Week 1- Mixing Tee

In this project, a simulation of a mixing tee will be conducted in ANSYS using the FLUENT solver.

A mixing tee is used for mixing two fluids with different velocities or temperatures or types, etc. It is used to ensure both fluids are properly mixed before exiting the tee.

In this project, the mixing tee contains of 2 perpendicular inlets converging into a single outlet. The fluids used are identical in all aspects except their temperatures vary at their respective inlets. One inlet has hot fluid flowing through it, and the other inlet has cold fluid flowing through it. The expectation is that the cold fluid will cool the hot fluid and provide outlet fluid at a much lower temperature. This setup is used in Fluid Conditioners.

The hot fluid inlet temperature is 36C and the cold fluid inlet temperature is 19C. The inlet velocity for the hot fluid inlet is 3 m/s.

The simulation will be divided into two cases, which are further divided into two sub-cases for each case.

Case 1 – Short tee

A short tee will be used, the intent is to gauge the effect of length in the mixing of the fluids.

Inlet hot fluid velocity: 3 m/s

Inlet cold fluid velocity: 6 m/s (subcase 1)

Inlet cold fluid velocity: 12 m/s (subcase 2)

The length of the tee in this case is about 0.2m and the cold fluid inlet is located at a distance of 0.03m from the hot fluid inlet.

The analysis is carried out in ANSYS workbench. The “Fluid Flow (Fluent)” module is selected and the geometry is imported in spaceclaim, this is the imported geometry seen in spaceclaim:

Since the analysis in this project is focussed upon fluid behaviour, the volume needs to be extracted from this geometry. For this, go to prepare -> volume extract -> edges and select the inlets and outlet edges to extract the volume. Supress this geometry and make sure volume is not supressed.

The model is meshed using the ANSYS mesher for an element size of 0.005m (5mm), the size was chosen accordingly to not exceed the cell count limitations for the ANSYS student version license.

A mesh metric evaluation was conducted to ensure proper quality for all cells, as seen most elements are in the 0.7 – 1 range, indicating they are of good quality.

An initial test simulation was conducted for subcase 1, with two turbulence models: k-omega-SST and k-epsilon. The results obtained were compared and k-omega-SST was deduced to be the superior model for this type of simulation due to the following reasons:

• Fewer iterations used (~270 for SST vs ~300 for k-epsilon)
• K-episilon is poor for near wall simulations and data
• K-omega SST is superior for wake flows (a wake occurs in this simulation near the nexus of hot and cold fluid)

Source: 3.7 RANS EQUATIONS AND TURBULENCE MODELS, CHAPTER 3 TURBULENCE AND ITS MODELLING, An Introduction to Computational Fluid Dynamics by H K Versteeg and W Malalasekera.

Thereafter, the k-omega SST will be used for all simulations in this project.

Subcase 1

Cold fluid inlet velocity: 6m/s

Hot fluid inlet velocity: 3m/s

Momentum Ratio: 2 (=6/3)

A simulation for these boundary conditions was conducted in ANSYS Fluent, the simulation took 265 iterations, and this is the residuals plot:

This is the area-averaged temperature at the outlet for every iteration:

As we can notice, the temperature is converged quite well.

To see the variation of temperature across the outlet face, this is the plot of the standard deviation of temperature across the outlet for every iteration:

The simulation is done, now to the post processing. Close FLUENT and open CFD-post, to generate the required plots.

1. Velocity and Temperature Contours

These contours show the velocity and temperature at a cut plane

 

 

2. Temperature and Velocity along axis

A line was created in CFD-post along the axis of the pipe, and a chart was created.

 

 

3. Temperature and Velocity across outlet

A line was created in CFD-post along the center of the outlet, and a chart was created.

 

Subcase 2

Cold fluid inlet velocity: 12m/s

Hot fluid inlet velocity: 3m/s

Momentum Ratio:  4 (=12/3)

A simulation for these boundary conditions was conducted in ANSYS Fluent, the simulation took 326 iterations, and this is the residuals plot:

This is the area-averaged temperature at the outlet for every iteration:

As we can notice, the temperature is converged quite well.

To see the variation of temperature across the outlet face, this is the plot of the standard deviation of temperature across the outlet for every iteration:

The simulation is done, now to the post processing. Close FLUENT and open CFD-post, to generate the required plots.

1. Velocity and Temperature Contours

These contours show the velocity and temperature at a cut plane

 

2. Temperature and Velocity along axis

A line was created in CFD-post along the axis of the pipe, and a chart was created.

 

 

3. Temperature and Velocity across outlet

A line was created in CFD-post along the center of the outlet, and a chart was created.

 

Case 2 – Long tee

A longer tee will be used, slightly longer than the one used in Case 1.

Inlet hot fluid velocity: 3 m/s

Inlet cold fluid velocity: 6 m/s (subcase 1)

Inlet cold fluid velocity: 12 m/s (subcase 2)

The length of the tee in this case is about 0.2m and the cold fluid inlet is located at a distance of 0.02m from the hot fluid inlet.

The analysis is carried out in ANSYS workbench. The “Fluid Flow (Fluent)” module is selected and the geometry is imported in spaceclaim, this is the imported geometry seen in spaceclaim:

Since the analysis in this project is focussed upon fluid behaviour, the volume needs to be extracted from this geometry. For this, go to prepare -> volume extract -> edges and select the inlets and outlet edges to extract the volume. Supress this geometry and make sure volume is not supressed.

