Week 1- Mixing Tee

Aim : Perform steady-state simulations to compare the mixing effectiveness in a mixing Tee of different lengths and using different models for the solution.

 

Objective:  

1 . compare mixing effectiveness for k-epsilon and k-omega SST models

2. compare mixing effectiveness for different lengths of mixing Tee 

3. Compare mixing effectiveness for different momentum ratios

 

Given:

Hot inlet temperature=36⁰C

Cold inlet = 19⁰C. 

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

Theory:

Mixing tees—in which two fluid streams with different physical and/or chemical properties mix—are widely used in the petrochemical industry. mixing tees are used to properly mix two fluids at different temperatures moving with different momentum to get the desired temperature at the output.

It has many applications in air conditioning and refrigiration systems, nuclear reactor cooling , in powerplants,petrochemical industries and many more.

When hot and cold air meet at the mixing point, the flow becomes turbulent becuaes of change in momentum and temperature of two fluids, this turbulance ensures proper mixing of the fluids so that we get desired temperature at the output, turbulence also ensures uniform mixing along the pipe.

To solve for this turbulance we use RANS based equations i.e Reynolds avergage navier-stokes equations, in addition to this to know know the different variables we solve additional equations. To solve these equations ANSYS fluent has differnt turbulent models, we will use following two models:

• k-epsilon realizable model with standard wall conditions
• k-omega SST 

Procedure: 

Geometry:

We open geometry and import short mexing Tee solidwork model. After importing we select "Prepare" option from the top toolbar and inside it select "volume extract" then select "Edge selection" and select hot-inlet,cold-inlet and outlet edges and apply. We then supress solid model for physics and now we have successfully extracted the volume for flow simulation.

 

Meshing:

First we name the faces through which flow interacts i.e hot-inlet,cold-inlet,walls and outlet, this is done by selecting the section to be named and press "N"

We now select mesh option and leave the options at default settings and right click on mesh option and select genrate mesh option.

Setup: 

1. Perform mesh check.

console shows meshing done, Therefore our meshing is good.

2. In general select following options.

3. Inside physics tick energy option and inside viscous option select the model to be used for calculation

 

4.Inside materials select medium as air

5. Now in zones select boundaries and set the value of velocity and temperature at the inlet aand outlet

Hot Inlet

 

Cold inlet

 

Outlet:

4. We now create reports for temperature deviation and average temperature.

 

Area-Weighted-Average

 

Temperature deviation

6.Select appropriate model from various viscous models available

7. Initialize and run caluclations for 300 iterations.

 

1. K-epsilon model: 

Results:

Area-averaged-temperature:

Standard-deviation:

 

Residuals:

Values of standard deviation and area weighted average temperature:

 

 2.K-Omega SST model

Results:

Standard deviation:

Area Area-Area-weighted average:

Residuals:

Values of standard deviation and area weighted average temperature:

 

Conclusion:

1.k-omega model takes more iterations to converge than k-epsilon model.

2.From area weighted average value k-epsilon shows less deviation than k-omega model as value of area weighted avergae temperature of k-epsilon model is less than k-omega sst model.

Therefore, We select k-epsilon as our viscous model

 

grid independence test:Since we have selected k-epsilon as our model we will do grid dependence test for it cahnging the element size and keeping all parameters same.

1. Element size = 0.005:

Mesh detail:

Quality:

Results:
Area weighted avergae temperature:

Standard deviation:

Residuals:

contour plot of temperature along the pipe:

2.Element size = 0.0025:

Mesh detail:

Quality:

Results:

Area weighted avergae temperature:

Standard deviation:

Residuals:

contour plot of temperature along the pipe:

3.Element size = 0.002:

Mesh detail:

 

Quality:

 

Results:

Area weighted avergae temperature:

 

Standard deviation:

 

Residuals:

 

contour plot of temperature along the pipe:

Discussion:

Based on the mesh dependency test run on epsilon model we can see from results that as the element size decreases the time taken to complete the simulation increases exponentially since the number of elements in the mesh increases since during simulation all required equations are solved at each and every element time required to complete simulation too increases, but if we see the contour plot of temperature along the length of the pipe the more finer the mesh the temperature distribution is lot smoother, also the residuals converge in a stable way for finer mesh.

