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Fig. 4. Demonstration of the method for measuring solid body added-mass (i.e.
Darwin, 1953). Axisymmetric
inviscid flow about a solid sphere is shown in cross section. Solutions were
computed using dimensional units to allow comparison with experimental
results. Sphere radius and propagation speed are 2.54 cm and 1 cm
s-1, respectively. Computational domain is 50 sphere radii axially
in both directions normal to the reference plane and approximately 12 cm
radially. Variables d0 and rL indicate
(qualitatively) finite upstream approach distance and reference plane radius,
respectively. Total fluid drift (i.e. for infinite domain) was computed using
measured partial drift in the computational domain and an analytical
asymptotic correction factor (i.e. Eq. 12;
Eames et al., 1994). (A)
Sphere approaches initially planar Lagrangian surface from left; t=0
s. (B) Streamwise distortion of Lagrangian surface occurs as the sphere passes
through the plane; t=4.45 s. Note that since only streamwise
Lagrangian displacement is plotted, the sphere appears to pass through the
plane. Plots of combined streamwise and transverse Lagrangian displacement
(e.g. D-F below) verify that the plane is actually distorted around the
sphere. (C) Volume between initial plane and horn-like distorted surface is
the drift volume, 
D, from which the added-mass coefficient
is computed; t=13.3 s. (D-F) Individual Lagrangian particle paths
corresponding to t=0 s, 4.45 s and 13.3 s, respectively.
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