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, AD-A1 523 Di T. OF AN ANOSPH "C iS D1DiT FND~AVG HAU
UNCLASSIFIED U h 3-" 6 9 2 4 M
AU
W= mI ~~~~~- 12 IIIIIII .
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'CROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDS-1963-A
, i i * .
Ln
Report No. CG-D-23-85
DEVELOPMENT OF ANATMOSPHERIC DISPERSION MODEL
FOR HEAVIER-THAN-AIR GAS MIXTURES
Volume II:Laboratory Calm Air Heavy Gas
Dispersion Experiments
' JERRY A. HAVENS
THOMAS 0. SPICER
This report Is evellable to the U.S. public through the NationalTechnical Informatlon Service, 8prlngfleld, Virginla 22181.
FINAL REPORTMAY 1985
Prepared for:
U.S. Department of TransportationUnited States Coast Guard
Office of Research and DevelopmentWashington, D.C. 20593
Technical Report Dcumentation Page1. R...'l No. 2. G....nmen? Acession He. 3. Seeip-e.nt' Ceeis-t N.
CG-D-23-85 Ar aeA l~ 2 ____5____
4 1,0q; end Swigb''le S. ftepoe Date
DEVELOPMENT OF AN ATMOSPHERIC DISPERSION MODEL FOR May 1985HEAVIER-THAN-AIR GAS MIXTURES 6. Po,fo,m~ng Otg.g.onw Code
VOLUME 11: LABORATORY CALM-AIR HEAVY GAS DISPERSION ______________
EXPERIMENTS I. Pefmn otoon.36t~of Report N.7 ANN,.,r's)
Jerry A. Havens and Thomas 0. Spicer Final Report
Chemical Enqi neeri ng Department 11. Cotc a, Giant N.University ofl Arkansas DT-CG-23-80-C-20029Fayetteville, Arkansas 72701 13 yo9 Repo. e.n. d e.o Co t
12 Sponsig,,,g Agency No.* and Addegg Final ReportU.S. Coast GuardSet 190My98Commandant (G-FCP-22F/TP64) Sept._______________1985 _
2100 Second Street, NW 4seS.eAgnyCd
4-ashington DC 20593 1 pnsa gnyCd15 svpplemoee.ty N...,
This volume accompanies: Volume I: Development of an Atmospheric Dispersion Modelfor Heavier-than-Air Gas Mixtures, and Volume III: DEGADIS Model User's
, {aboratory experimental instantaneous releases of right circular cylindrical3
initial height-to-diameter ratios of 0.4, 1.0, and 1.57 are reported. The heavy gasflow field surrounding the release is described by time series of gas concentrationat various radial and vertical coordinates with respect to release center. Measure-ments of the gravity current velocities are determined from time-of-onset of measuredaas concentration. V.'. - C '5L
Calm-air instantaneous vy/'gas releases are demonstrated to scale with acharac .grist- length V'', where Vi is the initial volume, and a characteristictime -' 76lv/ 'q1 here g' iS .the reduced gravi tational acceleration). The scaledlaboratory releases predi~Tc the gravity-spreading and iutoprcsocrinduring thelbuoyancy-dominated flow phase of the 2000 ,m Freon/air instantaneousreleases conducted by the British Health and Safety E'iecutive at Thorney Island, UK.
The gravity spread and dilution data are used to validate the buoyancy-dominatedflow submodel which is incorporated in DEGADIS, the general purpose heavy gasdispersion modeL--developed for theCoast Guard Hazard Assessment Computer System(HACS).
17. go, weodo Is. U0e,,#~.eh. Statement
Heavy Gas Dispersion Density CurrentsTurbulent Mixing Gravity CurrentsAtmospheric Dispersion Stratified FlowsBuoyancy-Driven Flows
to. sge,,#y Cloge.f. (of th.0 tooei) j3D. sooa....y CI...il. (of "big page) 21. No. *I Poqo* 22. Pt...
Fermi DOT F 1700.7 (872) R*ept.wti of ceepiteted Pogo oiniteda~d
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TABLE OF CONTENTS
Page
LIST OF FIGURES vii
LIST OF TABLES ix
LIST OF SYMBOLS xi
SUMMARY 1
I. INTRODUCTION 3
11. DESCRIPTION OF CALM-AIR HEAVY GAS DISPERSION EXPERIMENTS 5
11.1 Experimental Results 5
I1.1.1 Experimental Procedure 10
11.l.2 Gas Concentration Measurements 12
111. RESULTS OF CALM-AIR HEAVY GAS DISPERSION EXPERIMENTS 17
111.1 Cloud Extent 23
111.2 Concentration Measurements 26
111.2.1 Effect of Initial Volume 26
111.2.2 Effect of Initial Density 28
111.2.3 Effect of Initial Height-to-Diameter Ratio 28
111.3 Comparison with Field-Scale Experiments 32
111.4 Average Concentration 34
I.CONCLUSIONS 3
V.REFERENCES 3
APPENDIX A: Gas Concentration Measurements A-1
B: Experimental Data Summiaries B-1
C: Calculation of Average Cloud Concentration C-1
v
LIST OF FIGURES
Page
11.1 Schematic Plan of Heavy Gas Release Facility 6
11.2 135-Liter, Freon-12, H/D = 1.0 7
11.3 Gas Release Mechanism 7
11.4 Freestanding Gas Cylinder Initial Condition 9
11.5 Side Views--135-Liter Release 11
11.6 Overhead Views--135-Liter Release 11
11.7 Gas Sensor Positions 13
11.8 Schematic Diagram of Aspirated Hot Wire Gas Sensor 13
11.9 Gas Sensor Mounting 14
11.10 Aspirated Hot Wire Anemometry ConcentrationMeasurement System 15
I11.1 Nondimensional Cloud Radial Extent vs. Time 24
11.2 Predicted and Observed Nondimensional Cloud RadialExtent vs. Time 25
111.3 Peak Concentration vs. Distance from ReleaseCenter--Freon-12 ( a)i = 4.19, (H/D) i 1.0 27
111.4 Peak Concentration vs. Distance from ReleaseCenter--Freon-12/air mixtures, (H/D)i = 1.0 29
111.5 Peak Concentration vs. Distance from ReleaseCenter--Freon-12, (J a)i = 4.19 30
111.6 Peak Concentration vs. Distance from ReleaseCenter--Freon-12, (2pa)i = 4.19 31
111.7 Laboratory and Thorney Island Trial MaximumConcentration Measurements vs. Distance 33
111.8 Peak and Average Concentration Decay with RadialDistance Compared with Predicted Cloud AverageConcentration 35
111.9 Peak and Average Concentration Decay with Time 36
vii
LIST OF TABLES
Page
11 Container Removal Times
IIl Release Experiment Summnary 1
ixa
LIST OF SYMBOLS
cE constant in gravity intrusion formula
D cloud diameter, m
g gravitational acceleration, m/s2
g' reduced gravitational acceleration, gA', m/s2
H cloud height, m
H* dimensionless height, H/Z
r radial distance,m
R cloud radius, m
R* dimensionless cloud radius, R/V
R* initial dimensionless cloud radius, RO/Z00
t time, s
characteristic time, . / gA!
t* dimensionless time, t/-
V. initial cloud volume, m3
y gas concentration, mole
y cloud-averaged gas concentration, mole %
z vertical distance, m
Greek Symbols
A' reduced density, (, a- )/ a
frontal entrainment coefficient
2 cloud density, kg/m3
a air density, kg/m
3
characteristic length, V/3
Subscripts
i initial or indexxi
SUMMARY
Laboratory experimental instantaneous releases of right circular
cylindrical volumes of heavy gas (Freon-12/air) with initial volumes
ranging form 0.034 m3 to 0.531 m3 and specific gravities ranging from
2.2 to 4.2 are described. Releases with initial height-to-diameter
ratios of 0.4, 1.0, and 1.57 are reported. The heavy gas flow field
surrounding the release is described by time series of gas
concentration at various radial and vertical coordinates with respect
to release center. The gas concentration measurements, made using
aspirated hot wires, provide high frequency response gas concentration
data describing the rapidly slumping, laterally expanding gas cloud.
Measurements of the gravity current velocities are determined from
time-of-onset of measurable gas concentration.
Calm air, instantaneous heavy gas releases are demonstrated to scale
with a characteristic length Vi/, where V. is the initial volume, and a
characteristic time V)/6/ where g,',' is the reduced gravitational
acceleration. The scaled laboratory releases predict the gravity
spreading and dilution process occurring during the buoyancy-dominated
flow phase of the 2000 m3 Freon-air instantaneous releases conducted by
the British Health and Safety Executive at Thorney Island, UK.
The gravity spread and dilution data are used to validate a
buoyancy-dominated-flow submodel which is incorporated in DEGADIS, a
general purpose heavy gas dispersion model developed for the Coast
Guard Hazard Assessment Computer System (HACS).
3
1. INTRODUCTION
Mathematical models used to predict the dispersion of heavier-
than-air gases (HTAG) released into the atmosphere must provide a
description of the gravity-driven flow and attendant mixing (dilution)
processes that characterize the initial phases of rapid releases.
Since for rapid releases of "compact" gas volumes (i.e. height-to-
diameter ratto of order one), the initial gravity-driven flow and
mixing processes may result in cloud dilution by one or two orders
of magnitude; such processes can be an important determinant of the
maximum downwind distance to gas concentrations of the order 1%
characteristic of many hydrocarbon fuel lower flammability limits.
