The aerodynamics of aircraft at high angles of attack is a subject which is being pursued diligently, because the modern agile fighter aircraft and many of the current generation of missiles must perform well at very high incidence, near and beyond stall. However, a comprehensive presentation of the methods and results applicable to the studies of the complex aerodynamics at high angle of attack has not been covered in monographs or textbooks. This book is not the usual textbook in that it goes beyond just presenting the basic theoretical and experimental know-how, since it contains reference material to practical calculation methods and technical and experimental results which can be useful to the practicing aerospace engineers and scientists. It can certainly be used as a text and reference book for graduate courses on subjects related to high angles of attack aerodynamics and for topics related to three-dimensional separation in viscous flow courses. In addition, the book is addressed to the aerodynamicist interested in a comprehensive reference to methods of analysis and computations of high angle of attack flow phenomena and is written for the aerospace scientist and engineer who is familiar with the basic concepts of viscous and inviscid flows and with computational methods used in fluid dynamics.

Table of Contents:
1 Introduction.- 2 Description of Flows at High Angles of Attack.- 2.1. The Finite Lifting Wing of Medium and High AR at Low Subsonic Speeds.- 2.2. The Low AR Rectangular Wing at Low Subsonic Speeds.- 2.3. The Slender Delta Type Wings.- 2.3.1. Sharp Edges Delta Wings at Low Subsonic Speeds.- 2.3.2. Spiral Type Separations on Delta Wings at Very High Angles of Attack at Low Speeds.- 2.3.3. Slender Delta Wings in Supersonic Flows.- 2.4. The Flow Over Elongated Slender Bodies.- 2.4.1. The Symmetric Vortex Flows over Slender Bodies in Subsonic Flows.- 2.4.2. The Asymmetric Vortex Flow over Slender Bodies in Subsonic Flow.- 2.4.3. Symmetric and Asymmetric Vortex Flows over Elongated Bodies in Supersonic Flows.- 2.5. Aircraft Type Configurations.- 2.5.1. Aircraft Aerodynamics Characteristics.- 2.5.1.1. Effects of Symmetrical Vortex Flows at Subsonic Speeds.- 2.5.1.2. Effects of Asymmetric Vortex Flows at Zero Sideslip in Subsonic Flow.- 2.5.1.3. Effect of LEX at High Angles of Attack at Subsonic Flow.- 2.5.1.4. Closed Coupled Canard-Wing Configurations at High Angles of Attack at Subsonic Flows.- 2.5.1.5. Effect of Sideslip at Subsonic Speeds.- 2.6. Vortex Breakdown.- 2.7. Nonsteady Aerodynamics at High Angles of Attack on Slender Configurations.- 2.8. Effect of Separation at High Angles of Attack in Hypersonic Flows.- References.- 3 The Topology of Separating and Reattaching Vortical Flows.- 3.1. Equations for Vortical Flows.- 3.1.1. The Vorticity Transport Equation.- 3.1.2. The Biot-Savart Law.- 3.2. Topological Concepts for the Analysis of Vortical Flows.- 3.2.1. Attached and Separated Flows.- 3.2.2. The Equations for Surface Stream Lines and Surface Vortex Lines of Three-Dimensional Flows.- 3.2.3. The Characteristics of the Singular Point.- 3.2.4. Skin Friction Lines Near Separation in Three-Dimensional Flows.- 3.2.5. Rules of Topology Applied to Three-Dimensional Separated Flows.- References.- 4 Linear Aerodynamics of Wings and Bodies.- 4.1. Equations for Potential Subsonic Flows.- 4.2. Equations for the Lifting Wing at Low Speeds.- 4.3. The Linear Panel Methods for the Calculation of the Subsonic Aerodynamic Coefficients for Wings and Bodies.- 4.3.1. The Multhop Method.- 4.3.2. The Surface-Source Distribution Method.- 4.3.3. The Linear Vortex Lattice Method.- 4.4. Low and High Order Linear Panel Methods for Subsonic and Supersonic Flows.- 4.4.1. Low Order Method - USSAERO.- 4.4.2. Low Order Method - Supersonic Linear VLM-VORLAX.- 4.4.3. High Order Method - PAN AIR.- 4.5. Comparison of the Various Panel Methods.- References.- 5 Vortex Flows and the Rolled Up Vortex Wake.- 5.1. Vortex Core of the Rolled Up Wake.- 5.2. The Rolled Up Tip Vortices.- 5.3. The Rolling-Up of the Vortex Wake Behind Wings.- 5.3.1. The Rolling-Up of the Vortex Lines of the Zero Thickness Vortex Sheet.