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torch 1981
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. -EOTENTlAL-ELffi4.JgSEEL-EOR. GAUSSIAE-PLUME
INTERACTION WITH SB!?LE TERRAIN FEATURES
A. jBass
D. G. Strimaitis
B. A. Egan
Environmental Research 5 Technology, Inc.
Concord, Massachusetts 01742
9-1/8"
Contract No. 68-02-2759
I
Project Officer
i
i
John F. Clarke
i
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, NC 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
U. K
3/8'
EPA-287 ICin i
(4-70)
PAG- NUMBER
RXDDDD13afl5
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[EPA-600/4-8 1-008
3.
I*. TITLE AND SUBTITLE
POTENTIAL FLOW MODEL FOR GAUSSIAN PLUME INTERACTION
HITH SIMPLE TERRAIN FEATURES
7. AUTMOK(S)
A. Bass, D. G. Strimaitis,
B. A. Egan
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Research and Technology, Inc.
Concord, Massachusetts 01742
12. SPONSORING AGEWCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Rese?rch and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
IS. SUF^LEMENTAHY NOTES
\
\ '^
1 RECIPIENT'S ACCESSIOfPMO.
RS^ H °s 1 Q a 7
tin Js. ff K fc3y OKT NO.
10. PROGRAM ELEMENT NO.
CDTA1D/05-0625 (FY-81)
11. CONf RAC?/G«AWT MO.
68-02-2759
13. TYPE OF flEPOHT AWD PEBIOO COVERED
Final 1977 - 1979
1«. Sf'OWSORlWG AGENCY CODE
EPA/600/09
*©. ABST.KACT
The theory of turbulent plumes embedded within potential flow fields is dis-
cussed for flows modified by special complex terrain situations. Both two-dimen-
sional and three-dimensional isolated terrain obstacles are considered. Concen-
tration estimates are evaluated using a Gaussian solution to the appropriate
diffusion equation; dispersion coefficients are modified to account for terrain-
induced kinematic constraints, and plume centerlisie trajectory is obtained from s
stream line of the potential flow. Specific limitations to the theory and its
applicability are reviewed.
A computer algorithm is developed and documented to perform these calculations.
Dispersion estimates and ground-level concentrations are given for a variety of
meteorological situations. Parameters of the problem include obstacle height,
effective source height, distance between source and obstacle, crosswind aspect
ratio of the oihstacle, and atmospheric stability. The potential flow theory,
originally applicable to neutral flows, is extended by an empirical approximation
to slightly stable flows. Model computstions are coftipared to laboratory experi-
mental results for neutral and stable flows, and to field measurements from the
Tennessee Valley Authority UiuJow Creek Power Plant..'
17.
a: DESCRIPTORS
Meteorology
* Plumes
* Hills
* Three dimensional flow
* Two dimensional flow
* Mathematical models
KEY WOPOS AND OOCUMSNT ANALYSIS
8. DISTPIBUTION STATEROEMT
RELEASE TO PUBLIC
EPA Form 2228-1 (9-73}
b.lBEWTIFIERS/OPEN ENDED T£RMS
19. SECUH5TY CE.AS3 (Thte fteportf
UNCLASSIFIED
20. SECURilTV CLASS f Tiiti pagei
UNCLASSIFIED
c. COSATI fteld/Croup
048
218
08F
20D
12A
21 . WO. OF PAG ES " """ "
202
22. PRICE
1
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DISCL
This report h&s been reviewed by
Laboratory, U.Sr Environmental Protect
cation. Approval does not signify tha
views and policies of the U.S. Environ:
mention of trade names or eosnaereial p
recosaendation for UP®.
, _. 6-1 .''2"
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9-1/8"
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the Environsental Sciences Research
ion Agency, and approved for publi-
t the contents necessarily reflect the
aentai Protection Agency, nor doss
roduets constitute endorsement or
"^
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This report describes the _results; of a program to develop and evaluate a
transport/diffusion siodel for estimating asbient ground-level concentrations ]
from point sources in areas of complex terrain. j
At the beginning of the investigation, development of two modified I
Gsussian-type plums asodels was proposed, as guided by regulatory requirements^
The first model'was to be a worst-case, single-point-source Eiodel to be used ;
as a screening tool for esti&ating hourly-averaged ground-level air quality |
impact on a variety of individual temin features; the second model was to be
an extension to'handle multiple terraih features. At the conclusion ©f a j
project technical review held at the Meteorology Laboratory on 20-21 July 1978
at the request of the goveraraent project officer, it was mutually agreed _thatj
Implementation of'the worst-case screening model wouliT be" premature."'" Instead"^
the prograa was, directed toward furt", it model refinements and extensions, &nd\
included detailed comparisons of model predictions with field Eeasurenefits and
laboratory experiments. ; |
In the execution of this program, Environmental Research $ Technology, '
Inc. (ERT) has: j
i
e adapted the potential flow theory approach for neutral situations b^
including the effects of terrain-induced perturbations on pluase |
trajectory, and on vertical and crosswind dispersion;
e developed espirieal approximations to the potential flow theory to
address both: j
^lightly stable flows; and
obstacles of arbitrary crosswind aspect ratio;
e implemented and documented a' computer algorithm to perform these
potential flow theory calculations; »nd investigated the variations;
of results with changes in effective stack height, obstacle height,;
distance to obstacle, stability, and aspect ratio; and ;
e made a preliminary assessment cf the model through a comparison ©f !
model results with U.S. Environmental Protection Agency tow tenk and
wind tunnel experiments and with atmospheric data froo TVA's Widows
Creek Power Plant. j 1
BEG! I;
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F.PA-237
] F-OR TABLES
AMD ILLUS-
', THATIONS
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1 J
The theory jof turbulent plumes embedded within potential flew fields is
discussed for flows modified by special complex terrain situations. Both two-
dimensional and 'three-diraensional isolated terrain obstacles are considered. I
Concentration estimates are evaluated sising a Gaussian solution to the appro-j
priate diffusion equation; dispersion Coefficients are modified to account fa?
terrain-induced'kinematic constraints,land plume centerline trajectory is i
obtained frcaj alstreaia line of the potential flow. Specific limitations to j
the theory and its applicability are reviewed. j
A computer1algorithm is developed and documented to perform these cal- ;
culations. Dispersion estimates and ground-level concentrations are given fey
avaTiety_of Eeterolegieal_ situations ,J_ Parameters._pf._ the _problea_include__ .^J
'obstacle height, effective source height, distance between source and obstacle
crosswind aspect ratio of the obstacle^ and atmospheric stability. The j
potential flew theory, originally applicable to neutral flows, is extended by!
an empirical approximation to slightly;stable flows. Additionally, an inter-!
polation scheme-'is- proposed for objects of arbitrary crosswind aspect ratio [
between the limiting cases of a hemisphere and a half-circular cylinder. j
For neutral and slightly stable flows over two-dimensional obstacles, i
predicted Eaaxiaum ground level concentrations are similar to those expected i
over flat terrain. For flews over three-diraensional obstacles, however, the j
model predicts an order of magnitude increase in the ground level concen- j
tration. Model 'computations are compared to laboratory experimental results i
for neutral and.stable flows over an isolated obstacle with a crosswind aspect
ratio equal to that of the hemisphere,'and for neutral flows over obstacles :
with aspect ratios that vary between tfeose of the hemisphere and the circular
cylinder. Peak .concentrations at the erests of these obstacles are feuitd to
be overpredicted by no more than a factor of two- A preliminary test of the I
model against field measurements indicates that the model coisputations i
generally bracket the observed concentrations, with the major uncertainty
being the specification of the dispersion parameters.
The performance of the potential flow raodel differs markedly froa that i
of the level plums and the terrain-following plusis approaches to predicting ;
groraid-iev©! concentrations in complex!terrain. Th© level pluae predictions j
characteristically overpredict by one $o two orders of magnitude, end the i
terrain-following plume predictions characteristically underpredict by several
orders of magnitude at small aspect ratio. Consequently, the potential flow
approach provides a real potential for!simulating physical interactions of a ,
plume with terrain features in coaplex!terrain under conditions where the j
atssospheric stratification is neutral to slightly stable, and where direct ;
plume impingement on the hill -side is aot expected. i
Recomsendaticms are aad© for extending the applicability of the modelingi
approach, and for providing additional:data for adequate validation. Several
j"0f"'the areas cited for enhaaceaent and! extension include alternate turbulence'!
rTO',
iv
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, (RATIONS
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schemes,4&n algorithm for estimating concentrations in hill wakes,
generalized potential flow streass functions for additional terrain shapes, ap.3
additional laboratory data for stable flow over a variety of obstacle shapes.!
TOP OF
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AREA
This report is suteaittcd in fulfillment of Contract
Environmental Research § Technology,
Protection Agency.
3-02-2759 by
nc. under the sponsorship of the U.J
[
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(4-76)
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CONTENTS
Preface. . . . J iii
(Abstract . . . J iv
Figures. . . . J X
Tables ....
Abbreviations arid Symbols XV
Acknowledgement.' xvifi
1. Introductiqa 1
2. Summary an4 Conclusions 3
3. Recommendations 9
0 -t ^..
4. Complex Terrain Modeling: Technical Issues and Current Status.11
4.1 Terrali-Induced Kinematic Constraints on Dispersion
and Plume Trajectories . . i 11
! *
4.2 Enhanced Dispersion in Complex Terrain 12
4.3 Buoyant Entrairaaent Effects on Peak Plume Impact in
Complex Terrain ; 13
4.4 Plume ^Dispersion and Transport Under Stable Flow
Conditions j 14
5. Application of Potential Flow Theory. . . . 15
5.1 Modeling Criteria and Rationale 15
5.2 Gaussian Forauiations in Complex Terrain . 15
5.3 Modeling Approach, Applicability, and Limitations 18
i i
5.4 Theoretical Basis of Potential Flow Algorithms—
Neutral Flows ! 19
i I
5.5 PGT Scaling of Dispersion Coefficients .26
6. Neutral Flew 34
6.1 Ground-Level and Centerline Concentrations for
Neutral Flow j 34 BOTTOM OF
j |^A("-£ ARFA*
BFGIN 6.2 Dependence on Stack Height and Position 36 OUTSIDE''" '
LAST LINE) 6 3 E££ectl 0£ obstacle Size 43 — DIMENSION
OF TEXT Sy- , „ i FOR TABLES
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| !_' I iiiSli Vil Jj ( TRATIONS
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OF F
2*. Cozsparisonftifith Laboratory Experis
Over a S4ngle Mound
7.1 Background
7.2 Dispersion Coefficients, Fla
— - 7.3 Boundary Layer Enhanced Dispi
7.4 Comparison with Flat Terrain
7.5 Comparison in Presence of Tei
8. f4odifi cations for Effects of Strsi
8.1 Qualitative Observations frm
8.2 Incorporating Stratification
8.3 Application to the Atmosphen
9. Comparison with Laboratory Experii
"^ ~9T2 ~Dispersron' Coefficients", Tla;
9.3 Results in Presence of Terra
10. Modifications for Arbitrary Cross*
10.2 Adjustments to Pluse Center!
10.3 Adjustments to Velocity Fie
11. Comparison with Laboratory Experis
Flow Over Hills of Intermediate
11.1 Background
11.2 Comparison of Hill Shapes .
11.3 Dispersion Coefficients, Fl)
11.4 Comparison for Plurae Height
Obstacle Height
11.5 CoiEp4rison for Ploiss Height
the Obstacle Height . . .
i
116 Swsffsify pnd Conclusions . .
12. Model Comparison with Field Obser
1
12.2 The Widows Creek Steaa Elec
12.3 Case 'Selection for Model Cos
12.4 Predicted and Observed Cone
• j2 S Sjnspjsry sn*l Cone l unions . .
k 3/g.- '
PAGE r
EPA-2S7 (Cin.t
(4-761
JTER
'AGE ^
sents — Neutral Flow — -
45
45
Results 46
Tairi Obstacle ........ 50
:ification 60
i Laboratory ^?o^®liIls 60
Effects 60
i 65
lents— Stratified Flow .... 67
67
rferTalnT~.~7 7~.~7 ~~.~".' T ~67 **"
n Obstacle 70
sind Aspect Ratio. ...... 74
74
.in@ Trajectory
74
d 78
ients--Nsutral
Aspect Ratio 80
80
so
it Terrain 82
Equal to the
84
Equal to Half
92
101
rations (Widows Creek Data) . . 103
103
trie Power Plant 103
sparisons .105
Sntrations 120
132 —
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©renees . ,
Appendices
A. Progs-ass Dssicripticss - (^PLX
B. Prograa Flow Chart.
i
Source __Prpgrsa Listing.
