MIXING EFFICIENCY OF A CIRCULAR CROSS SECTION TEE MIXER
MIXING EFFICIENCY OF A CIRCULAR CROSS SECTION TEE MIXER
Project by: Rajat Kumar Dudheria
Email id : [email protected]
INTRODUCTION:
Mixing Tee configuration is used to mix two different fluid streams. Depending of inlet velocities, temperature, pressure, area of cross section and length of pipe, the outlet stream properties like outlet temperature, velocity, heat transfer and extent of mixing varies. Mixing Tee is widely used in Air conditionong system, mixing different fluids in industries and in drainage and water distribution system.
In this project, effect of inlet velocities of two streams and pipe length on outlet stream`s properties is studied using Computational fluid dynamic approach. For this one cold stream at temperature 10C and hot stream at temperature 25C as inlet stream is used. Outlet stream temperature, standard deviation of temperature and flow through the pipe is computed and analysed.
Momentum ratio (M) is defines as ratio of inlet velocities of two stream.
Here, M= Velocity of cold stream / velocity of hot stream.
CASES STUDIED:
1. Short pipe with hot inlet velocity = 3m/s and M= 2.
2. Long pipe with hot inlet velocity = 3m/s and M= 2.
3. Short pipe with hot inlet velocity = 3m/s and M= 4.
SOFTWARE USED: ANSYS R18.1
MODELLING OF NUMERICAL MODEL:
GEOMETRY AND MESH
Pipe opeing along x axis is taken as inlet for hot fluid and opening along y axis (smaller diameter opening) as cold fluid inlet. Outlet is obtained from 3rd opening.
Detail of Gemetry:
Diameter Length
Pipe type along x axis (m) along y axis (m) along z axis (m)
Long pipe 0.0339 0.017 0.2684
Short pipe 0.0339 0.017 0.1924
Fig No 1: Pipe model used for Tee mixing ( long pipe)
VOLUME EXTRACTION:
Volume is extracted from the model in all 3 cases using Design modular's Fill- tool using cavity approach.
Fig No2: Extracted volume.
MESHING:
Meshing of the extracted volume is done using Tetrahedral cell with predefined standard parameter for all cases.Relevance centre is set to fine type to obtain a good mesh.
Detail of Mesh:
TYPE OF ELEMENT: Tetrahedral
CELL COUNT: 40281 ( small pipe )
28452 ( long pipe )
Fig no 3: Meshed body ( short pipe )
Fig No 4: cut view of meshed body ( short pipe)
Meshing is done by setting the element quality above 5%. Element quality barchart for both small pipe ( Fig No:5) and long pipe (Fig No: 6) is shown below.
Following detail related to element quality for both pipes are:
Properties Short pipe Long Pipe
Minimum 0.2758 0.25374
Average 0.83475 0.83774
In above data, minimum value of element quality for both short pipe ( 27.58% ) and long pipe ( 25.37%) is well above the 5% minimum condition. Also the average value of element quality which is more than 80% for both the pipes shows that larger porportion of element are having quality above 85%. Same can be concluded from below mentioned element graph( Fig No: 5 & 6 )for both pipes. Thus a good mesh is obtained.
Fig No: 5 Element quality of short pipe.
Fig No: 6 Element quality of long pipe.
SETUP FOR SIMULATION:
Air is used as a fluid for both the inlets with the following properties-
Density- 1.225 kg/m3
Cp ( specific heat at constant pressure) - 1006.43 J/Kg-k
Thermal conductivity(K) - 0.0242 W/m-k
Viscosity - 1.7894e-05 Kg/ m-s.
Energy equation is solved to capture the temperature variation throughout the pipe. Also continuity and momentum equations are solved for flow and velocity analysis. K-epsilon (k-ε) turbulence model with Realizable standard wall function is used to descride the mean flow characteristics for turbulent flow condition.
Fluid flow is steady flow with constant pressure ( gauge pressure= 0 Pa). Pressure based solver with absolute velocity is used. Since flow velocities of streams are low, affect of compressibility is negligible. So density based solver is not used.
Boundary conditions for inlet and outlet fluid streams for different cases:
Case No. Pipe type Hot fluid velocity (m/s) Cold fluid velocity (m/s) Momentum ratio(M)
1. Short 3 6 2
2. Long 3 6 2
3. Short 3 12 4
In above all cases, velocities are normal to cross section and Turbulent intensity and Turbulent Viscosity Ratio are set at standard value of 5% and 10 respectively.
Adiabatic wall is defined with no slip condition. At outlet the gauge pressure is set to 0 Pa.
RESULT AND DISCUSSION:
Plot of Temperature at outlet, residual and standard deviation of temperature at outlet is obtained.
For convergence check, the residual obtain on solving various equations at each iteration is calculated and if it lies below 0.001, then it satisfy the convergence test.For energy equation this value is 1e-06.
The standard deviation of temperature at outlet and flow temperature at outlet corrospondes to last iteration value obtained in console. The simulation is done for 500 iterations.
CASE 1: Short pipe with momentum ratio = 2 and hot fluid velocity = 3m/s.
