适合复杂边界的波浪力的耦合模型计算
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摘要
非线性波浪对海上建筑物作用的时域计算是目前海洋工程中的一个重要课题。采用耦合计算模型可以发挥Boussinesq方程能够计算复杂地形、三维有限元势流模型可以适合复杂边界的优点。本文研究将时域三维耦合计算模型应用于计算边界较为复杂的海洋建筑物的波浪场的计算上。计算模型将计算域分为内域和外域：内域为包围模型的矩形区域,采用三维Laplace方程,用有限元方法求解；外域为内域外面到四周边界的水域,采用水平二维Boussinesq方程,用有限差分法求解。两域在交界面处相耦合。
首先,介绍了通用有限元分析软件ANSYS的网格生成技术并将其应用在圆柱模型和船体模型的内域网格的划分中。
其次,将三维耦合计算模型应用于计算圆柱物体上的非线性波浪压力和流场波面升高,并简要介绍了相关的模型实验。计算值与实验值的比较表明：相对于小周期情况(T=1.6s),该耦合计算模型在周期较大(T>≥2.0s)的情况下具有满意的精度。在短周期情况下(T=1.6s)波浪非线性特征不明显,但对较大周期(T=2.0s)非线性成分开始占有较大比例,特别是波高较大时(H=8cm)波面中二次谐波就有较大的值,对于长周期波(T=-3.0s),在与同样波高但较小的周期(T=2.0s)相比,波面中二次谐波幅值较大,并且同样存在着较大的三次到五次谐波。与波面升高相比,压力的非线性特征不很明显。
最后,将三维耦合计算模型应用于计算边界更为复杂的船体周围的波浪场,验证了该耦合计算模型的适用性较广。
The time-domain coupled model calculating nonlinear waves acting on marine structures is an important topic in ocean engineering. Using the coupled model to solve the wave propagation and the wave action on the offshore structures can avoid the limitation that scope of application is narrow, which is caused by simply using the potential flow model, viscous flow model or the Boussinesq equation model, etc. This paper study making the time-domain coupled model calculate the wave field acting on the marine structures that have more complex boundary. The whole computation domain is divided into inner domain and outer domain. The inner domain surrounding the cylinder is governed by the Laplace equation, which is solved by the finite element method. The other area is the outer domain and is governed by Boussinesq equations, which is solved by the finite difference method. Matching conditions on the interface boundaries are applied to couple the inner and outer domains.
Firstly, introduce mesh generation technology of the finite element analysis software-ANSYS and apply it to grid division of inner domain of the cylinder model and ship model.
Secondly, the nonlinear time-domain coupled numerical model is adopted to calculate the nonlinear wave pressure acting on a circular cylinder and wave surface elevation. Calculated values compared with the experiment values show that:compared to the situation of the short period(T=1.6s),the coupled computational model has satisfactory accuracy at the major period(T≥2.0s). In the case of short period (T=1.6s) the non-linear characteristics of wave aren't obvious, but at the major period (T=2.0s) they have a higher proportion. At the situation of large height(H=8cm),the second harmonic wave have larger values.Compared with the same wave height in smaller period(T=2.0s),the second harmonic of wave-front has larger amplitude and also has three to five times larger harmonic at the long period waves (T=3.0s). The non-linear characteristics of wave pressure isn't very clear compared to the case of wave elevation.
Finally, apply the three-dimensional calculation model to calculate wave acting on the hull. Verify the applicability of the coupled model.
首先,介绍了通用有限元分析软件ANSYS的网格生成技术并将其应用在圆柱模型和船体模型的内域网格的划分中。
其次,将三维耦合计算模型应用于计算圆柱物体上的非线性波浪压力和流场波面升高,并简要介绍了相关的模型实验。计算值与实验值的比较表明：相对于小周期情况(T=1.6s),该耦合计算模型在周期较大(T>≥2.0s)的情况下具有满意的精度。在短周期情况下(T=1.6s)波浪非线性特征不明显,但对较大周期(T=2.0s)非线性成分开始占有较大比例,特别是波高较大时(H=8cm)波面中二次谐波就有较大的值,对于长周期波(T=-3.0s),在与同样波高但较小的周期(T=2.0s)相比,波面中二次谐波幅值较大,并且同样存在着较大的三次到五次谐波。与波面升高相比,压力的非线性特征不很明显。
最后,将三维耦合计算模型应用于计算边界更为复杂的船体周围的波浪场,验证了该耦合计算模型的适用性较广。
The time-domain coupled model calculating nonlinear waves acting on marine structures is an important topic in ocean engineering. Using the coupled model to solve the wave propagation and the wave action on the offshore structures can avoid the limitation that scope of application is narrow, which is caused by simply using the potential flow model, viscous flow model or the Boussinesq equation model, etc. This paper study making the time-domain coupled model calculate the wave field acting on the marine structures that have more complex boundary. The whole computation domain is divided into inner domain and outer domain. The inner domain surrounding the cylinder is governed by the Laplace equation, which is solved by the finite element method. The other area is the outer domain and is governed by Boussinesq equations, which is solved by the finite difference method. Matching conditions on the interface boundaries are applied to couple the inner and outer domains.
