Amplitude Induced Nonlinearity in Piston Mode Resonant Flow: A Fully Viscous Numerical Analysis

Near field flow characteristics around catamarans close to resonant conditions involve violent viscous flow such as energetic vortex shedding and steep wave making. This paper presents a systematic and comprehensive numerical investigation of these phenomena at various oscillating frequencies and separation distances of twin sections. The numerical model is based on the solution of Navier–Stokes equations assuming laminar-flow conditions with a volume of fluid (VOF) approach which has proven to be particularly effective in predicting strongly nonlinear radiated waves which directly affect the magnitude of the hydrodynamic forces around resonant frequencies. Considered nonlinear effects include wave breaking, vortex shedding and wave-body wave-wave interactions. The method is first validated using available experiments on twin circular sections: the agreement in a very wide frequency range is improved over traditional linear potential flow based solutions. Particular attention is given to the prediction of added mass and damping coefficients at resonant conditions where linear potential flow methods fail, if empirical viscous corrections are not included. The results of the systematic investigation show for the first time how the so-called piston-mode motion characteristics are nonlinearly dependent on the gap width and motion amplitude. At low oscillation amplitudes, flow velocity reduces and so does the energy lost for viscous effects. On the other hand for higher oscillation amplitude, the internal free surface breaks dissipating energy hence reducing the piston mode amplitude. These effects cannot be numerically demonstrated without a computational technique able to capture free surface nonlinearity and viscous effects.