Mixing efficiency

Project title: Steady-state simulations on the mixing tee geometry

Goals:

1. The main objective of this project is to find out the aerage temperature at the outlet of the mixing tee geometry

2. To setup simulations to compare thermal mixing effectiveness in a t-junction.

3.To compare k-epsilon and k-omega turbulent models.

4. To perform mesh independency test for one simulation.

5. Discuss the results about the length of the pipe and momentum ratio about thermal mixing.

6. To plot the veocity contours, temperature contours, velocity line plot and temperature line plot along and across the length of the pipe.

we setup four different cases

• Case 1
  • Short mixing tee with a hot inlet velocity of 3m/s and cold inlet velocity of 6 m/s.
  • Momentum ratio of 2.

• Case 2
  • Long mixing tee with a hot inlet velocity of 3m/s and cold inlet velocity of 6 m/s.
  • Momentum ratio of 2

• Case 3
  • Short mixing tee with a hot inlet velocity of 3m/s and cold inlet velocity of 12 m/s.
  • Momentum ratio of 4.
• Case 4
• • • Long mixing tee with a hot inlet velocity of 3m/s and cold inlet velocity of 12 m/s.
    • Momentum ratio of 4.
• Momentum ratio = velocity at cold inlet / velocity at hot inlet

Note:

For all cases hot inlet is taken in x-direction and cold inlet is taken in y-direction. and the temperature of hot and cold inlet is taken as `36^@C`and `19^@C^` respectively.

Case 1:

In Case 1 we used the short mixing tee geometry with a hot inlet of velocity 3m/s and temperature taken at this boundary is 36 degree celsius and cold inlet of velocity 6 m/s and temperature taken at this boundary is 18 degree celsius. in case 1, we take the momentum ratio 2.

1.Geometry of T_Junction short pipe:

1.3D view in spaceclaim is shown below

Fig 1:solid body

2.The computational fluid domain can be extracted by using volume extraction tool available in space claim. The following edges used in the volume extraction

Fig 2:Edges used in volume extraction

3.After selecting the edges we click on the green right mark to create computational domain.

4.After the volume extraction the geometry would like as shown below.

Fig 3: Compuational domain

4. Also disable the solid part geometry and right click on the solid component part and select the suppress from physics. we only take the computational domain that\'s why we did this.

2.Meshing details

Details of mesh are given below

No of nodes:105952

No of elements:553368

Mesh of the geometry

Mesh Metric

3.Boundar Conditions

The boundaries are inlet_y for cold air, inlet_x for hot air and outlet for the mixed air.

4.Case Setup

Now we have to setup the simulations in ansys fluent. Basically in ansys fluent we solve all our mathematical equation.

• Now click on general and choos the pressure based solver ,choose the absolute in the velocity formulation and choose the steady in the time.
• Now going to models, in the viscous models choose the k-epsilon, realizable, standard wall function.
• Also choose the energy equation for temperature calculation.
• Then go to boundary conditions and choose the inlet_x boundary and set the inlet velocity 3 m/s and temperature 36 degree celsius. At the inlet_y boundary set the veocity 6 m/s and temperature 19 degree celsius. At the walls, we set the no-slip conditions and set the wall motion stationary. At the outlet wall, we set the gauage pressure 0 and retain the default temperature.
• go to solving tab and in the definitions set the monitors to calculate the average outlet temperature and standard deviation of the temperature. you may alos set many monitors for the study of other parameters.
• After seeting all the parameters and models, use the hybrid initializatio to initialize the the case.
• set the 500 iterations and click on calculate to run the simulation.

• The above graph shows the convergence history of the problem. we easily observe that solution is converges at 220 iterations and after 220 iterations plot is fairly parallel to x-axis.

Area weighted average

The above graph is the area weighted average of the temperature at the outlet boundary, we observe in the graph that at the outlet the average temperature is approximately 30.42.

Standard deviation

The above graph is the standard deviation of the temperature at the outlet boundary. we oberve that standard deviation of the temperature is 1.72 degree celsius approximately. Lower value of standard deviation is the indiction of batter results.

