Mixing efficiency

Objective: Compare the Steady State Analysis results of mixing tee with different length and momentum ratios and write a detailed report explaining the results obtained.

Question:

For this challenge, we have created two versions of the mixing tee. One of them is longer than the other.

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

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. Giving the reason for choosing a suitable model is compulsory.

• Case 1

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

• 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, compare the following values from the 2 cases.

• Cell count
• Average outlet temperature
• Number of iterations for convergence

Expected results:

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

For each simulation, you need to show the convergence plot

Introduction:

A Mixing Tee is used to mix the two different temperature fluids. A Mixing Tee is formed by two pipe sections joined at a right angle to each other. A good mixing happens when Standard deviation of outlet temperature is low. A good mixing can be achieved through either increasing the length of the tube or increasing the inlet velocity. In this challenge, the ANSYS fluent analysis is going to be performed for different length of mixing tees and different values of momentum ratio.

Two Turbulence model use in this analysis are:

Standard k-epsilon: The baseline two-transport-equation model solving for kinetic energy k and turbulent dissipation ε. Turbulent dissipation is the rate at which velocity fluctuations dissipate.

In the standard k-ε model, the eddy viscosity is determined from a single turbulence length scale, so the calculated turbulent diffusion is that which occurs only at the specified scale, whereas in reality, all scales of motion will contribute to the turbulent diffusion. The k-e model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity.

Performs poorly for complex flows involving severe pressure gradient, separation, strong streamline curvature. The most disturbing weakness is lack of sensitivity to adverse pressure gradients; another shortcoming is numerical stiffness when equations are integrated through the viscous sublayer which is treated with damping functions that have stability issues

Standard k-omega: A two-transport-equation model solving for kinetic energy k and turbulent frequency ω. This is the default k–ω model. This model allows for a more accurate near-wall treatment with an automatic switch from a wall function to a low-Reynolds number formulation based on grid spacing. Demonstrates superior performance for wall-bounded and low Reynolds number flows. Shows potential for predicting transition. Options account for transitional, free shear, and compressible flows.

Geometry:

Extracting Volume for performing simulation:

Mesh:

Element size of 5 mm is used and also in element quality checkup , all the elements are lying above 5% so we are good to run the simulation.

Named selection:

For Short Tee,

Case: 1 MR=2 with K epsilon Realizable

Boundary conditions:

• Inlet_x: Velocity: 3 m/s Temperature: 36°C
• Inlet_y: Velocity: 6 m/s Temperature: 19°C
• Outlet: Gauge pressure = 0 pascal

Convergence residual plots:

No. of Iterations to conevrge = 250.

Area-weighted average of temperature:

Area-weighted average of temperature is 30.251°C

Standard deviation of temperature:

Standard deviation of temperature is 1.422°C

Temperature contour with line chart along length of pipe:

Temperature contour with line chart across diameter of pipe:

Velocity contour with line chart along length of pipe:

Velocity contour with line chart across diameter of pipe:

Case: 2 MR=4 with K epsilon Realizable

Boundary conditions:

• Inlet_x: Velocity: 3 m/s Temperature: 36°C
• Inlet_y: Velocity: 12 m/s Temperature: 19°C
• Outlet: Gauge pressure = 0 pascal

Convergence residual plots:

No. of Iterations to conevrge = 200.

Area-weighted average of temperature:

Area-weighted average of temperature is 27.547°C

Standard deviation of temperature:

Standard deviation of temperature is 1.374°C

Temperature contour with line chart along length of pipe:

Temperature contour with line chart across diameter of pipe:

Velocity contour with line chart along length of pipe:

Velocity contour with line chart across diameter of pipe:

Case: 3 MR=2 with K omega SST

Boundary conditions:

• Inlet_x: Velocity: 3 m/s Temperature: 36°C
• Inlet_y: Velocity: 6 m/s Temperature: 19°C
• Outlet: Gauge pressure = 0 pascal

Convergence residual plots:

No. of Iterations to conevrge = 225.

Area-weighted average of temperature:

Area-weighted average of temperature is 30.25°C

Standard deviation of temperature:

Standard deviation of temperature is 1.99°C

Temperature contour with line chart along length of pipe:

Temperature contour with line chart across diameter of pipe:

Velocity contour with line chart along length of pipe:

Velocity contour with line chart across diameter of pipe:

Case: 4 MR=4 with K omega SST

Boundary conditions:

• Inlet_x: Velocity: 3 m/s Temperature: 36°C
• Inlet_y: Velocity: 12 m/s Temperature: 19°C
• Outlet: Gauge pressure = 0 pascal

Convergence residual plots:

No. of Iterations to conevrge = 130.

