Concentration Calculation

8/20/2019 Concentration Calculation

1/53

Understanding the USEPA’s

AERMOD Modeling System for

Environmental Managers

Ashok Kumar Kanwar Siddharth Bhardwaj

Abhilash Vijayan

University of Toledo

[email protected]

Concentration Calculation


2/53

AMBIENT AIR ONENTRATION

MODE!IN"

Ty#es of Poll$tant So$r%es

• oint Sour!es e.".# sta!ks or vents• Area Sour!es e.".# landfills# $onds# stora"e $iles• Volume Sour!es e.".# !onveyors# stru!tures with multi$le vents

&a%tors Affe%ting Dis#ersion of Poll$tants in the Atmos#here

Sour!e %hara!teristi!s• &mission rate of $ollutant• Sta!k hei"ht• &'it velo!ity of the "as

• &'it tem$erature of the "as• Sta!k diameter

(eteorolo"i!al %onditions• )ind velo!ity• )ind dire!tion• Ambient tem$erature• Atmos$heri! stability


3/53

ONENTRATION MODE!IN"

• lume rise !al!ulations

• %on!entration !al!ulations

• *is$ersion !oeffi!ients

• *ownwash !onditions

• &valuation


4/53

BAS+% S&,(&-TS / A- &0&VAT&* 0U(&


5/53

BASI SE"MENTS O& AN E!E'ATED

P!UME

+-+T+A0 1AS&• Verti!al 2et 3 &ffluents are not defle!ted immediately u$on enterin" the

!ross flow if 4Vs 5 U 6 7 8• Bent9ver 2et Se!tion 3 &ntrainment of the !ross flow is ra$id be!ause by

this time a$$re!iable "rowth of vorti!es has taken $la!e• Thermal Se!tion 3 Self "enerated turbulen!e !auses mi'in" and

determines the "rowth of $lume

T:A-S+T+- 1AS&• lume;s internal turbulen!e levels have dro$$ed enou"h so that the

atmos$heri! eddies in the inertial sub ran"e determines the $lume;s "rowth

*+//US+- 1AS&• The $lume;s own turbulen!e has dro$$ed and ener"y !ontainin" eddies

of atmos$heri! turbulen!e determine the "rowth of $lume


6/53

T


7/53

%0ASS+%A0 ,AUSS+A- 0U(&

(*&0S

Advantages

• rodu!e results that mat!h !losely with e'$erimental

data• +n!or$orate turbulen!e in an ad9ho! manner • Sim$le in their mathemati!s• =ui!ker than numeri!al models• *o not re>uire su$er !om$uters

Disadvantages

• -ot suitable if the $ollutant is rea!tive in nature

• /ails to in!or$orate turbulen!e in !om$rehensivesense• Unable to $redi!t !on!entrations beyond radius of

a$$ro'imately ? Km• /or "reater distan!es# wind variations# mi'in"

de$ths and tem$oral variations be!ome $redominant


8/53

SOURES O& ERROR IN A !ASSIA!

"AUSSIAN MODE!


9/53


10/53

&//&%T+V& SU:%& 1&+,1T

(&T1*

• +nde$endent of downwind distan!e# '• &ffe!tive sour!e hei"ht.4S!reen model8

h hs ∆h 9 htwhere#

hs hysi!al !himney hei"ht

ht (a'imum terrain hei"ht between

the sour!e and re!e$tor

VA:+AB0& 0U(& (&T1*• Takes into a!!ount the tilt of the $lume


11/53

0U(& *+S&:S+- A:A(&T&:S

• :elease 1ei"ht

• Terrain /eatures

• Velo!ity /ield

• Sam$lin" Time


12/53

P!UME RISE A!U!ATIONS

• -o $enetration

• %om$lete $enetration

• artial $enetration


13/53

INPUT PARAMETERS &OR

P!UME RISE• Buoyant /lu'

• (omentum /lu'

• Brunt9Vaisala /re>uen!y

• enetration arameter


14/53

P!UME RISE INPUT

"ravitytodueona!!elerati"

raturee'it tem$esta!kT

itye'it velo!sta!kw

T84TCT

downwashsta!k ti$for!orre!tedradiussta!kr

3where

r wTT/

/lu'(omentum

T

CTr "w/

/lu'Buoyant

s

s

Ss

s

?s

?s

s

m

s

s?

