Effect of Length and Momentum Ratio on Mixing Efficiency using ANSYS FLUENT
Abstract
The purpose of this project is to simulate the flow inside a T-junction pipe and compare the effect of different length geometry and speeds of two fluids at different temperatures on the mixing.
Introduction
A T-junction pipe, or mixing tee, as the name states is a t-shape pipe where two-fluid or air comes from two different inlets and mixes together before leaving from one outlet as shown in Fig. 1. Mixing tee can be used for varies reasons but for our case, we want to simulate the mixing effectiveness of two different mixing tee - short and long, and how does it affect the outcome.
Figure 1: Simple mixing tee geometry.
Objective
Set up a steady-state simulation to compare the mixing effectiveness of short and long mixing tee when the hot inlet is 36 (degree C), and the cold inlet is at 19 (degree C). For both cases, the velocity of the hot inlet is 3 (m/s). Momentum ratio of 2,4.
`Momentum Ratio = (v_(cold))/(v_(hot))`
For simplicity, I have chosen a momentum ratio of 3.
Procedure
The procedure is shown for Case 1 (short tee). For the other two cases, the procedure is identical. We will set up the Ansys Workbench with three Fluent Analysis Systems as shown in Fig. 2 below.
Figure 2: Ansys Workbench with three Fluent Analysis System.
Open SpaceClaim where we will prepare the geometry. You can open the SpaceClaim by right-clicking the geometry tab as shown in Fig. 2 and click \"Open Geometry in SpaceClaim\". Once the geometry is loaded in SpaceClaim, you should be able to view the geometry.
Preparing the Geometry: Under Prepare tab, choose the Volume Extract feature available in SpaceClaim. This will help us extract the fluid volume for the simulation. Using the edge selection, choose the three edges (two inlets and one outlet) as shown in Fig. 3 below.
Figure 3: SpaceClaim Volume Extract feature
This will extract the volume from the solid part as shown in Fig 4. We will have to disable the solid part of the geometry since we are doing fluid simulation. You can do so by right-clicking on Solid1 and choose Disable for Physics.
Figure 4: SpaceClaim Structure tree after volume extraction.
Thus, the geometry is prepared for the simulation as shown in Fig. 5. Notice that the geometry now only has the volume shape, all the unneccesary solid part is disabled.
Figure 5: Prepared geometry view in SpaceClaim.
Now we will move to the second step, Meshing the geometry. Referring to Fig 2, double click Mesh tab to open Ansys Meshing. By default, your mouse should be in Face selection mode. If not, use the shortcut Ctrl + F to select face selection mode. In face selection mode, only the faces of the geometry can be selected. Click one of the inlets and press N to name that face. Do the following for all other faces (hot inlet, cold inlet, outlet, and walls) as shown in Fig 6.
Figure 6: Name selection of the geometry shown in Ansys Meshing
Under Outline (Project Tree), right-click on Mesh to generate default mesh as shown in Fig 7.
Figure 7: Default Mesh generated by Ansys Meshing
By using default meshing parameters, the mesh quality is beyond the standard quality of mesh elements. If the element metric is below the standard metric (<0.05), then geometry should be refined. For our case, since it is a simple geometry the mesh quality is adequate as shown in Fig 8.
Figure 8: Mesh quality for short tee shown in Ansys Meshing.
Referring back to Fig. 2, we will Setup the simulation in Ansys Fluent. Once the model is loaded, perform a Mesh check under Setting Up Domain to make sure it passes standard mesh quality. If there are no errors, the console will print the following message:
Checking mesh .....
Done.
Under Setting Up Physics, make sure Steady State is selected for Time, Pressure-based for Type and Absolute for Velocity Formulation. By doing so, it models the type of simulation Fluent will perform once we finish setting up.
Select Energy and choose `k`-`epsilon` model in Viscous selection. We are choosing the `k`-`epsilon` model because we are not interested in capturing turbulence near the wall, and since it is a basic simulation, `k`-`epsilon` is selected also because of its convergence rate compared to `k`-`omega` model.
Under Material, air should be selected (by default it is set to air).
Under Zone, make sure volume_volume states that the type is set to the fluid.
Under Boundary, all the boundaries type should be set to its type (inlets as inlet, outlet as an outlet, walls as wall). This is because of our name selection as shown in Fig. 6. Fluent recognizes the names of each face and sets the type accordingly.
