基于NURBS高阶面元法的SWATH兴波阻力计算
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摘要
小水线面双体船(Small Waterplane Area Twin Hull，SWATH)船型设计的关键技术之一是其水动力性能(快速性、耐波性和操纵性)的预报和优化设计，而其静水阻力预报是其快速性预报的重要内容。和常规船型一样，预报SWATH船型的静水阻力可采用船模试验、理论和数值计算方法。随着计算机科学技术的发展及其在造船学科的日益广泛的应用，基于计算流体动力学(Computational Fluid Dynamics，CFD)技术的数值计算方法已成为预报船舶阻力和优化设计船型的有效工具。这类方法也为我们预报SWATH船型的静水阻力提供了一种有效工具。
为了尝试采用现代CFD方法数值预报SWATH船型的兴波阻力，本论文开发了一种基于非均匀有理B样条(Non-Uniform Rational B-Splines，NURBS)的高阶面元法，不但用NURBS表示物面及自由面的几何形状，而且还用其表示物面及自由面上的源强分布。NURBS的应用提高了几何及源强密度表达的精度，能够方便地满足所需的任意阶连续性的要求，不需要引入局部坐标，所以避免了局部坐标与整体坐标之间的转换。其具体做法是在物体表面和所选取的自由面上布置Rankine源来模拟厚度效应，通过满足物面边界条件、线性自由面边界条件来求解未知源强的控制网格，进而计算物体兴波波形和阻力。为了满足远前方无波的辐射条件，本论文采用了Jensen等提出的“网格错位”方法来满足，即将自由面源层上置一定高度，相应的自由面配置点向后错位一个面元纵向长度。
本文运用该方法计算了三维物体的绕流、兴波波形和兴波阻力，给出了Wigley、数学SWATH船型定常直航运动时的兴波波形和兴波阻力，其结果与实验结果、理论结果进行了比较，结果比较令人满意。
本论文的研究为用CFD方法预报SWATH船型的水动力性能打下了一定的基础，对提高我国SWATH船型的开发与设计水平具有一定的实用意义。
One of the key techniques in SWATH design is the prediction and optimum design of the hydrodynamic performances (resistance and propulsion, seakeeping, maneuverability), whereas the resistance prediction is the most important task of hydrodynamic performance prediction. As with conventional ships, the methods of model experiment, theoretical analysis and numerical calculation are applied to predict the resistance of SWATH. Along with the development of computer scientific techniques and wide appliance in shipbuilding, numerical method based on CFD technique has become an effective tool for predicting the resistance and optimum design of ships.
In order to predict the wave resistance of SWATH by applied CFD technique, this thesis presents a raised panel method based on NURBS for calculating flow, the wave pattern and wave resistance of a 3-D body advancing with forward speed on or beneath the free surface.
In this thesis, NURBS is applied not only to represent the body geometry, disturbed free surface, but also to represent the unknown source strength distribution. This makes the geometry representation of the body shape and the wave pattern more precise. Rankine sources are distributed on panels of body surface and free surface. The source strengths are determined by satisfying the body surface boundary condition and the linearity free surface boundary condition, so that the velocity potential, the wave pattern and the wave resistance could be obtained. The radiation condition is satisfied numerically with collocation points shifting upstream.
As applications of the method, flow around a 3-D body, the wave pattern and wave resistance of a ship are solved. The encouraging numerical results are achieved.
This research is useful for hydrodynamic calculation of the ship by using CFD technique and for improving the techniques in prediction and optimum
design of SWATH.
为了尝试采用现代CFD方法数值预报SWATH船型的兴波阻力，本论文开发了一种基于非均匀有理B样条(Non-Uniform Rational B-Splines，NURBS)的高阶面元法，不但用NURBS表示物面及自由面的几何形状，而且还用其表示物面及自由面上的源强分布。NURBS的应用提高了几何及源强密度表达的精度，能够方便地满足所需的任意阶连续性的要求，不需要引入局部坐标，所以避免了局部坐标与整体坐标之间的转换。其具体做法是在物体表面和所选取的自由面上布置Rankine源来模拟厚度效应，通过满足物面边界条件、线性自由面边界条件来求解未知源强的控制网格，进而计算物体兴波波形和阻力。为了满足远前方无波的辐射条件，本论文采用了Jensen等提出的“网格错位”方法来满足，即将自由面源层上置一定高度，相应的自由面配置点向后错位一个面元纵向长度。
本文运用该方法计算了三维物体的绕流、兴波波形和兴波阻力，给出了Wigley、数学SWATH船型定常直航运动时的兴波波形和兴波阻力，其结果与实验结果、理论结果进行了比较，结果比较令人满意。
本论文的研究为用CFD方法预报SWATH船型的水动力性能打下了一定的基础，对提高我国SWATH船型的开发与设计水平具有一定的实用意义。
One of the key techniques in SWATH design is the prediction and optimum design of the hydrodynamic performances (resistance and propulsion, seakeeping, maneuverability), whereas the resistance prediction is the most important task of hydrodynamic performance prediction. As with conventional ships, the methods of model experiment, theoretical analysis and numerical calculation are applied to predict the resistance of SWATH. Along with the development of computer scientific techniques and wide appliance in shipbuilding, numerical method based on CFD technique has become an effective tool for predicting the resistance and optimum design of ships.
