Environmental Engineering Reference
In-Depth Information
radiation leads to the production of NO and O
3
. The chemical reactions considered
by our model are:
k
J
NO
+
O
→
NO
+
O
NO
+
O
+
h
ν
→
NO
+
O
3
2
2
2
2
3
where
k
depends on temperature and is around 0.4 ppm
−1
s
−1
while
J
depends on
solar radiation and ranges between 0, during the night, and 0.4 min
−1
in the full
sunlight. The discretized form of the chemical equation is (for NO and similarly
for the other compounds):
( )
*
*
*
*
c
(
x
,
t
)
=
c
(
x
,
t
)
−
k
Δ
t
c
(
x
,
t
)
c
(
x
,
t
)
+
j
Δ
t
c
x
,
t
NO
j
1
NO
j
1
NO
j
1
O
j
1
NO
j
1
3
2
where * indicates the concentration in the cells after the turbulent dispersion but
before the chemical reaction. In the case of O
3
deficit of concentration was
introduced as described in Alessandrini and Ferrero (2009). Then the mass of the
different substances were redistributed to each particle in the cell.
3. Segregation Parameterization
In order to simulate the chemical reaction in a turbulent flow on a time scale less
than the typical equilibrium scale the cross covariance term between the concentration
fluctuation
A
cc
of the two compounds participating to the reaction should
be accounted for. The contribution of this term is often referred as “segregation”
<
'
'
>
B
<
c
'
c
'
>
A
B
α
=
and
is the segregation coefficient.
<
c
>
⋅
<
c
>
A
B
Looking at the Brown and Bilger (1998) wind tunnel measurements the covariance
term seems to experience an exponential decay with the distance. Thus a new
parameterization for the segregation coefficient (Alessandrini and Ferrero, 2009)
was obtained as a function of the downstream distance, “x”, by performing a best
fit of the experimental data presented in Brown and Bilger (1998):
x
−
0
12
N
D
x
α
where x
s
is the stoichiometric distance (the distance where the mixing ratio of the
plume becomes equal to the background mixing ratio) and N
D
the Damköhler
number (which represents the ratio between the time scales of turbulence and
chemical reactions). In this work we have adapted this parameterization to a real
atmospheric dispersion case. For x
s
the constant values 5,000 m was assumed and
N
D
, estimated from the chemical and turbulence parameters, was set to 0.22.
−
0
.
71
e
s
