EPA-650/3-74-003
October 1973
Ecological Research Series
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EPA-650/3-74-003
WIND TUNNEL TESTS OF
NEGATIVELY BOUYANT PLUMES
by
T. G. Hoot, R. N. Meroney, and J. A. Peterka
Fluid Dynamics & Diffusion Laboratory
College of Engineering
Colorado State University
Fort Collins , Colorado 80521
Grant AP-01186
Program Element No. 1AA009
EPA Project Officer: Willaim H . Snyder
Meteorology Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
October 1973
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This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
11
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ABSTRACT
WIND TUNNEL TESTS OF NEGATIVELY BUOYANT PLUMES
This study reports the results of tests made of negatively buoyant
emissions into a quiescent medium, laminar crosswind and turbulent
boundary layer. Measurements included the maximum rise height, horizon-
tal point of descent and behavior of emission concentrations.
in
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TABLE OF CONTENTS
Section Page
LIST OF TABLES vi
LIST OF FIGURES vii
LIST OF SYMBOLS ix
I. INTRODUCTION 1
1.1 Negatively Buoyant Emissions 1
1.2 Plume Rise 3
1.3 Moist Plumes 5
1.4 Velocity and Concentration Distributions 6
II. PLUME RISE EQUATIONS 9
2.1 Vertical Plumes in a Quiescent Medium 9
2.2 Bent Over Negatively Buoyant Plume in a Laminar 17
Crosswind
III. CONCENTRATION DETERMINATIONS 25
3.1 Plumes in a Laminar Crosswind 25
3.2 Dense Ground Source in a Turbulent Boundary Layer 27
3.2.1 Eulerian Diffusion Formulation 27
3.2.2 Lagrangian Formulations 29
3.2.3 Wind Tunnel Simulation of Diffusion 31
IV. EXPERIMENTAL MEASUREMENTS 33
4.1 Plume Rise 33
4.2 Concentration Measurements 35
4.2.1 Plumes in a Laminar Crosswind 35
4.2.2 Dense Ground Source in a Turbulent 35
Boundary Layer
V. APPARATUS AND INSTRUMENTATION 37
5.1 Wind Tunnels 37
5.2 Velocity and Temperature Measurements 37
5.3 Gas Mixing and Smoke Visualization 38
5.4 Vortex Generators 39
5.5 Concentration Measurements 40
5.5.1 Measuring Apparatus 40
5.5.2 Tube and Gas Calibration 40
5.5.3 Concentration Calculations and 41
Counting Statistics
VI. RESULTS OF EXPERIMENTS 43
6.1 Plume Rise 43
6.1.1 Vertical Plumes 43
6.1.2 Plumes in a Laminar Crosswind 44
6.1.3 Plume Rise in the Presence of a 46
Cubical Structure
IV
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Section Page
6.2 Concentrations 47
6.2.1 Plumes in a Laminar Crosswind 47
6.2.2 Dense Ground Source in a Turbulent 48
Boundary Layer
6.2.3 Decay of Concentration in Buoyancy 49
Dominated Plumes After Touchdown
VII. CONCLUSIONS 51
BIBLIOGRAPHY 52
TABLES , 55
FIGURES 60
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LIST OF TABLES
Table Page
I VERTICAL PLUMES SMOKE VISUALIZATION DATA 55
II PLUMES IN A LAMINAR CROSSWIND SMOKE VISUALIZATION
DATA 56
VI
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LIST OF FIGURES
Figure Page
1 CSU Thermal Wind Tunnel 60
2 Flow Mixing and Visualization System 61
3 Vortex Generator Details 62
4 Velocity Profile Laminar Flow 63
5 Velocity Profile at Source, Turbulent Boundary 64
Layer
6 Velocity Profiles, Tunnel Centerline, Turbulent
Boundary Layer 65
7 Turbulence Intensities, Tunnel Centerline 66
8 Temperature Profiles, Thermal Stratification 67
9 Gradient Richardson Number, Thermal Stratification 68
10 Radiation Detection System 69
11 Smoke Photographs 70
12 Dimensionless Rise Height vs. Froude Number-
Vertical Plumes 72
13 Dimensionless Rise Height vs. Rise Height Parameter 73
14 Dimensionless "Touchdown" Distance vs. "Touchdown
Parameter" 74
15 Isopleths of Plume in Laminar Crosswind 75
16 Maximum Concentration vs. Downstream Distance
Plumes in a Laminar Crosswind, R=5, D =1/8" 77
17 Maximum Concentration vs. Downstream Distance,
Plumes in a Laminar Crosswind, R=10, D =1/8" 78
18 Maximum Concentration vs. Downstream Distance,
Plumes in a Laminar Crosswind, R=15, D =1/8" 79
19 Maximum Concentration at Plume High Point vs.
H/D 80
VII
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Figure Page
20 Maximum Concentration at Plume Touchdown 81
vs. Fall Parameter
21 Maximum Concentrations vs. Downstream Distance,
Negatively Buoyant Ground Source, Neutral
Stratification 82
22 Maximum Concentrations vs. Downstream Distance,
Negatively Buoyant Ground Source, Inversion
Stratification 83
23 Lateral Spread 50 Percent Concentration Neutral
Stratification 84
24 Lateral Spread 50 Percent Concentration Inversion
Stratification 85
25 Lateral Spread 10 Percent Concentration Neutral
Stratification 86
26 Lateral Spread 10 Percent Concentration Inversion
Stratification 87
27 Vertical Spread 50 Percent Concentration Neutral
Stratification 88
28 Vertical Spread 50 Percent Concentration Inversion
Stratification 89
29 Vertical Spread 10 Percent Concentration Neutral
Stratification 90
30 Vertical Spread 10 Percent Concentration Inversion
Stratification 91
31 Cross-sectional Distribution of Concentration,
x=6 ft. Neutral Stratification 92
32 Decay of Plume Maximum Concentration Downstream
from Touchdown Point 93
van
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LIST OF SYMBOLS
b Plume Radius
b Stack Radius
o
D Stack Diameter
o
e Base of Natural Logarithm
F Flux of Negative Buoyancy
FR "Vertical" Densimetric Froude Number Based on Stack Exit
Velocity, Density and Density Difference
p
RH "Horizontal" Densimetric Froude Number Based on Crosswind
Velocity, Ambient Density and Stack Exit Density Difference
g Gravitational Acceleration
H Maximum Plume Rise Height Above Stack
h Stack Height Above Ground
O
h. Building Height Above Ground
R Velocity Ratio (Stack Exit Velocity Divided by Crosswind
Velocity)
Ri Richardson Number
Re Reynolds Number
S Distance Measured Along Plume
Trajectory From Stack Exit
SG Specific Gravity (Air = 1)
t Time
T Time of Maximum Plume Rise
T , T Reference Temperatures
o' r r
U Boundary Layer Longitudinal Velocity
U Plume Velocity
U Stack Exit Velocity
y Crosswind Velocity
W Plume Vertical Velocity
ix
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X Longitudinal Coordinate
X Longitudinal Coordinate of Plume
Maximum Rise
X Plume Touchdown Point (Longitudinal Coordinate)
y Lateral Coordinate
Z Vertical Coordinate
Greek Letters
a,3 Dimensionless Entrainment Constants
Y Ratio of Characteristic Length for Gaussian Concentration
Distribution to that for Velocity Distribution
6 Angle of Plume Trajectory with Horizontal
v Kinematic Viscosity
o Transverse Plume Standard Deviation
a Vertical Plume Standard Deviation
Z
p Plume Density
p Plume Density at Stack Exit
p. Ambient Air Density
X Local Concentration
X Concentration at Stack Exit
Subscripts
0 Denotes Stack Exit Quantities
A Denotes Ambient Quantities
D Denotes Quantities at Plume Touchdown
M Denotes Quantity at Plume Centerline
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SECTION I
INTRODUCTION
Negatively buoyant emissions into the atmosphere have been reported
by several observers. Scorer (23) reports the case of two power plants
emitting wet-washed plumes with apparently insufficient elimination of
free water, in which the subsequent evaporation of the free water cools
the plume and causes it to sink. According to the report the plant it-
self is obscured from view on many occasions. Chesler and Jesser (8)
and Bodurtha (3) have observed and discussed the descent of dense gases
from stacks and relief valves.
The consequences of such behavior are potentially drastic. When
the plume sinks rapidly to the ground, very little dilution will occur
in comparison with normal emissions and high ground level concentra-
tions of gases which may be toxic or explosive could result. In this
report experimental results of the dynamic behavior of negatively
buoyant emissions and the resulting concentration distributions are
reported.
1.1 Negatively Buoyant Emissions
Previous experimental work with negatively buoyant emissions
appears to be confined to three efforts. Bodurtha (3) conducted wind
tunnel tests of emissions of freon-air mixtures into a crosswind.
Various combinations of density, exit velocity, crosswind velocity and
stack diameter were used in obtaining smoke pictures. The results were
correlated by an expression for the maximum rise height:
H= 5.44 D °'5 R°'75
o
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In which H is the maximum rise height of the plume centerline, D
is the stack diameter and R is the ratio of the exit velocity to the
wind speed. This formula has the disadvantage of being dimensionally
inhomogeneous and .the absence of relative density terms makes its
application questionable as the specific gravity approaches unity.
