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Hydraulic jump is used to dissipate excessive flow energy in stilling basins to control erosion on the downstream side. The literature review revealed that the convergence of the side walls in a USBR type II stilling basin has enhanced energy dissipation by stabilizing the hydraulic jump. Taking this into account, a Computational Fluid Dynamics (CFD) model was created using CFD code to analyze the hydraulic efficiency of a USBR type III stilling basin with varying degrees of side wall convergence. Additionally, alterations were made to the standard Impact Blocks geometry to evaluate their effect on energy dissipation. The side walls of stilling basin were converged from 0.5° to 2.5° (with an increment of 0.5°). Study results indicated an increase in hydraulic jump efficiency from 1.6 to 14.5% due to increase in wall convergence. Modified Friction Blocks also enhanced the energy dissipation up to 2%. Post-jump Froude number values were found in acceptable range of 0.6 to 0.78. The optimal hydraulic performance of stilling basin was noted when wall convergence angle of 2.5° was used along with modified Friction Blocks. Hydraulic performance of modified stilling basin may be investigated during gated operation of the model.

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  • Walls convergence in stilling basin.

  • Navier–Stokes equations.

  • Computational Fluid Dynamics (CFD) code.

CFD, FLOW-3D, Froude number, hydraulic jump, Mohmand Dam, stilling basin
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Physical and numerical model studies play integral roles in hydraulic investigations, offering insights into the behavior of fluid systems and hydraulic structures. While physical models replicate real-world scenarios on a smaller scale, numerical models simulate hydraulic processes using mathematical equations. Both approaches have distinct advantages and are often used in tandem to complement each other. However, currently, numerical models are being used preferably because they are cost effective, allow researchers to simulate a wide range of hydraulic scenarios with ease, adjusting parameters and boundary conditions as needed, and simulate hydraulic processes with high precision and accuracy, particularly when calibrated and validated using field data or results from physical models. Recent research is developing a numerical model using physical model data for its calibration and validation, then carrying out scenario modeling on numerical models. Recently, Babaali et al. 2015; Ljubičić et al. 2018; Macián-Pérez et al. 2020a used a similar technique to assess the hydraulic performance of stilling. Murzyn & Chanson (2009); Lee & Wahab (2019); and Zaffar et al. (2023) employed a k-Ɛ model to study the turbulent flow characteristics of hydraulic jump numerically. Viti et al. (2018); Retsinis & Papanicolaou (2020); and Jayant & Jhamnani (2023) investigated the hydraulic jump through CFD modelling. Gomes et al. (2011) & Miao et al. (2023) evaluated numerical solutions for both turbulent and laminar flows and validated models by comparing experimental results and numerical solutions. The studies demonstrated the presence of downstream vortices near bottom that were hardly represented by physical models. In another study, Jian-gang et al. (2010) used two different turbulent models, i.e., VOF and mixture models and simulated the flows in stilling basins to assess their hydraulic efficiency. Literature survey indicated number of studies (Wu & Sugavanam 1978; Amorim et al. 2015; Tang & Lin 2015; Valero et al. 2016; Wang et al. 2016; Abbas et al. 2018; Karim & Mohammed 2020; Hunt & Kadavy 2021; Jiang et al. 2022) where numerical models were used to evaluate the hydraulic performance of stilling basins.

