A potential flow model has been formulated for scallop
swimming. Under the small-disturbance approximation, the problem
of the unsteady flow past the wing-like configuration of a
scallop is separated into two linear sub-problems: the steady
lifting problem and the unsteady symmetric thickness problem. The
latter is associated with the expansion and contraction of the
boundary surface of the scallop due to the shell opening and
closing. A quasi two dimensional analytical solution of the
thickness problem was obtained to give the time-dependent fluid
forces acting on the outer surfaces of the shells. In addition to
the added mass effect, which has been widely accepted in the
hydrodynamics of aquatic locomotion, there are two other
mechanisms in the fluid reaction: flow induced pseudo-elasticity
and pseudo-viscosity. The pseudo-elasticity provides a force
proportional to the gape angle displacement, and will assist
shell opening but resist shell closing. The pseudo-viscosity
force is proportional to the angular velocity of the gape, and
benefits both shell opening and closing. Their roles are
discussed through comparison with those of shell inertia, hinge
ligament elasticity and hinge damping. At 10 C the hinge damping
in the scallop was found to be almost compensated by the flow
induced pseudo-viscosity. The unsteady fluid reaction may have a
significant effect on the operation of the dynamic swimming
system of scallops.
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