smaller than the width of the channel, allowing 2.5 times the diameter of the PSFM on
either side of the device.
2.1.1 Flow Field Determination
The conceptual model laid forth in Klammler et al. (2004) provides equations for
determining the pressure difference as well as the local velocity at two openings on the
PSFM. The pressure and velocity distributions around the submerged body can then be
used to estimate the velocity of the flow field around it.
Since the shape of the PSFM defines the flow field around it, conformal mapping
may be used to relate the complex potential of the flow field to the complex coordinates
of the device. The flow field around a cylinder was adapted to that of a Joukowsky
(hydrofoil) profile by Klammler et al. (2004) as follows:
z, = [z, -(1-b).a]+ -(2-1)
[z, (1- b) a]
where z~ = x, + iy, represents the complex coordinates of an impermeable circle with a
radius of a [L], z = xJ + iy, are the transformed complex coordinates of the Joukowsky
profile in the z,-plane, b is a dimensionless parameter defining the shape of the profile by
the chord-to-width ration, which ranges between 0 to 1, where b = 0 defines a circular
(blunt) profile and b = 1 defines a profile that is a straight line (slender).
Using these transformed coordinates, Klammler et al. (2004) used v, [L/T], the
complex conjugate of the flow velocity around the PSFM to find vo [L/T], the velocity of
the flow field