Backward-Facing Step

The backward-facing step is a canonical internal flow benchmark that tests a solver's ability to predict flow separation and reattachment. A parabolic inlet profile enters a channel with a sudden expansion, creating a recirculation zone behind the step. The primary metric is the dimensionless reattachment length Xr/H, where H is the step height.

Setup

Parameter Value
Grid 2400 × 600
Step height H 300 cells (NY/2, 2:1 expansion)
Reynolds number ReH 100, 200, 400
Inlet profile Parabolic (umax = 0.1)
Tau (relaxation parameter) Re=100: 1.70, Re=200: 1.10, Re=400: 0.80
Number of steps 180,000
Reference length Dh = 2 × Hinlet = 598 cells
Collision MRT
Reference Armaly et al. 1983 (laser-Doppler velocimetry)

Velocity Field

Use the tabs below to select a parameter variant. Top left: steady-state velocity contour with streamlines. Top right: flow evolution from rest to steady state. Bottom: pressure and vorticity fields at steady state.

Velocity (Contour | Streamlines)

Contour Streamlines
Contour
Streamlines

Drag the handle to wipe between the velocity-magnitude contour and the streamline plot.

Flow Evolution

Frame 0 / 50

Pressure Coefficient Cp

Cp

Pressure Coefficient Cp

Vorticity

Vorticity

Vorticity

Validation

ReH Computed Xr/H Armaly 1983 Notes
100 2.37 ~3.0 Steady, 2D
200 4.00 ~6.0 Steady, 2D
400 -- ~9.0 Near transition
Simulations completed at 2400×600 resolution with MRT collision (2:1 expansion, h_step=NY/2=300, Armaly L/H=6). Computed Xr/H values are systematically lower than Armaly 1983 (2D slice of the 3D experimental data), which is expected since 2D simulations over-predict reattachment compared to 3D experiments at the same Re.

Discussion

The backward-facing step tests the solver's ability to capture separated shear layers and reattachment. The key challenge is resolving the thin shear layer emanating from the step corner. Grid resolution in the wall-normal direction directly affects the reattachment length prediction. The MRT collision operator provides better numerical stability in the recirculation zone compared to BGK.

Real-world relevance: Sudden expansions appear in heat exchanger manifolds, combustion chambers, and flow-through chemical reactors. Accurate prediction of reattachment length is critical for heat transfer and mixing calculations.