Turner (31) conducted experiments in which salt water jets were
injected vertically into calm fresh water. Maximum rise heights were
observed and correlated with various dimensionless parameters and an
expression was reported equivalent to:
H/DQ = 1.74 FR
In which H and D are as previously defined and FD is the
O K
densimetric Froude number based on the ambient density and original
density difference. This Froude number is defined as:
^"o
n = A °
^R
where p. = Ambient Density
/T.
U = Exit Velocity
p = Exit Density
D = Exit Diameter
o
This definition of the Froude number implies the Boussinesq assumption
for density in the inertial terms of the equations of motion; thus it
can be considered applicable in the density range in which that assump-
tion is valid. Although the constant of proportionality is reported by
Turner as equal to 1.74, a plot of values given in the original article
indicates the value of this constant was determined graphically to be
3.1.
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Holly and Grace (15) conducted tests of salt water jets injected
vertically into a fresh water open channel in which maximum rise
heights and downstream concentrations were measured. Expressions
obtained for rise height and concentration distribution were:
-148FR
. (3.47 X 10 )
o
and
0.4F
_ i! gs
em = (31. xlO R ) (£)'
o
In which H is the top edge of the jet and D the jet diameter at
maximum rise height, e is the least dilution (reciprocal of dimen-
sionless concentration), X is downstream distance and X the
distance to the point where the jet descends to the channel bottom.
The least dilution expression was stated to apply to both the regions
upstream and downstream from X = X .
1.2 Plume Rise
A large amount of work has been completed upon the rise of
buoyant plumes. The beginning point for most of the recent work is the
classic paper of Morton, Taylor and Turner (19) which examines the rise
of a buoyant plume in a quiescent medium. The analysis was based on
the conservation of volume, mass and momentum with assumptions of self
similarity, circular plume cross section and simple proportionality of
volumetric entrainment rate to plume velocity. Either Gaussian or
"top hat" profiles of velocity and buoyancy flux may be assumed with
appropriate modifications of the equations. With the assumption of a
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"virtual point source" located below the actual exit, the model
predicts a "straight sided" plume.
The "bent-over" plume rise models of Briggs (4) and Csanady (10)
incorporate this theory for the initial stage of buoyant, bent-over rise
which predicts a 2/3 power parabola as the plume trajectory. In both
models a second stage is introduced in which the rate of volumetric
entrainment is related to the turbulent energy dissipation per unit
mass. Criteria for transition is that the rate of entrainment thus
computed exceed that computed by the initial stage theory and is appli-
cable when environmental turbulence in the inertial subrange dominates
mixing. This predicts a leveling off to an asymptotic rise which
Briggs takes as the final rise height. Csanady introduces a third
stage in which the eddy diffusivity is taken as constant and a linear
rate of rise is predicted. In both these models the initial region of
momentum dominated rise is neglected as insignificant in contributing
to the final rise height.
Hoult, Fay and Forney (14) introduced a continuous model for the
rise of a buoyant plume in a laminar uniform crosswind. Utilizing the
Morton et al. assumptions of self similarity and conservation of mass
and momentum and employing entrainment constants for velocity differ-
ences parallel and perpendicular to the flow direction, the model pre-
dicts a momentum-dominated jet behavior close to the stack with a 1/2
power parabola trajectory. It subsequently suggests a buoyancy domi-
nated plume with a 2/3 power parabola trajectory far from the stack
similar to the initial stages of the Briggs and Csanady models. For a
bent-over jet in a laminar crosswind all of the above models predict
a 1/3 power parabola a trajectory.
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Several investigators (16), (24), (30) have observed and recorded
the internal and surrounding flows associated with jets and plumes
injected into a cross flow. The plume emerges as a jet from the stack
exit, traveling upward much like a typical momentum jet. The cross-
wind effect soon becomes dominant bending the plume over and convecting
it downstream with a lateral velocity essentially equal to the cross-
wind.
It has been further noted that as the plume rises, its cross-
sectional shape changes from circular to "kidney-shaped" (30), and
finally as it is bent over, the outside shear layer which envelopes
the plume tends to roll up behind the core and from two line vortices
of equal strength but opposite sign.
Noting this fact, Tulin and Schwartz (28) conducted investigations
into the rise and growth of a two-dimensional vortex pair passing
through neutral and stably stratified surroundings. As the plume falls
or rises in stably stratified surroundings a lateral spreading and
deviation from circular cross section was noted.
In all of the above cited models the Boussinesq approximation is
made, i.e. that the density in the inertial terms of the equations of
motion is approximately equal to ambient density, or more properly,
that potential density is equal to ambient potential density.
1.3 Moist Plumes
Morton (20) considered the case of a moist plume released
vertically into a quiescent atmosphere using entrainment theory and
conservation of mass, volume, momentum and specific humidity. Assuming
a linear variation in atmospheric humidity, he obtained an expression
for the plume specific humidity as a function of height.
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Csanady (10) and Slawson and Wigley (33) extended this analysis
and formulated a model for the dynamic behavior of a bent-over plume
containing both free water and water vapor. The model considers evapo-
ration and condensation along with the resulting effects on the buoyancy
flux. Wigley and Slawson (32) applied this analysis to the rise of a
saturated plume.
1.4 Velocity and Concentration Distributions
Prandtl's mixing length theory applied to circular turbulent jets
predicts a constant eddy viscosity and diffusivity (25) which in turn
predicts Gaussian distributions of velocity and effluent concentration
along with a decay rate of maximum values of these quantities that is
inversely proportional to downstream distance. Experimental measure-
ments have confirmed this theory.
Albertson et al. (1) measured velocity distributions in a simple
momentum jet. The profiles were determined to be Gaussian and the
rate of decay of maximum velocity inversely proportional to downstream
distance following the zone of flow establishment. Becker (2) et al.
measured concentrations in a jet and found them to be Gaussian also,
but flatter in profile than the velocity distributions measured by
Albertson. The decay rate of maximum concentration was found to be
inversely proportional to downstream distance, but decaying at a faster
rate than the velocity.
Rouse et al. (22) measured velocities and temperatures above a
point source of heat and obtained Gaussian profiles for both, though
slightly sharper in profile for those obtained for jets. Maximum
velocities and temperatures were observed to decay according to -1/3
and -5/3 powers of downstream distance respectively. Hewett (13)
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measured temperature distributions in heated plumes injected into a
laminar cross flow in a wind tunnel for neutral and stratified cases
and found the distributions to be qualitatively Gaussian, although he
proposed no model and did not report a decay rate with downstream
distance. It was noted that concentration gradients were much steeper
on the bottom than the top indicating the influence of buoyancy on the
local diffusion.
For turbulent diffusion phenomena in the lower atmosphere,
Button's equations have been widely used to estimate concentration dis-
tributions for a point source, but the application is restricted be-
cause of many ideal assumptions. Also, they are not sensitive to
atmospheric stratification situations. In an attempt to improve
sensitivity to real conditions Pasquill-Gifford's semi-empirical
formulas have become popular. A set of transverse and vertical standard
deviations of the dispersion are plotted as functions of downstream
distance. A "stability category" which classifies six different kinds
of possible atmospheric stratifications, relates the various plume
dispersions to different meteorological conditions.
Wind tunnel studies of diffusion over topographic models in
turbulent boundary layers indicate good correlation with Pasquill-
Gifford prediction techniques (18), In addition wind tunnel diffusion
studies have been conducted for idealized source conditions. Davar
(11) studied diffusion from a horizontal point source in a neutral
turbulent boundary layer, Malhotra (17) performed similar experiments
under unstable conditions, while Chaudhry (7) studied diffusion in a
stably stratified boundary layer. Shih (26) evaluated the effects of
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8
the growth of boundary layer thickness and free stream turbulent
intensity upon diffusion.
Yang and Meroney (35) studied the diffusion in the wake of a
cubical structure placed in a turbulent boundary layer. They found
that the critical conditions, such that the plume will not be trapped
in the building cavity region are:
R >. 1, hs/hb >_ 2
where R is the velocity ratio and h and h, are the stack and
building heights as measured from the ground.
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SECTION II
PLUME RISE EQUATIONS
2.1 Vertical Plumes in a Quiescent Medium
Smoke pictures of negatively buoyant plume rise in a quiescent
medium indicate that the behavior is such that the plume exists in a
jet with approximately linear growth of radius with vertical distance
to between 1/3 and 1/4 plume rise height. The plume width then grows
in a highly non- linear fashion, becoming quite large in the upper
regions. Although simple entrainment theory can not be expected to
give a complete description of this motion, especially as entrainment
occurs in a complex manner along the top of the plume and the bottom
of the plume "crown", it may serve as an aid to dimensional analysis in
predicting the relationship between pertinent parameters. Clearly,
some accounting for the entrainment is necessary since the assumption
of a frictionless plume with no entrainment leads to
H/Do = FR2/2
General Equations of Conservation:
If the effects of the descending fluid on the exterior of the plume
are neglected due to their much smaller density and velocities, the
equations of conservation (after Morton et al.) become:
Buoyancy:
d °° H °°
—• I pUZirrdr = p ~ j U2urdr
cu. Q A &L Q
Assuming p. to be a function of Z alone.
