EPA/600/A-97/079
7A.11
LABORATORY OBSERVATIONS OF THE RISE OF BUOYANT THERMALS
CREATED BY OPEN DETONATIONS
Roger S. Thompson*
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina
William H. Snyder
University of Surrey
Guildford, Surrey, England
Jeffrey C. Weil
National Center for Atmospheric Research
Boulder, Colorado
1. INTRODUCTION
The most common method of disposing of obsolete
munitions is by open detonation in an earthen pit.
Typically, small quantities (up to 500 Ibs.) are destroyed
in a detonation that creates a buoyant, turbulent cloud or
thermal which contains contaminants and rises through
the atmosphere. The detonations are scheduled for
daytime when the atmospheric conditions can be
described as a convective boundary layer surmounted by
a temperature inversion. Detonating larger quantities
would result in more complete combustion and more
economic disposal of the munitions. The environmental
effects of detonating larger quantities are being evaluated
with new dispersion models (Weil, et al, 1996) which
require new experimental data and descriptive algorithms
for their development and testing.
Laboratory experiments were carried out in a water
tank at the Fluid Modeling Facility of the U.S.
Environmental Protection Agency to study the rise and
growth of buoyant thermals and their penetration through
elevated density changes and into elevated stable layers.
A dense volume of salt water (herein referred to as a
thermal) was released at the top of the tank and observed
as it fell 1) through water of constant density, 2) through
a constant-density layer into a layer of greater density
with a step-change at the interface, or 3) through a
constant-density layer into a layer with a linear increase
of density with depth. The falling volume of water
simulated a buoyant thermal rising through the
atmosphere where density decreases with height. These
density profiles are first approximations to the profiles
observed during convective atmospheric conditions.
Visual observations and video recordings were used
to determine the rise and growth of the thermals as well
as estimates of the fraction of the thermal that penetrated
a step-change interface. Observations and concentration
measurements were used to determine the maximum
* Corresponding author address: Roger S, Thompson,
MD-81, National Exposure Research Laboratory, U.S.
Environmental Protection Agency, Research Triangle
Park, NC 27711; thompson.roger@epamail.epa.gov.
penetration distance and equilibrium height of thermals
that encounter an elevated linear gradient.
A criterion was obtained for predicting when a
thermal will penetrate a step-change in density as a
function of its initial buoyancy, the magnitude of the step-
change and the height of the interface. The maximum
penetration distance and equilibrium heights for the
elevated gradient cases are presented graphically.
2. EXPERIMENTAL DETAILS
The experiments were conducted in the towing tank
at the EPA Fluid Modeling Facility. The tank is 3.6 m wide
and was filled to a level of 108 cm using salt water. By
varying the salinity, the desired density stratification was
obtained. Thermals were simulated with the release of a
150 cm3 mixture of salt water and blue food dye from a
10-cm-diameter hemispherical cup. The cup was lowered
into the water until the surface of the fluid in the cup was
level with the water surface in the tank. By quickly
rotating the cup, its fluid was released with roughly the
initial shape of a thermal created by a detonation. This
technique has been used by Richards (1961) and
Saunders (1962) who performed similar experiments.
Releases into neutral and step-change environments
were made first. A video camera was used to record a
time history of the trajectory and growth of each thermal;
a mirror to the side at 45° provided a side view in addition
to the direct front view. Several frames of the video
recording of each thermal were input to a personal
computer and analyzed to determine the depth of the
leading edge, the depth of the centroid, the horizontal
dimension (diameter), and vertical thickness from both
front and side views. These dimensions were used to
compute the volume of the thermal by approximating its
shape as an oblate spheroid. For the experiments with a
neutral layer followed by a linear increase in density, a
visual observation of the maximum penetration distance
was made. In addition, the equilibrium height of the
thermal was computed from the concentrations of dye
samples collected with an array of sample ports that were
moved through the thermal after it reached its equilibrium
height.
-------
3, RESULTS
The variables used to describe the position of a
thermal are defined in Fig. 1 in an atmospheric setting
where z is measured upward from the earth's surface.
The height of the centroid of the thermal is zc and the
distance to the virtual origin, below the surface, where the
thermal can be considered to have originated at a point is
Zy. The height to the step-change interface or base of the
elevated linear gradient is z.,. For the tank experiments,
z was measured positive downward from the water
surface. To keep an atmospheric perspective, we will
discuss the laboratory results as if the tank were inverted;
that is, the falling volume of fluid will be described as a
rising thermal with its properties defined in terms of its
height.