This experimental study was sponsored by the Coast Guard as one
task area in the development of a general purpose HTAG dispersion
model for incorporation in the Coast Guard's Hazard Assessment
Computer System (HACS). The experimental program was designed to
provide accurate measurement of the gravity spreading velocities and
rates of dilution (by mixing with air) of HTAG volumes released
instantaneously in calm conditions in order to accurately describe
the buoyancy-dominated flow regime. The experiments were made
using Freon-12 and Freon-12/air mixtures with initial volumes
0.034 m3 to 0.53 m3, different initial cloud densities (Sp. Gr. 2.2
to 4.2), and different height-to-diameter ratios (0.4, 1.0, and
1.57).
Gas concentration measurements were made at a series of radial
and vertical positions in the cloud. Both peak gas concentration
and cloud average concentration data as a function of time and cloud
radial extent from release center are reoorted. Average spreading
velocities were measured by inferring time of cloud arrival from
gas concentration measurements.
The calm air HTAG release data have been used to validate a
gravity spread-dominated regime submodel which is proposed as part
of the general purpose HTAG dispersion model DEGADIS developed for
the Coast Guard.
5
11. DESCRIPTION OF CALM-AIR HEAVY GAS DISPERSION EXPERIMENTS
The experimental facility was designed to allow the instantaneous
release of up to one cubic meter HTAG onto a smooth solid surface
under calm conditions; it consists of a control room and a release
containment room (see Figure 11.1). The release containment area
is isolated from the ventilation and climate control of adjacent
rooms. A vertical curtain surrounds the 15.2 m diameter release
area to inhibit naturally occurring horizontal air motion during
an experiment. The release point is at the center of the
measurement area. Gas concentration and velocity measurement
stations are movable anywhere in the release area up to a height
of one meter. Instrument cables are carried overhead to the
control room. The gas for release and calibration is carried
from standard high pressure gas cylinders to the point of use
through Tygon tubing.
11.1 Experimental Results
Fiqure 11.2 shows a sector of the release area surrounding a
135 liter gas container filled with white smoke marked Freon-12 gas
with an initial height-to-diameter ratio one ((H/D)i = 1.). The
gas container is a 1/8 inch thick polycarbonate sheet rolled to form
a cylinder with vertical exterior support ribs which extend above the
cylinder to the end of a rod in a pneumatic cylinder. Figure 11.3shows the release mechanism with a 531 liter container. The release
mechanism is rigidly mounted in a framework hung from roof support
beams. A solenoid valve operated by the computer control and data
acquisition system admits air under the pneumatic cylinder piston for
a designated time period, moving the gas container vertically past
the gas volume. The container removal time is controlled by the
operating pressure of the air supply line and by the length of time
the solenoid valve is open; the removal time is measuredi by timing
the passage of a reflective tape marker on the cylinder between light
beams projected from optical fibers mounted to the side. Table II. I
6
____ ____ ____ ___ cm
r.o
(D-
E4
El E
Cu CO C
Cel7B V)
0
00
0 0
Cu a :
0 0z 00
~0 U
E C0 0
0.z
E
z E260 * CL
- c a * SE E %m a 40 0 m CU L)U QOaO
U
- - - Iv-.
Sr444;>
* .1
8
shows typical times required for the gas container to pass the topof the released gas, and its variability in repeat experiments.
TABLE 11.1
CONTAINER REMOVAL TIMES
Initial Volume Time to Pass(H/D)i = 1.0 Top of Gas
35 liter .12 + .002 sec.
54 liter .12 + .002 sec.
135 liter .24 + .01 sec.
531 liter .31 + .03 sec.
Container removal rates were studied using smoke-marked gasvolumes to determine operating conditions required to leave afreestanding, minimally perturbed, cylindrical gas volume after thecontainer had risen above the gas. Figure 11.4 shows photographs ofa 531 liter container ((H/D)i 1.0) initially containing smoke-marked CO 2 taken immnediately before and 0.31 seconds after initiationof container movement. The second frame indicates that the bottomof the container is past the top of the gas volume 0.31 seconds afterits vertical movement began, and the gas is shown to be freestanding
with only minimal perturbation. The slight perturbation of thecloud edge which appears as the container clears the gas volume maybe induced by vibration of the plastic container wall during itsvertical travel, although the local circulatory flows which aooearto be beginning at this time would be expected to arise as a result
of Kelvin-Helmholtz type instabilities of the density-stratified
shear flow at the interface. In any case, variability in the initialcondition of the release is assumed negligible in analysis of the
subsequent flow process. The variability which does occur in thetime series of concentration at a given position in different
I
tp
10
experiments is believed to be due to the random nature of the flow
itself but may be slightly affected by the impossibility of
eliminating the last traces of naturally induced air circulation in
the release area and by uncertainty in the gas concentrationmeasurements.
Fiqure 11.5 shows a 135 liter Freon-12 release at two successive
times; Figure 11.6 shows overhead views of the same release. In
Figure 11.6, the gas container is just hidden under the square plate
which is part of the release mechanism framework. The edge of the
spreading gas cloud has advanced to a radial distance of 1 .5 m at
0.7 s and 2.0 m at 1.0 s. The radial symmietry of the cloud is clearly
indicated. Observations of the cloud's movement beyond the edges of
the area photographed confirmed radially symmuetric cloud advance to
distances at which the peak gas concentration at floor level has
decreased to at least 1% of the initial value. The spreading gas
rapidly forms a torus or doughnut shape, as observed in previous
wind tunnel (Hall, 1982) and field (Pickne.tt, 1978) calm-air and
low-wind releases.
I1.1.1 Experimental Procedure
The gas container was filled by introducing the test gas through
a gas "diffuser" plate, with eight radial outlets to minimize mixing
effects due to jetting, at the bottom of the open-topped cylinder.
Horizontal overflow slots cut in the container wall determined the
gas height when filled. Experiments indicated that gas addition at
10 liters/minute for a period sufficient to add twice the gascontainer volume resulted in a HTAG interface at the horizontal
slots which was very sharp, with the gas concantration below the slots
esimtated to be greater than 98% pure gas. During cylinder filling,
the gas overflowing through the horizontal slots flowed down the
exterior wall of the container and was dispersed by four small (100
CFM) axial flow instrument cooling fans placed at floor level about
one cylinder radius away, at 900 angles.
Ii
Eli!!..i~.f. ~
12
After the cylinder was filled, all personnel moved to the
adjacent room housing the data acquisition and experimental controlcomputer system, and the room containing the spill area was sealed.A calming period of ten minutes was observed, then the computer
sequenced the actuation of photographic lights and cameras (when
used), the raising of the gas container, and the data acquisition.
Generally, experiments were repeated to give three experimental
data sets under (intended) identical conditions. Following completion
of the releases and the final calibration check (when gas concentra-
tion measurements were made), the exhaust fans were turned on to clear
the release area.
11.1.2 Gas Concentration Measurements
Figure 11.7 shows a sector of the release area with gas sensors
mounted on vertical support rods. Sensors are positioned on
different radii to aVoid interference in the flow caused by other
sensors. Figure 11.8 is a schematic description of a gas sensor,
and Figure 11.9 shows a sensor mounted on a support rod. A vacuum
pump aspirates gas through a 4 mmn diameter sample port fitted with a
fibrous filter; the sample flows over a 4 ui wire or 25 wi film mounted
on a TSI 1260 anemometer probe, and then through a 400 wi diameter
choke. The aspiration rate with the 400 11 choke was approximately
1.5 liters/minute, although some measurements were made with
aspiration rates as low as 300 mi/mmn. The high aspiration rates
were used to maximize the resolution of the peak concentrations in
the cloud.The hot wires or films were operated at overheat ratios of 1.32
and 1.16 respectively, corresponding to an operating temperature of
about 850C. This operating condition was determined to give good
resolution of the concentration of Freon-12/air mixtures without
appreciable deterioration of the sensors experienced in high Freon-12
concentration, high overheat ratio usage. The output of the TSI
10538 anemometers was fed to a reference voltage shifting circuit,
through a low pass filter (100 Hz) and amplifier, and input to a
13
r4
our 11-7. Gas sensor positioris.
TSI * 1260Probe -Hot Wire. Film
For Support Rod
Filter
ChokeInlet
~ i ~e~ ~. kceltic diarm of asrjira~ec ,,ot
q ure 119 Ga s senisor m ounti n'.
"I 'iC computur a -cqj si t ion syv 1ein ;.*
Co)nc n trat 41c n mea s werie nt J we re vC .7 je j, 21
seconds a~;cre -e.ase .
3as -a brat4 on m! t.; re.- w ' -Qfd t: *:a - se c
t1r thie conta 4 er and aua in at t e n 3 ~ce s- -
4dentical re ica ,s .-- le-ar 3 -- Q' i ng eiere a", -lade :tc
r-leases to ;-rrect f ?r eis,)r driftr wnicli -ia,. "~uV
.he r- rge 2 _-;C , O 0 ?- d- 7 g ",n Lne r irnce CI
reedii n the ara - concentration. bas cd on~ il s'
-ensors' c: rst ;. P,'mrndr standardzat-c' - ne
,,i xtL re 2r- y .*." vr '~ier.pers .4as ce1; :a - ,r.,r
15
TSI #1260Anemometer4y ie2pFl
Fibrous Filter
-Inlet
400p Choke Not to Scale
To Vacuum
Sensors
(8 Total) # 3 # 5 # 7 #
TSI ModelSignal TSI 8 CHANNEL ANEMOMETER
Conditioner I___Ref ereceVoltage ____[Reference
Shifter
PacificModel #3100-F
100OHZLow PassFilters
Variable GainAmplifiers v yy
COMPUTER DATA ACQUISITION SYSTEM
Figure 11.10. Aspirated hot wire anemometryconcentration measurement system.
