Dispersion of Air Pollutants

Depends on meteorological conditions:

wind speed and atmospheric stability class (adiabatic lapse rate,

see diagrams at left)

2

Effect of stack parameters

PLUMERISE

X

PLUMECENTERLINE

z

Z RELEASEHEIGHT

he

Plume rise: fairly complex, depends on velocity and temperature of flue gas, as well as on ambient atmospheric conditions

3

Turbulence• Circular eddies of air movements over short timescales than

those that determine wind speed (unstable)• Mechanical Turbulence: – Caused by air moving over and around structures/vegetation– Increases with wind speed– Affected by surface roughness

• Thermal Turbulence: – Caused by heating/cooling of the earth’s surface– Flows are typically vertical– Convection cells of upwards of 1000 - 1500 meters

What is the effect of turbulence on pollution?Is turbulence desired?

04/07/2023 4

Atmospheric Stability

• Concept that describes (non-)movement of air near the surface

• Characterized by vertical temperature gradients (Lapse Rates)– Dry adiabatic lapse rate () = 0.976 oC/100 m ~ 1 oC/100 m– International standard lapse rate = 0.0066 oC/m

Does dry or moist air have a larger temperature change for the same change in elevation? Why?

Does lapse rate have anything to do with air quality?

04/07/2023 5

• First Law of Thermodynamics

• Barometric Equation

gdZdP

dPdTCdPdhdq p 1

= 0 for adiabatic expansion

p

p

Cg

dZdT

gdZdPdTC

1

How much is dT/dZ if Cp = 1.0034103 m2/s2-K? What if Cp = 1.856103 m2/s2-K? (for dry air and moist air)

Lapse Rate

04/07/2023 6

Stability Conditions

Adiabatic lapse rate

Environmental lapse rate

04/07/2023 7

Superadiabatic Lapse Rates (Unstable)

• Temperature decreases are greater than -10o C/km• Occur on sunny days• Characterized by intense vertical mixing• Excellent dispersion conditions

04/07/2023 8

Neutral Lapse Rates• Temperature decreases are similar to the adiabatic lapse rate• Results from:

– Cloudy conditions– Elevated wind speeds– Day/night transitions

• Describes good dispersion conditions

Isothermal Lapse Rates (Weakly Stable)• Characterized by no temperature change with height• Atmosphere is somewhat stable• Dispersion conditions are moderate

04/07/2023 9

Inverted Lapse Rates (Strongly Stable)• Characterized by increasing temperature with height

Does it occur during the day or at night?Is it associated with high or low pressure systems?Does it improve or deteriorate air quality?

www.ew.govt.nz/enviroinfo/air/weather.htm

www.co.mendocino.ca.us/aqmd/Inversions.htm

Inversion

04/07/2023 10

Inverted Lapse Rates (Strongly Stable)• Characterized by increasing temperature with height

Does it occur during the day or at night?Is it associated with high or low pressure systems?Does it improve or deteriorate air quality?

www.ew.govt.nz/enviroinfo/air/weather.htm

www.co.mendocino.ca.us/aqmd/Inversions.htm

Inversion

04/07/2023 11

Inversion• Definition: temperature increases with altitude

04/07/2023 12

Inversion

http://www.co.mendocino.ca.us/aqmd/pages/Inversion-Art-(web).jpg

04/07/2023 13

Inversion• Two major types of inversion:– Subsidence Inversion: descent of a layer of air within a high

pressure air mass– Radiational Inversion: radiation at night from the earth’s

surface into the local atmosphere

04/07/2023 14

Radiational Inversions

• Result from radiational cooling of the ground• Occur on cloudless nights – nocturnal• Typically surface based• Are intensified in river valleys• Cause pollutants to be “trapped”

What happens to inversion when sun rises?

www.co.mendocino.ca.us/aqmd/Inversions.htm

Fig 3.3

04/07/2023 15

Radiational Inversions

• Elevated inversions are formed over urban areas– Due to heat island effect– Due to dust dome

Fig 3.4

04/07/2023 16

Radiational Inversions• Breakup after sunrise• Breakup results in elevated ground level

concentrations• Breakup described as a fumigation

de.wikipedia.org/wiki/Smog

04/07/2023 17

Radiational Inversions

• Elevated inversions are formed over urban areas– Due to heat island effect– Due to dust dome

Fig 3.4

04/07/2023 18

Subsidence Inversion• Associated with high-pressure systems• Inversion layer is formed aloft• Covers hundreds of thousands of square kms• Persists for days

Fig 3.5apollo.lsc.vsc.edu/.../smog_var_geo.html

04/07/2023 19

Subsidence Inversion• Migrating high-pressure systems: contribute to the hazy

summer conditions in Midwest, SE and NE• Semi-permanent marine high-pressure systems

www.oceansatlas.org/.../datard.htm

– Results in a large number of sunny calm days

– Inversion layer closest to the ground on continental side

– Responsible for air stagnation over Southern California

Where else on earth would have similar phenomenon?

04/07/2023 20

Inversions

• Frontal - warm air overrides cooler air• Advective - warm air flows over a cold surface or

cold air

www.atmos.ucla.edu/.../inversions/Note03.html

Qualitative Descriptions• Plume rise h

H=hs + h• Driving forces– Buoyancy– Momentum

• Different phases– Initial phase– Thermal phase– Breakup phase– Diffusion phase

Qualitative Descriptions

• Influencing factors– When there is no downwash

• Exit velocity• Stack diameter• Stack gas temperature• Ambient temperature• Wind speed• Atmospheric stability• Wind shear

– Downwash

Holland Plume Rise Formula

• Simple• More suitable for power plant• For neutral conditions

The wind speed ū is adjusted to the stack height.

