Wind-tunnel studies of roughness effects in gas dispersion

Pergamon

Amtmphrm

Enrwo,,mr,tr Vol 28. No I I, pp IM-1870.

1994.

1X2-2310!94 S700+0.00

WIND-TUNNEL

STUDIES

OF ROUGHNESS DISPERSION

EFFECTS IN GAS

P. T. ROBERTS* and R. E. J. FRYER-TAYLOR* Shell Research Limited. Thornton Research Centre. P.O. Box I, Chester CHI 3SH. U.K

and D. J.

HALL

*Warren Spring Laboratory, Stevenage SGI ZBX, U.K programme of work has been carried out using wind-tunnel modelling to investigate the effect of surface roughness on dense-gas dispersion from ground-level sources where the roughness height is large compared with the cloud depth. Neutrally buoyant gas releases were included as control experiments. The results are compared with results of a I : 100 scale simulation of dispersion in high roughness conducted by CPP Inc. for the American Petroleum Institute (API). For surface roughness lengths, z,,, smaller than about 0.5 cm (0.5 m full scale), dispersion is shown to be well described by a Gaussian plume model. Plume width and depth increase with I~ and are simple functions of distance from the source. For larger roughness, dispersion depends on the arrangement of the roughness elements. plume width, oY, can be restricted by channelling and plume depth, u,. becomes sensitive to run conditions.

Abstract-A

Key word index:

Wind-tunnel simulation. obstructed dispersion

1. INTRODUCTION

The dispersion of flammable and toxic materials at ground level on process sites is enhanced by the turbulence generated by flow around obstacles and pipework. It is reasonable that account should be taken of this when assessing hazards, but there is no validated method of predicting dispersion around obstacles whose dimensions are large compared with the cloud depth. A pragmatic, and commonly used, approach is to assume a large value for the surface roughness length, zo, perhaps up to 1 m, as input to a dense-gas dispersion model. This unsupported practice is abetted by available recommendations (Hanna and Drivas, 1987) for z,, values and produces qualitatively “expected” results-but the large-scale experiments used for validation (Hanna et ul., 1991) were carried out on very aerodynamically flat sites (China Lake, Frenchmann Flat, Maplin Sands) and provide no test of the possible effect of z. on dispersion. Given the current procedures and models, two important questions emerge. First, “is z. an appropriate parameter to use for on-site dispersion where obstacles are large compared with cloud height?’ Secondly, “what z. value should be assigned to a process site?” To answer these questions, we must make recourse to measurement and observation. A first step is to use physical fluid modelling to simulate boundary layers of varying zO, observe the resultant disper-

sion behaviour and compare this with model predictions. If this process is successful, then the question of how to parameterise real sites by roughness length can be investigated. We describe a series of dispersion experiments carried out in the Warren Spring Laboratory No. 1 wind tunnel, which is used for atmospheric dispersion modelling. Material was released from a ground-level area source into boundary layers that ranged from smooth wall to a roughness length of 9 mm (0.9m full-scale). The results are compared with some similar experiments conducted by Petersen and Ratcliff (1988) for the API. The range of conditions tested is set out in Table 1. We are aware of one other study that has addressed the effect of surface roughness on dispersion, a 1989/90 round-robin comparison conducted as part of the CEC Major Technical Hazards Research Program, project BA and involving Warren Spring Laboratory. U.K., TNO, the Netherlands and the University of Hamburg, Germany. Both continuous and instantaneous (Thorney Island style) dense gas releases were compared. In this paper we address only neutrally buoyant dispersion results. 2. EXPERIMENTAL

CONDITIONS

The No. I wind tunnel at Warren Spring Laboratory has a working section I.5 m high, 4.3 m wide and 20 m long. The

1861

1862

P. T. ROBERTS et al. Table

1. Summary

of continuous

Roughness length (mm) Smooth Rough Rough Rough Rough Rough Rough

wall wall wall wall wall wall wall

Release gas density (relative to air) 1, 1.4,5.74 I, 1.4,4.0 1, 1.4,5.74 1.1.4.5.74 I, 1.4,4.0 I, 1.4,5.74 1, 1.4,5.74

