突扩式水跃共轭水深的简化解

A simplified solution of the conjugated depth of abruptly expanding hydraulic jump

分析突扩水跃的水力特性,给出水跃方程的简化解。在分析突然扩散式水跃段流态的基础上对回流水深作出假设,考虑水跃扩散比对回流水深的影响,运用动量守恒定律建立突然扩散式水跃方程。通过级数展开方法,推导出突然扩散式水跃方程的显式简化解,并给出有关参数的经验公式。突扩比β=1.0时简化解与试验结果的平均误差为1.924%,在3.0<Fr1<9.0范围内二元水跃经典解与简化解误差随着水流弗劳德数Fr1的增加而减小,最大误差小于3.001%,简化解能够与试验和二元水跃经典解吻合很好。在不同扩散比情况下,简化解与试验结果的平均误差为5.511%,说明具有良好的精度。因此,可以应用它进行泄水建筑物下游水力计算。

The simplified solution of the hydraulic jump equation is provided by analyzing the hydraulic characteristics of a hydraulic jump in an abruptly expanding channel.Based on analyzing the flow pattern of a hydraulic jump in an abruptly expanding channel,a hypothesis is made for the depth in the back-flow region considering the effect of the abruptly expanding ratio on the depth in the back-flow region.The law of momentum conservation is used to establish the hydraulic jump equation in an abruptly expanding channel.Through the approximate treatment,the explicit simplified solution of the hydraulic jump equation in an abruptly expanding channel is derived.An empirical formula for the related parameters is given.The average error between the simplified solution and the experimental result is 1.924% at an abruptly expanding ratio when β=1.0.The error between the classical solution and the simplified solution in the range of 3.0<Fr1<9.0 decreases with the increase of the flow Froude number and the maximum error is less than 3.001%.The simplified solution well agrees with the experiment and the classical solution of 2D hydraulic jump.The average error of the simplified solution and the experimental result under different abrupt expanding ratio is 5.511%,indicating good accuracy.Therefore,it can be applied to carry out the hydraulic calculation in the downstream of the outlet structure.