EPA-450/4-79-015
C.I
DRAFT
for
Public Comment
GUIDELINE FOR USE OF FLUID MODELING
TO DETERMINE GOOD ENGINEERING PRACTICE STACK HEIGHT
June 1979
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
Office of Air, Noise, and Radiation
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
DRAF1
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EPA-450/4-79-015
DRAFT
GUIDELINE FOR USE OF FLUID MODELING
TO DETERMINE GOOD ENGINEERING PRACTICE STACK HEIGHT
June 1979
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
Office of Air, Noise, and Radiation
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
DRAFT
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ACKNOWLEDGMENT
This guideline was prepared by Alan Huber of the Monitoring and
Data Analysis Division, Office of Air Quality Planning and Standards,
Environmental Protection Agency. Appreciation is extended to Dr. William
Snyder of the Meteorology and Assessment Division, Environmental Sciences
Research Laboratory, for his helpful comments and discussion concerning
fluid modeling. His fluid modeling guideline document reference herein
serves well in establishing EPA standards to be followed in the conduct
of such studies.
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TABLE OF CONTENTS
Page
1.0 INTRODUCTION 1
2.0 BACKGROUND 2
3.0 BASIC CONCEPTS 5
3.1 Dynamic Similarity Criteria 7
3.2 Boundary Layer Conditions 13
3.3 Surface Roughness, Terrain,
and Building Scaling 14
3.4 Plume Rise 15
3.5 Concentration Measurements 18
4.0 REQUIREMENTS FOR A FLUID MODEL DEMONSTRATION 20
4.1 Preliminary Design 21
4.1.1 Model Surface and Its Boundary Layer ... 21
4.1.2 Plume Rise 27
4.1.3 Atmospheric Dispersion Comparability ... 31
4.2 Determination of 6EP Stack Height 35
4.2.1 Demonstration of Adverse Effects 37
4.2.2 6EP Stack Height 40
5.0 REPORT CHECKLIST 42
6.0 REFERENCES 46
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1.0 INTRODUCTION
This guideline contains specifications for the use of fluid model-
ing to determine Good Engineering Practice (GEP) stack height. The
guidance is intended for use by the U. S. Environmental Protection
Agency (EPA), by State and local air pollution control agencies, and by
industry and its consultants in the design and final review of a fluid
modeling study determinination of GEP stack height. The Agency issues
guidelines in association with regulations in order to make clear any
requirements for data and to present criteria the Agency will use in
evaluating the adequacy of that data. The specifications in this guide-
line are necessary to assure consistency among studies. It is very
important for both those conducting the fluid modeling study and those
reviewing the results to share a common set of criteria for reference.
The aim of fluid modeling is to produce an accurate representation
of the atmosphere using the flow of air or water in a test facility,
e.g., wind tunnel or water channel. Certain similarity criteria must be
considered if fluid modeling studies are to accurately reproduce at-
mospheric phenomena. A separate guideline entitled, "Guideline for
Fluid Modeling of Atmospheric Diffusion" (Snyder, 1979), reviews the
fundamental principles and practical applications of fluid modeling.
The aim of that guideline is to establish the capabilities and limitations
of fluid modeling, and to establish EPA standards for the conduct of
fluid modeling studies. This guideline is based on Snyder's state-of-
the-art review.
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2.0 BACKGROUND
Section 123 of the Clean Air Act Amendments of 1977 deals with
stack height. It defines GEP stack height as "the height necessary to
insure that emissions from the stack do not result in excessive con-
centrations of any air pollutant in the immediate vicinity of the source
as a result of atmospheric downwash, eddies and wakes which may be
created by the source itself, nearby structures or nearby terrain obstacles."
The scientific literature, in general, indicates that a case-specific
review is integral to assuring the prevention of adverse aerodynamic
effects in the immediate vicinity of a given source. However, the
literature also identifies a general formulation that establishes a
minimum height necessary to prevent significant effects of nearby
structures. The GEP formulation is a reasonable working rule, defined
as:
HG = H + 1.5 L (1)
where: HQ = GEP stack height
H = Height of the structure or nearby structure
L = Lesser dimension (height or width) of the structure or
nearby structure.
The basis of the formulation and a summary of extensive scientific
literature on the subject can be found in the "Technical Support Document
for Determination of Good Engineering Practice Stack Height" (EPA, 19785).
Proposed regulations (40 CFR Part 51) to implement Section 123 of
the 1977 Clean Air Act Amendment allow the stack heights near structures
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as determined by Equation 1 to be used as the maximum creditable stack
height which a source may use in establishing its applicable State
Implementation Plan emission limitation. The maximum creditable stack
height where nearby terrain features are of concern must be determined on a
case-by-case basis through the use of appropriate field or fluid modeling
studies. Field or fluid modeling studies may also be used by the source
operator to show that a stack height greater than that determined by
Equation 1 is needed to prevent excessive pollutant concentrations.
Likewise EPA or State and local air pollution control agencies may
require a field or fluid modeling study where Equation 1 is determined for
a particular situation to be inappropriate.
An excessive concentration for the purpose of determining GEP stack
height is defined in the proposed regulation as a concentration that is
greater than an ambient air quality standard and is 40 percent or more
in excess of the maximum concentration monitored or modeled in the
absence of downwash, wake, or eddy effects produced by nearby structures
or terrain. Similarly, for sources subject to Prevention of Significant
Deterioration CPSD) review, an excessive concentration is'a concentra-
tion greater than that permitted by the remaining PSD increment; such a
concentration must also be a least 40 percent in excess of the maximum
concentration monitored or modeled in the absence of downwash, wake, or
eddy effects produced by nearby structures or terrain.
In most instances where GEP stack height must be determined,
fluid modeling studies are preferable to field studies since field
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studies are much more expensive and time consuming. Moreover, diffi-
culties with relating measurements of excessive concentration to the
adverse effects of structures or terrain can arise in the field.
There must be an area near the site of the source where the atmos-
pheric flow is similar except for differences caused by the structures
or terrain nearby the source.
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3.0 BASIC CONCEPTS
The basic concepts for designing a fluid modeling study are out-
lined in the following subsections. The construct of a fluid model
requires that the flow in the test facility (e.g., wind tunnel) be
appropriately fixed and along with the surface roughness, terrain,
and/or buildings, scaled to accurately reproduce atmospheric phenomena.
