不规则波中浮体二阶水动力时域数值模拟
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摘要
随着我国近海油气资源日趋减少,油气开发逐渐走向深海,发展新型深海平台技术已经成为国际海洋工程界研究的热点问题,而在时域内能够有效地模拟非线性波浪力对深海平台的影响是非常重要的。为了满足深海平台设计中对准确预报载荷和运动的要求,本文将以非线性不规则波对浮体的影响特性及预报方法进行研究,旨在发展不规则波中深海平台二阶水动力的时域预报技术。
本文将研究一种稳定的三维时域数值模拟方法,预报和分析浮体在规则和不规则波中所受的线性以及非线性的水动力,在远方辐射面上采用多次透射边界条件(Multi-transmitting formula, MTF),在自由面上采用积分格式的自由面边界条件(Integral form of Free surface Boundary Condition, IFBC)。为此,本文着重在以下几个方面开展了研究工作：
1.本文从时域线性辐射和绕射问题入手,对基于MTF和IFBC边界元法的参数敏感性进行研究,其中包括附加因子、平滑函数、时间步长、水深、人工波速以及网格质量等因素的影响；并对时域数值模型的稳定性以及MTF的外传效率进行了研究：长时历的数值模拟,结果不会出现发散现象；同时,给出在水波领域能够满足数值精度要求的人工波速取值范围；此外还使用不同形状的人工边界对一般形状浮体的水波问题进行了研究。
2.将基于MTF和IFBC边界元法应用到不规则波问题的数值模拟中。对受不规则垂荡激励运动的半球辐射问题和直立圆柱桩的不规则绕射问题进行了研究,其中包括双色波、多色波以及基于海浪谱的不规则波问题。除在低海况外(h1/3=0.5m和k1/3=1:0m), MTF都能有效地将不规则的波动传出人工边界,在人工边界处达到无反射的效果。由于低海况的波能谱曲线比较平坦,绝大部分能量所占的频率范围比高海况要宽的多,仅使用MTF法还不能有效地将所有波动传出人工边界,因此本文采用一种新的水波透射器—阻尼区耦合MTF法(MTF+DZ)作为人工边界条件模拟基于海浪谱的不规则波问题,并比较了各种阻尼区耦合MTF法的消波效率,得到了最优的MTF+DZ的耦合形式,同时给出了有效的最短阻尼区长度,此外还使用MTF+DZ法模拟了半潜柱体和半潜式平台的不规则波绕射问题,并使用MATLAB软件对不规则的时历信号进行快速傅立叶变换,将得到的结果与Hydrostar软件的频域结果进行了比较。
3.本文对基于MTF和IFBC分布源法的数值精度进行了研究。以直立圆柱桩绕射为例,将一阶绕射势及其各阶导数与频域解析解进行了比较分析,得到面元法向突变处分布源法求得的面元切向速度精度较低的结论,并以三维圆球绕流为例,进一步验证了上述结论。此外本文就现有方法如何提高数值结果的精度进行了研究,得到基于Galerkin技术的分布源法可以提高面元切向速度的总体精度,但它对法向突变处面元切向速度的精度提高并不明显。
4.本文就基于MTF和IFBC边界元法对二阶水波辐射和绕射问题进行了研究。使用辅助函数求解二阶非线性自由面条件中与一阶速度势相关的高阶导数项(包括速度势对z的二阶导数项、速度势对z和t的三阶导数项),避免使用传统的差分方法,提高了数值精度及稳定性。
5.本文研究了作强迫垂荡的半潜柱体的辐射问题和直立圆柱的二阶绕射问题,由于所选人工边界条件的消波效率、自由面条件中微分处理方式以及物面上高阶导数的求解方法不同,最终导致目前二阶水动力结果之间存在较大离散度。同时,在二阶绕射问题中,本文将一阶速度势及其各阶次导数的解析解代入二阶非齐次自由面条件,得到的二阶水动力与频域解析解吻合的非常好,也得到了本文结果与频域半解析解相差较大的主要原因—通过分布源法得到的控制域形状突变处的面元切向速度精度比较低。此外,本文的时域二阶结果非常稳定。说明MTF和IFBC可以有效地用于时域二阶问题的数值模拟,在人工边界上达到无反射的效果。
6.本文还讨论了二阶自由面条件和物面条件齐次与非齐次对二阶结果的影响,得到了一些有指导意义的结论。对于辐射问题,二阶速度势产生的力主要是由非线性的物面条件引起,而非线性的自由面条件对这部分力的贡献非常小,但它对总的二阶力影响比较大。对于绕射问题,正好与辐射问题的结论相反,这里二阶速度势产生的力主要是由非线性的自由面条件引起,而二阶物面条件对这部分力的贡献随着频率的增加逐渐减小,同时,此处的二阶物面条件对总的二阶力幅值影响也比较大。
7.本文最后对受不规则激励运动半潜柱体的二阶辐射问题以及其在无限水深情况下二阶不规则波绕射问题进行了研究,得到的数值结果稳定性非常高,说明本文方法可以有效用于非线性不规则波问题的时域数值模拟。
With the continuous decline of inshore oil and gas resources in China, more and more oil and gas resources exploration activities have been moved to the deep sea. Under this circumstance, it has already become an international hot topic to develop new type of deep-water platforms in the field of the ocean engineering. It is very important to effectively simulate nonlinear wave body interaction in time domain. In order to meet the requirement of predicting the wave loads and movements on deep-water platforms precisely, the aim of this thesis is to develop a predictable method for time-domain simulation of second-order hydrodynamic force on deep-water platforms in irregular wave through investigating the characteristics of nonlinear and irregular wave body interaction.
