FPSO在波浪中的底部砰击载荷研究
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摘要
当前船舶底部砰击荷载的理论模型是二维楔形或三维锥体以恒定的速度进入初始静止水面，采用边界元方法求解。由于边界元求解方法受限于研究领域，且程序的通用性差，因而不能广泛地应用于工程领域。
本文提出了一种适用于浮式生产储油船(FPSO)的底部砰击荷载的计算方法。这种方法包含三部分内容：采用三维频域边界元法计算FPSO在波浪上的频域运动响应；采用时频转换法得到FPSO船体剖面与波面的垂向相对运动的时间历程，和确定砰击发生的时刻和砰击时船体入水的速度；采用计算流体力学方法(CFD)建立二维入水模型，直接剖面计算压力分布和垂向力。
数值计算结果表明，FPSO在压载斜浪入射状态下，相对运动的幅值和出水后的入水的速度幅值最大，最易发生砰击。砰击最大压力和发生砰击的船剖面的几何形状有很大的关系。其中底部平底半宽对砰击压力系数有重要的影响，特别对于类似于FPSO的大平底肥大型工程船影响尤为显著。本文以无因次化平底半宽为自变量得到估算砰击压力系数的回归公式，以供工程设计应用。
此方法可简便快速地用于预报FPSO在其工作海域下不同工况下的底部砰击载荷，具有工程上可接受的精度，其结果可为后续结构强度校核提供设计参数。
The Boundary Element Method (BEM) is a popular method used to solve the bottom slamming caused by the entering of the two-dimensional wedge or three-dimensional cone into the initial still water with a constant velocity. Because of the limited research field and bad generosity of program, this method can not be applied in practical engineering widely.
In this paper, a process which is easy to estimate the slamming load is proposed. The process has three steps. Firstly, the 3D BEM is applied to calculate the motions of the FPSO in frequency domain. Secondly the frequency-time transformation method is used to obtain the relative motions in time domain and get slamming occurrence time and its entry-water velocity. Finally, the two dimensional model established with the method of CFD(computational fluid dynamics) to directly calculate the distribution of the load and the vertical force on the FPSO section.
The numerical results show that the FPSO which have the largest relative motions and relative velocity amplitudes, will more likely lead to occur slamming on the condition of blast loads and the incident wave angle of 135 degree. The max slamming loads is greatly related to the shape of the ship section. the half-breadth of the flat bottom is one of the most important factors for slamming loads coefficients, especially for full-formed ship of FPSO shape with large flat bottom. In this paper, a regression formula to estimate the slamming load coefficient is obtained, with the independent variable of the half breadth of the flat bottom, which is conveniently applied in the engineering practice.
The method in this paper can be easily applied to estimate the slamming load magnitude with acceptable precision, and the results can be used for strength analysis of bottom frame.
本文提出了一种适用于浮式生产储油船(FPSO)的底部砰击荷载的计算方法。这种方法包含三部分内容：采用三维频域边界元法计算FPSO在波浪上的频域运动响应；采用时频转换法得到FPSO船体剖面与波面的垂向相对运动的时间历程，和确定砰击发生的时刻和砰击时船体入水的速度；采用计算流体力学方法(CFD)建立二维入水模型，直接剖面计算压力分布和垂向力。
数值计算结果表明，FPSO在压载斜浪入射状态下，相对运动的幅值和出水后的入水的速度幅值最大，最易发生砰击。砰击最大压力和发生砰击的船剖面的几何形状有很大的关系。其中底部平底半宽对砰击压力系数有重要的影响，特别对于类似于FPSO的大平底肥大型工程船影响尤为显著。本文以无因次化平底半宽为自变量得到估算砰击压力系数的回归公式，以供工程设计应用。
此方法可简便快速地用于预报FPSO在其工作海域下不同工况下的底部砰击载荷，具有工程上可接受的精度，其结果可为后续结构强度校核提供设计参数。
The Boundary Element Method (BEM) is a popular method used to solve the bottom slamming caused by the entering of the two-dimensional wedge or three-dimensional cone into the initial still water with a constant velocity. Because of the limited research field and bad generosity of program, this method can not be applied in practical engineering widely.
