Mixing efficiency

REPORT:

AIM:

• To find out the mixing efficiency of the short and long tee with different momentum ratio of 2 and 4, When the hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C with the hot inlet velocity of 3m/s.
• To 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.
• Comparing the values from the cases by creating a table.
• To plot the Velocity and temperature contour plots on the cut planes along and across the pipe.
• To plot the Velocity and temperature line plots along and across the length of the pipe.
• To Perform Mesh independent study for any one case.
• To Discuss the effect of length and momentum ratio on results.

INDRODUCTION:

To Perform a steady state simulation for a short and long tee joints using two different momentum ratios.The fluid we are using is Air. First we will be performing a mesh independent test by creating three meshes with different number of cells in it and we will be comparing all them to find out the best one required for doing the following simulation.After the mesh indepent test we will be doing the turbulence model test, We will be using the K-episilon and K-omega turbulence model which are basically known as RANS MODELS(REYNOLDS-AVERAGED NAVIER-STOKES) and perform two simulation to find out the best turbulence model according to the values obtaines.By obtaining the suitable mesh and turbulence model we will be simulating the mixing efficiency of short and long tee using the different momentum ratios.

SOFTWARE USED: ANSYS FLUENT.

THEORY:

MIXING TEE JOINT:

Tee joint is a T-Shaped joint having two inlets and one outlet,It is used in various conditions in various circumstances.For instance like the oil and gas industry,Automotive,Pharmacuetical etc.Mixing Tees utilizes a specifically engineered internal geometry to efficiently mix two fluid streams into one combined stream. Mixing Tees are ideal for microbore or analytical gradient HPLC. These mixing tees are specifically designed for high pressure applications.

K-EPSILON TURBULENCE MODEL:

K-epsilon (k-ε) turbulence model is the most common model used in Computational fluid Dyanamics (CFD) to simulate mean flow characteristics for turbulent flow conditions. It is a two equation model that gives a general description of turbulence by means of two transport equations (PDEs). The original impetus for the K-epsilon model was to improve the mixing length model, as well as to find an alternative to algebraically prescribing turbulent length scales in moderate to high complexity flows.

• The first transported variable is the turbulent kinetic energy (k).
• The second transported variable is the rate of dissipation of turbulent kinetic energy (ε).

Unlike earlier turbulence models, k-ε model focuses on the mechanisms that affect the turbulent kinetic energy. The mixing length models lacks this kind of generality. The underlying assumption of this model is that the turbulent viscosity is isotropic, in other words, the ratio between Reynolds stress and mean rate of deformation is the same in all directions.

The k-ε model has been tailored specifically for planar shear layers and recirculating flows. This model is the most widely used and validated turbulence model with applications ranging from industrial to environmental flows, which explains its popularity. It is usually useful for free-shear layer flows with relatively small pressure gradients as well as in confined flows where the Reynolds shear stress are most important. It can also be stated as the simplest turbulence model for which only initial and/or boundary conditions needs to be supplied.

K-OMEGA TURBULENCE MODEL:

In Computational fluid Dyanamics, the k–omega (k–ω) turbulence model is a common two-equation turbulence model, that is used as a closure for the Reynolds-averaged Navier-Stokes (RANS equations). The model attempts to predict turbulence by two PDE for two variables, k and ω, with the first variable being the turbulence kinetic energy (k) while the second (ω) is the specific rate of dissipation (of the turbulence kinetic energy k into internal thermal energy).

SST K-OMEGA MODEL:

The SST k-ω turbulence model [Menter 1993] is a two equation eddy viscosity equation model which has become very popular. The shear stress transport (SST) formulation combines the best of two worlds. The use of a k-ω formulation in the inner parts of the boundary layer makes the model directly usable all the way down to the wall through the viscous sub-layer, hence the SST k-ω model can be used as a Low returbulence model without any extra damping functions. The SST formulation also switches to a k-ε behaviour in the free-stream and thereby avoids the common k-ω problem that the model is too sensitive to the inlet freestream properties. Authors who use the SST k-ω model often merit it for its good behaviour in adverse pressure gradients and separating flow. The SST k-ω model does produce a bit too large turbulence levels in regions with large normal strain, like stagnation regions and regions with strong acceleration. This tendency is much less pronounced than with a normal k-ε model though.

