# Development of a Three-Dimensional CFD Model and OpenCV Code by Comparing with Experimental Data for Spillway Model Studies

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/s flow rate) and the obtained results were compared with experimental observations in the literature. Numerical and experimental results have shown that cavitation occurs after a particular downstream point on the surface, based on cavitation indices.

## 2. Case Study

^{3}, the lake area is 81.86 km

^{2}, and the reservoir volume is 2126 billion m

^{3}. The minimum operating level elevation of the Dam is 115 m, and the maximum operating level elevation is 125 m [29].

^{3}s

^{−1}, has 6 chambers, each of which is 11 m wide, 15.60 m high, and equipped with a radial gate. The discharge channel, which extends downstream of the Ogee crested sill, is 81 m wide, 567 m long, and ends with an energy-dissipating pool. The discharge channel slopes are 0.03 and 0.17 and are connected to a vertical curve (Figure 1) [29].

#### Theoretical Equations of Spillway

_{0}denotes discharge coefficient, L

_{0}denotes effective length of spillway crest or width, and H

_{0}denotes upstream head measured from the crest to the unaffected upstream water stage. Equation (2) is used to determine the effective length L

_{0}. L

_{n}is the net length of the crest, N is the number of piers, K

_{p}and K

_{a}are constants depending on the shape of piers and abutments. In this study, K

_{p}of 0.01 K

_{a}0.1 was used. The discharge coefficient, C

_{0}, uses different values. It is influenced by a variety of factors including the depth of approach, relation of the actual crest shape to the ideal nappe shape, upstream face slope, downstream apron interference, and downstream submergence. The C

_{0}coefficient was calculated as 1.97 for the discharge of Q

_{1000}= 10,055 m

^{3}s

^{−1}.

_{0}= slope of channel. The hydraulic radius is defined by dividing the cross-sectional area of the channel by the wet circumference.

## 3. Experimental Studies

## 4. CFD Model Studies

#### 4.1. Basic Equations

_{i}is the velocity components; x

_{i}is the coordinate components; ρ is the density; µ is the molecular viscosity coefficient; P is the correct pressure; µ

_{t}is the turbulent viscosity coefficient, which can be derived from the turbulent kinetic energy k and turbulent dissipation rates:

_{k}and σ

_{ε}are turbulence Prandtl numbers for the k and ε equation, respectively, σ

_{k}= 1.0, σ

_{ε}= 1.3, C

_{1ε}and C

_{2ε}are ε equation constants, C

_{1ε}= 1.44, and C

_{2ε}= 1.92. C

_{μ}= 0.09 is a constant determined experimentally, as described in [33].

#### 4.2. Volume of Fluid (VOF) Model

_{w}is the volume fraction of water. In each cell, the sum of the volume fractions of air and water is unity. Volume fractions of air, denote by α

_{a}, can be provided as shown in [33]:

#### 4.3. Boundary Conditions for Spillway

^{3}s

^{−1}, the covers were fully opened and the floodwater height was calculated as 25 m in the approach channel. In CFD analysis, this value was adjusted according to the model scale, and the water inlet height was defined as 12.5 cm. In addition, in accordance with the prototype spillway project, the approach channel length was 15 m, and the length between the approach channel and the spillway outlet was 402 m. At the beginning of the approach channel, numerical analysis was initiated with the velocity values provided in Table 2.

_{p}” is the average stream flow velocity at the “p” point; “K” is the von Karman constant (0.418); “y

_{p}” is the distance from point p to the wall; empirical constant “E” has the value of 9.79; and “u

_{*}” is the friction velocity. The “u” uniform velocity distribution is provided to the horizontal velocity component in the x-direction at the inflow boundary. The vertical velocity component “v” in the y-direction is set to zero. The inlet velocity field to the channel consists of a forward “u” horizontal velocity and zero “v” vertical velocities at all points except points close to the channel.

^{+}is a dimensionless distance similar to the local Reynolds number that is often used in CFD to describe how coarse or fine a mesh is for a given flow. It determines whether the effects in cells adjacent to the wall are laminar or turbulent.

