Numercial Study On Wave Attenuation Performance Of Vertical Multi-plates Based On Bragg Resonance

With the development of marine exploitation,offshore construction and the protection of offshore structures are particularly important.The free surface vertical multi-plates breakwater,as one of various breakwaters,has the advantages of protecting the seabed topography and can be used in deep water environment.When the wave interacts with the periodic structure,Bragg resonance will occur,which seriously affects the wave attenuation performance of the structure.Therefore,it is important to study the free surface vertical multi-plates breakwaters on the water surface and the wave interaction to the reasonable arrangement of the breakwater.Based on the potential flow theory,a three-dimensional time-domain numerical wave tank(NWT)is developed by the desingularized boundary element method(DBEM).The wave attenuation characteristic of the free surface vertical multi-plates breakwater and the Bragg resonance phenomenon were studied.The desingularized boundary element method is based on the Rankine source,and the source points are distributed outside the fluid domain.Mixed Euler-Lagrangian(MEL)time marching scheme is carried out to track the free surface.The fourth-order Adams prediction correction method is used to solve the next time step’s potential and wave elevation in the free surface.The artificial damping zone is used to eliminate the reflection of the end wall of the NWT.The first derivative of wave elevation in the free surface is solved by the spline interpolation technique.To eliminate the so-called “sawtooth”instability,the five-point smoothing method is used to smooth the velocity potential and wave elevation on the free surface.The ramping function is used to avoid computation instability caused by excessive initial values.Firstly,the influence of mesh size,time step and the desingularized distance is discussed for the numerical wave generation to determine the wave generation parameter.Then the numerical method of the wave generation is verified.The results indicate the mesh size and the desingularized distance have little effect on the numerical wave generation in a certain range,but if the parameters value is too largeor too small,the numerical calculation will fail.Then,the effect of the plate calculation parameters on the transmission characteristics of the single plate breakwater is also discussed.On these basis,the numerical method to compute the interaction between wave and single,double and three surface vertical plates is verified:(1)for the single plate,compare the numerical result with the analytical solution of previous literatures;(2)for the double and three plates,compare the numerical result with the experimental result.Finally the paper studies the wave attenuation characteristic and Bragg resonance phenomenon of the free surface vertical multi-plates breakwater,and the transmission coefficient and reflection coefficient of the breakwater with plate number and immersion depth are also discussed.The Bragg resonance condition and its values affected by the number of plates and the immersion depth are analyzed.The results are summarized as follows.(1)With the increase of the number of plates and the depth of immersion,the performance of free surface vertical multi-plates breakwaters is gradually enhanced in the Bragg resonance zone,while its performance is hardly improved in the harmful zone and the full reflection zone.(2)The Bragg resonance,which occurs at 2S/L=0.95,is less affected by the number of plates and the depth of the immersion,but the transmission and reflection coefficients in the Bragg resonance is greatly affected.The value of the reflection coefficient increases as the number of plates and the depth of immersion increases.The value of the transmission coefficient decreases as the number of plates and the depth of immersion increase.