Mixing efficiency
Aim:- The aim is to set up steady-state simulations & compare the mixing effectiveness between hot inlet temperature 360C & the Cold inlet at 190C. I have to use the k-epsilon and k-omega SST model for the first case and based on my judgment select the more suitable model for further cases and also justifying the answer.
Intoduction:- Here I will use the fluent module which includes the geometry, meshing, setup, solution & post processing. The structure given is a mixing tee that is designed for specific requirements and I have to solve for two cases one short tee and other one long tee.
Practical Importance:- This is used for rapid mixing.
Modelling Approach:- The geometry is already provided along with the course. This is the tee with two inlets along x & Y direction one for hot fluid and other is for cold fluid. The other section consists of the outlet section.
Case 1:-
- Short mixing tee with a hot inlet velocity of 3m/s.
- Momentum ratio of 2, 4.
- Momentum ratio = velocity at cold inlet / velocity at hot inlet
- Here we will use the k-epsilon model
In performing the simulation we do not need the solid boundaries because we are only measuring the temperature at the mixing junction so we eliminate the extra surfaces and consider only the fluid volume. The solid component will not be included in mesh generation process so we hide it by selecting suppress for physics.
After this we go to the meshing section and give names to the faces such as inlet-x, inlet-y, outlet-x direction & walls.
Then we provide the meshing with 0.004m and keep all the parameters unchanged. Now we cut the geometry into half along y axis so the we can visualise the flow internally. Also we check the element quality and find that our mesh quality lies between the minimum value 0.35 and maximum is 0.90. Next in the setup we get to see the console where we can find all the information regarding the mesh, geometry etc and any runtime error regarding them will show here. So here we also check the mesh quality and find that eveything is fine.
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The flow is steady with pressure driven and absolute velocity solver. Also we use the k-epsilon model with realiazable model and standard wall functions. This is a RANS based turbulence model & also we are interested to know the temperature distribution so we select the energy option. Now we select the material for which we will undergo the process from the material section. We find that air is already selected and so we dont change it and continue to work on that.
Next after selecting the material we go the the boundary section and set the given velocity and temperature for the inlet x and y direction. Velocity for inlet x & y are 3m/s and 1.5m/s & temperature for inlet x and y are 36`degree`Celsius and 19 degree celsius respectively.We dont provide any data at the outlet as it shows the gauge pressure as 0 which is atmospheric. In this case we will perform the mesh independent study for three mesh element size 0.003, 0.004 & 0.005 m. On the base of the study we will select the best suitable parameters .
Now we start with mesh size 0.002m and start our simulation by check the residuals and limit the iterations to 160. Also we are interested to find the area weighted average and standard deviation of temperature at the outlet section so we choose them from the definations section.Then we select the hybrid method and start the initialisation after which we run the calculation at first upto 160 iterations. Ansys fluent has found that the respectived criteria has gone below the respective convergence values so it stop automatically at 140 iterations and we can take it as converged. The standard deviation of temperature i.e. 2.5, area weighted of temperature which gives the temmperature at the outlet upto 33.9 degree celsius & the velocity and temperature contour are shown below.
The second simulation is done by increasing the mesh size to 0.003m and upto 300 iterations. Here we are using a larger mesh size and also increasing the no. of iterations so that we can find the convergence, standard deviation of temperature i.e. 2.5, area weighted of temperature which gives the temmperature at the outlet upto 33.8 degree celsius & the velocity and temperature contour. In this model of the residual plot we can see that the solution ran upto 300 iterations and after 150 iterations the residual plots are repeating each other and following the same pattern & values, so we can conclude that the solution has converged.
The third simulation is done by increasing the mesh size to 0.004m upto 1000 iterations. Here we are using a larger mesh size and also increasing the no. of iterations so that we can find the convergence, standard deviation of temperature i.e. 2.5, area weighted of temperature which gives the temmperature at the outlet upto 33.9 degree celsius & the velocity and temperature contour. In this model of the residual plot we can see that the solution ran upto 1000 iterations and after 300 iterations the residual plots are repeating each other and following the same pattern & values, so we can conclude that the solution has converged.
| Sl No. |
Mesh Size (m) |
Cell Counts |
Average outlet temperature(celsius) | No. of iterations |
| 1 | 0.002 | 106551 | 33.9 | 160 |
| 2 | 0.003 | 39868 | 33.8 | 500 |
| 3 | 0.004 | 21988 | 33.8 | 1000 |
According the above table we find that the there is not much difference in outlet temperature when different mesh size are used in this case but we find that the mesh size of 0.002m has a advantage that it is more refine and so the solution converges automatically and takes less time.