In order to predict the wave resistance of SWATH by applied CFD technique, this thesis presents a raised panel method based on NURBS for calculating flow, the wave pattern and wave resistance of a 3-D body advancing with forward speed on or beneath the free surface.
In this thesis, NURBS is applied not only to represent the body geometry, disturbed free surface, but also to represent the unknown source strength distribution. This makes the geometry representation of the body shape and the wave pattern more precise. Rankine sources are distributed on panels of body surface and free surface. The source strengths are determined by satisfying the body surface boundary condition and the linearity free surface boundary condition, so that the velocity potential, the wave pattern and the wave resistance could be obtained. The radiation condition is satisfied numerically with collocation points shifting upstream.
As applications of the method, flow around a 3-D body, the wave pattern and wave resistance of a ship are solved. The encouraging numerical results are achieved.
This research is useful for hydrodynamic calculation of the ship by using CFD technique and for improving the techniques in prediction and optimum
design of SWATH.
引文
1 李世谟．兴波阻力理论基础．北京：人民交通出版社，1986
2 王献孚，周树信，陈泽梁，等．计算船舶流体力学．上海：上海交通大学出版社，1992
3 吴望一．流体力学．北京：北京大学出版社，1982
4 李世谟．船舶阻力．北京：人民交通出版社，1989
5 施法中．计算机辅助设计与非均匀有理B样条(CAGD&NURBS)．北京：高等教育出版社，2001
6．朱心雄．自由曲线曲面造型技术．北京：科学出版社，2000
7．邹早建，罗青山，徐海祥，史一鸣．SWATH船型及其阻力性能计算．武汉理工大学学报(交通科学与工程)，Vol．26 No．3 June 2002
8．徐航，邹早建．基于NURBS的三维物体曲面构造及其CFD应用．2001年船舶与海洋工程研究专集(总第143期)
9．赵成璧．船舶曲面设计现代方法与软件系统的研究．武汉交通科技大学博士学位论文，1999
10．马岭．基于NURBS面元法的船舶兴波问题数值计算研究．武汉理工大学硕士论文，2002
11．徐航．基于NURBS的三维物体波浪载荷数值计算．武汉理工大学硕士论文，2002
12．徐海祥．高速多体船兴波水动力数值计算．武汉理工大学硕士论文，2001
13．陈惠民．世界小水线面双体船发展动向及我国开发对策文集．1999
14．李白齐．21世纪海洋高性能船．北京：国防工业出版社，2001
15.Y. Cao, W. Schultz, R. Beck. Three-Dimensional, Unsteady Computation of Nonlinear Waves Caused by Underwater Disturbances. Eighteeth Symposium on Naval Hydrodynamic, 1991
16.Lawrence J. Doctors, Robert F. Beck. Convergence Properties of the Neumann-Kelvin Problem for a Submerged Body. Journal of Ship Research, Vol. 31, No. 4,Dec. 1987
17.C.B. Zhao and Z.J. Zou. A 3D Potential Flow Computing Method Based on NURBS. 14th International Workshop on W.W&F.B. 1999
18.I.R. Park, H.H. Chun, S,H. Kim and D. D. Ha. Free-Surface Flow Analysis around Three Dimensional Hydrofoils By A Higher-Order Boundary Element Method.
