La Houille Blanche
Number 5-6, Septembre 1977
|Page(s)||459 - 469|
|Published online||01 December 2009|
Définition de la géométrie des structures ventilées à la base
Definition of the geometry of ventilated structures
Chef de la Division "Navires Spéciaux"
2 Ingénieur de la Division "Navires Spéciaux" Bassin d'Essais des Carènes
In the mind of a naval architect, the depth of submergence, the planform of the wing are imposed, as is the spanwise loading distribution. In order to create the most suitable flow, not only is the free-shock entrance condition imposed, but also a distribution of the wing load that is as constant as possible. Van Dycke's method of singular perturbations is used to link the Larrock and Street solution of the two-dimensional theory with the lift line. A) The two-dimensional problem In order to simplify the Larrock and Street theory, distribution of velocity on the profile in the transformed plane T is necessary (f being the complex potential, f = t + TE log (1 - t/TE)). A distribution of constant velocity on the greater part of the face and the back is considered, and these velocities are linked by sine-like laws. The free-shock entrance condition (dRc/dt = 0 for t = 0, Rc being the radius of curvature and t = 0, the stagnation point is : B"0/B'0 = q"0/(2 q'0) - 1/TE where B0 et q0 : argument and modulus of the velocity at origin, TE : transformed of the infinite dowstream of the physical plane. The closing points C and D of the cavity are determined by B(TE) = 0 and B1 = limt --> -∞ (B - B∞) t. By reiterating, the desired profile is rapidly obtained. B) The three-dimensional problem The span having been fixed, and the aspect-ratio tending towards the infinite, the infinite downstream flow tends towards that created by a simple vortex line (outer problem). On the other hand, the chord having been fixed and the aspect-ratio tending towards the infinite, the flow near the wing tends towards the two-dimensional flow studied at par. A (inner problem). There exists a region where, at the second order, the solutions of the inner and outer problems must be identical and both equally valid (in order to match these two solutions). The asymptotical development of the outer problem when x --> 0, must be equivalent to that of the inner problem when x --> - ∞ , which leads to the following conditions: U∞ = 1/cosB∞, tg(B∞) = a(z), B1 = - Γ(z)/π with B1= lim t --> ∞(B - B∞)t. It is thus sufficient to resolve the two-dimensional problem after taking account of these new conditions. This new result can also be employed in the purely twodimensional case, by dictating B1 = - Γ(Z)/π close to the general condition adopted (see Furuya f(TC) = f(TD) - Ref. 2).
© Société Hydrotechnique de France, 1977