Numerical Results

Temperature Contour

Summary of the Above Video:

1. Create a Contour Plot and name it Temperature Contours
2. Under Geometry > Locations, choose periodic 1 and set the variable of interest as Temperature.
3. Under View > Apply Scale, enter (1, 30, 1)
4. Default Transform
   1. Apply Reflection about ZX Plane

You can save the image to a file using the camera icon indicated in the image below or using the Snipping Tool in Windows (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

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?

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

The wall temperature values can be exported to a csv file (suitable for Excel) using the Export button highlighted below.

Importing Experimental Data and Chart Formatting

We can import experimental data from a csv file using the procedure shown below. The csv file should contain two columns, corresponding to the x-axis and y-axis values, respectively 

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

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

Mixed Mean Temperature at an Axial Location

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. 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.

Wall Temperature at an Axial Location

For calculating the Nusselt no. at an axial location, we need the wall temperature at that location. The wall temperature at an axial location can be calculated in two ways:

• By interpolating the Tw vs. x values exported to Excel from the wall temperature plot obtained above. 
• By directly extracting the wall temperature at the desired location using the Probe function in the post-processor. 

The following video shows you the procedure for extracting the wall temperature at x=2.67 m using the Probe function; this value can then be used to calculate the Nusselt number. 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.

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.  

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

The wall heat flux on the left hand side is known from the boundary condition. We have shown you how to get the wall temperature T_w at an axial location. Calculate the mixed mean 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. 

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?

Input Summary

In older versions of FLUENT, 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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