19.C. Wang and Z.J. Zou. A 3D Panel Method for Hydrodynamic Forces on Hydrofoils. Journal of Ship Mechanics, Vol.5 No.3 June 2001
20.Z.J. Zou. A 3-D numerical method for hydrodynamic forces on a plane in maneuvering motion. Proc. of the International Symposium on Maneuverability of Ship at Slow Speed. 1995
21.K.J. Kim.A Higher order panel method for calculating free surface potential flows with linear surface boundary conditions. SSPA Report No.2966-2 1989
22.H. Maniar. A B-spline based higher order method in 3D. The Ninth International Workshop on Water and Floating Bodies. 1994
23.J. S., Kouh, Y. B. Suen. A 3D potential-based and desingularized high order panel method. Ocean Engineering. 2001
24.G. B. Vaz, J. A .C . Falcao, L. Eca. A Numerical Study on Low and Higher-Order Potential Based BEM for 2D Inviscid Flows. IABEM2002 - Computational Mechanics Journal Special Issue
25.J. H. Yong, F. H. Cheng, et al. Dynamic highlight line generation for locally deforming NURBS surfaces. Computer-Aided Design. 2003
26.M.H. Kim, W.C. Koo, S.Y. Hong. Wave interactions with 2D structures on/inside porous seabed by a two-domain boundary element method. Applied Ocean Research .2000
27.H.C. Raven. Inviscid calculations of ship wave making---capabilities, limitations and prospects. 22nd Symp. on Naval Hydrodynamics, Washington DC, 1998
28.T. Katsuji, M.M. Makiko, S. Hiroshi. Estimation of Wave Drift Force by Numerical Wave Tank, 2nd Report. 10th International Offshore and Polar Engineering Conference.2000
29.W. K. Jang. A Numerical Study of Nonlinear Wave Interaction in Regular and Irregular Seas: Irrotational Green-Naghdi Model.
30.E. O. Tuck, L. Lazauskas. Free-surface pressure distributions with minimum wave resistance. ANZIAM J. 43 (E), 2001
31.D.C. Scullen, E.O. Tuck. Free-surface elevation due to moving pressure distributions in three dimensions, in preparation, January 2001.
32.M.H. Kim, W.C. Koo, S.Y. Hong. Wave interactions with 2D structures on/inside porous seabed by a two-domain boundary element method. Applied Ocean Research .2000
33.Y.S. Cao, W. Schultz. Three-dimensional desingularized boundary integral methods for potential problems. Int J Numer Meth Fluids. 1991
34.I.V. Sturova. The effect of internal waves on the hydrodynamic characteristics of a submerged body. Physics of Atmosphere and Ocean. 1993
35.N.G. Kuznetsov. Wave resistance of a semisubmerged cylinder on deep water. High Speed Hydrodynamics. 1990
36.O.V. Motygin, N. G. Kuznetsov. The Wave Resistance of a Two-Dimensional Body Moving Forward in a Two-Layer Fluid. Journal of Engineering Mathematics. 1997.
37.J.R. Cadby, C.M. Linton. Three-dimensional water-wave scattering in two-layer fluids.
38.Papanikolaou, A. D. Kaklis, P.D. On the Wave Resistance of Twin-Hull Floating Bodies with Non-Symmetric Demi-Hulls, 11th International Workshop on Water Waves and Floating Bodies, Hamburg, March.
39.Z.H. George, D. Spanos, P. Apostolos. Numerical and Experimental Study on the Wave Resistance of Fast Displacement Asymmetric Catamarans.
40.H.Sding. Drastic Resistance Reduction in Catamarans by Staggered Hulls, 4th Int. Conference on Fast Sea Transportation FAST'97, Sydney. 1997
41.D.SPANOS. Investigation of the Wave Resistance of Thin Catamarans with Symmetricand Non-Symmetric Demihulls, Diploma Thesis (in Greek), Dept. Naval Arch. & Marine Engineering, NTUA. 1995
42.A. Papanikolaou, D. Spanos. Systematic Resistance Tests of Catamaran Configurations with Non-Symmetric Wigley Demihulls, Lab. of Ship Design, Dept. of NAME, National Tech. Univ. of Athens, NTUA. 1999
43.T.M. Ralph, C. S. David. Plane Wave Radiation Resistance of a Source Mounted in the Side of an In_nite Duct in the Presence of Mean Flow
44.E. O. Tuck, D. C. Scullen, and L. Lazauskas. Wave Patterns and Minimum Wave Resistance for High-Speed Vessels.
45.M. Bessho. On a consistent linearized theory of the wave-making of ships, Journal of Ship Research, Vol. 38, 1994, pp. 83-96.
46.F. Noblesse. Analytical representation of ship waves (23rd Weinblum Memorial Lecture), Schiffstechnik, Vol. 48, 2001, pp. 23-48.
47.N. Salvesen, C. V. Kerczek, C.A. Scragg, C.P. Cressy, and M.J. Meinhold. Hydrodynmamic design of SWATH ships, Transactions of the Society of Naval Architects and Marine Engineers, Vol. 93, 1985, pp. 325-348.
