Week 1- Mixing Tee

Aim: 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 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. 

 

Mixing Tee:

Fluid mixing is represented in the form of mixing two coaxial jet flows with good mixing efficiency. It is generally used for applications that require an efficient mix of two fluid streams with different physical & chemical properties combination together to form one stream. For example, this mixing Tee is used in high pressurised application like an Air Conditioner. In the mixing of Fluids, thus viscosity is a prevailing property of the system mixing if it is in lower the value the turbulent mixing can be achieved quickly and mixing operation can be easily done. Moreover, the standard deviation method used to examine the mixing efficiency in tee simulation.

 

1. Case 1 
   • Short mixing tee with a hot inlet velocity of 3m/s.
   • Momentum ratio of 2, 4. 

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.

 

K-epsilon layer:

This model is essentially a high Reynolds number model, meaning the law of the wall must be employed and provide velocity “boundary conditions” away from solid boundaries (what is termed “wall-functions”). Another major drawback is the model's lack of sensitivity to adverse pressure-gradient. It was observed that under such conditions it overestimates the shear stress and by that delays separation.

This model is usually used where flow does not demand to integrate the solution through the viscous sublayer and wall-bounded effects are secondary. For such cases, the first cell away from the wall shall be placed at a y+ of 30-300. In such a scenario, the viscous sublayer and buffer layer (viscosity-affected inner region) are not resolved. Instead, semi-empirical formulas called “wall functions” are used to bridge the viscosity-affected region between the wall and the fully-turbulent region.  

 K-omega model:

This model is essentially a low Reynolds number model. This model takes 'elliptic' near-wall behaviour meaning that it has an inherent nature of being able to “communicate” with the wall and actually has Dirichlet (as in no-slip in this case) boundary conditions. The implication of such behaviour is the straightforward possibility of integrating through the laminar sublayer without additional numerically destabilizing damping functions or two additional transport equations.  

Commonly encountered situations where the flow demands integrating through the viscous sublayer include: heat transfer, calculation of aerodynamic drag, flows with adverse pressure gradients, etc. Integrating through the viscous sublayer would generally impose resolving the mesh to y+<1. The omega equation can be integrated through the viscous sublayer without the need for a two-layer approach.

 

Numerical solution for the outlet mixture:

where `m=rho_(air)*A*V`

`rho_(air)=1.225(Kg)/m^3`

Area of cold inlet=0.0002m^2

Area of hot let=0.0009m^2

For momentum ratio 2

`T_(mixture=30.76^0C`

For momentum ratio 4

`T_(mixture=27.78^0C`

Case 1:Short pipe

(i) For momentum ratio=2 ,element size =2mm and  k-epsilon model

• Geometry

Firstly we have to open the model in the geometry window then we have to extract the volume by specifying the correct edges

 

volume extraction:

 

 

• Mesh

Secondly, we have to give the name for faces and then meshing of the pipe by specifying the elemental size

cut section:

 

• setup

After the meshing, we have to specify the correct  boundary conditions for the specified inlets and outlet

Then we have to select the model

Residual plots:

Standard deviation plot

 Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

Across the pipe:

 

2.Velocity and temperature line plots  across the length of the pipe

 

(ii) For momentum ratio=2 and k-omega model

 

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

 

Area-weighted average of temperature:

Standard deviation plot:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

 

Across the pipe:

2.Velocity and temperature line plots  across the length of the pipe

 

(iii) For momentum ratio=2 and k-epsilon model

 

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

(iii) For momentum ratio=2 and k-epsilon model

 

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

(iii)(ii) For momentum ratio=2 and k-epsilon model

 

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

(iii)(ii) For momentum ratio=2 and k-eplison model

 

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

 

 

(iii) For momentum ratio=4 , elemental size=2mm and  k-eplison model

 

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

 

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

(iv) For momentum ratio=4, elemental size=2mm and k-omega

 residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

(v) For momentum ratio=4, elemental size=3mm and k-epsiloon model(mesh independence test)

 

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

(vi) For momentum ratio=4, elemental size=5mm and k-epsilon model(mesh independence test)

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

Case 2:Long pipe:

(i) For momentum ratio=2 , elemental size=2mm and k-epsilon model

 Geometry:

Mesh:

residual Plot:

Standard deviation plot

 

Area-weighted average of temperature:

Results

1.Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

(ii) For momentum ratio=2 , elemental size=2mm and k-omega model

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results

1.Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

 

(iii) For momentum ratio=4, elemental size=2mm and k-epsilon model

 

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results

1.Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

(iv) For momentum ratio=4 , elemental size=2mm and k-omega model

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results

1.Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

(v) For momentum ratio=2 , elemental size=3mm and k-epsilon model(mesh independence test)

residual Plot:

Standard deviation plot

Area-weighted average of temperature:

Results

1.Velocity and temperature contour plots on the cut planes along and across the pipe.

Along the pipe

 

across the pipe

2.Velocity and temperature line plots  across the length of the pipe

 

 

Comparison table :

type of pipe	momentum ratio	turbulence model	elemental size in mm	cell counts	outlet temperature	standard deviation	number of iterations to converge
short pipe	2	k-epsilon	2	106253	30.31	1.7108	160
short pipe	2	k-omega	2	106253	30.39	1.942	165
short pipe	4	k-epsilon	2	106253	27.56	1.093	180
short pipe	4	k-omega	2	106253	27.5428	1.026	190
long pipe	2	k-epsilon	2	140048	30.409	1.2104	160
long pipe	2	k-omega	2	140048	30.4336	1.08187	160
long pipe	4	k-epsilon	2	140048	27.5018	0.85377	180
long pipe	4	k-omega	2	140048	27.517	0.8433	190

 

 

Mesh independence test for short pipe:

momentum ratio	elemental size in mm	cells counts	outlet temperature	standard deviation
2	2	106253	30.31	1.7108
2	3	39769	30.2873	1.5525
2	5	14247	30.252	1.1421

Conclusion:

The resultant average temperature for both turbulence model Reliazable K -Epsilon & K omega SST looks similar, but for computing K omega  SST takes more time and more number of iterations for convergence.

For both case momentum ratio of 4, the outlet temperature drops significantly this occurs because of very high cold velocity air. So this clearly shows higher the momentum ratio greater the efficiency of the mixing.

We are getting an almost similar result for short tee & long tee for the momentum ratio of 4 from this we can get to know that the length of the pipe doesn't affect the efficiency of the pipe.

When it comes to standard deviation, the long tee gives very lower value compared to the short tee. Indeed, we can increase high inlet cold air velocity for the application so we can get pretty good mixing in nature for a short pipe instead of using the long pipe.

If we increase velocity will get better turbulent mixing. majority of the mixing is because of higher velocity and as we go along the length of the pipe there is additional mixing that occurs because of diffusion.

And there is no much difference in the analytical outlet temperature and numerical outlet temperature 

Overall, the short tee pipe gives a pretty good result, and also it saves material cost. Increasing the pipe length doesn't create any difference in the outlet temperature.