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Research Papers: Fundamental Issues and Canonical Flows

The Application of Eddy-Viscosity Stress Limiters for Modeling Cross-Flow Separation

[+] Author and Article Information
P. A. Gregory1

Department of Mechanical and Manufacturing Engineering, University of Melbourne, Victoria 3010, Australiapgregory@unimelb.edu.au

P. N. Joubert, M. S. Chong, A. Ooi

Department of Mechanical and Manufacturing Engineering, University of Melbourne, Victoria 3010, Australia

The phrase “vortex structure” is used here simply to describe the “spiraling” motion. The definition of a vortex is still a highly debated issue, and there exists several definitions of a vortex.

1

Corresponding author.

J. Fluids Eng 132(9), 091201 (Sep 03, 2010) (22 pages) doi:10.1115/1.4001967 History: Received September 21, 2008; Revised June 08, 2010; Published September 03, 2010; Online September 03, 2010

Abstract

The ability of eddy-viscosity models to simulate the turbulent wake produced by cross-flow separation over a curved body of revolution is assessed. The results obtained using the standard $k−ω$ model show excessive levels of turbulent kinetic energy $k$ in the vicinity of the stagnation point at the nose of the body. Additionally, high levels of $k$ are observed throughout the wake. Enforcing laminar flow upstream of the nose (which replicates the experimental apparatus more accurately) gives more accurate estimates of $k$ throughout the flowfield. A stress limiter in the form of Durbin’s $T$-limit modification for eddy-viscosity models is implemented for the $k−ω$ model, and its effect on the computed surface pressures, skin friction, and surface flow features is assessed. Additionally, the effect of the $T$-limit modification on both the mean flow and the turbulent flow quantities within the wake is also examined. The use of the $T$-limit modification gives significant improvements in predicted levels of turbulent kinetic energy and Reynolds stresses within the wake. However, predicted values of skin friction in regions of attached flow become up to 50% greater than the experimental values when the $T$-limit is used. This is due to higher values of near-wall turbulence being created with the $T$-limit.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Figure 11

Plots of sectional streamlines at x/L=1.05 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit. The streamlines are obtained by integrating the in-plane vector field for the experimental data and RANS simulations.

Figure 13

Contours of k/(U∞)2×103 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit at x/L=1.0. The contour interval is equal to 2.0. Selected contours are labeled.

Figure 1

Schematic of the experimental apparatus used to measure the cross-flow separation from the curved body of revolution. The orientation of the variable θ used to plot Cp and Cf values at cross sections along the body is also shown. θ=0 deg corresponds to the outboard side of body (the contracted side of the body), which faces the freestream. θ=180 deg corresponds to the inboard side of the body (the elongated side). θ=90 deg corresponds to locations above the centerline of the body.

Figure 2

View of the meshing scheme used to represent the working section of the wind tunnel (top), the rear of the body showing the support sting (middle), and the nose section of the curved body of revolution (bottom)

Figure 3

Schematic of the working section showing the extent of the flow domain where the flow was forced to remain laminar

Figure 4

Contours of k/(U∞)2×103 taken at the symmetry plane for (a) k−ω model, (b) k−ω model with laminar zone, (c) k−ω with T-limit, and (d) k−ω model with T-limit and laminar zone

Figure 5

Contours of νT/ν taken at the symmetry plane for (a) k−ω model, (b) k−ω model with laminar zone, (c) k−ω with T-limit, and (d) k−ω model with T-limit and laminar zone

Figure 6

Plots of Cp versus θ at various x/L. (—) Standard k−ω model, (–⋅–)k−ω model with laminar zone, (⋯⋯⋅⋅)T-limit model, (– – – –) T-limit model with laminar zone, and (○) experimental values.

Figure 7

Plots of Cp versus θ at various x/L. (—) Standard k−ω model, (–⋅–)k−ω model with laminar zone, (⋯⋯⋅⋅)T-limit model, – – – – T-limit model with laminar zone, and (○) experimental values.

Figure 8

Plots of Cf versus θ for various x/L. (—) Standard k−ω model, (–⋅–)k−ω model with laminar zone, (⋯⋯⋅⋅)T-limit model, (– – – –) T-limit model with laminar zone, and (○) experimental values.

Figure 9

Contours of ⟨U⟩/U∞ at x/L=1.0 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit. The contour interval is equal to 1.0. Selected contours are labeled.

Figure 10

Plots of sectional streamlines at x/L=1.025 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit. The streamlines are obtained by integrating the in-plane vector field for the experimental data and RANS simulations.