Literature has reported various research studies around the globe to optimize the energy dissipation phenomenon in stilling basins. In a few studies side walls of stilling basins were converged to enhance their hydraulic performance (Babaali et al. 2015; Ljubičić et al. 2018; Macián-Pérez et al. 2020a). The convergence of walls stabilized the jump within the basin which increased the energy dissipation in the stilling basin (Pirestani et al. 2011; Khadka et al. 2020; Macián-Pérez et al. 2020b). Soori et al. (2017) attempted to enhance energy dissipation by installing the obstacles (a sort of auxiliary device) in USBR stilling basin Type-II of Nazloochay spillway model in Iran. Authors used numerical models for the optimal design of obstacles. In an experimental study, Frizell et al. (2016) examined the efficiency of stilling basins with stepped spillways by testing USBR Type-III stilling basins on 3 different slopes. Akib et al. (2015) conducted experimental research to investigate how different shapes of artificial uneven/grooved beds influence the characteristics of hydraulic jumps. The study revealed that a circular-shaped tire waste grooved bed had a substantial impact on hydraulic jump by reducing its length and depth. Eshkou et al. (2018) investigated the impact of sloping baffle blocks on the hydraulic jump in a gradually diverging stilling basin with a negative bed slope. Al-Mansori et al. (2020) evaluated hydraulic performance of stilling basins by replacing the standard baffle blocks with the new blocks on the physical model. In 2021, Nasralla (2022) performed an experimental investigation on stepped spillways using baffled stilling basins to observe energy dissipation. The results showed that installation of baffles downstream of the stepped spillway increases energy dissipation. Daneshfaraz et al. (2020) investigated energy dissipation in supercritical fluid that showed a positive correlation between numerical and experimental study. Daneshfaraz et al. (2021a, 2021b, 2021c) studied the effect of the rough elements on energy dissipation. Babaali et al. (2019) investigated the hydraulic parameters of flow, i.e., Froude number, pressure, turbulent dissipation, and air entrainment in USBR Type II stilling basin utilizing FLOW-3D. An adverse slope (3: l) was installed at the end of the USBR Type II stilling basin. Adverse slopes were provided to increase the energy loss, but this did nothing to stabilize the hydraulic jump, especially for higher discharges. On the other hand, wall convergence yielded a favorable impact on energy dissipation and 5 degree of wall convergence showed the best performance. It is evident from the literature review that the hydraulic performance of stilling basin USBR Type-III by modifying the baffle block geometry along with wall convergence has not been studied yet. Hence, there is a need for systematic study to see the impact of wall convergence and modified baffle blocks on hydraulic performance of stilling basin USBR Type-III. For this purpose, the lower stilling basin of Mohmand Dam spillway, Pakistan was selected as a case study.

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The Mohmand Dam is under construction on the Swat River in Pakistan. The Swat River runs through Khyber Pakhtunkhwa (KPK) province of Pakistan. The dam has a gated spillway on its left abutment. The spillway has seven bays, each one having a width of 15 m with basin. Figure 1 shows the location of the Mohmand Dam spillway. Its capacity is approximately 833.84 million cubic meters (MCM) along with power generation of 800 megawatts.
Figure 1
Location of Mohmand Dam.
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Location of Mohmand Dam.

Figure 1
Location of Mohmand Dam.
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Location of Mohmand Dam.

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A comprehensive methodology was worked out and formulated after a detailed technical literature review and the gray area was assessed for current study. A numerical model of Mohmand Dam Spillway was developed in FLOW-3D by employing the following sequential steps.

Numerical simulations in CFD Code FLOW-3D

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Based on the capability to accurately simulate the free surface flows by applying the volume of fluid approach, the CFD code FLOW-3D was chosen for this study. This method incorporates precise pressure and kinetic boundary conditions, ensuring accuracy of the modeling process. FLOW-3D exhibits exceptional proficiency in solving time dependent, free-surface problems. The governing equation of FLOW-3D is the Reynolds averaged Navier-Stokes (RANS) equation that mathematically expresses the conservation of mass and momentum. The solver uses finite volume approximation to discrete the Continuity equation which may be expressed as given in Equation (1).
(1)
where fluid density is shown by time (t) and the flow velocity vector field by u. RANS equation can be expressed as Equation (2).
(2)
where the left hand side (L.H.S.) of the above equation represents change in mean momentum of fluid element that because of the mean body force ρi, the isotropic stress resulting from mean pressure field δij, the viscous stresses ⁠, and apparent stress as a result of the unstable velocity field, usually represented as the Reynolds stress.

Geometry and mesh

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The geometry of Mohmand Dam Spillway consists of an ogee type control structure, upper chute with 1:1.6 slope, upper stilling basin with impact blocks, and a weir of 10 m height at the end of the upper chute. The weir is followed by lower chute and lower stilling basin. The lower chute has a longitudinal slope of 1:1.6. Auxiliary devices, namely chute blocks, impact blocks and end sill, are installed in the lower stilling basin. Two bays of the spillway were selected for current study. Length and width of selected geometry was 592 and 30 m respectively. To enchase the computational efficiency of the model and given the specific area of focus, the computational domain was delimited from the weir of the upper stilling basin to the end sill of the lower stilling basin. Tail water levels of the upper stilling basin were used as a head water for computational domain after ensuring that the model is accurately representing the flow conditions and hydraulic behavior within the lower stilling basin. To ensure the accuracy and reliability of the model, results were validated against experimental data.