In this paper, a process which is easy to estimate the slamming load is proposed. The process has three steps. Firstly, the 3D BEM is applied to calculate the motions of the FPSO in frequency domain. Secondly the frequency-time transformation method is used to obtain the relative motions in time domain and get slamming occurrence time and its entry-water velocity. Finally, the two dimensional model established with the method of CFD(computational fluid dynamics) to directly calculate the distribution of the load and the vertical force on the FPSO section.
The numerical results show that the FPSO which have the largest relative motions and relative velocity amplitudes, will more likely lead to occur slamming on the condition of blast loads and the incident wave angle of 135 degree. The max slamming loads is greatly related to the shape of the ship section. the half-breadth of the flat bottom is one of the most important factors for slamming loads coefficients, especially for full-formed ship of FPSO shape with large flat bottom. In this paper, a regression formula to estimate the slamming load coefficient is obtained, with the independent variable of the half breadth of the flat bottom, which is conveniently applied in the engineering practice.
The method in this paper can be easily applied to estimate the slamming load magnitude with acceptable precision, and the results can be used for strength analysis of bottom frame.
引文
[1] O M Faltinsen, Maurizio Landrini, Marilena Greco. Slamming in marine applications. Journal of Engineering Mathematics 2004, 48: 187-217.
[2] 戴仰山，宋竞正．船体在海浪中的弯矩．中国造船，1980(3)：71-84．
[3] Marine Composites, 92-94.
[4] Ochi M K, Motter L E. Prediction of slamming characteristics and hull response for ship design. Trans. SNAME, 1973, Vol. 81: 144-176.
[5] T Von Karman. The impact of seaplane floats during landing. Nat. Adv. Com. for Aeronautics. Tech. Note321 (1929) 309—313.
[6] H Wagner. Ober Stoss- und Gleitvorgange an tier Oberflache yon Flussigkeiten. ZAMM 12 (1932) 192-235.
[7] Stavovy A B, Chuang S L. Analytical determination of slamming pressures for high-speed vehicle in wave. JSR, 1976, Vol. 20(4): 190-198.
[8] 胡嘉骏，蔡新钢．船舶表面点砰击压力的预报方法．船舶力学，2005，Vol．9(No．1)：63-70．
[9] G K Kapsenberg, A P van't Veer, J P HackeR, M M D Levadou. Aftbody Slamming and Whipping Load. Maritime Research Institute Netherlands, Northrop Grumman Ship Systems.
[10] Ferdinace I V. Theoretical consideration on the penetration of a wedge. ISP, 1966(4): 102-116.
[11] Korobkin A A, Pukhnachov V V. Initial stage of water impact. Ann. Rev. Fluid Mech, 1988, Vol. 20: 159-185.
[12] Coint R. Free surface flows close to a surface-piercing body. Mathematical Approaches in Hydrodynamic, 1991: 319-334.
[13] Howison S D, Ockendon J R, Wilsen, S K. Incompressible water-entry problems at small deadrise angles. J. Fluid Mech, 1991, Vol. 222: 215-230.
[14] Dobrovoi'skaya, Z N. On some problems of similarity flow of fluid with a free surface. J. Fluid Mech, 1969, Vol. 36: 805-829.
[15] Zhao R, Faltinsen O. Water Entry of two-dimension Body. Journal of Fluid Mechnies, 1993, Vol. 246: 593-612.
[16] Zhao R, Faltinsen O M, Aarsnes J V. Water entry of arbitrary two-dimensional sections with and without flow separation. Prec. 21st Symp. Naval Hydrodynamics. Trondheim, Norway, 1996: 408-423.
[17] Muzaferija S, Peric M, Sames P, et al. A two-fluid Navier-Stokes sokes solver to simulate water entry. Prec. 22nd Symp. Naval Hydrodynamics, Washington DC, USA, 1998: 277-289.
