# Numerical Simulation of Two-Dimensional Dam Failure and Free-Side Deformation Flow Studies

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## Abstract

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## 1. Introduction

## 2. Numerical Models and the Proposed Method

#### 2.1. Governing Equations

_{eff}= μ + μ

_{t}, μ is the dynamic viscosity, μ

_{t}is the turbulence viscosity, v is the flow velocity, t is the time, p is the pressure, ρ is the density, f

_{b}is the mean external strength of the body.

_{b}is the resultant of the body force (such as gravity or centrifugal forces).

#### 2.2. VOF Method

_{i}. The volume fraction of phase i is defined as:

_{i}is the volume of phase i in the cell and V is the volume of the cell. The volume fractions of all phases in a cell must sum up to one:

_{i}= 0 means that the cell is completely void of phase i;

_{i}= 1 means that the cell is completely filled with phase i;

_{i}< 1 means that values between the two limits indicate the presence of an interface between phases. The VOF model is shown in Figure 1.

_{i}is the density, μ

_{i}is the dynamic viscosity, and (Cp)

_{i}is the specific heat of phase i.

_{d,i}is the diffusion velocity, S

_{αi}is a user-defined source term of phase i, and Dρ

_{i}/Dt is the material or Lagrangian derivative of the phase densities ρ

_{i}.

## 3. Single Liquid Dam Failure Simulation with Different Shapes of Obstacles Downstream

#### 3.1. Basic Calculation Model Parameters

#### 3.2. Mesh Division and Boundary Conditions of Foundation Dam Failure Computational Model

#### 3.3. Data Analysis of Basic Dam Model Calculation Results

#### 3.4. Comparative Analysis of Dam Failure Models with Diverse Obstacles Shapes Down-Stream

## 4. Simulation and Analysis of Single Liquid Dam with Wet Bed Downstream

#### 4.1. Calculation Model of Wet Bed

#### 4.2. Computational Model of Grid Division with Wet Bed

#### 4.3. Distribution and Evolution of Free Surface Flow Field

_{0})0.5, where g is acceleration of gravity, which is 9.81 m/s

^{2}. The distribution and evolution of free surface flow field at T = 2.5–80 are shown in Figure 14, Figure 15, Figure 16 and Figure 17. Figure 14 shows that the potential energy of the upstream water is transformed into kinetic energy when the dam breaking water flow begins to move under the effect of gravity. The downstream water may impede the flow of the upstream water when there is 2.5 cm of still water downstream of the flume, causing the upstream water flow to travel upward in the form of a rolling wave.

#### 4.4. Free Surface Height Variation at Different Positions

_{0}, while the abscissa represents dimensionless time T. In general, the calculated values of water level at the six locations are in good agreement with the experimental values. As the dam break wave reaches the area, the water level at other regions will increase swiftly and remain constant for a long time. The position of P2 is the closest to the upstream water column, so the height of free surface here will rise rapidly after the dam break begins, and then the water level will remain constant before T = 33 and maintain at about h/h

_{0}= 0.43. The water levels of P1 and P2 gradually decreased between T = 32–48 and T = 33–46, respectively, and then rose rapidly to the peak. The second rapid rise in the free surface water level at each location is caused by reflected waves generated by the reflection of the dam break wave against the downstream right wall.

_{0}= 0.40 after the first rapid rise, which indicates that the free surface profile upstream of reflected wave is horizontal. As the dam wave reaches the right wall of the tank, it is reflected and carries on to the measurement section, producing wave columns in all measuring positions. With the passage of time, there is a gradual reduction in the amplitude of the travelling wave. The reflected wave height h/h

_{0}exceeds 1 at P5 and P6, which can be explained by the collision of the reflected wave moving upstream. The dam breaking wave moving downstream results in the superposition and the reflected wave also becomes steeper as it moves upstream.

## 5. Simulation and Analysis of Single Liquid Dam Failure during Gate Twitching

#### 5.1. Dam Breaking Model When the Gate Twitches

#### 5.2. Free Surface Flow Field Distribution

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**The free surface flow field of obstacles of different shapes at 0.1–0.5 s (from top to bottom, it is rectangular, semi-circular, triangular, regular trapezoid and inverted trapezoid).

**Figure 10.**The maximum height of the water column on the left wall of the obstruction container of different shapes.

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**MDPI and ACS Style**

Jiang, H.; Zhao, B.; Dapeng, Z.; Zhu, K.
Numerical Simulation of Two-Dimensional Dam Failure and Free-Side Deformation Flow Studies. *Water* **2023**, *15*, 1515.
https://doi.org/10.3390/w15081515

**AMA Style**

Jiang H, Zhao B, Dapeng Z, Zhu K.
Numerical Simulation of Two-Dimensional Dam Failure and Free-Side Deformation Flow Studies. *Water*. 2023; 15(8):1515.
https://doi.org/10.3390/w15081515

**Chicago/Turabian Style**

Jiang, Haoyu, Bowen Zhao, Zhang Dapeng, and Keqiang Zhu.
2023. "Numerical Simulation of Two-Dimensional Dam Failure and Free-Side Deformation Flow Studies" *Water* 15, no. 8: 1515.
https://doi.org/10.3390/w15081515