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  • Forced Convection - Numerical Results

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Does the flow become fully developed at the end of the first section?

Centerline Temperature Plot

Now let's look at the temperature variation along the center-line of the pipe. To do this we need to first create a line corresponding to the center-line:

Insert > Location > Line

Name it "Centerline" and click OK. On the lower left panel, you will see Details of Centerline. Enter the start and end locations of the line and the sampling frequency. Click Apply.

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You will see centerline created under User Locations and Plots.

Insert > Chart 
Please name this chart "Centerline Temperature". You will see Details of Centerline Temperature appear on the lower left.

We'll go through the tabs in the menu to specify the plot that we want. Select the General tab and name the chart "Temperature Variation along Pipe Axis".

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Select the Data Series tab. Change Name and Location.

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We want to see the variation of temperature with the length of the pipe. Therefore, temperature will be on the "y-axis" of the chart and axial position on the "x-axis" of the chart.

Click on X Axis tab. Next to Variable, choose X.
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Click on Y Axis tab. Next to Variable, choose Temperature.

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Click Apply. You will see Centerline Temperature created under Report in the Outline tab.

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Wall Temperature Plot

HTML
<iframe width="560" height="315" src="https://www.youtube.com/embed/-Cvn7HPp9eY?rel=0" frameborder="0" allowfullscreen></iframe>

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  1. In details of Chart > New Series > Import Data from file
    1. Find file and click okay
  2. Change how experimental data looks in CFD Post
    1. In Line Display under Series 2 > No Line > Symbols > Ellipse
  3. Chart Details > General
    1. Give Title
  4. Chart Details > Chart Display
    1. Font Sizes
    2. Grid Sizes

 

Pressure Plot

Create a plot of the pressure variation along the centerline of the pipe. Steps for this are similar to the plot of the centerline temperature that we did earlier.

There is no need to create a new line. We can use the "centerline" created earlier.

Insert > Chart 

Follow steps from the Centerline Temperature plot above, making appropriate modifications. You should see the following plot.

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Note that the centerline temperature and pressure variations can be plotted by duplicating this plot as mentioned in the video.

Mixed Mean and Wall Temperatures

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Wall Shear

We plot the wall shear using the procedure shown in the video below.  

HTML
<iframe width="640" height="360" src="//www.youtube.com/embed/WiK1uBTdK-M?rel=0" frameborder="0" allowfullscreen></iframe>

Summary of the above video:

  1. Click on the Chart Viewer tab
  2. Click chart in the top toolbar
    1. Name it Wall Shear
  3. Click on Data Series Tab
    1. In Location dropdown menu, choose Wall
  4. Click on X Axis tab
    1. under Variable, choose X
  5. Click on Y Axis tab
    1. under Variable, choose Wall Shear X or Wall Shear
  6. Go to Location in the tree
    1. Double click on Wall
    2. Increase Sampling from 50 to 200

We then consider the trends in the wall shear in the heated, mixing and flow development sections and try to justify them through physical reasoning.

HTML
<iframe width="640" height="360" src="//www.youtube.com/embed/NbdGrJTesZg?rel=0" frameborder="0" allowfullscreen></iframe>

Summary of the above video:

  1. As you heat flow, velocity increases
    1. Momentum at any any average is going to increase when heat is added
  2. The gradient of the velocity normal to the wall is higher, the wall shear is higher
    1. Wall shear increases in the heated region, as shown in the wall shear plot

You can spiff up your plot using the tips discussed below. This video also shows you how you could read in experimental results for comparing the wall shear between simulation and experiment.

HTML
<iframe width="640" height="360" src="//www.youtube.com/embed/6RNykoM86xA?rel=0" frameborder="0" allowfullscreen></iframe>

Summary of the above video:

  1. To edit how the Wall shear graph is displayed
    1. Select Wall shear in tree
    2. Click on General, check Title and enter title in Title blank
    3. in Data Series, enter series name in Name blank
    4. in X Axis, enter x axis label in Custom Label blank
    5. same for Y Axis
    6. in Line Display, uncheck "Use series..." and type within Legend Name blank
    7. in Chart Display, under Sizes, toggle with the line sizes and font
  2. To add another data series
    1. go to Data series tab of Wall Shear
    2. click on New button
    3. Scroll down, click File as  Data Source > browse for your file
  3. To export the chart
    1. Click the button next to undo
    2. Select location to save
    3. Rename

When the simulation was repeated for conditions for which experimental data are available, we got the comparison shown below. The difference in the average wall shear in the heated section between the simulation and experiment is a respectable 4%. Note that the wall shear in turbulent flows is difficult to predict accurately due to the steep velocity gradients at the wall. 

 Image RemovedImage Added

 

Fanning Friction Factor

The Fanning friction factor, also called the skin friction coefficient, can be plotted using the procedure outlined below. 

HTML
<iframe width="640" height="360" src="//www.youtube.com/embed/Jcht7CAPzAc?rel=0" frameborder="0" allowfullscreen></iframe>

Summary of the above video:

  1. Create Location > Point 
    1. (2.67, .0294, 0)
  2. Probe wall shear at point: 
    1. Create Expression > Right Click > New Expression
    2. probe(Wall Shear)@w267 / 1.483 (Pa/K) /Tm267
  3. Can duplicate for different locations for a plot

 

Final Plots

HTML
<iframe width="560" height="315" src="https://www.youtube.com/embed/x-flaXXU7xg?rel=0" frameborder="0" allowfullscreen></iframe>

Summary of the above video:

  1. Display Wall Temperature vs. Position in pipe and compare with experimental data
  2. Display Pressure Variation vs. Position in pipe and compare with experimental data
  3. Display Temperature at Centerline vs. Position in pipe and compare with experimental data

 

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