National Defeonce naticnalls UNCLASSIFIECdefeonce naticnalls unclassifiec suffield repo rt no. 500...
Transcript of National Defeonce naticnalls UNCLASSIFIECdefeonce naticnalls unclassifiec suffield repo rt no. 500...
U National D6fens*
Defeonce naticnalls UNCLASSIFIEC
SUFFIELD REPO RTNO. 500
________________UNLIMITED:u
SDNISTIBTION
AD-A 193 802 DSRBTO
A MODEL FOR CALCULATING,
DISPERSION AND DEPOSITION OF SMALL PARTICLES
FROM A LOW LEVEL POINT SOURCE (U)
by
Stanley B. Mellsen
PC 31 A DTIC-E-LECTE~7APR 141988~
February 1988-
DEFENCE RESEARCH ESTABLISHMENT SUFFIELD. RALSTON, ALBERTA
~~9A9() 88 4 iS -
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DEFENCE RESEARCH ESTABLISHMENT SUFFIELD
RALSTON ALBERTA
SUFFIELD REPORT 500
A MODEL FOR CALCULATING
DISPERSION AND DEPOSITION OF SMALL PARTICLES
FROM A LOW LEVEL POINT SOURCE
Accession For
by NTIS G;A&ID7IC TABUnannouncedJust IfIcatio i
Stanley 8. Melisen
Distribution/Availability Codes
PCN 351SA Dist L Special
N CLA
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DEFENCE RESEARCH ESTABLISHMENT SUFFIELD
RALSTON ALBERTA
SUFFIELD REPORT NO. 500
A MODEL FOR CALCULATING
DISPERSION AND DEPOSITION OF SMALL PARTICLES
FROM A LOW LEVEL POINT SOURCE
by
Stanley 3. Mellsen
ABSTRACT
1A mathfatical model for estimating concentrations and ground
deposi•ion"densities from a low level point source of particulates up
to 2•,_mi'n diameter has been developed. The model applies K theory to
account for vertical dispersion and Gaussian spread to account for la-
teral dispersion. Results for the limiting case of zero terminal velo-
city with negligible retention at the ground are compared directly to
field experimental data for a source near ground level to establish the
validity of using Gaussian lateral dispersion from an elevated source.
The vertical dispersion function and lower boundary condition for an
existing line source model were applied in the present point source
model. Previous comparison to ground deposition densities measured in
various field experiments indicate that estimates from the line source
model are reasonable, although further exoeriments would be useful.C.cy~c.AA •
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TABLE OF CONTENTS
Page No.
ABSTRACTTABLE OF CONTENTSLIST OF SYMBOLSLIST OF TABLESLIST OF FIGURES
INTRODUCTION ........................................... 1
K; OUTLINE OF THE LINE SOURCE MODEL ....................... 2Differential Equation .............................. 2Boundary Conditions ................................ 3Functional Forms of U(z), PS, q .................... 5
SOLUTION OF EQUATIONS .................................. 7Numerical Methods .................................. 7
POINT SOURCE MODEL ..................................... 8
CAlI rLATED RESULTS AND COMPARISON TO EXPERIMENT ........ 13
DISCUSSION OF RESULTS .................................. 39
CONCLUSIONS ............................................ 42
REFERENCES ............................................. 43
APPENDIX A COMPUTER PROGRAM "DIFFP", WITH SAMPLE RESULTS
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LIST OF SYMBOLS
A constant to account for variations in eddy diffusivity due
to atmospheric stability
B sublayer Stanton number
C (x,z) total dosage for an instantaneous line source, g s m-3 , or
steady state concentration from a continuous line source, g
m-3
C(x,y,z) total doscge for an instantaneous point source g s m-3, or
steady state concentration from a continuous point source gM-3
0 drop diameter, m
E efficiency of retention or capture by the subs4 rate
F(x,z) vertical flux of diffusing material, g m-2 for an instan-
taneous source and g m-2 s-' for a continuous source
h release height of line source, m
H upper boundary of the turbulent boundary layer, m
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K(z) coefficient of vertical eddy diffusivity at height z, m2
s-I
At length of the same order as the roughness length of the
substrate zo, m.
p exponent in power law wind velocity profile
Pa mean transport velocity between the turbulent atmosphere
and the rough surface, m sin
PS apparent mean transport velocity through the horizontal
plane at z=O m s"=
Q source strength, g m-' for an instantaneous line source and
g m-1 s-' for a continuous iine source
Qp source strength g for an instantaneous point source and g
s"- lor a continuous point source
q terminal velocity of particles, m s"i
R(z) vertical diffusive resistance of the atmosphere at height
z,mnsI 5
S total surface area of the roughness element per unit hori-
zontal area
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lh~uh~aIW~s -- ~
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u(z) mean horizontal wind speed in x direction at height z, mS'!
x horizontal dowii wind distance, m
y horizontal crosswind distance, m
z vertical height above ground, m
ay, az crosswind and vertical plume standard deviations, m
w conta-mination density, g M-2 from an instantaneous source
and g m-2 s"I from a continuous line source
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LIST OF TABLES
TABLE I Value of Constants
TABLE II Formulae for a Cx) and ca Cx) (102 < x < 10'nm)
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LIST OF FIGURES
Figure 1 Downwind Concentrations from a line source at 1 m Height in
Neutral Atmospheric Stability with 2 m Wind Speed of 5 mS-
Figure 2 Downwind Concentrations from a Point Source at 1 m. Height
in Neutral Atmospheric Stability with 2 m Wind Speed of 5 m
s-I
Figure 3 Downwind Concentrations from a Point Source at Various
Heights in Neutral Atmospheric Stability with 2 m Wind Speed
of 5 m s-'. K Theory with Gaussian Lateral Spread.
Figure 4 Downwind Concentrations from a Point Source at Various
Heights in Neutral Atmospheric Stability with 2 r Wind Speed
of 5 m s-1. Gaussian distribution.
Figure 5 Concentrations 100 m Downwind of a Line Source at 1 m Heightwith Various Retention Efficiencies in Neutral Atmospheric
Stability with 2 m Wind Speed of 5 m s'. E=O.0 to 0.2.
Figure 6 Concentratiuns 100 m Downwind of a Line Source at 1 m Heliht
with Various Retention Efficiencies in Neutral Atmospheric
Stability with 2 m Wind Speed of 5 m s-'. E=0.5 and 1.0.
Figure 7 Peak Concentrations Downwind of a Point Source at 1 m Height
with Various Retention Efficiencies in Neutral Atmospheric
Stability with 2 m Wind Speed of 5 m s 1 . E=O.0 to 0.2.
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LIST OF FIGURES (continued)
Figure 8 Peak Concentratio'os 100 m Downwind of a Point Source at 1 m
Height with Various Retention Efficiencies in Neutral Atmos-
pheric Stability with 2 m Wind Speed of 5 m s-'. E=0.5 and
1.0.
Figure 9 Downwind Concentrations of Monodisperse Particulate from a
Line Source at 1 m Height in Two Atmospheric Stability
Conditions.
Figure 10 Ground Deposition of Monodisperse Particulate from a Line
Source at 1 m Height in Stability Category .3 with 2 m Wind
Speed of 3 m s-1.
Figure 11 Ground Deposition of Mornodisperse Particulate from a Line
Source at 1 m Height in Stability Category F with 2 n, Wind
Speed of 1.5 m s".
Figure 12 Downwind Concentrations from a Point Source at 1 m Height
with Various Retention Efficiencies in Neutral Atmospheric
Stability with 2 m Wind Speed of 5 m s-1.
Figure 13 rownwind Cowi.entrations from a Point Source at 1 m Height in
Various Atmospheric Stability Conditions.
Figure 14 Ground Deposition from a Point Source at 1 m Height in
Various Atmospheric Stability Conditions.