(pA-p)U2Trrdr = [ U27rrdr]
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10
f\
For -r=- = 0 (neutral atmosphere)
/ (p.-p) U2irrdr = b U (PA~P ) 2ir (2.1)
0 ooo
00
/ pU2irrdr
One may define the average density p = as:
/ U2?rrdr
0
p = PA[I
(b 2U
U2irrdr
0
Momentum:
CO
i O
-r=- I pU 2irrdr = / (p -p)g2Trrdr
d/: o o A
Equations of Conservation (Top Hat Profile) :
If a "top hat" profile and the Morton et al. entrainment
CO
f\
hypothesis are employed / U2irrdr = b U
0
Volume:
~ (b2U) = 2abU (2.3)
where a is an entrainment constant of proportionality relating inflow
velocity of outside air to plume velocity. Similarly
Buoyancy :
(pA-p)b2U = pA(l-SG)bo2Uo (2,4)
where SG = p /p.. Also:
O A.
P = PA[1
A
b 2U (SG-1)
b U
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11
Momentum:
± (Pb2U2) = (pA-p)b2g (2.6)
Maximum Rise Time (Top Hat Profile) :
Combining equations (2.4), (2.6), and the relationship dZ/dt = U
one may obtain
i (pbV) - pA(l-SG)bo2Uog
or
pbV = pA(l-SG)bo2Uogt + pobo2Uo2
2 2
And since at maximum rise pb U =0, the time of rise can be
calculated as
P U
T = _ — ° ° (Time of Maximum Rise) (2.7)
O A
If a Gaussian distribution is assumed and if the ratio of a for
the two cases is adjusted so that the conservation of mass is
consistent at stack exit, the same expression for maximum rise results.
Equations of Conservation (Gaussian) :
If a Gaussian distribution is assumed such that b is a
characteristic length (different from the value of b in the top hat
model), following Morton, Taylor and Turner, and:
'-A - '
2., 2
u = u e-r /b
m
Y = Ratio of characteristic lengths for density and velocity
b = Initial Radius
Subscript m = Centerline Values
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12
The equations of conservation become:
, , Yb2Um
-r|- [ I pU 2iirdr] = (PA~P )b Yg (2.6a)
0
Maximum Rise Time (Gaussian):
If Z is measured along the plume centerline. dZ/dt = U , so
that:
If y is taken as unity to simplify the equations and initial
conditions are made to match, using (2.4a) we obtain:
GO
^ [ / pU227rrdr] = 2pA(l-SG)bo2Uog
and
oo
/ pU22Trrdr = 2pA(l-SG)b 2U gt + p b 2U 2 (A)
At maximum rise height the integral on the left hand side is zero and
an expression for time of maximum rise results as:
P U
O 0 /-
Maximum Rise Height (Gaussian) :
The assumption of nearly constant density i.e. in equation (A),
yields:
pU 2b2 = 4p.(l-SG)b 2U gt + 2p b 2U 2
m Ak •* o o6 o o o
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13
So that:
_ _ 4p.(l-SG)b 2U gt + 2p b 2U 2
,2 2 _ Av _ o os Ko o o
m p
If it is assumed that p~p then equation (2.8) becomes
b2U 2 = 4 1^1 b 2U gt + 2b 2U 2 (2.6b)
m SG o o6 o o ^ '
The conservation of volume expression is taken to be the same
here as for top hat velocity profiles with the understanding that the
value of a thus defined will in general be different from the top
hat value, and since dZ = U dt:
m
~ [b2U ] = 2abU 2 (2.3b)
dt L nr m *• '
Matching the fluxes of volume and momentum to stack exit quantities:
U = 2U
mo o
b = b //2~
mo o
The velocity and radius may be non-dimensionalized with their
initial values such that:
b* = b/b = b//?b
* o mo
U* = U/U = 2U/U
* o mo
Z* - Z/UQT
Thus utilizing the above and the definition of maximum rise time
equation (2.7a):
A 7 U T
;nr* (b* U *) = 2ab*U * (~) (2.3c)
dt* * m* * m b
o
(1 - Pm/PA) b*2U * = 2(1-SG) (2.4c)
b*V,2 = 2(l-tJ (2.6c)
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14
One can now eliraate b* from equation (2.3c) by utilizing equation
(2.6c) to obtain a differential equation in U * alone.
d ,(l-t*K rr~ n 2.
a F,, U
.
dt* u R
m
thus may be integrated to yield
U * = 2(l-t«)
m
'IGai^F,,2
Information is now available to calculate the maximum rise height H,
1
defined as II = U T / U * dt*. The result is
° 0 M
2 -
H !!Z N3/1° ,N dR
Do~ 5 M4/5 0
-/2
5 M /Z M
N
where ,
, F
P = (1-tJ x , M = - 1 — — , and N = 1+M.
Note R = -rr- and B is the Beta Function. The second integral
on the right can be evaluated by a series expansion as:
« rf-l
4/5 2J
The series can be shown to be convergent if Stirling's Formula for
T(n) as n gets large is assumed. For most Froude numbers, however,
M/N * 1 and
F 2 B(l/2, 4/5) 2.30F
£ i\ i\
r~ - = - r~n - TTo - f or
C2 ms/4cs)1/2^
FR
-------
15
H °-45 FR
D " ^ -
Gaussian
If a for the Gaussian and top hat cases are adjusted to make
equation (2.4) equivalent at stack exit for both top hat and Gaussian
assumptions:
ct = '2 ot
top hat Gaussian
and
0.515 F
H/D = — £-. (2.8a)
o i
top hat
And if it is assumed P~P4:
f\
0.515 SG1/4 F
H/Do = - (2.8b)
top hat
These expressions are identical to those obtained with the same
constant density assumptions and a top hat profile of plume quantities
if the top hat rise time is used.
In the above Fn is the densimetric Froude number based on stack
K
exit veloicty, density and density difference rather than the one
obtained using the Boussinesq approximation and is defined as:
U
n
8°,
po
Expressions (2.8) represent the rise computed by neglecting the
entrainment resulting from lateral velocities due to radial growth at
the top and bottom of the plume "crown" and predicts an infinite
radius at maximum rise height.
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16
Estimation of Entrainment Constant:
Equations (2.8) cannot be utilized experimentally to give a
precise estimate for the actual value of a. Good correlation with the
Froude number or Froude number and specific gravity is a valid expecta-
tion, however.
A method of evaluating a results from considering motion in the
jet region immediately downstream from the stack. The conservation of
momentum leads to:
pb2U2 = -(p -p.) b 2U gt+ p b 2U 2
o A o o6 o o o
— 22 22
In the jet region t is small and pb U » p b U
b 2U 2(SG-1)
From (2.5) p = p [1 + -2—°- ]
A b2U
This leads to:
_ -b 2U (SG-1) + /[b 2U (SG-1)]2 + 4SGb 2U V
2.. oo o o J oo
2
Substituting in (2.4) and integrating results in an expression for
a for a top hat profile which should be approximated close to the
stack.
a = •=•
b-b b (SG-1) /[b 2U (SG-l)]2+4SGb 2U 2b2+2v/SG~ b U b
o o , J L o ov J oo oo
+ In
4 SG /[b 2U (SG-l)]2+4SGb 4U 2+2/SG b 2U
I L f\ r\ ^ J -I f\ r\ r\ r
OO J OO OO
^
(2.9)
It should be noted here that the value of a computed in this manner
is of the order of half the value of a. as computed for a point source
of buoyancy where a is taken as db/dZ. The jet assumption is
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17
subject to the limitations of assuming that the buoyancy forces are
small in the jet region, while the point source is subject to the
limitations of ignoring finite momentum flux and the assumption of
a point source for a finite diameter. Briggs (5) gives an estimate
for the point source of a = 0.075.
2.2 Bent Over Negatively Buoyant Plume In a Laminar Crosswind
The effect of negative buoyance on plume behavior and resulting
downwind concentrations will be greatest when crosswinds are light, and
turbulence intensities are low. The sinking velocity of the plume
relative to the horizontal convective velocity will be much higher than
under "normal" conditions. In such cases, the entrainment of outside
air into the plume and the resulting diffusion is a function of this
interaction between the plume and the crosswind, and approaches the
behavior of a turbulent plume injected into a laminar crosswind.
General Equations of Conservation (Top Hat Profiles);
Assuming a crosswind of constant velocity, a "top hat" profile,
and the Hoult et al. model for the entrainment of outside air into the
plume, where entrainment due to "parallel" and "perpendicular" velocity
differences are assumed to superimpose, the equations of motion become:
(a) Conservation of "Volume"
•jg- (b2U) = 2ab(U-Vcos6) + 2BbV|sin0|; (2.10)
(b) Conservation of Horizontal Momentum:
(pbVcose) = PAV ^ (b2U) (2.11)
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18
(c) Conservation of Vertical Momentum:
5- (pb2UW) = (p,-p)b2g (2.12)
CIS f\
(d) Conservation of Mass
J) = PA dV ^^ C2-13)
which leads to the buoyancy flux relation:
d 2 2 dpA
^ (pA-p)bZUg = b^Ug -^ Sine (2.14)
where:
s = Distance measured along plume axis
U = Axial velocity = ds/dt
W = Vertical component of velocity
8 = Angle of plume axis with the horizontal
Trajectory Near Stack:
In the case of a neutral atmosphere equation (2.12) still leads
to equation (2.7) for the time of maximum rise. Examining the case of
the plume as it initially leaves the stack, where the trajectory is
approximately vertical, cos8 ~ 0, sin8 =• 1, U - W.
Equation (2.13) integrates to
pb2W2 = (p.-p ) b 2gU t + p b 2U 2
*-KA ^oj o 6 o ooo
And since t is still small:
2 ? 9 ?
