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    SimScale DocumentationValidation CasesAerodynamics: Flow around the Ahmed Body

    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]\(^1\).

    View Project

    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 dimensions
    Figure 1: Dimensions of the Ahmed Body
    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 TypeNumber of CellsComments
    1Standard3,826,602Far field mesh cell size 0.4 \(m\)
    2Standard4,673,973Far field mesh cell size 0.2 \(m\)
    3Standard8,594,246Far field mesh cell size 0.1 \(m\)
    4Standard10,351,196Body mesh cell size 3 \(mm\)
    5Standard24,257,180Body 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

    ParameterInletTop FaceBottom FaceLateral Faces OutletBody
    Velocity \([m/s]\)60 SymmetryWall FunctionSymmetryZero GradientFull Resolution
    k \([m^2/s^2]\)0.135 SymmetryWall FunctionSymmetryZero GradientFull Resolution
    \(\omega\) \([1/s]\)180.1 SymmetryWall Function SymmetryZero GradientFull Resolution
    Pressure \([Pa]\)Zero GradientSymmetryWall FunctionSymmetry0 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    		REFERENCEERROR [%]
    176.7586.54083.2980.3360.287516.87
    274.9926.63781.6290.3300.287514.78
    372.9696.52479.4930.3210.287511.65
    467.6718.85076.5210.3090.28757.48
    564.81910.38775.2060.3040.28755.74
    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

    Note

    If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.

    Last updated: April 17th, 2024

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