United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Triangle Park NC 27711
EPA-600/4-79-013
February 1979
Research and Development
Predictions of
Highway
Emissions by a
Second Order
Closure Model

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                RESEARCH REPORTING SERIES

Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology.  Elimination of traditional grouping  was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:

      1.  Environmental  Health Effects Research
      2.  Environmental  Protection Technology
      3.  Ecological Research
      4.  Environmental  Monitoring
      5.  Socioeconomic Environmental Studies
      6.  Scientific and Technical Assessment Reports (STAR)
      7.  Interagency Energy-Environment Research and  Development
      8.  "Special" Reports
      9.  Miscellaneous Reports

This report has been assigned to the ENVIRONMENTAL MONITORING series.
This series describes research conducted to develop new  or improved methods
and  instrumentation for the identification and quantification of environmental
pollutants at the lowest conceivably significant concentrations.  It also includes
studies to determine the ambient concentrations of pollutants in the environment
and/or the variance of pollutants as a function of time or meteorological factors.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.

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                                             EPA-600/4-79-013
                                             February 1979
                  PREDICTIONS OF
              HIGHWAY EMISSIONS BY A
            SECOND ORDER CLOSURE MODEL
                        by
          M. E. Teske and W. S. Lewellen
Aeronautical Research Associates of Princeton,  Inc.
         50 Washington Road, P.O. Box  2229
            Princeton, New Jersey 08540
              Contract No. 68-02-2285
                  Project Officer
               Francis S. Binkowski
       Meteorology and Assessment Division
    Environmental Sciences Research Laboratory
   Research Triangle Park, North Carolina   27711
    ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
        OFFICE OF RESEARCH AND DEVELOPMENT
       U.S. ENVIRONMENTAL PROTECTION AGENCY
   RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711

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

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                           ABSTRACT
     The dispersion of sulfur hexafloride tracer and sulfate from
automobile emissions in the immediate vicinity of a highway were
estimated for conditions similar to those existing during the
General Motors sulfate dispersion experiment conducted at a GM
test track.  A second-order closure model of turbulent transport
in the planetary boundary layer was used to predict the steady-
state dispersion under two conditions:  with the mean wind and
velocity component variances specified by the data or predicted
with the aid of an automobile wake model.  The GM measured wind
data apparently suffered from low vertical velocity variance
readings at the 1.5 meter height, and led to an overprediction of
the SF6 levels by an average factor of 1.77 for the 18 tower col-
lection points during the 15 test days.  The correlation fell
to 0.96 of the measured levels when the model also predicted the
wind fields.  The results indicate that close to the highway,
buoyancy effects were small even in the critical case when the
wind is light and aligned with the roadway.

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                       CONTENTS
Abstract	iii
Figures	 vi
Symbols	 ix

     1.   Introduction 	  1
     2 .   Conclusions and Recommendations	  3
     3 .   General Motors Experiment	  4
     4.   Numerical Simulation	  6
     5.   Automobile Wake Model	  9
     6.   Model Results	 13

References	31
Appendices
     A.   The programmed second-order closure
         equations for two-dimensional, unsteady
         flows	 33
     B.   Model dispersion predictions of SFfc and
         sulfate for 13 typical test periods in the
         GM experiment	 35
     C.   Model comparisons of the velocity and
         variance fields predicted by the closure
         model and measured by GM for the two
         critical test days 293 and 296	 62
                           v

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                            FIGURES


Number

   1   A sketch of the General Motors proving grounds
         test site, showing the relative positions of
         the data towers, instruments, and traffic
         pattern	
       Contours of predicted  AS04  levels (above
         background) using the measured GM mean wind
         fields and turbulence data for the second
         test period of day 293.  In this case the
         ambient winds were nearly cross-wind to the
         traffic, and  S = 28.9 mg/mile/vehicle.
         When the background 804 level is included,
         S = 16.2 mg/mile/vehicle, so that the  ASC>4
         levels shown here should be multiplied by a
         factor of 0.56 	  14

       Contours of predicted  ASC-4  levels (above
         background) using the measured GM mean wind
         fields and turbulence data for the second
         test period of day 296.  In this case the
         ambient winds were nearly aligned with the
         traffic and  S » 28.9 mg/mile/vehicle	  15

       A point-plot of the predicted vs  measured levels
         of  AS04  using the measured GM mean wind
         fields and turbulence data with an assumed
         emission level of  S = 28.9 mg/mile/vehicle.
         Each second-period sample from the 15 simulated
         days contributes 18 points to this plot.  The
         days are denoted as:  1 = day 275; 2 = day 276;
         3 = day 279;  4 = day 281; 5 = day 285;  6 =
         day 286; 7 = day 290; 8 = day 293; 9 = day 294;
         A = day 295;  B = day 296; C = day 297;  D =
         day 300; E = day 302; and F = day 303	  17

       A point-plot of the predicted vs measured levels
         of total 804 using the measured GM mean wind
         fields and turbulence data with an assumed
         emission level of  S = 16.2 mg/mile/vehicle
         based on the  ASC-4  levels plus the mean
         ambient background.  Each second-period sam-
         ple for the 15 simulated days contributes 18
         points to this plot, as denoted in Figure 4....  18

                               vi

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Number                                                    Page

   6   Contours of predicted SFfc levels using the
         measured GM mean wind fields and turbulence
         data for the second test period of day 293	 19

   7   Contours of predicted SF^ levels using the
         measured GM mean wind fields and turbulence
         data for the second test period of day 296	 20

   8   A point-plot of the predicted vs measured levels
         of SFg using the measured GM mean wind fields
         and turbulence data, showing a least-squares
         slope of  1.77 .   Each second-period sample
         from the 15 simulated days contributes 18
         points to the plot.  The days are numbered
         in ascending order with the keys explained
         in Figure 4	 21

   9   Contours of predicted  ASO^ levels (above back-
         ground) using the predicted mean wind fields
         and turbulence data for the second test
         period of day 293, with  S = 51.7 mg/mile/
         vehicle.  When the background 864 level is
         included,  S = 17.3 mg/mile/vehicle, so that
         the  ASC-4  levels shown here should be mul-
         tiplied by a factor of 0.33	 24

  10   Contours of predicted  ASC-4  levels (above back-
         ground) using the predicted mean wind fields
         and turbulence data for the second test
         period of day 296, with  S = 51.7 mg/mile/
         vehicle	 25

  11   A point-plot of the predicted vs measured
         levels of  AS04  using the predicted mean
         wind fields and turbulence data with an
         assumed emission level of  S = 51.7 mg/mile/
         vehicle.  The notation is discussed in Figure 4.. 26

  12   A point-plot of the predicted vs measured levels
         of total 864 using the predicted mean wind
         fields and turbulence data with an assumed
         emission level of  S = 17.3 mg/mile/vehicle
         based on the  ASC-A.  levels plus  the mean
         ambient background.  The notation is discussed
         in Figure 4	 27

  13   Contours of predicted SFg levels using the pre-
         dicted mean wind fields and turbulence data
         for the second test period of day 293	 28
                              via.

