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Simulation of Thermal Mixing in T-Junction using Ansys Fluent

AAhammed Shaneeb Nk2 May 2020
CFD

OBJECTIVE:-

  • To set up simulations to compare thermal mixing effectiveness in a T-Junction.
  • To compare k-epsilon and k-omega turbulent models.
  • To plot velocity contour, temperature contour, velocity line plot and temperature line plot along and across the length of the pipe.
  • To discuss the effect of length of the pipe and momentum ratio on thermal mixing.
  • To perform mesh independent study for one case.

GEOMETRIES:-

  • Two geometries have been used in this project.
    1. T-Junction Short Pipe:
      • The 3D view in SpaceClaim is shown below.
      • The computational fluid domain can be extracted by using Volume Extraction tool available in SpaceClaim. After the volume extraction operation, the geometry would like as shown below.
      • The front view of the geometry with dimensions and boundary names have been given below.
    2. T-Junction Long Pipe:
      • The 3D view of the long pipe is shown below.
      • After volume extraction operation, it would look like as given below.
      • The front view of the geometry with dimensions and boundaries is shown below.

TURBULENCE MODEL SELECTION:-

k-epsilon and k-omega are two turbulent models used in CFD simulations. To find out which model is better suitable for our problem, two sample simulations have been run with these conditions.

  • Geometry:-
    • T-Junction Short Pipe has been used to run the two sample simulations.
  • Meshing Details:-
    • Element Size: Default (1.0219e-2 m)
    • Nodes: 2797
    • Number of Elements: 12583
    • 3D view of mesh in both cases have been shown below.
    • Central sectional view of mesh is given below. The number of elements in the cold inlet part and in the junction is more. It is a default implementation by Ansys.
    • Meshing Quality Metrics has been shown below. Majority of the elements have more than 75% quality and there is no element which has less than 20% quality which is a good indication.
  • Case set-up Details:-
    • Solver type: Pressure-based
    • Fluid: Air is the fluid which is entering as well as in the fluid domain
    • Energy equation option was enabled since temperature change phenomenon needs to be studied in the case.
    • Boundary Conditions:
      • Hot Inlet: velocity-inlet type, 3m/s, 360C
      • Cold Inlet: velocity-inlet type, 6m/s (since momentum ratio = 2), 190C
        • Momentum Ratio = velocity of cold air / velocity of hot air
      • Outlet: pressure-outlet type, 0 gauge pressure, backflow total temperature 26.850C
      • Walls: wall type, No Slip condition
    • Initial Conditions: Hybrid initialization has been used
    • Number of Iterations: 500
    • Timestep method: Automatic
  • Results Comparison:-
  • Two separate simulations have been run with the above conditions, one with k-epsilon realizable model and other with k-omega SST model. Following results have been analysed to select the best model for the problem of this project. In each of the coming plots, the first one will be of k-epsilon model and the later will be of k-omega model.
    • Scaled Residuals Graph:-
    • In CFD calculations, a bunch of partial differential equations need to be solved. For this, descritiization techniqes have been used to convert these PDEs to solvable form. There would be some error during this conversion. The residuals are good indications for that deviation.
    • It has been observed that the solution has been converged very quickly in k-epsilon model (~180 iterations) compared to that in k-omega model (~450 iterations). When the equations used in a turbulence model is in accordance with the problem physics, the solution would converge after few iterations.
    • Standard Deviation of Outlet Local Temperature:-
    • Both model gave constant value for standard deviation after few iterations which is a good sign.
    • k-epsilon model gave lower standard deviation of local temperature at outlet compared to k-omega model (1.5694213 and 1.763489 respectively in degree celcius). Lower the standard deviation better the result.
    • Area-weighted Average of Outlet Temperature:-
    • Both model gave almost same outcome for area-weighted average temperature. k-epsilon model gave 30.206572 and k-omega model gave 30.231203 degree celcius. Both of them started to give a constant value for the same after very few iterations.
    • Temperature Contour Along the Pipe:-
    • The temperature contour along the pipe has been taken at the central plane of the pipe.
    • Both model gave temperature contours in the expected way.
    • The diffusion characteristic was observed more in the k-epsilon model compared to that in k-omega model after the t-junction.
    • Velocity Contour along the Pipe:-
    • The velocity contour along the pipe has been taken at the central plane of the pipe.
    • Both model gave almost similar velocity contour along the pipe.
    • After the t-junction, small region of recirculation has been observed in both contours.
    • More diffusion was observed in k-epsilon model.
    • Temperature and Velocity Contours Across the Outlet:-
    • Both model gave almost similar contours at the outlet except the fact that the diffusion was more in k-epsilon model and hence less temperature has been observed at the top of the outlet in k-epsilon model compared to that in k-omega model.
  • Model Selection:-
  • Due to the following reasons, k-epsilon realizable model has been selected to run the simulation in this thermal mixing problem.
    • The solution has been converged quickly in k-epsilon model.
    • k-epsilon model gave low value for standard deviation and area-weighted average of temperature at outlet.
    • Better diffusion was observed in k-epsilon model.
    • In general, k-omega turbulence model is used to capture the physics for near wall/boundary problems. Thermal mixing would happen more in the fluid domain bulk than near wall/boundary. k-epsilon model is better suitable for this application.