• For non-neutral conditions

ss

asss dTTT

Puvd

h 31068.25.1

hCFh

StCF

CF

)(

7.010

Briggs Plume Rise Formulas

• More complicated• Buoyancy flux parameter

• Momentum flux parameter

a

asssb T

TTdgvF

4

2

s

assm T

TdvF

4

22

Briggs Plume Rise Formulas• Determination of buoyancy dominated or

momentum dominated plumes– Calculate (T)c

• For unstable or neutral (A-D)– For Fb <55

– For Fb55

• For stable (E,F)

– If T (=Ts-Ta) (T)c , it’s buoyancy dominated– If T (=Ts-Ta) < (T)c , it’s momentum dominated

3

2

31

0297.0

s

ssc

d

VTT

3

1

32

00575.0

s

ssc

d

VTT

21

01958.0)( sVTT ssc

Briggs Plume Rise Formulas

• For buoyancy dominated plume under unstable or neutral conditions (A-D)– x* = distance at which atmospheric turbulence

begins to dominate entrainment• For Fb55 m4/sec3, x*=34 Fb

2/5

• For Fb<55 m4/sec3, x*=14 Fb5/8

– xf=distance to the final rise, m• xf=3.5x*

– Final plume rise:

uxF

h b3

2*31

)5.3(6.1

Briggs Plume Rise Formulas

• For buoyancy dominated plume under stable conditions (E and F)– Stability parameter, s

• Default values for

– 0.02 K/m for E stability– 0.035 K/m for F stability

TT

gsa

z

Briggs Plume Rise Formulas

– Final plume rise

– Distance to final rise

31

6.2

suF

h b

210715.2s

ux f

Briggs Plume Rise Formulas

• For momentum dominated plume under unstable or neutral conditions (A-D)

• For momentum dominated plume under stable conditions (E,F)

– Calculate both and use the lower one.

uvd

h ss3

31

5.1

suF

h m

Briggs Plume Rise Formulas

– Final plume rise

– Distance to final rise

31

6.2

suF

h b

210715.2s

ux f

Briggs Plume Rise Formulas

• For momentum dominated plume under unstable or neutral conditions (A-D)

• For momentum dominated plume under stable conditions (E,F)

– Calculate both and use the lower one.

uvd

h ss3

31

5.1

suF

h m

Briggs Plume Rise Formulas

• Gradual rise• Distance < distance to final rise (i.e., x<xf) and

Buoyancy dominated plume

uxF

h b3

23

1)(6.1

Briggs Plume Rise Formulas

• Distance < distance to final rise (i.e., x<xf) and momentum dominated plume– Jet entrainment coefficient

– Unstable conditions (A-D)3

1

22

3

u

xFh

j

m

sj v

u

31

Briggs Plume Rise Formulas• X=downwind distance with max value of:

Xmax=49Fb5/8 for 0<Fb<55 m4/sec3

xmax=119Fb2/5 for Fb> 55 m4/sec3

– Stable conditions (E,F)

• with

0)3(4 2

max

bs

ss FForuvuvd

x

31

2

/sin(3

suusx

Fhj

m

sux 5.0max

Briggs Plume Rise Summary

Unstable and neutral

Stable

Buoyancy

Momentum

uxF

h b3

2*31

)5.3(6.1

31

6.2

suF

h b

uvd

h ss3

31

5.1

suF

h m

Buoyancy Induced Dispersion• Air entrainment due to “boiling-like action” enlarges

the plume• Small impact on ground level concentration in most

cases• The impact can be reflected in – Initial plume size

– Effective dispersion coefficients5.300h

zy

5.020

2

5.020

2

)(

)(

zzze

yyye

• Calculate the final plume rise from a power plant for the following conditions:

• Atmospheric Stability D• Vs =19 m/s• ds =3 m • U 10 m =4 m/s • Ts =400 oK • Ta =283 oK • Stack Height= 67 m

• Deacon power law for calculating wind speed at stack height • u = u1 * (z/z1)p

• Where,• u = desired but unknown wind speed, (us)

• u1 = wind speed at known height, (u10)

• z = height where wind speed is unknown, hs

• z1 = height where wind speed is known, 10m• p = exponent from table 3-3 in the text = 0.15• Therefore, u = u1 * (z/z1)p = 4 * (67/10)0.15 = 5.3 m/sec

• 2) Check for downwash:• Vs / u >= 1.5 (downwash conditions need not

be considered) = 19.0/5.3 = 3.571 >1.5 (therefore downwash need not be considered)

• Where,• Vs = stack velocity in m/sec• u = wind speed at plume elevation

• 3) Calculate buoyancy flux parameter• Fb = g * vs * d2 * ΔT / (4 * Ts) • = 9.81 * 19* 32 * (400 - 283) / (4 *400) = 123 m4/s3 (Fb >

55m4/s3)• 4) Calculate temperature difference• ΔT = Ts - Ta = 400 - 283 = 1170K• 5) Calculate cross over temperature difference (ΔT)c

• for Fb > 55m4/s3

• (ΔT)c = 0.00575 * Ts * vs 2/3 / ds 1/3 = 0.00575 * 400 * 192/3 / 3 1/3

= 11.40K

• 7) Calculate final plume rise Δh• for Fb > 55m4/s3 Δh = 38.71 * (Fb

3/5 / u ) = 38.71 * (1233/5 / 5.3) = 130m

• 8) Calculate final effective plume height H• H = 130 + 67 = 197m • This is less than the typical 300m night time

inversion height; so plume rise may be reasonably accurate