# Numerical 3D Model Development and Validation of Curb-Cut Inlet for Efficiency Prediction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Site Characteristics

^{2}(2764 ft

^{2}) of depressed vegetated beds into this area, with curb-cut inlets hydraulically connecting them to the surrounding street. The site’s total catchment area is 1242.2 m

^{2}(13,500 ft

^{2}), making its total hydraulic loading ratio of 4.8 to 1. The actual dimensions of the street, apron, and inlet geometries of each of the two inlets are presented in Table 1. Although both inlets are on the same street, the longitudinal and transverse street slopes differ slightly between the two inlets. In addition, though the inlet length, inlet depth, apron width, and apron length are the same for both inlets, the tributary catchment area associated with the NW inlet is half of that of the SW inlet.

#### 2.2. Fieldwork

#### 2.2.1. Field Survey

#### 2.2.2. Field Experiments Using a Hydrant Test

#### 2.2.3. Selection of Flow Rates for Field Experiment

- Q—inflow (CMS),
- K—conversion factor from English to metric units = 0.0028,
- C—dimensionless runoff coefficient = 0.9 for impervious street [5],
- I—precipitation intensity (mm/hr), and
- A—drainage area (0.0325 ha for the NW inlet and 0.065 ha for the SW inlet).

#### 2.3. CFD Model Development

#### 2.3.1. Discretization and Surface Tracking Codes

^{TM}, Flow Science Inc., Santa Fe, NM, USA) [32,33]. The selection of specific mesh properties was also informed by the grid analysis, described in Section 2.3.4.

#### 2.3.2. Turbulence Model Selection

^{2}/s.

#### 2.3.3. Time Step and Initial Condition

#### 2.3.4. Mesh Size Selection and Definition of Boundary Conditions

#### 2.4. Grid Analysis

#### 2.5. Definition of Boundary Conditions

#### 2.6. Replicating Inlet Clogging

#### 2.7. Surface Roughness

#### 2.8. Inlet Performance Metric

^{2}), or flow rate (CMS)), was also computed per Equation (4)).

#### 2.9. Convergence Assessment

## 3. Validation Results

#### 3.1. Qualitative Validation

#### 3.2. Quantitative Validation

## 4. Scenarios for Sensitivity Analysis

#### 4.1. Effect of Flow Rate on Inlet Efficiency

#### 4.2. Effect of Clogging on Inlet Efficiency

## 5. Sensitivity Analysis Results

#### 5.1. Effect of Flow Rate on Inlet Efficiency

#### 5.2. Effect of Inlet Clogging on Inlet Efficiency

## 6. Discussion

#### 6.1. Possible Sources of Error in Model Validation

#### 6.1.1. Velocity Measurements

#### 6.1.2. Survey Data

#### 6.1.3. Differences in Street Slope and Apron Slope

#### 6.2. Effect of Inlet Hydraulics on Inlet Efficiency

#### 6.2.1. Inlet Hydraulics—Effect of Upstream Velocity and Its Effect on Formation of Inlet Clogging

#### 6.2.2. Effect of Upstream and Downstream Flow Condition on Inlet Efficiency

#### 6.3. Model Application—Effect of Inlet Clogging on the Stage-Discharge Curve of Flume Fitted into the Inlet

^{2}decreases from 0.96 to 0.7 as clogging increases from 0% to 75%. It further drops down to 0.5 as the clogging increases to 85%.

## 7. Conclusions

#### Design Implications

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Results of Error Analysis

# Cells | Modeled Inflow (CMS) | Observed Inflow (CMS) | Relative Error (%) | Modeled Inlet Efficiency (%) | Observed Inlet Efficiency (%) | Absolute Error (%) |
---|---|---|---|---|---|---|

