# Experimental and Numerical Study of Hydrodynamic Characteristics of Gullies for Buildings

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## Abstract

**:**

## 1. Introduction

## 2. Research Methods

#### 2.1. Experimental Method

^{3}. With the flow structure fully developed in the gully (6) at the tested flow rate of 0.8 L/s, the 3000 glass balls are falling into the entry tray (5) in 30 s. The discharged water stream carrying air bubbles and glass balls flows through the interceptor (7) into the tank (8). The glass balls out of the gully in the discharged stream are retained in the interceptor (7). Each test gully is made of transparent arctic block. A light sheet is emitted toward the transparent test gully at each set of test conditions. The air–water flow images with or without glass balls in the gully are taken by the charge-coupled device (CCD) at the rate of 60 fps. The images are recorded and stored via the computerized data acquisition system. The performance index of self-purification for the tested gully is calculated as the mass ratio between the intercepted and supplied glass balls.

#### 2.2. Numerical Method

_{F}is the fractional volume open to flow to feature a mass source and Ax, Ay, and Az are the fractional area open to flow in the x, y and z directions. The factor of CON = 0.45 is typically used to account for the worst case situations.

## 3. Results and Discussion

#### 3.1. Simulation Results

#### 3.2. Experimental Results

## 4. Conclusions

- The weak momentum flow region in front of the streamlined bump in the discharge pipe of each type of test gullies formulates an obstacle for air-bubble transportations out of the gullies. A considerable amount of trapped air-bubbles in the gully drum undermines the transportation of glass balls out of the gully.
- The mass ratios between the intercepted and supplied glass balls for both test gullies keep increasing by increasing the water flow rate to enhance the flow momentum. With the higher flow momentum for the beveled nozzle flow toward the exit pipe, the mass ratios between the intercepted and supplied glass balls for the gully with the beveled nozzle exit are consistently higher than those found for the gully with the downward nozzle exit. With the enhanced air-bubble discharges at the flow rate above 0.7 L/s, the mass ratio between the intercepted and supplied glass balls increases drastically for the gully with the beveled nozzle.
- The impacts of nozzle configuration on the sustainable static and dynamic pressure loadings for present type of shallow gullies with the streamlined bump in the exit pipe are not noticeable.
- With diminished air-bubble effects and constant water head of 20 mm, the gully with downward nozzle exit exhibits the higher flow rates. Justified by the superior purification performance for the shallow gully with the beveled nozzle exit, the moderation of velocity gradients at the nozzle exit is recommended for boosting the maximum flow rate.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

English Symbols | |

A | fractional area open to flow (m^{2}) |

f | volumetric source of external force vector (N m^{−3}) |

g | gravitational acceleration (m s^{−2}) |

h | grid interval (m) |

P | pressure (N m^{−2}) |

$\dot{\mathrm{Q}}$ | total volume flow rate through gully (m^{3} s^{−1}) |

u | fluid velocity vector (m s^{−1}) |

${u}_{\mathrm{diff}}$ | particle diffusion velocity vector (m s^{−1}) |

V_{F} | fractional volume open to flow (m^{3}) |

u, v, w | fluid velocity component in x, y, z directions (m s^{−1}) |

x, y, z | orthogonal coordinates (m) |

Greek symbols | |

α | drag coefficient per particle mass (s^{−1}) |

β | drag coefficient per particle mass (s^{−1}) |

μ | Fluid viscosity (kg m^{−1} s^{−1}) |

ρ | Fluid density (kg m^{−3}) |

Subscripts | |

p | particle |

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**Figure 1.**Test gullies with the convergent nozzle of: (

**a**) beveled discharge; and (

**b**) vertical discharge.

**Figure 2.**Experimental facilities for testing: (

**a**) sustainable positive and negative pressures at steady and unsteady conditions; (

**b**) maximum flow rate; and (

**c**) self-purification performance.

**Figure 3.**(

**a**) Simulated temporal u, v, and w variations at location P2 using the grids of h = 4 and 5 mm; and (

**b**) comparisons of water level elevation from drum bottom at water flow rates of 0.4, 0.5, 0.6, 0.7 and 0.8 L/s between numerical predictions and experimental measurements.

**Figure 4.**Distributions of velocity and static-pressure at t = 2, 4, 6, 10 s on: (

**a**) z = 0; and (

**b**) x = 0 planes for test gully with beveled nozzle flow with ${\dot{\mathrm{Q}}}_{\mathrm{floor}}$ = 0.6 L/s.

**Figure 5.**Distributions of velocity and static-pressure at t = 2, 4, 6, 10 s on: (

**a**) z = 0; and (

**b**) x = 0 planes for test gully with downward nozzle flow with ${\dot{\mathrm{Q}}}_{\mathrm{floor}}$ = 0.6 L/s.

**Figure 6.**Temporal variations of glass ball transportation through gully with beveled nozzle flow at entry water flow rate of 0.6 L/s.

