Introduction:

The hydraulic jump is often applied as an energy dissipator below weirs or spillways of dams, chutes, gates, drops and other structures might be utilized in this regard. In the hydraulic jump, the water depth increases abruptly and some of the kinetic energy is transformed into potential energy, with some energy irreversibly losses through the turbulence. Determining the dimensions of the stilling basin is an important task for the hydraulic engineers to design a safe and economical energy dissipator and to reduce the construction costs of stilling basin, a change in the plan and profile sections of the basins can be useful. Arbhabhirama and Abella (1971) studied radial hydraulic jumps in a gradually expanding channel of rectangular cross section with divergence angles from 0 to 13°. The results showed that the divergence of the walls causes reductions in the sequent depth and the length of jump and an increase in the energy loss as compared to the hydraulic jump in a straight rectangular channel. Ead and Rajaratnam (2002) conducted an experimental study of the hydraulic jump on corrugated beds and specified that the reduction of the tailwater depth depends on increasing of bed shear stresses, which in turn are generated by interaction of the supercritical flow with the bed corrugations. Channels with trapezoidal cross-sections was carried out by Omid et al (2007). They found that the sequent depth and the length of the hydraulic jump decreased, whereas the energy loss increased with the increasing bottom width. Abbaspour et al. (2009) investigated the effect of sinusoidal corrugated bed with different wave steepness on the basic features of the hydraulic jump. They showed that the length ratio and the tailwater depth ratio of the jump on corrugated beds are smaller than that of the corresponding jump on a smooth bed. Chanson and Carvalho (2015) using an integral form of the continuity and the momentum principles, proposed an equation for calculating the sequent depth ratio of the hydraulic jump in an irregular channel. Daneshfaraz et al. (2018) studied the effect of sand bed with median size 1.9 cm on S-jump characteristics. The results showed that the abruptly expansion stilling basins with a rough bed in all the expansion ratios reduced the depth ratio and average jump length compared to an abruptly expansion stilling basins with smooth bed.

The main purpose of this research is to study the effects of expansion ratio of the side walls channel and the discrete roughness elements height on the characteristics of the hydraulic jump such as the sequent depth, the jump length, the energy dissipation and the bed shear stress.



Methods:

The experiments were conducted in a hydraulic laboratory of the University of Tabriz in a metal-glass horizontal rectangular flume. The facility had been relatively large-size channel 0.5 m wide, 0.5 m high and 10 m long. The sidewalls had been made of glass for observational purpose with 0.5 m high and 2.1 m long. The inflow conditions were controlled by a vertical sluice gate with a semi-circular rounded shape (Ø = 0.2 m) and the downstream coefficient of contraction was about unity. Also, the downstream flow conditions were controlled by a vertical gate. The upstream gate opening was fixed (2.1 cm) in all of the conducted experiments. To investigate the effect of roughness, discontinuous dissipative elements of lozenge shape with two heights (1.4 and 2.8 cm) were installed on the horizontal bed. Three glass physical models were built with divergence ratio (B = b1/b2) of 0.4, 0.6 and 1 (where b1 and b2 are the widths of the stilling basin in upstream and downstream of the hydraulic jump, respectively). During the jump, flow depths were measured using ultrasonic sensors Data Logic US30 with operation range of 10–100 cm and accuracy of ±0.1 mm that were mounted above the channel. The length of the hydraulic jump was measured by a fabric ruler with a reading accuracy of ±1 mm installed along the channel.



Results:

In this paper, the main features of a hydraulic jump under both the effect of the height of bed roughness and expansion of basin walls condition were investigated. Experimental observations showed that installing roughness elements stabilized the hydraulic jump on the channel. Equations (8), (9) and (10) were proposed for estimating the sequent depth ratio (y2/y1), the relative length of the hydraulic jump (Lj/y1) and the relative loss of energy (EL/E1), respectively. The Equation (8) shows that the sequent depth ratio increased with the increasing inflow Froude number and the divergence ratio. Also, the sequent depth ratio decreased as the roughness elements ratio increased. The relative length of the hydraulic jump for a given inflow Froude number, decreased as the roughness elements ratio increased. A comparing between the measured values of EL/E1 and those calculated by Equation (10) showed that, Equation (10) allows an estimation for calculating the relative energy loss in expanding basin with roughened bed. Also, the results indicated that the value of ε in the hydraulic jump on rough beds is increased compared with the smooth bed in all expansion ratios. Furthermore, the roughness height of 2.8 cm is more effective in creating high turbulence, force and increasing the coefficient of bed shear force.