Aerodynamics: Flow around the Ahmed Body

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]$^1$.

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Geometry

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.

ahmed body geometry — Figure 2: Three dimensional view of the geometry used in the study

Analysis Type and Mesh

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 $mm$

Table 1: Mesh details

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).

ahmed body simulation mesh — Figure 3: Mesh used for the SimScale simulation, case number 5

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.

Simulation Setup

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

Table 2: Boundary Conditions for the Ahmed Body simulation

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$.

Reference Solution

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°:

$$ C_{d} = 0.2875 $$

Result Comparison

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

Table 2: Results comparison and computed errors

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

error percentage vs mesh cell count simscale — Figure 4: Mesh convergence plot for the different cases

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.

ahmed body wake velocity vectors — Figure 5: Velocity vectors and contours plotted with SimScale’s online post-processor

ahmed body wake experimental results — Figure 6: Experimental results for comparison showing a schematic of the streamlines over the Ahmed body

References

S.R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984

Note

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Last updated: April 17th, 2024

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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 \(mm\)