Experimental study of the hydraulic jump on reverse bed with porous screens
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Abstract
Nowadays, the porous screens have been used extensively in open channels to prevent erosion in ditches as the water in supercritical state flows past the screen which forces the formation of a hydraulic jump upstream of the screen and produces significant energy loss. In this investigation, the operation of screens has been studied for supercritical flow and the Froude number in the range of 4.5 to 10.6 on two reverse slopes experimentally. In this study, the parameters included arrangements of screens in both the single and double types, and the angle and distance of screens from the hydraulic jump toe. The screens were studied with a porosity of about 50% with square holes. The study results showed that using of screens on the reverse slope of − 0.025 dissipates more energy compared to reverse slope of − 0.015. The screens with double arrangement have better performance and dissipate more energy than the screens with single arrangement, while the distance of screens from the toe of the hydraulic jump does not have a significant effect on the energy dissipation.
Keywords
Energy dissipation Porous screens Reverse slope Sequent depth Hydraulic jumpIntroduction
A hydraulic jump occurs at the transition from supercritical flow to subcritical flow. It is characterized by a sudden increase in water depth and loss in the energy. The turbulent hydraulic jump is one of the significant problems in the hydraulic engineering.
Pagliara and Peruginelli (2000) were studied hydraulic jumps formed on adverse slopes experimentally. A general equation, for the sequent depth ratio, was proposed and corroborated by experimental data. Hydraulic jumps in sloping channels have been studied by Beirami and Chamani (2006, 2010). In this paper, the roller length and energy loss of a large variety of hydraulic jumps were investigated in horizontal and sloping channels experimentally. A stilling basin with bottom slopes of 0.0, − 0.025, − 0.050, − 0.075, and − 0.100 was used to generate the jumps. An empirical relationship is presented to predict the roller length.
Mudgal and Pani (2012) used sills to aid the formation of a hydraulic jump in a stilling basin. The drag force acting on a sill in forced hydraulic jump depends on the initial Froude number Fr_{1}, the height of the sill S, and its distance from the toe of the jump. Farhoudi and Khalili Shayan (2013) have investigated the stability of free hydraulic jump on adverse stilling basins from a theoretical point of view. In this research, a theoretical equation for estimating the minimum upstream Froude number to establish the free hydraulic jump on an adverse bed was presented. The hydraulic characteristics of forced jump due to perforated sill were measured and compared with the classical hydraulic jump by Behrouzi-Rad et al. (2013). The experiments results of this study certified the effect of the perforated sill on dissipation of energy. Cherhabil and Debabeche (2016) have studied the hydraulic jump in a sloped trapezoidal channel experimentally. The study was done to determine the impact of channel slope on the characteristics of the jump. An experimental investigation is done to determine the relationships between the sequent depth ratio of the jump and the initial Froude number and the channel slope. An investigation of hydraulic jump in the stilling basins with stepped sills has been done experimentally by Minaei Gigloo et al. (2016). They found that the sill with two steps has better efficiency to stabilize a jump in the stilling basin compared to sill with three steps. Parsamehr et al. (2017) have investigated the characteristics of hydraulic jump, including sequent depth, relative length of the jump, and energy loss on rough bed with discontinuous roughness elements of lozenge shape over adverse slope. It was found that by increasing the height of roughness elements and steeping the adverse slope, the sequent depth ratio, and relative length of the jump decreased, while the energy loss increased.
In recent years, the screens have been applied to prohibit the erosion in roadside ditches and steep bed surfaces. This screen is placed perpendicularly across the supercritical flow in the ditch which forces the formation of a free or forced hydraulic jump upstream of the screen and produces significant energy loss. The experimental study showed that the porous screens with a porosity of about 40% were used as effective energy dissipaters in the stilling basins. The results of these experiments are presented by Rajaratnam and Hurtig (2000). The relative energy loss was considerably larger than that created the similar classical hydraulic jump, and the sequent depth required was observed about one half of y_{2}*.
Bozkus et al. (2007) and Bozkus and Aslankara (2008) evaluated the energy dissipation of the screen in a flume with horizontal bed. The experiments were done with Froude numbers 2.5 up to 8.5, screen porosities of 40% and 50%, and distances of double screens between 1 and 5 cm The experiments show the screen porosity of 40% provided higher energy dissipation. The screens with double arrangement with the imposed hydraulic jump dissipated more energy.
Shaker et al. (2013) studied the effect of holes shape in the screen wall on the efficiency of the energy dissipation. Three holes of different shapes were used in screen walls, circular, square and two different dimensions for each model, with a fixed porosity of 40%. Sadeghfam et al. (2014) investigated the effectiveness of screens as the energy dissipaters in small hydraulic structures experimentally. In the experimental study, the experiments were done for a range of Froude numbers between 2.5 and 8.5, screen porosity of 40% and 50%, and gaps of double screens between 1 and 5 cm. The screens with double arrangement with the imposed hydraulic jump dissipated more energy. Singh (2018) has conducted laboratory experiments on screens or porous baffles with a porosity of about 50–60%. The single wall or double wall was used with the different angles at 45°, 90° and 135°. The experiments were done for a range of Froude numbers (Fr_{1}) from about 1.5 to 6. The downstream flow was found to be supercritical flow and tail water depth after the screen is equal to the 0.79 times to y_{2}.