PROCEDURE:

CASE 1:

Short Tee Joint with hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C with the hot inlet velocity of 3m/s and momentum ratio 2.(Using K-Epsilon turbulence model)

Formula to find cold inlet velocity:

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

Substituting the known values,

2 = velocity at cold inlet/3

velocity at cold inlet = 6m/s.

We are going to perform the mesh dependent test and turbulence model test using the first case and use the results for the upcoming cases.

GEOMETRY:

SPACECLAIM:

Open the geometry file in spaceclaim to view.

Procedure:

• Now we have to eliminate the umwanted volume in the geometry before the simulation.
• click on the prepare option and select volume extract option.
• After selecting the volume extract option select the select edges option.
• Now u have to select the edges inlet x,inlet y and outlet x.
• After select the edges click on Complete option.
• Now hide the solid option.
• Now u can view the required volume.

• Now near the solid option click your left mouse button and select the option Supress for physics.
• Now close space claim.

MESH:

Mesh element size(0.006)

procedure:

• Click on mesh option in Work bench.
• You can view the geometry directly.
• You have to select the face by clicking on ctrl+f and N.
• Now in elemet size change it to 0.006 from the default value.
• Click on Genrate mesh option.

• After creating the mesh u have to check the mesh quality.
• For instance u can see the above image having a element quality graph which depicts a lowest value of 0.35 which is good. For element quality the lowest value should not be less than 5%.
• Not only element quality there are many quality aspects in Mesh metrics.

Mesh quality

• orthogonality qaulity

If you get 1 as your orthogonality then it is good and 0 is considered to be bad.

• Skewness

For skewness 0 - 0.25 -excellent

0.25-0.95 moderate

0.95-0.97 Bad

0.97-1 Very bad

• Aspect ratio

For a mesh the aspect ratio should be less than 5.

• Jacobian quality

The value should be than 0.6 to attain a good jacobian value.

SETUP:

PROCEDURE:

By clicking you can see the geometry is automatically updated in the fluent.

You have to the select the Double precision and start the fluent.

In Domain select the Check option.

In check select the perform Mesh check option.

• In the physics select energy option.
• After selecting physics click on viscous model to select the turbulence model
• In viscous model select the K-epsilon turbulence model and select Realizable and Standard wall functions.

Now select the materials option.

Now give the desired fluid type or select from fluid database.

• Now click on Boundaries to give the conditions.
• After clicking on boundaries fluent automatically decides the inlets and outlets according to the name given
• Now click on inlet x and click edit option.
• Now you can give the velocity and temperature values,.

• After giving all the boundary conditions click on Solution.
• In solution click on Definition->Surface report->Area weighted Average.
• In that give Temperature in the outlet x to get the plot.
• Same way again click Definition->Surface report->Standard deviation.
• In that give Temperature in the outlet x to get the plot.
• Similary use the above options and give velocity instead of temperature to get the velocity graphs at the outlet.
• Now click on Initialize solution.
• Then give the required number of iterations and click on Calculate.

RESIDUAL GRAPH:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF VELOCITY GRAPHS:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF TEMPERATURE GRAPHS:

POST PROCESSING:

CFD POST:

• After opening the CFD post u can see the geometry is uploaded auromatically.
• Try to render the walls to see the simulation clearly.
• Now click on Insert->Location->Plane.
• Now select the XY plane and in variables select Temperature and click on apply.
• Now you can see the Temperature Contour,Similarly you can change Temperature to velocity to see the velocity contour.

• The above images show the Temperature and Velocity contours along the pipe.
• To view the contour across the length of pipe select Insert->Location->Plane.
• Now select the YZ axis and follow the above rules and click apply.

VELOCITY AND TEMPERATURE LINE GRAPHS ALONG THE LENGTH OF THE PIPE:

VELOCITY AND TEMPERATURE LINE GRAPHS ACROSS THE LENGTH OF THE PIPE:

You can observe that the velocity graphs are similar to the article which is mentiones in the references.

RESULTS FOR CASE 1:

We know the formula for the Temperature mixture to do the manual calculation,

Substituting the known values,

mass flow rate = `rhovA`

Density of air = 1.225 kg/3^3

Area = 0.0009 m^2

V of hot inlet = 3m/s

m_hot = 1.225*0.0009*3

m_hot = 0.003307 kg/s

m_cold = 1.225*0.0002*6

m_cold = 0.00147 kg/s

T_hot = 36C

T_cold = 19C

T(mixture) = 0.003307*36+0.00147*19/0.003307+0.00147

T(mixture) = 30.768 C

Value from the simulation,

303.355K Which is 30.205C

CASE 1 WITH MESH ELEMENT SIZE 0.003:

Upload the above geometry in the space claim and follow the same method mentioned above and close space claim.

