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    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].

    Geometry

    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:

    t-junction pipe dimensions validation case
    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:

    DimensionMeasurement \([m]\)
    Diameter of the pipes \((D)\)0.051
    Length of the main pipe1.275
    Length of the branch pipe0.612
    Length of the mixing pipe0.6375
    Table 1: Dimensions of the sections of the pipe

    Analysis Type and Mesh

    Tool Type: OpenFoam®

    Analysis Type: Incompressible

    Turbulence Model: k-omega SST

    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:

    MeshMesh TypeCellsy+Element Type
    CoarseStandard876174< 13D tetrahedral/hexahedral
    ModerateStandard1246164< 13D tetrahedral/hexahedral
    FineStandard2034350< 13D 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.

    standard mesh full resolution y+ <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.

    Simulation Setup

    Material:

    • Water
      • Viscosity model: Newtonian
      • \((\nu)\) Kinematic viscosity: 9.3379e-7 \(m^2/s\)
      • \((\rho)\) Density: 999 \(kg/m^3\)

    Boundary Conditions:

    Figure 3 will be used as a reference for the definition of the boundary conditions:

    validation case t junction pipe boundary conditions
    Figure 3: Overview of the boundary conditions used in the present validation case

    The following boundary conditions are used:

    BoundaryBoundary TypeVelocity \([m/s]\)Pressure \([Pa]\)Turb. kinetic energy \([m^2/s^2]\)Specific dissipation rate \([1/s]\)Phase Fraction
    Main pipe inletCustom0.5 in the y-directionZero gradientFixed at 9.375e-4Fixed at 15.8Fixed at 1
    Branch pipe inletCustom-0.5 in the x-directionZero gradientFixed at 9.375e-4Fixed at 15.8Fixed at 0
    Mixing pipe outletCustomZero gradientFixed at 0Zero gradientZero gradientZero gradient
    Pipe wallsCustomFixed at 0Zero gradientFull resolutionFull resolutionZero gradient
    SymmetrySymmetrySymmetrySymmetrySymmetrySymmetrySymmetry
    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:

    assessing results pipe scalar
    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.

    scalar distribution results validation
    Figure 5: Comparison of the scalar distribution 51 mm downstream of the T-junction
    scalar distribution results validation 91 mm
    Figure 6: Comparison of the scalar distribution 91 mm downstream of the T-junction
    scalar distribution results validation downstream of t-junction
    Figure 7: Comparison of the scalar distribution 191 mm downstream of the T-junction
    scalar distribution results validation
    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.

    t junction pipe scalar simulation results validation
    Figure 9: Fine mesh results, showing scalar distribution contours on several cutting planes

    Last updated: September 30th, 2020

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