- 5.3.2. The Rolling-Up of a Finite Thickness Vortex Sheet.- 5.4. The "Bursting"1 Introduction.- 2 Description of Flows at High Angles of Attack.- 2.1. The Finite Lifting Wing of Medium and High AR at Low Subsonic Speeds.- 2.2. The Low AR Rectangular Wing at Low Subsonic Speeds.- 2.3. The Slender Delta Type Wings.- 2.3.1. Sharp Edges Delta Wings at Low Subsonic Speeds.- 2.3.2. Spiral Type Separations on Delta Wings at Very High Angles of Attack at Low Speeds.- 2.3.3. Slender Delta Wings in Supersonic Flows.- 2.4. The Flow Over Elongated Slender Bodies.- 2.4.1. The Symmetric Vortex Flows over Slender Bodies in Subsonic Flows.- 2.4.2. The Asymmetric Vortex Flow over Slender Bodies in Subsonic Flow.- 2.4.3. Symmetric and Asymmetric Vortex Flows over Elongated Bodies in Supersonic Flows.- 2.5. Aircraft Type Configurations.- 2.5.1. Aircraft Aerodynamics Characteristics.- 2.5.1.1. Effects of Symmetrical Vortex Flows at Subsonic Speeds.- 2.5.1.2. Effects of Asymmetric Vortex Flows at Zero Sideslip in Subsonic Flow.- 2.5.1.3. Effect of LEX at High Angles of Attack at Subsonic Flow.- 2.5.1.4. Closed Coupled Canard-Wing Configurations at High Angles of Attack at Subsonic Flows.- 2.5.1.5. Effect of Sideslip at Subsonic Speeds.- 2.6. Vortex Breakdown.- 2.7. Nonsteady Aerodynamics at High Angles of Attack on Slender Configurations.- 2.8. Effect of Separation at High Angles of Attack in Hypersonic Flows.- References.- 3 The Topology of Separating and Reattaching Vortical Flows.- 3.1. Equations for Vortical Flows.- 3.1.1. The Vorticity Transport Equation.- 3.1.2. The Biot-Savart Law.- 3.2. Topological Concepts for the Analysis of Vortical Flows.- 3.2.1. Attached and Separated Flows.- 3.2.2. The Equations for Surface Stream Lines and Surface Vortex Lines of Three-Dimensional Flows.- 3.2.3. The Characteristics of the Singular Point.- 3.2.4. Skin Friction Lines Near Separation in Three-Dimensional Flows.- 3.2.5. Rules of Topology Applied to Three-Dimensional Separated Flows.- References.- 4 Linear Aerodynamics of Wings and Bodies.- 4.1. Equations for Potential Subsonic Flows.- 4.2. Equations for the Lifting Wing at Low Speeds.- 4.3. The Linear Panel Methods for the Calculation of the Subsonic Aerodynamic Coefficients for Wings and Bodies.- 4.3.1. The Multhop Method.- 4.3.2. The Surface-Source Distribution Method.- 4.3.3. The Linear Vortex Lattice Method.- 4.4. Low and High Order Linear Panel Methods for Subsonic and Supersonic Flows.- 4.4.1. Low Order Method - USSAERO.- 4.4.2. Low Order Method - Supersonic Linear VLM-VORLAX.- 4.4.3. High Order Method - PAN AIR.- 4.5. Comparison of the Various Panel Methods.- References.- 5 Vortex Flows and the Rolled Up Vortex Wake.- 5.1. Vortex Core of the Rolled Up Wake.- 5.2. The Rolled Up Tip Vortices.- 5.3. The Rolling-Up of the Vortex Wake Behind Wings.- 5.3.1. The Rolling-Up of the Vortex Lines of the Zero Thickness Vortex Sheet.- 5.3.2. The Rolling-Up of a Finite Thickness Vortex Sheet.- 5.4. The "Bursting" of the Rolled Up Vortices.- References.- 6 Nonlinear Aerodynamics of Wings and Bodies at High Angles of Attack.- 6.1. Analytical and Semi-Empirical Methods for Calculations of the Nonlinear Aerodynamic Characteristics.- 6.1.1. Cross Flow Model.- 6.1.2. Nonlinear Lifting Surface Theory for Low AR Wings.- 6.1.3. Leading Edge Vortex Models for Slender Delta Wing.- 6.1.3.1. Concentrated Line Vortices with Plane Feeding Sheet.- 6.1.3.2. The Spiral Vortex Sheet.- 6.1.4. Leading-Edge Suction Analogy.- 6.1.5. Semi-Empirical Correlation for the Nonlinear Lift of Low AR Wings.- References.- 7 The Nonlinear Panel Methods for Aircraft and Missile Configurations at High Angles of Attack.- 7.1. The Nonlinear Vortex Lattice Method (NLVLM) for Subsonic Flows.- 7.1.1. Mathematical Formulation of the NLVLM.- 7.1.2. The Nonlinear Calculation Method for Lifting Surfaces.- 7.1.2.1. Calculations of the Source and Vortex Strengths Distributions and the Trajectories of the Free Vortices.- 7.1.2.2. Calculations of the Pressure Distribution and Aerodynamic Coefficients.- 7.1.2.3. Schemes for Division of Delta Wing Surfaces to Panels.