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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.

Import validation project into workspace

Geometry

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

MultiPhase-geometry

Fig.1. Geometry used in the study

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 :

Table 1: Mesh Metrics
Mesh type Cells in x Cells in y Cells in z Number of nodes Type
snappyHexMesh 120 240 1 28800 2D hex
MultiPhase-mesh

Fig.2. Mesh used for the SimScale case

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.

Table 2: Fluid Properties for two cases
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:

Table 3: Boundary Conditions for multi-phase flow simulation
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.

C1Pr C2Pr

C1PrR C2PrR

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.

C1Vel C2Vel

C1COM C2COM

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

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.