Spar平台水动力载荷及垂荡—纵摇耦合运动分析
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摘要
本文研究深海Spar平台的波浪载荷和水动力系数,以及平台垂荡-纵摇耦合运动的马休稳定性问题。研究工作对于深海Spar平台的设计和开发具有重要的意义。
由于平台的结构特点,纵摇的回复力系数是平台排水量和纵摇初稳性高的函数,平台垂荡时排水量和初稳性高也随时间变化,因此平台的垂荡和纵摇耦合运动为可以用参数激励方程表示。当Spar平台有较大的垂荡运动,且平台垂荡运动频率和纵摇固有频率满足2:1内共振关系时,纵摇运动出现马休失稳。当马休不稳定出现时,垂荡运动能量向纵摇传递并显著的加大纵摇运动幅值。
对于主体波浪力的求解,文中用半解析方法研究孤立的截断的浮式Spar平台主体的一阶绕射问题,在Matlab平台上编制了波浪力计算程序。程序可以计算在不同波浪入射角时的纵荡激励力、垂荡激励力和纵摇激励力矩。对于水动力系数的求解,理论上用半解析方法研究了孤立截断浮式Spar平台主体的一阶辐射问题,推导了一阶辐射速度势的计算公式,在Matlab平台上开发了Spar平台主体水动力系数计算程序。程序可以求解纵荡附加质量系数、纵荡附加阻尼系数、垂荡附加质量系数、垂荡附加阻尼系数、纵摇附加质量系数和纵摇纵荡附加阻尼系数。两个程序得到的数值计算结果与WAMIT等软件计算结果一致。因此可应用于Spar平台的运动计算。文中运用集中质量方法模拟锚链,并编制了锚链和平台的耦合运动计算程序。
研究结果表明:平台的垂荡运动对于波面升高最为敏感;纵摇阻尼对于平台纵摇运动的稳定性起到了非常重要的作用;锚链对抑制纵摇失稳作用显著,但它不直接作用在纵摇上而是通过减小平台的垂荡运动幅值来影响纵摇稳定性。
The objectives of this study are to obtain wave loads and hydrodynamic coefficients for Spar platform and to evaluate heave-pitch coupling motion and Mathieu instability, which are referable in design and fabrication of spar platform.
According to the characteristic of Spar, the pitch restoring coefficient can be represented by a function of the displaced volume and the metacentric height of Spar. Due to heave motion, the displaced volume and the metacentric height of Spar platform change in time and this heave-pitch coupling can be represented by parameter excited equation. Mathieu instability for a Spar platform arises when there is large heave motion and the period of the heave motion is half of the pitch natural. In the process, kinetic energy is transferred from heave mode to pitch and the amplitude of pitch is magnified considerably.
For wave exciting force, the main body of the Spar platform is simplified as an isolated truncated float vertical cylinder. An exact semi-analytical method is described to solve one order diffraction problem of Spar platform and a computer program is developed for obtaining surge, heave wave exciting force and pitch wave exciting moment in different wave heading. For hydrodynamic coefficients, using the same simplified model, one order radiation problem of Spar platform is in detail deduced by using semi-analytical method in theory and also a computer program is developed for obtaining the added mass and damping coefficients of surge, heave and pitch respectively. The two Calculation program ware compiled using Matlab software. Comparisons between the numerical results given in the paper and those obtained from MOSES and WAMIT show excellent agreement. The results can be used for calculating motion of Spar. The mooring is simulated by lumped mass model and coupled with the hull of Spar to evaluate the motion of Spar by a coupled program.
The results in this paper show that the wave elevation effect is the main reason for inducing heave motion and the pitch damping coefficient significantly affects the Mathieu instability. The results also show that mooring effect can suppress the Mathieu instability by reducing the heave amplitude but not directly function on pitch.