48.J.S. Kouh, C.H. Ho. A High Order Panel Method Based on Source Distribution and Gaussian Quadrature, Ship Technology Reseaeh, Vol.43, 1996
49.G.Jensen and H. Sding. Rankine Source Methods for Numerical Solutions of the Steady Wave Resietaee Problem,
50．张小兔．基于B样条的三维船体水动力数值计算研究．武汉理工大学博士论文，2002．
51．滕斌，柏威．基于B-样条的边界元方法及其在波浪力计算中的应用．第十四届全国水动力学研讨会文集，2000．
52．高高．船波问题的辐射条件、自由面条件的研究及面元误差分析．武汉交通科技大学博士论文，1997
53．黄鼎良．小水线面双体船性能原理．国防工业出版社，1993
54.K .J. Bai, S. E. Kim. The Cross Flow Effect on the Force and Moment Acting on a SWATH Ship .Proc. of the 17th Symposium on Naval Hydrodynamics, 1988
55．刘应中．船舶兴波阻力理论．国防工业出版社，2003
2 王献孚，周树信，陈泽梁，等．计算船舶流体力学．上海：上海交通大学出版社，1992
3 吴望一．流体力学．北京：北京大学出版社，1982
4 李世谟．船舶阻力．北京：人民交通出版社，1989
5 施法中．计算机辅助设计与非均匀有理B样条(CAGD&NURBS)．北京：高等教育出版社，2001
6．朱心雄．自由曲线曲面造型技术．北京：科学出版社，2000
7．邹早建，罗青山，徐海祥，史一鸣．SWATH船型及其阻力性能计算．武汉理工大学学报(交通科学与工程)，Vol．26 No．3 June 2002
8．徐航，邹早建．基于NURBS的三维物体曲面构造及其CFD应用．2001年船舶与海洋工程研究专集(总第143期)
9．赵成璧．船舶曲面设计现代方法与软件系统的研究．武汉交通科技大学博士学位论文，1999
10．马岭．基于NURBS面元法的船舶兴波问题数值计算研究．武汉理工大学硕士论文，2002
11．徐航．基于NURBS的三维物体波浪载荷数值计算．武汉理工大学硕士论文，2002
12．徐海祥．高速多体船兴波水动力数值计算．武汉理工大学硕士论文，2001
13．陈惠民．世界小水线面双体船发展动向及我国开发对策文集．1999
14．李白齐．21世纪海洋高性能船．北京：国防工业出版社，2001
15.Y. Cao, W. Schultz, R. Beck. Three-Dimensional, Unsteady Computation of Nonlinear Waves Caused by Underwater Disturbances. Eighteeth Symposium on Naval Hydrodynamic, 1991
16.Lawrence J. Doctors, Robert F. Beck. Convergence Properties of the Neumann-Kelvin Problem for a Submerged Body. Journal of Ship Research, Vol. 31, No. 4,Dec. 1987
17.C.B. Zhao and Z.J. Zou. A 3D Potential Flow Computing Method Based on NURBS. 14th International Workshop on W.W&F.B. 1999
18.I.R. Park, H.H. Chun, S,H. Kim and D. D. Ha. Free-Surface Flow Analysis around Three Dimensional Hydrofoils By A Higher-Order Boundary Element Method.
19.C. Wang and Z.J. Zou. A 3D Panel Method for Hydrodynamic Forces on Hydrofoils. Journal of Ship Mechanics, Vol.5 No.3 June 2001
20.Z.J. Zou. A 3-D numerical method for hydrodynamic forces on a plane in maneuvering motion. Proc. of the International Symposium on Maneuverability of Ship at Slow Speed. 1995
21.K.J. Kim.A Higher order panel method for calculating free surface potential flows with linear surface boundary conditions. SSPA Report No.2966-2 1989
22.H. Maniar. A B-spline based higher order method in 3D. The Ninth International Workshop on Water and Floating Bodies. 1994
23.J. S., Kouh, Y. B. Suen. A 3D potential-based and desingularized high order panel method. Ocean Engineering. 2001
24.G. B. Vaz, J. A .C . Falcao, L. Eca. A Numerical Study on Low and Higher-Order Potential Based BEM for 2D Inviscid Flows. IABEM2002 - Computational Mechanics Journal Special Issue
25.J. H. Yong, F. H. Cheng, et al. Dynamic highlight line generation for locally deforming NURBS surfaces. Computer-Aided Design. 2003
26.M.H. Kim, W.C. Koo, S.Y. Hong. Wave interactions with 2D structures on/inside porous seabed by a two-domain boundary element method. Applied Ocean Research .2000
27.H.C. Raven. Inviscid calculations of ship wave making---capabilities, limitations and prospects. 22nd Symp. on Naval Hydrodynamics, Washington DC, 1998
28.T. Katsuji, M.M. Makiko, S. Hiroshi. Estimation of Wave Drift Force by Numerical Wave Tank, 2nd Report. 10th International Offshore and Polar Engineering Conference.2000
29.W. K. Jang. A Numerical Study of Nonlinear Wave Interaction in Regular and Irregular Seas: Irrotational Green-Naghdi Model.