For boundary, the following parameters were set:
Inlet hot: Velocity = 3 (m/s), Temperature = 36 (degree C)
Inlet cold: Velocity = 9 (m/s), Temperature = 19 (degree C)
Outlet: Pressure = 0 (Pascal), Temperature = default
Under Solving, new Definition were created as shown in Fig.9.a and Fig.9.b.
Figure 9(a): Outlet temperature definition in Fluent.
Figure 9(b): Standard Deviation for outlet temperature in Fluent.
Lastly, the case was Initialize by Hybrid Initialization as shown in Fig. 11.
Figure 10: Hybrid Initizilation message shown in the Fluent console.
Finally, time to run the simulation. Given a number of iterations, hit Calculate.
Results and Discussion
Case 1 - Short Tee with Default Mesh
Figure 11: Short Tee: (a) Residual Plot (b) Average Temperature Plot (c) Standard Deviation Plot
Fig.11.b shows us the average temperature at the outlet, which is 28.61 (degree C). From Fig.11.a, we can conclude that as the number of iteration increases, the solution converges. In fact, the solution converges after 200 iterations. One can also argue that the change in residual in very small after 40 iterations.
Figure 12: Case 1 (Short Tee) Temperature Contour Plot shown in Ansys Postprocessing.
Figure 13: Case 1 (Short Tee) Temperature Contour Plot near the t-section with mesh shown in Ansys Postprocessing.
Figure 14: Case 1 (Short Tee) Velocity Contour Plot shown in Ansys Postprocessing.
We can see how the two different temperature fluid mixes in Fig. 12, and velocity of the fluid before and after mixing in Fig. 14. This should be intuitive that if the hot fluid velocity is slow compared to cold fluid coming from the top and when they mix, it would create swirls after on where the two-fluid will mix and bring the temperature down. How much down will depend on two things: the length of the pipe after the two starts mixing and the speed of cold fluid compared to the hot fluid.
Case 2 - Short Tee with Different Mesh
Figure 15: Different Mesh on Short Tee shown in Ansys Meshing.
Figure 16: Mesh Quality for the different mesh short tee.
Figure 17: Short Tee Mesh: (a) Residual Plot (b) Average Temperature Plot (c) Standard Deviation Plot
Figure 18: Case 2 (Short Tee Mesh) Temperature Contour Plot shown in Ansys Postprocessing.
Figure 19: Case 2 (Short Tee Mesh) Velocity Contour Plot shown in Ansys Postprocessing.
Comparing Fig.17.a with Fig.11.a, we can compare the convergence rate of two simulations with different mesh. It is known that increasing the mesh cells increases the computational time and rate of convergence, which our result supports. The average outlet temperature is closer to 29 (degree C), 28.892 (degree C) to be exact. This improves our accuracy on the final temperature result at a cost of computational time and convergence rate. We would have to run the simulation (twice the original simulation iteration, >600) to get our result to converge.
There is always a trade-off but if we care about accuracy and want to know the result in detail, the finer mesh would be required (sizing of 0.001m).
Case 3 - Long Tee with Default Mesh
Figure 20: Default Mesh on Long Tee shown in Ansys Meshing.
Figure 21: Mesh Quality for the default mesh long tee.
Figure 22: Long Tee: (a) Residual Plot (b) Average Temperature Plot (c) Standard Deviation Plot
Figure 23: Case 3 (Long Tee) Temperature Contour Plot shown in Ansys Postprocessing.
Figure 24: Case 3 (Long Tee) Velocity Contour Plot shown in Ansys Postprocessing.
There is no surprise that long tee requires even more iteration before the result would converge to a solution as shown in Fig. 22. Since there is more number of element cells, the more time and iteration it would be required to converge (thus >>300 iterations) since the simulation was run for 300 iterations for all three cases.
Comparing Fig. 23 with Fig. 12, the are almost identical. As we mentioned earlier, the longer the pipe is, the two-fluid will mix well and give uniform temperature before the outlet. These results can be verified by the standard deviation plot for each case. For the long tee, the standard deviation of temperature at the outlet is much closer to zero than a short tee, indicating the mixing effect of a long tee.
Conclusion
In conclusion, we successfully simulate the mixing efficiency of mixing tee geometry. For such simulations where turbulence and capturing flow properties near the wall are not necessary than `k`-`\\eplison` model is recommended due to a faster rate of convergence and accurate result. It was found that a long tee was identical to a short tee with little higher mixing efficiency. However, similar results can be achieved with a short tee with a higher momentum ratio.