,133
.137
.147
D. Sespl© Output Listing 178
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1 I
1 Horizontal dispersion coefficients for neutral flow
; i 2 Vertical dispersion coefficients for neutral flow over a
> circular ridge I 29
3 Horizontal dispersion coefficients for neutral flow over a
1 hemispherical hill 30
^a--4_ _.„ ..Vertical dispersion coef f icieuts . for neutral _£ low _ovet a_ _SB
: 1
Sa Velocity speed up factors for neutral flow over a
". | 5b Velocity speed up factors for neutral flow over a
hemispherical 'hill 33
i 6 Centerline and ground- level (
shoissn in Figures 1 through
7 Domain of calculations perfoj
j cylindrical ridge and neutj
' '
J: j 8 Domain of calculations perfoi
vt' hemispherical hill and neu-
';s 9 ttexiaum ground- level concenti
•j ridge and various combinat:
-^ i position
Concentrations for cases
4 (neutral flow) 35
•raed for a two-diaensional
ral flow 37
iaed for a three-dimensional
tral flow 38
rations for a cylindrical
.ons of stack height and
39
'**3
't| 10 Position af maximum ground- level concentration for a
:-5 cylindrical ridge and various combinations of stack
'?h 11 Maximum ground- level concentrations for a spherical hill
;-:| and ^various combinations of stack height and
\\ 12 Position of maximum ground- level concentration for a
^ spherical hill and various combinations of stack
V,4 13 Maximina ground- level concentration as a function of
'^ „ , hill height 44
;j LAST LificL_i4 Position (distance 5rom hill
1 |s/S" ^ :::;i:;j:;-J
crest) o£ maximum ground-
mctioiLjcf. hill height ... 44
,,..,..;., ~^
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tL_15& Vertical concentration profile 39.2 cm downwind of a
12. § era stack in flat terrain 47
15b Vertical concentration profile 84.7 cm downwind of a
12.5 era stack in flat terrain 48
15c Vertical concentration profile 130.2 era downwind of a
16a Vertical concentration profile 39.2 era downwind of a
12.5 era stack in presence of a 23 csn hill 51
16b Vertical concentration profile 68.2 cm downwind of a
12.5 era stack in presence of a 23 cm hill 52 i
16c Vertical concentration profile 84.7 cm downwind of a
12.5 era ''tack in presence of a 23 cm hill 53
17 Height of the source streamline (n ) above the hill
crest (height = a) for various slack heights (H )
~v!8a Strearalines over s hemisphere . ...... 62 ,
18b Streamlines over a half circular cylinder 62
19 Vertical concentration profile 50 cm downwind of a
^ era stack for stratified flow in flat terrain 68 <
i
20 Vertical concentration profile 84.7 cm dcwr.wind of a
'. 9 da stack for stratified flou in flat terrain 69 '
21a Ground- level concentration for stratified flow as a
1 function of distance upwind along the ground from
the hill c~est for a 9 cm stack f/id 23 cm hill 71
21b Ground- level concentration for stratified flow as a
function of cross-wind distance alcr..1? the ground
from the hill crest for a 9 on stack and
23 cm hill » 73
22 Definition sketch for aspect ratio X - b/a for
hills of spherical, intermediate, and i
cylindrical shapes. ...i 75
23 Details of hills used in 3PA wind tunnel experiments. . . 81
24 Predicted and observed concentrations for stack
height equal to hill height (23.4 on) 86
25 Vertical plume spread at hill crest for stack
height equal to hill height (23,4 cm) 89
26 Predicted and observed plume height at hill crest
for stack height equal to hill height (23.4 on) .... 90
27 Vertical concentration profiles over CX, the
i i ~~"
i i 1 . . . x>
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;. -| HF.RF :«sK 28 Lateral pluase spread at hill' crest for stsek height
i f i equal to hill height (23.4,011). 93
~ - i '' I
DfcOP?:£D 29 Predicted and observed Gaussian rasss flux for stack
: M?AD; height equal to hill height (23.4 on) 94
. ' C-EG'N ' ' :
• , ^fcr'OM; ^° Predicted and observed concentrations for stack height
• '-'I Hrce *-^T~~ equal to half the hill heicht (11.7 cm) 96
- ;• i 31 Predicted and observed plune! height at hill crest
: .- for stack height equal to half the hill
*' height (11.7 cm) i, 97
; 32 Vertical piusae spread at hill crest for stack height
equal to half the hill height (11 7 cm) 98
• V 33 Lateral plume spread at hill crest for stack height
• •; equal to half the hill height (11.7 era) 99
34 The Widows Creek steam electric power plant and
surrounding features 104
, 35_. __ __Cosparison of tne idealized cross- section_o£Saud ^
\ '• feuntain to the southeast of Widows Creek pcwer
plant with the circular cylinder assumed in
the corapIeK terrain issodel 108
; 36 Temperature profile used to calculate pluaie rise
. -'"; and Froude number on day 3, hour 1300, 1978 113
'? :\-
;" ] 37 T^aperature profile used to calculate plume rise
-=* ! and Froude number on day 40, hour 1300, 1978 114
:- 4 | 38 Temperature profile used to calculate plume rise
-. ' -i ' and Froude msaber on day 1^0, hour 0900, 1978 115
• -=? i i
•-----' t 39 Temperature profile used to calculate plume rise
• : '• and Froude nusber on day 230, hour 1000, 1978 116
'^ i 40 Temperature profile used to calculate plume rise
r'-vi and Froude nuaber on day 4, hour 2100, 1978 117
i 41 Temperature profile used to calculate plume rise
—^ and Froude nusber on day 166, hour 240(', 1978 118'
'~ yj 42 Temperature profile used to calculate plume rise
;. , ' and Froude number on day 222, hour 2400, 1978 119
• '.-'." ' '
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JABLES.-
Number
i i '
I 1 Range 'of model parameters evaluated in laboratory
| and field tests of the potential flow model 6
2 Form Of vertical distribution and vertical spread
i implied by solutions of the clv;sical parabolic '
j equation of diffusion 17
j 3 Comparison of predicted and observed normalized
i concentrations and plume centerline height for
|or4_ the 12.5 on high stack in the_ presence, of _th« ._
22.9 cm high polynomial bill 54
4 Comparison of predicted and observed normalized
i concentrations and plume centerline height over
j the hill crest for the 9.0 cm height stack 55
j 5 Error ratio R*/R for 10% errors in o and n 57
I 6 Comparison of normalized concentrations and
j derived terrain correction factors at the hill crest. . 58
) , ;
i 7 Plume impact criteria based on Figure 17 65 j
| 8 Comparison of predicted and observed concentrations !
I at hill crest for the 9 cm stack tow tank experiments . 72 j
| 9 Representative,values_of speed-up factor S 77 i
10 Observed normalized concentrations at hill crest j
for stack height equal to hill height 84 i
|
11 Comparison of predicted and observed normalized
surface concentrations for stack height equal j
to hill height j 85
12 Comparison of surface concentrations at hill crest
between the potential flow model, the wind tunnel
observations, the half-height assumption, the
terrain-following plume assumption, and the level
plume assumption for a stack height equal to hill
height i 87
13 Predicted and observed normalized surface
concentrations for a stack height equal to QOTTO!,'. OF
half hill height J 95 IMAGE AREA.
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OF TEXT $&•__ , j I FOR TABLES
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TYPING GUIDE SHEt'T
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Comparison of observed to predicted ratios of
plume size parameters and speed-up f actor (s)
as ^ function of aspect ratio
Hours ' selected for aodel comparisons at Sand ^fountain . .
Hours selected for jaodel comparisons at Sumjnerhouse
Mountain '.
Cases of significant inpact that have associated
vertical profiles of temperature
Final pluas heights of emissions frosa boilers 7
and 8 both with and withe at full SO- scrubbing
Hourly uncontrolled SO- emissions from each boiler
unit Curing hours selected for raodel analysis
Sumiaary of results of Froude number calculations
Stability classification system
Ranges of dispersion stability class designations
appropriate to the case ho'ars based on temperature
profiles winds and tise of day
Results of Eodel calculations for hours showing
inpsct on the ne&rby ridge
Results of ssodel calculations for hours showing
impact on the isolated sc&Kid
Ihicontrolled SO- concentration normalization
factors for test cospari^oa hours ...........
Revised S0» emission rates for Units 7 and 8 and
cosbined concentration normalization factors
that include scrubber operations
Comparison of predicted and observed S02 concentrations
Cosparison of predicted and observed S0? concentrations
at Widows Creek
Comparison of observed concentrations at Widows Creek
and predicted concentrations based on the potential
flow sod el with buoyant plisae enhancement
SuEaary of comparisons of the potential flow model
with half-height ard level plume assumptions
i j
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TRATrOS..^
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TYPING GUIDE SHEET
c,(.-
[SYMBOL
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la1, b1
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LIST OF SYMBOLS AMD ABBREVIATIONS
TOP OF
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------- r?!S"
height of obstacl© ,'
I
coefficients of boundary layer enhanced dispersion coefficientj
I ;
half of the crosswind breadth of obstacle
plvaae path coefficient !
I ;
coefficients of polynomial fit for z™
normal and crosswind dimensionless diffusivities
-noraal and crosswind "effectiv©"" diffusivities •
i
trial solution functions
i i
Fronde rnsaber l
acceleration due to gravity
trial solution function'
gross boiler load
weighting functions for velocity in aspect ratio
i computation '
effective source height
local terrain height ,
final plume rise {
Monin-Obukhov length
experimental Bass flux
distance along normal fsroa pluea centerline to surface
i (assuming no errors)
distance along normal fro® plume centerlin© to surface
I (with errors) j
emission rate of pollutant
l
ratio of ground level to centorline concentration
i (assuming no errors)
ratio of ground level to centerline concentration
; (with errors) i
i
distance frraa axis of syraaetry to pisna® centerline
1 for axisyraetric obstacle
xv
—--' Pif/: r."'0\
•
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, TRATIONS
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H.LFit &
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SYMBOL 4
RS stack top radius (E)
s along pits® cer&teriine path
s»n,Y curvilinear coordinates for
— 1 pluae centerlin® j
s. ' J
... _ . ,. ._ ... , . ^
length
systea that follows the
^CYL SSPH $peed-up factor for cylindrical ridge and hessispherical hill
SC iteospheric dispersion Stability class
Ta
Ts
T(s)
T
I"
lu
U
oo
.V
!Vs
j w w
!HC¥L* WSPH
Ix
Xs
i ••ru
I CF
ZCYL' ZSPH
plus© center line Wveetion time
tebient average tensperai:ure
stack exhaust temperature
Crosswind line integral;
terrain correction factor
-along: streamline-velocity — ~ — •
!
horizontal wind speed
velocity at crest of obstacle
^'velocity field component assuaing potential flow
i over cylindrical ridge, hemispherical hill respectively
enifora velocity upwind' of source
Velocity normal to streaaline
stack exhaust velocity
i
weighting funetiorss for streamline height in aspect
' ratio
LAST LINE
OF TEXT Bd
distance along X axis fro® source
downwind distance froa source to obstacle center
height of streaialine above crest for neutral flow
height of streamline above crest for stratified flow
height of streamline above surface for flow over
I cylindrical ridge, hemispherical hill
roughness length
i
ratios of cosjplex terrain to flat terrain spread
j statistics j
aspect ratio terra in speed-up equation
Streamline depression at any x due to stratification
£treaa!ine depression at crest due to stratification
stream function gradient factor
5 3/8"
CFA-287 (Cin.)
(4-76)
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' '•" ' ' " V.
TYPING GUIDE SHEET ••'
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1 HfchE ^SYMBOL |
j? >—~™ f^
1
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j HEAD.
n pltsse height pertiirbatio-jn facto?
A obstacle crosswind sspett ratio
. -h , , ,. ..,,,.,...,..;.. ^ - _. ... .;;, ^i-,.'
TOP Of
,., ,. ...,,,. ^^ A n r A
" * ' ' ' J A^ilL>n
I BEGIN \\ limiting two-dimensioraak and three-dimensional aspect
1 SB'.T'ONS
1
I
I
;
i
— - -* j ratios !
o~", ~ ~?ros"swina"«nd •vertical "dispersion ~coeffic
y»z r
— „
'". '"-.
L^Slta , _ ,
o _ „ irosswind and vertical Dispersion coefficients in
' ' i flat terrain
' i
o ' boundary layer enhanced; vertical dispersion
! coefficient j
o * vertical dispersion coefficient with errors
HS) normal to streraline line integral
X Concentration
X*,X diaensionless concentration
- 1 -V . •
i
.
| ^lD,3D stream function for two-dimensional, axi symmetric three- j
t .
I
1
i
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j
' '
BEGIN
LAST Ll-'sE
OF TEXT ^
• dimensional flows •
i !
ty stream function through source
i
$ u- streassline equation of plume centerline
P i i
6 potential teaperature
; ', 1
ABSREVIATIC»iS
I
cm centimeter
1
EPA U.S. Environmental Protection Agency
ERT Environmental Research $ Technologys Inc.
* •
FMF fluid Itodeling Facility
i i
ka kiloaeter
1
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m meter
MAAQS National Ambient Air Quality Standards
PGT Pasquill-Gifford-Turner!
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PSD prevention of significant deterioration
TVA Tennessee Valley Authority
LT local time
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HERE ®
ACKNOWL
EDGMENT
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The suthori wish to acknowledge helpful review and suggestions of Dr. F.
Pasquill, a consultant to the project.! We also acknowledge the helpful
advice provided'by Drs. J. C. R. Hunt,jft. H. Snyder, and R. E. Britter.
Special thsnks are extended to John F.jClarke and to George C. Hoi worth,
for their overall judgment and direction on the project.
The major contributions of R. G. Isaacs and Dr. J. Caiman to earlier
versions of this report are gratefully^ acknowledged.
Laboratory,data was kindly furnished by Dr. William H. Snyder, Environ-
mental Sciences'Research Laboratory, UPS. Environmental Protection Agency,
and Widows Creek Power Plant data was fcindly furnished by Mr. John P. Blackwe|
Aijr_Re_spurces Program^ ,Tennesse9_Valley Authority._ _ _ ^
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I INTRODllCTION
I
This study has been motivated by the requirement for & treateent of
plum® dispersion in complex terrain that is practical for regulatory use,
yet retain- taieh of the essential physics of the problem. For regulatory
[purposes, the modeling approach shouldiemphasize cases with potential for
high ground-level concentrations. These include:
• stable conditions and low wiitd speeds, under which direct pluse j
_ __ _isjp_act or blodd.ng_ by nearby^terrain obstacles may occur, and_ , J
0 neutral or slightly stable conditions and moderate or high wind 1
speeds, under which the pluse centerline trajectory passes over j
and close to the terrain surface.
I :
This report addresses tlie development of modeling methods for neutral
and slightly stable conditions. The general approach employed follows the
theory of turbulent plua^s embedded within potential flow fields as developed
by Hunt end Mulhearn (1973) and Hunt and Snyder (1978). The theory is
[applied to the calculation of ground-level concentrations using a Gaussian
jforra of solution to the diffusi-n equation. Streaiafunctions proper to
•potential flow over a cylinder (aspect Jratio = «) astd to potential flow over
la sphere (aspect ratio = 1) form cornerstones of the model. These are
(extended to describe flows over terrairi features of intermediate crosswind
jaspect ratio by a weighting of the two limiting streamfunctions. This
weighting schema was derived in part using results froa wind tunnel experi-
ments for flows over obstacles of intermediate aspect ratio (Snyder et al.
1979). ' |
In addition, although the model is strictly applicable only to neutral
flows, an empirical approximation scheme is included to define streamline
lowering caused by increased stratification. The empirical basis for this
portion of the oodel is derived from stratified tow-tank experiments (Snyder
1977 and Snyder 1978). j
Other restrictions in the use of the raodel have not been addressed.
These limitations to the eodel arise ftfosi the neglect of boundary layer '\
phenomena such aa flow separation, unsteady wake effects, tisae-dependent \
effects of stability (e.g., lee wave generation), and surface heating j
effects. In addition, the theory is applicable in a strict sathematical i
sense only for thin plumes. | j
This report discusses the rational© for selecting particular modeling i
BEGIN approaches, provides full technical documentation for the algorithms developed
LAST LINE and presents, for a number of specific test situations, the results of
OF TEXT ^comparisons between sodel calculations'and laboratory and field observations.1
3/8'
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(4-7G»
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Ttia report Consists of twelve sections and four appendices. Section
presents a suBiBsfsy of the study md it^ conclusions, and Section 3 states
r«eos!2t©ndations jfor fiiture laboratory and/or field experiments to further
and validate the modeling approaches. Section 4 briefly overviews
th© technical aspects of cossplex terrain modeling.
Section S describes the theoretical basis for applying potential flow
Jtiraory to the sideling of plus© transport and diffusion in coaplex terrain.
T^K^m^^^srpr^s^r^^^TO^^gPTTt
TOP OF •
^IMAGE
AREA
lunt sud coworkers ar© reviewed and approximations ar© introduced for prac-
tical application of the theory. A method is presented for calibrating
sodsi dispersion coefficients to varies diffusion parameter systesis. In
Section 6 th® theory ir applied to the i calculation of ground-level and
centerliae concentrate /ras for a variety of cases that illustrate the model's
>©hsvior, under beuf.
