Validation Case: Scalar Transport in T-Junction Pipe
The scalar transport in a T-junction pipe validation case belongs to fluid dynamics. This test case aims to validate the following:
Scalar mixing distribution
In this project, a T-junction pipe is used to simulate passive scalar mixing. The SimScale results are compared to the experimental results reported in [1] and [2].
The geometry consists of a pipe with 3 sections: a main pipe, a branch pipe, and a mixing pipe. Figure 1 highlights the pipe dimensions:
Figure 1: Dimensions of the T-junction pipe sections
Due to the symmetrical nature of the geometry, only half of the pipe is captured. The pipes have a diameter \(D\) of 51 \(mm\), which is the same as used in the experimental setup. Details of the pipe dimensions are provided in Table 1:
Mesh and Element Types: This validation case uses a total of 3 meshes, to perform a mesh independence study. All meshes were created in SimScale with the standard mesher algorithm. In Table 2, an outline of the meshes is presented:
Mesh
Mesh Type
Cells
y+
Element Type
Coarse
Standard
876174
< 1
3D tetrahedral/hexahedral
Moderate
Standard
1246164
< 1
3D tetrahedral/hexahedral
Fine
Standard
2034350
< 1
3D tetrahedral/hexahedral
Table 2: Overview of the meshes used for the independence study
Figure 2 shows the discretization of the mixing pipe obtained with the fine mesh. A total of 10 inflation layers were used to resolve the boundary layer, aiming to achieve a y+ value smaller than 1.
Figure 2: Fine standard mesh created in SimScale, showing the end of the mixing pipe (outlet). Ten inflation layers are added to resolve the boundary layer.
Figure 3 will be used as a reference for the definition of the boundary conditions:
Figure 3: Overview of the boundary conditions used in the present validation case
The following boundary conditions are used:
Boundary
Boundary Type
Velocity \([m/s]\)
Pressure \([Pa]\)
Turb. kinetic energy \([m^2/s^2]\)
Specific dissipation rate \([1/s]\)
Phase Fraction
Main pipe inlet
Custom
0.5 in the y-direction
Zero gradient
Fixed at 9.375e-4
Fixed at 15.8
Fixed at 1
Branch pipe inlet
Custom
-0.5 in the x-direction
Zero gradient
Fixed at 9.375e-4
Fixed at 15.8
Fixed at 0
Mixing pipe outlet
Custom
Zero gradient
Fixed at 0
Zero gradient
Zero gradient
Zero gradient
Pipe walls
Custom
Fixed at 0
Zero gradient
Full resolution
Full resolution
Zero gradient
Symmetry
Symmetry
Symmetry
Symmetry
Symmetry
Symmetry
Symmetry
Table 3: Summary of the boundary conditions for the present validation case
Model:
\((Sc_{t})\) Turb. Schmidt number = 0.1
Diffusion coefficients = 2.3e-9 \(m^2/s\)
Note
The turbulent Schmidt number is the ratio of momentum diffusivity to mass diffusivity in a turbulent flow\(^3\).
Following the turbulent Schmidt number sensitivity tests performed by Frank et. al\(^2\), we will use a value of 0.1 in the simulations.
Result Comparison
The numerical simulation results for the mixing scalar are compared with experimental data provided by the Laboratory for Nuclear Energy Systems, Institute for Energy Technology (ETHZ), Zürich\(^1\), and also mentioned by Frank et. al\(^2\).
A comparison of the mixing scalar distribution obtained with SimScale and experimental results is presented. The scalar distribution is assessed over four lines, placed 51, 91, 191, and 311 mm downstream of the T-junction:
Figure 4: The results are assessed over the four red lines, positioned downstream of the T-junction.
Below, a series of figures show the comparison of results from SimScale to the experimental data for the scalar distribution.
Figure 5: Comparison of the scalar distribution 51 mm downstream of the T-junction
Figure 6: Comparison of the scalar distribution 91 mm downstream of the T-junction
Figure 7: Comparison of the scalar distribution 191 mm downstream of the T-junction
Figure 8: Comparison of the SimScale results for the coarse, moderate, and fine meshes, against experimental data
The SimScale results show a good agreement with the experimental data from [1]. Also, a great agreement is observed when comparing the SimScale results to the numerical studies presented by Frank et. al.
Figure 9: Fine mesh results, showing scalar distribution contours on several cutting planes
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