# Numerical Analysis of Pressure Profiles and Energy Dissipation across Stepped Spillways Having Curved Risers

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## Abstract

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^{3}/s followed by the model calibration. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the stepped spillway. It was estimated that curving the risers increases the energy dissipation up to three percent for lower flow rates, whereas it has no significant impact on energy dissipation for higher flow rates. It was found that in simply stepped spillway lower steps dissipate more energy as compared to curved risers stepped where energy dissipation is shifted to higher steps. On the other hand, curved risers stepped spillways showed lower values of negative pressures as compared to the simply stepped spillway. It was seen that a higher energy dissipating step as experienced more negative pressures as compared to the lower energy dissipating step.

## 1. Introduction

- (1)
- To estimate the total energy dissipation, energy dissipation distribution, and pressure profiles along the curved surface of the steps of the stepped spillway models (with curved risers) and along the vertical surface of steps for simple stepped spillways models under the skimming flow regime of flow.

^{3}/s.

## 2. Materials and Methods

#### 2.1. Model Validation

^{3}/s. The same model geometry was constructed in SOLIDWORKS software package and was named as Model 1. The geometry file was imported to numerical solver software package FLOW 3D. Grid Sensitivity analysis was performed at step no. 13 (for which the results are discussed later). Different mesh sizes 20 mm, 15 mm, 10 mm, and 5 mm were opted to run the simulation. It was 5 mm mesh which gave the lowest error (less than 10%) when the values were compared to experimental results for step no. 13 taken from [14].

#### 2.2. Modelling of the Spillways

#### 2.3. Properties of Model

#### 2.4. Boundary Conditions

#### 2.5. Flow 3D FEA Numerical Modelling

#### 2.5.1. Mass Continuity Equation

#### 2.5.2. Momentum Equation

#### 2.5.3. RNG k-ε Turbulence Model

#### 2.5.4. VOF Model

#### 2.5.5. Air Entrainment Model

#### 2.5.6. Density Evaluation Model

#### 2.5.7. Drift Flux Model

#### 2.6. General Simulation Setup

#### 2.7. Methodology Limitation

## 3. Results

#### 3.1. Model Validation

^{3}/s as used by the paper. Two parameters pressure profiles and free surface elevation were compared with results from [14] to look for the validity of the model. The same sub models that are given in Section 2 were adopted in FLOW 3D. To get a promising mesh size, grid sensitivity analysis was performed at step no. 13, as shown in Figure 5. We found that 20 mm mesh size gave the maximum error (more than 50%), while the error was less than 10 percent when the 5 mm mesh size was adopted. Therefore, for the further validation same 5 mm mesh size was adopted.

#### 3.1.1. Pressure Profiles

#### 3.1.2. Free Surface Elevation

#### 3.1.3. Pressure Profiles

^{3}/s. The pressure decreases along the vertical surface of the steps in the case of vertical riser and eventually becomes negative near the tip. This produces cavitation, which in real spillway cause damages to spillway [27]. This behavior of pressure profiles along the vertical surface of the steps have been studied by many researchers, such as [23]. The reduction in the negative pressure along the vertical surface of the steps will show a reduction in cavitation. Therefore, many researchers have tried different techniques to counter that pressure reduction. Curved risers as presented in the plots from 9 to 13, encounter fewer negative pressures as compared to simple stepped spillways. This reduction in negative pressures as compared to simple stepped spillways and previous studies [16,17,18] will reduce the cavitation damage.

#### 3.2. Total Energy Dissipation

^{3}/s.

#### 3.3. Energy Dissipation Distribution

## 4. Conclusions

- Total energy dissipations and pressure profiles were calculated for each of simulation. No increment in energy dissipation was obtained expect for lower flow rates like 0.020 m
^{3}/s where it increased to three percent in curved risers stepped spillways as compared to simple stepped spillways. - In a simple stepped spillway, the lower steps, such as step nos. 12, 13, and 14 were dissipating more energy as compared to higher steps. Moreover, this shifted to higher steps in the case of stepped spillways having curved risers.
- Pressure profiles, along the vertical surface of steps in the case of simple stepped spillways, and along curved risers in the case of curved stepped spillways, showed that simple stepped spillway possess more negative pressure values as compared to curved stepped spillways. This can cause more cavitation in the case of simple stepped spillways as compared to curved stepped spillways, when the local pressure across the step face decreases less than the vapor pressure of water.