THERMAL MIXING IN SHORT PIPE:-

In this case, thermal mixing has been simulated in short pipe with momentum ratio = 2 and 4. The ratio of velocity at cold inlet to that of hot inlet is called momentum ratio.

  • Geometry:-
    • T-Junction Short Pipe has been used to run this simulation.
  • Meshing Details:-
    • Element size: 0.003 m
    • Nodes: 8345
    • Number of Elements: 39774
    • 3D view of mesh is shown below.
    • Central sectional view of mesh is given below. Ansys automatically gave more number of elements near the wall and cold inlet part.
    • Meshing Quality Metrics is shown below. Most of the elements have 70%+ quality.
  • Case set-up Details:-
    • Solver type: Pressure-based
    • Fluid: Air is the fluid which is entering as well as in the fluid domain
    • Energy equation option was enabled since temperature change phenomenon needs to be studied in the case.
    • Turbulence model: k-epsilon realizable
    • Boundary Conditions:
      • Hot Inlet: velocity-inlet type, 3m/s, 360C
      • Cold Inlet: velocity-inlet type, 6m/s in first case and 12 m/s in second case, 190C
      • Outlet: pressure-outlet type, 0 gauge pressure, backflow total temperature 26.850C
      • Walls: wall type, No Slip condition
    • Initial Conditions: Hybrid initialization has been used
    • Number of Iterations: 600
    • Timestep method: Automatic
  • Results:-
  • Two separate simulations have been run with the above conditions, one with momentum ratio = 2 and other with momentum ratio = 4. In each of the coming plots, the first one will be the case with momentum ratio = 2 and the later will be with momentum ratio = 4.
    • Scaled Residuals Graph:-
    • It took atleast 300 iterations for the solution to converge in both cases (~340 in first case and ~320 in second case).
    • Standard Deviation of Outlet Local Temperature:-
    • After about 100 iterations, both cases started to give constant value for standard deviation (1.7341109 and 1.0708057 respectively in degree celcius). Lower the standard deviation better the result.
    • Area-weighted Average of Outlet Temperature:-
    • Both cases started to give constant value for area-weighted average temperature before even 100 iterations. The first case gave value as 30.257984 and the second case gave 27.630489 in degree celcius. Since the second case gave lower value, it indicates that better mixing has been happened when momentum ratio is increased.
    • Temperature Contour Along the Pipe:-
    • The region in the contours near the t-junction of the pipe clearly indicates that more thermal mixing has happened in the second case where the momentum ratio was more. It has been observed that the higher velocity fluid from cold inlet has pushed the hot air downwards more which reduces the temperature of the hot air in the bottom the pipe more than that at top. Hence there is high temperature at the top of the pipe just after the t-junction than the bottom of the pipe. Since this pushing is more in the second case, the more the thermal mixing.
    • Velocity Contour along the Pipe:-
    • The higher velocity condition given in the second case can be visually verified by using this contour. As stated before, the higher velocity fluid pushes the lower velocity hot air towards the bottom of the pipe. This causes a small recirculation zone near the t-junction somewhat close to the top of the pipe. Since the cold inlet air velocity is more in the secnod case, the more this phenomenon visible.
    • Temperature and Velocity Contours Across the Outlet:-
    • Since more thermal mixing was happened in the second case, the average outlet temperature is less in the second case.
    • Temperature and Velocity Contours in 3D:-
    • The above 3D contours show how the temperature and velocity change along and across the pipe. The evolution pattern is clearly visible and matches with the expectation.
    • Temperature Along the Pipe - Line Plot:-
    • The above line plots have been taken by considering a line which is at the very center of the pipe. This profile is helpful to study the mixing due to the high velocity of cold air and due to diffusion. The fluid slowly attains a value of temperature between the lower value of cold air and higher value of hot air after t-junction.
    • Velocity Along the Pipe - Line Plot:-
    • The above line plots have been taken by considering a line which is at the very center of the pipe. The fluid slowly attains a value of velocity between the lower value of hot air and higher value of cold air after t-junction.
    • Temperature Across the Outlet- Line Plot:-
    • The above line plots have been taken by considering a line across the oulet which is at the very center of the outlet. The variation of the air temperature inside the pipe compared to that near the wall is clearly visible.
    • Velocity Across the Outlet- Line Plot:-
    • The above line plots have been taken by considering a line across the oulet which is at the very center of the outlet. The variation of the air velocity inside the pipe compared to the zero velocity near the wall is clearly visible.