MESH(ELEMENT SIZE 0.003):

Follow the same method for the mesh stated above.

Now the only change is that,The mesh element size has to be changed to 0.003 from its default value.

Perform the quality check as mentioned above.Here you can see the quality as 0.28 which greater than 5% which states it is good.

check other parameters also.

SETUP:

Follow the same procedure as mentioned above select the same turbulence model and same materials.

Give the boundary condition as same as stated above

After the procedure click on Calculate.

After calculation u will get the following results

RESIDUAL GRAPH:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF VELOCITY GRAPHS:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF TEMPERATURE GRAPHS:

POST PROCESSING:

CFD POST:

Follow the same procedures as mentioned above select the xy plane for the contour along the length

Contour plots along the length:

Contour plots across the length:

VELOCITY AND TEMPERATURE LINE GRAPHS ALONG THE LENGTH OF THE PIPE:

VELOCITY AND TEMPERATURE LINE GRAPHS ACROSS THE LENGTH OF THE PIPE:

RESULTS:

We know the manual value is 30.768C

The value by the simulation is:

The value by simulation is 30.259C

CASE 1 WITH MESH ELEMENT SIZE 0.0018:

Upload the above geometry in the space claim and follow the same method mentioned above and close space claim.

MESH(ELEMENT SIZE 0.0018):

Follow the same method for the mesh stated above.

Now the only change is that,The mesh element size has to be changed to 0.0018 from its default value.

Perform the quality check as mentioned above.Here you can see the quality as 0.23 which greater than 5% which states it is good.

check other parameters also.

SETUP:

Follow the same procedure as mentioned above select the same turbulence model and same materials.

Give the boundary condition as same as stated above

After the procedure click on Calculate.

After calculation u will get the following results

RESIDUAL GRAPH:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF VELOCITY GRAPHS:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF TEMPERATURE GRAPHS:

POST PROCESSING:

CFD POST:

Follow the same procedures as mentioned above select the xy plane for the contour along the length

Contour plots along the length:

Contour plots across the length:

VELOCITY AND TEMPERATURE LINE GRAPHS ALONG THE LENGTH OF THE PIPE:

VELOCITY AND TEMPERATURE LINE GRAPHS ACROSS THE LENGTH OF THE PIPE:

RESULTS:

We know the manual value is 30.768C

The value by the simulation is:

The value by simultion is 30.271C

ELEMENT SIZE	NO.OF.ELEMENTS	ELEMENT QUALITY	AREA.AVG TEMPERATURE (T(mixture))	T(mixture) value by formula
0.006	12700	0.35	30.205C	30.768C
0.003	39817	0.28	30.259C	30.768C
0.0018	137296	0.26	30.271C	30.768C

RESULTS FOR MESH DEPENDENT TEST:

From the simulation it is clear that the smaller the elemental size that is 0.0018 shows the temperature without much distortion much clearly whereas larger the elemental size shows some distortion.We also know that the t(mixture) calculated by the formula is 30.768C and if you observe the t(mixture) obtained from the simulation you can see that the t(mixture) of smaller elemental is nearer to the manual value.This means that less the elemental size we get more accurate results.So we will be using the elemental size 0.0018 for our further simulations.

Short Tee Joint with hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C with the hot inlet velocity of 3m/s and momentum ratio 2.(Using K-Omega turbulence model)

CASE 1 WITH MESH ELEMENT SIZE 0.0018(k-omega model):

Upload the above geometry in the space claim and follow the same method mentioned above and close space claim.

MESH(ELEMENT SIZE 0.0018):

Follow the same method for the mesh stated above.

Now the only change is that,The mesh element size has to be changed to 0.0018 from its default value.

Perform the quality check as mentioned above.Here you can see the quality as 0.23 which greater than 5% which states it is good.

check other parameters also.

SETUP:

Follow the same procedure as mentioned above but the only difference here is in viscous model we will be using K-Omega turbulence model and select SST option.

Select the same materials as mentioned above.

Give the boundary condition as same as stated above

After the procedure click on Calculate.

