International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
Effect of Mesoscale Wind on the Pollutant Emitted from
an Area Source of Primary and Secondary Pollutants with
Gravitational Settling Velocity
Pandurangappa. C 1, Lakshminarayanachari. K 2, M. Venkatachalappa 3
1
Department of Mathematics, RajaRajeswari College of engineering, Bangalore -560 074, India.
2
Department of Mathematics, Sai Vidya Institute of Technology, Bangalore -560 064, India.
3
Department of Mathematics, Bangalore University, Central College Campus, Bangalore -560 001, India.
1
[email protected]
2
[email protected]
3
[email protected]
One of the most effective ways to assess the impact of
various pollutants on the environment of a particular area is
through mathematical modeling. Mathematical models are
important tools and can play crucial role as a part of
methodology developed to predict air quality.
Abstract— A comprehensive two-dimensional numerical
model for the dispersion of air pollutants is presented. This
model deals with the dispersion of both primary and
secondary pollutants emitted from an area source with
mesoscale wind along with large scale wind. The mesoscale
wind is chosen to simulate the local wind produced by urban
heat island. It is found that the mesoscale wind reduces the
concentration of primary and secondary pollutants in the
upwind side centre of heat island and enhances the
concentration in the downwind side of centre of heat island,
and as the gravitational settling velocity increases, the
concentration of secondary pollutants decreases. The
concentration of primary and secondary pollutants is less in
magnitude for neutral atmosphere when compared to stable
condition. The neutral atmospheric condition enhances
vertical diffusion carrying the pollutant concentration to
greater heights and thus the concentration of primary and
secondary pollutants is less at the surface region of the urban
city.
Sometimes the pollutant appears in the form of larger
particles on which the effect of gravitational acceleration
cannot be neglected (Calder, 1961). In this case the
pollutant will come down to surface by means of settling
velocity Ws. Particles less than about 20 m are treated as
dispersing as gases, and effects due to their fall velocity are
generally ignored. Particles greater than about 20 m have
appreciable settling velocity (Stern, 1984). Particulate
pollutants emitted into the atmosphere may be dislodged by
a number of natural processes. One of the primary removal
mechanisms is dry deposition onto the surface of the earth
as a result of gravitational settling and ground absorption
by the soil, vegetation, buildings or a body of water.
Surface deposited pollutants may have a significant impact
upon the local ecosystem as the pollutants enter into and
travel through the biological pathways. As secondary
pollutants are heavier, they may come down to the surface
of the earth by means of gravitational settling. Several
researchers have examined the effect of gravitational
settling and ground absorption in the study of air pollution
models.
Keywords— Mesoscale winds, Primary and Secondary
pollutants, Finite difference technique, Gravitational settling
velocity.
I. INTRODUCTION
The dispersion of atmospheric contaminant has become a
global problem in recent years due to rapid industrialization
and urbanization. The toxic gases and small particles could
accumulate, under certain meteorological conditions, in
large quantities over urban areas. This is one of the serious
health hazards in many of the cities in the world. Principal
sources of air-pollution are industries, automobiles and
thermal power plants. The life cycle of pollutants include
emission, dispersion and removal by dry deposition on the
surface of the earth as a result of deposition on the ground
surface by soil, vegetation, buildings or a body of water.
The study of chemically reactive heavy admixture and
its byproduct has generated considerable attention because
of its severe harmful effects on human society and the
environment. A part of an atmospheric contaminant and its
byproduct might occur in the form of particles due to
complexity of the atmosphere.
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
These particles (or heavy admixture) and their
movement by gravitational acceleration have significant
impact on the local eco-system. In the case of Bhopal gas
leakage, for example, a thick coating of dust was found on
the soil around 160 km of the leakage area. So, it is
imperative to have a mathematical model to consider
secondary pollutant due to chemical reaction and their
removal by means of gravitational settling. Rudraiah et al
(1997) have studied the atmospheric diffusion model of
secondary pollutants with settling. Sujit Kumar Khan
(2000) presented a time dependent mathematical model of
secondary air pollutant with instantaneous and delayed
removal. The above models do not deal with the effect of
mesoscale wind.
The effect of mesoscale wind is analyzed for both
primary and secondary pollutants in stable and neutral
atmospheric conditions.
II. MODEL DEVELOPMENT
The dispersion of chemically reactive pollutant
concentration in a turbulent atmospheric medium using Ktheory approach is usually described by the following
equation.
C
C
C
C
U
V
W
t
x
y
z
 
