T. Elperin1, A. Fominykh1, I. Katra2, and
B. Krasovitov1
1Department
of Mechanical Engineering, The Pearlstone Center for
Aeronautical Engineering Studies, Ben-Gurion University of the Negev,
P.O.B. 653, 8410501, Israel
2Department of Geography and Environmental Development, Ben-Gurion
University of the Negev, P.O.B. 653, 8410501, Israel
Scavenging of air pollutions
Ne'ot Hovav chemical
factoryand rain droplets
by cloud
(Northern Negev, Israel)
Power plant (Ashquelon, Israel)
Ben-Gurion University of the Negev
Gaussian Plume model
Scavenging of air pollutions
by cloud and rain droplets
Ben-Gurion University of the Negev
Pasquill-Gifford stability categories
Gradient Richardson
number reads
Richardson
number
Atmospheric stability
Pasquill–Gifford
stability class
Ri  0.25
Very stable
G
0  Ri  0.25
Stable
E–F
Ri  0
Neutral
D
 0.3  Ri  0
Unstable
C–B
Ri  0.3
Very unstable
A
where q is potential temperature that can be calculated as follows
Γ is the adiabatic lapse rate (
mixing depth)
K/m over the distance to the
Ben-Gurion University of the Negev
Pasquill-Gifford horizontal dispersion parameters
Pasquill Stability
Category
A
c
d
24.1670
2.5334
B
18.3330
1.8096
C
12.5000
1.0857
D
8.3330
0.72382
E
6.2500
0.54287
F
4.1667
0.36191
Ben-Gurion University of the Negev
Pasquill Stability Category
A*
B*
C*
D
E
F
x (km)
a
b
.10
0.10 - 0.15
0.16 - 0.20
0.21 - 0.25
0.26 - 0.30
0.31 - 0.40
0.41 - 0.50
0.51 - 3.11
3.11
.20
0.21 - 0.40
0.40
All
.30
0.31 - 1.00
1.01 - 3.00
3.01 - 10.00
10.01 - 30.00
30.00
.10
0.10 - 0.30
0.31 - 1.00
1.01 - 2.00
2.01 - 4.00
4.01 - 10.00
10.01 - 20.00
20.01 - 40.00
40.00
.20
0.21 - 0.70
0.71 - 1.00
1.01 - 2.00
2.01 - 3.00
3.01 - 7.00
7.01 - 15.00
15.01 - 30.00
30.01 - 60.00
60.00
122.800
158.080
170.220
179.520
217.410
258.890
346.750
453.850
**
90.673
98.483
109.300
61.141
34.459
32.093
32.093
33.504
36.650
44.053
24.260
23.331
21.628
21.628
22.534
24.703
26.970
35.420
47.618
15.209
14.457
13.953
13.953
14.823
16.187
17.836
22.651
27.074
34.219
0.94470
1.05420
1.09320
1.12620
1.26440
1.40940
1.72830
2.11660
**
0.93198
0.98332
1.09710
0.91465
0.86974
0.81066
0.64403
0.60486
0.56589
0.51179
0.83660
0.81956
0.75660
0.63077
0.57154
0.50527
0.46713
0.37615
0.29592
0.81558
0.78407
0.68465
0.63227
0.54503
0.46490
0.41507
0.32681
0.27436
0.21716
Pasquill-Gifford vertical
dispersion parameters
Ben-Gurion University of the Negev
Scavenging
air pollutions
Mass transfer of gaseous adsorbent in atmospheric boundary
layerof(ABL)
can be
by cloud and rain droplets
described using advection diffusion equation that reads
(1)
where is the mean concentration of gaseous adsorbent, are the components
of mean wind velocity,
are components of turbulent fluxes, is the rate of
gas adsorption. Hereafter we adopted the turbulence closure based on the
hypothesis of the gradient transport (K-theory)
(2)
where
are the diagonal components of eddy diffusivity.
