Numerical investigation of hydraulic jumps with USBR and wedge-shaped baffle block basins for lower tailwater

3D

three-dimensional

A_x, A_y, A_z

flow areas in x, y, and z directions

b

length scale

C_d

discharge coefficient

CFD

Computational Fluid Dynamics

D

orifice opening

F

fraction of fluid

FAVOR

Fractional Area–Volume Obstacle Representation

Fr₁

Froude number

FVM

finite volume method

g

acceleration due to gravity

G_x, G_y, G_z

body acceleration in x, y, and z directions

H₁

specific energy heads upstream of hydraulic jumps

h₁

water level in the supercritical region

H₂

specific energy heads downstream of hydraulic jumps

h₂

water level in the subcritical region

H_c

centreline head

H_d

designed head

H_e

effective head

K–ɛ

turbulence model

L_r

roller length of the hydraulic jump

L_r/d₁

dimensionless roller length

Q

volume flow rate

R²

coefficient of the determination

RANS

Reynolds Averaged Navier–Stokes equations

RNG K–ɛ

renormalization group

RSM

Reynolds stress model

Stl

stereo lithography

T_s

simulation time

TKE

turbulent kinetic energy

u, v, w

velocity components in x, y, and z directions

U_max

maximum velocity in the vertical section

U_rms

root mean square velocity

USBR

United States Bureau of Reclamation

VOF

volume of fluid

X

horizontal distance from hydraulic jump toe

X_min, X_max

upstream and downstream boundary

Y

flow depth

y₂/y₁

sequent depth

Y_min, Y_max

wall boundary in lateral direction

Z_min, Z_max

bottom and top boundary

turbulent dynamic viscosity

turbulent production

dynamic viscosity

dissipation of turbulent kinetic energy

δ

y value

fluid density

fluctuation of specific weight

⁠,⁠,⁠,

model parameters

efficiency of the hydraulic jump

Soon after the barrage operation in 1958, multiple problems occurred on the barrage downstream, such as uprooting of the impact baffle blocks due to their vertical face, damage to the basin's floor, lowering of tailwater levels, and bed retrogression (Zulfiqar & Kaleem 2015). During 1959–1962, repair works were carried out to cater to these issues, but the problems remained persistent. To resolve these issues, the Punjab Government constituted a committee of experts in 1966 and 1973, but no specific measures were taken, and the issues continued to aggravate (Zaidi et al. (2004). Additionally, these traditional impact blocks also face flow reattachment on the sides that decreases the drag force (Frizell & Svoboda 2012). On the contrary, after investigating the wedge-shaped baffle blocks (WSBBs) downstream of pipe outlets, research scholars (Pillai et al. 1989; Verma & Goel 2003; Verma et al. 2004; Goel 2007; Goel 2008; Tiwari et al. 2010) reported that these blocks increased the energy dissipation and created more eddies and wake regions on either side. These studies further mentioned that upon the use of WSBBs, the overall length of stilling basins was also reduced from 15 to 25%.

Habibzadeh et al. (2012) conducted experiments to investigate the role of baffle blocks for submerged HJs and energy dissipation downstream of low-head hydraulic structures. Chachereau & Chanson (2011) and Wang & Chanson (2015) investigated free surface profiles and turbulent fluctuation within the HJ for a wide range of initial Froude number (Fr₁). The velocity profiles showed a wall jet-like profile, and turbulence intensities were high due to the fluctuations at the free surface. Maleki & Fiorotto (2021) developed a semi-empirical method to investigate HJs on a rough bed. The results showed that the characteristic length scale was linearly changing with Fr₁. Macián-Pérez et al. (2020b) carried out experiments on the USBR-II stilling basin to investigate the characteristics of HJs. The results of sequent depths and HJ efficiency agreed with the experimental studies, which reached 99.2 and 97%, respectively. The results of the dimensionless free surface profile also agreed with the previous studies for which the value of the coefficient of determination (R²) reached 0.979. Murzyn & Chanson (2009) conducted experiments for a wide range of Fr₁ up to 8.3 to investigate bubbly and turbulence structure within the HJ. The results showed that void fraction (C_max) and bubble frequency (F_max) were found in the developing region, and vertical interfacial velocity agreed with the wall jet-like profile. Qasim et al. (2022) conducted experiments on bed discordance downstream of different weirs. The results indicated that as the bed discordance increased, the dimensionless flow depth decreased downstream of the discordance, which increased the Froude number. The results further showed that as the configuration of bed discordance was changed, the free surface profiles were also changed, which affected the flow depths and velocity profiles. Bhosekar et al. (2014) conducted experiments to investigate the characteristics of discharge downstream of orifice spillways. The results showed that free surface profiles were not elliptical due to the flat curve near the gate opening. The results further indicated that the flat curve developed a negative pressure on roof profiles, which reduced the discharge capacity of the spillway.

