EPA-650/3-74-003
October 1973
Ecological Research  Series

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                                   EPA-650/3-74-003
     WIND  TUNNEL TESTS  OF
NEGATIVELY  BOUYANT  PLUMES
                     by

      T. G. Hoot, R. N. Meroney, and J. A. Peterka

         Fluid Dynamics & Diffusion Laboratory
              College of Engineering
             Colorado State University
            Fort Collins , Colorado  80521
                 Grant AP-01186
            Program Element No. 1AA009
        EPA Project Officer: Willaim H . Snyder

              Meteorology Laboratory
        National Environmental Research Center
      Research Triangle Park, North Carolina 27711
                 Prepared for

       OFFICE OF RESEARCH AND DEVELOPMENT
      U.S. ENVIRONMENTAL PROTECTION AGENCY
            WASHINGTON, D.C.  20460

                 October 1973

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This report has been reviewed by the Environmental Protection Agency
and approved for publication.  Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
                                  11

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                               ABSTRACT




            WIND TUNNEL TESTS OF NEGATIVELY BUOYANT PLUMES






     This study reports the results of tests made of negatively buoyant




emissions into a quiescent medium, laminar crosswind and turbulent




boundary layer.  Measurements included the maximum rise height, horizon-




tal point of descent and behavior of emission concentrations.
                                 in

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                          TABLE OF CONTENTS


Section                                                        Page

            LIST OF TABLES                                      vi

            LIST OF FIGURES                                     vii

            LIST OF SYMBOLS                                     ix

    I.       INTRODUCTION                                         1
            1.1  Negatively Buoyant Emissions                    1
            1.2  Plume Rise                                      3
            1.3  Moist Plumes                                    5
            1.4  Velocity and Concentration Distributions        6

   II.   PLUME RISE EQUATIONS                                     9
        2.1  Vertical Plumes in a Quiescent Medium               9
        2.2  Bent Over Negatively Buoyant Plume in a Laminar    17
             Crosswind

  III.   CONCENTRATION DETERMINATIONS                            25
        3.1  Plumes in a Laminar Crosswind                      25
        3.2  Dense Ground Source in a Turbulent Boundary Layer  27
             3.2.1  Eulerian Diffusion Formulation              27
             3.2.2  Lagrangian Formulations                     29
             3.2.3  Wind Tunnel Simulation of Diffusion         31

   IV.   EXPERIMENTAL MEASUREMENTS                               33
        4.1  Plume Rise                                         33
        4.2  Concentration Measurements                         35
             4.2.1  Plumes in a Laminar Crosswind               35
             4.2.2  Dense Ground Source in a Turbulent          35
                    Boundary Layer

    V.   APPARATUS AND INSTRUMENTATION                           37
        5.1  Wind Tunnels                                       37
        5.2  Velocity and Temperature Measurements              37
        5.3  Gas Mixing and Smoke Visualization                 38
        5.4  Vortex Generators                                  39
        5.5  Concentration Measurements                         40
             5.5.1  Measuring Apparatus                         40
             5.5.2  Tube and Gas Calibration                    40
             5.5.3  Concentration Calculations and              41
                    Counting Statistics

   VI.   RESULTS OF EXPERIMENTS                                  43
        6.1  Plume Rise                                         43
             6.1.1  Vertical Plumes                             43
             6.1.2  Plumes in a Laminar Crosswind               44
             6.1.3  Plume Rise in the Presence of a             46
                    Cubical Structure
                                   IV

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Section                                                        Page

            6.2  Concentrations                                 47
                 6.2.1  Plumes in a Laminar Crosswind           47
                 6.2.2  Dense Ground Source in a Turbulent      48
                        Boundary Layer
                 6.2.3  Decay of Concentration in Buoyancy      49
                        Dominated Plumes After Touchdown

  VII.      CONCLUSIONS                                         51

            BIBLIOGRAPHY                                        52

            TABLES                                      ,        55

            FIGURES                                             60

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                            LIST OF TABLES


Table                                                          Page

  I        VERTICAL PLUMES SMOKE VISUALIZATION DATA             55

 II        PLUMES IN A LAMINAR CROSSWIND SMOKE VISUALIZATION
           DATA                                                 56
                                   VI

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                            LIST OF FIGURES


Figure                                                           Page


  1       CSU Thermal Wind Tunnel                                 60

  2       Flow Mixing and Visualization System                    61

  3       Vortex Generator Details                                62

  4       Velocity Profile Laminar Flow                           63

  5       Velocity Profile at Source, Turbulent Boundary          64
          Layer

  6       Velocity Profiles, Tunnel Centerline, Turbulent
          Boundary Layer                                          65

  7       Turbulence Intensities, Tunnel Centerline               66

  8       Temperature Profiles, Thermal Stratification            67

  9       Gradient Richardson Number, Thermal Stratification      68

 10       Radiation Detection System                              69

 11       Smoke Photographs                                       70

 12       Dimensionless Rise Height vs. Froude Number-
          Vertical Plumes                                         72

 13       Dimensionless Rise Height vs. Rise Height Parameter      73

 14       Dimensionless "Touchdown" Distance vs. "Touchdown
          Parameter"                                              74

 15       Isopleths of Plume in Laminar Crosswind                 75

 16       Maximum Concentration vs. Downstream Distance
          Plumes in a Laminar Crosswind, R=5, D =1/8"             77

 17       Maximum Concentration vs. Downstream Distance,
          Plumes in a Laminar Crosswind, R=10,  D =1/8"            78

 18       Maximum Concentration vs. Downstream Distance,
          Plumes in a Laminar Crosswind, R=15,  D =1/8"            79

 19       Maximum Concentration at Plume High Point vs.
          H/D                                                     80
                                  VII

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Figure                                                         Page

20       Maximum Concentration at Plume Touchdown               81
         vs. Fall Parameter

21       Maximum Concentrations vs. Downstream Distance,
         Negatively Buoyant Ground Source, Neutral
         Stratification                                         82

22       Maximum Concentrations vs. Downstream Distance,
         Negatively Buoyant Ground Source, Inversion
         Stratification                                         83

23       Lateral Spread 50 Percent Concentration Neutral
         Stratification                                         84

24       Lateral Spread 50 Percent Concentration Inversion
         Stratification                                         85

25       Lateral Spread 10 Percent Concentration Neutral
         Stratification                                         86

26       Lateral Spread 10 Percent Concentration Inversion
         Stratification                                         87

27       Vertical Spread 50 Percent Concentration Neutral
         Stratification                                         88

28       Vertical Spread 50 Percent Concentration Inversion
         Stratification                                         89

29       Vertical Spread 10 Percent Concentration Neutral
         Stratification                                         90

30       Vertical Spread 10 Percent Concentration Inversion
         Stratification                                         91

31       Cross-sectional Distribution of Concentration,
         x=6 ft. Neutral Stratification                         92

32       Decay of Plume Maximum Concentration Downstream
         from Touchdown Point                                   93
                                  van

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                            LIST OF SYMBOLS


b         Plume Radius

b         Stack Radius
 o

D         Stack Diameter
 o
e         Base of Natural Logarithm

F         Flux of Negative Buoyancy

FR        "Vertical" Densimetric Froude Number Based on Stack Exit
          Velocity, Density and Density Difference

p
 RH       "Horizontal" Densimetric Froude Number Based on Crosswind
          Velocity, Ambient Density and Stack Exit Density Difference

g         Gravitational Acceleration

H         Maximum Plume Rise Height Above Stack

h         Stack Height Above Ground
 O
h.         Building Height Above Ground

R         Velocity Ratio (Stack Exit Velocity Divided by Crosswind
          Velocity)

Ri        Richardson Number

Re        Reynolds Number

S         Distance Measured Along Plume
          Trajectory From Stack Exit

SG        Specific Gravity (Air = 1)

t         Time

T         Time of Maximum Plume Rise

T , T     Reference Temperatures
 o'  r                 r
U         Boundary Layer Longitudinal Velocity

U         Plume Velocity

U         Stack Exit Velocity

y         Crosswind Velocity

W         Plume Vertical Velocity

                                  ix

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X         Longitudinal Coordinate

X         Longitudinal Coordinate of Plume
          Maximum Rise

X         Plume Touchdown Point (Longitudinal Coordinate)

y         Lateral Coordinate

Z         Vertical Coordinate
                              Greek Letters

a,3       Dimensionless Entrainment Constants

Y         Ratio of Characteristic Length for Gaussian Concentration
          Distribution to that for Velocity Distribution

6         Angle of Plume Trajectory with Horizontal

v         Kinematic Viscosity

o         Transverse Plume Standard Deviation

a         Vertical Plume Standard Deviation
 Z

p         Plume Density

p         Plume Density at Stack Exit

p.        Ambient Air Density

X         Local Concentration

X         Concentration at Stack Exit


                              Subscripts

0         Denotes Stack Exit Quantities

A         Denotes Ambient Quantities

D         Denotes Quantities at Plume Touchdown

M         Denotes Quantity at Plume Centerline

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                               SECTION  I



                              INTRODUCTION





     Negatively buoyant emissions into the atmosphere have been reported



by several observers.  Scorer  (23) reports the case of two power plants



emitting wet-washed plumes with apparently insufficient elimination of



free water, in which the subsequent evaporation of the free water cools



the plume and causes it to sink.  According to the report the plant it-



self is obscured from view on many occasions.  Chesler and Jesser (8)



and Bodurtha (3) have observed and discussed the descent of dense gases



from stacks and relief valves.



     The consequences of such behavior are potentially drastic.  When



the plume sinks rapidly to the ground, very little dilution will occur



in comparison with normal emissions and high ground level concentra-



tions of gases which may be toxic or explosive could result.  In this



report experimental results of the dynamic behavior of negatively



buoyant emissions and the resulting concentration distributions are



reported.





1.1  Negatively Buoyant Emissions



     Previous experimental work with negatively buoyant emissions



appears to be confined to three efforts.   Bodurtha (3) conducted wind



tunnel tests of emissions of freon-air mixtures into a crosswind.



Various combinations of density, exit velocity, crosswind velocity and



stack diameter were used in obtaining smoke pictures.   The results were



correlated by an expression for the maximum rise height:




          H= 5.44 D °'5 R°'75
                    o

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In which  H  is the maximum rise height of the plume centerline, D



is the stack diameter and  R  is the ratio of the exit velocity to the



wind speed.  This formula has the disadvantage of being dimensionally



inhomogeneous and .the absence of relative density terms makes its



application questionable as the specific gravity approaches unity.



