Steady incompressible inviscid flow past a three-dimensional multiconnected
(toroidal) aerofoil
with a sharp trailing edge TE is considered, adopting for simplicity
a linearized analysis of
the vortex sheets that collect the released vorticity and form the trailing
wake. The main
purpose of the paper is to discuss the uniqueness of the bounded flow solution
and the
role of the eigenfunction. A generic admissible flow velocity u
has an unbounded singularity
at TE; and the physical flow solution requires the removal of
the divergent part of u (the
Kutta condition). This process yields a linear functional equation along
the trailing edge
involving both the normal vorticity ω released into the wake, and
the multiplicative factor
of the eigenfunction, a1. Uniqueness is then shown
to depend upon the topology of the
trailing edge. If δTE=[empty ], as, for example, in an annular-aerofoil
configuration, both ω and
a1 are uniquely determined by the Kutta condition,
and the bounded flow u is unique. If
δTE≠[empty ], as, for example, in a connected-wing configuration,
there is an infinity of bounded
flows, parametrized by a1. Numerical results of relevance
for these typical configurations are
presented to show the different role of the eigenfunction in the two cases.
A three-dimensional source-vorticity method for simulating incompressible potential flows around a deforming body without the Kutta condition
