A Correlation-Based Transition Model Using Local Variables—Part I: Model Formulation

[+] Author and Article Information
F. R. Menter

 ANSYS CFX Germany, 12 Staudenfeldweg, Otterfing, Bavaria 83624, Germanyflorian.menter@ansys.com

R. B. Langtry

 ANSYS CFX Germany, 12 Staudenfeldweg, Otterfing, Bavaria 83624, Germanyrobin.langtry@ansys.com

S. R. Likki

Department of Mechanical Engineering,  University of Kentucky, 216A RGAN Building, Lexington, KY 40502–0503srinivas@engr.uky.edu

Y. B. Suzen

Department of Mechanical Engineering,  North Dakota State University, Dolve Hall 111, P.O. Box 5285, Fargo, ND 58105bora.suzen@ndsu.edu

P. G. Huang

Department of Mechanical Engineering, University of Kentucky, 216A RGAN Building, Lexington, KY 40502-0503ghuang@engr.uky.edu

S. Völker

 General Electric Company, One Research Circle, ES-221, Niskayuna, NY 12309voelker@crd.ge.com

J. Turbomach 128(3), 413-422 (Mar 01, 2004) (10 pages) doi:10.1115/1.2184352 History: Received October 01, 2003; Revised March 01, 2004

A new correlation-based transition model has been developed, which is based strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) approaches, such as unstructured grids and massive parallel execution. The model is based on two transport equations, one for intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models) but form a framework for the implementation of correlation-based models into general-purpose CFD methods. Part I (this part) of this paper gives a detailed description of the mathematical formulation of the model and some of the basic test cases used for model validation, including a two-dimensional turbine blade. Part II (Langtry, R. B., Menter, F. R., Likki, S. R., Suzen, Y. B., Huang, P. G., and Völker, S., 2006, ASME J. Turbomach., 128(3), pp. 423–434) of the paper details a significant number of test cases that have been used to validate the transition model for turbomachinery and aerodynamic applications. The authors believe that the current formulation is a significant step forward in engineering transition modeling, as it allows the combination of correlation-based transition models with general purpose CFD codes.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 2

Relative error between vorticity Reynolds number (Rev) and the momentum thickness Reynolds number (Reθ) as a function of boundary layer shape factor (H)

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Figure 3

Profiles of the transported scalar R̃eθt for a flat plate with a rapidly decaying freestream turbulence intensity (T3A test case)

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Figure 4

Contours of transition onset momentum thickness Reynolds number from the empirical correlation (Reθt, top) and the transport equation (R̃eθt, bottom) for the Genoa turbine blade

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Figure 13

Normalized wall friction velocity distributions (uτ∕Uo) on the suction side of the Genoa cascade Ubaldi (19)

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Figure 1

Scaled vorticity Reynolds number (Rev) profile in a Blasius boundary layer

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Figure 5

Transition onset momentum thickness Reynolds number (Reθt) predicted by the new correlation as a function of turbulence intensity (Tu) for a flat plate with zero pressure gradient

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Figure 6

Transition onset momentum thickness Reynolds number (Reθt) predicted by the new correlation as a function of pressure gradient parameter (λθ) for constant values of turbulence intensity (Tu). Experimental data are from Fashifar and Johnson (15).

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Figure 7

Skin friction (Cf) for the T3A test case (FSTI=3.5%)

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Figure 8

Skin friction (Cf) for the T3B test case (FSTI=6.5%)

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Figure 9

Skin friction (Cf) for the T3A-test case (FSTI=0.87%)

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Figure 10

Skin friction (Cf) for the Schubauer and Klebanof (18) test case (FSTI=0.18%)

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Figure 11

Predicted skin friction (Cf) for the T3C4 test case with and without the modification for separated flow transition

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Figure 12

Intermittency (γ, top), effective intermittency (γeff, middle), and turbulence intensity (Tu, bottom) for the T3C4 test case





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