Figure 15 Downwind Concentrations from a Point Source of 5 pm Particles
at 3 m Height in Various Atmospheric 'tability Conditions.
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LIST OF FIGURES (continued)
Figure 16 Downwind Concentrations from a Point Source of 20 pm
Particles at 3 m Height in Various Atmospheric Stability
Conditions.
Figure 17 Ground Deposition of Monodisperse Particulate from a Point
Source at 3 m Height in Stability Category C with 2 m WindSpeed of 3m is"
FIgure 18 Ground Deposition of Monodisperse Particulate from a Point
Source at 3 m Heioht in Neutral Atmospheric Stability with 2
m Wind Speed of 5 m s-1.
Figure 19 Ground Deposition of Monodisperse Particulate from a Point
Source at 3 m Height in Stability Category E with 2 m Wind
Speed of 1.5 m s-1.
Figure 20 Ground Deposition of Monodisperse Particulate from a Point
qource at 3 m Height in Stability Category F with 2 m Wind
Speed of 1.5 m s-".
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DEFENCE RESEARCH ESTABLISHMENT SUFFIELD
RALSTON ALBERTA
SUFFIELD REPORT NO. 500
A MODEL FOR CALCULATING
DISPERSION AND DEPOSITION OF SMALL PARTICLES
FROM A LOW LEVEL POINT SOURCE
by
Stanley B. Mellsen
INTRODUCTION
1. A mathematical model which includes the effect of atmospheric
diffusion on dispersion and settling was developed at the Defence
Research Establishment Suffield [1,2]. Calculation of airborne concen-
trations and mass deposition densities downwind of an elevated line
source of non-evaporating spray or solid particles can be calculated
from this model. Knowledge of aerial concentration and mass deposition
density from a low level point source is also useful in applications
related to chemical and biological defence. Therefore, the line source
model has been extended to calculate these quantities from a point
source. The purpose of this report is to describe this point source
model 3nd to provide some comparision to previously available data from
field experiments of other workers.
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OUTLINE OF THE LINE SOURCE MODEL
2. The differential equation, boundary conditions and functional
forms for the wind velocity profile, transport velocity to the rough
surface, and particle terminal velocity were stated previously [1,2],
but are provided for convenience. The details of the solutions are
shown elsewhere [1,2].
Differential Equation
3. The equation used to describe turbulent diffusion of monodisperse
particulate matter in the atmosphere from a uniform infinite crosswind
line source is:
u(z) 3C(x,z)/ax = a/az[K(z)aC(x,z)/az} + qaC(x,z)/az (1)
where C total dosage for an instantaneous source
steady state concentration from a continuous sourcex =horizontal downwind distance
z vertical height above ground
K(z) =the coefficient of eddy diffusivity at zu(z) =mean horizontal wind speed at z
q terminal velocity of the particles
This equation and its boundary conditions have been discussed by Calder
[3], who indicated the problems in stating the lower boundary condition
with regard to the transport of material through this boundary of the
turbulent atmosphere to the ground or substrate. Monaghan and McPherson
[4] have proposed an equation for the transport of vapour to rough nat-ural surfaces based an wn-k by Chamberlain [5] which relates the trans-
A
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port of vapour to the substrate in terms of windspeed at 2 m above
ground, the roughness and specific area of the substrate, and an
absorption velocity, characteristic of the vapour, into the roughness
elements of the substrate. This equation has been modified to include
the terminal velocity of particulate matter and its retention by the
roughness elements. As for the case of vapour diffusion, it is assumed
that the turbulent airstream is bounded by the non-turbulent atmosphere
which acts as a lid to vertical diffusion.
Boundary Conditions
4. The vertical flux F(x,z) of diffusing material is given by:
F(x,z) = -{K(z)aC(x,z)/az + qC), (2)
where F is positive in the direction of increasing z,
and therefore,
u(z)aC(x,z)/ax = -aF(x,z)/az (3)
At the upper boundary z = H,
Lim F o (4)
z4H
At the lower botvndary,
Ltim [-F(x,z)= ES(Pa + q/S) rim C(x,z), (5a)
Z_+0 Z40
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= E(Ps + q) lim C(x,z), (5b)
Z4O
where E is the efficiency of retention (or capture), S is the total
surface area of the roughness elements per unit horizontal area, Pa is
the mean transport velocity of material between the turbulent
atmosphere and the rough surface. Ps is the apparent mean transport
velocity through the horizontal plane at z = o.
The upper and lower boundary conditions are given by:
Lim [K(z) aC(x,z)/az + qC(x,z)) = o (6)z4H
and
Lim {K(z) aC(x,z)/az + qC(x,z)J = ES(Pa + q/S) lim C(x,z) (7a)
Z40 Z40
= E(Ps + q) lim C(x,z) (7b)
z4o
Boundary Condition for a Material Source
5. Assuming a line source, then from mass balance considerations in
equation (1)
Lim C(x,z) Q6(x-h)/u(h) (8)
X4O
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where Q is source strength (mass per unit length for an instantaneous
line source), h is release height and 6 is the Dirac delta function.
Functional Forms of u(z), Ps, q
6. a. A number of functional forms for u(z) have been proposed. In
this model a power-law form is used:
u(z) = u(2) {(z + At)/(2 + AA)jp (9)
where z is in metres, p is a function of atmospheric
stability and Al is a length of the same order as the
roughness length zo0.
K(z) is given by:
K(z) = A(z +AJ)u(2) (10)
where A is a constant dependent upon atmospheric stability.
Monaghan and McPherson [4] have published values of A, At
and p for stable to slightly unstable conditions by fitting
their vapour diffusion model to field data and Pasquill's
data on vapour cloud height. Pa is related to the
reciprocal of the sublayer Stanton number B by the
approximate equation:
Pa = u,/B'IS (11)
Since u. is approximately a factor of 10 less than u(2)
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Pa a O.lu(2)/B-'S (12)
Chamberlain (1966) suggests values of B-1 between 5 and 8 for
grass with S equal to approximately 2. Hence the equation:
Pa = 0.01 u(2) (13)
is used for all stability categories.
b. Thoom [6] quotes values of B"1 for a variety of rough
surfaces which range from 5 for grassland to 2 for a pine
forest. Thus, if Pa is z•ssumed to be the same for all these
surfaces, S varies from 2 for grassland to 5 for the forest.
Suggested values of A, at, p, u(2) and H are given in Table
I for various Pasquill atmospheric stability categories.
c. Assuming the particulate is a liquid of approximately unit
specific gravity and diameter D, Best's equation [7] for
terminal velocity can be used:
q = A[1 - exp(--BDc)1; (14)q = 9.43 {1-exp[-(D/1.77) 1 ' 1 47 ]}for 0.3 5 0: 6.0
q is in m .-I for D in mm.
Below 0 = 0.3 mm equations for fluid drag on spheres are used.
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SOLUTIONS OF EQUATIONS
Numerical Methods
7. The diffusion equations are solved by finite difference methods
using a Crank-Nicolson formulation to reduce the difference scheme to a
tridiagonal matrix which is inverted by the Gauss elimination method
using a digital computer. Errors in discretization are reduced by
subdividing the atmosphere vertically intu equal increments of
diffusive resistance R rather than height, using the relationship
R(z) = fzdz/K(z) or dR(z)/dz = 1/K(z). (15)
8. This procedure also economizes on computer storage. The equationsare solved for C(x,z) and deposition of partiLilate in the substrate.
In the latter case, equation (7) will give rate of deposition for acontinuous source or deposition density (mass/unit horizontal area = w)
for an instantaneous source. As stated previously, the details are
described elsewhere [1,2].
