A Near-Wall Reynolds-Stress Closure Without Wall Normals

Turbulent wall-bounded complex flows are commonly encountered in engineering practice and are of considerable interest in a variety of industrial applications. The presence of a wall significantly affects turbulence characteristics. In addition to the wall effects, turbulent wall-bounded flows become more complicated by the presence of additional body forces (e.g. centrifugal force and Coriolis force) and complex geometry. Most near-wall Reynolds stress models are developed from a high-Reynolds-number model which assumes turbulence is homogenous (or quasi-homogenous). Near-wall modifications are proposed to include wall effects in near-wall regions. In this process, wall normals are introduced. Good predictions could be obtained by Reynolds stress models with wall normals. However, ambiguity arises when the models are applied in flows with multiple walls. Many models have been proposed to model turbulent flows. Among them, Reynolds stress models, in which turbulent stresses are obtained by solving the Reynolds stress transport equations, have been proved to be the most successful ones. To apply the Reynolds stress models to wall-bounded flows, near-wall corrections accounting for the wall effects are needed, and the resulting models are called near-wall Reynolds stress models. In most of the existing near-wall models, the near-wall corrections invoke wall normals. These wall-dependent near-wall models are difficult to implement for turbulent flows with complex geometry and may give inaccurate predictions due to the ambiguity of wall normals at corners connecting multiple walls. The objective of this study is to develop a more general and flexible near-wall Reynolds stress model without using any wall-dependent variable for wall-bounded turbulent flows. With the aid of near-wall asymptotic analysis and results of direct numerical simulation, a new near-wall Reynolds stress model (NNWRS) is formulated based on Speziale et al.'s high-Reynolds-stress model with wall-independent near-wall corrections. Moreover, only one damping function is used for flows with a wide range of Reynolds numbers to ensure that the near-wall modifications diminish away from the walls.