Week 1- Mixing Tee

MIXING TEE

OBJECTIVE:

• For this challenge, we have created two versions of the mixing tee. One of them is longer than the other.
• Our job is to set up steady-state simulations to compare the mixing effectiveness when the 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.

INTRODUCTION:

The function of the mixing Tee is to provide proper mixing of quantities to get the desired result at the outlet.

By controlling the velocity of chilled air we can get the desired temperature in the room.

ANSYS WORKFLOW:

GEOMETRY: Construct a two or three-dimensional representation of the object to be modeled using Ansys SpaceClaim or Ansys DesignModeler.

MESH: Now define how the modeled system should be broken down into finite pieces using Ansys Meshing.

SETUP: The case setup will be done using Ansys fluent.

SOLUTION: In this step the run-time result visualization is done in Ansys fluent.

RESULTS: Post-processing of results will be done here using Ansys CFD-post.

Case 1- SHORT TEE:

GEOMETRY SETUP:

The computational models are uploaded to the Ansys Space Claim as a step file.

• we are interested in performing fluid flow analysis through the geometry, hence we use the volume extraction option to extract the fluid volume from the geometry.
• Then the solid model is suppressed for physics from the fluid model to create mesh at the interested region.

MESH GENERATION:

• Boundary naming is done in Ansys Mesh before Mesh generation.
• The boundary names inlet- x, inlet- y, outlet, and wall are defined using the face selection and create named selection options.

• After generating the mesh, the number of nodes and elements is investigated using the statistics option.
• Then the mesh quality is checked by choosing the mesh metrics option in the quality section.

• The element quality should not be less than 5%.
• In our case minimum mesh quality is 30%, so we can move ahead.

SETUP AND SOLUTION:

CASE 1: Short tee

• Short mixing Tee with a hot inlet velocity of 3m/s
• Momentum ratio of 2,4
• Use the k-epsilon and k-omega SST model.

CASE 1 (i): Short tee (Momentum ratio 2)

• Short mixing Tee with a hot inlet velocity of 3m/s
• The cold inlet velocity is 6m/s for a Momentum ratio of 2.

• The energy equations are included as we are interested in temperature.
• The hybrid scheme is used for initialization and the no. of iterations is setup and then click on calculate option.

RESULTS:

K-EPSILON MODEL:

1) RESIDUAL PLOT:

2) AREA WEIGHTED AVERAGE:

3) STANDARD DEVIATION:

4) CONTOUR PLOT:

i) TEMPERATURE CONTOUR:

ii) VELOCITY CONTOUR:

5) STREAMLINE PLOT:

i) TEMPERATURE STREAMLINE:

ii) VELOCITY STREAMLINE:

K-OMEGA MODEL:

1) RESIDUAL PLOT:

2) AREA WEIGHTED AVERAGE:

3) STANDARD DEVIATION:

4) CONTOUR PLOT:

i) TEMPERATURE CONTOUR:

ii) VELOCITY CONTOUR:

5) STREAMLINE PLOT:

i) TEMPERATURE STREAMLINE:

ii) VELOCITY STREAMLINE:

CASE 1 (ii): Short tee (Momentum ratio 4)

• Short mixing Tee with a hot inlet velocity of 3m/s
• The cold inlet velocity is 12m/s for a Momentum ratio of 4.

• The energy equations are included as we are interested in temperature.
• The hybrid scheme is used for initialization and the no. of iterations is setup and then click on calculate option.

