Week 1- Mixing Tee

Aim:-

• Set up steady-state simulations to compare the mixing effectiveness when the hot inlet temperature is 36C, and the cold inlet is 19C.
• Try both the k-epsilon and k-omega SST models for the first case to get proper judgment about each method; later, use the most suitable model for further simulations.
• Simulate each case for the given velocity and momentum ratio.
• Compare results from the 2 cases about cell count, average outlet temperature, and the number of iterations for convergence.
• Plot the velocity and temperature contour plots on the cut plane along and across the pipe.
• Also, plot the velocity and temperature line plots along and across the length of the pipe.
• Perform Mesh independent study for any one case.
• Moreover, discuss the effect of length and momentum ratio on results.
• Lastly, for each simulation, show the convergence plot.

 

Objective:-

• Understand and define the problem statement for each case.
• Open Ansys workbench and set up a fluent simulation setup, and rename it accordingly.
• From fluent setup, open space claims, and Load the geometry. Extract the working fluid region from the loaded geometry to compute simulation in that particular region. And then close space claim.
• Next, in mesh setup, provide boundary names for each surface and generate mesh to the fluid flow volume. Close mesh setup and update the mesh.
• Later, in the setup section, provide all the required parameters according to the simulation, such as simulation type, input velocity and temperature, materials (working fluid), and other user-defined parameters. 
• In setup parameters, understand the concept of k-epsilon and k-omega SST and find out which is convenient for the current simulation.
• Afterward, simulate our problem setup for the number of iteration required to converge our results.
• Then, close and update the setup. Open the results section to see all the simulated results.
• Juxtapose generated results from each case for their cell count, average outlet temperature, and the number of iteration for convergence.
• Display contour plot on the cut plane to visualize velocity and temperature distribution along and across the mixing tee’s length.
• For a more detailed examination, plot velocity and temperature line chart along the mixing tee’s length.
• Validate the test by performing a mesh independence study on any one case.
• Study the effect of length and momentum ratio on the results of each case.
• Plot the convergence graph to verify that all the results are fully converged after running numerous iterations.

 

Problem Setup

Understand k-epsilon and k-omega SST by considering case-1

Case-1

Short mixing tee

a - Simulation-1

hot Inlet velocity - 3m/s

Momentum ratio - 4

 

 b - Simulation-2

hot Inlet velocity - 3m/s

Momentum ratio - 2

 

Case-2

Long mixing tee

a - Simulation-3

hot Inlet velocity - 3m/s

Momentum ratio - 4

 

b - Simulation-4

hot Inlet velocity - 3m/s

Momentum ratio - 2

 

Let us start with analyzing the best method to converge the solution for this particular case by studying two methods: k-epsilon and k-omega SST.

The aforementioned methods use simulation of turbulence modeling where k-epsilon models predict flow virtually far from the boundaries (wall), and the k-omega model predicts near the wall.

The selection of model depends on the specific problem; no turbulence model suit for every case. Fine-tuning requires the SST model that used good mesh at the boundary, and with wall treated usually works in the most case; it is a problem specific.

Our first study will set two setups, one for k-epsilon and another for k-omega SST. Here, we are going to use the same geometry and mesh for both cases of simulation. Hence, we are going to use a short mixing tee model and mesh it.

                                      

 

Start with dragging and dropping mesh setup to load the geometry and mesh it.

                                      

 

Then open space claim to load geometry in setup. Space claim is a beneficial CAD cleanup software to prepare CAD geometry for simulation setup; it could be for FEA or CFD.

Therefore, load the geometry and extract the fluid volume (working fluid volume).

                                                                            

 

Suppress the actual model, as we do not have to make any conduction simulation in this project. Lastly, close the space Claim.

                                                   

 

Now, we can go for meshing. So, click on the mesh button, which will start Ansys meshing, where we can generate the mesh and provide names for all the surface of the geometry.

Next, create two fluent setups—one for k-epsilon and another for k-omega SST. Drag the exiting mesh into the Fluent analysis Setup cell. Then update the mesh (Right-click on mesh and use the update button) to convert and write the mesh for the FLUENT analysis.

