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TECHNICAL PAPERS

# Detached-Eddy Simulation of the Separated Flow Over a Rounded-Corner Square

[+] Author and Article Information
Kyle D. Squires

Mechanical and Aerospace Engineering Department, Arizona State University, Tempe, AZ 85287-6106

James R. Forsythe

Cobalt Solutions, LLC, 4636 New Carlisle Pike, Springfield, OH 45504

Philippe R. Spalart

Boeing Commercial Airplanes, Seattle, WA 98124-2207

J. Fluids Eng 127(5), 959-966 (Sep 01, 2005) (8 pages) doi:10.1115/1.1990202 History:

## Abstract

Detached-eddy simulation (DES) is used to study the massively separated flow over a rounded-corner square. The configuration is an idealization of the flow around a forebody cross section rotating at high angle of attack. Simulations are performed at sub- and supercritical Reynolds numbers, between which experimental measurements show a reversal of the side force. DES predictions are evaluated using experimental measurements and contrasted with unsteady Reynolds-averaged Navier–Stokes (URANS) results. The computations are also subjected to a moderate grid refinement, a doubling of the spanwise period, an enlargement of the domain in the other directions, and the removal of any explicit turbulence model. The sub- and supercritical flows are computed at Reynolds numbers of $105$ and $8×105$, respectively, and with the freestream at $10deg$ angle of attack. Boundary-layer separation characteristics (laminar or turbulent) are established via the initial and boundary conditions of the eddy viscosity. Following boundary layer detachment, a chaotic and three-dimensional wake rapidly develops. For the supercritical flow, the pressure distribution is close to the measured values and both the streamwise and side forces are in adequate agreement with measurements. For the subcritical flow, DES side-force predictions do not follow the experimental measurements far enough to achieve reversal.

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Copyright © 2005 by American Society of Mechanical Engineers
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## Figures

Figure 1

Cross section of the rounded-corner square and angle of attack of the freestream flow. Corner radius is 1∕4 the “diameter” D of the forebody. Angles are measured positive counterclockwise from the aft-symmetry stagnation point.

Figure 2

Instantaneous vorticity isosurfaces colored by pressure. Pressure contours on the far plane; vorticity contours in the near plane. Subcritical flow at Re=105 shown in (a); supercritical flow at Re=8×105 shown in (b).

Figure 3

Particle pathlines colored by νt∕ν from tripless solution at Re=105. Threshold of νt∕ν from 0 (dark) to 1 (light).

Figure 9

Pressure coefficient distribution around the forebody. Laminar separation cases. Symbols are measurements from Polhamus (1959) (10). ——— case 4 (Re=1×105); --- case 7 (Re=4×105).

Figure 10

Instantaneous streamlines around the lower-front corner of the square in the laminar separation case showing the thin region of reversed flow

Figure 4

Contours of the instantaneous vorticity in three spanwise planes for case 1 (on the left) and case 3 (on the right). Vorticity contours are from the turbulent separation cases at Re=8×105.

Figure 5

Force coefficients Cx and Cy from two-dimensional URANS at Re=8×105, turbulent boundary layer separation. --- Cx; ——— Cy.

Figure 6

Force coefficients Cx and Cy from case 2, DES prediction at Re=8×105, turbulent boundary layer separation. --- Cx; ——— Cy.

Figure 7

Pressure coefficient distribution around the forebody. Turbulent separation cases, Re=8×105. Symbols are measurements from Polhamus (1959) (10) ——— case 1; --- case 3; -∙- case 4; ⋯ case 5; – – – case 6; -∙∙- case 7; ●———● case 8.

Figure 8

Force coefficients Cx and Cy from case 4, DES prediction at Re=1×105, laminar boundary layer separation. --- Cx; ——— Cy.

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