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Description
(Text)
Having worked on problems of three-dimensional boundary-layer flow for more than a decade, the authors decided to publish some of their results and ideas as a book. They believe this is worthwhile to do in spite of the availability of other books on boundary-layer theory. These books have their emphasis mainly on two-dimensional flow, on the modeling of turbulent flow, or on prediction techniques. The present book, on the other hand, is dedicated to the descrip tion of three-dimensional shear flow past realistic configurations and to the provision of formulations for prediction methods. To this end several sets of governing equations for the treatment of high-Reynolds number viscous flows are being discussed, together with approximations of the geometry of general configurations. Thus the book , which gives a uniform representation of the for mulation of the many problems, and not so much a review of the work done so far at different places, is aimed at the perspective in vestigator of three-dimensional viscous-flow problems. The reader should not allow himself to ‾e scared off'by the use of tensorial concepts and of the index notation, both not too familiar in classic fluid mechanics. The authors made the experience that the use of these concepts alleviates much the work on realistic flow problems. In the book they have emphasized the use of these concepts and not their mathematical proofs.
(Table of content)
1. Introduction.- 2. First-Order Boundary-Layer Equations.- 3. Boundary-Layer Parameters.- 4. Stagnation-Point Solution.- 5. Quasi-Two-Dimensional Boundary Layers.- 6. Initial Conditions for the Prediction of Boundary Layers on Wings and Fuselages.- 7. Higher-Order Boundary-Layer Equations.- 8. Thin-Layer Approximations of the Navier-Stokes Equations.- 9. On the Influence of Surface Curvature.- 10. Samples of Surface-Oriented Coordinate Systems.- 11.Conditions of Compatibility at the Body Surface.- 12. Local Topology of Three-Dimensional Separation and Attachment Lines.- 13. Similarity-Type Transformation of Boundary-Layer Equations in Contravariant Form.- Appendix A: Basic Geometrical Relations.- A. 1 General Coordinates.- A.2 Surface-Oriented Locally Monoclinic Coordinates.- A. 3 Covariant Base Vectors of Surface-Oriented Coordinate Systems.- A.4 Transformation of a Vector.- A.5 Partial Derivatives.- A.6 The Covariant Metric Tensor for Surface-Oriented Coordinates..- A.8 The Two Principal Curvatures of the Surface.- A.9 Directions of the Two Principal Curvatures of the Surface.- A.13 Christoffel Symbols and Metric Factors.- A.14 Shifters.- Appendix B: Series Expansion of Vector Quantities in General Coordinates.- Appendix C: The Vorticity Vector.- Appendix D: Dimensions and Boundary-Layer Stretching.- Appendix E. Calculation of Streamlines, Surface and Volume Element.- List of Symbols.- References.
Contents
1. Introduction.- 2. First-Order Boundary-Layer Equations.- 3. Boundary-Layer Parameters.- 4. Stagnation-Point Solution.- 5. Quasi-Two-Dimensional Boundary Layers.- 6. Initial Conditions for the Prediction of Boundary Layers on Wings and Fuselages.- 7. Higher-Order Boundary-Layer Equations.- 8. Thin-Layer Approximations of the Navier-Stokes Equations.- 9. On the Influence of Surface Curvature.- 10. Samples of Surface-Oriented Coordinate Systems.- 11.Conditions of Compatibility at the Body Surface.- 12. Local Topology of Three-Dimensional Separation and Attachment Lines.- 13. Similarity-Type Transformation of Boundary-Layer Equations in Contravariant Form.- Appendix A: Basic Geometrical Relations.- A. 1 General Coordinates.- A.2 Surface-Oriented Locally Monoclinic Coordinates.- A. 3 Covariant Base Vectors of Surface-Oriented Coordinate Systems.- A.4 Transformation of a Vector.- A.5 Partial Derivatives.- A.6 The Covariant Metric Tensor for Surface-Oriented Coordinates..- A.8 The Two Principal Curvatures of the Surface.- A.9 Directions of the Two Principal Curvatures of the Surface.- A.13 Christoffel Symbols and Metric Factors.- A.14 Shifters.- Appendix B: Series Expansion of Vector Quantities in General Coordinates.- Appendix C: The Vorticity Vector.- Appendix D: Dimensions and Boundary-Layer Stretching.- Appendix E. Calculation of Streamlines, Surface and Volume Element.- List of Symbols.- References.
