Steady State Analysis of mixing tee with different length and momentum ratio

Objective: Compare the Steady State Analysis results of mixing tee with different length and momentum ratios and write a detailed report explaining the results obtained.

Question:

For this challenge, we have created two versions of the mixing tee. One of them is longer than the other.

Your job is to set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 360 C & the Cold inlet is at 190 C.

Use the k-epsilon and k-omega SST model for the first case and based on your judgment use the more suitable model for further cases. Giving the reason for choosing a suitable model is compulsory.

• Case 1
  • Short mixing tee with a hot inlet velocity of 3 m/s.
  • Momentum ratio of 2, 4.
• Case 2
  • Long mixing tee with a hot inlet velocity of 3m/s.
  • Momentum ratio of 2, 4.
• Momentum ratio = velocity at cold inlet / velocity at hot inlet

In a table, compare the following values from the 2 cases.

• Cell count
• Average outlet temperature
• Number of iterations for convergence

Expected results:

• Velocity and temperature contour plots on the cut planes along and across the pipe.
• Velocity and temperature line plots along and across the length of the pipe.
• Perform Mesh independent study for any one case.
• Discuss the effect of length and momentum ratio on results.

For each simulation, you need to show the convergence plot

From above information, the following cases can be analysed for expected results.

• CASE-A: BEST MODEL FOR ANALYSIS
• CASE-AA: Short Tee, MR-2, Model: K-EPSILON, Default Mesh(10.219 mm).
• CASE-AB: Short Tee, MR-2, Model: K-OMEGA SST, Default Mesh(10.219 mm).
• CASE-B: MESH INDEPENDENT STUDY
• CASE-BA: Short Tee, MR-2, Model: Best model from CASE-A, Mesh - 7 mm.
• CASE-BB: Short Tee, MR-2, Model: Best model from CASE-A, Mesh - 5 mm.
• CASE-BC: Short Tee, MR-2, Model: Best model from CASE-A, Mesh - 3 mm.

• CASE-1a: Short Tee, MR-2, Model: Best model from CASE-A, Mesh: Best size from CASE-B.
• CASE-1b: Short Tee, MR-4, Model: Best model from CASE-A, Mesh: Best size from CASE-B.
• CASE-2a: Long Tee, MR-2, Model: Best model from CASE-A, Mesh: Best size from CASE-B.
• CASE-2b: Long Tee, MR-4, Model: Best model from CASE-A, Mesh: Best size from CASE-B.

• Following Parameters will be same for all Cases.
• Hot inlet Velocity - 3 m/s
• Hot inlet Temperature - 360 C
• Cold inlet Temperature - 190 C

Case Setup and Execution:

• CASE-A: BEST MODEL FOR ANALYSIS

• Geometry: Model is imported to ANSYS Spaceclaim.
• Volume is extracted using edges from prepare > volume extract option.
• 
  
• Mesh: Mesh is created for volume with default element size(10.219 mm).
• 
  
• Named Selections: Named selections are created for boundaries as shown below.
• 
  
• Boundaries:
• Inlet_x:
• Velocity: 3 m/s
• Temperature: 360 C
• Inlet_y:
• Velocity: 6 m/s
• Temperature: 190 C
• Outlet:
• Pressure Force Multiplier: 1
• Back flow Temperature: 26.850 C

• Material: Air is assigned as material for Volume.
• 
  

• CASE-AA: Short Tee, MR-2, Model: K-EPSILON, Default Mesh(10.219 mm).

• K-epsilon realizable Turbulence model with standard wall function.

  K-ε model focuses on the mechanisms that affect the turbulent kinetic energy. The underlying assumption of this model is that the turbulent viscosity is isotropic, in other words, the ratio between reynold tress and mean rate of deformations is the same in all directions.

