# Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

_{0}in the reservoir was constant at 0.25 m. On the right side, the initial tailwater depths ${h}_{1}$ were 0 m in the case of the dry bed and 0.025 and 0.1 m in the wet bed, so there were three different situations with water depth ratios $\mathsf{\alpha}={h}_{1}/{h}_{0}$ of 0, 0.1, and 0.4. The wet-bed conditions were created by using a low weir at the end of a flume. The water surface profiles were observed at the early stage using three high-speed digital cameras (50 frames/s), and the accuracy of the instrumental measurements was demonstrated in Reference [30]. In the following section, the corresponding numerical results refer to positions x = −1 m (P1), −0.5 m (P2), −0.2 m (P3), +0.2 m (P4), +0.5 m (P5), +1 m (P6), +2 m (P7), and +2.85 m (P8), where the origin of the coordinate system x = 0 is at the dam site. The three water depth ratios $\mathsf{\alpha}$ of 0, 0.1, and 0.4, where the $x,y$ coordinates are normalized by ${h}_{0}.$

#### 2.2. Model Performance Criteria

#### 2.3. Analytical Solution

#### 2.4. Numerical Model and Simulation Setup

#### 2.4.1. Flow-3D

#### 2.4.2. MIKE 3 FM

## 3. Comparison between Flow-3D, MIKE 3 FM, and 1D Exact Riemann Solver Predictions

#### 3.1. Free Surface

#### 3.1.1. Free Surface during the Early Stage

_{0})

^{1/2}. The simulated wavefront in the downstream region ($x/{h}_{0}>0$) using MIKE 3 FM moved more slowly than the measurements and the results of Flow-3D, indicating that the wavefront in the upstream reservoir ($x/{h}_{0}<0$) moved faster than the measurements and the other results. It was observed that the two numerical models and analytical solution generally had low values for the RMSE, with all of them below 0.08 at different times, which indicates that both types of solutions achieved acceptable results for the dry-bed case during the initial stage, while the Flow-3D model obtained the best RMSE result of 0.02 (Table 1). Significantly, as time passed, the error decreased from T = 1.127–6.637; the Flow-3D, MIKE 3FM, and 1D approaches improved the forecast by reducing the RMSE values by ~42.29%, ~22.87%, and ~54.84%, respectively, demonstrating that the differences between the values predicted by the three models to solve dam-break flows for dry beds were very small over time. Therefore, any of the three models can be selected as an appropriate model for predicting the free surface after the dam break for the dry-bed.

#### 3.1.2. Free Surface during the Late Stage ($T\ge 9.899$)

#### 3.2. Water Depth Variations

#### 3.3. Velocity

#### 3.3.1. Averaged Velocity Evolution

#### 3.3.2. Vertical Velocity Profiles

^{−1}at t = 0.8 s, indicating that the slope of the water surface sharply changed with a large u near the gate during the initial stage. The results clearly indicate that 3D effects are important in dam-break flows, and the comparisons demonstrate that the Flow-3D and MIKE 3 FM models could provide more detailed information, such as vertical velocity variations, than the 1D and 2D shallow-water models.

#### 3.4. Computational Costs

^{®}Core™ i5 PC. The comparison between the simulated and experimental results, as showed for the first test case in Ozmen-Cagatay and Kocaman [30], clearly shows that the 3D RANS approach has the ability to represent the water surface profiles quite well during the entire dam-break process, immediately during the initial stage and after the gate collapse, and it reproduced the free-surface profiles of the front wave well for dry- and wet-bed conditions while the wave-front modelled by the MIKE 3 FM model for the wet-bed case was a rectangular jump rather than a curved surface. For the dam-break flow under a dry bed, the results of the free surface profiles during the late stage using the MIKE 3 FM approach can be considered reasonable relative to the experimental measurements. The performances of the MIKE 3 FM models in relation to the water depth variations and velocity variation for the dry- and wet-beds were satisfactory. The previous research results show the practical advantage of using the MIKE 3 FM model to compute the water levels and velocity for large-scale dam-break problems [48]. A possible dam-break flow application in which the SW 3D mode might be needed is used for computing the hydrodynamic characteristic of a dam-break wave in large domains, and the water surface profiles of the front wave during the earliest stage is not very important. These two three-dimensional models of Flow-3D and MIKE 3 FM could be efficiently and effectively applied in the near-field region, and if given the computational effort and efficiency required by each method, the MIKE 3 FM approach should be considered a major candidate for computations involving large domains, leaving the RANS approach for fine calculations in which knowledge of the 3D structure of the flow is required. Often, in practical applications, both these requirements are necessary.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic view of the experimental conditions by Ozmen-Cagatay and Kocaman [30]: (

**a**) α = 0; (

**b**) α = 0.1; and (

**c**) α = 0.4.

**Figure 2.**Schematic view of the experimental conditions by Khankandi et al. [39]: (

**a**) α = 0 and (

**b**) α = 0.2.

**Figure 3.**Typical profiles of the dam-break flow regimes for Stoker’s analytical solution [9]: Wet-bed downstream.

**Figure 4.**Sensitivity analysis of the numerical simulation using Flow-3D for the different mesh sizes of the experiments in Reference [30].

**Figure 5.**Sensitivity analysis of the numerical simulation using MIKE 3 FM for the different mesh sizes of the experiments in Reference [30].

**Figure 6.**Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h

_{0})

^{1/2}and for dry-bed ($\mathsf{\alpha}=0$). The experimental data are from Reference [30].

**Figure 7.**Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h

_{0})

^{1/2}and for a wet-bed (α = 0.1). The experimental data are from Reference [30].

