Double sill stilling basin to enhance energy dissipation for a strong hydraulic jump with a high Froude number

Roller Compacted Concrete (RCC) is a new and viable construction material for concrete gravity dams. It is gaining popularity due to its low cost and fast deployment. The design of a stilling basin, part of a dam that controls the hydraulic jump and dissipates energy, is crucial. One of the important considerations is the Froude number at the spillway toe (F1), which determines the type of hydraulic jump that will occur. An energy dissipator is also required to prevent scour caused by the change in flow conditions from supercritical to subcritical. Double sills installed downstream of the steep chute way channel can be used as an energy dissipator. This study uses hydraulic modeling to evaluate the flow energy reduction and subcritical flow conditions in a stilling basin with double sills. The investigation is expected to provide better information on hydraulic jump control.


Introduction
Water flowing over a chuteway results in supercritical flow and generates a hydraulic jump at the toe.A hydraulic jump is a phenomenon that occurs when supercritical flow suddenly changes to subcritical flow.It is characterized by a standing wave that forms across the channel.Hydraulic jumps can occur in a variety of open-channel hydraulic structures, such as spillways, stilling basins, and steep chutes [1], [3], [4].Froude number is the important parameter that characterizes supercritical flow.A stilling basin is needed at the toe of the chute to reduce the energy of supercritical flow [2], [8].Hydraulic jumps are very useful as energy dissipators in supercritical flows.This energy attenuation is useful for preventing erosion by reducing the flow velocity to a point where the flow can no longer erode the downstream bottom channel [5], [6].
Several studies have been carried out to determine the velocity field and base shear stress in hydraulic jumps [2], [7].There have been many previous studies that discussed the effectiveness of energy dissipation [9], [10], [11], but there are still few studies that discussed the effectiveness of double sill stilling basins.
This study will investigate whether this research design will provide appropriate Froude values for the transition from supercritical to subcritical flow and whether it will effectively dissipate energy.In this research, the configuration of double sills, such as the shape, distance between the first and second sills, and height ratio of the first and second sills, will affect their performance in dissipating supercritical flow energy.This study discusses double sills' effectiveness in enhancing energy dissipation with variations in their height and distance.

Hydraulic Physical Model Data
The research was conducted in the River Engineering Laboratory, Department of Water Resources Engineering, Faculty of Engineering, Universitas Brawijaya.The hydraulic model uses several laboratory facilities and equipment, including the hydraulic physical model of the spillway with a height of 1.0 m, the chute way channel with a slope of 1:0.8, and the width of the channel, B = 0.4 m.A sketch of the double sill hydraulics model is shown in Figure 1.

Research Variables
In this research, sill 1 (Z 1 ) had a straight upstream with a curved (round) crest or ogee sill, and sill 2 (Z 2 ) had a straight upstream with a flat crest or trapezoidal prism sill.This is a double sill study with variations of three sill heights for the first sill and six sill heights for the second sill.The first sill (Z 1 ) was placed L 1 = 0.8 m from the toe of the spillway, and the second sill (Z 2 ) was placed L2 = 0.4 m from the first sill.The model test was flowed in 7 variations discharge, 15, 17, 19, 21, 23, 25, and 27 liters/second in each series.The shape and dimensions of the sill used are shown in Figure 2 and Figure 3. Details of the double sill form used in this study can be seen in Table 1.The detailed model treatment is explained in Table 1.Flow through an open channel is uniform flow if the various flow variables present, such as flow depth, wetted area, flow velocity, and flow rate at each section along the flow, are constant.In this uniform flow, the energy line, water level line, and channel bed are parallel so that the slopes of these lines are the same.The flow depth in uniform flow is called the normal depth, y n .Uniform flow cannot occur at large flow velocities or very large channel slopes [7].If the flow velocity exceeds a certain limit (critical velocity), then the water surface becomes unstable, and waves will occur.At a very high velocity (more than six m/s), air will enter the stream, and the flow may become unsteady.
The flow in open channels can be categorized as non-uniform, where flow variables such as flow depth, wetted area, and flow rate at each section along the flow are not constant and undergo variation.If this variation occurs over a short distance, it is termed rapidly varied flow, while if it occurs over a long distance, it is known as gradually varied flow.Steady flow is the term used when the flow at a specific point remains constant over time, while unsteady flow refers to a situation where the flow variables change with time [12], [13].Furthermore, flow in open channels can be classified into three types: subcritical flow, critical flow, and supercritical flow.The determination of these flow types is based on the Froude number.