TABLE I
VALUE S•--U- STANTS
CONSTANTS
STABILITY A p u(2) HCATEGORY m TS
C 0.08 0.025 0.2 2-4 1000D 0.04 0.025 0.23 ?3 500E 0.03 0.025 0.3 1.5-3 200F 0.02 0.025 0.5 1.5-2 100
AU is given for grassland
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POINT SOURCE MODEL
Description and Justification of the Method
10. The extension of the line source model was accomplished by
applying Gaussian lateral distribution to the solution calculated from
the K theory lini source model. The Justification for this is that in
practical applications the lateral distribution over simple terrain
without major obstacles is Gaussian [8]. This applies only to gaseous
clouds or particles small enough so that they follow the air movement
with negligible slip. Since particle dispersici as well as gas
dispersion is considered, sensitivity tests for the effect of particle
size on airborne concentrations and mass deposition densities were
performed by comparing results for various sizes of particles up to 20
pm diameter. In this way the assumption that particles closely
follow the air flow can be verified.
11. Vertical distributions are approximately Gaussian only for someelevated sources, yet it is common practice to assume the distribution
from pollutants emitted near the surface is also Gaussian [8]. The
"Gaussian vertical distribution assumes that the coefficient, K, is
independent of height which is not generally realistic. The vertical
diffusion coefficient as given by equation (10), with constants A and At
given in Table I, is realistic for open prairie terrain without major
obstacles [1,2,4].
12. The condition of conservation of mass, called the continuity
condition, must be satisfied. As for the line source model, the x
direction is downwind, and z vertical. The direction designated by y is
horizontal and 900 to the left of the x direction. A different meaning
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was used for y in the line source model, but since it does not appear
explicitly in this report, it can be used in the conventional manner.
The continuity conditions which assume no turning of wind with height
are given as follows. For a single continuous line source at right
angles to the mean wind direction the continuity condition is (steady
conditions)
Q = f C(x,z) u(z) dz (16)p
where Q is the source strength in mass per unit length per unit time,
C(x,z) is the concentration.
For a single continuous point source the continuity condition is (steady
conditions)
Q = Jf C(x,y,z) u(z)dy dz (17)
where Qp is the source strength in units of mass per unit time and
C(x,y,z' is the concentration. Equations (16) and (17) must be
satisfied for all distances x downwind.
13. Almost all the solutions to equations (16) and (17) are based on
the same general forms [8]. Three independent dispersion functions,
G(x), H(y) and l(z) that are independent of each other, are assumed.
The continuity conditions, equations (16) And (17) can be satisfied by
the solutions for the following equations. For the continuous line
source
Q 1(z) (18)SC(x,y) = uz
and for the point source
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C(x'y'z) = Q H(y) Ihz)u(z)y(19)
where H and I also depend upon x [8].
14. Solutlons (16) and (17) require that thL dispersion functions act
independently. This is usually the case, to a good approximation [8].
The most serious exception occurs when the wind direction changes withheight. In that case H(y) varies with height and therefore also depends
on z. Most observations of vapour dispersion indicate that K(z)increases with distance from the source [8]. T;,e reason is that in the
atmosphere there are eddies of all sizes. As the plume grows, larger
eddies become relatively more important, so K(z) must be allowed toincrease with travel time or distance. If the source is at or near the
surface, the centra of gravity of the plume will rise with downwind
distance. Therefore, since K(z) varies directly with height as shown in
equations (10), the effective value K(z) will increase with distance,
even if it is assumed to vary with height only, and the solutions of (1)
for q = 0, which represent dispersion of a gaseous cloud, are quite
realistic [8]. For particulate dispersion, the terminal velocity isgreater than zero, which corresponds to q > 0 in equation 1. Therefore
the height of the centre of gravity of the plume rises less with
* downwind distance. In the atmosphere, the characteristic vertical
dimension of eddies is of the same order as the distance above theground [9]. Therefore the effective value of K(z) can be expected to
increase less with down wind distance for particulates with considerable
terminal velocity than for gases. Again the physics is compatible withequation (10) in which K(z) is proportional to height.
15. Assuming then that I(z) is given by K theory and H(y) is a
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Gaussian distribution, the line source solution outlined in paragraphs 3
to 8 with q = 0 in equation (10) can be applied to calculate
concentrations downwind of a point source as follows. Substituting
equation (18) into equation (19) gives
C(x,y,z) = P C(x,z) H(y) (20)Q
"where H(y) is given by the basic form of the Gaussian lateral distribu-
tion as follows
H(y) = 1 exp-Y2) (21)VTW-yC (21)
Say
The term a is the standard deviation of y. Actual values of are
given by the numerical expressions developed by Briggs [8,10,11] who
revised the Pasquill-Gifford diagrams developed from observations over
smooth terrain. These are shown in Table IH. The plume width is
approximately 4 ay as 95% of the dispersed material is located within
the 2 ay to each side of the centre of the distribution.
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11111'11111 111ll~l III Jil I/M=/
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TABLE II
FORMULAS FOR aYWAND a z (X) (102 < X< 104 M)
Pasqu ill
Type a Qm z (m)
Open-Country Conditions
A. O.22X(1+O.OO0lx) 1f 0.20X
B 0.16x(1+O.OO0lx) tf 0.12x
C O.11x(1+0.0OO1x)-l O.08x(1+0.00O2x)-f
0 O.08x(1+0. OO0lx)*i 0.06x(1+0.0015x)-f
E 0.O6x(1+O.0001x)-f O.03x(1+O.0003x)'i
F O.04x(1+O.0004x)*f O.016x(1+O.0003x)-
Urban Conditions
A-B 0.32x(1+0.0004x) O.24x(1+O.O0lx)*
C O.22x(1+0.0004x) 1f 0.20x
0 0. 16x(1+0.0004x)*f 0. 14x(1+O. 0003x)*f
E-F 0. llx(1+O.0004x) 1i O.08x(1+0.00015x)-i
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Gaussian lateral spread is a good approximation for gaseous clouds, but
there is no evidence that it is suitable for particulate clouds with
considerable terminal velocity. However, the concentrations calculated
for a gaseous cloud can be shown to be close to those for particles with
diameters up to 20 pm, which is a size range of interest in practical
applications. This is accomplished by comparing concentrations and mass
deposition densities calculated for various particle sizes with the line
source model. Calculated results, provided later, will show that the
differences are small enough so that practical estimates can also be
made from the point source model. The mass desposition density for a
particle is not necessarily the same as for a gas' but this can be ac-
counted for independently of lateral spread by providing the appropriate
retention factor, E, in bhe lower boundary condition given by equations
(7a) and (7b). A non-reactive gas such as argon or helium is not ab-
sorbed at all by dry deposition, but once a particle encounters a
surface it is considered to have been absorbed [12]. Here E=O for the
non-reactive gaz and E=1 for the particle,
CALCULATED RESULTS AND COMPARISON TO EXPERIMENT
16. In this section calculated results are shown from the K theory
line source model and the point source model using K theory for the
vertical dispersion function and Gaussian distribution for the lateral
spread. The results for both types of sources are compared, to a set of
values based on carefully constructed diffusion experiments at Pr-ton,
England in the 1930's under O.G. Sutton. [8,13]. Also the ground level
concentration along the wind direction from a gaseous point source with
no retention is compared to the results calculated using Gaussian
distributions both horizontally and vertically.
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17. The line source model "DIFF", was applied using a Fortran
computer prugram [1) on the DRES Honeywell CP-6 system. The point
source model "DIFFP" was applied in a similar way. The program, which
was developed by modifying the one for the line source, is described in
Appendix A. The ground level concentrations using only Gaussian
dispersion was calculated from the following equation [8,11]
C(x,oo) P exp -h27,7-yUU (h) •z22.
y z z
Equation (22) is used with the dispersion functions, 7y and cz, given in
Table II. These dispersion functions were originally intended for use
in estimating ground level concentrations from elevated stack sources
[11] and have been developed over many years with industrial
applications in r,mind.
