Mixing efficiency in T-junction

Mixing in T-junction is used in several places like aerospace, refrigeration, nuclear reactors etc. It is direct contact heat exchanger. Generally, it is preffered for turbulent mixing.

Case 1:

In this study our aim is to find the mixing efficiency of short mixing tee. It is given that incoming hot and cold air has inlet temperature of 36⁰C & 19⁰C respectively. Hot air enters from horizontal inlet and cold air from vertical inlet. The geometry shown in the figure below is made using ANSYS SPACECLAIM.

Now, solid volume is extracted from the model. It is shown in figure below:

Before meshing is done, we apply name selections. This helps us later in setting boundary conditons. the name selection usedin this study are shown below.

Meshing is performed using body element size of 0.002 m as shown below:

Element quality is one of the important paramter to check the quality of mesh. It is checked in mesh metric. The element quality generated in this simulation is shown below. Here, most of the elememts generated are of high quality which are lying in the range of 0.7 - 1.0. Since, most of the elements are of good quality it can lead to expected results.

In setup, Turbulence k-epsilon model is selected to solve the governing equations. Since, we are calculating the final temperature so the energy equations box is also checked. Rest of the settings are left to default.

Velocity inlet and Pressure outlet boundary conditions are used to solve the equations. Fluid used is air.

The boundary conditions used here are:

Inlet Velocity of hot fluid = 3m/s

Inlet Temperature of hot fluid = 36⁰C

Inlet Velocity of cold fluid = 1.5m/s

Inlet Temperature of cold fluid = 19⁰C

Pressure at outlet is 0 gaunge.

Average surface temperature at outlet and standard deviation at outlet are plotted, they both are reduced to a constant value of 30.54 ⁰C and 2 ⁰C. The residuals have also decreased till certain value and became constant.

The mesh size is futher reduced to 0.0015 m. Now, average surface temperature at outlet and standard deviation at outlet obtained are 30.64⁰C and 2⁰C. The percentage variation in average surface temperature at outlet is about 0.3%, this is in feasible range thus the solution is grid independent.

After Post processing the data, the temperature and velocity plot obtained are shown below.

Outlet interface temperature and velocity are also shown below.

It is also simulated using k-omega SST model with same boundary conditions.Average surface temperature and standard deviation at outlet obatined are 34 ⁰C and 2.5 ⁰C. Average surface temperature at outlet is shown below.

The theoritical value of mixture temperature is obtained using formulae below.

• Theoritical mixture temperature obtained at outlet is 27.5 ⁰C.
• Average surface temperature at outlet obtained by Turbulence k-epsilon model is 30.54 ⁰C.
• Average surface temperature at outlet obtained by Turbulence k-omega SST model is 34 ⁰C.

Results(Outlet temperature) obtained by Turbulence k-epsilon model is closer to theoritical value. Hence, Turbulence k-epsilon model gives better results Turbulence k-omega SST model. Further in this study only Turbulence k-epsilon model is used in simultaion.

Case 2:

In this study our aim is to find the mixing efficiency of long mixing tee. It is given that incoming hot and cold air has inlet temperature of 36⁰C & 19⁰C respectively. Hot air enters from horizontal inlet and cold air from vertical inlet. The geometry shown in the figure below is made using ANSYS SPACECLAIM.

Now, solid volume is extracted from the model. It is shown in figure below:

Before meshing is done, we apply name selections. This helps us later in setting boundary conditons. the name selection usedin this study are shown below.

Meshing is performed using body element size of 0.002 m as shown below:

The element quality generated in this simulation is shown below. Here, most of the elememts generated are of high quality which are lying in the range of 0.7 - 1.0. Since, most of the elements are of good quality it can lead to expected results.

In setup, Turbulence k-epsilon model is selected to solve the governing equations. Since, we are calculating the final temperature so the energy equations box is also checked. Rest of the settings are left to default.

Velocity inlet and Pressure outlet boundary conditions are used to solve the equations. Fluid used is air.

The boundary conditions used here are:

Inlet Velocity of hot fluid = 3m/s

Inlet Temperature of hot fluid = 36⁰C

Inlet Velocity of cold fluid = 1.5m/s

Inlet Temperature of cold fluid = 19⁰C

Pressure at outlet is 0 gaunge.

Average surface temperature at outlet and standard deviation at outlet are plotted, they both are reduced to a constant value of 34.10 ⁰C and 2.5 ⁰C.The residuals have also decreased till certain value and became constant.

The mesh size is futher reduced to 0.0015 m. Now, average surface temperature and standard deviation at outlet becomes 34.13 ⁰C and 3⁰C. The percentage variation in average surface temperature at outlet is about 0.1%, this is in feasible range thus the solution is grid independent.

After Post processing the data, the temperature and velocity plot obtained are shown below.

Outlet interface temperature and velocity are also shown below.

• Theoritical mixture temperature obtained at outlet is 27.5 ⁰C.
• Average surface temperature at outlet obtained by Turbulence k-epsilon model is 3 ⁰C.

	Short mixing tee	Long mixing tee
Cell count	463268	637076
Average outlet temperature (0C)	30.64	34.13
Number of iterations for convergence	200	250

When Momentum ratio is increased to 2:3. Average surface temperature at outlet becomes 33.51⁰C.

Momentum ratio	Outlet temperature (0C)
2:3	33.51
3:4	33.27

CONCLUSION

• Mixing in short tee is more effective than in long tee. It can be seen from results that as the length of the tee increases the mixing effectiveness decreases. As the length increases, the outlet temperature increases thus deviating from the theoritical value.
• Momentum ratio also affects the Outlet temperature. As we increase momentum ratio, outlet temperature decreases, taking it towards theoritical predicted value.

This challenge was great but it is no where mentioned to simulate for different momentum ratios.