1. Mechanical Engineering 4J03
McMaster University
Project #1
Prepared For: Dr. Hamed
Date of Tutorial: February 6, 2015
Project Due Date: February 27, 2015
Prepared By: Shaun Chiasson, 1070043

2. Objective:
Two cases were to be examined of hot and cold air flow mixing in a duct in order to
determine grid independence and the understand flow and mixing characteristics to facilitate the
design an improved mixing system.
Results:
Before designing an improved mixing system an energy balance needed to be performed
in order to determine whether or not it is feasible to have an exit temperature of 200°C for two
streams of air, one at 50°C and another at 500°C. Information on the Cp of air is not available
for these exact temperatures so they were found from linear interpolation of known values close
to the specified temperatures. The Cp at the exit will be assumed to be that of air at the target
temperature 200°C. Densities of the air will be computed the same way where required.
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Performing an energy balance where the energy at the exit equals the energy of the two
inlets also substituting the mass flow rate at the exit to be the sum of the inlet mass flow rates,
rearranging to find the temperature at the exit the following equation results.
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The energy balance indicates that with perfect mixing of the two air streams it is possible
to bring the exit temperature very close to the required 200°C. The assumption for an exit Cp of
200°C has been validated. Since perfect mixing is not possible a limit on the high and low exit
temperatures has been provided and calculated hereafter.

3. Since the energy balance indicated a perfectly mixed temperature less than the required
200°C it makes sense that meeting the lower limit of the temperature range is the difficulty in
designing a mixing system for these air flows.
Figure 1: Temperature contour for no static mixing, mesh size of 1.5cm.
Figure 2: Temperature profile at start of mixing zone with no static mixing, mesh size 1.5cm.

4. Figure 3: Temperature profile at exit of mixing zone with no static mixing, mesh size 1.5cm.
Figure 4: Temperature contour for no static mixing, mesh size of 0.75cm.

5. Figure 5: Temperature profile at start of mixing zone with no static mixing, mesh size 0.75cm.
Figure 6: Temperature profile at exit of mixing zone with no static mixing, mesh size 1.5cm.

6. Figure 7: Temperature contour for tube bundle mixing, mesh size of 1.5cm.
Figure 8: Temperature profile at start of mixing zone with tube bundle mixing, mesh size 1.5cm.

7. Figure 9: Temperature profile at exit of mixing zone with tube bundle mixing, mesh size 1.5cm.
Figure 10: Temperature contour for tube bundle mixing, mesh size of 0.75cm.

8. Figure 11: Temperature profile at start of mixing zone with tube bundle mixing, mesh size 0.75cm.
Figure 12: Temperature profile at exit of mixing zone with tube bundle mixing, mesh size 0.75cm.

9. It is necessary to verify that there is grid independence in the solutions presented for the
two different mesh sizes used for the two mixing cases that have been presented. For the case of
no static mixing vales for the temperatures will be taken at the exit for a y coordinate of 0.125m.
For the case of the tube bundle mixing the temperatures will be taken at the exit for a y
coordinate of 0.1m.
With grid independence established for a 1.5cm mesh, test runs on designs for better
mixing were run at a mesh size of 3cm. Refinement of the results was done at the 1.5cm mesh
with the prescribed inflation layer information given in the project description. Many attempts
were made to come up with a feasible design that could meet the criteria for mixing temperature
at the exit as well as limiting the pressure drop to 4in of water or 996Pa. Some of the many trials
that were done will be presented here.
Figure 13: Examples of two failed design ideas.

10. Figure 14: Examples of two more failed design ideas.
Figure 15: Temperature contour of final design configuration.

11. Figure 16: Temperature profile at start of mixing zone for the final design.
Figure 17: Temperature profile at exit of mixing zone for the final design.

12. Figure 18: Graph of pressure drop for the first 2.5m of the hot duct showing a peak pressure of 1030kPa.
Figure 19: Dimension for the mixing section final design geometry.
Discussion:
Determining grid independence can be tricky because it can depend on where values are
taken. Some locations can have minimal changes in values for the solution as where other areas
can have greater changes in values. Overall the solutions between a 1.5cm mesh and a 0.75 cm
mesh did not change significantly.
It was very difficult to find a design to meet the given criteria, over forty designs were
attempted and only a few came close to meeting the specifications. This is an indication that
perhaps the limitations on the problem are not very realistic. The final design presented here
shows a maximum pressure drop of 1030Pa which is 34Pa greater than the allowed pressure

13. drop. The minimum temperature at the exit for the final design was not within the allowable
range; however the maximum temperature was within the limit. There was only a 12°C
difference between the final solution and the requirements of the design. This could be an
indication that with some more work on the geometry of the final design the temperatures and
pressure drop could be met within the specifications.
One of the major difficulties in finding solutions was problems with recirculation at the
exit of the duct. Ansys dealt with this by placing a wall boundary over a portion of the exit
boundary and iterating the solution to try and resolve the flow so that the wall would no longer
be required. Often times this wall due to recirculation at the exit caused the software to not
converge or experience longer simulation times with sinusoidal variations in the residuals.
Avoiding designs with recirculation at the exit helped to get quick convergence and avoid
possible errors in the final solution.
Conclusion:
Although the final design presented here does not exactly match the given criteria it is an
excellent solution and may still perform well in the real world. If the limitations on the problem
could be changed it would be wise to have a greater allowable pressure drop, or a longer duct. It
may also be advisable to have some turbulence generation prior to the mixing section to promote
mixing. Using a dynamic mixing method may be a much better approach to this problem if the
criteria cannot be changed. Dynamic mixing can provide excellent mixing with lower pressure
drops but will likely be more expensive.
Reference:
[1] Yunus A. Cengel and Michael A. Boles, Thermodynamics an Engineering Approach, Fifth
Edition. United States of America, Boston: McGraw-Hill College, 2006