C   
C    C 
   Kz
 Kx
   Ky
  RC , (1)
x 
x  y 
y  z 
z 
where C is the mean pollutant concentration in the air at
any location  x, y, z  and time t . K x , K y and K z are the

The effects of mesoscale winds on the diffusion and
dispersion of pollutants in an urban area along with
gravitational settling are presented in the present paper. It is
well known that large urban areas often generate their own
mesoscale winds due to the urban heat sources.
Consequently, as pointed out by Griffiths (1970),
knowledge of large-scale winds is not sufficient for air
pollution forecasts in urban areas. Griffiths has cited a
specific incident of Chicago city where the urban
mesoscale phenomena played an important role in shaping
the urban pollution pattern.
eddy – diffusivity coefficients U , V and W are the
horizontal and vertical components of wind velocity along
x , y and z directions respectively and R is the chemical
reaction rate coefficient for the chemical transformation.
The x – axis of the Cartesian coordinate system is aligned
in the direction of actual wind near the surface, the y – axis
is oriented in the horizontal cross wind direction and the z –
axis is chosen vertically upwards.
The physical problem consists of an area source which
is spread over the surface of the city with finite down wind
and infinite cross wind dimensions. We assume that the
pollutants are emitted at a constant rate from uniformly
distributed area source. The major source being vehicular
exhausts due to traffic flow and all other minor sources are
aggregated. The vertical height extends up to a mixing
height of 624 meters above which pollutants do not rise due
to the inversion layer of the atmosphere. The pollutants are
transported horizontally by large scale wind which is a
function of vertical height (z) and horizontally as well as
vertically by local wind caused by urban heat source, called
mesoscale wind. We have considered the centre of heat
island at a distance x  l / 2 i.e., at the centre of the city.
We have considered the source region within the urban area
which extends to a distance l in the downwind x direction
(0  x  l). In this problem we have taken l = 6km. We
compute the concentration distribution till the desired
downwind distance l = 6km i.e., 0  x  l. We have
considered two layers, surface layer and planetary
boundary layer to evaluate the large scale wind and
mesoscale wind velocities as accurate as possible. The
pollutants are considered to be chemically reactive and
form secondary pollutants by means of first order chemical
In this paper we have developed a numerical model for
primary and secondary pollutants with more realistic large
scale wind velocity, mesoscale wind velocity and eddy
diffusivity profiles by considering the various removal
mechanisms such as dry deposition, wet deposition and
gravitational settling velocity. The secondary pollutants are
formed by means of first order chemical reaction rate of
primary pollutants. In this model, we have made general
assumption that the secondary pollutants are formed by
means of first order chemical conversion of primary
pollutants. The horizontal homogeneity of pollutants and
constant eddy diffusivity are assumed. The model has been
solved using Crank-Nicolson implicit finite difference
technique. Concentration contours are plotted and results
are analyzed for primary as well as secondary pollutants in
stable and neutral atmospheric situations for various
meteorological parameters, terrain categories, and removal
mechanisms, transformation processes, with and without
mesoscale winds. Mesoscale wind increases the advection
on the left and decreases the advection on the right of
centre of heat island. Therefore, in general the mesoscale
wind decreases the concentration on the left and increases
the concentration on the right of the centre of heat island.
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
conversion. The physical description of the model is shown
schematically in figure 1.
viii)
Pollutants concentration does not vary in cross
wind direction; therefore, no y – dependence and also
lateral flux of pollutants is small and traversing the
center line of uniform area source i.e.,
C p
  C p 
V
and
K
0.
y
y 
y 
ix)
Horizontal advection is greater than the horizontal
diffusion for not too small values of wind velocity.
The horizontal advection by the wind dominates over
C p
C p 
 
horizontal diffusion i.e. U
  K x
.

x
x 
x 
x)
Vertical diffusion is greater than the vertical
advection since the vertical advection is usually
negligible compared to diffusion owing to the small
vertical component of the wind velocity.
Under the above assumptions equation (1) reduces to
C
 p
C p
C p
 U ( x, z )
 W ( z)
t
x
z
C p 
 
  K z ( z)
  k  kwp C p , (2)
z 
z 
where C p  C p ( x, z, t ) is the ambient mean concentration
Figure 1. Physical layout of the model.