0.15 0.5 3.0 5.25 6.0 9.0

forward part of the working section was used to generate a simulated atmospheric boundary layer about 1 m thick over the test section. The gas source was a uniformly emitting disc of 0.10 m diameter fitted flush with the tunnel floor. Air was used as a source gas with a small concentration (1.25 or 2.5% by volume) of methane tracer. Five different boundary layers, A. B. C. D and E, were generated by varying the size and distribution of roughness elements in the wind tunnel; details of these are given in Table 2. Condition E was a smooth wall boundary layer. Vertical velocity profiles were obtained using a pulsed-wire anemometer mounted on an automatic traverse. Velocity profiles were measured both upwind and downwind of the test section, and for at least two settings of the tunnel wind speed. From these measurements the aerodynamic roughness length of the boundary layer was determined and the tunnel settings required to establish the required release conditions were calculated. Several run conditions, coded l-6, were used; details of these are given in Table 3. Each run condition was associated with a particular friction velocity, u,*. In keeping u, constant across the roughness distributtons. the present work differs from that of Petersen and Ratcliff (1988) who maintained a constant tunnel speed. Details of their experiments, identified as R3 and R50, are also shown in Table 3.

Table

2. Roughness

Code

Geometry

A B D C E

Cylinder Rect. prism Rect. prism Rect. prism Smooth board

element

shape,

size and spacing

Height (mm)

Width (mm)

Depth (mm)

Pitch (mm)

10 20 35 35

10 10 10 35

10 10 35 10

50 50 180 180

Table Roughness

3. Matrix

code 1

A B C D E Friction (mm s-‘) R3 R50

releases

2

Study

This work Petersen and Ratcliff This work This work Petersen and Ratcliff This work This work

of experimental Run code 3 4

conditions

5

6

1

*

l

l

l

*

*

*

l

l

*

*

*

-

*

*

-

-

-

-

l

l

-

-

-

90

65

42

65

42

30

Roughness length (mm) 0.5 3.0 9.0 6.0

velocity velocity velocity

(1988)

Initial experiments, made with boundary layers A and B, used a full set of run conditions to investigate whether any systematic effect on dispersion was produced by changes in the tunnel wind speed for a fixed roughness distribution or by changes in the gas release rate for fixed wind conditions. No strong effects were found and, subsequently, only run conditions 2 and 3 were used in experiments with boundary layers C, D and E. The roughness elements for boundary layers A and B comprised regular extrusions from otherwise smooth-surfaced plastic tiles and for boundary layers C and D comprised wooden blocks glued to plywood sheet. To move from the C to D roughness configuration, the plywood sheets were rotated through 90”. In all the roughness, alternate rows were staggered to produce a diamond pattern. The layout of the roughness elements is shown schematically in Fig. I. To generate the smooth-wall boundary layer, E, it was necessary to introduce some roughness into the wind tunnel to accelerate the boundary layer development. Single strips of A roughness, 0.25 m deep, were laid at intervals across the tunnel upwind of the source. The closest strip was 4 m from the source. A full description of the HTAG measurement methods is given by Petersen and Ratcliff (1988). The experiments were made in an open-circuit wind tunnel and the boundary layers generated using arrays of cubic roughness elements. For the R3 condition, the cube side length was I3 mm and for the R50 condition it was 50 mm. Release conditions for the experiments are summarised in Table 4. The wind-tunnel speed was referenced to a fixed height; in the WSL wind tunnel, this was 300 mm and in the HTAG experiments it was 100 mm; here we also show calculated 300 mm values for comparative purposes. The range of operating conditions for the two studies are comparable except that the HTAG study used larger gas flow rates and a smaller diameter source.We used small release rates after Hall and Waters (1989) found that (dense) plume dispersion was very sensitive to source disturbances that arise either directly from source momentum or indirectly through vortex

*

Friction Friction

(1988)

37 mm s-’ 82 mm SK’

0.15 5.25

Roughness effects in gas dispersion shedding. Hall and Waters (1989) recommended that these source disturbances could he minimised if the momentum ratio satisfied:

this criterion in wind-tunnel simulations and release sufficient material to provide measurable concentrations. Our largest value of M was 0.43 for condition 6. In contrast, for the neutral R50 HTAG experiments, 0.7
M=U, pso.5<0.2 u,

1863

[1

lS
Pa

where U, is the release gas exit velocity. It is difficult to meet

3. BOUNDARY

LAYER

PROPERTIES

The velocity profile in the rough-wall boundary layer (Monin and Yaglom, 1987) above the roughness elements is described by two parameters; the aerodynamic roughness length z. and the friction velocity u,.