[18] Schumann C. Volume-of-fluid computatibns of water entry of bow sections. Proe.EUROMECH 374. Poitiers, France, 1998.
[19] Scolan Y M, Korobkin A A. Three-dimensional theory of water impact. Part 1: Inverse Wagner problem. Journal of Fluid Mechanics 2001, 440: 293-326.
[20] Sames P C, Schellin T E, Muzaferija S, et al. Application of a two-fluid finite volume method to ship slamming. Prec. 17nd Int. Conf. Off-(OMAE'98), Lisbon, Portugal.
[21] Ge Wang, Shaojie Tang, Yung Shin. A Direct Calculation Approach for Designing a Ship-shaped FPSO's Bow Against Wave Slamming Load. Proceedings of The Twelfth International Offshore and Polar Engineering Conference Kitakushu, Japan, 2002: 163-168.
[22] Ole A Hermundstad, Torgeir Moan, Hans Jorgen, et al. Motions and Slamming Loads on a Re-Re Ship. 9th Symposium on Practical Design of Ships and Other Floating Structures Luebeck-Travemuende, Germany. 2004.
[23] 刘应中，缪国平．船舶在波浪上的运动理论．上海：上海交通大学出版社，1986．
[24] 戴遗山，贺五洲．简单Green函数法求解三维水动力系数．中国造船，1986，Vol．93(2)：1-15p．
[25] Maniar H. A three dimensional higher-order panel method based on B-splines: [Ph.D. Thesis], Department of Ocean Engineering, MIT, Cambridge, Massachusetts, 1995.
[26] 缪国平，刘应中，杨勤正等．三维脉动源的Michell型表达式．中国造船，1995，13l：1-11．
[27] 宗智，黄鼎良．三维移动脉动源速度势的数值研究．水动力研究与进展．1991，6：56-63．
[28] 钱昆．浮体在大幅波浪中的运动和荷载计算研究：[博士学位论文]．大连：大连理工大学船舶工程系，2004．
[29] 戴愚志，余建星．一种船体及周围自由面的网格自动生成方法．船舶工程．2005，28(5)．1-4．
[30] Jonh L Hess, A M O Smith. Calculation of Nonlifting Potential Flow About Arbitrary Three-Dimensional Bodies. Journal of Ship Research. 1964, September: 22-43.
[31] 薛密．数值数学和计算．上海：复旦大学出版社，1991．
[32] Beck, R F. and Loken, K. Three dimensional effects in ship relative motion problems. JSR, 1989, Vol. 33.
[33] Inglis R B. A three dimensional analysis of the motion of arigid ship in waves[D]. Unversity of London, 1980.
[34] C J Garrison. Hydrodynamic Loading of Large Offshore Structures: Three- Dimensional Source Distribution Methods. In: Numerical Methods in Offshore Engineering. Chichester; Zienkiewicz, R. W. Lewis, K. G. Stagg. 1978: 87-141.
[35] Garrison C J. Hydrodynamics of large objects in the sea, Part Ⅰ-Hyrdrodynamic analysis. Journal of Hydronautics.1974, 8: 5-12.
[36] Faltinsen O M, Miehelsen. Motion of large structures in waves, in: The dynamics of marine vehicles and structures in waves. The institution of Mechanical engineers, 1974: paper 11
[37] G Telste, F Noblesse. Numerical Evaluation of the Green Function of Water-Wave Radiation and Diffraction. Journal of Ship Research. 1986, 30(2), 69-84.
[38] J N Newman. Double-Precision Evaluation of The Oscillatory Source Potential. Journal of The Ship Research. 1954, 25(3), sep: 151-154.
[39] Haskind M D. On Wave Motions of a Heavy Fluid. Prikladnaya Matematika I Mekahannika, 1954, 18: 15-26.
[40] 王言英，海洋工程导论，大连：大连工学院，1986．
[41] 俞聿修．随机波浪及其工程应用．大连：大连理工大学出版社，2000．222-232．
[42] 曾芬芳，黄国建．虚拟海洋场景中波浪的模拟．计算机应用，2001，Vol．21，No．4．
[43] Campell, Weynberg. Measurement of parameter Affecting Slamming. Southampton: University of Southampton, 1980.
