ISBN: 3-540-66277-4
TITLE: Aerodynamics of a Lifting System in Extreme Ground Effect
AUTHOR: Rozhdestvensky, Kirill V.
TOC:

1. Introduction 1
1.1 Some Definitions 1
1.2 A Brief Reference on Wing-in-Ground-Effect Craft 1
1.3 Asymptotic and Numerical Methods in the Aerodynamics of the Wings-in-Ground Effect 4
1.3.1 On the Mathematical Modelling of the Aerodynamics of a Lifting System in the Ground Effect 4
1.3.2 Asymptotics for Ground-Effect Lifting Flow Problems 7
1.3.3 Numerics: Euler Codes for Steady Flows 17
1.3.4 Numerics: Euler Codes for Unsteady Flows 19
1.3.5 Numerics: Viscous Flows, NavierStokes Solvers 20
2. Problem Formulation for the Flow Past a Lifting Surface in Proximity to a Solid Boundary 23
2.1 Formulation of the Three-Dimensional Unsteady Flow Problem 23
2.2 Flow Below the Lifting System and Its Wake (Channel Flow) 25
2.3 Flow Above the Lifting System and Its Wake 28
2.4 Flows in the Vicinity of Edges 29
2.5 Matching of Flow Descriptions in Different Regions 36
2.6 A Uniformly Valid Flow Description and Aerodynamic Coefficients 43
2.7 A Limiting Mathematical Model of the Extreme Ground Effect 45
3. The Linear Theory of a Lifting System Moving Close to the Ground 47
3.1 Features of a Linearized Formulation and an Algorithm of the Solution 47
3.2 Two-Dimensional Steady Flow Past a Slightly Curved Foil 51
3.3 A Wing of Small Aspect Ratio in a Steady Linearized Flow 58
3.4 Steady Flow Past a Wing of Arbitrary Aspect Ratio 63
3.5 Harmonic Oscillations of a Thin Foil in a Two-Dimensional Flow 73
3.6 Three-Dimensional Unsteady Linearized Lifting Flows 79
4. Nonlinear Flow Problems for a Lifting System in the Extreme Ground Effect 85
4.1 A Curved Thick Foil in a Two-Dimensional Ground Effect 85
4.2 A One-Dimensional Flow Model for a Flying Wing with Endplates 95
4.3 Steady-State Solutions for Flow Past a Wing with Endplates 101
4.4 Unsteady Flow Solutions for a Wing with Endplates 112
4.4.1 A Nonlinear Unsteady Solution for Small Gaps Under Endplates 112
4.4.2 Unsteady Perturbation of a Steady Flow 114
5. Compressible Flow Past a Wing in the Extreme Ground Effect 121
5.1 Channel Flow in a Compressible Fluid 121
5.2 Steady Linearized Compressible Flow Past a Wing of Finite Span 124
5.3 Compressible Linearized Unsteady Flow Past a Wing of Finite Span 127
5.4 Nonlinear Steady Compressible Flow Problem for a Foil 133
6. The Influence of Endplates, Flaps, and Slots 137
6.1 An Estimate of the Influence of Endplates 137
6.2 A Lifting System with a Jet Flap in the Extreme Ground Effect 146
6.3 Nonlinear Steady Flow Problem for a Foil with a Jet Flap 155
6.4 Steady Flow Past a Jet-Flapped Wing of Finite Span 158
6.5 A Wing with a Rotating Flap 166
6.6 Slotted Wings in the Ground Effect 171
7. The Aerodynamics of a Lifting System Near Curved Ground 183
7.1 The Influence of Waves on the Aerodynamics of a Lifting Surface 183
7.2 An Estimate of the Acceleration of a Lifting Surface in Flight over a Wavy Wall 200
7.3 The Aerodynamic Response of a Lifting System to Aperiodic Perturbations 205
Appendix: The Motion of a Wing Over a Wavy Wall at an Arbitrary Course Angle: Derivation of the Unsteady Lift and the Moment Coefficients 214
8. Schematized Flow Models for a Power-Augmented Lifting System 221
8.1 Local Flow Problems for Analysis of PAR Mode 223
8.1.1 Reentrant Jet Flow Near the Leading Edge 224
8.1.2 Reentrant Jet Flow Near the Leading Edge with a Deflected Tip 227
8.1.3 Local Separated Flow Past a Flap (Endplate) 229
8.2 Unseparated Flows Near Leading and Trailing Edges 231
8.2.1 Unseparated Coanda Flow Past a Leading Edge 231
8.2.2 Coanda Flow of Finite Width Past a Deflected Leading Edge 234
8.2.3 The Model of Flow Past a Leading Edge with a Winglet 237
8.2.4 Unseparated Flow Near a Trailing Edge with a Flap 239
8.2.5 Flow of Infinite Width Past a Trailing Edge with a Flap 241
8.3 Envelopes of the Efficiency of Power Augmentation for a Scheme with a Reentrant Jet 244
8.3.1 Estimate of the Efficiency and the Thrust Recovery of PAR Based on a Reentrant Jet Scheme 245
8.3.2 Margins of Efficiency of PAR Based on a Reentrant Jet Scheme 250
8.4 A Discussion of a Mathematical Model of PAR with the Coanda Effect 257
9. The Aerodynamic Efficiency of a Wing in the Extreme Ground Effect 263
9.1 Optimal Wing-in-Ground Effect 263
9.2 The Lift-to-Drag Ratio of a Wing in the Ground Effect 269
10. Integral Formulations for Lifting Surfaces in the Extreme Ground Effect 281
10.1 A Slightly Curved Foil in a Two-Dimensional Ground Effect 281
10.2 A Foil with a Jet Flap in Proximity to the Ground 283
10.3 A Wing of Small Aspect Ratio 284
10.4 Lifting Line(s) in Close Proximity to the Ground 285
10.4.1 A Single Lifting Line in the Extreme Ground Effect 285
10.4.2 A Comment on "Span-Dominated" and "Chord-Dominated" Extreme Ground Effects 288
10.4.3 A Tandem of Lifting Lines in the Extreme Ground Effect 289
10.5 Quadruplication of the Integral Equation for a Wing of Finite Span 292
11. Equations and the Stability of Motion of a Lifting System in the Extreme Ground Effect 295
11.1 Linear Equations of Longitudinal Dynamics 296
11.1.1 The Quartic Characteristic Equation 297
11.1.2 The Quintic Characteristic Equation 299
11.2 The Equations of Motion in the Extreme Ground Effect 300
11.2.1 Order Estimates and Assumptions 300
11.2.2 Asymptotic Form of the Equations of Motion for h -> 0 301
11.3 Static Stability and "Binding" Near the Ground 302
11.3.1 A Single Wing in the Extreme Ground Effect 306
11.3.2 A Tandem in the Two-Dimensional Extreme Ground Effect 311
11.3.3 The Degree of Binding of the Vehicle to the Ground 315
Appendix: Formulas for the Coefficients B_i(i = 1 5) 318
12. Simple Mathematical Models of Elastic and Flexible Wings in the Extreme Ground Effect 319
12.1 Evaluation of the Speed of Flutter of a Foil Close to the Ground 320
12.2 An Aeroelastic Wing in the Extreme Ground Effect 323
12.3 A Flexible Wing  a Simple Theory of a PARAWIG 328
Bibliography 337
Index 349
END
