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Documentation

Aerodynamics: Flow around the Ahmed Body

Overview

The aim of this test case is to validate the following parameters of steady-state incompressible turbulent flow around the Ahmed Body with a pre-referenced case 1:

  • Drag Coefficient
  • Velocity Profiles

The geometry is uploaded on to the SimScale platform and meshed using the snappyHexMesh tool. A fine resolution is provided behind the Ahmed Body to detect wakes.

See the validation project

Geometry

The geometry is created based on the simplified aerodynamic body used by Ahmed et al 2. See Fig.1.a for dimensions and Fig.1.b for the geometry. The slant angle (\(\psi\)) is set to 25 degrees. 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.

Fig.1.a. Dimensions of the Ahmed Body
Fig.1.b. Geometry used in the study

Analysis type and Domain

The snappyHexMesh tool was used to generate the mesh, with refinement near the walls and in the wake region (see Fig.2.).

Fig.2. Mesh used for the SimScale case

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.

  • 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. The \(k-\omega\) SST turbulence model was chosen, with full resolution for near-wall treatment of the flow.

Tool Type: OPENFOAM®

Analysis Type: simpleFoam

Mesh and Element types:

Mesh TypesNumber of VolumesType
snappyHexMesh38 million3D Hex
Table 1: Mesh Metrics

Simulation Setup

Fluid

Air with 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 3.

Boundary Conditions

ParameterInletTop FaceBottom FaceLateral Faces OutletBody
Velocity\(63.7\ m/s\)Symmetry\(63.7\ m/s\) (Moving Wall)SymmetryZero GradientFull Resolution
k21.9SymmetryWall FunctionSymmetryZero GradientFull Resolution
\(\omega\)29215SymmetryWall Function SymmetryZero GradientFull Resolution
PressureZero GradientSymmetryWall FunctionSymmetry0 PaFull Resolution
Table 2: Boundary Conditions for Ahmed Body simulation

The free stream velocity of the simulation is \(63.7\ m/s\), so that the Reynolds number based on the height of the body \(H\) is \(1.2 \times 10^{6} \). It is of the same order of magnitude used in the original experiment of Ahmed and Ramm 3.

Results

Drag Coefficient

The drag coefficient is defined as

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

where \(A_x\) (\(0.112m^2\)) is the projected area of the Ahmed body in streamwise direction and FD the drag force. The time-averaged drag force was determined by integration of surface pressure and shear stress over the entire Ahmed body. The resulting drag coefficient of the Ahmed body was computed to be \(0.306\) which is within a \(2.86%\) error margin of the measured value of \(0.298\) 4.

Wake Flow Patterns

The velocity streamline contour of mean flow obtained with the simulation is reported in Fig. 4 together with experimental results of reference 5.

Figure 3: Velocity Streamline contours
Figure 4: Experimental results
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