The stack and plume from the source must be similarly scaled. The fluid
model encompasses the entire situation within the four walls of the test
facility that is designed to accurately simulate atmospheric flow in the
field. Consideration of each of the concepts outlined in the following
subsections leads to requirements for data and the reporting of that
data as given later in Section 4. Specific references to requirements
given in Section 4 are underlined.
A detailed formulation and discussion of the fundamental principles
for fluid modeling of atmospheric phenomena is presented by Snyder
(1979). A summary of the important criteria is presented here. Certain
similarity criteria must be considered if fluid modeling is to accurately
reproduce atmospheric phenomena. The dynamics of the flow in the fluid
model must accurately simulate those in the field. The effects of
surface conditions in the field upstream of the modeled area must be
accounted for in the fluid model by developing appropriate boundary
layer conditions. The necessary surface roughness, terrain, and buildings
are included in the construct of the fluid model. The plume trajectory
in the fluid model should be similar to that in the field.
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The purpose of the fluid modeling study for determining GEP stack
height is to demonstrate the extent of adverse influences caused by near-
by structures or terrain obstacles on dispersion of stack emissions.
GEP stack height is appropriately determined for atmospheric conditions
that allow significant surface influences to extend highest into the
atmosphere.
Above some minimal reference wind speed, e.g., 3 m/s, the flow
pattern near the structure or terrain obstacle in the field is in-
dependent of wind speed, as is reasoned in the discussion presented in
Section 3.1 on Reynolds number independence. The excessive ground-level
concentration is highest when plume rise near the source is smallest.
For most sources, even those with a relatively high exit velocity, a
wind speed of 15-20 m/s, found to occur occasionally at most locations,
will result in significantly reduced plume rise and thus the greatest
potential for ground-level concentrations in excess of those in the
absence of structure or terrain obstacle influences.
The wind speed that will result in the determination of greatest
GEP stack height is seen for all foreseeable situations to exceed 6 m/s.
The atmosphere is characterized by a generally neutral state of stability
when the surface wind speed at a height of 10 m is greater than 6 m/s
(Turner, 1970). Thus, the critical conditions of stability for de-
termining GEP stack height are expected to be associated with a neutrally
stable (adiabatic) atmosphere. Specific guidance for fluid modeling of
an adiabatic atmosphere is given herein. Specific guidance for modeling
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a nonadiabatic atmosphere is not feasible; the need to model these situ-
ations are expected to be very infrequent and require case-by-case
consideration.
To define GEP stack height for a specific stack, measurements in
the wake of and in the absence of either the structure or terrain
obstacle are needed to assess the increase in maximum concentrations.
The concentration increase must be assessed to determine whether the in-
crease constitutes an excessive concentration. Concentrations in the
wake of the structure or terrain obstacle are considered excessive if
the ground-level concentrations exceed an ambient air quality standard
or PSD increment and are at least 40 percent greater than the maximum in
the absence of their influences. Wind-tunnel modeling is ideally suited
for this type of determination since the model structure or terrain
feature being studied can be easily removed to assess its effect. More
importantly, a properly designed wind-tunnel study can account for the
aerodynamically induced influences affecting the dispersion of the stack
effluent.
3.1 Dynamic Similarity Criteria
To rigorously model the dynamic behavior of atmospheric flow, five
nondimensional parameters must be matched between the model and the
field. These parameters, as discussed by Snyder (1979), are:
1. Froude number, Fr = IW V gL ^o/T ',
2. Rossby number, Ro = Un/LftR;
3. Reynolds number, Re = UJ-/v,
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4. Peclet number, Pe = URL/< ;
5. Reynolds-Schmidt number, Re-Sc = URL/a.
where:
IL = reference velocity;
L = reference length;
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The Rossby number represents the ratio of the inertial forces
to the Coriolis force on a local air parcel. Coriolis force results
in the wind vector changing direction with increasing height above the
surface. If the Rossby number is large, the Coriolis force is relatively
small and thus does not have a significant effect on a dispersing pollutant.
Snyder suggests that the Rossby number is sufficiently large at downwind
distances (L) less than about 5 km to ignore Coriolis force for modeling
dispersion in adiabatic atmospheric flow over flat terrain. No in-
formation is available to assess the effect of Coriolis force in regions
of complex terrain. This implies that fluid modeling should be limited
to areas within 5 km of the source, since Coriolis force cannot presently
be reproduced. Presently used mathematical models of atmospheric dis-
persion do not account for Coriolis forces. Therefore, while fluid
modeling should be limited to_ areas within 5^ Jon of_ the source, its use
for modeling greater areas may as_ for mathematical models be_ similarly
justified, when necessary. The Rossby number criterion is not a critical
modeling parameter, although i_t poses a_ 1 imitation on_ the use of fluid
modeling. There are no special data requirements to satisfy this similarity
criterion.
The Reynolds number represents the ratio of the inertial forces on
to the frictional forces on a local air parcel. When the modeling
medium is air, the reference velocity must be increased by the same
amount as the reference length is reduced in order to match the Reynolds
number. In water, the reference velocity need only be increased by 1/15
the reduction in the reference length, since the kinematic viscosity of
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water is 1/15 that of air. However, using water as the medium requires
much more energy for equal rates of flow. This physical limitation
generally results in water tunnels having to be smaller in size and
operated with lower flow rates than wind tunnels. The reference
length in atmospheric dispersion problems must be modeled at a reduced
scale of several orders of magnitude, making an equivalent increase in
the reference velocity impractical. Thus if strict adherence to the
Reynolds number criterion were required, no atmospheric flows could be
modeled.
Various arguments to justify the use of smaller Reynolds numbers in
fluid modeling compared to those in the atmosphere are found in the
literature. The best argument appears to be the principle of Reynolds
number independence. This principle is based upon the hypothesis that
in the absence of bouyancy and Coriolis effects, the pattern of tur-
bulent flow is similar at all sufficiently high Reynolds numbers. If the
Reynolds number is large, frictional forces are relatively small com-
pared to the inertial forces. For Reynolds number independence to hold,
the frictional forces must remain relatively small and have little
effect on the overall flow as the Reynolds number is decreased. A large
amount of experimental evidence now exists to support this principle.
For atmospheric flows, Reynolds number independence appears to apply
except in the very smallest scale of the turbulent flow very close to
the ground or other physical boundary. In effect, the reference length L
Cscale of flow structure examined! Is small where the frictional forces
are important. Flow very near structures or terrain features may not be
Reynolds number independent.
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Practice indicates that sufficiently large Reynolds numbers are
attainable at least for modeling the flow over sharp-edged geometrical
structures or terrain features in ordinary meteorological wind tunnels.