Mesh was applied considering the extent of computational domain. The accuracy of model results also depends upon the cell size of the mesh. The sensitivity analysis of mesh size for validation and scenario modeling was carried out using mesh sizes of 0.3, 0.6, and 1.2 m. The Grid Convergence Index (GCI), an analytical approach introduced by Mansour & Laurien (2018) was employed for all three grids as shown in Table 1, to assess the sensitivity of the mesh. In Table 1, f1, f2 and f3 represent the solutions generated from fine, medium, and coarse mesh as an expression of discharge. ɸ21 is the difference between volume flow rates of finer and medium mesh whereas ɸ32 is the difference between volume flow rates of medium and coarser mesh, respectively. ⁠, are the approximate relative errors with finer and coarser meshes, respectively. ⁠, are Grid Convergence Index for fine and coarse meshes respectively, where rp is the refinement factor with order of accuracy ‘p’ and it is defined as the ratio of the sizes of two consecutive grids such as r = hcourse/hfine. The order of accuracy p is calculated by using Equation (3).
(3)
Table 1

Results of discretization error for three grid sizes using grid convergence index

Sr. No.Reservoir ElevationVolume Flow Rate (m3/sec)
ɸ21ɸ32e21e32GCI21GCI32
m aslf1 (0.3 m)f2 (0.6 m)f3 (1.2 m)(m3/s)(m3/s)––%%
1 551 2,600 2,605 2,613 5 8 1.9 × 10−3 3.07 × 10−3 4 × 10−3 6.4 × 10−3 
2 555 4,871.4 4,873 4,882 1.60 9 3.3 × 10−4 1.8 × 10−3 8.8 × 10−5 4.8 × 10−4 
Sr. No.Reservoir ElevationVolume Flow Rate (m3/sec)
ɸ21ɸ32e21e32GCI21GCI32
m aslf1 (0.3 m)f2 (0.6 m)f3 (1.2 m)(m3/s)(m3/s)––%%
1 551 2,600 2,605 2,613 5 8 1.9 × 10−3 3.07 × 10−3 4 × 10−3 6.4 × 10−3 
2 555 4,871.4 4,873 4,882 1.60 9 3.3 × 10−4 1.8 × 10−3 8.8 × 10−5 4.8 × 10−4 
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The results, in Table 1, indicated that numerical solutions achieved with 0.3 m cell size have a smaller grid convergence index value (GCI21) as compared to coarse-grid convergence index (GCI32). Moreover, the approximate relative error also decreased with a decrease in cell size of grid. However, mesh was further refined (from 0.3 to 0.25 m) which showed a negligible difference in flow rate as indicated in Table 2. As a result, a grid size of 0.3 m was selected for scenario modelling.

Table 2

Comparison of flow rates at different mesh sizes for reservoir level 555 m asl

Mesh ConfigurationMesh Size (m) (cumecs)Computed Discharge
Coarse 1.2 4,882.14 
Medium 0.6 4,873.22 
Optimal 0.3 4,871.40 
Fine 0.25 4,871.36 
Mesh ConfigurationMesh Size (m) (cumecs)Computed Discharge
Coarse 1.2 4,882.14 
Medium 0.6 4,873.22 
Optimal 0.3 4,871.40 
Fine 0.25 4,871.36 
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Turbulence modelling

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Simulations were carried out using the Renormalization Group Turbulence (RNG) k-Ɛ model. The RNG k-Ɛ model is a refined form of standard k-Ɛ model. It is better than the standard k-Ɛ model because it is based on statistical methods and equation constants are derived explicitly which are found empirically in the standard k-Ɛ model. Moreover, the RNG model has wider applicability. Hence, the RNG model, being robust and most accurate, was used in simulations.

Free surface modelling

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Volume of Fluid (VOF) is employed in FLOW-3D to track the interface between air and water. The tracking of the interface(s) between phases is accomplished by the solution of a continuity equation for the volume fraction of one (or more) of the phases. For the qth phase, this equation has the following form:
(4)
where αq is the volume fraction of qth phase. The following three conditions are possible for each cell of the computational domain:

  • αq = 0: the cell is empty (of the qth phase)

  • αq = 1: the cell is full (of the qth phase)

  • 0< αq < 1: the cell contains the interface between qth phase and one or more other phases.

