Zahra Monemiyan

Hydraulic jump downstream of a vertical drop with a contraction transition and upstream subcritical flow

Abstract

A vertical drop is an abrupt change in elevation to offset the difference between the channel slope and the ground slope. The free falling jet impacts the channel floor and produces a recirculating pool. An air pocket is trapped in the area between the pool surface and the free falling jet. Due to the mixing process of the free falling jet, negative pressures develop in the air pocket, fill the pocket with air and increase the falling jet vibration. Usually, a ventilation shaft is provided to aerate the air pocket. In this investigation, contraction transitions are used to eliminate the negative pressures in the vertical drops. By using contraction transition at the brink of the drop, the falling jet width decreases and the air pocket vanishes.

The main objective of this study is to examine the effect of contraction transition on characteristics of hydraulic jump downstream of drop and the energy dissipation. The experimental work was conducted in two channels with three different drops and six different transitions. The relative critical depth d_c/h (where d_c is the critical depth and h is the vertical drop height) varied between 0.07 and 0.459. Empirical equations were presented to estimate brink depth profile, average bring depth, relative pool length and relative energy loss. Energy loss at the drop was calculated and compared with the result of the previous studies. It was observed that contraction transitions increase the energy loss about 10% to 15%. By using experimental observation, assumptions from previous researchers and assuming that the present hydraulic jump characteristics are similar to those of the classical hydraulic jump, six analytical models presented to estimate the energy loss. Estimations of the two analytical models were in good agreement with the experimental results. The shock waves formed at the downstream channel affect the hydraulic jump characteristics. It was observed that the shape and the roller length of the hydraulic jump are different from those in the classical hydraulic jump. Roller length data ware compared with previous studies formulas. It was shown that roller lengths were less than those of the classical hydraulic jump. The roller lengths decreased by increasing initial Froude number. Hydraulic jump had three different shapes. With initial Froude number (Fr₁) between 2 and 4, hydraulic jump forms like a classical hydraulic jump. An asymmetric V-jump forms with initial Froude number between 4 and 7. In 400-mm-high drop and with relative contraction (brink width divided by channel width) equal to 0.8, special hydraulic jump forms. The secondary depth of the hydraulic jumps are almost equal to those of the classical hydraulic jump. The maximum difference between experimental data and Rand’s secondary depth equation is about 11%.