To stabilize the HJ in the stilling basins, different shapes of baffle blocks are employed, i.e., baffle blocks (Habibzadeh et al. 2012), friction blocks (Chaudary & Sarwar 2014), end sill (Mansour et al. 2004) and vertical sill (Alikhani et al. 2010), splitter blocks (Verma & Goel 2003), curved (Eloubaidy et al. 1999), T-shaped and triangular (Tiwari & Goel 2016), and WSBB (Pillai et al. 1989; Goel 2007; Goel 2008). These arrangements control the HJs in case of fewer tailwater depths (Peterka 1984) and minimize the erosion downstream of structures (Zaffar et al. 2023). Sayyadi et al. (2022) investigated HJ characteristics for negative steps in the stilling basin. The results showed that the negative step increased the energy dissipation up to 11%. Pillai et al. (1989) compared three different stilling basins for the Fr₁ up to 4.5. The results showed that the stilling basin with the WSBB reduced the scour and overall length of the basin. Goel (2008), Goel (2007), and Tiwari et al. (2010) conducted experiments to investigate HJ characteristics downstream of square and circular pipe outlets using WSBBs. The results showed that as compared to the impact USBR-VI basin, the WSBB basin spread the fluid efficiently in the lateral direction and reduced the basin length up to 50%.

In the former section, the experimental studies on HJs, velocity distribution, free surface profiles, and turbulent kinetic energy (TKE) are discussed, which could be assisted by Computational Fluid Dynamics (CFD) models (Ghaderi et al. 2020). Furthermore, over these hydraulic structures, the flow is very complex and associated with secondary currents, which characterized it as highly turbulent in all directions. Hence, using laboratory and field experiments, it is hard to accurately measure the free surface profile, velocities, secondary currents, and TKE over these hydraulic structures (Jothiprakash et al. 2015). Furthermore, physical experiments and on-site measurements are usually expensive and time-consuming. In contrast, the improvements in computational speed, storage, and turbulence modeling have made CFD a viable complementary investigation tool for hydraulic modeling (Ghaderi et al. 2021). Consequently, the use of numerical modeling tools such as Open Foam (Bayon-Barrachina & Lopez-Jimenez 2015), ANSYS Fluent (Aydogdu et al. 2022), and FLOW-3D (Hirt & Sicilian 1985) has become prevalent to get hydraulic characteristics of grade-control structures. Such modeling tools are helpful, especially when the basic fundamental equations are unable to provide desired outputs, like in the case of multifaceted geometries (Herrera-Granados & Kostecki 2016). So far, many researchers have employed numerical models in the hydraulic investigations of HJs and energy dissipation, but only a few of the latest studies are highlighted here. FLOW-3D numerical models were employed to investigate the HJ (Zaffar & Hassan 2023a) and baffle blocks (Zaffar & Hassan 2023b) for different stilling basins of the Taunsa barrage. These studies focused on velocity distribution, TKE, free surface profiles, energy loss energy, and the effects of baffle blocks on the HJ characteristics. Macián-Pérez et al. (2020a) carried out a numerical investigation on a high Reynolds of 210,000 to study the HJ characteristics. Upon comparison, the FLOW-3D model showed 93% accuracy in the roller length of HJs. The results also indicated 94.2 and 94.3% accuracy for sequent depths and HJ efficiency, respectively. Nikmehr & Aminpour (2020) examined the HJ characteristics on rough beds using FLOW-3D, and compared results with the experiments. The results indicated that roughness height and its distance affected the HJ length. Gadge et al. (2018) conducted a numerical study to investigate the impact of roof profiles on the discharge capacity of orifice spillways and validated the models with experimental results. The study revealed that in addition to the pond level and height of orifice (d), the bottom and roof profiles also affected the discharge coefficient (C_d).

