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\(^1\).
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.
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 direction
Minimum \([m]\)
Maximum \([m]\)
x
-1.5
0.5
y
0
0.1143
z
0
0.05
Table 1: Dimensional limits of the geometry
The faces and their respective boundary types\(^2\) are mentioned in Table 2:
Face(s)
Type
A
Inlet
B+H (upto 0.3867 \(m\) from A )
Symmetry
C+D+E+G
Walls
F
Outlet
Table 2: Faces on the geometry and their respective boundary 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 type
Number of cells
Element type
blockMesh
550000
2D Hexahedral
Table 3: Mesh metrics for the structured hexahedral mesh
The mesh can be seen below.
Figure 2: Structured 2D hexahedral mesh created locally and imported to SimScale
Simulation Setup
Fluid:
Air
Viscosity model: Newtonian
\((\nu)\) Kinematic viscosity: 1.469e-5 \(m²/s\)
\((\rho)\) Density: 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:
Parameter
Inlet
Symmetry
Walls
Outlet
Velocity \([m/s]\)
44.2
Symmetry
No slip
Zero Gradient
Pressure \([Pa]\)
Zero Gradient
Symmetry
Zero Gradient
0
\(k\) \([m^2/s^2]\)
5.366
Symmetry
Wall Function
Zero Gradient
\(\omega\) \([s^-1]\)
182.399
Symmetry
Wall Function
Zero 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 \(m/s\).
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).
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.
Figure 5: All Velocity [node] contours with emphasis on the reattachment region
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