Mixing efficiency

AIM: -

To observe how the mixing is done is efficiently through user input values of velocity and temperature.

Introduction: -

Mixing tee problem is usually an example of pipe networking. Pipe Networking is mostly used in transfer of Fluids from one location to other.

For example, there are Water pipe networks around city, some parts of city are exposed to high temperature, but they cannot directly send the heated water to Houses/ Shops. So, there are connections from other sides, where the temperatures are less, by joining both water pipelines temperature is reduced by the time it reaches the destination. Not only Tee joint, Y- junction also used.

The pipe networking is very common in industries like Steam Power plants, Spices Manufacturing plants…etc.

Tee joints have 3 types of possibilities as shown below.

In this project, the second type of flow is selected

Theory: -

The quantity of mixing, scale up design of the mixer and the mixing efficiency were done on basis of using traditional design formulas. But those are limited to an extent. Through the computational methods such as using fluent solver, CFX solver. Etc. gives the approximations which saves the time complexity with good accuracy.

Applications such as Underground water and gas pipelines

Objective: -

To set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 36°C & the Cold inlet is at 19°C.

In a table, compare the following values from the 2 cases.

• Cell count.
• Average outlet temperature.
• Number of iterations for convergence.

Given:

Case1: 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.

As there are two geometries of mixing tee. So, For the Short pipe these are the boundary conditions.

Based upon the results of the physics model involved, physics for the long pipe is selected.

Modelling approach: -

Setup:

Click on workbench>Open.

From the toolbox drag the Fluid Flow(fluent) to the project schematic.

Geometry- Where the model is imported/ made by self and some of the operations like refining the model, extraction of volume…Etc.

Mesh- The mesh can be generated, the named selections can be given, can see the mesh through planes.

Setup-Here the actual physics can be selected based upon our requirements such as, if body is producing heat then the energy equation can turn on. Etc..

Solution-It intimates when the residuals reach its limits and is ready for the post processing.

Results-Post processing results can be viewed with help of contours, vectors, streamlines and particle path tracking.

Where,

Geometry and Mesh come’s under Pre-Processing.

Setup and Solution come’s under Solving.

Results come under Post-Processing.

Pre-Processing: -

Geometry:

Open space claim →Import Short Tee geometry .

To extract volume from the model, Go to Prepare →Volume Extraction →Select Edge option→ make edge selection →Click → Uncheck the solid structure, supress physics.

Here physics can be suppressed because the objective is how efficiently the mixing takes place.

Close the space claim →Mesh →Edit.

Mesh:

Click on the mesh, there will be a box in left bottom corner, click on sizing → Element size double click on the default value →0.006 i.e. 6e-3 due to the academic licence constrains, less element size is restricted. By default, the type of mesh is tetrahedron

As the report says the element quality is greater than 37%, make sure the element metrics or element quality should not be lower than 5%.

As a part of standard model of mesh size, every model is given with element size of 6e-3 m.

Now giving the named selection such as the Inlet, outlet, Wall. Etc.

Fluent Setup: -

Before setup, there are some challenges i.e.

Results: -

Case1:

Momentum Ratio 2:

Check the mesh quality before proceeding, Apply the below conditions.

By hybrid initialization and 500 iterations, calculate the solution.

Viscous model: Realizable K-Epsilon

Residuals: (Solution has been converged at 116^th iteration)

Average temperature at outlet: - (30.517° C)

Standard Deviation at outlet: - (0.913)

Temperature contour at midplane: -

Temperature at low pressure: - (303.842 K ~ 30.692° C)

Temperature at high velocity: - (308.331 K ~35.181° C)

Velocity streamlines: -

Summary:

Viscous model: - K-Omega (SST)

Check the mesh quality before proceeding, Apply the below conditions.

By hybrid initialization and 500 iterations, calculate the solution.

Residuals: (Solution has converged at 162^nd iteration)

Average Temperature at outlet: - (30.25° C)

Standard Deviation at outlet: - (1.685)

Temperature at mid plane: -

Temperature at low pressure: - (301.029 K ~ 27.879° C)

Temperature at high velocity: - (305.674 K ~ 32.524° C)

Velocity streamlines: -

Summary:

Momentum Ratio 4: -

Check the mesh quality before proceeding. Apply the below conditions.

By hybrid initialization and by 500 iterations, calculate the solution.