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Number                                                   Pagt

  14   Contours of predicted SFg levels using the
         predicted mean wind fields and turbulence
         data for the second test period of day 296	  29

  15   A point-plot of the predicted vs measured
         levels of SFg using the predicted mean
         wind fields and turbulence data, showing
         a least-squares slope of 0.96 .   The
         notation is discussed in Figure 4	  30
                             Vlll

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                        LIST OF SYMBOLS

SYMBOLS
c           -- concentration fluctuation
C           -- mean concentration
g           -- gravity
L           -- average distance between cars
L           -- average distance between trucks
p           -- pressure
q2          -- turbulent kinetic energy
     QTJ.QG  ~~ automobile source functions for turbulence, SF5,
               804, velocity and temperature
S           -- S04 emission level
t           -- time
u*          -- surface shear stress velocity
u.          -- velocity fluctuations (u,v,w)
U           -- mean horizontal  windspeed aligned with the road-
               way
U.          -- mean velocity
V           -- mean horizontal  windspeed normal to the roadway
Va          -- effective mean windspeed
W           -- mean vertical windspeed
x^          -- Cartesian directions (x,y,z)
zo          -- hydrodynamic roughness
                  „. ...     9V   3W
n           -- vortxcity  = — - y-
K           -- vonKarman constant
9           -- temperature fluctuation
0           -- mean potential temperature
00          -- reference temperature
A           -- turbulent macroscale
                               IX

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v           -- kinematic viscosity
a ,a        -- y,z Gaussian source spreads
V           -- stream function
                               x

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                           SECTION 1

                         INTRODUCTION
     For the last several years, the Environmental Protection
Agency  (EPA) has supported the development by Aeronautical
Research Associates of Princeton, Inc.  (A.R.A.P.) of a second-
order closure turbulence model.  The first summarization of the
model development is contained in Donaldson  (Ref. 1), with a
more recent recapitulation found in Lewellen and Teske (Ref. 2).
The strength of the model rests upon the added physics of the
Reynolds stress equations carried for the turbulence correla-
tions  u . u .  ,  u. 9  and  (p~  .  In the incompressible case, five
          J
constants must be evaluated exclusive of the constants appearing
in a companion equation for the turbulent scale length  A  .
These constants are determined by fitting a wide variety of
shear and wake flows (see Ref. 2 for details).  Once determined,
these constants are then unchanged when an application is made
to other, more complicated flow problems.  In the main, the
model has performed admirably in several two-dimensional un-
steady calculations (Refs. 3-5) and appears to give satisfactory
flow results when applied to other simple laboratory flows not
used to evaluate the modeling constants (Ref. 6).

     Of particular interest to EPA is the prediction by the
model of plume dispersal.  To date, the work has centered
around individual plume dynamics (Refs. 2, 6-9) and has not
yet been concerned with multiple plume dynamics.

     In September and October of 1975, General Motors conducted
what they termed their "Great Sulfate Experiment" using a large
fleet of test automobiles on their proving grounds in Milford,
Michigan.  Considerable data were taken of the ambient winds
and turbulence, the temperature, 804, and an SFfc tracer emitted
from several trucks.  The executive summary (Chock, Ref. 10)
highlights the results of a more detailed volume (Cadle, et al . ,
Ref. 11).  Subsequent comparisons of the data with predictions
by the standard Gaussian plume models used at EPA to estimate
roadway sulfate concentrations were not very favorable (Ref. 12).

     Eskridge and Demerjian (Ref. 13) assess this shortcoming
of the EPA model and advance their own "finite difference"
model.  They use an eddy viscosity approach in which the effects
of the automobile have been parameterized with coefficients

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dependent only upon the vertical direction, with the assumption
that the horizontal coefficient is five times larger than the
vertical coefficient.   They assume that the SFg release may be
taken as a steady phenomenon, and use the case with the wind
aligned with the traffic to determine the incremental eddy
viscosity caused by the wake turbulence of the cars.  With this
incremental eddy viscosity function held fixed, they do a
creditable job for the other simulation days.

     In this report, our A.R.A.P. model will be run in two dif-
ferent modes.  First,  the predictions are made using the
available wind and turbulence fields measured at the GM site
to establish the background into which a steady tracer source
is released.  Second,  the calculations are repeated with all
the turbulent correlations predicted by our planetary boundary
layer model with the addition of simulated car wakes.

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                           SECTION 2

                CONCLUSIONS AND RECOMMENDATIONS
     By modeling the automobile wake, it is possible to cal-
culate complete turbulence distributions in the immediate
vicinity of a roadway.  When these velocity variances are used
in the prediction of tracer dispersion, good agreement is ob-
tained with the measured distributions of SFg.  The predicted
turbulence field indicates that the GM measurements of  aw
near the surface are as much as a factor of 2 low.

     As a result of these numerical simulations, we estimate
that the effective average emissions rate of S04 is 17.3 mg/
mile/vehicle.  A great deal of uncertainty, however, surrounds
this number because of the assumptions made on the background
804 level.

     We also conclude that buoyancy is relatively unimportant
to dispersion in the immediate proximity of the roadway where
the towers were located.

     The computer time required for our program's prediction
(of up to 1 hour of c.p.u. time on a PDF 11/70) is probably too
long for it to be used as an integral part of a three-dimen-
sional air quality model.  However, we believe the code could
be streamlined to produce a viable three-dimensional unsteady
code using the A.R.A.P. second-order closure technique.  One
particularly attractive approach to trim the computational
restrictions considerably is to integrate across the vertical
direction (Ref.  6).

     Although the code's present speed is not very good for
regional modeling, it is still adequate for the solution of
local two-dimensional unsteady phenomena where second-order
closure yields the full modeled effect of turbulence.

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                           SECTION 3

                   GENERAL MOTORS EXPERIMENT
     A fleet of 352 late-model automobiles were driven on a
north-south track (two lanes each, Figure 1) of 10 km length
for 17 test days in 1975 (from Refs.  10 and 11).  The cars
were grouped into 32 packs of 11 cars each (16 packs per lane),
with the lead car averaging 80 km/hr.  Uniformly spaced through-
out the automobiles were eight pick-up trucks releasing SF^
tracer gas (one truck for every four packs).  The vehicles also
emitted from 2.6 to 52 mg/mile 804 sulfate into the air, to be
added to the environmental sulfate present at the site.  Tests
were conducted in the early morning hours.

     The traffic passed a tower grid at one pack per 29 seconds.
The towers were positioned on an angle to compensate for local
terrain, and were placed at distances from the center of the
test track of -42.7 m, -14.6 m, 0 m,  +16.5 m, +27.7 m and
+42.7 m as shown.  Two stands further to the east also recorded
wind data, but those results are not amenable to a rectangular
grid simulation.  Each tower measured the wind fields with Gill
model 27004 UVW anemometers at three heights:  1.5 m, 4.5 m and
10.5 m (the equipment on the +16.5 m tower was actually posi-
tioned back to +14.6 m).   Temperatures were recorded on towers 1
and 6 only at the same heights.  At different levels (0.5 m,
3.5m and 9.5 m), collectors measured SFg and 804 levels.

     The SF5 and 804 data are assembled in 30-minute averages
and presented in tables in Ref. 11.  We decided to discard
the first two recorded days (272 and 274) because of faulty
SF£ release data.  Because of the complexity and computer time
required to exercise our numerical code, we arbitrarily
selected the second 30-minute average for the other 15 reported
days.  The average temperatures on towers 1 and 6 are also
given for these periods in Ref. 11. In order to make accurate
predictions,  it was essential to gain access to the wind fields
and turbulence fluctuations.  These data were calculated at
EPA and given to us.  To be consistent with SF6 and 804 data, we
averaged the mean wind field turbulence data over the same second-
sampling period.  Thus, we have 15 cases to simulate, with wind
fields and turbulence given, and the results for both SF$ and
804 dispersion available.