18. The set of values, based on the Porton experiments [13], are
repeated for convenience as follows:
a. Experimental Data for Adiabatic Gradient Conditions
The following data are the mean results of many trials with
both smoke and gas clouds over level grass land. No diffe-
rence could be detected between the rates of diffusion of
gases and smokes.
(1) The concentration at any point in a continuously gene-
rated cloud is directly proportional to the strength of
the source, provided that the source itself does not
materially interfere with the natural air flow (e.g. by
producing intense local convection currents).
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(2) For a given strength of source the mean concentration
at any point in a continuously generated cloud is
approximately inversely proportional to the mean wind
speed measured at a fixed height.
(3) The time-mean width of the cloud from a continuous
point source measured at ground level, is about 35 m at
100 m downwind of the source and shows only very small
variations with the mean wind speed.
(4) The time-mean height of the cloud from an infinite
crosswind continuous line source is about 10 m at 100 m
downwind of the source and showns only very small
variations with wind speed.
(5) The central (peak) mean concentration from a continuous
point source decreases with distance downwind, x,
according to the law
concentration a x"1-76
(6) The peak (i.e. 9round level) mean concentration from an
infinite crosswind continuous line source decreases
with distance downwind, x, according to the law
concentration a x-649
(7) The absolute values of the peak mean concentrations at
100 m downwind are as follows:
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Mean Wind Peak
Type of S..urce Strength at 2 mn Height Concentration
Continuous Point 1 g sec'- 5 m sec" 1 2 mg m-3
Continuous infinite
line (across wind) 1 g sec, 1 m-1 5 m sec' 1 35 mg m-3
The above data constitutes a standard set of values to which
any theory of atmospheric diffusion must conform. It is
unfortunate that as yet no corresponding set has been
published for non-adiabatic temperature gradients, but it
- - should be emphasized that the general unsteadiness and
erratic behaviour of the light winds which are associated
with both large lapse rates and large inversions make the
experimental study of atmospheric diffusion in there
conditions a matter of considerahle difficulty.
b. Width and Height of Clouds
The width of a cloud from a continuous point source is the
distance between points on the skirts of the crosswind
'p concentration curve at which the concentrations is a fixed
fraction, normally one-tenth, of the peak value. Similarly,the height of the cloud is defined as the vertical distance
from the ground to the point at which the concentration has
fallen to one-tenth of the value on the ground.
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19. Downwind concentrations from a line source at 1 m height calcula-
ted from the DRES K theory model and from Sutton's mean field trial data
are shown in Figure 1. The wind speed at 2 m height is 5 m s"' in neu-
tral atmospheric stability. The terminal velocity, q, was set to zero
in equations (1) to simulate a gaseous cloud in the mathematical model.
The field trial results were obtained from the peak mean concentration
at 100 m and the law for decrease of concentration with downwind dis-
tance. Similar results for a point source are shown in Figure 2. Cal-
culated results are also shown for various point source release heights
in Figure 3 from the present K theory model with Gaussian lateral
spread, and in Figure 4 from Gaussian dispersion given by equation (22).
Concentrations 100 m downwind of a line source at 1 m height are shown
as functions of height for various retention efficiencies in Figures 5
and 6, for comparison to Sutton's cloud height data. Similar results
are shown for a point source for use in practical applications in
Figures 7 and 8.
20. The effect of particle size on concentration and ground deposi-
"tion density from a line source is shown in Figures 9, 10 and 11. Con-
centrations shown start at 30 m downwind, but one should note that less
reliability is expected at short distances than at distances greater
than 100 m from the source. The effect of fluctuations have not yet
smoothed out, and concentrations vary rapidly with distance at short
distances. Figures 9, 10 and 11 compare calculated results for 20 pm
diameter particles to particles of less than 1 pm diameter. The ter-
minal velocity of the the 20 pm particle was calculated using equations
for fluid drag on spheres [14]. The velocity which was obtained assu-
ming unit specific gravity was 0.01216 m s-1. The terminal velocity of
particles less than 1 p diameter was assumed to be zero. The downwind
concentrations are shown in Figure 9 for two atmospheric stability
categories, D and F and the guund deposition densities are shown in
Figure 10 for stability D and Figure 11 for stability F.
UNCLASSIFIED
J,/
UNCLASSIFIED /18
21. As mentioned previously, particles small enough so that their
terminal velocity is negligible and which therefore follow the air flow
will still not produce the sawe downwind concentrations as nonreacting
gaseous clouds. The reason is that they are affected by the ground sur-
face in different ways. Particles are assumed to have a retention
efficiency, E, of 1 and nonreacti'e gaseous clouds have a retention ef-ficiency of 0. The effect of various retention efficiencies on downwind
concentration from a point source is shown in Figure 12. Peak downwind
concentrations from a low level point source of particles which follow
the air flow are shown in Figure 13 for four atmospheric stability cate-
gories. Similarily, peak ground contamination densities are shown in
Figure 14.
22.- Downwind concentrations from a low level point source of 5 pm and
20 pm diameter particles are shown for four atmospheric stability cate-
gories in Figures 15 and 16, respectively. Ground deposition densitiesfor these two particle sizes are shown in Figures 17 to 20. The calcu-
lations were performed for particles of unit specific gravity using thepoint source K theory model with Gaussian lateral spread.
UNCLASSIFIED
//
UNCLASSIFIED
E
K THEORYoJ ZERO TERMINAL VELOCITY AND NO RETENTION
MEAN FIELD TRIAL DATA (SUTTON)0(n
"T" 100-
E
10"
z
/ Uj
0
,, , il-3 10-1 ,"a 100 1000 10000
z
' • OX DISTANCE FROM SOURCE (m)
- I-
-Figure 1
j" DOWNWIND CONCENTRATIONS FROM• A LINE SOURCE AT1 m HEIGHT IN NEUTRAL ATMOSPHERIC STABILITY WITH
2 m WIND SPEED OF 5 m s -1
" .- UNCLASSIFIED
S/S,.';!" / :' / :.'./: ' " > .... , ,/ ,./ ;, .,, i"•/ •/ " , , .z
UNCLASSIFIED /20
K THEORY WITH GAUSSIAN LATERAL SPREAD
ZERO TERMINAL VELOCITY AND NO RETENTIONE
10 MEAN FIELD TRIAL DATA (SUTTON)
w
Uj
z 10-1zN
0N
4%
+ .4.o N
-. Z 10-2-
LU-4
S..... ; ": • 0 -3 -
zi'+ •+o '
.- +.-
10'-41'•
100 1000 10000
" zX DISTANCE FROM SOURCE (m)
S,,,•:Figure 2
' DOWNWIND CONCENTRATIONS FROM A POINT SOURCEAT 1 m HEIGHT IN NEUTRAL ATMOSPHERIC STABILITY
SWITH 2m WIND SPEED OF 5ms-1
) UNCLASSIFIED
w N
-' "Nti .
UNCLASSIFIED /21
10 K THEORY WITH GAUSSIAN LArERAL SPREAD
ZERO TERMINAL VELOCITY AND NO RETENTION
E
0,E h=12m
0
S.......,- 10-1 '
Sh=20m
lo
0U..
z0"" 10-2
zUjz0
0 -3
j 10 1 h0 1000m
-J
z
0
10-4
100 1000 1000aX DISTANCE FROM SOURCE (m)
"Figure 3
DOWNWIND CONCENTRATIONS FROM A POINT SOURCE ATVARIOUS HEIGHTS IN NEUTRAL ATMOSPHERIC STABILITY
WITH 2 m WIND SPEED OF 5 m s 1
UNCLASSIFIED
/
UNCLASSIFIED /2210
4-
E0 h.. 2
. ,= h=2mE 1 GAUSSIAN DISTRIBUTION
LI
h=10m0
l-
'oS: ~h'-20m
0Z• ,• -. h=50m
zW -
w- -4z 10
0~
0
COD
100 1000 10000X DISTANCE FROM SOURCE (m)
Figure 4
DOWNWIND CONCENTRATIONS FROM A POINT SOURCE ATVARIOUS HEIGHTS IN NEUTRAL ATMOSPHERIC STABILITY
WITH 2 m WIND SPEED OF 5 m s
UNCLASSIFIED
1 P 1 F,
UNCLASSIFIED /23100.
