session 4, unit 7 plume rise. qualitative descriptions plume rise h h=h s + h driving forces...
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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