                                                                                                           

                                                           

 

We can check our meshing by cutting the fluid domain into the section as shown below to observe mesh flow. And we can also investigate the quality of mesh by clicking on the option called element quality in the quality section of the mesh panel.

                                                  

 

Then, double click on the setup option in the FLUENT cell for trying the k-epsilon method. It will open the FLUENT interface.

                                      

 

In the Fluent window, we will first see the console window which displays text, and it also accepts TUI (Text User Interface) commands. In the beginning, we will see a lot of text about loading meshing cells, text about achromatic setting boundary condition in fluent as per name provided to surfaces.

                                                     

 

After the complete loading of domain geometry, it will represent it in a graphical user interface very remarkable manner for the user to understand how imported boundary conditions will look.

                                                         

 

Next, in the domain panel by using the check button we can check our mesh preferable for fluent analysis or not. And we can improve the quality using modify option.

                                                        

 

After clicking on the check mesh quality button, it prints the following conformation in the console Window. The mesh check ensures that each cell is in a correct format and connected to other cells as expected. It is recommended to check every mesh immediately after reading it. Failure of any check indicates a badly formed or corrupted mesh that will need repairs prior to simulation.

                                                     

 

Click ‘units’ to change the units of temperature. FLUENT store values in SI units. Most post-processing can be converted into other units.

                                          

 

Then we will set the physics of the domain. Keep the general parameter setting as it is. Solver type -> pressure-based; velocity formulation -> Absolute; solver time -> steady.

                                                          

 

Next, activate models. First, Turn on the energy  Equation. Activating energy equation allows the temperature-dependent problem to be solved.

                                                             

 

In the viscus model, select ‘k-epsilon’,’ Realizable’ for our first type of simulation. Turbulence modeling is a complex area. The choice of model depends on the application. Here, the Realizable k-epsilon model is used which is an improvement on the well-established standard k-epsilon model. Accept the remaining default settings.

                                                             

 

In materials click “FLUENT Database’ to add new material. In this case, our working fluid is air so we keep the default material.

                                     

 

In the cell zone define the material, select the working fluid.

                                   

 

In ‘Boundary condition’ click on the ‘Inlet-x’ and edit the inlet parameter set velocity as 3m/s and temperature as 36^oC. For inlet_y set velocity as 12m/s as we are using momentum ratio of 4 and temperature as 19^oC.

                                   

                                                                

                                                                

 

Set outlet pressure condition as atmospheric pressure value which is also zero gauge pressure. The simulation may predict that flow enters the model through part of the outlet. The backflow will bring turbulence and energy back into the model. However, the model can not predict how much (because the flow is coming from outside of the model). It is, therefore, necessary to specify backflow conditions. Ideally, the geometry should be selected such that flow enters the model only at well-defined inlets. The backflow setting then does not affect the final solution (although they may be used in intermediate iterations).

                                        

 

In ‘Reports’, press ‘new’ for the surface report monitor. Select area-weighted average.

                                          

 

 here we want temperature average at outlet surface so select temperature. And check “report file” and “report Plot”.

                                                     

 

And, similar way create a plot for average velocity plot at outlet boundary condition.

Before running the program our final step will be to initialize the problem setup.

Initialization creates the initial solution that the solver will iteratively improve. Generally, the same converged solution is reached whatever the initialization, though convergence is easier if they are similar. Basic initialization imposes the same values in all cells. You can improve on this in various ways - for example, by patching different values into different zones. Several features, including patching and post-processing, are not available until after initialization.

The hybrid Initialization method is an efficient method of initializing the solution based purely on the setup of the simulation with no extra information required. These methods produce a velocity field that conforms to complex domain geometries and a pressure field that conforms to complex domain geometries and a pressure field that smoothly connects high and low-pressure values.

                                                                      

 

after hitting initialize button we will get the following data printed in the console window that says initialization is done.

                                                                        

 

Now, we can run the simulation just enter the number of iteration for which we want to run the simulation and press ‘calculate’.

                                     

 

When the solution will fully converge it will show the following massage

                                     

 

While calculating the solution we will also get our converge plot for the k-epsilon method. It also built up another plot report of temperature and velocity at the outlet that we set earlier.

