# Flow reattachment: Flow over a backward-facing step¶

## Overview¶

The aim of this test case is to validate steady-state flow over a backward-facing step. The incompressible, turbulent case is validated with the experimental results of Driver and Seegmiller [1] as archived in the NASA Turbulence Modeling Resource [2]. The following parameters have been analysed:

• Velocity Profiles
• Coefficient of Pressure
• Reattachment Length

The geometry was meshed locally and a mesh upload to the platform was performed.

Import validation project into workspace

## Geometry¶

The geometry is constructed based on the reference case [1], as shown in Fig.1. The height of the step is $$h = 12.7$$ cm, and the tunnel height is $$8h$$. The origin is located at the base of the step. The face details have been given in Table 1.

Fig.1. Geometry used in the study

Table 1: Domain Details
Face(s) Type
A Inlet
B+H Symmetry
C+D+E+G Walls
F Outlet

## Analysis type and Domain¶

The blockMesh tool was used to generate the mesh locally (see Fig.2. and Table 2.). A single-cell width was assigned in the z-direction to ensure a 2D mesh.

A typical property of the generated mesh is the $$y^+$$ (“y-plus”) value, which is defined as the non-dimensionalized distance to the wall; it is given by $$y^+ = u^*y/\nu$$. A $$y^+$$ value of 1 would correspond to the upper limit of the laminar sub-layer.

• Explicit resolution of the near-wall region: The first cell lies at most at the boundary of the laminar sub-layer and no further. Here, $$y^+$$ value is 1 or below.
• Use of wall-functions to resolve the near-wall region: There is no need to place cells very close to the laminar sub-layer, and typically $$30 \leqslant y^+ \leqslant 300$$.

A $$y^+$$ value of 30 was used for the inflation layer. The $$k-\omega$$ SST turbulence model was chosen, with wall functions for near-wall treatment of the flow.

Tool Type : OPENFOAM®

Analysis Type : simpleFoam

Mesh and Element types :

Table 2: Mesh Metrics
Mesh type Number of volumes Type
blockMesh $$5.5 \times 10^5$$ 2D hex

Fig.2. Mesh used for the SimScale case

## Simulation Setup¶

Fluid:

Kinematic Viscocity ($$\nu$$): $$1.4694 \times 10^{-5}\ m^2s^{-1}$$

The boundary conditions for the simulation are shown in Table 3.

Boundary Conditions:

Table 3: Boundary Conditions for Ahmed Body simulation
Parameter Inlet Symmetry Walls Outlet
Velocity $$44.2\ ms^{-1}$$ Symmetry $$0.0\ ms^{-1}$$ Zero Gradient
Pressure Zero Gradient Symmetry Zero Gradient $$0.0$$ Pa
$$k$$ $$5.336\ m^2s^{-2}$$ Symmetry Wall Function Zero Gradient
$$\omega$$ $$182.399\ s^{-1}$$ Symmetry Wall Function Zero Gradient

## Results¶

Velocity Profiles

Shown below in Figure 3 are comparisons of velocity profiles from SimScale simulation results with the reference [1] at different distances into the domain. All distances have been normalized with the step height $$h$$, and the velocity is normalized with respect to the inlet velocity $$v_{in} = 44.2\ ms^{-1}$$.

Fig.3. Vecloity profiles at different depths into the domain.

Coefficient of Pressure

Shown below in Figre 4 is the comparison of the cofficient of pressure $$C_p = \frac{P-P_{\infty}}{\frac{1}{2} \rho V_{\infty}^2}$$ from SimScale simulation results with the reference [1] at the lower and upper walls.

Fig.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. The reattachment length was calculated to be $$6.82\ cm$$, which lies within a $$12 \%$$ error limit of the experimental value of $$7.74\ cm$$ [2].

## Disclaimer¶

This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software and owner of the OPENFOAM® and OpenCFD® trade marks. OPENFOAM® is a registered trade mark of OpenCFD Limited, producer and distributor of the OpenFOAM software.