However, more work must be done to determine if simulation of flow over
more streamlined surfaces can be sufficiently modeled. Frictional
forces have very little effect if the general flow is detached from the
surface or other physical boundary. Flow over streamlined surfaces is
less susceptible to detachment and thus is more sensitive to the value
of its Reynolds number. Reynolds numbers in atmospheric flow generally
are sufficiently large for the independence principle to hold. Fortu-
nately flow similarity is generally observed at the lower values of
Reynolds number attainable in fluid modeling, provided the flow is
locally detached or if the area of study is sufficiently above the
surface. This has led modelers in some situations to force flow de-
tachment by adding roughness to the model structures or terrain features,
The Reynolds number criterion is a critical modeling parameter. Step 4
i_n Section 4.2.1 requires a_ test for Reynolds number independence.
The Peclet number is most easily discussed by writing it as the
product of the Reynolds Number and Prandtl Number:
URL
Pe = — = Re-Pr.
v <
The Reynolds-Schmidt Number can similarily be written as the product of
the Reynolds Number and the Schmidt Number:
URL v
Re-Sc = — ^-= Re-Sc.
v a
n
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Both the Prandtl number and the Schmidt number are properties of the
fluid. The Prandtl number is the ratio of the momentum diffusivity to
the thermal diffusivity. The Schmidt number is the ratio of the mo-
mentum diffusivity to molecular diffusivity. These numbers are somewhat
different between air and other fluids. This would seem to preclude
using any model medium other than air in simulations of atmospheric
flow. A high Reynolds number is necessary in the wind tunnel flow to
match the Peclet number or Reynolds-Schmidt number found in the field.
Arguments similar to those constructed for Reynolds number independence
are used to justify the neglect of the Peclet number and Reynolds-
Schmidt number as modeling criteria, provided the Reynolds number is
sufficiently large. Both heat and mass are regarded as passive
quantities in connection with most environmental atmospheric dispersion
problems. Thus, if the Reynolds number of the main structure of the
flow is sufficiently large, advection and the larger scale turbulent
motions are totally responsible for the transport and dispersion of a
passive pollutant. That is, molecular or thermal diffusion acts mostly
to smooth out the very small-scale discontinuities of concentration or
temperature. Molecular or thermal diffusion jjS_ assumed to contribute
negligibly tp_ the dispersion of_ the source plume within the simulated
turbulent atmosopheric boundary layer, provided the Reynolds number ij_
large enough with the Peclet number and Reynolds-Schmidt number being
themselves unimportant.
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3.2 Boundary Layer Conditions
The effects of upstream surface conditions on the velocity of the
wind result in a variation with height described generally by some
theoretical distribution such as a logarithmic or power law profile.
The profile is characterized by the depth of the boundary layer and a
representative surface roughness length. Turbulence intensity of the
wind naturally decreases with height above the surface roughness. The
profiles of mean velocity and turbulence intensity are very significant
characteristics that should be very closely matched in the model.
Measurement of vertical profiles of Reynolds stress throughout the
region of interest is especially useful in characterizing the surface
friction velocity u*, which is a parameter used in representing the
velocity near the surface by a logarithmic profile. Measured field
profiles will not likely be available at most sites where GEP stack
height is to be determined. In Section 4, general modeling criteria are
specified for use when field data are not available. Steps 2b, 2£ and
3b_« 3c_ jji Section 4.1.3 require mean velocity, turbulence intensity, and
Reynolds stress profiles tp_ be_ measured at several positions throughout
the model.
Consideration of additional flow characteristics of the atmospheric
boundary layer would be desirable. However, specific guidance is not
possible. The purpose of specifying necessary modeling criteria for the
boundary layer is to first insure that dispersion throughout the modeled
flow correctly provides dispersion patterns comparable to those given by
13
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recommended air quality modeling techniques as described in the "Guideline
on Air Quality Models" _(EPA, 1978a). Concern for the similarity of
additional flow characteristics is not necessary if the model boundary
layer dispersive characteristics are documented through measurements in
the test facility to fall between estimated values for Pasquill-Gifford
stability category C and D as prescribed by Turner (1970). Step 4 in
Section 4.1.3 requires documentation of_ dispersion from the source.
A Documentation and test of comparability of the fluid model
boundary layer conditions to flow over flat terrain in the absence of
any buildings can be done simply. Problems, however, arise in doing the
same for flow over complex terrain or over urban areas where local
differences near the surface result from different surface features.
Because of these differences one cannot establish that the fluid model
boundary is non-developing or that the dispersive characteristics can be
represented by a general categorization. In order to evaluate the fluid
model boundary layer conditions it is necessary to first document the
flow in absence of the complex terrain or urban structures as prescribed
above. Differences found for flow over the complex terrain or urban
area can then be related to the increased surface roughness. Secti on
4.2.1 requires measurements sufficient ^p_ document such differences.
3.3 Surface Roughness, Terrain, and Building Scaling
Obviously, minute geometric details of terrain or structures do not
significantly affect atmospheric flow. Thus, such detail need not be
considered in a fluid modeling simulation. Objects about the same size
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as the characteristic surface roughness length need not be produced in
geometrical form but air equivalent roughness must be established. For
example, gravel can be added to the surface of the terrain or buildings
to establish an equivalent roughness.
Major terrain features and building structures must be scaled
without geometric distortion. The amount of reduction in scale is
limited by the requirement for the flow to be Reynolds number independent.
Discussion and some guidance on selecting the proper model surface
roughness, terrain height and building height are given by Snyder
(1979). The fluid modeler's decisions must be based on a number of
interacting concerns, including the size of the area to be modeled, the
necessary boundary layer depth, the desired diffusion characteristics,
f
and Reynolds number independence. Often, the fluid modeler's experience
$
is the best guide. Data requirements and criteria which EPA will use to
evaluate the resulting study are given in Section 4. It is recognized
that each fluid modeler may have somewhat different^approaches to
selecting these, design parameters. This is acceptable if the results
«
meet the report requirements. Section 4.1.1 outlines the requirements
for modeling the surface and jts boundary layer.
3.4 Plume Rise
The plume trajectory should be matched between the model and the
field. However, field data will not be available at most sites where
GEP stack height must be determined. Vertical concentration profiles
through the elevated plume center!ine taken as part of the fluid
15
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modeling study can be used to determine the plume centerline and to
establish comparability to standard estimates of plume centerline
height. As indicated in previous sections, the atmospheric conditions
that are considered here in determining GEP stack height are characterized
as neutral stability (adiabatic) with high mean wind speed. Under such
conditions, plume rise near the source where its rise is dominated by
momentum flux, will be small while its rise farther downwind may be
largely due to buoyancy flux. A thorough review of the issues re-
lating to fluid modeling of plume rise is presented by Snyder (Section 3.1,
1979).