After calculation u will get the following results

RESIDUAL GRAPH:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF VELOCITY GRAPHS:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF TEMPERATURE GRAPHS:

POST PROCESSING:

CFD POST:

Follow the same procedures as mentioned above select the xy plane for the contour along the length

Contour plots along the length:

Contour plots across the length:

VELOCITY AND TEMPERATURE LINE GRAPHS ALONG THE LENGTH OF THE PIPE:

VELOCITY AND TEMPERATURE LINE GRAPHS ACROSS THE LENGTH OF THE PIPE:

RESULTS:

We know the manual value is 30.768C

The value by the simulation is:

The value by simultion is 30.457C

S.no	TURBULENCE MODEL	No.of.Iterations	T(mixture)	Manual T(mixture) value
1.	K-Epsilon	220	30.271	30.768
2.	K-Omega	210	30.457	30.768

From the above Table it is clear that the K-omega turbulence model is providing more accurate results than the K-epsilon turbulence model.T(mixture) value attaines by K-Omega is nearer to the manual T(mixture) value.Comparing the iterations also K-omega has converged in less iteration than K-Episilon model, So it is K-Omega model consumes less time than K-epsilon model.From the above theory we know that k- epsilon model poorly resolves the viscous layer unline K-Omega model. Furthermore, k-ω model is good in resolving internal flows, separated flows and jets and flows with high-pressure gradient and also internal flows through curved geometries. You always need to make sure that you have a proper mesh at the boundary wall by abiding by the correct Y Plus value.

So we will be using K-omega turbulence model for our upcoming simulations in this project.

CASE 2:

Short Tee Joint with hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C with the hot inlet velocity of 3m/s and momentum ratio 4.(Using K-Omega turbulence model)

Formula to find cold inlet velocity:

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

Substituting the known values,

4 = velocity at cold inlet/3

velocity at cold inlet = 12m/s.

We are going to perform the mesh dependent test and turbulence model test using the first case and use the results for the upcoming cases.

GEOMETRY:

SPACECLAIM:

Open the geometry file in spaceclaim to view.

Follow the steps mentioned above and prepare the required volume.

MESH(ELEMENT SIZE 0.0018):

Follow the same method for the mesh stated above.

Now the only change is that,The mesh element size has to be changed to 0.0018 from its default value.

Perform the quality check as mentioned above.Here you can see the quality as 0.23 which greater than 5% which states it is good.

check other parameters also.

SETUP:

Follow the same procedure as mentioned above but the only difference here is in viscous model we will be using K-Omega turbulence model and select SST option.

Select the same materials as mentioned above.

Give the boundary condition as same as stated above

After the procedure click on Calculate.

After calculation u will get the following results

RESIDUAL GRAPH:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF VELOCITY GRAPHS:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF TEMPERATURE GRAPHS:

POST PROCESSING:

CFD POST:

Follow the same procedures as mentioned above select the xy plane for the contour along the length

Contour plots along the length:

Contour plots across the length:

VELOCITY AND TEMPERATURE LINE GRAPHS ALONG THE LENGTH OF THE PIPE:

VELOCITY AND TEMPERATURE LINE GRAPHS ACROSS THE LENGTH OF THE PIPE:

RESULTS:

We know the manual value is 30.768C

The value by the simulation is:

The value by simultion is 27.608C

CASE 3:

Long Tee Joint with hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C with the hot inlet velocity of 3m/s and momentum ratio 2.(Using K-Omega turbulence model)

Formula to find cold inlet velocity:

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

Substituting the known values,

2 = velocity at cold inlet/3

velocity at cold inlet = 6m/s.

We are going to perform the mesh dependent test and turbulence model test using the first case and use the results for the upcoming cases.

GEOMETRY:

SPACECLAIM:

Open the geometry file in spaceclaim to view.

By following the above procedure you can extract volume which is needed. The extracted volume looks like the below image

MESH(ELEMENT SIZE 0.0018):

Follow the same method for the mesh stated above.

Now the only change is that,The mesh element size has to be changed to 0.0018 from its default value.

Perform the quality check as mentioned above.Here you can see the quality as 0.23 which greater than 5% which states it is good.

check other parameters also.

SETUP:

Follow the same procedure as mentioned above but the only difference here is in viscous model we will be using K-Omega turbulence model and select SST option.

