浮体在大幅波浪中的运动和荷载计算研究
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摘要
船舶和海洋平台在波浪中运动和荷载的数值分析和研究,具有重要的理论意义和实用价值。随着我国国民经济持续高速增长,对水运和海洋工程的要求也曰益提高,新船型和新型海洋平台不断出现,原有的规范已经逐渐不能满足新型船舶和海洋结构物的安全性计算的需要。尤其是随着计算机技术的发展和结构分析方法的进步,为结构三维有限元分析和可靠性分析提供波浪载荷的要求越来越多。这就对波浪载荷和运动计算预报方法提出了新的要求。本文以势流理论为基础,开发了基于NURBS的边界元法计算程序,应用频域格林函数法和时域完全非线性方法,对船舶和海洋结构物在非线性波浪中产生的运动和载荷问题进行了理论研究和数值计算。
浮体与波浪的相互作用计算十分复杂,尤其时域方法的计算量是十分巨大的。因此,提出和建立一个准确、高效的数值方法是十分必要的。本文首先开发了基于NURBS的边界元法计算程序。NURBS方法可以精确地表示复杂的三维空间物体,利用NURBS方法,可以方便准确的表达多种复杂的三维空间曲面和三维实体;应用基于NURBS的边界元法,能够保证面元边界上的几何连续性和物体表面速度势及其导数的连续性,并能方便的计算物体表面上的流体速度。基于NURBS的边界元法相对于传统的常数元方法计算结果更加精确,可以用较少的网格数量得到同样精度的结果,这样就降低了对CPU速度和内存的要求。目前,NURBS已经广泛的用于CAD软件中,并可方便的产生物体表面的网格,这些网格可直接作为面元用于流体力学计算,方便了CAD和CFD系统的集成。本文对基于NURBS的高阶边界元法进行了研究,建立和开发了高阶边界元方法计算程序,计算了无限域中物体绕流问题,对建立线性方程组的配置点法和Galerkin法进行了比较,并将计算结果与理论解进行了比较验证。
应用基于NURBS的边界元法,本文对频域中浮体在波浪中的水动力系数、运动和荷载进行了计算,并同已有的数值结果和实验结果进行了比较。对于航行船舶的耐波性问题,由于频域三维移动脉动源格林函数的复杂性,目前在实际计算中应用很少,常用方法还是二维的切片法。本文对该格林函数的数值计算进行了研究,应用分区自适应步长辛普森法积分和积分变换的方法,得到了满足精度和速度要求的有效算法。对浮体在波浪中的荷载与波浪参数的关系进行了计算和对比分析,并对船舶遭遇海况的超越概率和波浪载荷的长期分布进行了计算。
在时域计算中,本文采用混合欧拉—拉格朗日法对三维完全非线性波浪进行了分析。计算中每一时刻的边界条件在真实物面和自由表面上满足,使用基于NURBS的边界元法计算流场内的速度势,然后将得到的速度势带入自由表面条件和物体运动方程,采用四阶Adams-Bashforth-Moulton法和四阶库塔-龙格方法时间步进。辐射边界条件采用在外边界加人工阻尼层的方法处理。对于自山运动物体的受力计算中物面上速度势的时间导数的计算问题。使用迭代法建立求解物面上速度势的时间导数的积分方程,对于物面网格较多的模型,可以提高计算的速度。利用该数值模型对波浪水槽中的波浪产生和衰减,波浪与固定物体和运动物体的相互作用进行了计算研究。数值计算表明,该方法在数值上是稳定的,基于本方法实现的数值计算结果同实验结果以及相关文献给出的计算结果符合良好。
Numerical simulation and analysis of motions and loads of ship and ocean structure under waves with large amplitude are very important in theory and engineering application. With the development of Chinese economy, more and more new types of ship and ocean structure are developed. The new design method is required for achieving safe ships and ocean structures. With the wide use of the three-dimensional finite element method, the calculation of wave loads on floating body in the waves is in need more and more. In this paper, the interaction between non-linear waves and surface-piercing body with arbitrary shape in three dimensions is investigated on the basis of the potential theory. The Green-Function method both in frequency-domain and in time-domain with considering of fully non-linear effect is used in the calculation.As the wave simulation in the time-domain requires more memory and CPU-time than in the frequency-domain, an efficient NURBS approach based boundary element program is developed firstly in this paper. NURBS (Non-Uniform Rational B-Spline) is a new spline method that can express the complex three-dimensional surface exactly. By using the NURBS method, the continuity of potential function and its derivative between the grids can be affirmitived. And the fluid speed on boundary surface can be accurately calculated. Comparing with the traditional constant panel method, the NURBS based BEM is more accurate and can reduce the CPU time consuming and memory requirement. Now the NURBS method is widely used in the CAD software. The application of the NURBS based BEM can help the integration of CAD and CFD system. In this paper, the detail of NURBS based BEM is anylased and a computer program of NURBS based BEM is developed. The diffraction problem of body in infinity fluid is calculated. The computation result is compared with the analytic result satisfactorily.In this paper, the NURBS based BEM is used to calculate the wave-body interaction problem in the frequency-domain. By using the self-adaptive step size Simpson integral method and use a certain integral transform method, a numerical method for the