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Documentation

SimScale DocumentationValidation CasesValidation Case: Flow Reattachment: Flow Over a Backward-Facing Step

Validation Case: Flow Reattachment: Flow Over a Backward-Facing Step

The phenomenon of flow reattachment over a backward-facing step is a classic case in fluid mechanics. For this case, the following parameters have been validated:

  • Velocity Profiles
  • Coefficient of Pressure
  • Reattachment Length

The simulation results obtained through SimScale are compared against the experimental results of Driver and Seegmiller\(^1\).

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Geometry

The geometry used for validation is as shown in Figure 1. It has a backward-facing step with a height \(h\) of 0.0127 \(m\) at 1.5 \(m\) from the inlet face A.

backward facing step geometry used for simulation in simscale with faces, flow reattachment validation
Figure 1: Backward facing step geometry with faces described in Table 2

The minimum and maximum limits in the spatial directions are tabulated as follows:

Spatial directionMinimum \([m]\)Maximum \([m]\)
x-1.50.5
y00.1143
z00.05
Table 1: Dimensional limits of the geometry

The faces and their respective boundary types\(^2\) are mentioned in Table 2:

Face(s)Type
AInlet
B+H (upto 0.3867 \(m\) from A )Symmetry
C+D+E+GWalls
FOutlet
Table 2: Faces on the geometry and their respective boundary types

Analysis Type and Mesh

Tool Type: OpenFOAM®

Analysis Type: Incompressible steady state flow

Turbulence Model: k-omega SST

Mesh and Element Types:

The blockMesh tool was used to generate the hexahedral mesh locally and imported to the SimScale workbench. A single-cell width was assigned in the z-direction to ensure a 2D mesh.

The mesh near the walls is resolved for \(y^+\) > 30 meaning the first cell away from the wall lies in the logarithmic region. Read more about how to calculate y-plus (\(y^+\)) value here.

Note

  • For explicit resolution near the wall region, the first cell should lie in the laminar sub-layer region (\(y^+\) < 1). Such a wall is referred to as fully resolved.
  • Full resolution can be prevented by using wall-functions and placing the first cell in the logarithmic region (30 < \(y^+\) < 300).

    • The \(k-\omega\) SST turbulence model was chosen, with wall functions for the near-wall treatment of the flow.

    Mesh typeNumber of cellsElement type
    blockMesh5500002D Hexahedral
    Table 3: Mesh metrics for the structured hexahedral mesh

    The mesh can be seen below.

    two dimensional hex mesh with one cell thickness in the z direction
    Figure 2: Structured 2D hexahedral mesh created locally and imported to SimScale

    Simulation Setup

    Fluid:

    • Air
      • Viscosity model: Newtonian
      • Kinematic viscosity \((\nu)\): 1.469e-5 \(m²/s\)
      • Density \((\rho)\): 1 \(kg/m^3\)

    Boundary Conditions: Using the Custom boundary condition feature in SimScale. the parameters at the boundaries (Table 2) were set to the following values:

    ParameterInletSymmetryWallsOutlet
    Velocity \([m/s]\)44.2SymmetryNo slipZero Gradient
    Pressure \([Pa]\)Zero GradientSymmetryZero Gradient0
    \(k\) \([m^2/s^2]\)5.366SymmetryWall FunctionZero Gradient
    \(\omega\) \([s^-1]\)182.399SymmetryWall FunctionZero Gradient
    Table 3: Boundary conditions

    Result Comparison

    The comparisons for velocity, pressure coefficient, and the reattachment length were made between the experimental values\(^1\) and the simulation results from SimScale.

    Velocity Profiles

    Velocity profiles are compared across the domain height, normalized with the step height \(h\), at different distances into the domain. All distances have been normalized with \(h\) too while the velocity is normalized with respect to the inlet velocity 44.2 \(m/s\).

    velocity profile comparison across the height of the domain at various interval lengths
    Figure 3: Normalized velocity profiles across the domain height at different distances into the domain

    Coefficient of Pressure

    Shown below, in Figure 4, is the comparison of the coefficient of pressure \(C_p=\frac{P−P_∞}{\frac{1}{2}ρV^2_∞}\) with respect to the normalized distance from the inlet, obtained from the SimScale simulation with the experimental ones\(^1\) at the lower (faces C+D+E) and upper walls (face G).

    pressure coefficient comparison at lower and upper walls of the domain
    Figure 4: Coefficient of pressure at lower and upper walls

    Reattachment Length

    The reattachment length is the distance from the step at which the flow resumes in the positive flow direction all over the cross-section. Using the SimScale post-processor with the velocity vectors, checking the cell-velocity values for the reattachment length was calculated to be 6.84477 \(cm\), which lies within a 12% error limit of the experimental value\(^1\) of 7.74 \(cm\).

    A good look into the velocity contours, as observed in the SimScale post-processor, shows the reattachment region (blue) where the velocity is in the opposite direction of the dominant flow. This appears due to sudden change (step) in the geometry.

    velocity as observed in the simscale postprocessor showing the flow reattachment region
    Figure 5: All Velocity [node] contours with emphasis on the reattachment region

    References

    Last updated: February 20th, 2021

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