纵摇容器中液体晃荡的非线性数值模拟
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摘要
在海洋工程领域,液体晃荡是一种普遍存在的物理现象。对于船舶而言,转动比平动有着更重要的影响。该文针对纵摇容器中的液体晃荡问题,采用高阶边界元方法建立自由水面满足完全非线性边界条件的时域数学模型。通过大地坐标系和随体坐标系之间的坐标变换,使得计算域仅控制在随体坐标系内。求解中采用半混合欧拉—拉格朗日方法追踪流体瞬时水面,运用四阶龙格库塔方法更新下一时间步的波面和速度势。通过与已发表试验和数值结果的对比,验证了建立模型的准确性。进而开展大量数值试验研究容器纵摇运动频率、纵摇转动中心和容器中布置一竖直隔板对晃动波面与荷载的影响。
In the field of marine engineering, liquid sloshing is a kind of universal physical phenomenon.For the ship, the rotation has a more important influence than translation. Therefore, a time-domain numerical model is developed by higher-order boundary element method to solve the liquid sloshing in a tank subjected to pitch motion, in which the fully nonlinear boundary conditions satisfied on the free surface. With the coordinate exchanged between the global and local coordinates, the computational domain can be governed only in the local coordinates. In the solving process, a semi-mixed Eulerian-Lagrangian technique is applied to track the transient free surface and the 4th-order Runge-Kutta method is used to refresh wave elevation and velocity potential on the free surface at each time-step. The proposed numerical model was testified by comparison with the other published experimental and numerical results. On the base of validation, lots of numerical experiments are carried out to investigate the effect of pitch motion frequency, rotational center and a vertical baffle mounted on the container bottom on the sloshing surface and loads on the container.
In the field of marine engineering, liquid sloshing is a kind of universal physical phenomenon.For the ship, the rotation has a more important influence than translation. Therefore, a time-domain numerical model is developed by higher-order boundary element method to solve the liquid sloshing in a tank subjected to pitch motion, in which the fully nonlinear boundary conditions satisfied on the free surface. With the coordinate exchanged between the global and local coordinates, the computational domain can be governed only in the local coordinates. In the solving process, a semi-mixed Eulerian-Lagrangian technique is applied to track the transient free surface and the 4th-order Runge-Kutta method is used to refresh wave elevation and velocity potential on the free surface at each time-step. The proposed numerical model was testified by comparison with the other published experimental and numerical results. On the base of validation, lots of numerical experiments are carried out to investigate the effect of pitch motion frequency, rotational center and a vertical baffle mounted on the container bottom on the sloshing surface and loads on the container.
引文
[1]Faltisen O M.A nonlinear theory of sloshing in rectangular containers[J].Journal of Ship Research,1974,18:224-241.
[2]Nakayama T,Washizu K.Nonlinear analysis of liquid motion in a container subjected to forced pitching oscillation[J].International Journal for Numerical Methods in Engineering,1980,15:1207-1220.
[3]Nakayama T,Washizu K.The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems[J].International Journal for Numerical Methods in Engineering,1981,17:1631-1646.
[4]Chen B F,Chiang H W.Complete 2D and fully nonlinear analysis of ideal fluid in containers[J].Journal of Engineering Mechanics,1999,125(1):70-78.
[5]Chen B F,Chiang H W.Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating container[J].Ocean Engineering,2000,27:953-977.
[6]Chen B F,Nokes R.Time-independent finite difference analysis of fully non-linear and viscous fluid sloshing in a rectangular container[J].Journal of Computational Physics,2005,209:47-81.
[7]Chen B F,Asce M.Viscous fluid in container under coupled surge,heave and pitch motions[J].Journal of Waterway,Port,Coastal and Ocean Engineering,2005,131(5):239-256.
[8]Chen B F,Wu C H.Effects of excitation angle and coupled heave-surge-sway motion on fluid sloshing in a three-dimensional container[J].Journal of Marine Science and Technology,2011,16:22-50.
