ANALYSIS OF TWO-DIMENSIONAL CAVITY FLOW BY FINITE ELEMENTS

The variational principle in terme of stream function (?) for free surface gravity flowis discussed by the formulation of first-order variation in a variable domain. Because ofdifferent transversal conditions adopted, there are four forms of variational principle interms of (?).An air-filled cavity flow with given discharge and total energy is then analysed by finiteelement method.At the end of the cavity, the free stream line is tangent to a short fictitiousplate of given length, which joins the fixed boundary at an angle to be determined.Thecondition that the free stream line should be tangent to the fixed boundary at the point ofseparation makes the solution unique.Finally curves giving the cavity length as a function of the Froude number,cavitypressure and channel bottom slope are presented.     

重力场中二维空腔流动的有限元分析

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.     

Analysis of two-dimensional cavity flow by finite elements

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.A n 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.