K THEORY WITH ZERO TERMINAL VELOCITY
/ 10-E E 0.0 E 0.1 E 0.2
LU
0
N
0.1* I I10 20 30 40 0 10 20 30 40 0 10 20 30 40
C PEAK CONCENTRATION AT VARIOUS HEIGHTS FOR A 1 g m 1 s8 SOURCE (mg m- 3)
... Figure 5
CONCENTRATIONS 100 m DOWNWIND OF A LINE SOURCE
/ I AT 1 m HEIGHT WITH VARIOUS RETENTION EFFICIENCIES
IN NEUTRAL ATMOSPHERIC STABILITY
WITH 2 m WIND SPEED OF 5 m s 1
• /..-..
UNCLASSIFILI. /24
K THEORY WITH ZERO TERMINAL VELOCITY
10-EE 0.5 E 1.0
0.
11 20 300 6 20- 1
AT 1- mNEGTWT AIURTNINEFCECE
C PAKCONENRAION NETAT VARIOUSHEIHSFRC SAB1ILITY ORC 1g
WITH 2 m WIND SPEED OF 5 m s
7 UNCLASSIFIED
vy I I II I c/III0
10U NC LASS IFrIED / 25
K THEORY WITH GAUSSIAN LATERAL SPREADAND ZERO TERMINAL VELOCITY
10
z0
E 0.0 E 0.1 E 0.2wj
00
C'PEAKCNETAINA AIU -IHSFRAIgsSUC M 3
Fiur,
PEKCNETAIOS10mDWWIDO ON
NN
UNCLASSIFIED /26100-
"K THEORY W1l H GAUSSIAN LATERAL SP•/,ai)
AND ZERO TERMINAL VELOCITY
10E
z0
E - 0.5 E 1.0
0
o 2 0 1 2
" C PEAK CONCENTRATION AT VARIOUS HEIGHTS FOR A g s- SOURCE (mg M -3)
/• Figure 8
PEAK CONCENTRATIONS 100m DOWNWIND OF A POINT
SOURCE AT I m HEIGHT WITH VARIOUS RETENTION
EFFICIENCIES IN NEUTRAL A'TMOSPHERIC STABILITY
WITH 2 m WIND SPEED OF 5 m s-
S," UNCLASSIFIED
C,,
UNCLASSIFIED /27
1000-K THEORY WITH RETENTION
FACTOR OF 1
PARTICLE SPECIFIC GRAVITY = 1EE ks
F 2 m WIND SPEED0o100. 20m 1 pm STABILITY D 3 m- 1
,A .,STABILITY F 1.5 m s 1
Ez0pm <lpim
S• -.
D0
U.
l -Z1oz 1
10: 100 1000100
X DISTANCE FROM SOURCE (m)
• .. Figure 9
DOWNWIND CONCENTRATIONS OF MONODISPERSE
', PARTICULATE FROM A LINE SOURCE AT 1 m HEIGHT
IN TWO ATMOSPHERIC STABILITY CONDITIONS
UNCLASSIFIED
ME spy,
I-zF
0i
UNCLASSIFIED) /2810
K THEORY WITH RETENTIONFACTO R O F 1
PARTICLE SPECIFIC GRAVITY =1
Eb <l1 m 20 pmE
0(n
7~ 10-1
E
0U.-
LU
w
O10-241010 00 00
X ITNEFOMSUC m
Fiue1
GRUDDPSTONO OOIPRS ATCLT
FRMALNwOREX'1 EGTI TBLTCAEOYDWT0 WN PE F
UNLSSFE
14;Il
UNCLASSIFIED /2910"
" K THEORY WITH RETENTIONFACTOR OF 1
NPARTICLE SPECIFIC GRAVITY 1E
w 1I
w -0
<l~um 20 pm0conI--
Eo 10-1-
9--
0U.
zwI-
10-2-0 -LUJ
0.
3
10-3 i 1 '1 ' 1 1 I ''' a I I pI ipi10 100 1000 -... ....... 10000
X DISTANCE FROM SOURCE (m)Figure 11
GROUND DEPOSITION OF MONOD!SPERSE PARTICULATEFROM A LINE SOURCE AT 1 m HEIGHT IN STABILITY
CATEGORY F WITH 2 m WIND SPEED OF 1.5 m s
UNCLASSIFIED
n ~ I &
~ -%• " ' ,' I I iI I I
UNCLASSIFIED /30
10K THEORY WITH GAUSSIAN LATERAL SPREAD
E AND ZERO TERMINAL VELOCITY
v E
w
"o 10-1
S.• 10
U.
-• 10-3-
-~ 10-1-
Ilk
;10-4
*4 ,
lu
W 102
I C-
10 io-5
SX DISTANCE FROM SOURCE (m)
S--- Figure 12
I., DOWNWIND CONCENTRATIONS FROM A POINT SOURCE AT
i• 1 m HEIGHT WITH VARIOUS RETENTION EFFICIENCIES IN
CNEUTRAL ATMOSPHERIC STABILITY
. • •i•¢,WITH 2 m WIND SPEED OF S.,*n S-1
• ~U NCLASSI1F!IED
Al
UNCLASSIFIED
100 •K THEORY WITH GAUSSIAN LATERAL
SPREAD, ZERO TERMINAL VELOCITY
AND RETENTION EFFICIENCY OF 1
E 2 m WIND SPEED
E STABILITY C 3 m S 1
U 10 STABILITY D 3 m s
STABILITY E 1.5ms 1
STABILITY F 1.5 m s 1
• i \10-1"
o 1
0
ccz °I-
z0
S• 10-2"
LU
10-31
10 100 1000 10000X DISTANCE FROM SOURCE (m)
Figure 13
DOWNWIND CONCENTRATIONS FROM A POINT SOURCE
AT 1 m HEIGHT IN VARIOUS ATMOSPHERICSTABILITY CONDITIONS
UNCLASSIFIED
01,,/./ /
/ ,~
UNCLASSIFIED /32
2 m WIND SPEED
STABILITY C 3 m s 1
STABILITY D 3 m s 1
- STABILITY E 1.5 m s 1
STABILITY F 1.5ms 1'•, • 10-1
E K THEORY WITH GAUSSIAN LATERALSPREAD, ZERO TERMINAL VELOCITY
OAND RETENTION EFFICIENCY OF 1
10-2
1- CDE F
cr.
0
jI i
0
// , ICLL
1' ,
;' ,•10-4'll
10 100. 1000 10000
X DISTANCE FROM SOURCE (m)
/ i Figure 14
GROUND DEPOSITION FROM A POINT SOURCE AT 1 m
HEIGHT IN VARIOUS ATMOSPHERIC STABIUT'Y CONDITIONS
* ,UNCLASSIFIEDL ,M&••g•y,• . .q
UNCLASSIFIED '33
10E
EL K THEORY WITH GAUSSIAN LATERAL SPREAD,C., PARTICLE SPECIFIC GRAVITY = 1
0 12m WIND SPEED
STABILITY C 3 m s 1
4 STABILITY D 5 ms-1
0 10-1 STABILITY E 1.5 m s 1
!C D F STABILITY F 1.5 m s 1
z0
z
E10-2z0
10-
100 1000 10000O X DISTANCE FROM SOURCF (m)
I Figure 16
DOWNWIND CONCENTRATIONS FROM A POINT SOURCE OF
20 mm PARTICLES AT 3 m HEIGHT IN VARIOUS
.. ATMOSPHERIC STABILITY CONDITIONS
UNCLASSIFIED
- i2
z.- •"- , ._.. .. .. .-. . .. .. w
C.