In general, plume rise near the source in an adiabatic atmosphere
has proven to be well-described for most conventional sources by the
Briggs 09751 formulation,
2
Ah)3
FT
_ 3
"W
_ 3
"¥
P_W^
pjp"
a
M
^
2
D2
4H
FT
H
4.1
(2)
x
k
for a = 1/3 + U/W , & = 0.6 where L is a momentum length scale and LD
s m D
is a buoyancy length scale, defined as
1/2
H_
L^
H"
_ 1
"2
(3)
•B = 1
C Fr^
(4)
3/2
3/2
16
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where:
p = stack effluent density
p = ambient air density
a
W = stack effluent exit speed
D = stack exit diamater
HS = stack height
U = mean wind speed at height of stack
Frs = U/[gD(pa-ps/ps)]1/2
Fra = U/[gD(Pa-Ps/pa)]1/2 .
The first term in Equation 2 represents the contribution due to
source momentum and the second term represents the contribution from
source buoyancy. Close to the stack, the initial momentum term will be
important, whereas, the buoyancy term will ultimately dominate. Match-
ing the parameters in the above plume rise equation should insure
comparable plume rise in the fluid model so long as the plume is not
downwashed into the wake of the stack. This formulation is adopted as
the method for estimating plume centerline height in the field. The
plume centerline height in the fluid model should be shown to be com-
parable to the estimate by Eauation 2 in the absence of buildings or
terrain.
When stack downwash occurs, special consideration must be given to
the flow around the stack. It is essential to assure that the flow
within the boundary layer around the stack is turbulent. Common practice
in fluid modeling is to use a trip wire or fence or other surface
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roughness to force the boundary layer flow to be turbulent. This is not
necessary for modeling rectangular stacks since their sharp corners
force flow separation. In all cases, it is necessary to assure that the
stack effluent exhaust is fully turbulent. Data requirements and
criteria that EPA will use to evaluate the representativeness of the
plume rise jji the fluid model are presented in_ Section 4.1.2.
3.5 Concentration Measurements
Concentrations measured in a fluid modeling study should be related
to those in the field through the nondimensional concentration, C = xUH2/Q
as presented by Snyder (Section 3.5, 1979), where
x = mass concentration of pollutant (gm/m3),
U = reference wind speed (m/s),
H = characteristic length (m), and
Q = pollutant emission rate (gm/s).
The sampling time for measurements taken as part of the fluid
modeling study must be long enough to provide steady-state averages.
Fluid modeling is designed to correspond to conditions in the field for
which the wind direction is steady. It is essential that the maximum
ground-level concentrations be shown to represent the steady-state
average values since they are crucial in the demonstration of excessive
concentration. Data requirements and criteria which must be_ considered
lH establishing this fact are presented jn_ Section 4..
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In absence of effects of building and/or terrain, the pattern
of concentrations in the fluid model should be comparable to those
estimated by mathematical models recommended by EPA. Steady-state
average concentrations measured in the fluid model should thus correspond
to one-hour average concentrations in the field. In those situations
where persistence of the wind direction can be assumed, fluid modeling
can be used for estimating average concentrations for longer periods
of time. Fluid modeling studies can also be used for estimating
average concentrations for periods having variability in the wind
direction by including a separate examination of the flow for several
directions. Concentrations can then be estimated by considering the
frequency of wind direction.
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4.0 REQUIREMENTS FOR A FLUID MODEL DEMONSTRATION
Section 3 presented a summary of the basic design concepts used
in developing a fluid modeling study that is comparable to field
conditions. Elements necessary for determining a GEP stack height
are specified in this section. Specific guidance on requirements
for data and the reporting of that data are given. Fluid modeling
studies can be adapted to meet detailed specifications since essential
characteristics can be controlled. Atmospheric flow is extremely complex
in that profiles of its characteristics can vary with time and space.
In general, field profiles of atmospheric characteristics rarely are
available at the sites where a GEP stack height is to be determined.
Therefore, it is only necessary for the modeling study to be designed
to meet the general atmospheric conditions, given here as comparable
to those used in air quality models recommended by EPA. Where detailed
field information describing the situation is available, the modeling
study should be designed to best assimilate it. For these situations,
the fluid model should be shown to be comparable to the field.
The requirements given here are based on the general guidance
by Snyder (1979). Readers and users of this guideline should be
familiar with the presentation by Snyder. Deviation from his general
guidance occurs in this guideline only in a few instances where the
objectives were judged to be met without additional detail.
Section 4.1 presents important criteria that should be considered
prior to the construction of the fluid model for the actual situation.
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The model scale should first be determined. Then a test for atmospheric
dispersion comparability should be conducted as specified. Section 4.2
specifies the procedure and reporting requirements for determining a GEP
stack height. The step-by-step procedure leads simply to a satisfactory
study provided sufficient preliminary consideration is given to the
criteria presented in Section 4.1.
Specific reporting requirements presented here should be followed
as outlined. All supplementary data taken as part of the study should
also be incorporated into the report. A separate appendix describing
the fluid modeling facility and instrumentation used in the conduct of
the study should be attached. Normal operating conditions and associated
parameters should be described. A daily log should be kept during the
conduct of the study since the Agency reserves the right to conduct a
thorough audit and review. In some instances on-site visits and demonstration
of repeatability of some measurements may be requested.
4.1 Preliminary Design
4.1.1 Model Surface and its Boundary Layer
The size of all building structures and the general topography in
the vicinity of the source should be examined and the area to be deter-
mined. A roughly cubical building or other major structure, or a three-
dimensional hill upstream of the source should be included it its height
exceeds l/20th of the distance from the source. An obstruction whose
crosswind dimension is large compared to its height (width greater than
10 times its height) should be included if its height is greater than l/30th
of its distance upstream. For tall obstructions (height greater than
21
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width) the width replaces the height scale in the above determination
of the critical distances. If possible, ridges even farther upstream
should be included. In areas having undulating terrain, the hill or
ridge height is defined as the elevation difference between its peak and
local trough. A detailed topographic map and discussion concerning the
selection of the size of the modeled area should be presented in the
study report.
