Keywords

1 Introduction

Energy dissipation is not only required at downstream of the spillway of a dam and barrage but also an important phenomenon to prevent erosion at canal outlets and culvert outlets [1]. This is crucial for effective water resources planning and management, which is emphasized in most countries of the present world [2,3,4]. The failure or damage of many culverts, pipe outlets, and detention basin outlet structures is caused by unchecked erosion. Energy dissipators are structures designed to protect downstream areas as well as drainage structures from erosion and scouring by causing energy losses and reducing the velocity of flow to acceptable limits. One such structure known as the USBR type VI impact basin was developed at the US Bureau of Reclamation laboratory in 1957 [5]. The basin is contained in a box-like structure, which is relatively small and does not require any tail-water to perform successfully. Energy dissipation takes place as flow strikes the vertical portion of the hanging baffle and then deflected upstream by the horizontal portion of the baffle and finally hitting the floor, thereby creating horizontal eddies [6].

An experimental study to reduce scour at downstream and to shorten the basin length of USBR type VI impact stilling basin was carried out by Goel and Verma [7]. For this, various experiments were performed in laboratory with Froude number ranges from 1.70 to 5.50. Wedge shape splitter blocks, end sill, and baffle wall of different sizes were used at different locations from pipe outlet. It was concluded that new models developed performed better than typical USBR type VI and also the length of the basin reduced to 25% with smaller tail-water depth.

Tiwari and Goel in their experimental study carried out 57 tests in laboratory for the enhancement of energy dissipation caused by impact stilling basin [8]. These experiments were performed to find out the effect of size, shape, and position of impact wall and gap between impact wall and basin floor. The performance was evaluated in terms of the performance index. The indices are simple techniques and widely used in water resources for assessing the performance or specific characteristics [9,10,11]. All the dimensions of the impact stilling were calculated in terms of equivalent diameter (d). It was concluded that size, shape, and location of impact wall affect the flow condition which ultimately affects the scour downstream of the basin. Higher the perform index higher the energy dissipation, and the highest performance index was observed with impact wall of size 1.5d × 3d at a distance of 4d from the pipe outlet with length of basin reduced up to 30% as compared to USBR type VI stilling basin and with a gap of 1d between wall and basin floor.

Modeling and analysis of impact stilling basin has been done in ANSYS Fluent software [12]. This software uses numerical methods like finite element analysis (FEA) for simulation purposes. The process of numerical simulation involves three basic steps, viz. preprocessing, solver, and post-processing. The R15.0 version of ANSYS workbench is used which has its own software for drawing of geometry, i.e., design modular.

Reference Stilling Basin Model

Based on the experimental study carried out by previous studies [7, 8, 13, 14], six different models were developed and analyzed in ANSYS Fluent software in order to find the best model for energy dissipation downstream of a rectangular pipe outlet. These models were tested for three different scenarios, namely for Froude number = 1.85, 2.85, and 3.85, respectively, and the performance of stilling basin was evaluated by computing and comparing different parameters, viz. turbulent kinetic energy at outlet, kinetic energy and specific energy losses, and wall shear stress at outlet for different models in different scenarios. A general schematic diagram of stilling basin model is shown in Fig. 1 on which all the models were developed and analyzed in ANSYS.

Fig. 1
figure 1

Side view of the general basin model having dimensions in terms of equivalent diameter ‘d’. Note: This figure is modified version of the original figure proposed by Tiwari and Goel [8]

Full size image

2 Modeling in ANSYS

2.1 Calculation of Equivalent Diameter and Inlet Velocity

Equivalent diameter (d) is the most important parameter for designing an impact stilling basin as the dimensions of the basin (as well as model) is computed in terms of ‘d’ (see Fig. 1). If the pipe outlet is circular in shape, the diameter of pipe outlet is taken as ‘d’, but if the shape is rectangular or any other polygon, ‘d’ is calculated by equating the area of that polygon to a circle. Say, for a rectangular inlet, ‘d’ is calculated as the square root of (\(4*A/\pi\)), where A is the area of rectangle. In this study, rectangular pipe of size 10.8 cm × 6.3 cm is used for analysis, therefore for each model the value of d is fixed as 9.3 cm.

The Froude number (Fr) at the pipe outlet is defined as Fr = V/(gd)1/2, where V = velocity in m/s; g = acceleration due to gravity in m/s2, and d = diameter of the pipe. Therefore, for Fr = 1.85, 2.85, and 3.85, the inlet velocity is computed as 1.767 m/s, 2.722 m/s, and 3.677 m/s, respectively.

2.2 Geometry

In this study, there are total six different models of impact stilling basin whose geometry has been drawn in design modular. All the models are drawn in shape of a rectangular box with length = 7d (65.1 cm), width = 6.3d (58.6 cm), and height = 5.2d (50 cm) where ‘d’ is the equivalent diameter of pipe outlet (d = 9.3 cm).The geometry of six different models is shown in Fig. 2, and details of each model are given in Table 1.

Fig. 2
figure 2

Geometry of model M-I to M-VI drawn in design modular

Full size image
Table 1 Various models designed in design modular by ANSYS Fluent software
Full size table

2.3 Meshing

The meshing has been done in ICEM CFD software which is a part of ANSYS workbench. The meshing details of all the six models have been kept same. Tetrahedron method is used in assembly meshing with maximum eight inflation layers and growth rate of 1.4. Figure 3 shows the meshed model of the impact stilling basin.