  An immediate benefit of the realizable k-ɛ model is that it provides improved predictions for the spreading rate of both planar and round jets. It also exhibits superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and re circulation. In virtually every measure of comparison, Realizable k-ɛ demonstrates a superior ability to capture the mean flow of the complex structures.

  The calculation is done for 300 iterations.

  Results:

  Residual Plot: Number of iterations to converge - 160.

  Area Weighted Average temperature at outlet (30.25 ^oC)

  Standard deviation of temperature at outlet (1.6 ^oC)

  • Velocity contour plot on the cut planes along the pipe:
  • Velocity contour plot on the cut planes across the pipe:
  • Temperature contour plot on the cut planes along the pipe:
  • Temperature contour plot on the cut planes across the pipe:
  • Lines for creating Line Plots:
  • Velocity line plot on the cut planes along the pipe:
  • 
    
  • Velocity line plot on the cut planes across the pipe:
  • Temperature line plot on the cut planes along the pipe:
  • Temperature line plot on the cut planes across the pipe:
• • CASE-AB: Short Tee, MR-2, Model: K-OMEGA SST, Default Mesh(10.219 mm).

  • SST K-Omega Turbulence Model
    Shear Stress Transport (SST) is a variant of the standard k–ω model and used when there are wall effects present within the case.
    The SST model accounts for the transport of turbulent shear stress and gives highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients. SST is recommended for high accuracy boundary layer simulations. Dependency on wall distance makes this less suitable for free shear flows compared to standard k-w. It requires mesh resolution near the wall.

    The calculation is done for 300 iterations.

    Results:

    Residual Plot: Number of iterations to converge - 213.

    Area Weighted Average temperature at outlet (30.25 ^oC)

    Standard deviation of temperature at outlet (1.85 ^oC)

    • Velocity contour plot on the cut planes along the pipe:
    • Velocity contour plot on the cut planes across the pipe:
    • Temperature contour plot on the cut planes along the pipe:
    • Temperature contour plot on the cut planes across the pipe:
    • Velocity line plot on the cut planes along the pipe:
    • Velocity line plot on the cut planes across the pipe:
    • Temperature line plot on the cut planes along the pipe:
    • Temperature line plot on the cut planes across the pipe:
    • Conclusion for Case-A:

    • 	ITERATIONS FOR CONVERGENCE	OUTLET TEMPERATURE in Degree Celsius
      K-EPSILON	160	30.25
      K-OMEGA SST	213	30.25

    • From the above table, we can observe that the outlet temperature of mixing tee is same when we compare that for k-epsilon and k-omega turbulence model. Also we conclude with that fact that k-omega SST model takes more iteration to converge the solution.

      We choose k-omega SST over k-epsilon realizable with standard wall function. The reason for choosing that the realizable k-ɛ model is provides improved predictions for the spreading rate of both planar and round jets and captured turbulence in the bulk flow.

      The SST model accounts for cross-diffusion which better marries the k-epsilon and k-omega models. Using a blended function based on wall distance, engineers can include cross-diffusion when away from the wall but not near it. In other words, using the wall distance as a switch, SST works like k-epsilon in the far field and k-omega near the target geometry.

    The model has superior performance to the
    k
    -epsilon model in simulating boundary layers with adverse pressure gradients. Ultimately, though, the performance of SST
    k
    -omega is not very different from the realizable
    k
    -epsilon two-layer model.
    • CASE-B: MESH INDEPENDENT STUDY
    • All settings, conditions and geometry is same as Case-A except mesh.
    • CASE-BA: Short Tee, MR-2, Model: k-omega SST, Mesh - 7 mm.Mesh:
    • Mesh is created for volume with element size - 7 mm.

    • Results:

      Residual Plot:

      Area Weighted Average temperature at outlet (30.25 ^oC)

      Standard deviation of temperature at outlet (1.85 ^oC)

    • CASE-BB: Short Tee, MR-2, Model: k-omega SST, Mesh - 5 mm.
    • Mesh: Mesh is created for volume with element size - 5 mm.