_{τ}is the friction velocity, y is the height from the wall to the midpoint of the wall-adjacent cells, v is the kinematic viscosity, τ

_{w}is the wall shear stress, and ρ is the fluid density at the wall. Values of y

^{+}close to the lower bound (y

^{+}≈ 30) are most desirable for wall functions, whereas values of y

^{+}≈ 1 are better for near-wall modelling [37,38].

#### 4.4. Numerical Solver

## 5. Image Processing Studies

#### 5.1. Image Processing: Python-OpenCV

#### 5.2. Motion Detection and Tracking Algorithm

#### 5.3. Experimental Design and Equipment

#### 5.4. Video and Data Processing

## 6. CFD Model Results

^{3}s

^{−1}) transferred the flood discharge downstream safely. Figure 13 shows the general view of the flow resulting from the CFD analysis on the spillway model. When Figure 13 is examined, it is observed that the side walls of the spillway chute channel are sufficient for the flood flow. However, overflows were observed at some points near Cross-section 1 of the separating walls of the chute channel. The velocity and water depth of the physical model and numerical model results are compared in tables, figures, and graphs below. Comparisons, mean absolute error (MAE), root-mean-square error (RMSE), and average percent error (APE) values are calculated and shown in the tables. MAE, RMSE, APE equations provided as:

_{i observed}” is the experiment measured, and “Y

_{i estimate}” is the CFD measured.

#### 6.1. Comparison of Velocity

#### 6.2. Comparison of Water Depth

#### 6.3. Investigation of Pressure in CFD Model

#### 6.4. Investigation of Cavitation on Prototype Spillway

_{T}is the absolute pressure (P

_{a}), including atmospheric pressure; P

_{v}is the vapor pressure of the water (P

_{a}); $\mathsf{\rho}$ is the density; and U is the velocity of the water. The calculated cavitation indices are presented in Table 6. While making the calculations, we considered the average temperature as 20 °C, the vapor pressure (P

_{v}) value as 2338 Pa, and the atmospheric pressure (Patm) as 92,801 Pa. The pressure and velocity values obtained with the model were increased in scale ratio according to Froude similarity and the pressure and velocity values were determined for the prototype spillway.

