Page 88 - Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

Dynamics of Inviscid Fluids 73

affix of this sharp trailing edge of (c) and Zp = Re* be the affix of its
homologous from (C) (by the canonical conformal mapping considered
before). The function z = H(Z), in the neighborhood of Z = Zp behaves
10
as

z2-zp=A(Z-Zp)t+-:-,

the omitted terms in this expansion being of order higher than p in
Z—Zp. According to the above expansion ifa direction, passing through
Zr, is rotated with an angle a, then the homologous direction passing
through zp, will rotate with the angle pa. If we denote by éz (0 < 6 < 1),
the angle of the semitangents drawn to (c), at zp (that is the “jump”

of a semitangent direction passing through zp is 2a — 67, see Figure 2.4
A), one could see that the exponent p in the above expansion should
necessarily be 2 — 6, the “jump” of the homologous direction from the
plane Z, thus being a (see Figure 2.4 B).

ar (Z)

(Z) YA TL

(C), “

nn ares"
c)
/
(2-8)n “. _s

(A) (B)

Figure 2.4. Profile with sharp trailing edge

d
Consequently, in the vicinity of Zp, (=) = A(2—6)(Z—Zp)'>+
F
. oe . df dFdZ
- and this derivative vanishes at Z = Zr. But then, from de dz de’

one could see that the complex velocity in the neighborhood of the sharp

See, for instance, C. Iacob, * Introduction mathématique a la mécanique des fluides”, p.
645 [69].