# Ozone Transport in 311 MVA Hydrogenerator: Computational Fluid Dynamics Modelling of Three-Dimensional Electric Machine

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Review

#### 2.1. Partial Discharges in Hydrogenerators and Ozone Production

#### 2.1.1. Partial Discharges

#### 2.1.2. Partial Discharges and Ozone Production

#### 2.2. Mass Conservation Law for Ozone

^{3}, D is the diffusion coefficient (m${}^{2}$/s), R is the molar rate of species production per unit volume, given in mol/(m${}^{3}\xb7$s), and ${\overrightarrow{u}}_{m}$ is the average mass velocity vector field (m/s).

#### 2.3. Parameters of Ozone Fluid Dynamics

## 3. The Novel Hydrogenerator Numerical Model

#### 3.1. Geometry and Materials

#### 3.2. Boundary Conditions

#### 3.3. Finite Element Mesh and Computational Resources

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Ozone transmissions through numerical models of radiators as functions of air velocity: copper sheets and screen models.

**Figure A2.**Perspective views of ozone concentration distributions (ppb) in benchmark simulations obtained with (

**a**) the radiator screen model and (

**b**) the realistic copper representation of the radiator.

**Figure A3.**Magnitude of velocity field (m/s) on $yz$-plane in benchmark simulations: (

**a**) radiator screen model and (

**b**) realistic copper representation of the radiator and the source region indicated by the small square at the left side.

**Figure A4.**Ozone concentrations (ppb) on $yz$-plane in benchmark simulations: (

**a**) radiator screen model and (

**b**) realistic copper representation of the radiator.

**Figure A5.**Ozone concentrations (ppb) on $xz$-plane in benchmark simulations: (

**a**) radiator screen model and (

**b**) realistic copper representation of the radiator.

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**Figure 1.**Respective probabilities of factors leading to damages in insulation [26].

**Figure 2.**Overview of the finite element model of the hydrogenerator: labeling of the structural parts. Wall height ${w}_{h}$ and width ${w}_{l}$ are provided.

**Figure 3.**Hydrogenerator stator bars and their dimensions: (

**a**) the coil-type bar model and (

**b**) all the 378 stator bars as arranged in the model of the hydrogenerator. Dimensions ${b}_{w}$ and ${b}_{h}$ are provided.

**Figure 4.**Hydrogenerator stator core and its dimensions: (

**a**) perspective view and (

**b**) top view. Dimensions ${c}_{h},{c}_{t},{c}_{s},{c}_{r},{c}_{R},{t}_{l},{g}_{l},{t}_{h}$, and ${g}_{h}$ are given.

**Figure 5.**Hydrogenerator air directors and radiator: (

**a**) perspective view and (

**b**) top view. The dimensions ${d}_{l}$, ${r}_{l}$, ${r}_{h}$, and ${d}_{r}$ are given.

**Figure 7.**Overview of the finite element mesh conceived for representing the hydrogenerator structure. Yellowish regions are air directors.

**Figure 8.**Part of the conceived computational mesh for representing ozone sources (highlighted in blue) and stator bars.

**Figure 9.**Labels of each hydrogenerator radiator and angles of reference: (

**a**) perspective view and (

**b**) top view. Radiators are seen with shades of blue.

**Figure 10.**Ozone concentration (ppb) overview in the numerical model of the hydrogenerator for simulations (

**a**) A and (

**b**) B (with source ${S}_{10}$ additionally activated).

**Figure 11.**Overview of ozone concentration (ppb) in numerical model of hydrogenerator in simulations: (

**a**) C (source ${S}_{8}$ additionally activated) and (

**b**) D (source ${S}_{0}$ additionally activated).

**Figure 12.**Ozone concentration (ppb) overview in the numerical model of the hydrogenerator for simulation D (including vector velocity field with log-scale vector sizes).

**Figure 13.**Ozone distribution (ppb) and velocity field on the vertical plane perpendicular to sources ${S}_{4}$ and ${S}_{5}$ (simulation D, $\varphi =315$°).

