Mixing efficiency

Case 1

• Short mixing tee with hot inlet velocity of 3m/s
• Momentum ratio of 2

Initially the short mixing tee geometry is imported in space claim cleanup utility with the aim to prepare the volume fluid domain out of it. Then, volume fluid domain is assigned suitable names such as inlet, outlet and walls with the subsequent generation of mesh.

Fig No. 1: Baseline Mesh

Fig No. 2: Baseline Mesh Quality

Figure 1 depicts the baseline mesh with triangular dominant mesh with minimum element size of 0.0102 and number of element is to be 12657. To check whether the mesh element quality is less than 5% or not,the element matrix table showing the number of elements against the element metrices and the minimum mesh element quality turns out to be 39.676% which is acceptable for this case as shown in fig 2.

Further, the geometry is taken to a Fluent tool for setting up the physics i.e. steady, pressure based, K-epsilon turbulence model and velocity formulation under the solver setting with activated energy equation option. Under the zone tab, appropriate boundary conditions to mixing tee geometry has been aasigned such as hot air inlet and cold air inlet velocities as 3 m/s and 6m/s while the temperature of the respective streams at the inlet as 25 deg C and 10 deg C. Here, the hybrid method of initialization is used instead of standard initialization. After this, the case has been run for 350 iterations with residuals keep dropping after each iteration and reached the steady state value after certain iterations as shown in fig 3. To check, whether the proper mixing of two streams are taking place or not, standard deviation monitor plot of temperature at the outlet is monitored which seems to be 1.5 deg C approximately while that of average temperature of air at the outlet is 20 deg C approx. as shown in fig 4 and fig 5.

Fig No.3 Baseline Mesh Residuals

Fig No. 4 Average Temperature of air at Outlet

Fig No. 5 Standard Deviation of Temperature of air at Outlet

The velocity and temperature contours at the mid-section plane for the baseline mesh case are as shown in fig 6 and fig 7. The cold air enters in the regime of hot air in order to have proper mixing, but at the interface of two streams, proper heat transfer phenomena is not visible because of coarseness of mesh (i.e intended physics needs to be captured at the interface).Meanwhile, the velocity at the walls assumes the no-slip condition i.e. zero velocity which was clearly depicted in velocity contour. Here, the hot air velocity is half that of the cold air so, air at the outlet seems to have not achieved appropriate condition and thus there is need for refinement in mesh for capturing of intended physics that we looking for. Hence the mesh has been refined as per the requirement.

Fig No. 6 Temperature Contour at the Mid-section plane

Fig No. 7 Velocity Contour at the Mid-section plane

After, the mesh has been refined with minimum element size of 0.00108 as compared to baseline mesh which in turn increases the number of element to 480333.For such small element size, the minimum mesh element quality needs to be evaluated and turns out to be 23.24% compared to baseline mesh as shown in fig 8 & 9.

Fig No. 8: Refined Mesh

Fig No. 9: Refined Mesh Quality

After the mesh refinement, the geometry was loaded to Fluent solver with other settings remains unchanged.This time, the case has been run for larger iterations say 600 iterations for steady state to reach with average outlet temperature and standard deviation of temperatre at the outlet as shown in fig 10, 11 & 12. In fig 11, average temperature of air at the outlet was 20 deg C approx. while in fig 12, the standard deviation monitor plot of temperature at the outlet shows 2 deg C.

Fig No.10 Refined Mesh Residuals

Fig No. 11: Average Temperature of air at Outlet

Fig No. 12: Standard Deviation of Temperature of air at Outlet

Hence, the respective temperature and velocity contours for the refined mesh are shown in fig 13 and 14. In mesh refinement case, the temperature and velocity of cold air at the inetrface seems to be smooth and distinct.

Fig No. 13: Temperature Contour at the Mid-section plane

Fig No. 14: Velocity Contour at the Mid-section plane

Case 2

• Long mixing tee with hot inlet velocity of 3m/s
• Momentum ratio of 2

In this case, the long mixing tee with hot and cold air inlet velocities of 3 m/s and 6m/s respectively have been applied at the respective inlets. The same methodolgy has been adopted as shown in the above case of short mixing tee and corresponding baseline mesh and its quality are shown in fig 15 and 16.

Fig 15 shows the baseline mesh with triangular dominant mesh with minimum element size of 0.0138 and number of element turn out to be 15613. The minimum mesh element quality of 32.98%.

Fig No. 15: Baseline Mesh

Fig No. 16: Baseline Mesh Quality

Again, the geometry was taken to a Fluent tool for setting up the physics i.e. steady, pressure based, K-epsilon turbulence model and velocity formulation under the solver setting with activated energy equation option. The appropriate boundary conditions to long mixing tee geometry has been applied such as hot air inlet and cold air inlet velocities as 3 m/s and 6m/s while the temperature of the respective streams at the inlet as 25 deg C and 10 deg C. Here, the hybrid method of initialization was used instead of standard initialization. After this, the case has been run for 500 iterations with residuals plot as shown in fig. 17.

Fig No.17: Baseline Mesh Residuals

The standard deviation monitor plot of temperature at the outlet was monitored which seems to be 1 deg C approximately while that of average temperature of air at the outlet was 20 deg C approx. as shown in fig 18 and fig 19.