Numerical values of average temperature and standard deviation is

5.Post processing

Results

Temperture and velocity contours along the pipe

The temperature and velocity contours along the pipe has been taken at the central plane of the pipe.

Temperature Contours

Velocity Contours

Temperature and velocity contours across the pipe

Temperature Contours

Velocity Contours

Line plot along the length of the pipe

Temperature plot

In the above graph, we know that at the inlet_x temperature is 36 degree celsius and it is going to decrease at the distance -0.05 m, because at that point cold air is enter from the inlet_y and it decreases the temperature of hot air. whenever proper mixing occur temperature is again increases.

Velocity plot

In the above graph, we observe that at inlet_x, we take the velocity 3 m/s and at a -0.05 distance when cold air enter from the inlet_y with 6 m/s velocity it increases the flow velocity and after that it is going to slow down at a distance 0m. And after that distance velocity is again going to increases.

Line pot across the pipe

Temperature plot

Velocity plot

The above line plots have been taken by considering the a line across the outlet which is at the very center of the outlet. And the variation of temperature inside the pipe compared to that near the wall is clearly visible.

3D Temperature Contours

3D Velocity Contours

The above 3D contours show how the temperature and velocity changes along and across the pipe. The evolution pattern is clearly visible and matched with he expectation results.

Reference formula

To calculate the Temperature of the mixture and enthalpy of the mixture, we need the mass flow rate at the hot inlet (inlet_x) which we calculate in fluent. And also we calculate the mass flow rate at the cold inlet (inlet_y) in fluent.

And for the calculation of the enthalpy of the mixture, we also calculate the enthalpy at hot inlet (inlet_x) and enthalpy at cold inlet (inlet_y) in fluent. Values of all the calculations are given below.

By using all the above values

`T_(mixture)=frac{(0.0033103)(36)+(0.0016569)(19)}{0.0033103+0.0016569}=30.3293`

`h_(mixture)=frac{(0.0033103)(11075.216)+(0.0016569)(-6020.6348)}{0.0033103+0.0016569}=5372 J/kg`

For the comparisons we calculate the outlet values of mass flow rate and enthalpy, which are given below

Case 2

In case 2, we take the long mixing tee with a hot inlet velocity of 3m/s and cold inlet velocity is 6 m/s and momentumratio is 2. At hot inlet, we take the temperature 36 degree celsius and at the cold inlet, we take the temperature 19 degree celsius.

1.Geometry of T-junction long pipe

2.Meshing

Sizing

Mesh Metric

3.Boundary Conditions

4. Case setup

All the settings in fluent are remain are as we did in case 1. Here we only change the geometry and do the analysis.

Residuals

Ares weighted average

Standard deviations

Numerical Values

5.Post Processing

Results

Temperature and Velocity Contours along the pipe

Temperature Contours

Velocity Contours

Temperature and Velocity Contours across the pipe

Temperature contours

Velocity Contours

At global range velocity values

At local range velocity values

3D contours of Temperature

3D contours of Velocity

Temperature plot along the length of the pipe

Velocity plot along the length of pipe

Temperature and Velocity plot across the pipe

Velocity plot across the length of the pipe

For the verification of results we need to calaulate the value of the temperature of the mixture and enthaly of the mixture.

`T_(mixture)=frac{(0.003258)(36)+(0.0016337)(19)}{0.003258+0.0016337}=30.32244`

`h_(mixture)=frac{(0.003258)(11075.186)-(0.0016337)(6020.8943)}{0.003258+0.0016337}=5365`

Effect of length in thermal mixing

Case 3

• In case 3, we take the short mixing tee with a hot inlet velocity of 3m/s and cold inlet velocity 12 m/s and momentum ratio 4.
• we take inlet_x velocity=3 m/s and inlet_y velocity=12 m/s.
• we take inlet_x temperature= 36 degree celsius.
• we take inlet_y temperature= 19 degree celsius.
• At the outlet boundary we take the gauage pressure=0.