It can be assumed that free surface is on the volume fraction of 0.5.

Initial and boundary conditions

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The extents of computational domain were Xmin, Xmax, Ymin, Ymax, Zmin, and Zmax. The boundary conditions were employed for these extents of the computational domain as shown in Figure 2.
Figure 2
Initial and boundary conditions.
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Initial and boundary conditions.

Figure 2
Initial and boundary conditions.
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Initial and boundary conditions.

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The Xmin and Xmax represent the extent of computational domain in the upstream and downstream direction, respectively. Ymin and Ymax indicate the right and left sides of the computational domain. Whereas, Zmin represents the bottom of the computational domain and Zmax represents the top of the domain. ‘Wall Boundary Condition’ was used for Zmin. ‘Specified Pressure’ was opted for Xmin, Xmax, and Zmax. ‘Symmetry’ was applied at Ymin and Ymax. instead of ‘wall’ boundary condition. ‘Symmetry’ boundary condition was selected considering the balance between computational efficiency and accuracy in representing the physical phenomena of interest. In FLOW-3D, ‘wall’ is a boundary condition that describes a surface in the computational domain where the fluid velocity normal to the surface is zero. This is important for accurately simulating fluid behavior near solid surfaces. ‘Symmetry’ boundary condition is used to specify a plane of symmetry in the computational domain. This condition is used when there is a repeating pattern in the domain, and only one part of the domain needs to be simulated. The symmetry boundary condition specifies that the flow variables (pressure and velocity) on one side of the plane are equal to those on the other side of the plane. This reduces the size of the computational domain and makes the simulation more efficient. ‘Specific pressure’ boundary condition applies the pressure value at a specific location in the computational domain. This boundary condition is used when the pressure value at a certain point in the domain is known, such as at an inlet or outlet boundary. Fluid region is added in the domain by using the initial tab in Flow -3D. For fluid initialization, fluid elevation is used. In this study, fluid region, namely ‘Fluid Region I’ was added upstream of the structure. Limits of fluid region were then specified. Limits of fluid region I at Reservoir Level 555 m were 585 m and Z 492.6 m as shown in Figure 3.
Figure 3
Limits of fluid region I at Reservoir Level 555 m.
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Limits of fluid region I at Reservoir Level 555 m.

Figure 3
Limits of fluid region I at Reservoir Level 555 m.
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Limits of fluid region I at Reservoir Level 555 m.

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Model validation

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The numerical model was validated to verify the accuracy of numerically obtained results. For this purpose, discharge, flow depth and depth average velocity values were observed on the physical model which were then compared with the numerical model results. Physical modelling of Mohmand Dam spillway was carried out by the Water and Power Development Authority (WAPDA) in October 2017 at a scale of 1:60. Flow parameters (flow depth & velocity) computed by numerical model were noted at two locations, i.e., at start of basin and end of stilling basin. Table 3 shows the comparison of observed flow parameters, i.e. discharge, flow depth and flow velocity with that of computed values from the numerical model at reservoir levels of 555 m asl and 563 m asl. Comparison shows a difference of less than 3% which indicated that the numerical model is a good representative of prototype.

Table 3

Validation of Mohmand Dam spillway

Sr. No.Flow CharacteristicScale Model ResultsCFD Model Results
(a). (Operating Condition: Reservoir level = 555 m asl) 
1. Discharge (cumecs) 3,842.9 3,900 
2. Flow Depth (m) 26 25.7 
3. Depth average velocity (m/s) 11 11.3 
(b). (Operating Condition: Reservoir level = 563 m asl) 
1. Discharge (cumecs) 7,314.3 7,450 
2. Flow Depth (m) 32 32.4 
3. Depth average velocity (m/s) 13 12.7 
Sr. No.Flow CharacteristicScale Model ResultsCFD Model Results
(a). (Operating Condition: Reservoir level = 555 m asl) 
1. Discharge (cumecs) 3,842.9 3,900 
2. Flow Depth (m) 26 25.7 
3. Depth average velocity (m/s) 11 11.3 
(b). (Operating Condition: Reservoir level = 563 m asl) 
1. Discharge (cumecs) 7,314.3 7,450 
2. Flow Depth (m) 32 32.4 
3. Depth average velocity (m/s) 13 12.7 
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3.7. Model operation

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After validation of the numerical model, scenario modelling was performed to evaluate the hydraulic performance of the stilling basin. Flow parameters (flow depth, Froude number, and depth average velocity) were computed from the numerical model for each geometric scenario of wall convergence (0°, 0.5°, 1°, 1.5°, 2°, 2.5°) and impact blocks (standard and modified) by varying reservoir levels between 555 m asl (above sea level) and 563 m asl (555, 558, 561.3, 563) under free flow condition.

