Numerical Results

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.

Please make sure your project is saved in Workbench. Double click on Results in the Project Schematic window. This will open CFD-Post (the program used to analyze results from FLUENT computation.) Click on z axis in the triad (at the bottom right of the graphics window) to get the view along the z-axis.

Temperature Contour

Summary of the Above Video:

1. Create Contours > Name Temperature Contours
2. Under Details Plot Temperature
3. Under View > Scale > Enter (0, 30, 0)
4. Default Transform
   1. Mirror > Mirror about ZX Plane

You can save the image to a file using the camera icon highlighted below or using the Snipping Tool in Windows 7 (you can search for it under Start > Programs).

In developing the experiment, it was assumed that by the end of the adiabatic mixing stage, the flow will be well mixed. Do the results from the numerical solution simulation support this assumption?

Velocity Vectors

Our next challenge is to produce velocity vectors. This is a very similar process to creating the temperature contours above. 

Summary of the Above Video:

1. Click Vectors > Name Velocity Vectors
2. In Details plot Velocity 
3. In Variable > Color by Variable
   1. Color by temperature
      
      

We see that the flow speeds up as the density decreases in order to keep the same mass flow rate.  

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.

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".

Select the Data Series tab. Change Name and Location.

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.

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

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

Wall Temperature Plot

Summary of the Above Video:

1. Create location > Line
   1. Point 1: (0,.0294,0) Point 2: (6.045,.0294,0)
2. Create Chart
3. Under Data Series  > Location Select line you just created
4. X Tab 
   1. Plot X location
5. Y Tab
   1. Plot Temperature

Importing Experimental Data and Chart Formatting

Summary of the Above Video:

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.

Mixed Mean and Wall Temperatures

From energy conservation, we can show that the mixed mean temperature is constant in the flow development and mixing sections and varies linearly in the heated section. This is shown schematically in the following figure from the MAE 4272 lab manual.

The slope of Tm in the heated section can be obtained from the following equation which is derived from energy balance in the heated section:

Using the above equation, calculate the mixed mean temperature Tm at x=2.67 m. In the Verification & Validation section, you'll check that this value matches the Tm value calculated by integrating the temperature profile. This should be the case if energy is conserved in the simulation.

The following video show you the procedure for extracting the wall temperature at x=2.67 m. To repeat the calculation at a different axial location, you can right-click on appropriate items in the tree, duplicate and modify as necessary. You need to double-click on an item in the tree to modify it; this is easy to overlook.

Summary of the above video:

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.

To calculate the Nusselt no.:

• Export values from your Tw vs. x plot to an Excel file by clicking on the Export button, as previously discussed in the Wall Temperature Plot section. You'll see that the Excel worksheet contains many values of Tw vs. x.  
• Then calculate Nu directly in the same worksheet from Tw and Tm. 

This yields a nice curve of Nu vs x.

Input Summary

You can view the input summary (model, material properties, boundary conditions, etc) by clicking on Report in the menu bar of FLUENT. A small window will pop up and you can print the selected input summary directly in FLUENT.

Go to Step 7: Verification & Validation

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