                                     

 

After this, we can close the fluent and post-process the results. Click on the results in the workbench and it will open CFD-Post.

CFD-Post initially displays the outline (wireframe) of the model which can be turned on by checking the surface shown in the Outline panel in the fluid section.

Viewer toolbar buttons allow you to manipulate the view.

Create a plane - in the location menu, select ‘Plane’ -> accept the default name ‘Plane 1’ -> set ‘Method’ to be ‘YZ Plane’, accept ‘X’ as 0.0, and press ‘Apply’

Finally, select a plane from the Outline section and use color by temperature which will generate temperature contour on the selected plane.

                                                           

 

Now, create plane 2 for velocity contour.

                                                         

 

This time, we are going to use the same setting for the next simulation and solve the problem by the k-omega SST method. And compare all the results

For the k-omega SST method

                                         

 

Similar way, we will plot temperature and pressure contour. And compare with the k-epsilon method.

                                        

 

In the above contour chart, we can see the flow difference of k-epsilon Realizable and k-omega SST let just first understand why they are different

k-Epsilon

- as we saw in our first simulation, the K-epsilon turbulence model is the most common model used in CFD to simulate mean flow characteristics for turbulent flow conditions. It is a two-equation model that gives a description of turbulence by means of two transport equations (PDEs). the first transported variables are the turbulent kinetic energy (k) and the second transported variable is the rate of dissipation of turbulent kinetic energy.

k-epsilon focuses on the mechanism that affects the turbulent kinetic energy.

 

k-omega SST

The SST k-omega turbulence model is a two-equation eddy-viscosity model that is used for many aerodynamic applications. It is a hybrid model combining the Wilcox k-omega and the k-epsilon models. A blending function, F1, activates the Wilcox model near the wall and the k-epsilon model in the free stream. This ensures that the appropriate model is utilized through the flow field

 

Main difference

The k- omega model is well suited for simulating flow in the viscous sub-layer. On the contrary, The k-epsilon model is ideal for predicting flow in the regions away from the wall

The SST model exhibit less sensitivity to free stream conditions (Flow outside the boundary layer) than many other turbulence models.

The shear stress limiter helps the k-omega model avoid a build-up of excessive turbulent kinetic energy near stagnation points.

If we observe our simulated figure, we can notice, in the k-omega model flow is more like laminar and not giving proper turbulent results, in contrast, simulation by k-epsilon, is giving proper mixing of the two air stream.

 

In this particular case we are not dealing with walls, therefore, we are going to use the k-epsilon method for further simulations.

Now, let us start our simulation with case 1 -a

 

 

Case-1-a

Short mixing tee

a - Simulation-1

Inlet velocity - 3m/s

Momentum ratio - 4

Inlet velocity of cold air = 3x4 = 12m/s

 

We will create two FLUENT cells to compute problems for two momentum ratios separately.

                                      

 

Mesh file for short mixing Tee:

                                                                                                      

 

In our earlier simulation, we can notice because of the coarse meh structure near-wall its showing distorted contour near-wall surface. So if we add inflation layers near-wall surface we can minimize this effect.

                                                       

 

Results

The solution is converging at 118 iterations.

Residue plot:

                                                   

 

Temperature:

Area weighted average outlet temperature:

The average temperature at the outlet is 27.524769^oC.

                                                 

 

Velocity:

An area-weighted average of velocity magnitude at outlet:

The average velocity at the outlet is 6.0129226m/s.

                                                 

 

Temperature contour on the plane along the length of pipe

                                         

 

Velocity contour on the plane along the length of pipe   

                                                                     

 

Case-1-b

Short mixing tee

b - Simulation-1

Inlet velocity - 3m/s

Momentum ratio - 2

Inlet velocity of cold air = 3x2 = 6m/s

                                      

 

Results

The solution is converging at 105 iterations.

Residue plot:

                                       

 

Temperature:

Area weighted average outlet temperature:

The average temperature at the outlet is 30.419565^oC.

                                      

 

Velocity:

An area-weighted average of velocity magnitude at outlet:

The average velocity at the outlet is 4.5009896m/s.