#### Police Recommendations

- This research was conducted through the latest CFD commercial code FLOW3D. Though the calibration process provides enough accuracy through the use of fine grids, there is still possibility for inaccuracies. The finer meshing and the use of second-order advection options can be utilized in FLOW3D to find inaccuracies.
- Spillway models with curved risers demonstrate an increment of three percent energy dissipation for lower flow rates. These types of spillways can be utilized for dams that are subject to continuous low emissions. Compared with a simple stepped spillway, the curved risers efficiently diminish material costs and allow more energy dissipation.
- Spillways with curved risers do not significantly increase energy dissipation for high flow rates. Compared with simple stepped spillways, they dissipate almost the same amount of energy. It is important to use these types of flow rates instead of simple stepped spillways because they can save material costs, but can dissipate the same amount of energy.
- Cavitation is an important parameter studied by dam spillway researchers. The spillways of many dams have been damaged by cavitation. Current research has identified that simple stepped spillways have more negative pressure than spillways with curved risers. The practical use of stepped spillways with curved risers can reduce the possibility of cavitation because they dissipate the same amount of energy.
- The present research shows that the steps that consume more energy are experiencing more negative pressure. Thus, specific steps that dissipate more energy are more susceptible to cavitation. The energy dissipation distribution of the steps can be used to analyze the number of steps that consume more energy and endure more negative pressure. This fact is very useful in a practical sense because more resources can be utilized to build steps that dissipate more energy and are more prone to cavitation than steps that dissipate less energy and are less likely to occur. This can help the design of the spillway in the future, and can stimulate the life of the spillway.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 9.**Pressure profiles for (

**A**) simple stepped, (

**B**) 30°, (

**C**) 60°, and (

**D**) 90° curved risers spillway for the head of 100 mm.

**Figure 10.**Pressure profiles for (

**A**) simple stepped, (

**B**) 30°, (

**C**) 60°, and (

**D**) 90° curved risers spillway for the head of 120 mm.

**Figure 11.**Pressure profiles for (

**A**) simple stepped, (

**B**) 30°, (

**C**) 60°, and (

**D**) 90° curved risers spillway for the head of 160 mm.

**Figure 12.**Pressure profiles for (

**A**) simple stepped, (

**B**) 30°, (

**C**) 60°, and (

**D**) 90° curved risers spillway for the head of 200 mm.

**Figure 13.**Pressure profiles for (

**A**) simple stepped, (

**B**) 30°, (

**C**) 60°, and (

**D**) 90° curved risers spillway for the head of 220 mm.

**Figure 16.**(

**a**).EDD for the Q = 0.042 m

^{3}/s. (

**b**). EDD for the Q = 0.059 m

^{3}/s. (

**c**). EDD for the Q = 0.068 m3/s.

Reference | Author(s) | Country | Type of Spillway Model | Pressure Profiles | Total Energy Dissipation | Energy Dissipation Distribution | Methodology |
---|---|---|---|---|---|---|---|

28 | [1] | Iran | Vertical risers and Horizontal tread | × | √ | × | Physical Modelling/Laboratory setting |

29 | [2] | Algeria | Vertical and Horizontal Tread | × | × | × | Numerical Modelling/Ansys Fluent |

30 | [3] | China | Sky Jump/Vertical risers and Horizontal/Inclined Treads | × | √ | × | Physical Modelling/Laboratory setting |

31 | [4] | Vietnam | Vertical Risers and Horizontal Tread | × | × | × | Physical Modelling/Laboratory Settings. |

32 | [5] | Iran | Sloping steps, Separation between steps | × | √ | × | Physical Modelling & Numerical Modelling. |

27 | [6] | Canada | Smooth and Rough Vertical and Horizontal Treads/Steps with edges | √ | × | × | Numerical Modelling FLOW 3D |

33 | [7] | Thailand | Vertical Risers and horizontal treads | × | √ | × | Numerical Modelling/Physical Laboratory Model. |

34 | [8] | China | Vertical Risers and horizontal treads. | √ | × | × | Numerical Modelling/Physical Laboratory Model. |