17
III. RESULTS OF CALM AIR HEAVY GAS DISPERSION EXPERIMENTS
Subsequent to a development period during which the experimental
procedure was refined, 67 releases of Freon-12 and Freon-12/air
mixtures were conducted where gas concentration measurements were
made in order to determine air entrainment. The experimental
variables studied were: (1) initial gas volume, (2) initial gas
density, and (3) initial gas height-to-diameter (aspect) ratio. In
most tests, simultaneous gas concentration measurements were made at
eight different positions in the HTAG flow field. Table III.1
summarizes the relevant experiments, indicating the radial and
vertical coordinates (from ground level spill center) of the
concentration measurement positions. In Table Ill.1, the experiments
are grouped by experimental variable: initial volume (Vi), initial
specific gravity (p/p a)i, and initial height-to-diameter ratio
((H/D)i). Forty-three releases of pure Freon (Sp. Gr. = 4.19) with
(H/D)i= 1. were made, including 3 of 34 liters, 34 of 54 liters, 2
of 135 liters, and 4 of 531 liters initial volume. Seven releases,
at three different initial volumes, were made of a Freon-12/air
mixture with (p/p a)i = 2.92, all with (H/D)i = 1. Five releases,
at two different spill volumes, were made of a Freon-12/air mixturewith (p/p a)i= 2.16, again all with (H/D)i = 1. Finally, three releases
of 54 liters pure Freon-12 were made with (H/D). = 0.4, and nine
releases of 54 liters pure Freon-12 were made with (H/D)i = 1.57.
The experimental plan required measurements to be made at
different radial and vertical positions in a series of experiments
in order to determine radial and vertical concentration profiles.
Vertical concentration profile measurements were made to determine
cloud height and to provide cloud average concentration as a function
of time. Concentration time series measurements for all experiments
are given in Appendix A; a summary of time of arrival and peak
concentration data is given in Appendix B.
1 pc
5i 1c ! o oc
- ~ ~ ~~! .CD
W2 0 2 j
0D 0 CLD
0:z
t. =; * 0 0 0
Ui C4 ,- ; I; l;
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.-- -- I-0 0
0P hLuu
*D C -
'9. L6'.
C Lf n n'
cc Is
C* 00
0v 0 0 '
IA -l .. 0 00
N.. C,.~
=; CD, . . 0
41 N. .. .. . . .
. .. . . . . . . .
0. .c~ . .
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CG 0 o 0 o 0 000000
ONC
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co co E
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n P1 n nl lN- f f e
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-'C 0 0 0 0 0
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o 77
0jC C o 0C 00 00 n0
CD 0 DC 0 M cr C
0 CD
U- -L
4J %D - L JJr
o, 'Ucoc
.1.1
Nl .' . .J I
oc ic ic4o(c)
I Ioju
CDi'c CD lolo*y j m;< Ic" r~J
Cj CjIC'j~ k 'J4'N
o "D ,,
-K-
o~t 1c 1= 0-~--r-
_j0 0 -018 Cocc0Z~
11 I k ~ Int n I nU
C fn In H !fco 'u tn inI
co of0 co~ coha o w
U u c'z- -. Is :2 ,
23
I11.I Cloud Extent
Figure 1l1.1 shows the nondimensional cloud radial extent
determined from the onset of measured concentration as a function
of the nondimensional time t* = t/ [V 1 3 /" gp] 1/2 measured fromS1
the start of gas container removal for all of the experiments
reported. The DEGADIS source model-predicted radial extent as a
function of time is shown by the solid line. For the range of
data plotted, the predicted radial extent is essentially
independent of aspect ratio (H/D)i for the ratios tested. The
variation of observed cloud radial extent for earlier times can
be decreased if the radial extent is expressed as R* - R.
If the gravity intrusion formula is integrated for a right
circular cylinder of gas, the extent of the radially spreading
cloud expressed as R.2 - R*2 would be proportional to t* and0
the proportionality constant would be 2 CE/V - ; expressed with
logarithms,
log (R*2 - R*2) = log t* + log (2 CE/ /-T)
0 CE!
Figure 111.2 shows that the experimental data reflect this
functionality (dashed line with slope = 1.0) after the initial
acceleration of the gas cloud from rest. The intercept (t* 1 1.)
gives CE = 1.15. It should be noted that the predicted radial
extent of the cloud for these releases is very insensitive to the
value of CE, but the value of CE strongly affects the entrainment
rate and therefore the value of E. For CE = 1.15, E has been
determined to be 0.59.
24
CD
C\j - 0
CC
II>
-J
CC
25
A - 34.2 L
100 o - 54. 1 L MI
60
~~40
slope =1.0
DEGADIS prediction
6
V -~7 ______
1.0 2 4 6 10 20 40 60 100 200
Figure 111.2. Predicted and observed r'ondimensionalcloud radial extent vs. time.
26
111.2 Concentration Measurements
Analysis of the concentration measurements has been directed
to the following points considered most relevant to the use of
these data in the formulation of the DEGADIS model:
-- verification of scaling laws
-- determination of peak gas concentration decrease witn
distance from spill center
-- determination of effects of initial density and
height-to-diameter ratio
-- determination of average cloud concentration as a function
of time and cloud extent.
I11.2.1 Effect of Initial Volume
Calm air releases of cubic volumes of HTAG (Hall, 1982) should be
nondimensionalized with a characteristic length scale = vi/ andI/6
1
a characteristic time scale 7 = vi//- - (Hall, 1983). Figure
111.3 shows the maximum (peak) gas concentration measured at various
radial distances from release center for all (45) of the pure
Freon-12, (H/D)i = 1.0, releases summarized in Table III.I. The
measurements of gas concentration are for a 0.6 cm height for the
34, 54, and 135 liter releases (H* = 0.0185, 0.0158, and 0.0117,
respectively) and 1.3 cm height for the 531 liter release (H* = 0.0185).
All of the gas concentration data were digitized at 250 Hz, and the
maximum gas concentrations were obtained from a sliding three point
average of the digitized sample points. The peak measured concentra-
tions collapse to the same curve when plotted against the radial
position nondimensionalized by the scale length V1/3
27
80 -_ _
60 -
40 -
0
20 -
- 10 _____ ___
0
8
6
4
2 A 4 2 0. 60801082
c 2tr-Fen1 4/ ) 6 8 4.19 (HD)010R*1
28
111.2.2 Effect of Initial Density
Figure 111.4 shows the peak measured gas concentrations vs. the
nondimensionalized distance from release center, R*, for releases
with (H/D). = 1. and specific gravities of 2.16 and 2.92. These
specific gravities are for Freon-12/air mixtures of 36% and 60%
respectively.
Comparison of Fiqures 111.3 and 111.4 indicates the same peak
gas concentration decay with nondimensionalized distance from release
center for the releases with (/oa)i varied from 2.16 to 4.19.
111.2.3 Effect of Initial Heiqht-to-Diameter Ratio
Fiqure 111.5 shows the peak measured gas concentration vs. the
nondimensionalized distance R* for releases of pure Freon-12 with
(H/D)i of 0.4, 1.0, and 1.57. The data are for 54 liter releases
with initial heights 22 cm, 41 cm, and 55 cm, respectively. Although
there might be a trend to higher concentrations at the same distance
with small (H/D)i, the effect is certainly not pronounced in this
(H/D)i range. Furthermore, comparison of these data must be made
in the light of greater uncertainty (i.e., in terms of experimental
repeatability) for the (H/D)i releases. The low releases spread more
slowly, and the maintenance of the radial symmetry of the release out
to large radii is more affected by the presence of small air currents.
However, the data do indicate that for (H/D) i from 0.4 to 1.57, the
dilution mechanism is essentially the same.
Figure 111.6 shows the same peak measu-ed gas cuncentration
fron Figure 111.5 expressed as a function of the nondimensional
distance R* - R* in order to more accurately scale the data for
earlier experimental times.
29
416 8102
80ue114 ekcnetaio s itnefo eescentr--Feon-2/ai mitr Sp. Gr.) 21.0
100
80 S _ A (H/D)i 0.4___ o H/D)j = 1.0
60 U (H/DY 1.57
6-1
t2 --
10~
8 02
F6ue115 ekcnetaio s itnefo ees
4etr-ro-2.>'~>=49
31
100 --
80 tA (HID) 1 0.40 (H/D) 1 =1T0I-rn
60 -7 (H/D)1 1.57
40L... ..- 1 -_ - ---
_____ -4-
- 4 7- -
10 .z:::
8
4
2
12 4 6 8 10 20R* R*
Figure 111.6. Peak concentration vs. distance from releasecenter--Freon-12, (p/p a). 4.19.
32
111.3 Comparison with Field Scale Experiments
Figure 111.7 shows maximum measured concentrations taken from
the laboratory calm-air HTAG experiments as a function of radial
extent. The distance from release center has been nondimensionalized
by the characteristic length Vi . Figure 111.7 also shows peak
concentration measurements vs. the nondimensionalized distance from
release center for the Thorney Island Triais 7 through 16 (HSE, 1983).
The cloud dispersion process in the Thorney Island (2000 m 3 ) 'nstan-
taneous releases is initiated by a rapid gravity-driven flow phase
during which the gas flow field is relatively unaffected by the
wind (Spicer and Havens, 1985). During this time period, which extends
to times at which the cloud concentration has decreased to well below
10%, the laboratory experimental results (for 5A-530 liter volumes)
scale accurately to the 2000 m3 releases of Thorney Island, repre-
senting a characteristic length scale factor of about 50.
33
100.-:Thorney Trials
o centerline
x near centerline
C 10.
00
0 0
0o
X V
00.2- 1 1
1.0 10. 100.
Distance f rom Spill Center/i
Figure 111.7. Laboratory and Thorney Island Trial maximumconcentration measurements vs. distance.