      Turner (31) conducted experiments in which salt water jets were



injected vertically into calm fresh water.  Maximum rise heights were



observed and correlated with various dimensionless parameters and an



expression was reported equivalent to:





          H/DQ = 1.74 FR





In which  H  and  D   are as previously defined and  FD  is the
                   O                                  K


densimetric Froude number based on the ambient density and original



density difference.  This Froude number is defined as:







                  ^"o
          n  =      A °	
          ^R
where  p. = Ambient Density
        /T.


       U  = Exit Velocity



       p  = Exit Density



       D  = Exit Diameter
        o


This definition of the Froude number implies the Boussinesq assumption



for density in the inertial terms of the equations of motion; thus it



can be considered applicable in the density range in which that assump-



tion is valid.  Although the constant of proportionality is reported by



Turner as equal to 1.74, a plot of values given in the original article



indicates the value of this constant was determined graphically to be



3.1.

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     Holly and Grace (15) conducted tests of salt water jets injected

vertically into a fresh water open channel in which maximum rise

heights and downstream concentrations were measured.  Expressions

obtained for rise height and concentration distribution were:
                            -148FR
               .   (3.47 X 10       )
            o

                    and

                          0.4F
                          _ i!       gs
          em  =   (31. xlO  R  ) (£)'
                                   o

In which  H  is the top edge of the jet and  D  the jet diameter at

maximum rise height, e   is the least dilution (reciprocal of dimen-

sionless concentration), X  is downstream distance and  X   the

distance to the point where the jet descends to the channel bottom.

The least dilution expression was stated to apply to both the regions

upstream and downstream from  X = X .


1.2  Plume Rise

     A large amount of work has been completed upon the rise of

buoyant plumes.  The beginning point for most of the recent work is the

classic paper of Morton, Taylor and Turner (19) which examines the rise

of a buoyant plume in a quiescent medium.  The analysis was based on

the conservation of volume, mass and momentum with assumptions of self

similarity, circular plume cross section and simple proportionality of

volumetric entrainment rate to plume velocity.  Either Gaussian or

"top hat" profiles of velocity and buoyancy flux may be assumed with

appropriate modifications of the equations.  With the assumption of a

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"virtual point source" located below the actual  exit,  the  model




predicts a "straight sided" plume.




     The "bent-over" plume rise models of Briggs (4)  and Csanady (10)




incorporate this theory for the initial stage of buoyant, bent-over rise




which predicts a 2/3 power parabola as the plume trajectory.   In both




models a second stage is introduced in which the rate of volumetric




entrainment is related to the turbulent energy dissipation per unit




mass.  Criteria for transition is that the rate  of entrainment thus




computed exceed that computed by the initial stage theory  and  is appli-




cable when environmental turbulence in the inertial subrange  dominates




mixing.  This predicts a leveling off to an asymptotic rise which




Briggs takes as the final rise height.  Csanady introduces a  third




stage in which the eddy diffusivity is taken as  constant and  a linear




rate of rise is predicted.  In both these models the initial  region of




momentum dominated rise is neglected as insignificant in contributing




to the final rise height.




     Hoult, Fay and Forney (14) introduced a continuous model  for the




rise of a buoyant plume in a laminar uniform crosswind. Utilizing the




Morton et al. assumptions of self similarity and conservation  of mass




and momentum and employing entrainment constants for velocity  differ-




ences parallel and perpendicular to the flow direction, the model pre-




dicts a momentum-dominated jet behavior close to the stack with a 1/2




power parabola trajectory.  It subsequently suggests a buoyancy domi-




nated plume with a 2/3 power parabola trajectory far from  the  stack




similar to the initial stages of the Briggs and Csanady models.   For a




bent-over jet in a laminar crosswind all of the above models  predict




a 1/3 power parabola a trajectory.

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     Several investigators  (16),  (24),  (30) have observed and recorded




the internal and surrounding flows associated with jets and plumes




injected into a cross flow.  The plume  emerges as a jet from the stack




exit, traveling upward much like a typical momentum jet.  The cross-




wind effect soon becomes dominant bending the plume over and convecting




it downstream with a lateral velocity essentially equal to the cross-




wind.




     It has been further noted that as  the plume rises, its cross-




sectional shape changes from circular to "kidney-shaped" (30), and




finally as it is bent over, the outside shear layer which envelopes




the plume tends to roll up behind the core and from two line vortices




of equal strength but opposite sign.




     Noting this fact, Tulin and Schwartz (28) conducted investigations




into the rise and growth of a two-dimensional vortex pair passing




through neutral and stably stratified surroundings.  As the plume falls




or rises in stably stratified surroundings a lateral spreading and




deviation from circular cross section was noted.




     In all of the above cited models the Boussinesq approximation is




made, i.e.  that the density in the inertial terms of the equations of




motion is approximately equal to ambient density, or more properly,




that potential density is equal to ambient potential density.






1.3  Moist Plumes




     Morton (20) considered the case of a moist plume released




vertically into a quiescent atmosphere using entrainment theory and




conservation of mass, volume, momentum and specific humidity.  Assuming




a linear variation in atmospheric humidity,  he obtained an expression




for the plume specific humidity as a function of height.

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     Csanady (10) and Slawson and Wigley (33)  extended this analysis




and formulated a model for the dynamic behavior of a bent-over plume




containing both free water and water vapor.   The model considers evapo-




ration and condensation along with the resulting effects on the buoyancy




flux.  Wigley and Slawson (32) applied this  analysis to the rise of a




saturated plume.






1.4  Velocity and Concentration Distributions




     Prandtl's mixing length theory applied to circular turbulent jets




predicts a constant eddy viscosity and diffusivity (25) which in turn




predicts Gaussian distributions of velocity and effluent concentration




along with a decay rate of maximum values of these quantities that is




inversely proportional to downstream distance.  Experimental measure-




ments have confirmed this theory.




     Albertson et al.  (1) measured velocity distributions in a simple




momentum jet.  The profiles were determined to be Gaussian and the




rate of decay of maximum velocity inversely proportional to downstream




distance following the zone of flow establishment.  Becker (2) et al.




measured concentrations in a jet and found them to be Gaussian also,




but flatter in profile than the velocity distributions measured by




Albertson.  The decay rate of maximum concentration was found to be




inversely proportional to downstream distance, but decaying at a faster




rate than the velocity.




     Rouse et al. (22) measured velocities and temperatures above a




point source of heat and obtained Gaussian profiles for both, though




slightly sharper in profile for those obtained for jets.  Maximum




velocities and temperatures were observed to decay according to -1/3




and -5/3 powers of downstream distance respectively.  Hewett (13)

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measured temperature distributions in heated plumes injected into a




laminar cross flow in a wind tunnel for neutral and stratified cases




and found the distributions to be qualitatively Gaussian, although he




proposed no model and did not report a decay rate with downstream




distance.  It was noted that concentration gradients were much steeper




on the bottom than the top indicating the influence of buoyancy on the




local diffusion.




     For turbulent diffusion phenomena in the lower atmosphere,




Button's equations have been widely used to estimate concentration dis-




tributions for a point source, but the application is restricted be-




cause of many ideal assumptions.  Also, they are not sensitive to




atmospheric stratification situations.  In an attempt to improve




sensitivity to real conditions Pasquill-Gifford's semi-empirical




formulas have become popular.   A set of transverse and vertical standard




deviations of the dispersion are plotted as functions of downstream




distance.  A "stability category" which classifies six different kinds




of possible atmospheric stratifications, relates the various plume




dispersions to different meteorological conditions.



     Wind tunnel studies of diffusion over topographic models in




turbulent boundary layers indicate good correlation with Pasquill-




Gifford prediction techniques  (18),   In addition wind tunnel diffusion




studies have been conducted for idealized source conditions.  Davar




(11)   studied diffusion from a horizontal point source in a neutral




turbulent boundary layer,   Malhotra (17) performed similar experiments




under unstable conditions,  while Chaudhry (7) studied diffusion in a




stably stratified boundary layer.   Shih (26)  evaluated the effects of

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                                    8






the growth of boundary layer thickness and free stream turbulent




intensity upon diffusion.




     Yang and Meroney (35) studied the diffusion in the wake of a




cubical structure placed in a turbulent boundary layer.  They found




that the critical conditions, such that the plume will not be trapped




in the building cavity region are:




          R >. 1, hs/hb >_ 2





where  R  is the velocity ratio and  h   and  h,   are the stack and




building heights as measured from the ground.

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                              SECTION II



                          PLUME RISE EQUATIONS





2.1  Vertical Plumes in a Quiescent Medium



     Smoke pictures of negatively buoyant plume rise in a quiescent



medium indicate that the behavior is such that the plume exists in a



jet with approximately linear growth of radius with vertical distance



to between 1/3 and 1/4 plume rise height.  The plume width then grows



in a highly non- linear fashion, becoming quite large in the upper



regions.  Although simple entrainment theory can not be expected to



give a complete description of this motion, especially as entrainment



occurs in a complex manner along the top of the plume and the bottom



of the plume "crown", it may serve as an aid to dimensional analysis in



predicting the relationship between pertinent parameters.  Clearly,



some accounting for the entrainment is necessary since the assumption



of a frictionless plume with no entrainment leads to




          H/Do = FR2/2




General Equations of Conservation:



     If the effects of the descending fluid on the exterior of the plume



are neglected due to their much smaller density and velocities, the



equations of conservation (after Morton et al.) become:



Buoyancy:




          d   °°             H   °°
          —• I pUZirrdr = p  ~ j U2urdr
          cu. Q            A &L Q




Assuming  p.   to be a function of  Z  alone.
               (pA-p)U2Trrdr = [   U27rrdr]

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                                    10
       f\
For  -r=- = 0  (neutral  atmosphere)
          /   (p.-p)  U2irrdr = b  U (PA~P ) 2ir                      (2.1)
          0                    ooo


                                          00
                                         / pU2irrdr

One may define the average density  p = 	    as:

                                         / U2?rrdr
                                         0
          p = PA[I
                      (b  2U
                           U2irrdr
                         0
Momentum:
                            CO
           i      O
          -r=- I pU 2irrdr  =  / (p  -p)g2Trrdr
          d/: o             o  A

Equations of Conservation  (Top  Hat Profile) :

     If a "top hat"  profile and the Morton et al.  entrainment
                           CO
                                      f\
hypothesis are employed  / U2irrdr = b U
                         0

Volume:



          ~ (b2U) = 2abU                                          (2.3)


where  a  is an entrainment constant of proportionality relating inflow

velocity of  outside  air  to plume velocity.  Similarly

Buoyancy :


          (pA-p)b2U  = pA(l-SG)bo2Uo                               (2,4)


where  SG =  p /p..   Also:
             O  A.
          P = PA[1
               A
                      b  2U (SG-1)
                          b U

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                                    11
 Momentum:




          ±  (Pb2U2) =  (pA-p)b2g                                  (2.6)




Maximum Rise Time  (Top Hat Profile) :



     Combining equations  (2.4),  (2.6), and the relationship  dZ/dt = U



one may obtain




          i  (pbV) - pA(l-SG)bo2Uog




or




          pbV = pA(l-SG)bo2Uogt + pobo2Uo2



                             2 2
And since at maximum rise  pb U  =0, the time of rise can be



calculated as



                P U

          T = _ — ° °         (Time of Maximum Rise)                (2.7)

                O  A



     If a Gaussian distribution is assumed and if the ratio of  a  for



the two cases is adjusted so that the conservation of mass is



consistent at stack exit, the same expression for maximum rise results.



