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# 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$$^1$$.

## 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.

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

The faces and their respective boundary types$$^2$$ are mentioned in Table 2:

## 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.

The mesh can be seen below.

## 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:

## 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 $$m/s$$.

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).

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.

Last updated: February 20th, 2021