Boundary Conditions for case 3 is given in the following figure

Note:

we take the same geometry and mesh as we take in case 1 only change occur in the velocity of the inlet_y boundary which we take in this case is 12 m/s in ansys fluent,thats why i am not displaying the geometry and mesh. Here we only foscused on the results.

Results:

Residuals

Weighted average temperature

Standard deviation

Temperature and velocity contours along the length of the pipe

Temperature Contours

Velocity Contours

Temperature and velocity contours across pipe

velocity Contours at local values

Temperature and velocity plots along the length of the pipe

Temperaure and Velocity across the length of the pipe

3D contours of temperature and velocity

Calculation of T_mixture formulas

`T_(mixture)=frac{(0.0033103135)(36)+(0.0033138612)(19)}{0.0033103135+0.003138612}=28.242634`

`h_(mixture)=frac{(0.0033103135)(11075.216)-(0.0033138612)(5966.7487)}{0.0033103135+0.0033138612}=2549 J/kg`

Case -4

• in case-4 we take the long mixing tee geometry with momentum ratio 4.
• At the hot inlet_x, we take the velocity 3 m/s and at the cold inlet_y, we take the velocity 12 m/s.
• At the outlet, we take the gauge pressure is zero.
• At the walls, we take the no slip conditions
• we take the same geometry and mesh as we take in case-2. we only change the velocity of inlet_y 12 m/s in fluent. Remaining all the settings are retain.
• Here we only focus on the results that\'s geometry and mesh are not displayed.

Results description are given below

Results

Residuals

Area weighted average

Standard deviation

Temperature and Velocity plot along the length of the pipe

Temperature and velocity contours across the pipe

Temperature and velocity plot along the length of plot

Temperature and velocity plot across the length of plot

3D Contours of temp and velocity

Calaulation of T_mixture formulas

`T_(mixture)=frac{(0.003258051)(36)+(0.0032675203)(19)}{0.003258051+0.0032675203}=27.48766`

`T_(mixture)=frac{(0.003258051)(11075.168)-(0.0032675203)(5967.4475)}{0.003258051+0.0032675203}=2541.494`

Discussion of results about the effects of length and momentum ratio\'s:

Summary of all the cases are describe in the following table

Results discussion about the momentum ratio and Effect of length in thermal mixing:

we discuss all the results one by one.First of all we discuss the impact of momentum ratio in short mixing tee.

• The momentum ratio is the ratio of cold inlet velocity to hot inlet velocity.
• Since the hot inlet velocity is kept constant and increasing the cold inlet velocity.
• In a short pipe with momentum ratio 2 and 4 comparison with same geometry and mesh, we easily observe that with momentum ratio 4 more diffusion occur. And as a result more mixing occur.
• In a long pipe with momentum ratio 2 and 4 comparison with the same geometry and mesh, we easily observe that with momentum ratio 4 more diffusion occur. And as a result more mixing occur.
• It was observed that efficient mixing was happened near the t-junction, where the hot and cold inlet air meets with different temperature and velocity.
• The average temperature and standard deviation at the outlet has been reduced in the long mixing tee too much as compared to short mixing tee.
• Morevoer all the contours (temperature and velocity), temperature plots, velocity plots are given in above in which we observe the behaviour of the results.

Now we discuss the impact of length on thermal mixing

• As the length is increased after the t-junction, more diffusion was happened. And as a result more mixing was occur.
• This was easily observed in the above expalined temperature and velcity contours.
• The area weighted average and standard deviationat the outlet has been reduced in the long mixing tee to much as compared to the short mixing tee, which slightly support the observation.
• All the numerical description of results are given in the above table.
• There was a more mixing when length was increased, but it was not so high.
• One more obervation is that increasing the length is not the gurantee of increasing the mixing always.

Mesh Independency test

While performing the mesh independency test we take only the short mixing tee model. And mesh independency test has been conducted for three different cases varying the element size.