4 UNCLASSIFIED /34
E 10
E K THEORY WITH GAUSSIAN LATERAL SPREAD,
S "PARTICLE SPECIFIC GRAVITY = 1
S 1 2m WIND SPEED
STABILITY C 3 m s 1
STABILITY D 5 mrsSTABILITY E 1.5ms-1
STABILITY F 1.5ms-1o10
Z10-3
z
IL
0
NU 10-4
... 100 1000 10000
X DISTANCE FROM SOURCE (m)
Figure 15
DOWNWIND CONCENTRATIONS FROM A POINT SOUP.CE OF
5/pm PARTICLES AT 3 m HEIGHT IN VARIOUS ATMOSPHERIC
STABILITY CONDITIONS
UNCLASSIF'IED
, I
-.
/0
UNCLASSIFIED /35
10-1
E K THEORY WITH GAUSSIAN LATERALE • SPREAD, AND RETENTION FACTOR OF 1E PARTICLE SPECIFIC GRAVITY =1
0
5 14m 20 ym,/ 1 O-S10-2_
0
zW
10-3
0.
w
10-4
10 100 1000 10000
X DISTANCE FROM SOURCE (m)
Figure 17
GROUND DEPOSITION OF MONODISPERSE PARTICULATEFROM A POINT SOURCE AT 3m HEIGHT IN STABILITY
CATEGORY C WITH 2 m WIND SPEED OF 3 m s 1
UNCLASSIFIED
UNCLASSIFIED /36
K THEORY WITH GAUSSIAN LATERAL10-1 .SPREAD, AND RETENTION FACTOR OF 1
E PARTICLE SPECIFIC GRAVITY =1
E
0
5 pm 20Opm
0
U•
ca,0 1-
10 --
10 100 1000 10000X DISTANCE FROM SOURCE (mi
Figure 18GROUND DEPOSITION OF MONODISPERSE PARTICULATE
FROM A POINT SOURCE AT 3 m HEIGHT IN NEUTRALATMOSPHERIC STABILITY WITH 2 m WIND SPEED OF 5 m
U NCLASSI FIED
_2
1UNCLASSIFIED /37
K THEORY WITH GAUSSIAN LATERAL
~ b- 1 SPREAD, AND RETENTION FACTOR OF 1E PART'.LE SPECIFIC GRAVITY =1
E
0
50 p~m 20 pm
10-
U.
z
wa
10-
10 100 10010000
X DISTANCE FROM SOURCE (in)
Figure 19
GROUND DEPOSITION OF MONODISPERSE PARTICULATEFROM A POINT SOURCE AT 3 m HEIGHT IN STABILITY
CATEGORY E WITH 2 m WIND SPEED OF 1.5 m sUNCLASSIFIED
L)NC'LASSIFIFI 138
E o1
E 101K THEORY WITH GAUSSIAN LATERAL
Sj SPREAD, AND RETENTION FACTOR OF 1
o PARTICLE SPECIFIC GRAVITY =1
0
E.um 20,um
< 10-2-
0U.
U,
3
00- rT-T
10 100 1000 10000X DISTANCE FROM SOURCE (in)
Figure 20
GROUND DEPOSITION OF MONODISPERSE PARTICULATEFROM A POiNT SOURCE AT 3 m HEIGHT IN STABILITY
CATEGORY F WITH 2 m WIND SPEED OF 1.5 m s
UNCLASSI1:IL-I)
UNCLASSIFIED /39
DISCUSSION OF RESULTS
23. The results for the K theory line source model agree favorably
with Sutton's mean field trial data. As shown in Figure 1, the peak
concentration at 100 m downwind is 35 mg m-3 for both. At longer
downwind distances the calculated results are lower than those given by
"mean field trial data. The difference gradually increases until at 1000
m the calculated value is 9C% of that computed from Sutton's criteria
and 70% at 10000 m downwind. The calculated cloud height at 100 m
downwind of a line source is 11 m as compared to 10 m from the mean
field trial data. The calculated height is obtained from Figure 5, with
retention efficiency E = 0, where the concentration has fallen to
one-tenth of the value on the ground.
24. Tne results for the point source model using K the;.ry for
vertical dispersion and Gaussian lateral spread agree favorably with the
mean field trial data, althrugh less so than for the line sourc%. The
calculated peak concentration at 100 m downwind was 1.76 g (1-3 as
compared to 2 g m-3 from Sutton's mean field trial data. This
corresponds to a calculated value which is 88% of the measured vilue.
The difference gradually increases until the calculated value is 75% of
that computed from Sutton's criteria at 1000 m and 50% at 10000 m. The
calculated cloud width 100 m downwind of the point source using equation
(21) with ay from Table II is 34 m, as compared to 35 m from the mean
field trial data. The criteria used for the cloud width was that
specified by Sutton as the distance between points on the crosswind
concentration curve at which the concentration has fallen to one tenth
of the peak value. Using the criteria that the cloud width is 4 •y, as
previously described, the calculated value is 32 m. The cloud height
for a point source was not specified for the mean field trial data, but
oNCLASSIFIED
In
UNCLASSIFIED /40
the calculated value as shown in Figure 7 for retention efficiency, E=O,
is the same as for the line source. This is to be expected since the
same K theory is used for vertical dispersion.
25. Comparison of Figures 3 and 4 indicate that the downwind location
of the maximum ground level concentration for the two methods of
calculation is in good agreement for all release heights. The
difference in the values of the concentration is greatest for a release
height of 20 m whe-e K theory nodel with Gaussian spread gives results
about 75% of that by Gaussian dispersion. The former model tends to
give higher concentrations upwind of the peak and lower concentrations
downwind of the peak. There is no general agreement on the best method
to model elevated sources [8]. A review of various models is described
by Gifford [15].
26. The agreement between theory and experiment is favorable for the
line source. The calculated results in Figures 5 and 6 also show the
. behavior of concentration as a function of height Iz'r various retention
efficiencies. As retention efficiency increases, the height at which
the maximum concentration occurs increases, but the maximum
concentration, itself decreases. This is also true for a point source
as shown in Figures 7 and 8, which uses the same K theory for vertical
dispersion.
- 27. The concentrations at the source height downwind of a low level
line source is not affected appreciably by particle size less than 20 pm
in neutral atmospheric stability. Figure 9 indicates that the
concentrations of 20 pm particles are not less than 90% of the
concentrations for particles less than 1 pm in size over the whole
downwind distance range considered. For atmospheric stability F, which
UNCLASSIFIED
"- - !1- / "
UNCLASSIFIED /41
is the "worst case", the differences are considerably greater. The
reason is that the plume travels close to the ground at all distances,
so that even small differences in terminal velocity affect the number of
particles which come into contact with the ground and thu:. are removed
by retention. Figure 9 indicates that the difference between
concentrations of 20 pm particles and particles less than 1 pm in
diameter, gradually increases with do•,nwind distance. The
concentrations of 20 pm particles are 85% at 100 m, 65% at 1000 m and
50% at 10000 m of the concentration of particles less than 1 pm in
diameter. The ground deposition Oensities of 20 pm particles are not
less than 75% of those of the smallest particles over the whole distance
range in atmospheric stability D, but vary gradually from 50% at 100 m
'o 90% at 10000 m. For the wind speeds considered, which are realistic
in practical applications, the ground deposition densities are nearly
equal at 10000 m for the two atmospheric stability categories.
