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.

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).

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:

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.

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