• Geometry

• T-Junction short pipe geometry has been used

• Boundary Conditions

• Mesh Details

• Case-1

• Element size: 0.0102
• Number of nodes:2836
• Number of elements:12800

• Case-2

• Element size:0.0028
• Number of nodes:9776
• Number of elements:47115

• Case-3

• Element size:0.00102
• Number of nodes:105952
• Number of elements:553368

• The 3-D view of the meshes are given below.

• Case-1 mesh

• Case-2 mesh

• Case-3 mesh

• Case-1 Mesh-metric

• Case-2 Mesh-metric

• Case-3 Mesh-metric

• Residuals of Case-1

• Residuals of case-2

• Residuals of case-3

• Area weighted average of Case-1

• Area weighted average of Case-2

• Area weighted average of case-3

Standard deviation of case-1

Standard deviation of case-2

Standard deviation of case-3

• Temperature Contours of Case-1 along the length of the pipe

• Temperature Contours of Case-2 along the length of the pipe

• Temperature Contours of Case-3 along the pipe

• Velocity Contous of Case-1 along the pipe

• Velocity Contours of Case-2 along the pipe

• Velocity Contours of Case-3 along the pipe

• Temperature Contours of Case-1 across the pipe

• Temperature Contours of Case-2 across the pipe

• Temperature Contours of Case-3 across the pipe

• Velocity Contours of Case-1 across the pipe

• Velocity Contours of Case-2 across the pipe

• Velocity Contours of Case-3 across the pipe

Temperature and velocity line plot along the length of pipe

Temperature plots along the length of pipe for case-1

Temperature plots along the length of pipe for case-2

Temperature plots along the length of pipe for case-3

Velocity plots along the length of pipe for case-1

Velocity plots along the length of pipe for case-2

Velocity plots along the length of pipe for case-3

Temperature plots across the length of pipe for case-1

Temperature plots across the length of pipe for case-2

Temperature plots across the length of pipe for case-3

Velocity plots across the length of pipe for case-1

Velocity plots across the length of pipe for case-2

Velocity plots across the length of pipe for case-3

Mesh lines contours of Temperature for case-1

Mesh lines contours of Temperature for case-2

Mesh lines contours of Temperature for case-3

Mesh lines contours of velocity for case-1

Mesh lines contours of velocity for case-2

Mesh lines contours of velocity for case-3

3D Contours of temperature for case-1

3D Contours of temperature for case-2

3D Contours of temperature for case-3

3D Contours of Velocity for case-1

3D Contours of Velocity for case-2

3D Contours of velocity for case-3

Mixture formula\'s calculation for case 1

`T_(mixture)=frac{(0.0032580584)(36)+(0.00163375)(19)}{0.003258584+0.0016337557}=30.32236086`

`h_(mixture)=frac{(0.0032580584)(11075.191)-(0.00163375)(6020.8956)}{0.0032580584+0.0016337557}=5365.490254`

Mixture formula\'s calculation for case-2

`T_(mixture)=frac{(0.0032072537)(36)+(0.0016337558)(19)}{0.0032972537+0.0016337558}=30.36751`

`h_(mixture)=frac{(0.0032072537)(11075.211)-(0.0016337558)(6020.8581)}{0.0032972537+0.0016337558}=5410.0900`

Mixture formula\'s calculation for case-3

T_(mixture)=frac{(0.0033103)(36)+(0.0016569)(19)}{0.0033103+0.0016569}=30.3293

`h_(mixture)=frac{(0.0033103)(11075.216)+(0.0016569)(-6020.6348)}{0.0033103+0.0016569}=5372 J/kg`

Mesh Independency results discussion

• Basically when the mesh become finer, the number of elements to capture the physical phenomena is increases. And we got the batter solution.
• It is also depend on the problem nature that which kind of mesh refinement is required. Otherwise it predicts the over estimated values.
• In the above mesh independency study we observe that whenever mesh is refine behaviour of temperature and velocity contours looks smooth as compared to the coarse mesh.
• But one thing we observe in the above results is that whenever we refine the mesh values of standard deviation is increases this is happen due to deviation because he standard deviation is a measure of the amount of variation or dispersion of a set of values.
• All the numerical values comparion are given the above table.