Wind direction

k=0.41.

0 0

0 0

0

0 0

0

0 0

0

The value of z. for each roughness distribution was found by plotting U against In(z). Measurements were made for at least two tunnel operating speeds and at locations at both start and end of the test section. A common value of z. was found from the extrapolation U = 0 at z=zo. With z. fixed, u,, was found by minimising the (mean-square) error between equation (1) and the individual data sets. The tunnel operating speeds needed to achieve the desired values of u* for the gas release experiments were then calculated. The velocity profile (1) is only valid well above the roughness elements. In these experiments the departure of the velocity profile from equation (1) was apparent below about 10 z. and only data from greater heights was used in determining the values of z. and u*. The applicability of the logarithmic law can be extended somewhat for dense arrays of roughness elements by introducing a displacement thickness but can never apply below the roughness elements themselves. Because the roughness elements are large, equation (1) cannot be used to describe the change in wind velocity with height over the whole vertical extent of the dispersing gas cloud. We therefore choose to parameterise the velocity profile over the cloud extent by a simple power-law

0 0

0

0

_______---- c

0

II 0

0

II II

0

II 0

Fig. 1. Plan view of the roughness distributions used to generate boundary layers A, B, C and D. Roughness element dimensions are given in Table 2.

(4

Table 4. Summary of release conditions (neutral Run code

U30 (m s-7 A

B

C

D

E

1

1.40

1.01

-

-

-

2 3 4 5 6

1.01 0.66

0.73 0.47

0.52 0.34

0.60 0.38

1.65 1.00

1.01

0.73

-

-

-

0.66 0.47

0.47 0.34

-

-

-

HTAG R3 R50

28 138

144 31 141 147

(1)

fJ 30

u LO

0.66 0.66 0.66 0.77 0.77 0.77

0.56 0.56 0.56 0.56 0.56 0.56

u*

(mm s-l) 90 65 42 65 42 30

37 37 37 82 82 82

density

experiments) Release rate (m’s.10-6)

fJ, (mm s-l)

42 75 94 48 61

12.0

101

12.9

111

55.0 108.5 163.0 55.0 108.5

220 330

111 220 330

5.3 9.5 6.1 7.8

163.0

1864

P. T. ROBERTS er al.

where Urel is the wind speed at height z,,r. The powerlaw index a in equation (2) can be most simply determined by taking the logarithm of equation (2) and fitting the transformed equation In(U)=aln(z)+c

(3)

to the data, determining a by least-squares minimisation. In these experiments we have taken the reference height to be 300mm. We note that the power law index derived from the fitting procedures does depend upon the range of heights over which the power law is fitted. By giving emphasis to measurements below 300 mm our power-law index is likely to exceed values derived using the mixing layer depth as reference height. The smooth-wall boundary-layer velocity profile (Monin and Yaglom, 1987), is described by equation (4). The characteristic length scale, I~ = r/u,, decreases as tunnel speed, hence u*, increases. v=!ln u, k

E +5.5 0 :f

z$>--t.

(4)

Equation (4) was fitted to the measured velocity profiles by estimating a value for zr and calculating a value for u* by least-squares regression. A new estimate of cr was then calculated and the procedure repeated until a constant value of u, was determined. Power-law fits to the data were made in the same way as for the rough-wall boundary layers. Values of the power-law coefficient, a, are given in Table 5, as a function of friction velocity. We note that the tunnel speed settings used for the dispersion experiments were calculated using these velocity results and so there is not a direct correspondence between Tables 5 and 3. The power and logarithmic profile fits to the data are shown in Fig. 2. This shows that the power law is a good description of the very lowest part of the boundary layer. As might be expected for flow over the very largest roughness elements the velocity profiles were less repeatable and fewer measurements were made, than for the smaller roughness. Consequently, the value of a is less certain. For comparison purposes, z varies from about 0.1 over exceptionally smooth surfaces to about 0.35 in very rough terrain such as urban areas when the power law is fitted over the mixing layer height (Snyder, 1981). We also calculated an effective co for the smooth wall experiments, E, for comparison with Table I; it was about IO-times smaller than zr and decreased from 0.06 mm to 0.02 mm as u* increased from 22 to 67 mms-‘.

