Two-Phase Flow with Fluid-Structure Interaction

The following example demonstrates techniques for modeling a fluid-structure interaction containing two fluid phases in COMSOL Multiphysics. It illustrates how a heavier fluid can induce movement in an obstacle modifying the fluid flow itself. This model uses the arbitrary Lagrangian-Eulerian (ALE) technique along with a Two-Phase Flow, Phase Field predefined multiphysics interface.

The model geometry consists of a small container, in the middle of which is a thin obstacle. Initially, a heavier fluid (water) is present in the left domain and air is present everywhere else. The model is similar to a classic dam break benchmark, except the obstacle disrupts the flow of the water into the right domain. The obstacle begins to bend due to the inertial force of the heavier fluid.

Figure 1: Water sloshing in a tank with a flexible baffle.

The ALE method handles the dynamics of the deforming geometry and the moving boundaries with a moving grid. The fluid-fluid boundary is tracked using the phase-field method. On the obstacle surface, an Interior Wetted Wall boundary condition is applied, which allows a contact angle to be specified on a deforming wall. COMSOL Multiphysics computes new mesh coordinates for the channel area based on the movement of the structure’s boundaries and on mesh smoothing. Because of the small thickness of the obstacle, you can use shell elements to avoid adapting the mesh to the actual thickness.

Model Definition

Initially, the heavier fluid forms a dam. The container is 30 mm long, 5 mm wide, and 10 mm tall. The top of the soft obstacle is fixed to the container and it hangs freely inside the container. The obstacle is 9 mm in height, 4 mm wide, and 0.3 mm thick. An initial barrier of water is released, and when it reaches the obstacle, it pushes it away from its original position. The displaced air naturally feeds into the channel on the opposite side of the obstacle. If the obstacle would have been as wide as the channel, the water would not be able to penetrate into the right domain. In the real world, this effect is observed when pouring milk or orange juice from a container. The liquid tends to exit the container in a periodic motion. If the carton is pierced so that displaced air can reenter, a very smooth pour results. The two fluids are air and water, whose physical properties are defined at room temperature. The wetted wall contact angle is π/2 rad. The Young’s modulus of the obstacle is set to 2 MPa.

Figure 2: Initial fluid density inside the container. The soft obstacle hangs down from the container and is free to move.

Results and Discussion

Figure 3 shows the deformation of the nylon obstacle at t = 0.08 s. The water (indicated by the blue color) flows from left to right, and the return passage allows the displaced air to recirculate naturally between the two sides of the obstacle. After the initial release of the heavier fluid, the obstacle begins to relax back toward its original position and the liquid level starts to distribute evenly on both sides of the obstacle.

Figure 3: Plot of fluid density and deformed geometry at 0.08 s.

Figure 4 shows how the water has filled the box at the final computational time. The obstacle has nearly returned to its original position.

Figure 4: Plot of density at final solution time.

Figure 5 shows the solution at selected times during the computation.

Figure 5: Fluid propagation in the box and obstacle deformation (from right to left, top to bottom).

Figure 6 shows the structural displacement of the obstacle during the simulation period.

Figure 6: Horizontal (blue) and vertical (green) displacements of the obstacle.

Figure 7 shows the variation of the water volume. Note that the mass is well conserved.

Figure 7: Variation of the volume fraction of water during the analysis.

Modeling in COMSOL Multiphysics

This example implements the model using two predefined multiphysics coupling interfaces: Two-Phase Flow, Phase Field and Fluid-Shell Interaction. These multiphysics couplings add to the model a Laminar Flow interface, which computes the fluid’s velocity and pressure; a Phase Field interface, which computes the volume fraction of the two phases; and a Shell interface, which computes the structural displacement of the obstacle.

The fluid-domain deformations are obtained by computing a moving mesh that follows the structural deformation. The computational requirement is reduced by only computing the deformation of the mesh around the obstacle; in the rest of the fluid domain the mesh is considered to be rigid. The Fluid-Structure Interaction multiphysics node is fully coupled, the obstacle acts on the fluid as a moving wall, and the fluid applies face load on the structural part, see Figure 8.

Figure 8: Face load applied on the obstacle by the water

At walls in contact with the fluid interface, you can use the Wetted Wall condition. At the obstacle, whose geometry is not represented with a thickness, you can use the Interior Wetted Wall condition.

The simulation procedure consists of two steps. First the phase field and the level set functions are initialized, then the time-dependent calculation starts. These steps are automatically set up by the COMSOL Multiphysics software. You only need to specify appropriate times for the initialization step and the time-dependent analysis.

CFD_Module/Fluid-Structure_Interaction/twophase_flow_fsi

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the tree, select .

Click .

In the tree, select .

Right-click and choose .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
Hb	10[mm]	0.01 m	Box height
Wb	5[mm]	0.005 m	Box width
Lb	30[mm]	0.03 m	Box length
Xo	15[mm]	0.015 m	Position of obstacle
do	0.3[mm]	3E-4 m	Obstacle thickness
Ho	9[mm]	0.009 m	Obstacle height
Wo	4[mm]	0.004 m	Obstacle width
Xi	10[mm]	0.01 m	Initial position of the interface

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type Lb.

In the text field, type Wb.

In the text field, type Hb.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	Xi
Layer 2	Xi

Find the subsection. Select the check box.

Clear the check box.

Obstacle

In the toolbar, click

In the window for , type Obstacle in the text field.

Locate the section. From the list, choose .

In the text field, type Xo.

Locate the section. Select the check box.

Obstacle (wp1)>Plane Geometry

In the window, click .

Obstacle (wp1)>Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type Wo.

In the text field, type Ho.

Locate the section. In the text field, type Hb-Ho.

Obstacle (wp1)>Fillet 1 (fil1)

In the toolbar, click

On the object , select Point 2 only.

In the window for , locate the section.

In the text field, type Wo/2.

Definitions

Symmetry

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Boundaries 2, 7, and 13 only.

In the text field, type Symmetry.

Wall

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Boundaries 1, 3–5, 8–10, and 14–17 only.

In the text field, type Wall.

Laminar Flow (spf)

In the window, under click .

In the window for , locate the section.

Select the check box.

Specify the rref vector as


0	x
0	y
Hb	z

Initial Values 1

In the window, under click .

In the window for , locate the section.

In the p text field, type spf.rho*g_const*(Hb-z).

Clear the check box.

Symmetry 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Interior Wall 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Wall 2

In the toolbar, click

and choose .

Select Boundaries 8 and 10 only.

In the window for , click to expand the section.

From the list, choose .

Pressure Point Constraint 1

In the toolbar, click

and choose .

Select Point 20 only.

In the window for , locate the section.

Clear the check box.

Phase Field (pf)

Phase Field Model 1

In the window, under click .

In the window for , locate the section.

In the χ text field, type 5.

Initial Values, Fluid 2

In the window, click .

Select Domains 2 and 3 only.

Symmetry 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Interior Wetted Wall 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Shell (shell)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Thickness and Offset 1

In the window, under click .

In the window for , locate the section.

In the d text field, type do.

Fixed Constraint 1

In the toolbar, click

and choose .

Select Edge 19 only.

Symmetry 1

In the toolbar, click

and choose .

Select Edge 17 only.

Now, create materials because they will be required for the settings of the node.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Right-click and choose .

In the tree, select .

Right-click and choose .

In the toolbar, click

to close the window.

Materials

Nylon

In the toolbar, click

In the window for , type Nylon in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	2[MPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.4	1	Young’s modulus and Poisson’s ratio
Density	rho	1000	kg/m³	Basic