From the literature review, it is found that only a few studies are conducted on the flow characteristics downstream of the Taunsa barrage (Zaidi et al. 2004, 2011; Chaudhry 2010). These studies were carried out in laboratory flume and investigated the effects of tailwater on the location of HJs. However, the studies were lacking in providing the data for other essential hydraulic parameters, i.e., velocity distribution, free surface profiles, TKE, and relative energy loss in the stilling basin. On the contrary, the literature has revealed many experimental and numerical studies on different shapes of baffle blocks downstream of open-channel flow, but the use of WSBB downstream of river diversion barrage is found limited. In the previous studies (Pillai et al. 1989; Verma & Goel 2003; Verma et al. 2004; Goel 2008, 2007; Tiwari et al. 2010), these blocks have only been tested downstream of pipe outlet basins for the initial Froude number of 4.5. Therefore, in the present study, FLOW-3D numerical models are developed to investigate the effects of presently available USBR baffle blocks in the stilling basin of the Tuansa barrage. Due to the uprooting problems of these blocks, the study also investigates the suitability of WSBBs downstream of the studied barrage and draws a comparison between the results of modified USBR and WSBB basins. In this study, based on results from the literature, WSBB with a vertex angle of 150° and cutback angle of 90° is applied for Fr₁ up to 6.64. The main objective of this study is to investigate HJs and flow behavior with USBR baffle blocks and WSBB downstream of an investigated barrage at 44 m³/s discharge. At 44 m³/s discharge, the numerical models are operated at the minimum tailwater level of 129.10 m, and investigated free surface profiles, sequent depths, roller lengths, HJ efficiency, velocity profile, and TKE in the two different stilling basins.

Environmental flows are governed by the laws of physics and represented by Navier–Stokes Equations (NSEs), which are inherently nonlinear, time-dependent, and contain three-dimensional partial deferential schemes (Viti et al. 2018). These partial differential equations explain the procedures of continuity, momentum, heat, and mass transfer. For one- and two-dimensional models, these equations can be solved analytically, while for the solution of three-dimensional models, CFD models are employed to discretize the NSEs. In these models, flow equations, i.e., NSEs and continuity equations, are discretized in each cell. Generally, these models start with a mesh, which further contains multiple interconnected cells in the employed mesh blocks. These meshes subdivide the physical space into small volumes, which are associated with several nodes. The values of unknown parameters are stored on these nodes, such as velocity, temperature, and pressure. Different numerical techniques are available to discretize the NSEs, i.e., Direct Numerical Simulation (DNS) (Jothiprakash et al. 2015), Large Eddy Simulation (LES) (Ghosal & Moin 1995), and Reynold Averaged Navier–Stokes (RANS) Equation (Kamath et al. 2019). However, as compared to DNS and LES models, due to less computation cost and simulation time, the RANS model is frequently used in river and hydraulic investigations. Using the RANS model, two additional variables are generated, for which turbulence closure models are usually employed (Carvalho et al. 2008). These models find closure by averaging the Reynolds stress terms in NSEs and append additional variables for turbulent viscosity and transport equations.

Presently, FLOW-3D models are developed to investigate the effects of different shapes of baffle blocks on HJ downstream of the river diversion barrage. The models employ RANS equations to solve algorithms and equations of incompressible fluid in each computational cell. To further address the additional terms, i.e., Reynolds stresses and turbulent viscosity, the Renormalization group (RNG K–ɛ) method is applied. For the discretization of RANS and other algorithms, at present, the Volume of Fluid (VOF) method (finite volume method (FVM)) is employed, while the equations of the controlled volume are formulated with area and volume porosity functions. This formulation is called the ‘Fractional Area/Volume Obstacle Representation’ (FAVOR) method (Hirt & Sicilian 1985). The proceeding section describes the equations used for the present models.

In Equations (6)–(8) u, v, and w, are velocity components in x, y, and z directions, respectively. and p are total pressure and fluid density while the terms are known as the Reynolds stresses. A_x, A_y, and A_z are flow areas while R,⁠, and R_SOR are the model's coefficient, flow generic property, and mass source term, respectively.

Six turbulence models are available in FLOW-3D, which employs numerous equations to solve the closure problems. Among various models, the two-equation turbulence models such as standard K–ɛ (Bradshaw 1997, RNG K–ɛ (Yakhot et al. 1991), and K–ω (Wilcox 2008) are widely used in hydraulic investigations.

In FLOW-3D, the fluid fraction (F) in each cell is usually presented by three possibilities:

• (A)

  F = 0, cell is empty.

• (B)

  F = 1, a cell is fully occupied by fluid.

• (C)

  0 < F < 1, cell represents the surface between the two fluids.