## 7. Image Processing Results

#### 7.1. Velocity Algorithm Results

#### 7.2. Water Depth Algorithm Results

## 8. Conclusions

- -
- It was observed that both the physical model and the numerical model (10,055 m
^{3}s^{−1}) transfer the flood discharge downstream safely. - -
- The average velocity values measured with the ADV device generally increased along the discharge channel. We observed that the increase in velocity values was low in the cross-sections where the slope was 3%, and the velocity increase was higher in the cross-section where the slope was 17%. The velocity values increased from the wall edges to the center.
- -
- The error rates between the experimental and numerical analysis rates were obtained in Section 3, with the highest APE error percentage value of 13.8, as a result of the examination.
- -
- As a result of the studies, it was determined that the APE error rate between the experimental and numerical analysis’ water depth results was around 1.7–3.8% at most measurement points.
- -
- Cavitation index values were calculated as above 0.2 in all sections of the prototype spillway. Thus, there is no risk of cavitation in the spillway discharge channel.
- -
- It has been observed that the error rate of the water depths obtained with the newly developed float method based on image processing is higher than the simulation results when compared with the experiments.
- -
- With the developed float method, velocity correction coefficients were obtained for the chute spillway depending on the velocity of the floating object.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Willey, J.; Ewing, T.; Wark, B.; Lesleighter, E. Complementary Use of Physical and Numerical Modelling Techniques in Spillway Design Refinement. In Proceedings of the ICOLD, 24th Commission Internationale Des Grands Barrages, Kyoto, Japan, 2–8 June 2012. [Google Scholar]
- Olsen, N.R.B.; Kjellesvig, H.M. Three-Dimensional Numerical Flow Modelling for Estimation of Spillway Capacity. J. Hydraul. Res.
**1998**, 36, 775–784. [Google Scholar] [CrossRef] - Dargahi, B. Experimental Study and 3D Numerical Simulations for a Free-Overflow Spillway. J. Hydraul. Eng.
**2006**, 132, 899–907. [Google Scholar] [CrossRef] - Kumcu, S.Y. Investigation of Flow over Spillway Modeling and Comparison between Experimental Data and CFD Analysis. KSCE J. Civ. Eng.
**2017**, 21, 994–1003. [Google Scholar] [CrossRef] - Demeke, G.K.; Asfaw, D.H.; Shiferaw, Y.S. 3D Hydrodynamic Modelling Enhances the Design of Tendaho Dam Spillway, Ethiopia. Water
**2019**, 11, 82. [Google Scholar] [CrossRef] - Green, J. Comparison of Modelling Techniques for Assessment of Spillways. Dams Reserv.
**2019**, 29, 97–105. [Google Scholar] [CrossRef] - Gadhe, V.; Patil, R.G.; Bhosekar, V.V. Performance Assessment of Upgraded Spillway—Case Study. ISH J. Hydraul. Eng.
**2021**, 27, 327–335. [Google Scholar] [CrossRef] - Ge, M.; Petkovšek, M.; Zhang, G.; Jacobs, D.; Coutier-Delgosha, O. Cavitation Dynamics and Thermodynamic Effects at Elevated Temperatures in a Small Venturi Channel. Int. J. Heat Mass Transf.
**2021**, 170, 120970. [Google Scholar] [CrossRef] - Ge, M.; Manikkam, P.; Ghossein, J.; Subramanian, R.K.; Coutier-Delgosha, O.; Zhang, G. Dynamic Mode Decomposition to Classify Cavitating Flow Regimes Induced by Thermodynamic Effects. Energy
**2022**, 254, 124426. [Google Scholar] [CrossRef] - Ge, M.; Zhang, G.; Petkovšek, M.; Long, K.; Coutier-Delgosha, O. Intensity and Regimes Changing of Hydrodynamic Cavitation Considering Temperature Effects. J. Clean. Prod.
**2022**, 338, 130470. [Google Scholar] [CrossRef] - Aydin, M.C.; Isik, E.; Ulu, A.E. Numerical Modeling of Spillway Aerators in High-Head Dams. Appl. Water Sci.
**2020**, 10, 42. [Google Scholar] [CrossRef] [Green Version] - Yorke, T.H.; Oberg, K.A. Measuring River Velocity and Discharge with Acoustic Doppler Profilers. Flow Meas. Instrum.
**2002**, 13, 191–195. [Google Scholar] [CrossRef] - Al-Khatib, I.A.; Gogus, M. Prediction Models for Discharge Estimation in Rectangular Compound Broad-Crested Weirs. Flow Meas. Instrum.
**2014**, 36, 1–8. [Google Scholar] [CrossRef] - Sahu, M.; Khatua, K.K.; Mahapatra, S.S. A Neural Network Approach for Prediction of Discharge in Straight Compound Open Channel Flow. Flow Meas. Instrum.
**2011**, 22, 438–446. [Google Scholar] [CrossRef] - Chiu, C.-L.; Said, C.A.A. Maximum and Mean Velocities and Entropy in Open-Channel Flow. J. Hydraul. Eng.
**1995**, 121, 26–35. [Google Scholar] [CrossRef] - USGS.gov. USGS Science in Your Watershed—General Introduction and Hydrologic Definitions. Available online: https://www.usgs.gov/ (accessed on 12 October 2021).
- Genç, O.; Ardiçlioğlu, M.; Ağiralioğlu, N. Calculation of Mean Velocity and Discharge Using Water Surface Velocity in Small Streams. Flow Meas. Instrum.
**2015**, 41, 115–120. [Google Scholar] [CrossRef] - USBR. Water Masurement Manual; Water Resources Technical Publicationcations, Inc.: Highlands Ranch, CO, USA, 1997.
- Marjang, N.; Merkley, G.P. Surface Velocity Coefficients for Application of the Float Method in Rectangular and Compound Open Channels. Irrig. Sci.