    • Results:

      Residual Plot: Number of iterations to converge - 223.

      Area Weighted Average temperature at outlet (30.25 ^oC)

      Standard deviation of temperature at outlet (2 ^oC)

    • CASE-BC: Short Tee, MR-2, Model: k-omega SST, Mesh - 3 mm.
    • Mesh: Mesh is created for volume with element size - 3 mm.

    • Results:

      Residual Plot: Number of iterations to converge - 281.

      Area Weighted Average temperature at outlet (30.25 ^oC)

      Standard deviation of temperature at outlet (2 ^oC)

    • Conclusion for CASE-B:

    • From the above three plot, we can observe that as we take coarse mesh size, it takes lesser iterations to converge the solution. The phenomenon behind this is that when we create a mesh so that we just break a whole geometry into the many element cells and now we solve the governing equation for these elements. So for finer mesh, we construct more equations and these equation takes more computation time to solve, resultant we need more iterations to get a converged solution. But we get a solution near to the exact solution. Also, we cannot use a smaller mesh without proper justification.

    • But if we generate the coarser mesh so we get some diffusion in our solution and that why we should care about the mesh size.

      Also when we go coarser to finer mesh then after a limit of element size we get the same results that are called a mesh independent solution. In this case, we start from element size 7mm to 3mm. We clearly see that for element size 3mm and 7mm, we get nearly the same residual plot, Standard deviation of temperature plot and iteration number at which our solution to converge. So we can continue our simulation with element size 5mm so that the computational time can be saved.

      CASE-1a: Short Tee, MR-2, Model: k-omega SST, Mesh: 5mm.
    • Boundaries:
    • Inlet_x:
    • Velocity: 3 m/s
    • Temperature: 360 C
    • Inlet_y:
    • Velocity: 6 m/s
    • Temperature: 190 C
    • Outlet:
    • Pressure Force Multiplier: 1
    • Back flow Temperature: 26.850 C
    • Material: Air is assigned as material for Volume.
    • Mesh: Size of element - 5mm
    • Turbulence Model: K-omega SST.

    • Results:

      Residual Plot: Number of iterations to converge - 223.

      Area Weighted Average temperature at outlet (30.25 ^oC)

      Standard deviation of temperature at outlet (2 ^oC)

    • Velocity contour plot on the cut planes along the pipe:
    • Velocity contour plot on the cut planes across the pipe:
    • Temperature contour plot on the cut planes along the pipe:
    • Temperature contour plot on the cut planes across the pipe:
    • Velocity line plot on the cut planes along the pipe:
    • Velocity line plot on the cut planes across the pipe:
    • Temperature line plot on the cut planes along the pipe:
    • Temperature line plot on the cut planes across the pipe:
    • CASE-1b: Short Tee, MR-4, Model: k-omega SST, Mesh: 5mm.
    • Boundaries:
    • Inlet_x:
    • Velocity: 3 m/s
    • Temperature: 360 C
    • Inlet_y:
    • Velocity: 12 m/s
    • Temperature: 190 C
    • Outlet:
    • Pressure Force Multiplier: 1
    • Back flow Temperature: 26.850 C
    • Material: Air is assigned as material for Volume.
    • Mesh: Size of element - 5mm
    • Turbulence Model: K-omega SST.

    • Results:

      Residual Plot: Number of iterations to converge - 175.