Figure 12

Contours of ⟨U⟩/U∞ for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit at x/L=1.05. The contour interval is equal to 0.5. Selected contours are labeled.

Figure 14

Contours of k/(U∞)2×103 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit at x/L=1.025. The contour interval is equal to 2.0. Selected contours are labeled.

Figure 15

Contours of k/(U∞)2 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit at x/L=1.05. The contour interval is equal to 2.0. Selected contours are labeled.

Figure 16

Contours of ⟨uv⟩/(U∞)2 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit at x/L=1.0. The contour interval is equal to 1.0 for the experimental data and 0.5 for the RANS data. Selected contours are labeled.

Figure 17

Contours of ⟨uv⟩/(U∞)2 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit at x/L=1.05. The contour interval is equal to 1.0 for the experimental data and 0.5 for the RANS data. Selected contours are labeled.

Figure 18

Contours of ⟨uw⟩/(U∞)2 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit at x/L=1.0. The contour interval is equal to 1.0. Selected contours are labeled.

Figure 26

Contours of νT/ν for (a) standard k−ω model, (b) k−ω with laminar zone, (c) k−ω with T-limit, and (d) k−ω with T-limit model and laminar zone at x/L=1.0. The contour interval is equal to 1.0. Selected contours are labeled.

Figure 29

Plots of Cf versus θ for various x/L. (—) T-limit α=0.8, (–⋅–)T-limit with laminar zone α=0.8, (⋯⋯⋅⋅)T-limit α=1.0, (– – – –) T-limit model with laminar zone α=1.0, and (○) experimental values.

Figure 19

Contours of ⟨uw⟩/(U∞)2 for (a) experimental data, (b) k−ω model, (c) k−ω, laminar zone, and (d) k−ω with T-limit at x/L=1.05. The contour interval is equal to 0.5. Selected contours are labeled.

Figure 20

Individual streamline visualizations for the (a) experimental body, (b) k−ω model, (c) k−ω with laminar zone, and (d) k−ω with T-limit

Figure 23

Various views of the surface flow streamlines for the (a) experimental body, (b) k−ω model, (c) k−ω with laminar zone, and (d) k−ω with T-limit against a backing grid

Figure 24

Contours of k/(U∞)2×103 for (a) experimental data, (b) k−ω with laminar zone, (c) k−ω with T-limit, and (d) k−ω with T-limit model and laminar zone at x/L=0.9. The contour interval is equal to 1.0. Selected contours are labeled.

Figure 31

Contours of νT/ν for (a) T-limit α=0.8, (b) T-limit with laminar zone α=0.8, (c) T-limit α=1.0, and (d) T-limit model with laminar zone α=1.0 at x/L=1.0. The contour interval is equal to 2.0. Selected contours are labeled.

Figure 27

Plots of U/Uτ versus y+ for various x/L. (—) Standard k−ω model, (–⋅–)k−ω model with laminar zone, and (⋯⋯⋅⋅)T-limit model. The slope of the log law is also shown.

Figure 28

Plots of νT/ν versus y+ (left) and k/(U∞)2 versus y+ (right) for various x/L. (—) Standard k−ω model, (–⋅–)k−ω model with laminar zone, and (⋯⋯⋅⋅)T-limit model.

Figure 30

Contours of k/(U∞)×103 for (a) T-limit α=0.8, (b) T-limit with laminar zone α=0.8, (c) T-limit α=1.0, and (d) T-limit model with laminar zone α=1.0 at x/L=1.0. The contour interval is equal to 2.0. Selected contours are labeled.

Figure 32

Plots of U/Uτ versus y+ for various x/L. (—) T-limit α=0.8 and (⋯⋯⋅⋅)T-limit α=1.0. The slope of the log law is also shown.

Figure 33

Plots of νT/ν versus y+ (left) and k/(U∞)2 versus y+ (right) for various x/L. (—) T-limit α=0.8 and (⋯⋯⋅⋅)T-limit α=1.0.

Figure 21

Individual streamline visualizations for the (a) experimental data, overlaid with (b) k−ω model, (c) k−ω with laminar zone, and (d) k−ω with T-limit

Figure 22

Side view of surface flow patterns for the (a) experimental body, (b) k−ω model, (c) k−ω with laminar zone, and (d) k−ω with T-limit

Figure 25

Contours of k/(U∞)2×103 for (a) experimental data, (b) k−ω with laminar zone, (c) k−ω with T-limit, and (d) k−ω with T-limit model and laminar zone at x/L=1.0. The contour interval is equal to 1.0. Selected contours are labeled.

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