A coupled potential rotational method for viscous flow about large floating bodies in waves
Wave loads on (and responses of) a large floating body in incident regular water waves
of small amplitude are usually adequately predicted by linear potential flow theory, but in
certain cases viscous forces are important in damping the response. One example is the roll
response of vessels near resonance in beam waves. To obtain a mesh based Navier-Stokes
solution for these special response prediction cases is computationally expensive as underresolution
of the mesh can cause diffusion and dispersion of the wave-field, and no-exact
radiation condition exists to prevent reflection of outgoing waves from open boundaries and
thus the computational domain must be made large. To overcome these limitations, a new
formulation is investigated based on a Helmholtz decomposition of the flow field into the
linear potential flow solution, efficiently solved using a Diffraction/Radiation code, and a
rotational remainder, governed by a set of'decomposed' incompressible Navier-Stokes equations.
The rotational flow is not treated as a wave-like field, so that a radiation condition is
not required, and the mesh need only be resolved locally around the body.
The formulation has been validated in two-dimensions for a submerged stationary body
in regular waves, and for the forced steady sway/roll motion of rectangular barge sections.
These barge sections were also tested for forced oscillatory roll motions, where the important
eddy damping phenomenon of vortex pairs shed from sharp corners was simulated,
however the viscous damping was either underpredicted or overpredicted depending on the
beam-to-draught aspect ratio. The coupled sway and roll response of a rectangular barge in
beam waves at roll resonance was tested using a strip theory extension, which coupled the
three-dimensional linearised potential solution to the two-dimensional rotational solution
in cross-sectional planes along the vessel. A fast iteration procedure provided converged
linear body responses, but only irregular sea data was available for comparison. The comparisons
however suggested an underprediction of the viscous damping in agreement with
the forced roll experiments. The test cases above were simulated as laminar flows. A turbulence
model for large eddy simulation was validated for uniform freestream flow past a
fixed circular cylinder.