                                     

 

Temperature contour on the plane along the length of pipe

                                       

 

Velocity contour on the plane along the length of pipe

                                      

 

Case-2-a

Long mixing tee

a - Simulation-1

Hot Inlet velocity - 3m/s

Momentum ratio - 4

Inlet velocity of cold air = 3x4 = 12m/s

                                     

 

                                               

 

Results

The solution is converging at 104 iterations.

Residue plot:

                                             

 

Temperature:

Area weighted average outlet temperature:

The average temperature at the outlet is 27.479210^oC

                                             

 

Velocity:

An area-weighted average of velocity magnitude at outlet:

The average velocity at the outlet is 5.9916080m/s.

                                             

 

Temperature contour on the plane along the length of pipe

                                       

 

Velocity contour on the plane along the length of pipe

                                       

 

Case-2-b

long mixing tee

b - Simulation-1

Inlet velocity - 3m/s

Momentum ratio - 2

Inlet velocity of cold air = 3x2 = 6m/s

                                       

 

Results

The solution is converging at 95 iterations.

Residue plot:

                                             

 

Temperature:

Area weighted average outlet temperature:

The average temperature at the outlet is 30.431403^oC

                                             

 

Velocity:

An area-weighted average of velocity magnitude at outlet:

The average velocity at the outlet is 4.4927602m/s.

                                             

 

Temperature contour on the plane along the length of pipe

                                       

 

Velocity contour on the plane along the length of pipe

                                       

 

Effectiveness of mixing

In order to measure the effectiveness of the mixing, we can calculate the standard deviation of the temperature at the outlet of the mixing tee.

A high standard deviation means the mixing is bad, on the contrary, a low standard deviation means we are getting better mixing.

Below, the line chart exhibits the standard deviation of the temperature at the outlet of the mixing tee for each case we have studied.

Now we can see in both short and long pipe the standard deviation is constantly lower after 80^th iterations which have a higher velocity of 12m/s at the cold air inlet.

Therefore, we are getting the best mixing when the flow is high and the effectiveness of mixing is almost less dependent on the length of the mixing tee.

                                       

                                       

 

In the above figures, we took planes across the length of the mixing tee, from the middle part to the outlet of the flow.

Glimpse over the contour over plane depicts the same results of the effectiveness of mixing in is better when the flow of the fluid is higher.

                                       

 

We can see, little more effective mixing at the outlet of the long mixing tee. This occurs because of the diffusion over the length of the pipe.

                                       

 

A similar phenomenon we can notice in velocity contour plots over plane across the length of the mixing tee.

Mesh independence

A mesh independence (or grid independence) study is something an analyst can perform to determine the dependence of the results on the mesh density.  

Compare the results for various runs for different sizing of meshing elements. And in a bid to pass mesh independence results should obtain with proper precision.

So we will run 3 simulations on each case to verify the final results.

                                                

 

Output Result Table:-

                                     

After putting all the results in a single table we can compare our results where we can see the length of the mixing tee does not affect the results at the output that much if we ignore the diffusion criteria.

High-velocity flow showing good mixing results than low-velocity flow.

All results are passing the mesh independence criteria.

 

 

Conclusion:

• k-epsilon models predict flow virtually far from the boundaries (wall), and the k-omega model predicts near the wall. As in this case we need a flow simulation turbulent model far from the wall, therefore, the k-epsilon method is used.
• Solving the first simulation on the fluid domain using coarse mesh gives an initial overview of the analysis which converges results fast. As element number increases the convergence time also increases. Therefore, after obtaining the rough results using coarse mesh simulation successfully we can improve mesh quality and get to final accurate results doing this saves a lot of time which is also extremely helpful for mesh independence test.
• To get better mixing at outlet high velocity of flow is very effective. Therefore, a higher momentum ratio gives better mixing of hot and cold fluid stream at the outlet.
• As the Length of the mixing tee increases because diffusion flow always gives slightly better mixing of two-fluid.
• Finally, in the above cases, it is very important to use a short mixing tee with a momentum ratio of 4 to get precise results but one has to consider the diffusion of flow along the length of the mixing tee, a long mixing tee with momentum will be the greater option.