ss b

===

−==

=

=


15/53

P!UME RISE INPUT

( )

hei"htsta!kats$eedwindisu

hDCh

Chu-/

arameter nenetratio

E@@DtoDfromtakenisvalueTy$i!al

layer.stableelevatedin the"radientetemeratur otentialD

F

Datretem$eratu $otentialAmbientF

D

F

8F4D

" -

/re>uen!yVaisala9Brunt

sih

G

h

?

bs

ii

i

H5?

DDi i

−=

=

+

=∂∂ =

∂∂

=>


16/53

P!UME RISE IN T*E ON'ETI'E

BOUNDAR+ !A+ER

distan!edownwind'

@.I84J $arametertentrainmenJ

hatus$eedwindu

3where

u?J

'G/

uJ

'G/Ch

lume*ire!t

HH

s $

H5G

G

$

?

H

?

b

?

$

?

H

md

===

==

+=


17/53

INDIRET P!UME

$aramter8tentrainmenless4dimension.H and

?.GL .7MJH.7M 3

8h4DJr

se!tion!ross $lumeelli$ti!alassumedanof

dimensionsverti!aland0ateral

u'w

7L r r r

u

'

r r u

D?/ Ch

e

y?

si?h

?

$

??G5?

ye?

hDy

$

H5?

Dy $

i bi

=

===−=

≡

+=

=

∗

with

where:


18/53

P!UME RISE &OR PENETRATED

P!UME

h

H5GG

s

G

e>

e>is

e$

e>se$

ChG

? ?.ICh

[email protected]?

Dh h

n $enetratioartial3?%ase

Chhh

n $enetratio%om$lete3H%ase

+=

∆++

=

+=


19/53

P!UME RISE IN STAB!E

BOUNDAR+ !A+ER

.N- -3

' - !os9H

' -sin

/

/ -

-

/ ?.II

H

G5HHH

b

m

HG5H

?

b

=

+

=∆

where

uuuh

p p p

s

U $ and - are evaluated initially at sta!k hei"ht and

subse>uent $lume estimates are made iteratively by avera"in"them at sta!k to$ with those at hs Chs5?


20/53

T*E MA,IMUM &INA! RISE

O& STAB!E P!UME

risefinaltodistan!eThe 3

ar!tan -

u

u

/ ?.IIOPh

H

m

H

$

G5H

?

$

bs

≡

=

=∆

f

b

f

f

xwhere

F

N F x

N x


21/53

NEUTRA! ATMOSP*ERI

ONDITION -N./0

elo!ityfri!tion vu

s!alelen"thneutral0

rise $lumeneutralh3

uu

/ 0

80H.?4h0H.?h

n

n

?Q $

b

n

G5?

ns

E5G

nn

=

≡≡∆

=

+=∆

∗

where

and


22/53

A!M STAB!E ONDITION

G57

H57 b

s! -

/7 h =∆

/+-A0 STAB0& 0U(& :+S& &=UAT+-

RhMhMOP'hMh(+-hs!nf sss

∆∆∆∆=∆


23/53

SOURE *ARATERI1ATION

• Sour!e !an be !hara!teriDed as $oint# area# volume.

• Additional ability to a!!ount for irre"ular sha$ed areas

• oint Sour!e3 similar to +S%G

+n$ut3 0o!ation# &levation# &mission rate# Sta!k hei"ht# Sta!k inside

diameter# Sta!k "as e'it velo!ity# and Tem$erature.

• Area Sour!e3

o Treatment is enhan!ed from that available in +S%G

o +n$ut as s>uares# re!tan"les# !ir!les or $oly"ons

o oly"ons may be defined u$to ? verti!es.


24/53

SOURE *ARATERI1ATION

4%ontd..8

• Volume Sour!es3

o *iffers from +S%G in !onsiderin" the initial $lume siDe

o +n$ut in!ludes 0o!ation# &levation hei"ht# 1ei"ht of release#

&mission rate# +nitial lateral and verti!al $lume rise

o Unlike +S%G# A&:(* adds the s>uare of the initial $lume siDe

to the s>uare of ambient $lume siDe

y? yl? yo?