The model is meshed using the ANSYS mesher for an element size of 0.005m (5mm), the size was chosen accordingly to not exceed the cell count limitations for the ANSYS student version license.

A mesh metric evaluation was conducted to ensure proper quality for all cells, as seen most elements are in the 0.7 – 1 range, indicating they are of good quality.

Subcase 1

Cold fluid inlet velocity: 6m/s

Hot fluid inlet velocity: 3m/s

Momentum Ratio: 2 (=6/3)

A simulation for these boundary conditions was conducted in ANSYS Fluent, and this is the residuals plot:

The simulation never converged, and the residuals entered some sort of a periodicity. Since the residuals didn’t seem to vary that much, there was no further reason to continue until the residual conditions (energy <10 ^3) are met.

This is the area-averaged temperature at the outlet for every iteration:

As we can notice, the temperature is converged quite well.

To see the variation of temperature across the outlet face, this is the plot of the standard deviation of temperature across the outlet for every iteration:

The simulation is done, now to the post processing. Close FLUENT and open CFD-post, to generate the required plots.

1. Velocity and Temperature Contours

These contours show the velocity and temperature at a cut plane

 

2. Temperature and Velocity along axis

A line was created in CFD-post along the axis of the pipe, and a chart was created.

3. Temperature and Velocity across outlet

A line was created in CFD-post along the center of the outlet, and a chart was created.

Subcase 2

Cold fluid inlet velocity: 12m/s

Hot fluid inlet velocity: 3m/s

Momentum Ratio:  4 (=12/3)

A simulation for these boundary conditions was conducted in ANSYS Fluent, and this is the residuals plot:

The residuals never converge to the required criteria (energy <10^-6), hence any previous criteria must be changed to account for the new results.

This is the area-averaged temperature at the outlet for every iteration:

As we can notice, the temperature is converged quite well.

To see the variation of temperature across the outlet face, this is the plot of the standard deviation of temperature across the outlet for every iteration:

The simulation is done, now to the post processing. Close FLUENT and open CFD-post, to generate the required plots.

1. Velocity and Temperature Contours

These contours show the velocity and temperature at a cut plane

 

 

2. Temperature and Velocity along axis

A line was created in CFD-post along the axis of the pipe, and a chart was created.

3. Temperature and Velocity across outlet

A line was created in CFD-post along the center of the outlet, and a chart was created.

Grid Independence Test

To ensure that the solution is not skewed by the current mesh sizes, a grid independence test was conducted by varying the mesh size for Case 1 – Subcase 2. The area averaged outlet temperature and standard deviation of the same were used as metrics when comparing between different element sizes.

Mesh Size 1: 2mm/0.002m

Residuals report:

Area Weighted Average Temperature at outlet: 27.5727 C

Standard Deviation of Temperature at outlet: 1.049499594144189

Mesh2: 4mm/0.004m

Residuals report:

Area Weighted Average Temperature at outlet: 27.5647C

Standard Deviation of Temperature at outlet: 1.00254143128861

To summarise,

Mesh Size	Area Weighted Average Temperature at outlet (C)	Standard Deviation of Temperature at outlet
0.002m	27.5727	1.049499594144189
0.004m	27.5647	1.00254143128861
0.005m	27.5101	1.077492671014553

 

From the above table, since the values of Area Weighted Average Temperature at outlet and Standard Deviation of Temperature at outlet do not change significantly for a wide variation in mesh size, it can be stated that the simulation has passed the grid dependence test successfully. Or, we can say that the solution is independent of the grid size.

Summarising Table

	Momentum Ratio	Cell Count	Average Outlet Temperature	Number of iterations for convergence
Short Tee	2	14308	30.3	265
	4	14308	27.51	326
Long Tee	2	17904	30.37	500
	4	17904	27.54	500

 

Steamlines

These streamlines were taken in CFD-Post for Case 1 – Subcase 2, to understand the behaviour of how hot and cold fluids mix with each other.

The first picture is seen from the outlet show how fluid particles from the cold inlet move around the domain.

The next two pictures are seen from the outlet show how fluid particles from the hot inlet move around the domain.

 

 

Note: the colours of the steamlines do not hold any significance, they are just unique colours for each streamline.

Conclusions and Observations

1. Lower cold inlet velocity causes an un-uniform distribution of the fluid’s temperature at the outlet. (this is seen in the plots, and also seen in higher values of standard deviation of temperature). In other words, when momentum ratio is increased, a more uniform distribution of fluid is obtained at the outlet
2. Increased length of pipe does not cause a significant difference in uniform mixing of fluid. The majority of mixing occurs due to colliding hot and cold particles of fluid and not due to diffusion of individual particles in flow.
3. Increased cold inlet velocity causes overall lower fluid temperature at the outlet due to simply more cold fluid.

Recall the mixing formula, `T_(mixture) =( m_(hot) * T_(hot) + m_(cold) * T_(cold) )/(m_(hot) * m_(cold) )`

In this case, `m = V`, when `V_(cold)` is increased, `T_(mixture)` decreases.

 

4. There is a wake formed near the nexus of cold and hot fluid, which causes a drop in velocity in that region.
5. Decreasing grid size increases the residuals for the continuity and energy equations, which may cause previously reached convergence criteria to be invalid.
6. Decreasing grid size also increases computational time required, as there are simply more cells to solve equations in.
7. Both the hot and cold fluid form the shape of a double vortex as the flow progresses towards the outlet. The double vortex has two distinct streams of hot and cold fluid, the hot fluid is the outer layer and the cold fluid occupies the inner layer.