Hydraulic investigation of stilling basins of the barrage before and after remodelling using FLOW-3D

The hydraulic jump occurs when a supercritical flow changes into a subcritical. This phenomenon occurred to dissipate and reduce high kinetic energy downstream of the hydraulic structures. The classification of hydraulic jumps is based on the Froude number (Fr), and according to Bélanger (1841) after simplifying the momentum equation, Fr can be used to estimate the sequent depths of hydraulic jumps. Generally, hydraulic jumps are classified into four different categories, which include weak jump (1.7 < Fr₁ ≤ 2.5), oscillating jump (2.5 < Fr₁ ≤ 4.5), steady jump (4.5 < Fr₁ ≤ 9), and strong jump(Fr₁ > 9) (Murzyn & Chanson 2009).

Several experiments and numerical investigations are carried out on hydraulic jumps, and a few of the most recent studies are highlighted here. Wang & Chanson (2015) conducted experiments on the fluctuating characteristics of the free surface within the hydraulic jump, whereas Chachereau & Chanson (2011) & Murzyn & Chanson (2009) studied the effects of velocity and free-surface fluctuations within the hydraulic jump. They presented that the free turbulent fluctuation was found upstream of the hydraulic jump, and results of the free surface showed the characteristic frequencies between 1.4 and 4 Hz. Longo (2011, 2010) conducted experiments in a laboratory flume to investigate the turbulence beneath the free surface in a stationary flow created by Crump weir. Ultrasonic distance sensor and Ultrasonic Doppler velocity profiler were used to measure the velocity field. Results showed that the free-surface elevation power spectrum had a peak at a frequency of 2 Hz which was affected by the change of Fr. The results further indicated that with the small Fr values the free surface was flat with damping of turbulence and velocity, while with moderate Fr values the thickness of boundary layer increased which was equivalent to the root mean square wave height. Wu & Rajaratnam (1996) carried out experiments on the transition of the hydraulic jump into channel flow. Kucukali & Chanson (2008) conducted experiments on bubbly structures within the hydraulic jumps. Hager & Li (1992) carried out experiments on the characteristics of hydraulic jump in a rectangular channel to investigate the effects of the continuous and transverse sill. Hager & Bremen (1989) investigated the effects of wall function on the sequent depths of classical hydraulic jump and results showed that the sequent depths were influenced by incoming Reynolds numbers.

The performance of any hydraulic structure such as spillways, dams, barrages, and pipe outlets depends on the shape and size of the stilling basin (Babaali et al. 2015). Primarily, after the hydraulic jump, the leftover energy is needed to be dissipated by providing energy dissipators in the stilling basin. To avoid cavitation damages and scouring on downstream of the stilling basin necessary structural arrangements are made to restrain the hydraulic jump at certain locations. Furthermore, a substantial amount of energy is still to be dissipated at the downstream of stilling basin for which flexible aprons are provided. Many researchers have contributed to the design of stilling basins, and some of the most relevant studies are mentioned here. Bantacut et al. (2022) conducted experiments to investigate the energy dissipation in USBR-IV stilling basin, and modified the shape of energy dissipators, floor elevation, end threshold, and riprap length. Results showed that compared to energy dissipation values of 89.5 and 77.7% in the original stilling basin, the modified stilling basin dissipated more energy up to 98.4 and 84.8% for the discharges of Q₂ and Q₁₀ scenarios. Aydogdu et al. (2022) used ANSYS Fluent software to investigate the different shapes of central sills in the expanding stilling basin and the results of numerical models were validated by the laboratory experiments.

Ali & Kaleem (2015) investigated the performance of energy dissipation for stilling basins of Tuansa Barrage, Punjab, Pakistan, before and after remodelling. The study concluded that remodelling of the stilling basin was not rational which caused the launching of the stone apron and was responsible for the drifting of the river towards the left side of the barrage. Chaudhry (2010a) studied and reviewed the performance of Taunsa Barrage stilling basins for various discharges and tailwater levels (TWLs). The results indicated that TWLs for the old barrage design were adequate for the formation of hydraulic jumps. The study concluded that the stilling basins before and after remodelling had distinct hydraulics and flow behaviour. Chaudary & Sarwar (2014) reviewed and analyzed the hydraulics of Taunsa Barrage stilling basins for designed and altered TWLs. The study showed that remodelled stilling basin is dissipating less energy than the old basin and also indicated that the available TWLs were appropriate for hydraulic jumps. Results further showed that the construction of sub weir downstream of the main weir caused sedimentation between the two structures.

