Nonlinear k–ε models have been extensively used in technological applications. It is clear from the assessment of the existing nonlinear k–ε models using DNS databases that the nonlinear models can not satisfy and reproduce exactly the wall-limiting behaviour and the anisotropy of Reynolds normal stress components. Especially, the Reynolds normal stress component, u22, in the wall-normal direction, which is proportional to x24 near the wall is not satisfied. Since the wall limiting behaviour of Reynolds normal stress components in the nonlinear model is determined by the turbulence energy k, which is proportional to x22 in the model, the Reynolds stress components, u12, u22 and u32 are proportional to x22. In this study, we have proposed a new nonlinear k–ε model which satisfies exactly the wall limiting behaviour of Reynolds normal stress components in the inertial and the noninertial frames. The proposed model can also predict well the anisotropy of the Reynolds normal stress components near the wall.
Non-Linear Two-Equation Model Taking Into Account the Wall-Limiting Behaviour and Redistribution of Stress Components
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Hattori, H, & Nagano, Y. "Non-Linear Two-Equation Model Taking Into Account the Wall-Limiting Behaviour and Redistribution of Stress Components." Proceedings of the ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. Volume 2: Symposia, Parts A, B, and C. Honolulu, Hawaii, USA. July 6–10, 2003. pp. 2043-2050. ASME. https://doi.org/10.1115/FEDSM2003-45353
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