Figure 1. Variables to describe the rise of a
thermal in the atmosphere.
Thermals with high buoyancy compared to the
density difference at the interface will completely
penetrate into the upper -layer and continue to rise
indefinitely; Thermals with less buoyancy may, because
of their momentum, penetrate beyond :he interface only
to have a fraction return to the interface as the momentum
fades. The weakest thermals will not penetrate the
interface at all. In describing the final fraction of a thermal
that penetrates a step change Pf, Richards (1961) defined
a parameter S as a measure of the strength of the
interface relative to the buoyancy of the thermal. By
adapting his expression to the atmosphere, we get
S=V(p,-p2)/B, where V is the volume of the thermal when
it is centered on the interface (we use the volume when
the centroid is at z,), p,-p2 is the density difference
between the lower and upper layers and B is the mass
deficit of the thermal at its release (initial volume times its
density subtracted from that of an equal volume of the
surrounding fluid). In the water tank, B is replaced by M,
a similarly defined mass excess, and the density
difference is reversed. A comparison of our
determinations of Pf with those of Richards is shown in
Fig. 2 where it is seen that our results have a similar slope
but are offset to larger values of S. Based on the
following intuitive argument, our results seem more
reasonable. As a thermal with a value of S less than 1
approaches the interface, its average density is less than
that in the upper layer. Given this and its momentum, the
thermal may be expected to continue rising, resulting in
essentially total penetratbn. Our results are in better
agreement with this argument; Richards' results suggest
Pf of only 0,5 when S=0.9.
Figure 2. Final penetration versus Richards' S (uses-
measured volume). Open symbols and dashed line
are from Richards (1961).
-------
Because the volume of the thermal when it is
centered on the interface is not known prior to the
detonation, Richards' formula is not very useful in
modeling applications. To obtain a predictive formula, we
define a parameter A=Vp(p1-p2)/B, where V. is the
predicted volume of the thermal when its centroid is at the
interface. An expression for Vp as a function of z was
obtained from values computed from the video recordings
of the thermals. As shown in Fig, 3, for thermals in a
neutral environment and those encountering a step-
change in density with a P( 2 0.5, the volume can be
described by 0.058(zc-»-zv)3. Thermals that have a lower
final penetration, P, < 0.5, have a somewhat larger
volume. Using the volume formula above in our
expression for A (with zc=z1, i.e. Vp=0.058(z1-*-zv)3) we
obtain the results shown in Fig. 4. A vertical line at
4=1.35 divides the data into cases with large P, and
cases with low P, and leads to the simple criterion ,that
thermals penetrate for A < 1.35 and do not penetrate for
A a 1.35.
50000
'• step-change environment; P(>0.5
. o step-change environment; P, < 0.5
1 neutral environment
10000
o
1
1000
30
40 50
zc+zv, cm
60
Figure 3, Average measured volumes for all releases
into step-change and neutral environments.
When a thermal in the tank enters an elevated
gradient (layer of linearly increasing density), its
momentum causes it to overshoot its equilibrium height.
It will then reverse direction and soon approach an
equilibrium position. The maximum penetration distance
1 •
9
•
.8 -
.7 •
.6 •
.5 •
.4 •
.3 •
.2 -
.1 •
i t '
* ••*
• <
•
*
4
*•
<
•
l
1 I
1 1 1
»*
1* •
•
•
«
* Y
i
i
»* *
m mm .... ' •
Figure 4. Final penetration versus A.
type. After the thermal was seen to reach its equilibrium
height, an array of 100 sample tubes was drawn through
the thermal collecting water samples that were analyzed
for dye concentration. From these concentrations, the
vertical distribution of the dye in the thermal was
determined and used to calculate the height of its centroid
zeq. The values of these variables are shown in Fig. 5
plotted against PT, a measure of the initial buoyancy of
the thermal divided by the strength of the density gradient,
This nondimensional parameter is defined by
pT=FT1M/[(z1+zv)N1/2Jt where FT is the buoyancy of the
thermal and N is the Brunt- Valsala frequency of the stable
layer. In the water tank, FT=Bg/p, where g is the
acceleration due to gravity, p, is the density of the neutral
layer, and jV2=-&| -£• , where —£. is the density gradient
in the stable layer. While in the atmosphere, Fr= —.
where QT is the heat content of the thermal, cp is the
specific heat of air, pa is the density of air, 8a is the
potential temperature of the ambient air, and
, where — is the gradient of the potential
dz
of the leading edge of the thermal zmx was visually temperature in the stable layer. The solid line through the
observed and recorded during each experiment of this P°ints for z™ IS the theoretical prediction of Saunders
-------
(1962) with his constants evaluated using the empirical
results of this study. It is seen to provide a good fit to the
data. We know of no theoretical expression for zeq, but
given the prediction of zmx, a corresponding value of zeq
can be estimated from the empirical expression
(Zeq-z1)/(z1+ztf)=0.47[(zmx-z1)/(zl+zv)]1^2 shown as a
dashed line in Fig. 5.