PbV = p b nj * (B)
ooo
Noting that cos6 = -5— = , equation 2.11 becomes:
CIS j i/o
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19
= PA
/ \ I /
(1
or rearranging and utilizing equation (B) above,
b W ~ —^^i— + 1 b U
Z' oo
This may be substituted directly into equation (2.10)
~ (b2W) = b 2U ~ R^ = 2abW + 20bV
Q/i 0 O dZi L
One may replace the right hand terms by:
v/pT b U Sp b U /SG b U
hw = OOP _ o o o _ o o
1/PA(1
/R(SG)+Z'
b 2U (SG-1)
o o R+Z'
2.
hv . bWV _ rR(SG)+Z' / R+Z
bV ' -biT ' Vo C - P - 5 /RSG
o - P - R(SG)+Z'
R+Z
— can be taken as =1 the new continuity of volume
expression is:
2g R(SG) 2a
. _
dZ Z' Rb Z' b b R
0 O O
Integrating this differential expression results in:
2gZ
Rb 2
°
r --
Q R2b 2
o
x - 1 rQR+3)Z2 23 r(aR-HB)Z5
~ RSG L Rb 3Rb L Rb j ' ' ' J
RCSG) Rb 3Rb
0 00
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20
/CSG)boX
Z = R/ aR+g— for values of Z/bQ sufficiently small that
higher order terras will not be significant. This is identical to the
expression denoted by Hoult, Fay and Forney except for the specific
gravity term.
Evaluating pb U from this expression:
o
Subsequent Trajectory:
For the bent over case where cosS^l, sin8*Z', PKPA> U~V, the
assumption of Gaussian profiles in vertical component of velocity and
concentration (density difference) yields expressions that are identical
to those resulting from the "top hat" case with the exception that b
is now the radial distance at which the quantities described by the
Gaussian expression assume values equal to — of the centerline values.
"
In this case the entrainment hypothesis is equivalent to the assumption
of a mixing length proportional to the width of the plume, such that a
linear rate of growth of radius with Z and Gaussian profiles of
vertical velocity and density difference are predicted.
The new conservation of volume expression will be:
4r (b2V) = 2bV ^- - 2bVW
dt *• J dt m
or since dZ ~ W dt
m
If the constant of proportionality is taken as 6, then
~ = 3, and b = 3Z + C
Q.L
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21
If it is assumed that C can be taken as zero without large error
and if dp./dZ = 0 in equation (2.14) then equation (2.12) becomes:
A
or
, co 2,,2 (p.-p )b U gu
d t ..w -r /b . , ^A MoJ o o6
3V I VW e 2irrdr = r:
dX J m pAV
9 999 P f Y _ ^
b^VW * gZ V Z' = -L. I5-J
m ,,3 P,
or
Z =
H -
1/3
Which is a slight variation on the well known expression for positively
buoyant plumes. In the above F the buoyancy flux has been substi-
tuted for (p -p.)b U g, X is the horizontal distance to the point
O f\ O O
of maximum rise, and H is maximum plume rise. For this case
Expression for Maximum Plume Rise:
Using equation (2.12) in time derivative form:
pb2UW = -Ft + p b 2U 2
ooo
and
W =
-Ft + p b 2U 2
o o o
pb2U
The previously evaluated expressions for b U for the asymptotic
cases of the plume close to the stack and of the bent over plume
2 2
indicates b U = b U f(R, Z/d if the Boussinesq approximation is
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22
made for the density on the grounds that it is valid over most of the
rise. If the original density is retained in the time calculations
the result is:
-Ft + P b 2U 2
PAf(R,2D ) b 2U °
A v o o o
where R is constant.
Therefore maximum plume rise is in general:
dz _
or
H/D = <|>(R, (SG)(F 2)) (2.15)
O K
The jet region equations apply only when time is small and R(SG)/Z'«1,
however for purposes of comparison (2.15) can be calculated for this
assumption over the entire plume rise resulting in:
o 4(aR+3)
/T . 16(aR+g) p 2
R(SG) R
- 1
(2,16a)
For bent over plumes (if considered for the whole rise)(2.15) becomes:
3R(SG)F 2 ,
H/D = [ T~JH i/A (2.16b)
0 88
This predicts values of H/D which vary a maximum of =10 percent
in the range of specific gravities from 1.25 to 5 if the exit and
crosswind velocities are held constant. The minimum predicted rise is
at a specific gravity of two. This agrees qualitatively with the
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23
observations of Bodurtha who stated that the rise of plumes he observed
with roughly this range in specific gravities was independent of
specific gravity.
Traj ectory During Descent:
For the descending portion of the plume equation (2.10) can be
dx 1
transformed, noting that cos0 = -3— = 9 -, ,9 , to
CIS f~_~.&^\.lL.
' 7 i i
] = 2abZ' V + 28b|Z'|V
2 1 /2
For values of Z1 < 0.3, then 1. £ (1+Z1 ) ' <_ 1,05. Since
measurements discussed by Briggs (5) indicate 3 ^ (6 to 8)a for
these conditions, the bent over plume expressions will still apply
approximately. Hence,
b - BfH+H-Z)
and
p B2C2H-Z)2(dCH"^) = + JL (X-X)
d(X-X) V
which integrates to produce:
XjOT r8g2 {(2H-Z)3 - H3},1^2 FRH
D ~ ^ 3 3 •> r-
o •* D •* /R
o
Where F is the "horizontal" Froude Number - and X is
KH
the horizontal location of maximum plume rise. At ground level
Z = -h , the stack height. Then
Xn"X RB2 H 3 h= 3 1//2 FBH
~ = [^~ (jf) {(2+ -|f) -1}] -^ (2.17)
oo /R
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24
Where X is the horizontal point of plume touchdown. The position
of X can be estimated from the time of rise by assuming that the
plume is convected horizontally with crosswind velocity V. Thus
VpoUo -
_
- R
It should be noted that entrainment theory is not expected to provide
a completely accurate description of negatively buoyant motion due to
the low velocity differences in the region of maximum rise. However,
it is a useful tool in developing relationships between parameters for
experimental measurement.
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25
SECTION III
CONCENTRATION DETERMINATIONS
3.1 Plumes in a Laminar Crosswind
Rouse, Yih, and Humphries showed theoretically and experimentally
that the decay of maximum concentration in a vertical positively buoy-
-5/3
ant plume is ~X . Morton et al. obtained the same results using
entrainment theory. In that particular case mixing length theories are
consistent with the entrainment hypothesis and both predict a linear
rate of growth of radius with vertical distance, and Gaussian profiles
of velocity and concentration. If the same approach is taken and it
is noted that:
p -
where X is the concentration at any point and p is the correspond-
ing density. If Gaussian profiles are assumed, equation (2.4a) becomes:
VA - (SG-l)
0 *o
2 v
b , .. ,, m , ..,, , 2
1+Y ^o *AJ m
so that
X b 2U
_~ ° °
xo b2U
m
(p -PA) U — = (P -PA)U b = constant
^^
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26
Vertical Plumes:
For a negatively buoyant vertical plume, this predicts at maximum rise
height:
X U D 2
/ ruin i~l moO ,-,,/n -, ~ 1
xm/x0 - CH/DQ) or, —Q (H/DO)
Bent Over Plumes:
For plumes in a crosswind the concentration delay can be examined in
the asymptotic regions. Close to the stack, in the jet region,
X0 42M*!]
For the bent over region of the plume
b2u = P2V = b 2U [*- H- 1] : b 2U [
o olRD 2 o o RD
o o
2
since (Z/D ) » R over most of the rise and
R
' °r
Q V
o
so that the bounds on concentration are
2
~ Q D
o x o
For the descending plume region
JL ~ (b2V) X ~ (2H - Z) 2
xo
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27
which at large distances downstream approaches proportionality with
RH
_
(X-X)
Q R5/3
(X-X)
Implicit in the above is the assumption of a mixing length proportional
to the characteristic length b, similarity in the form of dif-
fusivities of mass and momentum, and similarity in profiles of
velocity and concentration at all cross sections.
3.2 Dense Ground Source in a Turbulent Boundary Layer
3.2.1 Eulerian Diffusion Formulation
In a field of small scale turbulence the diffusion may be
considered through the concept of an "eddy diffusivity" as analogous
to molecular diffusion. A coefficient k, the "diffusivity", is taken
as proportional to U'£, U' is the turbulent fluctuation velocity.
£ can be interpreted in terms of a proportionality coefficient be-
tween the average turbulent flux of a given substance C'U' and the
gradient of average concentration VC,
U'C1 = -KVC .
When the diffusion is considered in three dimensions, the concept is
generalized by introducing three such coefficients, k , k , ky which
X y LI
are assumed to be functions of position. Application of the conserva-
tion principle yields:
^£ + n l£ + v ^ + W -^ - — fk -1^1 + -L rk 9£i + J_ fk 2£i
3t U 3x V 3y W 3z ~ 3x L x 9xxJ 9y ly 8yJ 9z L z 3zJ
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28
If the boundary layer assumption of W=V=0 is combined with neglect of
the longitudinal dispersion term, the following equation results:
W + U 97 = 9y fky ly^ + 97 ^zTz^
The assumption of constant diffusivity k = k = k as formulated
y z
by Roberts leads to a Guassian distribution in the radial direction
and a longitudinal decay rate inversely proportional to X. The
predictions of this analysis unfortunately do not agree with observa-
tions. The observed decay rate of maximum concentration is much
greater than that predicted by this model. Several investigators
(see (29)) were able to obtain closed form solutions for the two
dimensional version of (3.4) for an infinite line source in a crosswind
by use of Schmidt's conjugate power.
