1 Introduction ............................................... 1
1.1 Phenomenological Models of Attached Viscous Flow ........... 2
1.2 Three Kinds of Interaction and the Locality Principle ...... 4
1.3 Short Survey of the Development of the Field ............... 7
1.4 Scope and Content of the Book ............................. 15
References ................................................ 18
2 Properties of Three-Dimensional Attached Viscous Flow ..... 23
2.1 Characterization of the Flow .............................. 23
2.2 Coordinate Systems and Velocity Profiles .................. 29
2.2.1 Cartesian Coordinates .............................. 30
2.2.2 External Inviscid Streamline-Oriented
Coordinates ........................................ 30
2.2.3 Surface-Oriented Non-Orthogonal Curvilinear
Coordinates ........................................ 32
2.3 Influencing Attached Viscous Flow and Flow Three-
Dimensionality ............................................ 35
2.3.1 Surface Suction .................................... 36
2.3.2 Surface-Normal Injection (Blowing) ................. 38
2.3.3 Thermal Surface Effects ............................ 40
2.4 Problems .................................................. 47
References ................................................ 48
3 Equations of Motion ....................................... 51
3.1 Material and Transport Properties of Air .................. 51
3.1.1 Equation of State and Specific Heat at Constant
Pressure ........................................... 51
3.1.2 Transport Properties ............................... 52
3.2 Equations of Motion for Steady Laminar Flow in Cartesian
Coordinates ............................................... 57
3.2.1 Transport of Mass: The Continuity Equation ......... 57
3.2.2 Transport of Momentum: The Navier-Stokes
Equations .......................................... 57
3.2.3 Transport of Energy: The Energy Equation ........... 59
3.3 Initial and Boundary Conditions ........................... 59
3.4 Similarity Parameters, Boundary-Layer Thicknesses ......... 61
3.3 Equations of Motion for Steady Turbulent Flow ............. 67
3.6 Problems .................................................. 72
References ................................................ 73
4 Boundary-Layer Equations for Three-Dimensional Flow ....... 75
4.1 Preliminary Notes ......................................... 75
4.1.1 Coordinate Convention .............................. 75
4.1.2 The Boundary-Layer Criteria ........................ 75
4.2 First-Order Boundary-Layer Equations for Steady Laminar
Flow ...................................................... 76
4.3 Boundary-Layer Equations for Steady Turbulent Flow ........ 80
4.3.1 Averaged Navier-Stokes Equations ................... 80
4.3.2 Scales ............................................. 81
4.3.3 Structure of the Flow .............................. 82
4.3.4 Boundary-Layer Equations ........................... 86
4.4 Characteristic Properties of Attached Viscous Flow ........ 87
4.5 Wall Compatibility Conditions ............................. 91
4.6 Problems .................................................. 95
References ................................................ 97
5 Boundary-Layer Integral Parameters ........................ 99
5.1 General Considerations .................................... 99
5.2 Mass-Flow Displacement Thickness and Equivalent Inviscid
Source Distribution ...................................... 100
5.3 Momentum-Flow Displacement Thickness ..................... 101
5.4 Energy-Flow Displacement Thickness ....................... 102
5.5 Problems ................................................. 102
References ............................................... 104
6 Viscous Flow and Inviscid Flow—Connections and
Interactions ............................................. 107
6.1 Introductory Remarks—The Displacement Effect ............. 107
6.2 Interaction Theory ....................................... 110
6.2.1 About the Beginnings .............................. 110
6.2.2 Weak Interaction .................................. 111
6.2.3 Strong Interaction ................................ 116
6.3 Viscous-Inviscid Interaction Methods ..................... 117
6.4 Examples ................................................. 120
6.4.1 Second-Order Boundary-Layer Effects ............... 120
6.4.2 Viscous-Inviscid Interaction Effects .............. 123
6.5 Problems ................................................. 125
References ............................................... 128
7 Topology of Skin-Friction Fields ......................... 131
7.1 Introduction ............................................. 131
7.1.1 General Remarks ................................... 131
7.1.2 The Concept of Limiting Streamlines ............... 132
7.1.3 General Issues of Three-Dimensional Attachment .... 133
7.1.4 General Issues of Three-Dimensional Separation .... 134
7.1.5 Detachment Points and Lines ....................... 136
7.2 Singular Points .......................................... 138
7.2.1 Introduction ...................................... 138
7.2.2 Flow-Field Continuation around a Surface Point .... 139
7.2.3 Singular Points on Body Surfaces .................. 141
7.3 Topological Rules ........................................ 144
7.4 Singular Lines ........................................... 147
7.4.1 Introduction ...................................... 147
7.4.2 Attachment Lines .................................. 150
7.4.3 Separation Lines .................................. 165
7.5 Attachment and Separation of Three-Dimensional Viscous
Flow- More Results and Indicators ........................ 172
7.6 Problems ................................................. 175
References ............................................... 175
8 Quasi-One-Dimensional and Quasi-Two-Dimensional Flows .... 179
8.1 Stagnation Point Flow .................................... 179
8.2 Flow in Symmetry Planes .................................. 183
