# Model Experiment Exploration of the Kinetic Dissipation Effect on the Slit Dam with Baffles Tilted in the Downstream Direction

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. DEM Method

#### 2.1.1. Numerical Simulation Model

#### 2.1.2. Parameters and Process of DEM

#### 2.2. Flume Experiment

#### 2.2.1. Experimental Device

#### 2.2.2. Experiment Particles

#### 2.2.3. Experimental Steps

_{total}= 1.5 kg were first naturally stacked on top of the flume and then released under gravity until the particles were completely stationary; the normal force on the inclined baffle during each parallel experiment was recorded using the pressure sensor with 0.2 s time interval. After each release, the particle mass trapped by the inclined baffle was recorded as m

_{trap}. Each experiment combination was measured at least 3 times until the deviation of the recorded impact force was less than 10%.

## 3. Results

#### 3.1. DEM Simulation Results

_{θ}

_{=0°}in the figure is the maximum impact force on baffles with θ = 0°. With the increase of θ, the maximum impact force on the baffle gradually decreased. When θ ≥ 30°, the maximum impact force on the baffle could be kept at a low level. Based on Figure 3, it can be found that with the same opening width, increasing θ can delay the impact of particles on the baffle and increase the collisions and frictions among particles at the same time, which may be a factor to reduce the maximum impact force of particles on the baffle. Therefore, considering the kinetic energy dissipation performance of the particle system and the maximum impact force on baffles, a θ = 45° baffle structure was selected for the flume experiment.

#### 3.2. Experimental Results of the Particle Impact Force

#### 3.3. Experimental Results of the Trapping Efficiency

_{trap}and m

_{total}are, respectively, the mass of particles intercepted by the baffle structure and the total mass of particles, where m

_{trap}takes the average value of multiple stable results.

## 4. Discussion

#### 4.1. Influence of Baffle Inclination Angle θ on Particle Kinetic Energy Dissipation (DEM Simulation)

#### 4.2. Influence of the Particle Arch Effect on Trapping Efficiency (Experimental Analysis)

#### 4.3. Trapping Impact Force under Different Relative Opening Widths (Experimental Analysis)

_{trap}. The specific expression can be given as in Equation (2):

_{max}is the maximum impact force measured by the sensor during the impact process; E is the trapping efficiency calculated by Equation (1). The trapping impact force F

_{trap}is a combined factor to evaluate both the impact force and the interception efficiency, which can reflect the change in the interception state. The calculation results of the trapping impact force of each group of experiments are given in Figure 10.

_{trap}of the three sized particles experience a process of first decreasing and then increasing; that is, the change in peak impact force F

_{max}is not linearly related to particle trapping efficiency E. There is an extreme value of b/d, which makes the inclined baffle rest in the ideal interception state. In Figure 10, the minimum value of the trapping impact force curve of 6 mm particles appears at about b/d = 1.0, while the minimum value of the trapping impact force curve of 10 mm and 14 mm particles appears at about 1 < b/d < 2. When b/d > 2, the decline rate of the trapping efficiency of the baffle to particles is much faster than the decline rate of the maximum impact force until the trapping efficiency is reduced to zero. This shows that when the particle size is in the range of 6~14 mm, the optimal width diameter ratio of the inclined baffle in the ideal interception state is 1 ≤ b/d ≤ 2.

## 5. Conclusions

- The DEM simulation results indicate that the change of the inclination angle θ of the tilted baffles affects the number of particle collisions, thereby affecting the ability of the baffle structure to dissipate the kinetic energy of particles; when the inclination angle is 30° ≤ θ ≤ 45°, the baffle structure bears less impact force and has better particle kinetic energy dissipation performance.
- The flume experiment results indicate that the particle size d and the baffle opening width b have an influence on the impact force and trapping efficiency of the inclined baffle structure; with the increase of the width diameter ratio b/d, the peak impact force of the inclined baffle structure decreases nearly linearly, while the trapping efficiency decreases nonlinearly; and the tilted baffles can successfully intercept the flowing down particles when the width diameter ratio range is 0 ≤ b/d ≤ 4.
- In this paper, the ratio of the maximum impact force to the trapping efficiency (trapping impact force) is proposed to evaluate the interception effect of the tilted baffles. By analyzing this index, it has been found that when the particle size is in the range of 6~14 mm, a suitable width diameter ratio lies in 1 ≤ b/d ≤ 2, which can ensure an ideal interception state for the tilted baffles with relatively weaker impact force and higher trapping efficiency.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) schematic diagram of DEM method simulating flume model; (

**b**) schematic diagram of flume experimental device; (

**c**) particle hopper; (

**d**) baffle impact force measuring sensor.

**Figure 3.**Schematic diagram of the velocity variation of the particle impacting the baffle structure with different inclination angles obtained from the DEM simulation. t is the time that the particles begin to move and fall.

**Figure 4.**DEM simulation statistical results of the particle system under different baffle angle conditions. (

**a**) changes in particle contact number; (

**b**) changes in kinetic energy of the system.

**Figure 5.**Maximum impact force under different baffle angle conditions, normalized with the maximum impact force of the baffle with θ = 0°.

