https://orcid.org/0000-0002-1085-1023
Abstract
The present experimental study analyzes the effects of lateral jet flow (LJF) in a stilling basin with abruptly expanding channels on the stabilization and the significant characteristics of spatial hydraulic jump. The experiments were carried out with three different inflow Froude numbers (8.77, 9.56, and 10.87), three different distances of the LJF from the abruptly expanding channel (0 m, 0.25 m, and 0.5 m), and one and two LJF (i.e., the number of active orifices in the LJF system). According to the results, the distances of the LJF from the narrow channel and the number of LJF improve the hydraulic jump's stabilization and flow pattern enhancement in the tailwater channel. Additionally, the average sequent depth and the spatial jump length decreased by 14% and 20%, respectively, compared to no LJF. Also, using LJF increases relative energy dissipation by 12.45% on average.
HIGHLIGHTS
Using lateral jet flow (LJF) to stabilize spatial hydraulic jump.
Reduction of sequent depth by LJF.
Reduction of hydraulic jump length by LJF.
Increasing energy dissipation in spatial hydraulic jump using LJF.
INTRODUCTION
The hydraulic jump in open channels is a sudden and fast transition of the flow regime from supercritical to subcritical. This transition is characterized by a sudden change in the flow depth with the development of large-scale turbulence, surface waves, energy loss, and air entrainment. The hydraulic jump is widely used as an energy dissipater downstream of hydraulic structures such as spillways, drop structures, chutes, and sluice gates (Chanson 2015). To reduce the costs of stilling basin construction and prevent erosion and cavitation, determining the optimal dimensions of a stilling basin is an essential issue for engineers from viewpoints of economics and safety.
.By ignoring channel resistance, Gill (1980) indicated that the values of sequent depth ratio were over-predicted. Other notable studies on the characteristics of the classical hydraulic jump have been conducted by Silvester (1964); Hager & Bremen (1989); Carollo et al. (2007); Chanson (2011); Carollo et al. (2012); and Türker & Valyrakis (2021).
There have been studies on using water jets as an energy dissipater in the stilling basin. Tharp (1966) analyzed the effects of submerged jets on the characteristics of hydraulic jumps. He showed that submerged jets are as effective as drop structures in decreasing the hydraulic jump length. Additionally, submerged jets reduced the required tailwater depth of a hydraulic jump at any angle. Deng et al. (2008) introduced a stilling basin with horizontal submerged jets with three significant advantages: high energy dissipation rate, low impact pressure, and low near-the-bed velocity. They also found that the high energy dissipation rate is due to the formation of shear areas in this basin. Varol et al. (2009) studied the water jet effects on hydraulic jump characteristics. They concluded that energy dissipation in hydraulic jumps with jets increases compared to free hydraulic jumps. Chen et al. (2010) conducted experimental research on the scale effects of two-phase air–water flows in a stilling basin with horizontal submerged jets. The results showed the minimum effect of the model scale on the flow's averaged time characteristics. Chen et al. (2014) analyzed velocity distribution in a stilling basin with horizontal submerged jets. They observed a 60% decrease in the near-bed velocity compared to the velocity of the jet at the outflow orifices. Alghwail et al. (2018) performed an experimental study of the effect of counterflow jets on hydraulic jump features downstream of an ogee spillway. They showed that a counterflow jet reduces hydraulic jump length by 19% compared to a scenario without a counterflow jet. Helal et al. (2020) numerically analyzed the effects of bed water jets on the submerged hydraulic jump. According to the results, the water jets installed at the bottom of the channel decreased the hydraulic jump length by 59%, and the jump efficiency improved to 85.4% compared to the non-jetted system. Moradi et al. (2022) conducted an experimental study on 3-dimensional velocity distribution in stilling basins with horizontal submerged jets. They concluded that increasing the jet's submergence leads to an increase in shear stress and the size of the vortices. They also showed that an increase in the submergence caused the maximum bed and sidewall shear stress to dwindle by 2.2% and 2.7%, respectively. Ibrahim et al. (2022) experimentally evaluated the effect of bed water jets on hydraulic jump features. The results revealed that bed water jets decreased jump length by an average of 48%. Zhou et al. (2022) examined jet flow in hydraulic jump-stepped spillways. They stated that compared with conventional stepped spillways, the hydraulic jump-stepped spillway could extend the practical application for large unit discharges by providing a better understanding of jet flow conditions. Sajjadi et al. (2022) investigated the impact of submerged counterflow jets on classical hydraulic jump features in stilling basins. They observed that the submerged counterflow jets decreased the hydraulic jump's average length and sequent depth by 32.8% and 19.6%, respectively. Wang et al. (2022) investigated the hydraulic characteristics of countercurrent jets on adverse-sloped beds. The results revealed that, compared to the horizontal bed, the bed slope did not increase the energy dissipation rate of countercurrent jets but decreased the return flow length and upstream water level. Sharoonizadeh et al. (2022) studied the hydrodynamic features of counterflow jets in an abruptly expanding channel. The results revealed the good performance of the counterflow jets in preventing flow instability associated with abruptly expanding stilling basins.
