经典式Spar平台非线性耦合动力响应研究
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摘要
海洋油气的勘探与开采活动正在向越来越深的水域发展。作为深水和超深水海域中极具竞争力的平台类型,Spar平台在常规海况下表现出良好的运动特性。然而近期一些的实验结果与数值模拟显示:由于耦合非线性因素的存在,使得当平台遭遇到长周期涌浪时将出现复杂的非线性耦合共振现象,导致平台主体运动的失稳和系缆张力的突然增大,危及平台的作业安全。目前对于Spar平台非线性运动稳定性与耦合动力响应方面的研究已成为海洋工程界关注的焦点。本文依据非线性动力学理论,研究经典式Spar平台主体运动的非线性稳定性问题;采用数值模拟方法,计算在规则波浪下主体-系泊系统的耦合动力响应。本文的主要工作与结论如下:
(1)概述了Spar平台的结构形式和总体性能,回顾了Spar平台的发展历程,综述了国外Spar平台的应用现状与发展趋势,介绍了国内外关于Spar平台的最新研究成果,确定了本文的主要研究方向与关键问题。
(2)计算经典式Spar平台主体所受到的波浪载荷。根据刚体动力学理论推导出Spar主体垂荡、纵荡、纵摇三自由度的运动方程。根据绕射辐射理论,以一座实验Spar平台为算例,计算了该平台主体所受到的一阶波浪激励力、一阶辐射阻尼力,二阶纵荡波浪力,为之后的理论分析打下了基础。
(3)研究Spar平台纵摇运动的Mathieu不稳定性。考虑垂荡运动对于纵摇稳性高度的影响,建立了Spar平台非线性参-强联合激励纵摇运动方程。应用摄动法求得了主参数共振时方程的近似解析解,根据李雅普诺夫稳定性定理对方程解的稳定性与局部分岔特性进行分析,揭示了纵摇运动出现参激失稳的机理,做出了发生大幅值纵摇运动的不稳定参数域,进而建立了预报平台发生参数激励纵摇运动的方法,分析了不同参数激励与纵摇阻尼对于纵摇运动响应的影响。
(4)研究Spar平台垂荡与纵摇运动的耦合内共振特性。考虑瞬时波面和一阶波浪激励力的影响,建立了两自由度耦合非线性方程。针对垂荡与纵摇固有频率间的准2:1关系,采用多尺度法导出了当波浪频率接近垂荡固有频率时耦合方程的近似解析解并数值验证,根据Floquet理论对定常周期解的稳定性进行分析。研究发现:当出现耦合内共振现象时垂荡运动存在能量饱和现象,当垂荡激励力继续增大时,多余的垂荡能量将向纵摇模态转移,导致出现不稳定纵摇运动。增加垂荡阻尼可降低垂荡共振幅值,而增加纵摇阻尼或扩大垂荡与纵摇固有频率间的差距将削弱两自由度间的耦合关系,从而避免耦合内共振运动的发生。
(5)研究Spar平台垂荡与纵摇运动的组合共振特性。采用摄动法导出当波浪频率接近垂荡与纵摇固有频率之和时响应方程的近似解析解并数值验证,根据Routh-Hurwitz判据对零解的稳定性和局部分岔特性进行了分析。研究发现:较大的纵摇激励力矩将导致解曲线发生局部分岔行为从而衍生出稳定的亚谐分量,是导致两自由度响应出现倍周期与幅值跳跃现象的根本原因。提高系统阻尼可减小零解的不稳定区从而提高此时平台运动的稳定性。
(6)计算规则波浪下Spar平台主体-系泊系统的耦合动力响应。应用集中质量法模拟系泊系统,考虑系泊缆绳所受到的流体载荷和其与主体之间的相互作用,建立了系泊-主体全耦合分析模型,根据龙格库塔法在MATLAB语言环境下开发大型耦合计算程序ANCMS。以一座实验Spar作为算例,得到了不同系缆长度时缆绳的静态预张力与缆绳水中构型,测出了缆绳的非线性系泊刚度,对比了在规则波浪下有无系泊系统时平台的运动响应,研究了系泊缆绳的粘性阻尼与质量惯性力对于平台运动响应的影响,得到了以波浪频率为分岔参数的主体运动幅值与系缆张力分岔图。
Offshore oil and gas drilling and production activities are being pushed into deeper and deeper waters. As the most attractive types of deep and ultra deep water production platforms, Spars have exhibited excellent dynamic characteristic in normal conditions. But some recent numerical research and experiments results showed that the compliant coupled resonant response appeared when the platform experiencing long periodic ground swell because of some nonlinear factors, which may cause unstable motion and tension increasing quickly in the cable. This phenomenon may endanger the security and production of the platform. More and more attention has been attracted to the motion stability and coupled dynamic response of the Spar platforms in the ocean engineering field presently.
