Mixing efficiency

Objective: To understand the mixing effectiveness of two fluids in tee junction pipe

There are variety of industrial applications of fluid mixing, like fluid transportation, evaporative cooling, etc. It has been observed that mixing of two fluids in a tee junction is a simple and effective method to achieve good quality mixing. Generally, the aim of mixing is not restricted to heat and mass transfer, but it is also done to achieve a mixture of particular form. However, in this study we will observing the heat transfer of two fluids at different temperatures. The junction used have perpendicular inlets which is known to have better mixing abilities than parallel or coaxial inlets. This helps in rapid mixing within a short distance of injection point.

Brief Description about analysis:

1. The analysis will be done on Ansys FLUENT workbench using a pressure based steady-state solver.

2. Two geometries will be used wherein one tee-pipe geometry is smaller in length as compared to other.

3. Here forth for sake of readability analysis on short pipe will be referred as Case 1 and that of long pipe will be referred as Case 2 . Models used in these cases will be mentioned explicitly.

4. The turbulence models used are realizable k-epsilon model and k-omega SST model. Calculations will be performed on Case 1 using both models and the model which performs better will be used for calculations on Case 2 and for grid dependence test.

5. We have defined a term Momentum Ratio to correlate the velocity of fluids at inlet and outlet i.e.

   ``Momentum Ratio` = `Velocity at cold inlet` / `Velocity at hot inlet``

6. Input and boundary conditions:

   1. Temp at hot inlet = 36°C = 309.15 K

   2. Temp at cold inlet = 19°C = 292.15 K

   3. Velocity at hot inlet = 3 m/s ;

   4. Velocity at cold inlet = 6 m/s for momentum ratio = 2

   5. Velocity at cold inlet = 12 m/s for momentum ratio = 4

   6. Pressure at outlet = atmospheric pressure = 1 atm

To analyze our output, the following output parameters are documented and analyzed:

1. Cell count

2. Average Outlet Temperature

3. Number of iterations for convergence

Steps Performed:

1. In Ansys FLUENT Workbench, a standalone system of Fluid Flow(Fluent) is created.

2. SpaceClaim

   1. Given geometry is imported into SpaceClaim

   2. Volume Extraction is performed to get body which comes in contact with fluid.

3. Meshing

   1. Named faces are created.

   2. Mesh is generated.

   3. Element size is marked as input parameter, while No of elements is marked as output parameter.

4. Setup

   1. Appropriate units is selected for calculations.

   2. Viscous model is selected depending upon the scenario.

   3. Input velocity at hot and cold inlet and temp at both inlets are marked as parameterized input.

   4. Reports for monitoring area weighted average temperature at outlet , standard deviation of temperature at outlet and scaled residuals for convergence are created. The same are marked as parameterized output.

   5. Convergence criteria is set to 1e-6 for each parameter.

5. Solution

   1. The solution is allowed to run for a minimum of 600 iterations so that solution gets converged.

6. Results

   1. Contour and Line plots of temperature and velocity along the length of pipe and across the width of pipe is created at various sections.

Comparison between k-epsilon and k-omega SST:

As seen from the above analysis chart, the difference between k-epsilon model and k-omega SST model is very minute in this case. However, it is important to note that the standard deviation of temperature at the outlet using k-epsilon model is slightly less and hence the mean temperature values will be more accurate and acceptable. This difference in values among the models can be attributed to the fact that k-epsilon model is known to work well in the bulk of flow, while k-omega SST does well in the proximity of the wall.

As we can see from above temperature contour plot along the length of pipe, the fluid mixing takes place in the bulk of flow near the tee-junction intersection not near the walls.

It is for this reason k-epsilon model has been used for calculations in Case-2 and for grid dependence test.

Analysis of output parameters:

1. Cell Count:

   • As we move on from Case 1 to Case 2 , we can observe that number of elements generated during mesh formation. This aligns with our basic concept that with a bigger geometry a finer mesh would yield better results.

2. Average Outlet Temperature:

   • The average outlet temperature in case of higher velocity of cold inlet is better as it closely aligns with experimental data[1] .This proves that at higher velocities of cold fluid the mixing of fluids is more effective. This can be observed in the below contour plots also. The plot in the left corresponds to inlet of cold fluid having lower velocity and right corresponds to inlet of cold fluid having higher velovity . We can see that the hot air seeps through and does not involve completely in mixing process while in case of higher velocity the two fluids get mixed effectively and temperature close to ambient is obtained at the outlet.

• • This ineffectiveness can be observed in Case 2 also as shown below. Hence, it can be said that increase in length of pipe does not help in reducing the mixing ineffectiveness of fluid, rather momentum ratio has greater correlation with mixing effectiveness. 

     3. Number of iterations for convergence:

• • In all the cases the absolute convergence was not reached, however after certain number of iterations the value of residuals were only oscillating around a range of values, hence the solution was said to converged.
  • Convergence plot of Case 1 k-epsilon model DP0 and DP1

• • Convergence plot of Case 2 k-epsilon model DP0 and DP1

Grid Dependence Test:

A grid dependence test is performed to check whether current solution is dependent on cell size and numebr of elements, if it so, then it has be refined further till the point it becomes independent of cell size and number of elements. In given scenario a grid dependence test is performed on Case 1 with element size as parameterized input and area weighted average temperature of outlet as output. 

It can be seen from above Grid Dependence Chart as we decreased the element size the number of mesh elements increased however, the outlet temperture parameter remained constant. Hence, the solution is independent of grid now. 

References:

[1]. Th.Franka C.Lifantea H.-M.Prasserb F.Mentera (2009) "Simulation of turbulent and thermal mixing in T-junctions using URANS and scale-resolving turbulence models in ANSYS CFX".