From residual graph ( Fig No: 7), It can be seen that except for continuity equation all other equations residual values are lower than 1e-04. The simulation converges somewhere between 425 and 450 iterations. It can be approximated to 435.Also the residual corresponding to energy equation goes below 1e-055 at 150 iteration.
The standard deviation of Temperature at outlet is 1.053 ( fig no: 8). This shows that solution obtained is well converged with small temperature variation at outlet.
Temperature at outlet: 293.09 K ( 19.94 C ) ( fig no 9).
Fig No: 7- convergence plot for small pipe with M=2 (case 1)
Fig No: 8 Standard deviation of Temperature
Fig No: 9 Temperature at outlet.
CONTOUR PLOT OF TEMPERATURE VARIATION AND VELOCITY ALONG MIDDLE PLANE:
Fig no 10: Contour plot of Temperature.
Fig No : 11 Contour plot for velocity.
CASE 2: LONG PIPE WITH HOT FLUID VELOCITY - 3m/s and M=2.
From residual graph ( Fig No: 12), It can be seen that except for continuity equation all other equations residual values are lower than 1e-04. The simulation converges somewhere between 375 and 400 iterations. It can be approximated to 385.Also the residual corresponding to energy equation goes below 1e-055 at 150 iteration.
The standard deviation of Temperature at outlet is 1.36 ( fig no: 14). This shows that solution obtained is well converged with small temperature variation at outlet.
Temperature at outlet: 293.13 K ( 19.98 C ) ( fig no 13).
Fig No 12- CONVERGENCE PLOT FOR LONG PIPE ,MR -2
Fig No 13- Outlet temperature
Fig No 14 Standard deviation ofoutlet temperature.
CONTOUR PLOT OF TEMPERATURE VARIATION AND VELOCITY ALONG MIDDLE PLAN
Fig no 15: Contour plot of Temperature.
Fig No : 16 Contour plot for velocity.
CASE 3: Short pipe with momentum ratio = 4 and hot fluid velocity = 3m/s.
From residual graph ( Fig No: 17), It can be seen that except for continuity equation all other equations residual values are lower than 1e-04. The simulation converges somewhere between 375 and 400 iterations. It can be approximated to 380. Also the residual corresponding to energy equation goes below 1e-055 after 350 iteration.
The standard deviation of Temperature at outlet is 0.91 ( fig no: 18). This shows that solution obtained is well converged with small temperature variation at outlet.
Temperature at outlet: 290.72 K ( 17.57 C ) ( fig no 19).
Fig No 17- CONVERGENCE PLOT FOR SHORT PIPE ,MR -4
Fig No: 18 Standard deviation of Temperature
Fig No: 19 Temperature at outlet.
CONTOUR PLOT OF TEMPERATURE VARIATION AND VELOCITY ALONG MIDDLE PLANE:
Fig no 20: Contour plot of Temperature.
Fig No : 21 Contour plot for velocity.
TABULATION:
| CASE | CELL COUNT | Avg. Outlet Temp | Number of iteration for convergence |
| 1 | 40281 | 293.09k | 435 |
| 2 | 28452 | 293.13k | 385 |
| 3 | 40281 | 290.72k | 380 |
DISCUSSION:
1. For same MR value as in case 1 & 2, the outlet stream temperature is almost same irrespective of pipe length.
2. Comparing the case 1 & 3 having same pipe length but different MR value, we observe lower outlet stream temperature (17.57 C ) in case 3 with higher MR value. Whereas in case 1 with lower MR value, outlet stream temperature is 19.94 C .
3. Standard deviation of outlet stream temperature is 1.053 for case 1 compared to 0.91 for case This is due to better mixing, higher turbulence and better heat exchange in case of higher MR value.
4. From temperature contour plot of case 1 & 3 we observe that the penetration of cold fluid stream is more for higher value of MR as represented by blue colour region in plot. Also at outlet section the variation in temperature is more in case 1 & 2 as compared to 3 .
5. From temperature contour plot we observe that variation in outlet temperature is more in lowe portion of flow. This variation decrease with increase of MR value.
6. From temperature contour plot of case 1 & 3 we observe that cold stream fluid exchanges heat with larger portion of incoming hot fluid stream at higher temperature difference in case 3 compared to case 1 & 2.
7. Comparing the velocity profile at pipe outlet from velocity contour plot of case 1, 2 and 3 we observe that for same MR value, case 1 with shorter pipe length have least symmetrical representation compared to case 2 with longer pipe length. This is due to extra region for mixing in longer pipe. In case 3 with higher MR value we observe well developed axis symmetric velocity profile at pipe outlet. Thus with higher value of MR, well develop velocity profile can be obtain in shorter pipe because of better mixing.
CONCLUSION:
The 3-D model of Tee mixing is developed for CFD stimulation and is stimulated and analysed using ANSYS FLUENT. It is observed that pipe length has less influence on outlet stream temperature and mixing efficiency compared to momentum ratio (MR). For same inlet conditions and pipe length better mixing is observed for higher MR case. Also the outlet stream is more homogenous with enhanced velocity profile. Thus higher MR value results in better mixing, higher heat exchange between streams, less temperature variation at outlet and more homogenised outlet stream.