[9]Akyildiz H,Unal E.Experimental investigation of pressure distribution on a rectangular container due to the liquid sloshing[J].Ocean Engineering,2005,32:1503-1516.
[10]Akildiz H,Unal E.Sloshing in a three-dimensional rectangular container:numerical simulation and experimental validation[J].Ocean Engineering,2006,33:2135-2149.
[11]Akildiz H.A numerical study of the effects of the vertical baffle on liquid sloshing in two-dimensional rectangular container[J].Journal of Sound and Vibration,2012,332:41-52.
[12]Armenio V,Rocca M L.On the analysis of sloshing of water in rectangular containers:numerical study and experimental validation[J].Ocean Engineering,1996,23(8):705-739.
[13]Bae H S,Yun Y W,Park M K.Flow response of magnetic fluid surface by pitching motion[J].Journal of Mechanical Science and Technology,2010,24(2):583-592.
[14]Celebi M S,Akyildiz H.Nonlinear modeling of liquid sloshing in a moving rectangular container[J].Ocean Engineering,2002,29:1527-1553.
[15]Xue M A,Lin P Z.Numerical study of ring baffle effects on reducing violent liquid sloshing[J].Computers and Fluids,2011,52:116-129.
[16]肖龙飞,杨建民,郭彬.浅水FPSO垂荡和纵摇运动的低频响应[J].舰船科学技术,2009,31(11):120-125.Xiao L F,Yang J M,Guo B.Low frequency heave and pitch motions of FPSO in shallow water[J].Ship Science and Technology,2009,31(11):120-125.
[17]尹立中,邹经湘,王本利.俯仰运动圆柱贮箱中液体的非线性晃动[J].力学学报,2000,32(3):280-290.Yin L Z,Zou J X,Wang B L.Nonlinear sloshing of liquid in a circular cylindrical container under pitching excitation[J].Chinese Journal of Theoretical and Applied Mechanics,2000,32(3):280-290.
[18]洪亮,朱仁传,缪国平,范菊.液舱晃荡对船舶横摇运动影响的数值研究[J].中国造船,2015,1:1-10.Hong L,Zhu R Z,Miu G P,Fan J.Numerical research on effect of sloshing on ship roll motion[J].Shipbuilding of China,2015,1:1-10.
[19]徐国徽,胡嘉骏,顾学康.耦合运动下液货舱晃荡压力预报研究[J].船舶力学,2016,20(7):884-891.Xu G H,Hu J J,Gu X K.Prediction of sloshing pressure in coupled motions for Liquid Cargo Carriers[J].Journal of Ship Mechanics,2016,20(7):884-891.
[20]李玉成,滕斌.波浪对海上建筑物的作用(第2版)[M].北京:海洋出版社,2002.Li Y C,Teng B.Wave action on marine structures(2nd Eidtion)[M].Beijing:Ocean Press,2002.
[21]宁德志.快速多极子边界元方法在完全非线性水波问题中的应用[D].大连:大连理工大学,2005.Ning D Z.Application of the fast multiple boundary element method to the fully nonlinear water wave problems[D].Dalian:Ph.D thesis,Dalian University of Technology,2005.
[22]Higuchi M,Tanaka T,Endo S.Study on hull vibration-induced container liquid sloshing in LPG containerers[R].Nippon Kokan Technology Report,1976,72:111-122.
[2]Nakayama T,Washizu K.Nonlinear analysis of liquid motion in a container subjected to forced pitching oscillation[J].International Journal for Numerical Methods in Engineering,1980,15:1207-1220.
[3]Nakayama T,Washizu K.The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems[J].International Journal for Numerical Methods in Engineering,1981,17:1631-1646.
[4]Chen B F,Chiang H W.Complete 2D and fully nonlinear analysis of ideal fluid in containers[J].Journal of Engineering Mechanics,1999,125(1):70-78.
[5]Chen B F,Chiang H W.Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating container[J].Ocean Engineering,2000,27:953-977.