由于平台的结构特点,纵摇的回复力系数是平台排水量和纵摇初稳性高的函数,平台垂荡时排水量和初稳性高也随时间变化,因此平台的垂荡和纵摇耦合运动为可以用参数激励方程表示。当Spar平台有较大的垂荡运动,且平台垂荡运动频率和纵摇固有频率满足2:1内共振关系时,纵摇运动出现马休失稳。当马休不稳定出现时,垂荡运动能量向纵摇传递并显著的加大纵摇运动幅值。
对于主体波浪力的求解,文中用半解析方法研究孤立的截断的浮式Spar平台主体的一阶绕射问题,在Matlab平台上编制了波浪力计算程序。程序可以计算在不同波浪入射角时的纵荡激励力、垂荡激励力和纵摇激励力矩。对于水动力系数的求解,理论上用半解析方法研究了孤立截断浮式Spar平台主体的一阶辐射问题,推导了一阶辐射速度势的计算公式,在Matlab平台上开发了Spar平台主体水动力系数计算程序。程序可以求解纵荡附加质量系数、纵荡附加阻尼系数、垂荡附加质量系数、垂荡附加阻尼系数、纵摇附加质量系数和纵摇纵荡附加阻尼系数。两个程序得到的数值计算结果与WAMIT等软件计算结果一致。因此可应用于Spar平台的运动计算。文中运用集中质量方法模拟锚链,并编制了锚链和平台的耦合运动计算程序。
研究结果表明:平台的垂荡运动对于波面升高最为敏感;纵摇阻尼对于平台纵摇运动的稳定性起到了非常重要的作用;锚链对抑制纵摇失稳作用显著,但它不直接作用在纵摇上而是通过减小平台的垂荡运动幅值来影响纵摇稳定性。
The objectives of this study are to obtain wave loads and hydrodynamic coefficients for Spar platform and to evaluate heave-pitch coupling motion and Mathieu instability, which are referable in design and fabrication of spar platform.
According to the characteristic of Spar, the pitch restoring coefficient can be represented by a function of the displaced volume and the metacentric height of Spar. Due to heave motion, the displaced volume and the metacentric height of Spar platform change in time and this heave-pitch coupling can be represented by parameter excited equation. Mathieu instability for a Spar platform arises when there is large heave motion and the period of the heave motion is half of the pitch natural. In the process, kinetic energy is transferred from heave mode to pitch and the amplitude of pitch is magnified considerably.
For wave exciting force, the main body of the Spar platform is simplified as an isolated truncated float vertical cylinder. An exact semi-analytical method is described to solve one order diffraction problem of Spar platform and a computer program is developed for obtaining surge, heave wave exciting force and pitch wave exciting moment in different wave heading. For hydrodynamic coefficients, using the same simplified model, one order radiation problem of Spar platform is in detail deduced by using semi-analytical method in theory and also a computer program is developed for obtaining the added mass and damping coefficients of surge, heave and pitch respectively. The two Calculation program ware compiled using Matlab software. Comparisons between the numerical results given in the paper and those obtained from MOSES and WAMIT show excellent agreement. The results can be used for calculating motion of Spar. The mooring is simulated by lumped mass model and coupled with the hull of Spar to evaluate the motion of Spar by a coupled program.
The results in this paper show that the wave elevation effect is the main reason for inducing heave motion and the pitch damping coefficient significantly affects the Mathieu instability. The results also show that mooring effect can suppress the Mathieu instability by reducing the heave amplitude but not directly function on pitch.
引文
[1]李润培,谢永和,深海平台技术的研究现状与发展趋势[J],中国海洋平台,2003,18(3),1～5
[2]董艳秋,深水采油平台波浪载荷及响应[M],天津:天津大学出版社,2005
[3]张智,董艳秋,芮光六,一种新型的深海采油平台Spar[J],中国海洋平台,2004,19(6):29～35
[4]John Halkyard,Spar Platform for Deep Water Oil and Gas Fields[J],Moring Technology Society Journal,1996,30(3):3～12
[5]Don Selle,Murphy Kikeh Project Achieves Major Milestones[J],INTEC Quarterly Journal,2006(4)