**Figure 6.**Variation of particle impact force with time in the flume experiment when θ = 45°. (

**a**) b = 0 mm; (

**b**) b = 10 mm; (

**c**) b = 15 mm; (

**d**) b = 20 mm; (

**e**) b = 25 mm; (

**f**) b = 30 mm; (

**g**) b = 35 mm; (

**h**) b = 40 mm; (

**i**) summary of maximum impact forces for different slit widths. All impact force time history curves were recorded from the moment the particles first contacted the baffle structure.

**Figure 7.**Particle trapping efficiency of inclined baffle structure with θ = 45° under different slit widths.

**Figure 8.**Schematic diagram of particle rebound form in baffle structure with different inclination angles (

**a**) θ = 0°; (

**b**) θ = 45°. The red arrow represents the part of particles that do not collide with the baffle structure, and the black arrow represents the part of particles that collide and bounce with the baffle structure.

**Figure 9.**Schematic diagram of particles jamming in the inclined baffle structure, in which the white circle is the divided particles that have different effects on jamming, and the red dotted line is the arch structure formed by the particles at the opening. (

**A**) is the arch forming area; (

**B**) is the extrusion area; (

**C**) is the impact area.

**Figure 10.**Trapping impact force of particles on inclined baffle structure under different relative opening widths.

Parameters | Values |
---|---|

Wall normal stiffness (N/m) | 1 × 10^{8} [42] |

Wall normal-to-shear stiffness ratio (dimensionless) | 1 [42] |

Particle normal stiffness (N/m) | 1 × 10^{8} [42] |

Particle normal-to-shear stiffness ratio (dimensionless) | 1 [42] |

Ball radius (mm) | 5 |

Ball density (kg/m^{3}) | 2550 |

Inter-ball friction coefficient (dimensionless) | 0.36 [42] |

Interface-ball friction coefficient (dimensionless) | 0.4 [42] |

Gravitational acceleration (m/s^{2}) | 9.81 [42] |

Coefficient of restitution (dimensionless) | 0.78 [42] |

Parameters | Values | ||
---|---|---|---|

Diameter(mm) | 6 | 10 | 14 |

Density (kg/m^{3}) | 2550 | 2550 | 2550 |

Initial bulk density (kg/m^{3}) | 1549 | 1487 | 1380 |

Young’s modulus (GPa) | 60 | 60 | 60 |

Poisson ratio | 0.25 | 0.25 | 0.25 |

Dynamic friction angle (°) | 17.2 | 16.6 | 14.7 |

Static friction angle (°) | 28 | 30 | 34 |

Experiment ID | Slit Size, b (mm) | Particle Diameter, d (mm) | Slit Size to Particle Size Ratio, b/d |
---|---|---|---|

B0-D6 | 0 | 6 | 0.00 |

B0-D10 | 0 | 10 | 0.00 |

B0-D14 | 0 | 14 | 0.00 |

B10-D6 | 10 | 6 | 1.67 |

B10-D10 | 10 | 10 | 1.00 |

B10-D14 | 10 | 14 | 0.71 |

B15-D6 | 15 | 6 | 2.50 |

B15-D10 | 15 | 10 | 1.50 |

B15-D14 | 15 | 14 | 1.07 |

B20-D6 | 20 | 6 | 3.33 |

B20-D10 | 20 | 10 | 2.00 |

B20-D14 | 20 | 14 | 1.43 |

B25-D6 | 25 | 6 | 4.17 |

B25-D10 | 25 | 10 | 2.50 |

B25-D14 | 25 | 14 | 1.79 |

B30-D6 | 30 | 6 | 5.00 |

B30-D10 | 30 | 10 | 3.00 |

B30-D14 | 30 | 14 | 2.14 |

B35-D6 | 35 | 6 | 5.83 |

B35-D10 | 35 | 10 | 3.50 |

B35-D14 | 35 | 14 | 2.50 |

B40-D6 | 40 | 6 | 6.67 |

B40-D10 | 40 | 10 | 4.00 |

B40-D14 | 40 | 14 | 2.86 |

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**MDPI and ACS Style**

Fang, Y.; Liu, H.; Guo, L.; Li, X.
Model Experiment Exploration of the Kinetic Dissipation Effect on the Slit Dam with Baffles Tilted in the Downstream Direction. *Water* **2022**, *14*, 2772.
https://doi.org/10.3390/w14182772

**AMA Style**

Fang Y, Liu H, Guo L, Li X.
Model Experiment Exploration of the Kinetic Dissipation Effect on the Slit Dam with Baffles Tilted in the Downstream Direction. *Water*. 2022; 14(18):2772.
https://doi.org/10.3390/w14182772

**Chicago/Turabian Style**

Fang, Yingguang, Hao Liu, Lingfeng Guo, and Xiaolong Li.
2022. "Model Experiment Exploration of the Kinetic Dissipation Effect on the Slit Dam with Baffles Tilted in the Downstream Direction" *Water* 14, no. 18: 2772.
https://doi.org/10.3390/w14182772