WEEK - 1 - CFD ANALYSYS OF A MIXING TEE EFFICIENCY USING ANSYS FLUENT

OBJECTIVE:

To set up the steady-state simulation to compare the mixing effectiveness of a mixing tee when hot inlet temperature is 36ᵒC the cold inlet is at 19ᵒC for the different cases using Ansys Fluent.

THE MAIN OBJECTIVE IS:

1. To find out the average temperature at the outlet of the geometry.
2. To compare the RANS-based turbulence models (K-epsilon & K-omega).
3. To compare cell count, No. of iterations for convergence and outlet temperature for two cases.
4. To perform mesh independent study for any one case.
5. To discuss the effect of length and momentum ratios on results.
6. To plot the velocity and temperature contour plots and line plots along and across the length of the pipe.

INTRODUCTION:

A tee joint is a connection of two members approximately perpendicular to one another, forming two right angles similar to the letter T. In this case, two inlets are oriented in X & Y directions, perpendicular to each other. Mixing tee utilizes a specially engineered internal geometry to efficiently mix two fluid streams into one combined stream.

In this project, we are simulating the flow through a Mixing Tee to measure the effectiveness of mixing. The outside air comes through one of the inlets and the chilled air comes through the other inlet. By adjusting the flow rate of chilled air, we can get the desired temperature at the outlet. CFD approach is applied to predict the outlet temperature and velocity of the pipe at steady-state conditions. To capture the turbulence, RANS-based solver K-epsilon and K-omega turbulence models have been used. By using different momentum ratios and physical parameters like cell count. No. of iterations for convergence, area-weighted average, the standard deviation of temperature at the outlet is predicted.

Software Used: Ansys 2019 R3

Ansys workflow for this project:

GEOMETRY SETUP:

Two geometries have been used in this project. These computational models are uploaded to the Ansys Space Claim geometry using the step file format.

1. Short Mixing Tee Pipe
2. Long Mixing Tee Pipe

In this project, our interest is to perform flow simulation so we don’t need some features. We need to extract the fluid volume. Basically, ‘Space Claim’ is a CAD cleaning software that is very helpful for preparing a CAD model for further simulation. So, by using the fluid volume extraction utility in space claim extract the fluid domain by selecting respective edges. Then suppress the solid model from the fluid model to create mesh at the interested region.

• SHORT TEE EXTRACTED VOLUME:

• LONG TEE EXTRACTED VOLUME:

MESH GENERATION:

After loading the geometry into the workbench, Perform a series of operations in the meshing part.

Using the normal selection option define the inlet_X, inlet_Y, outlet, and Wall.

Mesh Size: 3 mm, Mesh Type: Tetrahedral Mesh

After generating the mesh successfully, investigate the statistics related to elements and nodes by clicking the statistics option. Then check the mesh quality by clicking the mesh metrics option in the quality section. Check whether we achieved good quality or not.

Element quality is one of the important criteria to solve governing equations. It should not be less than 5%. In our case min mesh quality is 30%, so it's quite fine to move further analysis.

SETUP & SOLUTIONS:

CASE – 01:

Short mixing tee with a hot inlet velocity of 3m/s.

Momentum ratio of 2,4.

TURBULENCE MODELS:

Most of the CFD problems are based on turbulence modelling. The RANS based turbulence models which were applied to the present problem:

K-epsilon model – This is one of the most common CFD models used for turbulent flow modelling. This model basically utilizes two transport variable properties K-which is the turbulent kinetic energy and epsilon – which is the rate of dissipation of kinetic energy.

K-omega model – This is also one of the common RANS-based solvers used in turbulent flow problems. This model attempt to predict turbulence by solving two different partial differential equations, which is K (Turbulent Kinetic Energy) and omega (Specific rate of dissipation of Energy).

(K-epsilon model predicts the turbulence parameters well far from the boundaries (wall) and K-omega model predicts the turbulence parameters well near the wall)

Apply both turbulence models K-epsilon realizable and K-omega SST model for the Case-01. Based on the results, use the more suitable model for Case-02.

Momentum Ratio: The ratio of velocity at the cold inlet to that of velocity at the hot inlet.

Flowchart for Turbulence Model Selection:

Case 1.1: Tee – short with K-epsilon realizable:

Momentum ratio 2:

Solver: Pressure Based

From the General tab, select the pressure-based solver along with absolute velocity formulation and with a steady-state condition.

Fluid: Air is the fluid in the fluid domain

Energy parameters are activated science the temperature change phenomenon needs to be studied in this case.

Turbulence Model: Select the viscous model which is K-epsilon realizable.

Boundary Conditions:

Hot Inlet Temperature - 36ᵒC

Cold Inlet Temperature - 19ᵒC

Hot inlet air Velocity – 3m/s

Cold inlet air velocity – 6m/s (M.R - 2)

Outlet: Pressure outlet type, Zero-gauge pressure

Walls: Wall type, No-slip condition

Initialize the solver with hybrid schemes. And setup No. iterations and then click on the calculator option.