28. Figure 12 indicates that concentrations of particles which follow
the flow are lower than those of non reacting vapors downwind from a
' -, point source. The difference increases gradually as is shown by
comparing the results for E=O and E=1. The concentration for E=0.2 is
about midway, on the logarithmic scale, between those for the other two
retention efficiencies. Figures 13 and 14 give concentrations and
ground deposition densities downwind of a point source using zero
terminal velocity. They can be used as a good approximation for
"particles smaller than 5 pm in diameter. The concentrations for
particles between 5 and 20 pm in Oiameter can be estimated by comparing
Figures 15 and 16. A feel for the difference in ground deposition
densities downwind of a point source for various small particle sizes is
given in Figures 17 to 20, where the calculated results for 5 and 20 pm
particles are shown for four atmospheric stability categories.
UNCLASSIFIED
//..
UNCLASSIFIED /42
S29. Some comparisons of calculated ground contamination densities for
the line source model to field data for particles 30 pm and larger
[1,2,16,17] indicate that this model can be used with reasonable confi-
dence. The predicted location of the downwind peak agrees with experi-
ment but the calculated peak ground deposit densities are lower. The
point source model which uses the same vertical dispersion function and
lower boundary condition is supported by these results to a certain
extent, although further experiments would be useful.
CONCLUSIONS
30. A mathematical model has been developed from ',h'ch concentrations
and ground contamination densities from a low level point source of
particles less than 20 pm in diameter can be calculated. Confidence in
the model to predict concentrations accurately is supported by
experimental data for gaseous clouds, for which the model can be applied
using the limiting case of zero terminal velocity. Calculations for
particles within the specified size rarge show that the effect of
particle size is small enough so that predictions of concentrations can
be made with sufficient accuracy for many practical applications.
Ground contamination densities can also be calculated for the same range
of particle sizes. Reasonable confidence in their accuracy is supported
by comparisons with experiments reported previuusly [1,2,16,17].
UNCLASSIFIED
-i 2
/ _
UNCLASSIFIED /43
REFERENCES
1. Monaghan, J. and Mellsen, S.G., "Calculations of the Deposition
of Droplets from Aerial Spray using an Atmospheric Diffusion
"Model (U)", Suffield Report No. 393, 1985, UNCLASSIFIED.
2. Mellsen, S.B. and Monaghan, J., "Calculations of the Deposition
of Droplets from an Aerial Spray Using and Atmospheric Diffusion
Model", American Society of Mechanical Engineers, Paper No.
86-WA/HT-35, 1986.
3. Calder, K.L., Atmospheric Diffusion of Particulate Material
Considered as a Boundary Value Problem", J. Meteorology, Vol. 18,
1961, pp 413-416.
4. Monaghan, J. McPherson, W.R., "A Mathematical Model for
Predicitng Vapor Dosages on and Downwind of Contaminated Areas of
Grassland", Suffield Technical Paper No. 386, 1971,
UNCLASSIFIED.
5. Chamberlain, A.C., '-rraisport of Gases to and from Grass-like
Surfaces", Proc. Roy. Sac., Series A., Vol. 290, 1966, pp.
235-265.
6. Thom, A.S., "Momentum, Mass and Heat Exchange of Vegetation",
Quart. J.R. Met. Soc., Vol. 98, 1972, pp. 124-134.
7. Best, A.C., "Empirical Formulae for the Terminal Velocity of
Water Drops Falling Through the Atmosphere", Quart. J.R. Met.
Soc., Vol. 76, 1950, pp. 302-311.
UNCLASSIFIED
-i'
/
UNCLASSIFIED /44
8. Panofssky, Hans. A. and Dutton, John A., "Atmospheric Turbulence,Models and Methods for Engineering Applications", John Wiley &
Sons, 1984.
9. Seinfield, John H., "Atmospheric Chemistry and Physics of Air
Pollution", p. 491, John Wiley & Sons, 1986.
10. Hanna, Steven R., Briggs, Gary A. and Hosker, Rayford P.,"Handbook on Atmospheric Diffusion", Technical Information
Centre, U.S. Department of Energy DOE/TIC 11223, 1982.
11. American Society of Mechanical Engineers, "Recommended Guide forthe Prediction of the Dispersion of Airborne Effluents", 3rd
Edition, 1979.
12. Seinfield, John H., "Atmospheric Chemistry and Physics of AirPollution", pp. 639, 640, John Wiley & Sons, 1986.
13. Sutton, O.G., "Atmospheric Turbulence", Second Edition, Methuen &Co. Ltd., 1955.
14. Mellsen, Stanley B., "The Distance Travelled from Rest toTerminal Velocity by a Sphere in Air (U)", Suffield TechnicalNote No. 425, 1978. UNCLASSIFIED.
* 15. Gifford, G.A., "Atmospheric Dispersion Models for Environmental
Applications, Lectures on Air Pollution and Environmental ImpactAnalysis", American Meteorological Society, Boston, pp. 35-38,
1975.
UNCLASSIFIED
SII' ...
UNCLASSIFIED /45
16. Johnson, 0., McCallum, J.A. and Larson, B.R., "Diffusion and
Deposition of 30 Micron Particles from a Low Level Source (U)",
Suffield Technical Paper No. 367, 1974, UNCLASSIFIED.
17. Johnson, 0., "Diffusion and Ground Deposition of 100 Micron
Particles from a Point at a Height of 92 Metres (U)", Suffield
Report No. 284, 1980, UNCLASSIFIED.
UNCLASSIFIED
/
UNCLASSIFIED
, 1// I\
/
APPENDIX A
COMPUTER PROGRAM
"DIFFP"
WITH SAMPLE RESULTS
UNCLASSIFIED
UNCLASSIFIED
A-1
Al. The computer program for calculating concentrations and groundcontamination densities downwind of a point source using K theory forvertical dispersion and Gaussian lateral dispersion was developed fromthe line source program. The program called DIFFP is therefore verysimilar to the program DIFF, from which it was developed. The datainput required to execute the program is shown in Table Al, withrequired atmospheric constants in Table A2. Sample output and alisting of the program immediately follow the table. The proqram forthe line source, which contains several subroutines, is difficult tourderstand for the uninitiated because it is not thoroughly annotated.The modification to account for lateral spread from a point source washandled as simply and straightforwardly as possible with minimalmodifications.
A2. The modifications required to calculate concentrations andground deposition densities downwind of a point source were all made inthe subroutine PPOUT, the last subroutine in the program. A shortalgorithm was inserted to calculate the standard deviation: ay, and theassociated Gaussian lateral dispersion function at any distancedownwind. The concentrations and ground deposition densities were thenobtained by multiplying the concentrations and ground depositiondensities for the line source calnulated earlier in the program by thelateral dispersion function. The program was set up to calculateresults for any one lateral crosswind position, y, at each downwinddistance. The peak values are given by setting y = 0. Off axis valueswhich are symmetric about the axis are less according to the Gaussianlateral distribution.
A3. The algorithm for calculating the Gaussian lateral dispersionfunction is shown in lines 506 to 526 in the program listing. Themodified dosages are calculated in lines 532 to 534 and the modifiedground contamination densities are calculated in lines 541 to 543.Line 545 was inserted to include values of the lateral dispersionfunctions in the u~tput results. Also line 499 was modified to includethe new functions in DIMENSION statements and a few FORMAT statementswere added.
UNCLASSIFIED
UNCLASSIFIED
A-2
TABLE Al
DATA INPUT FOR DIFFUSION PROGRAM, DIFFP
RECORD VARIABLES FORMAT NOTES
1 PA,M,S,A,DL, 8F10.0 PA=O.01 U(2). U(2) is 2 mQ,E, SOURC windspeed (m s- 1 ).
S=2.0 for open ground; 5.0for forest.Q is terminal velocity ofdroplets or oarticles(m s'-).E is retention factor ofsubstrate; the value is 1for complete retentionSOURC is line sourcestrength, mass per unitlength (g m'-).M=p,A, DL=A1 are given inTable A2).
