Topological Analysis Of Computed Three Dimensional Viscous Flow Fields

Viscous flow is treated usually in the frame of boundary-layer theory and as two-dimensional flow. Books on boundary layers give at most the describing equations for three-dimensional boundary layers, and solutions often only for some special cases. This book provides basic principles and theoretical foundations regarding three-dimensional attached viscous flow. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers. This wider scope is necessary in view of the theoretical and practical problems to be mastered in practice. The topics are weak, strong, and global interaction, the locality principle, properties of three-dimensional viscous flow, thermal surface effects, characteristic properties, wall compatibility conditions, connections between inviscid and viscous flow, flow topology, quasi-one- and two-dimensional flows, laminar-turbulent transition and turbulence. Though the primary flight speed range is that of civil air transport vehicles, flows past other flying vehicles up to hypersonic speeds are also considered. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers, as this wider scope is necessary in view of the theoretical and practical problems that have to be overcome in practice. The specific topics covered include weak, strong, and global interaction; the locality principle; properties of three-dimensional viscous flows; thermal surface effects; characteristic properties; wall compatibility conditions; connections between inviscid and viscous flows; flow topology; quasi-one- and two-dimensional flows; laminar-turbulent transition; and turbulence. Detailed discussions of examples illustrate these topics and the relevant phenomena encountered in three-dimensional viscous flows. The full governing equations, reference-temperature relations for qualitative considerations and estimations of flow properties, and coordinates for fuselages and wings are also provided. Sample problems with solutions allow readers to test their understanding.

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.

This research is motivated by the need for accurate prediction of three-dimensional viscous flow in a turbine or compressor passage. As a major step towards the investigation of these problems, the three-dimensional entrance flow through ducts of various regular cross-sections, with longitudinal and transverse curvature effects, have been studied. The mathematical model has been formulated using time-averaged three-dimensional parabolized Navier-Stokes equations. The analysis has been developed using an existing two-equation turbulence model and is checked by obtaining satisfactory comparison of the present results for straight and curved circular pipes. The effects of the problem parameters on the flow fields are accurately evaluated and the limitations of the turbulence model have been briefly stated. Four related areas were identified and studied separately. These consist of the law of the wall, coordinate transformations and efficiency and accuracy of the numerical algorithm. The last three of these areas have been studied with some success already, and the additional analysis developed will be implemented in the basic turbulent-flow program to make the latter a truly predictive tool.

The present volume entitled "Recent Contributions to Fluid Mechanics" is dedicated to Professor Dr.-Ing. Alfred Walz in honour of his 75th birthday. Alfred Walz, born on 11 May 1907, began his outstanding career as an electrical engineer. A few years after obtaining his university degree he became extremely engaged in fluid dynamics. Walking in the footsteps of Prandtl he was able to direct the development of theoretical activities in an inimitable way. He had the great opportunity to work both as an engaged fluid dynamicist -always trying to get to the bottom of things -and as a popular and patient teacher. To all of these things - in his own words - he gave his heart. Consequently, it is a great pleasure to publish the following 34 contributions summarizing the efforts of 56 authors. These artic les in total cover the wide range of experimental as well as theore tical fluid dynamics and reflect the present state of the art. Moreover, all colleagues and friends of Alfred Walz wish that he may be able to continue his work and his influence on the work of all of us via his enlightening ideas. Friedrichshafen, August 1982 Werner Haase Chairman of the Scientific Committee Table of Contents SURVEY PAPER Shear Layer Studies - Past, Present, Future P. Bradshaw .......................................... .

The present volume, with the exception of the introductory chapter, consists of papers delivered at the workshop entitled "The Impact of Supercomputers on the Next Decade of Computational Fluid Dynamics," The workshop, which took place in Jerusalem, Israel during the week of December 16, 1984, was initiated by the National Science Foundation of the USA (NSF), by the Ministry of Science and Development, Israel (IMSD), and co-sponsored by the National Aeronautics and Space Administration (NASA), the Office of Scientific Research of the U.S. Air Force (AFOSR), Tel Aviv University and Massachusetts Institute of Technology. The introductory chapter attempts to summarize what transpired at the workshop. The genesis of the workshop was an agreement between NSF and Il1S, signed in the spring of 1983, to conduct a series of bi-national work shops and symposia. This workshop represented the first activity spon sored under the agreement. The undersigned were selected by their respective national bodies to act as co-coordinators and organizers of the workshop. The first question that we faced was to decide upon a topic. In the past few years the field of CFD has mushroomed and consequently there have been many meetings, symposia, workshops, congresses, etc.

A concise mathematical framework is constructed to study the topology of steady 3-D separated flows of an incompressible, or a compressible viscous fluid. Flow separation is defined by the existence of a stream surface which intersects with the body surface. The line of separation is itself a skin-friction line. Flow separation is classified as being either regular or singular, depending respectively on whether the line of separation contains only a finite number of singular points or is a singular line of the skin-friction field. The special cases of 2-D and axisymmetric flow separation are shown to be of singular type. In regular separation it is shown that a line of separation originates from a saddle point of separation of the skin-friction field and ends at nodal points of separation. Unsteady flow separation is defined relative to a coordinate system fixed to the body surface. It is shown that separation of an unsteady 3-D incompressible viscous flow at time t, when viewed from such a frame of reference, is topologically the same as that of the fictitious steady flow obtained by freezing the unsteady flow at the instant t. Examples are given showing effects of various forms of flow unsteadiness on flow separation. Hui, W. H. Unspecified Center NAGW-575; RTOP 505-31-01-01...