**2009**, 27, 457–470. [Google Scholar] [CrossRef] - Kra, E.Y.; Merkley, G.P. Mathematical Modeling of Open-Channel Velocity Profiles for Float Method Calibration. Agric. Water Manag.
**2004**, 70, 229–244. [Google Scholar] [CrossRef] - Misra, S.K.; Thomas, M.; Kambhamettu, C.; Kirby, J.T.; Veron, F.; Brocchini, M. Estimation of Complex Air–Water Interfaces from Particle Image Velocimetry Images. Exp. Fluids
**2006**, 40, 764–775. [Google Scholar] [CrossRef] - Lin, Y.-T.; Lin, Y.-C.; Han, J.-Y. Automatic Water-Level Detection Using Single-Camera Images with Varied Poses. Measurement
**2018**, 127, 167–174. [Google Scholar] [CrossRef] - Ljubicic, R.; Vicanovic, I.; Zindovic, B.; Kapor, R.; Savic, L. Image Processing for Hydraulic Jump Free-Surface Detection. In Proceedings of the 38th IAHR World Congress—“Water: Connecting the World”, The International Association for Hydro-Environment Engineering and Research (IAHR), Beijing, China, 1–6 September 2019; Volume 38, pp. 1073–1082. [Google Scholar]
- Shin, S.S.; Park, S.D.; Lee, S.K. ScienceDirect Measurement of Flow Velocity Using Video Image of Spherical Float. Procedia Eng.
**2016**, 154, 885–889. [Google Scholar] [CrossRef] [Green Version] - Shin, S.S.; Park, S.D. Application of Spherical-Rod Float Image Velocimetry for Evaluating High Flow Rate in Mountain Rivers. Flow Meas. Instrum.
**2021**, 78, 101906. [Google Scholar] [CrossRef] - Tsubaki, R.; Fujita, I.; Tsutsumi, S. Measurement of the Flood Discharge of a Small-Sized River Using an Existing Digital Video Recording System. J. Hydro-Environ. Res.
**2011**, 5, 313–321. [Google Scholar] [CrossRef] - Li, D.; Liang, B.; Zhang, W. Real-Time Moving Vehicle Detection, Tracking, and Counting System Implemented with OpenCV. In Proceedings of the 2014 4th IEEE International Conference on Information Science and Technology, Shenzhen, China, 26–28 April 2014; pp. 631–634. [Google Scholar]
- Chandan, G.; Jain, A.; Jain, H. Mohana Real Time Object Detection and Tracking Using Deep Learning and OpenCV. In Proceedings of the 2018 International Conference on Inventive Research in Computing Applications (ICIRCA), Coimbatore, India, 11–12 July 2018; pp. 1305–1308. [Google Scholar]
- DSI. Çatalan Dam Spillway Model Experiments Report; DSI: Ankara, Turkey, 1985. [Google Scholar]
- Reclamation, B. (Ed.) Design of Small Dams; U.S. Government Printing Office: Washington, DC, USA, 1977. [Google Scholar]
- Chaudhry, M.H. Open-Channel Flow, 2nd ed.; Springer: Boston, MA, USA, 2008; ISBN 9780387301747. [Google Scholar]
- Kirkgöz, M.S.; Ardiçlioğlu, M. Velocity Profiles of Developing and Developed Open Channel Flow. J. Hydraul. Eng.
**1997**, 123, 1099–1105. [Google Scholar] [CrossRef] - ANSYS. FLUENT Theory Guide; ANSYS Inc: Canonsburg, PA, USA, 2015. [Google Scholar]
- Hirt, C.W.; Nichols, B.D. Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries. J. Comput. Phys.
**1981**, 39, 201–225. [Google Scholar] [CrossRef] - Launder, B.; Spalding, D. Lectures in Mathematical Models of Turbulence; Academic Press: Cambridge, MA, USA, 1972. [Google Scholar]
- Üneş, F.; Ağiralioğlu, N. Numerical Investigation of Temporal Variation of Density Flow and Parameters. J. Appl. Fluid Mech.
**2017**, 10, 81–94. [Google Scholar] [CrossRef] - Gerasimov, A. Modelling Turbulent Flows with FLUENT; Fluent Europe Ltd.: Sheffield, UK, 2006. [Google Scholar]
- Lodh, B.K.; Das, A.K.; Singh, N. Investigation of Turbulence for Wind Flow over a Surface Mounted Cube Using Wall Y+ Approach. Indian J. Sci. Technol.
**2017**, 10, 1–11. [Google Scholar] [CrossRef] - Unes, F.; Varcin, H. 3-D Real Dam Reservoır Model for Seasonal Thermal Densıty Flow. Environ. Eng. Manag. J.
**2017**, 16, 2009–2024. [Google Scholar] [CrossRef] - Üneş, F.; Varçin, H. Investigation of Seasonal Thermal Flow in a Real Dam Reservoir Using 3-D Numerical Modeling. J. Hydrol. Hydromech.
**2015**, 63, 38–46. [Google Scholar] [CrossRef] - Üneş, F. Investigation of Density Flow in Dam Reservoirs Using a Three-Dimensional Mathematical Model Including Coriolis Effect. Comput. Fluids
**2008**, 37, 1170–1192. [Google Scholar] [CrossRef] - Üneş, F. Analysis of Plunging Phenomenon in Dam Reservoirs Using Three-Dimensional Density Flow Simulations. Can. J. Civ. Eng.
**2008**, 35, 1138–1151. [Google Scholar] [CrossRef] - Üneş, F.; Varçin, H. Investigation of Plunging Depth and Density Currents in Eğrekkaya Dam Reservoir. Tek. Dergi
**2012**, 23, 5725–5750. [Google Scholar] - OpenCV. OpenCV Official Website. Available online: https://opencv.org/about/ (accessed on 20 October 2021).
- Mukherjee, A. Motion Analysis in Video Surveillance Using Edge Detection Techniques. IOSR J. Comput. Eng.
**2013**, 12, 10–15. [Google Scholar] [CrossRef] - Chanson, H. Turbulent Air-Water Flows in Hydraulic Structures: Dynamic Similarity and Scale Effects. Environ. Fluid Mech.
**2009**, 9, 125–142. [Google Scholar] [CrossRef] [Green Version] - Falvey, H.T. Cavitation in Chutes and Spillways. Engineering Monograph 42. In Water Resources Technical Publication; US Printing Office, Bureau of Reclamation: Denver, CO, USA, 1990. [Google Scholar]

