Week 1- Mixing Tee

Week 1- Mixing Tee

Aim:

To set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C.

To use the k-epsilon and k-omega SST model for the first case and based on the judgment to use the more suitable model for further cases.

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

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

1. Cell count
2. Average outlet temperature
3. Number of iterations for convergence

Expected results:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.
2. Velocity and temperature line plots along and across the length of the pipe.
3. Perform Mesh independent study for any one case.
4. Discuss the effect of length and momentum ratio on results.

Introduction:

Fluids are transported through flow sections. Flow sections of circular cross sections are known as pipes. Most fluid especially liquids are transported in circular pipes. This is because, pipes with a circular cross section can withstand large pressure differences between the inside and outside without significant distortion. A typical piping system involves pipes of different diameters connected to each other by various fittings (T-Junction, Y-Junction) or elbow to ensure continuous transport of the fluid. In tee-Joint Frictional losses could occur in pipe flow. Added to that with the difference in temperature of the fluid passing through the inlets (x and y axis) could create certain changes in the temperature of the flow when mixing happens.

Mixing problems, such as the design and scale-up of a mixer and quantification of mixing, have been traditionally tackled by developing empirical design equations mainly due to the complexity of the fluid dynamics of mixing. Although this approach has proven to be satisfactory for many applications, it is rather limited because it neglects the complexity of flow in most mixing applications. Applications where pipeline mixing with tees is used include low viscosity mixing such as wastewater treatment and blending of some oils (injection of additives) and petrochemical products. Other applications include blending of fuel gas, and mixing of feed streams for catalytic reactors. A tee is formed by two pipe sections joined at a right angle to each other. One stream passes straight through the tee while the other enters perpendicularly at one side.

Tee pipes are commonly used in piping systems and multi-channel network in various industries like electronic, petrochemical, nuclear plant etc, the mixing of hot fluid and cold fluid give rise to temperature fluctuation in the vicinity of mixing zone. The flow pattern of fluid gives necessary information such as area, where thermal zones are high. Using different momentum ratio, the efficiency of the model and its effectiveness is checked.

Given Data:

Hot air inlet temperature (x-inlet) `T_h`= 36°c

Cold air inlet temperature (y-inlet) `T_c`= 19°c

Hot air inlet velocity = 3 m/s

Momentum ratio = 2 and 4

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

Calculation:

Cold Inlet velocity Calculation:

Cold Inlet velocity for the momentum ratio = 2:

Velocity at cold inlet = Momentum Ratio * Velocity at hot inlet

Cold inlet velocity = 2 * 3 = 6 m/s

Cold Inlet velocity for the momentum ratio = 4:

Velocity at cold inlet = Momentum Ratio * Velocity at hot inlet

Cold inlet velocity = 4 * 3 = 12 m/s

Analytical Calculation:

Given data:

Diameter of the x-inlet = 0.0338781 m

Diameter of the y-inlet = 0.0169626 m

Diameter of the outlet = 0.0338781 m

Cross Sectional Area Calculation:

Cross sectional area of the x-inlet (hot air) = `(pi*(0.0338781)^2)/4`

Therefore, the cross-sectional area of the x-inlet = `9.013138*10^-4` m^2.

Cross sectional area of the y-inlet (cold air) = `(pi*(0.0169626)^2)/4`

Therefore, the cross-sectional area of the y-inlet = `2.259823*10^-4` m^2.

Cross sectional area of the mixed air outlet = `(pi*(0.0338781)^2)/4`

Therefore, the cross-sectional area of the mixed air outlet = `9.0.13138*10^-4` m^2.

Mass Flow Rate Calculation:

Mass flow rate of hot air = Density of the fluid * Cross sectional area of the x-inlet * Velocity of the fluid at x-inlet

Mass flow rate of hot air = 1.225 * 9.013138 * 10^-4 * 3

Mass flow rate of hot air `m_(hot)`= 0.003312 kg/s

Mass flow rate of cold air = Density of the fluid * Cross sectional area of the y-inlet * Velocity of the fluid at y-inlet (6 m/s)

Mass flow rate of cold air at 6 m/s = 1.225 * 2.259823 * 10^-4 * 6

Mass flow rate of cold air at 6 m/s `m_(c1)`= 0.001661 kg/s

Mass flow rate of cold air = Density of the fluid * Cross sectional area of the y-inlet * Velocity of the fluid at y-inlet (12 m/s)

Mass flow rate of cold air at 12 m/s = 1.225 * 2.259823 * 10^-4 * 12

Mass flow rate of cold air at 12 m/s `m_(c2)`= 0.003322 kg/s

Calculating the velocity at mixed outlet:

For y-inlet velocity of 6 m/s:

Velocity at mixed outlet = (Mass flow rate of hot air + Mass flow rate of cold air at 6 m/s)/(Density of the fluid + Cross sectional area of the mixed outlet)

Velocity at mixed outlet =`(0.003312 + 0.001661)/(1.225+9.013138*10^-4)`

Therefore, Velocity at mixed outlet = 4.504358 m/s.