[6]John Halkyard,Spar General Response,CSO Aker Engineering,inc,2001
[7]A. N. Williams,Z. Demirbilek,Hydrodynamic Interactions in Floating Cylinder Array-I. Wave Scattering[J],Ocean Engineering,1988,15(6):549～583
[8]A. N. Williams,Z. Demirbilek,Hydrodynamic Interactions in Floating Cylinder Array-II. Wave Radiation,Ocean Engineering,1989,16(3):217～263
[9]D. D. Bhatta,M. Rahman,Wave Loadings on a Vertical Cylinder due to Heave Motion,International Journal of Mathematics & Mathematic science,1995,18(1):151～170
[10]Oguz Yilmaz,Hydrodynamic Interactions of Waves with Group of Truncated Vertical Cylinder,Journal of Waterway,Port,Coastal and Ocean Engineering,1998:272～279
[11]Oguz Yilmaz,Atilla Incecik. Analytical Solutions of the Diffraction Problem of a Group of Truncated Vertical Cylinder[J],Ocean Engineering,1998,25(6):385～394
[12]A. Sarkar,R. Eatock Taylor,Low-Frequency Responses of Nonlinear Moored Vessels in Random Waves: Coupled Surge, Pitch and Heave Motions[J],Journal of Fluids and Structures,2001,15:133～150
[13]Y. Drobyshevski,Hydrodynamic Coefficients of a Floating, Truncated Vertical Cylinder in Shallow Water[J],Ocean Engineering,2004,31:269～304
[14]李远林,近海结构水动力学[M],广州:华南理工大学出版社, 1999
[15]李玉成,腾斌,波浪对海上建筑物的作用[M],北京:海洋出版社,2002
[16]胡志敏,董艳秋,张建民,张力腿平台波浪载荷计算[J],中国海洋平台, 2002, 17(3):6～11
[17]胡志敏,董艳秋,张建民,张力腿平台水动力参数计算,海洋工程,2002,20(3): 14～22
[18]吴应湘,李华,曾晓辉等,深海采油平台发展现状和设计中的关键问题[J],中国造船,2002,43卷增刊:80～86
[19]曾晓辉,沈晓鹏,吴应湘等,深海平台分析和设计中的关键力学问题[J],船舶工程,2005,27(5):18～21
[20]张帆,杨建民,Spar平台的发展趋势及其关键技术[J],中国海洋平台,2005,20(2)6～11
[21]B. J. Koo,Evaluation Of The Effect Of Contact Between Risers And Guide Frames On Offshore Spar Platform Motions:[PhD Thesis],Texas;Texas A&M University,2003
[22]Haslum H. A.,Faltinsen O. M.,Alternative Shape of Spar Platforms for Use in Hostile Areas,Proceedings of the 31st Offshore Technology Conference,Huston,1999,217~288
[23]Jun B. Rho,Hang S,Heave and Pitch Motions of a Spar Platform with Damping Plate,Proceeding of the 12th inter Offshore and Polar Eng. Conf.,kitakyushu,japan,2002,26～31
[24]Jun B. Rho,Hang S,An Experimental Study for Mooring Effects on the Stability of Spar Platform,Proceeding of the 13th inter Offshore and Polar Eng. Conf.,Honolulu,Hawaii,USA,2003,25～30
[25]Zhang L.,Zou J.,Mathieu Instability Evaluation for DDVC/SPAR and TLP Tendon Design,Proceedings of the 11th Offshore Symposium, Society of Naval Architect and Marine Engineer,Houston,2002,41～49
[26]B. J. Koo,M. H. Kim,R. E. Randall,Mathieu Instability Of A Spar Platform With Mooring And Risers[J],Ocean Engineering,2004,31:2175～2208
[27]Jun B. Rho,Hang S,a study on Mathieu-type instability of conventional spar platform in regular waves[J],International Journal of Offshore and Polar Engineering,2005,15(2):104~108
[28]Yong-Pyo Hong,Dong-Yeon Lee,An Experimental Study on the Extreme Motion Responses of a Spar Platform in the Heave Resonant Waves ,Proceedings of the 15th inter Offshore and Polar Eng. Conf.,seoul,korea,2005,19～24
[29]贾启芬,刘习军,工程动力学,天津:天津大学出版社,1999
[30]Xiaohong Chen,Jun Zhang,Wei Ma,Studies On Dynamic Coupling Effects Between A Spar And Its Mooring Lines[J],Ocean Engineering,2001,28:863～887
[31]王家楣,张志宏,流体力学[M],大连:大连海事大学出版社,2002