**Figure 14.**Ozone distribution (ppb) and velocity field on the vertical plane perpendicular to radiator ${R}_{2}$ (simulation D, $\varphi =337.5$°).

**Figure 15.**Ozone distribution (ppb) and velocity field on the horizontal plane perpendicular to source ${S}_{4}$ (simulation D, $z=2.070$ m).

**Figure 16.**Ozone distribution (ppb) and velocity field on a horizontal plane at the top region of the hydrogenerator (simulation D, $z=3.750$ m).

**Figure 17.**Ozone concentrations (ppb) on the surface of radiator ${R}_{0}$ in the numerical model of the hydrogenerator for simulations (

**a**) A, (

**b**) B, (

**c**) C and (

**d**) D.

**Figure 18.**Ozone concentrations (ppb) on the surface of radiator ${R}_{1}$ in numerical model of the hydrogenerator for simulations (

**a**) A, (

**b**) B, (

**c**) C and (

**d**) D.

**Figure 19.**Ozone concentrations (ppb) on the surface of radiator ${R}_{2}$ in the numerical model of the hydrogenerator for simulations (

**a**) A, (

**b**) B, (

**c**) C, and (

**d**) D.

**Figure 20.**Ozone concentrations (ppb) on the surface of the radiator ${R}_{3}$ in numerical model of the hydrogenerator for simulations (

**a**) A, (

**b**) B, (

**c**) C, and (

**d**) D.

**Figure 21.**Ozone concentrations (ppb) on the surface of the radiator ${R}_{4}$ in the numerical model of the hydrogenerator for simulations (

**a**) A, (

**b**) B, (

**c**) C, and (

**d**) D.

**Figure 22.**Influence of sources ${S}_{12}$ ($\varphi =265$°) to ${S}_{16}$ ($\varphi =285$°) in simulations (

**a**) E and (

**b**) F.

**Figure 23.**Localized influence in the region of sources ${S}_{17}$ ($\varphi =75$°) and ${S}_{18}$ ($\varphi =75$°) in simulations (

**a**) E and (

**b**) F.

**Figure 24.**Localized influence in the region of sources ${S}_{19}$ ($\varphi =310$°) and ${S}_{20}$ ($\varphi =310$°) in simulations (

**a**) E and (

**b**) F.

**Figure 25.**Perspective view of ozone concentration (ppb) in numerical model of hydrogenerator in simulations (

**a**) E and (

**b**) F.

**Figure 26.**Ozone concentration (ppb) on the surfaces of the radiators ${R}_{0}$ and ${R}_{1}$ in the numerical model of the hydrogenerator: (

**a**) ${R}_{0}$ (simulation E), (

**b**) ${R}_{0}$ (simulation F), (

**c**) ${R}_{1}$ (simulation E), and (

**d**) ${R}_{1}$ (simulation F).

**Figure 27.**Ozone concentration (ppb) on the surfaces of the radiators ${R}_{2}$ and ${R}_{3}$ in the numerical model of the hydrogenerator: (

**a**) ${R}_{2}$ (simulation E), (

**b**) ${R}_{2}$ (simulation F), (

**c**) ${R}_{3}$ (simulation E), and (

**d**) ${R}_{3}$ (simulation F).

**Figure 28.**Ozone concentration (ppb) on the surfaces of the radiators ${R}_{4}$ and ${R}_{5}$ in the numerical model of the hydrogenerator: (

**a**) ${R}_{4}$ (simulation E), (

**b**) ${R}_{4}$ (simulation F), (

**c**) ${R}_{5}$ (simulation E), and (

**d**) ${R}_{5}$ (simulation F).

**Figure 29.**Ozone concentration (ppb) on the surfaces of the radiators ${R}_{6}$ and ${R}_{7}$ in the numerical model of the hydrogenerator: (