Results:

• Convergence Plot:

• Area Weighted Average of Temperature:

• Standard Deviation of Temperature:

Post Processing Results:

• Temperature contour along the pipe:

• Temperature contour across the pipe:

• Velocity contour along the pipe:

• Velocity contour across the pipe:

• Temperature line plot along the pipe:

• Temperature line plot across the pipe:

• Velocity line plot along the pipe:

• Velocity line plot across the pipe:

The post-processing results show the variation of temperature and velocity along and across the length of the pipe.

The average outlet temperature becomes 30.25°C, the Solution get converged at the 150th iteration and the standard deviation of temperature is 1.6.

Momentum ratio 4:

• Change the Cold inlet air velocity to - 12m/s (i.e., Momentum Ratio = 4). Keep the others as same as before.
• Initialize the solver with hybrid schemes. And setup No. of iterations and then click on calculate option.

Results:

• Convergence Plot:

• Area Weighted Average of Temperature:

• Standard Deviation of Temperature:

Post Processing Results:

• Temperature contour along the pipe:

• Temperature contour across the pipe:

• Velocity contour along the pipe:

• Velocity contour across the pipe:

• Temperature line plot along the pipe:

• Temperature line plot across the pipe :

• Velocity line plot along the pipe :

• Velocity line plot across the pipe :

• The post-processing results show the variation of temperature and velocity along and across the length of the pipe.
• The average outlet temperature becomes 27.5°C, Solution gets converged at the 134th iteration and the standard deviation of temperature is 1.2.

Case 1.2: Tee – short with K-omega SST:

Momentum ratio 2:

Solver: Pressure Based

Select the K - omega SST turbulence model

• Set the boundary conditions and initialize the solver with hybrid schemes. And setup No.of iterations and then click on calculate option.

Results:

• Convergence Plot:

• Area weighted average of temperature :

• The standard deviation of temperature:

Post-processing results:

• Temperature contour along the pipe:

• Temperature contour across the pipe :

• Velocity contour along the pipe :

• Velocity contour across the pipe:

• Temperature line plot along the pipe:

• Temperature line plot across the pipe:

• Velocity line plot along the pipe:

• Velocity line plot across the pipe:

• The post-processing results show the variation of temperature and velocity along and across the length of the pipe.
• The average outlet temperature becomes 30.25°C, the Solution get converged at the 216th iteration and the standard deviation of temperature is 2.5.

Momentum ratio 4:

• Change the Cold inlet air velocity to - 12m/s (i,e.. Momentum Ratio = 4). Keep the others as same as before.
• Initialize the solver with hybrid schemes. And setup No.of iterations and then click on calculate option.

Results:

Convergence plot:

• Area weighted average of temperature:

• The standard deviation of temperature:

Post-processing results:

• Temperature contour along the pipe:

• Temperature contour across the pipe:

• Velocity contour along the pipe:

• Velocity contour across the pipe:

• Temperature line plot along the pipe:

• Temperature line plot across the pipe:

• Velocity line plot along the pipe :

• Velocity line plot across the pipe:

• The post-processing results show the variation of temperature and velocity along and across the length of the pipe.
• The average outlet temperature becomes 27.5°C, Solution gets converged at the 197th iteration and the standard deviation of temperature is 1.5.

Comparison between the both turbulent models for short Tee geometry with an analytical solution:

K – Epsilon Realizable model
Geometry	Momentum Ratio	Average Outlet Temperature	Iteration to Converge	Standard deviation Temperature
Short Tee	2	30.25oC	150	1.2
Short Tee	4	27.6oC	134	2.5
K – Omega SST Model
Long Tee	2	30.25oC	216	1.7
Long Tee	4	27.5oC	197	1.5

Analytical Solution:

Momentum Ratio 2:

Mass of hot fluid (m_h) = ρ* A* V_h= 997*0.0009*3 = 2.69 kg/s

Mass of cold fluid (m_c) = ρ* A* Vc= 997*0.0009*6 = 1.35 kg/s

Temperature of mixture (T_mixture) = (m_h * T_h + m_c * T_c) / (m_c + m_h) = 30.319°C

Momentum Ratio 4:

Mass of hot fluid (m_h) = ρ* A* V_h= 997*0.0009*3 = 2.69 kg/s

Mass of cold fluid (m_c) = ρ* A* Vc= 997*0.0009*12 = 2.3928 kg/s

Temperature of mixture (T_mixture) = (m_h * T_h + m_c * T_c) / (m_c + m_h) = 27.99°C

Conclusions:

Avg. outlet temperature: On comparing the two turbulent models from the analytical solution, we got nearly same results.

Iterations to converge: No. of iterations taken by K-Omega SST to achieve convergence is higher than that taken by the K-epsilon realizable model.

Standard deviation of temperature: K-Omega SST model produced higher standard deviation that means less accuracy in predicting results for this model.

