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Forced Convection - Panel
Forced Convection - Panel
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FLUENT Google Analytics
FLUENT Google Analytics

Numerical Results

Note

To Cornell MAE 4272 Students: You Fall 2020: For the canvas quiz, you should use the FLUENT inputs from this tutorial. Later, you will need to repeat the FLUENT simulation with inputs from YOUR MEASUREMENTS in the lab and compare the FLUENT results with the experiment.

Some of the results shown below were obtained with a pipe length of 6.096 which is slightly different from the current length of 6.045. So your results might be slightly different from those shown below. 

Temperature Contour

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<iframe width="560" height="315" src="https://www.youtube.com/embed/7_P7arvK-4Q?rel=0" frameborder="0" allowfullscreen></iframe>

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Using the above equation, calculate the mixed mean temperature Tm at x=2.67 m. Remember to add the inlet temperature, otherwise you will just end up with the temperature difference between the mixed mean temperature and the inlet temperature (where we assumed the flow was fully mixed). An alternate procedure to calculate Tm involves integrating the temperature profile. This procedure is covered in the Verification & Validation section in the video entitled Check Energy Conservation via Mixed Mean Temperature Variation. If energy is conserved in the FLUENT simulation, the values calculated using the two procedures should match.

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  1. Create a line at x = 2.67
  2. Go to Expressions, right click and click New
    1. Name Tw267
  3. Right click in Definition box > Functions > CFD-Post > maxVal
  4. Right click within the parenthese of maxVal > Variables > Temperature
  5. Right click after the @ sign > Locations > x267

Nusselt No.

Cornell MAE 4272 students, Fall 2020: Please use the following procedure for calculating the Nusselt number at two axial locations in the heated section where the flow is thermally fully-developed.

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The convective heat transfer coefficient, h can be determined from Newton's law of cooling:

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The wall heat flux on the left hand side is known from the boundary condition. We Now that we have shown you how to get the wall temperature T_w at an axial location. Calculate the mixed mean and wall temperatures at any axial location, you can create an Excel spreadsheet to calculate the Nusselt number at different axial locations. You can then plot this data to get a nice curve of Nu vs x. temperature at the same axial location by evaluating the following integral using the procedure shown in the video in the Verification and Validation section. The title of the video is Check Energy Conservation via Mixed Mean Temperature Variation. 

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Once you determine h, you can non-dimensionalize it to get the Nusselt number.

 

The Nusselt number in the thermally fully-developed region should be the same at different axial locations. Why? Do your Nu values at the two axial locations compare reasonably well? Why or why not?


Wall Shear

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

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<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.

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


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.

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<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. 

 

Fanning Friction Factor

The Fanning friction factor, also called the skin friction coefficient, is obtained by non-dimensionalizing the wall shear. It can be calculated and plotted using the procedure outlined below. 

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<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

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

 

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