基于B样条面元法的浮体二阶水动力计算
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摘要
海洋结构物的二阶波浪力计算一直是在海洋工程技术研究领域的一个重要内容。本文基于B样条高阶面元法,对浮体的一阶、二阶水动力计算进行了研究,给出了一种有限水深格林函数的改进算法,并将对称性的应用引入到基于B样条面元法的二阶水动力计算中来提高计算效率。
对B样条面元的相关几何计算和B样条面元的生成方法进行了简单介绍,并给出了一种适用于任意三维浮体的基于PCL语言的浮体湿表面B样条面元生成方法。
根据三维频域线性理论,对基于B样条面元法的无航速浮体的水动力系数波浪激励力计算,不规则频率消除,运动响应求解,剖面载荷计算以及压力加载进行了研究,针对压力加载问题给出了一种基于最小二乘法的任意点的参数值反算方法,解决了一些采用B样条面元法波浪载荷计算时的基本问题。
为了考虑水深对水动力,尤其是二阶水动力的影响,本文提出了一种有限水深格林函数的改进高斯拉盖尔算法,这种方法对传统的高斯拉盖尔算法进行了两点改进,不仅提高了被积函数的收敛性,而且解决了传统方法高斯拉盖尔算法在频率较高时计算失真的现象,此外,本文将有限水深格林函数场点源点对称性引入到计算中,大大提高了计算精度和计算效率。
基于二阶频域理论,对基于B样条面元法的浮体二阶绕射力求解进行了研究。对物面非齐次项、近场自由面非齐次项和远场自由面非齐次项的计算进行了讨论。给出了一种速度势对直角坐标二阶偏导数的隐式计算公式,并验证了龙贝格积分和高斯拉盖尔积分相结合的方法用于计算三重亨格尔函数积分的有效性。
为了提高计算效率,介绍了对称性在B样条面元法中的应用。首先分析了格林函数的场点源点对称性和几何对称性,并由此入手,对对称性在速度势求解矩阵中的应用进行了分析。基于任何一函数均可写成一对称函数和反对称函数的思想,给出了物面一阶速度势的一阶和二阶偏导数以及自由面速度势一阶偏导数的对称性分解,进一步的得到了物面强迫项和自由面强迫项对称性分解,从而将对称性引入到二阶速度势求解中,使二阶速度势求解的计算量大大降低。
The second order wave loads calculation is one of the most vital research fields in offshore engineering. This thesis discussed the first order and second order velocity potential calculation of floating bodies based on B-Spline panel method. An improved calculation method of finite water depth Green function is presented, and the usage of symmetry property is introduced to improve the calculation efficiency.
Firstly, briefly introduced the geometric calculation of B-spline curves and surfaces that may be used in the B-spline panel method, and put forward a B-spline panel generation method based on PCL for wet surface of arbitrary shape three-dimensional floating structures. According to three-dimensional potential theory in frequency domain, the removal of the irregular frequencies, the calculation of hydrodynamic coefficients and wave exitation forces, motion responses, sectional loads and loading wave press for floating bodies are discussed. An interpolation algorithm based on least squares method for calculating the parameter coordinates is introduced to calculate the press of the centroid of the structural finite element, thus solved the basic problems in the wave loads calculation.
An improved Gauss-Laguerre calculation method of finite water depth Green function is presented to consider the influence of water depth on the hydrodynamics, especially the second-order hydrodynamics. Two improvements have been made for the traditional Gauss-Laguerre calculation method. The improvements not only greatly improve the convergence and computation efficiency of the integrals, but also solve the problem of numerical error in the high frequencies domain. In addition, the symmetry of the source point and field point is can be also utilized by this method, which can halve the required calculation magnitude.
Subsequently, according to second-order potential theory, the calculation of second order diffraction potential based on B-spline panel method is studied. The body forcing term, near field and far field free surface forcing term calculation are studied. An implicit formula is given for the potentials'second-order partial derivatives in right-angle coordinate, And a Romberg and Gauss-Laguerre combined method's validation for the tripled Hankel function integration calculation. At last, the influence of water depth to the second-order forces'QTFs is discussed.
Lastly, the symmetry properties are introduced in the B-spline panel method to reduce the computation burden. Firstly, the Green function's source point and field point symmetry and geometry symmetry are discussed, and based on these, symmetry properties used in the matrix solving are discussed. Based on the idea of any function can be divided into two parts, symmetrical part and antisymmetric part, the symmetry properties of the first-order potentials'first and second order derivatives are obtained through symmetry analysis. By the above results, the symmetry decomposition of body surface forced term and free surface forced term can be obtained and the symmetry property is introduced to the calculation of second-order potential, which reduces the calculating quantity greatly.