[32]JRME,WAMIT-MOSES Hydrodynamic Analysis Comparison Study,2000
[33]A.K. Agarwal,A.K. Jain,Dynamic Behavior Of Offshore Spar Platforms Under Regular Sea Waves,Ocean Engineering,2003,30:487～516
[34]A.K. Agarwal,A.K. Jain,Nonlinear Coupled Dynamic Response Of Offshore Spar Platforms Under Regular Sea Waves[J],Ocean Engineering,2003,30:517～551
[35]Sangsoo Ryu , Hull/Mooring/Riser Coupled Motion Simulations of Thruster-assisted Moored Platforms; [PhD Thesis],Texas;Texas A&M University,2003
[36]H. Ormberga,K. Larsenb,Coupled Analysis Of Floater Motion And Mooring Dynamics For A Turret-Moored Ship[J],Applied Ocean Research,1998,20:55～67
[37]J.I. Gobat,M. A. Grosenbaugh,Time-Domain Numerical Simulation Of Ocean Cable Structures[J],Ocean Engineering,2006,33:1373～1400
[38]Shan Huang,Dracos Vassalos,A Numerical Method For Predicting Snap Loading Of Marine Cables[J],Applied Ocean Research,1995,15:235～242
[39]易丛,Spar平台系缆张力及垂荡运动响应分析:[硕士学位论文],天津;天津大学,2007
[40]W. Raman-Nair,R. E. Baddour,Three-Dimensional Dynamics Of A Flexible Marine Riser Undergoing Large Elastic Deformations[J], Multibody System Dynamics,2003,10:393～423
[41]盛振邦,船舶静力学[M],北京:国防工业出版社,1979
[42]唐友刚,高等结构动力学[M],天津:天津大学出版社,2002
[43]Xiaohong Chen,Studies on Dynamic Interaction between Deep-Water Floting Structures and Their Mooring/Tendon Systems;[PHD Thesis], Texas;Texas A&M University,2002
[44]冯玮,由浅入深学Maple[M],北京:国防工业出版社,2002
[45]Reckten Wald G.,数值方法和Matlab实现与应用(伍卫国,万群,张辉)[M],北京:机械工业出版社,2004
[2]董艳秋,深水采油平台波浪载荷及响应[M],天津:天津大学出版社,2005
[3]张智,董艳秋,芮光六,一种新型的深海采油平台Spar[J],中国海洋平台,2004,19(6):29～35
[4]John Halkyard,Spar Platform for Deep Water Oil and Gas Fields[J],Moring Technology Society Journal,1996,30(3):3～12
[5]Don Selle,Murphy Kikeh Project Achieves Major Milestones[J],INTEC Quarterly Journal,2006(4)
[6]John Halkyard,Spar General Response,CSO Aker Engineering,inc,2001
[7]A. N. Williams,Z. Demirbilek,Hydrodynamic Interactions in Floating Cylinder Array-I. Wave Scattering[J],Ocean Engineering,1988,15(6):549～583
[8]A. N. Williams,Z. Demirbilek,Hydrodynamic Interactions in Floating Cylinder Array-II. Wave Radiation,Ocean Engineering,1989,16(3):217～263
[9]D. D. Bhatta,M. Rahman,Wave Loadings on a Vertical Cylinder due to Heave Motion,International Journal of Mathematics & Mathematic science,1995,18(1):151～170
[10]Oguz Yilmaz,Hydrodynamic Interactions of Waves with Group of Truncated Vertical Cylinder,Journal of Waterway,Port,Coastal and Ocean Engineering,1998:272～279
[11]Oguz Yilmaz,Atilla Incecik. Analytical Solutions of the Diffraction Problem of a Group of Truncated Vertical Cylinder[J],Ocean Engineering,1998,25(6):385～394
[12]A. Sarkar,R. Eatock Taylor,Low-Frequency Responses of Nonlinear Moored Vessels in Random Waves: Coupled Surge, Pitch and Heave Motions[J],Journal of Fluids and Structures,2001,15:133～150
[13]Y. Drobyshevski,Hydrodynamic Coefficients of a Floating, Truncated Vertical Cylinder in Shallow Water[J],Ocean Engineering,2004,31:269～304
[14]李远林,近海结构水动力学[M],广州:华南理工大学出版社, 1999
[15]李玉成,腾斌,波浪对海上建筑物的作用[M],北京:海洋出版社,2002
[16]胡志敏,董艳秋,张建民,张力腿平台波浪载荷计算[J],中国海洋平台, 2002, 17(3):6～11
[17]胡志敏,董艳秋,张建民,张力腿平台水动力参数计算,海洋工程,2002,20(3): 14～22
[18]吴应湘,李华,曾晓辉等,深海采油平台发展现状和设计中的关键问题[J],中国造船,2002,43卷增刊:80～86