K-epsilon provides standard results for overall region. If we are interested to capture the phenomenon in such regions nearer to wall, in such a case we should use K-omega with very fine meshing near to wall.

So based on above conclusions, it is recommended to use k-epsilon realizable turbulence model since it is predicting the results very accurately within less iterations.

Case 2 : Long mixing Tee with a hot inlet velocity of 3m/s,

Momentum of ratio of 2,4.

Case 2.1: Tee - Long with K-epsilon realizable :

Momentum ratio 2 :

• Set the conditions as above and initialize the solver with hybrid schemes. And setup No. of iterations and then click on calculate option.

Mesh Defining: Here inflation layer is defined at the walls to accurately capture the results.

Results:

• Convergence plot:

• Area weighted average of temperature :

• Standard deviation of temperature :

Post processing results:

• Temperature contour along and across the pipe:

• Velocity contour along the pipe :

• Temperature line plot along the pipe :

• Temperature line plot across the pipe :

• Velocity line plot along the pipe :

• The post processing results shows the variation of temperature and velocity along and across the length of the pipe.
• The average outlet temperature becomes 30.30°C, Solution get converged at 196th iteration and standard deviation of temperature is 1.9.

Momentum ratio 4 :

Change the Cold inlet air velocity to - 12m/s (i,e.. Momentum Ratio = 4). Keep the others as same as before.

Initialize the solver with hybrid schemes. And setup No.of iterations and then click on calculate option.

Results:

• Convergence plot:

• Area weighted average of temperature :

• Standard deviation of temperature :

Post processing results:

• Temperature contour along and across the pipe:

• Velocity contour along the pipe :

• Temperature line plot along the pipe :

• Temperature line plot across the pipe :

• Velocity line plot along the pipe :

• The post processing results shows the variation of temperature and velocity along and across the length of the pipe.
• The average outlet temperature becomes 27.5°C, At 250th iteration the standard deviation of temperature is 0.75.

Comparison between the both Geometries with analytical solution :

K – Epsilon Realizable model
Geometry	Momentum Ratio	Average Outlet Temperature	Iteration to Converge	Standard deviation Temperature
Short Tee	2	30.25oC	150	1.2
Short Tee	4	27.6oC	134	2.5
Long Tee	2	30.25oC	196	1.9
Long Tee	4	27.5oC	250	0.75

Discussions :

Avg. outlet temperature: Since we are interested on the fluid volume, the temperature at the outlet we got in case-01 and case-02 is near about the same irrespective of the length of mixing tee.

Momentum Ratio :

• Higher the momentum ratio, cold fluid entrance velocity will be higher therefore amount of cold fluid entering the pipe also be higher, and due to higher relative velocity between the fluids it experiences higher turbulence and thereby outlet fluid temperature drops.
• For momentum ratio=2, the average fluid outlet temperature is around 30.3°C whereas for momentum ratio=4 it is confined to 27.5°C, so there is a drop of temperature by almost 3°C at at outlet with the use of high momentum ratio.
• So, in order to attain better turbulent mixing, the velocity of the chilled air is very important. By increasing the velocity of chilled air the outlet temperature get reduced.

Iterations to converge : Longer configuration take more iterations to converge and to predict the desired results than the shorter configuration.

Conclusions :

• Higher the momentum ratio, higher the mixing efficiency of Tee-joint.

Increase in length of the pipe doesn't serve the mixing purpose efficiently, so it's Efficient to use short pipe.

Grid Independency Test :

Geometry Selected: Short- Tee model.

Mesh Generation:

3mm:

2mm:

1mm:

Results @ Mesh 3mm :

• Convergence plot :

• Area weighted average of temperature:

• Standard deviation of temperature:

Results @ Mesh 2mm :

• Convergence plot :

• Area weighted average of temperature:

• Standard deviation of temperature:

Results @ Mesh 1mm :

• Convergence plot :

• Area weighted average of temperature:

• Standard deviation of temperature:

Comparison between different Mesh sizes of short Tee @ MR2:

Mesh Size	No. of elements	No. of Nodes	Average Outlet Temperature	Iteration to converge
3 mm	11216	20014	30.25oC	250
2 mm	27120	47553	30.30oC	200
1 mm	115797	199388	30.40oC	300

Mesh Refinement:

• We're refining the mesh means we're adding more no. of cells. Solver going to take more iterations to converge to a particular value.
• Finer mesh means, more cells to be processed. More governing fluid dynamic equations are being solved on each & every cells. For this reason, simulation time is increasing. Whereas mesh is coarse means, we're having few no. of cells then linear solver can converge pretty fast.

Conclusion:

• From the grid independency test, it is seen that mesh size of 1 mm gives the best predicted results as compared to other mesh sizes.
• It is seen that on decreasing the mesh size the average outlet temperature also starts approaching towards the analytical results. Taking too finer mesh shows deviation from the analytical solution.
• The mesh grid independency test shows the effect of meshing parameter on the average outlet temperature distribution.