In this paper the nonlinear dynamics theory is adopted to study the motion stability of a classic Spar platform and the hull-mooring coupled dynamic response is calculated in regular waves by using the numerical method. The main contents and contribution are summarized as follows:
(1) The structure form and general characteristic of the Spar platforms are presented, the development process is reviewed, the application status and the development tendency at abroad are introduced, some recent research achievements of the Spars are summarized synthetically, the study direction and key problems of the thesis are presented.
(2) The wave loadings on the hull of a Classic Spar platform are calculated. The coupled differential equations for surge, heave and pitch of a Spar platform are deduced according to the rigid body dynamics theory. The first order wave exciting forces and the radiation damping forces of an experimental Spar model are calculated according to the diffraction/radiation theory, the second order wave exciting force of surge is also obtained which lay a foundation for the further theoretical analysis.
(3) The Mathieu instability of pitch motion of a Spar platform is studied. The nonlinear parametric and forcing excited equation for pitch motion is established with considering the effect of heave motion on the metacentric height of pitch. The approximate analytical solution of the differential equation is obtained for the prime parametric by using perturbation method. The stability and the local bifurcation characteristic of the solution are studied according to the Lyapunov's laws so as to reveal the mechanism of instable parametric pitch motion. The parametric field for the large amplitude pitch motion is obtained and the method is founded for predicting the instable pitch movement. The factors of different excited parameters and pitch damping for the response are also analyzed.
(4) The internal resonant characteristic of heave-pitch motion is studied. The nonlinear coupling equations for heave and pitch are established considering the effect of time-varying incident wave elevation and first order wave exciting forces. The steady-state response of the equations are solved by the method of multiple scales and validated by the numerical method in the presence of the quasi 2:1 internal relationship when the wave frequency get close to the natural heave frequency. The stabilities steady-state periodic solutions are analyzed according to the Floquet theory. It is observed that the heave motion exhibits saturation when the internal resonance occurs, as the heave exciting force increases further, the extra energy of heave mode is transferred to the pitch mode and induces unstable pitch response. Increasing heave damping can decrease the heave resonant amplitude, Increasing pitch damping or enlarge the disparity of the natural frequencies between heave and pitch motion can weaken the coupled relationship of the two modes, which can suppress the internal resonance response.
(5) The combination resonance response of heave-pitch motion is studied. The steady-state response of the equations are obtained when the incident wave frequency approaching to the sum of heave natural frequency and pitch natural frequency. The stabilities and the local bifurcation characteristic of the trivial solution are analyzed according to the Routh-Hurwitz criterion. The result shows that large pitch exciting moment can induce bifurcation behavior in two solution curves and trips stable sub-harmonic component, which leads to period doubling and jumping phenomena in both modes. Increasing system damping can reduce the instability domain of the trivial solution so as to improve the stability of Spar platform.
