The Scattering Of Water Waves By A Vertical Cylinder In Channel

In the hydrodynamics studies,numerical simulation and model test are both very important research methods.Physical mode tests are usually carried out in wave tanks,while the results are approximate to the results in open sea.However,the reflection tank walls have significant effect on the experimental results.Thus,it is important to launch numerical study on how the tank walls affect wave action on structures in a wave tank.Based on linear potential flow theory,the scattering problem of a fixed vertical cylinder with constant cross section is studied in the frequency domain.As the boundaries have the same horizontal section,this problem can be simplified as 2D-potential problem.The numerical model is established by higher-order boundary element method,with the boundary integral equation derived from source distribution method,using the channel Green function as kernel function.Furthermore,a technique is applied to remove the “irregular frequencies” from above numerical model.The reliability of the model is validated by comparing with analytic results and former literatures with using different methods.Applying our improved model,the numerical results is shown for a cylinder with filleted square sections in the center of channel and a circular cylinder eccentric in channel.Based on these works,the conclusions are as follows:1.By applying the closed virtual impedance surface method,the “irregular frequencies” can be removed in lower frequency,but they still exist in higher frequency range.With a larger closed virtual impedance surface,the first irregular frequency is higher,and the accurate numerical results can be obtained in larger frequency range.2.For the scattering of a filleted square cylinder,a smaller fillet radius will cause many effects.The total transmission frequency is lower and the reflection coefficient is higher,while the cylinder is in the center of channel.In open sea,the first-order force and mean second-order force is larger,and the mean second-order force on the cylinder in open sea will have two pikes.3.For the scattering of a symmetric cylinder in the center of channel,there is transverse resonance when w/L is integer.But when the boundary of the cylinder and the tank wall is parallel,the “pass” between it will have its own resonance and this will interfere the transverse resonance in entire channel.4.For the scattering of a circular cylinder eccentric in channel,the transverse resonance frequency is w L2/(28)i/,as i is integer;and the first-order force in y direction will not be zero as the symmetric case.When the transverse resonance happens in channel,the first-order force will have strong correspondence with the amplitude of resonance mode on the cylinder center.