Other dispersion predictions have been proposed for power law
profiles and constant flux atmospheres such that:
m du
U = U, (Z/Z,) , K -7— = constant
11 m dz
1 -m
which require K = K, (Z/Z.,) where U, and K, are the velocity
nmlvl 1 1
and diffusivity at the reference height Z . The solutions obtained
predict a power law decay rate in maximum concentration with X.
Several other investigations have obtained closed form solutions for
the three dimensional problem of ground and elevated point sources by
the assumption of variable lateral diffusivity combined with the
conjugate power laws. These proposals have varying degrees of success
in predicting the decay rate of maximum concentration and lateral
dispersion. (7, 27, 29)
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29
3.2.2 Lagrangian Formulations
Lagrangian formulation of duffusion assumes one follows the motions
of a specific particle in time. Taylor (27) considered the motion of a
fluid element with the assumptions of homogeneous, isotropic,
stationary turbulence and obtained:
'
Y 2(t) = 2U'2 I I
00
2 2
where Y. (t) is the variance in om dimensional motion, and U1 is
the RMS value of the turbulent velocity fluctuation in that direction.
The velocity correlation, RT (T) is defined by.
LJ
_ U'(t)U'(t+t)
Kj (^TJ —
^
when t is small R, (ipl and Y.2 = U'2 t2. As t-*», R, (t)-K) and
lj 1 L
oo . i —
/ R.(r)dT = const. Then Y.2(t) = Const x 2U'2.
0 L *
Sutton (29) on dimensional grounds proposed at an empirical form
for R (T)
RL(T) = —^—
r ii 1 2 ^n
(v+U' T)
with n as an adjustable constant. This led to the following solution
for a continuous point source:
on
2Q
''- ~ -2-n y z
TrC C Ux J
Y z
where C and C are generalized coefficients of diffusion in their
y z
respective directions. Button's formula has been widely used in
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30
practice even though it was developed under the assumption of
homogeneous isotropic turbulence. In use it is typically applied to
the shear flow of the lower atmosphere.
The principle of Lagrangian similarity has recently been utilized
by several investigators to provide a more rational approach to shear
flow diffusion, i.e. without postulating a diffusivity in advance.
Reasoning dimensionally Batchelor and Ellison related the time rate of
change of the vertical mean position of a particle to the shear
velocity and a universal function of z/L, where L is the stability
length. Assuming a probability density distribution about the mean
position and noting that for a ground source in neutral flow this
function as applied to maximum ground concentration is essentially the
dirac delta function, they obtained relations for the decay of maximum
concentrations for continuous point and line sources. Concentrations
from point sources were predicted to decay as X ' -X ' , while line
sources decay X . Gifford, Cermak, and Chaudhry (7) extended this
principle to diffusion in a stably stratified atmosphere.
The results of Lagrangian theory are usually incorporated into
statistical models in terms of the calculated first, second, or higher
moments. For a continuous ground source the expression obtained is:
xu i
0 ira a
v y z
2
2a 2
y
2
z "I
2a 2
z
Where:
Q is the flow rate in units of concentration per second
a (x) and a (x) are distribution moments found by the
Lagrangian theory
X is the average concentration
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31
3.2.3 Wind Tunnel Simulation of Diffusion
Cermak et al. (6) point out that for small scale diffusion, in
which there is no variation in the mean wind direction, and non-neutral
stratification, dynamic similarity of flows with geometrically similar
boundary conditions, is determined by three dimensionless parameters:
VL/v (Reynolds Number)
^
P— (Prandtl Number)
-—~- (Richardson Number)
T V
o
If the tunnel flow consists of air, Prandtl Number similarity is
assumed. If only micro scale eddy motion is considered, such that
there is no variation in the mean wind direction, experience has
shown that for shear flows of high Reynolds Number, that viscosity has
no effect on the scale components of the motion which contains nearly
all the energy which might effectively contribute to turbulent
diffusion. Plate and Lin, Chuang and Cermak, Malhotra and Cermak,
Arya and Chaudhry have all demonstrated the reliability of the use of
wind tunnel shear layers for modeling atmospheric flows, even though
a ratio in Reynolds Numbers between model and prototype is of the
order of 10 .
For flow of this sort, the gradient form of the Richardson Number
must be used i.e.
Ri - g
Rl ' T
If power law relationships in Z for profiles of temperature and
velocity are obtained such that:
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32
.. _ T-T
JL - f_L^n r Ii -
II 1-7 J J (.7. _rp J -
Ul Zl Tl r l
T -T
. _ g m ,Z m-2n+l(Z1) r_J IN
Rl - Y~ ~2 CZ7^ T \. 2 >
o n 1 U
since Ri = Buoyancy force therefore
Inertial force
<0 Unstable stratification
Ri =0 Neutral stratification
>0 Stable stratification
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33
SECTION IV
EXPERIMENTAL MEASUREMENTS
4.1 Plume Rise
Experiments on negatively buoyant plumes were conducted to check
previous and present theories for plume rise characteristics and to
obtain reliable data on the nature of the descending plume. Vertical
plume rise experiments with no crosswind were conducted in the
Industrial Aerodynamics wind tunnel in the Fluid Dynamics and Diffusion
Laboratory at Colorado State University. The 6x6 ft area of the test
section (which was closed at each end for this experiment to limit
corrective currents) provided a very still environment for the experi-
ment. The experiments with bent over plumes were performed in the
thermal tunnel in the Fluid Dynamics and Diffusion Laboratory. The
tunnel has a 24x24 inch cross section. Turbulent plumes were injected
into both laminar and turbulent crosswinds. Plumes were also injected
into a low-speed turbulent crosswind in the Industrial Aerodynamics
wind tunnel. These plumes were of large specific gravity and descended
quickly to the tunnel floor, where the longitudinal decay rate was
measured.
Additional details of the wind tunnels are described in Section 5.
The pertinent parameters regarding plume rise appeared in the
equations in Section 2. Values of these parameters applicable to
actual conditions can be duplicated in the wind tunnel. Implicit in
the assumptions was the existence of a Reynolds Number sufficiently
large to justify the assumptions of turbulent entrainment. The
Reynolds Numbers based on pipe flow calculations did not meet this
criteria for all cases studied so that the turbulence was artificially
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34
generated. A sharp edged orifice was placed in the stacks 8 diameters
upstream from the exit. Hewett (13) has shown that plume rise is
independent of Reynolds Number if the plume is turbulent at exit.
The range in parameters was as follows. For the vertical plumes,
specific gravities ranged from 1.08 to 3.0 and exit velocities from
~9 to 75. Stack diameters of 1/8 inch and 1/4 inch were used.
For the plumes in a laminar crosswind, velocity ratios ranged from
2.5 to 25, specific gravities from 1.10 to 4.16 and Froude Numbers from
-5.2 to 75. Two diameters, 1/4 inch and 1/8 inch were used and two
crosswind velocities -0.75 and =1.5 ft per second were employed. Stack
heights of 3 inch and 6 inch were employed at various points, both to
provide variations in this parameter and to avoid hitting the tunnel
roof with plumes of high exit velocity. The specific gravities were
obtained by mixing Freon 12 with Air in appropriate proportions. Freon
12 has a molecular weight of 121. Densities at appropriate pressures
and temperatures were obtained from applicable Mollier Chants.
The experiments were conducted as follows. Tunnel and stack flow
rates were set. The effluent was bubbled through TiCl. to produce
smoke. Extended time exposure photographs were taken against a black-
board divided into marked horizontal and vertical increments. Measure-
ments were then corrected for the parallax resulting from the fact that
this plume was in the center of the tunnel and the blackboard at the
tunnel wall. Several photographs are shown in Fig. 11,
In addition a 4% inches x 4% inches x 4% inches cubical structure
with a stack exiting in the center was installed in the Colorado State
University thermal tunnel in a turbulent shear flow. Velocity at this
top of the building was set at 6.75 ft per second for a Reynolds Number
-------
35
of -13,500. Smoke photographs were taken for specific gravities of
1, 1.5 and 2.5; velocity ratios of 1 and 2; and stack height to
building height ratios of 1, 1.5 and 2,
4.2 Concentration Measurements
4.2.1 Plumes in a Laminar Crosswind
Concentration measurements at the maximum rise height were made of
18 plumes injected into the laminar crosswind. Concentrations at the
points where these plumes touched the floor was also taken. These
plumes were from 1/4 inch and 1/8 inch diameter stacks with specific
gravities of 1.5, 2 and 3 respectively.
Detailed cross-sectional concentration measurements taken in
roughly equal longitudinal increments between the point of maximum
rise height and plume touchdown were made for six plumes of specific
gravities 2 and 3; and exit ratios of ~5, 10, and 15 from a 1/8 inch
diameter stack. The cross^sectional measurements were made so that
the plane of measurement was at right angles to the plume motion as
determined from the smoke pictures.
4.2.2 Dense Ground Source in a Turbulent Boundary Layer
Concentration measurements were taken in a turbulent boundary
layer of negatively buoyant ground sources. Specific gravities of 1.0
(Air),1.10, 1.25, 1.50, 2.0 and 3.0 were employed. Measurements were
made in neutral and inversion stratifications. Free stream velocity
was 6 ft for second and the boundary layer thickness was approximately
6 inches. Velocity of discharge from the source was set equal to
tunnel velocity at the height of the source centerline. The turbulent
boundary layer was artificially generated in the Colorado State
-------
36
University thermal tunnel by the use of vortex generators after the
method of Counihan (9). An approximate 1/7 law velocity profile was
obtained. Using the thermal stratification capabilities of the tunnel,
an approximate 1/7 law temperature profile was also generated. The
vortex generator arrangement is described in Section 5.