Additional parameters and criteria should also be considered in the
selection of the scale of the modeled area. The following list presents
such criteria that are further discussed in later sections. At this
stage of experimental design, the fluid modeler should select design
parameters that can be shown to satisfy necessary requirements. The
fluid modeler's experience is likely the best guide.
1. The buildings, other structures, and/or terrain should be im-
mersed in an appropriate boundary layer that can be characterized as
representing atmospheric dispersion between that for Pasquill-Gifford
category C and D over flat terrain (Turner, 1970). The depth of the
model boundary layer, 6, scaled to represent 600 m in the field, in-
dependent of surface roughness and wind speed. The design wind speed
should be less than the speed that is exceeded less than 2 percent of
the time for the given wind direction. This should be based on frequency
distributions from at least one year of wind records representative of
the source location.
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2. The surface roughness length z0 and the friction velocity u
should be derived from the mean velocity profile:
U*
. 2/5 in -4-, (5)
in the range, 1 .5 hr < z < 1 .5 hr + 100 m, where z is the height, hr is
the general height of the surface roughness elements, and d is the
displacement height (neglected for z0<0.2m, full scale). Simiu and
Scanlan (1978) suggest that reasonable values of d in cities may be
estimated using the formula
d=iT-z0/k, (6)
where H" is the general roof-top level and k is the von Karman constant
CO. 4). Values of the surface roughness length, z0, for various types of
surfaces are presented in Table 1 as a guide. Actual values over urban
areas with tall buildings or near elevated terrain may be substantially
larger. Values of the friction velocity, u*, are dependent on the value
of z0. Values for u* as suggested by Counihan (1975) are presented in
Figure 1 , as a guide. The vertical profile of the shear stress -uw
may also be used to estimate the value of u* as demonstrated in
Figure 2. The value of u| is equal to the surface shear stress.
3. The mean velocity profile through the entire depth of the
boundary layer should be represented by a power law U/U^ = (z/<$)p. The
power law fnde* p is dependent on the value of z0. Values for p as
suggested by Counihan (1975)_ are presented in Figure 1 , as a guide.
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Table 1. Values of Surface Roughness Length (ZQ) for Various Types
of Surface (from Simiu and Scanlan, 1978).
Type of Surface o
(cm)
Sand 0.01 - 0.1
Sea Surface 0.003a - 0.5b
Snow Surface 0.1 - 0.6
Mown Grass OvO.Olm) 0.01 - 1
Low Grass, Steppe 1 - 4
Fallow Field 2 - 3
High Grass 4 - 10
Palmetto 10 - 30
Pine Forest (Mean height of trees: 15m;
one tree per 10m2; zd=12m) 90 - 100
Outskirts of Towns, Suburbs 20 - 40
Centers of Towns 35 - 45
Centers of Large Cities 60 - 80
Wind speed at 10m above surface = 1.5m/sec.
Wind speed at 10m above surface > 15m/sec.
24
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CM
CM*
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
rn i—m
I p = 0.24 + 0.096loginzn + 0.
logiQZ0+ 0.016(109! QZ0)2
III I ill i
0.001
0.01
0.1
z0, m
1.0
10
Figure 1. Variation of power law index p, and surface friction
velocity u*, with roughness length z0 in the adiabatic
boundary layer from Counihan (1975). Dashed curve is
power law index from Irwin (1979).
25
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1.0
.8
.6
.4,
\ *
U. • !• m/MC
13
l
\ .
\«°
.5 1.0 1.5
2
Figure 2. Variation of shear stress with height measured at various
downwind positions in a wind tunnel boundary layer (adiabatic
flow). Data from Zoric and Sandborn (1972), (as in Snyder 1979)
26
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4. The surface of the model should be covered with roughness of
size e such that 20
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the source in the field. The plume center-line height in the fluid model
should be shown to be comparable at downwind distances less than that to
the point of maximum rise. Vertical profiles of concentration through
the plume center!ine can be used to provide a measurement of the center-
line in the fluid model, where reflection from the surface, and
influences from terrain, buildings or other structures are not significant.
There should be a comparison made for at least two positions prior to
the distance of final plume center!ine height. In general, vertical
profiles of concentration necessary to meet requirements presented in
Section 4.2 will provide sufficient data for this necessary comparison.
The following guidance should be considered in designing the study. For
special situations where the user believes a deviation is warranted,
full support and documentation is necessary.
The exhaust from stacks is usually fully turbulent in the field.
The effluent Reynolds number cannot be matched to assure similarity. It
is sufficient, however, for the fluid model effluent Reynolds number to
exceed a critical value following the arguments of Reynolds number
independence. The fluid model stack effluent Reynolds number, WsD/v, should
be guided (in order of decreasing "correctness") by the following:
(a) Fix the effluent Reynolds number to be as large as
possible, preferably greater than 15,000.
If it is necessary to reduce the effluent Reynolds number
below 2,000, trip the flow to ensure a fully turbulent
exhaust.
28
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(c) If it is desired to reduce the effluent Reynolds number
below 300, it will be necessary to do some experimentation to
determine under what conditions the plume will simulate the
behavior of a plume in the field.
To model situations with stack effluent downwash around the lip of
the stack the following criteria should be met:
1. Insure that the flow within the boundary layer around the stack
is turbulent; and,
2. Match each of the following ratios:
Ws> PS' Ws
us Pa [gD(pa-Ps)/Ps]1/2
To model the far-field rise of a buoyant plume from a stack, the
following criteria must be met:
1. Insure a fully turbulent effluent flow as discussed
above, and
2. Either (in order of decreasing "correctness");
Cal match psWs , _ Ws , and D_
(bl match L/H and L/H (See Equation 2, Section 3.4),
m$ BS
29
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(i) following geometric similarity, or
(ii) exaggerating the stack diameter, but avoiding
stack effluent downwash around the lip of the stack.
Obviously, if the stack diameter is exaggerated, other lengths are
to be referenced to the stack height and not the stack diameter. Notice
that under condition 2(b) an exaggeration in stack diameter will generally
be accompanied by a reduction in the momentum ratio. The momentum ratio
should not be reduced to the point where the plume is unrealistically
downwashed into the wake of the stack.
The above conditions should be met whenever possible. If this is
not possible, relaxed requirements may be sufficient when measurements
of the plume centerline height in the fluid model are equivalent to the
estimated plume centerline, or field data support an alternative. The
matched plume rise is essential in the determination of GEP stack height
because the degree of structure or terrain influence is sensitive to the
plume height. For special situations where correct plume rise modeling
is not possible, some allowances may be made to adjust the plume height
relative to the exact modeling requirements. In these instances, the
resulting GEP stack height should not exceed the height that would have
otherwise resulted.