34
111.4 Average Concentration
An extensive series of 54 liter Freon-12 releases, with
(H/D)i = 1. were made to determine the gas concentration time
series as a function of radial and vertical position relative to
the release center. For several successive times following the
release, the concentration data were volume averaged by integrating
the radial and vertical concentration distributions in the cloud
(Appendix C).
The cloud average concentration vs. radial extent (or time)
is useful for verification of box model simulations of the cloud
dilution process. Figure 111.8 shows the cloud concentration
decay with distance from release center (nondimensionalized)
predicted using zhe DEGADIS source model. The predicted average
cloud concentration decay with radius is in good agreement with
the cloud average concentration decay with distance determined
by volume averaging the radial and vertical concentrations.
Figure 111.9 shows the same information as Figure 111.8
plotted as a function of time. With this change, a direct
comparison of the peak and average concentrations can be made. For
this type of release, the ratio of the peak-to-average concentration
is not strictly constant but is a function of concentration level.
However for most approximations, it appears that a peak-to-ensemble-
average ratio of 2.0 to 2.5 appears justified.
35
100 -- -
80 ___
60
averag gaoncentrationio
20
a e a concentration 13L, I4
2 2 4.6.810.20
ditnecmae ihpeitdcodaverageconcentration.0
1 00 i--- -
TT2TTTTTEPeak Measured Concentrations80 ~ 34.2
0F 54. 1L07 135 1
40 A r
20
~10
6 7- __ _ _ __ _ _ __ _ _
4
TI EGAIS-predictedaverage
Taverace co r ren tra t .o r,
5 7 10 20 40 60 s0 100
Figure 141.?. Peak and average concentrat on decay with time.
37
IV. CONCLUSIONS
Laboratory, instantaneous releases of Freon/air mixtures in calm airhave been conducted to determine the gravity-spreading velocities and
rates of dilution with air which characterize such releases.
Deak gas concentration decay with distance from the release center
and cloud spreading velocity are demonstrated to scale with theoretically
predicted length and velocity scales over the range of release sizes
studied (54 liters to 531 liters), and the results are consistent with
measurements made during the gravity-dominated flow regime of the 2000 m3
Thorney Island Heavy Gas Trials.
Peak gas concentration decay with distance from the release center
shows essentially the same pattern for releases with initial specific
gravity ranging from 2.2 to 4.2 and initial volume height-to-diameter
ratios varying from 0.4 to 1.57.
The gas concentration development with time at a number of radial
and vertical positions relative to the release center has been determined
for 54 liter, H/D = 1.0 Freon-12 releases. The data have been analyzed
to provide cloud average concentration as a function of time and cloud
radial extent. The average cloud concentration data have been used to
validate a buoyancy-dominated regime submodel similar to that proposed by
van Ulden (1983). The buoyancy-dominated regime submodel is incorporated
in DEGADIS, the general purpose heavy gas dispersion model developed
for the Coast Guard Hazard Assessment Computer System.
39
V. REFERENCES
Hall, D. J. et al., "A Wind Tunnel Model of the Porton Dense Gas SpillField Trials," LR 394 (AP), Warren Spring Laboratory, Departmentof Industry, Stevenage, UK, 1982.
HSE--British Health and Safety Executive, Research and LaboratoryServices Division, Red Hill, Sheffield, UK--Heavy Gas DispersionTrials, Thorney Island 1982-83, Data Digests.
Picknett, R. G., Field Experiments on the Behavior of Dense Clouds,CDE Report PTN, IL 1154/78/1, Porton Down, UK, September 1978.
Spicer, T. 0. and J. A. Havens, "Modeling the Phase I Thorney IslandExperiments," Symposium on the Thorney Island Heavy Gas Trials,sponsored by the British Health and Safety Executive, Sheffield,UK, April, 1984.
van Ulden, A. P., "A New Bulk Model for Dense Gas Dispersion: Two-Dimensional Spread in Still Air," I.U.T.A.M. Symposium onAtmospheric Dispersion of Heavy Gases and Small Particles, DelftUniversity of Technology, The Netherlands, August 29-September 2,1983.
4
i
41
APPENDIX A
GAS CONCENTRATION MEASUREMENTS
The gas concentration measurements for the experiments
summarized in Table III.1 follow. Repeat measurements are plotted
together (i.e. Run 817831-3 designates 3 experiments). The experi-
ment run identification number is followed by the designated
sensor position number from Table III. (i.e. 871831-3:5 designates
3 experiments at position 5 (R = 3.0 m, H = 0.6 cm).
Repeat runs between two calibrations are plotted as follows:
Run Example Plotted Line Type
First MDDYYI:C 817831:5
Second MDDYY2:C 817832:5
Third MDDYY3:C 817833:5
where: M = single character month designation
DO = day of month
YY = two-digit year
C = channel number
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B-I
APPENDIX B
EXPERIMENTAL DATA SUMMARIES
A summary of some experimental results for each experiment, in
chronological order, follows. For each series of experiments, the
following information is summarized for each channel:
(*) Experimental initial conditions
(*) Ambient conditions
(*) Gas sensor position (dimensional and nondimensional)
(*) Cloud time of arrival (TOA) based on the onset of
measured concentration (dimensional and nondimensional)
(*) Maximum observed mole fraction (PEAK)
(*) Time of PEAK (TOP) (dimensional and nondimensional)
B-3
Experiment: 705830
13 max.Radius (m) R/V. Time Obs. Time
of Mole ofChannel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) TOA(s) TOA/T PEAK PEAK TOP(s) TOP/-r
1.33 .389 1.391 1.0/0.6 3.1/.019 1.24 9.91 .424 .371 1.44 11.3
1.31 .301 1.59
2.58 .174 2.642 1.5/0.6 4.6/.019 2.51 19.3 .207 .194 2.58 19.7
2.48 .202 2.51
4.38 .073 5.13 2.0/0.6 6.2/.019 4.23 32.2 .081 .090 4.77 35.6
3.99 .115 4.06
7.11 .036 9.94 2.5/0.6 7.7/.019 6.62 52.3 .040 .039 7.4 63.1
6.73 .042 7.4
11.2 .014 27.05 3.0/0.6 9.3/.019 9.42 78.0 .020 .018 12.0 163
9.92 .020 24.8
16.6 .O10 35.56 3.5/0.6 10.81.019 15.2 118 .014 .012 43.5 295
14.2 .014 36.3
Initial Volume (1): 34.2Initial Relative Density: 2.91Initial (H/D)6 1.0Temperature ( C): 28.0Pressure (mm Hq): 736.6Relative Humidity: 46%
V 1/3 (m) * .324
[ 3/ (q'g&)i1/2
(s) 0.132
B-4
Experiment: 719830
1/3 Max.Radius m) R/V1 / 3 Time Obs. Time
1 of Mole ofChannel,1/3 Arrival Avg. Fraction Avq. PEAK Avcg.Number Height (cm) H/vj TOA(s) TOA/ PEAK PEAK TOP(s) TOPir
1.04 .612 1.111 1.0/0.6 2.6/.016 1.07 7.49 .585 .599 1.18 8.13
1.99 .232 2.282 1.5/0.6 4.0/.016 2.00 14.2 .199 .216 2.40 16.6