Firstly, introduce mesh generation technology of the finite element analysis software-ANSYS and apply it to grid division of inner domain of the cylinder model and ship model.
Secondly, the nonlinear time-domain coupled numerical model is adopted to calculate the nonlinear wave pressure acting on a circular cylinder and wave surface elevation. Calculated values compared with the experiment values show that:compared to the situation of the short period(T=1.6s),the coupled computational model has satisfactory accuracy at the major period(T≥2.0s). In the case of short period (T=1.6s) the non-linear characteristics of wave aren't obvious, but at the major period (T=2.0s) they have a higher proportion. At the situation of large height(H=8cm),the second harmonic wave have larger values.Compared with the same wave height in smaller period(T=2.0s),the second harmonic of wave-front has larger amplitude and also has three to five times larger harmonic at the long period waves (T=3.0s). The non-linear characteristics of wave pressure isn't very clear compared to the case of wave elevation.
Finally, apply the three-dimensional calculation model to calculate wave acting on the hull. Verify the applicability of the coupled model.
引文
[1]董胜,孔令双.海洋工程环境概论[M].青岛：中国海洋大学出版社,2005.
[2]缪国平,刘应中.水波及其与结构物相互作用-新时期海洋高科技中的水波动力学问题之一[J].水动力学研究与进展A辑,2006,15(2)：156-151.
[3]Eatock Taylor R,Huang S M.Second-order diffraction forces on a vertical cylinder in regular waves[J].App.Ocean Res.1987,9(1):19-30.
[4]Huang J B, Eatock Taylor R.Semi-analytical solution for second-order wave diffraction by a truncated circular cylinderin monochromatic wave[J].Jour.Fluid Mech,1996,31(9):171-196.
[5]缪国平,刘应中.大直径圆柱上的二阶波浪力.中国造船[J],1987,3：12-24.
[6]邹志利,戴遗山.回转体二阶绕射压力和绕射力.中国造船[J],1992,1：1-18.
[7]Teng B,Li Y C,Dong G H.A method for third force on axisymmetric bodies. Jour. of Hydrodynamics[J],1999,11(4):109-117.
[8]邹志利.水波理论及其应用[M].北京：科学出版社,2005.
[9]Bowers B C.Harbour resonance due to set-down beneath wave group[J]J.Fluid Mech, 1997,79(1):71-92.
[10]王永学,任冰.波浪冲击过程的湍流数值模拟[J].水动力学研究与进展,1999,14(4)：409-417.
[11]王永学.无反射造波数值波浪水槽[J].水动力学研究与进展,1994,9(2)：205-214.
[12]邹志利,邱大洪,王永学.VOF方法模拟波浪槽中二维非线性波[J].水动力学研究与进展,1996,11(1)：93-103.
[13]万德成,缪国平.数值模拟波浪翻越直立方柱[J].水动力学研究与进展,1998,13(3)：363-370.
[14]Per A. Madsen,Ole R.Sφrensen.A new form of the Boussinesq equations with improved linear dispersion characteristics[J].Coast.Eng,1991,18(2),183-204.
[15]Okey Nwogu. Alternative form of Boussinesq equations for nearshore wave propagation [J]. J. Wtrwy, Port, Coast.and Oc. Engrg.,1993,119(6):618-638.
[16]Gobbi M F, Kirby J T. Wave evolution over submerged sills:tests of a high-order Boussinesq model[J]. Coast. Engrg.,1999,37:57-96.
[17]邹志利.高阶Boussinesq水波方程[J].中国科学(E辑),1997,27(5)：460-473.
[18]邹志利.高阶Boussinesq水波方程的改进[J].中国科学(E辑),1999,29(1)：87-96.