The formation and perseverance of hydraulic jumps in stilling basins depend on the tailwater depth. In conditions where the required depth for creating a hydraulic jump is insignificant and the excavation of the stilling basin's bed is impossible due to economic and implementation constraints, an expansion section is an effective solution to ensure the formation and perseverance of the jump in the stilling basin (Herbrand 1973). Based on the location of the jump toe and the tailwater depth, the hydraulic jump in the abruptly expanding channel is divided into repelled, spatial, and transitional hydraulic jumps (Bremen & Hager 1993). Alhamid (2004) carried out an experimental study on S-jump features in the sudden expanding stilling basin with three different expansion ratios of 0.67, 0.5, and 0.33. According to the results, the spatial hydraulic jump has greater efficiency than the classical hydraulic jump. Matin et al. (2008) investigated hydraulic jumps in an abruptly expanding sloping channel. They showed that the hydraulic jump in such channels contributes to lesser tailwater depth.
Neisi & Shafai Bejestan (2013) studied the effect of bed roughness elements on spatial hydraulic jump features. They concluded that jump efficiency increased by 20% compared to a classical hydraulic jump. Hassanpour et al. (2017) conducted experimental research on hydraulic jump features in expanding channels with a roughened bed. They found that the roller length of the hydraulic jump on a gradual expansion basin with a rough bed was smaller than classical hydraulic jumps in a rectangular basin with a smooth and rough bed. Eshkou et al. (2018) evaluated the effect of angled baffle blocks in an expanding channel. Analysis of experimental data illustrated that the best convergence angle is 30 degrees, which decreased jump length by up to 35%. Jesudhas et al. (2020) performed numerical research on the velocity distribution of submerged spatial hydraulic jumps. They deduced that the combined performance of the separation rollers, the jump roller, and the channel bed converts vortical structures into smaller scales, resulting in energy loss of the hydraulic jump. Hajialigol et al. (2021) examined a system of crossbeams to dissipate the flow's kinetic energy in the sudden expanding stilling basin. They showed that beam spacing and system slope are the most effective geometric parameters for the system's efficiency. In addition, the crossbeam system can improve the flow patterns in the tailwater channel and prevent any undesirable damage. Sharoonizadeh et al. (2021) examined the performance of counterflow jets to stabilize spatial hydraulic jumps. They showed that jet distance from the expansion section and the jet density play an essential role in the system's performance. Khanahmadi et al. (2022) investigated the effect of a rough bed on the hydraulic jump characteristics in the sudden expanding channel. They deduced that the length of the transitional hydraulic jump on the rough bed is smaller than the classic jump and the smooth bed. Aydogdu et al. (2022) evaluated the sill hydraulics for the sudden expanding stilling basin. They indicated that the hydraulic jump features are strongly influenced by sill geometry. In addition, hydraulic jumps in the sudden expanding channel have been studied by many scientists (e.g., Omid et al. 2010; Scorzini et al. 2016; Torkamanzad et al. 2019; Hassanpour et al. 2021).
According to the literature review, there are numerous studies on the hydraulic jump in an abruptly expanding stilling basin and the effects of a jet in the same direction as the flow (parallel to the flow) on the hydraulic jump. However, there has not been any research on the interaction effects of LJF on spatial jump characteristics downstream of the ogee spillway. As a result, the present study primarily aims to analyze the impact of LJF on S-jump characteristics, such as sequent depth, jump length, roller length, and efficiency.