In the thesis a stable three-dimensional time-domain method, based on Rankine source, has been applied to simulate linear and nonlinear hydrodynamics in regular or irregular waves. A Multi-Transmitting Formula method (MTF) with an artificial wave speed is employed to satisfy the radiation condition to minimize the wave reflection on the Artificial Boundary (AB), and a stable Integration form of Free surface Boundary Condition (IFBC) is used to update velocity potential on the free surface. Major works done in this thesis are as follows:
Firstly, the semi-sphere with heave motion and the cylinder with incident wave were simulated. The basic parameter sensitivity are studied by comparing the present results with frequency solution, including additional factor, modulation function, time step, water depth, artificial wave speed and the mesh on boundary etc. The stability and efficiency of MTF method also have been investigated by long time simulation without instability. Usually, it is not necessary to make the artificial wave speed equal to the physical wave speed so that the effective range of the artificial wave speed is obtained. Moreover, the floating bodies, for example LNG carrier and Semi-submersible platform, with arbitrary shape of AB have been simulated in time domain. It is indicated that MTF and IFBC can be used to simulate time-domain problems by long time simulation almost without reflecting waves.
Secondly, the irregular wave radiation and diffraction problems have been simulated by Boundary Element Method (BEM) upon MTF and IFBC method. The semi-sphere with irregular excitation frequencies and the surface piercing cylinder with irregular incident waves have been investigated, which includes bichromatic wave diffraction and fully irregular wave diffraction based on wave spectrum. The irregular wave can be transmitted out of AB except for low sea state (h1/3=0.5m and h1/3=1.0m) in the MTF method, since the range of frequency at low sea state is greater than that at high sea state. Therefore, the MTF method only can transmit the waves which have common artificial wave speed out of AB so that the MTF can not transmit all the out-going waves out of AB effectively and it is necessary to use a new absorbing boundary condition (MTF coupled with damping zone, MTF+DZ) to simulate the full irregular wave diffraction problems. In this thesis, the efficiency of four kinds of MTF+DZ method has been investigated, and the best one of them is obtained therefrom. The smallest length of DZ is provided. At last, a truncated cylinder and semi-submersible diffraction have been simulated by MTF+DZ method and the results are transformed to frequency domain by Fast Fourier Transform (FFT), which are almost consistent with the results of Hydrostar.
