Elliptic blending model: A new near-wall Reynolds-stress turbulence closure

Abstract

A new approach to modeling the effects of a solid wall in one-point second-moment ͑Reynolds-stress͒ turbulence closures is presented. The model is based on the relaxation of an inhomogeneous ͑near-wall͒ formulation of the pressure-strain tensor towards the chosen conventional homogeneous ͑far-from-a-wall͒ form using the blending function ␣, for which an elliptic equation is solved. The approach preserves the main features of Durbin's Reynolds-stress model, but instead of six elliptic equations ͑for each stress component͒, it involves only one, scalar elliptic equation. The model, called ''the elliptic blending model,'' offers significant simplification, while still complying with the basic physical rationale for the elliptic relaxation concept. In addition to model validation against direct numerical simulation in a plane channel for Re ϭ590, the model was applied in the computation of the channel flow at a ''real-life'' Reynolds number of 10 6 , showing a good prediction of the logarithmic profile of the mean velocity.

Toward an equivalence criterion for Hybrid RANS/LES methods

“…is modeled using an adaptation of the Elliptic-Blending Reynolds-Stress model [30,31] to the hybrid temporal LES framework [10]. In this equation, similar to the case of the Reynolds-stress transport equation used in RANS, P i j sfs , ε i j sfs , φ * i j sfs…”

Wall effects on pressure fluctuations in turbulent channel flow

“…According to the way wall-proximity is handled, smcs can be classified into three categories (a) Models which use wall-topology based (for instance distance from the wall or geometric normal to the wall) corrections of the quasi-homogeneous closures, tend to the homogeneous limit away from the wall (y + 30). Notice that elliptic blending models (Manceau & Hanjalić 2002) use the same family of tensorial representations for the redistribution φ ij , the velocity/pressure-gradient correlation Π ij or the dissipation ε ij terms, and introduce the knowledge of wall-topology via the boundary conditions of the scalar Helmholtz equation used to define the scalar blending parameter. Therefore, it can be argued that elliptic blending models belong to this category.…”

Reynolds Stress Closure in Hybrid RANS-LES Methods

“…The near wall form of the redistribution model was obtained in [10] such that the correct asymptotic behavior is obtained…”

“…The EB-RSM used in this paper is a modification of the original EB model [10] and the improved model presented by Thielen et al [11]. The modeled transport equation for the Reynolds stress tensor is given by…”

“…The elliptic relaxation model is based on the solution of six elliptic equations to adjust any homogeneous redistribution model to yield the correct near wall behavior. More recently, a simpler albeit slightly less accurate model that solves only one additional elliptic equation was proposed by Manceau and Hanajalić [10] and Thielen et al [11]. The model is based on a blending between any homogeneous redistribution model like the LRR model [12] and a near wall redistribution model that has the desired asymptotic behavior.…”