MATERIALS AND METHODS
Laboratory equipment
Schematic view of experimental setup and details.
(a) Centrifugal pump, (b) sudden expanding channel, and (c) sluice gate.
- 1.
Number of jets, i.e., the number of active orifices in the LJF system (n): 1 and 2
- 2.
Inflow Froude number (Fr1): 8.77, 9.56, and 10.87
- 3.
Distance of the lateral jets from the narrow section (d): 0, 0.25 and 0.5 m
View of positioning arrangement of the jets.
During each experimental test, the pump was initially turned on and the inflow discharge was adjusted using a valve located in the pipeline before the head tank. To create a spatial hydraulic jump, the toe position was set at the enlarged section using a sluice gate, and then the multistage centrifugal pump was switched on to supply the jet discharge. After stabilization flow conditions, the inflow depth at the toe (y1) and sequent depth (y2) were measured using a point gauge with ±1 mm reading accuracy. Furthermore, the length of the jump (Lj) was measured with a ruler on the sidewalls of the flume with an accuracy of ±1 mm. On the whole, the sequent depth of five cross sections of the flume was measured, and average depth was used. The jump length is defined as the distance between the jump and the location in which the water surface is horizontal and bubbles are not present (Hager 1992). The characteristics of the experiments performed in this research are shown in Table 1.
Main parameters of the current experimental study
| Run | QI (m3/s) | Qj (m3/s) | n | d (m) | Fr1 | y2 (m) | Lj (m) |
|---|---|---|---|---|---|---|---|
| No jet | 0.026–0.044 | 0 | 0 | 0 | 8.77–10.57 | 0.098–0.130 | 1–1.30 |
| S1 | 0.026–0.044 | 0.0015 | 1 | S1 = 0 | 8.77–10.57 | 0.078–0.114 | 0.75–1 |
| S2 | 0.026–0.044 | 0.0015 | 1 | S2 = 0 | 8.77–10.57 | 0.080–0.116 | 0.8–1.02 |
| S3 | 0.026–0.044 | 0.0015 | 1 | S3 = 0.25 | 8.77–10.57 | 0.085–0.117 | 0.8–1.02 |
| S4 | 0.026–0.044 | 0.0015 | 1 | S4 = 0.25 | 8.77–10.57 | 0.089–0.117 | 0.9–1.06 |
| S5 | 0.026–0.044 | 0.0015 | 1 | S5 = 0.5 | 8.77–10.57 | 0.091–0.120 | 0.95–1.05 |
| S6 | 0.026–0.044 | 0.0015 | 1 | S6 = 0.5 | 8.77–10.57 | 0.093–0.121 | 1–1.08 |
| S1-2 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S2 = 0 | 8.77–10.57 | 0.074–0.110 | 0.68–0.94 |
| S1-3 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S3 = 0.25 | 8.77–10.57 | 0.077–0.1105 | 0.74–0.97 |
| S1-4 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S4 = 0.25 | 8.77–10.57 | 0.076–0.111 | 0.72–0.96 |
| S1-5 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S5 = 0.5 | 8.77–10.57 | 0.081–0.113 | 0.84–1.02 |
| S1-6 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S6 = 0.5 | 8.77–10.57 | 0.080–0.112 | 0.81–1.00 |
| S2-3 | 0.026–0.044 | 0.0015 | 2 | S2 = 0, S3 = 0.25 | 8.77–10.57 | 0.078–0.111 | 0.75–0.98 |
| S2-4 | 0.026–0.044 | 0.0015 | 2 | S2 = 0, S4 = 0.25 | 8.77–10.57 | 0.079–0.1115 | 0.79–0.99 |
| S2-5 | 0.026–0.044 | 0.0015 | 2 | S2 = 0, S5 = 0.5 | 8.77–10.57 | 0.081–0.112 | 0.83–1.01 |
| S2-6 | 0.026–0.044 | 0.0015 | 2 | S2 = 0, S6 = 0.5 | 8.77–10.57 | 0.082–0.114 | 0.84–1.03 |
| S3-4 | 0.026–0.044 | 0.0015 | 2 | S3 = 0.25, S4 = 0.25 | 8.77–10.57 | 0.080–0.112 | 0.82–1.00 |
| S3-5 | 0.026–0.044 | 0.0015 | 2 | S3 = 0.25, S5 = 0.5 | 8.77–10.57 | 0.0835–0.114 | 0.845–1.03 |
