Fluid mechanical aspects of separated and vortical flow in aircraft wing aerodynamics are treated. The focus is on two wing classes: (1) large aspect-ratio wings and (2) small aspect-ratio delta-type wings. Aerodynamic design issues in general are not dealt with. Discrete numerical simulation methods play a progressively larger role in aircraft design and development. Accordingly, in the introduction to the book the different mathematical models are considered, which underlie the aerodynamic computation methods (panel methods, RANS and scale-resolving methods). Special methods are the Euler methods, which as rather inexpensive methods embrace compressibility effects and also permit to describe lifting-wing flow. The concept of the kinematically active and inactive vorticity content of shear layers gives insight into many flow phenomena, but also, with the second break of symmetry---the first one is due to the Kutta condition---an explanation of lifting-wing flow fields. The prerequisite is an extended definition of separation: "flow-off separation" at sharp trailing edges of class (1) wings and at sharp leading edges of class (2) wings. The vorticity-content concept, with a compatibility condition for flow-off separation at sharp edges, permits to understand the properties of the evolving trailing vortex layer and the resulting pair of trailing vortices of class (1) wings. The concept also shows that Euler methods at sharp delta or strake leading edges of class (2) wings can give reliable results. Three main topics are treated: 1) Basic Principles are considered first: boundary-layer flow, vortex theory, the vorticity content of shear layers, Euler solutions for lifting wings, the Kutta condition in reality and the topology of skin-friction and velocity fields. 2) Unit Problems treat isolated flow phenomena of the two wing classes. Capabilities of panel and Euler methods are investigated. One Unit Problem is the flow past the wing of the NASA Common Research Model. Other Unit Problems concern the lee-side vortex system appearing at the Vortex-Flow Experiment 1 and 2 sharp- and blunt-edged delta configurations, at a delta wing with partly round leading edges, and also at the Blunt Delta Wing at hypersonic speed. 3) Selected Flow Problems of the two wing classes. In short sections practical design problems are discussed. The treatment of flow past fuselages, although desirable, was not possible in the frame of this book.

This successful book gives an introduction to the basics of aerothermodynamics, as applied in particular to winged re-entry vehicles and airbreathing hypersonic cruise and acceleration vehicles. The book gives a review of the issues of transport of momentum, energy and mass, real-gas effects as well as inviscid and viscous flow phenomena. In this second, revised edition the chapters with the classical topics of aerothermodynamics more or less were left untouched. The access to some single topics of practical interest was improved. Auxiliary chapters were put into an appendix. The recent successful flights of the X-43A and the X-51A indicate that the dawn of sustained airbreathing hypersonic flight now has arrived. This proves that the original approach of the book to put emphasis on viscous effects and the aerothermodynamics of radiation-cooled vehicle surfaces was timely. This second, revised edition even more accentuates these topics. A new, additional chapter treats examples of viscous thermal surface effects. Partly only very recently obtained experimental and numerical results show the complexity of such phenomena (dependence of boundary-layer stability, skin friction, boundary-layer thicknesses, and separation on the thermal state of the surface) and their importance for airbreathing hypersonic flight vehicles, but also for any other kind of hypersonic vehicle.

Aircraft concepts are always driven by the requirements of the desired m- sion. A di?erent purpose for the use of the aircraft consequently results in a di?erent design. Therefore, depending on the intended outcome, con?i- ing requirements need to be ful?lled, for example, e?cient cruise speed and greatercargocapabilities, in combinationwith shorttake-o?andlanding ?eld lengths, or high speed and agility combined with variable payload demands. Due to the highly complex, non-linear physical environment in which aircraft operate, this task demands that the most advanced methods and tools are employed, to gain the necessary understanding of ?ow phenomena, and to exploit the ?ow physics to achieve maximum aircraft e?ciency. Inthe naturalsciences, researcherstry to create andextend humankno- edge by understanding and explaining the mechanisms of physical processes. In engineering, a designer is limited by certain requirements, and in order to ful?l these requirements the necessary technical tools need to be designed. In general, for a given problem the corresponding scienti?c or technical solution is sought. In order to successfully advance from a problem towards a solution, three main methods may be used. The two classical methods include theory and experiment, which are now being complemented by a third method, - scribedasnumericalsimulation.Theexperimentalapproachis basedonph- ical observation, measurement of relevant values, and methodical variation of the subject matter. For example, such experiments are used to gain a ph- ical understanding as well as to validate and investigate design alternative