**Figure 1.**Çatalan Dam spillway structure. 1–6 numbers indicate chambers and arrows indicate 3% and 17% slopes in the discharge channel.

**Figure 2.**Section of the Çatalan Dam spillway structure (flow inlet part) [29].

**Figure 4.**Model image of the spillway in the experiment: (

**a**) top view; (

**b**) flow inlet part; (

**c**) flow output part.

**Figure 5.**Velocity measurement points and location (distances from starting point) of the spillway model in the hydraulic water channel (top view).

**Figure 10.**The OpenCV code stages: (

**a**) reading current video image; (

**b**) image filtering for floating object detection and tracking; (

**c**) calculation of the velocity of the tracked object (Red lines indicate cross-section locations, blue lines indicate the distance of the float from the origin).

**Figure 11.**The OpenCV code stages: (

**a**) reading current video image; (

**b**) image filtering for floating object detection and tracking; (

**c**) calculation of the water depth according the tracked object (The yellow lines show the cross-section locations, the green line the base of the spillway model).

**Figure 12.**The OpenCV code screens: (

**a**) Cam 2, image velocity algorithm; (

**b**) Cam 1, image water depth algorithm (Yellow lines show cross-section locations, the green line is the base of the spillway model, and the purple line is the buoyancy trajectory).

**Figure 14.**CFD and experiment results for velocity fluctuations: (

**a**) Cross-section 1; (

**b**) Cross-section 2; (

**c**) Cross-section 3; (

**d**) Cross-section 4.

**Figure 20.**CFD and experiment results for water depths: (

**a**) Cross-section 1; (

**b**) Cross-section 2; (

**c**) Cross-section 3; (

**d**) Cross-section 4.

**Figure 29.**Floating object velocity values obtained with OpenCV code: (

**a**) Cross-section 1; (

**b**) Cross-section 2; (

**c**) Cross-section 3; (

**d**) Cross-section 4. (Red lines indicate cross-section locations, blue lines indicate the distance of the float from the origin).