Thirdly, the numerical accuracy of the Source distribution method based on MTF and IFBC was investigated. The method of the thesis is applied to compute wave diffraction by surface-piercing circular cylinder. It is found that the value of the tangential velocity on the boundary is inaccurate upon comparing the results thereof with frequency solutions by Source distribution method, especially at the place where the normal vector is changed rapidly. In order to validate the above conclusion, three-dimensional uniform flow over sphere has been simulated. The conclusion is almost the same as that of wave diffraction problem. Afterwards, the Source distribution based on Galerkin technique has been employed to improve the accuracy of the tangential velocity. However, this method is not sensitive if the normal vector is changed rapidly.
In fourth, the second-order wave radiation and diffraction problem have been investigated by the method of this thesis. The high-order derivatives of velocity potential are acquired by the auxiliary function, which includes second-order derivative in z direction and third-order derivative with time t and position z. The auxiliary function improves the numerical accuracy and stability without implementing finite difference method.
Then, the efficiency of Artificial Boundary Conditions (ABC) and the treatment of differential terms on the free surface condition and high-order derivatives on the body surface, which has rendered that the results different from each other have been obtained by a plurality of second-order methods. Furthermore, with regard to the second-order diffraction problems, the analytical solution and its derivatives of first-order velocity potential have been used into second-order free surface condition in the thesis so that the numerical results agree well with the second-order frequency solution. It is found that the difference between the aforesaid method and analytical solution is caused by the accuracy of the Source distribution method. Accordingly, MTF and IFBC can be used to the long time simulation in time-domain second-order problems.
Moreover, homogeneous and non-homogeneous second-order free surface condition and body surface condition are discussed in the thesis so as to acquire some useful conclusions. Concerning the radiation problem, the hydrodynamic force, due to second-order potential, is generated mainly by the non-homogeneous body surface condition. Although the contribution of non-homogeneous free surface condition is quite small, it has a significant influence on the overall second-order force. Concerning the diffraction problem, the result thereof is opposite to that of the radiation problem. The hydrodynamic force, due to second-order potential, is generated mainly by the non-homogeneous free surface condition. The contribution of non-homogeneous body condition gradually decreases while frequency is getting higher. However, it also greatly affects the overall amplitude of second-order force.
Finally, the floating body with irregular heave motion is simulated in time domain upto second order, while the calculation of second-order irregular wave diffraction by a floating body in deep water is also included in the thesis. Long time simulations are done without instability, which indicates that the present method can be used to simulate second-order irregular wave body interaction in time domain.
本文将研究一种稳定的三维时域数值模拟方法,预报和分析浮体在规则和不规则波中所受的线性以及非线性的水动力,在远方辐射面上采用多次透射边界条件(Multi-transmitting formula, MTF),在自由面上采用积分格式的自由面边界条件(Integral form of Free surface Boundary Condition, IFBC)。为此,本文着重在以下几个方面开展了研究工作：
