# Session 4, Unit 7 Plume Rise

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```					Session 4, Unit 7

Plume Rise
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
d s vs                3  Ts  Ta    
h         1.5  2.68  10 P T         d s 

u                           s      
The wind speed ū is adjusted to the stack height.
For non-neutral conditions
 St 
CF     0.7
 10 
hCF  (CF ) h
Briggs Plume Rise Formulas
More complicated
Buoyancy flux parameter
d s2    Ts  Ta 
Fb  gvs        
 T      
4          a   

Momentum flux parameter
v s2 d s2    Ta   
Fm              
T     

4        s    
Briggs Plume Rise Formulas
Determination of buoyancy dominated or
momentum dominated plumes
   Calculate (T)c
 For unstable or neutral (A-D)
1
For Fb <55                0.0297TsVs       3
T c 


2
ds 3
   For Fb55                            2
0.00575TsVs 3
T c            1
 For stable (E,F)                    ds 3
1
(T ) c  0.01958TsVs s               2

   If T (=Ts-Ta)  (T)c , it’s buoyancy dominated
   If T (=Ts-Ta) < (T)c , it’s momentum dominated
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 Fb55 m4/sec3, x*=34 Fb2/5
 For Fb<55 m4/sec3, x*=14 Fb5/8
   xf=distance to the final rise, m
 xf=3.5x*
   Final plume rise:         1
*
2
3               3
1.6 Fb (3.5 x )
h 
u
Briggs Plume Rise Formulas
For buoyancy dominated plume under stable
conditions (E and F)
   Stability parameter, s
g   
s          
Ta  T 
 Default values for   
    
 z 

   0.02 K/m for E stability
   0.035 K/m for F stability
Briggs Plume Rise Formulas
   Final plume rise
1
 Fb                  3
h  2.6  
 us 
   Distance to final rise
u
x f  2.0715       1
2
s
Briggs Plume Rise Formulas
For momentum dominated plume under
unstable or neutral conditions (A-D)
3d s v s
h 
u
For momentum dominated plume under
stable conditions (E,F)
1
 Fm  3
h  1.5
    

 u s
   Calculate both and use the lower one.
Briggs Plume Rise Formulas
Distance < distance to final rise (i.e.,
x<xf) and Buoyancy dominated plume
1        2
3        3
1.6 Fb ( x)
h 
u
Briggs Plume Rise Formulas
Distance < distance to final rise (i.e.,
x<xf) and momentum dominated plume
   Jet entrainment coefficient
1   u
j  
3   vs

   Unstable conditions (A-D)
1
 3F x        3

h   m 2 
 2 
ju 
Briggs Plume Rise Formulas
 X=downwind distance with max value of:

4d s (v s  3u ) 2
xmax                         For Fb  0
vs u
Xmax=49Fb5/8 for 0<Fb<55 m4/sec3
xmax=119Fb2/5 for Fb> 55 m4/sec3
   Stable conditions (E,F)
1
       sin( x s / u 
3

h  3Fm                 

         ju s 
2

 with
u
x m ax  0.5
s
Briggs Plume Rise Summary
Unstable and                           Stable
neutral

Buoyancy                  1               2                          1
 Fb 
3       *       3                          3
1.6 Fb (3.5 x )
h                                     h  2.6  
u                          us 

Momentum           3d s v s                                 Fm 
1
3
h                                     h  1.5    
u                                        
 u s
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
h
 y0   z0 
3.5
   Effective dispersion coefficients
 ye  ( y   y 0 ) 0.5
2     2

 ze  ( z2   z20 ) 0.5
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 month
Long-term: > 1 month
Averaging Time
If longer averaging time is desired, use
the following power law
p
 tk   
Cs  Ck 
t     

 s    

   P=0.17-0.75, suggested value is 0.17
Crosswind Averaging
Integrate y from - to 
2 Q
1
 1 H
2                    
2

Ccw    1    exp                 
       
 zu
2      2  z
                           


Average over a sector
2
1
2
Q          1 H         
2

C ( )                          exp           
       
             z u      2  z
                     

Crosswind Averaging
Average over a sector considering
distribution of wind speeds and stability
classes

2
1
2
Q          1 H     
2

C ( , u, S )  f n ( , u, S )                        exp       
       
             z u      2  z
                 


   ISCLT3 and STAR
Crosswind Averaging
Smoothing transition from sector to
sector
   Weighted smoothing function, WS
(  |  ad   |)
WS                      for |  ad   | 

WS  0 for |  ad   | 
   Smoothed average concentration
2
1
2
Q(WS )        1 H     
2

C ( , u, S )  f n ( , u, S )                        exp       
       
             z u      2  z
                 

Multiple Sources
The max from each source do not
exactly overlap
Use of multiple stack factor
More 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 base
Multiple stacks
Presentation of results
   Concentration isopleths
Example Calculation
Chapter 10
Chimney Effects
Stack tip downwash
   Low pressure behind stack
vs
When         1.5
u
 vs   
h  hs  2d s   1.5
'
s
u     
ū is at the stack top level
   No plume rise (“plume sink”)
Avoid stack tip downwash
vs
When          1.5
u
hs'  hs
Building Effects
General description
Expanded meaning of “building”
Reduce building effects – rule of thumb
hs>2.5hb
Too conservative for tall thin buildings
Briggs Procedure to Minimize
Downwash
Five steps:
1.   Correction for stack induced downwash
2.   Correction for building effects
3.   Determine if plume is entrained in the
cavity. If entrained, treat it as a ground
level source
4.   Buoyancy effect
5.   Calculate downwind concentration
Cavity
Description
Cavity length
   Short buildings (L/H2)
 L affects cavity length xr
xr   L   A(W H )
   
H H 1.0  B (W H )
   Long buildings (L/H>2)
 L does not affect cavity length xr
xr   1.75 (W H )

H 1.0  0.25 (W H )
Cavity
Max cavity width
2 yr                        W
 1.1  1.7 exp   0.55 
W                           H
   It’s location long x direction
xmy                      W
 0.3  2.0 exp  0.55 
W                       H

Max height
zr                       L
 1.0  1.6 exp   1.3 
H                        H
Cavity
Concentrations within cavity
Q
C
cu A p
OR
QK
C
u b
Wake Downwind of Cavity
Treated as a ground level source
Turner method (virtual source)
Gifford method
parameters)
Huber-Snyder method
Sources Downwind of
Buildings
Briggs method
   Beyond 3b  no building effect
   Within 3b  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
he
h 
'
e      z st
2
   Egan
z st
he'  he 
2
   Bowne
 Modified dispersion coefficients
   ISC3 (COMPLEX 1) – to be discussed later
GEP Stack Height
Definition
   Greater of
 65 m
 HG=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

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