| S3-6 | 0.026–0.044 | 0.0015 | 2 | S3 = 0.25, S6 = 0.5 | 8.77–10.57 | 0.081–0.113 | 0.84–1.02 |
| S4-5 | 0.026–0.044 | 0.0015 | 2 | S4 = 0.25, S5 = 0.5 | 8.77–10.57 | 0.083–0.115 | 0.86–1.04 |
| S4-6 | 0.026–0.044 | 0.0015 | 2 | S4 = 0.25, S6 = 0.5 | 8.77–10.57 | 0.082–0.1145 | 0.87–1.02 |
| S5-6 | 0.026–0.044 | 0.0015 | 2 | S5 = 0.5, S6 = 0.5 | 8.77–10.57 | 0.084–0.115 | 0.88–1.04 |
| Run | QI (m3/s) | Qj (m3/s) | n | d (m) | Fr1 | y2 (m) | Lj (m) |
|---|---|---|---|---|---|---|---|
| No jet | 0.026–0.044 | 0 | 0 | 0 | 8.77–10.57 | 0.098–0.130 | 1–1.30 |
| S1 | 0.026–0.044 | 0.0015 | 1 | S1 = 0 | 8.77–10.57 | 0.078–0.114 | 0.75–1 |
| S2 | 0.026–0.044 | 0.0015 | 1 | S2 = 0 | 8.77–10.57 | 0.080–0.116 | 0.8–1.02 |
| S3 | 0.026–0.044 | 0.0015 | 1 | S3 = 0.25 | 8.77–10.57 | 0.085–0.117 | 0.8–1.02 |
| S4 | 0.026–0.044 | 0.0015 | 1 | S4 = 0.25 | 8.77–10.57 | 0.089–0.117 | 0.9–1.06 |
| S5 | 0.026–0.044 | 0.0015 | 1 | S5 = 0.5 | 8.77–10.57 | 0.091–0.120 | 0.95–1.05 |
| S6 | 0.026–0.044 | 0.0015 | 1 | S6 = 0.5 | 8.77–10.57 | 0.093–0.121 | 1–1.08 |
| S1-2 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S2 = 0 | 8.77–10.57 | 0.074–0.110 | 0.68–0.94 |
| S1-3 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S3 = 0.25 | 8.77–10.57 | 0.077–0.1105 | 0.74–0.97 |
| S1-4 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S4 = 0.25 | 8.77–10.57 | 0.076–0.111 | 0.72–0.96 |
| S1-5 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S5 = 0.5 | 8.77–10.57 | 0.081–0.113 | 0.84–1.02 |
| S1-6 | 0.026–0.044 | 0.0015 | 2 | S1 = 0, S6 = 0.5 | 8.77–10.57 | 0.080–0.112 | 0.81–1.00 |
| S2-3 | 0.026–0.044 | 0.0015 | 2 | S2 = 0, S3 = 0.25 | 8.77–10.57 | 0.078–0.111 | 0.75–0.98 |
| S2-4 | 0.026–0.044 | 0.0015 | 2 | S2 = 0, S4 = 0.25 | 8.77–10.57 | 0.079–0.1115 | 0.79–0.99 |
| S2-5 | 0.026–0.044 | 0.0015 | 2 | S2 = 0, S5 = 0.5 | 8.77–10.57 | 0.081–0.112 | 0.83–1.01 |
| S2-6 | 0.026–0.044 | 0.0015 | 2 | S2 = 0, S6 = 0.5 | 8.77–10.57 | 0.082–0.114 | 0.84–1.03 |
| S3-4 | 0.026–0.044 | 0.0015 | 2 | S3 = 0.25, S4 = 0.25 | 8.77–10.57 | 0.080–0.112 | 0.82–1.00 |
| S3-5 | 0.026–0.044 | 0.0015 | 2 | S3 = 0.25, S5 = 0.5 | 8.77–10.57 | 0.0835–0.114 | 0.845–1.03 |
| S3-6 | 0.026–0.044 | 0.0015 | 2 | S3 = 0.25, S6 = 0.5 | 8.77–10.57 | 0.081–0.113 | 0.84–1.02 |
| S4-5 | 0.026–0.044 | 0.0015 | 2 | S4 = 0.25, S5 = 0.5 | 8.77–10.57 | 0.083–0.115 | 0.86–1.04 |
| S4-6 | 0.026–0.044 | 0.0015 | 2 | S4 = 0.25, S6 = 0.5 | 8.77–10.57 | 0.082–0.1145 | 0.87–1.02 |
| S5-6 | 0.026–0.044 | 0.0015 | 2 | S5 = 0.5, S6 = 0.5 | 8.77–10.57 | 0.084–0.115 | 0.88–1.04 |
Dimensional analysis
is the upstream Reynolds number, 
is the upstream Froude number, and 
is relative jet discharge. Due to the high Reynolds numbers, viscosity effects are omitted (Hager 1992). Moreover, parameters 
are ignored due to constant jet discharge and the channel expansion ratio. As a result, Equations (4) and (5) are re-written as follows:
RESULTS AND DISCUSSION
In fluid mechanics, the water jet is water from a nozzle at high speed, with a certain amount of kinetic energy. As the water jet strikes an object, it exerts a force on it, resulting in a loss of energy due to the jet's impact. This impressed force is called the impact of the jet, which is designated as a hydrodynamic force. This force is because of fluid motion that involves a change in momentum (Kumar 2019). In this study, the effect of LJF on energy dissipation, sequent depth, jump length, and roller length of S-jump is investigated.
