Mixing Efficiency in T section

Question :

Your job is to set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C.

Use the k-epsilon and k-omega SST model for the first case and based on your judgment use the more suitable model for further cases. Giving the reason for choosing a suitable model is compulsory.

1. Case 1
   • Short mixing tee with a hot inlet velocity of 3m/s.
   • Momentum ratio of 2, 4.
2. Case 2
   • Long 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

In a table, compare the following values from the 2 cases.

1. Cell count
2. Average outlet temperature
3. Number of iterations for convergence

Expected results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.
2. Velocity and temperature line plots along and across the length of the pipe.
3. Perform Mesh independent study for any one case.
4. Discuss the effect of length and momentum ratio on results.

For each simulation, you need to show the convergence plot.

Answer :

Given :- Hot Inlet Temperature = 36⁰C

Cold Inlet Temperature = 19⁰C

Hot inlet velocity = 3 m/s

Momentum ratio = velocity at cold inlet / velocity at hot inlet

Short T

Procedure :-

1] First we need to start the workbench and select fluid flow (fluent) solver. Then setup the steps shown in fluent solver as follows.

• Geometry

1. Open Geometry section which will be done through spaceclaim.
2. Then we need to import the given geometry i.e. short/long T.
3. After which we have to extract the required volume, now suppress the physics of not required volume. This completes the Geometry section.

• Mesh

1. Start the mesh section.
2. Then name all boundaries like inlets, outlet, wall.
3. After that, edit the mesh elment size and generate mesh (Here we have used 0.002 as mesh element size for all cases).
4. Then check the mesh quality to make sure it is more than 5%
5. Now close the window and update the mesh option in workbench.

• Setup

1. Open the setup and then in Domain section check the mesh.
2. After that open up physics section, in that first select the energy equation option.
3. Then select the viscous option present in physics section and set the K-epsilon(realizable) model.
4. Now create/edit the material if required.
5. Go to Zones section in which select boundaries option and set the inlet and outlet boundaries according the question.
6. Now Jump in solution section and go into report option and create definitions like area weighted average for temperature, standard deviation of temperature and set to report plots and graphs.
7. Then select hybrid initialization method and initialize the problem.
8. finally set up some amount of iterations and start the calculation, which will plot the residual, area weighted average for temperature, standard deviation of temperature plots, and when the solution is converged the process will stop at some iterations. This complets the setup.

• Results

1. Select the wall volume to make it visible.
2. After that, insert the plane and color it with variable like temperature and velocity which shows the temperature and velocity flow on plane.
3. Edit the legend according to requirement. this completes the results and hence the entire simulation.

2] We are going to simulate Short T and Long T according to above procedure and for momentum ratio of 2 and 4 for both short/long T which has inlet X velocity of 3 m/s.

3] Below are the results obtained from performed simulations on short T and Long T according to given Cases.

#############################{ CASE I : Short T/MR = 2 }#############################

• Geometry of Short T

• Mesh

Element size used here is 0.002/2e-003 m

For this particular Case we will use both K-epsilon and K-omega model to check which is more suitable for the problem and based on results select the same for further cases.

1] K-epsilon model results

• Residual

• Standard deviation of temperature

• Area Weighted Average of temperature

• Temperature Contour plot

• Temperature Contour plot across pipe

• Temperature line plots along and across pipe

1] Temperature along pipe

2] Temperature across pipe

• Velocity Contour plot

• Velocity Contour Plots across Pipe

• Velocity Line plots along and across pipe

1] Velocity along pipe

2] Velocity across pipe

2] K-Omega model results

• Residual

• Standard Deviation of Temperature

• Area Weighted Average of temperature

• Temperature Contour plot

• Temperature Contour Plots Across Pipe

• Temperature line plot along and across pipe

1] Temperature along pipe

2] Temperature across pipe

• Velocity Contour plot

• Velocity Contour Plots across Pipe

• Velocity Line plots along and across pipe

1] Velocity along pipe

2] Velocity across pipe

Results summary :

	K-epsilon model	K-Omega model
Cell count	105841	105841
Average outlet temperature(0C)	30.3400	30.4600
Number of iterations for convergence	175	357

1. Looking at the results we can say that, k-epsilon model is more suitable because its standard deviation of temperature is more efficient as it gives less deviation in values of temperature.
2. Also, the outlet temperatue is less compared to K-omega model.
3. No. of iterations taken by K-epsilon model are less, and it can be seen that there is a lot of diffusion in k-omega model.

