
240(1)
16.1.7 Pressure and External Tangential Velocity
241(1)
16.1.8 Application to Curved Surfaces
241(1)
16.2 Momentum Integral Equation
241(2)
16.3 Local Boundary Layer Parameters
243(5)
16.3.1 The Displacement and Momentum Thicknesses
243(1)
16.3.2 The Skin Friction Coefficient
243(1)
16.3.3 Example: Three Boundary Layer Profiles
244(4)
16.4 Exercises
248(1)
16.5 Further Reading
249(1)
References
249(2)
17 Laminar Boundary Layers
251(12)
17.1 Boundary Layer Profile Curvature
251(1)
17.1.1 Pressure Gradient and Boundary Layer Thickness
252(1)
17.2 Pohlhausen's Quartic Profiles
252(2)
17.3 Thwaites's Method for Laminar Boundary Layers
254(6)
17.3.1 F(λ) = 0.45 - 6λ
255(1)
17.3.2 Correlations for Shape Factor and Skin Friction
256(1)
17.3.3 Example: Zero Pressure Gradient
256(1)
17.3.4 Example: Laminar Separation from a Circular Cylinder
257(3)
17.4 Exercises
260(1)
17.5 Further Reading
261(1)
References
262(1)
18 Compressibility
263(10)
18.1 Steady-State Conservation of Mass
263(2)
18.2 Longitudinal Variation of Stream Tube Section
265(1)
18.2.1 The Design of Supersonic Nozzles
266(1)
18.3 Perfect Gas Thermodynamics
266(4)
18.3.1 Thermal and Caloric Equations of State
266(1)
18.3.2 The First Law of Thermodynamics
267(1)
18.3.3 The Isochoric and Isobaric Specific Heat Coefficients
267(1)
18.3.4 Isothermal and Adiabatic Processes
267(1)
18.3.5 Adiabatic Expansion
268(1)
18.3.6 The Speed of Sound and Temperature
269(1)
18.3.7 The Speed of Sound and the Speed
269(1)
18.3.8 Thermodynamic Characteristics of Air
270(1)
18.3.9 Example: Stagnation Temperature
270(1)
18.4 Exercises
270(1)
18.5 Further Reading
271(1)
References
271(2)
19 Linearized Compressible Flow
273(14)
19.1 The Nonlinearity of the Equation for the Potential
273(1)
19.2 Small Disturbances to the Free-Stream
274(1)
19.3 The Uniform Free-Stream
275(1)
19.4 The Disturbance Potential
275(1)
19.5 Prandtl-Glauert Transformation
276(3)
19.5.1 Fundamental Linearized Compressible Flows
277(1)
19.5.2 The Speed of Sound
278(1)
19.6 Application of the Prandtl-Glauert Rule
279(5)
19.6.1 Transforming the Geometry
279(1)
19.6.2 Computing Aerodynamical Forces
280(2)
19.6.3 The Prandtl-Glauert Rule in Two Dimensions
282(2)
19.6.4 The Critical Mach Number
284(1)
19.7 Sweep
284(1)
19.8 Exercises
285(1)
19.9 Further Reading
285(1)
References
286(1)
Appendix A Notes on Octave Programming
287(6)
A.1 Introduction
287(1)
A.2 Vectorization
287(3)
A.2.1 Iterating Explicitly
288(1)
A.2.2 Preallocating Memory
288(1)
A.2.3 Vectorizing Function Calls
288(1)
A.2.4 Many Functions Act Elementwise on Arrays
289(1)
A.2.5 Functions Primarily Defined for Arrays
289(1)
A.2.6 Elementwise Arithmetic with Single Numbers
289(1)
A.2.7 Elementwise Arithmetic between Arrays
290(1)
A.2.8 Vector and Matrix Multiplication
290(1)
A.3 Generating Arrays
290(1)
A.3.1 Creating Tables with bsxfun
290(1)
A.4 Indexing
291(1)
A.4.1 Indexing by Logical Masks
291(1)
A.4.2 Indexing Numerically
291(1)
A.5 Just-in-Time Compilation
291(1)
A.6 Further Reading
292(1)
References
292(1)
Glossary 293(12)
Nomenclature 305(4)
Index 309
Dr. Geordie Drummond McBain, Australia Geordie McBain is an engineering consultant based in Sydney, Australia. In 1995 he graduated top of his class from James Cook University with first class honours in mechanical engineering, earning him the Faculty Medal, and went on to receive his PhD there in 1999. In 2002 he was awarded a Sesquicentennial Postdoctoral Fellowship at the University of Sydney, researching fluid dynamics. During this period, he taught aerodynamics to students on the Aeronautical and Aerospace Engineering degree programmes.
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