Three-dimensional Separated Flow Topology Critical Points, Separation Lines and Vortical Structures

This book develops concepts and a methodology for a rational description of the organization of three-dimensional flows considering, in particular, the case where the flow is the place of separations. The descriptive analysis based on the critical point theory of Poincaré develops conventional but rather unfamiliar considerations from aerodynamicists, who face the understanding of complex flows including multiple separation lines and vortices. These problems concern industrial sectors where aerodynamics plays a key role, such as aerospace, ground vehicles, buildings, etc.

Contents

1. Skin Friction Lines Pattern and Critical Points.
2. Separation Streamsurfaces and Vortex Structures.
3. Separated Flow on a Body.
4. Vortex Wake of Wings and Slender Bodies.
5. Separation Induced by an Obstacle or a Blunt Body.
6. Reconsideration of the Two-Dimensional Separation.
7. Concluding Remarks.

About the Authors

Jean Délery is a Supaero (French National Higher School of Aeronautics and Space) engineer who has worked at Onera (French national aerospace research center) since 1964. He has participated in several major French and European aerospace programs, is the author of many scientific publications, and has occupied various teaching positions particularly at Supaero, the University of Versailles-Saint-Quentin, Ecole polytechnique in France and ?La Sapienza? University in Rome, Italy. He is currently emeritus adviser at Onera.

INTRODUCTION ix

CHAPTER 1. SKIN FRICTION LINES PATTERN AND CRITICAL POINTS 1

1.1. Basic properties of the three-dimensional boundary layer 1

1.2. Skin friction lines and surface flow pattern 5

1.3. Critical points of the skin friction line pattern 8

1.3.1. General solution and the eigenvalue problem 8

1.3.2. The different critical points 14

1.4. Critical points of the wall vorticity lines 24

CHAPTER 2. SEPARATION STREAMSURFACES AND VORTEX STRUCTURES 27

2.1. Generalization to the flow field and three-dimensional critical points 27

2.2. Separation and attachment lines 32

2.3. Streamsurfaces of separation and attachment 36

2.4. Vortical structures 40

2.5. Some properties of a vortical structure 42

CHAPTER 3. SEPARATED FLOW ON A BODY 47

3.1. Basic rules and definitions 47

3.2. General definition: the basic separated structures 49

3.3. Field associated with a separation with one saddle point and three nodes: the horseshoe vortex 56

3.4. Field associated with a separation with one point and two foci: the tornado-like vortex 62

CHAPTER 4. VORTEX WAKE OF WINGS AND SLENDER BODIES 69

4.1. Vortical structures over a delta wing 69

4.2. Vortical flow over a slender body 77

4.3. Vortex wake of a classical wing 82

4.3.1. Topological description 82

4.3.2. A scenario for the origin of vortices on a wing 88

CHAPTER 5. SEPARATION INDUCED BY AN OBSTACLE OR A BLUNT BODY 91

5.1. Separation in front of an obstacle 91

5.2. Flow induced by an obstacle of finite height or protuberance 97

5.4. The flow past an automobile 110

5.4.1. The surface flow pattern 110

5.4.2. Separation surfaces 116

CHAPTER 6. RECONSIDERATION OF THE TWO-DIMENSIONAL SEPARATION 121

6.1. Some definitions: a reminder 121

6.2. Two-dimensional separation 123

6.3. Special critical points 123

6.4. Three-dimensional structure of a two-dimensional separated flow 131

6.5. Axisymmetric afterbody 136

CHAPTER 7. CONCLUDING REMARKS 143

BIBLIOGRAPHY 147

LIST OF SYMBOLS 151

INDEX 153

Jean Délery is an engineer and?currently Emeritus adviser at Onera, Chalais-Meudon, France.