重力场中二维空腔流动的有限元分析

林炳尧; 许协庆

重力场中二维空腔流动的有限元分析

林炳尧¹,
许协庆²

1.
水利水电科学研究院;
2.
水利水电科学研究院清华大学

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出版历程
- 收稿日期: 1982-08-09
- 刊出日期: 1985-05-15

Analysis of Two-Dimensional Cavity Flow by Finite Elements

Lin Bin-yao¹,
Xu Xie-qing²

1.
Institute of Water Conservancy and Hydroelectric Power Research, Beijing;
2.
Institute of Water Conservancy and Hydroelectric Power Research, Qinghua University, Beijing

摘要

摘要: 本文利用可变域泛函一阶变分表达式讨论了现有的几种自由面重力流ψ模式变分原理.证明了几种变分原理所以有差别是因为在自由表面采用的贯截条件不同,据此将ψ模式变分原理概括成四种类型.分析重力场中二维空腔流动时,根据有限元特点在空腔尾部置放一虚拟平板.计算中,每给出一个空腔长度,均可得到一收敛的自由表面,选取在脱流点流线光滑的曲线作为解答,从而得到空腔流动的一组可能解.此算法适用于单宽流量及总能头给定时通气空腔流动计算.最后,给出不同Fr数、空腔压力及坝面坡度等各种情况下的空腔长度曲线.

Abstract: The variational principle in terms of stream function ψ for free surface gravity flow is discussed by the formulation of first-order variation in a variable domain. Because of different transversal conditions adopted, there are four forms of variational principle in terms of ψ.An air-gilled cavity flow with given discharge and total energy is then analysed by finite element method. At the end of the cavity, the free stream line is tangent to a short fictitious plate of given length, which joins the fixed boundary at on angle to be determined. The condition that the free stream line should be tangent to the fixed boundary at the point of separation makes the solution unique.Finally curves giving the cavity length as a function of the Fraude number, cavity pressure and channel bottom slope are presented.

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参考文献(9)

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[4]	许协庆,自由面重力流的一种有限元解法.水利学报.1(1980).
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[7]	柯朗、希尔伯特,《数学物理方法》,I,科学出版社,(1958).
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[9]	Knapp,R,T.,7.W.Daily and F.G,Hammitt,Cavitation,(1970).