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水跃曾经用物理模型广泛研究过;但是几乎还没有适用于原型水跃消力池内部流态的资料。为了有助于由物理模型对原型工况的预报,研究出了一个数学模型。这里应用的技术是纳莱阿兰(R.Narayanan)的分条积分法的一个推广。分条积分法应用流速形态函数使能对运动方程部分积分。在混掺区采用高斯流速分布,而内层则用指数定律。数学模型中计入了槽底切力、紊动切力、势流核心、掺气、离心力和紊动压强。模型对水跃长度、旋滚长度、流速分布、水面线以及槽底压强给出了良好的预报。边界层增长的预报不很好。模型表明掺气的主要作用是水流的膨胀。离心力和紊动压强的作用则随 F_1~2的增加而增大,当 F_1>5,作用就开始变得显著起来。
Hydrodynamics has been extensively studied using physical models; however, there is almost no data available for the flow patterns within the prototype hydrotaping tank. In order to facilitate the prediction of prototype conditions by physical models, a mathematical model has been developed. The technique used here is an extension of R. Narayanan’s method of the integral integral. Slice integral method enables the integration of part of the equations of motion by applying the flow rate morphological function. Gaussian flow velocity distribution in the mixed zone, while the inner law using exponential. The mathematical model includes the trough shear force, turbulent shear force, potential flow core, air entrainment, centrifugal force and turbulent pressure. The model gives a good prediction of the length of the hydrofoil, the length of the roll, the distribution of the flow velocity, the surface water line and the pressure at the bottom of the tank. The forecast of boundary layer growth is not very good. The model shows that the main effect of aeration is the expansion of the water flow. The effect of centrifugal force and turbulent pressure increased with the increase of F_1 ~ 2. When F_1> 5, the effect began to become remarkable.