For y-inlet velocity of 12 m/s:

Velocity at mixed outlet = (Mass flow rate of hot air + Mass flow rate of cold air at 12 m/s)/(Density of the fluid + Cross sectional area of the mixed outlet)

Velocity at mixed outlet =`(0.003312 + 0.003322)/(1.225+9.013138*10^-4)`

Therefore, Velocity at mixed outlet = 6.008705 m/s.

Calculating the mixed outlet temperature:

For y-inlet velocity of 6 m/s:

Temperature at mixed outlet = `((m_h*T_h)+(m_(c1)*T_c))/(m_h+m_(c1))`

By substituting the values we get,

Temperature at mixed outlet = `((0.003312*36)+(0.001661*19))/(0.003312+0.001661`

Temperature at mixed outlet for the velocity of 6 m/s at y-inlet = 30.32°c

For y-inlet velocity of 12 m/s:

Temperature at mixed outlet = `((m_h*T_h)+(m_(c2)*T_c))/(m_h+m_(c2))`

By substituting the values we get,

Temperature at mixed outlet = `((0.003312*36)+(0.003322*19))/(0.003312+0.003322`

Temperature at mixed outlet for the velocity of 12 m/s at y-inlet = 27.48°c.

Case 1

Short mixing tee with a hot inlet velocity of 3m/s.

Momentum ratio of 2, 4.

Geometry setup:

• The Ansys Workbench software was launched and under the Analysis systems "Fluid Flow (Fluent) was chosen. Rename the project according to the case.
• Right click on the "Geometry" and select "Import geometry" and select the "STEP" file of the particular case.
• After the file selection double click on the geometry so that we could modify the geometry as per the requirements.

• We need to create the wet region for setting up the fluid flow simulation. This can be done by using the following command. Prepare --> Volume Extract --> Select the Select Edges option --> Select the open edges and Select the green tick option so as to form the fluid flow region.
• After the formation of the wet region the solid region is need to be suppressed. The fluid flow region is displayed as follows.

• Once the geometry preparation is done, we have to create a named selection and meshing parameters under the Mesh category.
• For creating a named selection fix the selection mode to Face Selection. Select the faces and create the named selection.

The created named selections are as follows.

Y-inlet:

X-inlet:

Walls:

Outlet:

• In order to mesh the geometry, click on mesh and select the desired meshing parameters and click on generate mesh.

In this case we have set the element size to be 3e-3. The created mesh for the geometry is as follows.

Mesh Quality and Mesh Metrics:

Mesh Statistics:

After setting up the mesh close the mesh tab and update the mesh category for further proceedings.

Case Setup:

For the case 1 we have assigned the y-inlet velocities of 6 m/s and 12 m/s. Added to that in order to select the accurate model, we are using K-Epsilon and K-Omega SST models for comparison.

K-epsilon model:

• Open the "Setup". Once the setup is open click on General --> Units --> Temperature --> Select Celsius. Set the Solver Type as Pressure Based and Absolute under Velocity formulation.
• Under Models parameter check the energy equation box as we are involved in studying the temperature effectiveness. Under Viscous select the k-epsilon model and click ok.
• Then under Material set the fluid to be air.
• Under Cell Zone Conditions make sure that the selected fluid is air.
• Select the Boundary Conditions parameter and set the boundary conditions for the created named selections.

X-inlet:

Select the type to be velocity-inlet and assign the velocity and temperature of the fluid.

Y-inlet:

Select the type to be velocity-inlet and assign the velocity and temperature of the fluid.

Walls:

Retain the default values for walls.

Outlet:

Select the type to be pressure-outlet and make sure the pressure is set to atmospheric condition.

• Then under Report Definitions select the parameters that are needed to be calculated.
• Then under Initialization select the initialization method as Hybrid and then select initialise button.
• Then under Run Calculation parameter enter the desired number of iterations and click on calculate.