Numerical models are developed and implemented to investigate the complexity of spatial flow and are considered as a powerful tool to improve the stilling basin designs and performance. Recently, the developments in the information and computer technology have allowed the hydraulic engineers to address the problems, mainly by the use of turbulence models (Siuta 2018). These turbulence models (Carvalho et al. 2008) not only investigate the flow characteristics in the stilling basin but also have the ability to test the internal structure of the many important phenomena such as hydraulic jump and air entrainment (Chanson & Gualtieri 2008). The two equations turbulence models, i.e., Standard k–ε, Renormalization Group (RNG-k–ε), and hybrid models are very useful to model the complex flow behaviours (Wang et al. 2016) that cannot be measured through physical experiments. In recent times, FLOW-3D, Fluent-CFD, and Open Foam are useful software that use the above-mentioned turbulence models to investigate the performance of the hydraulic structure. These software divide the flow domain into grid blocks and resolve the geometry by discretization of the Navier–Stokes equation for each computational cell (Bayon-Barrachina et al. 2015). A few of the most recent numerical studies on the hydraulic jump and flow behaviour in different types of stilling basins are highlighted here.

Bayon-Barrachina & Lopez-Jimenez (2015) used OpenFoam numerical models to investigate the various characteristics of classical hydraulic jump in rectangular prismatic channel. Mukha et al. (2022) used OpenFoam to investigate the characteristics of classical hydraulic jump and used the Large Eddy Simulation (LES) model for the investigation of various hydraulic parameters and compared the results with Direct Numerical Simulation (DNS). Nikmehr & Aminpour (2020) used FLOW-3D models to investigate the effects of hydraulic jump on the rough bed and validated the outputs with the experimental data. Mirzaei & Tootoonchi (2020) conducted experiments to investigate the effects of sluice gate and bump on the characteristics of the hydraulic jump for various hydraulic conditions and validated the results using FLOW-3D. Macián-Pérez et al. (2020) analyzed the structural properties of the hydraulic jump such as the hydraulic jump shape, the free-surface profile (FSP) and the sequent depth ratio, and the hydraulic jump efficiency, using FLOW-3D models. Carvalho et al. (2008) used FLOW-3D models to investigate the characteristics of hydraulic jumps and compared the results with experiments. The study used volume of fluid (VOF) and RNG-k–ε models to compute pressure and velocity profiles. Chaudhry (2010b) implemented HEC-RAS to investigate the surface flow analysis in the stilling basins of Taunsa Barrage. The study mainly investigated tailwater, velocity, Froude number, and hydraulic jump location in the original and remodelled stilling basins. Results showed that in the original stilling basin, hydraulic jump locations and velocities were within the safe limits while in the remodelled stilling basin the flow depths became high which moved the hydraulic jump up on the glacis.

In Pakistan, barrages play a vital role to provide water to thousands of hectares of fertile land. Several barrages have suffered from aging, hydraulic, structural and sedimentation/retrogression problems. These problems have endangered some barrages and headwork, and even threatened their overall stability (Icr 2010). Taunsa Barrage, in Punjab, Pakistan, is one of the important diversion structures on the mighty Indus River. It was initially, a modified United Stated Bureau of Reclamation (USBR) type-III stilling basin was constructed for the design discharge of 28,313 m³/s. Soon after the completion, the barrage faced many problems, and after so many partial repairs, the barrage was rehabilitated from 2005 to 2008. Under rehabilitation, the stilling basin of the barrage was remodelled and some geometrical changes were made in the basin. Based on the bibliographical analysis, only a few (Chaudhry 2010a, 2010b; Chaudary & Sarwar 2014; Ali & Kaleem 2015) have studied the hydraulics of Taunsa Barrage stilling basins before and after rehabilitation. These studies have reviewed the previous reports and studied the effects of TWLs in the two different stilling basins. Additionally, in general, the above-mentioned literature indicated that after remodelling the barrage's stilling basin, the stone apron and inverted filter blocks washed away. However, the literature lacks to show the quantification of various hydraulic parameters such as FSP, flow depth, velocity profile, roller lengths of hydraulic, hydraulic jump efficiency, and turbulence kinetic energy in two different stilling basins of this barrage. Therefore, the present study aimed to investigate the flow behaviour for 44 m³/s (gated flow) within the stilling basins of Taunsa Barrage before and after remodelling using FLOW-3D numerical models. The study mainly investigated and compared the effects of changes in tailwaters on the hydraulic parameters such as FSPs, flow depth, Froude number, roller lengths of a hydraulic jump, velocity, hydraulic jump efficiency, and turbulent kinetic energy (TKE) in the two different stilling basins.

