2D Asymmetric Plane Diffuser (SST)

Overview

This case validates the solver's prediction of turbulent boundary-layer separation under an adverse pressure gradient in the asymmetric plane diffuser of Buice & Eaton, run with the k-omega SST turbulence model and compared to the WIND SST computation of NASA/TM-2005-213894. A fully developed plane-channel flow enters a one-sided diffuser: the lower wall is inclined at ${10}^{\circ }$ while the upper wall stays flat, so the cross-section opens to 4.7 times the inlet height. The resulting deceleration sets up an adverse pressure gradient that separates the boundary layer on the inclined wall, producing a recirculation bubble that reattaches downstream while the flat wall stays attached. Because the separation occurs on a smooth (geometrically un-forced) wall, its location and extent depend on the turbulence model's response to the pressure gradient, which makes the configuration a test of RANS closures. The skin-friction quantities the reference paper reports for its SST run are reproduced here: skin friction on the upper (flat) wall and skin friction on the lower (inclined) wall, with the Buice & Eaton measured skin friction overlaid for comparison.

Problem Setup

The geometry follows the reference paper, with the inlet channel height $H$ as the reference length. A straight inlet channel $110H$ long upstream of the diffuser lets the wall boundary layers develop naturally, so no profile-inlet boundary condition is needed. The inclined wall descends at ${10}^{\circ }$ over a length of $21H$ to an exit height of $4.7H$, rounded with fillets at the start and end of the ramp (matching the experiment's contoured corners); the start of the expansion is $x/H=0$. A recovery channel extends downstream so the separated shear layer reattaches and the boundary layer redevelops. The Reynolds number is $R{e}_H=2\times {10}^4$, based on the inlet centerline velocity and $H$, with the viscosity held constant to fix it. Turbulence is modelled with k-omega SST, integrated to the wall.

The mesh is the paper's recommended baseline $341\times 81$ grid at a near-wall spacing of $y^{+}\approx 1$. The paper's own grid-resolution study (coarse $341\times 41$, medium $341\times 81$, fine $341\times 161$, all at $y^{+}=1$) found the medium and fine grids essentially identical and selected the medium grid for all SST runs; the first off-wall cell here sits at $y^{+}\approx 1$. Because the comparison is against a single published SST curve set on this grid-independent mesh, a single converged grid is reported rather than a grid-convergence sweep.

The boundary conditions replicate the WIND deck by type, not merely by flow state: a compressible ideal-gas flow at Mach $0.0589$ (static $14.7$ psia, $530{}^{\circ }R$; incompressible in practice) with a subsonic total-pressure inflow holding the stagnation $p_0,T_0$ (the paper's "Arbitrary Inflow / hold totals" condition), no-slip adiabatic walls, and a static back-pressure outflow set to recover the experimental bulk velocity upstream of the diffuser, the same procedure WIND used. Matching the boundary-condition type keeps the comparison a code-to-code test on an identical setup. One model difference is noted: Luminary runs Menter's SST-2003m variant, whereas the paper's WIND "SST" is the standard Menter k-omega SST; the two differ in the separated, strong-pressure-gradient region.

Quantities of Interest

The two quantities compared to the WIND SST curves are the skin-friction coefficient $C_f(x/H)$ on the upper (flat) wall and the skin-friction coefficient on the lower (inclined) wall. Both are referenced to the inlet bulk dynamic pressure $\frac{1}{2}\rho U_b^2$: on the lower wall $C_f<0$ marks the separated recirculation region, and its zero crossings give the separation and reattachment locations, while the upper wall stays attached throughout. On the lower wall the Buice & Eaton measured skin friction is overlaid as symbols alongside the WIND SST and Luminary curves; the upper (flat) wall similarly shows the WIND SST, Luminary, and Buice & Eaton measured curves.