1 Chapter 8 Environmental Transport and Fate – Smokestack plumes Benoit Cushman-Roisin Thayer School of Engineering Dartmouth College A bit of history… We tend to entertain romantic ideas of pre-industrial life as somehow healthier and more environmentally conscious than our own today. In those days, nothing was more valuable to the survival of the human race than the use of fire for warmth, protection and early industry. But the same fire could do serious damage to human health and the environment. Until the invention of the chimney in Medieval Until the invention of the chimney in Medieval Europe in the 12 th century, people had to breathe the emissions from their own hearths. The smoke from their indoor fires, although vented through a roof opening, blackened the inside of their homes with soot and presumably the inside of their lungs, too. For those people living in the plains and arid regions who lacked wood, animal dung was the only source of fuel, adding disease vectors and odor problems to already Once the chimney was invented, its use became gradually universal, and by the 18 th century, once the industrial revolution got underway, chimneys were common features at factories, mills and forges. harsh living conditions. Living by the open flame was hardly idyllic.
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Transcript
1
Chapter 8
Environmental Transport and Fate
–
Smokestack plumes
Benoit Cushman-RoisinThayer School of Engineering
Dartmouth College
A bit of history…
We tend to entertain romantic ideas of pre-industrial life as somehow healthier and more environmentally conscious than our own today. In those days, nothing was more valuable to the survival of the human race than the use of fire for warmth, protection and early industry. But the same fire could do serious damage to human health and the environment.
Until the invention of the chimney in MedievalUntil the invention of the chimney in Medieval Europe in the 12th century, people had to breathe the emissions from their own hearths. The smoke from their indoor fires, although vented through a roof opening, blackened the inside of their homes with soot and presumably the inside of their lungs, too.
For those people living in the plains and arid regions who lacked wood, animal dung was the only source of fuel, adding disease vectors and odor problems to already
Once the chimney was invented, its use became gradually universal, and by the 18th century, once the industrial revolution got underway, chimneys were common features at factories, mills and forges.
y g p yharsh living conditions. Living by the open flame was hardly idyllic.
2
Basic plume types
A morning coning plume
another coning plume
3
A coning plume in Hanover, New Hampshire
A looping plume
(Scorer, 1997, page 390)
4
A looping plume
Plume from tannery in medina quarter of Fez, MoroccoPhotographs taken on the evening of 4 April 2008
(Photographs courtesy of Betsy Dain-Owens, ENGS-43 student in Winter 2008)
Looping plume in Hanover, New Hampshire(Photo by Benoit Cushman-Roisin)
5
A fanning plume
6
Examples of fumigation
Juarez Power Planthttp://windowoutdoors.com/FateXport/FateXport.html
Over Antarcticaphoto by J. Dana Hrubesdhrubes.home.att.net/march-05.html
It is assumed that the structure of the plume is Gaussian (bell curve) in both cross-wind and vertical directions.
I h d i d di iIn the downwind direction, a highly advective situation is assumed.
Note that the plume is considered as originating at a height H that may be greater than the physical stack height h, because of a possible buoyancy rise.
(Masters, 1997, page 408)
7
Question:
How Gaussian is the plume structure, really?
Snapshots reveal comple shapescomplex shapes.
But time averages over turbulent fluctuations show much simpler structures, with evident single maximum and smooth tapering away from it.
Question:
Is this tapering looking Gaussian?
Let’s plot to check…
8
In the vertical
In the horizontal cross-wind direction
Looks pretty Gaussian to me.
Don’t you agree?
With Gaussian distributions as the outcome, we view the problem as one of diffusion, in three dimensions:
cKz
cD
y
cD
x
cD
x
cu
t
czyx
2
2
2
2
2
2
y
steadystate
highlyadvective
nodecay
Note that, although the problem is 3D, diffusion is only acting in 2D.With x turned into travel time t = x/u, the solution is
tD
z
tD
y
tDtD
Mzytc
zyzy 44exp
44),,(
22
9
(Masters, 1997, p
z = H
page 407)
z = 0
Then, we mind the impermeable ground surface by adding an image below ground. With z = 0 at ground level, the actual source is at z = +H and the image is at z = –H:
tD
Hz
tD
Hz
tD
y
tDtD
Mzytc
zzyzy 4
)(exp
4
)(exp
4exp
44),,(
222
We are interested only in the ground-level concentration and set therefore z to zero:
tD
H
tD
y
tDtD
Mytcytc
zyzy 44exp
44
2)0,,(),(
22
ground
It is customary in this analysis to use values instead of Dy and Dz values, because it turns out that the latter ones are not constant (they tend to grow with the size of the plume and to be affected by buoyancy and atmospheric conditions). So, we define
2
2
242
242
zzzz
yyyy
tDtD
tDtD
Both are functions of t and hence of x. The solution is now expressed as
2
2
2
2
ground 22exp
2
2),(
zyzy
HyMyxc
It remains to determine the value of M.
