Verification & Validation
V&V Manual / Des-Les

Backward-Facing Step: DDES (Vogel-Eaton)

validation

VerificationValidation3DDES/LESSpalart–AllmarasIdeal gasUnsteadyEnergy equation
Instantaneous velocity magnitude \( |V|/U_{ref} \)
Instantaneous velocity magnitude on the spanwise mid-plane from the DDES; the resolved turbulent structures form in the separated shear layer downstream of the step and through reattachment.

Overview

The backward-facing step is a separated-flow benchmark: a turbulent boundary layer detaches at a sharp step, forms a recirculation bubble, and reattaches on the wall downstream. The reattachment length and the recovery of the wall shear stress are sensitive measures of how well a turbulence treatment represents the separated shear layer and its reattachment.

This case computes the Vogel & Eaton (1985) step at Reh=28,000 with Spalart-Allmaras Delayed Detached Eddy Simulation (DDES), a scale-resolving hybrid RANS-LES method that runs RANS in the attached boundary layer and resolves the turbulent eddies of the separated shear layer and wake. The result is compared two ways: against the Vogel-Eaton experiment, and against the enhanced-DDES simulation of Shur et al. (2015), which used the same vortex-tilting-measure length scale on this configuration.

Problem Setup

The geometry is a backward-facing step of height H=12.7 mm with a 5:4 channel expansion ratio. The domain is three-dimensional and spanwise-periodic over a width of 4H. The inflow develops along an upstream section (a slip-wall startup region followed by a no-slip wall long enough to establish δ99/H≈1.08 at the step edge), then expands over the step into a downstream channel of length 20H. The mesh is a structured-hexahedral grid of about 3.92 million cells with near-wall spacing giving y+≈1 on the resolved walls.

The fluid is treated as an ideal gas with Sutherland's-law viscosity. The boundary conditions are a total-pressure inlet (p0=101,868 Pa, T0=300.44 K), a static-pressure outlet, no-slip adiabatic walls on the step-side and opposite channel walls, slip walls on the upstream startup section, and a translational periodic pair across the span.

Turbulence is modeled with Spalart-Allmaras DDES using the 2015 vortex-tilting-measure length scale and an fd shielding function, with CDES=0.65. The convective scheme is a low-dissipation variant of FDS that blends upwind and centered contributions. Time integration is second-order implicit (BDF2) at a fixed step Δt=3×10−6 s; the simulation is first advanced until the flow is statistically stationary, after which time- and spanwise-averaged statistics are accumulated.

Quantities of Interest

The primary quantities are the skin-friction coefficient Cf along the step-side (lower) wall, whose zero crossing locates the mean reattachment point, measured at x/H≈6.97, and the mean streamwise velocity profiles U/Uref at four downstream stations, x/H=3.2,5.87,9.53,14.87. Both are compared against the Vogel-Eaton experiment and the Shur et al. (2015) DDES.

Sources

J. C. Vogel and J. K. Eaton, "Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step," Journal of Heat Transfer 107(4):922-929, 1985.: https://doi.org/10.1115/1.3247522
Backward-facing step experiment at Reh=28,000, expansion ratio 5:4; skin friction and reattachment on the step-side wall.
M. L. Shur, P. R. Spalart, M. Kh. Strelets, and A. K. Travin, "An Enhanced Version of DES with Rapid Transition from RANS to LES in Separated Flows," Flow, Turbulence and Combustion 95:709-737, 2015.: https://doi.org/10.1007/s10494-015-9618-0
Enhanced DDES with the vortex-tilting-measure length scale; the backward-facing step is one of its validation cases (Figs. 33-35), giving the code-to-code reference Cf and velocity profiles.

Results

Lower-wall skin friction Cf

Lower-wall skin friction \( C_f \)
Time- and spanwise-averaged skin-friction coefficient on the step-side (lower) wall versus the Vogel-Eaton experiment and the Shur et al. (2015) DDES; the zero crossing locates reattachment.

Reference: J. C. Vogel and J. K. Eaton, "Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step," Journal of Heat Transfer 107(4):922-929, 1985. (digitized from Shur et al. (2015), Figs. 33a, 35): https://doi.org/10.1115/1.3247522

Reattachment (C_f zero crossing): x_r/H = 6.97.

Mean streamwise velocity profiles U/Uref

Mean streamwise velocity profiles \( U/U_{ref} \)
Mean streamwise velocity profiles at x/H=3.2,5.87,9.53,14.87 versus the Vogel-Eaton experiment and the Shur et al. (2015) DDES, one panel per station.

Reference: J. C. Vogel and J. K. Eaton, "Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step," Journal of Heat Transfer 107(4):922-929, 1985. (digitized from Shur et al. (2015), Fig. 34): https://doi.org/10.1115/1.3247522

Solver configuration

features exercised
VerificationValidation3DDES/LESSpalart–AllmarasIdeal gasUnsteadyEnergy equation