30
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4.1.3 Atmospheric Dispersion Comparability
In the absence of buildings, other surface structures, or large
roughness and/or elevated terrain, dispersion in the fluid model must
show comparability to that described for the atmosphere by the basic
Gaussian plume distribution (Turner, 1970). Concentration measurements
for this test of comparability must be shown to have values representative
of field estimates given between estimates for Pasquill-Gifford category
C and D. The procedure for demonstrating this comparability is outlined
below. The purpose of this test is to provide an evaluation of the
model flow in absence of buildings, other surface structures or large
roughness, and/or elevated terrain. This test will insure that each
study shares some common ground and demonstrates comparability to
recommended modeling techniques for atmospheric dispersion over flat
terrain (EPA, 1978).
Step 1:
(a) Select model scale and the model flow velocity. In
choosing the scale, consideration should be given to all
criteria as outlined in Sections 4.1.1 and 4.1.2. The flow
velocity should be matched at the height of the proposed stack.
(b) Select the position where the model stack will be
placed.
(c) Select the method for providing a fully developed and
appropriate boundary layer at and downwind of the stack.
(d) Report a detailed description of the fluid model.
31
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Step 2:
(a) Take a vertical profile of the mean temperature e (°K)
and the intensity of temperature fluctuation C©'2)1/2/o
at the position where the model stack will be placed (one
profile each). Additional profiles are necessary if
operating conditions change.
(b) Take vertical profiles of the mean velocity U (m/s), and
the longitundinal and the vertical turbulence intensity
(IF)1/2/U and (wr)1/2/U at the position where the stack will be
placed, downwind at the end of the planned study area, and
midway between these two positions. Repeat profiles at positions
midway between the walls to both the left and right (9 profiles
each).
Step 3:
(c) Take a vertical profile of the shear stress -uw (m2/s2)
at the position where the stack will be placed, downwind
at the end of the area to be studied, and at the point
midway between these positions (3 profiles).
(a) Report and evaluate the temperature profiles. The
profile of mean temperature should be uniform. A
deviation from a uniform profile would indicate that air
temperature within the facility building is not well
mixed. An erratic profile for intensity of temperature
fluctuations would more strongly indicate the same. No
guidance can be given for deciding how much deviation
is unacceptable. These profiles should be used
only to provide a qualitative assessment.
(b) Report and evaluate the velocity profiles. Comparisons
in both the downwind direction and laterally should be
shown. Report the profiles of mean velocity on log-linear
scaled paper and estimate the values for the effective
surface roughness length z0 and the friction velocity u*
at each position, per Equation 5. Estimate these values by
determining the best fit to the data representing the lowest
100m full scale, above the height of the surface roughness
elements. Replot the profiles of mean velocity on linear
scaled paper and estimate the power law index p. The model
values of z0, u*, and p should be consistent with guidance
presented in Table 1 and Figure 1, representing atmospheric
flow over flat terrain with z0<0.2m and 6 = 600 m. Report
the profiles of turbulence intensity. Figure 3 is presented
for consideration to be used only as a guide. Values of
turbulence intensity representative of conditions in Figure 3
for z0>0.2m may indicate the model flow is too turbulent.
32
-------
Z/6
Figure 3. Variation of longitudinal turbulence intensity with height
under adiabatic conditions (from Snyder, 1979).
33
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The true test lies with the evaluation of concentration
measurements as discussed below. The profiles of mean veloc-
ity and profiles of turbulence intensity should all be similar
throughout the study area. Significant differences
in either the downwind direction and/or the lateral
direction may indicate a deficiency in the model design
or in the facility operation. No guidance can be given
for deciding how much deviation is unacceptable. These profiles
should be used only to provide a qualitative assessment.
Cc) Report and evaluate the profiles of shear stress after dividing
by its estimated value at the surface. The value of the
shear stress at the surface is equal to the surface friction
velocity squared, that should be comparable to the
estimate determined from the velocity profile. Figure 2
can be used as a guide for evaluating the measured profiles.
These profiles should be used only to provide a qualitative
assessment.
Step 4:
(a) Position a model stack, so that the top of the model stack is
at a height representing 100 m above the ground. It is desirable
that each demonstration of comparability use the same height.
A 100 m high stack was selected because it is believed to be
most representative of the height of stacks for which GEP
demonstrations are conducted. Design the model stack so that
its internal diameter is equal to 0.05 times the stack height.
Fix the flow rate of a non-buoyant stack exhaust containing
a tracer so that the exhaust velocity is 1.5 times the mean
velocity at stack top. This should allow concentration
measurements of the tracer to be taken in absence of either
plume rise or stack downwash. Concentration measurements for
this situation are required to demonstrate comparability to
atmospheric dispersion between that estimated using
Pasquill-Gtfford dispersion parameters for category C and D
as presented in Turner (1970).
(b) Take vertical and lateral profiles of concentration
through the plume centerline at the quarter intervals
between the source and the end of the planned study
area. Take ground-level longitudinal profiles of
concentration downwind along the plume centerline to the
end of the study area. (9 profiles)
(c) Convert model concentrations to equivalent field values
with the form xU /Q (m"2). Plot each vertical and lateral
profile of concentration measurement separately along
with plume estimates for both Pasquill-Gifford category
34
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C and D (Turner, 1970). Use the mean wind speed at the
height of the top of the stack U as the reference wind
speed. The distribution of measured values roust fall
between the two estimated distributions. The vertical and
lateral profiles of concentration can be used to provide a
check for conservation of mass. Calculate at each downwind
position of measurement,
Q =22 cu dydz-
Plot the ground-level longitudinal profile of concentration
measurement along with plume estimates for both Pasquill-
Gifford category C and D (Turner, 1970). The distri-
bution of measured values should fall between the two
estimated distribitions with an additional allowance
where these two distributions overlap as presented in
Figure 4. The dashed lines in Figure 4 allow a factor
of two difference in the overlapping region.
4.2 Determination of GEP Stack Height
Requirements and procedures for evaluating the model boundary layer
characteristics and dispersion for the actual situation are specified
below. The results of the previous section establish fluid model comparability
to atmospheric dispersion as estimated by recommended mathematical
models in the absence of buildings, other structures or large roughness,
and/or elevated terrain. Differences between the model boundary layer
characteristics and dispersion for the standard situation established in
the previous section and the actual situation analyzed below should be
related to real expected differences in the field due to the effects of
buildings, other structures or large roughness, and/or elevated terrain.
