Interesting and probing questions, Tom!
Only using source distributions results in a
symmetrical hull for a monohull, but is that still true for a
catamaran?
The side force on each demihull would be zero, of course, but
wouldn't the centerline of each demihull be much like a streamline of
the flow around the other demihull? This would result in a small
amount of camber in each hull.
Yes, it would more like that, but it wouldn't necessarily be a simple
concave or convex camber.
But it would seem that vortices would be necessary to calculate the
flow around the geometrically symmetrical hulls.
Yes. For a proper linearised calculation a transverse velocity, phi_y,
is necessary to counter-balance the velocity induced by the other
demihull. This can be done by including dipoles or vortices, and it
should lead to more accurate wave resistance predictions. (Satisfying
the Kutta condition at the sterns is a nuisance in actual calculations.)
Of course, there is also induced drag to consider in a full treatment
of the problem.
Looking at the same issue from the opposite
direction, if you had two symmetrical hulls in close proximity, there
will be a suction force trying to pull the two hulls together.
The sideforce can act to repel the demihulls at some Fr and hull
separations, or to pull them together at other Fr and separation.
Couser et al say that "...the presence of one demihull modifies the
flow so that the other demihull is effectively operating at an
effective angle of incidence (or yaw) to the free-stream."
See:
Couser, P.RR, Wellicome, J.F. and Molland, A.F.,
"Experimental measurement of sideforce and induced drag on catamaran
demihulls",
International Shipbuilding Progress,
Vol. 45(443), 1998, pp. 225-235.
I think that is a slight over-simplification. The effect is likely to
be a yaw angle and a wavy form of camber, sometimes inwards, sometimes
outwards, along the hull. That waviness would also be Froude-number
dependent, and dependent on the hull separation. Think of the waves
created by one demihull impacting along the length of the other
demihull.
Their experimental results show that the induced drag can be ignored
for practical purposes as it comprises less than 0.3% of the monohull
drag.
They also showed that using an effective yaw angle, like one does
in simple induced drag calculations, gives reasonable approximations,
so their slight "over-simplification" is of little actual consequence.
So do the source-only representations simulate symmetrical hulls,
or do they really simulate side-force-neutral hulls?
I have never given it much thought, but I suspect the latter.
I now have the means to actually calculate the flow along each
centreplane and, in fact, along the actual hull surfaces. I'll
try that some time, but I am only spending about one day per week on
ship hydro. As a recent semi-retiree I can play more fluid dynamics
and artificial life games these days without feeling like I should
be earning money at the same time.