- 7.1.2.4. The Relative Merit of the Various Panelling Schemes.- 7.1.3. Results of the NLVLM Calculations for Subsonic Flows.- 7.1.3.1. Rectangular and Trapezoidal Wings with or without Sweep.- 7.1.3.1.1. High Aspect Ratio Wings.- 7.1.3.1.2. Low Aspect Ratio Rectangular Wings.- 7.1.3.2. Delta Wings in Subsonic Flows.- 7.1.3.3. Multi Lifting Surfaces Configurations in Subsonic Flows.- 7.1.3.3.1. The Wing-Canard Configuration at Subsonic Speed.- 7.1.3.3.2. The Strake-Delta Wing Configuration at Subsonic Speed.- 7.1.4. Calculations of Subsonic Flows over Bodies at High Angles of Attack.- 7.1.4.1. The Position of Separation on Elongated Bodies.- 7.1.4.2. Calculation of the Aerodynamic Characterisitics for Symmetric and Asymmetric Vortex Separation over Elongated Bodies.- 7.1.4.2.1. Symmetric Vortex Separation.- 7.1.4.2.2. Asymmetric Vortex Separation.- 7.2. The Free Vortex Sheet (FVS) Method for Subsonic Flows.- 7.2.1. The Theoretical Model.- 7.2.1.1. Method of Computation.- 7.2.2. Results of the FVS Method Calculations.- 7.2.2.1. Delta Wings.- 7.3. The NLVLM for Supersonic Flow.- 7.3.1. Method of Calculations.- References.- 8 Solutions of the Euler Equations for Flows over Configurations at High Angles of Attack.- 8.1. The Euler Equations.- 8.2. Numerical Methods of Solution of the Euler Equations.- 8.2.1. Methods for Grid Generation.- 8.2.1.1. Grid Topology.- 8.2.1.2. Body Aligned Grid Systems.- 8.2.2. Finite Volume Methods.- 8.2.2.1. The Finite Volume Method of Jameson.- 8.2.2.1.1. Artificial Dissipation.- 8.2.2.1.2. Time Stepping.- 8.2.2.1.3. Methods of Accelerating Convergence to Steady State.- 8.2.2.1.4. Boundary Conditions.- 8.2.2.1.5. Mesh Generation Around Aircraft Configuration.- 8.2.2.2. The Finite Volume Method of Rizzi and Eriksson.- 8.2.2.2.1. Grid Generation.- 8.2.2.2.2. Numerical Procedure.- 8.2.2.2.3. The Trailing Edge Vorticity Generation - Kutta Condition.- 8.2.3. Finite Difference Methods.- 8.2.3.1. The Governing Equations.- 8.2.3.2. Numerical Solution Methods.- 8.2.3.3. Mesh Generation and Boundary Conditions.- 8.2.4. Finite Element Methods.- 8.2.4.1. Governing Equations.- 8.2.4.1.1. Artificial Dissipation Model.- 8.2.4.2. Mesh Generation.- 8.2.5. Multigrid Calculations with Cartesian Grids and Local Refinements.- 8.2.5.1. Numerical Scheme.- 8.2.5.2. Boundary Conditions.- 8.2.5.3. Computer Code.- 8.2.6. Results of Euler Computations on Three-Dimensional Configurations at High Angles of Attack.- 8.2.6.1. Delta Wings with Sharp and Rounded Edges.- 8.2.6.1.1. Calculation of Vortex Structure over Delta Wing.- 8.2.6.2. Strake-Wing-Body Configuration.- 8.2.6.3. Euler Solution Over Aircraft Missile Configuration.- References.- 9 Solutions to the Navier-Stokes Equations for Flows over Configurations at High Angles of Attack.- 9.1. Formulation of the Navier-Stokes Equations.- 9.1.1. The Navier-Stokes Equations in Cartesian Coordinates.- 9.1.2. Nondimensional Navier-Stokes Equations in Generalized Curvilinear Coordinates.- 9.1.3. Thin-Layer Approximation.- 9.1.4. The Parabolized Navier-Stokes Equations.- 9.1.5. The Reynolds-Averaged Equations and Turbulence Models.- 9.2. Numerical Methods for Solutions of the Navier-Stokes Equations.- 9.2.1. Solution of the Compressible Navier-Stokes Equations by a Time-Dependent Method.- 9.3. Method of solution of the Thin-Layer Equations.- 9.4. Grid Topology, Boundary and Initial Conditions.- 9.5. Solutions of the Navier-Stokes Equations for Flows over Three-Dimensional Configurations at High Angles of Attack.- 9.5.1. Navier-Stokes Solutions for Flows over Elongated Axisymmetric Bodies at High Angles of Attack.- 9.5.1.1. Flow on Prolate Spheroid and Ellipsoid in Subsonic Flow.- 9.5.1.2. Flow on Pointed Axisymmetric Bodies.- 9.5.1.2.1. Subsonic Flow Solutions.- 9.5.1.2.2. Supersonic Flow Solutions.- 9.5.1.3. Flow over Delta and Strake-Delta Wings.- 9.5.1.3.1. Subsonic Flow Calculations.- 9.5.1.3.2. Supersonic flow calculations.- 9.5.1.4. Calculation of Vortex Breakdown on Delta Type Wings.- 9.5.1.5. Flow over Canard-Wing-Body Configuration.- 9.5.1.6. Calculations on Aircraft Configurations.- References.- Credits.- Author Index.