Mixing Efficiency

Objective :

• performe steady-state simulations on the mixing tee geometry with different inlet temperatures.
• Analyze the mixing efficiency for shorter and longer length pipe.

The Simulations are done for different cases,

1. Short mixing tee with K-epsilon model, momentum ratio =2
2. Short mixing tee with K-omega SSTmodel, momentum ratio =2

The above two cases are different in terms of the turbulence model used. For further cases, the suitable model of these two are chosen.

3. Long Mixing tee momentum ratio = 2

4. Long Mixing tee momentum ratio = 4

Where, Momentum ratio = velocity at cold inlet / velocity at hot inlet

Hot inlet velocity = 3m/s for all cases.

CASE 1: Short mixing tee with K-EPSILON model, momentum raio 2.

• In ansys workbench, the geometry is imported and edited using spaceclaim so as to extract the flow volume alone for further processing. The pipe walls were suppressed for physics as it is not needed.

• Then spaceclaim is closed and we move on to meshing. In meshing, first we named all the boundries as,

1. Inlet_x - inlet in x direction

2. inlet_y - inlet in y direction

3. outlet - flow outlet

4. walls - the entire walls of the pipe

• The mesh is then generated and mesh sizes were default values.

No. of cells = 12657

• After closing the mesh, we move onto setup were we load the model in ansys fluent. Here the boundary conditions are updated.

Boundary conditions:

1. Inlet_x velotiy - 3 m/s

2. inlet_y velocity - 6m/s

3. Inlet_x temperature - 36 C

4. Inlet_y temperature - 19 C

5. Outlet pressure - 0 gauge

• In setup domain, we select presure based absolute steady state method for our simulation. In the physics, we include energy as we have to calculate temperature as well. The viscous model is selected as K-epsilon SST.
• Later, the boundary conditions are updated as above with working fluid as air.
• Then, we move on to the solutions domain, where report definitions are created.
• Finally, the flow is initialized and run for calculation.

CASE 2: Short mixing tee with K-OMEGA SST model, momentum raio 2.

• In this case, we change the viscous model for short mixing tee from k-epsilon to k-omega sst model and run the simulation again.

Results:

CASE 1: Short mixing tee with K-EPSILON model, momentum raio 2.

The solution converged after 126 iterations.

• Temperature distribution:

• Velocity Distribution:

• Residual plot

• Area Weighted average of temperature at outlet.

• Standard deviation of outlet temperature:

CASE 2: Short mixing tee with K-OMEGA SST model, momentum raio 2.

The solution converged after about 130 iterations.

• Temperature distribution

• Velocity Distribution:

• Residual plot

• Area Weighted average of temperature at outlet.

• Standard deviation of outlet temperature:

Outlet temperature obtained by both the cases:

• Case 1. k-epsilon model: 27.526 C
• Case 2. k-omega model: 27.531 C

For further cases, we use K-omega SST viscous model for solving.

Case 3: Long Mixing tee, Momentum ratio = 2

The same process as in short mixing tee is followed in this case, the difference being in the turbulance model used.

Boundary conditions:

• Inlet velocity in x direction: 3 m/s
• Inlet velocity in y direction: 6 m/s
• Inlet temperature in x direction: 36 degree
• Inlet temperature in y direction: 19 degree

Geometry of pipe:

Geometry after extractinf flow volume:

Mesh view:

The number of mesh cells = 15483

Case 4: Long Mixing tee, Momentum ratio = 4

Here, the momentum ratio is 4, which means the cold inlet velocity is doubled.

Boundary conditions:

• Inlet velocity in x direction: 3 m/s
• Inlet velocity in y direction: 12 m/s
• Inlet temperature in x direction: 36 degree
• Inlet temperature in y direction: 19 degree
• Outlet pressure - 0 gauge

Results:

Case 3: Long Mixing tee, Momentum ratio = 2

It took about 396 iterations for ansys to converge to the solution in this case.

• Temperature distribution:

• Velocity distribution:

• Residuals plot

• Area Weighted average of temperature at outlet.

• Standard deviation of outlet temperature:

Case 4: Long Mixing tee, Momentum ratio = 4

Ansys converged to a solution after 165 iterations in this case.

• Temperature distribution:

• Velocity Distribution:

• Residuals plot

• Area Weighted average of temperature at outlet.

• Standard deviation of outlet temperature:

Outlet temperature obtained by both the cases:

• Case 3: Outlet temperature = 30.334 C
• Case 4: Outlet temperature = 27.477 C

Comparison of 4 cases:

Cases	Geometry	Momentum ratio	Turbulence model used	No. of Mesh cells	No. of iterations for convergence	Average outlet temperature
1	Short tee	2	K- Epsilon Realizable	12657	126	27.526 C
2	Short tee	2	K- Omega SST	12657	130	27.531 C
3	Long tee	2	K- Omega SST	15483	396	30.334 C
4	Long tee	4	K- Omega SST	15483	165	27.477 C

Conclusions:

• When comparing the results obtained from k-epsilon and k-omega turbulence models, it was observed that k-epsilon took fewer iterations than k omega to converge. But, the temperature distribution at outlet was more even while using the k-omega sst model for solving. Even distribution of temperature at outlet is the main point of conducting this project. Hence, K-Omega SST model was chosen best for further cases.
• In the last two cases, where the momentum ratios were changed, it was observed that with higher momentum ratio, the mixing efficiency has had a great increase. The temperature distribution at the pipe endwas very much even when the momentum ratio was higher. Due to the uneven distribution of temperature in the case with lower momentum ratio, the average outlet temperature was greater than the desired value.
• When comparing the results based on the mixing Tee length, it is observed that with longer mixing tee, the mixing efficiency is greater by a small degree. But when taking into account factors like time and effort taken by the software for convergence, it can be inferred that longer mixing tee is more costly than shorter one and the degree of variance between the two results are considerably small. Hence, a shorter mixing tee will suffice.
• It can be also inferred that as the meshing is more finer and more mesh cells are generated, the finer and more accurate the results will become. But this will also incur more cost.