Steady state analysis of mixing of air at different temperature for a tee section using k-epsilon and k omega SST model in ANSYS FLUENT

OBJECTIVE:- To set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C in two different cases

Using K-Epsilon and k-omega SST model for first case, a model needs to be selected for the other case with appropriate reasons.

• Case I :-
  • Short Mixing tee with hot inlet velocity of 3 m/s and momentum ratio of 2 & 4.(Momentum ratio (MR) = Velocity of cold inlet / Velocity of hot inlet)
• Case II :-
  • Long Mixing tee with hot inlet velocity of 3 m/s and momentum ratio of 2 & 4.

Introduction:-

The mixing of two fluids at different temperatures is a common phenomena which needs to be studied. This type of phenomena is of prime importance because due to thermal stripping the joint or the tee section is subjected to thermal fatigue and thermal stresses which results into failure of the joint over time. In many cases the application is to have an efficient mixing of two fluids for optimium properties (in this case temperature) at outlet of the tee pipe. As shown in figure 1 a mixing tee having an inlet for hot fluid(outside air) and another inlet for cold fluid (chilled air) is mixed inside the pipe .The effectivness off the mixture and the outlet temperature will be shown in this work by CFD analysis using ANSYS Fluent.

Figure 1:- Mixing of two fluids in a pipe with T-Joint Image source:- Skill lync video

PROCEDURE OF SIMULATION OF CASE 1:-

• STEP 1 (PRE-PROCESSING):- The CAD model was already available of short T joint pipe which was imported in Spaceclaim in order to extract the volume . Extraction of Volume simply means filling up the inner domain of pipe with the fluid required to be simulated (AIR in this case). Using Volume extraction as shown in figure the fluid domain was formed and the body of the pipe was suppressed.The dimensional details of both the pipes are given below.

CAD models	Diameter of hot inlet (mm)	Diameter of cold inlet (mm)	Length (mm)
Short Pipe	33.876	16.963	192.38
Long Pipe	33.876	16.963	268.33

• STEP 2 (DISCRETIZATION):- Meshing the extracted volume of the fluid i.e discretizing the domain of fluid into smaller parts in order to perform the simulation. Tetra mesh was done followed by formation of inflation layer and finer meshing near the joining section by dividing the edge into number of divisions. The mesh size was taken to be 2 mm in order to capture the inside part of pipe for better convergence and results. Before this mesh independence test was done which will be shown further.

• Since its been shown in many literatures that the region near to wall are subjected to thermal stressses hence it was required to capture the physics at the near wall region hence inflation layer and finer meshing was done at the junction of T joint by edge sizing. Meanwhile the quality of tetra mesh was checked with Element quality of 11% minimum elements.
• The name selection was done using face selection tool. Four name selections were done namely Inlet cold, Inlet hot, Outlet and Walls . The vertical inlet was for cold fluid while the horizontal inlet was for passing hot fluid. The wall was the boundary or interface between the pipe inner surface and fluid.

• STEP 3 (SOLVING):- The meshing was then transfered to fluent in order to apply necessary boundary conditions and solving. Initially mesh check was done and then boundary conditions were applied.In the Physics option the energy option was checked because of the need of temperature as the output, the realizable k-epsilon turbulence model was selected initially. The following boundary condition were applied as shown in table from the boundaries menu in zones.

  Case 1:- Short T-mixing	Boundary conditions
  Input Parameters	Inlet cold fluid velocity	Inlet hot fluid velocity	Inlet cold fluid temperature	Inlet hot fluid temperature	Outlet gauge pressure
  6 m/s	3 m/s	19 ᵒ C	36 ᵒ C	0 Pa
  12 m/s	3 m/s	19 ᵒ C	36 ᵒ C	0 Pa

• The convergence criteria was selected and default values were changed to 1e-8 for energy equation and 1 e-4 for other parameters such as Velocity (u,v,w), Continuity,k (Turbulent kinetic energy) and Epsilon(Rate of disssipation of turbulent kinetic energy). This was done since lower residual values results to better results but also more time and iterations for convergence.
• In the output, Average values of temperature, velocity and standard deviation of the same were kept. Standard deviation helps finding the maximum change from the mean value that can be observed in the results hence useful for such problems.
• Hybrid initilization was done then and the initial calculations were done for 250 iterations. The following graphs and results of the output paramters weere found.

• Case 1 : k-epsilon model with MR= 4

• CASE 1 :- k-epsilon model with MR =2

CASE 1 :- k-omega SST model with MR =4

CASE 1 :- k-omega SST model with MR =2

• STEP 4 (POST-PROCESSING):- The results obtained from the fluent module was taken for post-processing of the results for analysis. In the Results section, Results< Insert<Plane/Line for selecting the plane along the mid length of the pipe i.e in XY Plane (along) and YZ plane (across). The variable was then changed to temperature and velocity for plotting the contours of temperature and velocity. Further for plotting the graphs of Velocity/Temperature VS length of pipe, a chart was prepared in order to plot the graph for analysis.

• RESULTS & DISCUSSIONS:-
• The results of average velocity, average temperature and std. deviations in there values are shown in the table.

