Mixing efficiency

Mixing Tee Simulation

Aim: Steady-state simulation of mixing tee with different momentum ratio and length to fluid mixing phenomenon and outlet temperature.

Physical model and simulation detail:

In the present study, a mixing tee geometry and meshing has been done in Ansys V. 20 to investigate the effectiveness of fluid velocity at outlet temperature. Grid independent, as shown in fig. 1 test has been done to ensure the reliability of obtained results and to read small property variation. A uniform grid size of 2 mm is taken in a radial direction as well in axial direction respectively. A total of 10,5858 numbers of elements as a grid-independent element is found.

Figure 1. Grid independence study.

Figure 2. Mesh cross-section view.

The governing equations for mass, momentum and energy are solved employing the CFD code. A 3-D geometry was prepared and transient simulation was carried out, where the implicit-coupled finite-volume method was used to discretize the governing equations. The coupled algorithm was used to solve the coupling model between velocity and pressure. The momentum and energy terms in the governing equations are iterated with a second-order upwind scheme that uses the upstream values and gradients to compute the control volume face values. For turbulence, Realizable k-epsilon turbulence model parameters (k-ε model.) are also iterated with a first-order upwind scheme. The second-order scheme is used to discretize the pressure term. No-slip boundary condition is used on the pipe walls. For the near-wall treatment, a standard wall function has been assumed in case of turbulent flow. Axial conduction and viscous dissipation in the fluid are considered, while axial conduction along the tube wall is incorporated as well. Convergence is obtained when various residuals of the parameters (temperature, velocity, pressure, etc.) change with the iterations within a pre-set convergence criterion of 10^-3 for the residuals of continuity equation and 10^-5 for the energy equation. Conservation of mass and energy are also checked for all the cases in the analysis.

Reason for selecting the k-ε model for analysis.

Figure 3. Turbulence diagram.

For this simulation, both the turbulence model almost show the same effect (shown in fig. 3.). I preferred the k-ε model because this technique offers good convergence and isn’t memory-intensive. However, the k-ω model is also susceptible to inlet boundary conditions, which is a disadvantage not seen in k-epsilon as well as it has the difficulty of convergence compared to k- ε model.

Results and discussion

Case 1: Short mixing tee

a. Residual Graphs

a b

Figure 4. Residual plot for short mixing tee (a) momentum ratio=2 (b) momentum ratio=4

b. Temperature contour

a b

Figure 5. Temperature contour for short mixing tee (a) momentum ratio=2 (b) momentum ratio=4

c. Velocity Contour

a b

Figure 6. Velocity contour for short mixing tee (a) momentum ratio=2 (b) momentum ratio=4

d. Velocity-temp line

a b

Figure 6. Velocity temperature line contour for short mixing tee (a) momentum ratio=2 (b) momentum ratio=4

e. Temperature line and Velocity line diagram

a b

Figure 7. Line diagram for short mixing tee (a) Temperature (b) Velocity

Case 2: Long mixing tee

a. Residual Graphs

a b

Figure 8. Residual plot for long mixing tee (a) momentum ratio=2 (b) momentum ratio=4

b. Temperature Contour

a b

Figure 9. Temperature contour for long mixing tee (a) momentum ratio=2 (b) momentum ratio=4

c. Velocity contour

a b

Figure 10. Velocity contour for long mixing tee (a) momentum ratio=2 (b) momentum ratio=4

d. Velocity-temp line

a b

Figure 10. Velocity temperature line contour for short mixing tee (a) momentum ratio=2 (b) momentum ratio=4

Table:1- Detail of simulation results.

	Short Mixing Tee	cell count	Outlet Temp	convergence
2 mm mesh	2 m.r.	105858	30.3	250
	4 m.r.	105858	27.5	300
	Long Mixing Tee
3 mm mesh	2 m.r.	56373	30.3	330
	4 m.r.	56373	27.5	330

Conclusion:

It is evident from the temperature contour that with the increase of momentum ratio (m.r.) outlet temperature is decreasing. The outlet temperature of m.r.=2 is equal to 30.3 ºC, while for m.r.=4 it is equal to 27.5 ºC. Mixing tee length has no significant effect on outlet temperature.