A. Primary Pollutant
In formulating the physical problem for primary
pollutant the following assumptions are made:
i)
The pollutants are emitted at a constant rate from a
uniformly distributed area source with steady emission
in the urban area (0  x  l)
ii)
The pollutants are advected downwind with
velocity U and W and are diffused vertically by
the turbulent eddies in the atmosphere
iii)
The pollutant is chemically reactive and converted
into secondary pollutant by first order chemical
reaction rate
iv)
Since larger particles are coming down by the
gravitational acceleration, the pollutants are deposited
on the ground by means of gravitational settling
velocity
v)
The pollutants can also be removed by dry
deposition on the surface of the earth as a result of
ground absorption by soil, vegetation, buildings or a
body of water.
vi)
The large scale wind velocity and eddy diffusivity
are the functions of vertical direction and mesoscale
wind velocity is a function of both horizontal and
vertical direction.
vii)
The mesoscale wind velocity is a function of height
and distance.

of pollutant species, U is the mean wind speed in x –
direction, W is mean wind speed in z-direction, kwp is the
washout coefficient of primary pollutant and k is the first
order chemical reaction rate coefficient for transformation.
We assume that the region of interest is free from
pollution at the beginning of the emission. Thus the initial
conditions are:
Cp = 0 at t = 0, 0  x  l and 0  z  H,
(3)
Cp = 0 at x = 0, 0  z  H and t > 0.
(4)
The air pollutants are being emitted at a steady rate
from the ground level and are removed from the
atmosphere by ground absorption.
Hence, the
corresponding boundary condition takes the form
C p
(5)
Kz
 Vdp C p  Q at z  0, 0  x  l  t  0 ,
z
C p
Kz
 0 at z = H, x > 0 t ,
(6)
z
where Q is the emission rate of primary pollutant species,
Vdp is the dry deposition velocity, l is the length of desired
domain of interest in the wind direction and H is the
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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
mixing height. The term kC p in equation (2) represents
conversion of gaseous pollutants to particulate matter, as
long as the process can be represented approximately by
first order chemical reaction. The concentration of Cs of
secondary pollutant such as sulphate is governed by the
following equation and the boundary conditions.
To solve the equations (2) and (7) we have used the
profiles of large scale wind velocity, mesoscale wind
velocity and eddy – diffusivity for stable and neutral
conditions and other meteorological parameters which are
discussed in the preceding section.
B. Secondary Pollutant
The basic governing equation for the secondary
pollutant Cs is
Cs
Cs
Cs
 U ( x, z )
 W ( z)
t
x
z
C 
Cs
 

K z ( z ) s   Ws
 kws Cs  Vg k C p . (7)

z 
z
z 
In deriving equation (7), we have assumed the
following:
i)
Secondary pollutants are produced by first order
chemical reaction rate.
ii)
Removal of pollutants Cs may occur by dry
deposition onto the surface of the earth as a result of
ground absorption by soil, vegetation, buildings etc.
iii)
Removal of Cs may occur by means of wet
deposition by rainout/washout and gravitational
settling of larger size particle pollutants.
where k ws is the first order wet deposition coefficient of
secondary pollutants, Vg is the mass ratio of secondary
particulate species to the primary gaseous species which is
being converted, Ws is the gravitational settling velocity
secondary pollutants.
To solve Eq. (2) and Eq. (7) we must know realistic
form of the variable wind velocity and eddy diffusivity
which are functions of vertical distance. The treatment of
Eq. (2) and Eq. (7) mainly depends on the proper
estimation of diffusivity coefficient and velocity profile of
the wind near the ground/or lowest layers of the
atmosphere. The meteorological parameters influencing
eddy diffusivity and velocity profile are dependent on the
intensity of turbulence, which is influenced by atmospheric
stability. Stability near the ground is dependent primarily
upon the net heat flux. In terms of boundary layer notation,
the atmospheric stability is characterized by the
parameter L (Monin and Obukhov 1954), which is also a
function of net heat flux among several other
meteorological parameters.
III. METEOROLOGICAL PARAMETERS
A. Eddy Diffusivity Profiles
The common characteristics of K x is that it has linear
variation near the ground, a constant value at mid mixing
depth and a decreasing trend as the top of the mixing layer
is approached. Shir (1973) gave an expression based on
theoretical analysis of neutral boundary layer in the form
(11)
K z  0.4u ze4 z H
*
where H is the mixing height.
For stable condition, Ku et al., (1987) used the following
form of eddy-diffusivity,
K z  [ u z  0.74  4.7 z / L ] exp(b )
(12)
*
b  0.91,   z /( L  ),   u* / | fL |.
The above form of K z was derived from a higher order
turbulence closure model which was tested with stable
boundary layer data of Kansas and Minnesota experiments.
Eddy-diffusivity profiles given by Eq. (11) and Eq. (12)
have been used in this model developed for neutral and
stable atmospheric conditions.
The appropriate initial and boundary conditions on Cs are:
Cs = 0 at t = 0, for 0  x  l and 0  z  H,
Cs = 0 at x = 0, for 0  z  H and t > 0.
(8)
Since there is no direct source for secondary pollutants and
they are removed from the atmosphere by ground
absorption and settling velocity. Hence the corresponding
boundary condition takes the form
Cs
(9)
Kz
 Wgs Cs  Vds Cs at z =0, 0  x  l,  t > 0 ,
z
where Vds is the dry deposition velocity and Wgs is the
gravitational settling velocity of secondary pollutants. The
pollutants are confined within the mixing height and there
is no leakage across the top boundary of the mixing layer.
Thus
Cs
(10)
Kz
 0 at z = H, x > 0  t .,
z
B. Mesoscale Wind
It is known that in a large city the heat generation causes
the rising of air at the centre of the city. Hence the city can
be called as heat island. This rising air forms an air
circulation and this circulation is completed at larger
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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
heights. But we are interested only what happens near the
ground level.
In case of neutral stability with z  0.1 u* / f we get
u   u*   ln   z  z0  z0 
p
 z  z sl 
  u sl ,
u  u g  u sl  
 H  z sl 
  zz p