RESULTS:

K-EPSILON MODEL:

1) RESIDUAL PLOT:

2) AREA WEIGHTED AVERAGE:

3) STANDARD DEVIATION:

4) CONTOUR PLOT:

i) TEMPERATURE CONTOUR:

ii) VELOCITY CONTOUR:

5) STREAMLINE PLOT:

i) TEMPERATURE STREAMLINE:

ii) VELOCITY STREAMLINE:

K-OMEGA MODEL:

1) RESIDUAL PLOT:

2) AREA WEIGHTED AVERAGE:

3) STANDARD DEVIATION:

4) CONTOUR PLOT:

i) TEMPERATURE CONTOUR:

ii) VELOCITY CONTOUR:

5) STREAMLINE PLOT:

i) TEMPERATURE STREAMLINE:

ii) VELOCITY STREAMLINE:

ANALYTICAL SOLUTION:

A_h = 901.3138 mm^2 = 901.3138e-6 m^2

A_c = 225.9823 mm^2 = 225.9823e-6 m^2

V_h = 3 m /s , T_h­­ = 36 ⁰C

V_c= 12 m /s, T_c = 19 ⁰C

MOMENTUM RATIO 2:

• Mass of hot fluid (m_h) = rho*a*V_h = 997*(901.3138e-6)*3 = 2.696 kg/s
• Mass of cold fluid (m_c) = rho*a*V_c = 997*(225.9823e-6)*6 = 1.352 kg/s
• Temperature of mixture (T_mixture) = (m_h*T_h + m_c*T_c)/(m_c + m_h) = 30.32⁰C

MOMENTUM RATIO 4:

• Mass of hot fluid (m_h) = rho*a*V_h = 997 * (901.3138e-6) * 3 = 2.69 kg/s
• Mass of cold fluid (m_c) = rho*a*V_c = 997 * (225.9823e-6) * 12 = 2.704 kg/s
• Temperature of mixture (T_mixture) = (m_h*T_h + m_c*T_c)/(m_c + m_h) = 27.49⁰C

CONCLUSION (case- 1):

AVERAGE OUTLET TEMPERATURE:

• On comparing both models with the analytical solutions we got nearly the same results.

ITERATIONS TO CONVERGE:

• No. of iterations taken to converge is less for the Realisable K-epsilon model than the K-omega SST model.

STANDARD DEVIATION:

• The standard deviation of the k-epsilon model is less than the k-omega model which shows better mixing efficiency in the k-epsilon model.

So based on the above observations the K-epsilon turbulence model is predicting the results accurately in less no. of iterations. So we can use the realisable k-epsilon model for case 2 (Long Tee).

Case 2- LONG TEE:

GEOMETRY SETUP:

The computational models are uploaded to the Ansys Space Claim as a step file.

• we are interested in performing fluid flow analysis through the geometry, hence we use the volume extraction option to extract the fluid volume from the geometry.
• Then the solid model is suppressed for physics from the fluid model to create mesh at the interested region.

MESH GENERATION:

• Boundary naming is done in Ansys Mesh before Mesh generation.
• The boundary names inlet- x, inlet- y, outlet, and wall are defined using the face selection and create named selection options.

• After generating the mesh, the number of nodes and elements is investigated using the statistics option.
• Then the mesh quality is checked by choosing the mesh metrics option in the quality section.

• The element quality should not be less than 5%.
• In our case minimum mesh quality is 30%, so we can move ahead.

SETUP AND SOLUTION:

CASE 2: Long tee

• Short mixing Tee with a hot inlet velocity of 3m/s
• Momentum ratio of 2,4
• Use the k-epsilon model.

CASE 2 (i): Long tee (Momentum ratio 2)

• Short mixing Tee with a hot inlet velocity of 3m/s
• The cold inlet velocity is 6m/s for a Momentum ratio of 2.

• The energy equations are included as we are interested in temperature.
• The hybrid scheme is used for initialization and the no. of iterations is setup and then click on calculate option.

RESULTS:

K-EPSILON MODEL:

1) RESIDUAL PLOT:

2) AREA WEIGHTED AVERAGE:

3) STANDARD DEVIATION:

4) CONTOUR PLOT:

i) TEMPERATURE CONTOUR:

ii) VELOCITY CONTOUR:

5) STREAMLINE PLOT:

i) TEMPERATURE STREAMLINE:

ii) VELOCITY STREAMLINE:

CASE 2 (ii): Long tee (Momentum ratio 4)

• Short mixing Tee with a hot inlet velocity of 3m/s
• The cold inlet velocity is 12m/s for a Momentum ratio of 4.