The barrage had a stilling basin similar to the USBR stilling basin type-III that consists of two rows of baffle and friction blocks. These auxiliary devices facilitate to dissipate the excessive kinetic energy, enhance turbulence, and stabilize hydraulic jump even in case of less tailwater. The barrage supplies water to 951,400 ha and diverts flows from the River Indus to the River Chenab through a Taunsa Panjnad Link Canal. The Barrage also works as an arterial road bridge, a railway bridge, crossing for gas, oil pipelines, telephone lines, and extra high voltage (EHV) transmission lines.

Soon after construction, in 1958, the barrage started facing multiple problems like oblique right-sided river approach caused heavy siltation in Dera Ghazi Khan Canal with the reduction in its capacity, extreme retrogression of water levels on the downstream, damage to stilling basin floor, and defects were developed in mechanical installations. During 1959–1962, repair works were carried out to cater to the problems mentioned above, but problems remained persistent. To resolve these issues, Punjab Government constituted committees of experts in 1966 and 1973, but no specific measures were taken and the issues continued to aggravate.

In the old stilling basin, the floor level of stilling basin was 126.79 m while after rehabilitation the floor level was changed to 127.10 m. In both the stilling basins, the crest of the weir was fixed at 130.44 m. The upstream and downstream glacis slopes were kept at 1:3 and 1:4 (H:V), respectively. In the old stilling basin, the first row of the baffle block was placed 14.63 m away from the weir crest. The length and height of the baffle blocks were 1.37 m while its width was 1.22 m which were placed in a staggered position. The overall distance between the two rows of baffle blocks was 1.37 m. The top width of the baffle block was 0.46 m which was angled at 45° from its rear end. Additionally, in the old stilling basin, two staggered rows of friction blocks were also placed at 28.95 m from the weir's crest. The overall length, width, and height of friction blocks were 1.37, 1.22, and 1.37 m, respectively, while the top surface of the friction block was similar to its bottom. In the new stilling basin, chute blocks were placed at the downstream glacis while a dentated sill in replacement of friction blocks was fixed at the end of the stilling basin. The length of the chute block was 4.82 m while its width and height were 1.70 m. The top surface of the chute blocks was 5% inclined in the flow direction. The distance between the two chute blocks was 3.45 m. A 1.52-m high dentated sill was placed along the width of the modelled bay. The top width of the sill was 0.30 m while its upstream and downstream faces were sloped as 2:1 (H:V). The overall width of the modelled bay was 18.29 m.

FlOW-3D software, is considered one of the most powerful tools for three dimensional (3D) flow analyses of hydraulic structures. The model uses numerical techniques to solve the equations of motion. The geometry of the solid and flow domain is divided into rectangular structured grids. These grids are easily developed and store important information on cell faces & nodes. Within these grids, specific numbers are assigned to each cell in all directions, I in the x-direction, j in the y-direction, and k in the z-direction. The fundamentals of finite difference and finite volume methods were also developed on such grids. These techniques have become the centre for FLOW-3D development. In FLOW-3D, finite volume method is used that holds all properties of fluid, derived directly from the conservation laws. The governing equations used in FLOW-3D for free-surface tracking and turbulence modelling are presented in Supplementary material, Annex A.

Models geometries were prepared in AutoCAD and converted into stereo-lithography file (.stl file). Before importing the geometries in FLOW-3D, errors were removed with the help of Netfabb software (recommended in FLOW-3D Manual) structured hexahedral meshes were used to resolve the geometries.

