Fundamentals of Aerodynamits
fth Ed t n n SI Un t
John D. Anderson, Jr. Curator of Aerodynamics National Air and Space Museum Smithsonian Institution and Professor Emeritus University of Maryland
M Gr ll
S n p r • t n • rr d , I • b , IA • M d n, WI • Y r • S n r n St. • n • K l p r • b n • nd n • M dr d M x C t • M l n • M ntr l • lh • S l • S dn • p • r nt r f t th fth Ed t n x x . 2 Appl d A r d n : h A r d n C ff nt — h r M n t d nd r t n . t r l t : h Ill v C nt r A f r r 8 nd nt l r n pl . 4 t r l t : A r d n C ff nt Ch pt r . S r A r d n : S Intr d t r . 6 r bl 8 h ht . I p rt n f A r d n : t r l Chapter 2 Ex pl A r d n : S nd nt l r n pl .2 A r d n : Cl f t n nd r t l nd E t n 0 Obj t v 2. . d M p f r h Ch pt r Intr d t n nd d M p 04 2.2 .4 S nd nt l A r d n v f t r l t n 0 r bl 2.2.1 Some Vector Algebra 106 1.4.1 Units 18 2.2.2 Typical Orthogonal Coordinate Systems 107 . A r d n r nd M nt 2.2.3 Scalar and Vector Fields 110 .6 C nt r f r r 2 2.2.4 Scalar and Vector Products 110 . n n l An l : h n h h r 4 2.2.5 Gradient of a Scalar Field 111 .8 l S l r t 4 2.2.6 Divergence of a Vector Field 113 . l d St t : n r 2 2.2.7 Curl of a Vector Field 114 . 0 p f l 62 2.2.8 Line Integrals 114 2.2.9 Surface Integrals 115 1.10.1 Continuum Versus Free Molecule Flow 62 2.2.10 Volume Integrals 116 1.10.2 Inviscid Versus 'Viscous Flow 62 2.2.11 Relations Between Line, Surface, and Volume Integrals 117 1.10.3 Incompressible Versus Compressible Flows 64 2.2.12 Summary 117 1.10.4 Mach Number Regimes 64 2. M d l f th l d: C ntr l l nd . l : Intr d t n t nd r l d El nt r 68 2.3.1 Finite Control Volume Approach 118
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2.3.2 Infinitesimal Fluid Element 3.2 Bernoulli's Equation 207 Approach 119 3.3 Incompressible Flow in a Duct: The Venturi 2.3.3 Molecular Approach 119 and Low-Speed Wind Tunnel 211 2.3.4 Physical Meaning of the Divergente 3.4 Pitot Tube: Measurement of of Velocity 120 Airspeed 224 2.3.5 Specification of the Flow Field 121 3.5 Pressure Coefficient 233 2.4 Continuity Equation 125 .6 Condition an Velocity for Incompressible 2.5 Momentum Equation 130 Flow 235 2.6 An Application of the Momentum Equation: 3.7 Governing Equation for Irrotational, Drag of a Two-Dimensional Body 135 Incompressible Flow: Laplace's 2.6.1 Comment 144 Equation 236 2.7 Energy Equation 144 3.7.1 Infinity Boundary Conditions 239 2.8 Interim Summary 149 3.7.2 Wall Boundary Conditions 239 2.9 Substantial Derivative 150 .8 Interim Summary 240 2.10 Fundamental Equations in Terms 3.9 Uniform Flow: Our First Elementary of the Substantial Derivative 156 Flow 241 2.11 Pathlines, Streamlines, and Streaklines 3.10 Source Flow: Our Second Elementary of a Flow 158 Flow 243 2.12 Angular Velocity, Vorticity, and Strain 163 . Combination of a Uniform Flow with a 2.13 Circulation 174 Source and Sink 247 2.14 Stream Function 177 . 