Fig No. 18: Average Temperature of air at Outlet

Fig No. 19: Standard Deviation of Temperature of air at Outlet

The velocity and temperature contours at the mid-section plane for the baseline mesh case are as shown in fig 20 and fig 21.

Fig No. 20: Temperature Contour at the Mid-section plane

Fig No. 21:Velocity Contour at the Mid-section plane

Again, the mesh has been refined with minimum element size of 0.00125 as compared to baseline mesh which in turn increases the number of element to 456044.For such small element size, the minimum mesh element quality needs to be evaluated and turns out to be 18.216% comapred to baseline mesh as shown in fig 22 & 23.

Fig No. 22: Refined Mesh

Fig No. 23: Refined Mesh Quality

After the mesh refinement, the geometry was loaded to Fluent solver with other settings unchanged.This time, the case has been run for larger iterations say 900 iterations for steady state to reach with average outlet temperature and standard deviation of temperatre at the outlet are as shown in fig 24, 25 & 26. In fig 25, average temperature of air at the outlet was 20 deg C approx. while in fig 26, the standard deviation monitor plot of temperature at the outlet shows 1.5 deg C.

Fig No.24: Refined Mesh Residuals

Fig No. 25: Average Temperature of air at Outlet

Fig No. 26: Standard Deviation of Temperature of air at Outlet

Hence, the temperature and velocity contours for the refined mesh are as shown in fig 27 and 28.

Fig No. 27: Temperature Contour at the Mid-section plane

Fig No. 28: Velocity Contour at the Mid-section plane

Case 3

• Short mixing with hot inlet velocity of 3 m/s
• Momentum ration of 4

In this case, the short mixing tee with hot and cold air inlet velocities of 3 m/s and 12 m/s respectively has been applied at the respective inlets. The same methodolgy has been adopted as shown in the previous case of short mixing tee and corresponding baseline mesh and its quality are shown in fig 29 and 30.

Fig 29 shows the baseline mesh with triangular dominant mesh with minimum element size of 0.0102 and number of element turn out to be 12657. The minimum mesh element quality of 39.67%.

Fig No. 29: Baseline Mesh

Fig No. 30: Baseline Mesh Quality

Again, the geometry was taken to a Fluent tool for setting up the physics i.e. steady, pressure based, K-epsilon turbulence model and velocity formulation under the solver setting with activated energy equation option. The appropriate boundary conditions to short mixing tee geometry has been applied such as hot air inlet and cold air inlet velocities as 3 m/s and 12 m/s while the temperature of the respective streams at the inlet as 25 deg C and 10 deg C. Here, the hybrid method of initialization was used instead of standard initialization. After this, the case has been run for 350 iterations with residuals keep dropping after each iteration as shown in fig 31.

Fig No.31: Baseline Mesh Residuals

The standard deviation monitor plot of temperature at the outlet was monitored which seems to be 1 deg C approximately while that of average temperature of air at the outlet was 17.5 deg C approx. are as shown in fig 32 and fig 33.

Fig No. 32: Average Temperature of air at Outlet

Fig No. 33: Standard Deviation of Temperature of air at Outlet

The velocity and temperature contours at the mid-section plane for the baseline mesh case is as shown in fig 34 and fig 35.

Fig No. 34: Temperature Contour at the Mid-section plane

Fig No. 35: Velocity Contour at the Mid-section plane

Again, the mesh has been refined with minimum element size of 0.001125 as compared to baseline mesh which in turn increases the number of element to 433574.For such small element size, the minimum mesh element quality needs to be evaluated and turns out to be 22.682% comapred to baseline mesh as shown in fig 36 & 37.

Fig No. 36: Refined Mesh

ig No. 37: Refined Mesh Quality

After the mesh refinement, the geometry was again loaded to Fluent solver with other settings remains unchanged.This time, the case has been run for larger iterations say 800 iterations for steady state to reach as shown in fig 38.

Fig No.38: Refined Mesh Residuals

The standard deviation monitor plot of temperature at the outlet was monitored which seems to be 1.5 deg C approximately while that of average temperature of air at the outlet was 17.5 deg C approx. as shown in fig 39 and fig 40.

Fig No. 39: Average Temperature of air at Outlet

Fig No. 40: Standard Deviation of Temperature of air at Outlet

Hence, the temperature and velocity contours for the refined mesh are as shown in fig 41 and 42.

Fig No. 41: Temperature Contour at the Mid-section plane

Fig No. 42: Velocity Contour at the Mid-section plane

From the above table, the results shows that with increase in the momentum ratio in case of short mixing tee, which increases the heat transfer phenomena of two streams and thus the achieving the desired comfort condition with ease which is clearly seen from the temperature contour of air at the mid section. In velocity contour also, there was large impingement length of cold air upto the outlet which increases the residence time for both the streams to have proper mixing. But when the length of the mixing tee was increased beyond the certain length, there was no phenomenal change in the average temperature of air at the outlet. Thus, there should be comprise between the length of mixing tee and velocity ratio chosen at the inlets so as to have intended comfort conditions