calculation of the Green function of three dimensional translating and pulsing source is developed and used in the computation of wave loads. Numerical examinations on first-order wave forces, first-order body responses, velocities of fluid particle and second-order mean drift forces in the frequency-domain show that the NURBS based BEM is more accuracy and more computational efficient than conventional const panel BEM. The relationship between wave parameters and wave loads is investigated. The exceeding probability of design waves with different wavelength is calculated based on the wave data of long-term distribution.In this paper, the fully non-linear problem in the time-domain is analysed. By using the mix Eurian-Lagrange method, the free surface boundary condition is satisfied on the instance free surface and on body surface. The standard fourth order Runge-Kutta method and the fourth order Adams-Bashforth-Moulton method are used as the time step method. The
NURBS based BEM method is used to calculate the velocity potential at each time step. An artificial damping zone is adopted as the far field radiation condition on the free surface to avoid the wave reflection from the outer boundary, and the present method is found to be numerically stable and accurate. The pressure on body can be obtained by solving a boundary integral equation of time derivative of velocity potential. The wave generation and attenuation in a numerical wave tank and the wave load on a cylinder are calculated. The time-domain wave-body interactive is also calculated in this paper. An iteration method is used in the calculation of time derivative of speed potential. The free motion of floating truncated cylinder and sphere is calculated and the results of wave forces and body motion are presented. All of the numerical results in this paper, including the time-domain results and the frequency-domain results, agree well with published e
浮体与波浪的相互作用计算十分复杂,尤其时域方法的计算量是十分巨大的。因此,提出和建立一个准确、高效的数值方法是十分必要的。本文首先开发了基于NURBS的边界元法计算程序。NURBS方法可以精确地表示复杂的三维空间物体,利用NURBS方法,可以方便准确的表达多种复杂的三维空间曲面和三维实体;应用基于NURBS的边界元法,能够保证面元边界上的几何连续性和物体表面速度势及其导数的连续性,并能方便的计算物体表面上的流体速度。基于NURBS的边界元法相对于传统的常数元方法计算结果更加精确,可以用较少的网格数量得到同样精度的结果,这样就降低了对CPU速度和内存的要求。目前,NURBS已经广泛的用于CAD软件中,并可方便的产生物体表面的网格,这些网格可直接作为面元用于流体力学计算,方便了CAD和CFD系统的集成。本文对基于NURBS的高阶边界元法进行了研究,建立和开发了高阶边界元方法计算程序,计算了无限域中物体绕流问题,对建立线性方程组的配置点法和Galerkin法进行了比较,并将计算结果与理论解进行了比较验证。
应用基于NURBS的边界元法,本文对频域中浮体在波浪中的水动力系数、运动和荷载进行了计算,并同已有的数值结果和实验结果进行了比较。对于航行船舶的耐波性问题,由于频域三维移动脉动源格林函数的复杂性,目前在实际计算中应用很少,常用方法还是二维的切片法。本文对该格林函数的数值计算进行了研究,应用分区自适应步长辛普森法积分和积分变换的方法,得到了满足精度和速度要求的有效算法。对浮体在波浪中的荷载与波浪参数的关系进行了计算和对比分析,并对船舶遭遇海况的超越概率和波浪载荷的长期分布进行了计算。
在时域计算中,本文采用混合欧拉—拉格朗日法对三维完全非线性波浪进行了分析。计算中每一时刻的边界条件在真实物面和自由表面上满足,使用基于NURBS的边界元法计算流场内的速度势,然后将得到的速度势带入自由表面条件和物体运动方程,采用四阶Adams-Bashforth-Moulton法和四阶库塔-龙格方法时间步进。辐射边界条件采用在外边界加人工阻尼层的方法处理。对于自山运动物体的受力计算中物面上速度势的时间导数的计算问题。使用迭代法建立求解物面上速度势的时间导数的积分方程,对于物面网格较多的模型,可以提高计算的速度。利用该数值模型对波浪水槽中的波浪产生和衰减,波浪与固定物体和运动物体的相互作用进行了计算研究。数值计算表明,该方法在数值上是稳定的,基于本方法实现的数值计算结果同实验结果以及相关文献给出的计算结果符合良好。
Numerical simulation and analysis of motions and loads of ship and ocean structure under waves with large amplitude are very important in theory and engineering application. With the development of Chinese economy, more and more new types of ship and ocean structure are developed. The new design method is required for achieving safe ships and ocean structures. With the wide use of the three-dimensional finite element method, the calculation of wave loads on floating body in the waves is in need more and more. In this paper, the interaction between non-linear waves