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-\omega $ 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.

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

D. Keith Walters

,
D. Keith Walters

Department of Mechanical Engineering,

walters@me.msstate.edu
Mississippi State University

, HPC2 SimCenter, P.O. Box ME, Mississippi State, MS 39762
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Davor Cokljat

Davor Cokljat

Ansys, Inc.,

davor.cokljat@ansys.com
Fluent Europe Ltd.

, Sheffield Business Park, 6 Europa View, Sheffield S9 1XH, UK
Search for other works by this author on:

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*. Dec 2008, 130(12): 121401 (14 pages)

**Published Online:**October 24, 2008

Article history

Received:

November 16, 2007

Revised:

July 24, 2008

Published:

October 24, 2008

Citation

Walters, D. K., and Cokljat, D. (October 24, 2008). "A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow." ASME. *J. Fluids Eng*. December 2008; 130(12): 121401. https://doi.org/10.1115/1.2979230

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