Specific Energy
The energy in a unit weight of water flowing through an open channel comprises three components: kinetic energy, pressure energy, and elevation energy relative to a reference level.The kinetic energy at a specific section in the open channel can be represented by the term V 2 /2g.Meanwhile, the pressure energy in the open channel is computed with respect to the water level, and the elevation of the flow is measured in relation to a horizontal reference line.The vertical distance from the reference line to the channel's bottom is commonly considered as the elevation energy (potential) at that section.For uniform flow conditions, then the energy line slope (S f ) = water slope (S w ) = channel bed slope (S 0 ) = Sin Ө.The equation used [15]: Eddy loss (h el ) can be obtained with the equation [16]: Assuming  1 = 2 =1, and h f =0, then: The energy at the cross-section of the channel, which is calculated against the bottom of the channel, is called the specific energy or specific height [17], [19]: With: A = wet cross-sectional area (m 2 ), B = channel bottom width (m), E = energy height (m), E s = specific energy, the energy measured from the bottom channel (m), E c = critical energy height (m), E 0 = energy head at upstream (m), E 1 = energy head at the toe of spillway (m), E 2 = energy head at downstream of spillway (m), ∆E = loss of energy head (m), g = acceleration of gravity (m/s 2 ), h = drop height (m), n = Manning roughness coefficient, Q = flow rate (m 3 /s), q = discharge per unit width (m 2 /s), q = Q/B, R = average hydraulic radius (m), S 0 = channel bottom slope, S f = slope of the energy line, V = average velocity (m/s), y = depth of water flow (m), y c = critical depth (m), z 1 = elevation height of channel section 1 from baseline (m), z 2 = elevation height of channel section 2 from baseline (m), x = horizontal distance (m), = energy coefficient.

Hydraulic Jump
A hydraulic jump occurs when a flow changes from supercritical to subcritical conditions.It leads to a swift rise in water level and a substantial energy dissipation.At the onset of the hydraulic jump, a significant turbulent vortex emerges, extracting energy from the main flow, and subsequently, the vortex disintegrates into smaller components as it moves downstream [18], [19].During a hydraulic jump, the momentum equation is the primary factor affecting energy computations.
Meanwhile, from the continuity equation: by combining the above equations, then: by simplifying the above equation, the equation is obtained: The water depths of the first section before the hydraulic jump, y 1 with Froude number (F 1 ), and after the hydraulic jump, y 2 with Froude number (F 2 ) play a significant role in hydraulic jumps.In a horizontal rectangular channel with supercritical flow, the flow energy experiences damping due to frictional resistance, resulting in reduced velocity and increased height in the flow direction.
Various types of hydraulic jumps occur on a horizontal surface, and the United States Bureau of Reclamation's research suggests that these jumps can be distinguished based on the flow's Froude number (F 1 ) [15]: a. Critical flow, for F 1 = 1, there is critical flow, so no jumps can be formed.b.Wavy jump, there are waves on the water's surface for F1 = 1 to F1 = 1.7.c.The jump is weak.For F 1 = 1.7 to F 1 = 2.5, a network of wave rolls is formed on the surface of the jump, but the water surface downstream remains smooth.Overall, the velocity is uniform, and the energy loss is small.d.Oscillating jumps, for F 1 = 2.5 to F 1 = 4.5, there are oscillating bursts accompanying the base of the jump moving to the surface and back again without a certain period.Each oscillation generates huge irregular waves and causes unlimited damage to the embankment.e. Steady jump, for F 1 = 4.5 to F 1 = 9, the edges of the downstream surface will roll, and the point where the jet velocity is high tends to break away from the flow.In general, both of these occur on the same vertical surface.The depth of the water below does not influence the movements and jumps.The hydraulic jump is perfectly balanced.The characteristics are the best.The energy dissipation is 45% -70%.f.Strong jumps, for F 1 > 9 and greater, high burst velocities will separate the crashing rolling waves from the braking surface, creating waves downstream.If the surface is rough, it will affect the waves that occur.Stepping movements are rare but effective because their energy dissipation can be up to 85%.

