Environmental Engineering Reference
In-Depth Information
to
1 standard deviation (note, values below 0 have been discard as meaningless).
As seen the 3D model results can be better compared with those of the LES, despite
differences in the modelling approaches. Even with the extreme case of comparing
instantaneous equations with Reynolds Averaged ones, when we consider the spatial
variability of the emissions we can generalize the results of the RANS model.
±
2.5 Conclusions
A simple method to account for variability of emission has been proposed.
The RANS model results compared to LES model are very encouraging. The
parameterization will allow error bars to be added to model results. The next step
will consider the analysis of different and more complex emission patterns and the
refinement of information on the spatial variability.
Appendix: Other Closures Used for Prognostic Equation for the
Variance of Pollutant Concentration
A description of the other closures used to solve the prognostic equation for the
variance of pollutant concentration is given.
The turbulent fluxes of (
G
) (2.1) are calculated for the eddy covariance (
w
c
)
K
z
Pr
∂
c
w
c
=−
(2.3)
∂
z
where the turbulent coefficient
K
z
is estimated using a K-l closure (Bougeault and
Lacarrère, 1989; Bélair et al., 1999),
w
is the vertical velocity, and Pr is the Prandtl
number. In this closure a prognostic equation for the turbulent kinetic energy (TKE)
e
is solved, and turbulent coefficients and TKE dissipation are derived using length
scales as follows:
c
k
l
k
e
1
/
2
K
z
=
(2.4)
e
3
/
2
l
ε
e
=
c
(2.5)
ε
ε
are calculated at a particular level from the possible upward
and downward displacements (
l
up
and
l
down
) that air parcels with kinetic energy
e
originating from the level
z
could accomplish before being stopped by buoyancy. In
the following
The lengths
l
k
and
l
ε
β
is the buoyancy coefficient.
z
+
l
up
β
θ
(
z
)
dz
=
(
z
)
−
θ
e
(
z
)
(2.6)
z
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