THERMAL MIXING IN LONG PIPE:-

In this case, thermal mixing has been simulated in long pipe with momentum ratio = 2 and 4.

  • Geometry:-
    • T-Junction Long Pipe has been used to run this simulation.
  • Meshing Details:-
    • Element size: 0.0035 m
    • Nodes: 8231
    • Number of Elements: 39070
    • 3D view of mesh is shown below.
    • Central sectional view of mesh is given below.
    • Meshing Quality Metrics is shown below. Most of the elements have 70%+ quality.
  • Case set-up Details:-
    • Solver type: Pressure-based
    • Fluid: Air is the fluid which is entering as well as in the fluid domain
    • Energy equation option was enabled since temperature change phenomenon needs to be studied in the case.
    • Turbulence model: k-epsilon realizable
    • Boundary Conditions:
      • Hot Inlet: velocity-inlet type, 3m/s, 360C
      • Cold Inlet: velocity-inlet type, 6m/s in first case and 12 m/s in second case, 190C
      • Outlet: pressure-outlet type, 0 gauge pressure, backflow total temperature 26.850C
      • Walls: wall type, No Slip condition
    • Initial Conditions: Hybrid initialization has been used
    • Number of Iterations: 600
    • Timestep method: Automatic
  • Results:-
  • Two separate simulations have been run with the above conditions, one with momentum ratio = 2 and other with momentum ratio = 4. In each of the coming plots, the first one will be the case with momentum ratio = 2 and the later will be with momentum ratio = 4.
    • Scaled Residuals Graph:-
    • It took almost 200 iterations for the solution to converge in both cases.
    • Standard Deviation of Outlet Local Temperature:-
    • The first case gave 1.1455713 and the second case gave 0.66012608 as standard devaiation of local outlet temperature in degree celcius.
    • Area-weighted Average of Outlet Temperature:-
    • The first case gave value as 30.332255 and the second case gave 27.511981 in degree celcius. Since the second case gave lower value, it indicates that better mixing has been happened when momentum ratio is increased.
    • Temperature Contour Along the Pipe:-
    • When the second case is compared with that with the short pipe, more diffusion was observed here due to more length of the pipe after t-juction. This phenomenon helps the air to get further mixed. The variation of the temperature between the bottom and top region of the pipe just after the t-junction is also clearly visible. This is due to the fact that the hot air was more pushed downwards due to high velocity of the cold air.
    • Velocity Contour along the Pipe:-
    • When compared with the short pipe, the recirculation region was observed as some more distributed in the long pipe cases.
    • Temperature and Velocity Contours Across the Outlet:-
    • When the second case is compared with that in short pipe case, the variation of temperature/velocity in various region of outlet is less. This is due to more diffusion happened becuase of the increased length after t-junction.
    • Temperature and Velocity Contours in 3D:-
    • The evolution pattern if temperature and velocity is clearly visible and matches with the expectation.
    • Temperature Along the Pipe - Line Plot:-
    • The above line plots have been taken by considering a line which is at the very center of the pipe. This profile is helpful to study the mixing due to the high velocity of cold air and due to diffusion. The fluid slowly attains a value of temperature between the lower value of cold air and higher value of hot air after t-junction. Since the length is more after t-junction, this phenomenon further continues.
    • Velocity Along the Pipe - Line Plot:-
    • The above line plots have been taken by considering a line which is at the very center of the pipe. The fluid slowly attains a value of velocity between the lower value of hot air and higher value of cold air after t-junction. Since the length is more after t-junction, this phenomenon further continues.
    • Temperature Across the Outlet- Line Plot:-
    • The above line plots have been taken by considering a line across the oulet which is at the very center of the outlet. The variation of the air temperature inside the pipe is less from that near the wall compared to that in short pipe.
    • Velocity Across the Outlet- Line Plot:-
    • The above line plots have been taken by considering a line across the oulet which is at the very center of the outlet. The variation of the air velocity inside the pipe from the zero velocity near the wall is very less compared to short pipe.