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 successful book gives an introduction to the basics of aerothermodynamics, as applied in particular to winged re-entry vehicles and airbreathing hypersonic cruise and acceleration vehicles. The book gives a review of the issues of transport of momentum, energy and mass, real-gas effects as well as inviscid and viscous flow phenomena. In this second, revised edition the chapters with the classical topics of aerothermodynamics more or less were left untouched. The access to some single topics of practical interest was improved. Auxiliary chapters were put into an appendix. The recent successful flights of the X-43A and the X-51A indicate that the dawn of sustained airbreathing hypersonic flight now has arrived. This proves that the original approach of the book to put emphasis on viscous effects and the aerothermodynamics of radiation-cooled vehicle surfaces was timely. This second, revised edition even more accentuates these topics. A new, additional chapter treats examples of viscous thermal surface effects. Partly only very recently obtained experimental and numerical results show the complexity of such phenomena (dependence of boundary-layer stability, skin friction, boundary-layer thicknesses, and separation on the thermal state of the surface) and their importance for airbreathing hypersonic flight vehicles, but also for any other kind of hypersonic vehicle.

Hypersonic ?ight and aerothermodynamics are fascinating topics. Design problems and aerothermodynamic phenomena are partly very di?erent for the various kinds of hypersonic ?ight vehicles. These are-and will be in the future-winged and non-winged re-entry vehicles as well as airbreathing cruise and acceleration and also ascent and re-entry vehicles. Both authors of the book worked for almost four decades in hypersonics: at the German aerospace research establishment (DVL/DFVLR, now DLR) to the end of the 1970s, then in industry (MBB/Dasa, now EADS). They were involved in many major technology programs and projects. First, in the early 1970s, the German ART program (Association for Re-Entry Te- nologies), and, in the 1980s, the European (ESA) HERMES project and the .. German Hypersonics Technology (SANGER) program. Then followed, in the 1990s, the Future European Space Transportation Investigations program (FESTIP), the Manned Space Transportationprogram(MSTP) with the - mosphericRe-EntryDemonstrator(ARD), theX-CRVProjectwiththe X-38 vehicle and, later, the German technology programs TETRA (Technologies for Future Space Transportation Systems), ASTRA (Selected Systems and Technologies for Future Space Transportation Systems Applications), and IMENS (Integrated Multidisciplinary Design of Hot Structures for Space - hicles). Research in the 1960s and 1970s placed great emphasis on low-density ?ows, high temperature real gas e?ects in ground-simulation facilities and, already, on discrete numerical computation methods. After the ?rst ?ights of the Space Shuttle Orbiter with its generally very good aerodynamic p- formance, interest in low-density problems diminished.

This volume contains twenty contributions of work, conducted since 1996 in the French- German Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). The main purpose of this publication is to give an overview over the work conducted in this programme, and to make the results obtained available to the pUblic. The reports are grouped under the four headings "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases" and "Turbulent Flows". AIl contributions to this publica- tion were reviewed by a board consisting of T. Alziary de Roquefort (Poitiers, France), P. Bontoux (Marseille, France), JA Desideri (Sophia-Antipolis, France), W. Kordulla (G6t- tingen, Germany), R. Peyret (Nice, France), R. Rannacher (Heidelberg, Germany), G. War- necke (Magdeburg, ,Germany), and the editor. The responsibility for the contents of the reports nevertheless lies with the authors. E. H. Hirschel Editor Preface The Colloquium on "Numerical Simulation of Flows", Marseille, November 21 and 22, th 1997, was the 6 Joint CNRS-DFG Colloquium organized in the frame of the French- German Research Collaboration on Computational Fluid Dynamics. This Collaborative Program was elaborated progressively since 1991, when the two major research groups were brought together: the Priority Program "Flow Simulation with Super Computers" from the DFG in Germany and the Groupement de Recherche de "Mecanique des Fluides NumCrique" (GDR MFN) from the CNRS in France.