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AND! CONCLUSIONS
In complex!terrain, two classes of meteorological conditions often are
associated with the likelihood of large ground-level concentrations:
(1) low wind speed, stable cases, and (2) moderate or high wind speed,
neutral or slightly stable cases. The first class of conditions generally
leads to high concentrations through direct plume impingement or terrain
blocking. The present model does not treat direct pluiae impingement or
terrain blocking under stable conditions. Specific recosaaendations for
Beating j3lume_dispessiGn under.sjtable. atmospheric, conditions are presented,-,
in Section 3. , " !
The second'class of situations promotes high concentrations because, as
the plume is transported over terrain features, it is forced to pass close !
to the terrain surface. Physical mechanisms relevant to this class of j
conditions inelude terrain-induced alteration of the plume centerline tra- i
jectory and kinematic constraints on horizontal and vertical dispersion. i
The dispersion process in these situations is modeled as a Gaussian plume j
embedded in a potential flow field. This approach falls between the two j
extremes found in present modeling approaches in neutral situations: j
i i I
a) the terrain-following method, where the plume rises everywhere over;
the terrain at a local elevation equal to the height of the pluae
above the stack base; and i
i i
b) the level plume method, where the local terrain height is sub-
tracted fri® the effective height of the plume.
i i
In Case a, maximum ground-level concentrations are about the same as over
flat terrain, while in Case b; near-plume axis concentrations are predicted
at ground level for terrain elevationsi approximately equal to effective
stack height. Neither extreme deals with terrain-induced changes in plume
trajectory and pluae dispfrrion rates.'
Various model modifications have been adopted (e.g., the CRSTER model
with terrain truncated at the height of the stack top) to remedy this situa
tion. However, such treatments are ad hoc; by contrast, the potential flow
theory as described here appears to offer a practical and more physically
justifiable method for incorporating these effects vjithin a Gaussian plurae
model. |
A research I computer algorithm based on the potential flow approach
computes ground-level pollutant concentrations; pluae center1in® concentra
tions; height of plus® trajectory above the surface; and horizontal and
EPA-287 (Cir,.)
(4-76)
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SECTIONS
vertical dispersion coefficisnts. In ihe method used, for example, the 1 |
equation of the ; plums centerline for fjow over a hemisphere provides the ' |
plume trajectory in neutral flow by:
i
M
2 / a3 \
2 S4 7 9 ?/7l *
ME«E -^T . _^__or*o-'7
1 ' 1
1 *
2 / a' \ x« » ' -1
H* f 1 ffl . , i f 2«. 11
s | 2 2 3/21 l '
?.;
In this equation, x and z ar© the horitontal and vertical- cartesian coordinates .{
\of a point on the streasaiina relative to the center of the obstacle, X and i
K are the position and height of the stack, and a is the height of the
jhfll. The velocity along the plume trajectory, u(s), is determined by the
gradient of the stream fimction, ^•3D, describing the trajectory of the pluss©
centerline, such that:
1 f- _,
/
3D 3D 1/2
1 3t« 2 ' »-iVu i */*
1 U(s) » (-r*- )
1
m««^A *• • f
•trt i 9 /
*au(x.t) = 0.5 U^ [l - -
i \ G
* (ft ) (2-2>
^
a3 \ r ,>
R2 + Z2} 3/2J U ^;
,
and U^ is equal to the velocity far upstream of the hill. A Gaussian fona
1
1
i
j
j
\
;
i
j
j
'-i
,
;
| of the dispersion equation using coordinates along and normal to the i
BEGIN
trajectory: :
1
x'(s-n'Y) f ifer exp [-fi (s)
2
n2 - f2 (s) y ] (2-4)
i i 2
provides diir.ensionless concentration estimates, x' " (x^ma /Q)» where by
definition, |
fj(s) = [u(s)R(s)]2/[
f,(s) - l/[4T(s)]
j * i
g(s) = 4it[4i(s)T(s)]
1-
and , i
1 I
f 2
^(s) * 1 D- (s') R (s1) u(s
/ X
o
1
! s
T(s) I j [D2(s')/[u(s')R2(
i O
i
i •
1
LASTLIN!f|____ |
•> TEXT S*1
.
l+(s)] (2-Sa)
(2-5b)
/2 (2-6)
')ds' (2-7)
s')]]ds' (2-8)
— _,
f - - i T "^^ *" t •<""
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FiRST TYPING GUIDE SHEET
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HERE »sk siailsr sequels® of Equations (see Section 5, Equations 5-7 through S-13)_ (
DROPPED
HEAD;
BEGIN
SECTIONS!
for flow over two-dimsasiossal obstacles uses the two-dimensional streaa
function for flow over a half -cylinder:
r''
I t
• • 1
ja i ,,_ -,,_
V IX, ZJ » U Z 11 - • - i v- -/
HERE *4~ , V ^X * Z ^ /
\
M n C-f-\ i
- 1
-1
-j
.-1
nj
i
i
To account for the effects of stability, an approximation consistent -;
with laboratory observations is adopted to lower the neutral stresalins
[(Section 8, Equations 8-1 through 8-8)
> The height of the neutral streas-
line within two obstacle heights of th© obstacle center is lowered by an
js&ount, 6:
/
\
6(x) = A ll - |4-l , for |x|<2a (2-10)
\ ai/
^^ _ -L - -w,yv r ~ w-»~ *v> ._IAI,
! where
i
*
i
A is z_ - z™,, and
'
]
)
j
-i
i
-'
ZC' ZCF ;ar® tjis streamline heights above the crest in neutral flow, ;
a$d in a flow characteriged by Froude number Fr, respectively. \ \
A second approxiaation is derived
(Section 10) to account for an
obscacle with arbitrary erosswind aspect ratio, \. In this case, two and
)
"•= tteee-diaensional streamlines are weighted to provide an intermediate pluse
1
j
ceaterline trajectory:
ZC ' IZSl4C*f X) " ZCYL W'x»x"
(
L1 * ZCYL ^'x) (2"H)
i
>
aiai the velocity components are weighted by the aspect ratio dependent
speed-up factor, S (Equations 10-13 and 10-14):
U(x,ZiX) = 2.0[S(?.; - 1.5] U
I !
+2.012.0 - S(X)]USpH(x,z) (2-12)
1
,
Model computations indicate that
ficantly with obstacle size, effective
aaximum concentrations vary signi-
stack height,, and relative distance
between the stack and the obstacle (Section 6) . Comparisons of model
predictions with available observations test the model perfonaanee for a
limited number of possible combinations of these and other factors. Table 1
BEGIN
suESBarizes the range of sodel parameters involved in the comparisons. Note
LAST LINE
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PiGE K
} EPA-287 (Gin.!
1 (4-76)
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UF TEXT *
TYPING GUiDE SHEET
CENTER
OF FAGt /
Slat X is the c&sswind aspect ratio of the obstacle (Section 10), Fr is the..
Froude number characterizing the iaportance of density stratification in
defining the flow (Section 8), X /a is j the distance between th© stack and
the otctacle normalized by th-j oBstacl® height, and H /& is the effective
stack height normalized by the obstacl^ height. s
~ TA^LE 1. RANGE OF MODEL PARAMETERS EVALUATED IN
1 LABORATORY AND FIELD TESTS OF 'THE POTENTIAL " " ' ' '
I FLOW MODP*.
_MI_>
Comparison Study X Fr X /a H /a
Smooth Tunnel , J. „.„ 939 3.7 0.4,0.6
(Section 7) j
Tow Tank , 1 OJ97 3.7 0.4
(Section 9) !
Rough Tunnel 1,2,3,» 999 3.7 0.5,1.0
^, —(Section. 11) _ ,_,.-, <_•• _ . ._^.
Widows Creek 4 1.3-1.7 32 >1
(Section 12) » 0.4-1.0 12 >1
9-1/o '
The "smooth 'tunnel" comparisons (Section 7) and the "tow tank" com-
parisons (Section 9) test the model under conditions that minimize the
influence of processes not contained iii the model. They show that the model
is able to predict the observed maximum surface concentration within a
factor of two (generally, overpredicting) , depending on the interpretation
of the observed plume properties in the absence of the obstacle.
The "rough tunnel" comparisons (Section 11) include t«ie effects of a
strong boundary layer on flow over obstacles with a triangular cross section.
Model predictions of maximum surface concentrations art again within a
factor of two (overprediction) for obstacles of aspect ratio 1. However, as
the crosswind aspect ratio increases, the concentration predictions fall
below th6 observations. The data indicate that the plume size is signi-
ficantly enhanced upstream and over hills with the larger aspect ratios.
The deformations included in the potential flow field approximation are only
partly responsible. A better understanding of plume dispersion in a deforming
boundary layer ijlow is likely to be needed to describe these experiments
more accurately.
The "Widows1 Creek" full-scale comparisons (Section 12) also show the
importance of accurately describing plume dispersion in the atmosphere. In
most cases, predicted surface concentrations aro extremely sensitive to the
dispersion paraS'-ters assumed. The limited comparisons of the modal with
fie\d data show that most of the observations fall between model predictions
when the two most appropriate dispersion parameter classes are used. But,
much more field data will bo required to adequately evaluate the model for
full-scale applications in the atmosphere.
, ,. i
( t • • • •
a&.
- i 3/e- w *:- -•••• ••••+m ^'
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PAGE NUMLiER
FPA-287 (Cin.)
(4-76)
TOP OF '!
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~ " • ' i • • •• i
Tr^ft .^*fMT(T"IS8T>a «rt* tc wl ^ti 1 «ahnT«fl^nw rlafra fava m
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HEHE
IL
ta are put into perspective by —j
comparing the observed peak concentrations with predictions of a level plume i
approach and a terrain-following approach. FOT the level plume approach, j
the predicted concentrations in th© cases studied equal the centerline I
concentrations (in the absence of reflection), which range frosi a factor of j
two ordersiof magnitude greater than the observed surface concentra- j
ons. In tliejase of the terrain-following approach, predicted concen- ___j
"^rations ar¥~e«bh^IaTIy~zef6"r"Tn~tefiasn6T"a"''lp"artial height correction^ 1
approach, whichjis an intermediate approach between the level pluxae and the [
terrain-following plume approaches (Section 7), the observations as well as i
the potential flow aodel indicate that a plume path coefficient of 0.35 is
needed to simulate unstratified flow over the symmetric hill (not a ridge) i
in the smooth tunnel, and a plume path' coefficient of 0.15 to 0.18 may be an j
approximate choice for a moderately stratified flow (Froude number nearly !
1.0) or or a symmetric hill in the tow tank. In the rough tunnel, plume path
coefficients based on the observations] and the potential flow model pre-
dictions vary between 0.46 and 0.76. I
These preliminary assessments suggest that with verification and
refinement, the]approach may be applicable to the following situations: 1
e isolated, single terrain obstacles of arbitrary height, of cross-
section approximately circular in a plane parallel to the wind
direction, and of arbitrary aspect ratio in the crosswind direc-
tion i1and j
, *~ !
9 neutral to slightly stable stratification (depending on effective
stack|height).
i
A number of limitations arise mainly from physical effects that are not
described by the potential flow model.: The model should not be applied to
the following situations:
• stable flow cases in which the plume may directly impact the
hill; | i
• dispersion cases dominated by surface boundary layer effects;
• unstable cases (e.g., strongly ccnvective situations) for which
potential theory is unsuitable; and
e cases dominated by wake effects.
1 i
The range of suitable applications of the model is also limited by the
theoretical approximations made, and by the limited configurations studied
experimentally.i These limitations incjude:
« the "thin plume" approximation (o /n « 1.0 where n is the
heigh^ of the plume centerline above the hill crest);
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the surface boundary layer effects not considered in the model;
the Gaussian beha-.io-1 assumed in the model in contrast to non-
Gaussian behavior seen in some of the experimental results;
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« restriction of the available experiments to a small number of
stack heights, and to fixed configuration of obstacle relative to
stack;! and
o the hill shapes used in the laboratory experiments, as compared to
the spherical hill shape asswaed in the theoretical calculations.
^ ' _ I ~
KowevHr, frbaTfio preliminary comparisons of tJie""mo^eT'witir~laljbfat6"ry~lafa,
jit is noted that the "thin pluse" approxiraation iuay effectively be relaxed
jto o /n <0.3. Indeed, tlie errors introduced by such a relaxation are not
as serious as those introduced with either the level plume or the terrain-
following pkrae approaches.
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RECOMMENDATIONS
The following reccsBsendations are proposed for extending the applica-
bility of the Eodel and for its verification.
e The complex terrain ssodei uses the PGT diffusion coefficients
derived froa observations made in flat terrain to predict what
will happen in cosplex terrain. The accuracy of the model taight
be improved by using updated dispersion curves. These updated
curves would include, for exaspie, changes with roughness length
or'intensity of the wind "direction" fluctuations ^ "^
The changes in the properties of the boundary layer over a hill
are not well understood theoretically. Further laboratory studies
of th© behavior o£ the boundary layer could lead to better engi-
neering approximations to so®e of the effects.
Developing an approximate treatment for computation of ground-
level concentrations in the wake of a hill would extent the
applicability of the present model.
The applicability of the model could also be extended by incor-
porating known solutions to the potential flows around bodies of
different shapes, e.g., a bluff, or an elliptical ridge. The
problem of very stable flow around an ellipsoidal hill, or ©f a
stack positioned away from the plane of syissetry, taight also be
addressed. Specific laboratory experiments of these flows fcreuld
be important in testing the generalized model.
The present model does not treat a situation in which the wind
direction is oriented at sosse arbitrary (not perpendicular) angle
to an elongated terrain obstacle. Experiments should be Hade to
gather the data to model the effect of nonnoraal wind incidence.
The effects of varying aspect ratio and of varying stratification
have been independently incorporated into the model and are
assumed to be additive. This superposition of effects seems
reasonable in the absence «f any data to the contrary. Experi-
aents including stratification and varying aspect ratio would
provide useful data from which the approximation could be refined.
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Although not discussed in the present work, it is recosmeisded that
the Epdeling technique used ifor stable esses should incorporate
recent suggestions to include (1) effects of enhanced crosswiad
plume meander, (2) buoyar.cy effects, (3) modified turbulence
typing schemes, and (4) physically realistic treatment of surface
reflection. A coaples©ntary* set of sispl© modeling algorithms
should be linked to the present @odel to handle those cases not ™!
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of such modifications would -enhance the credibility of the
approaches substantially.
i
Routine application of the model in the ateosphere requires th«j
determination of the Froude mosber for the flew at the terrain
elevation. Where only limited data ar© available at this height,
it aay be necessary to infer the Froude rasber frea surface
observations. Observational data should be analysed to reveal
the uncertainties in correspondence estmp Froude nsmbsrs obtained
frosa data st terrain elevation and those inferred fros standard
airport observations; and model sensitivity to these uncertainties
should be evaluated,. ' _. _^.
