Analytical & Numerical Solution Of Hydrodynamic Force & Motion Of A Vertical Circular Cylinder Oscillating In A Free Surface

In this paper,the floating vertical circular cylinder is studied.On the basis of summarizing the previous research results,this paper studies the hydrodynamic force and motion of the cylinder by the analytical method.This paper studies the floating vertical circular cylinder(floating point device)for surge,heave and pitch motion in linear plane waves.Based on the potential flow theory and linear wave theory,study on hydrodynamic and motion of the cylinder,solve the velocity potential boundary value problem which including Laplace equation and boundary conditions.The method of separation of variables is used to solve the velocity potential equation in cylindrical coordinate system.The velocity potential boundary value problem is decomposed into diffraction problems and surge,heave and pitch radiation problems.In the process of solving each problem,the water is divided into inner and outer waters.Then,through the continuity condition at the interface between the inner and outer waters,the undetermined coefficients in the expression of the velocity potential are determined.The hydrodynamic additional mass and damping coefficient are obtained in the radiation problem.Based on the hydrodynamic force,the equation of motion of the cylinder is established,and the analytical solution is obtained.The detailed derivation process is given in this paper.The velocity potential of the fluid is the analytic expressions of the series form,and the undetermined coefficients are expressed as simple complex algebraic equations by means of mathematical transformation in order to facilitate numerical solution.Using MATLAB programming language to solve the undetermined coefficients,so as to obtain the numerical solution of the hydrodynamic and movement of the float cylinder.In this paper,the convergence of unknown coefficients is studied.In a given wave number,the radius of the cylinder,the draught and water depth conditions,programme and solve the the added mass,damping coefficient,motion response amplitude ratio,the resultant force and moment of the cylinder,and the numerical results are given.For different depth-radius and draft-radius ratio of the cylinder,the added mass,damping coefficient,motion response amplitude ratio,the resultant force and moment changing with wave number are solved,and the results are discussed.The numerical results are compared with the results in other literatures,and the validity of the analytical procedure and the correctness of the program are obtained.The results show that the general trend of the additional mass,damping coefficient and motion response amplitude ratio is consistent.There are some differences in the smaller wave numbers.The analytical solution has a certain sensitivity and difference at low wave numberIn addition,the results based on the commercial software ANSYS CFX,are compared with the results based on the potential flow analysis method.It shows that there are differences near the resonance region,which needs to be further studied.