Area-weighted average of temperature:

Area-weighted average of temperature is 27.577°C

Standard deviation of temperature:

Standard deviation of temperature is 1.55°C

Temperature contour with line chart along length of pipe:

Temperature contour with line chart across diameter of pipe:

Velocity contour with line chart along length of pipe:

Velocity contour with line chart across diameter of pipe:

The k-ε model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. Whereas k-ω Solves one equation for turbulent kinetic energy k and a second equation for the specific turbulent dissipation rate (or turbulent frequency) ω. This model performs significantly better under adverse pressure gradient conditions.

The k-ω model predicts well near the wall and also mixing can be seen in k-ω turbulent model . Therefore K-ω is selected for future calculations.

For Long Tee

Geometry:

Mesh:

Element size is 5 mm with quality greater than 5%.

Case: 1 MR=2

Boundary conditions:

• Inlet_x: Velocity: 3 m/s Temperature: 36°C
• Inlet_y: Velocity: 6 m/s Temperature: 19°C
• Outlet: Gauge pressure = 0 pascal

Convergence residual plots:

No. of Iterations to conevrge = 225.

Area-weighted average of temperature:

Area-weighted average of temperature is 30.34°C

Standard deviation of temperature:

Standard deviation of temperature is 1.11°C

Temperature contour with line chart along length of pipe:

Temperature contour with line chart across diameter of pipe:

Velocity contour with line chart along length of pipe:

Velocity contour with line chart across diameter of pipe:

Case: 2 MR=4

Boundary conditions:

• Inlet_x: Velocity: 3 m/s Temperature: 36°C
• Inlet_y: Velocity: 6 m/s Temperature: 19°C
• Outlet: Gauge pressure = 0 pascal

Convergence residual plots:

No. of Iterations to conevrge = 275.

Area-weighted average of temperature:

Area-weighted average of temperature is 27.49°C

Standard deviation of temperature:

Standard deviation of temperature is 0.74°C

Temperature contour with line chart along length of pipe:

Temperature contour with line chart across diameter of pipe:

Velocity contour with line chart along length of pipe:

Velocity contour with line chart across diameter of pipe:

Comparing Short and Long Tee with K omega model:

	Short Tee with k omega		Long Tee with k omega
	MR=2	MR=4	MR=2	MR=4
Average Weighted Temperature (outlet)	30.25	27.577	30.34	27.49
Cell count	14247	14247	17771	17771
Number of Iteration to Converge	225	130	225	275
Standard Deviation of Temperature (outlet)	1.99	1.55	1.11	0.74

Mesh independent study:

Long Tee Using the K-omega model with momentum ratio 4

Boundary Condition

Hot inlet velocity -3m/s

Cold inlet Velocity-12m/s

Hot inlet temperature 36°C and cold inlet temperature 19°C

Mesh size -7mm, 4mm, 3mm

7mm

Convergence residual plots:

No. of Iterations to conevrge = 200.

Area-weighted average of temperature:

Area-weighted average of temperature is 27.48°C

Standard deviation of temperature:

Standard deviation of temperature is 0.76°C

Area-weighted average of velocity:

Area-weighted average of velocity is 6.051 m/s

4 mm

Convergence residual plots:

No. of Iterations to conevrge = 350.

Area-weighted average of temperature:

Area-weighted average of temperature is 27.51°C

Standard deviation of temperature:

Standard deviation of temperature is 0.86°C

Area-weighted average of velocity:

Area-weighted average of velocity is 6.035 m/s

3 mm

Convergence residual plots:

No. of Iterations to conevrge = 500.

Area-weighted average of temperature:

Area-weighted average of temperature is 27.54°C

Standard deviation of temperature:

Standard deviation of temperature is 0.64°C

Area-weighted average of velocity:

Area-weighted average of velocity is 6.039 m/s

Comparing results of different mesh sizes:

	7mm	4mm	3mm
Average Weighted Temperature (outlet)	27.54	27.51	27.54
Cell Count	15384	29071	56334
Average Weighted velocity (outlet)	6.051	6.035	6.039
Standard Deviation of Temperature (outlet)	0.76	0.86	0.64

By varying the element size and making mesh finer we can observe that by changing element size from 4 to 3 mm Average weighted temperature and Average weighted velocity remains almost constant. Thus by this we can conclude that grid dependency is achieved further refinement of mesh will not affect the results much it will just increase number of element and computational time.

Conclusion:

After reviewing all the above cases it is conformed that increase in length resulted in the better mixing of fluid although there is not much difference in average outlet temperature with specific momentum ratio. The standard deviation of the longer tee is lesser than the shorter tee in all the conditions. We can see the phenomena clearly in the figure shown above. There are more orange zones in a shorter tee than the longer tee.

But with the higher momentum ratio not only the mixing of fluids happened efficiently but even there is a significant drop in the average outlet temperature.

Longer Tee with a higher momentum ratio produced a better result than rest other cases.