35 | [9] | Sweden | V type of steps with vertical and horizontal risers. | √ | √ | × | Numerical Modelling FLOW 3D |

36 | [10] | China | V type of steps with vertical and horizontal risers. | × | √ | × | Numerical Modelling FLOW 3D |

37 | [11] | Iran | Vertical Risers and Pooled horizontal treads. | × | × | × | Numerical Modelling |

38 | [12] | Iran | Vertical Risers and Horizontal Treads. | × | × | × | Artificial Neural Network, Support Vector Machine |

39 | [13] | Germany | Vertical Risers and Horizontal Treads. | × | × | × | Laboratory Experimentation |

40 | [14] | United Kingdom | Vertical Risers and Horizontal Treads. | × | √ | × | Laboratory Experimentation |

This Research Work | Pakistan | Curved Risers and Horizontal Treads with different angle. | √ | √ | √ | Numerical Modelling FLOW 3D, ArcGis |

Items | Description |
---|---|

Location | Taxila on Haro River (Pakistan) |

Catchment Area | 308 square miles |

Design Flood discharge | 166,000 cusecs |

Main Dam type | earth and Rock fill |

Maximum dam height | 167 ft |

No. of spillways | 5 |

Items | Description |
---|---|

Type of spillway | Stepped |

No of steps | 14 |

Maximum design head | 213 mm |

Maximum design discharge | 0.064 m^{3}/s |

Sr No | Part | Model 2 | Model 1 (Validation Model) |
---|---|---|---|

1 | Total Height | 1.06 m | 78.9 cm |

2 | Total Width | 30 cm | 30 cm |

3 | No of Steps | 14 | 13 |

4 | Riser Height | 6 cm | First 5 steps (2, 2.4, 3, 4, and 5 cm) others 6 cm |

5 | Tread length | 5 cm | First 5 steps (1.5, 1.8, 2.25, 3, and 3.75 cm) others 6 cm |

6 | Equation of Crest | y = 2.632x^{1.64} | y = 3.632x^{1.85} |

7 | Tread Shape | Horizontal | Horizontal |

8 | Riser Shape | Vertical/Curved | Vertical |

9 | Slope of spillway | 1 V:0.80 H | 1 V: 0.75 H |

10 | Radius of Bottom Curve | 116 mm | 28 cm |

Sr No | Property | Value |
---|---|---|

1 | Source Material | acrylic |

2 | Specific Gravity | 1.18 |

3 | Refractive index | 1.49 |

4 | Modulus of Elasticity | 450,000 psi |

Riser Type | Q = 0.027 | Q = 0.042 | Q = 0.059 | Q = 0.068 | Q = 0.0208 |
---|---|---|---|---|---|

Vertical | 59.17% | 52.58% | 43.81% | 37.93% | 61.42% |

30° | 59.91% | 52.53% | 42.08% | 36.28% | 64.61% |

60° | 59.99% | 52.33% | 40.12% | 36.11% | 65.48% |

90° | 59.63% | 51.4% | 42.27% | 34.8% | 65.12% |

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**MDPI and ACS Style**

Saqib, N.u.; Akbar, M.; Pan, H.; Ou, G.; Mohsin, M.; Ali, A.; Amin, A.
Numerical Analysis of Pressure Profiles and Energy Dissipation across Stepped Spillways Having Curved Risers. *Appl. Sci.* **2022**, *12*, 448.
https://doi.org/10.3390/app12010448

**AMA Style**

Saqib Nu, Akbar M, Pan H, Ou G, Mohsin M, Ali A, Amin A.
Numerical Analysis of Pressure Profiles and Energy Dissipation across Stepped Spillways Having Curved Risers. *Applied Sciences*. 2022; 12(1):448.
https://doi.org/10.3390/app12010448

**Chicago/Turabian Style**

Saqib, Najam us, Muhammad Akbar, Huali Pan, Guoqiang Ou, Muhammad Mohsin, Assad Ali, and Azka Amin.
2022. "Numerical Analysis of Pressure Profiles and Energy Dissipation across Stepped Spillways Having Curved Risers" *Applied Sciences* 12, no. 1: 448.
https://doi.org/10.3390/app12010448