Thermal Mixing Efficiency in T-junction

1.Problem Specifications

This simulation considers the thermal mixing of hot and cold fluid at different flow rate to study the mixing effectivness in T-junction.

Three dimensional steady state analysis is performed using Ansys Fluent for three cases.

Case 1-Short mixing tee with hot inlet velocity of 3m/s and momentum ratio of 2.

so, cold inlet velocity=2 x 3

=6 m/s

Case 2-Long mixing tee with hot inlet velocity of 3m/s and momentum ratio of 2.

so, cold inlet velocity=2 x 3

=6 m/s

Case 3-Short mixing tee with hot velocity of 3m/s and momentum ration of 4.

so, cold inlet velocity=4x 3

=12 m/s

For all the above three cases temperature of hot fluid is taken as 300K and temperature of cold fluid is taken as 283.15K.

2.Pre-Analysis

2.1 Governing Equations:

The governing equation we solved here are Reynolds Averaged Navier Stokes Equations, which consists of continuity,momentum and energy equation.

2.2 Numerical Solutions Procedure Methods

Ansys fluent converts above (RANS) into huge set of algebraic equations. These algebraic equations are then inverted using iterative process to get the value of velocities(u,v,w), pressure (p)and temperature(T) at cell centres. Everything else is derived from these cell centres values.

3. Geometry

The mixing tee file is imported in the SpaceClaim. Then volume is extracted, as it is the domain over which the equations are solved.

Fig 3.1-Short mixing tee for case1 and case3

Fig 3.2-Long mixing tee for case2

4. Mesh Generation

The mesh generation process is done by trail and error method and mesh independency test is performed to achieve the good quality mesh so that solving the governing equations does not become computationally expensive.

4.1 Case 1 and Case 3 Final Mesh:

Fig 4.1- Final Mesh(front view)

Fig 4.2- Close up view of Mixing region

4.2 Case 2 Final Mesh:

Fig 4.3- Final Mesh(front view)

Fig 4.4- Close up view around the mixing region

5.Solver Setup

5.1 Solution Modelling:

Steady:pressure based:Energy:Reliazable k-ε:standard wall function

5.2 Materials:

Air

5.3 Boundary conditions:

6. Results

6.1 Grid indepency test data:

Four different meshes have been tested for Case 1 to achieve the convergence of residuals.

6.2 Datas obtained for all three cases

6.3 Convergence plot

Case1:

Fig 6.1- Resiuals vs number of iterations

Fig 6.2- Average temperature at outlet vs number of iteration

Case 2:

Fig 6.4- Resiuals vs number if iterations

Fig 6.5- Average temperature at outlet vs number of iteration

Case 3:

Fig 6.5- Resiuals vs number if iterations

Fig 6.6- Average temperature at outlet vs number of iteration

6.4 Temperature and Velocity distributions

Case 1:

Fig 6.7- Temperature distribution on the plane though the middle of the pipe

Fig 6.8- velocity distribution on the plane though the middle of the pipe

Case 2:

Fig 6.9- Temperature distribution on the plane though the middle of pipe

Fig 6.10 - velocity distribution on the plane though the middle of the pipe

Case 3:

Fig 6.11- Temperature distribution on the plane though the middle of pipe

Fig 6.12- velocity distribution on the plane though the middle of the pipe

7. Conclusion

The investigations have shown that

• For the same momentum ratio and the same temperature difference between the hot and cold fluid, the length of main pipe has negligible effect on the thermal mixing efficiency of cold and hot fluid as seen from the value of average temperature at the outlet. Since case1 and case2 has the different length of main pipe for same momenum ratio of 2 but the average outlet temperature is 294.5K in both cases.
• For the same length of main pipe, for same temperature difference between hot and cold fluid but with different momentum ratio, it is seen that thermal mixing efficiency changes. As the momentum ratio increases (ratio of velocity of cold fluid to hot fluid), the thermal mixing becomes more efficient.Because it is seen that when the momentum ratio is increased in Case3, the average outlet temperature drops from 294.5K in case1 to 291.5 in case 3.
• As the flow develops in the main pipe after intermixing, there is additional mixing due to diffusion but it is not dominant.