[44] 王福军，计算流体动力学分析—CFD软件原理与应用．北京：清华大学出版社，2004．
[45] Sheng-Lun Chuang. Experiments on Slamming of Wedge-Shaped Bodies. Journal of Ship Research 1967, 11:190-198.
[46] 陈震，肖熙．二维楔形体入水砰击仿真研究．上海交通大学学报．2007，4l(9)：1425-1428．
[47] M K Ochi, L E Motter. A Method to Estimate Slamming Characteristics for Ship Design. Marine Technology. 1971, april:219-232.
[2] 戴仰山，宋竞正．船体在海浪中的弯矩．中国造船，1980(3)：71-84．
[3] Marine Composites, 92-94.
[4] Ochi M K, Motter L E. Prediction of slamming characteristics and hull response for ship design. Trans. SNAME, 1973, Vol. 81: 144-176.
[5] T Von Karman. The impact of seaplane floats during landing. Nat. Adv. Com. for Aeronautics. Tech. Note321 (1929) 309—313.
[6] H Wagner. Ober Stoss- und Gleitvorgange an tier Oberflache yon Flussigkeiten. ZAMM 12 (1932) 192-235.
[7] Stavovy A B, Chuang S L. Analytical determination of slamming pressures for high-speed vehicle in wave. JSR, 1976, Vol. 20(4): 190-198.
[8] 胡嘉骏，蔡新钢．船舶表面点砰击压力的预报方法．船舶力学，2005，Vol．9(No．1)：63-70．
[9] G K Kapsenberg, A P van't Veer, J P HackeR, M M D Levadou. Aftbody Slamming and Whipping Load. Maritime Research Institute Netherlands, Northrop Grumman Ship Systems.
[10] Ferdinace I V. Theoretical consideration on the penetration of a wedge. ISP, 1966(4): 102-116.
[11] Korobkin A A, Pukhnachov V V. Initial stage of water impact. Ann. Rev. Fluid Mech, 1988, Vol. 20: 159-185.
[12] Coint R. Free surface flows close to a surface-piercing body. Mathematical Approaches in Hydrodynamic, 1991: 319-334.
[13] Howison S D, Ockendon J R, Wilsen, S K. Incompressible water-entry problems at small deadrise angles. J. Fluid Mech, 1991, Vol. 222: 215-230.
[14] Dobrovoi'skaya, Z N. On some problems of similarity flow of fluid with a free surface. J. Fluid Mech, 1969, Vol. 36: 805-829.
[15] Zhao R, Faltinsen O. Water Entry of two-dimension Body. Journal of Fluid Mechnies, 1993, Vol. 246: 593-612.
[16] Zhao R, Faltinsen O M, Aarsnes J V. Water entry of arbitrary two-dimensional sections with and without flow separation. Prec. 21st Symp. Naval Hydrodynamics. Trondheim, Norway, 1996: 408-423.
[17] Muzaferija S, Peric M, Sames P, et al. A two-fluid Navier-Stokes sokes solver to simulate water entry. Prec. 22nd Symp. Naval Hydrodynamics, Washington DC, USA, 1998: 277-289.
[18] Schumann C. Volume-of-fluid computatibns of water entry of bow sections. Proe.EUROMECH 374. Poitiers, France, 1998.
[19] Scolan Y M, Korobkin A A. Three-dimensional theory of water impact. Part 1: Inverse Wagner problem. Journal of Fluid Mechanics 2001, 440: 293-326.
[20] Sames P C, Schellin T E, Muzaferija S, et al. Application of a two-fluid finite volume method to ship slamming. Prec. 17nd Int. Conf. Off-(OMAE'98), Lisbon, Portugal.
[21] Ge Wang, Shaojie Tang, Yung Shin. A Direct Calculation Approach for Designing a Ship-shaped FPSO's Bow Against Wave Slamming Load. Proceedings of The Twelfth International Offshore and Polar Engineering Conference Kitakushu, Japan, 2002: 163-168.
