# Flow Velocity Distribution Towards Flowmeter Accuracy: CFD, UDV, and Field Tests

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Electromagnetic Flowmeters

## 3. Equipment and Layout

#### 3.1. Flow Meter Installation

#### 3.2. UDV Installation

_{max}) exists for each pulse repetition frequency (${F}_{prf}$) [11]:

_{max}) is also defined by the pulsed repetition frequency Equation (5), and consequently the product of P

_{max}and V

_{max}is constant, and is given by Equation (6) [13,14]:

#### 3.3. Experimental Facility

^{3}/h were tested. In each UDV measurement, the velocity was captured in 100 different points in a total of 100 profiles.

^{3}/h for both layouts.

^{3}/h and 12 m

^{3}/h, respectively.

## 4. CFD Model

#### 4.1. Governing Equations

^{3}and $1.0097\times {10}^{-6}$ m

^{2}/s, respectively.

#### 4.2. Mesh Definition and Solution Convergence

#### 4.3. Calibration and Validation

^{3}/h are bigger than 100 m

^{3}/h (Table 3). For the volume flow rate of 100 m

^{3}/h it is verified that the error associated to geometry 1 is the smallest one. From the two experimental tests, geometry 2 corresponds to the worst scenario, since the pipe is not long enough to dissipate the flow perturbations caused by the profile vertical curves.

## 5. Case Study

#### 5.1. Geometry Layout

#### 5.2. Simulations

#### 5.3. Solution

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Electromagnetic flowmeters components: (

**a**) primary element; (

**b**) convertor (adapted from [1]).

**Figure 2.**Electromagnetic flowmeter accuracy curve [1].

**Figure 3.**Operating principle of an electromagnetic flow meter [1].

**Figure 6.**Ultrasonic Doppler velocimetry (UDV) operating principle (adapted from [12]).

**Figure 7.**System layouts 1 and 2: (

**a**) facility scheme; (

**b**) lab installation, with flow direction identified by the blue arrow.

**Figure 13.**Comparison of velocity distribution profiles obtained through CFD model and experiments: (

**a**) for 100 m

^{3}/h; (

**b**) for 12 m

^{3}/h.

**Figure 15.**Weighting function distribution of uniform magnetic field point electrode electromagnetic flowmeter. Calculated limits (black continuous lines) analogous to Figure 4. Data provided by the model represented by the blue ticks.

**Figure 16.**The best function for the calculus of the factor for the region near the electrodes to fit the experiments (blue marks represent the experimental data used).

**Figure 17.**Pumping station layout (

**a**); photographs of the different parts of the hydraulic system (

**b**); modelling geometry—pump location identified by the green pipe section, flowmeter identified by the red line, flow direction identified by the blue arrow (plan view on the left and 3D view on the right) (

**c**).

**Figure 18.**System layout modelling geometry—with the flowmeter section identified by the red arrow and flow direction identified by the blue arrow.

**Figure 19.**Streamlines simulation along the hydraulic circuit for the pipe branch system layout (flowmeter section identified by the red arrow), in m/s (

**a**); Velocity distribution in the cross section of the flow meter (

**b**).

**Figure 20.**System layout proposed modelling geometry—the flowmeter section represented by the red arrow; flow direction identified by the blue arrow (added pipe in red).

**Figure 21.**Streamlines simulation along the hydraulic circuit for the proposed system layout (flowmeter section identified by the red arrow), in m/s (

**a**); velocity distribution in the electrodes cross section for the proposed geometry (

**b**).

**Table 1.**Test results: experiments and relative errors achieved in section A, for different volume flow rates.

Geometry | Q_{theoretical} (m³/h) | Tests Results | Error | |||||
---|---|---|---|---|---|---|---|---|

V_{ND100} (L) | V_{reference} (L) | t_{theoretical} (s) | t_{real} (s) | Q_{reference} (m^{3}/h) | ND100 (%) | Re (-) | ||

1 | 100 | 4980 | 5000 | 180 | 173 | 104 | −0.40% | 365,631 |

12 | 1006 | 1018 | 305 | 285 | 13 | −1.18% | 45,704 | |

2 | 100 | 5026 | 5000 | 180 | 172 | 105 | 0.52% | 369,147 |

12 | 1035 | 1020 | 306 | 295 | 12 | 1.47% | 42,188 |

Characteristics | 100 m^{3}/h | 12 m^{3}/h |
---|---|---|

Inlet | 5.6 bar | 5.8 bar |

Outlet | 0.59 m/s | 0.07 m/s |

Wall | No-slip | |

Mesh | Physics-controlled | |

Flow conditions | Steady state |

Geometry | Q = 100 m^{3}/h | Q = 12 m^{3}/h | ||
---|---|---|---|---|

Error | Error | |||

Experimental | Model | Experimental | Model | |

1 | −0.40% | −0.48% | −1.18% | −1.27% |

2 | 0.52% | 1.11% | 1.47% | 1.61% |

Material | Steel |
---|---|

Expansion | ND700 to ND800 |

Remaining pipes | ND800 |

Flowmeter | ND800 |

Inlet | 9.5 bar |
---|---|

Outlet | 1.5 m/s |

Wall | No-slip |

Mesh | Physics-controlled |

Flow conditions | Steady state |

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**MDPI and ACS Style**

Simão, M.; Besharat, M.; Carravetta, A.; Ramos, H.M.
Flow Velocity Distribution Towards Flowmeter Accuracy: CFD, UDV, and Field Tests. *Water* **2018**, *10*, 1807.
https://doi.org/10.3390/w10121807

**AMA Style**

Simão M, Besharat M, Carravetta A, Ramos HM.
Flow Velocity Distribution Towards Flowmeter Accuracy: CFD, UDV, and Field Tests. *Water*. 2018; 10(12):1807.
https://doi.org/10.3390/w10121807

**Chicago/Turabian Style**

Simão, Mariana, Mohsen Besharat, Armando Carravetta, and Helena M. Ramos.
2018. "Flow Velocity Distribution Towards Flowmeter Accuracy: CFD, UDV, and Field Tests" *Water* 10, no. 12: 1807.
https://doi.org/10.3390/w10121807