2 (1) XO,DYH, HH, U2M, 8F10.0 XO is the maximum downwinddistance considered.DY = 0.01 (2)H is the height of theatmospheric lid (see TableI). HH is the effectiverelease height (m). U2M is 2m windspeed (m s-1) (seeTable A2.
3 THETA,NZ(IC,ICI) F10.0,313 THETA = 0.5NZ is the size of thevertical array (usually 48but % 100). IC and ICI wereused to "debug" the programand to provide auxiliaryinformation: no entryrequired. Their use isdescribed in foot note (3)below.
UNCLASSIFIED
UNCLASSIFIED
A-3
TABLE Al
DATA INPUT FOR DIFFUSION PROGRAM, DIFF
continued
RECORD VARIABLES FORMAT NOTES
5 NUMOX,NOVES, 412 NUMOX is the number of down(ICZXIK) wind distances for output
(maximum 20)NOVES is the number ofheight intervals in printout. This is furtherdescribed in the notes withrecord 7. ICZX, IK are usedonly to provide auxiliaryinformation. No entry isrequired. Their use isdescribed in foot note (3)below.
6 XOUT(I), 8F10.0 Downwind distance from sprayI=1,NUMJX line (m). Maximum number of
positions is twenty.
7a,b,c .... STATZ(I), 8F10.0 STATZ and ENDZ are bottomENDZ(I), and top of chosen intervalZOUIN(I) of height, NOVES. ZOUIN is
height increment. Thus 0.0,10.0, 2.0 will give valuesof dosage at Z = 0.0, 2.0,4.0 .... 10.0 m. Thispermits height increments tobe varied from one intervalto the next. One recird isneeded for each interval.Total number is NOVESrecords (not to exceed 25).
8 Not used unless ICZX?1( 3 )
UNCLASSIFIED
UNCLASSIFIED
A-4
TABLE A-i
DATA INPUT FOR DIFFUSION PROGRAM., DIFF
continued
RECORD VARIABLES FORMAT NOTES
9 YC IPSC F1O.O, 13 YC is crosswind coordi-nate (m). IPSC is 1,2,3,4for stability categoriesCDEF.
9 YC IPSC F1O.O, 13 YC is crosswind coordi-nate (m). IPSC is 1,2,3,4for stability categoriesCDEF.
UNCLASSIFIED
S.-UNCLASSIFIED
A-5
FOOTNOTES
(1) X0 must exceed XOUT(NUMOX) card 6.(27) The calculated output position may vary slightly from the chosen
"XOUT(I) in card 6, because DY is a logarithmic increment of downwinddistance.
(3) IC = 0, ICI = 0, ICZX = 0, IK = 0No auxiliary information in output.IC = 1, ICI = 0, ICZX = 0, IK = 0Run parameters outputDR NZ DY NY THETAH HR RHHH HHR RHH IHHMatrix constants outputALPHA BETA GAM:A LAMBA Al D1IC = 2, IC1 = 0, ICZX = 0, IK = 0As for IC = 1 plus:Output controlsVertical intervalsSTART END INCREMENT for each i;ttervalVertical arrayZ RZ ID THETA (portion of full increment for Bessel's interpolation"formula)Horizontal output positionsX X-OUT IY
IC = 3, IC1 ; 0, ICZX = 0, IK = 0As for IC = 2 with the other three variables equal to zero.
IC = 4, IC1 a 0, ICZX a 0, IK > 0As for IC = 2 and 3 in the two preceding modes, except that no mainresults are printed out. Moreover, no downwind concentrations andground contaminations are calculated in the program.
IC = 3, IC1 2 0, ICZX = 0, IK = 0As for IC = 3 ICI = 0 except that vertical profile and matrix inter-rogation is printed out for iteration intervals separated by the valueof ICI. For example, if ICI = 10, iterations 10, 20, 30 ..... are prin-ted out until the specified maximum value of downwind distance has beenreached. This mode results in a large array of numbers printed out ateach iteration determined by ICI and could result in a great deal ofoutput paper from the printer.
UNCLASSIFIED
UNCLASSIFIED
A-6
IC = 2, IC1 = 0, ICZX 0 0, IK Ž 0
ICZX = 1: Peak concentrations and vertical locations of peaks in thetransformed plane for downwind positions IK.DY starting at Y = DY areprinted out. For example, if DY = 0.01, IK = 3, values are printed outat DY 0.01, 0.04, 0.07 .....
ICZX = 2: As for ICZX = 1 except that concentrations are also given atone user specified height, Z, at the same downwind positions. An extradata record is needed if ICZX a 1, which specifies heights Z, asfollows. XZ(I), FORMAT 2F10.0. Only one value of ZX(I) is required ifICZX = 2.
ICZX = 3: As for ICZX 2 except that concentrations are printed out attwo user specified heights, Z. Peak concentrations are not given.
U'SS
UNCLASSIFIED
UNCLASSIFIED
A-7
TABLE A2
VALUES OF CONSTANTS
CONSTANTS
STABILITY A ___ u(2) H
CATEGORY m m s"1 m
C 0.08 0.025 0.2 2-4 1000
D 0.04 0.025 0.23 k3 500
E 0.03 0.025 0.3 1.5-3 200
F 0.02 0.025 0.5 1.5-2 100
At is given for grassland
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B - 4 LINCLASSIFIFDThis Sheer Security Classification
DOCUMENT CONTROL DATA - R & DISecu,.ev clm, sacatboe oO •tie. body of oweet ued ndaing mneoaWtln mm be e dtee wtwn the everdl simcment is cseampfdo
I ORIGINATING ACTIVITY 2L DOCUMENT SECURITY CLASWFICATiONHNM!AýMFT QTr
Defence Research Establishment Suffield 2 GROUP
J DOCUMENT TITLE
Dispersion and Deposition of small particles from a low level point source
4. DECRIPTIVE NOTES IT ss of rowt end mckiszve detl...Suff J eld _[luort
' AUTHORIS) iLast neen. Iwo# rme. middle IntIe)
Mellsen, Stanley B.
D. DOCUMENT OATE February 1988 7L. TOTAL NO. OF PAGES 7b, NO. OP REFS
ft PROJECT OR GRANT NO. S. ORIGINATORS DOCUMENT NUMSIRSIN
351SA500
Ob CONTRACT NO. Wlb OTHER OOCUM!NT NO.jS) (Any otter numbre tha meW be
10. OISTRIGUTION STATEMENT
UNLIMITED
it. SUPPLEMEINTARY NOTIS 12, SPONSORING ACTIVITY
13. AMURACT
A mathematical model for estimating concentrations and grounddeposit densities from a low level point source of particulates up to20 urn in diameter has been developed. The model applies K theory toaccount for vertical dispersion and Gaussian spread to account for la-teral dispersion. Results for the limiting case of zero terminal velo-city with negligible retention at the ground are compared directly tofield experimental data for a source near ground level and to establishGaussian dispersion from an elevated source. The vertical dispersionfunction and lower boundary condition for an existing line source modelwere applied in the presbnt point source model. Previous comparison toground deposit densities measured in various field experiments indicatethat estimates from the line source model are reasonable, although fur-ther experiments would be useful.
Is-Off'.4,.l
UNCLASSIFIED
______________This Sheet Security Classificationj
KEY 111000
Diffusion ModelsAerosols - DispersionAerosols - SettlingAtmospheric DispersionLiquid Drops
01STRUCTIONS
I OIRIGINA IING ACTIVITY Eniet, the name wand a eeasof the 91& OTHER DOCUME NT NUMIERMS: It the document hal beaa,.Who#,almot. o.su..n.. liha iocutngnt. aIIIaI any other document foumraokw (eitherw by the ori~In~~
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ipu) iidestined to% Append..a MWao the ORB Security Reguationse. (1) *Oallified requeeters emay obtains copies of thisdocument from thewr delocs documenstation canfr.ý
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