[22] Ole A Hermundstad, Torgeir Moan, Hans Jorgen, et al. Motions and Slamming Loads on a Re-Re Ship. 9th Symposium on Practical Design of Ships and Other Floating Structures Luebeck-Travemuende, Germany. 2004.
[23] 刘应中，缪国平．船舶在波浪上的运动理论．上海：上海交通大学出版社，1986．
[24] 戴遗山，贺五洲．简单Green函数法求解三维水动力系数．中国造船，1986，Vol．93(2)：1-15p．
[25] Maniar H. A three dimensional higher-order panel method based on B-splines: [Ph.D. Thesis], Department of Ocean Engineering, MIT, Cambridge, Massachusetts, 1995.
[26] 缪国平，刘应中，杨勤正等．三维脉动源的Michell型表达式．中国造船，1995，13l：1-11．
[27] 宗智，黄鼎良．三维移动脉动源速度势的数值研究．水动力研究与进展．1991，6：56-63．
[28] 钱昆．浮体在大幅波浪中的运动和荷载计算研究：[博士学位论文]．大连：大连理工大学船舶工程系，2004．
[29] 戴愚志，余建星．一种船体及周围自由面的网格自动生成方法．船舶工程．2005，28(5)．1-4．
[30] Jonh L Hess, A M O Smith. Calculation of Nonlifting Potential Flow About Arbitrary Three-Dimensional Bodies. Journal of Ship Research. 1964, September: 22-43.
[31] 薛密．数值数学和计算．上海：复旦大学出版社，1991．
[32] Beck, R F. and Loken, K. Three dimensional effects in ship relative motion problems. JSR, 1989, Vol. 33.
[33] Inglis R B. A three dimensional analysis of the motion of arigid ship in waves[D]. Unversity of London, 1980.
[34] C J Garrison. Hydrodynamic Loading of Large Offshore Structures: Three- Dimensional Source Distribution Methods. In: Numerical Methods in Offshore Engineering. Chichester; Zienkiewicz, R. W. Lewis, K. G. Stagg. 1978: 87-141.
[35] Garrison C J. Hydrodynamics of large objects in the sea, Part Ⅰ-Hyrdrodynamic analysis. Journal of Hydronautics.1974, 8: 5-12.
[36] Faltinsen O M, Miehelsen. Motion of large structures in waves, in: The dynamics of marine vehicles and structures in waves. The institution of Mechanical engineers, 1974: paper 11
[37] G Telste, F Noblesse. Numerical Evaluation of the Green Function of Water-Wave Radiation and Diffraction. Journal of Ship Research. 1986, 30(2), 69-84.
[38] J N Newman. Double-Precision Evaluation of The Oscillatory Source Potential. Journal of The Ship Research. 1954, 25(3), sep: 151-154.
[39] Haskind M D. On Wave Motions of a Heavy Fluid. Prikladnaya Matematika I Mekahannika, 1954, 18: 15-26.
[40] 王言英，海洋工程导论，大连：大连工学院，1986．
[41] 俞聿修．随机波浪及其工程应用．大连：大连理工大学出版社，2000．222-232．
[42] 曾芬芳，黄国建．虚拟海洋场景中波浪的模拟．计算机应用，2001，Vol．21，No．4．
[43] Campell, Weynberg. Measurement of parameter Affecting Slamming. Southampton: University of Southampton, 1980.
[44] 王福军，计算流体动力学分析—CFD软件原理与应用．北京：清华大学出版社，2004．
[45] Sheng-Lun Chuang. Experiments on Slamming of Wedge-Shaped Bodies. Journal of Ship Research 1967, 11:190-198.
[46] 陈震，肖熙．二维楔形体入水砰击仿真研究．上海交通大学学报．2007，4l(9)：1425-1428．
[47] M K Ochi, L E Motter. A Method to Estimate Slamming Characteristics for Ship Design. Marine Technology. 1971, april:219-232.