| The ship motion mathematical model in waves not only plays an important role in ship's design,manufacture and operation,but also is the key technology to maritime simulator's behavioral realism.In order to avoid the inaccuracy problem of ship motion modeling by approximate formula,this dissertation establishes reliable and practical ship motion mathematical model in waves based on two-dimensional(2-D)strip theory and three-dimensional(3-D)time-domain theory respectively for maritime simulator.Within 2-D strip theory and 3-D time-domain theory,a deep theoretical study is carried out for ship motion mathematical models in waves,and the numerical computational software is developed to applied for the maritime simulator and marine engineering.2-D strip methods and 3-D time-domain methods are widely applied to marine engineering,but the ship motion models of maritime simulator are different from those of marine engineering,in which the real time and combination with visual system problems should be considered.The dissertation conducts an in-depth theoretical study of ship motion modeling in waves from three aspects,which are the application study of the multi-parameter conformal mapping method,numerical calculation and application of 3-D time-domain Green function and calculation of F-K forces respectively,and the reliable and practical ship motion models in waves are expected to established for maritime simulator.Finally,numerical validation is carried out for various ship types.The main research work and achievements of this dissertation are shown below:1.The ship six degrees of freedom(6DOF)motion model in waves is established based on the multi-parameter conformal mapping method.Based on the 2-D strip theory,ship transverse section is transformed into unit semicircle by the multi-parameter conformal mapping method,the singularity velocity potential is distributed on the unit semicircle to solve the perturbation velocity potential of 2-D flow field.Added mass,damping coefficients and wave exciting forces,which vary with frequency,are obtained,and the differential equation of ship 6DOF motion is established.The numerical calculation software of ship motion in waves is developed independently based on Visual Studio,and applied to the simulation platform of maritime simulator.Numerical calculations for S175 container ship,VGY8004 fishing vessel model,YUKUN vessel and Mariner ship's motions in waves are carried out,the numerical results indicate:1)Under head sea condition,the motion response amplitude operator(RAO)results of S175 container ship,VGY8004 fishing vessel model and Mariner vessel are in good agreement with the experimental results in most frequency ranges;and the time history of heave and pitch motions for YUKUN vessel are stable under different wave directions.2)When Mariner vessel is turning in waves,its heave,pitch and roll motions are obviously different from those of straight line motions.The time history of heave,pitch and roll motions is no longer harmonic,but it still presents some regularity,the period of heave,pitch and roll motions is about the time needed for turning a circle.Therefore,the ship 6DOF motion mathematical model established in this dissertation can effectively simulate ship motions in waves.2.Three-dimensional time-domain Green function numerical calculation is studied.Due to unclear dividing line between small values of time and large values of time,the numerical accuracy can't be guaranteed for 3-D time-domain Green function calculation.Thus,this dissertation further enlarges the transition time region between small values of time and large values of time,and the precise integration method is used to solve the fourth-order ordinary differential equation satisfied by the 3-D time-domain Green function.After the nodes of the three-dimensional time-domain Green function are tabulated,and the precise integration method is proposed to interpolate the nodes of the 3-D time-domain Green function.The numerical results indicate:when the field point and source point are both on the mean free surface,in transition time region,the accuracy of 3-D time-domain Green function solved by the precise integration method is seven orders higher than that of the fourth-order Runge-Kutta method.Thus,the method of this dissertation has better numerical results than fourth-order Runge-Kutta method.3.Based on the three-dimensional linear time-domain theory,the ship radiation problem and diffraction problem calculation model in waves is established.The initial and boundary conditions of radiation velocity potential and diffraction velocity potential are derived in body-fixed coordinate system.The boundary integral equations of radiation velocity potential and diffraction velocity potential are established based on the impulse response function method,and the numerical discretization of the boundary integral equations is solved by the constant panel method.Radiation forces,diffraction forces,hydrostatic restoring forces and F-K forces are solved on the mean wet hull surface,and a numerical calculation software for ship motion in waves is developed based on the 3-D linear time-domain method.To solve the hydrodynamic calculation numerical divergence problem for ships with flare using 3-D time-domain Green function method,and the geometry of the ship's panels near waterline should be properly processed.Thus,the ship's panels near the waterline are perpendicular to the mean free surface,which is suitable for hydrodynamic calculation of the ships with flare.The numerical calculations are carried out for Wigley I hull and S175 container ship with flare,when Wigley I hull sails in head seas at Froude number 0.2 and the ratio of wavelength to ship length is 1.5,the heave RAO calculated by 3-D time-domain method is 1.0%smaller than the experimental result;the heave RAO calculated by 3-D frequency-domain method is 9.4%larger than the experimental result,and the result of 3-D linear time-domain method is closer to the experimental result than 3-D frequency-domain method.When S175 container ship sails in head seas at Froude number 0.275,the calculation results of memory function obtained by the hull modification method presented in this dissertation converge.The numerical results indicate:based on 3-D linear time-domain theory,the numerical calculation software developed in this dissertation is effective and reliable for the ship's hydrodynamics and motions.4.The ship motion mathematical model in waves is established based on the three-dimensional Froude-Krylov force non-linear time-domain method.Linear perturbance force is calculated by 3-D time-domain Green function method on the mean wet hull surface,while non-linear F-K forces and hydrostatic restoring forces are solved on the instantaneous wet hull surface.An adaptive mesh generation method based on quad-tree subdivision is proposed to generate the instantaneous wet hull surface.The wave profile correction method is used to calculate the pressure induced by incident wave.For panels below mean free surface,the pressure analytical integral expression for F-K forces acting on panel is derived,which avoids the errors caused by numerical integration method.At different wave lengths and wave directions,the influence of flow field depth on F-K forces acting on ship hull is also investigated.The numerical prediction of motions for Wigley I hull sailing in waves at Froude number 0.2 is carried out,the calculation results indicate:when the water depth of the flow field is seven times greater than the ship's draft,the Froude-Krylov force acting on the hull is close to the Froude-Krylov force of the infinite depth flow field gradually;when the incident wave amplitude is 0.018m,due to the F-K force non-linear factors,compared with the 3-D linear time-domain method,the equilibrium position of the time history of ship's heave motion moves downward for a certain distance;in most of the wavelength range,the relative error between pitch RAO calculation results obtained by the 3-D Froude-Krylov force non-linear time-domain method and the experimental results is less than 10.9%,while the relative error between the RAO calculation results of pitching motion obtained by the 3-D linear time domain method and the experimental results is less than 22.0%,thus,the calculation results of the 3-D Froude-Krylov force non-linear time-domain method are closer to the experimental results. |
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