A single mesh block of 55.47 m long, 20.42 m wide, and 10 m high was implemented. Initially, the coarse mesh of 0.50 m was applied to resolve the geometries, but some of the model components were found unresolved. Gradually reducing the mesh size to 0.168 m, the geometry showed an appropriate resolution to run the simulation.

In total, 2,697,420 cubic mesh cells were used for solid and flow domains. The details of other indicators for mesh quality are presented in Table 1. Table 2 shows the summary of numerical methods used for the present models.

Table 2

Summary of setup for numerical models

Sr. no. .	3D modelling method .	Model setup .	Sr. no. .	3D modelling method .	Model setup .
1	Meshing	3D structured cubic cell	4	Advection scheme	Explicit second order limited
2	Turbulence model	RANS RNG-k–	5	Multiphase treatment	VOF with one fluid
3	Solid contours	Wall boundary	6	Free-surface tracking	Donor–acceptor method

Sr. no. .	3D modelling method .	Model setup .	Sr. no. .	3D modelling method .	Model setup .
1	Meshing	3D structured cubic cell	4	Advection scheme	Explicit second order limited
2	Turbulence model	RANS RNG-k–	5	Multiphase treatment	VOF with one fluid
3	Solid contours	Wall boundary	6	Free-surface tracking	Donor–acceptor method

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In field, barrage gates are not opened on the same levels and the openings of gates are set according to the flows. For the study, only one bay of the barrage is modelled and the total model length is 55.4 m, out of which 38.10 m comprises downstream. For reproducing the field condition, initially, the models were set for free flow analysis, and H_e/H_d = 0.998 (Savage & Johnson 2001; Johnson & Savage 2006; Gadge et al. 2018) was implemented, whereas H_e and H_d are effective and designed heads, respectively. For the designed discharge of studied barrage, the models were operated on 135.93 and 133.80 m ponds and TWLs, respectively. Furthermore, the models were also operated at three different TWLs, i.e., 129.10, 129.70, and 130.30 m.

The accuracy of numerical models' was checked by comparing the designed and gated discharges with the models values. For designed flow discharge in the old stilling basin, the numerical model produced 440.5 m³/s discharge that underestimated only 0.79% discharge compared to the designed value of 444 m³/s. However, in the new stilling basin, this error increased up to 0.89%, that produced 440 m³/s discharge. For gated flow in the old stilling basin, the model produced 0.32% higher discharge compared to orifice discharge of 44 m³/s. However, in the new stilling basin, the model underestimated the discharge up to 1.2%. These validation results indicated that the present numerical models using FLOW-3D have produced acceptable results, and allowed for further analysis of hydraulic jump characteristics in the stilling basins under study. The results of different characteristics of hydraulic jump in the two stilling basins are presented in Table 4.

Results of FSPs of hydraulic jumps at different tailwater in the new stilling basin are shown in Figure 9(b) which show a different pattern compared to the old stilling basin. Near the jump initiating location, the profile matched with the previous studies (Bayon-Barrachina & Lopez-Jimenez 2015; Wang & Chanson 2015) but as the distance from jump initiating location increased FSPs showed large deviations up to the jump termination point. After the jump, the FSP was found close to the Wang & Chanson (2015) experiment. Figure 9(b) also shows that as the TWLs in the new stilling basin increased, the FSP also increased which showed a curve pattern. Additionally, the FSPs of hydraulic jumps in the new stilling basin also showed deviation from the numerical study of (Bayon-Barrachina & Lopez-Jimenez (2015) and experiments of Wang & Chanson (2015). The reason for such deviation was the removal of stilling basin appurtenances such as baffle and friction blocks which normally stabilize the hydraulic jump.

On the other hand, in the new stilling basin higher velocities were found on the basin's floor and travelled halfway in the basin, as shown in Figure 16(c). From Figure 19(b) and 19(c), it was noted that as tailwater increased in the old stilling basin, the velocities in the basin reduced, and the roller lengths region produced lesser negative velocities. However, as tailwater increased the recirculation region increased, producing higher negative velocities, and in the lower zones of fluid near the floor, the velocities were higher than the old stilling basin.