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SECTION 4
OMPLEX|TERRAIN MODELING: TEOWICAL ISSUES AND CURRENT STATUS
The current Guideline on Mr gusalat^ j^dgls_ (EPA 1978) lists no ssodsl
as being generally epplicsble to complex terrain situations,, leaving the
matter to the discretion of the EPA Regional Adainisteator snd to "expert
advice." Eecsu^® Esodsiirag is tssed to ^certain whether a proposed pollutant'
sourc© will ESS©$ asbieat air quality standards [e.g., national Ambient Air
Standards (MA&QS) and prevention of significant deterioration (PSD)
thf decision to permit nsfr or expanded industrial astd energy
facilities i0..e«plex terrain areas iaay_be_jiighly_sensi._tive_to__
~~ ' " '
As baekgresmd to the ms&elivtg appffoach adopted, this section provides a
brief overview ^£ the present state-o£>the-srt for c^splex terrain aodeling,
including key t^ctsaieal areas of interest, r©eeut advances and current
research, anid-,rec«jnt field a?id laboratory expsriiaents .
Physical processes of interest in^ cc^Ies terrain include:
terrain-induced perturbatioas on wind speed sad direction and
pluaa|trajectories for different stability conditions;
©n the kinematics of plume shape,
ted atmospheric turbulfenc© levels and increased plus® dis
psrsidn coefficients;
4.1
© effects em plyrae rise owing to buoyant entrainsaeBt and vertical
shesrjj and, th®rsfore, ©n ®sti®^tes of masiraa ground- level tepsct
ia coapi@x terrain; and
e speci4l aarodyn^ic effects, such as plum® stagnation on the wind-
ward s.id® of terrain features under stable flow conditions, and
wake Effects en the leeward jside of terrain features.
Terrain- Xrafuced Kin©®aiie Constraants on Dispersion and Plurae Tra-
jectories I
As a resul^ of distortion due to air flow around terrain obstacles, a
plum© will pass ithrough phases ©f acceleration and deceleration along its
trajectory. To 'first ordsr, these effects are independent ' of the effects ©f
turbulent diffusion. In particular, f^r an incoaspressibl© fluid, raass con-
tinuity requires that an increase in velocity along a streamtub® will result
in a decrease ii| streastub© cross-sectional area, and vie© versa. Thus, for
®5a®pl©» a pltm^ passing up and over ail elevated ridge is expected to _
velocity over the crest; correspondingly, the plusae vertical spread
~
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)$fcntt and l&ilheam (1973) applied two-dimensional potential
jflow theory to quantitatively describe(the resulting ground-level concentra-
tion distribution. Their method involved superimposing diffusion effects
iato streamline trajectories defined by the potential flow theory. The
methods used included both simple gradient-trimsfer (K-theory) assumption
jctnd the statistical theory of turbulent diffusion extended to deforming
~~®n&. The results for flow over a cylindrical hill shewed that for a
jsouree'Ts ~te&~ htll~h@TghtS ""upwind ;~the~ "grmiM-Tever^onceritratldM~ffipproac!ie3~
those expected in the absence of the hill. Egan (1975) used potential flow
assumptions to describe the closeness of approach of a pluiae to ground
level, and the plus® spread due to kinematic defamation effects, for too
cases: flow nonsal to a half-cylinier, and flow normal to a hemisphere.
; For two-dimensional flow noraal to a half-cylinder, an elevated pli&se
that follows a streaaline is constrained to pass nearest to the ground just
above the crest of the cylinder. However, above the crest the streamline
'spacing is narrower than elsewhere, which tends to decrease a over the
jcrest. These two effects tend to cospsnsate, such that the ground-level
'^concentrations may not be markedly larger than those expected in the absence
bf the hill. This result should apply .qualitatively to flow norsal to
jridge-type-terrain features.- - - - • - ~,~ " 1Bsa
! For three-disensional neutral flow normal to a hemisphere, the stream-
lines approach the surface more closely, and converge more than in the flow
over a half cylinder. Axial symmetry results in distortion of a streastube
element as it passes over the crest. The flow kinematics cause a marked
local increase of a and a marked local decrease of a over the crest, and
the effects eosabine^to increase ground-level concentrations significantly in
jthe vicinity of the hill top.
i Hunt and telhearn (1973) could not extend their statistical theory
approach to predict the concentrations at the surface; rather, they developed
an asymptotic thin plume solution to the advection-diffusion e«$uation. This
solution foras the basis of the method adopted for this analysis.
j In sore recent work, Britter et al. (1976) generalized the Hunt and
Muihesrn model to calculate dispersion 'in inhorogeueous turbulent flows
around hills and other obstacles. They showed th*it wakes downwind of terrain
ban produce a 30% increase in ground-level concentrations at downwind dis-
jtances as great as 30 hill heights. They investigated dispersion over low
lls and compared theoretical results with experimental laboratory measure-
to show that hills with small slopes say have a large effect on surface
concentrations. In general, they conduct 1, terrain-induced convergence and
divergence in the flow field will dominate small-scale turbulent diffusion
in controlling plume spread. Hunt and Snyder(1978) provided further evidence
bf the increase of ground-level concentrations for three-dimensional flows
over obstacles. . i
J4.2 Enhanced Dispersion in Complex Terrain
i ! |
Field studies (e.g., Miller 1978) suggest that the routine use of the
dispersion estimates in complex terrain situations can lead to erroneous j BOTTOM OF
estimates of ground-level concentrations. Systematic errors are noteJ both i IMAGE ^~£f-
an near-field and far-field regimes. It appears that dispersion coefficients
a
Ki
often be modified toward less stable values.
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in eouplsx terrain settings, a shift of ona stability __
classification tcnuard unstable is appropriate (Hinds 1970 „ Leahey et ai.
1973, Leahey 1974, MscCready et al. 197,4, Cr«aar 1975, Start et al. 1975,
Start et al. 197^6, and Shearer et al. 1977).
During stable conditions th© effect of terrain upwind of an elevated
source is prissrily to increase th® crdsswind spread or ae&nder of th©
ijjiluae, perhaps because of eddies created in th© horizontal plan®. __Airborne__
measurements 'bF|>Iuiie" "growth" under "differing wind~direc'tlon-terrain~con-
figurations (Schierseier and Niesaeyer $970) show that upwind terrain is
important in increasing the crosswind spread, but has lesser effect in
jenhancing vertical dispersion rates. For settings in which the upwind fetch
does not include high terrain capable of creating eddy flows, one does not
pxpect to observe large crosswind iat)cnder at high elevations. Crosswind
peander is observed to be largest, othu-- things be equal, for low horizontal
Wind speeds. i j
' !
Buoyant Entrairaient Effects on Peak Plume Impact in Complex
Terrain \ >.
"Coliveetive "activity may cause buoyant" plumes to grow" rapidly'liy "entrain-
bent of Gobient air. This buoyancy- induced growth becomes less important as j
the pluse travels downwind; and ultimately, the effects of aebient tur- j
bulence dominate the pluae growth. ' j
I Over level terrain, tlie maxiaua ground- level concentration occurs at j
jdownwind distances where the vertical spread of the plume is a large fraction ;
jof the final plume elevation. At such distances the dimensions of the plusse j
>are largely the result of asbient turbulence and are largely independent of i
{the initial buoyancy- induced entrainment. For this reason, Sr-oyancy effects '•.
'on the plirae growth rates are often ignored in sir quality iapact analyses; i
Irather, use is srnde of dispersion coefficients based on experiments with I
passive, nonbtsoyant pluses [e.g., the PGT or American Society of Mechanical i
Engineers (A^IE 1968) coefficients]. : j
j For a plume traveling toward complex terrain the location of maxiisra )
jground- level iispact isay not be far downwind, and plume dimensions in the
{region of EraxiEism ispact ssay be dominated by buoyancy effects rather than by j
ambient turbulence levels. j
j The growth caused by buoyancy can be estimated on the basis of assusp-
jtions in the Briggs plume rise formulae (Briggs 1969). Specifically, Briggs j
noted from observations of rising plumes that the radius, T, is about one- j
half the plume centerline rise. This implies that plume growth is pro- i
jportional to pluae rise. Cramer (1975) incorporated this observation into j
jestimates of plume expansion by defining a virtual source distance using sn j
Initial plume dimension of AH/4.3. Pasquill (1978) suggested that the |
jgravth is about AH//lCf and that it can be incorporated by smsming the squares ;
jof buoyant growth and ambient turbulent growth. j
j Egan et al.: (1976) present exasspiss of the difference between o , the I
passive (nonbuoyant) PGT vertical dispersion coefficient, and (a ) ,sthe
buoyancy- enhanced dispersion coefficient, for a typical 1,000 megawatt j
[fossil-fuel fired power plant under various atmospheric stability conditions. •
BEGIN1 n^jg largest differences occur for stable atmospheric conditions and low wind j
LAST !-!r'lF (speeds; at a downwind distance of about 1,900 ra (about the location of final -';
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rise), sigjdficastt differences iij ground level concentration estimates.
would be expected on high terrain.
Th® potential flow model results with and without buoyancy enhancement
are ccspsred with the Widows Creek Pow«*;r Plant data. But the FMF laboratory
Jexpsriaeaits used! only neutrally buoyant plumes, so for those comparisons
nly th© no-enhancement calculations a?e appropriate.
Stable Flow Conditions
Stably stratified flow experiments in th© laboratory draonstrate that
the flow properties determining the trajectory ©£ the plums around an
jobs tad e ere sensitive to the ratio of'inertia! and buoyancy forces. Flow
jnorraal to a two-dimensional ridge unde£ stable atmospheric conditions may
pass over the ridge—if stratification .is weak and wind speed is sufficiently
high. If the teaperature inversion is 'strong and winds light, the flew may
f"block" upwind of the terrain; that is,; a plume may not have sufficient
pdnstic energy to flew over th® ridge.i These situations require special
'itreatEent of crosswind dispersion and reflection from the ground surface.
Different modeling approaches have beert taken to characterize enhanced
jhsrizontal- dispersion by pltaa® aeander during-light" wind-conditions." TtieSfe*3*
Include: (a) explicit sector averaging with a variable stability-dependent
sector width (e.g., EPA VALLEY eodsl); (b) multiple sector averaging (e.g.,
JERT ERTAQ model); and (c) statistical sector averaging using randomized wind
fields (e.g., EPA CRSTER modal). j
In flat terrain, the zero surface flux boundary condition leads to the
inage source argument (Csanady 1973), implying a doubling of ground-level
concentrations at large downwind distances. This doubling factor may be
(incorrect in many coisplex terrain situations. A rasesber of investigators
j(Briggs 1973, Cabe 1977, and Williams 1977) have suggested that in abruptly
(rising terrain Gaussian models should be used without doubling the surface
Concentrations (the 'reflection effect*). Britter, Kant and Puttock (1976)
jand Iftint, Puttock and Snyder (1979) report, on the basis of physical model
istudies of terrain objects, that the peak surface concentration is close to
the peak pluiae centerline v?lue upwind of the obstacle; doubling of con-
centrations is not observed. Egan et al. (1979) have recently developed an
plgoritha for quantitative estimates of the reflection coefficient as a
function of terrain slope, pluiae height, and downwind distance. This
algorithm gives a reflection coefficient of one for flat terrain, and zero
for the limit of direct incidence on a vertical bluff. The algorithm has
pot yet been tested with field or physical raodel experiments.
The potential flow theory described in Section 5 does not address these
stable flow incidence situations. i
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APPLICATION OF POTENTIAL FLOW THEORY
5.1 Modeling Criteria and Rationale
As a practical matter, it is neither feasible nor necessary to model
jail possible cossbinatioi's of topography and meteorological flow. For regu-
latory purposes,. th«* required modeling'approach should emphasize those cases
*ith a demonstrated potential for high ground-level concentrations.
The modeling approach described in this report addresses the develop-
aent of methods for neutral and slightly stable conditions. For neutral
afedspheric "stability conditions",""potential flow theory predicts that" flow **
close to the surface and perpendicular 'to an infinite, semicircular ridge (a
two-dimensional terrain obstacle) will accelerate and will lift over the
ridge. A typical streamline is only about one-half as high above the ridge
crest as it is above the surface upwind of the obstacle. (Streamlines for
potential flow over a cylinder are shown in Figure 18b in Section 8).
Because the flow accelerates, streamline spacing d creases and the
vertical dimensions cf a non-diffusing plume decrease by approximately a
factor of two. Thus, the ratio of plirae centerline height to vertical
dispersion coefficient a remains approximately the same as the ratio over
flat terrain. i i
But when the flow approaches a sphere under neutral flow conditions,
the comparable streamline approaches the surface much more closely, and (it
can be shown) this ratio is much smaller. This results in much larger
jround-level concentrations.
I
5.2 Gaussian Formulations in Complex Terrain
Many of the1 characteristics of flow fields in flat terrain are j:ijnifi-
cantly altered by the presence of terrain obstacles. Flow field assumptions
explicit to the application of Gaussian diffusion models include:
i i
• uniform (non-accelerating) velocity fields,
• constant plume centerline height (equal to stack height plus plume
rise) jabove a flat surface, and
* dispersion coefficients (o , ;a ) determined by ambient turbulence
levels independent of the mean flow.
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Because th^jse assumptions are not
use of a Gaussim plusae eodal requires,
features in & terrain-influenced situation. This section discusses the
modifications sjgide in order to Iceep a Saussian description of pluae disper
thought as to how to include these
>
: terrain,
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PARABOLIC EQUATION OF DIFFUSION*
Wind Speed Form of B in
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s = distance along plume center line trajectory.
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.on; note that the choices
Ms is an assumed form, not a derivat
1 • a « o » l.p reduce Equation 5-1 tj> the flat terrain Gaussian saodel.
This foraSla conceptually distinguish©
or shrinkage (decrease in o ) by flow Reformation and" (b) change of the
>Iuse centurlin4 trajectory owing to tie presence of a terrain obstacle.
Changes in th® concentration duel to the accompanying changes to the
velocity field are not explicitly accounted for in Equation 5-1 because
S&al 1
the transport velocity will result in small, inverse changes to the scaling
factor or centeriine concentration. j
The plume centeriine concentrations will also depend on the product of
the paraseters o and o . The groundx^evel concentration, on the other
land, will vary with the ratio (n/cs ) |in the exponential term. Egan (1975)
has argued thatlfor neutral flow over two-dimensional obstacles—where
a s i.o—£io% deformation has little or no effect on ground-level values;
for flows approaching a three-dimensional obstacle, however, n/a < 1.0,
leading to ground-level concentrationsilarger that those in analogous flat
terrain situations. j
In the discussion in Section 5.4, the quantity nz, the height of the
ptume «enterline above the-terra±n,~lsTeva:luated"by-a~partiTOl^r two^" or'
three-dimensional stream function (seeiSection 5.4.3) and the values of
a ,a in Equation 5-1 are defined (see'Equations 5-56, 5-57; Section 5.5) in
term! of particular line integrals. Tfeus, the method adopted is essentially
a modified Gaussian dispersion model.
