# Numerical and Experimental Approaches to Estimate Discharge Coefficients and Energy Loss Coefficients in Pressurized Grated Inlets

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{d}is the discharge coefficient, Q is the discharge passing through the grate (m

^{3}/s), ${A}_{g}$ is the area of gaps in the grate (m

^{2}), $g$ is the gravitational acceleration (9.81 m/s

^{2}), and $\Delta h$ is the average water depth above the grate (taking the grate as a datum) (m).

_{d}for the grate, Equation (1) was considered, and for each surcharge grate, water levels were measured over the grate inlet at 20 points in order to achieve the average flow depth.

^{2}), and v is the velocity of discharge through the grate, calculated as Flowrate divided by area of gaps (m/s

^{2}).

#### 2.1. Experimental Set-Up

#### 2.2. Data Collection

#### 2.3. Numerical Simulation

#### 2.3.1. Numerical Model

_{F}is the fractional volume open to flow, $\rho $ is the density, $u$, $v$, $w$ are the velocity components, A

_{x}, A

_{y}, A

_{z}are the fractional areas in the $x$, $y$ and $z$ directions, respectively, and the source term of density is R

_{SOR}.

_{x}, G

_{y}, G

_{z}are body accelerations in the coordinate directions (x, y, z) and (f

_{x}, f

_{y}, f

_{z}) are the viscos accelerations in the coordinate direction (x, y, z), respectively.

^{2}, using the first order method. The parameter of gravity in the “x” and “y” directions changed according to the inclination of the platform for the different combinations of geometry (longitudinal and transversal slopes) studied.

_{i}is the coordinate in the i-axis, u is the dynamic viscosity, u

_{t}is the turbulent dynamic viscosity, and P

_{k}is the production of TKE. The term of turbulence viscosity was estimated using Equation (9):

#### 2.3.2. Pre-Processing

_{min}) as a flowrate between 10 l/s and 50 l/s.

#### 2.3.3. Post-Processing

## 3. Results

_{d}are between 0.18 (10 l/s) and 0.46 (50 l/s). The values of the discharge coefficient obtained for the three different types of grates through experimental and numerical simulation demonstrate that a numerical approach could substitute for experimental tests to achieve accurate discharge coefficient values. Furthermore, it was demonstrated that discharge coefficient values are quite far from the usual value of 0.6 and vary depending on grate type and outflow rate.

_{d}presents a good approximation of the experimental values. This creates the opportunity to simulate more inlet grates and outflows using the numerical model, which is significantly less time consuming.

## 4. Conclusions

_{d}are related to the same physical phenomenon: the energy lost by the flow through the grate. This paper analyzes these two parameters at experimental and numerical levels.

_{d}present a good approximation in comparison with the experimental values. This creates the opportunity to simulate more inlet grates and flow rates using the numerical model, which is a faster and less expensive approach.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Depth location of water level measurement over the grate [15].

**Figure 6.**Mesh domain of the model [57].

**Figure 8.**Comparison of discharge coefficients from experimental data vs. numerical simulation for grate 1.

**Figure 9.**Comparison of discharge coefficients from experimental data vs. numerical simulation for grate 2.

**Figure 11.**Comparison of energy loss coefficients from experimental data vs. numerical simulation for grates 1, 2 and 3.

Cell Size (cm) | Time (mins) | Total Number of Cells (Unit) |
---|---|---|

0.5 | 920 | 25,292,512 |

0.75 | 139 | 772,701 |

1 | 25 | 324,064 |

1.25 | 11 | 164,240 |

1.5 | 5 | 94,875 |

2 | 2 | 40,508 |

3 | 0.8 | 12,285 |

Flowrate (l/s) | Grate Type 1 Exp. C _{d} | Grate Type 1 Num. C _{d} | Grate Type 2 Exp. C _{d} | Grate Type 2 Num. C _{d} | Grate Type 3 Num. C _{d} |
---|---|---|---|---|---|

10 | 0.14 | 0.15 | 0.18 | 0.15 | 0.18 |

20 | 0.22 | 0.22 | 0.23 | 0.23 | 0.26 |

30 | 0.29 | 0.29 | 0.31 | 0.30 | 0.34 |

40 | 0.36 | 0.36 | 0.36 | 0.36 | 0.42 |

50 | 0.41 | 0.40 | 0.41 | 0.40 | 0.46 |

Flowrate (l/s) | Grate Type 1 Exp. k | Grate Type 1 Num. k | Grate Type 2 Exp. k | Grate Type 2 Num. k | Grate Type 3 Num. k |
---|---|---|---|---|---|

20 | 3.41 | 1.56 | 1.35 | 0.56 | 0.65 |

30 | 2.02 | 0.79 | 0.44 | 0.49 | 0.46 |

40 | 0.44 | 0.35 | 0.39 | 0.29 | 0.14 |

50 | 0.42 | 0.22 | 0.25 | 0.15 | 0.16 |

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**MDPI and ACS Style**

Tellez-Alvarez, J.; Gómez, M.; Russo, B.; Amezaga-Kutija, M.
Numerical and Experimental Approaches to Estimate Discharge Coefficients and Energy Loss Coefficients in Pressurized Grated Inlets. *Hydrology* **2021**, *8*, 162.
https://doi.org/10.3390/hydrology8040162

**AMA Style**

Tellez-Alvarez J, Gómez M, Russo B, Amezaga-Kutija M.
Numerical and Experimental Approaches to Estimate Discharge Coefficients and Energy Loss Coefficients in Pressurized Grated Inlets. *Hydrology*. 2021; 8(4):162.
https://doi.org/10.3390/hydrology8040162

**Chicago/Turabian Style**

Tellez-Alvarez, Jackson, Manuel Gómez, Beniamino Russo, and Marko Amezaga-Kutija.
2021. "Numerical and Experimental Approaches to Estimate Discharge Coefficients and Energy Loss Coefficients in Pressurized Grated Inlets" *Hydrology* 8, no. 4: 162.
https://doi.org/10.3390/hydrology8040162