Week 1- Mixing Tee
Mixing Tee
Objective
To simulate the flow of air through mixing tee and understand the effect of length of pipe and momentum ratio of velocity for mixing of air by using two different types of pipe i.e. short pipe and long pipe.
About
In industrial process engineering, mixing is a unit operation that involves the manipulation of a heterogeneous physical system with the intent to make it more homogeneous. Mixing is performed to allow heat and/or mass transfer to occur between one or more streams, components, or phases. Modern industrial processing almost always involves some form of mixing. A mixing tee is a type of mixing mechanism. Mixing Tees utilizes a specifically engineered internal geometry to efficiently mix two fluid streams into one combined stream. Mixing tees are widely used in the petrochemical, HVAC industry, etc. in which two fluid streams with different physical and/or chemical properties mix together.
GEOMETRY:
SHORT-LENGTH MIXING TEE
LONG-LENGTH MIXING TEE
Hot air flowing in the main pipe is mixed with cold air flowing through a tee. The standard deviation of temperature is computed to quantify the degree of mixing. The velocity and temperature fields are also computed. The effects of the mesh size and turbulence model on results were examined.
For this, we have created two versions of the mixing tee. One of them is longer than the other.
It is set up as steady-state simulations to compare the mixing effectiveness when the hot inlet temperature is 360C & the Cold inlet is 190C.
Problem Setup
Understand k-epsilon and k-omega SST by considering case-1
Case-1
Short mixing tee
Simulation-1
hot Inlet velocity - 3m/s
Momentum ratio - 2
Simulation-2
hot Inlet velocity - 3m/s
Momentum ratio - 4
Case-2
Long mixing tee
Simulation-3
hot Inlet velocity - 3m/s
Momentum ratio - 2
Simulation-4
hot Inlet velocity - 3m/s
Momentum ratio - 4
K-epsilon Turbulence Model :
- This model is used in CFD to simulate mena flow characteristics for turbulent flow conditions.
- It is known as the simplest turbulence model for which only initial and boundary conditions need to be supplied.
- Realizable k-epsilon model exhibits superior performance for flows involving rotation and boundary layers under strong adverse pressure gradients.
- The k-epsilon model is ideal for predicting flow behavior in regions away from the wall.
K-omega SST Turbulence Model :
- SST stands for Shear Stress Transport.
- This model can be used for boundary layer problems, where the formulation works from the inner part through the viscous sub-layer until the walls. Hence this model can be used for low Reynolds flow applications without additional damping functions.
- The k-omega SST model accounts for its good behavior in adverse pressure gradients and separating flow. It produces large turbulence levels in regions with large normal strain. This effect is less with a normal k-epsilon model.
- The SST models exhibit less sensitivity to free stream conditions (flow outside the boundary layer)than many other turbulence models.
Case-1
SHORT TEE:
GEOMETRY SETUP:
The computational models are uploaded to the Ansys Space Claim as a step file.
In this project, we are interested in performing fluid flow analysis through the geometry, hence we used 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:
The boundary names inlet_x, inlet_y, outlet, and wall are defined using the named selection option.
After generating the mesh, the number of nodes and elements are 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.
Simulation-1:
- Short mixing Tee with a hot inlet velocity of 3m/s
- Momentum ratio of 2
|
SETUPS |
SHORT TEE (MR=2 AND HOT INLET VELOCITY = 3m/s)
|
|
|
K-EPSILON |
K-OMEGA |
|
|
SOLVER TYPE |
Pressure based |
Pressure based |
|
VELOCITY FORMULATION |
Absolute |
Absolute |
|
TIME |
Steady |
Steady |
|
VISCOUS MODEL |
Realizable K-epsilon with standard wall function |
K-omega SST model |
|
MATERIAL |
Air |
Air |
|
CELL ZONES |
Fluid type: air |
Fluid type: air |
|
BOUNDARIES |
· Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature - 360c · Inlet_y (velocity inlet) Velocity magnitude 6m/s Temperature – 190c · Outlet (pressure outlet) Gauge pressure – 0 pa · Walls – stationary walls |
· Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature - 360c · Inlet_y (velocity inlet) Velocity magnitude 6m/s Temperature – 190c · Outlet (pressure outlet) Gauge pressure – 0 pa · Walls – stationary walls |
The hybrid scheme is used for initialization and the no. of iterations is set up and then click on calculate option.
