Experimental study of the effect of horizontal screen diameter on hydraulic parameters of vertical drop


 The horizontal screen is one of the energy dissipater structures used on the brink of vertical drop. These structures increase the energy dissipation and the turbulence in the flow by causing air entrainment. In the present study, the effect of the diameter of the screen with constant porosity at three different diameters on the hydraulic parameters of the vertical drop was investigated. The experiments were performed in the relative critical depth range of 0.13 to 0.39. The results showed that by increasing the relative diameter of the horizontal screen, the relative wetting length and turbulence length increased, the residual energy remained constant and the pool depth decreased. Compared to the stilling basin, the horizontal screen significantly reduces turbulence length and residual energy. The results also showed that the application of horizontal screens at the brink of the drop, with and without a downstream rough bed, could be a suitable alternative for a stilling basin.


INTRODUCTION
Vertical drops also known as a grade control, or over-fall, is typically built in irrigation channels to pass water to a lower elevation or used in mountainous areas to reduce the steep slopes. Flow downstream of the drops, due to the slope, has a destructive kinetic energy. If this destructive energy is not controlled and reduced, downstream structures will be exposed to erosion and destruction. A hydraulic jump in the stilling basin is therefore commonly used to dissipaters was also studied experimentally by Sharif & Kabiri-Samani (). The results showed that as the tailwater depth increases, air entrainment decreased.
The first studies on screens were performed by (Rajaratnam & Hurtig ) as energy-decreasing devices.

Çakir () carried out experiments on screens and
showed that the use of screens for energy dissipation is effective. They also found that the thickness of the screens has an insignificant effect on energy dissipation. Studies were also carried out on the use of vertical screens; the results showed that the thickness of the screen had no effect on the energy loss but modifications in the number of screens and the shape of the square aperture had an impact ( Recently, the application of a horizontal screen at the brink of a vertical drop has been considered as a horizontal dissipater. Air entrainment is one of the factors commonly used for energy loss. These plates increase the energy loss by creating several falling jets and increasing turbulence downstream of the vertical drop. Screens on a vertical drop brink were studied by Kabiri-Samani et al. (). The results of their study revealed that when a vertical drop is equipped with screens, there is a decrease in the total length of the stilling basin downstream of the structures by about 60-75%.
Sharif & Kabiri-Samani () also investigated the effect of tailwater depth on a vertical drop equipped with a screen.
The results showed that by increasing the tailwater depth, air entrainment decreases and the relative pool depth increases. Hasanniya () investigated the hydraulic parameters of a vertical drop equipped with a horizontal screen with the subcritical flow. The results revealed that the relative depth of the pool, the relative downstream depth and reduction in the total energy of the system increase.
From this prior research, it is evident that the simultaneous application of a vertical drop and a horizontal screen can lead to a significant increase in energy loss downstream of these structures. There is still a significant need to better understand and analyze the geometric parameters affecting the hydraulic performance of a horizontal screen.
Consequently, the current study aims to investigate the performance of the vertical drop equipped with a horizontal screen with constant porosity at three different diameters of holes. To validate the obtained results, the current study is also compared with previous research data. Figure 1 shows the physical and hydraulic parameters of the flow for a vertical drop equipped with horizontal screens; these parameters are indicated in Equation (1):

DIMENSIONAL ANALYSIS
where Q is the flow discharge, H is the vertical drop height, P is the porosity of screen, y 0 is the upstream depth, y c is the critical depth (y c ¼ (q 2 /g) 1/3 ), y 1 is the downstream depth, y p is the pool depth, L wet is the wetted length of the screen, L D is the mixing length of the pool, D is the diameter of hole in screen, E 0 is the total energy upstream of the drop, E 1 is the specific energy downstream of the drop, ρ is the density of water, μ is the dynamic viscosity and g is the gravitational acceleration.
Using the π-Buckingham's theorem and with ρ, g and H as repeated variables, the relative mixing length of the pool was obtained on the basis of the independent dimensionless parameters in Equation (2): By applying the same method, Equation (3) was obtained for the wetted length of horizontal screens, the depth of the pool and the normalized residual energy: Here, Re 0 is the upstream Reynolds number, Fr 0 is the upstream Froude number, D/H is the relative diameter of hole in screen, y p /H is relative pool depth, y c /H is relative critical depth, L wet /y c is relative wetting length of screen, tal screen has no effect on the relative residual energy.
Moreover, the 50% porosity of the plates leads to a wetting length of screen and a mixing length of the pool smaller than a 40% porosity one. In the present study, therefore, the porosity of horizontal screen was considered to be 50%. The flow upstream of the vertical drop is subcritical and the Froude numbers are low (0.69 Fr 0 0.86), so the effect of this parameter on Equations (2) and (3) is neglected (Aza- Equations (4) and (5) are modified as follows:

Experimental setup
The experiments were performed in a horizontal, rectangular cross-section channel with Plexiglas walls and a length, In total, the depth at five locations was measured and the average value was used. A ruler with a precision of 1 mm was used to measure the respective lengths. Figure 2 illustrates a flow structure of the experimental model and the investigated ranges of the parameters are presented in Table 1.

