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

"4

-I

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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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S. AUfl4OI4I1SI Emote thie nemelsil of authsorts) as 04fowtn on or 13. ABSTRACT: Enter an absatract goivrot a beiet and factualmn the douitumets Eitee fotest noarre. tlot none. mieddlet initial. vamr of the document, even though. it may also IppeaIf inlititery. shWe 11111. The wn am of the principal author ie an elsewhere in the body of the document Itself. It '0 highlyasinsflut minimum rqiiien.desirable that the abstract of classified documents be uncleasse-

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to. TOTAL NUMBER OF PAGES The total pop count ahotldIfolinoi ncormal pegiisetsont aresoadures. i.e.. enter the niamba The length of the dwsract should be l1mitead to 20sitapaiM stagesn ieesoleinting .isormation. standwirt typewritten hoese; 7% 0nce s eng.

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he followeed by an Indication of technical content.Rb CONTI4ACT NUMBER It iqulpioprisle. enter the applicabe

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