# 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
• Wake Flow Patterns

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.

Import validation project into workspace

## Geometry¶

The geometry is created based on the simplified aerodynamic body used by Ahmed et al [1]. 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 ($$0.4\ m \times 7.2\ m \times 0.7\ m$$) symmetric about the z-plane. The domain of interest is a 2-dimensional rectangular space $$2\ m$$ high and $$1\ m$$ wide as shown in Fig.1.

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.).

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 1: Mesh Metrics
Mesh type Number of volumes Type
snappyHexMesh $$3.35 \times 10^6$$ 3D hex

Fig.2. Mesh used for the SimScale case

## 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:

Table 2: Boundary Conditions for Ahmed Body simulation
Parameter Top and Left Symmetry Plane Inlet Outlet Ahmed Body Walls and Road
Velocity Zero Gradient Symmetry From File Zero Gradient $$0.0\ ms^{-1}$$
Pressure Zero Gradient Symmetry Zero Gradient $$0.0\ Pa$$ Zero Gradient
$$k$$ Zero Gradient Symmetry $$0.287\ m^2s^{-2}$$ Zero Gradient Wall Functions
omega Zero Gradient Symmetry $$0.215\ s^{-1}$$ Zero Gradient Wall Functions

The velocity at inlet is assigned through the file-upload option provided on the platform. The file corresponds to the velocity profile provided by experiments [1]. The mean flow velocity is $$40\ ms^{-1}$$.

## Results¶

Drag Coefficient

The drag coefficient of the Ahmed body was computed to be $$0.280$$, which is within a $$2\%$$ error margin of the measured value of $$0.283$$ [1].

Velocity Profiles

Variation of velocity with height was compared with reference data [1] on the symmetry plane at different lengths into the wind tunnel. These comparisons have been shown in Fig.3., with the simulation results in blue and reference data in red.

$$\ \$$ $$\$$

$$\ \$$ $$\$$

Fig.3. Comparison of velocity profiles with reference data on the symmetry plane at different distances into the wind tunnel. Simulation results are in blue, while reference data is in red.

Wake Flow Patterns

Shown below in Fig.4. are the comparisons of the velocity contours (left-half of the figures) at different tunnel cross-sections in the wake region of the Ahmed Body. They have been compared to the analytical results (shown in the right half of the figures) [2].

$$\ \$$ $$\$$

Fig.4. Velocity contours $$80$$ mm (left figure) and $$200$$ mm (right figure) behind the Ahmed body compared with experimental measurements.

## 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.