Residuals and Convergence: (converged at 120^th iteration)

Average Temperature at outlet: (27.809° C)

Standard Deviation of temperature at outlet: (1.230)

Temperature at mid plane: -

Temperature at low pressure: - (301.722 K ~ 28.572° C)

Temperature at high velocity: - (293.373 K ~ 20.223° C)

Velocity Streamlines: -

Summary:

Viscous model: K-Omega (SST)

Check the mesh quality before proceeding. Apply the below conditions.

By hybrid initialization and by setting up 500 iterations calculate.

Residuals and convergence:

From the graph, there are repetitions of the pattern after 280^th iteration. So, the convergence is at 280^th Iteration.

Average temperature at outlet: - (27.842° C)

Standard Deviation of the temperature at outlet: - (2.065)

Temperature at mid plane: -

Temperature at low pressure: - (302.087 K ~ 28.937° C)

Temperature at high velocity: (293.618 K ~ 20.468° C)

Velocity Streamlines: -

Summary:

Summary for Case 1:

• As per the info from graphs the results of both viscous models are similar but, the standard deviation of the K-Omega (SST) is higher and the time complexity of K-Omega (SST) is higher compare to Realizable K-Epsilon
• If the temperature contours are compared, there is less clarity in K-Omega (SST) than Realisable K-Epsilon
• As the inlet cold velocity doubles by initial velocity, the outlet temperature reduces almost by 8.874% i.e. 2.708° C in Realizable K-Epsilon Viscous model.
• So, for less time complexity, good accuracy Realizable K-Epsilon for the viscous models.

Case 2: -

Long Tee:

Geometry:

Open space claim →Import Short Tee geometry.

To extract volume from the model, Go to Prepare →Volume Extraction →Select Edge option→ make edge selection →Click → Uncheck the solid structure, supress physics.

Here physics can be suppressed because the objective is how efficiently the mixing takes place.

Close the space claim →Mesh →Edit.

Mesh:

Click on the mesh, there will be a box in left bottom corner, click on sizing → Element size double click on the default value →0.006 i.e. 6e-3 due to the academic licence constrains, less element size is restricted.

As the report says the element quality is greater than 33%, make sure the element metrics or element quality should not be lower than 5%. By default, the type of mesh is tetrahedron

As a part of standard model of mesh size, every model is given with element size of 6e-3 m.

Now giving the named selection such as the Inlet, outlet, Wall. Etc.

Momentum Ratio 2: -

Check the mesh quality before proceeding. Apply the below conditions.

By hybrid initialization and by setting up 500 iterations calculate.

Residuals and convergence: - (converged at 164^th iteration)

Average Temperature at outlet: - (30.272° C)

Standard Deviation of temperature at outlet: - (1.300)

Temperature at mid plane: -

Temperature at low pressure: - (300.875 K ~ 27.725° C)

Temperature at high Velocity: - (305.252 K ~ 32.102° C)

Velocity streamline: -

Summary:

Momentum Ratio 4: -

Check the mesh quality before proceeding. Apply the below conditions.

By hybrid initialization and by setting up 500 iterations calculate.

Residuals and convergence: - (solution is converged at 146^th iteration)

Average Temperature at outlet: -

Standard Deviation of temperature at outlet: -

Temperature at mid plane: -

Temperature at low pressure: - (306.755 K ~ 33.605° C)

Temperature at high velocity: - (306.563 K ~ 33.413° C)

Velocity Streamline: -

Summary:

Summary for Case 2: -

• As there is reduction of temperature by 9.21% i.e. 2.789° C by increasing the inlet cold velocity by 2 time by initial velocity.
• Viscous model is Realizable K-Epsilon because, in Case 1 the results were good, less time complexity, same accuracy as K-Omega.

Conclusion: -

The below points are based on overall summary for Case 1 & Case 2.

• The length of short tee and long tee models are
  1. 192.38 mm
  2. 268.33 mm

The below table represents difference in temperature and difference in distance for equal Momentum ratios.

• In M.R 2 for both cases, there is 0.8% decrease in temperature by increasing 28.3% of initial length.
• In M.R 4 for both cases, there is 1.17% decrease in temperature by increasing 28.3% of initial length.
• K-Omega (SST) model have distorted contours compared to Realisable K-Epsilon.
• Velocity of inlet cold/hot air plays vital role in mixing applications.
• There are vortices that are generating that can be seen in velocity streamlines.
• There is only 0.8% & 1.17% decrease in temperature in case of increasing length.
• Now by comparing the M. R’s in came case,
  1. Temperature is decreased by 87% by doubling the velocity for CASE 1
  2. Temperature is decreased by 21% by doubling the velocity for CASE 1

So, the velocity variations are way forward for efficient mixing.