chapter 8 – smokestack plumes

20
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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Page 1: Chapter 8 – Smokestack plumes

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.

Page 2: Chapter 8 – Smokestack plumes

2

Basic plume types

A morning coning plume

another coning plume

Page 3: Chapter 8 – Smokestack plumes

3

A coning plume in Hanover, New Hampshire

A looping plume

(Scorer, 1997, page 390)

Page 4: Chapter 8 – Smokestack plumes

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)

Page 5: Chapter 8 – Smokestack plumes

5

A fanning plume

Page 6: Chapter 8 – Smokestack plumes

6

Examples of fumigation

Juarez Power Planthttp://windowoutdoors.com/FateXport/FateXport.html

Over Antarcticaphoto by J. Dana Hrubesdhrubes.home.att.net/march-05.html

Unknown locationhttp://www.cmar.csiro.au/airquality/index.html

The Gaussian model for smokestack plumes

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)

Page 7: Chapter 8 – Smokestack plumes

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…

Page 8: Chapter 8 – Smokestack plumes

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

Page 9: Chapter 8 – Smokestack plumes

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.

Page 10: Chapter 8 – Smokestack plumes

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)

Page 11: Chapter 8 – Smokestack plumes

11

Some of the values depend on the state of the atmosphere.

Traditional classification of common atmospheric conditions (Turner, 1970)

Surface

wind speed

Day

solar radiation

Night

cloudiness

( m/s) strong moderate slight overcast overcast cloudy clear

< 2 A A – B B D D E F

2 – 3 A – B B C D D E F

3 – 5 B B – C C D D D E

5 – 6 C C – D D D D D D

> 6 C D D D D D D

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

Page 12: Chapter 8 – Smokestack plumes

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

Page 13: Chapter 8 – Smokestack plumes

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

Page 14: Chapter 8 – Smokestack plumes

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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)

Page 15: Chapter 8 – Smokestack plumes

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

Page 16: Chapter 8 – Smokestack plumes

16

Vertical plume in Hanover on a cold winter morning

For y = 0(downwind direction)

(Source: Masters, 1997, page 416)

Page 17: Chapter 8 – Smokestack plumes

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

Page 18: Chapter 8 – Smokestack plumes

18

Watch out for the sea breeze!

Danger of fumigation in a sea-breeze

Page 19: Chapter 8 – Smokestack plumes

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.

Page 20: Chapter 8 – Smokestack plumes

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Note how single plumes merge to make super-plumes.

These profiles give an idea of how high the pollution reached in the atmosphere.

http://www.panoramio.com/photo/25258369 http://materialstechnology.tms.org/edu/article.aspx?articleID=2535

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