Figure 18(b) illustrates the comparison of hydraulic jump efficiency with the previous numerical and experimental studies. Models' results in the two stilling basins showed that as the TWL increased the hydraulic jump efficiency was found reduced from with previous studies. However in the old stilling basin, at the lower tailwater, i.e., 129.10 m, hydraulic efficiency was in good agreement with the numerical results of Bayon-Barrachina & Lopez-Jimenez (2015) and difference of results were only up to 3.5%. However, in the new stilling basin, the difference reached up to 5%. Results comparison with the experiments of Kucukali & Chanson (2008) showed that in the old stilling basin the present model at 129.10 m tailwater produced acceptable result of hydraulic efficiency which underestimated only 7.9%. However, the errors increased in the new stilling and reached to 9.6%. Similarly, the comparison with Wu & Rajaratnam (1996) experiments that the presents underestimated hydraulic efficiency up to 9.4 and 11% in the old and new stilling basins, respectively. Overall, it was found that the present models at lower tailwater produced acceptable accuracy of hydraulic jump with the previous studies, however much deviation were seen the higher tailwater. Compared to the old stilling basin, models' results in the new stilling basin were more deviated from the previous studies as shown in Figure 18(b).

The VOF RNG-k–ε (Yakhot et al. 1991) turbulence model was used to obtain the distribution of TKEs within the stilling basins. Figure 19 shows that in all models, the maximum TKEs were found within and foreside the hydraulic jumps in the old stilling basin. After the hydraulic jump, the TKEs declined along the length of stilling basins. The flows near the foreside of the stilling basin were found strongly turbulent, dissipating most of the kinetic energies. The effects of stilling basin appurtenances were prominent in dissipating the upstream kinetics energies of the hydraulic jump. After the hydraulic jump and baffle blocks rest of the energy was dissipated by the friction blocks, but the energy dissipation process was very weak at the end of the stilling basin. The results showed that at 129.10 m tailwater, in the supercritical flow, the TKE reached 5 m²/s² as shown in Figure 19(a). However, as the flow proceeded to the hydraulic jump, the TKE increased to 5.2 m²/s². After the hydraulic jump, the TKE was reduced to 2.9 m²/s² in the subcritical flow. At 129.40 and 130.30 m TWLs, the maximum kinetic energies were 4.2 and 4.9 m²/s², respectively, as shown in Figure 19(b) and 19(c).

In the new stilling basin, the maximum TKEs were found in the central region of the hydraulic jump and decreased after the hydraulic jump. At 129.10 m TWL, 4.9 m²/s² value of TKEs were produced in the new stilling basin. These values were found high in the middle region of the hydraulic jump and were found higher than the upper and lower zones. Compared to the old stilling basin, the new stilling basin has allowed the TKE in the forward region of the stilling basin, as shown in Figure 19(d). After the hydraulic jump, the TKE was reduced but found more than the old stilling basin. The results further revealed that the high TKEs travelled downstream of the stilling basin and slightly reduced above and behind the end sill. At 129.70 and 130.30 m TWLs, the maximum TKEs were in the hydraulic jumps and reached up to 6.6 and 4.8 m²/s², respectively, as shown in Figure 19(e) and 19(f). The results further indicated that the new stilling basin had produced more TKEs in the basin, which travelled downstream. On the other hand, in the old stilling, at higher TWLs, more energy was dissipated in the foreside of the stilling basin within the hydraulic jump and allowed less energy to travel downstream.

The present numerical study was carried out to investigate the hydraulics of the Taunsa Barrage's stilling basins before and after its remodelling. During the remodelling process, the stilling basin geometry was altered, in which baffle & friction blocks were replaced with chute blocks and end sill. FLOW-3D models were developed to investigate the hydraulic jump and flow characteristics such as FSP, flow depths, Froude number, roller lengths, longitudinal velocity, hydraulic jump efficiency, and TKE for a gated flow of 44 m³/s. The VOF and RNG-k– models captured the free surface and turbulence. The following conclusions are drawn from the study:

• In the old stilling, the numerical model underestimated the discharge (440.5 m³/s) nearly by 0.79% error as compared to the design discharge of 444 m³/s. However, in the new stilling basin, for the free flow analysis, the error in the discharge measurement was 0.89% (440 m³/s). For a gated flow of 44 m³/s, FLOW-3D models showed 0.32 and 1.2% errors in old and new stilling basins, respectively.