N
•f
1.5
N
.5 •
dp/dz = 0.0001 gm/cm
dp/dz = 0.0004 gm/cm4
dp/dz = 0.0001 gm/cm4
dp/dz = 0.0004 gm/cm4.
5. ACKNOWLEDGEMENTS
The authors wish to acknowledge Mr. Van Hursey
and Mr. G. Leonard Marsh of Geophex, Ltd. for their
support in the laboratory setup, data collection and data
analysis portions of this experimental study.
6. REFERENCES
Lawson, R.E. Jr., Snyder, W.H., and Shipman, M.S. 1998;
A laboratory model of diffusion in the convective boundary
layer. Preprints 10th Joint Conference on Applications of
Air Pollution Meteorology with the AWMA, Amer. Meteor,
Soc., Boston.
Richards, J.M., 1961: Experiments on the penetration of
an interface by buoyant thermals. J. Fluid Mech., 11, 369-
384.
Saunders, P.M., 1962; Penetrative convection in stably
stratified fluids. Tellus, 14,178-194.
Weil, J.C., Templeman, B.T., Banta, R., and Mitchell, W.
1996; Dispersion model development for open burn/open
detonation sources. Preprints 9th Joint Conference on
Applications of Air Pollution Meteorology with AWMA,
Amer. Meteor. Soc., Boston, 610-616.
DISCLAIMER: The information in this document has been
funded by the U.S. Environmental Protection Agency. It
has been subjected to the Agency's peer and
administrative review and approved for publication.
Mention of trade names or commercial products does not
constitute commercial endorsement or recommendation
for use.
Figure 5. Maximum penetration height beyond interface
(solid symbols) and equilibrium height of centroid (open
symbols) for elevated gradient environments.
4. SUMMARY AND DISCUSSION
Laboratory results have been presented that can be
used in the development of dispersion models for
assessing the impact of detonation of surplus munitions.
In particular, a simple criterion for predicting the
penetration of a thermal through a step-change in density,
data to support a theoretical prediction of the maximum
height, and an empirical expression for the equilibrium
height of thermals that encounter an elevated temperature
gradient will provide basic algorithms for such models.
Further work is underway in a convection tank (Lawson,
et at., 1998) with a heated floor and an elevated
temperature gradient to more closely model the
convective nature of the atmosphere.
-------
• • . TECHNICAL
REPORT DATA
1. REPORT NO. 2.
EPA/600/A-97/079
4. TITLE AND SUBTITLE
Laboratory observations of the rise of buoyant thermals created
detonations
by open
7. AUTHOR(S)
'Thompson, R.S., 2W.H. Snyder, and 3J.C. Weil
9. PERFORMING ORGANIZATION NAME AND ADDRESS
'Same as Block 12
2Universtiy of Surry
Guilford, Surrey, England
'National Center for Atmospheric Research
Boulder, CO
12. SPONSORING AGENCY NAME AND ADDRESS
National Exposure Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 277 1 1
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
10.PROGRAM ELEMENT NO.
1 1 . CONTRACT/GRANT NO.
13.TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/9
IS. SUPPLEMENTARY NOTES
16. ABSTRACT
The most common method of disposing of obsolete munitions is by open detonation in an earthen pit. Typically, small quantities
(up to 500 Ibs.) are destroyed in a detonation that creates a buoyant, turbulent cloud or thermal which contains contaminants that
rises through the atmosphere. The detonations are scheduled for daytime when the atmospheric conditions can be described as a
convective boundary layer surmounted by a temperature inversion. Detonating larger quantities would result in more complete
combustion and more economic disposal of the munitions. The environmental effects of detonating larger quantities are being
evaluated with new dispersion models (Weil, et al, 1996) which require new experimental data and descriptive algorithms for
their development and testing.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
^IDENTIFIERS/ OPEN ENDED TERMS o.COSATl
18. DISTRIBUTION STATEMENT
1 9, SECURITY CLASS (This Report) 21 .NO. OF PAGES
20. SECURITY CLASS (This Page) 22. PRICE
------- |