# Investigate Impact Force of Dam-Break Flow against Structures by Both 2D and 3D Numerical Simulations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{0}) were considered as variables that affect the maximum value of the impact force.

## 2. Methodology

#### 2.1. 2D Shallow Water Equations

**U**indicates the vector of conserved variables;

**F**and

**G**are flux vectors and

**S**is a source term accounting for the bed slope term

**S**

_{1}and friction term

**S**; x, y are orthogonal space coordinates on a horizontal plane; t is time; h and z

_{2}_{b}represent water depth and bottom elevation; u, v are velocity components in the x and y directions; S

_{0x}, S

_{0y}, S

_{fx}, S

_{fy}are bed slopes and friction slopes along the same directions; n is the Manning roughness coefficient; g is gravity acceleration.

**A**(

**U**) and

**B**(

**U**) are Jacobian matrices corresponding to the fluxes

**F**(

**U**) and

**G**(

**U**), respectively. The expressions of two matrices are expressed as

**S**

_{2}.

#### 2.2. 3D Navier Stokes Equations

**f**accounts for the body force per unit of mass; ν is the kinematic viscosity of the fluid; p is pressure; t is time; ρ is fluid density;

**v**is the vector variable of the 3 velocity components u, v, w.

## 3. Result and Discussion

#### 3.1. Dam-Break Wave on an Obstruction

#### 3.2. Force Due to Dam-Break Wave on a Group of Structures

_{0}) was 0.2 m, and downstream was dry. Ten square pillars (0.06 m wide and 0.2 m high) were placed in the flood plain. The coordinates of the 6 columns which were studied are shown in Figure 3.

_{e}= 10

^{−4}m was utilized to indicate whether the cell was wet or dry. The Manning coefficient n was equal to 0.007.

- a
- Mesh sensitivity analysis

^{®}Core ™ i5-7300HQ CPU @ 2.5GHz and an installer memory (RAM) of 8 GB, the resulting file size and computational time correspondence of 4 meshes were 87 GB, 27 GB, 12 GB, 4 GB and 9 h 17 min 28 s, 2 h 53 min 44 s, 2 h 34 min 56 s and 2 h 8 min 31 s, respectively. The cost-effective PC showed that the finest mesh generated the largest result file while the grid size of 0.015 m gave a much smaller one. Afterwards, the influence of the mesh resolutions on the accuracy of the models in predicting the flow depth (h) and velocity components (u and v) at the two study points a and b were evaluated employing the normalized root mean square error (NRMSE).

_{i,exp}, X

_{i,sim}, X

_{exp,max}and X

_{exp}

_{,min}represented the empirical, numerical, maximum and minimum values of the X variables:

- b
- Forces acting on groups of building

^{3}).

_{i}is the depth and F

_{ri}= u

_{i}/(gh

_{i})

^{0.5}is the Froude number of the incident wave (Figure 7).

_{dynamic,front}and F

_{static,back}.

#### 3.3. Effect of Dam-Break Width and Initial Water Level on Static Force and Dynamic Force Against Structures

_{0}) on the peak intensity of impact load generated by a discontinuous flow against the buildings using Flow 3D with the LES turbulence model. Table 2 shows different scenarios.

^{3}/s/m) at the damsite was estimated by the following expression:

^{2}b/h

_{0}and force per unit width (F) at columns A and E were quite good (0.979 and 0.967 for static force and 0.925 and 0.853 for dynamic force, respectively). When q

^{2}b/h

_{0}was small, the effect of velocity-induced force was minor, so the dynamic force was close with static force. The difference between the two types of force was increased significantly when q

^{2}b/h

_{0}increased. Thus, dynamic force instead of static force should be estimated for design purposes in a floodplain. Column A was directly in the path of the dam-break wave propagation; hence, both its static and dynamic impact loads were the largest. Meanwhile, the location of column E was further from the path and so had smaller impact force results. On the other hand, a poor R-square value was seen at column D, which was in the second array, so the Froude number in the vicinity of this column was reduced dramatically. So, dynamic force was approximately equal to static force, and both of them were much smaller than those at columns A and E.

## 4. Conclusions

- (1)
- To formulate water depth or velocity profiles, both 2D and 3D numerical solutions are quite similar. The proposed 2D numerical model is suitable for predicting hydraulic characteristics involving water depth and a velocity component as well as the maximum value of the static force. However, the 3D hydrodynamic model with the LES and RANs turbulent modules can well capture two peaks of impact load while the 2D shallow flow model presents only one. In general, the 3D result is closer to the experimental one.
- (2)
- Both the static and dynamic forces against several buildings were computed by Flow 3D with the LES module. The role of velocity-induced force and pressure force on a building varies with location. Near the damsite, the velocity-induced force is more prevalent while away from main direction of dam-break wave or in the second array the pressure force is the more important. The impact of velocity-induced force is quantified by parameter α, which is carried out as a function of the Froude number and water depth of the incident wave. The linear regression relation between q
^{2}b/h_{0}and the peak intensity of the static force and dynamic force is worked out with reasonable R-square quantities.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Configuration of experiment test (dimension in meters); (

**b**) Gauges on the vertical front face of building.

**Figure 2.**(

**a**) Distributed pressure profiles at centerline of front face of column; (

**b**) Comparison of load-time histories simulated by different numerical models.

**Figure 8.**Snapshots of streamlines of Froude number at different times: 1.0 s, 2.0 s, 5.0 s and 10 s.

Gauges | X | Grid Sizes and Models | ||||
---|---|---|---|---|---|---|

3D Model | 2D Model | |||||

0.01 m | 0.015 m | 0.02 m | 0.03 m | 0.01 m | ||

a | h | 0.445 | 0.449 | 0.449 | 0.457 | 0.441 |

u | 0.155 | 0.201 | 0.224 | 0.251 | 0.317 | |

v | 0.277 | 0.277 | 0.294 | 0.407 | 0.454 | |

b | h | 0.264 | 0.345 | 0.438 | 0.619 | 0.697 |

u | 0.126 | 0.183 | 0.133 | 0.234 | 0.221 | |

v | 0.311 | 0.248 | 0.213 | 0.443 | 0.242 |

**Table 2.**Case studies with different value of initial water level in reservoir and the damsite width.

Case | Initial Water Level (h_{0}) (m) | Damsite Width (b) (m) |
---|---|---|

1 | 0.2 | 0.25 |

2 | 0.2 | 0.50 |

3 | 0.4 | 0.50 |

4 | 0.2 | 0.75 |

5 | 0.6 | 0.50 |

6 | 0.4 | 0.75 |

7 | 0.6 | 0.75 |

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Hien, L.T.T.; Van Chien, N. Investigate Impact Force of Dam-Break Flow against Structures by Both 2D and 3D Numerical Simulations. *Water* **2021**, *13*, 344.
https://doi.org/10.3390/w13030344

**AMA Style**

Hien LTT, Van Chien N. Investigate Impact Force of Dam-Break Flow against Structures by Both 2D and 3D Numerical Simulations. *Water*. 2021; 13(3):344.
https://doi.org/10.3390/w13030344

**Chicago/Turabian Style**

Hien, Le Thi Thu, and Nguyen Van Chien. 2021. "Investigate Impact Force of Dam-Break Flow against Structures by Both 2D and 3D Numerical Simulations" *Water* 13, no. 3: 344.
https://doi.org/10.3390/w13030344