On Near-Wall Treatment in (U)RANS-Based Closure Models

The present work is concerned with computational evaluation of a recently formulated near-wall relationship providing the value of the dissipation rate ε of the kinetic energy of turbulence k through its exact dependence on the Taylor microscale λ: ε = 10νk/λ ², (Jakirli? and Jovanovi?, J. Fluid Mech. 656:530–539, 2010). Dissipation rate determination benefits from the asymptotic behavior of the Taylor microscale resulting in its linear variation in terms of the wall distance (λ?∝?y) being valid throughout entire viscous sublayer. Accordingly, it can be applied as a unified near-wall treatment in all computational frameworks relying on a RANS-based model of turbulence (including also hybrid LES/RANS schemes) independent of modeling level—both main modeling concepts eddy-viscosity and Reynolds stress models can be employed. Presently, the feasibility of the proposed formulation was demonstrated by applying a conventional near-wall second-moment closure model based on the homogeneous dissipation rate ε _h ( ${varepsilon_h =varepsilon -0.5partial left( {{nu partial k}/ {partial x_j }} right)} / {partial x_j }$ ; Jakirli? and Hanjali?, J. Fluid Mech. 539:139–166, 2002) and its instability-sensitive version, modeled in terms of the inverse turbulent time scale ω _h (ω _h ?=?ε _h /k; Maduta and Jakirli?, 2011), to a fully-developed channel flow with both flat walls and periodic hill-shaped constrictions mounted on the bottom wall in a Reynolds number range. The latter configuration is subjected to boundary layer separation from a continuous curved wall. The influence of the near-wall resolution lowering with respect to the location of the wall-closest computational node, coarsened even up to the viscous sublayer edge situated at $y_P^+ approx 5$ in equilibrium flows, is analyzed. The results obtained follow closely those pertinent to the conventional near-wall integration with the wall-next node positioned at $y_P^+ le 0.5$ .