35
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2x10'5r
5x10'b ~
E
d"
* 2x10-6
2x10'7
5x10-7 —
0.5
1 2 5
DISTANCE, km
10
Figure 4. Ground-level concentration with distance for a 100m high
plume, estimated with Pasquill-Gifford dispersion parameters
for stability category C and D (Turner, 1970).
36
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4.2.1 Demonstration of Adverse Effects
The procedure for demonstration and documentation of the adverse
effects of buildings and/or elevated terrain nearby the source is outlined
below.
Step 1: Place the model topography into the test facility.
(a) For modeling the situation of a few isolated buildings in
flat terrain this is a simple matter. The buildings are
simply immersed in the boundary layer designed for satisfying
the requirements of Section 4.1.3.
(b) Additional complexity arises for a model of flow over a
general urban area and/or elevated terrain. In addition
to constructing the model of buildings and/or elevated
terrain, surface roughness used in covering the model and
general roughness elements upwind of the model to provide
appropriate boundary layer characteristics for the situation
may be different from those used in the atmospheric dis-
persion comparability test (Section 4.1.3.).
(c) Report a detailed description of the fluid model.
Step 2:
(a) Follow Step 2 (b) Section 4.1.3. It is not necessary to
repeat profiles at the positions midway between the
walls to both the left and right (3 profiles each).
(b) Follow Step 2c, Section 3.1.3 (3 profiles each).
Step 3:
(a) Follow Step 3 (b) Section 4.1.3 to determine the model
values of z0, u*, and p. They should be consistent with
guidance presented in Table 1 and Figure 1. Specific
guidance for flow over areas of elevated terrain is not
available since little data correlating the flow character-
istics to the height and separation distances of terrain
features has been taken. In general, z0 in areas with elevated
terrain should be much larger than the largest values
found in Table 1. Significant differences may be found
at each location due to differences in the local surface
roughness. A discussion of such differences should be pre-
sented in the study report.
37
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(bl Follow Step 3 (c) Section 4.1.3.
Step 4: Test for Reynolds number independence.
(al For sharp-edged obstacles haying a Reynolds number U-l/v
greater than 11,000 no demonstration test is required.
(b) Where the effects of flow over elevated terrain or
smooth-shaped obstacles are being evaluated, a Reynolds
number test is required. A full evaluation of Reynolds
number independence would require a demanding research
project for each situation. The simple test required here
should, however, be sufficient enough to provide a critical
evaluation. Position a small source emitting a tracer at the
site of the GEP stack in question at a height equal to the
building or elevated terrain whose effects are in question.
The source should be nonbuoyant and have no plume rise. Take
a longitudinal surface-level profile of concentration along
the downwind direction. Repeat the profile after doubling the
freestream wind speed Uro. Take a vertical profile of the mean
velocity at the site of"the stack for this new situation.
Plot and compare the two profiles of concentration
xU/Q (nf2) using the freestream wind speed as the reference
speed. Differences in concentration should not be greater
than 10 percent. Reconsideration of the model design is
necessary where greater differences are observed.
Step 5: An evaluation of the plume from the stack in question must be
made. In general, the fluid modeler should first examine the plume
through a visualization technique, i.e., photographs of smoke exhaust.
Then a decision can be made as to the height for which GEP credit can be
justified. Photographs and/or measured data taken as part of this
process must be included in this report. Full documentation as outlined
below is required for the actual determination of GEP stack height.
(a) Take vertical and lateral profiles of concentration through
the plume center!ine at positions one-fourth and one-half of
the distance between the source and the end of the study area.
Also, do the same at the end of the study area and at the
position of maximum ground-level concentrations. The value of
maximum ground-level concentration must be unquestionably
determined. This requires a longitudinal surface-level
profile along the plume centerline, supported by 2 to 4
lateral profiles including one across the position of maximum
concentration.
In some situations, it may be necessary to model at a scale
such that the likely maximum ground-level concentration falls
downwind beyond the modeled area. This is very undesirable,
and should be avoided whenever possible. The diffusive
38
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characteristics for a limited region beyond the modeled area
may be obtained by extrapolating the measured values, only for
situations of flovf over generally homogeneous terrain and/or
uniform urban environments. For these situations, additional
vertical and lateral profiles of concentration at the position
three-fourths between the source and the end of the study area
should be made in lieu of measurements at the maximum. Extrap-
olation should be limited to distances equivalent to one-half
the distance between the source and end of the modeled area.
Ground-level concentration profiles for several stack
heights having their maximum value falling within the
modeled area should be made. These profiles can be used
to extrapolate a maximum value for higher stack heights,
and support the value obtained by extrapolating the measured
vertical and lateral profiles of concentration.
(b) Convert model concentrations to equivalent field values with
form xll /Q(m~2). Take the mean wind speed at the height of
the top of the stack U as the reference wind speed. Report
each vertical profile Of concentration measurement. In absence
of reflection from the surface, the plume center!ine can be
estimated as the vertical position of the maximum concen-
tration. At least two values must be compared to the esti-
mated plume rise as discussed in Section 4.1.2. Additional
vertical profiles must be measured if the above required
profiles do not provide sufficient information. Report
each vertical and lateral profile of concentration measure-
ments separately along with estimated plume distributions
incorporating estimated dispersion parameters.
In areas of elevated terrain downwind from the source, such
estimates may be difficult and perhaps meaningless. In
these instances a discussion relating the plume behavior to
anticipated effects of the terrain is needed. Plot the longi-
tudinal and lateral profiles of concentration measurements.
The maximum must be unquestionably determined. Two repeated
measurements at the position of the maximum should be taken
and reported as support that the concentration does, in fact,
represent the steady-state average. Differences in the
three concentrations should not be greater than 10 percent
of their values.
In some situations of flow over generally homogeneous terrain
and/or uniform urban environments the maximum value may be
obtained by extrapolation as discussed above. For these
instances, it is necessary that the appropriate dispersion
parameters can be derived from the vertical and lateral
profiles of concentration measurements. The maximum ground-
level concentration can then be estimated by inserting
the derived dispersion parameters into the Gaussian plume
39
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formula (Turner, 1970). Extrapolation of measured longitudinal
ground-level profiles should support the estimated maximum
ground-level concentration. Approval for such a study plan
must be granted by the reviewing agency prior to the study to
allow agency experts to provide a critical assessment.
