# Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system

## Abstract

Direct numerical simulations of bubbly multiphase flows are utilized to find closure terms for a simple model of the average flow, using Neural Networks (NNs). The flow considered consists of several nearly spherical bubbles rising in a periodic domain where the initial vertical velocity and the average bubble density are homogeneous in two directions but non-uniform in one of the horizontal directions. After an initial transient motion the average void fraction and vertical velocity become approximately uniform. The NN is trained on a dataset from one simulation and then used to simulate the evolution of other initial conditions. As a whole, the resulting model predicts the evolution of the various initial conditions reasonably well.

- Authors:

- Univ. of Notre Dame, IN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)

- OSTI Identifier:
- 1565344

- Grant/Contract Number:
- AC05-00OR22725; CBET-1335913

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Fluids

- Additional Journal Information:
- Journal Volume: 27; Journal Issue: 9; Journal ID: ISSN 1070-6631

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Ma, Ming, Lu, Jiacai, and Tryggvason, Gretar. Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system. United States: N. p., 2015.
Web. doi:10.1063/1.4930004.
```

```
Ma, Ming, Lu, Jiacai, & Tryggvason, Gretar. Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system. United States. doi:10.1063/1.4930004.
```

```
Ma, Ming, Lu, Jiacai, and Tryggvason, Gretar. Tue .
"Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system". United States. doi:10.1063/1.4930004. https://www.osti.gov/servlets/purl/1565344.
```

```
@article{osti_1565344,
```

title = {Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system},

author = {Ma, Ming and Lu, Jiacai and Tryggvason, Gretar},

abstractNote = {Direct numerical simulations of bubbly multiphase flows are utilized to find closure terms for a simple model of the average flow, using Neural Networks (NNs). The flow considered consists of several nearly spherical bubbles rising in a periodic domain where the initial vertical velocity and the average bubble density are homogeneous in two directions but non-uniform in one of the horizontal directions. After an initial transient motion the average void fraction and vertical velocity become approximately uniform. The NN is trained on a dataset from one simulation and then used to simulate the evolution of other initial conditions. As a whole, the resulting model predicts the evolution of the various initial conditions reasonably well.},

doi = {10.1063/1.4930004},

journal = {Physics of Fluids},

number = 9,

volume = 27,

place = {United States},

year = {2015},

month = {9}

}

*Citation information provided by*

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Web of Science

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