Page 121 - Aerodynamics for Engineering Students

Potential flow

3.1 Introduction

The concept of irrotational flow is introduced briefly in Section 2.7.6. By definition
the vorticity is everywhere zero for such flows. This does not immediately seem a very
significant simplification. But it turns out that zero vorticity implies the existence of a
potential field (analogous to gravitational and electric fields). In aerodynamics the
main variable of the potential field is known as the velocity potential (it is analogous
to voltage in electric fields). And another name for irrotational flow is potentialflow.
For such flows the equations of motion reduce to a single partial differential equa-
tion, the famous Laplace equation, for velocity potential. There are well-known
techniques (see Sections 3.3 and 3.4) for finding analytical solutions to Laplace’s
equation that can be applied to aerodynamics. These analytical techniques can also
be used to develop sophisticated computational methods that can calculate the
potential flows around the complex three-dimensional geometries typical of modern
aircraft (see Section 3.5).
In Section 2.7.6 it was explained that the existence of vorticity is associated with
the effects of viscosity. It therefore follows that approximating a real flow by a
potential flow is tantamount to ignoring viscous effects. Accordingly, since all real
fluids are viscous, it is natural to ask whether there is any practical advantage in