### Abstract

The bubble size distribution plays an important role in interfacial mass, momentum and energy transfer between bubbles and their carrier liquid in bubbly flow. Accurate modeling of the size distribution is therefore key. A Log-Normal presumed Number Density Function (LNpNDF) approach is proposed, which is embedded into the two-fluid model. Two additional moment transport equations are formulated which are shown to be consistent with the two-fluid model. From the moments, the size distribution can be fully reconstructed using the assumption that its underlying shape is log-normal. This methodology offers closure for the modeling of processes such as bubble coalescence, break-up and bubble poly-celerity. Special attention is paid to the concept of poly-celerity, which is shown to play an important role in the evolution of finite-width size distributions. A new average diameter, which is based on the fifth and third moment of the size distribution, is proposed, and it is shown that this diameter is a more suitable quadrature node for the modeling of bubble–liquid Stokes-like drag. The paper lays the mathematical foundation for a pragmatic, computationally efficient and effective poly-dipsersed method for the modeling of dispersed two-phase flow.

Language | English |
---|---|

Pages | 237-246 |

Number of pages | 10 |

Journal | Chemical Engineering Science |

Volume | 201 |

DOIs | |

State | Published - 29 Jun 2019 |

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### Keywords

- Bubbly flow
- Log-normal
- Moment modeling
- Population balance
- Size distribution
- Two-fluid model

### Cite this

*Chemical Engineering Science*,

*201*, 237-246. DOI: 10.1016/j.ces.2019.02.013

}

*Chemical Engineering Science*, vol. 201, pp. 237-246. DOI: 10.1016/j.ces.2019.02.013

**Poly-dispersed modeling of bubbly flow using the log-normal size distribution.** / Frederix, E.M.A. (Corresponding author); Cox, T.L.W.; Kuerten, J.G.M.; Komen, E.M.J.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Poly-dispersed modeling of bubbly flow using the log-normal size distribution

AU - Frederix,E.M.A.

AU - Cox,T.L.W.

AU - Kuerten,J.G.M.

AU - Komen,E.M.J.

PY - 2019/6/29

Y1 - 2019/6/29

N2 - The bubble size distribution plays an important role in interfacial mass, momentum and energy transfer between bubbles and their carrier liquid in bubbly flow. Accurate modeling of the size distribution is therefore key. A Log-Normal presumed Number Density Function (LNpNDF) approach is proposed, which is embedded into the two-fluid model. Two additional moment transport equations are formulated which are shown to be consistent with the two-fluid model. From the moments, the size distribution can be fully reconstructed using the assumption that its underlying shape is log-normal. This methodology offers closure for the modeling of processes such as bubble coalescence, break-up and bubble poly-celerity. Special attention is paid to the concept of poly-celerity, which is shown to play an important role in the evolution of finite-width size distributions. A new average diameter, which is based on the fifth and third moment of the size distribution, is proposed, and it is shown that this diameter is a more suitable quadrature node for the modeling of bubble–liquid Stokes-like drag. The paper lays the mathematical foundation for a pragmatic, computationally efficient and effective poly-dipsersed method for the modeling of dispersed two-phase flow.

AB - The bubble size distribution plays an important role in interfacial mass, momentum and energy transfer between bubbles and their carrier liquid in bubbly flow. Accurate modeling of the size distribution is therefore key. A Log-Normal presumed Number Density Function (LNpNDF) approach is proposed, which is embedded into the two-fluid model. Two additional moment transport equations are formulated which are shown to be consistent with the two-fluid model. From the moments, the size distribution can be fully reconstructed using the assumption that its underlying shape is log-normal. This methodology offers closure for the modeling of processes such as bubble coalescence, break-up and bubble poly-celerity. Special attention is paid to the concept of poly-celerity, which is shown to play an important role in the evolution of finite-width size distributions. A new average diameter, which is based on the fifth and third moment of the size distribution, is proposed, and it is shown that this diameter is a more suitable quadrature node for the modeling of bubble–liquid Stokes-like drag. The paper lays the mathematical foundation for a pragmatic, computationally efficient and effective poly-dipsersed method for the modeling of dispersed two-phase flow.

KW - Bubbly flow

KW - Log-normal

KW - Moment modeling

KW - Population balance

KW - Size distribution

KW - Two-fluid model

UR - http://www.scopus.com/inward/record.url?scp=85062607908&partnerID=8YFLogxK

U2 - 10.1016/j.ces.2019.02.013

DO - 10.1016/j.ces.2019.02.013

M3 - Article

VL - 201

SP - 237

EP - 246

JO - Chemical Engineering Science

T2 - Chemical Engineering Science

JF - Chemical Engineering Science

SN - 0009-2509

ER -