**a**) ${R}_{6}$ (simulation E), (

**b**) ${R}_{6}$ (simulation F), (

**c**) ${R}_{7}$ (simulation E), and (

**d**) ${R}_{7}$ (simulation F).

**Figure 30.**Maximum concentrations of ozone on the radiators as a function of $\varphi $ (numerical model).

Material | $\mathit{\gamma}$ | Reference |
---|---|---|

Stainless steel | 1.8 × 10${}^{-7}$ | Mueller et al. [36] |

Concrete | 7.9 × 10${}^{-5}$ | Simmons and Colbeck [37] |

Semiconductor coating layer | 1.11 × 10${}^{-6}$ | Cataldo and Ursini [38] |

Epoxy | 2.0 × 10${}^{-6}$ | Reiss et al. [39,40] |

Copper | 5.5 × 10${}^{-7}$ | Gusakov et al. [41] |

**Table 2.**The represented components and structural parts of the hydrogenerator, materials, and geometric details.

Components and Structural Parts | Material | Geometric Details |
---|---|---|

Floor and external walls | Concrete | Figure 2 |

Rotor | Surface of epoxy | Figure 2 |

378 coil-type stator bars | Copper covered by mica and a semiconductor coating layer | Figure 3 |

Stator core | Stainless steel | Figure 4 |

Air directors | Stainless steel | Figure 5 |

Radiator | Copper | Figure 5 |

**Table 3.**Ozone source locations in simulations A to D: vertical and angular coordinates, height category, and sectors.

Source | Vertical Coordinate z (m) | Height Category | Angular Coordinate $\mathit{\varphi}$ | Sector |
---|---|---|---|---|

${S}_{0}$ | 2.074 | intermediary | 270° | between ${R}_{0}$ and ${R}_{1}$ |

${S}_{1}$ | 2.074 | intermediary | 280° | ${R}_{1}$ |

${S}_{2}$ | 2.074 | intermediary | 292.5° | ${R}_{1}$ |

${S}_{3}$ | 0.574 | bottom | 305° | ${R}_{1}$ |

${S}_{4}$ | 2.074 | intermediary | 315° | between ${R}_{1}$ and ${R}_{2}$ |

${S}_{5}$ | 3.574 | top | 315° | between ${R}_{1}$ and ${R}_{2}$ |

${S}_{6}$ | 4.020 | top | 330° | ${R}_{2}$ |

${S}_{7}$ | 0.574 | bottom | 330° | ${R}_{2}$ |

${S}_{8}$ | 1.574 | intermediary | 340° | ${R}_{2}$ |

${S}_{9}$ | 2.074 | intermediary | 350° | ${R}_{2}$ |

${S}_{10}$ | 4.020 | top | 22.5° | ${R}_{3}$ |

${S}_{11}$ | 0.272 | bottom | 0° | between ${R}_{3}$ and ${R}_{4}$ |

Source | Dimensions (mm) | Volume (mm${}^{3}$) | Ozone Average Volumetric Concentration (ppb) |
---|---|---|---|

${S}_{0}$ | 20.2×20×15 | 6060 | 22,000 |

${S}_{1}$ | 20.2 × 15 × 10 | 3030 | 11,000 |

${S}_{2}$ | 20.2 × 15 × 10 | 3030 | 11,000 |

${S}_{3}$ | 47.2 × 25 × 15 | 17,700 | 64,257.43 |

${S}_{4}$ | 30 × 20.2 × 15 | 9090 | 33,000 |

${S}_{5}$ | 20.2 × 20 × 15 | 6060 | 22,000 |

${S}_{6}$ | 15 × 15 × 15 | 3375 | 12,252.48 |

${S}_{7}$ | 20.2 × 15 × 15 | 4545 | 16,500 |

${S}_{8}$ | 20.2 × 20.2 × 15 | 6120.6 | 22,220 |

${S}_{9}$ | 20.2 × 15 × 10 | 3030 | 11,000 |

${S}_{10}$ | 15 × 15 × 15 | 3375 | 12,252.48 |

${S}_{11}$ | 15×15×15 | 3375 | 12,252.48 |

**Table 5.**Ozone concentrations (ppb) in personnel circulation corridor and on surface of radiators for each simulation (from A to B).