For all further cases we select k-epsilon model and with mesh elemnt size of 0.002 

 

Case 1 :

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

mesh detail:

From mesh detail, number of elements = 106544

Subcase 1:

Momentum ratio = 2

Hot-inlet velocity = 3 m/s

Cold-inlet velocity = 6m/s

Hot-inlet temperature = `35^o c`

Cold-inlet temperature = `19^o c`

 

Solution:

Computed value of standard deviation and area weighted average temperature:

plots:

Area-weighted average temperature:

Standard deviation of temperature:

Residuals:

Post processing:

Contour plots of Temperature and velcoity along the length of the pipe:

Temperature plot:

 Velocity plot:

Contour plots of Temperature and velocity across the pipe:

Temperature plot:

 Velocity plot:

Variation of Temperature and velocity along the length of pipe:

Variation of Temperature and velocity across the length of pipe:

Subcase 2:

Momentum ratio = 4

Hot-inlet velocity = 3 m/s

Cold-inlet velocity = 12m/s

Hot-inlet temperature = `35^o c`

Cold-inlet temperature = `19^o c`

Steps:

 

Solution:

Computed value of standard deviation and area weighted average temperature:

 

plots:

Area-weighted average temperature:

Standard deviation of temperature:

Residuals:

Post processing:

Contour plots of Temperature and velcoity along the length of the pipe:

 Temperature plot:

 Velocity plot:

Contour plots of Temperature and velocity across the pipe:

Temperature plot:

  Velocity plot:

Variation of Temperature and velocity along the length of pipe:

Variation of Temperature and velocity across the length of pipe:

Case 2 :

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

mesh detail:

From mesh detail, number of elements = 140811

Subcase 1:

Momentum ratio = 2

Hot-inlet velocity = 3 m/s

Cold-inlet velocity = 6m/s

Hot-inlet temperature = `35^o c`

Cold-inlet temperature = `19^o c`

Solution:

Computed value of standard deviation and area weighted average temperature:

 

plots:

Area-weighted average temperature:

 

Standard deviation of temperature:

Residuals:

Post processing:

Contour plots of Temperature and velcoity along the length of the pipe:

 Velocity plot:

Contour plots of Temperature and velocity across the pipe:

 Temperature plot:

  Velocity plot:

Variation of Temperature and velocity along the length of pipe:

Variation of Temperature and velocity across the length of pipe:

Subcase 2:

Momentum ratio = 4

Hot-inlet velocity = 3 m/s

Cold-inlet velocity = 12m/s

Hot-inlet temperature = `35^o c`

Cold-inlet temperature = `19^o c`

Steps:

Solution:

Computed value of standard deviation and area weighted average temperature:

 

plots:

Area-weighted average temperature:

 

Standard deviation of temperature:

 

Residuals:

Post processing:

Contour plots of Temperature and velcoity along the length of the pipe:

 Temperature plot:

Velocity plot:

Contour plots of Temperature and velocity across the pipe:

Temperature plot:

Velocity plot:

Variation of Temperature and velocity along the length of pipe:

Variation of Temperature and velocity across the length of pipe:

 

Table comparing all the cases:

Discussion:

Effect of length on mixing:

Standard deviation is more in case of short mixing tee compared to long mixing tee because the length is not long enough to ensure proper mixing of fluids before reaching the outlet, there is not enough sapce for proper mixing of fluids.

Effect of momentum ratio on mixing:

Standard deviation is less in higher momentum ratio compared to low momentum ratio because as the momentum ratio increases the chilled air arrives at much higher velocity comapred to hot air and this increases the turbulence, by theory we know that turbulence helps in mixing of fluids, but in short mixing tee even tho the momentum ratio is high the standard deviation is high because the length is not enough to ensure proper mixing due to high turbulance before the fluids reach the outlet, therefore high momentum ratio ensures more proper mixing

Conclusion:

From the simulation and result we can arrive at the conclusion that the long mixing tee with high momentum ratio is optimum design to ensure proper mixing of the fluids.