596311 | 0.00535 | 0.00552 | -3.07971 | 14.39000 | 11.95000 | 2.44000 |

397833 | 0.00553 | 0.00553 | 0.05134 | 11.98535 | 11.95000 | 0.03535 |

227896 | 0.00558 | 0.00552 | 1.08696 | 15.45000 | 11.95000 | 3.50000 |

198032 | 0.00586 | 0.00552 | 6.15942 | 15.87000 | 11.95000 | 3.92000 |

194635 | 0.00590 | 0.00552 | 6.88406 | 16.00000 | 11.95000 | 4.05000 |

162023 | 0.00600 | 0.00552 | 8.69565 | 18.28000 | 11.95000 | 6.33000 |

93754 | 0.00660 | 0.00552 | 19.56522 | 26.23000 | 11.95000 | 14.28000 |

#### Appendix A.2. Additional Validation Parameters

**Figure A1.**Simulated and observed flow profile over the street surface. Dotted blue lines represent the location of the inlet. The inlet was located between −0.82 and 0 m. The upstream flow depths were measured from 0 to 6 m, and downstream flow depths were measured at −0.82 and −1 m.

**Figure A2.**Comparison of simulated and observed flow rate, velocity, and depth in flume for the NW and SW model for validation scenarios. Simulation results and observed data for all three parameters are linearly correlated. The grey bands around the line represent the standard error of regression line.

#### Appendix A.3. Site Photographs

#### Appendix A.4. Additional Explanation on Effect of Upstream and Downstream Flow Condition on Inlet Efficiency

- F—Froude number (unitless),
- V—the average velocity upstream of the inlet (m/s),
- G—acceleration due to gravity (m/s
^{2}), - D—depth of flow upstream of the inlet (m),

**Figure A4.**Variation of Froude number for 0.00755 CMS presented flow rate scenario for non-clogging NW and SW inlets model.

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**Figure 1.**(

**A**) Location of site; (

**B**) site setting—flow direction, inlets with tributary drainage areas (TDA), location of data collection points; (

**C**) detailed sketch of inlet with dimensions of inlet, apron, and flow definitions; and (

**D**) photograph of the southeast (SE) and southwest (SW) inlets fitted with the inlet channel and flume for flow monitoring.

**Figure 2.**Schematics of research methods illustrating the process of developing the computational fluid dynamic (CFD) model and validating it against field data.

**Figure 3.**CFD—model setup boundary conditions. Yellow dots represent the probes, and blue planes represent the flux planes to measure the modeled volume flow rate and depth in FLOW-3D. Teal lines show meshes defined in the model.

**Figure 4.**(

**A**) Photograph of inlet clogging during hydrant test; (

**B**) Screenshot of modeled inlet clogging; 90% clogging validation scenario. Observed and modeled inflow and inlet bypass.

**Figure 5.**(

**A**) Photograph of inlet bypass during hydrant test for 0.0033 CMS flowrate; (

**B**) Screenshot of modeled inlet bypass for 0.0033 CMS flowrate. Observed and modeled inflow and inlet bypass at the SW inlet.

**Figure 7.**Effect of increased flow rate and inlet clogging on inlet efficiency for the northwest (NW) inlet.

**Figure 9.**Graphical presentation of depth-averaged velocity for 0% (

**left**) and 50% (

**right**) clogging scenarios for the SW inlet.

**Figure 10.**Application of CFD model to evaluate the effect of inlet clogging on the stage-discharge curve.

Physical Characteristics | Validation |
---|---|

Street width, curb to crown | 3.5 m |

Length of inlet | 0.82 m |

Opening depth of inlet | 0.154 m |

Upstream (U/S) gutter depression (apron) length | 0.425 m |

Downstream (D/S) apron length | 0.425 m |

Apron width | 0.445 m |

NW inlet upstream street slopes (Sx, SL) | 1.50%, 1.18% |

SW inlet upstream street slopes (Sx, SL) | 1.15%, 1.30% |

**Table 2.**Flow rate selection—peak flow rate calculations based on peak rainfall intensity with a 15-min duration storm (NOAA, 2017).

