Experimental study of hydraulic jump characteristics in an inclined convergent channel

Dissipating high kinetic energy of supercritical flows for the purpose of protecting downstream structures has always been a concern of hydraulic structure engineers. One of the approaches to tackle this problem is the utilization of hydraulic jump phenomena in which a great amount of kinetic energy is dissipated through turbulence which is more pronounce in roller part and conversion to potential energy in term of depth increase at downstream end and turbulence. A hydraulic jump may occur in prismatic or non-prismatic, converged or diverged and horizontal or inclined channels. However, there are oblique shock waves initiating at the start of a contracted channel, interact with each other and sidewalls and may create a complex flow pattern which is detrimental to the channel itself and downstream facilities. The present research aims at studying hydraulic jumps taken place in a converging inclined channel. The main parameters of a hydraulic jump such as its location, initial depth, ratio of conjugate depths, jump length and energy dissipation are studied for various inclination and convergence ratios and inflow conditions.

The experiments were conducted in a channel with different bed slopes of 0, 5, 10, and 15 percent, and convergence angles of 3.66 and 5.4 degrees. The end sills of 0.75 to 11 cm high were installed at the end, depending on the bed slope, to fix the jump location in the channel. The entrance was set carefully to produce the least disturbance due to sharp edges and protruding elements appeared in the flow; hence, a symmetric hydraulic jump may be observed all over a cross section. In order to double-check the accuracy of measurements, clips of various hydraulic jump were shot through sidewalls, converted into the images and digitized using GrapherTM.
Discussion and

The length of a hydraulic jump, was mainly a function of bed slope, such that by increasing the slope to 15%, the increase in the jump length was about 37.5% in average. Specifying a unique initial depth in a converging channel was challenging. There were oblique waves originated from the concave corners and coincided at the center line of the channel. In cases where the hydraulic jump occurred before the coincidence of the oblique waves there were three different depths at the start of the jump. In this work, the centerline depth was selected as depth of reference in the development of equations. By enhancing the bed slope, the mean initial depth decreased and the conjugate depth ratio increased. The energy dissipation increased by both the bed slope and convergence ratio. However, the effect of bed slope was more significant such that the average growth of dissipation in a horizontal bed was about 30% compared to a sloping bed. By increase of initial Froude number the difference between energy dissipation in various bed slopes approached to that of a horizontal bed. Using regression models, empirical relationships were developed for the estimation of length, conjugate depths ratio and energy dissipation of a hydraulic jump in an inclined converging channel.