RESULTS:
K-EPSILON MODEL:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE:
STANDARD DEVIATION:
CONTOUR PLOT:
TEMPERATURE CONTOUR:
VELOCITY CONTOUR:
STREAMLINE PLOT:
TEMPERATURE:
VELOCITY:
K-OMEGA MODEL:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE:
STANDARD DEVIATION:
CONTOUR PLOT:
TEMPERATURE CONTOUR:
VELOCITY CONTOUR:
STREAMLINE PLOT:
TEMPERATURE:
VELOCITY:
SUMMARY:
|
|
SHORT TEE (MR = 2) |
|
|
K-EPSILON |
K-OMEGA |
|
|
AVERAGE OUTLET TEMPERATURE [K] |
303.413 |
303.458 |
|
STANDARD DEVIATION |
1.5 |
1.6 |
|
NO OF ITERATIONS |
150 |
170 |
Simulation-2:
- Short mixing Tee with a hot inlet velocity of 3m/s
- Momentum ratio of 4
|
SETUPS |
SHORT TEE (MR=4 AND HOT INLET VELOCITY = 3m/s)
|
|
|
K-EPSILON |
K-OMEGA |
|
|
SOLVER TYPE |
Pressure based |
Pressure based |
|
VELOCITY FORMULATION |
Absolute |
Absolute |
|
TIME |
Steady |
Steady |
|
VISCOUS MODEL |
Realizable K-epsilon with standard wall function |
K-omega SST model |
|
MATERIAL |
Air |
Air |
|
CELL ZONES |
Fluid type : air |
Fluid type : air |
|
BOUNDARIES |
· Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature - 360c · Inlet_y (velocity inlet) Velocity magnitude 12m/s Temperature – 190c · Outlet (pressure outlet) Gauge pressure – 0 pa · Walls – stationary walls |
· Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature - 360c · Inlet_y (velocity inlet) Velocity magnitude 12m/s Temperature – 190c · Outlet (pressure outlet) Gauge pressure – 0 pa · Walls – stationary walls |
The hybrid scheme is used for initialization and the no. of iterations is set up and then click on calculate option.
RESULTS:
K-EPSILON MODEL:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE:
STANDARD DEVIATION:
CONTOUR PLOT:
TEMPERATURE CONTOUR:
VELOCITY CONTOUR:
STREAMLINE PLOT:
TEMPERATURE:
VELOCITY:
K-OMEGA MODEL:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE:
STANDARD DEVIATION:
CONTOUR PLOT:
TEMPERATURE CONTOUR:
VELOCITY CONTOUR:
STREAMLINE PLOT:
TEMPERATURE:
VELOCITY:
SUMMARY:
|
|
SHORT TEE (MR = 4) |
|
|
K-EPSILON |
K-OMEGA |
|
|
AVERAGE OUTLET TEMPERATURE [K] |
300.396 |
300.38 |
|
STANDARD DEVIATION |
1.1 |
1.2 |
|
NO OF ITERATIONS |
130 |
160 |
ANALYTICAL SOLUTION:
Formula:
MOMENTUM RATIO 2:
- Mass of hot fluid (mh) = rho*a*Vh = 997*0.0009*3 = 2.69 kg/s
- Mass of cold fluid (mc) = rho*a*Vc = 997*0.0009*6 = 1.35 kg/s
- Temperature of mixture (Tmixture) = (mh*Th + mc*Tc)/(mc + mh) = 30.3190c = 303.319k
MOMENTUM RATIO 4:
- Mass of hot fluid (mh) = rho*a*Vh = 997*0.0009*3 = 2.69 kg/s
- Mass of cold fluid (mc) = rho*a*Vc = 997*0.0009*12 = 2.3928 kg/s
- Temperature of mixture (Tmixture) = (mh*Th + mc*Tc)/(mc + mh) = 27.990c = 300.99k
CONCLUSION:
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 realizable k-epsilon model for case 2
CASE-2
LONG TEE:
GEOMETRY SETUP:
The computational models are uploaded to the Ansys Space Claim as a step file.
In this project, we are interested in performing fluid flow analysis through the geometry, hence we used 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:
The boundary names inlet_x, inlet_y, outlet and wall are defined using the named selection option.
After generating the mesh, the number of nodes and elements are investigated using the statistics option. Then the mesh quality is checked by choosing the mesh matrices 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.
Simulation-3:
- Long mixing tee with a hot inlet velocity of 3m/s.
- Momentum ratio of 2.
|
SETUPS |
LONG TEE (MR=2 AND HOT INLET VELOCITY 3m/s) |
|
K-EPSILON |
|
|
SOLVER TYPE |
Pressure based |
|
VELOCITY FORMULATION |
Absolute |
|
TIME |
Steady |
|
VISCOUS MODEL |
Realizable K-epsilon with standard wall function |
|
MATERIAL |
Air |
|
CELL ZONES |
Fluid type : air |
|
BOUNDARIES |
· Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature - 360c · Inlet_y (velocity inlet) Velocity magnitude 6m/s Temperature – 190c · Outlet (pressure outlet) Gauge pressure – 0 pa · Walls – stationary walls |
The hybrid scheme is used for initialization and the no. of iterations is set up and then click on calculate option.
