掺气减蚀设施后二维空腔流动计算

本文发展了文献4]中提出的求解自由面重力流的h2类边值问题理论。运用解析函数的Riemann-Hilbert混合边值问题的h3类边值问题理论，导出了计算有重力作用情况下双自由表面二维空腔势流流动的边界程分方程，提出了确定空腔区水舌下自由表面的计算格式，并在物理平面上进行了数值求解。表明，该数值方法具有收敛速度快、边界适应能力强、计算量小、计算精度高和对初值要求不高等特点。计算结果与实测资料对比分析表明，来流佛氏数Fr<7情况下，无需考虑阻力影响，采用势流模型即可获得与实测值相符合的结果；而在来流佛氏数Fr>7情况下，由于射流掺气加剧，需引入阻力修正。

Numerical calculation for two dimensional cavity flow downstream of an aerator

The boundary integral equations for calculating the 2-D potential cavity flow down stream of the aerator are derived by using Riemann-Hilbert mixed boundary problem technique of analytical function. The numerical scheme for determining the lower free surface is proposed. The calculation result shows that this method is applicable to the complex shaped boundary without special requirement to the initial input value. Comparison between the calculated results and measured data indicates that the adoption of potential flow model is suitable under the condition of low Froude number (Fr<7) when air friction is neglected. Contrarily, the friction force correction must be made if Fr>7 and aeration of free jet is intensified.