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Flow velocity profiles

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The high flow velocity causes erosion downstream of the spillway. Assessment of flow velocity is essential to find out the potential for erosion.

Figure 4 shows that pre-jump flow velocity is much higher as compared to post-jump velocity. Post-jump velocities are comparatively less with modified impact block as compared to standard impact block which indicates that modified blocks are more effective in dissipating the flow energy. Table 4 illustrates the variation in velocity at different converging angles of the stilling basin wall with modified blocks at three selected locations: pre-jump, post-jump, and end sill. Meanwhile the model was operated at a maximum reservoir level of 563 (m asl). Table 4 shows that pre-jump velocities for all models (M1–M6) are approximately equal. It indicates that pre-jump velocities remained consistent in all models. However, post-jump velocities and end sill velocities are decreasing with the increase in wall convergence angle. It implies that the performance of the hydraulic jump has improved with the convergence of side walls. Figure 5 shows the model output for velocity in the stilling basin at the maximum reservoir level. Velocity contours show the velocity variation in the stilling basin and along the spillway chute. Flow velocity is highest, i.e. 57 m/s at the lower part of the chute which is reduced to 6 m/s in the stilling basin near the end sill. It indicates that the stilling basin has performed its function.
Table 4

Velocity variation at 563 m asl with different converging walls of basin

Location Points with Coordinates (x,y,z)Flow Velocity at 0° Wall convergenceFlow Velocity at 0.5° Wall convergenceFlow Velocity at 1.5° Wall convergenceFlow Velocity at 2.5° Wall convergence
(m) (m/s) (m/s) (m/s) (m/s) 
Pre-Jump (505.6, 90.5, 348) 57 57.1 57.09 57.11 
Post Jump (550, 90.5, 353.2) 13.5 13 12.88 11.3 
At the End Sill (591.6, 90.5, 353.2) 9 7.5 7 6.48 
Location Points with Coordinates (x,y,z)Flow Velocity at 0° Wall convergenceFlow Velocity at 0.5° Wall convergenceFlow Velocity at 1.5° Wall convergenceFlow Velocity at 2.5° Wall convergence
(m) (m/s) (m/s) (m/s) (m/s) 
Pre-Jump (505.6, 90.5, 348) 57 57.1 57.09 57.11 
Post Jump (550, 90.5, 353.2) 13.5 13 12.88 11.3 
At the End Sill (591.6, 90.5, 353.2) 9 7.5 7 6.48 
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Figure 4
Velocity changes along the Stilling Basin at 563 m asl.
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Velocity changes along the Stilling Basin at 563 m asl.

Figure 4
Velocity changes along the Stilling Basin at 563 m asl.
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Velocity changes along the Stilling Basin at 563 m asl.

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Figure 5
Model Output displaying Velocity Profile at Maximum Reservoir Level.
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Model Output displaying Velocity Profile at Maximum Reservoir Level.

Figure 5
Model Output displaying Velocity Profile at Maximum Reservoir Level.
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Model Output displaying Velocity Profile at Maximum Reservoir Level.

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Computation of flow depths

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Figure 6 shows the comparison of flow depth variation in the stilling basin at the specified locations (pre-jump, post-jump, and near-end sill) with standard and modified impact blocks. It is noted that the post-jump flow depth is slightly higher with modified impact blocks as compared to the standard blocks. High flow depths reduced the flow velocity and improved the efficiency of hydraulic jumps.
Figure 6
Flow Depth variation at 563 m asl.
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Flow Depth variation at 563 m asl.

Figure 6
Flow Depth variation at 563 m asl.
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Flow Depth variation at 563 m asl.