4. CONCENTRATION

MEASUREMENTS

Concentration measurements used a tracer gas sampled through small-bore probes connected to two flame ionisation (FID) via a scanning valve system. Up to

methane aspirated detectors 36 probes

Fig. 2. Comparison between logarithmic and powerlaw representations of the wind profile for the different roughness conditions.

Roughness Table

effects

5. Values of the power law index a derived ments in boundary layers of different Friction

Roughness code A B C D E

20

0.12

OF LATERAL

90

0.18 0.32

0.20 0.30 0.33 *0.05 0.30 f 0.05 0.13

0.21 0.30

0.22 0.30

0.12

DISPERSION

-$ Y> ( from the plume centreline.

(5) The

measure-

(u,,), mm s-l values) 65

Full-scale and model experiments show that the concentration profile across a neutrally buoyant plume is Gaussian in the form

where y is measured

from velocity roughness

45

COEFFICIENTS

C(x,y,z)=C(x,O,z)exp

velocity (nominal

1865

35

were used in two gangs of 18. Sampling was continuous; each line was connected to a FID for a minimum of 2 min. more usually 3, and the FID output sampled at a rate of 10 Hz. Experiments with boundary layers A and B were conducted first. The measured concentrations were averaged on-line and summary statistics collected. In later experiments, the full time-series were recorded and post-processed to give the concentration statistics. All concentrations were normlised with respect to the initial source tracer concentration to give a fractional dilution for the plume. At least three sets of measurements were made for each combination of roughness distribution and wind speed. Firstly, samples were taken along the expected plume centreline and across two plume cross-sections to determine the approximate shape of the plume. Detailed cross-wind measurements were then made at four or more downwind stations, typically including 0.21, 0.61, 1.5 and 4 m. All measurements were taken with the sampling inlet fixed to the floor. The order in which each measurement set was obtained was determined by the effort required to set out the measurement arrays. Thus, for a given roughness distribution, an array was set out and measurements for a range of wind speeds carried out both for the neutrally buoyant releases and for those dense gas releases that used methane as a tracer. The array was then changed. Results presented here for each combination of roughness and wind speed are therefore the composite of at least three time-separated experiments. Several common sampling positions were included, results from which showed the repeatability of the measurements to be good.

5. DERIVATION

in gas dispersion

105

0.44*0.05 0.35 f 0.05 0.16

parameter a,(x) is a measure of plume-width and many experiments have been carried out to establish appropriate values for cry,as a function of distance, for use in dispersion calculations. Alternatively, oY can be viewed as the standard deviation of the concentration distribution defined by

dy I w(y) dy s(Y-r1)’4~) CT;= ; v=p

J

4~)

dy

Jc(y)dy

(6)

and as such is defined for non-Gaussian distributions associated with dense gas releases. For this reason, we have chosen to evaluate try using definition (6) rather than attempt to fit the Gaussian distribution (5) to the experimental data. Of course, for a Gaussian profile, the two definitions of uY are equivalent. 6. RESULTS

6.1. Effect o/roughness length on uy(x) We found no effect of wind speed (friction velocity) or release rate on a, in experiments with boundary layers A and B. We henceforth report average values of cry(x) for each boundary layer. Figure 3 shows that, beyond about 1 m downwind, a,(x) exhibits a power-law dependence on downwind distance for all boundary layers. The value of oY in this region increased with increasing roughness, similar to those of A. We interpret this to indicate that the arrangement of roughness elements for condition D encouraged flow channelling in the streamwise direction and thus reduced lateral spread. At distances closer than 1 m to the source, Fig. 3 shows that, for the smooth floor results in particular, uY approaches a constant value of about 30 mm at the source. If we assume a uniform concentration across the centre of the source, diameter D, then uv = D/245 = 28.8 mm at x=0. An effective point origin for the plume can be estimated if a, is expressed as cT,=o(x+Xe)“=Qyo(l

+x/&J)“.

(7)

A suitable value for the origin x0 for each boundary layer can be found by trial and error.

P. T. ROBERTS et al.

1866 I

Roughness code

0.01

I 0.1

0.05

I

I

0.2

0.5

I 1.0

Diitance Fig.

Code 50 30

0 A 0 B AC

20

AD * l

1

I

5.0

10.0

from source. m

3. Values of oY for the different boundary layers.

X, 36 14 5 17

E

vR3

ho % 10

I

2.0

R50

2

38 7 2.5

vr

v

.

a

.

v

5

10

20

50

100

.

