孤立波对浸没平板作用的二维边界元数值分析
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摘要
该文采用二维边界元方法研究孤立波与浸没固定式平板的相互作用,研究相对波高、相对宽长和相对浸没深度对水动力载荷的影响规律。通过孤立波在台阶上传播与分裂及孤立波中平底上浸没固定式平板的波浪载荷等算例,验证了基于势流理论与完全非线性自由表面条件的二维边界元计算方法的正确性。系列数值模拟结果表明,孤立波作用下浸没平板的上举力随相对板长的增大而增大,而向下的垂向力增大趋于一常数。与平底情况相比,浸没平板下的斜坡会使得垂向力增大。通过分析波形、流场速度分布以及板表面压强分布等角度分析了水动力载荷的变化机理。
A numerical analysis on the two dimensional problem of hydrodynamic loads on a submerged plate in a solitary wave and is presented in this article. A two-dimensional boundary integral element method is developed to solve the potential flows with a fully nonlinear free surface. The boundary integral element method is validated though comparing with numerical results with the theoretical solution of the propagation and fission of a solitary wave over a step bottom. For the case of the horizontal bottom, the experimental measurements and numerical results of hydrodynamic loads acting on the submerged plate in a solitary wave are adopted to verify the BIEM model. Variations of the extreme wave loads values with the plate length to depth ratio, wave amplitude depth ratio and submergence depth ratio are discussed. It turns out that, for a given relative wave amplitude of a solitary wave, the maximum lift force on the submerged plate is proportional to the relative plate length, while the maximum downward vertical force approaches to a constant as the plate width becomes greater. The slope beneath the submerged plate generates difference of the hydrodynamic loads acting on the pl ate in a horizontal bottom. The velocity fields and the pressure distribution on the plate are discussed to understand the mechanism o f the variations of the wave loads induced by a solitary wave.
A numerical analysis on the two dimensional problem of hydrodynamic loads on a submerged plate in a solitary wave and is presented in this article. A two-dimensional boundary integral element method is developed to solve the potential flows with a fully nonlinear free surface. The boundary integral element method is validated though comparing with numerical results with the theoretical solution of the propagation and fission of a solitary wave over a step bottom. For the case of the horizontal bottom, the experimental measurements and numerical results of hydrodynamic loads acting on the submerged plate in a solitary wave are adopted to verify the BIEM model. Variations of the extreme wave loads values with the plate length to depth ratio, wave amplitude depth ratio and submergence depth ratio are discussed. It turns out that, for a given relative wave amplitude of a solitary wave, the maximum lift force on the submerged plate is proportional to the relative plate length, while the maximum downward vertical force approaches to a constant as the plate width becomes greater. The slope beneath the submerged plate generates difference of the hydrodynamic loads acting on the pl ate in a horizontal bottom. The velocity fields and the pressure distribution on the plate are discussed to understand the mechanism o f the variations of the wave loads induced by a solitary wave.
引文
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[11]GRILLI S T,SKOURUP J,SVENDSEN I A.An efficient boundary element method for nonlinear water waves[J].Engineering Analysis with Boundary Elements,1989,6(2):97-107.
[12]LIU L F,HSU H W,MENG H L.Applications of boundary integral equation methods for twodimensional non-linear water wave problems[J].International Journal for Numerical Methods in Fluids,1992,15(9):1119-1141.
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[14]刘桦,吴卫,王本龙,等.完全非线性孤立波的直墙反射[J].海洋工程,2000,18(1):1-6.LIU Hua,WU Wei,WANG Ben-long,et al.Vertical wall reflection of a fully nonlinear solitary[J].The Ocean Engineering,2000,18(1):1-6.
[15]JI L U,YU X P.Numerical study of solitary wave fission over an underwater step[J].Journal of Hydrodynamics Ser B,2008,20(3):398-402.
[16]HAYATDAVOODI M,ERTEKIN R C.Wave forces on a submerged horizontal plate-Part II:Solitary and Cnoidal waves[J].Journal of Fluids&Structures,2015,54:580-596.
[2]PATARAPANICH M.Forces and moment on a horizontal plate due to wave scattering[J].Coastal Engineering,1984,8(3):279-301.
[3]BROSSARD J,CHAGDALI M.Experimental investigation of the harmonic generation by waves over a submerged plate[J].Coastal Engineering,2001,42(4):277-290.
[4]LIU C,HUANG Z,TAN S.Nonlinear scattering of nonbreaking waves by a submerged horizontal plate:Experiments and simulations[J].Ocean Engineering,2009,36:1332-1345.
[5]DONG J,WANG B L,ZHAO X,et al.Wave forces exerted on a submerged horizontal plate over an uneven bottom[J].Journal of Engineering Mechanics,144(6):04018030.
[6]CHEONG H F,SHANKAR N J,NALLAYARASU S.Analysis of submerged platform breakwater by eigenfunction expansion method[J].Ocean Engineering.1996,23(8):649-666.
[7]LO H Y,LIU L F.Solitary waves incident on a submerged horizontal plate[J].Journal of Waterway Port Coastal&Ocean Engineering,2014,140(3):04014009.
[8]HAYATDAVOODI M,SEIFFERT B,ERTEKIN R C.Experiments and computations of solitary-wave forces on a coastal-bridge deck.Part II:Deck with girders[J].Coastal Engineering,2014,88(88):210-228.
[9]POUPARDIN A,PERRET G,PINON G,et al.Vortex kinematic around a submerged plate under water waves.Part I:Experimental analysis[J].European Journal of Mechanics B/Fluids 34(2012):47-55.
[10]DONG J,WANG B L,LIU H.Wave forces on a submerged horizontal plate over a sloping beach due to a solitary wave[C].Proceedings of the Twelfth ISOPEPacific/Asia Offshore Mechanics Symposium,4-7October,Gold Coast,Australia,2016.
[11]GRILLI S T,SKOURUP J,SVENDSEN I A.An efficient boundary element method for nonlinear water waves[J].Engineering Analysis with Boundary Elements,1989,6(2):97-107.
[12]LIU L F,HSU H W,MENG H L.Applications of boundary integral equation methods for twodimensional non-linear water wave problems[J].International Journal for Numerical Methods in Fluids,1992,15(9):1119-1141.
[13]GRIMSHAW R H J.The solitary wave in water of variable depth Part 2[J].Journal of Fluid Mechanics,1970,42(3):639-656.
[14]刘桦,吴卫,王本龙,等.完全非线性孤立波的直墙反射[J].海洋工程,2000,18(1):1-6.LIU Hua,WU Wei,WANG Ben-long,et al.Vertical wall reflection of a fully nonlinear solitary[J].The Ocean Engineering,2000,18(1):1-6.
[15]JI L U,YU X P.Numerical study of solitary wave fission over an underwater step[J].Journal of Hydrodynamics Ser B,2008,20(3):398-402.
[16]HAYATDAVOODI M,ERTEKIN R C.Wave forces on a submerged horizontal plate-Part II:Solitary and Cnoidal waves[J].Journal of Fluids&Structures,2015,54:580-596.