      Area Weighted Average temperature at outlet (27.5 ^oC)

      Standard deviation of temperature at outlet (1.5 ^oC)

    • Velocity contour plot on the cut planes along the pipe:
    • Velocity contour plot on the cut planes across the pipe:
    • Temperature contour plot on the cut planes along the pipe:
    • Temperature contour plot on the cut planes across the pipe:
    • Velocity line plot on the cut planes along the pipe:
    • Velocity line plot on the cut planes across the pipe:
    • Temperature line plot on the cut planes along the pipe:
    • Temperature line plot on the cut planes across the pipe:
    • CASE-2a: Long Tee, MR-2, Model: k-omega SST, Mesh: 5mm.
    • Boundaries:
    • Inlet_x:
    • Velocity: 3 m/s
    • Temperature: 360 C
    • Inlet_y:
    • Velocity: 6 m/s
    • Temperature: 190 C
    • Outlet:
    • Pressure Force Multiplier: 1
    • Back flow Temperature: 26.850 C
    • Material: Air is assigned as material for Volume.
    • Mesh: Size of element - 5mm
    • Turbulence Model: K-omega SST.

    • Results:

      Residual Plot: Number of iterations to converge - 253.

      Area Weighted Average temperature at outlet (30.35 ^oC)

      Standard deviation of temperature at outlet (1.25 ^oC)

    • Velocity contour plot on the cut planes along the pipe:
    • Velocity contour plot on the cut planes across the pipe:
    • Temperature contour plot on the cut planes along the pipe:
    • Temperature contour plot on the cut planes across the pipe:
    • Velocity line plot on the cut planes along the pipe:
    • Velocity line plot on the cut planes across the pipe:
    • Temperature line plot on the cut planes along the pipe:
    • Temperature line plot on the cut planes across the pipe:
    • CASE-2b: Long Tee, MR-4, Model: k-omega SST, Mesh: 5mm.
    • Boundaries:
    • Inlet_x:
    • Velocity: 3 m/s
    • Temperature: 360 C
    • Inlet_y:
    • Velocity: 12 m/s
    • Temperature: 190 C
    • Outlet:
    • Pressure Force Multiplier: 1
    • Back flow Temperature: 26.850 C
    • Material: Air is assigned as material for Volume.
    • Mesh: Size of element - 5mm
    • Turbulence Model: K-omega SST.

    • Results:

      Residual Plot: Number of iterations to converge - 197.

      Area Weighted Average temperature at outlet (27.5 ^oC)

      Standard deviation of temperature at outlet (0.75 ^oC)

    • Velocity contour plot on the cut planes along the pipe:
    • Velocity contour plot on the cut planes across the pipe:
    • Temperature contour plot on the cut planes along the pipe:
    • Temperature contour plot on the cut planes across the pipe:
    • Velocity line plot on the cut planes along the pipe:
    • Velocity line plot on the cut planes across the pipe:
    • Temperature line plot on the cut planes along the pipe:
    • Temperature line plot on the cut planes across the pipe:
    • Results Comparison & Conclusion:
  • Results Comparison:
    

    	Cell count	Average outlet temperature in oC	Number of iterations for convergence
    Case-1a:Short Tee, MR-2	14247	30.25	223
    Case-1b:Short Tee, MR-4	14247	27.5	175
    Case-2a:Long Tee, MR-2	18175	30.35	253
    Case-2b:Long Tee, MR-4	18175	27.5	197

• From the above table, the increase in the length does not affect much on the mixing tee of the same velocity, Temperature. While the change in velocity (momentum ratio 2 to 4) showed some better result in outlet temperature and took less iterations for the solution to converge.
• For the same momentum ratio, we get approx the same result for both geometries. So we can say that velocity is more dominant as compared to the length.
• For the same momentum ratio, we get approx the same result for both geometries. However it takes more execution time for the Longer tee to solve and produce about same results, which makes the shorter Tee joint more useful in this very specific observation.
• It was observed that efficient mixing was happened near the t-junction, where the hot and cold inlet air meets with different temperature and velocity.
• The average temperature and standard deviation at the outlet has been reduced in the long mixing tee too much as compared to short mixing tee.
• In momentum ratio 2 and 4 comparison with same geometry and mesh, we easily observe that with momentum ratio 4 more diffusion occur. And as a result more mixing occur.
• Increasing the momentum ratio causes the more mixing near the t_junction. This is a good idea to increase mixing efficiency.