Equations of Conservation (Gaussian) :



     If a Gaussian distribution is assumed such that  b  is a



characteristic length (different from the value of  b  in the top hat



model), following Morton, Taylor and Turner, and:
          '-A - '



                   2., 2

          u = u e-r /b
               m



          Y = Ratio of characteristic lengths for density and velocity



          b  = Initial Radius



          Subscript m = Centerline Values

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                                    12






The equations of conservation  become:













           ,     , Yb2Um
          -r|- [ I pU 2iirdr] =  (PA~P  )b  Yg                          (2.6a)

               0
Maximum Rise Time  (Gaussian):
     If  Z  is measured along the plume  centerline.   dZ/dt = U ,  so
that:
If  y  is taken as unity to simplify  the  equations and initial




conditions are made to match, using  (2.4a)  we  obtain:



                GO


          ^  [ / pU227rrdr] = 2pA(l-SG)bo2Uog







and



           oo


          / pU22Trrdr = 2pA(l-SG)b  2U  gt + p b  2U  2               (A)






At maximum rise height the integral on the  left hand side is zero and




an expression for time of maximum  rise results as:




                 P U

                  O 0                                             /-
Maximum Rise Height  (Gaussian) :



     The assumption of nearly  constant  density i.e.  in equation (A),



yields:




          pU 2b2 = 4p.(l-SG)b  2U gt  + 2p  b  2U  2
            m        Ak     •* o  o6      o o o

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                                    13
So that:




           _  _   4p.(l-SG)b 2U gt + 2p b 2U 2
          ,2  2 _   Av   _   o  os	Ko o  o

             m                  p



If it is assumed that  p~p   then equation  (2.8) becomes




          b2U 2 = 4 1^1  b 2U gt + 2b 2U 2                     (2.6b)
             m        SG     o  o6      o  o                      ^     '



     The conservation of volume expression is taken to be the same



here as for top hat velocity profiles with the understanding that the



value of  a  thus defined will in general be different from the top



hat value, and since  dZ = U dt:
                            m



          ~ [b2U ] = 2abU 2                                      (2.3b)
          dt L   nr       m                                       *•     '



Matching the fluxes of volume and momentum to stack exit quantities:



          U   = 2U
           mo     o



          b   = b //2~
           mo    o



     The velocity and radius may be non-dimensionalized with their



initial values such that:



          b* = b/b  = b//?b
           *      o         mo



          U* = U/U  = 2U/U
           *      o       mo
          Z* - Z/UQT




     Thus utilizing the above and the definition of maximum rise time



equation (2.7a):




          A      7                U T

          ;nr* (b* U *) = 2ab*U * (~)                           (2.3c)
          dt*   *  m*       * m    b
                                   o



          (1 - Pm/PA) b*2U * = 2(1-SG)                           (2.4c)




          b*V,2 = 2(l-tJ                                      (2.6c)

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                                   14
One can now eliraate  b*  from equation (2.3c) by utilizing equation



(2.6c) to obtain a differential equation in  U * alone.




          d   ,(l-t*K    rr~   n 2.
                             a F,, U
            .
          dt*    u              R

                  m
thus may be integrated to yield





          U * =       2(l-t«)
           m
                'IGai^F,,2
Information is now available to calculate the maximum rise height  H,

                     1

defined as  II = U T / U * dt*.  The result is


                 °  0         M
                  2           -


          H    !!Z  N3/1°    ,N      dR


          Do~   5    M4/5    0
                             -/2
                  5          M /Z               M

                                                N



where                                ,
                      ,             F

          P = (1-tJ x , M = - 1 — — ,  and N = 1+M.




     Note  R = -rr-  and  B  is the Beta Function.  The second integral



on the right can be evaluated by a series expansion as:



                    « rf-l

              4/5       2J
The series can be shown to be convergent if Stirling's Formula for



T(n)  as  n  gets large is assumed.  For most Froude numbers, however,



M/N * 1  and




                    F 2 B(l/2, 4/5)        2.30F
                 £   i\                          i\
                 r~  -  = - r~n - TTo - f  or

                            C2        ms/4cs)1/2^


                            FR

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                                   15
          H      °-45 FR

          D  " ^ -

                 Gaussian



If  a  for the Gaussian and top hat cases are adjusted to make



equation  (2.4) equivalent at stack exit for both top hat and Gaussian



assumptions:



          ct        = '2 ot
           top hat       Gaussian
and
                 0.515 F

          H/D  =      — £-.                                        (2.8a)
             o    i

                   top hat




And if it is assumed  P~P4:
                         f\




                 0.515 SG1/4 F

          H/Do = -                                               (2.8b)


                     top hat




These expressions are identical to those obtained with the same




constant density assumptions and a top hat profile of plume quantities




if the top hat rise time is used.




     In the above  Fn  is the densimetric Froude number based on stack
                    K


exit veloicty, density and density difference rather than the one




obtained using the Boussinesq approximation and is defined as:



                   U
                 n
                8°,
                      po
Expressions (2.8) represent the rise computed by neglecting the



entrainment resulting from lateral velocities due to radial growth at



the top and bottom of the plume "crown" and predicts an infinite



radius at maximum rise height.

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                                   16
Estimation of Entrainment Constant:



     Equations (2.8) cannot be utilized experimentally to give a



precise estimate for the actual value of  a.  Good correlation with  the



Froude number or Froude number and specific gravity is a valid expecta-



tion, however.



     A method of evaluating  a  results from considering motion in the



jet region immediately downstream from the stack.  The conservation  of



momentum leads to:




          pb2U2 = -(p -p.) b 2U gt+ p b 2U 2
                     o  A   o  o6    o o  o


                                    — 22       22
In the jet region  t  is small and  pb U  » p b  U





                       b 2U 2(SG-1)

From (2.5)  p = p [1 + -2—°-	 ]

                 A         b2U



This leads to:
           _    -b 2U (SG-1) + /[b 2U  (SG-1)]2 + 4SGb 2U V
           2..     oo            o  o      J        oo
                                    2



Substituting in (2.4) and integrating results in an expression for



a  for a top hat profile which should be approximated close to the



stack.
a = •=•
       b-b   b (SG-1)     /[b 2U  (SG-l)]2+4SGb 2U  2b2+2v/SG~ b U b
          o   o       ,  J  L o  ov     J      oo          oo
            +	 In
               4 SG       /[b 2U  (SG-l)]2+4SGb 4U 2+2/SG b  2U
                         I   L f\  r\ ^    J -I      f\  r\        r\  r
                             OO      J      OO        OO
                                                                ^



                                                                  (2.9)



It should be noted here that the value of  a  computed in this manner




is of the order of half the value of  a.  as computed for a point  source




of buoyancy where  a  is taken as  db/dZ.  The jet assumption is

-------
                                   17






subject to the limitations of assuming that the buoyancy forces are




small in the jet region, while the point source is subject to the




limitations of ignoring finite momentum flux and the assumption of




a point source for a finite diameter.  Briggs (5) gives an estimate




for the point source of  a = 0.075.






2.2  Bent Over Negatively Buoyant Plume In a Laminar Crosswind




     The effect of negative buoyance on plume behavior and resulting




downwind concentrations will be greatest when crosswinds are light, and




turbulence intensities are low.  The sinking velocity of the plume




relative to the horizontal convective velocity will be much higher than




under "normal" conditions.  In such cases, the entrainment of outside




air into the plume and the resulting diffusion is a function of this




interaction between the plume and the crosswind, and approaches the




behavior of a turbulent plume injected into a laminar crosswind.




General Equations of Conservation (Top Hat Profiles);




     Assuming a crosswind of constant velocity,  a "top hat" profile,




and the Hoult et al. model for the entrainment of outside air into the




plume, where entrainment due to "parallel" and "perpendicular" velocity




differences are assumed to superimpose, the equations  of motion become:






     (a)  Conservation of "Volume"







          •jg- (b2U) = 2ab(U-Vcos6) + 2BbV|sin0|;                  (2.10)






     (b)  Conservation of Horizontal Momentum:
             (pbVcose) = PAV ^ (b2U)                         (2.11)

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                                   18






      (c)  Conservation of Vertical Momentum:






           5- (pb2UW) = (p,-p)b2g                                 (2.12)
           CIS             f\




      (d)  Conservation of Mass







                  J) = PA dV ^^                                C2-13)




which leads to the buoyancy flux relation:




           d         2      2   dpA
          ^ (pA-p)bZUg = b^Ug -^ Sine                           (2.14)




where:



          s = Distance measured along plume axis



          U = Axial velocity = ds/dt



          W = Vertical component of velocity



          8 = Angle of plume axis with the horizontal



Trajectory Near Stack:



     In the case of a neutral atmosphere equation  (2.12) still  leads



to equation (2.7) for the time of maximum rise.  Examining the  case of



the plume as it initially leaves the stack, where  the trajectory  is



approximately vertical, cos8 ~ 0, sin8 =• 1, U  - W.