• At the investigated tailwaters, the locations of the hydraulic jumps in both stilling basin were noticed on the glacis. However, in the new stilling basin, the hydraulic jump moved up on the glacis at lower tailwater.

• Results of FSPs and flow depths in both the stilling basin revealed that in the new stilling basin the elevations of the free surface and flow depths were found high at all the investigated tailwaters, i.e., 129.10, 129.70, and 130.30 m. In the old stilling basin, the coefficient of determination (R²) for dimensionless FSPs and their comparison to the previous numerical and experimental studies, reached 0.97 at 129.10 m tailwater. For the other tailwaters in the old stilling basin, the FSPs at the jump initiation point and in the subcritical region after hydraulic jumps were close to the previous studies while much deviation was noticed in the region of hydraulic jump. However, for all the investigated tailwaters in the new stilling basin, a curve pattern of FSPs was noticed which deviated from the previous studies. At 130.30 m tailwater, in the new stilling basin after the hydraulic jump, the FSP was found close to the compared experimental study.

• In the old stilling basin, sequent depths were increased as the tailwater increased and reduced the initial Froude number (Fr₁). Conversely, in the new stilling basin, as the tailwater increased, the sequent depths and Fr₁ also increased. In the old stilling basin, comparison of sequent depths at 129.10 m tailwater agreed well with the previous experiments and numerical data. On the other hand, in the new stilling basin with chute blocks and dentated sill, the sequent depths deviated from the previous studies. In the old stilling basin, a linear trend of tailwaters against Fr₁ was noticed while in the new stilling basin a relative weak trend was observed.

• In the old stilling basin, the dimensionless roller lengths of hydraulic jumps were less than the roller lengths in the new stilling basin. Results revealed that due to removal of baffle blocks in the new stilling basin, the roller lengths of hydraulic jumps were not controlled and become larger with an increase in tailwater. At the lower tailwater (129.10 m) in the old stilling basin, the dimensionless roller lengths were found less than the compared experimental and numerical studies while at 130.30 m TWL, the roller length was found closer to previous experimental and numerical studies. Additionally, in the old stilling basin, a direct correlation of roller lengths against tailwaters was observed. On the other hand, at the lower tailwater (129.10 m) in the new stilling basin, the roller lengths of hydraulic jump were found less than those found in the literature. At higher tailwaters large roller lengths were observed which deviated from the compared experimental and numerical studies.

• In both the stilling basins, a maximum value of longitudinal velocity was observed in the supercritical regions which reached up to 10.7 and 11 m/s in old and new stilling basins, respectively. The maximum values of negative velocities were observed in the roller region of hydraulic jumps which reached up to 3 and −2.4 m/s in new and old stilling basins, respectively. Additionally, at all the investigated tailwaters, high velocity flows were observed at the floor in the new basin compared to the old stilling basin.

• In both the stilling basins, minimum difference of hydraulic jump efficiency was found at tailwater of 129.10 m; that efficiency was 56 and 55% for old and new stilling basins, respectively. At all other tailwaters, the deference of efficiencies between old and new stilling basins was much more reaching up to 5%. In the old stilling basin, a strong correlation of hydraulic efficiency with the investigated tailwaters was observed which showed a linear trend. On the contrary, relatively a weak correlation of hydraulic jump efficiency with tailwaters was seen in the new stilling basin.

• In both the stilling basins, the maximum values of TKE were found in supercritical and hydraulic jump regions. Results showed that flow in the hydraulic jump region was turbulent and the turbulent energy started decaying after the hydraulic jump to the end of the stilling basin. In the old stilling basin at 129.10 m tailwater, the maximum TKE was 5.2 m²/s² which reduced as the tailwater increased. In the old stilling basin, the maximum turbulent dissipate rate was found in the region of baffle and friction blocks. Conversely, in the new stilling basin, as the tailwater increased more turbulent flow was developed and maximum TKE reached up to 6.8 m²/s², at 129.70 m tailwater. In the new stilling basin, 2D analysis revealed higher amount of TKE at the end of basin.

In conclusion, based on the results of hydraulic parameters in the new stilling basin, the study suggests to investigate the flow characteristics by implementing other discharges, TWLs and turbulence models. To further investigate the performance of the new stilling basin, the study suggests to include erodible bed downstream of the rigid floor.

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.