25/53

ONENTRATION

• %on!entration# % is "iven by the e>uation

)here#

= &mission rate

U &ffe!tive wind s$eed

y $df in lateral dire!tion

D $df in verti!al dire!tion

Dy.U

=% =


26/53

ONENTRATION 4!ontd..8

• A&:(* assumes a traditional ,aussian $.d.f. for both the lateral andverti!al distributions in the SB0 and for the lateral distribution in the%B0.

• The %B0s verti!al distribution of $lume material refle!ts the distin!tlynon9,aussian nature of the verti!al velo!ity distribution in !onve!tivelymi'ed layers.

• )ei"htin" of the ? states de$ends on the

o *e"ree of atmos$heri! stability

o )ind s$eed

o lume hei"ht relative to terrain

• Under stable !onditions horiDontal $lume dominates thus "iven "reaterwei"ht# while in unstable and neutral !onditions terrain risin" $lume iswei"hted more.


27/53

"ENERA! STRUTURE &OR

OMP!E, TERRAIN

• +n stable flows a stable two layer stru!ture is used3 lower layer remains

horiDontal while u$$er layer tends to rise over terrain

• 0ayers are distin"uished by the dividin" stream line 1!. lume below

the 1! remains horiDontal and the $lume above 1! follows the hill and

rises.

• +n neutral and unstable !ases lower layer disa$$ears and entire flow

rises u$ the hill.


28/53

T2O STATE APPROA* &OR

ONENTRATION A!U!ATIONS IN T*E

PRESENE O& A *I!!

The total !on!entration $redi!ted by A&:(* is the wei"hted sum of thetwo e'treme $ossible $lume states


29/53

T2O !A+ER ONEPT

• The !on!entrations on a hill lies between values asso!iated with two

$ossible e'treme states of a $lume3o %ase H3 A horiDontal $lume that o!!urs under stable !onditions

where he flow is for!ed to "o around the hill

o %ase ?3 Terrain flowin" state where the $lume rises over terrain

-ote3 /or sim$le terrain the two !ases are e>uivalent.


30/53

ONENTRATION IN T*E PRESENE

O& A *I!!

)here3

%T P'r # yr # Dr O Total %on!entration

%!#s P'r # yr # Dr O %on!entration from the horiDontal $lume state

%!#s P'r # yr # D $O %on!entration from the terrain followin" $lume state f lume state wei"htin" fun!tion

D $ 1ei"ht of re!e$tor above terrain

Dr &levation of re!e$tor above sta!k base

Dt &levation of terrain above sta!k base

OD#y#P'f8.%4HOD#y#P'f.%OD#y#P'% $r r s!#r r r s!#r r r T −+=

tr $ DDD −=


31/53

DI'IDIN" STREAM!INE *EI"*T 3 *

• 1! is !al!ulated usin" the al"orithm in %T*(0US usin" h! from

A&:(A as3

)here3

- Brunt9Vaisala fre>uen!y

u41!8 )ind s$eed at hei"ht 1!

h! :e!e$tor s$e!ifi! terrain s!ale

{ } ( )dDDh -1.u?

H !

!

h

1

!

?

!

?

∫ −=

H5?

D

F

F

" -

∂

∂=


32/53

DI'IDIN" STREAM!INE *EI"*T 4 * 4%ontd..8

• The fra!tion of the $lume mass below 1!# as

• )ei"htin" fa!tor f is related to the fra!tion by

{ }

{ }∫

∫ ∞=Φ

@r r r T

1

@

r r r T

$

dDD#y#'%

dDD#y#'%!

[email protected] $Φ+=


33/53

T*REE P!UME APPROA* 3

&UNDAMENTA! &EATURE O&

AERMOD’S ON'ETI'E MODE!

A&:(*s Three lume Treatment of the %B0


34/53

ONENTRATIONS IN B!• *owndrafts more $revalent in %B0 than the u$draftsM the verti!al

!on!entration distribution is not ,aussian.