One fluid (water) with a free surface is considered in the present models, for which FLOW-3D automatically selects the free surface method from the availableVOF advection scheme. For the free surface tracking, 0.5 value is assigned in each computation cell.

One of the major issues in solving the NSEs is pressure–velocity coupling, and for that, a network of algorithms (SIMPLE (Patankar & Spalding 1972) and PISO (ISSA 1985)) has been developed. These above-mentioned algorithms use under- and over-relaxing factors for pressure correction in the continuity and momentum equations, which contain large memory. Additionally, due to the relaxation factors, sometimes the solution becomes unstable and does not find convergence. On the contrary, FLOW-3D employs the Generalized Minimum Residual Method (GMRES) (Joubert 1994) because it possesses good convergence, high speed, and uses less memory. Additionally, GMRES does not apply any relaxation factor and possesses an additional algorithm, ‘Generalized Minimum Residual Solver (GCG),’ to treat the viscous terms.

It is essential to mention that in both meshing scenarios, fine mesh blocks were used on the downstream side of the bay because the focus of the present investigation was made around the baffle blocks and in the HJ regions. The details of mesh cell size and mesh quality indicators for the various mesh blocks are provided in Tables 1 and 2, respectively. Notably, except for discharge analysis, the results of other hydraulic parameters are produced from the fine meshing.

A vertical gate of 18.5-m width, 0.53-m length, and 6.10-m height was mounted upstream of the weir crest. Pond levels of 135.93 and 136.24 m were maintained for free and orifice flows, respectively. Table 3 shows the conditions used for models' operation.

For the first mesh block, the upstream and downstream boundaries were set as pressure (P), while for the second block upstream boundary was set as symmetry (S). The lateral sides were set as rigid boundaries (W), and no-slip conditions were expressed as zero tangential and normal velocity (u=v=w = 0), where u, v, and w are the velocities in x, y, and z directions, respectively. These boundaries indicate a wall law velocity profile, which further expresses that the average velocity of turbulent flows is proportional to the logarithm of the distance from that point to the fluid boundary. For all variables (except pressure (P) (which was set to zero), upper boundaries (Z_max) were set as atmospheric pressure to allow water to null von Neumann. For both mesh blocks, the lower boundaries (Z_min) were set as walls.

For the present models, the stability and convergence at each iteration were checked by Courant number (Ghaderi et al. 2020), which affected the time steps from 0.06 to 0.0023 and 0.015 to 0.0025 for free and gated flow, respectively. It is worth mentioning here that for the free flow analysis of higher discharge such as 444 m³/s, the steady state solution can only be achieved by mass-averaged fluid kinetic energy (MAFKE) and volume flow rate (VFR) at the inlet and outlet boundaries. Therefore, the time at which the MAFKE and VFR reach the steady state is assigned as the simulation time (T_s) of models. Presently, VFRs at the inlet and outlet boundaries are considered as the stability and convergence indicators. Based on the criterion mentioned above, the present free and gated models achieved hydraulic stability at T_s = 60 s while the actual time (T_a) of models ranged between 30 and 48 h. However, to accommodate free surface fluctuations, the models were run for T_s = 80 s.

For performance assessment of the numerical models, H_e/H_d = 0.998 (Johnson & Savage 2006; Gadge et al. 2019; Zaffar & Hassan 2023a, 2023b) was implemented for free flow analysis, where H_e and H_d are effective and designed heads, respectively. This was the design discharge of the Taunsa barrage, for which the models were operated on the pond and tailwater levels of 135.93 and 133.8 m, respectively, as provided in Table 3.

Due to the limited results of investigated hydraulic parameters on the studied barrage, the models' results are compared with the previous relevant experimental and numerical studies. For such comparison, the models require some similarity in boundary and initial conditions, as obtained from Bayon-Barrachina & Lopez-Jimenez (2015) and Wang & Chanson (2015). Similar to the studies by Bayon-Barrachina & Lopez-Jimenez (2015) and Wang & Chanson (2015), in the present gated models, the upstream and downstream initial conditions are set to fluid elevation, i.e., pond and tailwater level, with hydrostatic pressure boundaries, while upstream boundaries are set to atmospheric pressure. Additionally, the sides and bottom are set to wall boundaries as described in Bayon-Barrachina & Lopez-Jimenez (2015) and Wang & Chanson (2015). However, the present models differ from the basin appurtenances as the compared studies have investigated HJ and other parameters on the horizontal flat beds. Furthermore, Bayon-Barrachina & Lopez-Jimenez (2015) and Wang & Chanson (2015) have investigated hydraulic parameters such as sequent depths, roller lengths, free surface profiles, energy dissipation, and TKE for Fr₁ of 6.10 and 3.8 < Fr₁ < 8.5, respectively. Similar to the above-mentioned study, the present modified USBR and WSBB basins are investigated for the Fr₁ of 6.5 and 6.64, respectively. Hence, to confirm the results of free surface profiles, the studies of Bayon-Barrachina & Lopez-Jimenez (2015) and Wang & Chanson (2015) are utilized, for which the relevant discussion is made in the proceeding paragraphs.

