High Angle of Attack Aerodynamics

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.