Equation (2.13) integrates to




          pb2W2 = (p.-p ) b 2gU t + p b 2U 2
                  *-KA ^oj  o 6 o     ooo



And since  t  is still small:



            2 ?       9  ?
          PbV = p b nj *                                        (B)
                   ooo



Noting that  cos6 = -5— = 	 , equation 2.11 becomes:
                    CIS       j   i/o

-------
                                   19
                        = PA
                  /  \ I /

          (1



or rearranging and utilizing equation  (B) above,




          b W ~  —^^i— + 1  b  U
                   Z'        oo



This may be substituted directly into  equation  (2.10)





          ~  (b2W) =  b 2U  ~ R^  =  2abW  +  20bV
          Q/i          0  O dZi   L



One may replace the  right hand terms by:
               v/pT b U           Sp  b U           /SG  b  U
          hw =   OOP _ 	 o  o o	 _  	o o
                          1/PA(1





                    /R(SG)+Z'
                                  b 2U  (SG-1)
                o o   R+Z'



                2.
hv . bWV _       rR(SG)+Z'   / R+Z

bV ' -biT ' Vo  C - P - 5 /RSG
                         o  - P -   R(SG)+Z'
       R+Z
            —  can be taken as  =1 the new continuity of volume
expression is:
                       2g  R(SG)   2a
            .         _
          dZ   Z'      Rb   Z'     b    b R
                         0          O    O


Integrating this differential expression results in:


                              2gZ

                              Rb                         2

                                °
                                                  r  --
                                                  Q   R2b 2
                                                         o
x -   1   rQR+3)Z2    23   r(aR-HB)Z5

  ~ RSG  L  Rb       3Rb   L  Rb    j    '  '  ' J
              RCSG)    Rb       3Rb
                         0         00

-------
                                   20
                /CSG)boX

          Z = R/  aR+g—  for values of  Z/bQ  sufficiently small that



higher order terras will not be significant.   This is identical to the



expression denoted by Hoult, Fay and Forney except for the specific



gravity term.



     Evaluating  pb U  from this expression:
                                    o


Subsequent Trajectory:



     For the bent over case where  cosS^l, sin8*Z', PKPA> U~V, the



assumption of Gaussian profiles in vertical component of velocity and



concentration (density difference) yields expressions that are identical



to those resulting from the "top hat" case with the exception that  b



is now the radial distance at which the quantities described by the



Gaussian expression assume values equal to  —  of the centerline values.
                                            "


In this case the entrainment hypothesis is equivalent to the assumption



of a mixing length proportional to the width of the plume, such that a



linear rate of growth of radius with  Z  and Gaussian profiles of



vertical velocity and density difference are predicted.



     The new conservation of volume expression will be:




          4r (b2V) = 2bV ^- - 2bVW
          dt *•   J       dt       m



or since  dZ ~ W dt
                m
If the constant of proportionality is taken as  6, then




          ~ = 3, and  b = 3Z + C
          Q.L

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                                    21
      If it is assumed that  C  can be taken as zero without large error



 and if  dp./dZ = 0  in equation (2.14) then equation (2.12) becomes:
           A
 or
           ,   co      2,,2         (p.-p )b  U gu
          d  t ..w  -r /b  .  ,     ^A MoJ o  o6
          3V I  VW e       2irrdr = 	r:	
          dX J    m                     pAV
            9       999     P  f Y _ ^
           b^VW  * gZ V Z'  = -L. I5-J

               m              ,,3   P,
or
          Z =
 H -
                             1/3
Which is a slight variation on the well  known  expression for positively



buoyant plumes.  In the above  F  the  buoyancy flux  has  been substi-



tuted for  (p -p.)b  U g, X  is the horizontal distance  to the point
             O  f\  O  O


of maximum rise, and  H  is maximum plume  rise.   For this case
Expression for Maximum Plume Rise:



     Using equation  (2.12) in time derivative  form:




          pb2UW = -Ft + p b 2U 2
                         ooo
and
          W =
-Ft + p b 2U 2
	o o  o


     pb2U
The previously evaluated expressions for  b U  for the asymptotic



cases of the plume close to the stack and of the bent over plume


            2      2
indicates  b U = b  U  f(R, Z/d   if the Boussinesq approximation is

-------
                                   22
made for the density on the grounds that it is valid over most of the



rise.  If the original density is retained in the time calculations



the result is:




                -Ft + P b 2U 2
              PAf(R,2D ) b 2U °
               A v    o   o  o



where  R  is constant.



     Therefore maximum plume rise is in general:
                         dz _
or




          H/D  = <|>(R, (SG)(F 2))                                   (2.15)
             O             K



The jet region equations apply only when time is small and  R(SG)/Z'«1,



however for purposes of comparison (2.15) can be calculated for this



assumption over the entire plume rise resulting in:
             o   4(aR+3)
/T .  16(aR+g) p 2

       R(SG)    R
                                             - 1
(2,16a)
For bent over plumes (if considered for the whole rise)(2.15) becomes:




                  3R(SG)F 2   ,

          H/D  = [	T~JH i/A                                   (2.16b)

             0      88



This predicts values of  H/D   which vary a maximum of =10 percent



in the range of specific gravities from 1.25 to 5 if the exit and



crosswind velocities are held constant.  The minimum predicted rise is



at a specific gravity of two.  This agrees qualitatively with the

-------
                                   23
observations of Bodurtha who stated that the rise of plumes he  observed



with roughly this range in specific gravities was independent of



specific gravity.



Traj ectory During Descent:



     For the descending portion of the plume equation  (2.10) can be


                                 dx        1
transformed, noting that  cos0 = -3— = 	9 -, ,9 , to
                                 CIS    f~_~.&^\.lL.
                         '          7        i   i
                           ] = 2abZ' V + 28b|Z'|V




                                         2  1 /2
For values of  Z1  <  0.3, then  1. £ (1+Z1 )  '   <_ 1,05.   Since



measurements discussed by Briggs  (5) indicate   3 ^  (6  to  8)a  for



these conditions,  the bent over plume expressions will  still apply



approximately.  Hence,



          b - BfH+H-Z)



and




          p B2C2H-Z)2(dCH"^)  = + JL (X-X)

                      d(X-X)      V



which integrates to produce:




          XjOT   r8g2 {(2H-Z)3  - H3},1^2 FRH

          D   ~ ^  3         3      •>     r-
           o       •*       D •*           /R
                           o
Where  F    is the "horizontal" Froude Number  -  and   X   is
        KH
the horizontal location of maximum plume rise.  At ground  level



Z = -h , the stack height.  Then




          Xn"X    RB2   H  3      h= 3     1//2 FBH
          ~ = [^~ (jf)  {(2+ -|f)  -1}]    -^                 (2.17)

            oo                     /R

-------
                                   24
Where  X   is the horizontal point of plume touchdown.   The position


of  X  can be estimated from the time of rise by assuming that  the


plume is convected horizontally with crosswind velocity  V.  Thus




                    VpoUo                                         -
                              _
                          -  R



It should be noted that entrainment theory is not  expected to provide


a completely accurate description of negatively buoyant motion due to


the low velocity differences in the region of maximum rise.   However,


it is a useful tool in developing relationships between parameters for


experimental measurement.

-------
                                   25





                              SECTION III



                     CONCENTRATION DETERMINATIONS





3.1  Plumes in a Laminar Crosswind



     Rouse, Yih, and Humphries showed theoretically and experimentally



that the decay of maximum concentration in a vertical positively buoy-


                -5/3
ant plume is  ~X    .  Morton et al.  obtained the same results using



entrainment theory.  In that particular case mixing length theories are



consistent with the entrainment hypothesis and both predict a linear



rate of growth of radius with vertical distance, and Gaussian profiles



of velocity and concentration.  If the same approach is taken and it



is noted that:
           p -
where  X  is the concentration at any point and  p  is the correspond-



ing density.  If Gaussian profiles are assumed, equation (2.4a) becomes:
             VA -    (SG-l)

          0        *o
           2            v
          b   ,     .. ,,   m    ,     ..,, ,  2
         1+Y  ^o *AJ  m



so that
          X   b 2U
          _~ °  °

          xo   b2U
                  m
              (p -PA) U  — =  (P -PA)U b   = constant
                 ^^

-------
                                   26
Vertical Plumes:



For a negatively buoyant vertical plume, this predicts at maximum rise



height:




                               X U D 2
            /     ruin i~l      moO    ,-,,/n -, ~ 1
          xm/x0 - CH/DQ)   or, —Q	(H/DO)



Bent Over Plumes:



For plumes in a crosswind the concentration delay can be examined in



the asymptotic regions.  Close to the stack, in the jet region,
          X0   42M*!]
For the bent over region of the plume
          b2u = P2V = b 2U [*- H- 1] : b 2U  [
                       o  olRD 2          o  o   RD

                              o                    o

             2
since  (Z/D )  » R  over most of the rise and
                  R

                      '       °r
                                       Q       V
                  o



so that the bounds on concentration are


                            2
                   ~      Q          D
            o             x           o
For the descending plume region
          JL ~ (b2V) X ~ (2H - Z) 2

          xo

-------
                                   27
which at large distances downstream approaches proportionality with
           RH
                 _
              (X-X)
            Q      R5/3
                         (X-X)
Implicit in the above is the assumption of a mixing length proportional



to the characteristic length  b, similarity in the form of dif-



fusivities of mass and momentum, and similarity in profiles of



velocity and concentration at all cross sections.





3.2  Dense Ground Source in a Turbulent Boundary Layer



     3.2.1  Eulerian Diffusion Formulation



     In a field of small scale turbulence the diffusion may be



considered through the concept of an "eddy diffusivity" as analogous



to molecular diffusion.  A coefficient  k, the "diffusivity", is taken



as proportional to  U'£,  U' is the turbulent fluctuation velocity.



£  can be interpreted in terms of a proportionality coefficient be-
tween the average turbulent flux of a given substance  C'U'  and the



gradient of average concentration  VC,
          U'C1 = -KVC .



When the diffusion is considered in three dimensions, the concept is



generalized by introducing three such coefficients, k ,  k ,  ky  which
                                                     X   y   LI


are assumed to be functions of position.   Application of the conserva-



tion principle yields:




     ^£ + n l£ + v ^ +  W -^ - — fk  -1^1 + -L rk  9£i  + J_ fk  2£i
     3t   U 3x   V 3y   W 3z ~ 3x L x 9xxJ   9y ly 8yJ    9z L z 3zJ

-------
                                   28
If the boundary layer assumption of  W=V=0  is combined with neglect of



the longitudinal dispersion term, the following equation results:





          W + U 97 = 9y fky ly^ + 97 ^zTz^



     The assumption of constant diffusivity  k  = k  = k  as formulated
                                              y    z


by Roberts leads to a Guassian distribution in the radial direction



and a longitudinal decay rate inversely proportional to  X.  The



predictions of this analysis unfortunately do not agree with observa-



tions.  The observed decay rate of maximum concentration is much



greater than that predicted by this model.  Several investigators



(see  (29)) were able to obtain closed form solutions for the two



dimensional version of (3.4) for an infinite line source in a crosswind



by use of Schmidt's conjugate power.



     Other dispersion predictions have been proposed for power law



profiles and constant flux atmospheres such that:



                       m     du
          U = U, (Z/Z,) , K  -7— = constant
               11     m dz


                            1 -m
which require  K  = K, (Z/Z.,)     where  U,  and  K,  are the velocity
        nmlvl              1        1


and diffusivity at the reference height  Z .  The solutions obtained



predict a power law decay rate in maximum concentration with  X.