Select the same materials as mentioned above.

Give the boundary condition as same as stated above

After the procedure click on Calculate.

After calculation u will get the following results

RESIDUAL GRAPH:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF VELOCITY GRAPHS:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF TEMPERATURE GRAPHS:

POST PROCESSING:

CFD POST:

Follow the same procedures as mentioned above select the xy plane for the contour along the length

Contour plots along the length:

Contour plots across the length:

VELOCITY AND TEMPERATURE LINE GRAPHS ALONG THE LENGTH OF THE PIPE:

VELOCITY AND TEMPERATURE LINE GRAPHS ACROSS THE LENGTH OF THE PIPE:

RESULTS:

We know the manual value is 30.768C

The value by the simulation is:

The value by simultion is 30.521C

CASE 4:

Long Tee Joint with hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C with the hot inlet velocity of 3m/s and momentum ratio 4.(Using K-Omega turbulence model)

Formula to find cold inlet velocity:

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

Substituting the known values,

4 = velocity at cold inlet/3

velocity at cold inlet = 12m/s.

We are going to perform the mesh dependent test and turbulence model test using the first case and use the results for the upcoming cases.

GEOMETRY:

SPACECLAIM:

Open the geometry file in spaceclaim to view.

Upload the above geometry in the space claim and follow the same method mentioned above and close space claim.

MESH(ELEMENT SIZE 0.0018):

Follow the same method for the mesh stated above.

Now the only change is that,The mesh element size has to be changed to 0.0018 from its default value.

Perform the quality check as mentioned above.Here you can see the quality as 0.21 which greater than 5% which states it is good.

check other parameters also.

SETUP:

Follow the same procedure as mentioned above but the only difference here is in viscous model we will be using K-Omega turbulence model and select SST option.

Select the same materials as mentioned above.

Give the boundary condition as same as stated above

After the procedure click on Calculate.

After calculation u will get the following results

RESIDUAL GRAPH:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF VELOCITY GRAPHS:

AREA WEIGHTED AVERAGE AND STANDARD DEVIATION OF TEMPERATURE GRAPHS:

POST PROCESSING:

CFD POST:

Follow the same procedures as mentioned above select the xy plane for the contour along the length

Contour plots along the length:

Contour plots across the length:

VELOCITY AND TEMPERATURE LINE GRAPHS ALONG THE LENGTH OF THE PIPE:

VELOCITY AND TEMPERATURE LINE GRAPHS ACROSS THE LENGTH OF THE PIPE:

RESULTS:

We know the manual value is 30.768C

The value by the simulation is:

The value by simulation is 27.553C.

REVIEW OF ALL THE CASES:

SHORT TEE JOINT

CASE.NO	MOMENTUM RATIO	MESH SIZE	NO.OF.CELLS	NO.OF.ITERATIONS	T(MIXTURE) OR AREA AVERAGED TEMPERATURE VALUE	MANUAL T(MIXTURE) VALUE
1.	2	0.0018	137296	210	30.457C	30.768C
2.	4	0.0018	137296	260	27.608C	30.768C

LONG TEE JOINT:

CASE.NO	MOMENTUM RATIO	MESH SIZE	NO.OF.CELLS	NO.OF.ITERATIONS	T(MIXTURE) OR AREA AVERAGED TEMPERATURE VALUE	MANUAL T(MIXTURE) VALUE
1.	2	0.0018	137296	140	30.521C	30.768C
2.	4	0.0018	137296	680	27.553C	30.768C

CONCLUSION:

MOMENTUM RATIO:

From the above simulations we can say that the momentum ratio influences the outlet temperature.Higher the momentum ratio reduses the temperature at the outlet.It means that the velocity at the cold inlet is increased the temperature at the outlet is decreased.We can also change the diameter of the inlet to influence the velocity.

EFFECT OF LENGTH:

We simulated with short tee joint and long tee joint to see the difference and to see the effect in length.It was found that almost the temperature at outlet was same with some little difference.By watchin the standard deviation graphs mentioned above in both cases we can say that the mixing in long tee joint is considered to be good compared to short tee joint.So varying the length does not give much change in the average outlet temperature.

For the faster manufacturing and cost-cutting process short tee joint is recommended.we can get the desired outlet temperature by adjusting the inlet velocities.

REFERENCES:

https://www.sciencedirect.com/science/article/pii/S0029549309005676