Chapter 2 - Lifting bodies, two-dimensional aerofoils and cascades

Summary

Introduction

An outline computational scheme was developed in Chapter 1 for application of the surface vorticity method to two-dimensional flow past non-lifting bodies of arbitrary shape. In the fields of aeronautics and engine aerodynamics on the other hand there is a special interest in lifting bodies and control surfaces such as aerofoils, struts and turbine, compressor or fan blades. The objective of this chapter is to extend the analysis to deal with these important applications which exhibit three features not yet considered, namely:

1. (i) Such devices are required to generate lift, associated with net bound circulation on the body.

2. (ii) In the applications cited the lifting surfaces are normally thin foils for which special computational problems arise due to the close proximity of vorticity elements on opposite sides of the profile.

3. (iii) A device may involve an assembly of several lifting bodies, taking deliberate advantage of their mutual aerodynamic interference.

We will deal with these matters in turn beginning with an extension of flow past a circular cylinder, Section 1.6, to the case of the Flettner rotor or lifting rotating cylinder, Section 2.2. Progressing to the closely related problem of flow past an ellipse, Sections 2.3 and 2.4, problems of type (ii) will be dealt with for the treatment of thin non-lifting and lifting bodies. This leads naturally into the case of generalised thin aerofoils, Section 2.5, for which comparisons will be provided from Joukowski's exact solutions.