Calculations
The downstream Froude number (Fr d ) is calculated using Equation (6) (Rand ): Prior researchers, for instance Esen et al. (), presented their studies using the relative downstream depth, as in Equation (7): The Froude number of downstream of the plain vertical drop can therefore be expressed as: In the present study, the relative critical depth range is between 0.13 and 0.39, and so the range of the downstream Froude number of plain vertical drop is 3.9 to 5.3. If a Type I stilling basin downstream of the drop is used to dissipate the flow energy, the total drop length is obtained from Equation (9) (see in Figure 3): In the Equation (9)

RESULTS AND DISCUSSION
In order to validate the results of a vertical drop, results from the present study were compared with those of Rajaratnam & Chamani () (Figure 4), which showed a good agreement.   Moreover, the performance criteria (the determination coefficient (R 2 ) and the normalized root-mean-square error (NRMSE)) were calculated and are presented in Table 2.
The existence of horizontal screens, with turbulence in the falling water jet and air entrainment, causes a loss of the jet. The wetted length, mixing length, pool length and residual downstream energy were measured and calculated.

Relative wetted length
The length of the screen that the flow passes through its holes is called the wet length of the screen (see Figure 5).
Since the relative wetted length (L wet /y c ) can be used to optimize vertical drops with horizontal screens, it is important to investigate the influence of this parameter. Figure 6 shows the relative wetted length versus the Froude number, taking in account three relative diameters of the screen porosities.
It can be seen that as the upstream Froude number

Relative pool depth
The falling jets, after impacting with the downstream bed, causes some flow to return to the vertical drop wall and form a pool behind the jet. The depth formed by the back flow near the wall of the vertical drop structure is called the pool depth (see Figure 8).
In Figure 9 shows the relative depth of the pool at three relative diameters of the screen versus the relative critical depth. It can be seen that by increasing the relative critical depth, the relative depth of the pool increases in all three relative diameters. Also, the pool's    Compared to the horizontal screen with a relative diameter of 0.067, the use of a screen with a relative diameter of 0.2 reduced the relative depth of the pool by 8.5%.
For the laboratory data, Equation (13) was used to estimate the relative depth of the pool with three relative screen diameters of the present study.
Equation (14) leads to an R 2 and NRMSE of 0.96 and 0.023, respectively. This equation estimates laboratory values of relative depth of the pool with a maximum relative error of 5.7%. Figure 13 shows the comparison between the laboratory and calculated values of the mixing length.

Normalized residual energy
The normalized residual energy is equal to the difference between downstream and upstream energy. Figure

DISCUSSION
In the present study, the hydraulic parameters of the vertical drop equipped with a horizontal screen were investigated by considering three different relative diameters of holes. The experiments were performed using a constant screen porosity and a relative critical depth ranging from 0.13 to 0.39.
The parameters of relative wetted length, relative pool depth, mixing length and normalized residual energy were investigated. The following results can be drawn:   • The relative diameter of the screen is inversely related to the mixing length and the use of these screens reduces the mixing length by more than 38%.
• The relative diameter of the screen has no effect on the normalized residual energy of the vertical drop; however, using the vertical drop equipped with a horizontal screen reduces the residual relative energy by 30% compared to the stilling basin.

CONCLUSION
The range of the Froude number downstream of the vertical slope in the present study is between 3.9 and 5.3. A Type 1 stilling basin is commonly used to dissipate energy downstream of the vertical drop (Rand ). In the design of stilling basins, an attempt is usually made to make the hydraulic jump inside the basin, and this requires to take into account the tailwater depth. To form the hydraulic jump inside the stilling basin, the end sill or a change in the pond bed level are sometimes used. However, the horizontal screen at the vertical drop does not require the tailwater depth to reduce the normalized residual energy or to form the hydraulic jump. It also reduces the normalized residual energy further with respect to the stilling basin. On the other hand, due to the decrease in the relative energy of the horizontal screen compared to the stilling basin, it is obvious that these screens have a lower relative tailwater depth. Therefore, using horizontal screens at the vertical drop compared to stilling basin has the following advantages: • There is no need for the tailwater depth, or to take into account the arrangements for the hydraulic jump inside the stilling basin.
• There is a reduction in the size of the stilling basin required for energy dissipation due to a decrease in the mixed length.
• There is a decrease in the normalized residual energy or an increase in flow energy dissipation However, due to their emergence, these screens have not been implemented in practical projects so far, and if they are implemented, they also have disadvantages.

DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.