Flow, Turbulence and Combustion

, Volume 91, Issue 4, pp 849–866 | Cite as

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

  • S. JakirlićEmail author
  • J. Jovanović
  • R. Maduta


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, (Jakirlić and Jovanović, 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 (\({\varepsilon_h =\varepsilon -0.5\partial \left( {{\nu \partial k}/ {\partial x_j }} \right)} / {\partial x_j }\); Jakirlić and Hanjalić, 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 Jakirlić, 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 \(y_P^+ \le 0.5\).


Computational fluid dynamics RANS Instability-sensitive URANS model Near-wall treatment Near-wall turbulence models Attached and separating flows 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of Fluid Mechanics and Aerodynamics/Center of Smart InterfacesTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Institute of Fluid MechanicsFriedrich-Alexander University of Erlangen-NurembergErlangenGermany

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