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  10.5m
     9.5m
          xO
                      7
o	  I
4-1 1.5ml
                 Jm4-51*
                t

              -.5m
                                 O
                          6 Road  O  RoadO-
         TOWER
           i
                      .7m
                                  z,W
                    6.8m —
                             u
                             iZ
                                TOWER
                                  3
                              — 6.8m
                                     ,,
                                   Ay \J
                                             O UVW anemometer
                                             x Temperature probe
                                             • S04  8 SF6
                                               collectors
Figure 1.   A sketch of the General Motors  proving  grounds  test
           site,  showing the relative positions  of the  data
           towers,  instruments and traffic pattern.

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                           SECTION 4

                     NUMERICAL SIMULATION
     For the last several years, A.R.A.P. has been engaged in
the formulation and development of an invariant, second-order
closure model of turbulent flows.  In the application of this
technique, we retain the Reynolds stress correlations

            ,  and  F2"  in the momentum and energy equations

         and  0 , and write exact equations for the correla-
tions themselves.  Our closure comes from modeling the higher-
order correlations that necessarily appear in these exact
equations in terms of known second-order correlations and mean
flow gradients.   Such a procedure introduces several modeling
constants that are evaluated by examining simple flow configura-
tions in which individual constants are important.  A fairly
complete examination and verification of the current state of
our incompressible modeling may be found in Ref. 2.  The as-
sumption of invariance requires us to select a fixed set of
modeling constants that do a reputable job of predicting
several simple flow configurations.  These constants are then
used in the equations of motion to predict more complicated
flows.  Appendix A gives the modeled equations.

     The code itself uses an alternating-direction-implicit
algorithm to solve the centered-space, forward-time finite
difference equations in a  y-z  rectangular grid mesh.  A
divergence-free flow is maintained by solving a Poisson equa-
tion for the stream function  ¥  and differentiating to obtain
the velocity fields.  This feature requires the time-dependent
solution of a vorticity equation.

     In application to the near-highway environment, the equa-
tions of motion are solved in an unsteady, two-dimensional
rectangular grid stretching from -60 m to +60 m in  y  (normal
to the roadway)  and 0.2 m to 20 m above the surface.  Nonuniform
mesh is used in both directions.  The +60 m in  y  is used so
that the boundaries are well beyond the positions of towers 1
and 6, but not so far as to force too large a minimum spacing
in  y  (in this case  Ay .   = 1 m).  The lowest  z  location
    •   v               •'mm      '
of 0.2 m is well above the assumed  zo = 3 cm (Ref. 10) and
permits a sufficient number of grid points to establish the
wall layer before the 0.5 m tower stations are reached.  Like-
wise, the 20 m top permits several points above the last tower

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height of 10.5 rn.

     Two types of calculations are performed.  In the first,
we take as given the basic velocity and turbulence fields
(interpolated and extrapolated from the 18 measuring points
to every one of the grid points in the 32 by 31 mesh).  Since
the temperature is known only at towers 1 and 6, we initially
linearly interpolate its value across the mesh.  We then hold
the kinetic energy components and velocity field fixed through-
out the calculation while the temperature adjusts inside the
mesh to a wake source function  QQ .  The passive tracer
is run to establish a steady-state tracer level based on a
steady-state wake source.  The steady-state solution for
is appropriately renormalized to give the steady-state
dispersion predictions.

     The second type of calculation involves solving for all
the second-order turbulent correlations and mean flow variables
with the wake source functions described in the next section.
Thus, a consistent set of Reynolds stress correlations is ob-
tained, along with compatible SFg and 804 levels.

     It was necessary to make a correction to the mean wind
field data before using them for the first calculation.
Namely, the mean wind fields had to satisfy continuity.  In
order to effect this, we used the cross-wind velocity levels
V  to obtain the vorticity  r\ = 3V/3z  (the  W  contributions
to  n  are negligible), solve the  Poisson   equation for the
stream function,  and differentiate to obtain divergence-free
flow profiles for  V  and  W .   In all cases, the resulting  V
profiles are relatively unchanged from the measured levels,
while the  W  profiles show some cross-sectional variation from
the values measured.   With the satisfaction of continuity,
however, we can be sure that no extraneous sources or sinks
are introduced into the simulation.

     For boundary conditions we assumed that the neutral law-of-
the-wall held along the lowest  z  row at 0.2 m, and that no
heat or tracer mass was transferred to the surface  (30/3z = 0 ;
3C/3z = 0).   The inflow boundary (either at +60 m) was held
at the conditions measured at the closest tower, while the out-
flow boundary and the top were permitted a zero slope condition.
This assumption enabled the tracer to pass easily through the
downstream boundary in any of the strong cross-wind cases
studied.  Since the critical fluxes  uw ,   vw ,  cw  and  wB"
were not given, we also assumed that they exhibited a zero
slope inflow condition.  Such an assumption could prove am-
biguous at an inflow boundary,  but in this case, it does not
seem to have bothered the results.

     The initial values of the vorticity and stream function
are obtained by differentiation and integration of the cross-

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wind velocity  V  as mentioned above.  The procedure  is  as
follows.

     We assume that
                       u*
                                 u'

                         KC I z x/n\zI z  ) *~ z ~t*  z  i
                                   o         o

from the neutral wall conditions, where

                  _ - -J-«      T T
                  HI = 	/ ,  ,                           m
                  i/>    0 v\ i *7 I *7  \

and  V  is taken from the  z =  1.5 m upstream tower.   For
1.5m
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                           SECTION 5

                     AUTOMOBILE WAKE MODEL


     It is beyond the scope of the present work to develop com-
pletely rigorous wake source functions for all the variables.
Due to the mixture of cars used and the spacing chosen, con-
siderable uncertainty exists in both the drag characteristics
and the S04 emissions.  This was a principal reason for choosing
to take a first cut at simulation using the turbulence and winds
measured by GM.  For the first mode of calculation, then, only
the models for heat release and SF5 release had to be determined.
Much of the desirability of this type of calculation is under-
mined_by an apparent error in the data fields (particularly
the  ww  correlation).  An examination of the wind and turbulence
left by the cars is then needed to make an estimate of the
appropriate source terms for the second calculation where the full
turbulence fields are predicted.

     The effect of the automobile traffic on the equations of
motion will center on several source terms added to the equations
for the velocity  U , temperature  0 ,  passive tracer  C  , and
energies  q2 ,   uu ,   vv ,  and  ww ..  For simplicity, we choose
to parameterize the wake of the automobiles in each pair of
lanes as a single Gaussian source centered about the middle of
each dual lane at +9.3 m as seen in Figure 1.  Since the auto-
mobiles are close to the ground, we assume a ground release,
so that only a half Gaussian actually exists.

