A new model for the transport equation for the turbulence energy dissipation rate
ε and for the anisotropy of the dissipation rate tensor εij,
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 εh of the energy dissipation rate. The algebraic
expression for the components of εij was then reformulated in terms of
εh, 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 εij, as well
as solving the new dissipation equation as a whole using DNS data for quantities other than
εij, 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 (uiui) All Overbar,
using εh instead of ε, agree well with the direct numerical simulations.
PARTICULAR SOLUTION OF BOUNDARY PROBLEMS FOR THE HEAT DISSIPATION EQUATION USING THE APPROXIMATION METHODS.
