Documentation

This validation case belongs to fluid mechanics, representing the aerodynamics of the Ahmed body study. The aim of this test case is to validate the following parameters:

- Drag coefficient computation
- Velocity profiles

The simulation results of SimScale were compared to the experimental data presented in [Ahmed]\(^1\).

The geometry is created based on the simplified aerodynamic body used by Ahmed et al\(^1\). See Figure 1 for dimensions and Figure 2 for the geometry. The slant angle (\(\phi\)) is set to 25°. The body is placed in a wind tunnel (\(6 m \times 5 m \times 13.5 m\)) in order to limit the aerodynamic blockage effect.

**Tool Type**: OpenFOAM®

**Analysis Type**: Turbulent Incompressible fluid flow

**Mesh and Element Types**:

Mesh # | Mesh Type | Number of Cells | Comments |
---|---|---|---|

1 | Standard | 3,826,602 | Far field mesh cell size 0.4 \(m\) |

2 | Standard | 4,673,973 | Far field mesh cell size 0.2 \(m\) |

3 | Standard | 8,594,246 | Far field mesh cell size 0.1 \(m\) |

4 | Standard | 10,351,196 | Body mesh cell size 3 \(mm\) |

5 | Standard | 24,257,180 | Body mesh cell size 2 \(mm\) |

The **Standard Mesher **algorithm with tetrahedral and hexahedral cells was used to generate the mesh, with refinements near the walls and in the wake region (see Figure 3).

A typical property of the generated mesh is the \(y^+\) (“*y-plus*“) value, which is defined as the non-dimensionalized distance to the wall, learn more. A \(y^+\) value of 1 would correspond to the upper limit of the laminar sub-layer.

Wall treatment

*Full Resolution in 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 \(30 \le y^+ \le 300\).

An average \(y^+\) value of 1 was used for the inflation layer around the body, and 150 for the floor. The \(k-\omega\) SST turbulence model was chosen, with full resolution for near-wall treatment of the flow around the body and with wall function for the floor.

**Fluid**

Air with a kinematic viscosity of \(1.5 \times 10^{-5}\ kg/ms\) is assigned as the domain fluid. The boundary conditions for the simulation are shown in Table 2.

**Boundary Conditions**

Parameter | Inlet | Top Face | Bottom Face | Lateral Faces | Outlet | Body |

Velocity \([m/s]\) | 60 | Symmetry | Wall Function | Symmetry | Zero Gradient | Full Resolution |

k \([m^2/s^2]\) | 0.135 | Symmetry | Wall Function | Symmetry | Zero Gradient | Full Resolution |

\(\omega\) \([1/s]\) | 180.1 | Symmetry | Wall Function | Symmetry | Zero Gradient | Full Resolution |

Pressure \([Pa]\) | Zero Gradient | Symmetry | Wall Function | Symmetry | 0 | Full Resolution |

The free stream velocity of the simulation is \(60\ m/s\), so that the Reynolds number based on the length of the body \(L\) is \(4.29 \times 10^{6} \). Those are the same values presented in the original experiment of Ahmed and Ramm\(^1\).

The experimental solution is presented in Figure 4 in the reference paper\(^1\) giving the value for the drag force coefficient for the slant angle \(\phi\) = 25°:

$$ C_{d} = 0.2875 $$

**Drag Coefficient**

The drag force is defined as

$$ F_{d}={\frac {1}{2}}\rho \,U^{2}\,C_{d}\,A_x $$

where \(A_x\) (0.115 \(m^2\)) is the projected area of the Ahmed body in the streamwise direction and \(F_{d}\) the drag force. The time-averaged drag force was determined by the integration of surface pressure and shear stress over the entire Ahmed body. The resulting drag coefficient of the Ahmed body, closest to the reference solution as yielded by the finer mesh (case number 5), was computed to be \(0.304\) which is within a \(1.94%\) error margin of the measured value.

Table 3 shows the result of the mesh independence study:

Mesh # | PRESSURE FORCE \([N]\) | VISCOUS FORCE \([N]\) | TOTAL DRAG \([N]\) | DRAG COEFFICIENT | REFERENCE | ERROR [%] |
---|---|---|---|---|---|---|

1 | 76.758 | 6.540 | 83.298 | 0.336 | 0.2875 | 16.87 |

2 | 74.992 | 6.637 | 81.629 | 0.330 | 0.2875 | 14.78 |

3 | 72.969 | 6.524 | 79.493 | 0.321 | 0.2875 | 11.65 |

4 | 67.671 | 8.850 | 76.521 | 0.309 | 0.2875 | 7.48 |

5 | 64.819 | 10.387 | 75.206 | 0.304 | 0.2875 | 5.74 |

Figure 4 shows the decreasing error trend in a mesh convergence plot:

**Wake Flow Patterns**

The velocity streamline contour of mean flow obtained with the simulation is reported in Figure 5 together with experimental results of reference.

Note

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Last updated: April 17th, 2024

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