sl
  u sl 
u e   ax  x0  
  H  z sl 

(13)
It is assumed that the horizontal mesoscale wind varies in
the same vertical manner as u . The vertical mesoscale
wind We can then be found by integrating the continuity
equation and obtain.
ue   a  x  x0  ln  ( z  z0 ) z0 
(14)
where a is proportionality constant. Thus we have
U  x, z   u  ue  u*   a  x  x0   ln   z  z0  z0 
(15)
W  z   we  a  z ln   z  z0  z0   z  z0 ln  z  z0 
(16)
u*   z  z0   
ln 
  z
   z0  L 
.
  z  z0
u e   ax  x0 ln 
  z0
  
  z 
 L 
u
   z  z0   
U  x, z   u  ue   *  a  x  x0   ln 
  z


   z0  L 

 z  z0
W  z   we  a  z ln 
 z0

For 1 
p
 z  zsl 
  ug  usl   a  x  x0   
  1  a  x  x0   usl (27)
 H  zsl 
p


 z  zsl   z  zsl 
W  z   we  a  ug  usl 

  z usl  (28)
p  1  H  zsl 


where, u g is the geostrophic wind, z sl the top of the surface
layer,
(17)
(18)
(19)
z
 6 we get
L
U x, z   u  ue
IV. NUMERICAL METHOD
(21)
Equations (2) and (7) are solved numerically using the
implicit Crank-Nicolson finite difference method in this
paper. We note that it is difficult to obtain the analytical
solution for equations (2) and (7) because of the
complicated form of wind speed U(x,z) and eddy
diffusivity Kz(z) considered in this paper (see section 3).
Hence, we have used numerical method based on CrankNicolson finite difference scheme to obtain the solution.
The detailed numerical method and procedure to solve the
partial differential equations (2) and (7) is described below
(Roache 1976, Wendt 1992).
(22)

u
  z  z 0 
  5.2
  *  ax  x0  ln 

  z 0 

W z   we
x 0 is the x co-ordinate of centre of heat island, H
is the mixing height and p is an exponent which depends
upon the atmospheric stability. Jones et al., (1971)
suggested the values for the exponent p , obtained from the
measurements made from urban wind profiles, as follows:
for neutral conditions
0.2

p  0.35 for slightly stable flow
0.5
for stable flow .

Wind velocity profiles given by equations (13), (17),
(21) and (25) are due to Ragland (1973) and equations (15),
(16), (19), (20), (23), (24), (27) and (28) are modified as
per Dilley –Yen (1971) are used in this model.

 2
z 
  z  z0 ln  z  z0  
2 L 

(20)

u   z  z0 
  5.2 .
u  * ln 
   z0 

  z  z0 

  5.2
u e   ax  x0 ln 
  z0 

(26)
U  x, z   u  ue
In case of stable For 0  z L  1 we get
u
(25)
(23)


 z  z0 
(24)
  z 0 ln z  z 0   4.2 z 
 a  z ln 
 z0 


In the planetary boundary layer Z / L   6 , above the
The governing partial differential equation (2) is
C p
C p
C p
 U ( x, z )
 W ( z)
t
x
z
surface layer, power law scheme has been employed.
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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)

(29)
  k  kwp C p .