Finally, five plumes were examined in the Colorado State
University Industrial Aerodynamics Tunnel (briefly described in Section
5) with a free stream velocity of approximately 2.5 ft per second and
a boundary layer thickness of approximately 12 inches. These plumes
were emitted from 1/4 inch stacks with velocity ratios ranging from
5 to 25 and specific gravity of 3 and thus tended to intercept the
tunnel floor at relatively short distances from the stack. The decay
rate of maximum concentration downstream from point of touchdown was
then determined to provide information supplementing that of the plumes
injected into the laminar crosswind. This provided data concerning
dispersion of heavy plumes due to background turbulence as opposed to
plumes which entrain fluid as a result of their own vertical motion.
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37
SECTION V
APPARATUS AND INSTRUMENTATION
5.1 Wind Tunnels
The thermal wind tunnel (Fig. 1) at the Fluid Dynamics and
Diffusion Laboratory, Colorado State University, was designed to
provide a low speed wind tunnel with vertical thermal gradient capabil-
ity. The section is 15 ft long with a two ft square cross section.
A bank of metal plates with electrical resistance heaters placed in the
tunnel inlet allows an initial thermal gradient to be established.
Water cooled panels on the tunnel floor and electrical resistance
heaters on the tunnel roof subsequently maintain the gradient along the
test section. In addition, the longitudinal pressure gradient along
the test section can be controlled by the tunnel roof which can be
adjusted vertically. The fan speed can be adjusted, thus controlling
the air speed in the tunnel. Maximum air velocity obtainable is
~10 ft per second.
The Colorado State University Industrial Aerodynamics tunnel has
a six ft square cross section and a test section which is 30 ft in
length. An adjustable pitch fan allows wind speeds up to 60 ft per
second. The boundary layer thickness ranges from -3 inches at the
start of the test section to ~16 inches at the end.
5.2 Velocity and Temperature Measurements
Extremely low velocities were measured utilizing the vortex
shedding properties of circular cylinders .id known relationships between
shedding frequency and approach velocity in the form of the Strouhal
Number of cylinder Reynolds Number. The device is similar to one
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38
described by Hewett (13), and requires a "hot wire" probe positioned
in the cylinder wake to measure the eddy shedding frequency. The
trace of the signal was observed on an oscilloscope and the probe
position adjusted so that only frequency of vortex shedding from the
bottom of the cylinder was counted. The signal appeared in wave form
and thus was counted on a digital counter. Velocity was determined
from Roshko's data relating Strouhal Number to Reynolds Number. This
method of velocity measurement was checked with a smoke wire.** The
measurements are good within three percent.
Velocities of higher magnitude were measured with a pitot-static
tube and a Transonic pressure meter, with the exception that velocity
and turbulence inten.sity profiles in boundary layers were measured with
a hot wire anemometer.
Measurements of temperature were made using a movable bank of
eight copper constant and thermocouples mounted vertically. Their
voltage output was measured by a sensitive millvolt potentiometer.
5.3 Gas Mixing and Smoke Visualization
The dense gas was formed by mixing air and Freon 12 in a flow tee
in the desired proportions. The air and Freon flow rates were measured
by Fisher and Porter "flowrators" which were calibrated for each gas.
Smoke was generated by impinging the mixture in jet form on the surface
of titanium tetrachloride in a container. The smoke thus formed was
then transported to the stack inside the tunnel where it was released.
A schematic of this arrangement is shown in Fig. 2.
**
See Orgill, M. M. et al., "Laboratory Simulation and Field Estimates
of Atmospheric Transport-Dispersion Over Mountainous Terrain,"
FDDL Dept. CER70-71MMO-JEC-LOG40, 1971.
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39
5.4 Vortex Generators
Since concentrations from a negatively buoyant ground source were
measured in the thermal tunnel to utilize the thermal inversion capabil-
ity, it was necessary to generate a turbulent boundary layer. This was
done using the method of Counihan by constructing eight "elliptic
wedge" vortex generators with the shape of a quarter ellipse with
minor axis equal to one-half major axis and a wedge angle of six
degrees. The generators were six inches high and three inches long at
the base. A serrated barrier was located six inches upstream from the
generators. A metal honeycomb section was placed immediately down-
stream of the heaters but upstream of the serrated barrier. It was
found that best results were obtained when the barrier was placed at
a 60 degree angle with the tunnel floor such that the top of the
barrier was placed adjacent to the downstream metal "Honeycomb" section.
The barrier was 1 1/8 inches high at the serrations and 7/8 inches
high elsewhere. Downstream from the generators a three inch wide
plate with 3/16 inch steel shot placed in staggered rows on the surface
was installed. Downstream from the shot-covered plate a four-inch
wide layer of 3/8 inch gravel was placed on the tunnel floor. A
sketch of the arrangement with details of the vortex generators and
serrated barrier is shown in Fig. 3. Velocity profiles produced
closely approximated a 1/7 power law profile. The "Boundary Layer"
was developed within twenty-five inches downstream from the generators.
Velocity, turbulence intensity and temperature profiles in the boundary
layer are shown in Fig. 5 to 9.
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40
5.5 Concentration Measurements
5.5.1 Measuring Apparatus
Concentration measurements were made using Krypton-85. Krypton-85
is a radioactive noble gas produced by nuclear fission. With the
atomic number 36, atomic mass unit 85, and the maximum energy of 0.67
M.E.V., Kr-85 has been widely used as an effective tracer gas in
recent years because of its long half life (10.3 years) and its pure
Beta emitting property. The Beta particles emitted by Kn-85 ionize
K
gas molecules as it passes through them. With these ionization prop-
erties gas concentrations can be detected by Geiger Mueller counters.
The counter tube consists of two electrodes, a fine metal wire, the
anode, surrounded by a hollow conducting cylinder, the cathode. Gas
samples were removed from the test section by a rake of sampling
probes and flushed through the tube jackets for a period of three
minutes. Sampling ceased, and the samples isolated by valves. Concen-
trations were then determined by counting the tube pulses. The tubes
used were Halogen-Quenched, stainless steel, thin-walled G-M tubes
(Tracer-lab 1108),
5.5.2 Tube and Gas Calibration
G-M tubes and radioactive source gas were calibrated by u<=ing the
following procedure. A reference G-M tube was calibrated using the
scalar counter and a radioactive source of known strength. This source
was placed inside a lead-shielded safe containing the reference G-M
tube. The reference tube is then calibrated in counts per minute vs.
source strength in curies. The radioactive strength of either a
calibrating or a source gas was then determined by passing the gas
through a plastic container with a Mylar cover at the same position in
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4:
the lead safe as the reference source. Using the known volume of the
container, concentrations of the gases was determined in yCi/cc.
A calibrating gas may then be passed through the test G-M tubes which
permits final calibration in counts per minute vs. concentration.
5.5.3 Concentration Calculations and Counting Statistics
Gas concentrations were determined by first eliminating the
"background" count corresponding to the naturally occurring radiation.
This was done by subtracting the background counts per minute from the
sample plus background count, and multiplying this by the "tube
constant" previously determined for each tube. The tube constant was
determined by passing the calibrating gas through the tube jacket,
subtracting the background (obtained by counting ambient air samples)
and correcting for "dead time", which is the time required for the
positive space charge to move far enough from the anode for further
pulses to occur. The result is then a tube constant in CPM/pyCi/cc.
The details are shown below:
CPM = CPM - Background
CPM_ = - 7 - (dead time correction)
l-(2xlO
CPM
Tube constant =
Source strength (ypCi/cc)
The standard deviation in the net counting rate (sample plus back-
ground) a for a sample is
R +b R,
-------
42
where R , is the observed sample-plus-background count, R, is the
background count and t and t, are the sample and background
counting times respectively. Since R, is of this order of 20 CPM and
was determined with 15 minute counts for each tube, the background
contribution is constant and small. If R , is large, t does not
have to be large to obtain a small value of an in terms of
K
S
percentage of R , . As R , goes down however, t must be
increased. In these experiments the following procedure for counting
was used.
+b - !00°> ts = 1 minute, OR £ 3.2 percent
100 1 R +5 < 1000, t = 2 minutes, OR £ 7.2 percent
s
R , < 100, t = 3 minutes
-------
43
SECTION VI
RESULTS OF EXPERIMENTS
6.1 Plume Rise
6.1.1 Vertical Plumes
The vertical plumes emitted into a quiescent atmosphere were
observed to rise initially in a jet with almost linear growth of
radius with vertical distance. This jet region appeared to encompass
from -1/4 to -1/3 the total rise height. Measurements of the point
of maximum rise of the top of the plume indicated better correlation
with Froude Number than with Froude Number multiplied by the one-
fourth power of specific gravity. Actual least squares correlation
08
indicated a proportionality to SG' F . This indicates the assumption
p~p produces better results than p~p». This at first seems com-
O f\
pletely unreasonable, particularly since it is later shown that for
bent over plumes, P~PA produces good results. There are, however,
important physical differences between two situations. Measurements
indicate that the entrainment constant perpendicular to the flow
direction is greater than the one for the parallel flow by a factor
of from six to eight; thus the presence of a crosswind greatly
increases the entrainment. The negatively buoyant vertical plume may
also reentrain some of the falling dense fluid, so that the flux of
negative buoyancy increases with distance, rather than being constant.
