Mixing Tee

 Mixing Tee

GIVEN PROBLEM:

1.For this challenge, we have created two versions of the mixing tee. One of them is longer than the other.

2. our 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. 

3.Use the k-epsilon and k-omega SST model for the first case and based on judgment use the more suitable model for further cases.

4.

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.

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

5.

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

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

6.

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

 solution:

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.

 k-epsilon models predict flow virtually far from the boundaries (wall), and the k-omega model predicts near the wall.

We are starting from the k-omega model for case-1-a:

1.First start ansys workbench and then drag Fluid flow(fluent) and drop on the white space . Then right click on Geometry→Import Geometry→Browse and load the certain file.

2.Then again right click on Geometry and select space Claim . In space Claim Geometry is loaded like this

3. In the spaceClaim select prepare→volume extract→edges .Then select the edges in the following way

Then click on the green button and deselect the shell1 button so that we can ignore the solid portion and use only fluid volume.on shell portion right click and select  'supress for physics' so that physical portion does not come into when meshing.

Then the geometry will looks like this

4.Then close spaceClaim and the geometry will be saved and the righ click on mesh and select edit mesh.Mesh will be loaded

5. Then click ctrl+F to name the faces of the geometry. select  two inlet portion as inlet-x and inlet-y ,outlet portion as outlet and walls . select their name by clicking 'n' on keyboard after selecting the portion.

Then on the left portion select mesh(outline→project→Model(A3)→mesh) .Then right click on it and Generate mesh.

Mesh will be like this

 

Then below at the 'Details of mesh' portion select elment size at Defaults as .010219meter. This is the size of one cell in the mesh.Then again right click on mesh ,update and Generate mesh.Then at the details portion below it in the quality section choose mesh metric and choose element size.Before that we can check our quality of mesh by cutting the plane by'section plane' command.

 

 

 

6. Then close the mesh portion and at the workbench make two copy of it for case-1-a(epsilon) and case-1-b . After generating mesh of long tee for case-2-a make a copy  of it for case-2-b and another for case-2-b_mesh_independent.

 

 7.Then at the case-1-a(omega) right click on set up and choose portions like below and start.

 Then after starting Fluent we can see this

At the physics portion choose energy equation .Activating energy equation allows the temperature-dependent problem to be solved.In the viscous model select K-omega,SST.

In the material portion fluid type is air

Then in the zones portion select the boundaries as inlet-x,inlet-y,outlet,walls.At inlet-x select edit and choose velocity 3m/s and thermal portion choose temperature as 36c

At inlet-y choose velocity as 12m/s and temperature as 19c.Before that change the unit of temperature from kelvin to celcius at the Domain portion.

Then at the solution-Defination-New-surface report-Area weighted average choose to get report and plot of weighted average and standard deviation of temperature and velocity at the outlet.

After setting up boundaries at the solution portion initialize at 't=0' portion and at the console we can see this

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.

Then take 141 as no of iteration and calculate and the solution will converge and the graphs will be shown.

Graphs are shown below:

RESIDUALS:

 AREA WEIGHTED AVERAGE TEMPERATURE AT OUTLET

 AREA WEIGHTED AVERAGE VELOCITY AT OUTLET:

 STANDARD DEVIATION ON TEMPERATURE OUTLET:

 STANDARD DEVIATION ON VELOCITY OUTLET:

 

 At the result portion we have to select the portion of the boundaries of the geomatry and then open insert-location-plane

 Then in the plane-1 section in color-mode-variable-temperature,Range-user specified,min-19c ,max-36c . In geometry for along length xy plane ,for along cross section YZ portion and apply.

 

 

In the walls portion select white color and Render-transperancy-.816 and apply

 

In 'default legend view 1' Defination-Horizontal,appearence-precision-2 & fixed view

 

TEMPERATURE ALONG THE LENGTH OF PIPE:

 

 

TEMPERATURE ALONG CROSS SECTION:

VELOCITY ALONG THE LENGTH OF PIPE:

VELOCITY ALONG CROSS SECTION:

K-EPSILON MODEL FOR case -1-a :

We have to follow same case as previous like creating geometry,load it , creating mesh metric same as previous.

Then in set up portion all are same but in physics choose k-epsilon and Realizable model.

GRAPHS:

RESIDUAL:

AREA WEIGHTED AVERAGE TEMPERATURE AT OUTLET

 AREA WEIGHTED AVERAGE VELOCITY AT OUTLET:

 STANDARD DEVIATION TEMPERATURE OUTLET:

 STANDARD DEVIATION VELOCITY  OUTLET:

 

 RESULTS:

TEMPERATURE ALONG THE LENGTH OF PIPE:

 

 

TEMPERATURE ALONG THE CROSS SECTION OF PIPE:

 

 

VELOCITY ALONG THE LENGTH OF PIPE:

 

VELOCITY ALONG THE CROSS SECTION OF PIPE:

comparison between two model:

k-omega sst                                                                k-epsilon realizable

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.

case-1-b:

Follow same geometry,mesh and set up but the boundary condition at  inlet-y will be diffferent for velocity as the momentum ratio is 2 so velocity at inlet-y will be 6m/s

GRAPHS:

 

 

RESULTS:

 

 

TEMPERATURE                                                              VELOCITY

 

case-2-a:

following the same process we can have geometry,mesh,setup,Results as mentioned above.

GRAPHS:

 

RESULTS:

TEMPERATURE                                                                         VELOCITY

 

case-2-b

following the same process we can have geometry,mesh,setup,Results as mentioned above,but momentum ratio is 2 in this case.

GRAPHS:

 RESULTS:

TEMPERATURE                                                             VELOCITY

MESH INDEPENDENT STUDY FOR case-2-b

changing the element size in mesh of case-2-b to .0059 study the following

mesh metric:

graphs:

results:

temperature                                                                                 velocity

 Mesh independent test allows mesh refinement without affecting results. After some tests we can be ensured by solution that mesh refinement won’t affect the result. The following graphs are showing the results after mesh refinement on long mixing tee, earlier element size is used as 0.010219 and now it got 0.0059.

 EFFECT OF LENGTH ON RESULTS:

comparison of case-1-b and case-2-b for describing the effect of length on results.

 temperature:

case-2-b                                                                           case-1-b

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.

for case-1-b

 

 for case-2-b:

 

 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.

 EFFECTIVENESS OF  MIXING(BOTH MOMENTUM AND LENGTH DEPENCY TEST):

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 case-1-b and case-2-b we have studied.

Now we can see in both short and long pipe the standard deviation is constantly lower after 80th 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.

case-1-b (momentum ratio=2)                                                                                            

 

 

 

 case-2-b(momentum ratio=4)

 

 

 Also For high momentum ratio highest standard deviation is lower so for High momentum ratio more diffusion occur and more effective mixing occur.

 DATA TABLE:

 Short Mixing Tee:

 

momentum ratio	Element size	no.of element	average velocity at outlet(m/s)	average temperature at outlet(degree c)	number of iteration
4	.010219	4129	6.0135793	27.526442	141
2	.010219	4129	4.4941822	30.236709	184

 

Long  Mixing Tee:

momentum ratio	Element size	no.of element	average velocity at outlet(m/s)	average temperature at outlet(degree c)	number of iteration
4	.013853	4359	6.004734	27.485368	500
2	.013853	4359	4.4929729	30.309233	181

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.

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.