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Tables 5 and 6 shows flow depth variation computed at selected converging angles. The modified impact blocks consist of a ramp between the baffle blocks and the bed of the stilling basin which caused an increase in flow depth. Post jump flow depth increased up to 3% due to wall convergence and modified impact block. Figure 7 shows the contours of flow depth at the spillway chute and stilling basin for maximum reservoir level. At the spillway chute, the flow depth has been reduced from 16 to 8 m. It increased to 33 m in the stilling basin which indicates that the flow profile has changed from super-critical to sub-critical.
Table 5

Flow depth variation in stilling basin with Standard Impact Blocks

Sr. No.Operating Condition
Free Flow (563 m asl)
Block Type
Standard Blocks
Convergence of Wall (Degrees)0°0.5°1.5°2.5°
1 Flow Depth (m) Pre-Jump 7.98 7.99 8.00 8.05 
2 Post-Jump 32.70 33.30 33.70 33.90 
3 Near end sill 30 31 32.5 33 
Sr. No.Operating Condition
Free Flow (563 m asl)
Block Type
Standard Blocks
Convergence of Wall (Degrees)0°0.5°1.5°2.5°
1 Flow Depth (m) Pre-Jump 7.98 7.99 8.00 8.05 
2 Post-Jump 32.70 33.30 33.70 33.90 
3 Near end sill 30 31 32.5 33 
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Table 6

Flow depth variation in stilling basin with Modified Impact Blocks

Sr. No.Operating Condition
Free Flow (563 m asl)
Block Type
Modified Blocks
Convergence of Wall (Degrees)0°0.5°1.5°2.5°
1 Flow Depth (m) Pre-Jump 8.00 8.00 8.00 8.05 
2 Post-Jump 33.00 33.70 33.80 34.00 
3 Near end sill 30.5 31.8 32.70 33.5 
Sr. No.Operating Condition
Free Flow (563 m asl)
Block Type
Modified Blocks
Convergence of Wall (Degrees)0°0.5°1.5°2.5°
1 Flow Depth (m) Pre-Jump 8.00 8.00 8.00 8.05 
2 Post-Jump 33.00 33.70 33.80 34.00 
3 Near end sill 30.5 31.8 32.70 33.5 
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Figure 7
Model Output displaying Flow Depth Variation at Maximum Reservoir Level.
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Model Output displaying Flow Depth Variation at Maximum Reservoir Level.

Figure 7
Model Output displaying Flow Depth Variation at Maximum Reservoir Level.
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Model Output displaying Flow Depth Variation at Maximum Reservoir Level.

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Computation of Froude number

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In dam spillways, the Froude number of the incoming flow lies within the range of 4.5–9. When the flow enters the stilling basin, a stabilized jump is formed. In this case, surface rollers tend to occur which helps in dissipating the energy by more than 70%. Froude number variation is shown in Figure 8. Contours show that the pre-jump Froude number is 6.65 whereas the post-jump value is 0.66. It further decreased to 0.24 near the end sill. Post-jump Froude number values indicated that the jump has dissipated most of the flow energy in the stilling basin.
Figure 8
Model Output displaying Froude Number at Maximum Reservoir Level.
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Model Output displaying Froude Number at Maximum Reservoir Level.

Figure 8
Model Output displaying Froude Number at Maximum Reservoir Level.
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Model Output displaying Froude Number at Maximum Reservoir Level.

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Energy loss

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Energy loss is computed in terms of head loss by the model at maximum reservoir of 563 m asl with different converging angles of side walls (0̊, 0.5̊, 1.5̊, 2.5̊) as shown in Figure 9. Results showed that energy dissipation in the stilling basin with modified impact blocks is considerably greater than that of standard blocks configuration. Head loss varied between 14.47 and 16 m. Maximum head loss was noted at 2.5° wall convergence. Consequently, two-meter (2 m) loss in head was achieved through wall convergence and modified impact blocks. Head loss in hydraulic jump was calculated using the relation given below:
(5)
where, y1 is flow depth just before the hydraulic jump, y2 is flow depth after the formation of hydraulic jump and is head loss.
Figure 9
Head loss at 563 m asl.
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Head loss at 563 m asl.

Figure 9
Head loss at 563 m asl.
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Head loss at 563 m asl.