Now we will find the mixture temperature by using the temperature referance formula in the guildelines.
Here the mass of hot fluid is calculated by using the formula-- density X area X velocity= 1 X 0.00089674 X 3= 0.002689 kg/s
mass of cold fluid is calculated by using the formula-- density X area X velocity= 1 X 0.000222 X 1.5= 0.000333 kg/s
By using the formula Tmix = 34.27 degree celsius.
Enthalpy of hot fluid are calculated by using the formula--- mass X Cp X T= 0.002689 X 1006.43 X 309.15= 836.64 J/s
Enthalpy of cold fluid are calculated by using the formula--- mass X Cp X T= 0.000333 X 1006.43 X 292.15= 97.911 J/s
Enthalpy of mixture= 755.238 J/s
Now we are changing the momentum ratio to 1/4, which makes the velocity of cold air to be 3 m/s, velocity of hot air to be 12 m/s. By increasing the velocity ratio there is a drop in the standard deviation of temperature which is at 2.125 degree celsius and the average weighted temperature is 34.875 degree celsius which is larger than the one obtain by the original VR. But the no of iteration has to be more when compared with the same VR for the same mesh of 0.003m and also the diffusion in this case is less.
Case 1:-
- Short mixing tee with a hot inlet velocity of 3m/s.
- Momentum ratio of 2, 4.
- Momentum ratio = velocity at cold inlet / velocity at hot inlet
- Here we will use the k-omega model
- The mesh is 0.003m
Now we will find the mixture temperature by using the temperature referance formula in the guildelines.
Here the mass of hot fluid is calculated by using the formula-- density X area X velocity= 0.00269 kg/s
mass of cold fluid is calculated by using the formula-- density X area X velocity= 0.0003333 kg/s
By using the formula Tmix = 35.14 degree celsius.
Enthalpy of hot fluid are calculated by using the formula--- mass X Cp X T= 0.00269 X 1006.43 X 309.15=836.96 J/s
Enthalpy of cold fluid are calculated by using the formula--- mass X Cp X T= 0.0003333 X 1006.43 X 292.15= 97.911 J/s
Enthalpy of mixture= 755.54J/s
So according to the above analysis we can predict that according to the given criteria k-epsilon model is more preferable due to the highest rate of convergence and good diffusion. Also due to the realizable k epsilon model we can precisiley predict the variation of flow.
- Case 2
- Long mixing tee with a hot inlet velocity of 3m/s.
- Momentum ratio of 2, 4.
- Here we will use the k-epsilon model
- The mesh is 0.002m
Now we start with mesh size 0.002m and start our simulation by check the residuals and limit the iterations to 140. Also we are interested to find the area weighted average and standard deviation of temperature at the outlet section so we choose them from the definations section.Then we select the hybrid method and start the initialisation after which we run the calculation at first upto 140 iterations. Ansys fluent has found that the respectived criteria has gone below the respective convergence values so it stop automatically at 123 iterations and we can take it as converged. The standard deviation of temperature i.e. 4.5, area weighted of temperature which gives the temmperature at the outlet upto 33.5 degree celsius & the velocity and temperature contour are shown be above.
| Sl no. | Mesh Count and cells | Avg Outlet temp(Celsius) | No of iterations |
| Case 1 | 0.002(106551) | 33.9 | 160 |
| Case 2 | 0.002 (141811) | 33.5 | 123 |
Also it is seen thatwith increase in lenght there is not much change in the outlet temperature except the convergence happens in less iterations and automatically stops.
Now we will find the mixture temperature by using the temperature referance formula in the guildelines.
Here the mass of hot fluid is calculated by using the formula-- density X area X velocity= 1 X 0.00089920 X 3= 0.002697 kg/s
mass of cold fluid is calculated by using the formula-- density X area X velocity= 1 X 0.00022394 X 1.5= 0.0003359 kg/s
By using the formula Tmix = 34.26 degree celsius.
Enthalpy of hot fluid are calculated by using the formula--- mass X Cp X T= 0.002697 X 1006.43 X 309.15= 839.138 J/s
Enthalpy of cold fluid are calculated by using the formula--- mass X Cp X T= 0.0003359 X 1006.43 X 292.15= 98.76 J/s
Enthalpy of mixture= 757.139 J/s