1.本文从时域线性辐射和绕射问题入手,对基于MTF和IFBC边界元法的参数敏感性进行研究,其中包括附加因子、平滑函数、时间步长、水深、人工波速以及网格质量等因素的影响；并对时域数值模型的稳定性以及MTF的外传效率进行了研究：长时历的数值模拟,结果不会出现发散现象；同时,给出在水波领域能够满足数值精度要求的人工波速取值范围；此外还使用不同形状的人工边界对一般形状浮体的水波问题进行了研究。
2.将基于MTF和IFBC边界元法应用到不规则波问题的数值模拟中。对受不规则垂荡激励运动的半球辐射问题和直立圆柱桩的不规则绕射问题进行了研究,其中包括双色波、多色波以及基于海浪谱的不规则波问题。除在低海况外(h1/3=0.5m和k1/3=1:0m), MTF都能有效地将不规则的波动传出人工边界,在人工边界处达到无反射的效果。由于低海况的波能谱曲线比较平坦,绝大部分能量所占的频率范围比高海况要宽的多,仅使用MTF法还不能有效地将所有波动传出人工边界,因此本文采用一种新的水波透射器—阻尼区耦合MTF法(MTF+DZ)作为人工边界条件模拟基于海浪谱的不规则波问题,并比较了各种阻尼区耦合MTF法的消波效率,得到了最优的MTF+DZ的耦合形式,同时给出了有效的最短阻尼区长度,此外还使用MTF+DZ法模拟了半潜柱体和半潜式平台的不规则波绕射问题,并使用MATLAB软件对不规则的时历信号进行快速傅立叶变换,将得到的结果与Hydrostar软件的频域结果进行了比较。
3.本文对基于MTF和IFBC分布源法的数值精度进行了研究。以直立圆柱桩绕射为例,将一阶绕射势及其各阶导数与频域解析解进行了比较分析,得到面元法向突变处分布源法求得的面元切向速度精度较低的结论,并以三维圆球绕流为例,进一步验证了上述结论。此外本文就现有方法如何提高数值结果的精度进行了研究,得到基于Galerkin技术的分布源法可以提高面元切向速度的总体精度,但它对法向突变处面元切向速度的精度提高并不明显。
4.本文就基于MTF和IFBC边界元法对二阶水波辐射和绕射问题进行了研究。使用辅助函数求解二阶非线性自由面条件中与一阶速度势相关的高阶导数项(包括速度势对z的二阶导数项、速度势对z和t的三阶导数项),避免使用传统的差分方法,提高了数值精度及稳定性。
5.本文研究了作强迫垂荡的半潜柱体的辐射问题和直立圆柱的二阶绕射问题,由于所选人工边界条件的消波效率、自由面条件中微分处理方式以及物面上高阶导数的求解方法不同,最终导致目前二阶水动力结果之间存在较大离散度。同时,在二阶绕射问题中,本文将一阶速度势及其各阶次导数的解析解代入二阶非齐次自由面条件,得到的二阶水动力与频域解析解吻合的非常好,也得到了本文结果与频域半解析解相差较大的主要原因—通过分布源法得到的控制域形状突变处的面元切向速度精度比较低。此外,本文的时域二阶结果非常稳定。说明MTF和IFBC可以有效地用于时域二阶问题的数值模拟,在人工边界上达到无反射的效果。
6.本文还讨论了二阶自由面条件和物面条件齐次与非齐次对二阶结果的影响,得到了一些有指导意义的结论。对于辐射问题,二阶速度势产生的力主要是由非线性的物面条件引起,而非线性的自由面条件对这部分力的贡献非常小,但它对总的二阶力影响比较大。对于绕射问题,正好与辐射问题的结论相反,这里二阶速度势产生的力主要是由非线性的自由面条件引起,而二阶物面条件对这部分力的贡献随着频率的增加逐渐减小,同时,此处的二阶物面条件对总的二阶力幅值影响也比较大。
7.本文最后对受不规则激励运动半潜柱体的二阶辐射问题以及其在无限水深情况下二阶不规则波绕射问题进行了研究,得到的数值结果稳定性非常高,说明本文方法可以有效用于非线性不规则波问题的时域数值模拟。
With the continuous decline of inshore oil and gas resources in China, more and more oil and gas resources exploration activities have been moved to the deep sea. Under this circumstance, it has already become an international hot topic to develop new type of deep-water platforms in the field of the ocean engineering. It is very important to effectively simulate nonlinear wave body interaction in time domain. In order to meet the requirement of predicting the wave loads and movements on deep-water platforms precisely, the aim of this thesis is to develop a predictable method for time-domain simulation of second-order hydrodynamic force on deep-water platforms in irregular wave through investigating the characteristics of nonlinear and irregular wave body interaction.
In the thesis a stable three-dimensional time-domain method, based on Rankine source, has been applied to simulate linear and nonlinear hydrodynamics in regular or irregular waves. A Multi-Transmitting Formula method (MTF) with an artificial wave speed is employed to satisfy the radiation condition to minimize the wave reflection on the Artificial Boundary (AB), and a stable Integration form of Free surface Boundary Condition (IFBC) is used to update velocity potential on the free surface. Major works done in this thesis are as follows:
Firstly, the semi-sphere with heave motion and the cylinder with incident wave were simulated. The basic parameter sensitivity are studied by comparing the present results with frequency solution, including additional factor, modulation function, time step, water depth, artificial wave speed and the mesh on boundary etc. The stability and efficiency of MTF method also have been investigated by long time simulation without instability. Usually, it is not necessary to make the artificial wave speed equal to the physical wave speed so that the effective range of the artificial wave speed is obtained. Moreover, the floating bodies, for example LNG carrier and Semi-submersible platform, with arbitrary shape of AB have been simulated in time domain. It is indicated that MTF and IFBC can be used to simulate time-domain problems by long time simulation almost without reflecting waves.