2 Doublet Flow: Our Third Elementary 2.15 Velocity Potential 181 Flow 251 Nonlifting Flow over a Circular 2.16 Relationship Between the Stream Function . and Velocity Potential 184 Cylinder 253 2.17 How Do We Solve the Equations? 185 . 4 Vortex Flow: Our Fourth Elementary Flow 262 2.17.1 Theoretical (Analytical) Solutions 185 . Lifting Flow over a Cylinder 266 2.17.2 Numerical Solutions-Computational Fluid Dynamics (CFD) 187 . 6 The Kutta-Joukowski Theorem and the Generation of Lift 280 2.17.3 The Bigger Picture 194 Nonlifting Flows over Arbitrary Bodies: 2. 8 Summary 194 . The Numerical Source Panel 2.19 Problems 198 Method 282 . 8 Applied Aerodynamics: The Flow over a Circular Cylinder-The Real Case 292 A 2 . Historical Note: Bernoulli and Euler-The Inv d, In pr bl l 20 Origins of Theoretical Fluid Dynamics 300 Ch pt r .20 Historical Note: d'Alembert and His nd nt l f Inv d, In pr bl Paradox 305 l 20 .2 Summary 306 3.1 Introduction and Road Map 204 .22 Problems 309 C nt nt x
Ch pt r 4 fh pt r Incompressible Flow over Airfoils 313 Incompressible Flow over Finite Wings 411 4.1 Intr d t n 5.1 Intr d t n: n h nd Ind d 4.2 A rf l n l t r 8 r 4 4.3 A rf l Ch r t r t 20 5.2 h rt x l nt, th t S v rt , 4.4 h l ph f h r t l S l t n nd l h ltz h r 420 f r Sp d l v r A rf l : h 5.3 r ndtl Cl l ft n n rt x Sh t 2 h r 424 4.5 h K tt C nd t n 0 5.3.1 Elliptical Lift Distribution 430 4.5.1 Without Friction Could We Have 5.3.2 General Lift Distribution 435 Lift? 334 5.3.3 Effect of Aspect Ratio 438 4.6 K lv n C r l t n h r nd th 5.3.4 Physical Significance 444 St rt n rt x 4 5.4 A r l nl n r ft n n 4.7 Cl l h n A rf l h r : h M th d 4 S tr A rf l 8 5.5 h ft n S rf h r nd th rt x 4.8 h C b r d A rf l 48 tt r l M th d 4 4.9 h A r d n C nt r: Add t n l 5.6 Appl d A r d n : h lt C n d r t n W n 464 4.10 ft n l v r Arb tr r 5.7 t r l t : n h t r nd d : h rt x n l r ndtl h E rl v l p nt f r l M th d 6 n t W n h r 4 6 4.11 M d rn Sp d A rf l 6 5.8 t r l t : r ndtl h 4.12 l : A rf l r M n 480 4.12.1 Estimating Skin-Friction Drag: 5.9 S r 48 Laminar Flow 372 5.10 r bl 484 4.12.2 Estimating Skin-Friction Drag: Turbulent Flow 374 Ch pt r 6 4.12.3 Transition 376 Three-Dimensional Incompressible 4.12.4 Flow Separation 381 Flow 487 4.12.5 Comment 386 6.1 4.13 Appl d A r d n : h l v r Intr d t n 48 n A rf l h l C 8 6.2 hr n n l S r 488 4.14 t r l t : E rl A rpl n 6.3 hr n n l bl t 4 0 n nd th l f A rf l 6.4 l v r A Sph r 4 2 h n 8 6.4.1 Conzment an the Three-Dimensional 4.15 t r l t : K tt , , Relieving Effect 494 nd th C r l t n h r 6.5 G n r l hr n n l l : n l f ft 40 hn 4 4.16 S r 40 6.6 Appl d A r d n : h l v r 4.17 r bl 40 Sph r h l C 4 x v C nt nt
