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a realizable reynolds stress algebraic equation modelThe invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.
Document ID
Document Type
Conference Paper
Shih, Tsan-Hsing
(NASA Lewis Research Center Cleveland, OH, United States)
Zhu, Jiang
(NASA Lewis Research Center Cleveland, OH, United States)
Lumley, John L.
(Cornell Univ. Ithaca, NY., United States)
Date Acquired
September 6, 2013
Publication Date
January 1, 1993
Subject Category
Report/Patent Number
NAS 1.15:105993
Meeting Information
Symposium on Turbulence Shear Flows(Kyoto)
Funding Number(s)
PROJECT: RTOP 505-62-21
Distribution Limits
Work of the US Gov. Public Use Permitted.

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NameType 19930007407.pdf STI