Theoretical and Computational Aerodynamics

Series Preface xv Preface xvii Acknowledgements xxi 1 Introduction to Aerodynamics and Atmosphere 1 1.1 Motivation and Scope of Aerodynamics 1 1.2 Conservation Principles 4 1.3 Origin of Aerodynamic Forces 6 1.4 Flow in Accelerating Control Volumes: Application of RTT 9 1.5 Atmosphere and Its Role in Aerodynamics 11 1.6 Static Stability of Atmosphere 17 Bibliography 20 2 Basic Equations of Motion 21 2.1 Introduction 21 2.2 Conservation Principles 23 2.3 Conservation of Linear Momentum: Integral Form 25 2.4 Conservation of Linear Momentum: Differential Form 26 2.5 Strain Rate of Fluid Element in Flows 28 2.6 Relation between Stress and Rate of Strain Tensors in Fluid Flow 32 2.7 Circulation and Rotationality in Flows 35 2.8 Irrotational Flows and Velocity Potential 36 2.9 Stream Function and Vector Potential 37 2.10 Governing Equation for Irrotational Flows 38 2.11 Kelvin's Theorem and Irrotationality 40 2.12 Bernoulli's Equation: Relation of Pressure and Velocity 41 2.13 Applications of Bernoulli's Equation: Air Speed Indicator 42 2.14 Viscous Effects and Boundary Layers 46 2.15 Thermodynamics and Reynolds Transport Theorem 47 2.16 Reynolds Transport Theorem 48 2.17 The Energy Equation 49 2.18 Energy Conservation Equation 52 2.19 Alternate Forms of Energy Equation 54 2.20 The Energy Equation in Conservation Form 55 2.21 Strong Conservation and Weak Conservation Forms 55 2.22 Second Law of Thermodynamics and Entropy 56 2.23 Propagation of Sound and Mach Number 60 2.24 One-Dimensional Steady Flow 61 2.25 Normal Shock Relation for Steady Flow 62 2.26 Rankine--Hugoniot Relation 64 2.27 Prandtl or Meyer Relation 65 2.28 Oblique ShockWaves 69 2.29 Weak Oblique Shock 71 2.30 Expansion of Supersonic Flows 74 Bibliography 76 3 Theoretical Aerodynamics of Potential Flows 77 3.1 Introduction 77 3.2 Preliminaries of Complex Analysis for 2D Irrotational Flows: Cauchy--Riemann Relations 78 3.3 Elementary Singularities in Fluid Flows 81 3.4 Blasius' Theorem: Forces and Moment for Potential Flows 90 Mechanism 94 3.5 Method of Images 99 3.6 Conformal Mapping: Use of Cauchy--Riemann Relation 101 3.7 Lift Created by Jukowski Airfoil 111 3.8 Thin Airfoil Theory 116 3.9 General Thin Airfoil Theory 129 3.10 Theodorsen Condition for General Thin Airfoil Theory 134 Bibliography 135 4 FiniteWing Theory 137 4.1 Introduction 137 4.2 Fundamental Laws of Vortex Motion 137 4.3 Helmholtz's Theorems of Vortex Motion 138 4.4 The Bound Vortex Element 140 4.5 Starting Vortex Element 140 4.6 Trailing Vortex Element 141 4.7 Horse Shoe Vortex 142 4.8 The Biot-Savart Law 142 4.9 Theory for a Finite Wing 146 4.10 Consequence of Downwash: Induced Drag 147 4.11 Simple Symmetric Loading: Elliptic Distribution 149 4.12 General Loading on a Wing 154 4.13 Asymmetric Loading: Rolling and Yawing Moment 157 4.14 Simplified Horse Shoe Vortex 161 4.15 Applications of Simplified Horse Shoe Vortex System 162 4.16 Prandtl's Lifting Line Equation or the Monoplane Equation 167 Bibliography 169 5 Panel Methods 171 5.1 Introduction 171 5.2 Line Source Distribution 172 5.3 Panel Method due to Hess and Smith 176 5.4 Some Typical Results 183 Bibliography 188 6 Lifting Surface, Slender Wing and Low Aspect RatioWing Theories 189 6.1 Introduction 189 6.2 Green's Theorems and Their Applications to Potential Flows 