# Multi-phase Flow: Rising Bubble¶

## Overview¶

The aim of this test case is to validate the following parameters of laminar transient multi-phase flow with a pre-referenced case [1]:

- Bubble vertical velocity
- Bubble center of mass
- Bubble profile

The mesh was created locally using the blockMesh tool and then imported on to the SimScale platform.

## Geometry¶

The domain of interest is a 2-dimensional rectangular space \(2\ m\) high and \(1\ m\) wide as shown in Fig.1.

## Analysis type and Domain¶

A uniformly-spaced hexahedral mesh was generated using the blockMesh tool (see Fig.2.). In order to keep the flow two-dimensional, the mesh was designed to have only one layer in the \(y\) direction.

**Tool Type** : OPENFOAM®

**Analysis Type** : Multi-phase (Laminar)

**Mesh and Element types** :

Mesh type | Cells in x | Cells in y | Cells in z | Number of nodes | Type |
---|---|---|---|---|---|

snappyHexMesh | 120 | 240 | 1 | 28800 | 2D hex |

## Simulation Setup¶

*Fluids:*

The domain is filled with fluid \(f_1\) (see Table 2). A bubble of fluid \(f_2\) with diameter \(0.5\ m\) is placed at \(t = 0\) in the domain at a height of \(0.5\ m\) (with bubble center as reference) on the central vertical line. Two cases are then simulatedwith different fluid properties as per [1]. Gravity was assumed to be \(0.98\ ms^{-2}\) in the negative \(y\) direction.

Case | \(rho _1\) | \(rho _2\) | \(mu _1\) | \(mu _2\) | \(sigma\) |
---|---|---|---|---|---|

Case 1 | \(1000\) | \(100\) | \(10\) | \(1\) | \(24.5\) |

Case 2 | \(1000\) | \(1\) | \(10\) | \(0.1\) | \(1.96\) |

*Boundary Conditions:*

Parameter | Top and Bottom (A,B) | Left and Right (C,D) | Front and Back (E,F) |
---|---|---|---|

Velocity | \(0.0\ ms^{-1}\) | Slip | Empty |

Pressure | Fixed Flux Pressure \((0)\) | Fixed Flux Pressure \((0)\) | Empty |

Phase Fraction | Zero Gradient | Zero Gradient | Empty |

## Results¶

A comparison of the bubble profiles for the two cases with the referenced case solutions is given in Fig.3. below.

Fig.3. Visualization of Bubble Profiles and comparison with reference for case 1 (left) and case 2 (right)

Shown in Fig.4. are graphs for the development of bubble center of mass and bubble velocity over time compared with referenced results.

Fig.4. Development of bubble center of mass and bubble velocity over time compared with referenced results.

## References¶

[1] | (1, 2) FeatFlow Benchmark Suite: Rising Bubble |

## Disclaimer¶

This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software and owner of the OPENFOAM® and OpenCFD® trade marks. OPENFOAM® is a registered trade mark of OpenCFD Limited, producer and distributor of the OpenFOAM software.