5.3 Modeling Approach, Applicability, and Limitations
i
This technique applies potential flow theory to a Gaussian point source
model. It permits explicit evaluationjof the terrain-induced kinematic
constraints andjtrajectory variations.! In adopting the present technique,
an attempt has been made to broaden its applicability. Approximations have
been developed to extend tho neutral formulation to slightly stable cases
and to allow for terrain obstacles with crosswind shapes intermediate between
those of a. cylinder and a sphere. These approximations are based both on
theoretical and Isemi-erapirical grounds! As presented in the folloifing
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sections, the approach may be suitable
meteorological situations:
BEGIN
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OF TEXT E
for the following topographic and
• isolated, single terrain obstacles of arbitrary height, with
approximately circular cross-rsection in the downwind direction and
arbitrary aspect ratio in the crosswind direction; and
I j
9 neutral to slightly stable stratifications.
I i
At the outset, the limitations ofJthe present model should be clearly
stressed. Thes^ limitations arise maialy from physical effects that are not
described by thd pot«"tic.l flow model.j The following cases are excluded:
I
luiae
flow cases, where plumes are constrained to flow around
ratheij than over the obstacle;
cases (dominated by surface boundary layer effects;
S 3/8"
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..
!
i
1
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, -,
I__ • unstable cases (e.g., convec
9 cases 'dominated by wake effei
i
Specific recommendations based on thesi
Section 3. '
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TYPING GUIDE SHEET
CENTER
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Sipensional difgysivities (length squa:
between these d^ffusivities and the PG'
1970) is explored in Section 5.5.
Substituting the continuity equat
«»• on oS
into Equation 5-43 yields:
U(S) 3s" 1 " 3? 9n" = D1(S)
Solutions to Equation 5-6 are sought tl
XI f f •% 1 1»*^ - _ _._._^ r .
».s,njiyj - , j exp 1 -
•ed/unit time}. The relationship
r dispersion coeff -,ients (Turner
ion:
0 (5-5)—
2 , 2 ,
i-| * D2(s) ^- (5-6)
lat are Gaussian in form:
fjCs) n2 - f2 (s) y2] (5-7)
and also satisfy the additional constraint that the mass flux across the ^
pfeffiS is conStarit, i'.e.r
1 +0> +OD
f f u(s) x
9-1 /R" i 1
This constraint, requires that:
g(s) = IT u(s) /
— — — ~ ^^ — j&-=*~
dndy =1.0 (5-8)
1/2
ifjCs) f2(s)] (5-9)
Substituting Equation 5-7 into 5-6 yields:
fjCs) = [u(s)]2/
\
f2(s) = l/[4T(s);
where :
s
4>(s) =| D..(s
0
and
s
T(s) = | [D20
o
Kf
|
[4 4>(s)] (5-10a)
(5-10b)
;') u(s')ds' (5-11)
;')/u(s')]ds' (5-12)
^
5 3/8" | ;:;;:;:;• Vx;:;
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|
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j
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LINE OF CENTER TOP OF
L-IINt VJr llf ArT
TFXT OF PAGE _>IWAbE <•
'"1 XP^AOCA
HERE as
DROPPED
: HEAD;
i BEGIN
SECTIONS
HERE ft
Jy_ Equation S-9&
g(s) » 4ir[i(>(s) T
,
[n more familiar terms, the dispersion
fee diffusion equation solution, a anc
•» n
fjCO = i/t;
i
f2(s) = i/[:
or
a 2 = I/ [2 f.(s)]
n i
.- . —
s) ]1/2 (5-13)
coefficients in the Gaussian form of
o , are given by: —
a 2] (5-14a)
ay2] (5-14b)
= 2* (s)/[u(s)]2 (5-15)
a 2 = I/ [2 f (3)] = 2T(s) (5-16)
7 *
1
TTie arguments for three dimensions proceed imzch the same as in the
previous section!. 'F-e appropriate non-
:-- t
9-1/8"
t
5-
J.
^
!
BEGIN
LAST LINE
U(S) -jjA- + n -T— -r^— = DI (s]
s n n
dimensional diffusion equation is:
2 , 2 ,
>
«'
'
i
!
1
]
1
i-Ky + D (s) ?-*j (5-17)
3n 3y
tfhere the coordinate system is now with respect to (s,n,y). Here, y is the
angular, azimuthal coordinate from the ;axis of symmetry along the flow with:
y - YR(s) (5-18)
1
*here R(s) is the distance from the axis of symmetry of the obstacle to the
jlume centarline, and y is the cross-wind distance from the plume center-
Liae. The continuity equation in this coordinate system becomes:
i 3v 1 d ,
I "alT UsT dT '
u(s)R(s)] = 0 (5-19)
ITie trial solutipn sought is of the form:
i
X (s,n,y) - g(s) exp[
subject to the constraint:
1
i2n +<»
I j u(s) x'(s,n,Y)
f '
' O —
Cf- TEXT S5!~
jCs) n2 -f2(s)Y2] (5-20)
1
r
f
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LINEO
TEXT
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, TYPING GUIDE SHEET
,* CENTER
OF PAGE ^
&ihs,itutl(s) R(s)]
o 2 = 2 [R(s)]2 T(s)
(5-26)
(5-27) i
5.4.3 Role of Potential Flow Theory
Values of the dispersion coefficients (Equations 5-15, 5-16, 5-26,
'and 5-27) are determined at a particular distance, s, along the pluae center-!
! line by line integrals (such as Equations 5-23 and 5-24) which are functions j
jof the velocity along the plume centerline streamline, u(s), and (in the j
ithree-diaensional case) by the distance, R(s), frosa the axis of syiametry. |
jIn the potential flow approach adopted, s, u(s), and R(s) are determined for j
ja particular terrain shape, by a stream function, $. That is, the variation ;
'of velocity along the pluse centerline and the distance of the plume center- i
[line froa the surface (defining the plume trajectory) are evaluated ai>ily- i
tically using the stresaline equation. I
i It is assumed that the plunie centerline follows tlie stre^line through j
jthe point source at the effective source height, H . Along a streamline, j
jthe value of tha streum function is constant, and the particular value of
'the pluzse centerline streas function is denoted by ij> . The va'ue of
(2) blight
idetermined by three parameters: (1) effective source height H ;
lof the obstacle, a; and (3) distance along the x-axis frosa the base of the
isource to the center of the obstacle, X . The streaaline associated with a
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•VW*.-x»«*- - -t"**z?^~?^
FIRST
LINE OF
TEXT
HERE s^grticular stre^a function, *, is determined by the shape and dmensioa of-
the terrain obstacle. The streamline taken to be the pluae ceaterline is:
CENTER
OF
DROPPED
HEAD;
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SECTIONS
HERE ^Skia
*(x,z)
(5-28)
is gives the height of the pluse centerline above the surface at any
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i—3Js«-¥el0©irty—£i«fl4,-j-£®03— is-^eteOTtsed-fey^t&e-atifem-
function, i|/, such that the along-streaeline velocity, u(s), is:
f3*!
(If)
(5-29)
The cases examined in subsequent sections include flow ever a two-
dimensional ridge and over a three-dimensional axisysaetric hill. In the
two-dimensional case, the stream function (Mlns-Thosson 1960, p. 156) is:
=U
l; -
where U^ is the magnitude of the uniform wind velocity far upstream of the
source. The value of the stream function through the source is then:
U-Hs
H
(5-31)
and the equatioa of the pluiae centerline is:
>u z 1 -
>S2D
(5-32)
> I
JFor exazsple, the height of the plume centerline, z , at x = 0 (over
crest of the ridge) is given by solving the quadratic equation:
(5-33)
I !
Analogous equations are valid in three-dijaensions for flow over a
hemispherical hill. The stream function in this case (f4ilne-Thcason I960,
p. 464) is: ,
BEGIN ;
LAST'JNE' ,
OF TEXT ttr-
0.5 UZ
Z2,s/;
(5-34)
3/8"
.]
tl
J iiLL 23
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LINt OF
TFYT
* C.A I
HERE jsf
DROPPED
u» c A rv
r.CMU,
BEGIN
The value of
SECTIONS!
HERE nf^
'
1
H
i
1
--,,-. »7^,-,f,t-.- r--* ,.-" --,> ,.-v- -i; *^,, T i-^r--rvTT>f*T'.-,'-<"-i ^~^«--=T-r-,^_^a'-^^"-7^-fVc-7/'^^p.;^rv ^?^
CENTER ' TOP OF :|
OF PAGE . ^1WAGE 1
th£ stream function throukh
j
i
1
?
3D
C s* s} "
" S
2
and the equatiea ©f the pluae cessterliH®
22
«•
1
1-
**
•
\
(2 2^ 3/2
X
H 2
s "s
,s-7 «r,r^ a
a source at (2 , H ) is:
S S
a3
(X 2 + H 2) 3/2
s s J
is:
a3 1
" ** ' ' ** '? /"& v3""<*uj
rw A . u A ^/-£
(X5 * HS } J
5.4.4 Reduction of Solution to Fiat Terrain Case
To clarify
situation of
developed in
'•"Soyr- -*•
tion reduces
the discussion ia tine previous sections, consider the
uniform flow with velocity I
^Sections -5.4.1, _5.4...?i._ai»4. !
"to
J^ over flat terrain. "Hie equations
j^4,3 are OTPiicsfole, ,asd_.tlie solu.~«M..
a recogisizsbl© for®. '•
The starting poimt is the appropriate stream function, $, which in this
case Oiilue-Hioason 1960) is:
9-1
Note that there
j the x-axis.
3
t
j
1
i
|
'8"
I
4»(z) = Uc
1
j
D z (5-37)
is no dependence OB x, and streamlines are thus parallel to
Th© value of the
!
and, therefore,
!
| 'or
1
t
t
i
\
I
BEGIN
LAST LINE
This is also
so that R(s)
$
stream function through the source, $ 9 is
CHS) = ^
the equation of the pl<
*(z) =
iim?
*,
z * H;
f
HS (5-38)
3 center line is:
,(HS) (5-39a)
(5-39b)
equal to the distance- from the x-axis to the plume centerline,
= t
I .
I
•s
|
j
\
\
-
>
Substituting Equation S-A7 into Equation 5-29, the velocity along the >
pluEe trajectory is constant and equal to:
OF TEXT **>-
5 3/B-
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EPA-287 (Gin.)
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!
N^ _
i
u(s)
i
! --
= constj «
i
.•.•.-.•-•.•.• L J • •
_ 1^24
PAGE Nm
= U^ (5-40)
—
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IbtR i
i
}
i
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l
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solution in tie fora of Equation 5-20 can now b© evaluated. In flat te:
th® aiossg-streasiline coordinate, s, isj just the downwind distance from the-
source, x, ami the noy®si to the streamline, n, is just the vertical distance
fro® th® plume eenterline, z. The line integrals $, T, (Equations S-23 sad
5-24) reduce toi
TOP OF
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'AREA
DL(x) H
U x
-98.
(S-
I T(x) - D2(x)
!
and f., f2, and,g are by substitution:'
j V0 - U./[4D1(x)xJ
I f2(x) - UJIs2/[4p2(x)x]
cg(x) -* -~4inr
(5-42)
(5-43)
(5-44)
----- !•
Noting that the crosswind distance froas plume centerline, y, is given by:
y = Hs
and substituting Equations 5-43 through 5-46 into Equation 5-20:
i
!
1
x'
4»
,1/2
(S-46)
(5-47)
This is the solution given by Sutton (1953) for a continuous point source.
The familiar Gaussian dispersion coefficients o ,o (see Equations 5-26 and
5-27) becesse: I I y z
BEGIN
LAST LINE
OF TEXT »
2D2(x)x/U
2D1(x)x/U
(5-48)
(5-49)
5.4.51 Uraitations
Although iaportant features of the terrain-influenced flow field are
reproduced by th© potential flow theory approach, inherent limitation
resain: '
-— I
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HEPE E
TYPING GUIDE SHEET
CENTER
OF PAGE
DROPPED
HEAD.
BEGIN
SFC TICK'S
HEBE p
• tb« p|eser.se of a realistic surface boundary leyer is ignored; .
• relevant physical phenomenon such as velocity shear, radiative
heatipg, gad flow separation are esitted; and
• the theoretical aodel requires that the pluae remain "thin"
coshered to its height above the terrain. For short stacks this
criterion is often violated oear the hill crest.
TOP OF
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'AREA
[Strictly speaking, the first two of these limitations also restrict the
theoretical validity of a conventional Gaussian solution in flat terrain
situations (Pasquill 197S), unless the set of dispersion coefficients assumed!
specifically account for these effects.] It is prudent to apply the poten-
tial flow theory approach only to the windward side of obstacles and not to
situations dominated by lee wake or separation effects not treated in the
Eodel. In many; of the results to be presented, the cosputed plume dimension
will violate tho restriction to "thin plumes", but it is not unreasonable to
•push1 the theoretical formulation in these cases (Hunt, Puttock, and Snyder I
1979). j j
BEGIN
LAST LiNE
OF TEXT &
PGT-Scslisg ^sf Dispersion Coefficients
I 1
Evaluating the terrain-influenced dispersion coefficients (Equations 5-26
and 5-27) with this femulation requires specifying the crosswind and the
normal diffusivities, D- and D,. To compare sodel calculations with
analogous flat terrain situatiSns, an approximation scheme was implemented,
using the PGT dispersion coefficients (Turner 1970) as a calibrating scale.
Qualitatively, the diffusivity at a given distance froa the source along the j
plume centerlin© stre^line is taken as that for the same transit time in j
flat terrain. The consequence of this assumption is that nodel calculations |
of dispersion coefficients reduce to flat terrain values in the limits of
large downwind distances or saall obstacles.
Newer and possibly superior formulations of dispersion coefficients
have been suggested (e.g., Pasquill 1978 and Irwin 1979), but have not yet
been adopted in EPA regulatory sodels.! Therefore, for ease of ccsparison,
the familiar PGT values have been used in the calculations discussed in this
report. Other dispersion coefficient systems can be easily incorporated
within the basic sethodology used here.
Substituting Equations 5-23 and 5-24 into Equations 5-26 and 5-27
gives explicit expressions for a and c . (From here on, the dispersion
coefficient in the norsal direction is denoted as a .) At a distance, s,
froa the source along the streamline, the dispersion coefficients are given
by:
a,! Cs)
z
2 D. (s) s i
1 / 'FTCs') u(s')ds-
R (s) o
(5-50)
_ 1 ___ I ______
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FIRST
LINE OF
TEXT
HERE 2«
DROPPED
HEAD;
BEGIN
SECTIONS
HERE *
TYPING GUIDE SHFET
— °As) » 2R2fs) D
where D^, oT are typical mean
These values are assumed
— t
. [ —
i Vs>
1
CENTER
OF PAGE ^
rS 2
2(s) / ds'/[R (s1) u(s')J (5-S£f
o
dif£usiv|lty values at distance s.
to be gissren by the PGT values (a -, a -j :
7
« oz£ (s)/2t • (S-52)
- oy2! (s)/2t (5-53)
where s is the integrated path length ^long the plume trajectory and t is
the advection time:
I
1
i
i s
I
^^ ^ P , /7 .