[19]邹志利.含强水流高阶Boussinesq水波方程[J].海洋学报,2000,22(4)：41-50.
[20]ZouZL. Higher order Boussinesq equations. Ocean Engrg.,1999,26(8):767-792.
[21]邹志利.适用复杂地形的高阶Boussinesq水波方程[J].海洋学报,2001,23(1)：109-119.
[22]C. Yang, R.C. Ertekin.Numerical simulation of nonlinear wave diffraction by a vertical cylinder[J].Journal of offshore mechanics and arctic engineering,1992,114(1),36-44.
[23]Buchmann B,Skourup J,Cheung K F.Run-up on a structure due to second-order waves and a current in a numerical wave tank[J].Applied Ocean Research,1998,20(5),297-308.
[24]Bai W,Teng B.Second-order wave diffraction around 3-D bodies by a time-domain method[J].China Ocean Engineering,2001,15(1),73-85.
[25]孙大鹏,李玉成.数值水槽内的阻尼消波和波浪变形计算[J].海洋工程,200,18(1)：1-6.
[26]张晓兔.三维完全非线性数值波浪水槽的模拟研究[R].大连：大连理工大学,2004.
[27]Wu G X,Eatock Taylor R.Finite element analysis of two-dimensional non-linear transient water waves[J].Applied Ocean Research,1994,16(6),363-372.
[28]Wu G X,Eatock Taylor R.Time stepping solutions of the two-dimensional nonlinear wave radiation problem[J].Ocean Engng,1995,22(8),785-798.
[29]Takagi K,Naito S,Hirota K.Hydrodynamic force acting on a floating body in a harbor of arbitrary geometry[C].Proc.3nd Int.Offshore and Polar Engineering Conference,1993,4(1):192-199.
[30]齐鹏,王永学,邹志利,等.非线性波浪时域计算的三维耦合模型[J].海洋学报,2000,22(6)：102-109.
[31]Qi Peng, Zou Zhi-li,Wang Yong-xue.A 3-D composite model for numerical simulation of nonlinear waves[C]. Proceedings of the Tenth International Offshore and Polar Engineering Conference, Seattle, USA,2000:68-73.
[32]王大国,邹志利,唐春安.波浪对箱形船作用的三维耦合计算模型[J].船舶力学,2007,11(4)：533—544
[33]Wang DaGuo,Zou Zhili,L G Tham, Tang ChunAn. A three-dimensional coupled numerical model of nonlinear waves in a harbor[J]. Sci China Ser E-Tech Sci,2008,51(12):2185-2196.
[34]张晓莉.应用高阶Bougssinesq方程模拟复杂地形上波浪传播与变形[D].大连：大连理工大学,2001.
[35]邓凡平.ANSYS10.0有限元分析自学手册[M].北京：人民邮电出版社,2007.
[36]王大国.港口非线性波浪耦合计算模型[D].大连：大连理工大学，2005.
[37]章本照,印建安,张宏基.流体力学数值方法[M].北京：机械工业出版社,2003.
[38]VAN OORTMERSSEN G. THE MOTION OF A SHIP IN SHALLOW WATER[J]. Ocean Engng, 1976,3(4):221-255.
[2]缪国平,刘应中.水波及其与结构物相互作用-新时期海洋高科技中的水波动力学问题之一[J].水动力学研究与进展A辑,2006,15(2)：156-151.
[3]Eatock Taylor R,Huang S M.Second-order diffraction forces on a vertical cylinder in regular waves[J].App.Ocean Res.1987,9(1):19-30.
[4]Huang J B, Eatock Taylor R.Semi-analytical solution for second-order wave diffraction by a truncated circular cylinderin monochromatic wave[J].Jour.Fluid Mech,1996,31(9):171-196.
[5]缪国平,刘应中.大直径圆柱上的二阶波浪力.中国造船[J],1987,3：12-24.
[6]邹志利,戴遗山.回转体二阶绕射压力和绕射力.中国造船[J],1992,1：1-18.
[7]Teng B,Li Y C,Dong G H.A method for third force on axisymmetric bodies. Jour. of Hydrodynamics[J],1999,11(4):109-117.
[8]邹志利.水波理论及其应用[M].北京：科学出版社,2005.
[9]Bowers B C.Harbour resonance due to set-down beneath wave group[J]J.Fluid Mech, 1997,79(1):71-92.
[10]王永学,任冰.波浪冲击过程的湍流数值模拟[J].水动力学研究与进展,1999,14(4)：409-417.
