Numerical Results

After the solution is complete, close the FLUENT window to return to the Workbench window. Double click Results in the main Workbench window to open CFD Post, where we will be viewing the results. For a basic orientation on how to use CFD Post, pl. see the videos in the [results step of the Laminar Pipe Flow tutorial].

The following instructions show only how to view results using the "chart" option. But one should really start by viewing velocity vectors, velocity/pressure/TKE contours etc. and check that the solution looks basically right. The [Laminar Pipe Flow tutorial] walks you through the steps to view vectors and contours in CFD Post.

Locations

Before viewing the results, we need to define the locations in CFD Post where we would like to view the results, namely the wall, centerline, and outlet.

Insert > Location > Line

Rename this location "Pipe Wall". Avoid naming locations in CFD Post with identical names to those used in FLUENT, this can cause problems. We will define the line by two points. Enter (0,0.1,0) for Point 1 and (8,0.1,0) for Point 2. Change Samples to 100.

Repeat the process for the two other locations needed:

y+

Turbulent flows are significantly affected by the presence of walls. The k-epsilon turbulence model is primarily valid away from walls and special treatment is required to make it valid near walls. The near-wall model is sensitive to the grid resolution which is assessed in the wall unit y+(defined in section 10.9.1 of the FLUENT user manual). We'll gloss over the details for now and use the following rule of thumb: select the near-wall resolution such that y+ > 30 or < 5 for the wall-adjacent cell when using the Enhanced Wall Treatment option. Look at section 10.9, Grid Considerations for Turbulent Flow Simulations, for details.

Let's plot y+ values for wall-adjacent cells to check how it compares with the recommendation mentioned above.

Insert > Chart

Let's rename the graph "Wall Y plus". Also, change Title to "Wall Y plus".

Data Series Tab
Rename the data series to "Y plus". Next, change Location to Pipe Wall.

X Axis Tab
Change Variable to X.

Y Axis Tab
Change Variable to Yplus.

Click Apply and our chart should appear.

As we can see, the wall _y+_value is between roughly 1.35 and 2.45. Since this is less than 5, the near-wall grid resolution is acceptable.

Export the data to a .csv file ("comma separated values") by clicking on Export. This file can be opened in Excel.

Centerline Velocity

Next, we would like to make a graph of the axial velocity along the centerline. We will do this by creating another chart.

Insert > Chart
Rename this chart "Centerline Velocity", and change the title of the chart as well.

Data Series
Change Name to "Centerline Velocity", and this time set Location to "Pipe Centerline".

X Axis
Once again, change Variable to X.

Y Axis
Change Variable to Velocity u, which corresponds to the Axial Velocity.

Click Apply and our chart should appear.

Coefficient of Skin Friction

The definition of the skin friction coefficient was discussed in the laminar pipe flow tutorial.

Once again, insert another chart, naming and titling it Coefficient of Skin Friction. Rename the data series and choose Pipe Wall for Location. Plot X on the X Axis and the Skin Friction Coefficient on the Y Axis. When complete, your chart should match the image below:

We can see that the fully-developed value is 0.0085. Compare this with what you'd expect from the Moody chart.

Velocity Profile

We'll plot the axial velocity at the outlet as a function of the distance from the center of the pipe.

Insert another chart, naming and titling it "Outlet Velocity". Change the name of the data series, and set the Location to Pipe Outlet. This time, put Velocity u on the X Axis and Y on the Y Axis. When complete, your chart should appear as below:

The axial velocity is maximum at the centerline and zero at the wall to satisfy the no-slip boundary condition for viscous flow. Compare qualitatively the near-wall velocity gradient normal to the wall with the laminar case. Which is larger? From this, what can you say about the relative strengths of near-wall mixing in the laminar and turbulent cases?

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