190 6.3 Irrotational External Flow Field due to a Lifting Surface 192 6.4 Slender Wing Theory 201 6.5 Spanwise Loading 205 6.6 Lift on Delta or TriangularWing 206 6.7 Vortex Breakdown 214 6.8 Slender Body Theory 218 Bibliography 221 7 Boundary Layer Theory 223 7.1 Introduction 223 7.2 Regular and Singular Perturbation Problems in Fluid Flows 224 7.3 Boundary Layer Equations 225 7.4 Boundary Layer Thicknesses 230 7.5 Momentum Integral Equation 233 7.6 Validity of Boundary Layer Equation and Separation 235 7.7 Solution of Boundary Layer Equation 237 7.8 Similarity Analysis 238 7.9 Use of Boundary Layer Equation in Aerodynamics 252 Bibliography 258 8 Computational Aerodynamics 259 8.1 Introduction 259 8.2 A Model Dynamical Equation 260 8.3 Space--Time Resolution of Flows 263 Methods 265 8.4 An Improved Orthogonal Grid Generation Method for Aerofoil 275 8.5 Orthogonal Grid Generation 279 8.6 Orthogonal Grid Generation for an Aerofoil with Roughness Elements 284 8.7 Solution of Navier--Stokes Equation for Flow Past AG24 Aerofoil 287 Bibliography 291 9 Instability and Transition in Aerodynamics 295 9.1 Introduction 295 9.2 Temporal and Spatial Instability 298 9.3 Parallel Flow Approximation and Inviscid Instability Theorems 299 9.4 Viscous Instability of Parallel Flows 301 9.5 Instability Analysis from the Solution of the Orr--Sommerfeld Equation 304 9.6 Transition in Three-Dimensional Flows 318 9.7 Infinite Swept Wing Flow 320 9.8 Attachment Line Flow 321 9.9 Boundary Layer Equations in the Transformed Plane 322 9.10 Simplification of Boundary Layer Equations in the Transformed Plane 324 9.11 Instability of Three-Dimensional Flows 325 9.12 Linear Viscous Stability Theory for Three-Dimensional Flows 328 9.13 Experimental Evidence of Instability on Swept Wings 332 9.14 Infinite Swept Wing Boundary Layer 334 9.15 Stability of the Falkner--Skan--Cooke Profile 337 9.16 StationaryWaves over Swept Geometries 340 9.17 Empirical Transition Prediction Method for Three-Dimensional Flows 340 Bibliography 343 10 Drag Reduction: Analysis and Design of Airfoils 347 10.1 Introduction 347 10.2 Laminar Flow Airfoils 350 10.3 Pressure Recovery of Some Low Drag Airfoils 358 10.4 Flap Operation of Airfoils for NLF 361 10.5 Effects of Roughness and Fixing Transition 362 10.6 Effects of Vortex Generator or Boundary Layer Re-Energizer 364 10.7 Section Characteristics of Various Profiles 364 10.8 A High Speed NLF Aerofoil 365 10.9 Direct Simulation of Bypass Transitional Flow Past an Airfoil 369 Bibliography 378 11 Direct Numerical Simulation of 2D Transonic Flows around Airfoils 381 11.1 Introduction 381 11.2 Governing Equations and Boundary Conditions 382 11.3 Numerical Procedure 384 11.4 Some Typical Results 387 Bibliography 406 12 Low Reynolds Number Aerodynamics 409 12.1 Introduction 409 12.2 Micro-air Vehicle Aerodynamics 412 12.3 Governing Equations in Inertial and Noninertial Frames 413 12.4 Flow Past an AG24 Airfoil at Low Reynolds Numbers 425 Bibliography 442 13 High Lift Devices and Flow Control 445 13.1 Introduction 445 13.2 Passive Devices: Multi-Element Airfoils with Slats and Flaps 449 13.3 Flow Control by Plasma Actuation: High Lift Device and Drag Reduction 465 13.4 Governing Equations for Plasma 468 13.5 Governing Fluid Dynamic Equations 475 13.6 Results and Discussions 476 Bibliography 484 Index 487