3.03 .178 3.083 2.0/0.6 5.3/.016 3.21 22.2 .105 .142 4.09 25.5
4.77 .075 5.464 2.5/0.6 6.6/.016 4.60 33.2 .088 .081 5.45 38.7
7.05 .038 7.94 57.55 3.0/0.6 7.9/.016 7.01 49.9 .035 .037 8.25
9.37 .026 23.86 3.5/0.6 9.3/.016 9.82 68.1 .022 .024 19.3 153
11.6 .025 28.77 4.010.6 10.6/.016 NR -- .012 .019 40.5 246
Initial Volume (1): 54.1Initial Relative Density: 2.91Initial (H/D)- 1.0Temperature ( C): 28.4Pressure (m Hg): 736.0Relative Humidity: 54%
V1 /3 (a) - .375
[ 1/3 / (qg 11 2
() j 0.142
B-5
Experiment: 728830
Max.Radius (a) R/V 1 3" Time Obs. Time
of Mole of
Channel e Arrival Avg. Fraction Avg. PEAK Avg.Number H/V. TOA(s) TOAI PEAK PEAK TOP(s) TOP/r
1.53 .438 1.651 1.0/0.6 3.1/.019 1.70 9.67 .334 .386 1.78 10.3
3.33 .162 4.292 1.5/0.6 4.61.019 3.32 19.9 .135 .149 3.68 23.9
5.69 .083 6.443 2.0/0.6 6.2/.019 5.22 32.7 .082 .082 5.79 36.6
NR --
4 2.5/0.6 7.7/.019 UR -- -- -- -- --
21.8 .014 25.85 3.0/0.6 9.3/.019 19.7 124 -- -- --
6 3.5/0.6 10.8/.019 28.2 169 -- 50.1 300
NR -
7 4.0/0.6 12.3/.019 47.6 285.0 -- 49.9 299
8 4.5/0.6 13.9/.019 M R -- -- --
Initial Volume (1): 34.2Initial Relative Density: 2.16Initial (MID)6 1.0Temperature (-C): 34.5Pressure (ma Hq): 734.4Relative Humidity: 43%
V 1/3 (a) * .324
[ (&) (3) 0.169
B-6
Experiment: 802830
1/3 Max.Radius (m R/V 3 Time 0bs. Time
of Mole ofChannel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) TOA(s) TOA/r PEAK PEAK T0P(s TOP/
0.80 .933 .991 1.0/0.6 1.9/.011 0.83 4.97 .897 .915 .98 6.01
1.38 .757 1.581.5/0.6 2.9/.011 1.36 8.36 .511 .634 1.65 9.85
2.48 .299 2.493 2.3/0.6 4.3/.011 2.70 15.8 .213 .256 2.91 16.5
4.61 .128 4.674 3.2/0.6 5.95/.011 4.75 28.5 .125 .127 5.11 29.8
7.65 .0585 4.05/0.6 7.53/.011 7.52 46.3 .049 .054 8.3
10.8 .043 24.66 4.7/0.6 8.7/.011 9.57 62.1 .040 .041 15.8 123
17.0 .030 37.67 5.5/0.6 10.2/.011 13.3 92.4 .031 .030 32.2 213
23.5 .025 60.18 6.3/0.6 11.7/.011 21.0 136 .028 .027 69.7 396
Initial Volume (1): 135Initial Relative Density: 2.91Initial (H/D)6 1.0Temperature ( C): 30.7Pressure (mm Hq): 736.9Relative Humidity: 54%
V 1 /3 () " .513
[Vi13 (S) . 0.165
B-7
Experiment: 805830
Max.Radius m R/VI/3 Time Obs. Time
of Mole of
Channel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) H/V1 TOA(s) TOA/T PEAK PEAK TOP(s) TOP/T
0.70 .932 1.011 1.0/0.6 1.9/.011 5.66 .934 7.78
0.74 .935 0.97
1.13 .623 1.372 1.5/0.6 2.92/.011 9.08 .611 10.7
1.18 .598 1.36
2.10 .276 2.263 2.3/0.6 4.3/.011 17.3 .223 19.9
2.30 .170 2.80
4.15 .087 4.564 3.2/0.6 5.95/.011 31.2 .103 32.9
3.78 .119 3.82
6.20 .079 7.735 4.05/0.6 7.53/.011 46.6 .072 53.6
5.67 .066 5.91
8.83 .034 15.16 4.7/0.6 8.7/.011 64.9 .042 143
7.70 .051 21.2
13.0 .020 37.57 5.5/0.6 10.2/.011 92.3 .029 255
10.5 .038 27.3
18.6 .0150 60.08 6.3/0.6 11.7/.011 130 .021 362
14.4 .027 32.1
Initial Volume (1): 135Initial Relative Density: 4.19Initial (H/D). 1.0Temperature ( C): 31.0Pressure (mm Hq): 735.8Relative Humidity: 46%v113 (m) • .513
V g')]l'2 (s) • 0.128
B-8
Experiment: 807830
Max.Radius (m) R/Vi Time 0bs. Time
Sof Mole ofChannel Arrival Avg. Fraction Ava. PEAK Avq.Number Height (cmi H/Vi TOA(s) TOA/T PEAK PEAK TOF(s) TOPT
1.02 .746 1.191 1.0/0.6 1.9/.011 1.03 4.84 .779 .773 1.14 5-.38
1.00 .795 1.06
1.83 .409 2.112 1.5/0.6 2.9/.011 1.82 8.69 .453 .422 1.84 9.33
1.83 .403 1.93
3.53 .154 3.773 2.3/0.6 4.5/.011 3.71 17.2 .113 .148 3.73 18.2
3.61 .177 .400
6.45 .094 7.184 3.2/0.6 6.2/.011 6.19 29.67 .125 .109 6.26 31.3
6.06 .109 6.30
9.42 .055 17.05 4.05/0.6 7.9/.011 9.32 44.8 .058 .058 9.57 76.1
9.52 .061 21.4
11.7 .042 33.36 4.7/0.6 9.2/.011 12.8 59.5 .050 .047 44.1 205
13.0 .049 52.0
16.3 .030 37.57 5.5/0.6 10.7/.011 16.6 76.6 -- .038 -- 225
15.5 .047 56.9
19.9 .023 43.78 6.3/0.6 12.3/.011 22.2 100 -- .033 -- 2i6
N .042 47.1
Initial Volume (1): 135Initial Relative Density: 2.16Initial (H/D). 1.0Temperature ( C): 30.4Presaure (mm Hg): 735.2Relative Humidity: 55%
V 1 3 (a) .513
T / (qa')i]112 (s) - 0.212
[V
B-9
Experiment: 808830
Max.Radius (a) R/V1 /3 Time Obs. Time
of Mole ofChannel 1/ Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) H/V. TOA(s) TOA/T PEAK PEAK TOP(s) TOP/t
0.83 .719 1.041 i.0/0.6 2.65/.016 0.92 7.87 622 .697 1.11 9.61
0.84 .750 1.01
1.45 .489 1.962 1.5/0.6 3.97/.016 1.49 13.4 .440 .469 2.28 19.6
1.43 .479 2.19
2.60 .213 2.943 2.2/0.6 5.82/.016 2.81 24.5 .170 .195 4.81 31.9
2.62 .203 2.71
4.18 .106 8.064 2.9/0.6 7.67/.016 4.75 40.9 .073 .090 9.08 75.3
4.46 .093 7.52
6.03 .053 11.35 3.5/0.6 9.26/.016 7.00 60.6 .040 .047 20.5 140
6.83 .048 14.0
8.02 .036 18.96 4.1/0.6 10.8/.016 9.57 80.5 .030 .033 28.1 215
NR -- --
10.6 .023 33.67 4.7/0.6 12.4/.016 NR 110 -- .028 -- 316
13.5 .032 35.4
NR -- --
8 5 .3 / 0 .6 1 4 .0 / .0 1 6 N R - -. .. .. . ..
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (MID)s 0.4Temperature ( C): 26.9Pressure (m Hq): 733.2Relative Humidity: 58%V11 3 (a) - .378
[Vl / (gs)i (
B-10
Experiment: 809830
Max.
Radius inm /V1 3 Time Obs. Timeof Mole of
Channel Arrival Avg. Fraction Avg. PEAK Avg.NuamDer Height tcm) H TOA(s) TOA/i PEAK PEAK TOP(s) TOP/i
0.94 .541 1.091.0/0.6 2.65/.016 0.91 8.4 .6UC .581 1.01 9.37
0.90 .602 0.97
1.50 .313 1.712 1.5/0.6 3.97/.016 1.62 14,3 .307 .276 1.80 16.3
1.55 .207 1.83
3.10 .098 3.453 2.2/0.6 5.82/.016 3.02 27.2 .085 .112 3.16 28.8
2.78 .152 2.82
4.55 .086 4.714 2.9/0.6 7.67/.016 4.89 43.0 .058 .069 5.96 47.6
4.65 .064 4.92
6.32 .036 15.55 3.5/0.6 9.26/.016 6.43 58.3 .037 .036 8.14 94.7
6.34 .034 7.36
9.12 .031 22.46 4.1/0.6 10.8/.016 8.03 78.6 .033 .030 17.0 184
8.60 .024 20.8
11.0 .027 27.47 4.7/0.6 12.4/.016 10.1 98.0 .022 .0243 33.3 305
11.0 .024 39.i
8 5.3'C.6 14.0/.016 12.5 -- .0207 -- 37.6 --
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D)A 1.57Temperature C): 27.2Pressure (," Hg): 733.6Relative Humidity: 60%
V113 (a) .378
S /Vl3 (qa) i2 (s) - 0.110
B-11
Experiment: 811830
1/3 Max.Radius m R/V. Time Obs. Time
of Mole ofChannel /3 Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cu . TOA(s) TOAIT PEAK PEAK TOP(s) TOP /
1 1.0/0.6 2.65/.016 .90 8.21 .441 .465 1.09 9.63.89 .488 1.01
2 1.5/0.6 3.97/.016 1.58 15.0 .258 .219 2.05 18.71.69 .180 2.03
3 2.2/0.6 5.82/.016 2.94 28.0 .121 .110 3.38 33.43.16 .100 3.94
4 2.9/0.6 7.67/.016 4.71 45.0 .066 .065 4.93 48.65.10 .065 5.66
5 3.5/0.6 9.26/.016 6.50 67.1 .041 .036 7.65 78.88.12 .031 9.52
6 4.1/0.6 10.8/.016 9.59 98.6 .021 .022 13.8 13111.9 .023 14.7
7 4.7/0.6 12.4/.016 15.0 194 .015 .012 21.8 30527.3 .008 44.6
8 5.3/0.6 14.0/.016 22.1 -- .012 -- 43.1 --NR -- - -
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D) 1.57Temperature C C): 28.9Pressure (mm Hg): 733.3Relative Humidity: 78%
I13 (a) ) .378
S1/3 1 (g')]/ 2 Cs) . 0.110
IV-
B-12
Experiment: 815830