4.2.2 GEP Stack Height
The stack height for which full documentation has been provided in
the previous sub-section is GEP if the maximum surface-level concen-
tration is 40 percent or more in excess of the maximum in the absence of
downwash, wake, or eddy effects produced by nearby structures or terrain
and if a shorter stack would result in an air quality violation as
specified in Section 2. The procedure for validating the proposed GEP
stack height is presented below.
Step 1:
Remove the building(s) or elevated terrain in question. This
is a simple matter in the case of buildings nearby the stack.
/ The situation near elevated terrain is complicated since
removal of the terrain feature in question may result in an
unrealistic discontinuity in the topography. A similar difficulty
arises where a high plateau is upwind of the source. In
such instances it may be necessary to remove all upwind
terrain and replace its area with appropriate surface roughness.
The surface roughness elements must be shown to result in an
appropriate z0 and u*. This requires that a vertical profile
of mean velocity, longitudinal turbulence intensity, and
shear stress be measured upwind of the source at the position
where the elevated terrain feature was located. Estimate z0
and u* guided by Step 3 (a,b) Section 4.2.1. The boundary
layer should be appropriately characterized as with the
actual topography.
Step 2:
Determine the maximum ground-level concentration. Document
fully as required by Step 5, Section 4.2.1.
40
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Step 3:
The proposed GEP stack height may be creditable if the maximum
ground-level concentration determined in Step 5, Section
4.2.1 is 40 percent in excess of maximum ground-level con-
centration determined in Step 2 above. Discussion relating
the increased maximum ground-level concentration measured
in the presence of the building(s) or terrain in question
to anticipated effects due to downwash, wakes, or eddies
should be presented in the report.
\J
41
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5.0 REPORT CHECKLIST
The fluid modeling study report should include the five items that
are outlined below. The report should completely document the design
and operation of the model study. Three tests should be conducted. The
data collected for these tests must allow for conclusions to be drawn
concerning the atmospheric conditions simulated by the fluid model, and
the cause of increased maximum ground-level concentrations for a stack
in the presence of building(s) and/or terrain. The height of the stack
examined in the study is creditable as GEP if the maximum ground-level
concentration is at least 40 percent greater in the presence of the
nearby building(s) and/or terrain than that measured in their absence,
provided the GEP stack height is the minimum height that allows an
ambient air quality standard or a PSD increment to be met.
1. A detailed topographic map and discussion concerning the
selection of the size of the modeled area.
2. Documentation for the dispersion comparability test in absence
of building(s), other surface structures, or large roughness and/or
elevated terrain should include:
(a) detailed description of the fluid model including features
of the scale model, surface roughness, freestream wind speed, and method
used to provide the fully developed boundary layer,
(b) one vertical profile of mean temperature,
(c) one vertical profile of intensity temperature fluctuations,
42
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(d) nine vertical profiles of mean velocity,
(e) nine vertical profiles of vertical and longitudinal turbulence
intensity,
(f) three vertical profiles of shear stress,
(g) effective surface roughness length z0, friction velocity
u*, and velocity power law index p, determined by evaluating the mean
velocity profiles and the shear stress profiles,
(h) four vertical and lateral profiles of concentration
through the plume center!ine,
(i) one ground-level longitudinal profile of concentration
downwind along the plume center!ine,
(j) evaluation of comparability of measured concentrations to
plume estimates for Pasquill-Gifford category C and D (Turner, 1970).
3. Documentation for the GEP stack height test in the presence of
building(s), other surface structures, or large roughness and/or elevated
terrain should include:
(a) detailed description of the fluid model including features
of the scale model, surface roughness, freestream wind speed, and the
method used to provide the fully developed boundary layer,
(b) three profiles of mean velocity,
(c) three vertical profiles of vertical and longitudinal
turbulence intensity,
43
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(d) three vertical profiles of shear stress,
(e) effective surface roughness length z0, friction velocity
u*, and velocity power law index p, determined by evaluating the mean
velocity profiles and the shear stress profiles,
(f) test for Reynolds number independence,
(g) four vertical and lateral profiles of concentration
through the plume centerline including profiles at the position of
maximum ground-level concentration,
(h) one ground-level longitudinal profile of concentration
downwind along the plume centerline,
(i) two to four lateral ground-level profiles including one at
the position of maximum ground-level concentration,
(j) discussion supporting the unquestionable determination of
the maximum ground-level concentration.
4. Documentation for the GEP stack height test in the absence of
building(s) or elevated terrain considered in justifying the stack
height should include:
(a) the same as steps (g), (h), (i), and (j) above,
(b) discussion relating the increased maximum ground-level
concentration measured in the presence of the building(s) or elevated
terrain in question to anticipated effects due to downwash, wakes, or
eddies.
44
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j
5. An appendix describing the fluid modeling facility, instrumentation v
used in the conduct of the study, and their normal operating conditions
and associated parameters.
45
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6.0 REFERENCES
Counihan, J., 1975: Adiabatic Atmospheric Boundary Layers: A Review
and Analysis of Data from the Period 1880-1972. Atmos. Envir., 9, 10,
pp. 871-905. ~
Environmental Protection Agency, 1978a: Guideline on Air Quality
Models. EPA-450/2-78-027, Research Triangle Park, North Carolina 27711,
Apri1.
Environmental protection Agency, 1978b: Technical Support Document for
Determination of Good Engineering Practice Stack Height (July Draft),
EPA-450/2-78-046, Research Triangle Park, North Carolina 27711.
Environmental Protection Agency, 1979: 1977 Clean Air Act Amendments
for Stack Heights — Proposed Regulatory Revisions. Federal Register,
44, 9, Friday, January 12.
Irwin, J. S., 1979: A Theoretical Variation of the Wind Profile Power-
Law Exponent as a Function of Surface Roughness and Stability. Atmos.
Envir., 13_, 1, pp. 1.1-194.
Simui, E. and Scanlan, R.H., 1978: Wind Effects on Structures, John
Wiley and Sons, NY, NY, 458 p.
Snyder, William H., 1979: Guideline for FJiiid Modeling ..of-Atmospheric
Diffusion (June Draft}. EPA-450/4-79-016, Research Triangle Park, North
Carolina 27711.
Turner, D. B., 1970: Workbook of Atmospheric Dispersion Estimates.
Publication No. AP-26, Office of Air Programs, Environmental Protection
Agency, Research Triangle Park, North Carolina 27711.
Zoric, D. L. and Sandborn, V. A., 1972: Similarity of Large Reynolds
Number Boundary Layers. Boundary-Layer Meteorol., 2_, p. 326-33.
46
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