Modeling a Bubble in a Channel with ANSYS Fluent

Adam D. Foltz

Problem Statement

The initial condition involves an air bubble lodged simultaneously in a small and large channel of water. The goal of this simulation is to find the final form of a bubble as it moves out of the small channel

and into the larger channel.

The driving force for this problem comes from a high capillary pressure on the left side of the meniscus, causing a hindrance of the expansion of the left meniscus [1].

Simulated Region

CAD Model

The problem was modeled as a 2D flow, so a simple surface was created in CREO. CAD Steps:

The first step was to create the channel, which was made by creating a sketch and using the Fill tool to create a surface. Once this was complete, the bubble had to be sketched and cut from the channel. The bubble was modeled using the

Spline tool, with a 30 incident angle.

Finally, the Fill tool was used to create the second surface for the bubble. Two surfaces were required for selection purposes in Fluent. Making the two surfaces as part of the same part, guaranteed a

conformal mesh.

30

920 m

460 m 460 m

150 m

Meshing

The mesh is dominated by linear quadrilateral elements (Quad4), with a few linear triangular elements (Tri3). The average element size is 1E-5 m. Inflation was used along the walls (three layers), to help resolve the boundaries. The whole domain was finely meshed, rather than using adaptive meshing, for efficiency.

Solver Settings

The pressure-based solver is the standard solver to use. The density based solver is for supersonic flows.

Gravity is neglected. The problem is transient based on the assumption that

the bubble will move to the right.

The energy equation is not solved for, so temperature is decoupled from the problem.

The flow is assumed to be laminar. The PISO scheme was chosen, which is standard for

transient problems.

Volume of Fluid

The volume of fluid method tracks the volume fraction of each of the fluids throughout the domain.

An additional equation, the volume fraction equation, is solved at each iteration. The method includes the effects of surface tension and wall adhesion, and

requires the pressure-based solver. The Implicit Body Force option is turned on, because the effects of

surface tension are included. This option enforces that the partial equilibrium of pressure gradient and body

forces is achieved.

The Level Set option is also turned on, since the effects of surface tension are included.

This option produces more accurate estimates of the interface curvature and surface tension force caused by the curvature.

Phases The two phases consist of air and water. The primary phase is chosen to be air, which is standard. The initialization of the problem involved patching the

bubble to consist of air, and the channel to consist of water. The material properties came from the Fluent material library.

Pressure Boundary Conditions

The problem is a 1 inlet and 1 outlet problem. The boundary conditions at both the inlet and the outlet are set to be 0 Pa. The most robust boundary conditions would be a velocity at the inlet and pressure at the outlet. Specifying the pressure at both the inlet and the outlet causes the problem to be sensitive to the initial

guess.

Wall Contact A no slip boundary condition was imposed on

all of the walls.

In addition, the wall adhesion model was used, which was also proposed by Brackbill [2].

This model does not impose the boundary condition on the wall itself, but rather the contact angle the fluid makes with the wall is adjusted via the surface normal in cells near the wall.

The contact angle is assumed to be 30 from the problem statement.

Surface Tension The capillary number is a dimensionless number which represents the relative effects of viscous forces versus surface

tension. Low velocity flow gives a low capillary number, which means the surface tension effects are dominant.

The continuum surface force model is used, which was proposed by Brackbill [2]. The pressure drop across the surface depends on the surface tension coefficient and the surface curvature.

The calculation of surface tension effects on triangular meshes is not as accurate as on quadrilateral meshes.

: dynamic viscosityV : reference velocity : surface tension

=

2 1 = 11 + 12p : pressure : surface tension coefficientR : surface curvature

Moving Forward

The solution is failing to converge, even with a very small time step.

An error appears, saying that the Global courant number is greater than 250.

I am attending an ANSYS workshop for Multi-Phase Flow in November, so I will ask the advice of the instructor at that time.

References1. [1] BubbleFlow.pdf 2. [2] ANSYS Users Guide

Modeling a Bubble in a Channel with ANSYS FluentProblem StatementCAD ModelMeshingSolver SettingsVolume of FluidPhasesPressure Boundary ConditionsWall ContactSurface TensionMoving ForwardReferences