Several other investigations have obtained closed form solutions for



the three dimensional problem of ground and elevated point sources by



the assumption of variable lateral diffusivity combined with the



conjugate power laws.  These proposals have varying degrees of success



in predicting the decay rate of maximum concentration and lateral



dispersion. (7, 27, 29)

-------
                                    29
     3.2.2  Lagrangian Formulations



     Lagrangian formulation of duffusion  assumes  one follows the motions



of a specific particle in time.  Taylor  (27)  considered the  motion of a



fluid element with the assumptions of homogeneous,  isotropic,



stationary turbulence and obtained:
                               '
          Y 2(t) = 2U'2  I  I

                         00
         2                                                        2
where  Y.  (t)  is the variance in om dimensional motion,  and   U1    is




the  RMS  value of the turbulent velocity fluctuation  in that  direction.




The velocity correlation, RT (T) is defined by.
                           LJ



                _ U'(t)U'(t+t)
          Kj (^TJ — 	



                     ^
when  t  is small  R, (ipl  and  Y.2 = U'2 t2.  As  t-*»,  R, (t)-K)   and
                    lj             1                        L
 oo                        	            . i —


/ R.(r)dT = const.  Then  Y.2(t) = Const x 2U'2.

0  L                       *

     Sutton (29) on dimensional grounds proposed  at an  empirical  form




for  R (T)






          RL(T) = —^—
                   r  ii 1 2 ^n
                   (v+U' T)



with  n  as an adjustable constant.  This led to the following  solution



for a continuous point source:
                         on

                         2Q
             ''-  ~      -2-n          y     z
                     TrC C Ux             J
                       Y z




where  C   and  C   are generalized coefficients of diffusion in their
        y        z


respective directions.  Button's formula has been widely used in

-------
                                   30
practice even though it was developed under the assumption of




homogeneous isotropic turbulence.   In use it is typically applied to




the shear flow of the lower atmosphere.




     The principle of Lagrangian similarity has recently been utilized




by several investigators to provide a more rational approach to shear




flow diffusion, i.e. without postulating a diffusivity in advance.




Reasoning dimensionally Batchelor and Ellison related the time rate of




change of the vertical mean position of a particle to the shear




velocity and a universal function of  z/L, where  L  is the stability




length.  Assuming a probability density distribution about the mean




position and noting that for a ground source in neutral flow this




function as applied to maximum ground concentration is essentially the




dirac delta function, they obtained relations for the decay of maximum




concentrations for continuous point and line sources.  Concentrations




from point sources were predicted to decay as  X  ' -X  ' , while line




sources decay X  .  Gifford, Cermak, and Chaudhry (7) extended this




principle to diffusion in a stably stratified atmosphere.



     The results of Lagrangian theory are usually incorporated into




statistical models in terms of the calculated first, second, or higher




moments.  For a continuous ground source the expression obtained is:
xu i
0 ira a
v y z
2
2a 2
y
2
z "I
2a 2
z
Where:




     Q  is the flow rate in units of concentration per second




     a (x)  and  a (x)  are distribution moments found by the




                        Lagrangian theory




      X is the average concentration

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                                   31



     3.2.3  Wind Tunnel Simulation of Diffusion


     Cermak et al.  (6) point out that for small scale diffusion, in


which there is no variation in the mean wind direction, and non-neutral


stratification, dynamic similarity of flows with geometrically similar


boundary conditions, is determined by three dimensionless parameters:


          VL/v  (Reynolds Number)

           ^
          P—   (Prandtl Number)



          -—~-  (Richardson Number)
          T V
           o


If the tunnel flow consists of air, Prandtl Number similarity is


assumed.  If only micro scale eddy motion is considered, such that


there is no variation in the mean wind direction, experience has


shown that for shear flows of high Reynolds Number, that viscosity has


no effect on the scale components of the motion which contains nearly


all the energy which might effectively contribute to turbulent


diffusion.  Plate and Lin, Chuang and Cermak, Malhotra and Cermak,


Arya and Chaudhry have all demonstrated the reliability of the use of


wind tunnel shear layers for modeling atmospheric flows, even though


a ratio in Reynolds Numbers between model and prototype is of the

order of 10 .


     For flow of this sort, the gradient form of the Richardson Number


must be used i.e.
         Ri - g
         Rl ' T
If power law relationships in  Z  for profiles of temperature and


velocity are obtained such that:

-------
                                   32
          ..      _                T-T
          JL - f_L^n           r	Ii -
          II    1-7 J J          (.7. _rp J -
          Ul    Zl              Tl  r       l

                                     T -T
           .  _ g   m   ,Z  m-2n+l(Z1) r_J	IN
          Rl - Y~  ~2  CZ7^        T  \. 2  >
                o  n    1            U
since  Ri = Buoyancy force    therefore
            Inertial force
          <0  Unstable stratification

     Ri   =0  Neutral stratification

          >0  Stable stratification

-------
                                   33






                              SECTION IV




                       EXPERIMENTAL MEASUREMENTS






4.1  Plume Rise




     Experiments on negatively buoyant plumes were conducted to check




previous and present theories for plume rise characteristics and to




obtain reliable data on the nature of the descending plume.  Vertical




plume rise experiments with no crosswind were conducted in the




Industrial Aerodynamics wind tunnel in the Fluid Dynamics and Diffusion




Laboratory at Colorado State University.  The 6x6 ft area of the test




section (which was closed at each end for this experiment to limit




corrective currents) provided a very still environment for the experi-




ment.  The experiments with bent over plumes were performed in the




thermal tunnel in the Fluid Dynamics and Diffusion Laboratory.  The




tunnel has a 24x24 inch cross section.  Turbulent plumes were injected




into both laminar and turbulent crosswinds.  Plumes were also injected




into a low-speed turbulent crosswind in the Industrial Aerodynamics




wind tunnel.   These plumes were of large specific gravity and descended




quickly to the tunnel floor, where the longitudinal decay rate was




measured.




     Additional details of the wind tunnels are described in Section 5.




     The pertinent parameters regarding plume rise appeared in the




equations in Section 2.  Values of these parameters applicable to




actual conditions can be duplicated in the wind tunnel.  Implicit in




the assumptions was the existence of a Reynolds Number sufficiently




large to justify the assumptions of turbulent entrainment.   The




Reynolds Numbers based on pipe flow calculations did not meet this




criteria for all cases studied so that the turbulence was artificially

-------
                                   34
generated.  A sharp edged orifice was placed in the stacks 8 diameters




upstream from the exit.  Hewett (13) has shown that plume rise is




independent of Reynolds Number if the plume is turbulent at exit.




     The range in parameters was as follows.  For the vertical plumes,




specific gravities ranged from 1.08 to 3.0 and exit velocities from




~9 to 75.  Stack diameters of 1/8 inch and 1/4 inch were used.




     For the plumes in a laminar crosswind, velocity ratios ranged from




2.5 to 25, specific gravities from 1.10 to 4.16 and Froude Numbers from




-5.2 to 75.  Two diameters, 1/4 inch and 1/8 inch were used and two




crosswind velocities -0.75 and =1.5 ft per second were employed.  Stack




heights of 3 inch and 6 inch were employed at various points, both to




provide variations in this parameter and to avoid hitting the tunnel




roof with plumes of high exit velocity.  The specific gravities were




obtained by mixing Freon 12 with Air in appropriate proportions.  Freon




12 has a molecular weight of 121.  Densities at appropriate pressures




and temperatures were obtained from applicable Mollier Chants.




     The experiments were conducted as follows.  Tunnel and stack flow




rates were set.  The effluent was bubbled through  TiCl.  to produce




smoke.  Extended time exposure photographs were taken against a black-




board divided into marked horizontal and vertical increments.  Measure-




ments were then corrected for the parallax resulting from the fact that




this plume was in the center of the tunnel and the blackboard at the




tunnel wall.  Several photographs are shown in Fig. 11,




     In addition a 4% inches x 4% inches x 4% inches cubical structure




with a stack exiting in the center was installed in the Colorado State




University thermal tunnel in a turbulent shear flow.  Velocity at this




top of the building was set at 6.75 ft per second for a Reynolds Number

-------
                                   35
of -13,500.  Smoke photographs were taken for specific gravities of




1, 1.5 and 2.5; velocity ratios of 1 and 2; and stack height to




building height ratios of 1, 1.5 and 2,






4.2  Concentration Measurements




     4.2.1  Plumes in a Laminar Crosswind




     Concentration measurements at the maximum rise height were made of




18 plumes injected into the laminar crosswind.  Concentrations at the




points where these plumes touched the floor was also taken.  These




plumes were from 1/4 inch and 1/8 inch diameter stacks with specific




gravities of 1.5, 2 and 3 respectively.




     Detailed cross-sectional concentration measurements taken in




roughly equal longitudinal increments between the point of maximum




rise height and plume touchdown were made for six plumes of specific




gravities 2 and 3; and exit ratios of ~5, 10, and 15 from a 1/8 inch




diameter stack.  The cross^sectional measurements were made so that




the plane of measurement was at right angles to the plume motion as




determined from the smoke pictures.




     4.2.2  Dense Ground Source in a Turbulent Boundary Layer




     Concentration measurements were taken in a turbulent boundary




layer of negatively buoyant ground sources.   Specific gravities of 1.0




(Air),1.10,  1.25, 1.50, 2.0 and 3.0 were employed.  Measurements were




made in neutral and inversion stratifications.  Free stream velocity




was 6 ft for second and the boundary layer thickness was approximately




6 inches.   Velocity of discharge from the source was set equal to




tunnel  velocity at the height of the source centerline.   The turbulent




boundary layer was artificially generated in the Colorado State

-------
                                  36






University thermal tunnel by the use of vortex generators after the




method of Counihan (9).   An approximate 1/7 law velocity profile was




obtained.  Using the thermal stratification capabilities of the tunnel,




an approximate 1/7 law temperature profile was also generated.   The




vortex generator arrangement is described in Section 5.




     Finally, five plumes were examined in the Colorado State




University Industrial Aerodynamics Tunnel (briefly described in Section




5) with a free stream velocity of approximately 2.5 ft per second and




a boundary layer thickness of approximately 12 inches.  These plumes




were emitted from 1/4 inch stacks with velocity ratios ranging from




5 to 25 and specific gravity of 3 and thus tended to intercept the




tunnel floor at relatively short distances from the stack.  The decay




rate of maximum concentration downstream from point of touchdown was




then determined to provide information supplementing that of the plumes




injected into the laminar crosswind.  This provided data concerning




dispersion of heavy plumes due to background turbulence as opposed to




plumes which entrain fluid as a result of their own vertical motion.

