FLOWLAB SOLUTION
8.131 Use the results from Problem 8.130 to examine the flow separation region for the
three different expansion ratios, R2/R1, considered. For one of the expansion ratios,
provide a qualitative visualization of the flow separation past the expansion by plotting
the streamlines as well as the velocity vectors. Comment on the velocity profiles in the
reversed flow region, particularly in the reattachment zone. In addition, compare the
flow separation regions for the three expansion ratios. Export the data for the wall shear
stress, τw , in the exit pipe and on one graph plot shear stress as a function of the distance
along the exit pipe for all three cases of the radius ratio. Develop a method to
quantitatively determine the extent of the flow separation region for each expansion ratio.
Also provide reasoning for the trends seen in the wall shear stress data.
Problem Setup
See Problem 8.130 solution for details.
Answer
For one of the expansion ratios, the students should present plots of streamlines and
velocity vectors in the expansion region to qualitatively visualize the flow separation.
For R2/R1 = 2.0, the following two plots show the streamlines and velocity vectors.
From the streamline plot, the separation region is clearly visible past the pipe expansion
(also a secondary recirculating region in the corner).
In the velocity vector plot, a close-up of the separated flow region clearly shows reversed
flow with the arrows pointing in the opposite direction. It can also be seen that in the
core of the primary recirculating region, the velocity values are quite small.
Note: The default length of the vectors was increased by clicking on the Modify button in
the post-processing window and clicking on the Edit button in the Velocity Vectors
category. To increase the size of the vector arrows, change the Scale value.
Next, the students are to compare the flow separation regions for the three different
expansion ratios. As outlined in the problem statement, the wall shear stress values for
the exit pipe were exported for the three cases and incorporated into a spreadsheet for
plotting – see below.
0.001
0.0005
Wall Shear Stress (Pa)
0
1
3
5
7
9
11
13
-0.0005
R2/R1 = 2.0
-0.001
R2/R1 = 2.5
R2/R1 = 3.0
-0.0015
-0.002
-0.0025
-0.003
Exit Pipe Location (m)
The students are also asked to develop a quantitative method of determining the extent of
the flow separation region for the three expansion ratios. In this case, we can use the wall
shear stress plot; where the curve crosses the x = 0 axis represents the reattachment point
of the separation bubble. Students are to discuss the trends in the wall shear stress plot,
such as positive and negative shear, differences in expansion ratio, etc.
Note: for each of the three expansion ratio cases, the wall shear stress was plotted from
the Reports section of Flowlab under the XY Plots. In the XYplot window, the File
button was clicked to bring up the import/export window. Export was selected to output
the data to a text file.
The reattachment points are summarized in the table below.
R2/R1 Reattachment point (m)
2.0
2.17
2.5
2.56
3.0
3.01
As both the graph and table show, an increase in the expansion ratio produces a larger
overall separation region, with the separation point always at the expansion location and
the reattachment point values shown above.