200

l

500

1+xlx, Fig. 4. Values of u, relative lo a virtual source at -X0

The results of this exercise are shown in Fig. 4, where we have also included small area source data from Petersen and Ratcliff (1988), for which bvo = 14.4 mm. Plotting uY/~Yo against (1 +x/x0) on a logarithmic scale shows that all of the data collapses on to essentially two straight lines. The low roughness boundary layers, our A condition and Petersen’s R3 condition, show a more rapid increase in og with

distance than the high roughness boundary layers, C, D and R50. Our B condition lies just outside of the scatter on the high roughness line and might form an intermediate condition. Curiously, the smooth floor results also collapse on to the high roughness line. Figure 4 also lists the virtual origin positions; these do not form a consistent set when ordered by roughness length.

Roughness

6.2.

E&-t

of roughness

length

effects

on concentrations

It is convenient to interpret the concentration measurements within the framework of the Gaussian plume model, although we note that there is evidence (Van Ulden, 1978: Robins, 1978) that the vertical concentration profile departs slightly from the Gaussian form for ground-level releases. We assume that the plume has a concentration profile

in gas

dispersion

an eight-fold difference in concentration, consistent with the ratio of flow rate to wind speed. It is therefore interesting to see whether scaling equation (10) removes the differences between the runs. In fact, because we have seen that aJx) was independent of run condition, successful scaling of equation (10) also implies that a:(x) is also not very dependent on run condition and may be estimated from the measured value of a,(x) and of co(x). Figure 6 shows the (dimensioned) scaled concentration :

cow c*(x)=&&-(y 2”,2Urcf ( > zXr Q

where co(x) is the concentration on the plume centreline and oY and ez are functions of downwind distance, X. We also assume that the plume advects with a depth-averaged velocity given by

where we have used the power-law velocity profile. Combining equations (8) and (9) we can evaluate the centreline concentration for a source strength Q

When a=O, the wind is constant with height and equation (10) reduces to the standard Gaussian plume equation for a ground-based source. Figure 5 shows centreline concentration measurements for the A roughness distribution and for run conditions l-6. Between conditions 1 and 6, there is

1867

1 c*(x)=

0.2

0.5

(1+.) ay 6,

does collapse to a single line to a very good approximation. Similar results were found for the B roughness distribution and for the smooth floor. For the C distribution, the scaling did not work so well and there was a small but discernible effect of wind speed. These data are compared in Fig. 7. E concentrations are 24-times greater than C concentrations. Run condition D did not scale, the derived concentrations being quite different for the two run conditions tested. Results are shown in Fig. 8. The failure to scale is not accounted for by the +0.05 uncertainty in the power index, a. Similarly, there is no evidence of large run-condition effects in the Q, data. We infer that Q, is sensitive to wind speed for this configuration.

10

0.1

1.0

0

1

+

2

0

3

x

4

A *

5 6

2.0

5.0

Distance from source.m Fig.

AE 28:11-E

5. Centreline

(11)

concentration for run conditions l-6, boundary layer A, showing normalization. Run conditions are those of Table 4.

spread

ofvalues

before

1868

P. T. ROBERTSet al.

0

1

+ x

2 3 4

A *

5 6

q

10 8 t 8 1ca 1

0.1 Distant%from source, m Fig. 6. Centreline concentrations of Fig. 5 scaled for release rate and wind speed, boundary layer A.

Distance from source. m Fig. 7. Effect of roughness distribution on dilution. Symbols indicate effectiveness of scaling for wind speed and release rate, c.f. Fig. 5.

6.3.

Inferred

values

We can calculate

for

a, as a function

of roughness

values of 6, as a function

of

downwind distance from equation (12). Results are shown in Fig. 9 for the A, B, C and E experiments. For

case C, separate 0, values are derived for run conditions 2 and 3. Measurements of gr from Petersen and Ratcliff (1988) are also shown. Figure 9 shows that O, is a power-law function of distance, with a power-law index value of about 2/3.

1869

Roughness effects in gas dispersion

0 +

e 10

r

2 3

8 3

3 I 8

-

+

:

8.

Be

i +

$

8444) +++

1

VJ l-

++++

* 8

4 0 + +;e +@

0.1’

I 0.50

I 0.20

’ 0.10

t % # O@ +*+ +$ *+* ( I 2.0 5.0

I 1.0

Fig. 8. Failed concentration scaling for roughness distribution speed on dispersion.