**Figure 8.**Comparison between observed and simulated free surface profiles at dimensionless times T = t(g/h

_{0})

^{1/2}and for the wet-bed (α = 0.4). The experimental data are from Reference [30].

**Figure 9.**Experimental and numerical comparison of free surface profiles $h/{h}_{0}\left(x/{h}_{0}\right)$ during late stages at various dimensionless times T after the failure in the dry-bed by Khankandi et al. [39].

**Figure 10.**Measured and computed water level hydrograph at various positions for dry-bed by Khankandi et al. [39]: (

**a**) G1 (−0.5 m); (

**b**) G2 (−0.1 m); (

**c**) G3 (0.1 m); (

**d**) G4 (0.8 m); (

**e**) G6 (1.2 m); (

**f**) G8 (5.5 m).

**Figure 11.**Measured and computed water level hydrographs at various positions for the wet-bed by Khankandi et al. [39]: (

**a**) G1 (−0.5 m); (

**b**) G2 (−0.1 m); (

**c**) G4 (0.8 m); and (

**d**) G5 (1.0 m).

**Figure 12.**Average velocity for the dry-bed at G4 (0.8 m) and G6 (1.2 m) by Khankandi et al. [39].

**Figure 13.**Comparison of simulated velocity profiles at various locations upstream and downstream of the dam at t = 0.8 s, 2 s, and 5 s for water depth ratios α = 0.1 by Ozmen-Cagatay and Kocaman [30]: (

**a**) P1(−1 m); (

**b**) P3 (+0.2 m); (

**c**) P5 (+1 m); and (

**d**) P6 (+2 m).

**Table 1.**RMSE values for the free surface profiles observed by Ozmen-Cagatay and Kocaman [30].

Water Depth Ratios | Time T (-) | RMSE | ||
---|---|---|---|---|

Analytical Solution | Flow 3D | MIKE 3 FM | ||

0 | 1.127 | 0.07 | 0.04 | 0.05 |

2.755 | 0.05 | 0.06 | 0.06 | |

3.882 | 0.04 | 0.02 | 0.04 | |

5.009 | 0.03 | 0.02 | 0.04 | |

6.637 | 0.03 | 0.02 | 0.04 | |

0.1 | 1.565 | 0.10 | 0.09 | 0.09 |

2.379 | 0.07 | 0.05 | 0.07 | |

4.007 | 0.10 | 0.08 | 0.09 | |

6.511 | 0.10 | 0.08 | 0.10 | |

8.891 | 0.05 | 0.04 | 0.05 | |

0.4 | 1.565 | 0.09 | 0.06 | 0.09 |

2.379 | 0.08 | 0.02 | 0.07 | |

4.007 | 0.07 | 0.05 | 0.06 | |

6.511 | 0.05 | 0.03 | 0.04 | |

8.891 | 0.04 | 0.04 | 0.03 |

**Table 2.**RMSE values for the free surface profiles observed by Khankandi et al. [39].

Water Depth Ratios | Time T (-) | RMSE | ||
---|---|---|---|---|

Analytical Solution | Flow 3D | MIKE 3 FM | ||

0 | 9.899 | 0.03 | 0.03 | 0.04 |

14.845 | 0.04 | 0.04 | 0.04 | |

49.497 | 0.26 | 0.02 | 0.02 |

**Table 3.**RMSE values for the water depth variations observed by Khankandi et al. [39] at the late stage.

Water Depth Ratios | Probe | RMSE | |
---|---|---|---|

Flow 3D | MIKE 3 FM | ||

0 | G1 | 0.02 | 0.02 |

G2 | 0.01 | 0.02 | |

G3 | 0.03 | 0.04 | |

G4 | 0.01 | 0.01 | |

G6 | 0.02 | 0.02 | |

G8 | 0.01 | 0.01 | |

0.1 | G1 | 0.02 | 0.03 |

G2 | 0.04 | 0.03 | |

G4 | 0.02 | 0.02 | |

G5 | 0.02 | 0.02 |

**Table 4.**RMSE values for the averaged velocity evolution at G4 and G6 based on experimental data by Khankandi et al. [39].

Water Depth Ratios | Probe | RMSE | |
---|---|---|---|

Flow 3D | MIKE 3 FM | ||

0 | G4 | 0.26 | 0.23 |

G6 | 0.29 | 0.26 |

**Table 5.**The required computational time for the two models to address dam break flows in all cases.

Experimental Group | No. of Grids | Computation Time (s) | ||
---|---|---|---|---|

MIKE 3 FM | Flow-3D | MIKE 3 FM | Flow-3D | |

Test 1 ($\mathsf{\alpha}=0)$ | 267 | 106,800 | 5 min | 120 min |

Test 2 ($\mathsf{\alpha}=0.1)$ | 267 | 106,800 | 5 min | 120 min |

Test 3 ($\mathsf{\alpha}=0.4)$ | 267 | 106,800 | 5 min | 120 min |

Test 4 ($\mathsf{\alpha}=0)$ | 2860 | 256,000 | 9 min | 480 min |

Test 5 ($\mathsf{\alpha}=0.2)$ | 2860 | 256,000 | 9 min | 480 min |

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**MDPI and ACS Style**

Hu, H.; Zhang, J.; Li, T.
Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data. *Appl. Sci.* **2018**, *8*, 2456.
https://doi.org/10.3390/app8122456

**AMA Style**

Hu H, Zhang J, Li T.
Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data. *Applied Sciences*. 2018; 8(12):2456.
https://doi.org/10.3390/app8122456

**Chicago/Turabian Style**

Hu, Hui, Jianfeng Zhang, and Tao Li.
2018. "Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data" *Applied Sciences* 8, no. 12: 2456.
https://doi.org/10.3390/app8122456