Comparison of mixing effectiveness in a Mixing Tee
Abstract:
A numerical investigation is carried out to compare the effectiveness of mixing of hot air stream with a cold air stream in a mixing tee using ANSYS Fluent. A steady-state simulation is performed for cases with different outlet length and different momentum ratio. The effectiveness of mixing is measured by observing the temperature at the outlet and its standard deviation. It is observed that a high velocity of the cold fluid is necessary to achieve a higher effective mixing.
Introduction:
A mixing tee is a device used to split or combine fluid flows. It is used in many applications including HVAC, blending of fuels and injection of additives. This report focuses on the HVAC application and considers an air cooler in particular. In order to achieve the temperature specified by the user, some quantity of atmospheric air is mixed with the cold air produced by the air cooler to reach the user-specified temperature without decreasing the efficiency of the air cooler.
The 3D model of the mixing tee is imported from SOLIDWORKS into ANSYS workbench to simulate the flow. The numerical solver FLUENT was used to solve the governing equations. Three different cases were defined as shown in Table.1. with different outlet length and different momentum ratios and the three cases were simulated independently. The momentum factor is the ratio of the velocity of the hot stream to the velocity of the cold stream. The effectiveness of mixing, used as the main factor for comparison, was measured indirectly through the temperature and its standard deviation at the outlet.
The geometry is cleaned and meshed using tetrahedral cells with an element size of 2e-3 for all the three cases. It is solved using FLUENT. A standard Pressure based solver was used with the Realisable k-epsilon viscous model. Since the report focuses on an air cooler, the material of the fluid stream was chosen to be air. The cell count, the number of iterations for convergence and the average outlet temperature are tabulated for discussion.
Case Description:
Case 1: Mixing Tee with short downstream length
The hot air enters at the intel to warm the cold air entering through the mixing tee. After mixing, the stream travels for a distance of 0.16 m before entering the atmosphere as shown in figure 1a. The model volume is extracted to have meshed. Figure 1b displays the model after it has meshed.
Figure 1a.3-D model of mixing tee - Case 1
Figure 1b. Meshed structure of mixing tee - Case 1
Case 2: Mixing Tee with long downstream length
Figure 2a. 3-D model of mixing tee - Case 2
The initial conditions, in this case, are similar to the base case except the mixed stream has to travel a downstream length is 0.23 m before contacting with the atmosphere. The model and its mesh are displayed in figure 2a and figure 2b.
Figure 2b. Meshed structure of mixing tee - Case 2
Case 3: Short Mixing Tee with higher cold stream velocity
The third case is similar to the base case in terms of geometry but the cold air enters through the inlet at a higher velocity of 12 m/s as shown in figure 3a and the meshed structure is shown in figure 3b.
Figure 3a. 3-D model of mixing tee - Case 3
Figure3b. Meshed structure of mixing tee - Case 3
The inlet conditions for the three cases are summarized in table 1.
Table 1. Definition of different inlet condition for the simulation
Results and Discussion:
The outlet temperature and its standard deviation are calculated for individual cases to determine the effectiveness of mixing.
Case 1: Mixing Tee with short downstream length
It is observed from the outlet temperature plot (figure 4a), that the average temperature is 19.9 degC and from figure 4b, the standard deviation of outlet temperature is observed as 1.4. This is assumed as the base case and the other two cases are compared with this base case.
Figure 4a. Convergence plot of average outlet temperature - Case 1
Figure 4b. Convergence plot of the standard deviation of outlet temperature - Case 1
Case 2:
It can be observed from the outlet temperature plot (figure 5a), that the average temperature is 19.97 degC and from figure 5b, the standard deviation of outlet temperature is observed as 0.78.
Figure 5a. The convergence of outlet temperature - Case 2
Figure 5b. Convergence plot of outlet temperature - Case 2
Case 3:
It can be observed from the outlet temperature plot (figure 6a), that the average temperature is 17.55 degC and from figure 6b, the standard deviation of outlet temperature is observed as 0.9. The lower standard deviation is due to an additional mixing that occurs towards the end of the pipe
Figure 6a. The convergence of outlet temperature - Case 3
Figure 6b. The convergence of standard deviation of outlet temperature - Case 3
The Mesh attributes and the solution obtained after the simulation are summarized for the three cases in table 2. The size of the mesh elements was kept constant at a value of 5E-3 m for the three cases. This leads to a larger number of elements in case 2 compared to the other two cases because of longer downstream length in case 2.
Table 2. Summary of results for the three cases of simulation
Temperature and velocity are plotted along the length of the model at the mid-Z-plane as shown in figure 7 for comparison.
It can be observed from figure 7 that most of the mixing takes place in near the joint with some diffusion occurring in the downstream direction. This implies that the downstream length of the mixing Tee has very little influence on the average outlet temperature.
The standard deviation of temperature implies the uniformity of temperature at the outlet. The standard deviation is influenced more by the downstream length as observed in case 2 which has a lower standard deviation of the output for the same initial conditions. But the outlet temperature is largely influenced by the velocity of the cold stream, evident from case 3.
Figure 7. The plot of temperature (on the left vertical side) and velocity (on the right vertical side) for three cases along the mid-Z plane
Conclusion:
This report examined the effectiveness of mixing of two air streams by observing the temperature and its standard deviation at the outlet of mixing tee in three different cases. It is reported that the velocity of the cold air stream leads to higher effectiveness of mixing of two air streams.