SUMMARY OF MESH AND CONVERGENCE DETAILS:-

The mesh details and the number of iterations took in different cases have been summaries below as a table.

EFFECT OF LENGTH IN THERMAL MIXING:-

Since the length is increased after the t-junction, more diffusion was happened. Hence more mixing happened. This was observed from the above explained temperature and velocity contours and line plots. Following is a comparison of short pipe and long pipe results when the simulation was run with momentum ratio = 4. The area-weighted average of outlet temperature has been slightly reduced which supports the observation. The standard deviation was also reduced in great extent. The temperature and velocity contours at the outlet and the actual values obtained have been given below. More details have been provided under the respective contours above. Though there was more mixing when the length has been increased, it was not so high. Only slight difference was observed. This indicates that increasing length is not an effective method to increase the mixing efficiency.

EFFECT OF MOMENTUM RATIO IN THERMAL MIXING:-

The momentum ratio is the ratio of the cold inlet velocity to that of hot inlet velocity. Since the hot inlet velocity was made constant, increasing momentum ratio here means higher the cold inlet velocity. It was observed that increasing so is increasing the mixing efficiently. Also, more and efficient mixing was happened near the t-juntion where these hot and cold air with different temperatures meet up. Following is a comparison of long pipe simulation results when it was run with momentum ratio = 2 and 4 respectively. The area-weighted average of outlet temperature has been reduced which supports the observation. The standard deviation was also reduced in great extent. The temperature contours along the pipe and the actual values obtained have been given below. More details have been provided under the respective contours above. Per the observations and results, it is an effective method to increase the momentum ratio for increasing the mixing efficiency.

MESH INDEPENDENT STUDY:-

The mesh independent study has been conducted for three cases by varying the element size.