• The energy equations are included as we are interested in temperature.
• The hybrid scheme is used for initialization and the no. of iterations is setup and then click on calculate option.

RESULTS:

K-EPSILON MODEL:

1) RESIDUAL PLOT:

2) AREA WEIGHTED AVERAGE:

3) STANDARD DEVIATION:

4) CONTOUR PLOT:

i) TEMPERATURE CONTOUR:

ii) VELOCITY CONTOUR:

5) STREAMLINE PLOT:

i) TEMPERATURE STREAMLINE:

ii) VELOCITY STREAMLINE:

ANALYTICAL SOLUTION:

A_h = 901.3138 mm^2 = 901.3138e-6 m^2

A_c = 225.9823 mm^2 = 225.9823e-6 m^2

V_h = 3 m /s , T_h­­ = 36 ⁰C

V_c= 12 m /s, T_c = 19 ⁰C

MOMENTUM RATIO 2:

• Mass of hot fluid (m_h) = rho*a*V_h = 997*(901.3138e-6)*3 = 2.696 kg/s
• Mass of cold fluid (m_c) = rho*a*V_c = 997*(225.9823e-6)*6 = 1.352 kg/s
• Temperature of mixture (T_mixture) = (m_h*T_h + m_c*T_c)/(m_c + m_h) = 30.32⁰C

MOMENTUM RATIO 4:

• Mass of hot fluid (m_h) = rho*a*V_h = 997 * (901.3138e-6) * 3 = 2.69 kg/s
• Mass of cold fluid (m_c) = rho*a*V_c = 997 * (225.9823e-6) * 12 = 2.704 kg/s
• Temperature of mixture (T_mixture) = (m_h*T_h + m_c*T_c)/(m_c + m_h) = 27.49⁰C

CONCLUSION (case- 2):

AVERAGE OUTLET TEMPERATURE:

• On comparing both models with the analytical solutions we got nearly the same results.

COMPARISON OF BOTH LONG AND SHORT TEE:

K- Epsilon Realizable Model:

CONCLUSION (cases 1 and 2):

AVERAGE OUTLET TEMPERATURE:

• Irrespective of the length of the mixing Tee, the average outlet temperature in both cases is almost the same.

MOMENTUM RATIO:

• For momentum ratio 2, the average outlet fluid temperature is 30.32⁰C whereas for momentum ratio 4 the average outlet fluid temperature is 27.49⁰C.
• From these, we can say that there will be a drop in temperature if the momentum ratio increases.
• This is because, as the momentum ratio increases, the velocity of cold inlet fluid increases, and due to the high relative velocity between the fluid, it experiences higher turbulence, and therefore the outlet fluid temperature decreases.

NO. OF ITERATIONS:

• The number of iterations to converge seems to be less for a higher momentum ratio.

LENGTH OF TEE:

• Increasing the length of the pipe doesn’t serve the purpose of effective mixing.
• Thus, Short pipes are more efficient.

GRID INDEPENDENCY TEST:

• The Short Tee (MR = 2) solved using K- Epsilon model is selected for the grid dependence test.

MESH GENERATION:

5mm:

4mm:

3mm:

MESH METRICS:

5mm:

4mm:

3mm:

RESIDUAL PLOT:

5mm:

4mm:

3mm:

AREA WEIGHTED AVERAGE OF TEMPERATURE:

5mm:

4mm:

3mm:

STANDARD DEVIATION OF TEMPERATURE:

5mm:

4mm:

3mm:

OBSERVATION:

CONCLUSION:

• 3 mm has the finest mesh, which means that should produce the most accurate results.
• But as the number of elements increases, the computational time also increases. So computational time is high for a 3mm mesh.
• From the above tables, we can say that our mesh is independent which means there are no large changes in outlet temperature by increasing the number of elements.
• Thus 5mm or 4mm element size is preferred.