• Sin!e lar"er $er!enta"e of the $lume is affe!ted by the downdrafts thisensembla"e avera"e has a "eneral downward trend.

+nstantaneous and !orres$ondin" ensembla"e9avera"ed $lume in the %B0


35/53

ONENTRATIONS IN B! 4!ontd..8

• The instantaneous $lume is assumed to have a ,aussian !on!entrationdistribution about its randomly varyin" !enterline

• The mean !on!entration is found by summin" the !on!entrations due torandom !enterline dis$la!ements. This results in a skewed distribution

whi!h A&:(* $resents as a bi9,aussian $.d.f.• A&:(* a$$roa!h e'tends ,iffords model to a!!ount for $lume rise.

• The $.d.f. of the $lume !enterline hei"ht D! is

)here hs is the sta!k hei"ht# u is the mean wind s$eed and ' is the

downwind distan!e# h is the $lume rise in!ludin" sour!e momentumand buoyan!y effe!ts

u

w'ChhD

s! ++=


36/53

T*REE P!UME APPROA* 4!ontd..8

• *ire!t or :eal Sour!e 9 des!ribes the dis$ersion of the $lume material

that rea!hes "round dire!tly from sour!e via downdrafts

• +ndire!t Sour!e 9 treats the $lume se!tions that initially rise to the%B0 to$ in u$drafts and return to the "round via downdrafts

• enetrated Sour!e 9 a!!ounts for the material that initially $enetrates

the elevated inversion hei"ht


37/53

ONENTRATION IN B!

• The total !on!entration in the %B0 for the horiDontal $lume state is

)here3

%! P'r # yr # Dr O Total !on!entration in %B0

%d P'r # yr # Dr O *ire!t Sour!e !on!entration !ontribution

%r P'r # yr # Dr O +ndire!t Sour!e !on!entration !ontribution

% $ P'r # yr # Dr O enetrated Sour!e !on!entration !ontributionThe total !on!entration for the terrain res$ondin" state has the form of

the above e>uation by re$la!in" Dr with D $.

O###PO##PO##PO##P r r r pr r r r r r r d r r r c z y xC z y xC z y xC z y xC ++=


38/53

ONENTRATION IN SB!

• &>uation for !on!entration in SB0

meander84withfun!tionondistributi0ateral/

Sour!eStableof 1ei"hth

on!ontributiion!on!entratSour!eStableOD#y#P'%

3where

?

8Dm?h4De'$

?

8Dm?9h94De'$

/.

u?W

= OD#y#P'%

y

es

r r r s

9m?

Ds

?ieff es

?

Ds

?ieff es

y

Ds

Xr r r s

≡≡

≡

++−+

−⋅

≡

∑∞

∞→


39/53

P!UME SIMU!ATION IN AERMOD• E different $lume ty$ed simulated based on the atmos$heri! stability and

on the lo!ation and in and above the boundary layer

o *ire!t

o +ndire!t

o enetrated

o +nje!ted

o Stable

• *urin" stable !onditions# $lumes are modeled with the familiar horiDontaland verti!al ,aussian formulations

• *urin" !onve!tive !onditions 40Y8 the horiDontal distribution is still,aussianM the verti!al !on!entration distribution results from a !ombination

of the first three $lume ty$es.

• *urin" !onve!tive !onditions# A&:(* also handles a s$eai!l !asereferred to as an inje!ted sour!e where the sta!k to$ 4or release hei"ht8 is"reater than the mi'in" hei"ht.


40/53

ESTIMATION O& DISPERSION

OE&&IIENTSy Standard deviation for lateral !on!entration

D Standard deviation for verti!al !on!entration

%ase H3 )ithout a buildin"

Z Ambient turbulen!e Z Turbulen!e due to buoyan!y

%ase ?3 resen!e of a buildin"

Z Buildin" wake effe!ts


41/53

DISPERSION OE&&IIENT IN

B!

?

Dd

?

Db

?

Da

?