To further assess the performance and gain deeper insight into the models' efficiency, residual plots are drawn for the investigated hydraulic parameters. These errors referred to the difference between the observed (literature) and predicted data, which monitored the regression quality (Hassanpour et al. 2021). At a 5% level of significance, a homo-scedasticity analysis measured the residual errors, and the results of predicted residual errors were compared with the previous study.

The sequent depths obtained from WSBB and modified USBR basins were 8.96 and 8.68, respectively, which were found to agree with the experimental results of other studies (Hager & Bremen 1989 and Belanger 1841), as shown in Figure 11(a). The results were also compared with the experiments of Kucukali & Chanson (2008), in which the value of Fr₁ was 6.9. However, the Fr₁ values obtained from present numerical models were 6.5 and 6.64 within WSBB and USBR basins, respectively. The comparison indicated that the present models overestimated the sequent depths, for which the errors reached 8.6 and 5.7% in WSBB and modified USBR basins, respectively. Furthermore, upon comparison with Bayon-Barrachina & Lopez-Jimenez (2015), results showed that present models underestimated the sequent depths, for which the maximum errors reached −13.2 and −9.8% errors in WSBB and USBR basins, respectively.

Figure 11(b) shows the comparison of residual errors of sequent depths with the previous studies. The maximum positive and negative residual values of 0.250 and −0.222 were found in WSBB and USBR baffle block stilling basins, respectively. The pattern of residual errors indicated an equal variance along the agreement line, which showed normal destitution of residual errors, thereby a homoscedastic pattern was noticed. The residual errors of sequent depths in both the tested basins were found within the ranges of Bayon-Barrachina & Lopez-Jimenez (2015) and Kucukali & Chanson (2008).

The results of numerical models showed 57.9 and 58.6% efficiencies in WSBB and modified USBR basins, respectively. The efficiencies for both the basins were also computed by Equation (2) and the results indicated 61.2 and 61.9% efficiencies for WSBB and modified USBR basins, respectively. The comparison further revealed that the present model underestimated the efficiencies, which reached the maximum errors of 5.41 and 5.45% in WSBB and modified USBR basins, respectively.

Figure 15(b) indicates the residual errors of for modified USBR and WSBB basins and compares the errors with the previous experimental and numerical studies. Upon comparison with the modified USBR basin and with the literature, the HJ efficiency in the WSBB basin showed a close agreement with the zero residual line, for which the maximum error reached 0.001. On the other hand, the residual error in the modified USBR basin reached 0.003. Figure 14 also showed that the maximum residual error in the HJ efficiencies was found to be less than that was observed in previous studies, which remained within the limits of the compared studies (Wu & Rajaratnam 1996; Kucukali & Chanson 2008; Bayon-Barrachina & Lopez-Jimenez 2015).

From Figure 19, results showed that as the distance from the HJ toe increased, the vertical distance of U_max and inner layer thickness also increased. The analysis further indicated that as the distance from the initial location of HJs increased, the position of U_max was increased, which leveled off after the HJ, as can be seen in sections (C-C) of Figures 17 and 18. In both stilling basins, at X = 2 m, from the HJ initial location, the forward velocity profiles were found well agreed with the profile of Ead & Rajaratnam (2002) and the values of R² reached 0.937 and 0.887 for WSBB and modified USBR basins, respectively, as shown in Figures 18(a) and 18(b), respectively. However, at X = 5.4 m, as compared to velocity (U/U_max = 0.36) in the modified USBR basin, the results showed less forward velocity (U/U_max = 0.21) in the WSBB basin at the upper fluid region.