1/- Max.Radius () R/V1 '3 Time Obs. Time
of Mole ofChannel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cU) H/V. TOA(s) TOA/T PEAK PEAK TOP(s) TOP/T
S0.88 .575 1.21
1 1.0/0.6 2.65/.016 0.92 8.42 .618 .564 1.14 10.80 . 96 .500 i. 19
1.60 .321 1.692 1.5/0.6 3.97/.016 1.69 15.2 .175 .244 1.95 16.3
1.69 .237 1.71
2.98 .098 3.873 2.2/0.6 5.82/.016 2.90 27.3 .153 .118 3.36 33.2
3.05 .104 3.64
4.70 .064 5.134 2.9/0.6 7.67/.016 4.96 44.0 .064 .062 5.00 45.5
4.76 .057 4.79
6.60 .030 6.905 3.5/0.6 9.26/.016 7.75 65.0 .022 .028 8.88 72.2
6.94 .033 7.87
8.54 .029 19.36 4.1/0.6 10.8/.016 9.42 82.0 .025 .026 25.0 202
8.92 .024 21.8
10.9 .017 31.77 4.7/0.6 12.4/.016 11.6 104.0 .028 .017 30.3 286
11.5 .015 31.6
14.4 .015 39.78 5.3/0.6 14.0/.016 14.4 135.0 .018 .017 26.8 355
15.3 .017 49.8
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D)6 1.58Temperature ( C): 28.9Pressure (mm, Hq): 734.7Relative Humidity: 54%. (m) = .378
[113i (ga')i11/2 (3) 0.110
B-13
Experiment: 815834
1/3 Max.Radius (m) R/V1 1 Time Obs. Time
of Mole ofChannel /3 Arrival Avg. Fraction Avg. PEAK( Avg.Number Height (cm)HV TOA(s) TOA/r PEAK PEAK TOP(s) T0P/,r
0.87 .650 0.921 1.0/0.6 2.65/.016 0.89 8.15 .740 .673 1.04 9.34
0.90 .628 1.09
1.50 .272 2.382 1.5/0.6 3.97/.016 1.76 14.9 .285 .269 2.27 19.7
1.63 .249 1.82
2.94 .106 3.513 2.2/0.6 5.82/.016 3.12 28.1 .116 .099 3.87 33.8
3.16 .075 3.69
4.80 .070 5.694 2.9/0.6 7.67/.016 5.02 48.9 .062 .064 9.95 62.9
4.86 .059 4.99
6.77 .026 16.75 3.5/0.6 9.26/.016 7.51 66.5 .023 .024 12.5 120
7.53 .024 10.1
9.02 .028 24.26 4.1/0.6 10.8/.016 11.2 94.0 .020 .029 30.4 211
10.6 .021 14.7
11.9 .017 28.97 4.7/0.6 12.4/.016 13.7 123 .012 .013 34.1 280
14.6 .011 28.6
14.6 .018 45.58 5.3/0.6 14.0/.016 NR -- .0095 .012 31.2 386
UR .0066 49.9
Initial Volume (1): 1.0Initial Relative Density: 4.19Initial (H/Dy. 1.0Temperature (C): 28.7Pressure (ma Hg): 734.7Relative Hunidity: 58%
"1/3
V 1 / (a) .378
V 1 / (g&')112 (3) *0.110
ii
B-14
Experiment: 817830
Max.Radius (m) R/V 1 !3 Time Obs. Time
of Mole ofChannel 1/3 Arrival Ava. Fraction Avg. PEAK Avg.Number Height (cm) H/V. TOA(s) TOA/I PEAK PEAK TOP(s) TOPur
0.97 .416 1.171.0/0.6 3.09/.019 1.01 9.82 .435 .420 1.12 11.3
1.00 .410 1.13
1.95 .188 2.192 1.5/0.6 4.63/.019 1.90 18.9 .166 .175 2.20 21.3
1.90 .172 2.06
2.70 .119 3.453 2.0/0.6 6.17/.019 2.86 27.7 .122 .119 3.83 36.4
2.86 .116 3.78
4.40 .051 4.464 2.5/0.6 7.72/.019 4.61 44.5 .050 .049 4.92 46.4
4.51 .046
6.71 .023 10.55 3.0/0.6 9.26/.019 6.32 45.1 .027 .024 15.1 158
6.74 .021 22.3
9.08 .020 12.26 3.5/0.6 10.8/.019 8.46 89.2 .026 .022 19.6 190
9.52 .021 25.9
12.0 .015 44.57 4.0/0.6 12.3/.019 11.7 124 .014 .014 43.0 406
14.0 .012 35.6
12.0 .020 45.28 4.0/0.6 12.3/.019 13.7 131 .015 .017 42.4 444
14.1 .015 47.2
Initial Volume (1): 34.2Initial Relative Density: 4.19Initial iH/D)6 1.0Temperature ( C): 28.3Pressure ( m Hq): 734.4Relative Humidity: 54%
V 13 (S) .324
S[vl/1 (q&)j1/2 ) 0.102
B-15
Experiment: B08830
Max.Radius (a) R/V1 /3 Time Obs. Time
of Mole ofChannel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) TOA(s) TOA/r PEAK PEAK TOP(s) TOP/
1.26 0.0021 2.951 1.5/16. 4.0/0.423 2.78 18.5 0.0006 -- --
1.56 0.426 1.662 1.5/0.6 4.0/0.016 1.59 14.4 0.304 .365 1.73 15.5
5.52 0.015 6.073 2.9/8.0 7.7/0.212 5.67 51.1 0.020 .017 5.87 54.5
5.08 0.060 6.224 2.9/0.6 7.7/0.016 5.40 47.9 0.053 .056 6.66 58.8
NR NR5 2.9/16. 7.7/0.423 NR -- NR -- -- --
13.3 0.0054 14.76 4.1/8.0 10.8/0.212 12.9 120 0.0072 .0063 13.1 127
12.8 0.015 28.57 4.1/0.6 10.8/0.016 12.7 116 0.014 .015 31.2 273
NR R8 4.1/16. 10.8/0.423 NR -- NR -- --
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D)S 1.0Temperature ( C): 18.8Pressure (m Hg): 732.9Relative Humidity: 62%
V1/3 (a) 0.378
S1/ 3 (qa)iJ112 S) 0.110
B-16
Experiment: B09830
Max.Radius (m R/V Time Obs. Time
1 of Mole ofChannel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) . TOA(s) TOA/ PEAK PEAK TOP(S) TOP/
1.67 0.095 2.831 1.5/6.0 4.0/0.159 1.58 14.8 0.154 .125 1.64 15.9
1.52 0.401 1.552 1.5/0.6 4.0/0.016 1.52 13.9 0.308 .355 1.81 15.3
5.21 0.038 5.683 2.9/3.0 7.7/0.079 4.88 46.0 0.047 .042 4.90 48.3
5.25 0.069 6.894 2.9/0.6 7.7/0.016 4.94 46.5 0.060 .064 8.20 68.9
5.26 0.027 5.625 2.9/6.0 7.7/0.159 5.01 46.9 0.028 .028 5.10 49.0
NR NR NR6 4.1/3.0 10.8/0.079 10.0 NR NR
NR NR NR7 4.1/0.6 10.8/0.016 10.3 NR NR
NR NR NR8 4.1/6.0 10.8/0.0159 10.3 NR NR
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D): 1.0Temperature ( C): 18.0Pressure (mm Hq): 730.0Relative Humidity: 62%V1/3 (m) * 0.378
i
[Vl, 3 /(g&,)i]112 s)=0.110
B-17
Experiment: B11830
Max.Radius (a) R/V 3 Time Obs. Time
of Mole ofChannel Arrival Avg. Fraction Avg. PEAK( Avg.Nuaber Height (cm) TOA(s) TOA/T PEAK PEAK TOP(s) TOP/-r
1.72 0.252 1.931 1.5/0.6 4.0/0.016 1.62 15.3 0.322 .304 1.81 17.1
1.68 0.337 1.88
1.72 0.144 1.782 1.5/4.0 4.0/0.106 1.67 15.6 0.141 .149 1.82 16.4
1.72 0.161 1.79
5.49 0.053 6.383 2.9/0.6 7.7/0.016 5.44 50.4 0.060 .055 7.71 66.4
5.64 0.053 7.73
5.63 0.042 5.994 2.9/4.0 7.7/0.106 5.57 52.2 0.037 .035 5.62 54.6
5.95 0.026 6.34
6.00 0.012 6.175 2.9/11.0 7.7/0.291 A 54.8 A ....
11.90 0.019 15.16 4.1/0.6 10.810.016 12.0 114 0.017 .016 14.1 163
13.6 0.013 24.3
12.1 0.015 13.67 4.1/2.0 10.8/0.053 11.9 114 0.014 .014 12.2 120
13.2 0.013 13.7
12.3 0.0080 13.28 4.1/4.0 10.8/0.106 12.0 114 0.0094 .0085 12.3 120
13.3 0.0080 13.8
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D): 1.0Temperature (6C): 19.8Pressure (mm Hq): 734.4Relative Humidity: 43%V1 /3 (a) - 0.378i
*[V11 3 / q&6']112 s)-0.110
ANo significant gas levels were detected.
B-18
Experiment: B15830
Max.Radius (m) R/V1 /3 Time Obs. Time
C of Mole ofChannel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) H/V. TOA(s) TOA/T PEAK PEAK TOP(s) TOP/i:
1.56 0.297 1.841 1.5/0.6 4.0/0.016 1.58 14.8 0.281 .304 1.83 16.8
1.73 0.333 1.86
1.57 0.223 1.82- 1.5/2.0 4.0/0.053 1.59 14.9 0.194 .193 1.75 16.5
1.73 0.163 1.87
3.11 0.116 3.673 2.2/0.6 5.8/0.016 3.20 29.8 0.111 .108 3.97 35.5
3.49 0.096 3.83
3.12 0.091 3.194 2.2/4.0 5.8/0.106 3.23 29.6 0.079 .076 3.32 30.6
3.37 0.056 3.55
3.30 - 0.023 3.485 2.2/8.0 5.8/0.212 3.27 31.5 0.040 .026 3.39 34.4
3.79 0.016 4.43
8.66 0.022 10.26 3.5/0.6 9.25/0.016 7.71 75.6 0.031 .027 8.73 88.1
8.46 0.027 10.0
8.82 0.012 9.407 3.5/4.0 9.25/0.106 7.92 77.7 0.024 .018 8.00 80.7
8.79 0.018 9.11
9.21 0.007 9.368 3.5/8.0 9.25/0.212 8.24 81.3 0.012 .0074 8.54 83.1
9.24 0.004 9.39
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (HI/D) 1.0Temperature I C): 21.5Pressure (mm Hg): 734.8Relative Humidity: 47%V1 / 3 (m) * 0.378iT [Vl fqg ,)i] 2 (s) • 0.110
. .. .... .. ... .. . .... .... -- e .