This volume contains eighteen contributions of work, conducted since 2000 in the French - German Research Programme "Numerical Flow Simulation," which was initiated in 1996 by the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). The main purpose of this third publication on the research programme is again to give an overview over recent progress, and to make the obtained results available to the public. The reports are grouped, like those in the first and the second publi cation (NNFM 66, 1998, and NNFM 75, 2001), under the four headings "Devel opment of Solution Techniques," "Crystal Growth and Melts," "Flows of React ing Gases, Sound Generation" and "Turbulent Flows." All contributions to this publication were reviewed by a board consisting of T. Alziary de Roquefort (Poi tiers, France), H. W. Buggisch (Karlsruhe, Germany), S. Candel (Paris, France), U. Ehrenstein (Nice, France), Th. Gallouet (Marseille, France), W. Kordulla (Gottingen, Germany), A. Lerat (Paris, France), 1. Piquet (Nantes, France), R. Rannacher (Heidelberg, Germany), G. Warnecke (Magdeburg, Germany), and the editor. The responsibility for the contents of the reports nevertheless lies with the contributors."

Der Band enthalt den Abschlussbericht des DFG-Schwerpunktprogramms "Flusssimulation mit Hochstleistungsrechnern." Es fuhrt die Arbeiten fort, die schon als Band 38 in der Reihe "Notes on Numerical Fluid Mechanics" erschienen sind.Work is reported, which was sponsored by the Deutsche Forschungsgemeinschaft from 1993 to 1995. Scientists from numerical mathematics, fluid mechanics, aerodynamics, and turbomachinery present their work on flow simulation with massively parallel systems, on the direct and large-eddy simulation of turbulence, and on mathematical foundations, general solution techniques and applications. Results are reported from benchmark computations of laminar flow around a cylinder, in which seventeen groups participated."

The last two decades have brought two important developments for aeroth- modynamics. One is that airbreathing hypersonic flight became the topic of technology programmes and extended system studies. The other is the emergence and maturing of the discrete numerical methods of aerodyn- ics/aerothermodynamics complementary to the ground-simulation facilities, with the parallel enormous growth of computer power. Airbreathing hypersonic flight vehicles are, in contrast to aeroassisted re-entry vehicles, drag sensitive. They have, further, highly integrated lift and propulsion systems. This means that viscous eflFects, like boundary-layer development, laminar-turbulent transition, to a certain degree also strong interaction phenomena, are much more important for such vehicles than for re-entry vehicles. This holds also for the thermal state of the surface and thermal surface effects, concerning viscous and thermo-chemical phenomena (more important for re-entry vehicles) at and near the wall. The discrete numerical methods of aerodynamics/aerothermodynamics permit now - what was twenty years ago not imaginable - the simulation of high speed flows past real flight vehicle configurations with thermo-chemical and viscous effects, the description of the latter being still handicapped by in sufficient flow-physics models. The benefits of numerical simulation for flight vehicle design are enormous: much improved aerodynamic shape definition and optimization, provision of accurate and reliable aerodynamic data, and highly accurate determination of thermal and mechanical loads. Truly mul- disciplinary design and optimization methods regarding the layout of thermal protection systems, all kinds of aero-servoelasticity problems of the airframe, et cetera, begin now to emerge."

From the pioneering glider flights of Otto Lilienthal (1891) to the advanced avionics of todaya (TM)s Airbus passenger jets, aeronautical research in Germany has been at the forefront of the birth and advancement of aeronautics. On the occasion of the centennial commemoration of the Wright Brothera (TM)s first powered flight (December 1903), this English-language edition of Aeronautical Research in Germany recounts and celebrates the considerable contributions made in Germany to the invention and ongoing development of aircraft.

Featuring hundreds of historic photos and non-technical language, this comprehensive and scholarly account will interest historians, engineers, and, also, all serious airplane devotees. Through individual contributions by 35 aeronautical experts, it covers in fascinating detail the milestones of the first 100 years of aeronautical research in Germany, within the broader context of the scientific, political, and industrial milieus. This richly illustrated and authoritative volume constitutes a most timely and substantial overview of the crucial contributions to the foundation and advancement of aeronautics made by German scientists and engineers.

This volume contains eighteen reports on work, which has been conducted since 2000 in the Collaborative Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). French and German engineers and mathematicians present their joint research on the topics: "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases, Sound Generation" and "Turbulent Flows". In the background of their work is still the strong growth in the performance of super-computer architectures, which, together with large advances in algorithms, is opening vast new application areas of numerical flow simulation in research and industrial work. Results of this programme from the period 1996 to 1998 have been presented in NNFM 66 (1998), and NNFM75 (2001).