! t
i
[
s
= / ds« (S-54)
° 1
J_ ^
= 7 ^L. (5-55)
' U (s • )
the final form of the dispersion coefficients:
s
yf
[I R2
o
t u
R2(s)
t
(s1)
i
2{s)
rs
r
u(s')ds'~
R2(s)
ds'
7
R (s«) u(s')
(5-56)
(5- 57)
The bracketed qfiantities approach 1 asi streaioline deformation becomes
negligible, and|0 ,a reduce to their flat terrain values.
Figures 1 and ^illustrate the plume spread statistics a and o ,
respectively, for neutral flow over a circular ridge. The riSge is f.O km
high; the point^source, 200 ra high, is! 4.5 kia from the ridge center.
Calculations ar® shown for diffusivities scalx^I to reproduce the- PGT neutral
stability class[values for a and o ip the flat case. This illustrates
that only the vertical dimensions of the plume (as characterized by a )
differ from flat terrain values in floV over tv/o-diiaensional obstacles. (In
each of Figuresjl through 4, the center of the ridge is indicated by a short
vertical bar at'the downwind distance 4.5 km; the horizontal bar extending
frost 3.5 km to 5.5 km denotes the windward-leeward extent of the ridge.)
1 i
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I
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flaa&i&fflaaiatfiiaai&aMi
,xl&e*at*£ U^t^£££Afe^.*a
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HERE x4-
*v^.^,.,,--,,,,,™,,^^^^,.^^
WING GUIDE SHEET * ' , ' ' ' ' ' ' "" ' "'•-.<;... '' :' '' ' '"••'•''$
CENTER ' , TOP OF -•.;;;
OK PAGE "• "^}M^G^ ' :
AREA
DROPPED
HEAD, fl-
BFG1N '
SECTIO'-J!
Computed Stability Ctass 0 (tidga)
— — (2) PGT Stabiittv Class D (fl»t)
3 4 5 7 10 20
Downwind Distance from Source (km)
BEfi ,\ I Figure 1. Horizontal dispersion coefficients for neutral flow
LASfI 8 over a circular ridge.
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. I
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i
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w^^^^^ssw^Tnfsywj^^^^iTO-w^y^^ifi • T"=rrr«,-;i>-
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1
.,^_?^,r^^,.^,^,v,,^;,., ,_ ,,_,^_,.-r., ,;. . .i.j_., ,_, ,.... -;^- •, .• .-.
CENTER ; ' TOPOF
OF PAGE ^IMAGE
...... __,.__ . .. J<|S*^ApCA
BEGIN
SECTIOi!
HERE !
BEGIN
LAST L,
OF TEX
1000
•§ 100
10
Computed Stability Class 0 (ridge)
—.__ (2) PGT StatxJity Class D (Rat)
Crest
I
I
J_
3 4 5 7 10 20
Downv/ind Distance from Sourca (km)
Figure 2.
Vertical dispersioh coefficients for neutral flow
over a circular ridge.
(Cin.)
;ii< 29 Ji:
PAGE ND^UER
rTOW OF
\GE AREA,
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dt;\'S;oN
.ft 1 ABLES
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-f i' i 'i i" '; r- ' ' i'^i nr r ...... 7' rtirTi ii n r fi -ri •• ' i -
-------
^r
[•; f^r*-!^r~rrt^ arrV*~ f^Sf^SfV^Sfr^f^f
FIRST
LINE CF.
TEXT
TYPING GUIDE SHFET
• CENTER
OF PAGE
J~
HERE S&j-__
DROPPED. l._
HEAD)
BEGIN
SF.CTU
HERE ;
i
i
TOP OF
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AREA
1000
100
10
(1) Computed Stability Class D IhiEl)
(21 PGT Stability Class D (flat)
Crest
I
I
I
3457 10 20
Downwind Distance from Source (km)
BEG!!.'
LAST I.
OF TE)
Figure 3.
Horizontal dispersion coefficients for neutral flow
over a hemispherical hill.
EPA-Z-37 iCm.j
{•5-76}
iiiii 30 ili
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..^
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l!C?^^°"^r5^^W?'*^*J*^^
.FIRST ;Vvr .'-^'TYPING GUIDE SHEET ' '"•'-."'/• ' : :;';"-\"V <;'':-"'-;'' 'V - ;;'/ '. '' -^v'.' '••' '- ' p'v ;"••'••'
- .- -;' , . •<,-.-'. CENTER -...•• '. -- . -.-. / .-,.- >.-..-,-• TOP OF- •
OF PAGE - -. ^IMAGE
LINE OF
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BEGIN f
SECTIOr]
HERE •!
BFGIW
LAST L!
OF TEXT
1000
3 4 5 7 10 20
Downwind Distance from Source (km)
Figure 4.
f
Vertical dispersion coefficients for neutral flow
over a hemispherical hill.
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DROPPED
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SECTIONS
HERE
As streamlines diverge to the leeward and~windward side of the hill, o
increases. Oveif the ridg®, vertical c|jaipression of the streamlines leads to
a drastic decrease in o . Over the ridge crest the vertical plume thickness
Ls about equal io the height of the pl^me center!ine above the surface, n .
This marginally I obeys the thin plume approximation. s
Retaining the saiae source-obstacle geometry, but changing the terrain
e&stacle type from a circular ridge to a hemispherical hill, Figures 3 and->t~
iplay-tha-th-Fdo-disefis^iMki-ftetttrai-f^^
tions 5-26 and -f-27. In this case, both o and o are affected by the
potential flow field, as evidenced by a marked increase in 0 over the hill
top. Comparing |az values in Figures 2Jand 4 at x - 4.5 km reveals that the
vertical thickness of the plume is mor£ severely restricted in three-dimen-
sional flow than two-dimensional flow.) In fact, as indicated in Figure 4,
downwind of the(hill o never recovers|from the deformation over ths hill
top. At the crest, thl quantity a /n j is approximately 2, clearly violating
the thin plume criterion. The pote'nti^l flow theory would not, strictly, be
applicable in this situation; however,iat least to the hill crest, useful
estimates should be obtained. Downwind of the crest, a is affected by two
factors that tend to increase its value over that predicted by potential
:E4pw_calculatio4s-alcne2 These-are^ {I>rincrease4-diffysi«a acr0ss-st*eaas*s>
lines because of smaller streamline spacing, and (2) terrain separation
phenomena, which enhance turbulent mixing over that given by ambient tur-
bulence rates. 'Because of these effects, the model should only be applied
to the upwind side of terrain obstacles.
Figure S^shows the evolution of the velocity speed up factor (the ratio
of the source streamline velocity in the presence of the hill to that in the
absence of the hill) for potential flows over the circular ridge and over
the hemispherical hill. Both streamline patterns upwind and downwind of the
obstacle crests are symmetric, so the speed-up factor has beer plotted only
from source to
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SEO
HE.
TYPING GUIDE SHEET
CI-WER
01" PAGE
m 1.5 -
a
3
1.0 2.0 3-0 4.0
Downwind Distance from Sourco (km)
W^M'WW'Wfl
TOP OF'
Figure Sa. Velocity speed up factors for neutral flow over a
circular vidge.
Sphere
(3D)
1.0
2.0 3.0
Downwind Distance from Sourn (km)
4.0
Velocity speed up factors for neutral flow over a
hemispherical hi11.
'.1_J 33
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NEUTRL FLOW
6.1 Ground-Leve>l and Centerline Concentrations for Neutral Flow
BEGIN
LAST LINE
TOPOF
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AREA
The terraiii-influenced dispersion estimates developed for neutral two-
and three-dimensional flow cases were used to compute the plume centerline an normalized by |
Uraa2/Q (Equatiori 5-4a). Note that results are not independent of obstacle j
lieight a. Introduction of the PGT calibration of diffusivities (Section 5.5)]
which are not linear in the length scale, require that all results are
specific for th£ particular obstacle height cited.
At plume centerline, the concentrations for the three-dimensional case,
as well as for the two-dimensional case (not shown) are not appreciably
different from tjhe flat-terrain case. jBut they are strikingly different at
ground level; compare curve 3, the ground-level concentration in the flat-
terrain case, with curves 4 and 5, thejground-level concentrations in the
three-dimensional and two-dimensional cases.
For the two-dimensional ridge the magnitude of the maximum ground-level
concentration is about equal to the maximum in flat terrain, but the maximum
occurs at about ;ridge top (4.5 km downwind from the source), whereas in the
flat terrain case the maximum occurs about 9 km downwind.
For the th^ee-diiaensional case the maximum ground-level, concentration is
roughly 10 times larger than in the flat terrain case, and occurs at the
leading edge of(the hemispherical hilli the concentrations remain very high
as the plume parses over the hill. j
The ground-level concentrations for the two-dimensional flow are similar
to those for th^ flat case because of flow acceleration effects: the reduc-
tion of a in the vicinity of the two-dimensional ridge crest is largely
OF TEXT Compensated by £ reduction of about equal magnitude in the closeness of
i" 1——' \ • j~- ' •
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HERS:
. TYPING GUIDE SHEET
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OF PAGE
TOP Orc
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'AREA
DROP?!
HEAD]
BEGIN;
SECTl)
HERE !
BrGI
LAS: a
OF'I
100
10
0.1
Hs =0.2
a= 1 km
cl = centerline; gl = ground level
a = hill height
(2) XsdMll) 3-D
(3) $^0W
(4) ^(hill) 3-D
(5)
, (hill) 2-D
10
20
109
ind Distance from Souna (X = -j)
Figure 6. Centerline and ground-level concentrations for cases
shown in Figures 1 through 4 (neutral flow).
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TEXT
HERE
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roach of the^plisae to the ridge. Ik three-dimensional flow over the —
[hemispherical hill, however, the pluse approaches such closer to the hill top
~l
DaOrx>
HEAD
BEG.'N
SECT i
HEP.E
ED
8111*
ground-level concentrations can substantially increase.
Dependence on Stack Height and Position
gr~ lltc ground-level concentrations, shown in Figure^6^ as ^_func_tipi^of j
36wiwiiia~diytMce~f6rn&e~hli^ ridge, were j
jcoaputed for a particular geometry; that is, hill (or ridge) height of 1 ka, i
jstack height =0.2 [hill (ridgo) height], and stack located 4.5 km upwind of !
the hill (ridge). For each choice of geoaetry, the maxisaim ground-level |
iconcentration occurs at a unique location downwind. Calculations of raaxisua ,
ground-level concentration, as well as the position of the maximua, were Bade
ifor various gcabinaticas of stack height, H , and distance betwc ,n stack and
hill center X., both normalized by hill heifht a. Figures 7 and 8 illustratej
;the regions in paraseter space in which calculations were performed for the i
jtwo- and three-disensional cases, respectively. For exaaple, in the case of j
'the hemispherical hill (Figure 8), assuaing a hill height of 0.5 km and a '•
diasiisionless effective stack height of H = 0.6t calculations were done __j
Varying the cimensionless distance between stact and hill center, X , froa j
'values of 10 to 100. Results of this series of nodel calculations are shown i
in Figures 9 and 10 for the cylindrical ridge and in Figures 11 and 12 for j
:the spherical hill, respectively. j
j Figure 9 shows that the maximum ground-level concentrations are not I
affected very ssich by the cylindrical ridge, especially for stack heights i
saaller than O.S tises the ridge height. (In each instance, the dashed line
is the value of the concentration for flat terrain.) For a nondisensional ;
stack height of 0.8, and for stacks positioned between about 20 and 100 times;
!the ridge height upwind of the ridge, the eaxisum ground-level concentration ;
increases sosewhat above the value corresponding to flat terrain. The
position of the saxiEua shifts from leewards of the ridge crest to the crest,
as shown in Figure 10, as X goes froa 20 to 100. j
A spherical hill exert! a isuch stronger influence on ground-level concen-
trations than does a cylindrical ridge. For short stacks not far froa the
hill, the laaifitana occurs on the crest of the hill and can be considerably
greater than in the flat terrain case (see Figures 11 and 12). Farther froa
the hill, the naxisaag ground-level concentration occurs before the pluzae
'reaches the hill. This limiting behavior is shown in Figure 11, where, for
:the smaller stack heights, all the aaximua ground-level concentrations are
constant for large X . The hill exerts negligible effect on the maxisum
ground-level concentration when the stack is a distance of approximately 10
.hill heights or sore away from the hill center.
! For the higher stacks, the behavior is considerably different. Figure ll
shows that when the taller stacks are fairly close to the hill, the maxims
ground-level concentration is insensitive to stack position. When the stack
is positioned farther froa the hill, however, the concentration increases by
as such as an order of aagnitude before decreasing to its value for flat
terrain. This behavior can be understood by looking at the variation in
position of the ground-level isaxiEais, as shown in Figure 12. For tall stacks
/relatively close to the hill, the saxiEua occurs far downwind of the hill.
However, when the stack is farther froa the hill, the maxims! shifts to the
OF
1 ON
r'-ES
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TEXT
HERE Bs
CENTER
OF DAGE
- TOP OF
AREA
LAS i LIFN
OF TEXT
Figure 7. Domain of calculations performed for a two-dimensional
cylindrical ridge and neutral flow.
37
IT ; ruf }C
AGE AREA
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ME,',S!CN
)R TABLES
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JATiOfJS
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-3
l~*"
I1CO40
1
60
40
*%rt
20
io
- —
-
rp ""
-l|
IN
\i
j
«
1
i
•
B
I
31 :
1S1 9
JJ8 i
L:
I
f
j! j.._
l._..-_.._ 1
-
iii11
0.2 0.4
1
»„_ .J
Legend
Valuet oft (Hill Hsight)
"•"—'""••""• «0.g *m
— — — - 1.0 km
«ra» «• • ?.g ftW
«•> . . «.»> "20 km
l, / | i l t i l i
-T
A^^-
«^~^_
i
i
I
0.6 O.S 1.0 1.2 1.4 1.6
A fi4a
1 & 1 • 1 "391 1 Mmifl!Rn>u«tlAnj!il &h»4r ltej^5.»
Figure 8, Domain of calculations performed for & three-dimensional j
hemispherical hill and neutral flow. wj__
,'
i
.4
i
I
I
1
4
1
'-I
Tl
-T! "^ •''
o 3-
rn _:
f
-1
i
1
^
" J
'j
1
,1
-J
•"M
^
-j
^t
>j
v -1
~" " % c^i
ri > T>2
>' 5tJ Ol
-------
H
n
We 0*
'.EXT ,'
Hfc'RP 2
D^OPf'tO,
HcAP1,
BtGif;
SCCTiGN-
BEGIN _
LAST L|
OF Tt)I
10.0
o
1.0
1
o
10-
I
i
10-
—•—Flat Terrain
Ridge Height a = 0.5 km
10
20
DsstSRsss Hell to Soui^g
Hg°0.2
H s - 0.4
H$-0!8
100
Figure 9.
ground- level concentrations for a cylindrical
ridge and various combinations of stack height and
position. >
TOP OP
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AREA
(-"~STT .""•*• * c".r
uv •' i t win L-'1"
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TEXT!