Inlet | Flow Rate Tested at the Field (CMS) | Peak Flow Rate Calculated Based on the Rain Intensity Q (CMS) | The Nearest Equivalent to 15-min Duration Rain Intensity (mm/hr) | Corresponding Return Period (Years) |
---|---|---|---|---|

SW | 0.0090 | 0.01032 | 63 | 1 |

NW | 0.0055 | 0.00516 | 63 | 1 |

0.0068 | 0.00614 | 75 | 2 | |

0.0075 | 0.00778 | 95 | 5 | |

0.0090 | 0.00909 | 111 | 10 |

Inlet | Test | Simulated Inflow (CMS) | Observed Inflow (CMS) | Relative Error—Inflow Flowrate (%) | Simulated Intercepted Flow (CMS) | Observed Intercepted Flow (CMS) | Relative Error—Intercepted Flowrate (%) | Modeled Inlet Efficiency (%) | Observed Inlet Efficiency (%) |
---|---|---|---|---|---|---|---|---|---|

NW | T1 | 0.00735 | 0.00736 | −0.13 | 0.00179 | 0.00049 | −265.30 | 24.35 | 6.65 |

NW | T2 | 0.00567 | 0.00566 | 0.17 | 0.00150 | 0.00041 | −265.85 | 26.45 | 7.24 |

NW | T3 | 0.00322 | 0.00330 | −2.42 | 0.00120 | 0.00034 | −252.94 | 37.26 | 10.30 |

SW | T4 | 0.00794 | 0.00755 | −5.16 | 0.00103 | 0.00108 | −4.62 | 12.97 | 14.30 |

SW | T5 | 0.00586 | 0.00552 | −6.15 | 0.00093 | 0.00066 | 40.90 | 15.87 | 11.95 |

SW | T6 | 0.00315 | 0.00314 | −0.31 | 0.00075 | 0.00057 | 31.57 | 23.80 | 18.15 |

NW | T1 | 0.01212 | 0.01016 | −19.24 | 0.93313 | 0.48263 | −93.34 | 0.48263 | −93.34 |

NW | T2 | 0.01232 | 0.01143 | −7.75 | 0.82539 | 0.46904 | −75.97 | 0.46904 | −75.97 |

NW | T3 | 0.01350 | 0.01270 | −6.31 | 0.74312 | 0.39904 | −86.22 | 0.39904 | −86.22 |

SW | T4 | 0.01953 | 0.02032 | 3.88 | 0.91998 | 0.91575 | −0.46 | 0.91575 | −0.46 |

SW | T5 | 0.01484 | 0.01524 | 2.62 | 0.96437 | 0.86207 | −11.86 | 0.86207 | −11.86 |

SW | T6 | 0.01412 | 0.01397 | −1.07 | 0.74851 | 0.67295 | −11.22 | 0.67295 | −11.22 |

Flow Rate (CMS) | Selection Reference |
---|---|

0.00044 | Observed inlet capacity during precipitation event dated July 29,2019 |

0.001 | Interpolation |

0.0028 | Interpolation |

0.0033 | Hydrant test |

0.0055 | Hydrant test and intensity corresponding to 15 min duration, 1-year return period with NW inlet |

0.0068 | Interpolation |

0.00755 | Hydrant test and intensity corresponding to 15 min duration, 5-year return period with the NW inlet, and less than 1-year return period for the SW inlet |

**Table 5.**Model scenario matrix depicting the number of model runs at each flow and clogging condition.

Clogging Conditions | Flow Rate (CMS) | Total for NW Inlet | Total for SW Inlet | ||||||
---|---|---|---|---|---|---|---|---|---|

0.00044 | 0.001 | 0.0028 | 0.0031 | 0.0055 | 0.0068 | 0.00755 | |||

0% | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 7 |

10% | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 7 |

25% | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 7 |

50% | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 7 |

75% | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 7 |

90% | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 7 |

Total | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 42 | 42 |

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## Share and Cite

**MDPI and ACS Style**

Shevade, L.J.; Lo, L.J.; Montalto, F.A. Numerical 3D Model Development and Validation of Curb-Cut Inlet for Efficiency Prediction. *Water* **2020**, *12*, 1791.
https://doi.org/10.3390/w12061791

**AMA Style**

Shevade LJ, Lo LJ, Montalto FA. Numerical 3D Model Development and Validation of Curb-Cut Inlet for Efficiency Prediction. *Water*. 2020; 12(6):1791.
https://doi.org/10.3390/w12061791

**Chicago/Turabian Style**

Shevade, Leena Jaydeep, L. James Lo, and Franco A. Montalto. 2020. "Numerical 3D Model Development and Validation of Curb-Cut Inlet for Efficiency Prediction" *Water* 12, no. 6: 1791.
https://doi.org/10.3390/w12061791