Session 4, Unit 7

Plume Rise

Qualitative Descriptions

Plume rise hH=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

SimpleMore suitable for power plantFor neutral conditions

The wind speed ū is adjusted to the stack height.

For non-neutral conditions

ss

asss dT

TTP

u

vdh 31068.25.1

hCFh

StCF

CF

)(

7.010

Briggs Plume Rise Formulas

More complicatedBuoyancy 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

32

31

0297.0

s

ssc

d

VTT

31

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, mxf=3.5x*

Final plume rise:

u

xFh b

32*3

1)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

gs

a

z

Briggs Plume Rise Formulas

Final plume rise

Distance to final rise

31

6.2

su

Fh b

21

0715.2s

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.

u

vdh ss3

31

5.1

su

Fh m

Briggs Plume Rise Formulas

Gradual riseDistance < distance to final rise (i.e., x<xf) and Buoyancy dominated plume

u

xFh b

32

31

)(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)31

22

3

u

xFh

j

m

sj v

u3

1

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

b

s

ss FForuv

uvdx

31

2

/sin(3

su

usxFh

j

m

s

ux

5.0max

Briggs Plume Rise Summary

Unstable and neutral

Stable

Buoyancy

Momentum

u

xFh b

32*3

1)5.3(6.1

31

6.2

su

Fh b

u

vdh ss3

31

5.1

su

Fh m

Buoyancy Induced Dispersion

Air entrainment due to “boiling-like action” enlarges the plumeSmall impact on ground level concentration in most casesThe impact can be reflected in Initial plume size

Effective dispersion coefficients

5.300

hzy

5.020

2

5.020

2

)(

)(

zzze

yyye

Session 4, Unit 8

Averaging Time, Multiple Sources, and Receptors

Chimney, Building, and Terrain Effects

Averaging Time

The concentration calculated from the Gaussian equations should represent the averaging time that is consistent with the averaging time of Short-term: 1 monthLong-term: > 1 month

Averaging Time

If longer averaging time is desired, use the following power law

P=0.17-0.75, suggested value is 0.17

p

s

kks t

tCC

Crosswind Averaging

Integrate y from - to

Average over a sector

2

21

21

2

1exp

2

zz

cw

H

u

QC

221

2

1exp

2)(

zz

H

u

QC

Crosswind Averaging

Average over a sector considering distribution of wind speeds and stability classes

ISCLT3 and STAR

221

2

1exp

2),,(),,(

zz

n

H

u

QSufSuC

Crosswind Averaging

Smoothing transition from sector to sector Weighted smoothing function, WS

Smoothed average concentration

221

2

1exp

)(2),,(),,(

zz

n

H

u

WSQSufSuC

||0

|||)|(

ad

adad

forWS

forWS

Multiple Sources

The max from each source do not exactly overlapUse of multiple stack factorMore accurate method – modeling with a consistent coordinate system

Receptors

Receptor grid Cartesian coordinate system Polar coordinate system

Single stack, but the origin of the coordinate system is not at the stack baseMultiple stacksPresentation of results Concentration isopleths

Example Calculation

Chapter 10

Chimney EffectsStack tip downwash Low pressure behind stack

ū is at the stack top level No plume rise (“plume sink”)

Avoid stack tip downwash

5.12

5.1

'

u

vdhh

u

vWhen

ssss

s

ss

s

hh

u

vWhen

'

5.1

Building Effects

General descriptionExpanded meaning of “building”Reduce building effects – rule of thumbhs>2.5hb

Too conservative for tall thin buildings

Briggs Procedure to Minimize Downwash

Five steps:1. Correction for stack induced

downwash2. Correction for building effects3. Determine if plume is entrained in the

cavity. If entrained, treat it as a ground level source

4. Buoyancy effect5. Calculate downwind concentration

Cavity

DescriptionCavity length Short buildings (L/H2)

L affects cavity length xr

Long buildings (L/H>2) L does not affect cavity length xr

)(0.1

)(

HWB

HWA

H

L

H

xr

)(25.00.1

)(75.1

HW

HW

H

xr

Cavity

Max cavity width

It’s location long x direction

Max height

H

W

W

yr 55.0exp7.11.12

H

W

W

xym 55.0exp0.23.0

H

L

H

zr 3.1exp6.10.1

Cavity

Concentrations within cavity

b

p

u

QKC

OR

Auc

QC

Wake Downwind of Cavity

Treated as a ground level sourceTurner method (virtual source)Gifford methodGifford-Slade method (total dispersion parameters)Huber-Snyder method

Sources Downwind of Buildings

Briggs method Beyond 3b no building effect Within 3b treat them as ground

level sources

Complex Terrain

Definition Simple terrain Complex terrain Intermediate terrain

Plume behavior in complex terrain

Complex Terrain

Modeling approaches Briggs

Egan

BowneModified dispersion coefficients

ISC3 (COMPLEX 1) – to be discussed later

ste

e zh

h 2

'

2' st

ee

zhh

GEP Stack Height

Definition Greater of

65 mHG=H+1.5L (for stacks in existance on Jan

12, 1979, HG=2.5H)

Structures to be considered: within 5L

In modeling analyses, no credit is given for stack height above the GEP