### Abstract

Governing equations of multigroups two-fluid model for two-phase bubbly flow has been derived on the basis of the two-fluid formulation. The governing equations are derived from the compressible Navier-Stokes equations of fluid mechanics by using temporal averages of the state variables. The equations are simplified for incompressible flows, using Boussinesq approximation and with a constant drift velocity or a constant bubble terminal velocity. The resulting equation system is similar to the Reynolds-averaged Navier-Stokes equation. Several additional terms are appeared in the averaged two-fluid equations representing the coupling between the phases. These coupling terms are representing a mass exchange between the phases, an interfacial momentum exchange, an interfacial energy exchange and an also momentum and energy exchange due to mass exchange as well as a two-phase turbulence. These additional terms require to be modeled appropriately. This paper describes the modeling of the additional terms arise in the momentum equation. The interfacial momentum exchange is modeled using drag force between liquid and bubble. Due to discrepancy between the evaluated bubble terminal velocity calculated from the standard drag equation and the bubble terminal velocity from the experiment, polynomial correlations are used to evaluate the terminal velocity as a function of the bubble radius. The two-phase turbulent terms is modeled by using a very simple turbulent model i.e. the eddy viscosity model. The phasic turbulence or also know as the turbulent mass diffusion is modeled using the turbulent Schmidt number. The modeling of interfacial momentum transfer has been verified by simulation of bubble column experiment by Durst et.al. Also presented are simulation results of bubble column with 5-group air bubbles of different size for laminar and for turbulent two-phase flows.

Original language | English |
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Title of host publication | Proceedings of the 9th International Conference on Thermofluids 2017, THERMOFLUID 2017 |

Editors | Thomas Hohne, Indro Pranoto, Deendarlianto, Akmal Irfan Majid, Ardi Wiranata, Adhika Widyaparaga, Masahiro Takei |

Publisher | American Institute of Physics Inc. |

ISBN (Print) | 9780735417175 |

DOIs | |

Publication status | Published - 16 Aug 2018 |

Event | 9th International Conference on Thermofluids 2017, THERMOFLUID 2017 - Yogyakarta, Indonesia Duration: 9 Nov 2017 → 10 Nov 2017 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2001 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 9th International Conference on Thermofluids 2017, THERMOFLUID 2017 |
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Country | Indonesia |

City | Yogyakarta |

Period | 9/11/17 → 10/11/17 |

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## Cite this

*Proceedings of the 9th International Conference on Thermofluids 2017, THERMOFLUID 2017*[030002] (AIP Conference Proceedings; Vol. 2001). American Institute of Physics Inc.. https://doi.org/10.1063/1.5049974