D indicating influence of wind

A - peterscoR50 -PeterserlR3 C 100 \ A/’ /

1

1 0.10

I 0.20

I 0.50

I 1.0

I 2.0

Distancefrom source.m Fig. 9. Calculated values of O, for the difference boundary layers

I 5.0

I

P. T. ROBERTS et al.

1870

The value of 0, increases with increasing roughness length. Over low roughness and’over a smooth wall. CT, appears to increase slightly faster with distance, compared with high roughness. The Petersen and Ratcliff R50 experiments give virtually identical values to our boundary-layer B. Their R3 results approach our smooth floor values downwind but show a larger value of ur close to the source, perhaps the effect of their much larger release momentum. The D series experiments gave values of CT,slightly larger than the B results for run condition 3. For run condition 2, 0, was a factor I.5 smaller and comparable with A results. 7. SUMMARY

AND

in neutrally

buoyant

CONCLUSIONS

dispersion

for

roughness

elements increasing in size. We have found that, for low roughness, zo < 3 mm (full scale equivalent 0.3 m), dispersion is consistent with a Gaussian plume interpretation; the measured plume width, aY(x), and the inferred vertical plume depth, a,(x), are independent of the tunnel operating speed and hence the friction velocity, u,. The value of u,(x) is dependent on both the source and on the roughness

distribution.

Source

influences

u*(x),

compared

well.

Experiments

with

a smooth

wall

plume width and plume depth were the rough-wall boundary layers values of friction velocity.

We have described and presented results from an atmospheric wind-tunnel study of ground-based, neutrally buoyant dispersion in rough-wall boundary layers. Experimental conditions were similar to those used by Petersen and Ratcliff (1988) in their I : 100 scale study of dispersion in the neutral boundary layer. Our overall objective was to determine a sensible upper bound to the use of aerodynamic roughness length when parameterising dense gas dispersion in boundary layers where the roughness elements are very large compared with the cloud dimensions. In this investigation we have sought qualitative trends

and the manner in which they are arranged affects dispersion; a#) is affected by the geometric arrangement of roughness elements, in particular flow channeling can restrict lateral plume growth, but is invariant or weakly dependent on wind speed. We infer an increased sensitivity of ur to run conditions particularly when flow chanelling occurs. Comparisons have been made with similar experiments conducted by Petersen and Ratcliff at the same scale but with different source characteristics and different roughness distributions. Values for u,(x) and

diminish

as

roughness length increases, and both u,(x) and (T&Y) increase as roughness length increases. For large roughness, z,, > 6 mm (full-scale equivalent 0.6 m), the size and shape of roughness elements

showed

that

smaller than for comparable

for

REFERENCES

Hall D. J. and Waters R. A. (1989) Investigation of two features

of continuously

released

heavy

gas plumes.

WSL

Report LR 707 (PA). Hanna S. R. and Drivas P. J. (1987) Guidelines for the use of Vapour Cloud Dispersion Models. Centre for Chemical Process Safety, A.1.Ch.E. Hanna S. R., Strimatis D. G. and Chang J. C. (1991) Hazard response modelling uncertainty (a quantitative method), Vol. II. Sigma Research Corporation, 234 Littleton Road, Suite 2E. Westford, Massachusetts 01886. Available NTIS. Monin A. S. and Yaglom A. M. (1987) Sratistical Fluid Mechanics,

Volume

1. MIT

Press,

MA.

Petersen R. L. and Ratcliff

M. A. (August 1988) Eflect of homogeneous and heterogeneous surface roughness on heavier than air gas dlsperslon. Report CPP-87-0417, CPP Wind Enginiering Consultants,. 1415 Blue Spruce Drive. Fort Collins. CO 80524. U.S.A. Robins A. G. (1978) Plume dispersion from ground level sources in simulated atmospheric boundary layers. Atmospheric Ennironmenr 12, 103311044. Snyder W. H. (1981) Guideline for fluid modelling of atmospheric diffusion. Environmental Sciences Research La-

boratory, report No. EPA-60018-81-009. Van Ulden A. fi. (1978) Simple estimates for vertical from

sources

2 125-2 129.

near the group.

Atmospheric

diffusion

Enr~ironment

12,