Loss of Energy
The energy loss in a jump equals the difference in specific energy before and after the jump [18], [19].The amount of energy loss is:

Efficiency
The ratio between the specific energies after and before the jump is defined as the jump efficiency.So, the magnitude of the jump efficiency is: The equation demonstrates that the jump efficiency is a dimensionless function solely reliant on the Froude number of the flow after the hydraulic jump.Similarly, the relative loss, denoted as 1 -E 2 /E 1 , is also a dimensionless function based on the Froude number [19], [20].

Hydraulic Jump Height
The height of the jump can be defined as the difference between the depth before and after the jump.y j = y 2 -y 1 (25)

Hydraulic Jump Length
The distance from the front surface of the hydraulic jump to a point on the downstream surface of the wave roll defines the length of the hydraulic jump.Although the theoretical determination of this length presents challenges, several hydraulic experts have conducted experimental investigations to explore it [21], [22].

Result and Discussion
The present invention was developed to provide energy dissipation due to supercritical flow at initial design conditions of Q = 15-27 l/s and slope = 1:0.8.It will result in a supercritical flow with a Froude number of 11-13, which will cause strong jump hydraulics.The present invention was developed to obtain a double sill composition with the best energy-dissipation results.This invention uses a double sill stilling basin with modification to be placed downstream of the channel.This study has 6 series, each carried out by flowing 7 flow rates (15,17,19,21,23,25, and 27 l/s.The hydraulic model was carried out with as many as 7 discharges, 1 variation of sill distance, 2 variations of sill 1 height (Z 1 ), and 2 variations of sill 2 height (Z 2 ), resulting in 42 running models.Based on the measured water level, the Froude numbers at y 1 and y 2 can be calculated, presented in Table 2. Based on Table 2, it shows that the obtained Froude number varies.At y 1 , the resulting Froude number is F 1 = 2.5 until 4.5 (oscillating jump).At y 2 , the Froude number, F 2 <1 (subcritical flow).In this case, it shows that energy dissipation is very influential on the amount of the resulting Froude number.So it can be seen that the minimum F 2 yield is in Series 4 with (L 1 = 80 cm; L 2 = 40 cm; Z 1 = 8 cm; Z 2 = 4 cm).A Froude number of 0.18 indicates a subcritical flow condition.This means that the flow velocity is less than the critical velocity, which is the velocity at which the flow changes from supercritical to subcritical.
In previous studies, a Froude number has been observed in a variety of hydraulic structures, including spillways, stilling basins, and steep chutes.For example, a study by Smith and Watts (2018) [23], and A study by Shen and Wang (2016) [24] found that a low Froude number is considered to be a good value for dissipating energy in supercritical flows.This is because the flow velocity is low enough to cause significant turbulence and mixing, which can dissipate energy.
Based on the measurement, results in each series will be analyzed and produce dimensionless parameters.The equation with the number of R 2 results from the relationship curve of each number being compared.The following Table 3 is the result of the correlation curve among dimensionless parameters..g 1/2 ) + 6.5783 0.779 7 L 1 /y 2 q/y 2 3/2 g 1/2 (q/(y 2 3/2 g 1/2 )) = -1.1092(L 1 /y 2 ) + 8.1155 0.779 8 y 2 /y 1 y j /y 1 (y j /y 1 ) = (y 2 /y 1 ) -1 1.000 From Table 3 above, the best regression equation relationship is taken, and the best graph can be seen in Figure 5 until Figure 10.Energy efficiency will be analyzed in each series based on the measurement results in each series.It can be seen in Table 4.The effectiveness of energy dissipation can be seen by comparing the specific energy before and after the hydraulic jump.The greater of jump efficiency rate, the more effective energy dissipation.Based on Table 4, Series 1 of the double sill stilling basin (L 1 = 80 cm; L 2 = 40 cm; Z 1 = 10 cm; Z 2 = 7.5 cm) gave the highest average jump efficiency, E 2 /E 1 = 0.59 or 59% is considered able to reduce the flow energy effectively compared to the other series.Previous studies [24], [25] found that spillways effectively dissipate energy.The 48-60 % energy efficiency indicates the effective way to dissipate the energy of supercritical flows.This energy dissipation is accompanied by the loss of energy that occurs due to hydraulic jumps, E 1 -E 2 whose nature varies depending on the difference in specific energy before and after the hydraulic jump.The hydraulic jump results obtained are in the form of the length and height of the hydraulic jump, as follows: It is shown that the greater the flow, the longer the hydraulic jump (Table 5).Based on the results, the minimum hydraulic jump length is in the double sill energy dissipator variation series 4 (L1 = 80; L2 = 40; Z1 = 8; Z2 = 4), with Lj = 208 cm.With this composition, a short hydraulic jump is formed, indicating the energy dissipator's effectiveness and efficiency in reducing the energy of a flow [23], [24].This is also related to the height of the jumps formed in all series, as follows: Based on the table above, it shows that the greater the flow, the higher the hydraulic jump.The results of the minimum hydraulic jump height are in the double sill stilling basin variation series 1 (L1 = 80; L2 = 40; Z1 = 10; Z2 = 7.5), with yj = 4.1 cm, which shows the effectiveness of the distance and height of the sill tested.
This case shows that the sill composition in the double sill stilling basin channel hydraulic model greatly influences the Froude number and the length and height of the resulting hydraulic jump.The following are the conclusions presented in Table 7. Modification with physical models can be done by developing other alternative modifications stilling basins at various flow rates.Research on the use of double stilling basins still needs further research to produce the best choice that can be applied efficiently.Therefore, this modified stilling basin becomes an alternative solution for the economical use of stilling basins.This modeling is expected to be very useful in the optimization method of planning a dam building.