**Figure 30.**OpenCV code display of the water depth obtained according to the position of the floating object: (

**a**) Cross-section 1; (

**b**) Cross-section 2; (

**c**) Cross-section 3; (

**d**) Cross-section 4.

**Table 1.**Coefficients to correct surface float velocities to average channel velocities [18].

Average Depth (m) | Coefficient |
---|---|

0.30 | 0.66 |

0.61 | 0.68 |

0.91 | 0.70 |

1.22 | 0.72 |

1.52 | 0.74 |

1.83 | 0.76 |

2.74 | 0.77 |

3.66 | 0.78 |

4.57 | 0.79 |

>6.10 | 0.80 |

Parameters | Dimension | Froude Scale Ratio | Prototype Value | Similarity Account | Model Value | |
---|---|---|---|---|---|---|

Spillway | Width | L | λ = (1/200) | 82.5 m | L_{p}∗λ | 41.25 cm |

Height | 34 m | 17 cm | ||||

Length | 402 m | 201 cm | ||||

Discharge (Q) | L^{3}T^{−1} | λ^{5/2} | 10,055 m^{3} s^{−1} | Q_{p}∗λ^{5/2} | 17.7 lt s^{−1} | |

Velocity (V) | Inlet 1 | LT^{−1} | λ^{1/2} | 6.5 m s^{−1} | V_{p}∗λ^{1/2} | 0.46 m s^{−1} |

Inlet 2 | 6 m s^{−1} | 0.42 m s^{−1} | ||||

Inlet 3 | 5.52 m s^{−1} | 0.39 m s^{−1} | ||||

Inlet 4 | 5.42 m s^{−1} | 0.38 m s^{−1} | ||||

Inlet 5 | 5.4 m s^{−1} | 0.36 m s^{−1} | ||||

Inlet 6 | 5.9 m s^{−1} | 0.42 m s^{−1} |

Solver Set | Solver | Pressure-Based |
---|---|---|

Space–Time | 3D, Unsteady | |

Model | Multiphase Model | VOF |

Viscous Model | k-ε | |

Phase | Primary Phase | Air |

Secondary Phase | Water | |

Discretization | Pressure | Presto |

Momentum | Second Order Upwind | |

Pressure–Velocity Coupling | Method | Coupled |

Convergence Criterion | Residuals | 0.001 (Continuity) |

0.001 (Momentum) |

Cross-Section No. | Column No. | Location at y Direction (m) | Experimental Results (m s^{−1}) | CFD Results (m s^{−1}) | MAE | RMSE | APE% |
---|---|---|---|---|---|---|---|

Cross-Section 1 | N1 | 0.0250 | 1.205 | 1.377 | 0.161 | 0.167 | 13.4 |

N2 | 0.1150 | 1.094 | 1.332 | ||||

N3 | 0.2025 | 1.378 | 1.266 | ||||

N4 | 0.2900 | 1.403 | 1.276 | ||||

N5 | 0.3775 | 1.144 | 1.299 | ||||

Cross-Section 2 | N1 | 0.0250 | 1.101 | 1.321 | 0.084 | 0.115 | 7.2 |

N2 | 0.1150 | 1.208 | 1.31 | ||||

N3 | 0.2025 | 1.288 | 1.28 | ||||

N4 | 0.2900 | 1.294 | 1.288 | ||||

N5 | 0.3775 | 1.223 | 1.305 | ||||

Cross-Section 3 | N1 | 0.0250 | 1.068 | 1.381 | 0.158 | 0.180 | 13.8 |

N2 | 0.1150 | 1.298 | 1.231 | ||||

N3 | 0.2025 | 1.143 | 1.327 | ||||

N4 | 0.2900 | 1.175 | 1.281 | ||||

N5 | 0.3775 | 1.224 | 1.342 | ||||

Cross-Section 4 | N1 | 0.0250 | 1.491 | 1.821 | 0.160 | 0.196 | 10.0 |

N2 | 0.1150 | 1.785 | 1.725 | ||||

N3 | 0.2025 | 1.602 | 1.861 | ||||

N4 | 0.2900 | 1.806 | 1.700 | ||||

N5 | 0.3775 | 1.793 | 1.748 |

Cross-Section No. | Column No. | Location at y Direction (cm) | Experimental Results (cm) | CFD Results (cm) | MAE | RMSE | APE% |
---|---|---|---|---|---|---|---|

