Abstracts - KTH Mechanics

182
Nonlinear interaction of a pair of sails in a flow:
comparison between theory and observation
T. Sugimoto a
Many efforts have been introduced into the study of interaction between a sail and
a viscous or inviscid flow in two- and three-dimensions. These problems are known to
have multiple equilibria and hence hysteresis in aerodynamic and structural
characteristics. But there are only a couple of studies on the interaction among a flow,
jib and main sails. Also, the former studies could treat only special cases. The
limitation is due to difficulty in finding a physically meaningful set of tensions in two
structurally independent sails.
The present study deals with the problem by formalism of a two-dimensional
inviscid flow. This offers quite tractable basic equations, that is, a couple of Fredholm
integral equations of the second kind, accompanied by a couple of nonlinear integral
constraints upon sail length.
We shall look for shapes of sails and tensions acting upon sails in equilibrium by
giving the angle of attack, the stagger angle between sails, and sail length. The
developed method of solution consists of a panel method as a flow-field solver and
Newton-Raphson method for tensions search. This method is very robust and leads
us to multiple solusions depending on initial guesses in terms of tensions.
Three types of configuration between two sails are studied: largely overlapping
sails with the same size or different sizes; less overlapping sails with the same size. In
each case there exist multiple equilibria and complex hysteresis in aerodynamic and
structural characteristics. Too much overlap of sails is found to fail to obtain high lift
that would be expectedly developed by the jib sail.
To verify the theory, we conduct experiments to observe shapes of sails by use of
an upright wind tunnel. In case of the same-length sails for example, we observe three
types of shapes as shown in figure 1: a pair of concave and convex sails; a pair of
sigmoid and convex sails; a pair of convex sails. The theory exactly predicts these.
a Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa Ward, Yokohama, Japan
(a) (b) (c)
Figure 1: In the circular window shapes of the same-length sails in a flow are shown;
the stagger angle is 5 degrees; air blows from top to bottom. The angles of attack are
-20, +6.0, and +20 degrees for (a), (b), and (c), respectively.