Mixing efficiency

MIXING EFFICIENCY 

Performing steady-state simulations to compare the mixing effectiveness when the hot inlet temperature is 36C(309.15K) and 19C(292.15)

are entrained from the X-Axis and Y-Axis respectively.

We will also determine what is the effect of changing the momentum ratio.

Also, different turbulence models(K-Epsilon and K-Omega) will also be tried out to determine which suits the best for our case and why.

In the end, we will analyze and determine the effect of length on Mixing efficiency.

Geometry Preparation 

Before starting the simulation we will first define our computational domain.

The concerned geometry is a Mixing-TEE.

We need to extract the Computational from the geometry.

Space claim has a Volume extract option which automatically extracts the volume from the Geometry.

MESHING

Element size - 0.001

Maximum size - 0.002

No. of Elements  - 574320

 

                                                                                                                                                                                  CASE 1

 Short mixing Tee                                                                                                                                                                                  

hot air velocity = 3m/s                                                                       

Momentum ratio = 2

Cold air velocity = 6m/s

Turbulence model = k-epsilon.

Solver Configuration 

Solver =  pressure-based 

Velocity Formulation = Absolute

 Time = Steady-State

Definitions

Area-weighted-average = Outlet Temprature

Standard-Deviation =   Outlet Temprature.

Solution Methods

Pressure-Velocity coupling

Scheme - Coupled

Spatial Discretization 

Gradient - Least squares Cell-Based

Pressure - Second order

Momentum - Second order upwind

Turbulent Kinetic Energy -  First order upwind

Specific dissipation rate - First order upwind

Energy - Second-order Upwind.

Results and Post-Processing

 Average Outlet Temprature - 303.55K

Standard Deviation of Temperature at the Outlet - 1.75K

Residuals

No. of iterations for convergence - 128

CONTOUR PLOT

Temperature Distribution along the plane

 

Velocity Distribution along the Plane

                                                                                                                                                                                    CASE 2

In this case, we are using the K-omega turbulence model with all other configurations kept the same, To determine which model suits the best for our case.

Short mixing tee

hot air velocity = 3 m/s

Momentum ratio = 2

Cold air velocity = 6 m/s

Turbulence model = k-omega.

Keeping the same Solution method as in the previous case, Convergence COULD NOT be achieved even after 4100 iterations.

In order to achieve convergence certain changes were made in the solution methods

Solution Methods

Pressure-Velocity coupling

Scheme - SIMPLE

Spatial Discretization 

Gradient - Least squares Cell-Based

Pressure - STANDARD

Momentum - First order upwind

Turbulent Kinetic Energy -  First order upwind

Specific dissipation rate - First order upwind

Energy - First order Upwind.

 With these settings in the solution-scheme, convergence was achieved in 586 iterations

Number of iterations for convergence - 589

Also, the standard deviation is higher than the k-epsilon model.

 Standard deviation - 1.50K                                                                                           Average temperature - 303.5K

For these reasons, the K-Epsilon model will be preferred over the K-Omega model in further cases.

                                                                                                                                                                                      Case 3

In this case, we are only interested in noticing the change at the outlet if the momentum ratio is changed from 2 to 4

Short mixing tee

hot inlet air velocity = 3 m/s

Momentum ratio = 4

Cold inlet air velocity = 12 m/s

Turbulence model = k-Epsilon.

Solution Methods

Pressure-Velocity coupling

Scheme - Coupled

Spatial Discretization 

Gradient - Least squares Cell-Based

Pressure - Second order

Momentum - Second order upwind

Turbulent Kinetic Energy -  First order upwind

Specific dissipation rate - First order upwind

Energy - Second-order Upwind.

Results and Post-Processing 

Residuals

Number of iterations for convergence - 206

Average Temperature at the outlet - 300.75K                                                                          Standard-Deviation - 1.4K

   

Temperature distribution along the plane.

   

The effect of an increased momentum ratio can be observed by comparing the results of CASE -1 and CASE - 3.

The average outlet temperature is lower when the momentum ratio is higher.

We can also notice "hot-spots" in the periphery of the outlet in CASE-1 which is noticeably missing in CASE-3.

Velocity Distribution along the plane 

   

                                                                                                                                                                          CASE -4 

Long Mixing TEE 

MESHING

Element size - 0.001

Maximum size - 0.002

Number of elements - 762276

Basic Parameters

Hot air velocity - 3

Momentum ratio - 2

Cold air velocity - 6

Turbulence model - K-Epsilon

The solution method and solver configurations are the same as defined in the previous K-Epsilon cases.

Solution Methods

Pressure-Velocity coupling

Scheme - Coupled

Spatial Discretization 

Gradient - Least squares Cell-Based

Pressure - Second order

Momentum - Second order upwind

Turbulent Kinetic Energy -  First order upwind

Specific dissipation rate - First order upwind

Energy - Second-order Upwind.

Results and Post-Processing

Number of iteration for convergence - 138

 Average Temperature at the Outlet - 303.6K                                                                                     Standard Deviation- 1.25K

Velocity distribution along with the Tee 

Temperature Distribution along with the Tee

                                                                                                                                                                       CASE - 5 

Basic Parameters

Hot air velocity - 3

Momentum ratio - 4

Cold air velocity - 12

Turbulence model - K-Epsilon

The solution method and solver configurations are the same as defined in the previous K-Epsilon cases.

Solution Methods

Pressure-Velocity coupling

Scheme - Coupled

Spatial Discretization 

Gradient - Least squares Cell-Based

Pressure - Second order

Momentum - Second order upwind

Turbulent Kinetic Energy -  First order upwind

Specific dissipation rate - First order upwind

Energy - Second-order Upwind.

Results and Post-Processing

Number of iterations for convergence - 209

 Average Temperature at the outlet - 300.75                                                                                                                     Standard deviation - 0.8

Velocity distribution along with the TEE 

Temperature distribution along with the TEE

CONCLUSION

K-Epsilon model was preferred over the K-omega model since it takes way less number of iterations.

Since,

The observed results from the simulations can be tabulated as follows.

We can observe that the effective average temperature doesn't change much with the length of the TEE.

Even though the Standard deviation does reduce by 28% and 43% for momentum ratio's 2 & 4 respectively.

Case Number	Geometry	Turbulence model	Element count	Momentum ratio	Average temperature	Standard - deviation	Iterations
1	Short-TEE	K-Epsilon	574320	2	303.55K	1.75K	128
2	Short- TEE	K-Omega	574320	2	303.50K	1.75K	589
3	Short - TEE	K-Epsilon	574320	4	300.75K	1.40K	206
4	Long-TEE	K-Epsilon	762276	2	303.60K	1.25K	138
5	Long-TEE	K-Epsilon	762276	4	300.75K	0.80K	209