Simulation of Mixing Tee problem using ANSYS Fluent, comparing K-epsilon and k-omega turbulence models and performing a grid independence test
AIM: To study the factors affecting the output temperature in an air mixing tee simulation and deciding which turbulence model is best suitable in this case and performing mesh independence test on one of the cases.
INTRODUCTION:
Mixing Tee:
Mixing Tees are used for efficiently mixing two fluid streams into one stream. They can be used for mixing of two air-air, air-liquid, liquid-liquid flows.
Examples: Mixing of air streams at a different temperature for cooling or heating, mixing two acids in the chemical industry, mixing of two liquid products in the food industry, etc.
PROBLEM DEFINITION: In this study, we will be simulating 2 cases on the length and long length mixing tee geometrical models.
Hot temperature - `36^@C` and Cold temperature - `19^@C`
Density of air (`rho`) = 1.225 `(kg)/(m^3)`
Specific heat (`C_p`) = 1006.43 `j/(kg-k)`
Viscosity = 1.7894e-05 `(kg)/(m-s)`
Surrounding temperature ( atmospheric temperature) = `26.85^@C`
Case 1:
Hot inlet velocity - 3 m/s
cold inlet velocity - 6 m/s
Momentum ratio = 2
Momentum ratio = velocity at cold inlet / velocity at hot inlet
Case 2:
Hot inlet velocity - 3 m/s
cold inlet velocity - 12 m/s
Momentum ratio = 2
Momentum ratio = velocity at cold inlet / velocity at hot inlet
Mesh Independence test:
Performing mesh independence test using a coarse, fine, and average mesh size on short length geometry for case 1 condition.
GEOMETRY:
Short length
Long length
MESH:
Meshing for short length geometry
Meshing for long length geometry
TURBULENCE MODEL:
Selecting between k -`epsilon` and k -`omega` model is to be done for each simulation case. Simulations were ran using ANSYS Fluent for both the cases on short and long geometry models and the number of iterations was considered before convergence for the selection between two models. The solution provided by both the turbulence models is accurate and acceptable for this study. Since the solutions are quite similar, the selection of turbulence models was done on the basis of the number of iterations.
CASE 1
Short length geometry - case 1 - ( k - `epsilon` model) number of iterations vs residual plot simulated up to 1500 iterations.
Short length geometry - case 1 - ( k - `omega` model) number of iterations vs residual plot simulated up to 1500 iterations.
For case 1 [ Hot velocity = 3m/s and Cold velocity = 6 m/s] it can be concluded that the k -`epsilon` model is better than the k -`omega` model in terms of convergence rate per iteration.
k - `epsilon` = 410 iterations
k -`omega` = 850 iterations
Hence for the case -1 k -`epsilon` turbulence model is selected
CASE 2
Short length geometry - case 2 - ( k - `epsilon` model) number of iterations vs residual plot simulated up to 1500 iterations.
Short length geometry - case 2 - ( k - `omega` model) number of iterations vs residual plot simulated up to 1500 iterations.
For case 2 [ Hot velocity = 3m/s and Cold velocity = 12 m/s] it can be concluded that the k -`omega` model is better than the k -`oepsilon` model in terms of convergence rate per iteration.
k - `epsilon` = 250 iterations
k -`omega` = 180 iterations
Hence for the case -2 k -`omega` turbulence model is selected
RESULTS:
SHORT LENGTH - CASE 1
Residual plot for short length geometry using case 1 conditions and k -`epsilon` model
Temperature contour plot on the cut planes along and across the pipe
Temperature streamline plot on the cut planes along and across the pipe
Velocity contour plot on the cut planes along and across the pipe
Velocity streamline plot on the cut planes along and across the pipe
SHORT LENGTH - CASE 2
Residual plot for short length geometry using case 2 conditions and k -`omega` model
Temperature contour plot on the cut planes along and across the pipe
Temperature streamline plot on the cut planes along and across the pipe
Velocity contour plot on the cut planes along and across the pipe
Velocity streamline plot on the cut planes along and across the pipe
LONG LENGTH CASE 1
Residual plot for long length geometry using case 1 conditions and k -`epsilon` model
Temperature contour plot on the cut planes along and across the pipe
Temperature streamline plot on the cut planes along and across the pipe
Velocity contour plot on the cut planes along and across the pipe
Velocity streamline plot on the cut planes along and across the pipe
LONG LENGTH CASE 2
Residual plot for long length geometry using case 2 conditions and k -`omega` model
Temperature contour plots on the cut planes along and across the pipe
Temperature streamline plot on the cut planes along and across the pipe
Velocity contour plot on the cut planes along and across the pipe
Velocity streamline plot on the cut planes along and across the pipe
| Case | Case 1 short | Case 2 short | Case 1 long | Case 2 long |
| Nodes | 4771 | 4771 | 6262 | 6262 |
| Elements | 22238 | 22238 | 29213 | 29213 |
| Average outlet temperature [C] | 28.503 | 28.501 | 28.73 | 27.138 |
|
Number of iterations for convergence |
420 | 180 | 350 | 160 |
MESH INDEPENDENCE TEST:
Simulation 1 - Mesh size = 0.004 m
nodes - 4771
elements - 22238
simulation time - 14.8 seconds
Mesh body
Temperature contour plots on the cut planes along and across the pipe
Simulation 2 - Mesh size = 0.0005 m
nodes - 582534
elements - 3147996
simulation time - 6.56 seconds
Mesh body
Temperature contour plots on the cut planes along and across the pipe
Simulation 3 - Mesh size = 0.5 m
nodes - 2033
elements - 8854
simulation time - 2709 seconds
Mesh body
Temperature contour plots on the cut planes along and across the pipe
CONCLUSION:
1) We can conclude that by changing the length of mixing tee the drop in temperature obtained is more as compared to the drop in temperature obtained by increasing the velocity of the cold air.
2) The effect of change in length is more as compared to the effect of change in momentum ratio from 2 to 4.
3) By improving the quality of mesh the accuracy of the results can be improved as shown in the mesh independent test. But the time taken for simulation increases very rapidly. hence, a proper balance should be maintained between mesh size and simulation time depending on the nature of the problem and application. Unnecessarily increasing mesh time increases the simulation time and will need higher resources resulting in inexpensive hardware requirements. But problems, where the investment on a product is higher, should be simulated on comparatively smaller mesh sizes to avoid loss due to failure of product, safety, and complexity of the problem.