Cases	Average temperature (ᵒ C)	Average velocity (m/s)	No. of iterations to converge	Std .deviation of velocity (m/s)	Std .deviation of temperature (ᵒ C)
k-epsilon model with MR= 2	30.406	4.502	150	1.105	1.411
k-epsilon model with MR= 4	27.54	6.021	250	1.228	1.201
k-omega model with MR= 2	30.434	4.504	250	1.2562	1.881
k-omega model with MR= 4	27.823	6.031	300	1.52	2.15

• • The following results clearly indicates that k-omega model do take higher number of iterations to converge than k epsilon model while the values are negligible. The major importance we need to see is the diffusuion that occurs in the regions closer to the mixing region.
  • The k epsilon model according to literatures are useful in the region of mixing or regions far from walls while regions near to walls are captured better by k omega model. An advance model which is k omega SST (SHEAR STRESS TRANSPORT) is useful for capturing the physics containing both the phenomena.
  • Here in k epsilon model for MR= 2 i.e for low reynolds number,and k omega SST model it can be seen that the temperature at the walls and the diffusion after mixing are better shown in the k omega SST model i.e better diffusion and turbulence by mixing of air. The wall temperatures and velocities were not captured in detail by k epsilon model hence k omega SST model was chosen for Case 2.
  • In velocity , at the boundaries due to application of no slip condition the velocity at the walls is approximately zero and also at the junctional wall. This phenomena is well seen in the k omega SST model than k epsilon for both the momentum ratio cases.
  • The magnitude was not varying enough w.r.t the model but the overall diffusion of the air was seen better in the k omega SST model hence k omega model was chosen for the case 2.
  • The actual results needs to be validated with the experiment.

Figure :- Temperature and velocity contours for short tee with MR= 2 & 4 along the plane obtained from k-epsilon model

Figure :-Temperature and velocity contours for short tee with MR= 2 & 4 along the plane obtained from k-omega SST model

Figure :-Temperature and velocity contours for short tee with MR= 2 & 4 across the plane obtained from k-epsilon model

Figure :-Temperature and velocity contours for short tee with MR= 2 & 4 across the plane obtained from k-omega SST model

Figure:- Line plot of velocity and temperature for k omega model having MR =4

Figure:- Line plot of velocity and temperature for k omega model having MR =2

Figure:- Line plot of velocity and temperature for k epsilon model having MR =2

Figure:- Line plot of velocity and temperature for k epsilon model having MR =4

• MESH INDEPENDENCY TEST:- This test was performed in order to ensure that the variation in the output temperature and velocity is minimum depending on the change in the grid size. This was performed on short T joint pipe with MR =2 and the turbulence model used was k omega SST. The table shows the number of nodes, elements and output parameters wrt change in the mesh size. The mesh size was changed from coarse to fine in 4 total steps.

Mesh size (mm)	No. of nodes	No. of elements	Min. Quality (Based on element quality)	Average Quality (Based on element quality)	Avg. Temperature (ᵒC)	Avg. velocity (m/s)	Std. dev Temperature (ᵒC)	Std dev. velocity (m/s)
10	10304	26822	0.1433	0.551	30.481	4.51	1.82	0.95
6	13114	36159	0.1435	0.577	30.482	4.51	1.9	0.98
4	23387	68483	0.1242	0.603	30.461	4.499	1.98	1.12
2	58371	171754	0.111	0.61	30.434	4.504	1.26	1.88

• The temperature distribution at the interface mixing region was smooth for mesh going from coarse to fine. The wall temperature was also see to be varying alongwith the mesh size. The variation in the mixing can be seen from the figure where plane is across the pipe.

CASE 2:- Long Mixing tee with hot inlet velocity of 3 m/s and momentum ratio of 2 & 4.

• Based on the above discussion k omega SST model was chosen and following results were found.
• The residual, average temperature, average velocity and std. deviations of velocity and temperature are shown below.

Figure :-Residual vs iteration plot for long tee with MR =2

Figure :-Temperature vs iteration plot for long tee with MR =2

Figure :- Velocity vs iteration plot for long tee with MR =2

Figure :- Std deviation of temperature vs iteration plot for long tee with MR =2

Figure :- Std. deviation of Velocity vs iteration plot for long tee with MR =2

Figure :-Residual vs iteration plot for long tee with MR =4

Figure :-Temperature vs iteration plot for long tee with MR =4

Figure :- Velocity vs iteration plot for long tee with MR =4

Figure :- Std. deviation of Temperature vs iteration plot for long tee with MR =4

Figure :-Std. deviation of velocity vs iteration plot for long tee with MR =4

Figure:- Temperature contour for long tee along and across pipe

Figure:- Velocity contour for long tee along and across pipe

Momentum ratio	No. of nodes	No. of elements	Min. Quality (Based on element quality)	Average Quality (Based on element quality)	Avg. Temp. (ᵒC)	Avg. velocity (m/s)	Std. dev Temp. (ᵒC)	Std dev. velocity (m/s)
2	74995	216666	0.128	0.597	30.41	4.497	1.27	1.33
4	74995	216666	0.128	0.597	27.803	6.00	2.056	1.80

The following conclusions were made based on the results obtained:-

• The magnitude of temperature and velocity were not found to be dependent on the length of pipe.
• On the other side the values were greatly affected by the momentum ratio i.e majorly by jet velocity of the cold fluid insertion in the pipe. The higher the velocity lead to lower the temperature because of good heat dissipation which was due to efficient mixing of fluid inside the pipe.
• According to analytical equation given,

• Based on this the Temperature was found to be 30.273 deg C and 27. 226 deg C for MR =2 and 4 respectively which is near to the values found from the analysis.