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Efficiency of the hydraulic jump

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The efficiency of the jump was calculated for all geometric scenarios. It was higher in the case of modified impact blocks as compared to standard impact blocks. Figure 10 shows that the efficiency of the jump is increasing by increasing the converging angle of side walls of stilling basin. The maximum efficiency of the jump was observed at 2.5̊ converging angle for 563 m asl reservoir level. In the current study, maximum 83% efficiency of stilling basin was noted with all geometric modification which is more than the standard one.
Figure 10
Variation in jump efficiency at 563 m asl R/L.
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Variation in jump efficiency at 563 m asl R/L.

Figure 10
Variation in jump efficiency at 563 m asl R/L.
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Variation in jump efficiency at 563 m asl R/L.

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The efficiency of the jump was computed in terms of relative energy loss by using the following relation given below:
(6)
where E1 is the specific energy of the supercritical flow, i.e., prior to hydraulic jump formation, E2 is specific energy of the subcritical flow, i.e. after the formation of the hydraulic jump, and η is the relative energy loss that shows the efficiency of the hydraulic jump.

Comparison of results with previous studies

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This section aims to compare hydraulic efficiency across various converging angles of a stilling basin with findings from prior research (Babaali et al. 2015; Raza et al. 2023). Analyzing the data from both the current and past studies allowed for a comprehensive understanding of how changes in converging angles impact the hydraulic performance of stilling basins. Figure 11 showing an increasing trend in hydraulic efficiency with the increase in covering angle. In all three cases hydraulic efficiency of the stilling basin has increased after wall convergence. Maximum hydraulic efficiency is noted at 2.5 degree wall convergence. By examining the trends in efficiency, researchers can identify optimal design parameters for stilling basins, contributing to the safety and economy of hydraulic structures.
Figure 11
Comparison of hydraulic efficiency of stilling with previous studies.
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Comparison of hydraulic efficiency of stilling with previous studies.

Figure 11
Comparison of hydraulic efficiency of stilling with previous studies.
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Comparison of hydraulic efficiency of stilling with previous studies.

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Improved design

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Different simulations were performed in a standard stilling basin at different flow rates. The modification in the standard geometry of the stilling basin was carried to assess its hydraulic performance. The side walls of the stilling basin were converged at different angles 0.5° to 2.5°; with an increment of 0.5°. Based on improved hydraulic performance of the stilling basin with modified geometry, an improved design of the stilling basin was suggested. The improved design is shown in Figure 12. It comprises side walls converged at 2.5 degree. The length of converged walls is 79 m which is 7 m shorter than the parallel one. It will reduce the overall cost of the structure. Improved design also includes modified shape of impact blocks known as ‘super cavitating impact blocks’. These blocks increased the efficiency of the stilling basin by up to 1% in comparison to standard wedge shape impact blocks. Modified impact blocks may be useful in avoiding the cavitation phenomenon. Improved design of the USBR Type-III stilling basin is an effort to achieve economy in the length of the basin with optimum hydraulic efficiency.
Figure 12
2-D Plan and 3-D view of improved design of stilling basin.
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2-D Plan and 3-D view of improved design of stilling basin.

Figure 12
2-D Plan and 3-D view of improved design of stilling basin.
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2-D Plan and 3-D view of improved design of stilling basin.

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A CFD model study was conducted on the lower stilling basin of Mohmand Dam spillway by varying the reservoir levels at free flow conditions. The study was conducted to investigate the effect of wall convergence and modified impact block on the hydraulic efficiency of the stilling basin. The side walls of the stilling basin were converged from 0.5° to 2.5° (with an increment of 0.5°). At all operating conditions, converged walls improved the hydraulic performance of stilling and contained the hydraulic jump in the stilling basin. The optimum efficiency of the hydraulic jump was observed at 2.5̊ wall convergence with modified impact blocks. The replacement of modified impact blocks with standard blocks increased the flow depth which in turn reduced the post-jump velocity. As a result, modified impact block increased the hydraulic efficiency up to 1%. Even with these modification, pre-jump and post-jump Froude numbers were found in an acceptable range of 4.83 to 6.75 and 0.66 to 0.78, respectively. Consequently, the current study provided improved design of USBR Type-III stilling basin. Improved design is an effort to achieve economy in the length of the basin with optimum hydraulic efficiency. The present study recommends checking the hydraulic performance of the modified stilling basin for gated flow condition. Moreover, for implementation of modified design, economic feasibility is required.

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The authors have no competing interests to declare that are relevant to the content of this article.

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No funding was received for conducting this study.

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

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The authors declare there is no conflict.

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