# Experimental Study of Void Fraction Measurement Using a Capacitance-Based Sensor and ANN in Two-Phase Annular Regimes for Different Fluids

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup of the Concave Capacitive Sensor and Measurements

## 3. Numerical Simulations

#### 3.1. Modelled Configuration

_{2}= 32 mm, an outer radius of R3 = 33 mm and a length of 120 mm. Also, the separation between the electrodes was set at 5 mm, as shown in Figure 7. Water (chemical formula of H

_{2}O, relative permittivity of 81 and density of 997.77 kg/cm

^{3}) and air (relative permittivity of 1 and density of 1.204 kg/m

^{3}) were considered as the liquid and gas phases, separately. A 3-dimensional view of the electrodes pattern, a volumetric view of the simulated setup and the meshed model of the capacitance-based sensor in a typical void fraction are illustrated in Figure 8. Moreover, void fractions of 0, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 percentage were also considered in the simulation in the annular flow, as shown in Figure 9. Additionally, the fluid component was divided into 17,832 3D tetrahedral fundamentals using FEM. The voltage and electric field dispersions of the FEM simulation results are illustrated in Figure 10. The results of the simulations are presented in Table 2.

#### 3.2. Validation of Simulations

## 4. Artificial Neural Network

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Bubble flow, (

**b**) Plug slug flow, (

**c**) Foam flow, (

**d**) Annular streak flow, (

**e**) Annular flow.

**Figure 7.**Cross-section diagram of the simulated capacitance-based sensor in the middle of the electrode.

**Figure 8.**(

**a**) 3-Dimensional view of the electrodes pattern. (

**b**) Volumetric view the simulated setup. (

**c**) Meshed model of the simulated structure.

**Figure 10.**(

**a**) Cross-section diagram of the voltage dispersion in the middle of the electrode. (

**b**) Cross-section diagram of the electric field dispersion in the middle of the electrode. (

**c**) Sketch of the electric field direction. (

**d**) 3D view of the electric field.

**Figure 13.**Regression diagrams of the predicted and simulated results for the void fractions: (

**a**) training set and (

**b**) testing set.

**Table 1.**Measured results by the experimental setup for the concave sensor in the annular water–air regime.

Void Fraction (%) | Measured Capacitance (pF) |
---|---|

100 | 27.21 |

90 | 44.73 |

80 | 53.19 |

70 | 57.65 |

60 | 60.83 |

50 | 61.80 |

40 | 63.22 |

30 | 64.38 |

20 | 65.23 |

10 | 66.65 |

0 | 68.11 |

**Table 2.**Simulation results calculated by COMSOL Multiphysics for the concave sensor in the annular water–air regime.

Void Fraction (%) | Simulated Capacitance (pF) |
---|---|

100 | 10.067 |

90 | 15.317 |

80 | 18.957 |

70 | 21.178 |

60 | 22.967 |

50 | 24.391 |

40 | 25.481 |

30 | 26.389 |

20 | 27.113 |

10 | 27.749 |

0 | 28.341 |

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**MDPI and ACS Style**

Veisi, A.; Shahsavari, M.H.; Roshani, G.H.; Eftekhari-Zadeh, E.; Nazemi, E.
Experimental Study of Void Fraction Measurement Using a Capacitance-Based Sensor and ANN in Two-Phase Annular Regimes for Different Fluids. *Axioms* **2023**, *12*, 66.
https://doi.org/10.3390/axioms12010066

**AMA Style**

Veisi A, Shahsavari MH, Roshani GH, Eftekhari-Zadeh E, Nazemi E.
Experimental Study of Void Fraction Measurement Using a Capacitance-Based Sensor and ANN in Two-Phase Annular Regimes for Different Fluids. *Axioms*. 2023; 12(1):66.
https://doi.org/10.3390/axioms12010066

**Chicago/Turabian Style**

Veisi, Aryan, Mohammad Hossein Shahsavari, Gholam Hossein Roshani, Ehsan Eftekhari-Zadeh, and Ehsan Nazemi.
2023. "Experimental Study of Void Fraction Measurement Using a Capacitance-Based Sensor and ANN in Two-Phase Annular Regimes for Different Fluids" *Axioms* 12, no. 1: 66.
https://doi.org/10.3390/axioms12010066