For Momentum ratio = 2.

Reports:

Scaled Residual:

Area Weighted Average of temperature:

Standard Deviation of temperature:

The velocity at the outlet is computed to be 4.504217 m/s

The temperature at the outlet is computed to be 30.33838°c

Temperature contour along the mid plane:

Velocity Profile along mid plane:

Temperature contour across the outlet:

Velocity contour across the outlet:

Temperature contour across the body at different locations:

Velocity contour across the body at different locations:

Temperature plot along the mid plane

Velocity plot along the mid plane:

Temperature plot across the outlet:

Velocity plot across the outlet:

K-omega SST model:

The K-omega SST model was selected under Models --> Viscous parameters.

Reports:

Scaled Residual:

Area Weighted Average of temperature:

Standard Deviation of temperature:

The velocity at the outlet is computed to be 4.509521 m/s

The temperature at the outlet is computed to be 30.34256°c

Temperature contour along the mid plane:

Velocity Profile along mid plane:

Temperature contour across the outlet:

Velocity contour across the outlet:

Temperature contour across the body at different locations:

Velocity contour across the body at different locations:

Temperature plot along the mid plane

Velocity plot along the mid plane:

Temperature plot across the outlet:

Velocity plot across the outlet:

Comparison of values between the Computational and Analytical Calculation:

K-epsilon Model:

The velocity at the outlet is computed to be 4.504217 m/s

The temperature at the outlet is computed to be 30.33838°c

K-omega SST Model:

The velocity at the outlet is computed to be 4.509521 m/s

The temperature at the outlet is computed to be 30.34256°c

Analytical Calculation:

The velocity at outlet = 4.504358 m/s.

The temperature at outlet = 30.32°c

RANS Model Selection:

Generally, k-epsilon turbulence model is used for the free stream simulations and k-omega SST turbulence model is for capturing the phenomenon from the turbulence sublayer. Here our interest is free stream properties thus k-epsilon model is preferred over k-omega SST turbulence model. Also, it could be observed from the above comparison that the results from k-omega SST model have relatively larger errors and higher standard deviation values for outlet temperature than the results from k epsilon turbulence models thus k-epsilon turbulence model is considered for further simulations.

For Momentum Ratio = 4

Y-inlet:

Select the type to be velocity-inlet and assign the velocity and temperature of the fluid.

Reports:

Scaled Residual:

Area Weighted Average of temperature:

Standard Deviation of temperature:

The velocity at the outlet is computed to be 6.046101 m/s

The temperature at the outlet is computed to be 27.57612°c

Temperature contour along the mid plane:

Velocity Profile along mid plane:

Temperature contour across the outlet:

Velocity contour across the outlet:

Temperature contour across the body at different locations:

Velocity contour across the body at different locations:

Temperature plot along the mid plane

Velocity plot along the mid plane:

Temperature plot across the outlet:

Velocity plot across the outlet:

Case 2

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

The geometry setup is done the same as setup done for short mixing tee.

The extracted wet region is as follows.

The regions are named after the wet region extraction.

Mesh:

Mesh Quality and Mesh Metrics:

Mesh statistics:

After setting up the mesh close the mesh tab and update the mesh category for further proceedings.

• Open the "Setup". Once the setup is open click on General --> Units --> Temperature --> Select Celsius. Set the Solver Type as Pressure Based and Absolute under Velocity formulation.
• Under Models parameter check the energy equation box as we are involved in studying the temperature effectiveness. Under Viscous select the k-epsilon model and click ok.
• Then under Material set the fluid to be air.
• Under Cell Zone Conditions make sure that the selected fluid is air.
• Select the Boundary Conditions parameter and set the boundary conditions for the created named selections.

X-inlet:

Select the type to be velocity-inlet and assign the velocity and temperature of the fluid.

Y-inlet:

Select the type to be velocity-inlet and assign the velocity and temperature of the fluid.

Walls:

Retain the default values for walls.

Outlet:

Select the type to be pressure-outlet and make sure the pressure is set to atmospheric condition.

• Then under Report Definitions select the parameters that are needed to be calculated.
• Then under Initialization select the initialization method as Hybrid and then select initialise button.
• Then under Run Calculation parameter enter the desired number of iterations and click on calculate.

For Momentum ratio = 2.