This volume contains twenty contributions of work, conducted since 1996 in the French- German Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). The main purpose of this publication is to give an overview over the work conducted in this programme, and to make the results obtained available to the pUblic. The reports are grouped under the four headings "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases" and "Turbulent Flows". AIl contributions to this publica- tion were reviewed by a board consisting of T. Alziary de Roquefort (Poitiers, France), P. Bontoux (Marseille, France), JA Desideri (Sophia-Antipolis, France), W. Kordulla (G6t- tingen, Germany), R. Peyret (Nice, France), R. Rannacher (Heidelberg, Germany), G. War- necke (Magdeburg, ,Germany), and the editor. The responsibility for the contents of the reports nevertheless lies with the authors. E. H. Hirschel Editor Preface The Colloquium on "Numerical Simulation of Flows", Marseille, November 21 and 22, th 1997, was the 6 Joint CNRS-DFG Colloquium organized in the frame of the French- German Research Collaboration on Computational Fluid Dynamics. This Collaborative Program was elaborated progressively since 1991, when the two major research groups were brought together: the Priority Program "Flow Simulation with Super Computers" from the DFG in Germany and the Groupement de Recherche de "Mecanique des Fluides NumCrique" (GDR MFN) from the CNRS in France.

The last decade has seen a dramatic increase of our abilities to solve numerically the governing equations of fluid mechanics. In design aerodynamics the classical potential-flow methods have been complemented by higher modelling-level methods. Euler solvers, and for special purposes, already Navier-Stokes solvers are in use. The authors of this book have been working on the solution of the Euler equations for quite some time. While the first two of us have worked mainly on algorithmic problems, the third has been concerned off and on with modelling and application problems of Euler methods. When we started to write this book we decided to put our own work at the center of it. This was done because we thought, and we leave this to the reader to decide, that our work has attained over the years enough substance in order to justify a book. The problem which we soon faced, was that the field still is moving at a fast pace, for instance because hyper sonic computation problems became more and more important."

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.

Aircraft concepts are always driven by the requirements of the desired m- sion. A di?erent purpose for the use of the aircraft consequently results in a di?erent design. Therefore, depending on the intended outcome, con?i- ing requirements need to be ful?lled, for example, e?cient cruise speed and greatercargocapabilities,in combinationwith shorttake-o?andlanding ?eld lengths, or high speed and agility combined with variable payload demands. Due to the highly complex, non-linear physical environment in which aircraft operate, this task demands that the most advanced methods and tools are employed, to gain the necessary understanding of ?ow phenomena, and to exploit the ?ow physics to achieve maximum aircraft e?ciency. Inthe naturalsciences,researcherstry to create andextend humankno- edge by understanding and explaining the mechanisms of physical processes. In engineering, a designer is limited by certain requirements, and in order to ful?l these requirements the necessary technical tools need to be designed. In general, for a given problem the corresponding scienti?c or technical solution is sought. In order to successfully advance from a problem towards a solution, three main methods may be used. The two classical methods include theory and experiment, which are now being complemented by a third method, - scribedasnumericalsimulation.Theexperimentalapproachis basedonph- ical observation, measurement of relevant values, and methodical variation of the subject matter. For example, such experiments are used to gain a ph- ical understanding as well as to validate and investigate design alternatives.

The goal of the GAMM-Committee for Numerical Methods in Fluid Mechanics (GAMM- Fachausschuf3 fUr Numerische Methoden in der Stromungsmechanik) is to bring together European research workers from different fields who are working on fluid mechanica I problems and develope and use Numerical Methods as mathematical tools, and to foster communication and cooperation between these people and the mathematicians working on the theory of Numerical Methods. The GAMM-Conference on Numerical Methods in Fluid Mechanics, which supplements the other activities of the committee, e. g. the GAMM-Workshops, is held every second year. The Third GAMM-Conference on Numerical Methods in Fluid Mechanics was held at the DFVLR, Koln, October 10 to 12, 1979. Approximately 100 scientists from 13 European countries attended the conference. In 32 papers problems were treated rang- ing from basic numerical questions to the application of Numerical Methods to basic fluid mechanical problems in Aerodynamics, Atmospheric Research, Nuclear Energy Techniques, Solar Energy Research, Turbomachines and Cascades. In two presentations the results of the GAMM-Workshops "Finite Element and Finite Volume Methods for Transonic Flow" (Chairmen W. Schmidt and F.G. Sator), and "Computation of Inviscid Transonic Flow" (Chairmen A. Rizzi and H. Viviand) were discussed. The report on the latter workshop will appear in "Notes on Nurnerical Fluid Mechanics" of Vieweg, too.