Cross-Section 1 | H1 | 1.0000 | 2.900 | 2.865 | 0.074 | 0.080 | 2.2 |

H2 | 6.4375 | 3.000 | 3.085 | ||||

H3 | 11.8750 | 3.500 | 3.435 | ||||

H4 | 14.6250 | 3.200 | 3.135 | ||||

H5 | 20.2500 | 3.000 | 2.955 | ||||

H6 | 25.8750 | 3.000 | 2.945 | ||||

H7 | 28.6250 | 3.800 | 3.655 | ||||

H8 | 34.0625 | 3.600 | 3.525 | ||||

H9 | 39.5000 | 3.500 | 3.405 | ||||

Cross-Section 2 | H1 | 1.0000 | 3.500 | 3.615 | 0.137 | 0.143 | 3.8 |

H2 | 6.4375 | 3.600 | 3.515 | ||||

H3 | 11.8750 | 3.600 | 3.405 | ||||

H4 | 14.6250 | 3.600 | 3.405 | ||||

H5 | 20.2500 | 3.700 | 3.525 | ||||

H6 | 25.8750 | 3.500 | 3.405 | ||||

H7 | 28.6250 | 3.500 | 3.395 | ||||

H8 | 34.0625 | 3.900 | 3.765 | ||||

H9 | 39.5000 | 4.000 | 3.865 | ||||

Cross-Section 3 | H1 | 1.0000 | 3.400 | 3.515 | 0.081 | 0.084 | 2.3 |

H2 | 6.4375 | 3.600 | 3.615 | ||||

H3 | 11.8750 | 3.700 | 3.615 | ||||

H4 | 14.6250 | 3.500 | 3.415 | ||||

H5 | 20.2500 | 3.500 | 3.415 | ||||

H6 | 25.8750 | 3.500 | 3.415 | ||||

H7 | 28.6250 | 3.600 | 3.515 | ||||

H8 | 34.0625 | 3.500 | 3.415 | ||||

H9 | 39.5000 | 3.500 | 3.415 | ||||

Cross-Section 4 | H1 | 1.0000 | 3.000 | 2.95 | 0.050 | 0.050 | 1.7 |

H2 | 6.4375 | 2.900 | 2.85 | ||||

H3 | 11.8750 | 2.800 | 2.75 | ||||

H4 | 14.6250 | 3.000 | 2.95 | ||||

H5 | 20.2500 | 3.000 | 2.95 | ||||

H6 | 25.8750 | 3.000 | 2.95 | ||||

H7 | 28.6250 | 3.000 | 2.95 | ||||

H8 | 34.0625 | 3.000 | 2.95 | ||||

H9 | 39.5000 | 3.000 | 2.95 |

Cross-Section No. | Column No. | Location at y Direction (m) | Model Pressure Pm (Pa) | Prototype Pressure Pp (Pa) | Total Pressure Pt (Pa) | Model Velocity Um (m s^{−1}) | Prototype Velocity Up (m s^{−1}) | $\mathbf{Cavitation}\text{}\mathbf{Index}\text{}\mathit{\sigma}$ |
---|---|---|---|---|---|---|---|---|

Cross-Section 1 | N1 | 0.0250 | 324.360 | 64,872.000 | 157,673.000 | 1.377 | 19.474 | 0.82 |

N2 | 0.1150 | 381.476 | 76,295.200 | 169,096.200 | 1.332 | 18.837 | 0.94 | |

N3 | 0.2025 | 320.449 | 64,089.800 | 156,890.800 | 1.266 | 17.904 | 0.97 | |

N4 | 0.2900 | 357.581 | 71,516.200 | 164,317.200 | 1.276 | 18.045 | 1.00 | |

N5 | 0.3775 | 310.582 | 62,116.400 | 154,917.400 | 1.299 | 18.371 | 0.91 | |

Cross-Section 2 | N1 | 0.0250 | 350.546 | 70,109.200 | 162,910.200 | 1.321 | 18.682 | 0.92 |