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                                   37






                               SECTION V



                     APPARATUS AND INSTRUMENTATION






5.1  Wind Tunnels




     The thermal wind tunnel  (Fig. 1) at the Fluid Dynamics and




Diffusion Laboratory, Colorado State University, was designed to




provide a low speed wind tunnel with vertical thermal gradient capabil-




ity.  The section is 15 ft long with a two ft square cross section.




A bank of metal plates with electrical resistance heaters placed in the




tunnel inlet allows an initial thermal gradient to be established.




Water cooled panels on the tunnel floor and electrical resistance




heaters on the tunnel roof subsequently maintain the gradient along the




test section.  In addition, the longitudinal pressure gradient along




the test section can be controlled by the tunnel roof which can be




adjusted vertically.  The fan speed can be adjusted, thus controlling




the air speed in the tunnel.  Maximum air velocity obtainable is




~10 ft per second.




     The Colorado State University Industrial Aerodynamics tunnel has




a six ft square cross section and a test section which is 30 ft in




length.  An adjustable pitch fan allows wind speeds up to 60 ft per




second.  The boundary layer thickness ranges from -3 inches at the




start of the test section to ~16 inches at the end.






5.2  Velocity and Temperature Measurements




     Extremely low velocities were measured utilizing the vortex




shedding properties of circular cylinders  .id known relationships between




shedding frequency and approach velocity in the form of the Strouhal




Number of cylinder Reynolds Number.   The device is similar to one

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                                   38
described by Hewett (13), and requires a "hot wire" probe positioned

in the cylinder wake to measure the eddy shedding frequency.   The

trace of the signal was observed on an oscilloscope and the probe

position adjusted so that only frequency of vortex shedding from the

bottom of the cylinder was counted.  The signal appeared in wave form

and thus was counted on a digital counter.   Velocity was determined

from Roshko's data relating Strouhal Number to Reynolds Number.   This

method of velocity measurement was checked with a smoke wire.**   The

measurements are good within three percent.

     Velocities of higher magnitude were measured with a pitot-static

tube and a Transonic pressure meter, with the exception that  velocity

and turbulence inten.sity profiles in boundary layers were measured with

a hot wire anemometer.

     Measurements of temperature were made using a movable bank  of

eight copper constant and thermocouples mounted vertically.  Their

voltage output was measured by a sensitive millvolt potentiometer.



5.3  Gas Mixing and Smoke Visualization

     The dense gas was formed by mixing air and Freon 12 in a flow tee

in the desired proportions.  The air and Freon flow rates were measured

by Fisher and Porter "flowrators" which were calibrated for each gas.

Smoke was generated by impinging the mixture in jet form on the  surface


of titanium tetrachloride in a container.  The smoke thus formed was

then transported to the stack inside the tunnel where it was released.

A schematic of this arrangement is shown in Fig. 2.
**
  See Orgill, M. M. et al., "Laboratory Simulation and Field Estimates
  of Atmospheric Transport-Dispersion Over Mountainous Terrain,"
  FDDL Dept. CER70-71MMO-JEC-LOG40, 1971.

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                                   39
5.4  Vortex Generators




     Since concentrations from a negatively buoyant ground source were




measured in the thermal tunnel to utilize the thermal inversion capabil-




ity, it was necessary to generate a turbulent boundary layer.  This was




done using the method of Counihan by constructing eight "elliptic




wedge" vortex generators with the shape of a quarter ellipse with




minor axis equal to one-half major axis and a wedge angle of six




degrees.  The generators were six inches high and three inches long at




the base.  A serrated barrier was located six inches upstream from the




generators.  A metal honeycomb section was placed immediately down-




stream of the heaters but upstream of the serrated barrier.  It was




found that best results were obtained when the barrier was placed at




a 60 degree angle with the tunnel floor such that the top of the




barrier was placed adjacent to the downstream metal "Honeycomb" section.




The barrier was 1 1/8 inches high at the serrations and 7/8 inches




high elsewhere.  Downstream from the generators a three inch wide




plate with 3/16 inch steel shot placed in staggered rows on the surface




was installed.  Downstream from the shot-covered plate a four-inch




wide layer of 3/8 inch gravel was placed on the tunnel floor.  A




sketch of the arrangement with details of the vortex generators and




serrated barrier is shown in Fig. 3.  Velocity profiles produced




closely approximated a 1/7 power law profile.  The "Boundary Layer"




was developed within twenty-five inches downstream from the generators.




Velocity, turbulence intensity and temperature profiles in the boundary




layer are shown in Fig.  5 to 9.

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                                   40
5.5  Concentration Measurements




     5.5.1  Measuring Apparatus




     Concentration measurements were made using Krypton-85.   Krypton-85




is a radioactive noble gas produced by nuclear fission.   With the




atomic number 36, atomic mass unit 85, and the maximum energy of 0.67




M.E.V., Kr-85 has been widely used as an effective tracer gas in




recent years because of its long half life (10.3 years)  and its pure




Beta emitting property.  The Beta particles emitted by Kn-85 ionize
                                                        K



gas molecules as it passes through them.  With these ionization prop-




erties gas concentrations can be detected by Geiger Mueller counters.




The counter tube consists of two electrodes, a fine metal wire, the




anode, surrounded by a hollow conducting cylinder, the cathode.  Gas




samples were removed from the test section by a rake of sampling




probes and flushed through the tube jackets for a period of three




minutes.  Sampling ceased, and the samples isolated by valves.  Concen-




trations were then determined by counting the tube pulses.  The tubes




used were Halogen-Quenched, stainless steel, thin-walled G-M tubes




(Tracer-lab 1108),




     5.5.2  Tube and Gas Calibration




     G-M tubes and radioactive source gas were calibrated by u<=ing the




following procedure.  A reference G-M tube was calibrated using the




scalar counter and a radioactive source of known strength.  This source




was placed inside a lead-shielded safe containing the reference G-M




tube.  The reference tube is then calibrated in counts per minute vs.




source strength in curies.  The radioactive strength of either a




calibrating or a source gas was then determined by passing the gas




through a plastic container with a Mylar cover at the same position in

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                                   4:


the lead safe as the reference source.  Using the known volume of the

container, concentrations of the gases was determined in  yCi/cc.

A calibrating gas may then be passed through the test G-M tubes which

permits final calibration in counts per minute vs. concentration.

     5.5.3  Concentration Calculations and Counting Statistics

     Gas concentrations were determined by first eliminating the

"background" count corresponding to the naturally occurring radiation.

This was done by subtracting the background counts per minute from the

sample plus background count, and multiplying this by the "tube

constant" previously determined for each tube.  The tube constant was

determined by passing the calibrating gas through the tube jacket,

subtracting the background (obtained by counting ambient air samples)

and correcting for "dead time", which is the time required for the

positive space charge to move far enough from the anode for further

pulses to occur.  The result is then a tube constant in  CPM/pyCi/cc.

The details are shown below:

          CPM  = CPM - Background
          CPM_ = - 7 -   (dead time correction)
                 l-(2xlO
                                 CPM
          Tube constant =
                          Source strength (ypCi/cc)


The standard deviation in the net counting rate (sample plus back-

ground)   a    for a sample is


                 R +b   R,

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                                   42
where  R  ,   is the observed sample-plus-background count, R,   is the



background count and  t   and t,   are the sample and background



counting times respectively.  Since  R,   is of this order of 20 CPM and



was determined with 15 minute counts for each tube, the background



contribution is constant and small.  If  R  ,   is large, t   does not



have to be large to obtain a small value of  an   in terms of
                                              K
                                               S

percentage of  R  , .   As  R  ,   goes down however, t   must be



increased.  In these experiments the following procedure for counting



was used.
            +b - !00°> ts = 1 minute, OR  £ 3.2 percent
          100 1 R +5 < 1000, t  = 2 minutes, OR  £ 7.2 percent

                                               s



          R  ,  < 100,  t  = 3 minutes

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                                   43






                              SECTION VI




                        RESULTS OF EXPERIMENTS






6.1  Plume Rise




     6.1.1  Vertical Plumes




     The vertical plumes emitted into a quiescent atmosphere were




observed to rise initially in a jet with almost linear growth of




radius with vertical distance.  This jet region appeared to encompass




from -1/4 to -1/3 the total rise height.  Measurements of the point




of maximum rise of the top of the plume indicated better correlation




with Froude Number than with Froude Number multiplied by the one-




fourth power of specific gravity.  Actual least squares correlation


                                   08
indicated a proportionality to  SG'  F .  This indicates the assumption




p~p   produces better results than  p~p».  This at first seems com-
   O                                   f\



pletely unreasonable, particularly since it is later shown that for




bent over plumes, P~PA  produces good results.  There are, however,




important physical differences between two situations.  Measurements




indicate that the entrainment constant perpendicular to the flow




direction is greater than the one for the parallel flow by a factor




of from six to eight; thus the presence of a crosswind greatly




increases the entrainment.  The negatively buoyant vertical plume may




also reentrain some of the falling dense fluid, so that the flux of




negative buoyancy increases with distance, rather than being constant.




This would have the effect of reducing rise time.  Since correlation




with specific gravity yields such a small power,  the correlation was




made with Froude Number.   The least squares value of the proportionality




constant was determined to be 2.96.  So that (See Fig. 12):

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                                   44






          H/DQ = 2.96 FR                                         (6.1)





This value is close to that indicated by Turner which appears to yield



a relationship of



          H/D  * 3.1 FD
             O        K




     The value of the entrainment constant, a, was determined for the



"top hat" region immediately downstream from the stack exit.  Matching




radial and height measurements from the smoke photographs to



equation (2.09) suggests that:



          a * 0.045.



When this value of  a  is used in equation (2.8a) to calculate plume



rise one predicts:



          H/D  = 2.43 Fn
             0         K



This relation somewhat underestimates rise height.  Apparently, in the



upper regions of the plume where velocities are low, the proportional



entrainment theory over-predicts entrainment.



     6,1.2  Plumes in a Laminar Crosswind



     Bodurtha noted that over a given range in specific gravities, the



plume rise is independent of specific gravity.  This was also found



in the present experiments for plume rise in a laminar crosswind.



Rise height was obtained by measuring the maximum centerline plume



height from the smoke pictures.  Froude Number dependence was deter-



mined by comparing rise heights from 1/4 inch and 1/8 inch diameter



stacks of equal specific gravity and velocity ratio.  Dimensionless



rise height was determined to be proportional to  (diameter ratio)  ,



with least squares value of  n  as 0.35.  Velocity ratio dependence



was determined by comparing rise heights for equal Froude Numbers and

-------
                                   45
specific gravities but differing velocity ratios i.e.  H r R .   The



least squares value of  m  was found to be 0.32.  Thus correlation



appears to follow the expression suggested by equation (2.16).   H/D



is plotted vs.  R   SG   F      in Fig. 13.  The least squares value
                          K


for the constant of proportionality is 1,32 so that:




          H/D  = 1.32 R1/3SG1/3Fn2/3                             (6.2)
             O                  K



     The correlation with this equation is good except for the lowest



Froude Numbers, where the rise is moderately less than predicted.