Now this equation is replaced by the equation valid at time
step n  1 2 and at the interior grid points (i, j ) . The spatial
derivatives are replaced by the arithmetic average of its
finite difference approximations at the nth and (n  1)th
time steps and we replace the time derivative with a central
difference with time step n  1 2 . Then equation (29) at the
grid points (i, j ) and time step n  1 2 can be written as

n
C p
t
1
2
ij
C p
 
 K z ( z )
z
z 
C p
1
 U ( x, z )
2
x

n
ij


C p
 U ( x, z )
x
C p
1
 W ( z )
2
z

n
ij
n 1
ij
n 1
ij
C p 
C p 
1   
 
 K z ( z)
   Kz (z)

2  z 
z 
z 
z 
ij
ij

1
n
n 1
 k  kwp C pij
 C pij
2
n 1




Cp
t
1
2

n 1
n
C pij
 C pij
t
ij
C p
U ( x, z )
x
U ( x, z )
W ( z)
W ( z)
C p
x
C p
z
C p
z
n
ij
n
ij
ij
n 1
 C pij
 C pn i 11 j 
 U ij 
 ,
x


n
 C pij
 C pn i 1 j 
 Wj 
,
z


C
 Wj 

C p 

 Kz  z 

z 
z 
n 1
pij
C
z
n 1
p i 1 j

,

 C
n 1
pij 1
 


n 1
n 1
n 1 
 C pij
 K j  K j 1 C pij
 C pij
1 
(37)
n
n
n
n 1
 Fij C pin ij  G j C pij
1  M ij C pij  N j C pij 1  Aij C pi ij
(38)
for each i = 2,3,4,….. i max , for each j=2,3,4,……jmax-1
and n=0,1,2,3,…….
t
t
Here
, Fij  U ij
,
Aij   U ij
2x
2x



 t

t
Bj   
( K j  K j 1 ) 
Wj  ,
2
2

z
4

z


 t

t
Gj  
( K j  K j 1 ) 
Wj  ,
2
2 z 
 4 z
t
t
Ej  
( K j  K j 1 ) , N j 
( K j 1  K j ) ,
4 z 2
4z 2




,
Dij  1 
t
t
U ij 
Wj
2x
2 z

(31)
n
 C pij
 C pn i 1 j 
 U ij 
 ,
x


n 1
n 1
ij
,
ij
Equation (30) can be written as
n 1
n 1
n 1
B j C pij
1  Dij C pij  E j C pij 1
for each
i  2,3, 4,....i max, j  2,3, 4,.... j max1, n  0,1, 2..... (30)
Using
n
n 1
1 

K j 1  K j
2 z 2 



C p
W ( z)
z
n
C p 
 
 Kz  z 

z 
z 
M ij  1 
t
1
( K j 1  2 K j  K j 1 )  k  kwp ,
2
4 z 2


t
t
U ij 
Wj
2x
2 z
(33)
t
1
(K
 2 K  K j 1 )  k  kwp .
j 1
j
2
4 z 2
and imax is the i value at x = l and jmax is the value of j at
z = H.
(34)
The initial condition (3) can be written as
0
C pij
 0 for j  1, 2,......... j max , i  1, 2,.........i max .
(32)



The condition (4) becomes
n 1
C pij
 0 for j  1, 2,...... j max , i  1 and n  0,1, 2,.......
(35)
The boundary condition (5) can be written as

z  n 1
z
n 1
,
1  Vd
 C pij  C pij 1  Q


K
K
j 
j

for j =1, i = 2,3,4,…….. imax and n = 0,1,2,3…,
The boundary condition (6) can be written as
C pin 1j1  C pin 1j  0 ,
n
ij
1
n
n
n
n
 K j 1  K j   C pij


1  C pij    K j  K j 1   C pij  C pij 1  
2(z )2 
(36)
for j = jmax, i= 2,3,4…., imax
330
(39)
(40)
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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
A similar procedure is adopted to obtain the finite
difference equations for the secondary pollutant Cs for the
partial differential equation (7) can be written as
B j Csijn 11  Dij Csijn 1  E j Csijn 11
above computational cycle is then repeated for each of the
next time levels and steady state solution is obtained when
the following convergence criterion for the residual defined
as
Cijn 1  Cijn
 ,
Cijn 1
 F ij Csin ij  G j Csijn 1  M ij Csijn  N j Csijn 1  Vg kC pijn  Aij Csin 1ij
(41)
for each i = 2,3,4,….. i max , for each j=2,3,4,……jmax-1
and n=0,1,2,3,……..
The initial and boundary conditions on secondary pollutant
Cs are
Csij0  0 for
is satisfied. Here, C is the concentration which stands for
both C p and Cs , n refers to time, i and j refer to the space
coordinates. The value of  is chosen as 10-5. In the system
of equations (38) the values of C pi 1 j are known at (n+1)th
j  1, 2,......... j max , i  1, 2,.........i max
Csn1j1  0 for i  1, j  1, 2,3..... jmax ,
time level. Therefore we are forcing the system of
equations (38) to (40) to tridiagonal system. Thus the
system of equations (38) to (40) has tridiagonal structure
but is coupled with equations (41) to (43). First, the system
n
of equations (38) to (40) is solved for C pij
, which is
n  0,1, 2,3....... ,