6. Appl d A r d n : A rpl n ft 8. Sp d f S nd nd r 00 8.3.1 Comments 563 6.7.1 Airplane Lift 500 8.4 Sp l r f th En r 6.7.2 Airplane Drag 502 E t n 64 6.7.3 Application of Computational Fluid 8. Wh n I A l C pr bl ? 2 Dynamics for the Calculation of Lift and 8.6 C l l t n f r l Sh W v Drag 507 r p rt 6.8 S r 8.6.1 Comment on the Use of Tables to Solve 6. r bl 2 Compressible Flow Problems 590 8. M r nt f l t n C pr bl l 8.7.1 Subsonic Compressible Flow 591 A Inviscid, Compressible Flow 513 8.7.2 Supersonic Flow 592 8.8 S r 6 8. r bl Ch pt r C pr bl l : S r l n r A p t Ch pt r 9 . Intr d t n 6 Obl Sh nd Exp n n W v 60 .2 A r f v f h r d n 8 . Intr d t n 602 7.2.1 Perfect Gas 518 .2 Obl Sh l t n 608 7.2.2 Internal Energy and Enthalpy 518 . S p r n l v r W d 7.2.3 First Law of Thermodynamics 523 nd C n 622 7.2.4 Entropy and the Second Law of 9.3.1 A Comment on Supersonic Lift and Drag Thermodynamics 524 Coefficients 625 7.2.5 Isentropic Relations 526 .4 Sh Int r t n nd fl t n 626 . f n t n f C pr b l t 0 . t h d Sh W v n r nt f l nt .4 G v rn n E t n f r Inv d, d 6 2 C pr bl l 9.5.1 Comment on the Flow Field behind a . f n t n f t l (St n t n Curved Shock Wave: Entropy Gradients C nd t n and Vorticity 636 .6 S A p t f S p r n l : Sh .6 r ndtl M r Exp n n W v 6 6 W v 40 . Sh Exp n n h r : Appl t n t . S r 44 S p r n A rf l 648 .8 r bl 46 .8 A C nt n ft nd r C ff nt 6 2 Ch pt r 8 . h nd It W d l 6 2 r l Sh W v nd l t d p 4 . 0 l : Sh W v nd r r Int r t n 6 8. Intr d t n 0 . t r l t : Ern t M h A 8.2 h r l Sh E t n r ph l S t h 6 C nt nt xv
. 2 S r 662 . Appl d A r d n : h l nd d . r bl 66 W n d 4 . 2 t r l t : h Sp d A rf l E rl r h nd Ch pt r 10 v l p nt 60 C pr bl l thr h zzl , ff r , . t r l t : h Or n f h nd W nd nn l 66 S pt W n C n pt 64 0. Intr d t n 6 0 . 4 t r l t : h rd . 0.2 G v rn n E t n f r Wh t b Ar h t t f th Ar l Q On n n l l 6 2 nd th S p r r t l W n 0. zzl l 68 . S r 4 10.3.1 More on Mass Flow 695 . 6 r bl 6 0.4 ff r 6 6 S p r n W nd nn l 6 8 0. Ch pt r 12 0.6 l : Sh W v nd r r Int r t n n d n r z d S p r n l n zzl 04 2. Intr d t n 80 0. S r 06 2.2 r v t n f th n r z d S p r n 0.8 r bl 0 r r C ff nt r l 80 2. Appl t n t S p r n A rf l 84 Ch pt r 11 2.4 l : S p r n A rf l S b n C pr bl l v r A rf l : r 0 n r h r 2. S r . Intr d t n 2 2.6 r bl 4 .2 h l t t nt l E t n 4 . h n r z d l t t nt l Ch pt r E t n Intr d t n t r l hn .4 r ndtl Gl rt C pr b l t f r nl n r S p r n l C rr t n 22 . I pr v d C pr b l t . Intr d t n: h l ph f C p t t n l C rr t n 2 l d n 8 .6 Cr t l M h b r 28 .2 El nt f th M th d f Ch r t r t 800 11.6.1 A Comment on the Location of Minimum Pressure (Maximum Velocity) 737 13.2.1 Internal Points 806 . r v r n M h b r: h 13.2.2 Wall Points 807 S nd rr r . S p r n zzl n 808 .8 h Ar l 4 .4 El nt f n t ff r n . h S p r r t l A rf l 4 M th d 8 . 0 C Appl t n : r n n A rf l 13.4.1 Predictor Step 817 nd W n 4 13.4.2 Corrector Step 817 xv C nt nt
