Nonlinear two-equation model taking into account the wall-limiting behavior and redistribution of stress components

Nonlinear k– models have been extensively used in technological applications. It is clear from the assessment of the existing nonlinear k– models using DNS databases that the nonlinear models can not satisfy and reproduce exactly the wall-limiting behavior and the anisotropy of Reynolds normal stress components. Especially, the Reynolds normal stress component, , in the wall-normal direction, which is proportional to x₂⁴ near the wall, is not satisfied. Since the wall-limiting behavior 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, , and , are proportional to x₂². In this study, we have proposed a new nonlinear k– model which satisfies exactly the wall-limiting behavior 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. PACS 47.27.Eq, 47.27.Ak, 47.27.Nz