### Abstract

A porous media solution PORFLO has been developed for the 3-dimensional two-phase flow by describing the process facility with Cartesian or cylindrical coordinates. The local porosity fraction is applied for distinguishing the fluid filled volumes from the solid structures. The solid structure contribute the two-phase flow through the wall friction, flow area and heat transfer.

The solid structure may contain heat input by steam generator tubes, steam condenser tubes or internal heating of solid particles. The first phase of the model development has included the modelling for these applications. The thermohydraulic solution is based on 5-equation approach, where the conservation equations are solved for the liquid and gas mass, mixture momentum, liquid and gas energy.

The first application for the model was the calculation of the particle bed dryout cooling experiments. In experiments the core debris coolability on the containment pedestal floor has been studied to verify the severe accident management strategy adapted in Olkiluoto BWRs. The decay power heating of the real core debris is generated by electrical resistance heaters. The second application is related to passive safety systems of BWR plants. In the isolation condenser the steam from the reactor vessel is flows through the heat transfer tubes. The tube bundle has been submerged into the cold water pool.

After a short heating period vigorous boiling takes place in the poll creating strong two-phase circulation. The 3-dimensional flow two-phase flow circulation was calculated for the pool. The work was a part of the new nuclear plant evaluation concept for the nuclear power plant candidates for Finland. After the EPR plant was selected, the more detailed analyses were not continued. The steam condensation inside the heat transfer tube may be modelled by using an 1-dimensional model. As a future application the characteristics of the horizontal steam generator is studied.

The primary fluid flow inside the heat transfer tubes creates the heat transfer boundary condition. Some scattered data from the local void fractions exists for the facility and at least the shape of the two-phase level during the steady state operation has been recorded. The present PORFLO model is based on the drift-flux model with five conservation equations, when the complete two fluid model includes six conservation equations, mass, momentum and energy equations for both phases. The question is, would the drift flux model be too limited for the 3D two-phase flow?

The author's opinion is that the approach gives just for the large facilities a good modelling possibility. The drift-flux formalism with two input parameters is a clear-cut formulation, and rather much experimental data has been formulated by using the drift-flux formalism. In the three reference facility of the PORFLO application the local void fractions are in the range of 0 to 0.4, where liquid is continuous phase and vapour exists in the form of bubbles.

For this flow regime the vapour phase does not transmit any momentum. Additionally the drift flux model is capable for modelling the sharp void fraction gradient at the two-phase level. The three applications demonstrate that the porous media approach based on the drift-flux model is applicable for modelling the real process facilities, where the water level exists and the two-phase flow patterns is generated mainly by the local gravitational pressure differences.

The particle bed dryout experiment, the BWR isolation condenser and the horizontal VVER steam generator are examples of such facilities. (author)

The solid structure may contain heat input by steam generator tubes, steam condenser tubes or internal heating of solid particles. The first phase of the model development has included the modelling for these applications. The thermohydraulic solution is based on 5-equation approach, where the conservation equations are solved for the liquid and gas mass, mixture momentum, liquid and gas energy.

The first application for the model was the calculation of the particle bed dryout cooling experiments. In experiments the core debris coolability on the containment pedestal floor has been studied to verify the severe accident management strategy adapted in Olkiluoto BWRs. The decay power heating of the real core debris is generated by electrical resistance heaters. The second application is related to passive safety systems of BWR plants. In the isolation condenser the steam from the reactor vessel is flows through the heat transfer tubes. The tube bundle has been submerged into the cold water pool.

After a short heating period vigorous boiling takes place in the poll creating strong two-phase circulation. The 3-dimensional flow two-phase flow circulation was calculated for the pool. The work was a part of the new nuclear plant evaluation concept for the nuclear power plant candidates for Finland. After the EPR plant was selected, the more detailed analyses were not continued. The steam condensation inside the heat transfer tube may be modelled by using an 1-dimensional model. As a future application the characteristics of the horizontal steam generator is studied.

The primary fluid flow inside the heat transfer tubes creates the heat transfer boundary condition. Some scattered data from the local void fractions exists for the facility and at least the shape of the two-phase level during the steady state operation has been recorded. The present PORFLO model is based on the drift-flux model with five conservation equations, when the complete two fluid model includes six conservation equations, mass, momentum and energy equations for both phases. The question is, would the drift flux model be too limited for the 3D two-phase flow?

The author's opinion is that the approach gives just for the large facilities a good modelling possibility. The drift-flux formalism with two input parameters is a clear-cut formulation, and rather much experimental data has been formulated by using the drift-flux formalism. In the three reference facility of the PORFLO application the local void fractions are in the range of 0 to 0.4, where liquid is continuous phase and vapour exists in the form of bubbles.

For this flow regime the vapour phase does not transmit any momentum. Additionally the drift flux model is capable for modelling the sharp void fraction gradient at the two-phase level. The three applications demonstrate that the porous media approach based on the drift-flux model is applicable for modelling the real process facilities, where the water level exists and the two-phase flow patterns is generated mainly by the local gravitational pressure differences.

The particle bed dryout experiment, the BWR isolation condenser and the horizontal VVER steam generator are examples of such facilities. (author)

Original language | English |
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Title of host publication | Proceedings |

Subtitle of host publication | 15th International Conference on Nuclear Engineering, ICONE15 |

Publisher | Japan Society of Mechanical Engineers |

Number of pages | 9 |

Publication status | Published - 2007 |

MoE publication type | B3 Non-refereed article in conference proceedings |

Event | 15th International Conference on Nuclear Engineering, ICONE15 - Nagoya, Aichi, Japan Duration: 22 Apr 2007 → 26 Apr 2007 |

### Conference

Conference | 15th International Conference on Nuclear Engineering, ICONE15 |
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Abbreviated title | ICONE15 |

Country | Japan |

City | Nagoya, Aichi |

Period | 22/04/07 → 26/04/07 |

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### Keywords

- 3D-flow
- porous media solution

### Cite this

Miettinen, J., & Ilvonen, M. (2007). Solving Porous Media Flow for LWR Components. In

*Proceedings: 15th International Conference on Nuclear Engineering, ICONE15*Japan Society of Mechanical Engineers.