     It was assumed that the effective steady-state cross-
section of the automobile wake is twice the roadway width,
ay = 6.8 m .  From a Masters' thesis by Brander (Ref. 14),
wherein he concluded that a single body wake is half as tall
as wide, we take  az = 1.7 m  since we are dealing with two
lanes of traffic.  The total area under the Gaussian half source
is then  QTrayoz/4  with  Q  the maximum source strength.  With
the automobiles traveling in packs of 11 every 29 seconds, we
can estimate average steady distance between cars to be


           ,    /80 km\ (29 sec/pack)     co .,  ,
           Lc = (	h?) (11 cars7pack)  = 58'6 m/Car

     The effective rate of heat release is given as an average
of 0.11 megajoules/sec/vehicle (Ref. 10).   For a typical hydro
carbon  CgH^g  (heat of formation = 11.4 Kcal/gm; density =

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= 0.7 Kg/&) this figure would correspond to 15.6 mpg.  With the
Cp  of air factored in, this yields an incremental temperature
release of 93 m3°C/sec.  Thus, the amplitude of the continuous
source function for heat from two lanes of traffic when modeled
as a Gaussian ground release is given by
                   ira a
              LCQ9 —3p- = 2(93 m3°C/sec)                (6)

or

                      Q0 = 0.175°C/sec

     The velocity source term should come from the effective
drag of the vehicles.  Thus, we would expect

              QTTira a L
               U  £ZC - %CDV*A                         (7)

where  C-Q  is the automobile drag coefficient,  Va  is the
effective ambient wind and  A  is the automobile frontal area.
An average drag coefficient from White (Ref.  15) is taken as
CD = 0.4-> assuming that each car sees a mean wind of  Va = 80 km/hr
(Since the cars follow in packs, this assumption is not a
particularly good one, because the interactive dynamics of 11
cars would tend to decrease either the effective  CQ  or wind
Va .  The precise amount of this reduction is difficult to
predict.)  For purposes of the second set of calculations, we
choose a maximum value for the axial momentum source strength
for our assumed wake geometry of

                      QD = 0.100 m/s2                    (8)

This corresponds to a car frontal area  A = 1.5 m2 and the total
effective drag reduced by 64 percent.

     Since the energy lost to drag goes directly into turbulent
kinetic energy, it is consistent to take

                2CnV3A
          V =^VlT= Va-2-22»2'8'              (9)
           H      y z c
     The release of the 864 sulfate was determined in Ref. 11
to fall anywhere between 2.6 and 52 mg/mile per vehicle.  This
is quite a wide range.  For our analysis we assume that the
average release was S mg/mile, and determine  S  by matching
our predictions of 804 with a least-squares fit of the measured
values over the 15 test periods studied.   If the GM experiment
pinpointed the overall average release of the 864, that number
could have  been used and no parameterization would have been
necessary.  The S mg/mile figure translates to a release of
0.0138S ing/sec; to give

                               10

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                        Ira a Lp
                   Qso    V G - 0.0138S                 (10)
                      4
or

                Qcn  = 0.026S microgms/m3sec              (11)
                 bU4

     The experiments attempted to maintain an SFg flow rate of
0.5 £/min, although some departure from this rate did occur as
shown in Table VII of Ref.  11, particularly when one of the
trucks did not release the  tracer.  In these cases, the actual
released average must be ratioed with a "perfect" average of
4 &/min (eight trucks) to establish the release rate for each of
the 15 cases to be simulated.  Since the density of SF6 is
6.6 gm/£  and its molecular weight is 146.05, the effective flow
rate of the SF5 gas is


        c = (0.5 &/min)(6 .6 gm/Jl) = 9   1Q_6 m3/sec
        c         6.18 kg/m3        y x lu   m /sec

Thus, for a steady-state emission of the SF/- ,
                          TTCJ a L           D
or
                   Qqi,  = 0.380 ppb/sec                   (14)
                    b-6
where  Lt  is the average distance between trucks
     A possible discrepancy in using  QSFA  as a steady-state

release might lie in the frequency at which the trucks pass the
instruments.  Since the trucks are also moving at 80 km/hr, we
see that the time between truck passages is


                    Att " 80 km/hr ' 12° sec              <16>

Since the average winds recorded by the data are about 2  to 3
m/s, even a light cross-wind will convect the released SF5 past
the towers before the next truck passes the instruments.  How-
ever, since the experiment involves integrating over the  time
dependence of the SFg release, and the diffusion equation is
linear with respect to species concentration, a steady release
is mathematically equivalent to a series of intensive puff re-
leases .
                                11

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     The critical assumption is that the turbulent velocity
fluctuations are stationary during the diffusion process.  This
may be questionable since the truck wake into which the SF6
was released may be expected to be somewhat different from the
ensemble mean car wake.
                               12

-------
                           SECTION 5

                         MODEL RESULTS


     We present the results of 30 different simulations.  One
averaging period for each of the 15 reported test days has been
simulated using both calculation modes.  In this section of the
report, we present detailed results for two representative days
(293 and 296) and summary comparisons between all the simula-
tions and data.  Appendix B contains the SFg and 804 contour
predictions for the other 13 test days.

FIXED TURBULENCE PREDICTIONS

     Because there exists a considerable amount of uncertainty
in the wake source parameters (e.g.,  °y »   CTz >  Va ,   A  and
CD),  we first predicted the SFg and 804 fields by fixing the
turbulence and mean wind (satisfying continuity) and solving
for the dispersion of a steady source representing the sulfate
and SFg tracer emissions.  To this end, then, we selected the
second averaging period for each of the reported test days
after the first two, established the input conditions from the
data supplied to us by EPA personnel or found in Ref.  11, and
then ran the code to see the effects of our temperature and
species source strengths.  Figures 2 and 3 present the contour
curves for the  AS04  predictions for days 293 and 296.  Here
we have removed the background sulfate level to give the auto-
mobile emission effect.

     In order to use our results to predict the S04 distributions,
we needed to make several auxiliary assumptions.  First, we have
a priori assumed that no chemistry occurs.   Therefore,  our
steady-state passive tracer levels may be conveniently scaled
to give the 804 levels.  To do this, we averaged the three up-
wind S04 levels recorded by Cadle, et al. (Ref. 11) and assumed
that this value was the ambient value for the particular run
in question.  Subtracting this value everywhere gives us a  AS04
level at each tower point for each of the 15 runs.   A least-
squares fit is then used to determine the effective 804 emission
rate; in this case,  8 = 28.9 mg/mile for each vehicle.  This
level of emission then multiplies our steady-state prediction
for each of the 15 test periods to obtain our  AS04  predic-
tions through all simulations.  The rest of the contours are
shown in Appendix B.  A plot of the predicted levels at the 18
tower positions against the measured levels for all 15  test days


                               13

-------
       10
        8
AS04(^g/m  ) =
  fsl
         -45
Figure 2.   Contours of predicted  AS04   levels  (above background)
           using the measured GM mean wind  fields and turbulence
           data for the second test  period  of day 293.  In this
           case the ambient winds were nearly cross-wind to the
           traffic, and  S = 28.9 mg/mile/vehicle.  When the
           background SO^ level is included,  S = 16.2 mg/mile/
           vehicle, so that the  AS04  levels shown here should
           be multiplied by a factor of  0.56  .
                              14

-------
                 ASO
        10
         8
   M   4
        z.
          -45     -30     -IS     0       IB
                             Y  (  M )
30
Figure 3.  Contours of predicted  AS04 levels  (above  background)
           using the measured GM mean wind fields  and turbulence
           data for the second test period of  day  296.   In this
           case the ambient winds were nearly  aligned with the
           traffic, and  S = 28.9 mg/mile/vehicle.
                               15

-------
is shown in Figure 4.  Since the data were used to correlate
with the predictions, the points on Figure 4 are forced to
scatter about a 45° line.  When the assumed average background
levels of 804 are added to the  AS04  levels, the considerably
less-scatter point plot of Figure 5 results, where a match of
the data with the predictions gives an emissions level of  S =
16.2 mg/mile/vehicle.  Clearly, our assumption on the background
level is very important.

