A new approach to modelling near-wall turbulence energy and stress dissipation

Abstract

A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor ε_ij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanović, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part ε^h of the energy dissipation rate. The algebraic expression for the components of ε_ij was then reformulated in terms of ε^h, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of ε_ij, as well as solving the new dissipation equation as a whole using DNS data for quantities other than ε_ij, for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for (u_iu_i) All Overbar, using ε^h instead of ε, agree well with the direct numerical simulations.