Reports:

Scaled Residual:

Area Weighted Average of temperature:

Standard Deviation of temperature:

The velocity at the outlet is computed to be 4.504486 m/s

The temperature at the outlet is computed to be 30.420909°c

Temperature contour along the mid plane:

Velocity Profile along mid plane:

Temperature contour across the outlet:

Velocity contour across the outlet:

Temperature contour across the body at different locations:

Velocity contour across the body at different locations:

Temperature plot along the mid plane:

Velocity plot along the mid plane:

Temperature plot across the outlet:

Velocity plot across the outlet:

For Momentum ratio = 4

Reports:

Scaled Residual:

Area Weighted Average of temperature:

Standard Deviation of temperature:

The velocity at the outlet is computed to be 6.022326 m/s

The temperature at the outlet is computed to be 27.47948°c

Temperature contour along the mid plane:

Velocity Profile along mid plane:

Temperature contour across the outlet:

Velocity contour across the outlet:

Temperature contour across the body at different locations:

Velocity contour across the body at different locations:

Temperature plot along the mid plane:

Velocity plot along the mid plane:

Temperature plot across the outlet:

Velocity plot across the outlet:

Mesh Independent study:

Geometry: Long Mixing Tee

Mesh size: 1.3853e-2

Mesh statistics:

Model: K-epsilon

Momentum ratio: 2

Reports:

Scaled Residual:

Area Weighted Average of temperature:

Standard Deviation of temperature:

The velocity at the outlet is computed to be 4.493143 m/s

The temperature at the outlet is computed to be 30.26125°c

Temperature contour along the mid plane:

Velocity Profile along mid plane:

Temperature contour across the outlet:

Velocity contour across the outlet:

Temperature contour across the body at different locations:

Velocity contour across the body at different locations:

Temperature plot along the mid plane:

Velocity plot along the mid plane:

Temperature plot across the outlet:

Velocity plot across the outlet:

Comparison:

Effect of Length and Momentum ratio on results:

Case 1(Short Mixing Tee):

Temperature:

Velocity:

1. The average outlet velocity of the k-epsilon model of momentum ratio - 2 is 4.504217 m/s

2. The average outlet velocity of the k-epsilon model of momentum ratio - 4 is 6.046101 m/s

Case 2(Long Mixing Tee):

Temperature:

1. The average outlet temperature of the k-epsilon model of momentum ratio - 2 is 30.420909⁰C

2. The average outlet temperature of the k-epsilon model of momentum ratio - 4 is 27.47948⁰C

Velocity:

1. The average outlet velocity of the k-epsilon model of momentum ratio - 2 is 4.504486 m/s

2. The average outlet velocity of the k-epsilon model of momentum ratio - 4 is 6.022326 m/s

Analytical Calculation:

Short Mixing Tee:

The velocity at outlet = 4.504358 m/s

The temperature at outlet = 30.32°c

Long Mixing Tee:

The velocity at outlet = 6.008705 m/s

The temperature at outlet = 27.4876°c

By comparing the above cases we could observe that, there is no much difference in the outlet temperature and velocity. So, the change in the length of the pipe should not affect the mixing of the flow. If the velocity increases the temperature is reduced at the outlet. Which means if the momentum ratio is increased the temperature decreases.

Observation table:

Conclusion:

• The flow in a mixing tee geometry was simulated successfully using Ansys Fluent Software.
• The flow in a mixing tee geometry was also calculated analytically for the comparison with the computational results.
• The wet region (fluid flowing region) was extracted and the regions are named successfully. Once the naming is done the geometry is meshed under certain parameters and finally the case is setup.
• The first case is setup with K-epsilon and k-omega SST models to choose which have the most effectiveness with the analytically calculated value.
• By comparing the computational results with the analytical results, K-epsilon model is more suitable for this type of simulation as this flow doesn't involve boundary layer or surface phenomenon.
• The study of flow in short mixing tee and long mixing tee have no difference in the outlet velocity and temperature. This means that, the change in the length of the pipe should not affect the mixing of the flow.
• The cold stream velocity from the inlet-y creates an impact on the outlet temperature. If the velocity is increased in the inlet-y the temperature decreases significantly.
• From the mesh independent study we could observe that if we use a coarse mesh, the computational time is getting lower but when we compare the results with the finer mesh and analytical value we could observe a lot of change in the value.
• The contour plots along the pipe and across the pipe was displayed. The temperature and velocity plot along and across the pipe was also displayed.