**Figure 7.**Temporal variations of glass ball transportation through gully with downward nozzle flow at entry water flow rate of 0.6 L/s.

**Figure 9.**Flow snapshots for glass ball transportation through gullies with: (

**a**) beveled; and (

**b**) downward nozzle flows at 0.8L/s.

**Figure 10.**Variations of mass ratio between intercepted and supplied glass balls against ${\dot{\mathrm{Q}}}_{\mathrm{floor}}\text{}$.

**Figure 11.**Temporal variations of water trap level and air pressure in gully drums with (

**a**) beveled and (

**b**) downward nozzle flows.

**Figure 12.**Temporal variations of air pressure and water trap height at: (

**a**) positive; and (

**b**) negative pressure loadings for test gullies with beveled and downward nozzle exits.

Type of Tests | Test Conditions | |
---|---|---|

Experiment | CFD | |

Sustainable pressures | ˇ(Tested) | |

Flow structures | 0.6, 0.8 L/s | 0.6, 0.8 L/s |

Maximum flow rate | ˇ(Tested) | |

Self-purification | 0.5, 0.6, 0.7, 0.8 L/s | 0.5, 0.6, 0.7, 0.8 L/s |

Diameter | Density | Number of Particles | Duration of Falling Particles into Gully |
---|---|---|---|

5 mm | 2500 kg/m^{3} | 3000 | 0–30 s |

Flow Entry Condition | Gully with Beveled Nozzle Exit | Gully with Downward Nozzle Exit |
---|---|---|

${\dot{\mathrm{Q}}}_{\mathrm{floor}}$ (L/s) | 1.12 | 1.51 |

${\dot{\mathrm{Q}}}_{\mathrm{side}1}$ (L/s) | ≥0.92 | ≥0.89 |

${\dot{\mathrm{Q}}}_{\mathrm{side}2}$ (L/s) | ≥0.86 | ≥0.89 |

${\dot{\mathrm{Q}}}_{\mathrm{side}3}$ (L/s) | ≥0.84 | ≥0.96 |

${\dot{\mathrm{Q}}}_{\mathrm{side}4}$ (L/s) | ≥0.88 | ≥0.86 |

${\dot{\mathrm{Q}}}_{\mathrm{side}}$+${\dot{\text{}\mathrm{Q}}}_{\mathrm{floor}}$ (L/s) | ${\dot{\mathrm{Q}}}_{\mathrm{side}}$ = 0.8, ${\dot{\mathrm{Q}}}_{\mathrm{floor}}$ = 0.22 | ${\dot{\mathrm{Q}}}_{\mathrm{side}}$ = 0.8, ${\dot{\mathrm{Q}}}_{\mathrm{floor}}$ = 0.52 |

${\dot{\mathrm{Q}}}_{\mathrm{side}1}$+${\dot{\text{}\mathrm{Q}}}_{\mathrm{side}2}$ (L/s) | ${\dot{\mathrm{Q}}}_{\mathrm{side}1}$ = 0.8, ${\dot{\mathrm{Q}}}_{\mathrm{side}2}$ = 0.09 | ${\dot{\mathrm{Q}}}_{\mathrm{side}1}$ = 0.8, ${\dot{\mathrm{Q}}}_{\mathrm{side}2}$ = 0.39 |

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**MDPI and ACS Style**

Lo, D.-C.; Chang, S.W.; Liu, H.-F.; Chen, C.-Y.
Experimental and Numerical Study of Hydrodynamic Characteristics of Gullies for Buildings. *Water* **2018**, *10*, 165.
https://doi.org/10.3390/w10020165

**AMA Style**

Lo D-C, Chang SW, Liu H-F, Chen C-Y.
Experimental and Numerical Study of Hydrodynamic Characteristics of Gullies for Buildings. *Water*. 2018; 10(2):165.
https://doi.org/10.3390/w10020165

**Chicago/Turabian Style**

Lo, Der-Chang, Shyy Woei Chang, Hsin-Feng Liu, and Chao-Yan Chen.
2018. "Experimental and Numerical Study of Hydrodynamic Characteristics of Gullies for Buildings" *Water* 10, no. 2: 165.
https://doi.org/10.3390/w10020165