B-19
Experiment: B16830
Max.Radius (m) R/V1 /3 Time Obs. Time
1 of Mole of
Channel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) H/V 3 TOA(s) TOA/r PEAK PEAK TOP(s) TOP/'
1.65 0.322 1.731 1.5/0.6 4.0/0.016 1.66 15.3 0.266 0.294 1.95 17.0
1.71 0.294 1.91
1.87 0.051 1.952 1.5/8.0 4.0/0.212 1.82 16.8 0.042 .052 2.17 18.2
1.82 0.063 1.86
3.30 0.120 3.713 2.2/0.6 5.8/0.016 3.28 29.7 0.14 .121 3.90 34.5
3.19 0.11 3.73
3.68 0.034 3.794 2.2/6.0 5.8/0.159 3.33 31.8 0.045 .037 3.41 33.2
3.44 0.032 3.71
3.89 0.013 4.035 2.2/11.0 5.8/0.291 A 35.5 A A
8.54 0.024 13.46 3.5/0.6 9.25/0.016 8.77 79.2 0.019 .020 10.2 107.
8.72 0.016 11.6
8.52 0.016 8.637 3.5/6.0 9.25/0.159 9.46 81.3 0.0049 .0092 9.77 82.9
8.72 0.0070 8.83
8 3.5/11.0 9.25/0.291 -- -- -- -- --
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D)' 1.0Temperature C C). 21.6Pressure (m Hg): 735.8Relative Humidity: 42%
V1/3 (a) - 0.378
T [V/ 3 / (ga,)]/ 2 (S) . 0.110
ANo significant gas levels were detected.
mt
B-20
Experiment: 424844
Max.Radius (a) R/V1/ 3 Time Obs. Time
1 of Mole of
Channel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) H/V TOA(s) TOA/T PEAK PEAK TOP(s) TOP/T
0.89 0.698 1.011 1.0/0.6 2.65J.016 0.86 7.95 0.562 .605 0.90 9.13
0.86 0.555 1.09
0.89 0.555 0.992 1.0/2.0 2.65/.053 0.89 8.07 0,676 .609 1.03 8.9z
0.87 0.596 0.91
2.07 0.242 2.273 1.8/0.6 4.76/.016 2.20 19.5 0.187 .206 2.38 22.1
2.13 0.188 2.62
2.00 0.211 2.064 1.8/2.0 4.76/.053 2.03 18.4 0.166 .167 2.07 19.1
2.02 0.124 2.13
2.19 0.112 2.225 1.8/6.0 4.76/.159 2.28 20.4 0.055 .065 2.43 21.2
2.24 0.026 2.32
3.98 0.097 5.016 2.4/0.6 6.35/.016 3.74 35.9 0.114 .100 4.49 43.6
4.06 0.090 4.81
3.76 0.075 4.507 2.4/2.0 6.35/.053 3.90 35.0 0.069 .072 4.33 40.0
3.82 0.073 4.30
4.05 0.029 4.528 2.4/6.0 6.35/.159 3.85 36.8 0.020 .020 4.14 39.3
4.18 0.012 4.26
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (HID16 1.0Temperature ( C): 23.6Pressure (= Hq): 726.2Relative Humidity: 44%
Vi1 3 (a) * .378
[V1/3 (q&)]1/2 3) *0.110
B-21
Experiment: 426840
Max.Radius (a) R/V/ 3" Time Obs. Time
of Mole ofChannel 1/3 Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) H/V / TOA(s) TOA/T PEAK PEAK TOP(s) TOP/t
0.89 .589 1.071 1.0/0.6 2.65/.016 0.85 7.96 .712 .671 0.87 8.63
0.86 .711 0.89
0.92 .364 0.932 1.0/4.0 2.651.106 0.92 8.29 .375 .374 1.04 8.72
0.88 .382 0.89
2.02 .194 3.223 1.8/0.6 4.76/.016 2.17 19.5 .189 .202 2.92 25.5
2.19 .222 2.23
2.03 .126 2.054 1.8/4.0 4.761.106 2.05 18.5 .099 .110 2.11 19.1
2.00 .106 2.11
2.33 .021 2.365 1.8/8.0 4.76/.212 2.40 21.6 .034 .037 2.56 22.3
2.37 .057 2.40
3.68 .083 4.426 2.4/0.6 6.35/.016 3.52 33.1 .109 .091 4.29 42.0
3.66 .082 5.07
3.80 .054 3.927 2.4/4.0 6.35/.106 3.64 34.6 .061 .059 3.68 35.4
3.90 .062 4.01
4.03 .0034 NRa 2.4/8.0 6.35/.212 3.87 36.4 .0074 .0050 3.99 36.9
4.04 .0043 4.07
Initial Volume (I): 54.1Initial Relative Density: 4.19Initial (H/D)6 1.0Temperature ( C): 25.5Pressure (mm Hg): 722.6Relative Humidity: 54%
V 1 3 (a) s .378
S[1/ 3/ C 0.110
B-22
Experiment: 430840
Max.Radius m R/V1 1 3 Time Obs. Time
L of Mole of
Channel Arrival Avg. Fraction Avg. PA Avg.Number Height (cm) H/i TOA(sa TOA/T PEAK PEAK TOP(s) TOP/t
0.89 0.620 1.081 1.0/0.6 2.651.016 0.89 8.13 0.515 .586 1.11 9.44
0.89 0.623 0.91
0.96 0.285 0.972* 1.0/6.0 2.651.159 0.93 8.68 0.148 .235 0.94 8.83
0.96 0.203 0.99
2.63 0.169 2.843 2.0/0.6 5.291.016 2.81 24.7 0.148 .156 2.95 28.4
2.68 0.152 3.53
2.70 0.138 2.974 2.0/2.0 5.29/.053 2.50 23.9 0.131 .129 2.58 25.5
2.66 0.118 2.82
2.82 0.037 2.905 2.0/6.0 5.29/.159 2.98 26.4 0.044 .044 3.13 27.3
2.85 0.050 2.93
4.31 0.075 4.796 2.6/0.6 6.88/.016 4.34 40.7 0.095 .084 4.98 46.5
4.72 0.081 5.50
4.13 0.078 4.617 2.6/2.0 6.88/.0 3 4.31 39.3 0.075 .068 5.12 43.5
4.48 0.052 4.55
4.47 0.020 4.528 2.6/6.0 6.881.159 4.46 41.9 0.028 .022 4.62 42.7
4.84 0.018 4.88
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (HID)' 1.0Temperature ( C): 25.0Pressure (im Hq): 738.6Relative Humidity: 45%
V/3 () .378
[ /1 (96,)1]112 (a) . 0.110
hCaliration subject to question.
B-23
Experiment: 501841
1/3 Max.Radius (m R/V1 /3 Time Obs. Time
a of Mole of
Channel - /3 Arrival Avg. Fraction Avg. PEAK Avg.Number Height (c) H/V. TOA(s) TOAiT PEAK PEAK TOP(s) TOP/
.88 NR MR1 1.0/0.6 2.65/.016 .87 8.04 NR -- NR --
.88 NR NR
.98 .220 1.012 1.0/8.0 2.65/.212 .99 9.14 .0929 .150 1.15 9.80
1.03 .137 1.05
2.73 .126 3.493 2.0/0.6 5.29/.016 2.84 25.9 .124 .120 3.51 32.2
2.92 .116 3.58
2.59 .100 2.644 2.0/4.0 5.29/.106 2.75 24.1 .092 .097 3.10 25.7
2.58 .099 2.70
2.98 .020 3.155 2.0/8.0 5.29/.212 3.02 27.6 .027 .027 3.07 28.9
3.05 .034 3.26
4.60 .062 6.166 2.6/0.6 6.88/.016 4.59 40.7 .070 .070 5.81 51.4
4.18 .077 4.91
4.48 .031 4.572.6/4.0 6,88/.106 4.42 40.4 .045 .042 4.63 41.6
4.37 .044 4.44
4.76 .012 4.818 2.6/8.0 6.88/.212 4.86 43.6 .0079 .010 5.21 45.8
4.68 HR NR
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D)= 1.0Temperature (°C): 26.5Pressure (m Hq): 732.5Relative Humidity: 42%Vl3 (a) * .378
V1 /3 (q&,)11 12 (s) 0.110
B-24
Experiment: 507840
Max.Radius im R/V Time Obs. Time
of Mole ofChannel Arrival Ava. Fraction Avg. PEAK Avg.Number Heiaht (cM) H/" TOAs) TOA/T PEAK PEAK TOP(s) TCP/T
0.92 0.607 1.20..30.6 2.65'.016 0.87 8.14 0.672 0.637 0.97 10.0
0.88 0632 1.12
0.86 0.582 1.071.0/0.6 2.65/.016 0.90 8.14 0.543 0.578 0.91 9.39
0.90 0.609 1.10
2.64 0.143 3.3632.0/0.6 5.29/.016 2.63 25.1 0.159 0.143 3.22 30.5
2.96 0.128 3.43
2.60 0.163 2.914* 2.0/0.6 5.29/.016 2.80 24.5 0.149 0.149 3.36 27.8
2.64 0.135 2.85
2.80 0.056 2.875 2.0/6.0 5.29/.159 2.81 26.4 0.034 0.051 3.00 27.3
3.04 0.064 3.08
4.28 0.094 5.996* 2.6/0.6 6.88/.016 4.60 40.2 0.084 0.088 5.66 52.2
4.29 0.087 5.47
4.14 0.090 5.0874 2.6/0.6 6.88/.016 4.50 40.0 0.077 0.082 5.52 48.2
4.47 0.077 5.20
4.36 0.035 4.418 2.6/6.0 6.88/.159 4.68 40.9 0.032 0.028 4.75 41.8
4.39 0.018 4.56
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (HID) 1.0Temperature 6C): 21.1Pressure (a 8q): 733.8Relative Humidity: 75%V1 /3 (a) .378
S 113/ (qL,)i (s) * 0.110
*Filters removed from these sensors.
