Backward-Facing Step Flow at Re = 400 (Armaly et al. Benchmark)

Internal Hydrodynamics (CFD)PASS · 2.37%

Laminar flow separation, recirculation bubble, and sudden expansion pressure recovery over a backward-facing step (step height S = 5 mm, expansion ratio ER = 2.0) at Reynolds number Re = 400, verified against the benchmark of Armaly et al. and the Borda-Carnot… show full text

Tolerance:: 5%

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Problem statement

Geometry: Two-stage channel with sudden backward-facing step: inlet channel height h = 5 mm, downstream channel height H = 10 mm (step height S = 5 mm, expansion ratio ER = 2.0, width W = 10 mm), total length L = 200 mm.
Material: Air at 20 °C (density rho = 1.204 kg/m³, dynamic viscosity mu = 1.825e-5 Pa·s, kinematic viscosity nu = 1.516e-5 m²/s), incompressible steady laminar Navier-Stokes model.
Boundary conditions: Inlet uniform velocity U_in = 0.3032 m/s (Re = 400 based on hydraulic diameter D_h = 2h), outlet gauge pressure 0 Pa, symmetry on spanwise side walls (surface numbers 6, 8), no-slip viscous wall on channel walls and step face (surface numbers 1, 2, 4, 7).
Measured quantity: Step and downstream channel wall drag coefficient Cd = 1.150, verified against benchmark simulation of Armaly et al.; secondary checks on Borda-Carnot sudden expansion pressure recovery Delta p > 0, recirculation zone formation, and mass conservation |Delta m| <= 2%.

WebCAE Terminal

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

units mm
import path="cfd_backward_facing_step.step" format=step
mesh tet size=2
cfd fluid air
cfd set mode=steady speed=0.30316 turbulence=laminar iterations=350 tol=1e-5 threads=8 cfl=5 multigrid=0
cfd inlet surface number 5 speed=0.30316 intensity=0.01
cfd outlet surface number 3 pressure=0
cfd symmetry surface number 6
cfd symmetry surface number 8
cfd wall surface number 1 monitor=on
cfd wall surface number 2 monitor=on
cfd wall surface number 4 monitor=on
cfd wall surface number 7 monitor=on
solve cfd

Results comparison

Reference value	1.150
Our result	1.123
Deviation	2.37%
Tolerance	5%
Status	PASS · 2.37%
Element family	Finite-volume CFD
Mesh details	4799 узлов, 18371 тет (Netgen P1 tet mesh, канал с внезапным расширением Re=400)

Updated: 2026-10-19 · WebCAE solver