Therefore for further cases we will use K-epsilon model as it gives us better results.

#############################{ CASE II : Short T/ MR = 4 }#############################

CAD cleanup will be the same as we are using same Short T pipe, but with higher Momentum Ratio i.e. 4

Setup changes are as follows

Boundaries	Velocity	Temperature
Inlet X	3	36
Inlet Y	12	19

• Residual

• Standard Deviation of temperature

• Area Weighted Average of Temperature

• Temperature Contour plot

• Temperature Contour Plots across Pipe

• Temperature Line plots along and across pipe

1] Temperature along pipe

2] Temperature across pipe

• Velocity Contour plot

• Velocity Contour Plots across Pipe

• Velocity Line plots along and across pipe

1] Velocity Along pipe

2] Velocity across pipe

#############################{ CASE III : Long T/ MR = 2 }#############################

LONG T

Steps are same as in short T procedure steps

• Extracted volume of Long T

• Mesh

Element size used here is 0.002/2e-003 m

• Residual

• Standard Deviation of Temperature

• Area Weighted Average of Temperature

• Temperature Contour plot

• Temperature Contour Plots across Pipe

• Temperature line plots along and across pipe

1] Temperature along pipe

2] Temperature across pipe

• Velocity Contour plot

• Velocity Contour Plots across Pipe

• Velocity line plots along and across pipe

1] Velocity along pipe

2] Velocity across pipe

#############################{ CASE IV : Long T/ MR =4 }#############################

CAD cleanup will be the same as we are using same Long T pipe, but with higher Momentum Ratio (4)

Setup changes are as follows

Boundaries	Velocity	Temperature
Inlet X	3	36
Inlet Y	12	19

• Residual

• Standard Deviation of Temperature

• Area Weighted Average of Temperature

• Temperature Contour Plot

• Temperature Contour Plot across Pipe

• Temperature line plots along and across pipe

1] Temperature along pipe

2] Temperature across pipe

• Velocity Contour Plot

• Velocity Contour Plots across Pipe

• Velocity line plots along and across pipe

1] Velocity along pipe

2] Velocity across pipe

	Short T	Short T	Long T	Long T
Case	CASE I	CASE II	CASE III	CASE IV
MR	2 / 2	4	2	4
Model	K-Epsilon / K-Omega	K-Epsilon	K-Epsilon	K-Epsilon
Cell count	105841 / 105841	105841	140023	140023
Average outlet temperature(0C)	30.34 / 30.45	27.60	30.36	27.55
Number of iterations for convergence	200 / 357	215	157	206

#############################{ Mesh Independence test }#############################

CASE III : Long T/ MR = 2

we are considering case 3 for mesh independence test

• Mesh Size = 0.0017

• Mesh Size = 0.0015

• Mesh Size = 0.0013

Results for mesh independence :

Element Size	Iterations for Convergence
0.0013	127
0.0015	134
0.0017	153

• Acoording to above results of mesh independence we can say that as the element size decreases the iterations required for convergence decreases.
• Hence the solution is not mesh independent.

############################# [ CONCLUSION ] #############################

• Looking at above results we can conclude that Length of pipe dont affect much with the results.
• Momentum ratio plays a vital role in this poject as it affects the mixing efficiency.
• Higher the velocity of cold inlet, higher will be the mixing efficiency and thus lower will be the outlet temperature.