溢流反弧段紊流边界层变化规律的数值模拟

Numerical Simulation of Development of Boundary Layer in Bucket of Spillway

在溢流反弧段流线同心圆假定的基础上，通过理论推导，建立了表征反弧段动水压强、壁面势流流速、壁面切应力的相应表达式；将描述边界层发展变化规律的连续方程、动量积分方程、动能积分方程联立，并运用列主元高斯消去法将其转化为一阶微分方程组，采用双边法求其数值解，从而模拟出反弧段水深、边界层厚度以及流速分布指数的沿程变化规律．

On the basis of the hypothesis of streamline concentric circles,by means of theoretical derivation,the formulas to describe the hydrodynamic pressure,wall potential velocity and wall shear stresses in the bucket of a spillway have been deduced.The continuity equation of water flow,momentum integral equation and kinetic energy integral equation of the boundary layer have been developed and a simultaneous equation has been formed.By column major element Gauss elimination method,they have been transformed into the first order differential equations.With the linear multistep two side method,the numerical solution has been obtained.Thus,the law of the development of the water depth and the thickness of turbulent boundary layer and the velocity distribution index in the direction of water flow have been simulated.