[19]曾晓辉,沈晓鹏,吴应湘等,深海平台分析和设计中的关键力学问题[J],船舶工程,2005,27(5):18～21
[20]张帆,杨建民,Spar平台的发展趋势及其关键技术[J],中国海洋平台,2005,20(2)6～11
[21]B. J. Koo,Evaluation Of The Effect Of Contact Between Risers And Guide Frames On Offshore Spar Platform Motions:[PhD Thesis],Texas;Texas A&M University,2003
[22]Haslum H. A.,Faltinsen O. M.,Alternative Shape of Spar Platforms for Use in Hostile Areas,Proceedings of the 31st Offshore Technology Conference,Huston,1999,217~288
[23]Jun B. Rho,Hang S,Heave and Pitch Motions of a Spar Platform with Damping Plate,Proceeding of the 12th inter Offshore and Polar Eng. Conf.,kitakyushu,japan,2002,26～31
[24]Jun B. Rho,Hang S,An Experimental Study for Mooring Effects on the Stability of Spar Platform,Proceeding of the 13th inter Offshore and Polar Eng. Conf.,Honolulu,Hawaii,USA,2003,25～30
[25]Zhang L.,Zou J.,Mathieu Instability Evaluation for DDVC/SPAR and TLP Tendon Design,Proceedings of the 11th Offshore Symposium, Society of Naval Architect and Marine Engineer,Houston,2002,41～49
[26]B. J. Koo,M. H. Kim,R. E. Randall,Mathieu Instability Of A Spar Platform With Mooring And Risers[J],Ocean Engineering,2004,31:2175～2208
[27]Jun B. Rho,Hang S,a study on Mathieu-type instability of conventional spar platform in regular waves[J],International Journal of Offshore and Polar Engineering,2005,15(2):104~108
[28]Yong-Pyo Hong,Dong-Yeon Lee,An Experimental Study on the Extreme Motion Responses of a Spar Platform in the Heave Resonant Waves ,Proceedings of the 15th inter Offshore and Polar Eng. Conf.,seoul,korea,2005,19～24
[29]贾启芬,刘习军,工程动力学,天津:天津大学出版社,1999
[30]Xiaohong Chen,Jun Zhang,Wei Ma,Studies On Dynamic Coupling Effects Between A Spar And Its Mooring Lines[J],Ocean Engineering,2001,28:863～887
[31]王家楣,张志宏,流体力学[M],大连:大连海事大学出版社,2002
[32]JRME,WAMIT-MOSES Hydrodynamic Analysis Comparison Study,2000
[33]A.K. Agarwal,A.K. Jain,Dynamic Behavior Of Offshore Spar Platforms Under Regular Sea Waves,Ocean Engineering,2003,30:487～516
[34]A.K. Agarwal,A.K. Jain,Nonlinear Coupled Dynamic Response Of Offshore Spar Platforms Under Regular Sea Waves[J],Ocean Engineering,2003,30:517～551
[35]Sangsoo Ryu , Hull/Mooring/Riser Coupled Motion Simulations of Thruster-assisted Moored Platforms; [PhD Thesis],Texas;Texas A&M University,2003
[36]H. Ormberga,K. Larsenb,Coupled Analysis Of Floater Motion And Mooring Dynamics For A Turret-Moored Ship[J],Applied Ocean Research,1998,20:55～67
[37]J.I. Gobat,M. A. Grosenbaugh,Time-Domain Numerical Simulation Of Ocean Cable Structures[J],Ocean Engineering,2006,33:1373～1400
[38]Shan Huang,Dracos Vassalos,A Numerical Method For Predicting Snap Loading Of Marine Cables[J],Applied Ocean Research,1995,15:235～242
[39]易丛,Spar平台系缆张力及垂荡运动响应分析:[硕士学位论文],天津;天津大学,2007
[40]W. Raman-Nair,R. E. Baddour,Three-Dimensional Dynamics Of A Flexible Marine Riser Undergoing Large Elastic Deformations[J], Multibody System Dynamics,2003,10:393～423
[41]盛振邦,船舶静力学[M],北京:国防工业出版社,1979
[42]唐友刚,高等结构动力学[M],天津:天津大学出版社,2002
[43]Xiaohong Chen,Studies on Dynamic Interaction between Deep-Water Floting Structures and Their Mooring/Tendon Systems;[PHD Thesis], Texas;Texas A&M University,2002
[44]冯玮,由浅入深学Maple[M],北京:国防工业出版社,2002
[45]Reckten Wald G.,数值方法和Matlab实现与应用(伍卫国,万群,张辉)[M],北京:机械工业出版社,2004