N2 | 0.1150 | 313.742 | 62,748.400 | 155,549.400 | 1.310 | 18.526 | 0.89 | |

N3 | 0.2025 | 319.891 | 63,978.200 | 156,779.200 | 1.280 | 18.102 | 0.94 | |

N4 | 0.2900 | 297.647 | 59,529.400 | 152,330.400 | 1.288 | 18.215 | 0.91 | |

N5 | 0.3775 | 345.269 | 69,053.800 | 161,854.800 | 1.305 | 18.455 | 0.94 | |

Cross-Section 3 | N1 | 0.0250 | 231.060 | 46,212.000 | 139,013.000 | 1.381 | 19.530 | 0.72 |

N2 | 0.1150 | 224.240 | 44,848.000 | 137,649.000 | 1.231 | 17.409 | 0.89 | |

N3 | 0.2025 | 197.060 | 39,412.000 | 132,213.000 | 1.327 | 18.767 | 0.74 | |

N4 | 0.2900 | 214.194 | 42,838.800 | 135,639.800 | 1.281 | 18.116 | 0.81 | |

N5 | 0.3775 | 222.327 | 44,465.400 | 137,266.400 | 1.342 | 18.979 | 0.75 | |

Cross-Section 4 | N1 | 0.0250 | 134.874 | 26,974.800 | 119,775.800 | 1.821 | 25.753 | 0.35 |

N2 | 0.1150 | 149.620 | 29,924.000 | 122,725.000 | 1.725 | 24.395 | 0.41 | |

N3 | 0.2025 | 153.900 | 30,780.000 | 123,581.000 | 1.861 | 26.319 | 0.35 | |

N4 | 0.2900 | 151.555 | 30,311.000 | 123,112.000 | 1.700 | 24.042 | 0.42 | |

N5 | 0.3775 | 130.170 | 26,034.000 | 118,835.000 | 1.748 | 24.720 | 0.38 |

Cross-Section No. | Location at x Direction (m) | Section Slope% | Average Water Velocity (m s^{−1}) | Average Floating Object Velocity (m s^{−1}) | Coefficient |
---|---|---|---|---|---|

Crossssection 1 | 0.366 | 3 | 1.094 | 1.061 | 1.03 |

Cross-section 2 | 0.766 | 3 | 1.288 | 1.394 | 0.92 |

Cross-section 3 | 1.266 | 3 | 1.143 | 2.788 | 0.41 |

Cross-section 4 | 2.01 | 17 | 1.602 | 4.424 | 0.36 |

Cross-Section | Observation No. | Location at x Direction (m) | Experimental Water Depth Results (cm) | OpenCV Code Water Depth Results (cm) | MAE | RMSE | APE% |
---|---|---|---|---|---|---|---|

1 | 0.166 | 3.500 | 4.300 | 0.592 | 0.628 | 18.8 | |

Section 1 | 2 | 0.366 | 3.500 | 4.200 | |||

3 | 0.566 | 3.300 | 3.900 | ||||

Section 2 | 4 | 0.766 | 3.500 | 4.000 | |||

5 | 0.966 | 3.400 | 4.000 | ||||

6 | 1.166 | 3.100 | 4.100 | ||||

Section 3 | 7 | 1.266 | 3.400 | 4.200 | |||

8 | 1.316 | 3.400 | 3.900 | ||||

9 | 1.366 | 2.800 | 3.300 | ||||

10 | 1.566 | 2.500 | 3.100 | ||||

11 | 1.766 | 2.500 | 2.300 | ||||

Section 4 | 12 | 1.966 | 2.500 | 2.300 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Varçin, H.; Üneş, F.; Gemici, E.; Zelenakova, M.
Development of a Three-Dimensional CFD Model and OpenCV Code by Comparing with Experimental Data for Spillway Model Studies. *Water* **2023**, *15*, 756.
https://doi.org/10.3390/w15040756

**AMA Style**

Varçin H, Üneş F, Gemici E, Zelenakova M.
Development of a Three-Dimensional CFD Model and OpenCV Code by Comparing with Experimental Data for Spillway Model Studies. *Water*. 2023; 15(4):756.
https://doi.org/10.3390/w15040756

**Chicago/Turabian Style**

Varçin, Hakan, Fatih Üneş, Ercan Gemici, and Martina Zelenakova.
2023. "Development of a Three-Dimensional CFD Model and OpenCV Code by Comparing with Experimental Data for Spillway Model Studies" *Water* 15, no. 4: 756.
https://doi.org/10.3390/w15040756