HERE;
HEAD;
SECX
ioao
<*
F.
3
G
10.0
1.0
——Flat Terrain
Ridgo Height a = 0.5 km
Hf - 0.8
H
0.4
/s
H
0.2
H s = 0.1
10
20
100
— E*>"
TOP Of
IMAG£
AREA
0 Tf
Figure 10.
Distsnca Hill to SGWCB fs^ » iSj/a)
Position of maximim ground-level concentration for a
cylindrical ridge and various combinations of stack
height and position. * -
__- -_ , ^_ 40 rrrr -=:.- -=.. -_- -_=
W3TTOM (M- i
IMAGE ARfcA; |
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PORTABLES
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UISE-C
TEXT •
HERE j
DROPPED
SEGIW
LAST LIN
CF TEXT
10.0
o
^
Dest«nce Kin to Sourea (
x,,/8)
Figure 11.
Maximum ground-level concentrations for a spherical
hill and various combinations of stack height and
position. 41
~
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MFPP tet
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SEGi
SECT
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OF PAGE
100.0
x
•
o
•5
§
to.o _
TOP OF
IMAGE
"ARffA
Distsnca Hill to Source (x\ •* Kg/a)
BEG In
LAST'
OF It
Figure 12.
Position of maximum ground-level concentration for a
spherical hill and various combinations of stack height
and position.
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•crest of the hi|l. A notable feature <
maximum concentration occurs at the hi
as 100 hill heights from the hill cent
0.3 Effect of Obstacle Size
i
>f the taller stacks is that the
LI crest, even for stacks as far away
sr.
TOP OF
^IMAGE
AREA
In one setiof calculations the obstacle size was changed with all other—
(4.5 km) upwindlof the spherical hill, and computations were made for hills
varying between 1500 m and 2,000 m in height. Variations of fflsxisura ground-
level concentration are shown in Figure 13. For these hill heights greater
than the stack height, the maximum ground-level concentration increases
rapidly. The position at which this maximum ground-level concentration
occurs is shown!in Figure 14.
-4
BEGIN
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;: .TYPING GUIDE SHEET
'
CENTER
10
v
a
J L
0.5 1.0 1.5 2.0
b',61 Height a (km)
Figure 13. Maxisum ground-level concentration as a function
of hill height.
1 20<
i "5
I -10
a
) tf
* f
,
«
i
0.5 1.0 1.5 2.0
HSH Height a (km)
Figure 14.
Position (distance from hill crest) of maximum
ground-level concentration as a function of hill
height.
44
CPA-237 (Cm.)
!4-76!
" ' ' . i''J ' .'f. ,'.v :' '.' ' ; •- -
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OK PAGE
OF
SECTION 7
COMPAR|SON KITH LABORATORY EXPERIMENTS—NEUTRAL FLOW OVER
A SINGLE MOUND
BEGIN
LAST LINE
OF TEXT S
7.1 Background!
Model computations were compared with experiments conducted at the EPA
Fluid Modeling facility (FMF) (Hunt etial. 1978) to study the flow and
diffusion of pollutants in idealized cbinplex terrain under neutral conditions
(and also stably stratified conditionsr-see Section 9). The primary purpose
of these neutral and stably stratified! flow experiments was to understand the
effects of stability on,.the flow structure over_a bell-shaped _hill_. TheJhiJ.1
fls~placed hear4the entrance "to the~wind"turnei~whefei ~the~flow~~was ess.en- s j
tially uniform and non-turbulent except for a thin boundary layer small j
compared with the hill height. (The thickness of this boundary layer in the
wind tunnel matched that observed over; the baseplate in the towing tank, so
that the approach flow structures in bpth the tank and the tunnel were
essentially identical except for the stability—see Section 9.) In later
experiments (Snyder and Britter 1979) the hill was placed in a simulated
atmospheric boundary layer, but the earlier experiments are more suitable for
the model coaparisons because (a) the potential flow model is expected to
more accurately.predict the behavior of a uniform, non-turbulent air stream
and (b) the "thin plume" assumptions ate more closely met. Calculations werej
performed using the complex terrain model for the characteristic dimensions
used in the EPA experiments (on the centimeter scale). Therefore, it was
first necessary}f determine the appropriate dispersion estimates on the
laboratory scale i.i the absence of terrain features, so that the line
integrals
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•; BEGIN
FIRST
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'TEXT
HERE js
TYPING GUIDE SHEET
CENTER
OF PAGE
'Stas fitted to
DROPPED
HEAD;
BEGIN
SECTIONS
HERE Sal1®1"* usetl *n the'model.
sigmas,, a lineal1 functional form, a
data. The measured
(1977) as experiments HHSWTN.398, .401
the three downwind distances 39.2, 84.
shown in Figures
Snyder and MarsS
iata are catalogued by Snyder and Mar-sli
and .403 for the vertical profiles at
7, and 130.2 cm. These data points are
15a, 15b and 15c, along with the curves given explicitly by
as best Gaussian fits to the data points. Using these
i + bx, was fitted to the three points_
(y
According~ko the Gaussian plume equation, at the plume centerline
0, z « H) ^he normalized mass flux parameter & defined by:
U
(7-2)
In
is equal to uni^y.
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FIRST
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TEXT '
.Hf-RE-iJ
TYPING GUIDE SHEET
DRCJ
HE/4
BEQ
SEC
HEF
200
180
160
140
120
100
80
60
40
20
CENTER;.,,
OF PAGEV
JL
I
* Experimant
© Computed Using o
s Computed Using o'
— Best Fit Curva (Snyder
and Marsh)
I
I
TOP OF
IMAGE
AREA
.001 .005 .01 .05 .1
.5 1
x
5 10
50 100 500 1000
Source: Snydar and Marsh 1977
BEG; §
LAS; 2
OF1 S
Figure 15a. Vertical concentration profile 39.2 cm downwind of a
12.5 cm stack in flat terrain.
I J „
EPA-287 (Cin.t
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iii 47 £|v
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'. BEGIN ' '• '""'•' • •>* '• '•"••-'•-""• ' ':
FIRST • TYPING GUIDE SHEET
L'NE OF . • '
TEXT
HERE £s|"- | - -
'" • '•- '" ' V.;**33^;1 .••• ; , • , -'•. ' -•••"-• • • ;- * -"^"^
-' CRNTER >
Of- PAGE
1
JO? OF
x IMAGE
J.y|
"'ii
-<
3
j
j
?
HEAl
S£C1
HERS
180
160
140
120
• 100
N
8°
60
40
20
I
I
A Experiment
9 Computed Using a
s Computed Using a'
• Best Fit Curve (Snyder
and Marsh)
I
.001 .005 .01
.05 .1
.51
5 10
50 100 5OO 1000
BF.G
LAS
Source: Snyder and Marsh 1977
Figure 15b.
Vertical concentration profile 84.7 cm downwind of a
12.5 cm stack in flat terrain.
48
EPA-287 (Cm.)
(4-76)
TTOM OF
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ITilDE
^BvSiON
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ID I'JJJS-
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LINE OF
TEXT
UROFF]
HE AC1!
BiGlf
TYPSNG GUiDE SHF.T
BEG: -
LAS' 2
CENTER
, OF PAGE
TOP OF
.IMAGE
Zl.
AKEA
200
180
160
140
120
N
80
60
40
20
I
I
Experiment
Computed Using a
Computed Using o'
Best Fit Curva (Snydar
and Marsh)
I
I
.001 .005 .01 .05 .1
Source: Snyder and Marsh 1977
.5 1
5 10 50 100 500 1000
Figure 15c.
Vertical concentration profile 130.2 cm downwind of a
12.5 cm stack in flat terrain.
OF *:
__. J
OP TABl ZS
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j
FIRST " TYPING GUIDE SHEET
LINT 0;r
TEXT
HEKE asjiiiteaded (since) the observed si
ToEserved concentrations isust be
potential flow saodel must coae
DSOrFL.. terrain obstacle is present.
HEAD |
REG.u 75 Comparison ^ Presence of
?r' . ' i'jN^ j
HRF Ssk
Mhea a *!>olvnaraial hill' w
CENTER
OF MGfc ^
gmas are input to the calculation, the
reproduced). The crucial test of the
froa comparison with experiments in w^ich &
\
i
Terrain Obstacle
1
as imtredMced in the wind tunnel, the con-
TOPOF
-IMAGE
AREA
i
I
1
Icentratien profiles differ substantially from those measured in flat terrain.!
.The resulting profiles at several dc&mdnd distances froa the stack are shown1
jin Figures 16a,'16b, and 16c. The three profiles were iseasured upstreas of !
;the hill, on the j>ide of the hill, and at the crest of the hill, respec- \
tively. The curves drawn are given explicitly in Snyder and Marsh (1977), I
drasts smoothly *hrough the experimental data points. Using the dispersion ;
parmeters derived frcs the flat terrain experiments, the centerline and )
ground-level concentrations cossputed with ,the model are indicated in i
i Figures 16a, 16b, and 16c. The fundamental equations used include 5-20 >,
Ithrough 5-25, 5-56,. and 5-57. !
i Centerline values are predicted within a factor of two using either a ,? ]
rat a* at alImpositions; the centerline concentrations predicted using a lie
'very close to the observed values at distances 39.2 and 84.7 csa from the I
stack. At the aost upstream position (Figure 16a) the ground-level value is ;
'not well predicted because of the boundary layer. The corresponding flat i
;terrain useasursaeat (Figure ISa) did not extend close enough to the ground to'
|enter the boundary layer (height of lowest issasurement was 7.5 cm). i
! The next measurement is part-aay up the hill. Using the original values
of o^, the model predicts an essentially zero ground-level concentration. i
.However, using the flat terrain boundary layer-enhanced a * gives a value |
joore than double the experimental value. j
At the crest of the hill (84.7 on) where the ground-level concentration ,
is highest, the predictions bracket the observed concentration. The observed'
concentration at the crest is the average of four Beasureaents which ranged j
•froa 0.2S3 to 0.506, laade through the sampling port at the center of the i
hill. |
i The predicted concentration using the best-fit o is 1/3 of the observed;
lvalue, while that computed with the enhanced a * is aBout five tisses the
^observed value. The difference in shape between the polynomial hill used in
;the laboratory experisents and the hemisphere used for the computations ccoild;
Icontribute to sc®e of the differences in concentrations predicted and I
iobserved sway ."TOD the hill crest, but the difference in shape alone cannot i
'explain the discrepancy observed in the surface concentrations over the j
.'crest. ' ' i
I Further inspection of the plums profiles in the absence of the hill !
| (Figures 15a-c) reveals that the centerline of the pluae does not ressain at ;
;the release height of 12.5 cza. Instead, the profiles suggest the effective ;
.pluae centerline height is about 11.5 as. Because this is evident 45.5 oa
i upwind of the location of the hill center, it is reasonable to assume that a
Isiiailar depression also affects the plume in the presence of the hill. I
i Results of additional computations using a (best-fit) with an assumed i
stack height of 11.5 cm are suuBaarized and compared with the observations and
the previous calculations in Table 3. Predictions of the centerline —j
T
^ so
TOM Ci
.;:•: A'lEA.;
'AMD ILuUS-
TPA7IOWS
(Cio.l
• 4-76)
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? TEXT
CCTJTER
OF PAGE
h?E£ &4-
TOPOf
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'AREA
200
Experiment
Computed Using o
e Computed Using
.001
Source: Snydar and K&reh 1977
Figure 16a.
Vertical concentration profile 39.2 cm downwind of
12.5 oa stack in presence of a 23 cm hill. (Hill
crest is 84.7 cm downwind of stack.)
1
51
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T?P?MG GUIDE SHEET"--7""
(T\'7f;R
•'T'C r^ p"rT--r "r -- - - ' '-^-—^-f-'nT^ifV".-
•' TOP OF
ijRO?1^:1 t
200
N
Computed Using o
a Computed Using o
Source: Sr ytter and ftSarsh 1S77
Figure 16b. Vertical concentration profile 68.2 raa dwmwirad of a
12.5 CT stack in presence of a 23 cs hill. (Hill
crest is 84.7 oa de&siwind of stack.)
4
K "5-
52
I 1
! j
-------
11 ME OF
TE;;T
200
15G
SHEET
CCNTt-lR
OF P~G>:
- t-T..-> - .—!r^-","-:Tf-f -i—sjc"-:"V.'1~
TOP OF
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* Experiment
® Computed Using o
m Computed Using a'
.(K)1 .005 .01
.05 .1
.5 1
/"s
X
5 10
50 IK)
500 1000
Source: Snyt&r and Meisfi 1977
Figure I6c.
iff. 257 (O-, '
(4-7PJ
Vertical conces&tratiozi profile 84.7 ca downwind of a
12.5 c® stack in presence 'of a 23 cm hill. (Hill
crest is 84.7 ca downwind of stack.)
.,_..
.53
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DROPPED j
HEAD. ,
SECTIONS __ TABLE 3. COMPARISON OF PREDICTED AND OBSERVED _J
' "~ *&f^ Wrir7?^A T T 7PH (TVT*iTPPf JT*0 A*TT
- nUiVvVuI. £«XrfiJ 4_>V^ld.Cr« 1 X\J\ 1 J
ONS AND PUS4E CENTERLINE -j
', HEIGHT FOR THE 12.5 CM HIGH STACK IN THE
— : PRESENCE OF THE 22.9
CM HIGH POLYNOMIAL HILL
i
i
Observed Value Predicted Value j
Parameter
j X=84.7 on (hill crest):
*C:r Surface Concentration
Hs=12.5 Hs=11.5
0.391 0.118 0.520 H
Centerline Concentration 47.9 53.2 51.4
i Centerline Height (cm)
X=68.2 on:
2.3 2.2 1.9
', 1
Surface Concentration <0.007*
Centerline Concentration 60.4 91.4 91.1
X=39.2 era:
Surface Concentration
0.003*
; Centerline Concentration 181.8 187 187
, !
i
i
-•
1
!
j
3
.1
]
1
'\
- i
i
*These concentrations were not Beasured right at the surface, !
but 2 to 3 ma above.
-k
j
"4
i
BEG'N
LASTLir
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.concentrations gemain nearly the same,! but the surface concentration at the—
crest has increased considerably. Now; the predicted value has risen froa
DROPPED °* tne observed(value, to 133%. Surface concentrations at the two locations
HEAD; upwind of the crest remain too small fpr a meaningful coaparison.
BEGIN Also included in Table 3 is the centerline height over the hill crest.
SECTIONS JShen the model ^ssuues the upwind plume height equals 12.5 ca, the predicted!
