Flow Reattachment: Flow over a Backward-Facing Step

Analysis type and Domain

The blockMesh tool was used to generate the mesh locally (see Fig.2. and Table 2.). A single-cell width was assigned in the z-direction to ensure a 2D mesh.

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/ν

. A y+

 value of 1 would correspond to the upper limit of the laminar sub-layer.

• Explicit resolution of the near-wall region: The first cell lies at most at the boundary of the laminar sub-layer and no further. Here, y+
  $y^{+}$

   

  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⩽y+⩽300
  $30⩽y^{+}⩽300$

   

  .

A y+

 value of 30 was used for the inflation layer. The k−ω

 SST turbulence model was chosen, with wall functions for near-wall treatment of the flow.

Tool Type : OPENFOAM®

Analysis Type : simpleFoam

Mesh and Element types :

Simulation Setup

Fluid:

Kinematic Viscocity (ν

$\nu$

): 1.4694×10−5 m2s−1

$1.4694\times {10}^{-5}{m}^2{s}^{-1}$

 

The boundary conditions for the simulation are shown in Table 3.

Boundary Conditions:

Table 3: Boundary Conditions for Ahmed Body simulation¶

Parameter	Inlet	Symmetry	Walls	Outlet
Velocity	44.2 ms−1 $44.2m{s}^{-1}$	Symmetry	0.0 ms−1 $0.0m{s}^{-1}$	Zero Gradient
Pressure	Zero Gradient	Symmetry	Zero Gradient	0.0 $0.0$  Pa
k $k$	5.336 m2s−2 $5.336m^2{s}^{-2}$	Symmetry	Wall Function	Zero Gradient
ω $\omega$	182.399 s−1 $182.399s^{-1}$	Symmetry	Wall Function	Zero Gradient

Results

Velocity Profiles

Shown below in Figure 3 are comparisons of velocity profiles from SimScale simulation results with the reference [1] at different distances into the domain. All distances have been normalized with the step height h

$h$

, and the velocity is normalized with respect to the inlet velocity vin=44.2 ms−1

$v_{in}=44.2m{s}^{-1}$

.

 

 

Fig.3. Velocity profiles at different depths into the domain.

Coefficient of Pressure

Shown below in Figure 4 is the comparison of the coefficient of pressure Cp=P−P∞12ρV2∞

$C_p=\frac{P-P_{\mathrm{\infty }}}{\frac{1}{2}\rho V_{\mathrm{\infty }}^2}$

 from SimScale simulation results with the reference [1] at the lower and upper walls.

 

Fig.4. Coefficient of Pressure at lower and upper walls

Reattachment Length

The reattachment length is the distance from the step at which the flow resumes in the positive flow direction all over the cross-section. The reattachment length was calculated to be 6.82 cm

$6.82cm$

, which lies within a 12%

$12\mathrm{\%}$

 error limit of the experimental value of 7.74 cm

$7.74cm$

 [2].

References

[1]	(1, 2, 3, 4) Driver, D. M. and Seegmiller, H. L., “Features of Reattaching Turbulent Shear Layer in Divergent Channel Flow,” AIAA Journal, Vol. 23, No. 2, Feb 1985, pp. 163-171.

[2]	(1, 2) Langley Research Center: Turbulence Modeling Resource – 2D Backward Facing Step

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.

Last updated: January 29th, 2019

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