流体流动中波状游动平板最优运动的数值方法

钱勤建; 孙德军

doi:10.3879/j.issn.1000-0887.2011.03.008

流体流动中波状游动平板最优运动的数值方法

doi: 10.3879/j.issn.1000-0887.2011.03.008

中国科学技术大学近代力学系, 合肥 230026

详细信息

作者简介:
钱勤建(1981- ),男,浙江人,博士生(E-mail:qqj@mail.ustc.edu.cn);孙德军(1967- ),男,教授,博士,博士生导师(联系人.Tel:+86-551-3606797;E-mail:dsun@ustc.edu.cn).

中图分类号: O352
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出版历程
- 收稿日期: 2010-11-20
- 修回日期: 2011-01-19
- 刊出日期: 2011-03-15

Numerical Method for Optimum Motion of Undulatory Swimming Plate in Fluid Flow

Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, P. R. China

摘要

摘要: 提出了一种求解波状游动平板最优运动方式的优化方法．最优化问题表述为固定推力的条件下，使得输入功率最小．由于存在不可见模态，使得该问题具有奇性，用通常的Lagrange乘子法计算得到的可能不是最优解，而是一个鞍点值．为了消除这一奇性，增加了一个关于幅值的不等式约束，并利用逐步二次规划的优化方法求解该问题．将该方法运用到二维和三维的波动板的几个例子上，获得了最优解．
- 波动板 /
- 最优化 /
- 面元法 /
- 逐步二次规划
Abstract: A numerical method for optimum motion of an undulatory swimming plate was presented.The optimal problem was stated as minimizing the power input under the condition of fixed thrust.The problem was singular for the invisible modes and the commonly used Lagrange method may not predict an optimum solution but just a saddle point.To eliminate the singularity,an additional amplitude inequality constraint was added to the problem.A numerical optimization code with a sequential quadratic programming method was used to solve the problem.The method was applied to several cases of two-dimensional and three-dimensional undulatory plates' motions and the optimum results were obtained.
- undulating plate /
- optimization /
- panel method /
- sequential quadratic programming

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参考文献(17)

[1]	Wu T Y. Swimming of a waving plate[J]. Journal of Fluid Mechanics, 1961, 10: 321-344. doi: 10.1017/S0022112061000949
[2]	Liu P, Bose N. Propulsive performance from oscillating propulsors with spanwise flexibility[J]. Proceeding of the Royal Society of London, 1997, 453 (1963):1763-1770. doi: 10.1098/rspa.1997.0095
[3]	Zhu Q, Wolfgang M J, Yue D K P, Triantafyllou M S. Three dimensional flow structures and vorticity control in fish-like swimming[J]. Journal of Fluid Mechanics, 2002, 468: 1-28.
[4]	DONG Gen-jin, LU Xi-yun. Numerical analysis on the propulsive performance and vortex shedding of fish-like traveling wavy plate[J]. International Journal for Numerical Methods in Fluids, 2005, 48:1351-1373. doi: 10.1002/fld.984
[5]	LU Xi-yun, YIN Xie-zhen. Propulsive performance of fish-like traveling wavy wall[J]. Acta Mechanica, 2005, 175:197-215. doi: 10.1007/s00707-004-0117-y
[6]	WU Chui-jie, WANG Liang. Where is the rudder of a fish?—the mechanism of swimming and control of self-propelled fish school[J]. Acta Mechanica Sinica, 2010, 26 (1):45-65. doi: 10.1007/s10409-009-0305-z
[7]	Lighthill M J. Mathematical Biofluiddynamics[M]. Philadelphia: Society for Industrial and Applied Mathematics, 1975.
[8]	Lighthill M J. Note on the swimming of slender fish[J]. Journal of Fluid Mechanics, 1960, 9: 305-320. doi: 10.1017/S0022112060001110
[9]	Lighthill M J. Aquatic animal propulsion of high hydromechanical efficiency[J]. Journal of Fluid Mechanics, 1970, 44: 265-301. doi: 10.1017/S0022112070001830
[10]	Wu T Y. Hydromechanics of swimming propulsion. part 1: swimming of a two-dimensional flexible plate at variable forward speeds in an invisid fluid[J]. Journal of Fluid Mechanics, 1971, 46: 337-355. doi: 10.1017/S0022112071000570
[11]	Wu T Y. Hydromechanics of swimming propulsion. part 2: some optimum shape problems[J]. Journal of Fluid Mechanics, 1971, 46: 521-544. doi: 10.1017/S0022112071000685
[12]	CHENG Jian-yu, ZHUANG Li-xian, TONG Bing-gang. Analysis of swimming three-dimensional waving plates[J]. Journal of Fluid Mechanics, 1991, 232: 341-355. doi: 10.1017/S0022112091003713
[13]	Kagemoto H, Wolfgang M J, Yue D K P, Triantafyllou M S. Force and power estimation in fish-like locomotion using a vortex-lattice method[J]. Journal of Fluids Engineering, 2000, 122: 239-253. doi: 10.1115/1.483251
[14]	Lan C E. A Quasi-vortex-lattice method in thin wing theory[J]. Journal of Aircraft, 1974, 11(9): 518-527. doi: 10.2514/3.60381
[15]	Ahmadi A R, Widnall S E. Energetics and optimum motion of oscillating lifting surfaces of finite span[J]. Journal of Fluid Mechanics, 1986, 162:261-282. doi: 10.1017/S0022112086002045
[16]	Spellucci P. An SQP method for general nonlinear programs using only equality constrained subproblems[J]. Mathematical Programming, 1998, 82(3): 413-448.
[17]	Spellucci P. A new technique for inconsistent problems in the SQP method[J]. Mathematical Method of Operations Research, 1998, 47: 355-400. doi: 10.1007/BF01198402