where [??] is the velocity vector, [D.sub.AB] is the molecular diffusion coefficient, [v.sub.t] is the turbulent (eddy) viscosity, and [Sc.sub.t] is the turbulent Schmidt number. From the solved concentration field, a corrected density field is obtained as
The diffusion coefficient DAB and the turbulent Schmidt number [Sc.sub.t] were set to 2.0 x [10.sup.-5] [m.sup.2]/s and 1.25, respectively, for both cases.
The transport has been modeled with a turbulent Schmidt number of 0.7 (the value of 0.7 is recommended for high-Reynolds-number jet flows by Yimer et al.
Jiang, "Estimation of the turbulent Schmidt number from experimental profiles of axial velocity and concentration for high-Reynolds-number jet flows," Canadian Aeronautics and Space Journal, vol.
where [[sigma].sub.c] is the turbulent Schmidt number. We can put these two formulae together by defining [[sigma].sub.i], i [member of] [w, c} where [[sigma].sub.c] = 1.
[epsilon]]: Normalising constants (--) [alpha], [[gamma].sub.w], [[gamma].sub.c]: Auxiliary model constants (--) [delta], [phi]: Model constants (--) [epsilon]: Turbulent kinetic energy dissipation rate ([m.sup.2][s.sup.-3]) [lambda]: Taylor microscale (m) v: Molecular kinematic viscosity ([m.sup.2] [s.sup.-1]) [v.sub.T]: Turbulent kinematic viscosity ([m.sup.2] [s.sup.-1]) [[sigma].sub.c]: Turbulent Schmidt number (--) [[sigma].sub.w]: 1, auxiliary notation (--) [xi], [zeta], [eta]: Dimensionless coordinates (--).
In most of the cases in CWE, [D.sub.jk] is defined as a scalar field computed from the turbulent viscosity [v.sub.t] divided by the turbulent Schmidt number S[c.sub.t]:
As one of the most argued and important constants of the conceptual model in dispersion calculations is the turbulent Schmidt number, [Sc.sub.t], as discussed already in (1), the effect of its value on the dispersion results was investigated.
as can be done by tuning the turbulent Schmidt number.
The proportionality factor, the mass diffusivity, is obtained from the momentum diffusivity by the turbulent Schmidt number. In the LES approach, an unsteady solution is obtained, and only SGS turbulent mass fluxes need to be modeled, by analogy between momentum and mass transfer and the specification of a turbulent SGS Schmidt number.
By using the turbulent Schmidt number
Sc, the turbulent diffusivity may be defined
[[[sigma].sup.d].sub.ij] stands for the turbulent Schmidt numbers
and in our case we only need to Consider the case i = j.