Page 234 - Introduction to Naval Architecture

PROPULSION 219

Figure 9,9 Flow round aerofoil without circulation

At points A and B the velocity is zero and these are called stagnation
points. The resultant force on the cylinder is zero. This flow can be
transformed into the flow around an aerofoil as in Figure 9,9, the
stagnation points moving to A' and B'. The force on the aerofoil in
these conditions is also zero.
In a viscous fluid the very high velocities at the trailing edge produce
an unstable situation due to shear stresses. The potential flow pattern
breaks down and a stable pattern develops with one of the stagnation
points at the trailing edge, Figure 9.10.

Figure 9.10 Flow round aerofoil with circulation

The new pattern is the original pattern with a vortex superimposed
upon it. The vortex is centred on the aerofoil and the strength of its
circulation depends upon the shape of the section and its angle of
incidence. Its strength is such as to move B' to the trailing edge. It can
be shown that the lift on the aerofoil, for a given strength of circulation,
T, is:

Lift = L = pVr

The fluid viscosity introduces a small drag force but has little influence
on the lift generated.

Three-dimensional flow
The simple approach assumes an aerofoil of infinite span in which the
flow would be two-dimensional. The lift force is generated by the
difference in pressures on the face and back of the foil. In practice an