Match Method In Frequency Domain On Motions And Wave Loads Of Ship With Forward Speed

When ships sail in waves,higher speed induces larger wave loads which will threaten the safety of ship structure.Therefore,it is of vital importance for the ship design to evaluate wave loads on ships and induced motions accurately and efficiently.A lot of research work has been done last decades.At present,Rankine source method and forward speed Green function method are the two main methods for predicting the motions and wave loads of ship with forward speed.The Rankine source has a simple form and suits for various free surface conditions,which can be successfully applied to the seakeeping problems of ships with forward speed.However,large amount of elements need to be distributed on the free surface which reduce its efficiency,at the same time,the results obtained by different numerical processing methods are different as the numerical beach technology to damp waves is induced to satisfy appropriate radiation condition.The method based on forward speed Green function satisfying the boundary condition on the free surface and radiation condition just needs to be integrated on the body surface and water line,however its form is complicated,when the field point and source point are both on the free surface,there are problems of singularity and high oscillations.To make full use of the advantages of the two popular methods and avoid their disadvantages,the match method in frequency domain based on analytical cylinder control surface is studied to predict the wave induced motions and loads of ship with forward speed in this study.A analytical cylinder surface is proposed to be the control surface which divides the whole fluid domain into the interior domain and exterior domain.The Rankine source is adopted in the interior domain;only the part of free surface inside the control surface is needed to be divided,which promotes the efficiency.The forward speed Green function is used in the exterior domain without need to set the numerical beach,meanwhile,as the control surface is meshless,the integration of the forward speed Green function on the waterline of control surface can be performed analytically,and the numerical difficulties induced by the singularity and high oscillations are avoid.To this end,the following aspects are mainly studied in this paper.1.The study of theory in frequency domain match methodThe fluid domain in which ship sails is analyzed and the linearized boundary conditions are derived.The theoretical system of frequency domain match method is discussed.The analytical cylinder surface is proposed to be the control surface making the vertical variable and circumferential variable independent which reduce the difficulty of calculation,and the technical route to study the frequency domain match method is given out.2.The study of solution in the exterior domainThe velocity potential and its normal derivative on the meshless cylinder control surface are expanded into Laguerre-Fourier series and the method to calculate the coefficients of the series is given.The integral equations are established in the external domain with application of forward speed Green function based on the second Green’s identity,and the relationship called DN between the velocity potential and its normal derivative is obtained on the control surface,which connects the interior domain and exterior domain together.3.The calculation of the integration of forward speed Green functionThe integrations of forward speed Green function on cylinder control surface are included in matrix DN.To solve DN easily,the method to compute the integration of forward speed Green function in cylindrical coordinate system is proposed for the first time.We start with the original formulation of Green function expressed by a double Fourier integral.Unlike all classical formulations based on the integration in wavenumber first,the integration in circumference variable is performed analytically by using the theorem of residues.The resultant expression in single wavenumber integral is well suited for its integration on the control surface.4.The study of solution in the interior domainThe higher order derivatives of the velocity potential on the free surface of the interior domain are computed based on cubic B spline,The unknowns in the free surface condition of interior domain are translated into the control points of cubic B spline from the velocity potential and its higher order derivatives.The integral equations are established in the internal domain with application of Rankine source based on the second Green’s identity,and the velocity potentials of the fluid domain are solved with the boundary conditions of interior domain and the relationship DN.5.The numerical computation and the validation of resultsThe process of numerical computation for the match method in this paper is revealed and programs are written with Fortran 90 language for predicting the motions and wave loads of ship with forward speed.The hemisphere,barge,submerged sphere and A,B,C ships are taken for examples,the hydrodynamic coefficients,motions and wave loads are calculated and the results are analyzed by comparing with the analytical solution,results calculated by the software or experimental measurements,the correctness of the match method in this paper is checked.