3D Duineveld Rising Bubble

3D rising bubble validation against Duineveld (1995) experimental data, using the ALE moving-mesh interface tracking method.

Repository path: tutorials/multiphaseFlow/3dDuineveldRisingBubble

Reference: Alkafri et al. (2024), multiRegionFoam: A Unified Multiphysics Framework, Sect. 7.3

Overview

A single air bubble rises in still pure water (FluidA), following the experimental setup of Duineveld (1995). The moving-mesh ALE interface tracking method (Hirt et al., originally implemented in OpenFOAM by Tuković and Jasak) is used to track the deforming bubble surface.

The bubble starts as a sphere of radius $r_b$ at rest and accelerates to its terminal rise velocity. The computational domain consists of two regions:

  • FluidB (bubble / air) — polyhedral mesh
  • FluidA (surrounding water) — prismatic mesh with polyhedral base

The outer domain is a sphere of radius $20 r_b$. The bubble mesh is bounded by the interfaceShadow patch on the bubble side and the interface patch on the liquid side where the coupled boundary conditions are applied.

Bubble radii simulated: $r_b = 0.5,\, 0.6,\, 0.7,\, 0.8,\, 0.9\,\text{mm}$

Time step: $\Delta t = 10^{-5}\,\text{s}$

Computational domain

Fig. 13 — Sketch of the computational domain. FluidB (bubble) is enclosed in FluidA (water) with radius 20 r_b. The interfaceShadow patch on the bubble side coincides with the interface patch on the liquid side.

Fig. 13 — Sketch of the computational domain. FluidB (bubble) is enclosed in FluidA (water) with radius 20 r_b. The interfaceShadow patch on the bubble side coincides with the interface patch on the liquid side.

Mesh

Fig. 14 — Mesh for the rising bubble simulation. Polyhedral cells for the bubble (FluidB) and prismatic cells with a polyhedral base for the water (FluidA).

Fig. 14 — Mesh for the rising bubble simulation. Polyhedral cells for the bubble (FluidB) and prismatic cells with a polyhedral base for the water (FluidA).

Boundary conditions

Table: Boundary conditions for the rising bubble simulation

BoundaryPressureVelocity
FluidA
interfaceregionCoupledPressureValueregionCoupledVelocityFlux
spacezeroGradientinletOutlet
FluidB
interfaceShadowregionCoupledPressureFluxregionCoupledVelocityValue

Physical properties

Table: Physical properties of air (FluidB) and water (FluidA)

PropertyUnitFluidB (air)FluidA (water)
Densitykg/m³1.205998.3
Dynamic viscositykg/ms1.82 × 10⁻⁵10⁻³
Surface tension coefficientN/m0.0727–

Numerical schemes

Table: Numerical schemes

SchemeSetting
ddtSchemebackward
gradSchemeGauss linear
divScheme div(phi,U)Gauss GammaVDC 0.5
divScheme div(phi,T)Gauss linearUpwind Gauss linear
laplacianSchemeGauss linear corrected
interpolationSchemelinear
snGradSchemecorrected
Finite area schemes
gradSchemeGauss linear
divSchemeGauss linear
interpolationSchemelinear

Results summary

Fig. 15 — Rise velocity over time for a bubble with r_b = 0.5 mm converging to the experimental terminal velocity.

Fig. 15 — Rise velocity over time for a bubble with r_b = 0.5 mm converging to the experimental terminal velocity.

Fig. 16 — Terminal rise velocity for varying equivalent bubble radii. Comparison of simulation results with Duineveld (1995) experiments and Tuković & Jasak simulations.

Fig. 16 — Terminal rise velocity for varying equivalent bubble radii. Comparison of simulation results with Duineveld (1995) experiments and Tuković & Jasak simulations.

Fig. 17 — Velocity field visualisation for the rising bubble with r_b = 0.9 mm at terminal state.

Fig. 17 — Velocity field visualisation for the rising bubble with r_b = 0.9 mm at terminal state.

The terminal rise velocity for $r_b = 0.5\,\text{mm}$ converges to the experimental value from Duineveld. Across all radii the simulated terminal velocities show a high level of agreement with both the Duineveld experimental data and the earlier OpenFOAM simulations by Tuković and Jasak, confirming that the ALE moving-mesh implementation handles significant mesh deformation robustly.

Running the case

cd $FOAM_RUN/../multiPhysicsFoam/tutorials/multiphaseFlow/3dDuineveldRisingBubble
./Allrun