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

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.

Face(s) | Type |
---|---|

A | Inlet |

B+H | Symmetry |

C+D+E+G | Walls |

F | Outlet |

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/ν. 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⩽y+⩽300.

A y+ value of 30 was used for the inflation layer. The k−ω 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 type | Number of volumes | Type |
---|---|---|

blockMesh |
5.5 * 105 | 2D hex |

*Fluid:*

Kinematic Viscocity (ν = 1.4694×10−5 m2s−1)

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

*Boundary Conditions:*

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 m2s−2 | Symmetry | Wall Function | Zero Gradient |

ω | 182.399 s−1 | Symmetry | Wall Function | Zero Gradient |

**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 vin=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 Cp=P−P∞12ρV2∞ 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.

[1] | (1, 2, 3, 4) Driver, D. M. and Seegmiller, H. L., “Features of Reattaching Turbulent Shear Layer in Divergent Channel Flow,” AIAA Journal, Vol. 23, No. 2, Feb 1985, pp. 163-171. |

[2] | (1, 2) Langley Research Center: Turbulence Modeling Resource – 2D Backward Facing Step |

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