(6) The coupled dynamic response for the hull-mooring system of a Spar platform is calculated under regular waves. The mooring system is modeled by using the lumped masses method, the fluid loads and the coupled effects are taken into account so that a full coupled analysis model of hull/mooring system is established. The large computer program ANCMS is developed adopting Runge-Kutta method with MATLAB. By taken an experimental Spar model for example, the pretension at the fairlead and configuration underwater are obtained with different cable lengths, the mooring stiffness are calculated. The dynamic responses under regular waves with/without mooring lines are compared. The viscous damping and mass inertia effects of the mooring lines on the responses are analyzed, the bifurcation diagram of motion and tension is obtained with the wave frequency as the bifurcation parameter.
(1)概述了Spar平台的结构形式和总体性能,回顾了Spar平台的发展历程,综述了国外Spar平台的应用现状与发展趋势,介绍了国内外关于Spar平台的最新研究成果,确定了本文的主要研究方向与关键问题。
(2)计算经典式Spar平台主体所受到的波浪载荷。根据刚体动力学理论推导出Spar主体垂荡、纵荡、纵摇三自由度的运动方程。根据绕射辐射理论,以一座实验Spar平台为算例,计算了该平台主体所受到的一阶波浪激励力、一阶辐射阻尼力,二阶纵荡波浪力,为之后的理论分析打下了基础。
(3)研究Spar平台纵摇运动的Mathieu不稳定性。考虑垂荡运动对于纵摇稳性高度的影响,建立了Spar平台非线性参-强联合激励纵摇运动方程。应用摄动法求得了主参数共振时方程的近似解析解,根据李雅普诺夫稳定性定理对方程解的稳定性与局部分岔特性进行分析,揭示了纵摇运动出现参激失稳的机理,做出了发生大幅值纵摇运动的不稳定参数域,进而建立了预报平台发生参数激励纵摇运动的方法,分析了不同参数激励与纵摇阻尼对于纵摇运动响应的影响。
(4)研究Spar平台垂荡与纵摇运动的耦合内共振特性。考虑瞬时波面和一阶波浪激励力的影响,建立了两自由度耦合非线性方程。针对垂荡与纵摇固有频率间的准2:1关系,采用多尺度法导出了当波浪频率接近垂荡固有频率时耦合方程的近似解析解并数值验证,根据Floquet理论对定常周期解的稳定性进行分析。研究发现:当出现耦合内共振现象时垂荡运动存在能量饱和现象,当垂荡激励力继续增大时,多余的垂荡能量将向纵摇模态转移,导致出现不稳定纵摇运动。增加垂荡阻尼可降低垂荡共振幅值,而增加纵摇阻尼或扩大垂荡与纵摇固有频率间的差距将削弱两自由度间的耦合关系,从而避免耦合内共振运动的发生。
(5)研究Spar平台垂荡与纵摇运动的组合共振特性。采用摄动法导出当波浪频率接近垂荡与纵摇固有频率之和时响应方程的近似解析解并数值验证,根据Routh-Hurwitz判据对零解的稳定性和局部分岔特性进行了分析。研究发现:较大的纵摇激励力矩将导致解曲线发生局部分岔行为从而衍生出稳定的亚谐分量,是导致两自由度响应出现倍周期与幅值跳跃现象的根本原因。提高系统阻尼可减小零解的不稳定区从而提高此时平台运动的稳定性。
(6)计算规则波浪下Spar平台主体-系泊系统的耦合动力响应。应用集中质量法模拟系泊系统,考虑系泊缆绳所受到的流体载荷和其与主体之间的相互作用,建立了系泊-主体全耦合分析模型,根据龙格库塔法在MATLAB语言环境下开发大型耦合计算程序ANCMS。以一座实验Spar作为算例,得到了不同系缆长度时缆绳的静态预张力与缆绳水中构型,测出了缆绳的非线性系泊刚度,对比了在规则波浪下有无系泊系统时平台的运动响应,研究了系泊缆绳的粘性阻尼与质量惯性力对于平台运动响应的影响,得到了以波浪频率为分岔参数的主体运动幅值与系缆张力分岔图。
Offshore oil and gas drilling and production activities are being pushed into deeper and deeper waters. As the most attractive types of deep and ultra deep water production platforms, Spars have exhibited excellent dynamic characteristic in normal conditions. But some recent numerical research and experiments results showed that the compliant coupled resonant response appeared when the platform experiencing long periodic ground swell because of some nonlinear factors, which may cause unstable motion and tension increasing quickly in the cable. This phenomenon may endanger the security and production of the platform. More and more attention has been attracted to the motion stability and coupled dynamic response of the Spar platforms in the ocean engineering field presently.
