Arthur Rizzi

Henri Viviand

This is one in a series of workshops organized by the GAID1 Specialist Group for Numerical Methods in Fluid Hechanics (GAMM-Fachausschuss flir Numerische Hethoden in der Stromungs­ mechanik) whose purpose is to bring together the small group of researchers actively working on a sharply defined topic in order to discuss in detail their problems and experiences, to promote direct comparison and critical evaluation of algorithms, and to stimulate new ideas for numerical methods in fluid dynamics. The chairmen of this workshop were A. Rizzi of FFA, Sweden, and H. Viviand of ONERA, France. 2. INTRODUCTION Practically ten years have passed since it was first demonstrat­ ed that the nonlinear potential equation of mixed type which governs inviscid transonic flow could be solved in a numerical procedure. These years have seen an interest in the computation of transonic flow that continues to grow because of the develop­ ing and ever-increasing ability of the numerical methods to solve more and more complex flows and because of the great practical use to which their solutions can be put. From the question of whether we can solve the equations of transonic flow we have now progressed to the question of how accurately can we solve them. Any attempt to answer it must by necessity include a collective comparison of the results obtained from the com­ putational methods that are being applied today for the numerical solution of inviscid steady transonic flow.

A GAMM Workshop

Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves

Ernst Heinrich Hirschel

Albrecht Eberle

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.

Numerical Solutions of the Euler Equations for Steady Flow Problems

Christian Breitsamter

Werner Staudacher

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.

Arthur Rizzi

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