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Research Papers: Fundamental Issues and Canonical Flows

Performance of Two-Equation Turbulence Models for Flat Plate Flows With Leading Edge Bubbles

[+] Author and Article Information
S. Collie, M. Gerritsen, P. Jackson

 Stanford Yacht Research, 367 Panama Street, Stanford, CA 94305-2220

J. Fluids Eng 130(2), 021201 (Jan 24, 2008) (11 pages) doi:10.1115/1.2829596 History: Received June 06, 2005; Revised July 26, 2007; Published January 24, 2008

This paper investigates the performance of the popular k-ω and SST turbulence models for the two-dimensional flow past the flat plate at shallow angles of incidence. Particular interest is paid to the leading edge bubble that forms as the flow separates from the sharp leading edge. This type of leading edge bubble is most commonly found in flows past thin airfoils, such as turbine blades, membrane wings, and yacht sails. Validation is carried out through a comparison to wind tunnel results compiled by Crompton (2001, “The Thin Aerofoil Leading Edge Bubble,  ” Ph.D. thesis, University of Bristol). This flow problem presents a new and demanding test case for turbulence models. The models were found to capture the leading edge bubble well with the Shear-Stress Transport (SST) model predicting the reattachment length within 7% of the experimental values. Downstream of reattachment both models predicted a slower boundary layer recovery than the experimental results. Overall, despite their simplicity, these two-equation models do a surprisingly good job for this demanding test case.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of the flow past a flat plate at shallow incidence

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Figure 2

Schematic of the leading edge bubble illustrating the secondary bubble near the leading edge

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Figure 3

Model dimensions

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Figure 4

Details of the domain for the flat plate

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Figure 5

Computational grid for the flat plate (medium resolution)

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Figure 6

Grid convergence of the lift and drag coefficients (α=3deg)

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Figure 7

Reattachment lengths versus angle of attack for the CFD compared with Crompton’s data

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Figure 8

Flow streamlines and the measurement stations for the flate plate at α=1deg (SST model)

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Figure 9

Chordwise velocity profiles within the leading edge bubble (α=1deg). (a) x/c=0.031, (b) x/c=0.125.

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Figure 10

Near-wall chordwise velocity profiles within the leading edge bubble (α=1deg). (a) x/c=0.031, (b) x/c=0.125.

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Figure 11

Chordwise velocity profiles downstream of reattachment (log scale, α=1deg). (a) x/c=0.250, (b) x/c=0.875.

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Figure 12

Pressure coefficient plot (α=1deg)

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Figure 13

Chordwise velocity profiles within the leading edge bubble (α=3deg). (a) x/c=0.031, (b) x/c=0.125, (c) x/c=0.250, (d) x/c=0.375.

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Figure 14

Near-wall chordwise velocity profiles at x∕c=0.031(α=3deg)

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Figure 15

Turbulent kinetic energy profiles within the leading edge bubble (α=3deg)

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Figure 16

Turbulent kinetic energy contours around the leading edge (α=3deg). (a) SST, (b) k-ω.

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Figure 17

Thin flat plate geometry and auxiliary block numbers

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Figure 18

LES chordwise velocity profiles within the leading edge bubble (α=1deg). (a) x/c=0.031, (b) x/c=0.125.

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Figure 19

LES near-wall chordwise velocity profiles within the leading edge bubble (α=1deg). (a) x/c=0.031, (b) x/c=0.125.

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Figure 20

LES boundary layer profile just downstream of reattachment (x∕c=0.25)

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