n1
 z  n1
1  (Vd  Wgs )
 Cs ij  Cs ij 1  0 j=1, i=2,3,…imax.
Kj 

(42)
n1
n1
Cs i j 1  Cs i j  0 ,
independent of the system (41) to (43) at every time step n.
This result at every time step is used in equations (41) to
(43). Then the system of equations (41) to (43) is solved for
(43)
 C  at
for j = jmax, i  2,3, 4i max
where
t
Ws ,
Aij  Aij , B j  B j 
2 z
Dij  Dij 
n
s ij
equations are solved using Thomas algorithm. Thus, the
solutions for primary and secondary pollutant
concentrations are obtained.
t
1
1
W  k  kwp   kws  , E j  E j ,
2 z
2
2
F ij  Fij , G j  G j 


The above sets of equations are tridiagonal system of
equations and they are solved by using Thomas algorithm.
This method is very efficient for use on the digital
computer and has been found to be stable to round off error
for finite difference equations. The ambient air
concentrations were obtained for stable and neutral
atmospheric conditions by a computer program developed
to solve the above system of equations.
t
Ws
2 z
t
1
1
W  k  kwp   kws  , N j  N j .
2 z
2
2
Vg is the mass ratio of the secondary particulate species to
the primary gaseous species which is being converted and
Wgs is the gravitational settling velocity of the secondary
M ij  M ij 

