Comparing the effectiveness of mixing tee for different momentum ratio.

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

Abstract: The steady-state simulation will be set up for the two cases by choosing the suitable turbulence model.

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

Application of mixing tee

Application where pipeline mixing with tee includes 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.

Geometry description

A tee is formed by joining two pipe sections at the right angle to each other. One stream passes straight through the tee (hot inlet air with a velocity of 3 `frac{m}{sec}` at a temperature of `36^@C` while the other enters perpendicularly at one side (cold inlet air with the varying velocity at a temperature of `19^@C`). The velocity at the cold inlet is increased to observe the effect of the mixing of air at the outlet.

The first set of simulations is carried for the default mesh size in "ANSYS-FLUENT" with varying turbulence models (`k-omega` and `k-epsilon`) to know the suitable turbulence model.

Case-1: Short tee

Default mesh size: 0.01029

Number of elements: `12760`

Momentum ratio:2

Turbulence model: `k-epsilon`

• Resulting geometry

• Residual plot

• Standard deviation of temperature

• Temperature at the outlet

• Velocity at the outlet

Contour

• Temperature plot

• Velocity plot

Case-1(a): Short tee

Default mesh size: 0.01029

Number of elements: `12760`

Momentum ratio:2

Turbulence model: `k-omega`

• Residual plot

• Standard deviation of temperature

• Temperature at the outlet

• Velocity at the outlet

Conclusion

It can be inferred that the `k-epsilon` is best suited for flow away from the wall whereas `k-omega` is best suited for near the wall-flow region, in this project we are not dealing with the wall, so for further simulation `k-epsilon` will be used.

Case-1(b): Short tee

Default mesh size: 0.002

Momentum ratio:2

Turbulence model: `k-epsilon`

Number of elements: `105865`

• Resulting geometry

• Residual plot

• Standard deviation of temperature

• Temperature at the outlet

• Velocity at the outlet

Contour

• Temperature plot

• Velocity plot

Case-1(c): Short tee

Default mesh size: 0.002

Momentum ratio:4

Turbulence model: `k-epsilon`

Number of elements: `105865`

• Residual plot

• Standard deviation of temperature

• Temperature at the outlet

• Velocity at the outlet

Contour

• Temperature plot

• Velocity plot

Case-2(a): Long Tee

Default mesh size: 0.002

Momentum ratio:2

Turbulence model: `k-epsilon`

Number of elements: `140272`

• Resulting geometry

• Residual plot

• Standard deviation of temperature

• Temperature at the outlet

• Velocity at the outlet

Contour

• Temperature plot

• Velocity plot

Case-2(b): Long Tee

Default mesh size: 0.002

Momentum ratio:4

Turbulence model: `k-epsilon`

Number of elements: `140272`

• Residual plot

• Standard deviation of temperature

• Temperature at the outlet

• Velocity at the outlet

Contour

• Temperature plot

• Velocity plot

Calculating exact temperature of the mixture

`T_(mixture)=frac{m_(hot)**T_(hot)+m_(cold)**T_(cold)}{m_(cold)+m_(hot)}`

`m_(hot)=m_(cold)=m_(air)=1.293kg`

`T_(hot)=309K`

`T_(cold)=292K`

Thus, `T_(mixture)=300.5K`

Demonstration of mesh independent study

Description	Element size	Number of elements	Number of iterations for convergence	Temperature at the outlet degree Celcius	Exact temperature of the mixture
Long tee momentum ratio 4	`0.002 m`	`140272`	`140-150`	`27.375^@C`	`27.50^@C`
	`0.003 m`	`56451`	`140-150`	`27.375^@C`
	`0.004 m`	`29044`	`120-130`	`27.50^@C`
	`0.006m`	`15590`	`100-120`	`27.50^@C`

Thus by performing mesh independent test, it can be inferred that the simulation result closely resembles the exact temperature value at element size `0.006m` which requires `100-120` iterations to converge which means it takes less computational time and less expensive, the element size should comply CFL number, an important criteria for the stability, otherwise, there may be a chance that solution will blow up.

Comparison of all cases

Description	Number of element	Number of iterations for convergence	Temperature at the outlet degree Celcius
Short tee momentum ratio 2	`105865`	`150`	`30.30^@C`
Short tee momentum ratio 4	`105865`	`140-150`	`27.40^@C`
Long tee momentum ratio 2	`140272`	`150`	`30.40^@C`
Long tee momentum ratio 4	`140272`	`140-150`	`27.375^@C`

Conclusion

• The turbulent mixing is well done in a short and long tee with high momentum ratio (in this case is 4), because of which there is a high-temperature drop at the outlet, justifying the absence of hot air at the outlet.
• The turbulent mixing is not well done enough in the case of the short and long tee with a low momentum ratio (which is 2), because of which there is a low-temperature drop at the outlet, justifying the presence of hot air at the outlet.
• The standard deviation of the long tee with high momentum ratio is low meaning the value of the temperature is more reliable.
• Thus for proper mixing long tee with high momentum ratio is preferred.