[6]Chen B F,Nokes R.Time-independent finite difference analysis of fully non-linear and viscous fluid sloshing in a rectangular container[J].Journal of Computational Physics,2005,209:47-81.
[7]Chen B F,Asce M.Viscous fluid in container under coupled surge,heave and pitch motions[J].Journal of Waterway,Port,Coastal and Ocean Engineering,2005,131(5):239-256.
[8]Chen B F,Wu C H.Effects of excitation angle and coupled heave-surge-sway motion on fluid sloshing in a three-dimensional container[J].Journal of Marine Science and Technology,2011,16:22-50.
[9]Akyildiz H,Unal E.Experimental investigation of pressure distribution on a rectangular container due to the liquid sloshing[J].Ocean Engineering,2005,32:1503-1516.
[10]Akildiz H,Unal E.Sloshing in a three-dimensional rectangular container:numerical simulation and experimental validation[J].Ocean Engineering,2006,33:2135-2149.
[11]Akildiz H.A numerical study of the effects of the vertical baffle on liquid sloshing in two-dimensional rectangular container[J].Journal of Sound and Vibration,2012,332:41-52.
[12]Armenio V,Rocca M L.On the analysis of sloshing of water in rectangular containers:numerical study and experimental validation[J].Ocean Engineering,1996,23(8):705-739.
[13]Bae H S,Yun Y W,Park M K.Flow response of magnetic fluid surface by pitching motion[J].Journal of Mechanical Science and Technology,2010,24(2):583-592.
[14]Celebi M S,Akyildiz H.Nonlinear modeling of liquid sloshing in a moving rectangular container[J].Ocean Engineering,2002,29:1527-1553.
[15]Xue M A,Lin P Z.Numerical study of ring baffle effects on reducing violent liquid sloshing[J].Computers and Fluids,2011,52:116-129.
[16]肖龙飞,杨建民,郭彬.浅水FPSO垂荡和纵摇运动的低频响应[J].舰船科学技术,2009,31(11):120-125.Xiao L F,Yang J M,Guo B.Low frequency heave and pitch motions of FPSO in shallow water[J].Ship Science and Technology,2009,31(11):120-125.
[17]尹立中,邹经湘,王本利.俯仰运动圆柱贮箱中液体的非线性晃动[J].力学学报,2000,32(3):280-290.Yin L Z,Zou J X,Wang B L.Nonlinear sloshing of liquid in a circular cylindrical container under pitching excitation[J].Chinese Journal of Theoretical and Applied Mechanics,2000,32(3):280-290.
[18]洪亮,朱仁传,缪国平,范菊.液舱晃荡对船舶横摇运动影响的数值研究[J].中国造船,2015,1:1-10.Hong L,Zhu R Z,Miu G P,Fan J.Numerical research on effect of sloshing on ship roll motion[J].Shipbuilding of China,2015,1:1-10.
[19]徐国徽,胡嘉骏,顾学康.耦合运动下液货舱晃荡压力预报研究[J].船舶力学,2016,20(7):884-891.Xu G H,Hu J J,Gu X K.Prediction of sloshing pressure in coupled motions for Liquid Cargo Carriers[J].Journal of Ship Mechanics,2016,20(7):884-891.
[20]李玉成,滕斌.波浪对海上建筑物的作用(第2版)[M].北京:海洋出版社,2002.Li Y C,Teng B.Wave action on marine structures(2nd Eidtion)[M].Beijing:Ocean Press,2002.
[21]宁德志.快速多极子边界元方法在完全非线性水波问题中的应用[D].大连:大连理工大学,2005.Ning D Z.Application of the fast multiple boundary element method to the fully nonlinear water wave problems[D].Dalian:Ph.D thesis,Dalian University of Technology,2005.
[22]Higuchi M,Tanaka T,Endo S.Study on hull vibration-induced container liquid sloshing in LPG containerers[R].Nippon Kokan Technology Report,1976,72:111-122.