Secondly, the irregular wave radiation and diffraction problems have been simulated by Boundary Element Method (BEM) upon MTF and IFBC method. The semi-sphere with irregular excitation frequencies and the surface piercing cylinder with irregular incident waves have been investigated, which includes bichromatic wave diffraction and fully irregular wave diffraction based on wave spectrum. The irregular wave can be transmitted out of AB except for low sea state (h1/3=0.5m and h1/3=1.0m) in the MTF method, since the range of frequency at low sea state is greater than that at high sea state. Therefore, the MTF method only can transmit the waves which have common artificial wave speed out of AB so that the MTF can not transmit all the out-going waves out of AB effectively and it is necessary to use a new absorbing boundary condition (MTF coupled with damping zone, MTF+DZ) to simulate the full irregular wave diffraction problems. In this thesis, the efficiency of four kinds of MTF+DZ method has been investigated, and the best one of them is obtained therefrom. The smallest length of DZ is provided. At last, a truncated cylinder and semi-submersible diffraction have been simulated by MTF+DZ method and the results are transformed to frequency domain by Fast Fourier Transform (FFT), which are almost consistent with the results of Hydrostar.
Thirdly, the numerical accuracy of the Source distribution method based on MTF and IFBC was investigated. The method of the thesis is applied to compute wave diffraction by surface-piercing circular cylinder. It is found that the value of the tangential velocity on the boundary is inaccurate upon comparing the results thereof with frequency solutions by Source distribution method, especially at the place where the normal vector is changed rapidly. In order to validate the above conclusion, three-dimensional uniform flow over sphere has been simulated. The conclusion is almost the same as that of wave diffraction problem. Afterwards, the Source distribution based on Galerkin technique has been employed to improve the accuracy of the tangential velocity. However, this method is not sensitive if the normal vector is changed rapidly.
In fourth, the second-order wave radiation and diffraction problem have been investigated by the method of this thesis. The high-order derivatives of velocity potential are acquired by the auxiliary function, which includes second-order derivative in z direction and third-order derivative with time t and position z. The auxiliary function improves the numerical accuracy and stability without implementing finite difference method.
Then, the efficiency of Artificial Boundary Conditions (ABC) and the treatment of differential terms on the free surface condition and high-order derivatives on the body surface, which has rendered that the results different from each other have been obtained by a plurality of second-order methods. Furthermore, with regard to the second-order diffraction problems, the analytical solution and its derivatives of first-order velocity potential have been used into second-order free surface condition in the thesis so that the numerical results agree well with the second-order frequency solution. It is found that the difference between the aforesaid method and analytical solution is caused by the accuracy of the Source distribution method. Accordingly, MTF and IFBC can be used to the long time simulation in time-domain second-order problems.
Moreover, homogeneous and non-homogeneous second-order free surface condition and body surface condition are discussed in the thesis so as to acquire some useful conclusions. Concerning the radiation problem, the hydrodynamic force, due to second-order potential, is generated mainly by the non-homogeneous body surface condition. Although the contribution of non-homogeneous free surface condition is quite small, it has a significant influence on the overall second-order force. Concerning the diffraction problem, the result thereof is opposite to that of the radiation problem. The hydrodynamic force, due to second-order potential, is generated mainly by the non-homogeneous free surface condition. The contribution of non-homogeneous body condition gradually decreases while frequency is getting higher. However, it also greatly affects the overall amplitude of second-order force.
Finally, the floating body with irregular heave motion is simulated in time domain upto second order, while the calculation of second-order irregular wave diffraction by a floating body in deep water is also included in the thesis. Long time simulations are done without instability, which indicates that the present method can be used to simulate second-order irregular wave body interaction in time domain.
引文
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