Week 1- Mixing Tee

Aim

To set up steady-state simulations to compare the mixing effectiveness when the hot inlet temperature is 36°C & the Cold inlet is at 19°C. The air mixes with each other at different velocities. The length of the mixing T is also changed for further analysis as described in the below cases. 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.

• 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.

In a table, compare the following values from the 2 cases.

1. Cell count
2. Average outlet temperature
3. Number of iterations for convergence

Governing equation

• Momentum ratio = velocity at cold inlet / velocity at hot inlet
• Analytical formula for T_mix value at outlet is

T_mix = [(m_hot * T_hot) + (m_cold * T_cold)] / (m_hot + m_cold)

Where, m – mass flow rate = ρ * A*V

T_cold - Temperature at cold inlet = 19^oC

T_hot - Temperature at hot inlet = 36 ^oC

T_mix - outlet temperature after mixing

Introduction

Mixing tee is a device that uses specifically engineered internal geometry to mix two fluid streams into one steam, efficiently. In this study, we are going to find the effectiveness of mixing tee. Hot air and cold air are going to be mixed in a mixing tee. They will have different velocities. We will use two different mixing tees distinguished with length and analyze the effect of length on mixing.

Setup

1. Simulations- Steady State
2. Hot inlet temperature- 36°C
3. Cold inlet temperature- 19°C
4. Use the k-epsilon and k-omega SST model
5. Hot inlet velocity of 3m/s
6. Table to compare the values for the 2 cases
   • Cell count
   • Average outlet temperature
   • Number of iterations for convergence

Procedure

• Open a new project, by clicking on Fluid flow (Fluent) in the Ansys workbench.

• Now click on geometry to import mixing tee model. It will redirect to Spaceclaim, Ansys’s geometry model manipulator.

• Now Go to prepare menu and click on volume extract. Switch to edge selection and select three outer edges and click on green check button. Exit from Spaceclaim and click on mesh to open mesh menu.

• Select outer face and press right click of mouse, it will open a menu. Click on option create named selection and write suitable name for face. Repeat for other faces.

• Now click on mesh option and choose generate mesh.

• Select the option element quality to see, how many elements are defying quality. Quality is measured on the scale of 0 to 1. In our graph, most of the element are near 1 so we can say it is good quality. Section plane can be created to see inner portion of geometry.

• Exit mesh and open setup. First, Check mesh, it is throwing no error then only we can proceed further. We are going to do pressure based steady state simulation, so choose these options on task page.

• Go to physics menu and select viscous model. It will open a menu, choose realizable k-epsilon model and close it.

• Click on material and choose air as working fluid.

• Now go to boundaries option to set boundary conditions. Select inlet_x and click on option edit. It will open a menu, where all the parameter can be set whether it is thermal, radiation, momentum etc. Put the required value of velocity and go to thermal parameter to set temperature for hot fluid.

• Repeat the same procedure for cold fluid coming.
• We want to generate temperature report of outlet and standard deviation of temperature. Go to solutions tab and select definition and select area weighted average. In the opened menu select temperature as field variable. Similarly select standard deviation in definitions menu.
• Now click on initialization to calculate approximate values of velocity and pressure for required iterations.
• Exit setup and double click on result to open CFD post. Check boxes to see walls and other parts. Click on walls and go to render set transparency to inside of wall. Colour can also be changed to white for clear visibility.
• Now insert a XY plane in wall by clicking on plane in location option of insert.

• Go to colour of plane and change it by variable choose option temperature.
• Right click on plane which we created and select streamline. Go to appearance and select velocity to see plot line on plane.

Case solving

Short mixing Tee

Case 1-Short mixing Tee (using K-epsilon Realizable )

Velocity Streamline

Long Mixing Tee

Case 1-Long mixing Tee (using K-epsilon Realizable )

Input Conditions

Viscus Model	K-epsilon Realizable
Momentum Ratio	2
Input 1	Cold air at 19°C
Input 1 Velocity	6 m/s
Input-2	Hot air at 36°C
Input-2 Velocity	3 m/s

Output Result

Avg. Temperature	30.25
Avg. Std Deviation	2.5
Number of iterations for convergence	75
Number of Cell	10885

Scaled Residuals

Standard Deviation of Temperature

Average Weighted Average of Temperature

Fluid flow

Velocity Streamline

Case 1-Long mixing Tee (K-omega Model ,SST )

Input Conditions

Viscus Model	K-omega Model ,SST
Momentum Ratio	2
Input 1	Cold air at 19°C
Input 1 Velocity	6 m/s
Input-2	Hot air at 36°C
Input-2 Velocity	3 m/s

Output Result

Avg. Temperature	30.25
Avg. Std Deviation	2.5
Number of iterations for convergence	75
Number of Cell	10885

Scaled Residuals

Standard Deviation of Temperature

Average Weighted Average of Temperature

Fluid flow

Velocity Streamline

Case 2-Long mixing Tee (using K-epsilon Realizable )

Input Conditions

Viscus Model	K-epsilon Realizable
Momentum Ratio	4
Input 1	Cold air at 19°C
Input 1 Velocity	12 m/s
Input-2	Hot air at 36°C
Input-2 Velocity	3 m/s

Output Result

Avg. Temperature	30.250
Avg. Std Deviation	2.5
Number of iterations for convergence	75
Number of Cell	10885

Case 2-Long mixing Tee (K-omega Model ,SST )

Input Conditions

Viscus Model	K-omega Model ,SST
Momentum Ratio	4
Input 1	Cold air at 19°C
Input 1 Velocity	12 m/s
Input-2	Hot air at 36°C
Input-2 Velocity	3 m/s

Output Result

Avg. Temperature	30.25
Avg. Std Deviation	2.5
Number of iterations for convergence	75
Number of Cell	10885

Mesh independence

A mesh independence (or grid independence) study is something an analyst can perform to determine the dependence of the results on the mesh density.

Compare the results for various runs for different sizing of meshing elements. And in a bid to pass mesh independence results should obtain with proper precision.

So we will run 3 simulations on each case to verify the final results.

Conclusion

The k- omega model is well suited for simulating flow in the viscous sub-layer. On the contrary, The k-epsilon model is ideal for predicting flow in the regions away from the wall

The SST model exhibit less sensitivity to free stream conditions (Flow outside the boundary layer) than many other turbulence models.

If we observe our simulated figure, we can notice, in the k-omega model flow is more like laminar and not giving proper turbulent results, in contrast, simulation by k-epsilon, is giving proper mixing of the two air stream.