30.E. O. Tuck, L. Lazauskas. Free-surface pressure distributions with minimum wave resistance. ANZIAM J. 43 (E), 2001
31.D.C. Scullen, E.O. Tuck. Free-surface elevation due to moving pressure distributions in three dimensions, in preparation, January 2001.
32.M.H. Kim, W.C. Koo, S.Y. Hong. Wave interactions with 2D structures on/inside porous seabed by a two-domain boundary element method. Applied Ocean Research .2000
33.Y.S. Cao, W. Schultz. Three-dimensional desingularized boundary integral methods for potential problems. Int J Numer Meth Fluids. 1991
34.I.V. Sturova. The effect of internal waves on the hydrodynamic characteristics of a submerged body. Physics of Atmosphere and Ocean. 1993
35.N.G. Kuznetsov. Wave resistance of a semisubmerged cylinder on deep water. High Speed Hydrodynamics. 1990
36.O.V. Motygin, N. G. Kuznetsov. The Wave Resistance of a Two-Dimensional Body Moving Forward in a Two-Layer Fluid. Journal of Engineering Mathematics. 1997.
37.J.R. Cadby, C.M. Linton. Three-dimensional water-wave scattering in two-layer fluids.
38.Papanikolaou, A. D. Kaklis, P.D. On the Wave Resistance of Twin-Hull Floating Bodies with Non-Symmetric Demi-Hulls, 11th International Workshop on Water Waves and Floating Bodies, Hamburg, March.
39.Z.H. George, D. Spanos, P. Apostolos. Numerical and Experimental Study on the Wave Resistance of Fast Displacement Asymmetric Catamarans.
40.H.Sding. Drastic Resistance Reduction in Catamarans by Staggered Hulls, 4th Int. Conference on Fast Sea Transportation FAST'97, Sydney. 1997
41.D.SPANOS. Investigation of the Wave Resistance of Thin Catamarans with Symmetricand Non-Symmetric Demihulls, Diploma Thesis (in Greek), Dept. Naval Arch. & Marine Engineering, NTUA. 1995
42.A. Papanikolaou, D. Spanos. Systematic Resistance Tests of Catamaran Configurations with Non-Symmetric Wigley Demihulls, Lab. of Ship Design, Dept. of NAME, National Tech. Univ. of Athens, NTUA. 1999
43.T.M. Ralph, C. S. David. Plane Wave Radiation Resistance of a Source Mounted in the Side of an In_nite Duct in the Presence of Mean Flow
44.E. O. Tuck, D. C. Scullen, and L. Lazauskas. Wave Patterns and Minimum Wave Resistance for High-Speed Vessels.
45.M. Bessho. On a consistent linearized theory of the wave-making of ships, Journal of Ship Research, Vol. 38, 1994, pp. 83-96.
46.F. Noblesse. Analytical representation of ship waves (23rd Weinblum Memorial Lecture), Schiffstechnik, Vol. 48, 2001, pp. 23-48.
47.N. Salvesen, C. V. Kerczek, C.A. Scragg, C.P. Cressy, and M.J. Meinhold. Hydrodynmamic design of SWATH ships, Transactions of the Society of Naval Architects and Marine Engineers, Vol. 93, 1985, pp. 325-348.
48.J.S. Kouh, C.H. Ho. A High Order Panel Method Based on Source Distribution and Gaussian Quadrature, Ship Technology Reseaeh, Vol.43, 1996
49.G.Jensen and H. Sding. Rankine Source Methods for Numerical Solutions of the Steady Wave Resietaee Problem,
50．张小兔．基于B样条的三维船体水动力数值计算研究．武汉理工大学博士论文，2002．
51．滕斌，柏威．基于B-样条的边界元方法及其在波浪力计算中的应用．第十四届全国水动力学研讨会文集，2000．
52．高高．船波问题的辐射条件、自由面条件的研究及面元误差分析．武汉交通科技大学博士论文，1997
53．黄鼎良．小水线面双体船性能原理．国防工业出版社，1993
54.K .J. Bai, S. E. Kim. The Cross Flow Effect on the Force and Moment Acting on a SWATH Ship .Proc. of the 17th Symposium on Naval Hydrodynamics, 1988
55．刘应中．船舶兴波阻力理论．国防工业出版社，2003