# 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 [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 ($$6 m \times 5 m \times 13.5 m$$) 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 $$30 \leqslant y^+ \leqslant 300$$.

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:

Table 1: Mesh Metrics
Mesh type Number of volumes Type
snappyHexMesh $$38\ million$$ 3D Hex

## 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 Inlet Top Face Bottom Face Lateral Faces Outlet Body
Velocity $$63.7\ m/s$$ Symmetry $$63.7 m/s$$ (Moving Wall) Symmetry Zero Gradient Full Resolution
$$k$$ $$21.9$$ Symmetry Wall Function Symmetry Zero Gradient Full Resolution
Omega $$29215$$ Symmetry Wall Function Symmetry Zero Gradient Full Resolution
Pressure Zero Gradient Symmetry Wall Function Symmetry 0 Pa Full Resolution

The free stream velocity of the simulation is $$U = 63.7\ m/s$$, so that the Reynolds number based on the height of the body $$H$$ is $$Re = 1.2 \times 10^{6}$$. It is of the same order of magnitude used in the original experiment of Ahmed and Ramm [1].

## Results¶

Drag Coefficient

The drag coefficient is defined as

$$CD = Fd/0.5 \times rho \times U2 \times Ax$$

where $$Ax (0.112\ m^{2})$$ 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 $$0.298$$ [1].

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 [2].

## 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.