    Although Figure 5 looks like a much better correlation, it
is partially illusory because the relatively large value of the
background 304 tends to dominate the automobile wake contribu-
tion.  If the background level were completely determined, then
Figure 4 would be the more accurate way to present the comparison
between measurements and predictions.  Unfortunately, a sig-
nificant part of the scatter in Figure 4 appears to be directly
traceable to the uncertainty in the background level caused by
variation in the three upwind 804 measurements.   We are led to
the conclusion that the emissions estimate based on Figure 5
is more valid than that based on Figure 4.

     Figures 6 through 8 show the corresponding curves for the
SFg predictions.  As can be seen from Figure 8 these predictions
are consistently higher than the data.  Since we have no
flexibility in adjusting the SFg levels, we must either fault
the prediction or the data.

     A least-squares fit through Figure 8 gives a line with a
slope of 1.77.  Thus, we are, in general, overpredicting the
data by 77 percent.

     Because we apparently have too much SF6 near the source
and too little above it, we are led to the conclusion that
vertical diffusion is being underpredicted.  Vertical diffusion
depends critically on  ww .  Chock (Ref. 10), in fact,  lays
doubt upon these estimates by noting that for light wind con-
ditions the true value of  aw  may be greater than measured
due to the Gill model UVW anemometer response time.  This ap-
parent discrepancy in the data led us to consider solving for
the complete wind fields; those results and a further examina-
tion of our automobile model are now presented.

FULL TURBULENCE PREDICTIONS

    Since the  ww  levels at the 1.5m height in the GM data
are considered to be too low to give a good prediction of the
SF5 results,  we proceeded to compute the full solution of the
wind and turbulence field using second-order closure, enabling
                              16

-------
  o
  O)
  LU
  o

  o
  LJ
  h-
  CJ
  M
  a
  Ul
  or
  a
                 3      6       9       12
              MEASURED  DELTA  S04
16
Figure 4.   A point-plot of the predicted vs measured levels  of
           AS04 using the measure Gil mean wind fields and tur-
           bulence data with an assuucd enission level of
           S = 2".9 n^/"die/vehicle.  3ach second period sam-
           ple from the 15 simulated days contributes 13 points
           to this plot.   The days are denoted as:  1 = day  275;
           2 = day 276; 3 = day 279; 4 = day 281; 5 = day 283;
           6 = day 286; 7 = day 290; 8 = day 293; 9 = day 294;
           A = day 295; B = day 296; C = day 297; D = day 300;
           E = day 302; and F = day 303.
                              17

-------
           30 „
  Q
  Ul
  K
  o
  H
  O
  UJ
  Or
  Q.
                             10      15      20
                           MEASURED  S04
25
30
Figure 5.   A point-plot of the predicted vs measured levels  of
           total S04 using the measured GM mean wind fields  and
           turbulence data with an assumed emission level of
           S =  16.2 mg/mile/vehicle based on the  AS04  levels
           plus the mean ambient background.  Each second-
           period sample for the 15 simulated days contributes
           18 points to this plot,  as denoted in Figure 4.
                              18

-------
   NJ    4
          -45
Figure 6.  Contours of predicted SFg levels using the measured
           GM mean wind fields and turbulence data for the
           second test period of day 293.
                              19

-------
                      SFe  (ppb) =
       10,.
          -45
Figure 7.   Contours of predicted SFg levels using  the measured
           GM mean wind fields and turbulence  data for  the
           second test period of day 296.
                               20

-------
        7.
        6..
   CD
   U.
   Q
   Ul
   H
   0
   UJ
               MEASURED  SF6
Figure 8.  A point-plot of the predicted vs measured levels of
          SF6 using the measured GM mean wind fields and  tur-
          bulence data showing a least-square slope of 1.77.
          Each second-period sample from the 15 simulated days
          contributes 18 points to the plot.  The days are
          numbered in ascending order with the keys explained
          in Figure 4.
                             21

-------
us to provide at least a consistent  ww  prediction for the tur-
bulent background of the S04 and SFg predictions.  Since we
are now dealing more directly with the wind fields and the tur-
bulence levels, and not the SF£ profile, we first examined the
effect of the source functions and automobile model on the
generation of turbulent kinetic energy  q2  and momentum  U .

     To perform the study, we looked more closely at the two
days 293 and 296, where the ambient wind is aligned nearly
cross-wind and parallel, respectively, to the flow of traffic.
Since the  U  velocity gradients are present only in the  uu
equation, we choose to set  Q — =62,  Q — = Q: — = 0
 ^      '                    niu   ^    '  x     ^
Isotropy and turbulent shear interactions will feed into the
equations for  vv  and  ww  to enable these variables to reflect
the presence of the automobiles.

     When the first car in a pack goes by, that car certainly
encounters an effective wind  Va = 80 km/hr , since 25 or so
seconds have elapsed since the last car of the previous pack
went by.  But the next car in the pack will see a reduced ef-
fective wind because this car is trapped in the wake of the
first (drafting in auto racing) , not also incidentally reducing
its effective drag coefficient.  Cars further back in the pack
feel the effects of the cars in front of them to create a very
difficult engineering problem.  For comparison in the laboratory
experiment of Chevray for wakes behind spheres (Ref. 2), we saw
that the velocity defect was about 35 percent of freestream at
a station five diameters downstream of the sphere.  This number
would give an effect of  (.65)3  in  Q 2 .

     Taking this effect into account in our source functions ,
we obtain a consistent set of mean and turbulence profiles for
all simulation days.  The specific days 293 and 296 are compared
with the smoothed interpolated GM data in Appendix C.  We
believe that these comparisons reflect a reasonable representa-
tion of the wake source functions.  Using these functions, we
now repeat the calculations for the  AS04  and SFg emission
levels .

     The biggest difference is in_the  ww  field measured by GM.
Near the surface the predicted  ww  is approximately twice the
reported data value.  We believe this is a reflection of the
relatively slow response time of the Gill anemometer.  Even on
the upwind towers,  ww  at the bottom measuring station (at 1.5m)
reports a value which is a factor of 2 lower than reported at
4.5 m.  In the nearly neutral surface layer,   ww  should be
constant with height.   However, the characteristic time of the
vertical fluctuations is a factor of 3 shorter at 1.5 m height
than it is at the 4.5 m station.
                               22

-------
     The new predictions for 804 dispersion using the predicted
turbulence and a steady pollutant source are given in Figures 9
and 10 for days 293 and 296 and may be compared with Figures 2
and 3.  The new summary plots of predicted vs measured for all
the cases predicted in this manner are given in Figures 11 and
12.  The best estimate of the 804 emission rate based on  ASQ-4
levels is 51.7 mg/mile/vehicle, with a root-mean-square error
from the linear curve fit of 0.574 .   The 804 emission rate
based on total 804 level is 17.3 mg/mile/vehicle, with a re-
duced root-mean-square error of 0.326 .   As previously discussed,
we believe the latter emissions estimate to be the more valid.

