Numerical Study On Parametric Roll Based On Impulse Response Function Method

The investigation on parametric roll resonance is significant and necessary because the induced large-amplitude roll motion threatens the ship safety greatly.The numerical prediction is one of the most effective method to study parametric roll,which practically provides guidance for the preliminary ship design and the establishment of ship maneuver guidelines.For study on parametric roll,this thesis first investigates the timedomain simulation with the Impulse Response Function method.Base on the frequency-domain results calculated with 3D translating and pulsating source,this thesis takes into the speed effect into account and derives the speed effect terms according to the linearity of the initial boundary value problem.The high-frequency hydrodynamic coefficients are obtained from asymptotic expressions,and the linear time-domain radiation and wave forces are calculated with inverse Fourier transform of the damping coefficients.Through the establishment of 6-DOF coupled motion equations,a linear time-domain model is constructed.The numerical results prove the feasibility of the present method and indicate that the speed effect should not be neglected in order to assure the concurrence between frequency and time domain as well as the simulation accuracy.Furthermore,a new Kramers-Kronig relations with the speed effect included is derived and validated in the thesis.In order to further improve the accuracy,the linear model is extended to a weakly nonlinear time-domain program based on the weakly nonlinear assumptions.The radiation and diffraction forces are kept linear and calculated based on the Impulse Response Function concept while the nonlinear Froude-Krylov forces and the nonlinear restoring forces are obtained through pressure integral calculated on the instantaneous submerged hull.The gird processing and the numerical integral method are discussed explicitly in the thesis.Through validation with three ship models with different ship hull forms and different speeds,it is shown that,although the simulated pitch amplitude is larger than the experiment,the weakly nonlinear model is more accurate than the linear model and has good adaptability to ship hull forms and speeds.Particularly,when the ship speed is low,the simulation results are rather accurate.The weakly nonlinear time-domain model is employed to simulate parametric roll resonance of a ship in regular head waves.Both zero and non-zero speed case are considered.In the zero-speed case,the nonprinciple parametric resonance occurring at the frequency around the roll natural frequency is investigated,with frequency-domain results calculated by 3D pulsating source.In the non-zero speed case,the principle parametric resonance at the encounter frequency twice the roll natural frequency is considered,and the frequency-domain results are calculated with 3D translating and pulsating source.The roll damping is obtained through roll decay test.Two types of parametric roll are analyzed with focus on motion symmetries,and the influence of the initial heeling angle,wave frequency and wave steepness on the roll amplitude in both the developing and the steady-state stage.The numerical results suggest that the non-principle parametric roll is also very dangerous and should not be neglected.Furthermore,the results of 4-DOF model and 6-DOF are compared and indicate qualitatively that surge and yaw have an impact on the roll amplitude.