${\mathit{O}}_{3}$ Concentration Parameter | Simulation A | Simulation B | Simulation C | Simulation D |
---|---|---|---|---|

Maximum concentration in personnel circulation corridor | 209.37 | 209.32 | 209.35 | 209.32 |

Average concentration in personnel circulation corridor | 3.9630 | 3.9602 | 3.9515 | 4.3975 |

Maximum concentration on radiator ${R}_{0}$ | 0 | 0 | 0 | 25 |

Average concentration on radiator ${R}_{0}$ | 0 | 0 | 0 | 0.2431 |

Maximum concentration on radiator ${R}_{1}$ | 159 | 159 | 159 | 159 |

Average concentration on radiator ${R}_{1}$ | 3.7132 | 3.7122 | 3.7124 | 4.1252 |

Maximum concentration on radiator ${R}_{2}$ | 209 | 209 | 209 | 209 |

Average concentration on radiator ${R}_{2}$ | 2.47 | 2.4715 | 3.0153 | 3.0152 |

Maximum concentration on radiator ${R}_{3}$ | 51.1 | 51.7 | 51.3 | 51.3 |

Average concentration on radiator ${R}_{3}$ | 0.2605 | 0.49 | 0.4842 | 0.4842 |

Maximum concentration on radiator ${R}_{4}$ | 7.61 | 7.62 | 7.54 | 7.54 |

Average concentration on radiator ${R}_{4}$ | 0.0728 | 0.1169 | 0.1172 | 0.1172 |

Region | ${\mathbf{PD}}_{\mathbf{max}}^{\mathit{A},\mathit{B}}(\%)$ | ${\mathbf{PD}}_{\mathbf{max}}^{\mathit{A},\mathit{C}}(\%)$ | ${\mathbf{PD}}_{\mathbf{max}}^{\mathit{A},\mathit{D}}(\%)$ | ${\mathbf{PD}}_{\mathbf{max}}^{\mathit{B},\mathit{C}}(\%)$ | ${\mathbf{PD}}_{\mathbf{max}}^{\mathit{B},\mathit{D}}(\%)$ | ${\mathbf{PD}}_{\mathbf{max}}^{\mathit{C},\mathit{D}}(\%)$ |
---|---|---|---|---|---|---|

Personnel circulation corridor | 0.0239 | 0.0095 | 0.0239 | 0.0143 | 0 | 0.0143 |

Radiator ${R}_{0}$ | – | – | 100 | – | – | – |

Radiator ${R}_{1}$ | 0 | 0 | 0 | 0 | 0 | 0 |

Radiator ${R}_{2}$ | 0 | 0 | 0 | 0 | 0 | 0 |

Radiator ${R}_{3}$ | 1.1742 | 0.3914 | 0.3899 | 0.7737 | 0.7737 | 0 |

Radiator ${R}_{4}$ | 1.6 | 0.5333 | 0.5305 | 1.0499 | 1.0499 | 0 |

**Table 7.**Percentage differences between the spatial average ozone concentrations among the simulations.

Region | ${\mathbf{PD}}_{\mathbf{avg}}^{\mathit{A},\mathit{B}}(\%)$ | ${\mathbf{PD}}_{\mathbf{avg}}^{\mathit{A},\mathit{C}}(\%)$ | ${\mathbf{PD}}_{\mathbf{avg}}^{\mathit{A},\mathit{D}}(\%)$ | ${\mathbf{PD}}_{\mathbf{avg}}^{\mathit{B},\mathit{C}}(\%)$ | ${\mathbf{PD}}_{\mathbf{avg}}^{\mathit{B},\mathit{D}}(\%)$ | ${\mathbf{PD}}_{\mathbf{avg}}^{\mathbf{C}},\mathbf{D}(\%)$ |
---|---|---|---|---|---|---|

Personnel circulation corridor | 0.0706 | 0.2902 | 9.8806 | 0.2197 | 11.0424 | 11.2868 |