    The difference in the SFg predictions is more striking
since there is no uncertainty in the emissions rate in this
case.  Figures 13 and 14, which show the results of the simula-
tion with the predicted turbulence, may be compared with Figures
6 and 7.  By increasing  ww  near the surface, more of the SFg
is moved away from the wake source to the top measuring sta-
tions.  The comparison between predicted and measured values is
now quite favorable (0.96) as seen in Figure 15.  In this case,
the root-mean-square error is 0.306.

     The reason the difference between measurements and predic-
tions shows a larger scatter for SOA (Figure 11), than for
SFfc (Figure 15) is most likely a reflection of the uncertainty
in the background level.  The upwind tower seldom showed the
same 804 level at all three instruments.  This indicates an
ambient transfer of 804 between the surface and the atmosphere
which would be disturbed by the automobile wake turbulence even
without any 804 emissions.  There is also the possibility of
chemical transformations affecting the 804 dispersion.

     The relative influence of buoyancy in the problem may be
found by ratioing the integrated buoyancy term in the turbulent
energy equation to the integrated dissipation rate.  Thus,  we
write
8fJ
If
                                  w9 dA
                                   dA
Evaluating  B  for the predicted turbulence fields gives a
value of  B  no larger than 0.109 for the aligned cases and
0.06-5 for the cross-wind cases.  The effects of buoyancy in
setting the turbulence field are thus quite small.  A funda-
mental reason why the Gaussian plume model does not predict
the GM data well is then the lack of any substantial influence
of the wake turbulence fields, not the fact that buoyancy is
not included.
                              23

-------
        10 AS04 (/ig/m3) =
         8
         6
   N    4
          -45
Figure 9.  Contours of predicted  ASO^.   levels  (above background)
           using the predicted mean wind fields and turbulence
           data for the second test period  of day 293, with
           S = 51.7 mg/mile/vehicle.  When  the background S04
           level is included,   S = 17.3  mg/mile/vehicle, so that
           the  AS04  levels  shown here  should be multiplied
           by a factor of 0.33 .
                               24

-------
          AS0
  Nl    4
         -45
Figure 10.
Contours of predicted  AS04  levels  (above background)
using the predicted mean wind fields  and  turbulence
data for the second test period of day  296,with
S = 51.7 mg/mile/vehicle.

                  25

-------
   -J
   UJ
   o

   a
   u
   H
   O
   H
   a
   UJ
   a
   CL
         0      3       6      9       12
             MEASURED  DELTA  S04
                                   15
Figure  11.
A point-plot of the predicted vs measured levels
of  AS04  using the predicted mean wind fields and
turbulence data with an assumed emission level of
S = 51.7 mg/mile/vehicle.  The notation is dis-
cussed  in Figure 4.
                             26

-------
           30,
           25..
   a
   LU
   h-
   a
   M
   a
   LU
   ce
   a.
                     5      10      15      20      25

                          MEASURED  S04
                                                30
Figure 12.
A point-plot of the predicted vs measured levels of
total 804 using the predicted mean wind fields  and
turbulence data with an assumed emission level  of
S = 17.3 mg/mile/vehicle based on the  AS04  levels
plus  the mean ambient background.  The notation is
discussed in Figure 4.
                             27

-------
   N    4.
          -45
Figure 13.
Contours of predicted SFg levels using the predicted
mean wind fields and turbulence data for the second
test period of day 293.
                              28

-------
                          SF6  (ppb) =
          -45    -30
              -IS     0
                 Y   ( M  )
Figure 14.
Contours of predicted S?£  levels using the predicted
mean wind fields and turbulence data for the second
test period of day 296.
                              29

-------
       7..
       6..
  CD
  U.
       5..
  Q
  Ul
  h-
  CJ
  H
  a
  UJ
  or
  a.
4..
3.
       2.
                123
              MEASURED  SF6
Figure 15.
    A point-plot of the predicted vs.measured levels of
    SFc using the predicted mean wind  fields and tur-
    bulence data, showing a least-square  slope of 0.96.
    The notation is discussed in Figure 4.
                             30

-------
                          REFERENCES
1.  Donaldson, C.duP.  Atmospheric Turbulence and the Dispersal
    of Atmospheric Pollutants.  In: Proceedings of the Workshop
    on Micrometeorology (D.A. Haugen, ed.), American Meteoro-
    logical Society, 1973.  pp. 313-390.

2.  Lewellen, W.S., and M.E. Teske.  Turbulence Modeling and
    Its Application to Atmospheric Diffusion. EPA-600/4-75-016,
    U.S. Environmental Protection Agency, Research Triangle
    Park, NC, 1975.

3.  Teske, M.E., and W.S.  Lewellen.  Turbulence Transport Model
    of a Thunderstorm Gust Front.  In: Proceedings of 10th
    Conference on Severe Local Storms, American Meteorological
    Society, Omaha, NE, 1977.  pp. 143-150.

4.  Lewellen, W.S., and M.E. Teske.  Turbulent Transport Model
    of Low-Level Winds in a Tornado.   In: Proceedings of 10th
    Conference on Severe Local Storms, American Meteorological
    Society, Omaha, NE, 1977.  pp. 291-298.

5.  Bilanin, A.J., M.E. Teske, and J.E. Hirsh.  The Role of
    Atmospheric Shear, Turbulence and a Ground Plane on the
    Dissipation of Aircraft Vortex Wakes.  AIAA 16th Aerospace
    Sciences Meeting, Paper 78-110, 1978.

6.  Teske, M.E., W.S. Lewellen, and H. Segur.  Turbulence
    Modeling Applied to Buoyant Plumes. U.S. Environmental
    Protection Agency, Research Triangle Park, NC, 1977.

7.  Lewellen, W.S., M.E.  Teske, R. Contiliano, G.  Hilst, C.duP.
    Donaldson.  Invariant Modeling of Turbulence and Diffusion
    in the Planetary Boundary Layer.  EPA-650/4-74-035, U.S.
    Environmental Protection Agency,  Research Triangle Park, NC,
    1974.

8.  Teske, M.E., and W.S.  Lewellen.  Example Calculations of
    Atmospheric Dispersion Using Second-Order Closure Modeling.
    In: Proceedings 3rd Symposium on Atmospheric Turbulence,
    Diffusion and Air Quality, American Meteorological Society,
    Raleigh, NC, 1976.  pp. 149-154.

9.  Teske, M.E., W.S. Lewellen, and H. Segur.  Example Calcula-
    tions of Buoyant Plume Dispersal Into Stable Atmospheres.
    In: Proceedings of Joint Conference on Applications of Air

                               31

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     Pollution Meteorology,  American Meteorological Society,  1977.
     pp.  283-290.

10.   Chock,  D.P.  General Motors Sulfate Dispersion Experiment:
     An Overview of the Wind,  Temperature and Concentration Fields.
     GMR-2231.

11.   Cadle,  S.H.,  D.P. Chock,  J.M.  Heuss, P.R. Monson.
     Results of the General Motors  Sulfate Dispersion Experiment.
     GMR-2107.

