Page 143 - Aerodynamics for Engineering Students

126 Aerodynamics for Engineering Students

Suppose there is an oval of breadth 2bo and thickness 2to set in a uniform flow
of U. The problem is to find m and c in the stream function, Eqn (3.31), which will
then represent the flow round the oval.
(a) The oval must conform to Eqn (3.31):

(b) On streamline T+!J = 0 maximum thickness to occurs at x = 0, y = to. Therefore,
substituting in the above equation:

and rearranging
2sUto - 2toc
tan- - - (3.34)
m ti - c2

(c) A stagnation point (point where the local velocity is zero) is situated at the 'nose'
of the oval, i.e. at the pointy = 0, x = bo, Le.:

w
-=- m 1 (2 + y2 - c2)2c - 2y 2cy -u
ay 2s 1 + (&) (x2+3 - c2)2

and putting y = 0 and x = bo with w/ay = 0:

m (bg - c2)2c
O=- U
2s (b; - c2)2
Therefore

b; - c2
m = TU- (3.35)
C
The simultaneous solution of Eqns (3.34) and (3.35) will furnish values of m and c
to satisfy any given set of conditions. Alternatively (a), (b) and (c) above can be used
to find the thickness and length of the oval formed by the streamline + = 0. This
form of the problem is more often set in examinations than the preceding one.

3.3.8 Doublet
A doublet is a source and sink combination, as described above, but with the separation
infinitely small. A doublet is considered to be at a point, and the definition of the
strength of a doublet contains the measure of separation. The strength (p) of a doublet
is the product of the infinitely small distance of separation, and the strength of source
and sink. The doublet axis is the line from the sink to the source in that sense.