RESULTS:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE:
STANDARD DEVIATION:
CONTOUR PLOT:
TEMPERATURE CONTOUR:
VELOCITY CONTOUR:
STREAMLINE PLOT:
TEMPERATURE:
VELOCITY:
Simulation-4:
- Long mixing tee with a hot inlet velocity of 3m/s.
- Momentum ratio of 4.
|
SETUPS |
LONG TEE (MR=4 AND HOT INLET VELOCITY 3m/s) |
|
K-EPSILON |
|
|
SOLVER TYPE |
Pressure based |
|
VELOCITY FORMULATION |
Absolute |
|
TIME |
Steady |
|
VISCOUS MODEL |
Realizable K-epsilon with standard wall function |
|
MATERIAL |
Air |
|
CELL ZONES |
Fluid type: air |
|
BOUNDARIES |
· Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature - 360c · Inlet_y (velocity inlet) Velocity magnitude 12m/s Temperature – 190c · Outlet (pressure outlet) Gauge pressure – 0 pa · Walls – stationary walls |
The hybrid scheme is used for initialization and the no. of iterations is set up and then click on calculate option.
RESULTS:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE:
STANDARD DEVIATION:
CONTOUR PLOT:
TEMPERATURE CONTOUR:
VELOCITY CONTOUR:
STREAMLINE PLOT:
TEMPERATURE:
VELOCITY:
SUMMARY:
|
|
LONG TEE (MR = 2) |
LONG TEE (MR = 4) |
|
AVERAGE OUTLET TEMPERATURE [K] |
303.367 |
300.449 |
|
STANDARD DEVIATION |
1.2 |
0.8 |
|
NO OF ITERATIONS |
180 |
130 |
COMPARISON OF BOTH LONG AND SHORT TEE:
|
K-EPSILON REALIZABLE MODEL |
|||||
|
GEOMETRY |
MOMENTUM RATIO |
CELL COUNT |
AVERAGE OUTLET TEMPERATURE [K] |
NO. OF ITERATIONS |
STANDARD DEVIATION |
|
SHORT TEE |
2 |
12583 |
303.413 |
150 |
1.5 |
|
SHORT TEE |
4 |
12583 |
300.396 |
130 |
1.1 |
|
LONG TEE |
2 |
15368 |
303.367 |
180 |
1.2 |
|
LONG TEE |
4 |
15368 |
300.449 |
130 |
0.8 |
OVERALL DISCUSSION:
AVERAGE OUTLET TEMPERATURE:
Irrespective of the length of the mixing Tee, the average outlet temperature in both cases is quite the same.
MOMENTUM RATIO:
- 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.
- For momentum ratio 2, the average outlet fluid temperature is 303k whereas for momentum ratio 4 the average outlet fluid temperature is 300k. From these, we can say that there will be a drop in temperature if the momentum ratio increases.
- In order to obtain better mixing, the velocity of cold air is important. By increasing the cold fluid velocity the outlet temperature gets reduced.
NO. OF ITERATIONS:
The longer Tee takes more time to converge than the short Tee.
CONCLUSION:
- The higher the momentum ratio, the higher will be the mixing efficiency of the Tee joint.
- Increasing the length of the pipe doesn’t serve the purpose of mixing efficiently. So, it is efficient to use the short pipe.
GRID INDEPENDENCY TEST:
The short Tee model is selected for the grid independence test.
5mm:
MESH GENERATION:
RESULTS:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE OF TEMPERATURE:
STANDARD DEVIATION OF TEMPERATURE:
4mm:
MESH GENERATION:
RESULTS:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE OF TEMPERATURE:
STANDARD DEVIATION OF TEMPERATURE:
3mm:
MESH GENERATION:
RESULTS:
RESIDUAL PLOT:
AREA WEIGHTED AVERAGE OF TEMPERATURE:
STANDARD DEVIATION OF TEMPERATURE:
SUMMARY:
|
MESH SIZE |
NO. OF ELEMENTS |
NO. OF NODES |
AVERAGE OUTLET TEMPERATURE |
NO. OF ITERATIONS |
|
5mm |
16143 |
3460 |
303.251 |
250 |
|
4mm |
23007 |
4925 |
303.246 |
175 |
|
3mm |
39921 |
8369 |
303.292 |
210 |
CONCLUSION:
- The mesh size of 3mm gives the best-predicted results than the other two mesh size
- Decreasing the mesh size, the average outlet temperature starts approaching towards the analytical results.