COMSOL 6.4 - Results

Results

By default you end up in the settings window for the Particle Trajectories (fpt) plot group when the study is complete. Since the default wall condition at the outlet is the Freeze condition, particles are still displayed at the outlet. The color expression of these stopped particles indicates their speed at the time they reached the outlet.

The default Particle Trajectories plot. Particles are colored according to their speed at the final time.

Particle Trajectories (fpt)

In the Settings window for 3D Plot Group, locate the Color Legend section.

Clear the Show legends checkbox.

Click to expand the Title section. From the Title type list, choose None.

Particle Trajectories 1

In the Model Builder expand the Results > Particle Trajectories (fpt)

node and click Particle Trajectories 1

In the Settings window for Particle Trajectories, locate the Coloring and Style section.

Find the Point style subsection. From the Type list, choose Comet tail. The comet tails will show the magnitude and direction of each particle’s velocity.

In the Model Builder window, expand the Particle Trajectories 1

node and click Color Expression 1

In the Settings window for Color Expression, locate the Expression section.

In the Expression text field, type at(0,qx<0).

The at operator evaluates the second input argument at the solution time given by the first. The above expression will return 1 for particles that have a negative initial x-coordinate, or return 0 otherwise.

Locate the Coloring and Style section. From the Color table list, choose RainbowLight. This gives a bit more contrast compared to the default Rainbow.

Surface 1

In the Particle Trajectories (fpt) toolbar, click

Surface.

In the Settings window for Surface, locate the Expression section.

In the Expression field, type 1.

Locate the Coloring and Style section. From the Coloring list, choose Uniform.

From the Color list, choose Black.

From the Particle Trajectories (fpt) toolbar, click

Selection.

In the Settings window for Selection, locate the Selection section.

From the Selection list, choose Blade surfaces.

Surface 2

In the Particle Trajectories (fpt) toolbar, click

Surface.

In the Settings window for Surface, locate the Expression section.

In the Expression field, type 1.

Locate the Coloring and Style section. From the Coloring list, choose Uniform.

From the Color list, choose Gray.

From the Particle Trajectories (fpt) toolbar, click

Selection.

In the Settings window for Selection, locate the Selection section.

From the Selection list, choose Outer surfaces.

In the Model Builder, right-click Surface 2

and choose

Transparency.

In the Settings window for Transparency, locate the Transparency section.

In the Fresnel transmittance text field, type 1, or drag the slider to the right.

Click the Plot button

Click Zoom Extents

in the Graphics toolbar. The plot should look like the following figure. Fresnel transmittance makes surfaces look more transparent if they are viewed normally, or more opaque when viewed at an angle.

You can also view the trajectories at different times by selecting other solution times in the Settings window for the Particle Trajectories (fpt)

node. You can also cycle through

In the next section, create a copy of this trajectory plot in which the trajectories are rendered as lines instead of points.

Particle Trajectories (fpt) 1

To clean up the Model Builder window, you can collapse the Particle Trajectories (fpt)

node.

In the Model Builder window, right-click Particle Trajectories (fpt)

and choose Duplicate. This will create a copy called Particle Trajectories (fpt) 1

Particle Trajectories 1

Expand the Results > Particle Trajectories (fpt) 1

node and click Particle Trajectories 1

In the Settings window for Particle Trajectories, locate the Coloring and Style section.

Find the Point style subsection. From the Type list, choose None.

Find the Line style subsection. From the Type list, choose Line.

In the Model Builder window, expand the Particle Trajectories 1

node and click Color Expression 1

In the Settings window for Color Expression, locate the Expression section.

In the Expression text field, type at(0,qx).

Locate the Coloring and Style section. From the Color table list, choose Dipole.

Click the Plot button

Click Zoom Extents

in the Graphics toolbar.

Now evaluate the transmission probability using the Particle Counter that was created earlier. For this purpose, transmission probability is defined as the fraction of the released particles to reach the outlet by the final time.

In the Results toolbar click Global Evaluation

In the Settings window for Global Evaluation locate the Data section.

From the Dataset list, choose Study 2/Solution 2 (sol2).

From the Time selection list, choose Last.

Click Replace Expression

in the upper-right corner of the Expression section. From the menu, choose Model > Component 1 > Particle Tracing for Fluid Flow > Particle Counter 1 > fpt.pcnt1.alpha – Transmission probability.

Click the Evaluate button

. The transmission probability should be about 0.8.

Poincaré Map

One useful way to visualize how particles mix is to use a Poincaré Map plot. The Poincaré map places a colored dot for each particle at the location at which the particle passes through a cut plane (known as a Poincaré section).

The first step is to define the cut planes where the intersections with the particle trajectories will be taken. These cut planes are defined as datasets.

In the Results toolbar click Cut Plane

In the Settings window for Cut Plane locate the Data section. From the Dataset list, choose Particle 1.

Locate the Plane Data section.

From the Plane list, choose xz-planes.

In the y-coordinate text field, type 0.006.

Select the Additional parallel planes checkbox.

In the Distances text field, type 0.006 0.016 0.026 0.036 0.042.

Click the Plot button

The cut planes will be shown in the Graphics window as shown below.

Cross-sections at which Poincaré maps will be plotted are shown in red.

Poincaré Map

In the Home toolbar click Add Plot Group

and choose 3D Plot Group

In the Settings window for 3D Plot Group locate the Data section. From the Dataset list, choose Particle 1.

The plots only display particle positions in each cut plane, but the plot group should still use Particle 1 or one of the Solution datasets as its data source, since this is used to render the dataset edges in the Graphics window.

On the 3D Plot Group 4 toolbar, click More Volume Plots

and choose Poincaré Map

In the Settings window for Poincaré Map locate the Data section. From the Cut plane list, choose Cut Plane 1.

Locate the Coloring and Style section.

Select the Radius scale factor checkbox.

In the associated text field, type 0.4. This scaling factor is multiplied by the Point radius expression to determine the size of each point in the plot.

Click the Plot button

Right-click Poincaré Map 1

and choose Color Expression

In the Settings window for Color Expression locate the Expression section. In the Expression text field, type at(0,qx<0).

The at operator evaluates an expression at the time specified in the first argument. Here, it is a logical expression based on the initial particle position.

Locate the Coloring and Style section.

From the Color table list, choose RainbowLight.

Clear the Color legend checkbox.

Next add a Surface plot to render the cut planes where the intersection points are computed.

Surface Plot

On the 3D Plot Group 4 toolbar click Surface

In the Settings window for Surface locate the Data section. From the Dataset list, choose Cut Plane 1.

Locate the Expression section. In the Expression text field, type 1.

Locate the Coloring and Style section.

From the Coloring list, choose Uniform.

From the Color list, choose Gray.

Click the Plot button

Click the Go to Default 3D View

button in the Graphics toolbar. The plot should look like the following figure.

In the above figure, the location of the particles at 6 Poincaré sections are shown. The color represents the location of the particle at its initial position. So, particles marked as red had an initial position of x < 0 and particles marked as blue had an initial position of x > 0. The at() operator is used to mark the particles with the color of their initial position. The first Poincaré section (the one furthest to the left in the above figure) clearly indicates which particles start with coordinates of x < 0. As the particles follow the flow field, they begin to mix together. By the end of the mixer, the particles have not mixed completely — there are still significant pockets of only red and only blue particles.

Phase Portrait

Another way to visualize particle positions is using the Phase Portrait plot. A Phase Portrait is a 2D plot in which the axes can be arbitrary expressions in terms of the particle position, velocity, or any other variable that can be evaluated on the particles.

In the Home toolbar click Add Plot Group