Figure 1
Figure 1 Hydraulic model of double sill stilling basin at the laboratory

Figure 4
Figure 4 Rech Box.In this invention, calculation of the inflow discharge model, control of elevation above sills, and examination of flow hydraulics along the chute channel and double sill stilling basin are carried out.Overflow discharge over the spillway is determined based on the capacity of the Rechbox weir which

Figure 5 Figure 6 9 Figure 7 Figure 8 10 Figure 9
Figure 5 Correlation of y 1 /y 2 and y j /y 2 in each series

Figure 10
Figure 10 Correlation of y j /y 2 and y j /y 1 for all series

13 Table 7 .
The optimum result of specific parameters on the double sill stilling basin The research of double sill stilling basin had a variation of 6 series by modifying the height of the sill.The physical model test carried out on the double sill stilling basin was tested at flow rates at 7 flow rates:15,17,19,21,23, 25, and 27 l/s in each series.The best series variation is in series 4 with sill dimensions L 1 /L 2 = 2 and Z 1 /Z 2 = 2 with the following details: L 1 = 80 cm; L 2 = 40 cm; Z 1 = 8 cm; Z 2 = 4 cm, which has the lowest Froude number and the shortest hydraulic jump length.Distance from the overflow to sills 1 as far as 80 cm.The second sills are 4 cm high, and the distance between sills 1 and 2 is 20 cm), with not much difference in the Froude number, the flow properties are the same.As for Series 4 shows the smallest Froude number at y2, namely F2 = 0.18, and the smallest average Froude number at y 2 , F = 0.21.Series 4 exhibited the lowest Froude value, indicating supercritical flow.This demonstrates that Series 4 has a form that can reduce flow energy from supercritical to subcritical conditions in stilling basins with double sills.

Table 1 .
Research Design of double sill stilling basin (Ogee sill and trapezoidal prism sill)

Table 2 .
Recapitulation of the results of the Froude number

Table 3 .
Results of analysis of combined dimensional variables

Table 4 .
The efficiency of Hydraulic jump in the double sill

Table 5 .
Recapitulation of the hydraulic jump length of the double sill stilling basin

Table 6 .
Recapitulation of hydraulic jump height in double sill energy dissipator