The objective of this research is to investigate the effect of single or double screens on the characteristics of a jump on a new type of stilling basin with adverse slope. This paper reports the results of a laboratory investigation on energy loss and the depth of jump, y_{2}, of both sill-controlled hydraulic jump and single and double screens on the smooth beds. Finally, this note is to offer theoretical and experimental results for the case of an end sill-controlled hydraulic jump on an adverse slope to estimate sequent depth and energy loss of jump. It is thought that the experiments conducted within the domain of this study (Bozkus et al. (2007), Bozkus and Aslankara (2008), Sadeghfam et al. (2014)) extended the information about porous screen on reverse bed stilling basins as the alternative energy dissipaters.
Materials and methods
Theoretical background
The experiments were conducted in a metal–glass flume with a rectangular cross section. The flume was 0.25 m wide, 0.5 m deep, and 10 m long. The bed slope of the channel was 0.002, but the portion of the channel was with a slope of 0.015 and 0.025 for the length of 2 m. The flume was provided with a sluice gate at the entry, and the discharge was measured by a triangular weir at the end of the flume. The supercritical depth y_{1} and subcritical sequent depth y_{2} of the jumps were continuously measured using ultrasonic sensors, and the data were saved on a computer and processed by VisiDAQ software. Then, the average of jump depths was computed.
Summary of experimental parameters
Exp. | N | R (cm) | Fr _{1} | Y_{1} (cm) | Q (lit/s) | S _{0} |
---|---|---|---|---|---|---|
A | 1 | 40–45, 45–50, 50–55, 55–60 | 4.5–10.6 | 2.5 | 12–36 | 0.015, 0.025 |
B | 2 | 30, 40, 50 | 4.5–10.6 | 2.5 | 12–36 | 0.015, 0.025 |
In this study, the water depths were measured at different sections of a jump in the centerline of the flume with a point gauge (accuracy of 0.1 mm). The supercritical depth and sequent depth y_{1}, y_{2} were measured as shown in Table 1. The sequent depth was controlled by an adjustable gate at the end of the channel such that the jumps were formed at the beginning of the reverse bed slope.
Results and discussion
In order to study a hydraulic jump on a reverse sloped bed, with porous screens or end sill its characteristics in different sections were analyzed.
The depth ratio
The dimensionless depth deficit parameter, D, was defined by Rajaratnam and Hurtig (2000) as \( D = \frac{{y_{2}^{*} - y_{2} }}{{y_{2}^{*} }} \), where y _{2} ^{*} is the sequent depth of a hydraulic jump on a smooth bed with the same upstream conditions. It is found that, for the hydraulic jump with single screen for two slopes S_{0} = 0.015 and S_{0} = 0.025., D varies 0.1–0.4 and 0.3–0.45, respectively, that the average values of 0.3 and 0.37 are obtained. These values indicate that the depth ratio formed by single screen is appreciably smaller than depth ratio in the classical hydraulic jump and the depth deficit parameter of hydraulic jump on the reverse bed of 0.025 is greater than slope of 0.015 for the same upstream Froude number.
Figure 3 compares the results of double screens with distances 40–45, 45–50, 50–55, and 55–60 cm. Based on this figure, for screen with distances of 50–55, the sequent depth ratio increases for a given value of the upstream Froude number.
It can be seen that, for the hydraulic jump with double screens in different distances (40–45, 45–50, 50–55 and 55–60 cm) for two slopes S_{0} = 0.015 and S_{0} = 0.025, D is constant value of 0.4.
The energy dissipation
In this case, the energy loss on reverse bed slope with single screen for slopes of 0.015 and 0.025 is increased by 13% and 19%, respectively, compared to classical jump energy. Also the energy loss on reverse bed slope with double screens for two slopes of 0.015 and 0.025 is increased by 18% and 23%, respectively, compared to classical jump energy.
In the Froude number range in this study, the supercritical flow in collision with double screens creates more energy loss due to the extra turbulences compared to jump behaviors with a single screen. The analysis of results shows that, for each screen distance, the relative energy loss increases with increasing the bed slope.
Conclusions
- 1.
Due to the instability of such jumps, the results are more scattered compared to the classic hydraulic jump in a horizontal channel. A hydraulic jump on an adverse slope has a complex flow configuration.
- 2.
The presence of a sill stabilizes the jump. In the reverse bed with a slope of 0.025, the values of sequent depth ratio (y_{2}/y_{1}) are less compared to slope of 0.015.
- 3.
Comparison of results shows that the sequent depth reduces with increase in the bed slope for both single and double screens.
- 4.
Results show the relative energy loss produced by screen is greater than that produced by the classical hydraulic jump for the same Froude number, Fr_{1}, and the double screen dissipates a little more energy than single screen. So the use of screens on reverse bed stilling basin in downstream of the hydraulic structures will be a good alternative to the stilling basins.
- 5.
It should be noted that in an adverse bed stilling basin with the presence of the porous screen, the relative loss of energy increases by increasing the bed slope.
Notes
References
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