12.   Maugh,  T.H. II.  Sulfuric Acid From Cars: A Problem That
     Never Materialized.  Science,  198:280-234, 1976.

13.   Eskridge, 3..E., and K.L.  Demerjian.  A Highway Model for
     the Advection, Diffusion and Chemical Reaction of Pollutants
     Released by Automobiles:  Part  I - Advection and Diffusion
     of SFfc Tracer Gas.  In: Proceedings of Joint Conference on
     Applications of Air Pollution Meteorology, American Meteoro-
     logical Society, 1977.   pp. 337-342.

14.   Brander, J.A.  Dispersion of Pollutants in the Wakes of Blunt
     Objects.  M.S. Thesis,  Massachusetts Institute of Technology,
     1974.

15.   White,  R.G.S.  A Method of Estimating Automobile Drag Coef-
     ficients.  SAE Transactions, 78:829-835, 1969.
                                 32

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                          APPENDIX A

              THE PROGRAMMED  SECOND-ORDER CLOSURE
                EQUATIONS FOR TWO-DIMENSIONAL,
                        UNSTEADY  FLOWS
     The ensemble-averaged  equations  of motion,  including the
invariantly modeled terms,  may be  summarized  in  tensor  form as
       DU.      92U.    3u.u.    a
       BIT - *  rrr -  -sir1  -  llr
                dx.       j       J.
     Du.u.    _  3U    _  3U.   g. _   g
     -Dp" = -uiuk  9^  - ukuj  HT + 
-------
     Dt      2
        	 ou.                  ,.       _ .

        uiui 33r + °-075ci + °-3 dr (C*A  fx~ >
         1  1 oX.                dX.      OA.
           J   J                  11
        0.375
                                   Q.8A   i
                                0  V
                                                          (A7)
     Si =  (0,0,g)

The equations for  C  and  its  correlations  may be found from
equations  similar to  those for  0   and its  correlations:
DC
Dt
                    9uC
= v
                        +  Q
                           Q
                                                  (A8)
   Du.c
                  3U.
                9x.
              (v + 0.3qA)
                                  3u..
                                  0.75q

                                    A
                                           u. c
                                                          (A9)
    Dc9
    Dt
= -u. c ^— u. e
                 3C
                        x
                         k
                             (v
                                     0.3,A)||!L]
                                              rC -J

                                                          (A10)
    Dt
                                       ^.45q
                                         A
                                                          (All)
     The cross-wind velocities  are actually determined by cross-
differentiating Eq.  (Al)  to  obtain an equation for
                       n  =
                           3V   3W
                           3z    3y

from which we may  solve  for the stream function:
                                                  (A12)
where
                         V = -
                               3y
                                                          (A13)
                                                          (A14)
                               34

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                          APPENDIX B

              MODEL DISPERSION PREDICTIONS OF SF6
            AND SULFATE FOR 13 TYPICAL TEST PERIODS
                     IN THE GM EXPERIMENT
     Figures B-l through B-13 present the predicted  AS04  levels
(above background) using the predicted mean wind fields and tur-
bulence data for the second test period in each day.  These
figures are drawn with the assumption that  S = 51.7 rag/mile/
vehicle.  When the ambient background is included in the SO^
levels, the value of  S  decreases to  S = 17 . 3 mg/mile/vehicle,
and all of the contours in Figures B-l through B-13 should be
multiplied by a factor of 0.33 .
     Figures B-14 through B-26 present the predicted SFfc levels
under the same conditions for the same days.  Here the emissions
level is fixed by the data.  The figure title contains the
specific day simulated.
                               35

-------
          AS0
   N   4
          -45
Figure B-l.
Predicted  AS04   levels for the second test period
of day 275.
                             36

-------
N    4..
       -45
Figure B-2.  Predicted
             of day 276.
                           levels for the second test period
                           37

-------
       10,.
        8
            ASO
   M    4.
          -45
Figure B-3.
Predicted  ASO^   levels  for  the  second test period
of day 279.
                              38

-------
             AS04(^tg/m
          -45
Figure B-4.
Predicted  ASOA  levels for the second test period
of day 281.
                             39

-------
  M    4.
         -45
Figure B-5.
Predicted  AS04  levels for the second test period
of day 283.
                              40

-------
        10.,
          -45
Figure B-6.
Predicted  AS04  levels for the second test period
of day 286.
                              41

-------
       10,
        8
         -45     -30
            -15     0
                Y  ( M )
30
45
Figure B-7.
Predicted  AS04   levels for the second test period
of day 290.
                              42

-------
         AS04(/ug/m3) =
  M    4
        -45
Figure B-8.
Predicted  AS04  levels  for the second test period
of day 294.
                            43

-------
               AS04(/ug/m3) -
  M   4
         -45
Figure  B-9.
Predicted  AS04  levels for the second test period
of day 295.
                            44

-------
   N    4..
          -45
Figure B-10  Predicted  ASOA  levels for the second test period
             of day 297.
                               45

-------
          ASO,
       10,.
  fSl    4..
         -45
Figure B-ll.
Predicted  AS04  levels for the second test  period
of day 300.
                             46

-------
          AS0
  N    4
         -45
Figure B-12.
Predicted  AS04  levels for the second test period
of day 302.
                             47

-------
          -45
Figure B-13.
Predicted  AS04  levels for the second test period
of day 303.
                              48

-------
               SFfi  (ppb) =
 Nl    4
        -45
Figure B-14.
Predicted SFg levels  for  the  second test period
of day 275.
                             49

-------
                SF6  (ppb) =
 N    4.
        -45
Figure B-15.
Predicted SFg levels for  the  second test period
of day 276,
                             50

-------
              SF6  (ppb) =
 N
        -45
Figure B-16.
Predicted SFg levels  for  the second test period
of day 279.
                              51

-------
              SF6  (ppb)>
  M    4
         -45
                                    02
Figure B-17.
Predicted SFg  levels for the second test period
of day 281.
                             52

-------
   N   4
                  SF6  (ppb) =
          -45     -30
             •15     0       15
                Y  ( M )
30
45
Figure B-18.
Predicted SF/-  levels  for the second test period
of day 283.
                             53

-------
                 SFfi  (ppb) =
 N
        -45
   -30
-16     0
    Y  (  M )
Figure B-19.
Predicted SF6  levels for the second test period
of day 286.
                             54

-------
                   SFfi  (ppb) =
   N   4
          -46
                                     02
Figure B-20.
Predicted SFfi levels  for  the  second test period
of day 290.
                              55

-------
      10,.
                 SFfi (ppb) =
  N    4
         -45
Figure B-21.
Predicted SFg  levels  for the second test period
of day 294.
                              56

-------
                     SF6  (ppb) =
                                        02
  N
         -45     -30
           -15     0
               Y  ( M )
45
Figure B-22.
Predicted SFg levels  for the second test period
of day 295.
                              57

-------
             SF6  (ppb) =
  N
         -45
Figure B-23.
Predicted SF6  levels for the second test period
of day 297.
                              58

-------
            SF6  (ppb)*
   N    4.
         -45
    -30
-IS     0
    Y  (  M )
Figure B-24.
Predicted SF^  levels for the second  test period
of day 300.
                              59

-------
                 SF6 (ppb) =
   N   4.
          -46
Figure B-25.
Predicted SF^  levels for the second test period
of day 302.
                              60

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  N
                            SF6 (ppb) =
         -45     -30
           -15     0
               Y  ( M )
15
Figure B-26.
Predicted SF^  levels for the second test period
of day 303.
                             61