This would have the effect of reducing rise time. Since correlation
with specific gravity yields such a small power, the correlation was
made with Froude Number. The least squares value of the proportionality
constant was determined to be 2.96. So that (See Fig. 12):
-------
44
H/DQ = 2.96 FR (6.1)
This value is close to that indicated by Turner which appears to yield
a relationship of
H/D * 3.1 FD
O K
The value of the entrainment constant, a, was determined for the
"top hat" region immediately downstream from the stack exit. Matching
radial and height measurements from the smoke photographs to
equation (2.09) suggests that:
a * 0.045.
When this value of a is used in equation (2.8a) to calculate plume
rise one predicts:
H/D = 2.43 Fn
0 K
This relation somewhat underestimates rise height. Apparently, in the
upper regions of the plume where velocities are low, the proportional
entrainment theory over-predicts entrainment.
6,1.2 Plumes in a Laminar Crosswind
Bodurtha noted that over a given range in specific gravities, the
plume rise is independent of specific gravity. This was also found
in the present experiments for plume rise in a laminar crosswind.
Rise height was obtained by measuring the maximum centerline plume
height from the smoke pictures. Froude Number dependence was deter-
mined by comparing rise heights from 1/4 inch and 1/8 inch diameter
stacks of equal specific gravity and velocity ratio. Dimensionless
rise height was determined to be proportional to (diameter ratio) ,
with least squares value of n as 0.35. Velocity ratio dependence
was determined by comparing rise heights for equal Froude Numbers and
-------
45
specific gravities but differing velocity ratios i.e. H r R . The
least squares value of m was found to be 0.32. Thus correlation
appears to follow the expression suggested by equation (2.16). H/D
is plotted vs. R SG F in Fig. 13. The least squares value
K
for the constant of proportionality is 1,32 so that:
H/D = 1.32 R1/3SG1/3Fn2/3 (6.2)
O K
The correlation with this equation is good except for the lowest
Froude Numbers, where the rise is moderately less than predicted.
Apparently the rise time is low enough that the net entrainment is
rather low; hence the Boussinesq approximation is not valid over a
sufficient range of the height.
The fact that plumes correlate well with this equation is for-
tuitous, since a significant portion of plume rise over the range of
variables examined takes place in a near-vertical configuration,
whereas equation (2.16) was obtained under assumptions of a near
horizontal plume. The fact that rise heights of plumes with specific
gravities from 1.5 to 3 would not significantly differ seems strange
since in the jet region plume rise is predicted as /SCf.
Measurements also indicate that equation (2.18) gives a good
estimate for the horizontal position of the point of maximum rise.
For plumes such that the point where the lower edge of the plume
touched the floor could be determined with reasonable certainty
(diffusion of the smoke downstream made some plumes visually indeter-
minate at larger distances) the results indicate that strong correla-
tion of touchdown distance with the "horizontal" Froude Number occurs
for plumes of equal diameter, velocity ratio and rise height, but
-------
46
differing specific gravities. Linear proportionality was noted.
Correlation with equation (2.17) was noted but with a fair amount of
scatter. The correlation of variables of equation (2.17) is plotted
in Fig. 14. A least squares value of the constant of proportionality
of 0.56, was found, so that:
= 0.56 ((-)[(2 + 1) - l]} (6.3)
oo /R
where X is the horizontal distance from the stack to the point
where the lower edge of the plume touches the tunnel floor.
6.1.3 Plume Rise in the Presence of a Cubical Structure
The plumes emitted from the center of a cubical structure
exhibited no variation with specific gravity as far as avoiding
entrainment into the cavity immediately behind the building. All
plumes were found to obey the criteria of Meroney and Yang that for
R _> 1 and h /h, ^L 2 entrainment in this region will be avoided.
Farther downstream, the negatively buoyant plumes were observed to
fall into the wake region of the building at distances beyond X as
calculated from (2.18), but in this region subsequent entrainment into
the building will not occur as it does in the cavity region. The
criteria to avoid such entrainment into the cavity region for nega-
tively buoyant plumes, in addition to that of Yang and Meroney,
appears to be that (from equation 2.18)
F 2
x = Doir ^ 3hb
For a cubical structure 3h, is the downstream extent of the cavity
region as found by Halitsky (12).
-------
47
6.2 Concentrations
6.2.1 Plumes in a Laminar Crosswind
The plumes injected into a laminar crosswind exhibited the
following behavior regarding diffusion. The plume cross section iso-
pleths at the maximum rise height (See Fig. 15) indicate a serai-
elliptic cross section at this point. The concentration gradients are
much steeper at the top of the plume than at the bottom, which would be
expected since a condition analogous to diffusion in unstable stratifi-
cation exists at the lower plume boundary. The negative buoyancy of
individual plume particles contributes to diffusion in this direction
since if a particle is displaced from the center of the plume in a
downward direction, it tends to continue due to the increased density
over that of the surrounding fluid, During the rise period, this trend
is accentuated since the direction of greatest diffusion is opposite
to the mean plume motion, thus increasing the relative displacement.
As the plume descends, the cross sections become more nearly circular
and the vertical distribution of concentration becomes 'more symmetrical
with the skew decreasing. The longitudinal rate of decay of the "non-
dimensional" concentration — ^ — approaches proportionality with
- -4/1?
(X-X) ' as the plume approaches XD (See Figs, 16-18). Plots of
maximum values of non-dimensional concentration at the plume high
point and at the point where plume centerline touches the tunnel floor
_2
vs. H/D indicate approximate proportionality with (H/D ) . Thus
simple mixing length theory predicts good approximations for the decay
in maximum concentrations for the "worst case" of negatively buoyant
-------
48
plumes injected into light winds such that the diffusion is essentially
controlled by plume turbulence. The proportionality constants
indicated are:
— ^ — = 2.15(H/D ) ' at point of maximum rise (6.4)
XVD 2 2H+h -1.95
— 0^- = 3.10 (-rr — -) at point of plume "touchdown" (6.5)
^ o
6.2.2 Dense Ground Source in a Turbulent Boundary Layer
Density differences were observed to have a significant effect on
the downstream diffusion pattern of a ground source. This effect was
primarily multiplicative, however, rather than a change in the power
law of decay with downstream distance as is normally observed with an
inversion stratification. Fig, 21 and 22 show the rate of decay of
maximum values of the quantity of xU/Q. With downstream distances
from the source U in this case is taken as the velocity at the source
centerline. In this case U was taken as 3.5 ft per second. Decay
rates of maximum concentration with downstream distance for a specific
gravity of pne were observed to be proportional to power laws of -1.68
and -1.45 for the neutral and inversion cases respectively, which is
in good agreement with previously observed values (7 , 27). The maximum
concentrations of the denser gases decay at a slightly greater rate
when the concentrations slowly approach those of air since the density
effects are attenuated by diffusion. Over the range of downstream
distances examined, a specific gravity of two, for example, increases
maximum ground concentrations by a factor of approximately 30 percent
in both neutral and inversion stratifications.
-------
49
The lateral and vertical plume dimensions for the 50 and 10 percent
levels reveal the following behavior (See Figs. 23-30). As the dense
plumes leave the source, the radial density gradients inhibit vertical
diffusion and accelerate lateral spread, so that initially the lateral
values of the spread rate are greater while the vertical values are
smaller. As the plume proceeds downstream, the 50 percent concentra-
tion plume dimension becomes larger for the less dense gases as the
concentration distributions for the denser gases exhibit sharper
"peaks. See Fig. 31. Apparently a "core" of dense gas resistant to
vertical diffusion is formed as the density differences in the outer
lateral regions of the plume are attenuated by diffusion. The lighter
gases thus arrive at heights where they are transported laterally
faster by diffusion than the heavier gases can move laterally at ground
level solely due to gravitational effects. The vertical spread of the
50 and 10 percent concentration levels is shown to be less for the
dense gases over the distance studied, but they approach that of air as
the plume proceeds downstream.
6.2,3 Decay of Concentration in Buoyancy Dominated Plumes
After Touchdown
The plumes injected into the turbulent boundary layer with free
stream velocity of 2,5 ft per second exhibited the following behavior.
An extremely large lateral spreading occurred immediately after touch-
down. The concentration profiles in the lateral direction were quite
flat. The initial decay rate is approximately proportional to X
(See Fig. 32), which is similar to the behavior noted by Holly and
Grace with salt water plumes in an open channel, The decay rate
appears to approach ground source behavior as all plumes approach a
2
-1.7 power law decay rate. (Values of velocity in the x^Z /Q are
-------
50
free stream velocity.) Such behavior is expected to occur only in
those plumes where as a result of high densities and/or low exit
velocities and crosswinds, the plume touches down a short distance
from the stack.
-------
51
SECTION VII
CONCLUSIONS
1. The rise height of a negatively buoyant plume is increased by
increasing the discharge velocity. For a given flow rate, this can be
accomplished by decreasing the stack or relief valve diameter. For a
-3/2
constant flow rate, rise height is proportional to D for vertical
-4/3
plumes in a quiescent atmosphere and to D for plumes in a cross-
wind. The horizontal position of plume descent to the ground will also
be increased by decreasing the stack diameter for a given flow rate and
_2
stack height. This horizontal distance is proportional to D , and
is of course increased with increased stack height being approximately
3/2
proportional to (2+h /H) for significant values of h /H .