In this paper the nonlinear dynamics theory is adopted to study the motion stability of a classic Spar platform and the hull-mooring coupled dynamic response is calculated in regular waves by using the numerical method. The main contents and contribution are summarized as follows:
(1) The structure form and general characteristic of the Spar platforms are presented, the development process is reviewed, the application status and the development tendency at abroad are introduced, some recent research achievements of the Spars are summarized synthetically, the study direction and key problems of the thesis are presented.
(2) The wave loadings on the hull of a Classic Spar platform are calculated. The coupled differential equations for surge, heave and pitch of a Spar platform are deduced according to the rigid body dynamics theory. The first order wave exciting forces and the radiation damping forces of an experimental Spar model are calculated according to the diffraction/radiation theory, the second order wave exciting force of surge is also obtained which lay a foundation for the further theoretical analysis.
(3) The Mathieu instability of pitch motion of a Spar platform is studied. The nonlinear parametric and forcing excited equation for pitch motion is established with considering the effect of heave motion on the metacentric height of pitch. The approximate analytical solution of the differential equation is obtained for the prime parametric by using perturbation method. The stability and the local bifurcation characteristic of the solution are studied according to the Lyapunov's laws so as to reveal the mechanism of instable parametric pitch motion. The parametric field for the large amplitude pitch motion is obtained and the method is founded for predicting the instable pitch movement. The factors of different excited parameters and pitch damping for the response are also analyzed.
(4) The internal resonant characteristic of heave-pitch motion is studied. The nonlinear coupling equations for heave and pitch are established considering the effect of time-varying incident wave elevation and first order wave exciting forces. The steady-state response of the equations are solved by the method of multiple scales and validated by the numerical method in the presence of the quasi 2:1 internal relationship when the wave frequency get close to the natural heave frequency. The stabilities steady-state periodic solutions are analyzed according to the Floquet theory. It is observed that the heave motion exhibits saturation when the internal resonance occurs, as the heave exciting force increases further, the extra energy of heave mode is transferred to the pitch mode and induces unstable pitch response. Increasing heave damping can decrease the heave resonant amplitude, Increasing pitch damping or enlarge the disparity of the natural frequencies between heave and pitch motion can weaken the coupled relationship of the two modes, which can suppress the internal resonance response.
(5) The combination resonance response of heave-pitch motion is studied. The steady-state response of the equations are obtained when the incident wave frequency approaching to the sum of heave natural frequency and pitch natural frequency. The stabilities and the local bifurcation characteristic of the trivial solution are analyzed according to the Routh-Hurwitz criterion. The result shows that large pitch exciting moment can induce bifurcation behavior in two solution curves and trips stable sub-harmonic component, which leads to period doubling and jumping phenomena in both modes. Increasing system damping can reduce the instability domain of the trivial solution so as to improve the stability of Spar platform.
(6) The coupled dynamic response for the hull-mooring system of a Spar platform is calculated under regular waves. The mooring system is modeled by using the lumped masses method, the fluid loads and the coupled effects are taken into account so that a full coupled analysis model of hull/mooring system is established. The large computer program ANCMS is developed adopting Runge-Kutta method with MATLAB. By taken an experimental Spar model for example, the pretension at the fairlead and configuration underwater are obtained with different cable lengths, the mooring stiffness are calculated. The dynamic responses under regular waves with/without mooring lines are compared. The viscous damping and mass inertia effects of the mooring lines on the responses are analyzed, the bifurcation diagram of motion and tension is obtained with the wave frequency as the bifurcation parameter.
引文
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