  • Geometry:-
    • T-Junction Short Pipe has been used to run the simulations.
  • Meshing Details:-
    • Case - 1:
      • Element Size: 0.01 m
      • Nodes: 2797
      • Number of Elements: 12583
    • Case - 2:
      • Element Size: 0.006 m
      • Nodes: 2813
      • Number of Elements: 12630
    • Case - 3:
      • Element Size: 0.0028 m
      • Nodes: 9698
      • Number of Elements: 46548
    • The 3D view and central sectional view of the mesh in three cases have been shown below.
    • Meshing Quality Metrices of three cases have been shown below. In all cases, majority of the elements have more than 70% quality. Highest quality was observed in third case.
  • Case set-up Details:-
    • Solver type: Pressure-based
    • Fluid: Air is the fluid which is entering as well as in the fluid domain
    • Energy equation option was enabled since temperature change phenomenon needs to be studied in the case.
    • Turbulence model: k-epsilon realizable
    • Boundary Conditions:
      • Hot Inlet: velocity-inlet type, 3m/s, 360C
      • Cold Inlet: velocity-inlet type, 12m/s (momentum ratio = 4), 190C
      • Outlet: pressure-outlet type, 0 gauge pressure, backflow total temperature 26.850C
      • Walls: wall type, No Slip condition
    • Initial Conditions: Hybrid initialization has been used
    • Number of Iterations: 800
    • Timestep method: Automatic
  • Results Comparison:-
  • Three separate simulations have been run with the above conditions, for case 1, 2 and 3. Following results have been analysed. In each of the coming plots, the first one will be of case 1, the second will be of case 2 and the last one will be of case 3.
    • Scaled Residuals Graph:-
    • Huge variation was observed in the residual plots in the first case after each iteration. This variation is observed to be reducing when the mesh becomes finer. Less variation is observed in the third case. It took more number of iterations to attain convergance in the first case. After about 250 iterations, the second case attained convergance and after about 220 iterations, the third case attained convergance.
    • Standard Deviation of Outlet Local Temperature:-
    • The standard deviation values of local outlet temperature obtained are 1.1837748, 1.091106 and 1.0606693 in case 1, 2 and 3 respectively. As the mesh became finer, lesser standard deviation was observed.
    • Area-weighted Average of Outlet Temperature:-
    • The area-weighted average values of outlet temperature obtained are 27.543249, 27.529984 and 27.580208 degrees respectively. Every case gave almost same value.
    • Temperature Contour Along the Pipe:-
    • The physics of thermal mixing was more clearly visible in third case compared to that in second and first case.
    • Temperature Contour Along the Pipe with Mesh:-
    • Third case gave more clear physics due to finer mesh used. This would increase the number of elements to capture the physical phenomenon.
    • Velocity Contour along the Pipe:-
    • Case 2 gave more clear visualization in the physical phenomenon than case 1. Case 3 gave even more clarity in the contour.
    • Velocity Contour along the Pipe with Mesh:-
    • As the mesh become finer, the number of elements used to capture the physics will be more and hence more clear physics can be observed in the third case.
    • Temperature Contour Across the Outlet:-
    • Since the mesh was more coarser in first and second case, the circular geometry of the outlet was slightly changed. Third case retained the circular shape due to finer mesh and hence it is the better and trusted result compared to that in case 1 and case 2.
    • Velocity Contour Across the Outlet:-
    • Since third case retained the circular shape of the outlet, the physics observed in third case is more trusted. Also it was as per the expectation.
    • Temperature Along the Pipe - Line Plot:-
    • The line plot of the temperature along the pipe gave almost similar trend in all the three cases even though slight differences in the values were observed.
    • Velocity Along the Pipe - Line Plot:-
    • The line plot of the velocity along the pipe gave almost similar trend in all the three cases even though slight differences in the values were observed.
    • Temperature Across the Outlet- Line Plot:-
    • The line plot of the temperature across the outlet of the pipe gave almost similar trend in all the three cases even though slight differences in the values were observed.
    • Velocity Across the Outlet- Line Plot:-
    • The line plot of the velocity across the outlet of the pipe gave almost similar trend in all the three cases even though slight differences in the values were observed.
  • Outcome:-
    • As the mesh become finer, the number of elements to capture the physical phenomenon increases. As the information from more number of nodes/elements are used to solve the equations, it would give better solution. This way, the finer mesh will give better result which can be visually examined/analysed by using contours and line plots as discussed above.

CONCLUSIONS:-

  • For thermal mixing problems, k-epsilon realizable turbulence model is better suitable than k-omega SST model.
  • Increasing length of the pipe after the t-junction causes more diffusion to happen thereby increases the mixing effectiveness. Though, the increased mixing was not so high.
  • Increasing the momentum ratio (velocity of cold air/velocity of hot air) causes more mixing near the t-junction which increase the mixing efffectiveness in great extend. It is a good and recommended idea to increase the momentum ratio for high mixing efficiency.
  • Since there would be more number of elements to capture the physical phenomenon, finer mesh would give better result compared to coarser mesh compromising on the time taken and the memory consumption.
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