the same time step n. Both the systems of

V. RESULTS AND DISCUSSION
A numerical model for the computation of the ambient
air concentration emitted from an urban area source
undergoing
various
removal
mechanisms
and
transformation process is presented. The results of this
model have been presented graphically in figures 3 - 8 to
analyze the dispersion of air pollutants in the urban area
downwind and vertical direction for stable and neutral
conditions of atmosphere. The concentration of primary
and secondary pollutants increase in the downwind
direction of the source region, because we have considered
the area source till the end of the urban city region and the
advection is along x - direction. The effect of mesoscale
wind on primary and secondary pollutants for stable and
neutral cases is studied. The concentration of primary and
pollutant Cs.
We have computed concentration residue obtained after
every time step against the number of time steps and
analyzed. Accuracy depends on the fall in residue. It is seen
that the residue settles to around 10-7. For the gridindependence study we have computed concentration for
20 ×156, 40 ×312, 80×624 and 160×1248 grids and
analysed. The analysis reveals that concentration for 20
×156 and 40 ×312 grids differ considerably against those
on 80 × 624 grids. Further, there is no perceptible change
occurring on 160 ×1248 grids from that of 80 x 624 grids.
It is therefore reasonable to assume that the solution
obtained on 80 × 624 grids is an independent solution. The
331
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
Secodary Pollutants Cs vd=0.0
0.06
z=2
ws=0.0
Secondary Pollutants Cs
0.06
x=6000
vd=0.0
ws=0.0
ws=0.001
0.05
0.05
ws=0.001
ws=0.002
0.04
ws=0.002
-3
Concentration(gm )
ws=0.004
-3
Concentration( gm )
0.04
0.03
0.02
0.01
ws=0.004
0.03
0.02
0.01
0.00
0.00
0
1000
2000
3000
4000
5000
0
6000
10
20
30
40
50
60
70
Height(m)
Distance(m)
(a)
(a)
0.018
0.018
vd=0.005
z=2
Secondary Pollutants Cs
0.016
ws=0.001
-3
-3
Concentration(gm )
0.010
0.010
ws=0.004
0.008
ws=0.002
0.008
0.006
ws=0.004
0.006
ws=0.002
0.012
Concentration(gm )
0.012
ws=0.001
0.014
0.014
vd=0.005
x=6000
Secondary Pollutants Cs
ws=0.0
0.016
ws=0.0
0.004
0.004
0.002
0.002
0.000
0.000
-0.002
-0.002
0
1000
2000
3000
4000
5000
0
10
20
30
50
0.012
z=2
Secondary Pollutants Cs
0.010
ws=0.002
-3
-3
Concentration(gm )
vd=0.0
ws=0.0
0.008
0.008
Concentration(gm )
x=6000
Secondary Pollutants Cs
vd=0.0
ws=0.0
ws=0.001
70
(b)
Figure 5. Concentration versus height of secondary pollutants for stable
case.
0.012
0.010
60
Height(m)
(b)
Figure 3. Concentration versus distance of secondary pollutants for stable
case.
0.006
0.006
0.004
0.004
ws=0.004
ws=0.008
0.002
ws=0.008
0.002
0.000
ws=0.004
0.000
0
1000
2000
3000
4000
5000
6000
0
50
100
Distance(m)
150
250
300
(a)
0.007
Secondary Pollutants Cs
200
Height(m)
(a)
0.007
vd=0.005
z=2
Secondary Pollutants Cs
0.006
x=6000
vd=0.005
0.006
ws=0.0
0.005
ws=0.0
0.005
ws=0.002
ws=0.002
-3
0.003
0.004
Concentration(gm )
0.004
Concentration(gm )
-3
40
6000
Distance(m)
0.003
ws=0.004 ws=0.008
0.002
ws=0.004
ws=0.008
0.002
0.001
0.001
0.000
0.000
0
1000
2000
3000
4000
5000
6000
0
50
100
150
200
250
300
Height(m)
Distance(m)
(b)
Figure 6. Concentration versus height of secondary pollutants for neutral
case.
(b)
Figure 4. GLC versus distance of secondary pollutants for neutral case.
332
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
secondary pollutants is less on upwind side of the centre of
heat island and more on downwind side of the centre of
heat island in the presence of mesoscale wind
(a =
0.00004) compared to that in the absence of mesoscale
wind (a = 0). This is because the horizontal component of
the mesoscale wind is along the large scale wind on the left
and against it on the right. The results are well agreed with
Laxminaranachari K et al., (2012) in the absence of
mesoscale wind  a  0.0  .
220
200
180
Primary Pollutants Cp
a=0
a=0.00004
z=2
ws=0.0
vd=0.0
140
-3
Concentration(gm )
160
120
100
80
60
40
20
0
0
1000
2000
3000
4000
5000
6000
Distance(m)
(a)
0.07
Secondary Pollutants Cs z=2
0.06
a=0
a=0.00004
vd=0.0
In figures 3 and 4 the plots of concentration of
secondary pollutants versus distance with the removal
mechanisms such as gravitation settling velocity and
deposition velocity for stable and neutral cases are
presented. The effect of settling velocity on secondary
pollutants for Vd  0.0 and Vd  0.005 is studied in figure 3
for the stable case. As settling velocity increases the
concentration of secondary pollutant decreases. If Vd  0.0
the maximum concentration of secondary pollutants is
0.06 (figure 3a) and if Vd  0.005 the maximum
concentration of secondary pollutants is 0.016 (figure 3b).
This shows that as deposition velocity Vd increases the
concentration of secondary pollutants decreases. In figure
4, a similar effect is observed in neutral case but the
magnitude of secondary pollutants is less when compared
to the stable case.
ws=0.0
-3
Concentration(gm )
0.05
0.04
0.03
0.02
0.01
0.00
0
1000
2000
3000
4000
5000
6000
Distance(m)
(b)
Figure 7. Concentration versus distance of primary & secondary pollutants
for stable case.
60
Primary Pollutants Cp z=2 ws=0.0
vd=0.0
-3
Concentration(gm )
50
In figures 5 and 6 the plots of concentration of
secondary pollutants versus height with the removal
mechanisms such as gravitational settling velocity and
deposition velocity for stable and neutral cases are
presented. In figure 5 the effect of gravitational settling
velocity and dry deposition velocity on secondary pollutant