Apparently the rise time is low enough that the net entrainment is



rather low; hence the Boussinesq approximation is not valid over a



sufficient range of the height.



     The fact that plumes correlate well with this equation is for-



tuitous, since a significant portion of plume rise over the range of



variables examined takes place in a near-vertical configuration,



whereas equation (2.16) was obtained under assumptions of a near



horizontal plume.  The fact that rise heights of plumes with specific



gravities from 1.5 to 3 would not significantly differ seems strange



since in the jet region plume rise is predicted as /SCf.



     Measurements also indicate that equation (2.18) gives a good



estimate for the horizontal position of the point of maximum rise.



     For plumes such that the point where the lower edge of the plume



touched the floor could be determined with reasonable certainty



(diffusion of the smoke downstream made some plumes visually indeter-



minate at larger distances) the results indicate that strong correla-



tion of touchdown distance with the "horizontal" Froude Number  occurs



for plumes of equal diameter, velocity ratio and rise height,  but

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                                   46
differing specific gravities.   Linear proportionality was noted.

Correlation with equation (2.17)  was noted but with a fair amount of

scatter.  The correlation of variables of equation (2.17) is plotted

in Fig. 14.  A least squares value of the constant of proportionality

of 0.56, was found, so that:
               = 0.56 ((-)[(2 + 1)  - l]}                     (6.3)
            oo                      /R

where  X   is the horizontal distance from the stack to the point

where the lower edge of the plume touches the tunnel floor.

     6.1.3  Plume Rise in the Presence of a Cubical Structure

     The plumes emitted from the center of a cubical structure

exhibited no variation with specific gravity as far as avoiding

entrainment into the cavity immediately behind the building.  All

plumes were found to obey the criteria of Meroney and Yang that for

R _> 1  and  h /h,  ^L 2  entrainment in this region will be avoided.

Farther downstream, the negatively buoyant plumes were observed to

fall into the wake region of the building at distances beyond  X  as

calculated from (2.18), but in this region subsequent entrainment into

the building will not occur as it does in the cavity region.  The

criteria to avoid such entrainment into the cavity region for nega-

tively buoyant plumes, in addition to that of Yang and Meroney,

appears to be that (from equation 2.18)

                F 2
          x = Doir ^ 3hb

For a cubical structure  3h,  is the downstream extent of the cavity

region as found by Halitsky (12).

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                                   47
6.2  Concentrations



     6.2.1  Plumes in a Laminar Crosswind



     The plumes injected into a laminar crosswind exhibited the



following behavior regarding diffusion.  The plume cross section iso-



pleths at the maximum rise height (See Fig. 15) indicate a serai-



elliptic cross section at this point.  The concentration gradients are



much steeper at the top of the plume than at the bottom, which would be



expected since a condition analogous to diffusion in unstable stratifi-



cation exists at the lower plume boundary.  The negative buoyancy of



individual plume particles contributes to diffusion in this direction



since if a particle is displaced from the center of the plume in a



downward direction, it tends to continue due to the increased density



over that of the surrounding fluid,   During the rise period, this trend



is accentuated since the direction of greatest diffusion is opposite



to the mean plume motion, thus increasing the relative displacement.



As the plume descends, the cross sections become more nearly circular



and the vertical distribution of concentration becomes 'more symmetrical



with the skew decreasing.  The longitudinal rate of decay of the "non-
dimensional" concentration  — ^ —  approaches proportionality with


   - -4/1?
(X-X)  '   as the plume approaches  XD  (See Figs, 16-18).  Plots of



maximum values of non-dimensional concentration at the plume high



point and at the point where plume centerline touches the tunnel floor


                                                           _2
vs.  H/D   indicate approximate proportionality with (H/D )  .   Thus



simple mixing length theory predicts good approximations for the decay



in maximum concentrations for the "worst case" of negatively buoyant

-------
                                   48
plumes injected into light winds such that the diffusion is essentially

controlled by plume turbulence.   The proportionality constants

indicated are:
          — ^ — = 2.15(H/D )  '    at point of maximum rise       (6.4)



          XVD 2         2H+h  -1.95
          — 0^- = 3.10 (-rr — -)      at point of plume "touchdown" (6.5)
            ^             o

     6.2.2  Dense Ground Source in a Turbulent Boundary Layer

     Density differences were observed to have a significant effect on

the downstream diffusion pattern of a ground source.   This effect was

primarily multiplicative, however, rather than a change in the power

law of decay with downstream distance as is normally observed with an

inversion stratification.  Fig,  21 and 22 show the rate of decay of

maximum values of the quantity of  xU/Q.  With downstream distances

from the source  U  in this case is taken as the velocity at the source

centerline.  In this case  U  was taken as 3.5 ft per second.  Decay

rates of maximum concentration with downstream distance for a specific

gravity of pne were observed to be proportional to power laws of -1.68

and -1.45 for the neutral and inversion cases respectively, which is

in good agreement with previously observed values (7 , 27).  The maximum

concentrations of the denser gases decay at a slightly greater rate

when the concentrations slowly approach those of air since the density

effects are attenuated by diffusion.  Over the range of downstream

distances examined, a specific gravity of two, for example, increases

maximum ground concentrations by a factor of approximately 30 percent

in both neutral and inversion stratifications.

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                                   49



     The lateral and vertical plume dimensions for the 50 and 10 percent


levels reveal the following behavior (See Figs. 23-30).  As the dense


plumes leave the source, the radial density gradients inhibit vertical


diffusion and accelerate lateral spread, so that initially the lateral


values of the spread rate are greater while the vertical values are


smaller.  As the plume proceeds downstream, the 50 percent concentra-


tion plume dimension becomes larger for the less dense gases as the


concentration distributions for the denser gases exhibit sharper


"peaks.  See Fig. 31.  Apparently a "core" of dense gas resistant to


vertical diffusion is formed as the density differences in the outer


lateral regions of the plume are attenuated by diffusion.   The lighter


gases thus arrive at heights where they are transported laterally


faster by diffusion than the heavier gases can move laterally at ground


level solely due to gravitational effects.  The vertical spread of the


50 and 10 percent concentration levels is shown to be less for the


dense gases over the distance studied,  but they approach that of air as


the plume proceeds downstream.


     6.2,3  Decay of Concentration in Buoyancy Dominated Plumes
            After Touchdown


     The plumes injected into the turbulent boundary layer with free


stream velocity of 2,5 ft per second exhibited the following behavior.


An extremely large lateral spreading occurred immediately after touch-


down.  The concentration profiles in the lateral direction were quite


flat.  The initial decay rate is approximately proportional to  X


(See Fig. 32),  which is similar to the behavior noted by Holly and


Grace with salt water plumes in an open channel,  The decay rate


appears to approach ground source behavior as all plumes approach a

                                                       	2
-1.7 power law decay rate. (Values of velocity in the  x^Z  /Q  are

-------
                                  50






free stream velocity.)  Such behavior is expected to occur only in




those plumes where as a result of high densities and/or low exit




velocities and crosswinds, the plume touches down a short distance




from the stack.

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                                    51





                               SECTION VII



                               CONCLUSIONS




     1.  The rise height of a negatively buoyant plume is increased by



increasing the discharge velocity.  For a given flow rate, this can be



accomplished by decreasing the stack or relief valve diameter.  For a


                                                      -3/2
constant flow rate, rise height is proportional to  D       for vertical


                                           -4/3
plumes in a quiescent atmosphere and to  D       for plumes in a cross-



wind.  The horizontal position of plume descent to the ground will also



be increased by decreasing the stack diameter for a given flow rate and

                                                              _2
stack height.  This horizontal distance is proportional to  D    , and



is of course increased with increased stack height being approximately


                         3/2
proportional to  (2+h /H)     for significant values of  h /H .



     2.  For plumes of relatively high density exhausted into light



winds, such that the density difference and resulting vertical motion



dominates diffusion, the ground concentration will be approximately



proportional to  (2H+h )   .   The downstream decay rate from this point

    YT T     ~\n i   v    £r

is  p—  = (77-)n(V-3 '    where  D  is the point of plume touchdown.  The
    x      V     D


-.65  power law decay rate can be extended to the intersection with the



ground source decay rate and that rate assumed from that point on.



     3.  The effect of negative buoyancy on the behavior of ground



source is primarily multiplicative as the decay relationship is  not changed



in form.   Large specific gravities produce only moderate percentage



increases in downstream concentration values rather than order of mag-



nitude changes.  Negative buoyance causes larger lateral and smaller



vertical  plume dimensions than are observed in cases of neutral  buoyancy.

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                                   52
                             BIBLIOGRAPHY
 (1)   Albertson,  M.  L.,  Dai,  Y.  B.,  Jenson,  R.  A.,  and Rouse,  H.,
      "Diffusion  of Submerged Jets," ASCE Transactions, 115,  pp.  639-697
      (1950).

 (2)   Becker,  H.  A.,  Hottel,  H.  C.,  and Williams,  G.C., "The  Nozzle-
      Fluid Concentration Field  of  the Round Turbulent Free Jet,"
      Journal  of  Fluid Mechanics, 30, pp.  285-304  (1968).

 (3)   Bodurtha, F.  T.  "The Behavior of Dense Stack Gases,"  J.  Air
      Pollution Control  Assoc.,  11,  431-437  (1961).

 (4)   Briggs,  G.  A.,  "A  Simple Model for Bent Over Plume Rise," Ph.D."
      Dissertation,  Pennsylvania State University,  (1970).

 (5)   Briggs,  G.  A.,  Plume Rise,  Atomic Energy Commission Critical
      Review Series,  Division of Technical Information, TID-25075,
      (1969).

 (6)   Cermak,  J.  E.  et al.,  "Simulation of Atmospheric Motion by Wind
      Tunnel Flows,"  Colorado State University,  Report No.  CER66-67
      JEC-VAS-EJP-GJB-HC-RNM-SI-17,  (1966).

 (7)   Chaudhry, F.  H.  and Meroney,  R. N.,  "Turbulent Diffusion in  a
      Stably Stratified  Shear Layer," FDDL Report  CER69-70FHC-RMN12
      (U.S.  Army  Electronics  Command Technical  Report C-0423-5),  (1969).