Experimental observations
Flow pattern in abruptly expanding channel.
As seen in Figure 4, in the presence of LJF, the collision between the main flow and the LJF causes severe turbulence, strong air entrainment, a break in the main flow leading to local radial vortices, and diffusivity of the S-jump. In all LJF experiments, flow depth increases and decreases velocity in the tailwater depth.
Experiments with the LJF system showed that the closer the lateral jet is to the narrow channel, the more effective it is in dispersing the main flow in the basin and creating uniform and regular width subcritical flow conditions in the tailwater depth. The lateral jet impact is more effective because the main flow structure associated with the S-jump in the stilling basin has not yet formed.
Preliminary experiments show that the S-jump is an asymmetric jump and its formation location at the right or left end of the narrow channel is entirely random. Therefore, designing the LJF system on both channel sides is necessary.
Sequent depths ratio
Sequent depths ratios versus initial Froude number.
As shown in Figure 5(a), as the number of jets increases, the sequent depth ratio decreases, and this decrease is more significant at higher Froude numbers. The average reduction of sequent depth ratio for one-jet and two-jet positions is 11.3% and 16.6%, respectively. Figure 5(b) shows the average sequent depth ratios of one-jet, two-jet, and non-jet states with the Herbrand (1973) and Alhamid (2004) equations (Equations (8) and (9), respectively). The difference between the non-jet experiments of this study and Equations (8) and (9) is due to the high Froude number and the creation of a shallow and fast main flow in the spatial hydraulic jump.
Figure 5(c) shows y2/y1 versus Froude numbers for different one-jet positions. The figure shows that the maximum deduction for the S1 place (zero distance from the narrow channel) and Froude number 10.87 is 20.4%. Also, the minimum reduction of sequent depth in the S6 position (farthest distance from the narrow channel) and Froude number 10.87 is 5.1%. Figure 5(d) shows a reduction in the ratio of sequent depths for some cases of two jets at different Froude numbers. For better figure clearance, some of the two-jet places with similar results were removed. The results show that the maximum sequent depth reduction for the S1-2 position (the closest operating distance of two jets to the narrow section) and the Froude number 10.87 is 24.5%. The minimum reduction for the S5-6 position (the farthest distance between two jets from the narrow channel) and the Froude number 8.77 is 11.5%.
Sequent depth ratios for various jet placement distances.
The dimensionless parameter 
illustrates the reduction in the sequent depth of the hydraulic jump; in this equation, y2* denotes the sequent depth of the jump with no jet. Table 2 demonstrates the average percentage of the sequent depth reduction of the S-jump for the observed data in the present study.