. h p nd nt hn : 4. Appl d p r n A r d n : Appl t n t S p r n l nt p r n W v r d r 8 6 d 8 8 14,9.1 Viscous Optimized Waveriders 882 13.5.1 Predictor Step 822 4. 0 S r 8 0 13.5.2 Corrector Step 822 4. r bl 8 0 .6 l v r C n 826 13.6.1 Physical Aspects of Conical Flow 827 13.6.2 Quantitative Formulation 828 A 4 13.6.3 Numerical Procedure 833 l 8 13.6.4 Physical Aspects of Supersonic Flow Over Cones 834 Ch pt r . S r 8 .8 r bl 8 8 Intr d t n t th nd nt l r n pl nd E t n f l 8 . Intr d t n 8 4 Ch pt r 4 .2 Q l t t v A p t f El nt f p r n l 8 l 8 4. Intr d t n 840 . t nd h r l C nd t n 0 4.2 Q l t t v A p t f p r n .4 h v r St E t n 08 l 84 . h l En r E t n 2 4. t n n h r 84 .6 S l r t r t r 6 4.4 h ft nd r f W n t p r n . S l t n f l : A r l n r Sp d : t n n lt f r t l t n 20 t An l f Att 84 .8 S r 2 14.4.1 Accuracy Considerations 856 . r bl 2 4. p r n Sh W v l t n nd An th r t t n n h r 860 Ch pt r 6 4.6 M h b r Ind p nd n 864 A Sp l C : C tt l 2 4. p r n nd C p t t n l l d n 866 6. Intr d t n 2 4.8 p r n l : A r d n 6.2 C tt l : G n r l n 28 t n 86 6. In pr bl (C n t nt r p rt 14.8.1 Aerodynamic Heating and Hypersonic C tt l 2 Flow—the Connection 869 16.3.1 Negligible Viscous Dissipation 938 14.8.2 Blunt versus Slender Bodies in 16.3.2 Equal Wall Temperatures 939 Hypersonic Flow 871 16.3.3 Adiabatic Wall Conditions (Adiabatic 14.8.3 Aerodynamic Heating to a Wall Temperature) 941 Blunt Body 874 16.3.4 Recovery Factor 944 C nt nt xv
16.3.5 Reynolds Analogy 945 Ch pt r 16.3.6 Interim Summary 946 rb l nt nd r r 0 6.4 C pr bl C tt l 48 . Intr d t n 020 16.4.1 Shooting Method 950 .2 lt f r rb l nt nd r r 16.4.2 Time-Dependent Finite-Difference n l t l t 020 Method 952 19.2.1 Reference Temperature Method 16.4.3 Results for Compressible Couette for Turbulent Flow 1022 Flow 956 19.2.2 The Meador-Smart Reference 16.4.4 Some Analytical Considerations 958 Temperature Method for Turbulent 6. S r 6 Flow 1024 19.2.3 Prediction of Airfoil Drag 1025 Ch pt r 17 . rb l n M d l n 02
Intr d t n t nd r r 6 19.3.1 The Baldwin Lomax Model 1026 .4 n l C nt 028 . Intr d t n 66 . S r 02 .2 nd r r r p rt 68 .6 r bl 0 0 . h nd r r E t n 4 .4 W S lv th nd r r E t n ? Ch pt r 20 . S r v r St S l t n : S Ex pl 0 Ch pt r 8 20. Intr d t n 0 2 n r nd r r 8 20.2 h Appr h 0 2 20. Ex pl f S S l t n 0 8. Intr d t n 8 20.3.1 Flow over a Rearward-Facing Step 1033 8.2 In pr bl l v r l t l t : h l S l t n 82 20.3.2 Flow over an Airfoil 1033 8. C pr bl l v r l t l t 8 20.3.3 Flow over a Complete Airplane 1036 20.3.4 Shock-Wave/Boundary-Layer Interaction 18.3.1 A Comment on Drag Variation 1037 with Velocity 1000 h f r n p r t r M th d 00 20.3.5 Flow over an Airfoil with a Protuberance 8.4 1038 18.4.1 Recent Advances: The Meador-Smart Reference Temperature Method 1004 20.4 h I f A r f r th r d t n f S n r t n r 040 8. St n t n nt A r d n 20. t n 00 S r 04 8.6 nd r r v r Arb tr r d : n t ff r n S l t n 0 App nd x A I ntr p l r p rt 04 18.6.1 Finite Difference Method 1012 8. S r 0 App nd x 8.8 r bl 0 8 r l Sh r p rt 0 xv C nt nt
App nd x C bl r ph 0 r ndtl M r n t n nd M h Ind x 0 An l 0 App nd x St nd rd At ph r 06