concentration versus height at a distance x  6000m is
studied. As height increases the concentration of secondary
pollutants decrease and reaches zero at about 60m height.
As the gravitational settling velocity is increased, the
concentration of secondary pollutants decreases for the
deposition velocity of Vd  0.0 and Vd  0.005 under stable
case. Whereas in neutral case the concentration of
secondary pollutants reaches higher levels and is zero
around 300m . This shows that the vertical mixing takes
place in neutral case and the pollutants are carried to the
higher heights. Hence neutral condition of the atmosphere
is favorable for air pollution point of view.
40
30
20
a=0
a=0.00004
10
0
1000
2000
3000
4000
5000
6000
Distance(m)
(a)
0.012
Secondary Pollutants Cs z=2 vd=0.0 ws=0.0
a=0
a=0.00004
0.010
-3
Concentration(gm )
0.008
0.006
0.004
0.002
0.000
0
1000
2000
3000
4000
5000
6000
Distance(m)
In figures 7 and 8 the effect of mesoscale wind on
primary and secondary pollutants for both stable and
neutral cases are presented. The concentration of primary
(b)
Figure 8. Concentration versus distance of primary and secondary
pollutants for neutral case.
333
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)
and secondary pollutants is less in upwind side of the
centre of heat island and more in the downwind side of the
centre of heat island in the case of mesoscale wind when
compared to that of without mesoscale wind. This is
because the mesoscale wind increases the velocity in the
upwind direction and decreases in the downwind direction
of the centre of heat island. The similar effect is observed
in neutral case. But the magnitude of primary and
secondary pollutant concentration is more in the stable case
and is less in the neutral case because neutral case enhances
vertical diffusion and the stable case suppresses the vertical
diffusion.
[5] Grying, S. E, Van Ulden, A. P., Larsen, S. E. 1983. Dispersion from
VI. CONCLUSIONS
[10] Lettau, H. H. 1959. Wind profile, surface stress and geostrophic drag
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R. Met. Soc, 109, 355-364.
[6] John, F. Wendt. 1992. Computational fluid dynamics-An
introduction (Editor) A Von Karman Institute Book Springer-Verlag.
[7] Jones, P. M., Larrinaga M, A. B., Wilson, C. B. 1971. The urban
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[8] Ku, J. Y., Rao, S. T., Rao, K. S. 1987. Numerical simulation of air
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[9] Lakshminarayanachari, K, Pandurangappa C, M. Venkatachalappa.
2012. Mathematical model of air Pollutant emitted from a time
dependent area source of primary and secondary pollutant with
Chemical reaction, International Journal Of Computer Applications
in Engineering, Technology and Sciences, Vol 4, 136-142.
coefficients in the atmospheric surface layer.
Geophysis, Academic Press, New York, 6, 241.
The effect of mesoscale wind on a two dimensional air
pollution due to area source is presented using a
mathematical model to simulate the dispersion processes of
primary and secondary pollutants in an urban area with
gravitational settling velocity. The results of this model
have been analyzed for the dispersion of air pollutants in
the urban area downwind and vertical direction for stable
and neutral conditions of atmosphere. The concentration of
secondary pollutants decreases as gravitational settling
velocity increases in both stable and neutral cases. The
concentration of primary and secondary pollutants is less in
upwind side of the centre of heat island and more in the
downwind side of the centre of heat island in the case of
mesoscale wind when compared to that in the absence of
mesoscale wind, because the mesoscale wind increases the
velocity in the upwind direction and decreases in the
downwind direction of the centre of heat island. The
concentration of primary and secondary pollutants is less in
magnitude for neutral atmosphere when compared to stable
condition. The neutral atmospheric condition enhances
vertical diffusion carrying the pollutant concentration to
greater heights and thus the concentration is less at the
surface region of the urban city.
Advances in
[11] Lettau, H. H. 1970. Physical and meteorological basis for
mathematical models of urban diffusion processes. Proceedings of
symposium on Multiple Source Urban Diffusion Models, USEPA
Publication AP-86.
[12] Monin, A. S., Obukhov, A. M. 1954. Basic laws of turbulent mixing
in the ground layer of the atmosphere. Dokl. Akad. SSSR, 151, 163.
[13] Nokes, R. I., Mcnulty, A. J., Wood, I. R. 1984. Turbulent dispersion
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[14] Peterson, T. W., Seinfeld, J. H. 1977. Mathematical model for
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Atmospheric
Environment 11, 1171.
[15] Ragland, K. W. 1973. Multiple box model for dispersion of air
pollutants from area sources. Atmospheric Environment 7, 1071.
[16] Reiquam, H. 1970. An atmospheric transport and accumulation
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[17] Roache, P. J. 1976. Computational fluid dynamics.
Hermosa
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[18] Roth, P. M. et al, 1971. Developments of a simulation model for
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repared for USEPA by Systems Applications, Inc.
[19] Rudraiah, N., M. Venkatachalappa, Sujit kumar Khan,
1997.
Atmospheric diffusion model of secondary pollutants, Int.J. Envir.
Studies., 52, pp 243- 267.
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334