Page 44 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

CONCEPTS, DEFINITIONS AND METHODS 27

Figure 2.5 (a) A slender body of revolution in uniform flow at a small angle of attack, a. (b) A
flexible slender body performing lateral oscillations of long wavelength, such that each segment
may be considered to be part of an infinitely long cylinder; a = tan-'(&/&).

and
V4 = 0 at infinity. (2.77b)

If the angle of attack is a, then in the (r, 8, x)-frame equations (2.77a,b) lead to (Karam-
cheti 1966)
aF aF
(V, sin a sin 8 + ur)- + (V, cos a + ux)- = 0 on F(r, 6, x) = 0 (2.78)
ar ax

and
ur = ue = u, = 0 at infinity, (2.79)

in which ur, ug and u, are the components of V4, and aF/ar = 1, aF/ax = -dR/dx from
(2.74). Hence, the surface condition (2.78) becomes
dR
L.
= (V, cos a + ux)- - V, sin a sin 8, 0 I I (2.80)
x
r=R dx