D

?

yd

?

yb

?

ya

?

y

++=

++=

Db b

Ddyd#

Db b#

Daya#

Dy#

thatassumesA&:(*3 -ote

+8[4*9dis$ersionindu!ed*ownwash

+8[4*9dis$ersionindu!edBuoyan!y

+8[4*9dis$ersionindu!edrbulen!eAmbient tu

+8[4*9+ndire!tand*ire!t9dis$ersionTotal3

σ σ

σ

σ

σ

σ

=

≡

≡

≡

≡

y

y

where


42/53

DISPERSION OE&&IIENT &OR

A PENETRATED P!UME

489dis$ersionindu!edBuoyan!y

+8[4*9dis$ersionindu!edrbulen!eAmbient tu

48sour!eenetrated9dis$ersionTotal

3

b$

Da$ya$#

D$y$#

≡

≡

≡

σ

σ

σ

where

?

b$

?

Da$

?

D$

?

b$

?

ya$

?

y$

+=

+=


43/53

DISPERSION OE&&IIENT IN

SB!-In5e%ted So$r%es0

?

Dd

?

bs

?

Das

?

Ds

?

yd

?

bs

?

yas

?

ys

++=

++=

4S89dis$ersionindu!ed*ownwash

sour!e4S8Stable9dis$ersionindu!edBuoyan!y

4SB089dis$ersionindu!edrbulen!eAmbient tu

sour!establefordis$ersionTotal3

Ddyd#

Dasyas#

Dsys#

≡

≡

≡

≡

σ

σ

σ

σ

bs

where


44/53

!ATERA! DISPERSION DUE TO

AMBIENT TURBU!ENE -B! 6

SB!0

i

X

X

.G

X

X

D.u

' '

8'N\H4u

'

v

v

ya

σ

σ σ

=

+

=


45/53

!ATERA! DISPERSION DUE TO AMBIENT

TURBU!ENE

-PENETRATED SOURE0

[ ]e$

,ma'

,

ma'

,

hDDD#(a'D

@.7ImDhei"htrelease,rassrairie

DDN\

3followsasN\S!ale

= =

=


46/53

BUO+AN+ INDUED DISPERSION

OE&&IIENTS-DIRET SOURE0

rise $lumeSour!e*ire!tCh

3where

?

[email protected]

d

d

b

=

∆=


47/53


OE&&IIENTS

-STAB!E P!UME RISE0

rise $lumeSour!e*ire!tCh

3where

?

[email protected]

s

s b

=

∆=


48/53


OE&&IIENTS

-PENETRATED SOURE0

downwashsta!k ti$for!orre!tedhei"htSta!kh

basesta!kaboveSour!e

enetratedtheof 1ei"hth

hh

rise $lumeSour!eenetratedCh

3where

?

[email protected]

s

e$

se$

$

$

b$

=

=

−=

=

∆=


49/53

'ERTIA! DISPERSION DUE TO

AMBIENT TURBU!ENE

-SB!0

DasDes

DasD"s

sses

es

Des

i

esD"s

i

esDas

of $ortion&levatedof $ortionSurfa!e

Chhh

"roundabovehei"ht $lumesour!eStableh

3where

,round&levated

D

h

D

hH

==

+==

+

−=


50/53

' *ownwind distan!e from the u$wind of the buildin"to the re!e$tor

y %rosswind distan!e from the buildin" !enterline to the

re!e$tor

D :e!e$tor 1ei"ht above "round

'" 0on"itudinal dimension of the wake

y" *istan!e from the buildin" !enterline to the lateral ed"e

of the wake

D"

1ei"ht of the wake at the re!e$tor lo!ation

ONENTRATION A!U!ATIONS UNDER

DO2N2AS*


51/53


52/53

TREATMENT O& BUI!DIN" DO2N2AS*

Use of numeri!al $lume rise model

Use of A&:(* dis$ersion !oeffi!ients


53/53

AERMOD3*o7 it is different from other

models

Air dis$ersion fundamentally based on the $lanetary

boundary layer turbulen!e stru!ture and s!alin" !on!e$ts

The treatment of both surfa!e and elevated sour!es in

in!luded

Both sim$le and !om$le' terrains are treated with the same

set of e>uations

Concentration Calculation

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