Page 135 - Aerodynamics for Engineering Students

1 18 Aerodynamics for Engineering Students

3.3.4 Solid boundaries and image systems
The fact that the flow is always along a streamline and not through it has an
important fundamental consequence. This is that a streamline of an inviscid flow
can be replaced by a solid boundary of the same shape without affecting the
remainder of the flow pattern. If, as often is the case, a streamline forms a closed
curve that separates the flow pattern into two separate streams, one inside and one
outside, then a solid body can replace the closed curve and the flow made outside
without altering the shape of the flow (Fig. 3.12a). To represent the flow in the region
of a contour or body it is only necessary to replace the contour by a similarly shaped
streamline. The following sections contain examples of simple flows which provide
continuous streamlines in the shapes of circles and aerofoils, and these emerge as
consequences of the flow combinations chosen.
When arbitrary contours and their adjacent flows have to be replaced by identical
flows containing similarly shaped streamlines, image systems have to be placed within
the contour that are the reflections of the external flow system in the solid streamline.
Figure 3.12b shows the simple case of a source A placed a short distance from an
infinite plane wall. The effect of the solid boundary on the flow from the source is
exactly represented by considering the effect of the image source A' reflected in the
wall. The source pair has a long straight streamline, i.e. the vertical axis of symmetry,
that separates the flows from the two sources and that may be replaced by a solid
boundary without affecting the flow.

Fig. 3.12 Image systems