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.
Figure 1: Dimensions of the Ahmed Body
Figure 2: Three dimensional view of the geometry used in the study
The Standard Mesheralgorithm with tetrahedral and hexahedral cells was used to generate the mesh, with refinements near the walls and in the wake region (see Figure 3).
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
\(60\ m/s\)
Symmetry
Wall Function
Symmetry
Zero Gradient
Full Resolution
k
0.135
Symmetry
Wall Function
Symmetry
Zero Gradient
Full Resolution
\(\omega\)
180.1
Symmetry
Wall Function
Symmetry
Zero Gradient
Full Resolution
Pressure
Zero Gradient
Symmetry
Wall Function
Symmetry
0 Pa
Full Resolution
Table 2: Boundary Conditions for 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 reference solution is of the experimental type, as presented in [Ahmed]\(^1\). It is given in terms of the drag force coefficient:
where \(A_x\) (0.115 \(m^2\)) is the projected area of the Ahmed body in streamwise direction and \(F_{d}\) 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, 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
0.298
12.91
2
74.992
6.637
81.629
0.330
0.298
10.64
3
72.969
6.524
79.493
0.321
0.298
7.75
4
67.671
8.850
76.521
0.309
0.298
3.72
5
64.819
10.387
75.206
0.304
0.298
1.94
Table 2: Results comparison and computed errors
Figure 4 shows the mesh convergence plot:
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.
Figure 5: Velocity vectors and contours plotted with SimScale’s online post-processorFigure 6: Experimental results for comparison
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