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Research Papers: Techniques and Procedures

A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow

[+] Author and Article Information
D. Keith Walters

Department of Mechanical Engineering, Mississippi State University, HPC2 SimCenter, P.O. Box ME, Mississippi State, MS 39762walters@me.msstate.edu

Davor Cokljat

Ansys, Inc., Fluent Europe Ltd., Sheffield Business Park, 6 Europa View, Sheffield S9 1XH, UKdavor.cokljat@ansys.com

J. Fluids Eng 130(12), 121401 (Oct 24, 2008) (14 pages) doi:10.1115/1.2979230 History: Received November 16, 2007; Revised July 24, 2008; Published October 24, 2008

An eddy-viscosity turbulence model employing three additional transport equations is presented and applied to a number of transitional flow test cases. The model is based on the k-ω framework and represents a substantial refinement to a transition-sensitive model that has been previously documented in the open literature. The third transport equation is included to predict the magnitude of low-frequency velocity fluctuations in the pretransitional boundary layer that have been identified as the precursors to transition. The closure of model terms is based on a phenomenological (i.e., physics-based) rather than a purely empirical approach and the rationale for the forms of these terms is discussed. The model has been implemented into a commercial computational fluid dynamics code and applied to a number of relevant test cases, including flat plate boundary layers with and without applied pressure gradients, as well as a variety of airfoil test cases with different geometries, Reynolds numbers, freestream turbulence conditions, and angles of attack. The test cases demonstrate the ability of the model to successfully reproduce transitional flow behavior with a reasonable degree of accuracy, particularly in comparison with commonly used models that exhibit no capability of predicting laminar-to-turbulent boundary layer development. While it is impossible to resolve all of the complex features of transitional and turbulent flows with a relatively simple Reynolds-averaged modeling approach, the results shown here demonstrate that the new model can provide a useful and practical tool for engineers addressing the simulation and prediction of transitional flow behavior in fluid systems.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Dimensionless velocity (a) and turbulent kinetic energy (b) profiles for fully developed turbulent channel flow at Reτ=395

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Figure 2

Domain and computational meshes used for ZPG flat plate test cases: (a) overall mesh; and (b) close-up view of leading-edge region

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Figure 3

Streamwise decay of freestream turbulence for test case T3A

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Figure 4

Distribution of skin friction coefficient for ZPG flat plate cases: (a) T3A−, (b) T3A, and (c) T3B

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Figure 5

Boundary layer profiles of mean velocity (a), total fluctuation kinetic energy (b), laminar kinetic energy (c), and turbulent kinetic energy (d), showing development from pretransitional to fully-turbulent regions in T3A flat plate case

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Figure 6

Comparison between model and empirical correlations for transition start versus freestream turbulence intensity, in cases T3A−, T3A, and T3B.

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Figure 7

Distribution of skin friction coefficient for flat plate cases with streamwise pressure gradient: (a) T3C2, (b) T3C3, (c) T3C4, and (d) T3C5

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Figure 8

Periodic domain and hybrid 2D mesh for VPI cascade test case

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Figure 9

Surface heat transfer coefficient distribution for VPI Cascade test cases: (a) Tu∞=10% and (b) Tu∞=19.5%

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Figure 10

Periodic domain and hybrid 2D mesh for VKI cascade test case

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Figure 11

Surface heat transfer coefficient distribution for VKI Cascade test cases with no suction side shock: (a) Tu∞=1%, (b) Tu∞=4%, and (c) Tu∞=6%

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Figure 12

Surface heat transfer coefficient distribution for VKI Cascade test cases with suction side shock: (a) Tu∞=1%, and (b) Tu∞=4%

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Figure 13

Structured C-type 2D mesh for A-airfoil test case

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Figure 14

Comparison of predicted and measured skin friction coefficients for the A-airfoil test case

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Figure 15

2D mesh for S809 airfoil test case

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Figure 16

Comparison of predicted and measured transition locations versus angle of attack for S809 airfoil test case: (a) pressure surface and (b) suction surface

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