The results further showed that upon the use of WSBBs, no flow reattachment was witnessed on either side of the baffle blocks. Due to reduced reattachment, more wake areas were generated on the side of the WSBB basin, and the results showed agreement with the statement of other authors (Verma & Goel 2003; Verma et al. 2004; Goel & Verma 2006). At Z = 0.47 m, 0.93 m, and 1.39 m, the maximum TKEs were noticed in the HJ region, which reached 4.3, 4.6, and 3.5 J/kg, respectively, as shown in Figure 22(b)–22(d), respectively. In the WSBB basin, after the HJ, the baffle blocks declined the TKEs due to the development of sharp discontinuities in the flow. After Z = 1.39 m, the value of TKEs up to the free surface gradually reduced, as shown in Figure 22(e) and 22(f). Figure 22(g) shows 2D illustrations of TKEs on the free surface, and the results indicate that as compared to the modified USBR basin, the magnitude of TKEs was lower and traveled less distance in the WSBB basin.

This study developed numerical models on the rigid bed to investigate the effects of USBR and WSBB baffle blocks on the HJ downstream of the river diversion barrage using FLOW-3D. VOF and RNG K–ɛ models were employed to track the free surface and turbulence, respectively. For the proposed new basin (WSBB basin), WSBB with a vertex angle of 150° and cutback of 90° is employed in the baffle block region, while the friction block region remained unchanged. The performance of the two different basins is assessed by HJs and other hydraulic parameters such as free surface profile, sequent depths, roller lengths, HJ efficiency, velocity profile, and TKE. Furthermore, the results of the present modified USBR Type-III and WSBB basins are compared with the relevant literature, for which regression analysis is performed and residual error diagrams are plotted. However, the present models are limited to the single discharge of 44 m³/s and employ only one turbulence model, i.e., RNG K–ɛ. Additionally, the present models were designed for a single bay of the barrage.

• Upon use of fine meshing, in comparison to the designed discharge, the present models showed 0.80 and 0.90% of errors in modified USBR Type-III and WSBB basins, respectively. Similarly, for the gated flow, the results indicated 0.32 and 1.14% errors in the modified USBR Type-III and WSBB basins, respectively.

• After employing regression analysis, the results of free surface profiles showed agreement with the previous studies for which R² reached 0.980 and 0.970 in WSBB and modified USBR basins, respectively. From the results, it can be believed that as compared to the modified USBR Type-III, the newly proposed WSBB basin produced a better free surface profile of HJs.

• Due to the inclusion of the baffle blocks in the studied basins, the roller lengths of HJs were contained efficiently, and thereby, as compared to the literature, lesser roller lengths were observed in the modified USBR Type-III and WSBB basins.

• The overall efficiency of HJs in modified USBR and WSBB basins reached 58.60 and 57.90%, respectively, which showed good agreement with the literature. Based on the results of the efficiency of HJs, the accuracy of the present models reached 93%.

• In the hydraulic regions, the results of dimensionless velocity profiles indicated a wall jet-like structure, which agreed well with the literature. In addition, as compared to the modified USBR Type-III basin, the velocity profiles in the WSBB basin were found to be more promising, for which R² reached 0.937. Additionally, after the HJ, as compared to the USBR Type-III basin, the forward velocity (U/U_max) in the WSBB basin was found to be less. Conclusively, it can be said that in comparison to the modified USBR Type-III basin, at the lower discharges, the WSBB basin decays the velocities more efficiently.

• The results of TKEs indicated that the flow was strongly turbulent near the foreside of the HJs, and the maximum TKEs were noted in the central fluid depths. In the WSBB basin, no fluid reattachment was observed on either side of the baffle blocks, and the results further indicated that as compared to the modified USBR Type-III basin, fewer TKEs were found at the end of the WSBB basin.

Based on the models' results, the study confirms the suitability of WSBB downstream of the barrage for lower tailwater conditions. From the results, it is believed that FLOW-3D is a very effective and efficient tool for the hydraulic investigation of flow behavior downstream of the barrage. However, in Pakistan, the use of such modeling tools is found very limited, therefore, the study results will help hydraulic and civil engineers to assess different energy dissipation arrangements within the stilling basins and will provide suitable alternative solutions. The present study was limited to the fixed geometry of the WSBB, therefore, it is suggested to investigate HJ and flow characteristics with other vertex and cutback angles. In addition, it is also recommended to study the hydraulics of WSBB downstream of barrages by employing multiple bays of barrage and other turbulence models.

The authors acknowledge Mr Jalil, AutoCAD operator, for his support in the development of different drawings relevant to the present study.

The authors received no research grants or funding.

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

The authors declare there is no conflict.