Fig. 3
figure 3

Mesh diagram drawn in ICEM CFD

Full size image

2.4 Boundary Condition in Fluent Setup

The following steps are followed to set up the Fluent software for analysis: (1) In Fluent launcher 3D, double precision and serial processing option is selected and setup is started. In General tab, pressure type solver, absolute velocity formulation, transient time, and direction of gravity in −ve Y-direction are selected. (2) Then in Models tab, multiphase, number of Eulerian phases 2, implicit scheme, and ‘k–ε’ viscous model are selected. (3) In the third tab, fluid from materials is selected, as air is already present new fluid water-liquid is added from database of ANSYS. Thereafter, primary phase (i.e., Phase I) to air and secondary phase (i.e., Phase II) to water are assigned. (4) Thereafter, boundary conditions and initial conditions are entered, inlet is taken as velocity inlet and velocity of flow entering the basin is entered and ‘intensity and hydraulic diameter’ specification method is chosen. Also Phase II volume fraction is taken as 1 to insure only water entered from the inlet. Outlet is taken as pressure outlet. (5) The solution is initialized using hybrid initialization method and after that liquid region is patched using patch option which ensures that at the start of the simulation which portion is filled with water and which portion of basin is filled with air. (6) The last step is running simulations where time step size 1 s, number of time steps 40, and maximum iteration per time step 5 are entered and simulations are allowed to run.

3 Results and Discussion

After simulations are run for each model, the software builds stream lines plot for every model (Fig. 4) showing the simulated flow of water through the stilling basin especially after the water strikes the impact wall. As the distance between impact wall and inlet increases from 2d (18.6 cm) to 4d (37.2 cm), gap between impact wall and basin floor increases from 0.5d (4.65 cm) to 1.5d (13.95 cm).

Fig. 4
figure 4

Stream lines plot for each model (first row for the models M-I, M-II, and M-III corresponding to Fr = 1.85, second row corresponding to Fr = 2.85, and third row corresponding to Fr = 3.85; fourth row for the models M-IV, M-V, and M-VI with Fr = 1.85, fifth row corresponding to Fr = 2.85, and sixth row corresponding to Fr = 3.85)

Full size image

The stream line plots from Fig. 4 give an idea of the velocity as well as the energy of the flow. The yellow and red color of stream lines denote high velocity, whereas blue and indigo colors signify low velocities; it also depicts the formation of eddies after the water strikes the impact wall as the distance between inlet and wall; the gap between basin floor and wall increases. Changes in the color of stream lines signify energy loss. Even though the stream line plots gave an idea about the energy losses and velocity vectors but the clear idea can only be known by computing the actual values of turbulent kinetic energy (TKE), kinetic energy (KE) and specific energy (SE) losses, and wall shear stress (WSS) at outlet. The results obtained from the analysis by Fluent are presented in Fig. 5 in the form of bar graphs comparing values of TKE, SE and KE losses, and WSS for different models with Froude numbers of 1.85, 2.85, and 3.85.

Fig. 5
figure 5figure 5

TKE, WSS, and the change in KE and SE between inlet and outlet for different models (M-I to M-VI) at different Fr (i.e., 1.85, 2.85, and 3.85)

Full size image

From Fig. 5, the following observations can be made:

For M-I model, the average as well as maximum value of TKE (in m2/s2) at the outlet of basin is highest (0.08 for Fr = 1.85, 0.104 for Fr = 2.85, and 0.126 for Fr = 3.85). This is because the impact wall is so close to the inlet that the jet of water strikes with more power causing more turbulence, which leads to the formation of horizontal as well as vertical eddies. This can be checked by seeing the stream lines for M-I, M-II, and M-III model. For low Froude number (1.85), this effect is more prominent, but as the value of the Froude number increases (Fr = 3.85), this effect lessens.

For M-III model, the value of shear stress (in Pa) at bottom outlet is least (5.43 for Fr = 1.85, 5.52 for Fr = 2.85, and 6.26 for Fr = 3.85), and for M-I model, it is highest (5.61 for Fr = 1.85, 6.19 for Fr = 2.85, and 6.95 for Fr = 3.85). This may be because of the stream lines of the jet of water are partially hitting the wall causing more portion of jet to pass between the gaps, hence causing more shearing. This effect is more prominent for high values of Froude number.

Kinetic energy as well as specific energy loss (in m) is highest in case of M-III model (0.127 for Fr = 1.85, 0.331 for Fr = 2.85, and 0.634 for Fr = 3.85) and lowest in case of M-I model (0.109 for Fr = 1.85, 0.317 for Fr = 2.85, and 0.618 for Fr = 3.85). This may be attributed to the shearing effect and because eddies formation at the outlet is least in case of M-III model. The inferences are in agreement with the previous experimental study [8, 14].

For M-V model, the gap between the impact wall and basin floor is least (i.e., 0.5d); hence, the shearing area is least which causes value of TKE and WSS at outlet bottom to be more than other models (M-III, M-IV, and M-VI). But the value of above two parameters is least for M-III model and not M-VI model. This may be because as gap between impact wall and basin floor increases beyond 1d the jet of water that flows between this gap gets shear form one side only as the bottom portion of the wall not able to apply shear to the jet floe which can be seen from the stream lines plot.

4 Conclusion

From the different model simulations of impact stilling basin through ANSYS Fluent software, the model M-III (impact wall size 1.5d × 3d, the distance between inlet and impact wall = 4d, and a gap of 1d between the basin floor and the wall) can be concluded as the best option. It produces less turbulent kinetic energy, less outlet velocity, less shear stress at the bottom outlet, and more energy losses, which lead to lesser chances of scouring in the downstream of the end sill.