 (8)   Chesler, S.  and Jesser,  B.  W., "Some Aspects  of Design  and
      Economic Problems  Involved in Safe Disposal  of Inflammable
      Vapors from Safety Relief  Valves," Transactions of the  ASME,
      pp.  229-246 (Feb.  1952).

 (9)   Counihan, J.,  "An  Improved Method of Simulating an Atmospheric
      Boundary Layer  in  a Wind Tunnel," Atmospheric Environment, Vol.  3,
      pp.  197-214 (1969).

(10)   Csanady, G.  T.,  "Bent Over Vapor Plumes," Journal of  Applied
      Meteorology,  10, pp.  36-42 (1970).

(11)   Davar, K. S.,  "Diffusion from a Point  Source  Within a Turbulent
      Boundary Layer," Ph.D.  Dissertation, Colorado State University,
      (1961).

(12)   Halitsky, J.,  "Gas Diffusion  Near Buildings," Meteorology and
      Atomic Energy,  pp.  221-225 (1968).

(13)   Hewett,  T.  A.,  "Model Experiments of Smokestack Plumes  in a
      Stable Atmosphere," Ph.D.  Dissertation, M.I.T., (1971).

(14)   Hoult, D. P.,  Fay,  J.  A.,  and Forney,  L.  J.,  "A Theory  of Plume
      Rise Compared with Field Observations," Paper No. 68-77, Air
      Pollution Control  Association, Pittsburgh, (1968).

-------
                                   S3
(15)  Holly, F. M. and Grace, J. L., "Model Study of Dense Jets in
      Flowing Fluid," Proceedings of the Hydraulics Division No. 9365,
      ASCE, (1972).

(16)  Keefer,  J. F. and Baines, W. A., "The Round Turbulent Jet in a
      Crosswind," Journal of Fluid Mechanics, 15, pp. 481-496 (1963).

(17)  Malhotra, R. C., "Diffusion From a Point Source of Buoyancy in a
      Turbulent Boundary Layer with Unstable Density Stratification,"
      Ph.D. Dissertation, Colorado State University, (1962).

(18)  Meroney, R. N.  and Chaudhry, F.  H.,  "Wind Tunnel Analysis of Dow
      Chemical Facility at Rocky Flats, Colorado," Colorado State
      University Report No.  CER71-72  RNM-FC-45 (1972).

(19)  Morton,  B. R.,  Taylor, G, I., and Turner, J. S., "Turbulent
      Gravitational Convection from Maintained and Instantaneous
      Sources," Proc. Royal  Society A23, pp. 1-23 (1956).

(20)  Morton,  B. R.,  "Buoyant Plumes in a Moist Atmosphere," Journal of
      Fluid Mechanics, 2, pp. 127T143  (1957),

(21)  Plate, E. J. and Lin,  C. W., "Investigations of the Thermally
      Stratified Boundary Layer," Fluid Mechanics Paper No. 5, Colorado
      State Unviersity, (1966).

(22)  Rouse, H., Yih, C.  S.  and Humphries, H. W., "Gravitational
      Convection from a Boundary Source,"  Tellus, 4, p. 201ff. (1952).

(23)  Scorer,  R. S.,  "The Behavior of  Chimney Plumes," Int. J. Air
      Pollution, 1, pp. 198-220 (1959).

(24)  Scorer,  R, S.,  "Experiments on Convection of Isolated Masses of
      Buoyant  Fluid," Journal of Fluid Mechanics, 2, pp.  583-594 (1957).

(25)  Schlichting, H., Boundary Layer  Theory, McGraw-Hill,  New York,
      6th Edition (1966).

(26)  Shin, C.  C., "Continuous Point Source Diffusion in a Turbulent
      Shear Layer," M.S.  Thesis, Colorado  State University, (1966).

(27)  Slade, D. H,, Editor,  Meteorology and Atomic Energy,  U.S.  Atomic
      Energy Commission,  Division of Technical Information, (1968).

(28)  Slawson,  P.  R.  and  Csanady,  G. T., "On the  Mean Path of Buoyant
      Bent Over Chimney Plumes," Journal of Fluid Mechanics, 28,
      Part 2,  pp.  311-312 (1967).

(29)  Sutton,  0. G.,  Micrometeorology,  McGraw-Hill Book Co., Inc.,  New
      York (1953).

(30)  Tulin, M. P. and Schwartz, J,, "Chimney Plumes in Neutral  and
      Stable Surroundings,"  Journal of Atmospheric Environment,
      Vol 6 (1), pp.  19-35 (1972).

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                                  54
(31)   Turner,  J.  S.,  "Plumes  with Negative or Reversing Buoyancy,"
      Journal  of  Fluid Mechanics,  26,  pp.  779-792 (1966).

(32)   Wigley,  T.  M.  L.  and Slawson,  P.  R., "A Comparison of Wet and
      Dry Bent Over  Plumes,"  Journal of Applied Meteorology,   11,
      No.  2, pp.  335-340 (1972).

(33)   Wigley,  T.  M.  L.  and Slawson,  P.  R., "On the Condensation of
      Buoyant  Moist  Bent Over Plumes," Journal of Applied Meteorology,
      10,  (1971).

(34)   Yang,  B. T.  and Meroney,  R.  N.,  "Gaseous Dispersion Into
      Stratified  Building Wakes," Colorado State University Report
      No.  CER70-71 BTY-RNM-8, (1970).

(35)   Yang,  B. T.  and Meroney,  R.  N.,  "Wind Tunnel Study on Gaseous
      Mixing due  to  Various Stack Heights  and Injection rates above
      an Isolated Structure," FDDL Report, CER71-72 RNM-BTY 16, (1971)

-------
            55
         TABLE I
     VERTICAL PLUMES
SMOKE VISUALIZATION DATA
Stack Exit
Velocity Ft.
Per Second
5.44
5.44
5.62
7.39
8.13
8.03
7.50
7.50
7.50
3.70
7.39
14.61
22.07
15.19
22.34
20.10
22.08
7.38
14.85
20.30
22.18
14.80
Stack
Diameter
Inches
.250
.250
.250
.250
.250
.250
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
.125
Specific
Gravity
1.50
2.00
1.24
1.25
1.52
1.97
1.09
1.25
1.50
1.09
2.00
1.96
2.00
1.49
1.50
1.42
1.42
1.35
1.35
1.35
1.35
3.00
Rise
Height
Inches
8.29
6.39
11.95
19.33
14.00
9.05
13.70
13.00
10.86
8.10
6.53
13.00
20.23
16.43
23.55
23.96
25.44
8.89
18.28
26.10
27.30
11.35

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                          62
                             Vortex  Generotor
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-------
                                    63
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-------
                                      64
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-------
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-------
                                   64
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-------
     67
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-------
                                                        69
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-------
                 70
R=10.44, FD=12.95, SG=2, U =7.50 ft/sec
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      Fig.  11.   Smoke  Photographs

-------
                  71
         ^ = 54, SG = 2.0, D  = 1/8"
       FR = 75, SG = 1,36, DQ = 1/8"
Fig. 11. (Cont.)  Smoke Photographs

-------
                                72
  280
  240
  200
  160
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  120
   80
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        Fig. 12.  Dimensionless Rise Height vs.  Froude Number-
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-------
                                  73
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-------
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                        75
                                   Isopleths  o_re
                                   Values of XVD02
                                                   XIO4
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  b) Downstream  in  Near  Horizontal Region
Fig.  15.   Isopleths of Plume in Laminar Crosswind

-------
                                76
                                                   100
c ) Downstream  in  Rapidly Sinking  Region
    Fig. 15. (Cont.)   Isopleths of Plume in Laminar Crosswind

-------
                                            77
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                                 80
                           o- SG=!.5,  R=5.05, 10.20,  15.45, D0 = 1/8"
                           0- SG=ZO,  R=5.05, 10.20,  15.45, D0=l/3"
                           A-SG=3.0,  R=5.05, 10.20,  15.45, D0= 1/8"
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                           A-SG=3.0,  R = 5.5I, 11.10,16.88,0=1/4"
M 0
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              vs.  H/D

-------
                                    81
  Itf'r
                                         O- SG= 3, Do = 1/8"
                                         o-SG = 2, D0= 1/8"
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-------
  10°
                                  82
                               O -SG=30
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  102
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   Fig.  21.  Maximum Concentrations vs.  Downstream  Distance,
              Negatively Buoyant Ground  Source, Neutral
              Stratification.

-------
                                   83
   10"
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   10
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Downstream Distance from Source,  inches
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     Fig.  22.   Maximum Concentrations vs. Downstream Distance,
                Negatively Buoyant  Gro\ind Source,  Inversion
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-------
                                               84
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                              92
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   Fig. 31.  Cross-sectional  Distribution of Concentration,
             x=6ft. Neutral Stratification

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                                   93
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                                    TECHNICAL REPORT DATA
                             (Please read Instructions on the reverse before completing)
 1. REPORT NO.
     EPA-650/3-74-003
                              2.
                                                             3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE

     WIND TUNNEL TESTS OF NEGATIVELY BUOYANT PLUMES
              5. REPORT DATE
                   October 1973
                                                             6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
     T.  G. Hoot,  R.  N.  Meroney  and J.  A. Peterka
                                                             8. PERFORMING ORGANIZATION REPORT NO.
                  RNM-JAP-13
9. PERFORMING ORGANIZATION NAME AND ADDRESS

     Fluid Dynamics  and Diffusion  Laboratory
     Colorado State  University
     Fort Collins,  Colorado  80521
              10. PROGRAM ELEMENT NO.

                  1AA009
              11. CONTRACT/GRANT NO.

                  AP-01186
 12. SPONSORING AGENCY NAME AND ADDRESS
                                                             13. TXPE OR.REPORT AND PERIOD COVERED
     Meteorology  Laboratory -  EPA
     National Environmental Research Center
     Research Triangle Park, North Carolina   27711
              14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
          The results of tests  made of negatively buoyant emissions into  a quiescent
     medium, laminar crosswind  and turbulent boundary layer  conducted in  a wind
     tunnel and  reported.  Measurements include  the maximum  rise height,  horizontal
     point of descent and behavior of emission  characteristics.
 7.
                                 KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS  C. COSATI Field/Group
     Wind tunnel  tests
     Nagatively buoyant plumes
     Plume dispersion
     Plume ruse
     Air pollution meteorology
13. DISTRIBUTION STATEMENT

     Unlimited
19. SECURITY CLASS (ThisReport)
21. NO. OF PAGES
      104
                                               20. SECURITY CLASS (Thispage}
                            22. PRICE
EPA Form 2220-1 (9-73)

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