Average percentage of the sequent depth reduction
| D (%) | n | Fr1 |
|---|---|---|
| 12.25 | 1 | 10.87 |
| 18.95 | 2 | 10.87 |
| 12 | 1 | 9.56 |
| 17.2 | 2 | 9.56 |
| 9.74 | 1 | 8.77 |
| 13.5 | 2 | 8.77 |
| D (%) | n | Fr1 |
|---|---|---|
| 12.25 | 1 | 10.87 |
| 18.95 | 2 | 10.87 |
| 12 | 1 | 9.56 |
| 17.2 | 2 | 9.56 |
| 9.74 | 1 | 8.77 |
| 13.5 | 2 | 8.77 |
Relative length of the hydraulic jump
Relative length ratios versus initial Froude number.
As shown in Figure 7(a), the LJF system reduces the relative hydraulic jump length in all tests, and the use of two jets performed better than one jet in the LJF system. The average relative hydraulic jump length reduction for two-jet and one-jet modes is 23% and 17.5%, respectively. Although increasing the Froude number increases the relative hydraulic jump length, applying the LJF system at higher Froude numbers has a better performance in reducing the relative hydraulic jump length.
Figure 7(b) compares the mean Lj/y1 values in the one-jet, two-jet, and non-jet modes of LJF with the Silvester (1964) and Hager (1992) equations (Equations (10) and (11), respectively). According to the observations in the hydraulic conditions leading to the S-jump, the main flow continues as a sinusoidal wave to the end of the flume (Hajialigol et al. (2021) and Sharoonizadeh et al. (2021) experiments also confirms this), and the first wavelength is selected as the S-jump length. It shows the possibility of erosion and scouring downstream of the basin with a length equal to Equations (10) and (11), and therefore, using the LJF system, especially with two jets, significantly affects spatial jump control.
Figure 7(c) shows the relative lengths of hydraulic jumps versus Froude numbers for different one-jet locations. The S1, with the shortest distance from the narrow channel, has the most significant effect in reducing the jump length, and the maximum reduction is 31.8% at a Froude number of 10.87. The minimum decrease of jump length in the S6 position (farthest distance from the narrow channel) and Froude number 10.87 is 9.1%. Figure 7(d) shows the changes in Lj/y1 versus Fr1 for deploying two concentric jets and two non-centric jets. The results show that the maximum Lj/y1 decrement for the S1-2 position, the closest operating distance of two jets to the narrow section, and the Froude number 10.87 is 38.2%. The minimum reduction for the S5-6 position, the farthest distance two jets from the narrow channel, and the Froude number 8.77 is 13.3%.
Relative length ratios for various jet placement distances.
In addition, Table 3 shows the percentage reduction in S-jump length when using the LJF system compared to the non-LJF mode. According to this table, the percentage reduction of the hydraulic jump length increases with the number of jets in the LJF system.
Average percentage of the jump length reduction
| D (%) | n | Fr1 |
|---|---|---|
| 21.2 | 1 | 10.87 |
| 28 | 2 | 10.87 |
| 17.8 | 1 | 9.56 |
| 24 | 2 | 9.56 |
| 13.5 | 1 | 8.77 |
| 17 | 2 | 8.77 |
| D (%) | n | Fr1 |
|---|---|---|
| 21.2 | 1 | 10.87 |
| 28 | 2 | 10.87 |
| 17.8 | 1 | 9.56 |
| 24 | 2 | 9.56 |
| 13.5 | 1 | 8.77 |
| 17 | 2 | 8.77 |
Relative roller length
Relative roller length ratios versus initial Froude number.
Relative roller length ratios for various jet placement distances.
Figure 9 shows that the relative roller length decreased in all the experiments with the presence of side jets compared to the non-jet system. According to Figure 9(a), the average reduction of roller length for one-jet and two-jet modes is 16% and 27.8%, respectively. Figure 9(b) depicts the roller length ratios of one-jet, two-jet, and non-jet states compared to the values obtained by Equations (12) and (13). It is discernible that the values of the S-jump roller length decrease compared to the classical hydraulic jump due to the effects of the sudden expansion section and the LJF system. Furthermore, it can be observed that with the increasing number of jets (i.e., the number of active orifices), the roller length ratio decreases.
