Chapter 1 - The basis of surface singularity modelling

Summary

Introduction

The principal aims of this book are to outline the fundamental basis of the surface vorticity boundary integral method for fluid flow analysis and to present a progressive treatment which will lead the reader directly to practical computations. Over the past two and a half decades the surface vorticity method has been developed and applied as a predictive tool to a wide range of engineering problems, many of which will be covered by the book. Sample solutions will be given throughout, sometimes related to Pascal computer programs which have been collated for a selection of problems in the Appendix. The main aims of this introductory chapter are to lay down the fundamental basis of both source and vorticity surface panel methods, to explain the fluid dynamic significance of the surface vorticity model and to introduce a few initial applications to potential flow problems.

As numerical techniques, surface singularity methods were not without progenitors but grew quite naturally from the very fertile field of earlier linearised aerofoil theories. Such methods, originally contrived for hand calculations, traditionally used internal source distributions to model profile thickness and vortex distributions to model aerodynamic loading, a quite natural approach consistent with the well known properties of source and vortex singularities. On the other hand it can be shown that the potential flow past a body placed in a uniform stream can be modelled equally well by replacing the body surface with either a source or a vortex sheet of appropriate strength, Fig. 1.1.