工程科学与技术   2019, Vol. 51 Issue (2): 115-120

Characteristics of the Wall Pressure in Impacting Zone at the End of Vertical Plug
HAN Haoran, TIAN Zhong, LIU Wen
State Key Lab. of Hydraulics and Mountain River Eng., Sichuan Univ., Chengdu 610065, China
Abstract: The vertical plug is a new way to dissipate water energy, in which the flow can be regarded as a submerged jet, and the construction leads to the high velocity and pressure on the wall. In order to explore the wall pressure distribution at the impinging zone and offer some scientific evidence for structural and hydraulic design, based on a spillway project, the characteristics of the wall pressure is analyzed by theoretical derivation, experimental test and numerical simulation under the condition of submerged jet with different flow rate. The results indicate that the measured pressure on the bottom axes agrees well with the numerical one, and both results have good agreement with the theoretical curve when the ratio of the distance between the test point and largest pressure point and the length of half maximum pressure is less than 1, but they are much larger than the theory when it is more than 1. The pressure gradually tends to the theoretical curve with the increasing of distance between press-slope and the center of the jet. The half-pressure length, which does not depend on the position of press-slope at the impacting zone downstream when the distance is 2.35 times larger than the jet diameter, is nearly equal to 0.3 times the diameter of the jet. Furthermore, the pressure of the top and side wall is decreasing when approaching to the center of the jet.
Key words: vertical plug    submerged jet    wall pressure    half-pressure length    numerical simulation

1 试验模型及测试方法

 图1 模型及测压点分布图 Fig. 1 Model and test point drawing

2 试验数据分析

 图2 冲击区壁面压强分布 Fig. 2 Pressure on the wall in impacting zone

3 底板轴线压强的理论分析

 ${J_0} = 2{b_0}\rho u_0^2$ (1)

 $\int_{{\rm{ - }}x}^x {\rho {u^2}{\rm{d}}y} = 2{b_0}\rho u_0^2$ (2)

 $\frac{u}{{{u_{\rm{m}}}}} = \exp \left[ {{\rm{ - }}{{\left( {{X / b}} \right)}^2}} \right]$ (3)

 $\frac{p}{{{p_{\rm{m}}}}} = \exp \left[ {{\rm{ - }}\alpha {{\left( {{X / b}} \right)}^2}} \right]$ (4)

 图3 压强实测值和理论曲线对比 Fig. 3 Comparison between the test results and theory curve

4 数值模拟研究

4.1 控制方程及边界条件设定

 $\frac{{\partial \rho }}{{\partial t}} + \frac{{\partial \rho {u_i}}}{{\partial {x_i}}} = 0$ (6)

 $\frac{{\partial \rho {u_i}}}{{\partial t}} + \frac{\partial }{{\partial {x_i}}}\left( {\rho {u_i}{u_j}} \right) = {\rm{ - }}\frac{{\partial p}}{{\partial {x_i}}} + \frac{\partial }{{\partial {x_j}}}\left[\mu \frac{{\partial {u_i}}}{{\partial {x_j}}}{\rm{ - }}\rho u_i'u_j'\right]$ (7)

k方程：

 $\frac{{\partial (\rho k)}}{{\partial t}} + \frac{{\partial (\rho {u_i}k)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left[(\mu + {\mu _t}){\alpha _k}\frac{{\partial k}}{{\partial {x_j}}}\right] + {G_k} + \rho \varepsilon$ (8)

ε方程：

 $\frac{{\partial (\rho \varepsilon )}}{{\partial t}} + \frac{{\partial (\rho \varepsilon {u_i})}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left[(\mu + {\mu _t}){\alpha _\varepsilon }\frac{{\partial k}}{{\partial {x_j}}}\right] + \frac{{C_{1\varepsilon }^*}}{k}{G_k}{\rm{ - }}{C_{2\varepsilon \rho }}\frac{{{\varepsilon ^2}}}{k}$ (9)

 ${G_k} = {\mu_t}\left(\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}\right)\frac{{\partial {u_i}}}{{\partial {x_j}}}$ (10)
 $C_{{\rm{1}}\varepsilon }^{\rm{*}} = {C_{{\rm{1}}\varepsilon }}{\rm{ - }}\frac{{\eta (1{\rm{ - }}{\eta / {{\eta _{\rm{0}}}}})}}{{{\rm{1}} + \beta {\eta ^{\rm{3}}}}}$ (11)

 图4 计算网格 Fig. 4 Computational grid

4.2 计算结果分析

 图5 底板压强计算结果 Fig. 5 Simulation result of the bottom pressure

 图6 计算模型图 Fig. 6 Computation model drawing

 图7 压强半宽值 Fig. 7 Length of half-pressure

 图8 底板轴线压强分布 Fig. 8 Bottom axes pressure distribution

5 结　论

1）垂直洞塞冲击区底板的压力半宽值与压坡段所处的位置无关，其值约为射流直径的0.3倍；

2）底板轴线压强分布规律可分为两个部分：当–4<X/b<1时，轴线压强（p/pm）分布近似为高斯分布（式（4），0.64< $\alpha$ <0.67）；当X/b>1时，在压坡段距离射流中心较近时，压强分布的理论曲线不适用，随着压坡段和射流中心之间距离的增加，压力分布逐渐吻合理论曲线；当L=2.35d时，底板轴线压强对称分布；说明压坡段仅在距离射流中心较近时才会对底板轴线的压强分布产生影响。

3）冲击区内，顶板和侧壁的压强越靠近射流中心，压强值越小；且由于压坡段的存在，理论曲线不再适用于原体型下底板轴线上的压强分布，下游压坡侧的压强明显大于上游。

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