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                          APPENDIX C

             MODEL COMPARISONS OF THE VELOCITY AND
            VARIANCE FIELDS PREDICTED BY THE CLOSURE
             MODEL AND MEASURED BY GM FOR THE TWO
                 CRITICAL TEST DAYS 293 AND 296
     Figures C-l through C-5 give the predicted contours of the
mean flowfields and turbulence levels for the second test period
of day 293.  Figures C-6 through C-10 give the corresponding
measured levels linearly interpolated from the data recorded at
the 18 tower positions.  Figures C-11 through C-15 and C-16
through C-20 give the predicted and measured levels for the
nearly-aligned day 296.
                               62

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        8..
        6.
  M    4.
                        U  (m/sec) =
         -45
Figure C-l.
Predicted contour levels of the  U  velocity  for
the second test period  of day 293.
                              63

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        61
   N    4
          -45
                  V (m/sec) =
                      1.75
Figure C-2.
Predicted contour levels of  the  V  velocity for
the second test period of  day 293.
                               64

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                      W  (m/sec) =
  N   4..
                 -30
            -15     0
                Y  C M )
15      30      45
Figure C-3.
Predicted contour  levels of the  W  velocity for
the second test period of day 293.
                             63

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  M    4..
         -45     -30
                         q2(m2/s2)
            -15     0
                Y  ( M )
Figure C-4.
Predicted contour  levels of the  q2  velocity  for
the second test period of day 293.
                               66

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              	    2  2
        10    ww  (m /s
   N    4.
          -45
Figure C-5.
Predicted contour levels of the  ww  velocity  for
the second test period of day 293.
                              67

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               U  (m/sec) =
  N
         -45
Figure C-6.
The measured contours of the  U  velocity  for
day 293.
                              68

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       10,.
        8..
                 V (m/sec) =
  N    4..
         -45     -30
            -15     0
                Y  ( M )
Figure C-7.
The measured contours of the   V  velocity for
day 293.
                              69

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                    W  (m/sec) =
   N
          -45    -30
                                                      .05
             -15    0
                Y   ( M  )
Figure C-8.
The measured  contours of the  W  velocity for
day 293.
                             70

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   N   4
                  q2{m2/s2) =
          -45    -30
             -IS    0
                Y   ( M  )
30      45
Figure C-9.
The measured contours of the  q2  correlation
for day 293.
                             71

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                              w w (m2/s2) =
  N
         -4S
Figure C-10.
The measured contours of the  ww  correlation
for day 293.
                             72

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   N    4.
          -45     -30
            -15     0
                Y  ( M )
IS      90
45
Figure C-ll.
The predicted contours  of  the  U  velocity for
day 296.

-------
                          V (m/sec) =
  N
         -45     -30
           -IS     0
               Y  ( M )
15      30
Figure C-12.
The predicted contours of the  V  velocity for
day 296.
                              74

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                      W  (m/sec) =
  M    4.
         -4S     -30
-15     0
    Y  [  M )
Figure C-13.  The predicted contours  of  the  W  velocity for
             day 296.

-------
                                 q2(m2/s2) =
  N
         -45
Figure C-14.
The predicted contours  of  the  q2  correlation
for day 296.
                             76

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                              ww (m2/s2)
   N   4.
          -46
Figure C-15.
The predicted contours  of  the  ww  correlation
for day 296.
                             77

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                   U (m/sec) =
   N
         -45     -30
           -15     0
               Y  ( M )
30      45
Figure C-16.
The measured  contours of the  U  velocity for
day 296.
                             78

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             V (m/sec) =
  N    4
         -45     -30
           -15     0
               Y  (  M )
30      45
Figure C-17.
The measured  contours of the  V  velocity for
day 296.
                             79

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              W  (m/sec) =
  N   4.
         -45    -30
           -15    0
              Y  ( M )
15      30      45
Figure C-18.
The measured contours of the  W  velocity for
day 296.
                             80

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             q2 (m2/s2) =
  N    4.
         -45    -30
           -15    0
              Y  ( M )
15      30      45
Figure C-19.
The measured contours of the  q2  correlation
for day 296.
                            81

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            ww (m2/s2) =
  N    41
        -45     -30
Figure C-20.
The measured  contours of the  ww  correlation
for day 296.
                             82

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                                   TECHNICAL REPORT DATA
                            (Please read Instructions on the reverse before completing)
 1. REPORT NO.
    EPA-600/4-79-013
                              2.
                                                           3. RECIPIENT'S ACCESSION-NO.
 4. TITLE ANDSUBTITLE
 PREDICTIONS OF HIGHWAY EMISSIONS
 BY A  SECOND ORDER CLOSURE MODEL
                                      5. REPORT DATE
                                        February  1979
                                      6. PERFORMING ORGANIZATION CODE
 7. AUTHOR(S)

  M.E.  TESKE and W.S. LEWELLEN
                                                           8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS

 Aeronautical  Research Associates  of  Princeton
 50  Washington Rd.
 Princeton, N. J.  08540
                                      10. PROGRAM ELEMENT NO.

                                       1AA601B  CA-31  (FY-78)
                                      11. CONTRACT/GRANT NO.


                                       68-02-2285
 12. SPONSORING AGENCY NAME AND ADDRESS
  Environmental Sciences Research  Laboratory - RTP,NC
  Office  of Research and Development
  U.S.  Environmental Protection  Agency
  Research Triangle Park, NC  27711
                                                           13. TYPE OF REPORT AND PERIOD COVERED
                                       Final   3/77-3/78
                                      14. SPONSORING AGENCY CODE
                                       EPA/600/09
 15. SUPPLEMENTARY NOTES
 16. ABSTRACT
       The dispersion of sulfur  hexafloride tracer and sulfate  from automobile emiss-
  ions  in  the immediate vicinity of a  highway were estimated  for  conditions similar to
  those existing during the General  Motors sulfate dispersion experiment conducted at a
  GM  test  track.  A second-order closure model of turbulent transport in the planetary
  boundary layer was used to predict the steady-state dispersion  under two conditions:
  with  the mean wind and velocity component variances specified by the data or pre-
  dicted with the aid of an automobile wake model.  The GM measured wind data apparently
  suffered from low vertical velocity  variance readings at the  1.5 meter height, and
  led to an overprediction of  the SF,.  levels by an average factor of 1.77 for the 18
  tower collection points during the 15 test days.  The correlation fell to 0.96 of the
  measured levels when the model  also  predicted the wind fields.   The results indicate
  that  close to the highway, buoyancy  effects were small even in  the critical case when
  the wind is light and aligned  with the roadway.
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
                                              b.IDENTIFIERS/OPEN ENDED TERMS
                                                   c.  cos AT I Field/Group
 *Air  pollution
  Automobiles
 *Exhaust emissions
 *Su1fates
 *Predictions
 *Mathematical models
 *Boundary layer
*Turbulent flow
    13B
    13F
    21B
    07B
    12A
    20D
 3. DISTRIBUTION STATEMENT

 RELEASE  TO PUBLIC
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                          UNCLASSIFIED
21. NO. OF PAGES

    93
                                              20. SECURITY CLASS (Thispage)
                                               UNCLASSIFIED
                                                                        22. PRICE
EPA Form 2220-1 (9-73)
                                            83

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