and surface-piercing body with arbitrary shape in three dimensions is investigated on the basis of the potential theory. The Green-Function method both in frequency-domain and in time-domain with considering of fully non-linear effect is used in the calculation.As the wave simulation in the time-domain requires more memory and CPU-time than in the frequency-domain, an efficient NURBS approach based boundary element program is developed firstly in this paper. NURBS (Non-Uniform Rational B-Spline) is a new spline method that can express the complex three-dimensional surface exactly. By using the NURBS method, the continuity of potential function and its derivative between the grids can be affirmitived. And the fluid speed on boundary surface can be accurately calculated. Comparing with the traditional constant panel method, the NURBS based BEM is more accurate and can reduce the CPU time consuming and memory requirement. Now the NURBS method is widely used in the CAD software. The application of the NURBS based BEM can help the integration of CAD and CFD system. In this paper, the detail of NURBS based BEM is anylased and a computer program of NURBS based BEM is developed. The diffraction problem of body in infinity fluid is calculated. The computation result is compared with the analytic result satisfactorily.In this paper, the NURBS based BEM is used to calculate the wave-body interaction problem in the frequency-domain. By using the self-adaptive step size Simpson integral method and use a certain integral transform method, a numerical method for the calculation of the Green function of three dimensional translating and pulsing source is developed and used in the computation of wave loads. Numerical examinations on first-order wave forces, first-order body responses, velocities of fluid particle and second-order mean drift forces in the frequency-domain show that the NURBS based BEM is more accuracy and more computational efficient than conventional const panel BEM. The relationship between wave parameters and wave loads is investigated. The exceeding probability of design waves with different wavelength is calculated based on the wave data of long-term distribution.In this paper, the fully non-linear problem in the time-domain is analysed. By using the mix Eurian-Lagrange method, the free surface boundary condition is satisfied on the instance free surface and on body surface. The standard fourth order Runge-Kutta method and the fourth order Adams-Bashforth-Moulton method are used as the time step method. The
NURBS based BEM method is used to calculate the velocity potential at each time step. An artificial damping zone is adopted as the far field radiation condition on the free surface to avoid the wave reflection from the outer boundary, and the present method is found to be numerically stable and accurate. The pressure on body can be obtained by solving a boundary integral equation of time derivative of velocity potential. The wave generation and attenuation in a numerical wave tank and the wave load on a cylinder are calculated. The time-domain wave-body interactive is also calculated in this paper. An iteration method is used in the calculation of time derivative of speed potential. The free motion of floating truncated cylinder and sphere is calculated and the results of wave forces and body motion are presented. All of the numerical results in this paper, including the time-domain results and the frequency-domain results, agree well with published e
引文
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