Ben-Gurion University of the Negev
Scavenging
of air pollutions
Boundary
conditions
Governing equation
by cloud and rain droplets
at
(3)
(4)
at
 rate of loss of active gas due to adsorption by aerosol particles
 height of ABL
For stable boundary layer (SBL) coefficient
reads (Blackadar, 1979):
(5)
where l is the turbulent mixing length, zm = 200 m, k = 0.4, RiC = 0.25
Ben-Gurion University of the Negev
Gas adsorption by PM
Scavenging of air pollutions
Time derivative of the radius-average concentration
of theand
adsorbed
gas in
by cloud
rain droplets
a porous particle reads:
(6)
Henry’s constant of adsorption
specific surface area of a particle
For an ensemble-average concentration field
(7)
Ben-Gurion University of the Negev
Gas adsorption by PM
from Eqs. (17) and (16) we obtain:
Scavenging of air pollutions
by cloud and rain droplets
(8)
solution of Eq. (8) reads:
(9)
Consequently
(10)
Ben-Gurion University of the Negev
Scavenging of air pollutions
expression for scavenging coefficient is the following:
by cloud and rain droplets
(11)
m
DG
 Henry’s adsorption constant
 coefficient of molecular diffusion
 volume fraction of particles
 scavenging coefficient
Ben-Gurion University of the Negev
Scavenging
of air
Table 1. Henry’s law constant of adsorption of active
gases NO
2, pollutions
by cloud
HNO3 and I-131 by carbon-based aerosols at temperature
T =and
298rain
K droplets
Gas
NO2
HNO3
I-131
HA [cm]
25 (a)
104 (c)
104 (d)
Dg [cm2/s]
0.14 (b)
0.11(b)
0.08 (d)
aKalberer
et al. (1999); bSeinfeld & Pandis (2016); cMunoz et al. (2002)
dNoguchi et al. (1988)
or
- linear form of isotherm of adsorption
U - adsorbed amount of active gas
Ben-Gurion University of the Negev
Scavenging of air pollutions
by cloud and rain droplets
Fig. 4. Dependence of adsorbed amount of
iodine vs. time (
,
,
)
Fig. 3. Dependence of adsorbed amount of
iodine vs. time (
,
,
)
Ben-Gurion University of the Negev
Scavenging
In ABL the wind profile can be described by the logarithmic
law of air pollutions
by cloud and rain droplets
(6)
 friction velocity
 shear stress at the surface level
 air density
 aerodynamic surface roughness length that is 1/30
of the field roughness elements
σ
 standard deviation of velocity fluctuations
Ben-Gurion University of the Negev
Scavenging of air pollutions
by cloud and rain droplets
Fig. 6. A cup anemometer
Measuring range
0 – 50 m/s
Accuracy
 0.49 m/s
Fig. 5. A 10-m wind mast
Ben-Gurion University of the Negev
Scavenging of air pollutions
by cloud and rain droplets
For each height the average wind velocity
was calculated as follows
Ben-Gurion University of the Negev
Scavenging
of air pollutions
Boundary
conditions
Governing equation
by cloud and rain droplets
at
(3)
(4)
at
 rate of loss of active gas due to adsorption by aerosol particles
 height of ABL
For stable boundary layer (SBL) coefficient
reads (Blackadar, 1979):
(5)
where l is the turbulent mixing length, zm = 200 m, k = 0.4, RiC = 0.25
Ben-Gurion University of the Negev
Scavenging
of air
pollutions
- Parabolic partial differential Eq. (3) was solved using
the method
of lines
by cloud and rain droplets
developed by Sincovec and Madsen [1975].
- Spatial discretization on a three-point stencil with uniformly distributed
mesh points was used in order to reduce partial differential equation (3) to
the approximating system of coupled ordinary differential equations.
- The resulting system of ordinary differential equations was solved using a
backward differentiation method.
Sincovec, R.F., Madsen, N.K. [1975] Software for nonlinear partial differential
equations. ACM T. Math. Software, Vol. 1, pp. 232–260.
Ben-Gurion University of the Negev
Scavenging ofFig.
air 7.
pollutions
by cloud and Concentration
rain droplets
distributions in the
XZ-plane,
evaluated at Y=0.
NO2
HNO3
Ben-Gurion University of the Negev
The model is based on an application of theory of turbulent
diffusion in the atmospheric boundary layer (ABL) in conjunction
with plume dispersion model and model of gas adsorption by
porous solid particles.
The wind velocity profiles used in the simulations were fitted from
data obtained in field measurements conducted in the Northern
Negev (Israel) using the experimental wind mast.
The adsorbate concentration distributions are calculated for the
particulate matter PM2.5-10, which is typical for industrial
emissions.
It is shown that the concentration of the gases adsorbed by aerosol
plume strongly depends on the level of atmospheric turbulence.
The results of present study can be useful in the analysis of
different atmospheric pollution models including gas adsorption by
aerosol plumes emitted from industrial sources.
Ben-Gurion University of the Negev