Figure 9(c) indicates Lr/y1 against initial Froude numbers for various one-jet positions. In one-jet mode, the maximum decline in roller length was 24.5% for the S1 position (jet with zero distance from the narrow channel) and a Froude number of 10.87. In contrast, the minimum reduction in jump roller length in the S6 position (farthest distance from the narrow channel) and a Froude number of 10.87 is 9.5%. Figure 9(d) illustrates a decrease of the roller length for some cases of the two-jet mode at various Froude numbers. The results indicate that the maximum roller length reduction for the S1-2 position (the closest operating distance of two jets to the narrow section) and a Froude number of 10.87 is 37%. While the minimum decline was 21% for the S5-6 position (the farthest distance double-jet mode from the narrow channel) and a Froude number of 8.77.
Relative energy loss ratios versus initial Froude number.
Average percentage of the roller length reduction
| D (%) | n | Fr1 |
|---|---|---|
| 17.9 | 1 | 10.87 |
| 28.4 | 2 | 10.87 |
| 16.5 | 1 | 9.56 |
| 29.6 | 2 | 9.56 |
| 13.5 | 1 | 8.77 |
| 25.1 | 2 | 8.77 |
| D (%) | n | Fr1 |
|---|---|---|
| 17.9 | 1 | 10.87 |
| 28.4 | 2 | 10.87 |
| 16.5 | 1 | 9.56 |
| 29.6 | 2 | 9.56 |
| 13.5 | 1 | 8.77 |
| 25.1 | 2 | 8.77 |
Relative energy loss ratios for various jet placement distances.
Energy dissipation
According to Bremen & Hager (1993), the X1 coefficient for the S-jump in Equation (17) is 0.05.
According to Figures (11) and (12), it can be concluded that using side jets increases the relative energy dissipation compared to the non-jet mode. This can be attributed to the interaction between the main flow issued from the narrow section and the LJF. It is clear that the efficiency of the spatial hydraulic jump increased with an increasing number of jets. In addition, relative energy dissipation decreases with an increase in jet distance from the expansion section. Hence, the S1 and S1-2 (shortest jet distance from the narrow channel) have the best performance (18.5% and 23%, respectively, and a Froude number of 10.87) in rising energy loss for single-jet and double-jet modes. In contrast, the S6 and S5-6 (farthest distance from the narrow channel) were found to have the worst performance in the reduction of flow energy. Moreover, the relative energy dissipation increases with an increase in the Froude number.
CONCLUSION
The high velocity of flow downstream of spillways is responsible for the destruction of the natural riverbed and covered channels. Energy dissipaters such as stilling basins, block ramps, and flip buckets are therefore used to dissipate the kinetic energy of the flow. To reduce the construction cost of a stilling basin, changes in their cross-section plans are essential.
In the present study, the use of side jets as a novel method of flow energy dissipation was introduced. The energy dissipation mechanism obtained from the interaction between the supercritical inflow over the spillway and the outflow from the LJF causes severe turbulence, strong air entrainment, and a break in the main flow leading to local radial vortices and diffusivity of the spatial hydraulic jump. Preliminary experiments indicate that spatial hydraulic jump is an asymmetric jump and its formation location at the right or left end of the narrow channel is entirely random. As a result, designing the LJF system on both channel sides is necessary. According to the results, using side jets reduces the length and depth of sequent S-jumps by 20% and 14%, respectively, compared to the non-jet mode.
Moreover, the jump's most significant sequent depth reduction stands at 19% in a discharge of 26 L/s in a two-jet mode. The relative length of the hydraulic jump increases by an increase in the initial Froude number, the distance of the jet from the expansion section, and a reduction in the number of jets. It is discernible that the values of the S-jump roller length decrease compared to the classical hydraulic jump due to the effects of the sudden expansion section and the LJF system. In addition, relative energy dissipation decreases with an increase in jet distance from the expansion section. Hence, the S1 and S1-2 (shortest jet distance from the narrow channel) have the best performance in rising energy loss for one-jet and two-jet modes, respectively. Overall, the results achieved from the present research indicate that side jets, as a novel energy dissipation system, significantly improve the flow pattern and primary characteristics of the hydraulic jump. As a result, using side jets can help prevent extreme damage to downstream hydraulic structures.
ACKNOWLEDGEMENTS
We are grateful to the Research Council of the Shahid Chamran University of Ahvaz for financial support (GN: SCU.WH99.343).
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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