Radiator ${R}_{0}$ | – | – | 100 | – | – | – |

Radiator ${R}_{1}$ | 0.0269 | 0.02154 | 9.9874 | 0.0054 | 11.1255 | 11.1195 |

Radiator ${R}_{2}$ | 0.0607 | 22.0769 | 18.0817 | 22.0028 | 21.9988 | 0.0033 |

Radiator ${R}_{3}$ | 88.1517 | 85.9211 | 46.2093 | 1.1856 | 1.1937 | 0.0083 |

Radiator ${R}_{4}$ | 60.4591 | 60.9258 | 37.8467 | 0.2909 | 0.2652 | 0.0256 |

Source | Vertical Position z (m) | Height Class | Azimuth Position $\mathit{\varphi}$ | Sector |
---|---|---|---|---|

${S}_{12}$ | 3.524 | top | 265° | ${R}_{0}$ |

${S}_{13}$ | 3.624 | top | 270° | between ${R}_{0}$ and ${R}_{1}$ |

${S}_{14}$ | 3.574 | top | 275° | ${R}_{1}$ |

${S}_{15}$ | 3.674 | top | 280° | ${R}_{1}$ |

${S}_{16}$ | 3.424 | top | 285° | ${R}_{1}$ |

${S}_{17}$ | 2.074 | intermediary | 75° | ${R}_{4}$ |

${S}_{18}$ | 1.574 | intermediary | 75° | ${R}_{4}$ |

${S}_{19}$ | 0.674 | bottom | 310° | ${R}_{1}$ |

${S}_{20}$ | 0.574 | bottom | 310° | ${R}_{1}$ |

Source | Dimensions (mm) | Volume (mm${}^{3}$) | Ozone Average Volumetric Concentration (ppb) |
---|---|---|---|

${S}_{12}$ | 20.2 × 15 × 15 | 4545 | 16,500 |

${S}_{13}$ | 47.2 × 20 × 15 | 14,160 | 51,405.94 |

${S}_{14}$ | 25 × 20.2 × 15 | 7575 | 27,500 |

${S}_{15}$ | 47.2 × 20 × 15 | 14,160 | 51,405.94 |

${S}_{16}$ | 47.2 × 20 × 15 | 14,160 | 51,405.94 |

${S}_{17}$ | 60 × 20.2 × 10 | 12,120 | 44,000 |

${S}_{18}$ | 30 × 20.2 × 10 | 6060 | 22,000 |

${S}_{19}$ | 47.2 × 15 × 15 | 10,620 | 38,554.46 |

${S}_{20}$ | 47.2 × 25 × 15 | 17,700 | 64,257.43 |

Radiator | Angular Position $\mathit{\varphi}$ (°) | Maximum Ozone Concentration (ppb) |
---|---|---|

${R}_{0}$ | 247.5° | 268.96 |

${R}_{1}$ | 292.5° | 342.42 |

${R}_{2}$ | 337.5° | 68.309 |

${R}_{3}$ | 22.5° | 209.83 |

${R}_{4}$ | 67.5° | 103.77 |

${R}_{5}$ | 112.5° | 111.92 |

${R}_{6}$ | 157.5° | 107.27 |

${R}_{7}$ | 202.5° | 473.83 |

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**MDPI and ACS Style**

de Oliveira, R.M.S.; Girotto, G.G.; de Alcantara, L.D.S.; Lopes, N.M.; Dmitriev, V.
Ozone Transport in 311 MVA Hydrogenerator: Computational Fluid Dynamics Modelling of Three-Dimensional Electric Machine. *Energies* **2023**, *16*, 8072.
https://doi.org/10.3390/en16248072

**AMA Style**

de Oliveira RMS, Girotto GG, de Alcantara LDS, Lopes NM, Dmitriev V.
Ozone Transport in 311 MVA Hydrogenerator: Computational Fluid Dynamics Modelling of Three-Dimensional Electric Machine. *Energies*. 2023; 16(24):8072.
https://doi.org/10.3390/en16248072

**Chicago/Turabian Style**

de Oliveira, Rodrigo M. S., Gustavo G. Girotto, Licinius D. S. de Alcantara, Nathan M. Lopes, and Victor Dmitriev.
2023. "Ozone Transport in 311 MVA Hydrogenerator: Computational Fluid Dynamics Modelling of Three-Dimensional Electric Machine" *Energies* 16, no. 24: 8072.
https://doi.org/10.3390/en16248072