MOF test case with periodic boundary conditions in the axisymmetric coordinate system

This test case simulates a domain of fluids in the axisymmetric coordinate system.

The verification criteria is:

• The main volume fraction;
• The symmetric difference area.

Configurations

Physical domain and geometry

The simulations take place in a box of fluid of coordinates (0,0) and (1,1). The second fluid is placed in a pacman centred at the position (0.5,0.5).

Fluids' properties

Both of the fluids considered have the same properties :

where \(\rho\) is the density, \(\mu\) the dynamic viscosity coefficient, \(\sigma\) the conductivity, C the specific heat capacity, \(\alpha\) the thermal expansion coefficient and \(T_{0}\) the reference temperature.

Boundary conditions

We consider periodic boundary conditions along the vertical axis.

Velocity

The velocity field is uniform along the vertical axis.

Phase advection

The numerical method used for phase advection is MOF.

Runtime parameters

Spatial discretization

A regular randomly perturbed mesh with \(\dfrac{L}{\Delta x}=100\) for each direction is considered.

Time discretization

The time step is fixed and equals to \(4.10^{-3}s\). The final time is set to 1s and corresponds to one period.

UseSymmetric choice

The UseSymmetric variable permits choosing whether the symmetric reconstruction or minimization. The tolerance angle and derivative are respectively set to \(10^{-5}\) and 0.

UseFilaments choice

The UseFilaments variable is included to use Filaments at MOF method.

GoUP choice

Following the variable GoUp, the direction of the velocity field can be changed.

Comments

By visualizing the eight cases given by the three choices. It is observed that only enabling or disabling filaments in MOF method which makes the difference in the quality of the numerical result.

Results

Numerical results

Figure 1 shows the volume fraction of the fluids at three different times ( initial, intermediate and final time) in the case of using filaments.

Figure 2 shows the volume of fraction of fluids at different times in the case of disabling filaments.

The difference between the two cases is observed in the pacman eye area which is better with filaments.

Area of symmetric difference

The value of symmetric difference area is clearly smaller in the case of using Filaments. The average area of symmetric difference is:6.881521288248423e-05 m².