Turbulence Model selection

In this problem, we take the two turbulence models k-epsilon and k-omega model. To find out which model is best, we run two simulations

• Geometry

• T-junction short pipe has been used to run the simulations

• Boundary conditions

• Meshing Details

• Element size(max face size)=1.02e-02
• No of nodes=2836
• No of elements=12800
• 3D mesh view has been shown below.

2D mesh view has been shown below

• Case setup details

• Solver type:pressure based
• Fluid: we take the air as fluid.
• Energy equation was enabled because the temperature change phenomena is studied.
• Boundary Conditions:

• At the hot inlet we take the velocity inlet_x=3 m/s, temperature inlet_x=36 degree celsius.
• velocity inlet_y=6 m/s, temperature inlet=19 degree celsius.
• At the outlet wall, we take the gauge pressue is zero and we retain the default value of temperature, which is 26.85.
• At the walls we take the no-slip condition.
• Hybrid initialization has been done.
• No of iterations=500.

Results Comparison

Two separate simulations have been run using the above condiions, one with k-epsilon model and other with k-omega sst model.

Residuals graph of k-epsilon model

Residuals graph of k-omega SST model

Area weighted average graph of k-epsilon model

Area weighted average graph of k-omega SST model

Standard deviation graph of k-epsilon model

Standard deviation graph of k-omega SST model

Temperature Contours of k-epsilon model along the length of pipe

Temperature Contours of k-omega SST model along the length of pipe

Velocity Contours of k-epsilon model along the length of pipe

Velocity Contours of k-omega SST model along the length of pipe

Temperature line plot of k-epsilon model along the length of pipe

Temperature line plot of k-omega SST model along the length of pipe

Temperature line plot of k-epsilon across the length of pipe

Temperature line plot of k-omega across the length of pipe

Velocity line plot of k-epsilon model along the length of pipe

Velocity line plot of k-omega SST model along the length of pipe

Velocity line plot of k-epsilon across the length of pipe

Velocity line plot of k-omega SST across the length of pipe

3D temperature contours of k-epsilon model

3D temperature contours of k-omega model

3D velocity contours of k-epsilon model

3D velocity contours of k-omega SST model

Temperature contours of k-epsilon model across the pipe

Temperature contours of k-omega SST model across the pipe

Velocity Contours of k-epsilon model across the pipe

Velocity Contours of k-omega SST model across the pipe

T_mixrure formulas calculation for k-epsilon model

T_(mixture)=frac{(0.0032580584)(36)+(0.00163375)(19)}{0.003258584+0.0016337557}=30.32236086

h_(mixture)=frac{(0.0032580584)(11075.191)-(0.00163375)(6020.8956)}{0.0032580584+0.0016337557}=5365.490254

T_mixture formulas calculation for k-omega SST model

`T_(mixture)=frac{(0.0032580584)(36)+(0.00163375)(19)}{0.003258584+0.0016337557}=30.32238299`

`h_(mixture)=frac{(0.0032580584)(11075.188)+(0.00163375)(6020.9029)}{0.003258584+0.0016337557}=5365.47880`

Results Discussion

• Both model gave almost same temperature and velocity contours.
• After t_Junction small recirculation has occured in both cases.
• By observing the numerical values given in the above table, k-epsilon model gave the batter results. there is no too much difference occur in both models results.
• K-epsilon model gave the lower value of standard deviation and average temperature at the outlet as compared to the k-omega SST model.
• Batter diffusion was observed in k-epsilon model.
• There is a lot of complex mathematics behind the k-omega SST model as compared to the k-epsilon.

Conclusions

• Increasing the length of pipe after the t_junction increase the more diffusion compared to the short length pipe.
• Increasing the momentum ratio also causes the more mixing near the t_junction. This is a good idea to increase the momentum ratio for the batter mixing efficiency.
• At a fine mesh physical phenomena are captured well as compared to the coarse mesh but we fine the mesh according to the nature of the problem. Sometimes it predicts the overestimated values.
• In thermal mixing type problems k-epsilon model is best as compared to the k-omega SST model.