8.3 The Infinite Swept Wing .................................. 187
8.4 The Locally Infinite Swept Wing .......................... 191
8.5 Initial Data for Infinite-Swept-Wing Solutions ........... 193
8.6 Two-Dimensional and Axisymmetric Flow .................... 195
8.7 The Mangier Effect ....................................... 195
8.8 Problems ................................................. 196
References ............................................... 198
9 Laminar-Turbulent Transition and Turbulence .............. 201
9.1 Laminar-Turbulent Transition—An Introduction ............. 201
9.2 Instability/Transition Phenomena and Criteria ............ 203
9.2.1 Some Basic Observations ........................... 204
9.2.2 Outline of Stability Theory ....................... 207
9.2.3 Inviscid Stability Theory and the Point-of-
Inflection Criterion .............................. 210
9.2.4 The Thermal State of the Surface, Compressible
Flow .............................................. 212
9.3 Real Flight-Vehicle Effects .............................. 213
9.3.1 Attachment-Line Instability ....................... 214
9.3.2 Leading-Edge Contamination ........................ 215
9.3.1 Cross-Flow Instability ............................ 217
9.3.4 Gцrtier Instability ............................... 219
9.3.5 Relaminarization .................................. 220
9.4 Receptivity Issues ....................................... 221
9.4.1 Surface Irregularities and Transition ............. 222
9.4.2 Free-Stream Fluctuations aqd Transition ........... 223
9.5 Prediction of Stability/Instability and Transition ....... 225
9.5.1 Stability/Instability Theory and Methods .......... 226
9.5.2 Transition Models and Criteria .................... 227
9.6 Turbulence Phenomena and Models .......................... 231
9.7 Boundary-Layer Control ................................... 232
9.8 Problems ................................................. 233
References ............................................... 237
10 Illustrating Examples .................................... 245
10.1 The Locality Principle: Flow Past a Helicopter Fuselage
and Past Finite-Span Wings ............................... 246
10.2 Flow Patterns Upstream of and at Trailing Edges of
Lifting Wings with Large Aspect Ratio .................... 251
10.3 Aspects of Skin-Friction Line Topology: Flow Past an
Airplane Configuration ................................... 259
10.4 Extrema of the Thermal State of the Surface: Flow Past
a Blunt Delta Wing ....................................... 273
10.5 The Location of Laminar-Turbulent Transition: Flow Past
an Ellipsoid at Angle of Attack .......................... 278
References ............................................... 284
11 Solutions of the Problems ................................ 287
Appendix A: Equations of Motion in General Formulations ....... 319
A.l Navier-Stokes/RANS Equations in General Coordinates ...... 319
A.2 Boundary-Layer Equations in General Coordinates .......... 321
A.2.1 First-Order Equations in Non-orthogonal
Curvilinear Coordinates ........................... 322
A.2.2 Small Cross-Flow Equations ........................ 325
A.2.3 The Geodesic as Prerequisite for the Plane-of-
Symmetry Flow ..................................... 328
A.2.4 Equations in Contravariant Formulation ............ 329
A.2.5 Higher-Order Equations—The SOBOL Method ........... 332
A.3 A Note on Computation Methods ............................ 332
A.3.1 Navier-Stokes/RANS Methods ........................ 332
A.3.2 Boundary-Layer Methods ............................ 333
A.3.3 Similarity Solutions .............................. 334
References ............................................... 334
Appendix В: Approximate Relations for Boundary-Layer
Properties .................................................... 337
B.l Introduction ............................................. 337
B.2 The Reference-Temperature Concept ........................ 337
B.3 Generalized Reference-Temperature Relations .............. 339
B.3.1 Flap Plate ........................................ 339
B.3.2 Stagnation Point .................................. 343
B.3.3 Attachment-Line at a Swept Cylinder ............... 344
B.4 Virtual Origin of Boundary Layers at Junctions ........... 346
References ............................................... 349
Appendix C: Boundary-Layer Coordinates: Metric Properties,
Transformations, Examples ..................................... 351
C.l Metric Properties of Surface Coordinates ................. 351
C.2 Transformations .......................................... 354
C.3 Example 1: Fuselage Cross-Section Coordinate System ...... 356
C.4 Example 2: Wing Percent-Line Coordinate System ........... 360
References ............................................... 365
Appendix D: Constants, Atmosphere Data, Units, and
Conversions ................................................... 367
D.l Constants and Air Properties ............................. 367
D.2 Atmosphere Data .......................................... 368
D.3 Units and Conversions .................................... 368
References ............................................... 370
Appendix E: Symbols, Abbreviations, and Acronyms .............. 371
E.l Latin Letters ............................................ 371
E.2 Greek Letters ............................................ 373
E.3 Indices .................................................. 374
E.3.1 Upper Indices ..................................... 374
E.3.2 Lower Indices ..................................... 374
E.4 Other Symbols ............................................ 375
E.5 Abbreviations, Acronyms .................................. 375
Permissions ................................................... 377
Name Index .................................................... 379
Subject Index ................................................. 385
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