10
u
S
xxM
speed wind
rateemission
time/length
time/mass
length
mass
dimension missing
amount
Sketch shows how the wind acts as a diluting mechanism.It makes sense therefore that the wind speed u should be in the denominator.
The solution now takes the form:
2
2
2
2
ground 22exp),(
zyzy
Hy
u
Syxc
in which
cground = ground concentration distribution (in mg/m3)S = emission rate from the smokestack (in mg/s)u = wind speed at height H (in m/s)y = horizontal transverse dispersion coefficient (in m)z = vertical dispersion coefficient (in m)
[Both y and z are functions of downwind distance x.]y = cross-wind distance (in m)
[Take y = 0 for downwind direction]H = h + h = effective stack height (in m)
with h = physical stack height (in m)h = height adjustment (in m)
11
Some of the values depend on the state of the atmosphere.
Traditional classification of common atmospheric conditions (Turner, 1970)
A = very unstableB = moderately unstableC = slightly unstableD = neutralE = slightly stableF = stable
Notes:- Surface wind is measured 10 m above ground.- A “cloudy night” is one with more than half cloud cover.- A “clear night” is one with less than half cloud cover.
Wind velocity profile and rotation
pH
mzu
Hzu
m 10) 10(
)(
Stability class Exponent pA 0.15B 0.15C 0.20D 0.25E 0.40F 0.60
12
Pasquill curves to obtain the pair of dispersion coefficients
(Source: Masters, 1997, page 412)
If you don’t want to use the graphs (ex. in creating a Matlab code), you may rely on:
fxc
xad
z
y
894.0
with x in kilometers and values obtained in meters
13
Or, if you are lazy and want a value from a table…
We have yet to determine the effective smokestack height H, the height at which the plume appears to be originating.
h
hhH
downwash possiblerisebuoyancy
db hh
py y
Downwash occurs in strong wind (u) and with weak gas ejection velocity (ws) and is caused by low pressure in the wake of the smokestack.
Rule:
)(5.14
Hu
wrh s
d
if ws < 1.5 u(H) and in which r = inner stack radius
14
A way to avoid downwash
Helix on outside of the stack forces wind to rise upon approaching stack
To determine the buoyancy rise hd (more common than downwash), we first need to calculate the buoyancy flux F:
fumes
airs T
TwrgF 12
f
in which
F = buoyancy flux (in m4/s3)g = 9.81 m/s2, the earth’s gravitational accelerationr = inner stack radius at tip (in m)ws = fumes vertical ejection velocity (in m/s)Tair = absolute ambient temperature (in K), at stack heightTfumes = absolute temperature of gas fumes (in K)
(Recall: Absolute temperature in degree Kelvin = temperature in oC + 273.15)
15
Then, we need to distinguish whether the plume is “bent-over” or “vertical”.
1) Bent-over plume: for stability classes A, B, C and D (unstable and neutral states)
F
FxF
FxF
f
f
3/23/1
5/234
8/534
119thens/m55If
49thens/m55If
u
xFh f
b
3/23/1
6.1
xf
Distance over which plume rises
2) Vertical plume: for stability classes E and F only (stable states)
3/1
4/1
34/1
2
0.4then)(275.0If
with ,
N
FhFNu
C
g
dz
dT
T
gN
b
p
air
air
3/1
24/1 6.2then)(275.0If
uN
FhFNu b
16
Vertical plume in Hanover on a cold winter morning
For y = 0(downwind direction)
(Source: Masters, 1997, page 416)
17
Graph to determine maximum ground concentration and its distance from the stack
3
(Source: Masters, 1997, page 417)9 x 10-6
Capping by inversion
L
y
XxLu
Syxc 2for
2)0,(
then
First determine the distance xL over which the capping inversion is reached:
LzL XxHLX at)(47.0such that is
18
Watch out for the sea breeze!
Danger of fumigation in a sea-breeze
19
Downdraft in wake of building
Kuwait oil fires of 1st Gulf War (1991)About 600 naturally pressurized oil wells were set on fire in Kuwait by Saddam Hussein’s retreating army in late February 1991, injecting massive quantities of smoke, unburned hydrocarbons, sulfur dioxide and nitrogen oxides into the atmosphere.
20
Note how single plumes merge to make super-plumes.
These profiles give an idea of how high the pollution reached in the atmosphere.