2. For plumes of relatively high density exhausted into light
winds, such that the density difference and resulting vertical motion
dominates diffusion, the ground concentration will be approximately
proportional to (2H+h ) . The downstream decay rate from this point
YT T ~\n i v £r
is p— = (77-)n(V-3 ' where D is the point of plume touchdown. The
x V D
-.65 power law decay rate can be extended to the intersection with the
ground source decay rate and that rate assumed from that point on.
3. The effect of negative buoyancy on the behavior of ground
source is primarily multiplicative as the decay relationship is not changed
in form. Large specific gravities produce only moderate percentage
increases in downstream concentration values rather than order of mag-
nitude changes. Negative buoyance causes larger lateral and smaller
vertical plume dimensions than are observed in cases of neutral buoyancy.
-------
52
BIBLIOGRAPHY
(1) Albertson, M. L., Dai, Y. B., Jenson, R. A., and Rouse, H.,
"Diffusion of Submerged Jets," ASCE Transactions, 115, pp. 639-697
(1950).
(2) Becker, H. A., Hottel, H. C., and Williams, G.C., "The Nozzle-
Fluid Concentration Field of the Round Turbulent Free Jet,"
Journal of Fluid Mechanics, 30, pp. 285-304 (1968).
(3) Bodurtha, F. T. "The Behavior of Dense Stack Gases," J. Air
Pollution Control Assoc., 11, 431-437 (1961).
(4) Briggs, G. A., "A Simple Model for Bent Over Plume Rise," Ph.D."
Dissertation, Pennsylvania State University, (1970).
(5) Briggs, G. A., Plume Rise, Atomic Energy Commission Critical
Review Series, Division of Technical Information, TID-25075,
(1969).
(6) Cermak, J. E. et al., "Simulation of Atmospheric Motion by Wind
Tunnel Flows," Colorado State University, Report No. CER66-67
JEC-VAS-EJP-GJB-HC-RNM-SI-17, (1966).
(7) Chaudhry, F. H. and Meroney, R. N., "Turbulent Diffusion in a
Stably Stratified Shear Layer," FDDL Report CER69-70FHC-RMN12
(U.S. Army Electronics Command Technical Report C-0423-5), (1969).
(8) Chesler, S. and Jesser, B. W., "Some Aspects of Design and
Economic Problems Involved in Safe Disposal of Inflammable
Vapors from Safety Relief Valves," Transactions of the ASME,
pp. 229-246 (Feb. 1952).
(9) Counihan, J., "An Improved Method of Simulating an Atmospheric
Boundary Layer in a Wind Tunnel," Atmospheric Environment, Vol. 3,
pp. 197-214 (1969).
(10) Csanady, G. T., "Bent Over Vapor Plumes," Journal of Applied
Meteorology, 10, pp. 36-42 (1970).
(11) Davar, K. S., "Diffusion from a Point Source Within a Turbulent
Boundary Layer," Ph.D. Dissertation, Colorado State University,
(1961).
(12) Halitsky, J., "Gas Diffusion Near Buildings," Meteorology and
Atomic Energy, pp. 221-225 (1968).
(13) Hewett, T. A., "Model Experiments of Smokestack Plumes in a
Stable Atmosphere," Ph.D. Dissertation, M.I.T., (1971).
(14) Hoult, D. P., Fay, J. A., and Forney, L. J., "A Theory of Plume
Rise Compared with Field Observations," Paper No. 68-77, Air
Pollution Control Association, Pittsburgh, (1968).
-------
S3
(15) Holly, F. M. and Grace, J. L., "Model Study of Dense Jets in
Flowing Fluid," Proceedings of the Hydraulics Division No. 9365,
ASCE, (1972).
(16) Keefer, J. F. and Baines, W. A., "The Round Turbulent Jet in a
Crosswind," Journal of Fluid Mechanics, 15, pp. 481-496 (1963).
(17) Malhotra, R. C., "Diffusion From a Point Source of Buoyancy in a
Turbulent Boundary Layer with Unstable Density Stratification,"
Ph.D. Dissertation, Colorado State University, (1962).
(18) Meroney, R. N. and Chaudhry, F. H., "Wind Tunnel Analysis of Dow
Chemical Facility at Rocky Flats, Colorado," Colorado State
University Report No. CER71-72 RNM-FC-45 (1972).
(19) Morton, B. R., Taylor, G, I., and Turner, J. S., "Turbulent
Gravitational Convection from Maintained and Instantaneous
Sources," Proc. Royal Society A23, pp. 1-23 (1956).
(20) Morton, B. R., "Buoyant Plumes in a Moist Atmosphere," Journal of
Fluid Mechanics, 2, pp. 127T143 (1957),
(21) Plate, E. J. and Lin, C. W., "Investigations of the Thermally
Stratified Boundary Layer," Fluid Mechanics Paper No. 5, Colorado
State Unviersity, (1966).
(22) Rouse, H., Yih, C. S. and Humphries, H. W., "Gravitational
Convection from a Boundary Source," Tellus, 4, p. 201ff. (1952).
(23) Scorer, R. S., "The Behavior of Chimney Plumes," Int. J. Air
Pollution, 1, pp. 198-220 (1959).
(24) Scorer, R, S., "Experiments on Convection of Isolated Masses of
Buoyant Fluid," Journal of Fluid Mechanics, 2, pp. 583-594 (1957).
(25) Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York,
6th Edition (1966).
(26) Shin, C. C., "Continuous Point Source Diffusion in a Turbulent
Shear Layer," M.S. Thesis, Colorado State University, (1966).
(27) Slade, D. H,, Editor, Meteorology and Atomic Energy, U.S. Atomic
Energy Commission, Division of Technical Information, (1968).
(28) Slawson, P. R. and Csanady, G. T., "On the Mean Path of Buoyant
Bent Over Chimney Plumes," Journal of Fluid Mechanics, 28,
Part 2, pp. 311-312 (1967).
(29) Sutton, 0. G., Micrometeorology, McGraw-Hill Book Co., Inc., New
York (1953).
(30) Tulin, M. P. and Schwartz, J,, "Chimney Plumes in Neutral and
Stable Surroundings," Journal of Atmospheric Environment,
Vol 6 (1), pp. 19-35 (1972).
-------
54
(31) Turner, J. S., "Plumes with Negative or Reversing Buoyancy,"
Journal of Fluid Mechanics, 26, pp. 779-792 (1966).
(32) Wigley, T. M. L. and Slawson, P. R., "A Comparison of Wet and
Dry Bent Over Plumes," Journal of Applied Meteorology, 11,
No. 2, pp. 335-340 (1972).
(33) Wigley, T. M. L. and Slawson, P. R., "On the Condensation of
Buoyant Moist Bent Over Plumes," Journal of Applied Meteorology,
10, (1971).
(34) Yang, B. T. and Meroney, R. N., "Gaseous Dispersion Into
Stratified Building Wakes," Colorado State University Report
No. CER70-71 BTY-RNM-8, (1970).
(35) Yang, B. T. and Meroney, R. N., "Wind Tunnel Study on Gaseous
Mixing due to Various Stack Heights and Injection rates above
an Isolated Structure," FDDL Report, CER71-72 RNM-BTY 16, (1971)
-------
55
TABLE I
VERTICAL PLUMES
SMOKE VISUALIZATION DATA
Stack Exit
Velocity Ft.
Per Second
5.44
5.44
5.62
7.39
8.13
8.03
7.50
7.50
7.50
3.70
7.39
14.61
22.07
15.19
22.34
20.10
22.08
7.38
14.85
20.30
22.18
14.80
Stack
Diameter
Inches
.250
.250
.250
.250
.250
.250
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
Specific
Gravity
1.50
2.00
1.24
1.25
1.52
1.97
1.09
1.25
1.50
1.09
2.00
1.96
2.00
1.49
1.50
1.42
1.42
1.35
1.35
1.35
1.35
3.00
Rise
Height
Inches
8.29
6.39
11.95
19.33
14.00
9.05
13.70
13.00
10.86
8.10
6.53
13.00
20.23
16.43
23.55
23.96
25.44
8.89
18.28
26.10
27.30
11.35
-------
56
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69
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Fig. 11. Smoke Photographs
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Negatively Buoyant Gro\ind Source, Inversion
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-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-650/3-74-003
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
WIND TUNNEL TESTS OF NEGATIVELY BUOYANT PLUMES
5. REPORT DATE
October 1973
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
T. G. Hoot, R. N. Meroney and J. A. Peterka
8. PERFORMING ORGANIZATION REPORT NO.
RNM-JAP-13
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Fluid Dynamics and Diffusion Laboratory
Colorado State University
Fort Collins, Colorado 80521
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
AP-01186
12. SPONSORING AGENCY NAME AND ADDRESS
13. TXPE OR.REPORT AND PERIOD COVERED
Meteorology Laboratory - EPA
National Environmental Research Center
Research Triangle Park, North Carolina 27711
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The results of tests made of negatively buoyant emissions into a quiescent
medium, laminar crosswind and turbulent boundary layer conducted in a wind
tunnel and reported. Measurements include the maximum rise height, horizontal
point of descent and behavior of emission characteristics.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Wind tunnel tests
Nagatively buoyant plumes
Plume dispersion
Plume ruse
Air pollution meteorology
13. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (ThisReport)
21. NO. OF PAGES
104
20. SECURITY CLASS (Thispage}
22. PRICE
EPA Form 2220-1 (9-73)
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