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Documentation

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 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 3, 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.

[IMAGE MISSING]

Figure 1: Geometry used in the study
Face(s)Type
AInlet
B+HSymmetry
C+D+E+GWalls
FOutlet
Table 1: Domain details

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 \(30 \le y^+ \le 300\).

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 :

Mesh typeNumber of VolumesType
blockmesh/(5.5 times 10^5\)2D Hex
Table 2: Mesh Metrics
Figure 2: Mesh used for the SimScale case

Simulation Setup

Fluid:

Kinematic Viscocity (\(5.5 \times 10^5\)): \(\nu\)

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

Boundary Conditions:

ParameterInletSymmetryWallsOutlet
Velocity\(44.2\ ms^-1\)SymmetryNo slipZero Gradient
PressureZero GradientSymmetryZero Gradient
\(k\)\(5.336m^2s^-2\)SymmetryWall FunctionZero Gradient
\(\omega\)\(182.399s^-1\)SymmetryWall FunctionZero Gradient
Table 3: Boundary Conditions for

Results

Velocity Profiles

Shown below in Figure 3 are comparisons of velocity profiles from SimScale simulation results with the reference 4 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 \(44.2\ ms^{-1}\).

Coefficient of Pressure

Shown below in Figure 4 is the comparison of the coefficient of pressure \(C_p=\frac{P−P_∞}{1/2ρV^2_∞}\) from SimScale simulation results with the reference 5 at the 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 \(7.74\ cm^2\) 6.

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