B-25
Experiment: 508840
1/3 Max.Radius (a) R/V3 Time Obs. Time1 of Mole of
Channel Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) H/Vi TOA(s) TOA/ PEAK PEAK TOP(s) TOP/
0.90 .607 1.05i* 1.0/0.6 2.65/.016 0.88 8.04 .681 0.644 0.91 9.32
0.86 .644 1.09
0.89 .654 1.172 1.0/0.6 2.65/.016 0.87 8.04 .767 0.693 0.88 9.7
0.88 .657 1.14
2.86 .126 3.473 2.0/0.6 5.29/.016 2.89 25.7 .122 0.134 3.69 32.1
2.68 .155 3.39
2.64 .198 3.0640 2.0/0.6 5.29/.016 2.68 24.5 .172 0.179 2.99 28.7
2.73 .166 3.37
2.96 .063 3.315^ 2.0/6.0 5.29/.159 2.97 26.5 .078 0.076 3.02 28.1
2.77 .087 2.89
4.26 .084 5.726 2.6/0.6 6.88/.016 4.51 40.1 .059 0.076 4.62 48.3
4.39 .085 5.52
4.08 .101 5.317A 2.6/0.6 6.88/.016 4.08 40.0 .084 0.090 4.84 47.7
4.31 .084 5.52
4.44 .0023 4.478A 2.6/6.0 6.88/.159 4.58 41.2 .0025 0.0046 4.79 42.1
4.51 .0089 4.57
Initial Volume (1): 54.1Initial Relative Density: 4.19Initial (H/D). 1.0Temperature ( 6C): 22.1Pressure (ma Hq): 739.1Relative Humidity: 54%V 1/3 (a) .378vi
=[V113 /(gA.),]l
1 2 (3) . 0.110
*Filters removed from these sensors.
B-26
Experiment: 706840
1/3 Max.Radius (m) R/V Time Obs. Time
1 of Mole ofChannel l/I3 Arrival Ava. Fraction Avg. PEAK Avg.Number Height (cm) . TOA(s) TOA/r PEAK PEAK TOP(s) TOP/T
0.451* 1.0/0.6 1.23/.0074 0.46 2.84 *
0.84 0.877 1.042 1.6/0.6 1.97/.0074 0.83 5.22 0.866 .872 0.90 6.1
1.37 0.585 1.873* 2.410.6 2.961.0074 1.36 8.53 0.642 .614 1.91 11.8
1.97 0.526 3.834* 3.2/0.6 3.94/.0074 2.14 12.8 0.387 .457 3.53 23.0
3.20 0.299 3.595 4.05/0.6 4.99/.0074 3.45 20.8 0.223 .261 5.72 22.8
4.41 0.182 5.346* 4.7/0.6 5.79/.0074 4.10 26.6 0.176 .179 5.08 32.6
5.75 0.187 7.257* 5.5/0.6 6.77/.0074 5.76 36.0 0.142 .165 7.69 46.7
7.41 0.116 9.818* 6.4/0.6 7.88/.0074 7.70 47.2 0.123 .120 10.1 62.3
Initial Volume (1): 535Initial Relative Density: 4.19Initial (H/D)6 1.0Temperature ( C): 25.7Pressure (m Hg): 733.1Relative Humidity: 64%
V113 (a) .812i
v '/ (qa')i]1/2 Is) . 0.161
*Filters removed from these sensors.**Sensor saturated.
B-27
Experiment: 710840
1/3 Max.Radius (a) RIV.I Time Obs. Time- of Mole of
Channel /1/3 Arrival Avg. Fraction Avg. PEAK Avg.Number Height (cm) H/V. TOA(s) TOA/T PEAK PEAK TOP(s) TOP/T
0.45 .989 0.68I* 1.0/1.3 1.23/.016 0.46 2.84 .944 .962 0.81 4.66
0.82 .944 0.892 1.6/1.3 1.97/.016 0.85 5.22 .830 .887 0.87 5.50
1.44 .662 1.783A 2.4/1.3 2.96/.016 1.31 8.60 .610 .636 1.38 9.88
2.32 .390 2.574* 3.2/1.3 3.941.016 2.09 13.8 .308 .349 2.50 15.9
3.45 2.47 3.685 4.05/1.3 4.99/.016 3.39 21.4 .198 .223 4.12 24.4
4.14 .152 4.65
6A 4.7/1.3 5.79/.016 4.50 27.0 .111 .132 5.01 30.2
5.46 .128 6.5370, 5.5/1.3 6.77/.016 6.05 36.3 .104 .116 7.34 43.4
6.97 .089 8.488A 6.4/1.3 7.88/.016 7.80 46.2 .089 .089 9.32 55.6
Initial Volume (1): 535Initial Relative Density: 4.19Initial (H/D)- 1.0Temperature ( C): 28.0Pressure (ma Hg): 735.1Relative Humidity: 14%V1 / 3 (m) = .812
[V1 / (ga, 1]1 2 (s) - 0.161
AFilters removed from these sensors.
c-1
APPENDIX C
CALCULATION OF AVERAGE CLOUD CONCENTRATION
The result of the experimental program described in Section
III was a large number of concentration time series at several
locations for a particular release type (Appendix A). The most
obvious parameters available from these traces were the time of
arrival (TOA) of the cloud, the Deak gas concentration, and the
time when the peak occurred (TOP). However, in order to compare
the data with predictions of a spatially averaged model (i.e. a box
model), the data itself must be spatially averaged. Superimposed
on the spatial average of the measured concentrations, a temporal
average is necessary in order to try and eliminate such questions
as sensor frequency response, concentration fluctuations due to
the turbulence, and variability of the experiment. Large
averaging times alleviate these problems, but too large an
averaging time will unduly reduce the average concentration. Note
~t)
that this is not true for determining the exposure f( t as a
0
function of time. The 54.1 1 and (HID). = 1.0 experiments were
chosen to make vertical concentration measurements in order to
determine an average concentration.
The first step in determining the "average" (in space and time)
concentration from the data was to determine the time period overwhich the concentration time series for each sensor would be
averaged. The following outline was used for a particular radius
where concentration data were taken:
C-2
(1) tl:= earliest TOA at the lowest sensor
(2) t2:= latest TOP at the highest sensor
(3) t0 := (t1 + t 2 ) / 2
At:= (t 2 - t l ) /2
It should be noted that for t3 := latest TOA at the highest sensor,
tI < t3 < t2 always held. With to and At defined, the concentration
data for each sensor were averaged over a centered time interval
(2At) about tO using
y(r,z,t) = 2t y(r,z,t) dt (C-l)
to-At
This temporal average over the specified At was carried out for
each sensor position in the cloud at the specified to. Note that
the parameters t0 and At were different for each cloud radius R.
Using these ideas, concentration as a function of height was
summarized for each experiment, and the experiments were averaged
for each run (a set of 2 or 3 experiments). From these numbers,
two methods for determining an average concentration were pursued.
A local cloud height H(r,t), defined as the height where the cloud
concentration is zero, was determined by linear interpolation and
extrapolation as follows:
(1) If the top sensor showed the presence of gas, H(r,t)
was estimated by linear extrapolation between
concentrations. Let Yi and zi denote the concentration
and height at the top sensor and Yi-l and zi- l denote
the same quantities for the next lowest sensor. Then
H(r,t) = zi + -_ (z i - zi- l ) (C-2)-l Yi
C-3
unless > in which case
H(r,t) z i (C-3)
(2) If the top sensor showed no gas present, the same
procedure as above was used except that position i
denotes the top sensor in the gas cloud. If the
value of H(r,t) exceeded the height of the lowest
sensor not in the gas cloud (i + 1), the local height
was set to this position (i.e. H(r,t) = zi+l).
(3) If only one sensor showed the presence of gas, the
cloud height was estimated as the average height of
the two lowest sensors. Or,
H(r,t) = (z1 + z2 ) / 2 (C-4)
With the local cloud height known, the volume of the cloud was
determined by
R H(r,t) R
R2 H= 2 rJ J r dzdr = 2r rH(r,t) dz (C-5)
0 0 0
using the tradezoidal rule. Note that the time dependency on R andH is not explicitly noted. Appealing to the conservation of mass,
the time-dependent averaged concentration is given by
ViH (C-6)
where Vi denotes the initial cloud volume.
The second approach for estimating y is to estimate the
integralR H(r,t)
TR2H = 21rf f y(r,z,t) dzrdr (C-7)
0 0
C-4
H(r,t)
since J y(r,z,t) dz is easily estimated using the trapezoidal
0
rule and the concentration data. First, however, i(r,O,t) = 76
must be estimated. The following rules were used for each run:
(1) If the two lowest sensors showed the presence of gas,
the ground level concentration was estimated by linear
extrapolation. Or,
+o = y1 + ( l 2 z (C-8)
If yo > 1.1 y , the yo0 was set to yl.
(2) If only one sensor showed the presence of gas, YO = Yl.
Upon completion,
- RZH (C-9)
2-Of course, the quantity nR Hy should be conserved and there-
fore represents a measure of the accuracy of the data. The reported
values are summarized below.
C-5
TABLE C-1
ESTIMATED AVERAGE CONCENTRATION FOR RELEASE OFPURE FREON-12, Vi = 54.1 1, and (H/D)i = 1.0
Time rrR 2 H Vi IR 2 HT V il
(tO + 6t) Radius R2 H Viir R H ~ RTH1
(s) (m)
1.00 1.11 0.168 0.132 0.27
2.23 1.84 0.067 0.103 0.35
3.69 2.36 0.043 0.057 0.24
8.08 3.49 0.030 0.026 0.14