对B样条面元的相关几何计算和B样条面元的生成方法进行了简单介绍,并给出了一种适用于任意三维浮体的基于PCL语言的浮体湿表面B样条面元生成方法。
根据三维频域线性理论,对基于B样条面元法的无航速浮体的水动力系数波浪激励力计算,不规则频率消除,运动响应求解,剖面载荷计算以及压力加载进行了研究,针对压力加载问题给出了一种基于最小二乘法的任意点的参数值反算方法,解决了一些采用B样条面元法波浪载荷计算时的基本问题。
为了考虑水深对水动力,尤其是二阶水动力的影响,本文提出了一种有限水深格林函数的改进高斯拉盖尔算法,这种方法对传统的高斯拉盖尔算法进行了两点改进,不仅提高了被积函数的收敛性,而且解决了传统方法高斯拉盖尔算法在频率较高时计算失真的现象,此外,本文将有限水深格林函数场点源点对称性引入到计算中,大大提高了计算精度和计算效率。
基于二阶频域理论,对基于B样条面元法的浮体二阶绕射力求解进行了研究。对物面非齐次项、近场自由面非齐次项和远场自由面非齐次项的计算进行了讨论。给出了一种速度势对直角坐标二阶偏导数的隐式计算公式,并验证了龙贝格积分和高斯拉盖尔积分相结合的方法用于计算三重亨格尔函数积分的有效性。
为了提高计算效率,介绍了对称性在B样条面元法中的应用。首先分析了格林函数的场点源点对称性和几何对称性,并由此入手,对对称性在速度势求解矩阵中的应用进行了分析。基于任何一函数均可写成一对称函数和反对称函数的思想,给出了物面一阶速度势的一阶和二阶偏导数以及自由面速度势一阶偏导数的对称性分解,进一步的得到了物面强迫项和自由面强迫项对称性分解,从而将对称性引入到二阶速度势求解中,使二阶速度势求解的计算量大大降低。
The second order wave loads calculation is one of the most vital research fields in offshore engineering. This thesis discussed the first order and second order velocity potential calculation of floating bodies based on B-Spline panel method. An improved calculation method of finite water depth Green function is presented, and the usage of symmetry property is introduced to improve the calculation efficiency.
Firstly, briefly introduced the geometric calculation of B-spline curves and surfaces that may be used in the B-spline panel method, and put forward a B-spline panel generation method based on PCL for wet surface of arbitrary shape three-dimensional floating structures. According to three-dimensional potential theory in frequency domain, the removal of the irregular frequencies, the calculation of hydrodynamic coefficients and wave exitation forces, motion responses, sectional loads and loading wave press for floating bodies are discussed. An interpolation algorithm based on least squares method for calculating the parameter coordinates is introduced to calculate the press of the centroid of the structural finite element, thus solved the basic problems in the wave loads calculation.
An improved Gauss-Laguerre calculation method of finite water depth Green function is presented to consider the influence of water depth on the hydrodynamics, especially the second-order hydrodynamics. Two improvements have been made for the traditional Gauss-Laguerre calculation method. The improvements not only greatly improve the convergence and computation efficiency of the integrals, but also solve the problem of numerical error in the high frequencies domain. In addition, the symmetry of the source point and field point is can be also utilized by this method, which can halve the required calculation magnitude.
Subsequently, according to second-order potential theory, the calculation of second order diffraction potential based on B-spline panel method is studied. The body forcing term, near field and far field free surface forcing term calculation are studied. An implicit formula is given for the potentials'second-order partial derivatives in right-angle coordinate, And a Romberg and Gauss-Laguerre combined method's validation for the tripled Hankel function integration calculation. At last, the influence of water depth to the second-order forces'QTFs is discussed.
Lastly, the symmetry properties are introduced in the B-spline panel method to reduce the computation burden. Firstly, the Green function's source point and field point symmetry and geometry symmetry are discussed, and based on these, symmetry properties used in the matrix solving are discussed. Based on the idea of any function can be divided into two parts, symmetrical part and antisymmetric part, the symmetry properties of the first-order potentials'first and second order derivatives are obtained through symmetry analysis. By the above results, the symmetry decomposition of body surface forced term and free surface forced term can be obtained and the symmetry property is introduced to the calculation of second-order potential, which reduces the calculating quantity greatly.
引文
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