[11]王永学.无反射造波数值波浪水槽[J].水动力学研究与进展,1994,9(2)：205-214.
[12]邹志利,邱大洪,王永学.VOF方法模拟波浪槽中二维非线性波[J].水动力学研究与进展,1996,11(1)：93-103.
[13]万德成,缪国平.数值模拟波浪翻越直立方柱[J].水动力学研究与进展,1998,13(3)：363-370.
[14]Per A. Madsen,Ole R.Sφrensen.A new form of the Boussinesq equations with improved linear dispersion characteristics[J].Coast.Eng,1991,18(2),183-204.
[15]Okey Nwogu. Alternative form of Boussinesq equations for nearshore wave propagation [J]. J. Wtrwy, Port, Coast.and Oc. Engrg.,1993,119(6):618-638.
[16]Gobbi M F, Kirby J T. Wave evolution over submerged sills:tests of a high-order Boussinesq model[J]. Coast. Engrg.,1999,37:57-96.
[17]邹志利.高阶Boussinesq水波方程[J].中国科学(E辑),1997,27(5)：460-473.
[18]邹志利.高阶Boussinesq水波方程的改进[J].中国科学(E辑),1999,29(1)：87-96.
[19]邹志利.含强水流高阶Boussinesq水波方程[J].海洋学报,2000,22(4)：41-50.
[20]ZouZL. Higher order Boussinesq equations. Ocean Engrg.,1999,26(8):767-792.
[21]邹志利.适用复杂地形的高阶Boussinesq水波方程[J].海洋学报,2001,23(1)：109-119.
[22]C. Yang, R.C. Ertekin.Numerical simulation of nonlinear wave diffraction by a vertical cylinder[J].Journal of offshore mechanics and arctic engineering,1992,114(1),36-44.
[23]Buchmann B,Skourup J,Cheung K F.Run-up on a structure due to second-order waves and a current in a numerical wave tank[J].Applied Ocean Research,1998,20(5),297-308.
[24]Bai W,Teng B.Second-order wave diffraction around 3-D bodies by a time-domain method[J].China Ocean Engineering,2001,15(1),73-85.
[25]孙大鹏,李玉成.数值水槽内的阻尼消波和波浪变形计算[J].海洋工程,200,18(1)：1-6.
[26]张晓兔.三维完全非线性数值波浪水槽的模拟研究[R].大连：大连理工大学,2004.
[27]Wu G X,Eatock Taylor R.Finite element analysis of two-dimensional non-linear transient water waves[J].Applied Ocean Research,1994,16(6),363-372.
[28]Wu G X,Eatock Taylor R.Time stepping solutions of the two-dimensional nonlinear wave radiation problem[J].Ocean Engng,1995,22(8),785-798.
[29]Takagi K,Naito S,Hirota K.Hydrodynamic force acting on a floating body in a harbor of arbitrary geometry[C].Proc.3nd Int.Offshore and Polar Engineering Conference,1993,4(1):192-199.
[30]齐鹏,王永学,邹志利,等.非线性波浪时域计算的三维耦合模型[J].海洋学报,2000,22(6)：102-109.
[31]Qi Peng, Zou Zhi-li,Wang Yong-xue.A 3-D composite model for numerical simulation of nonlinear waves[C]. Proceedings of the Tenth International Offshore and Polar Engineering Conference, Seattle, USA,2000:68-73.
[32]王大国,邹志利,唐春安.波浪对箱形船作用的三维耦合计算模型[J].船舶力学,2007,11(4)：533—544
[33]Wang DaGuo,Zou Zhili,L G Tham, Tang ChunAn. A three-dimensional coupled numerical model of nonlinear waves in a harbor[J]. Sci China Ser E-Tech Sci,2008,51(12):2185-2196.
[34]张晓莉.应用高阶Bougssinesq方程模拟复杂地形上波浪传播与变形[D].大连：大连理工大学,2001.
[35]邓凡平.ANSYS10.0有限元分析自学手册[M].北京：人民邮电出版社,2007.
[36]王大国.港口非线性波浪耦合计算模型[D].大连：大连理工大学，2005.
[37]章本照,印建安,张宏基.流体力学数值方法[M].北京：机械工业出版社,2003.
[38]VAN OORTMERSSEN G. THE MOTION OF A SHIP IN SHALLOW WATER[J]. Ocean Engng, 1976,3(4):221-255.