HERE ge&eight over thejcrest agrees closely with the observation. fejJLJjhjLTL-thjL—-—]
fassumed height is 1J.5 on, the predicted height over the crest is 80% of that]
observed. I j
/ In the absence of the obstacle, the dispersion parameters for release
(points above the boundary layer were determined using a stack height of
J12.5 era. To determine whether these flat terrain dispersion parameters for
the 12.5 cm stack can be used for other stacks, calculations were made for a
9 cm stack with the best-fit a . The results are compared to experiment in
jTable 4. The centerline concentration is overpredicted by 50%, the surface
jconcentration is underpv*dicted by 50%, and the centerline height is over-
I predicted by 30%. It is expected that the predicted concentrations would be j
(closer to the observations if specific plume spread data for the 9.0 OP stack-
Jin the absence of the hill had been obtained andLincorporated in jthe calcula-J
«•"•(! *»• m . <- - J" I
I I
TABLE 4. COMPARISON OF PREDICTED AND OBSERVED
,, JWRMALIZED CONCENTRATIONS AND PLUME CENTERLINE
HEIGHT OVER TOE HILL CREST FOR THE 9.0 CM HEIGHT STACK
Ion.
Parameter
Observed Value
Predicted Value
X = 84.7 cm:
Surface Concentration
Centerline Concentration
Centerline Height (cm)
16.6
30.0
0.9
8.0
45.5
1.2
Assessment>of model performance begins by comparing predicted concen-
trations with observed concentrations. In comparing results from the model
and laboratory experiments, sources of uncertainty are present. One measure
of their effect is the change in the ratio R of ground level to centerline
concentrations. From the basic Gaussian plume equation, the ratio R is:
*Cl
-•"ST
(7-3)
BEGIN
LASTLINE
OF TEXT
where n is the height of the streamline above the surface and a is the
vertical dispersion coefficient. For a typical wind tunnel experiment, (X ,
84.7 cm; a, 23.5 oa; H , 12.5 cm; and aspect ratio, 1) the model calculations
[predict, at the crest of the hill: j
0 ai o.58 cm, n = 2.16cm.
Z _ . ___ '__ S ______ ,
is th~en~ computed" by Equation 7-3.
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HERE
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Tnp
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^"2__ Now assume4 for example, that n
DROPPED
HEAD;
BEGIN
SECTIONS
HERE 55
or
(1
V
as:
. , o may be as much as
too low. Th* new retio R* is computed from Equation 7-3 with o
± 0.1)a, and,nc* = (1 ± 0.1)n ' ------
too high _
(1 ±-C2)n> '
then the error ratio
cu iroai cijus!_jLUii / - j KJ.UJ u «•
e generally, if o * » (1 ± £1)0. and
R*/R from Equation 7-3 can be written
(7-4)
AREA
Note that this ratio is sensitive not only to the size of the errors repre-
sented by C. and C_, but also to the value of (n^/a ).
Several computations were made for the particular values of n and o
given above (n 2/a 2 ~ j
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r
i
"1^"" TABLE 5. ERROR RATIO R*/R FOR 10% ERRORS
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-- - _.]
IN a_ AND n.
: Case I: (n_/oj2 = 14t
Usjf:
I
j
{
5
i
i
Case II:
i
0.9 ns
ns
1.1 n
S
0.9 a a
Z Z
1.1 az
1.0 3.7 9.9
0.20 1.0 2.3
0.033 0.23 1.0 ^
i
Cn./aJ2 = 3.5 j
0.9 ng
ns
1.1 ns
-1/2
R* = e
TCase I corresponds to
a =0.58 cm.
, z
i
EEGH;
or TEXT s^__
1
! _
£ 3/3-
1 . _
1
1
j
1
t
f
n
»'
,°Z*J
the
2
0.9 a a
1.1 a
Z
1.0 1.4 1.8
0.66 1.0 1.4
0.42 0.69 1.0
Kl
-1/2 —
R = e I'rj
specific choices n = 2
[
i
2
16 cm,
BO 7 TO'.' '.'*-
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f AND 'LL1..S-
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terrain correction factor is all that is needed to predict the surface
concentration in the presence of terrain from surface concentrations pre-
dicted in the abjsence of terrain. The j terrain correction factors can be
derived from thd potential flow model Results by solving Equation 7-6 for T
in terms of thejknown flat terrain dispe^ion parameters, and the ground-
level concentration calculated in the presence of the terrain (x
(7-7)
Similarly,'if an observed terrain*influenced surface concentration is
!known (as in the wind tunnel experiments), an observed terrain correction
factor may be calculated using Equation 7-7. FIT example, Table 6 lists
ground-level concentrations as observed at the hill crest; as predicted with
the potential flow model (also as predicted by the "half-height assumption"
be discussed shortly); and the corresponding terrain correction factors.
Note that if th6 source-obstacle relationship is fixed, a smaller surface
concentration gives a larger terrain correction.Jfaeior^ _Jh§L correction n
factors based on the observed ground concentrations vary roughly from .33 to
.35, while those based on the potential flow model vary from .36 to .34.
is seen that suall differences in the terrain factors are derived from much
greater differences in the maximum surface concentration.
9-1/8" j
TABLE 3. COMPARISON OF NORMALIZED CONCENTRATIONS AND DERIVED
t TERRAIN CORRECTION FACTORS AT THE HILL CREST
BEGIN
It
Observed Data:
H = 12.5 cm
H = 11.5 cm
Potential Flow Model:
Normalized Concentration
H
12.5
11.5
Half-Height Assumption:
H
12.5
11.5
0.325
0.353
0.357
0.344
0.5
O.S
0.391
0.391
0.118
0.520
0.0001
0.0011
Two modeling approaches can he readily compared with the wind tunnel
data: (1) a level trajectory, and (2) a specific partial height trajectory.
In the level trajectory model the plume centerline does not rise over terrainj
features. When ,the terrain exceeds the plume height (as is the case in these;
wind tunnel experiments) the centerline concentration is assumed to represent
LAST LINEuJxe highest ground concentration (no surface reflection doubling is
OF TEXT eftncluded)_._
l
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The partial height trajectory approach assumes that the plume rises ov.gr..
the hill. The glume's height above th© surface is described as a fraction of
the initial plusje height. The fractio^ (which lay vary continuously with
downwind distance—see below) depends 6n the initial plume height H ; on the
terrain height ty ; and on an assumed 'plums path coefficient,1 C. the
fractional displacement of the plume atsove the terrain enters into Equa-
(7-5) as a'multiplier of the ratio H/o --that is, as a terrain correc-
f actor T-rtFOT^pliaae3~lBt ti ally" 1 wer~ihan~ttt5~te'lfrliln~TH^-^TTpl
(7-8)
and for plusse heights greater than the terrain height (H
\ ht '
T - 1 - r± (1-C)
>ht):
(7-9)
The plume path coefficient may vary between 0 (level trajectory) and 1
(terrain following trajectory). One common choice for the plume path
coefficient is the "half-height." assumption: C = 0.5.
_^Predicted ground-level concentrations^ from_.the_ppten.ti.a_l fJLow_ model
jcorapared with those based on the half-height assumption in Table 6. The
(half-height assumption underpredicts the surface concentrations at the crest
of the hill by two to three orders of magnitude. (If a pluiae path coeffi-
cient of 0.35 is used instead, the partial height approach gives a concen-
tration of O.lSSrfor H = 12.5 cm, and>0.432 for H = 11.5 cm. These con-
centrations lie !much closer to the observed concentration, and to the con-
centrations calculated with the potential flow model.)
These additional comparisons of surface concentration predictions using
level plume and half-height assumptions emphasize the sensitivity of this
particular plume configuration to the ratio (H/a ). (It appears the thin
plume restriction (oz/n «1) is not a serious restriction even for ratios
as large as a /it *• O.sf which is the ease in the laboratory experiment with
the 12.5 cm release height.) In light of this sensitivity, the performance
of the potential flow model in reproducing the laboratory observations is
acceptable, and ^demonstrates the usefulness of this approach to complex
terrain problems where the potential flow approximation is applicable.
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MODIFICATIONS FOR EFFECTS OF STRATIFICATION
8.1 Qualitativls Observations from Laboratory Modeling
i i
Ambient stratification can significantly affect plume behavior and
resultant atmospheric pollutant concentrations. For moderate plume heights
relative to hill size, and for moderately stable stratification, laboratory
experiments suggest that the plume will go over the top of the hill, but the
path of the plume will be closer to the surface, and the flow over the crest
will be fasterjthan in neutral flow. |For small plume heights_under_strpng ^^
"ftratificatibnTl t¥e plume will tend to" go around the hill rather than over "°
it. If the hill is a long ridge, the flow may be "blocked1 and stagnate
upwind. To approximate first-order effects of moderate stratification,
results of FMF experiments on plume behavior in a stratified water channel
flow over a po^ywmial hill (Snyder 19,78) have been incorporated into the
complex terrain; model.
8.2 Incorporating Stratification Effects
I
Experimental results of the FMF tow-tank experiments on plume behavior
in stratified flow over a polynomial hill are reproduced in Figure 17 (Hunt
et al. 1978). The height of a streamline at the hill crest (n ) is shown as ,
a function of stack height (H ) for various stratifications denoted by Froude
number, Fr, including the neutral flowi case, Fr = °°. For any given stack
height and Froude number, the height of the streamline at the hill crest can
be compared with the neutral flow case'. To calculate the streamline displace'*-
ment at positions upwind of the hill crest, an approximation is made.
The approximation begins from the! streamlines for neutral flow over a
sphere (shown in Figure 18a), and over a circular cylinder (shown in Figure
18b). Note that the effect of the sphere or the cylinder on the flow is
negligible for distances greater than jabout two hill radii from the hill
center; it is a$suiaed that this remains true in the stratified case. Hence,
the difference between the plume centerline streamline heights for neutral
and for stratified flows is a maximum at the hill crest and is negligible at
| a distance approximately two hill radii from the center of the hill.
In the absence of additional experimental data and a sore complete i
theory, a linear interpolation scheme is applied to compute the height of the
streamline at intermediate distances from the hill. This linear approxima-
tion should be adequate; however, the interpolation scheme can easily be
changed in future refinements of the model. The procedure is incorporated
into the model in the following way.
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J1ENTFR
92 0.3 0.4 0.5
BEGIN g
LAST L «
OF TE> S
Source: Hunt et al. 1978
Figure 17. Height of the source streamline (ns) above the hill crest
(height = a) for various stack heights (Hg) and Fruude
numbers (Fr).
61
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Figure 18a. Streamlines over a hemisphere.
Circular Cylinder
Figure ISb. Streamlines over a half circular cylinder.
LTA-PS7 (C.i.)
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TEXT
HERE 3*
DROPPED
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SECTIONS
HERE &
tti
1_ As describ^l in Section 5.4.3,
center line is gjven by
1
1
where ij> is the $tream
if r££er-_to_-Eaua£ioas. ~5*-.
•
s,x)
(8-2)
(e.g., Equation^ 5-32, 5-36). In particular, the height of the streamline
at the center of the terrain obstacle,:zr, (at x = 0.0) is given by
1 i *~
I zr = zj (*.,0)
v> \ S
(8-3)
A^similarjrelationship can be .formed from_the_data in Figure 17_for.the- _a
iFroude number dependent height of the streamline over the terrain obstacle
center, zcp:
"CF
= n^. (Fr, H , a) + a
(8-4) j
,H
land fitting the data in the figure for the range of data shown (^s_ < 1) by [
(second-degree polynomials of the form: a |
|H
H 2
jwhere the coefficients depend on the Froude number, Fr.
Define: ! 1
- Z
CF
(8-5)
(8-6)
The height of the streamline, zp, for the stable flow is then computed by
z - 6
(8-7)
where z is completed for neutral flow according to Equation 8-2, and 6 is
given by: ' j
P.EGIN
LAST [
OF TEXT
or
6(x) = 0 ; |x| >J2a
6(x) =
2a
(8-8)
TTie net effect of modifying the neutral streamline is to lower the
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the obstacleicenter. The plurae cenierline is depressed sost at the crestJ
Iof the obstacle. ! . !
I This streaaline depression schesie is, strictly, limited to flows similar!
jto that investigated in Figure 17. The coefficients for Equation 8-5 hsve j
Ibeen derived for seven Froude nusiber ranges, and for stack heights less than j
•or equal to the height of the polynomial hill. In practice, the model uses j
^thls scheme for any stack height and any hill shap®._ _ __
i Where 'Equation"S-5" is 'applied"tc"'Ftac&"he"ights~"6utsi3e tSe range"©?
,experimental data, two physical constraints are iaposed on the calculated i
!value of 2-_. First, the streamline East not pass through the surface of the'
'sphere. If it does, zrc/a is set equal to 1.001. Second, the depressed i
streamline saist not drop belo& its original height at the source. If it does,
the stresaline height is set equal to the stack height. Not© that this ;
ilatter condition only becomes important for stack heights isuch greater than j
the hill heights. Also, extrapolation of thfc curves contained in Figure 17 ;
for stack heights above the hill height possibly introduces errors signi- ;
ficant for the wsre stable applications. More observations are needed to
'refine the algorithm for taller stacks.
An extension of Equations 8-5 through 8-8 frcsa flow over an isolated
three-dimensional mound to flow over a two-dimensional ridge" raus€~await>3a~
additional experiments to redefine the coefficients of Equation 8-5. Con-
sequently, the nodel now uses the same depression for all crosswind aspect
ratio hills. In practice, 6(x) (obtaiaed frosa Equations 8-5, 8-6, and 8-8)
for the two-dimensional hill is set equal to 6(x) for the three-dimensional
hill. This depression is then subtracted from the source streamline asso-
ciated with the two-diasensional hill. '
In addition to the lowering of the pluae csnterline streamline, changes
in the along streamline velocity, U(s), nust be computed. It is observed
that stratification speeds up the flow over the obstacle. The velocity
change owing to stratification is modeled by assuming that the along stream-
line velocity is given by the gradient of the neutral flow stream function,
ty, (Equation 5-29) defined along the lower streamline computed by the
stability modification described above. Since the gradient of the streamline
function increases nearer the surface, the along streamline velocity, U(s),
increases as stability lowers the plums centerline.
; A final point concerns the case of direct plume impact on the obstacle.
The potential flow theory approach can only be applied when the pluae center-
line streamline goes over the obstacle. The EPA tow tank experiments have
shown that as the stratification is made stronger and the stack is made ;
'shorter relative to the obstacle height, & point is reached at which the
plume no longer goes over the obstacle, but impacts and/or goes around the
obstacle. Using the c'ata in Figure 17, a minimum relative stack height,
,H /a, can be determined for a given Frjude number in order that the plume go
over the obstacle. This is the value of H /a (in Figure 17) for which a
given Froude nusaber curve intersects the ordinate (i.e., its height above the
crest of the obstacle is zero). Note that as stratification increases
(smaller Fr), the height of the minimum H /a required for passage over the
obstacle increases. ;
TabJe 7 summarizes the plume impact criteria currently incorporated into
the model. If H /a is less than the given value for a specified Froude :
ra^ber, it is assumed that the plume impacts the obstacle and the case is —-!
tf*~
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but not otherwise treated. The plu&e ispsct criteria have been _
tTncorporated in a discrete fora, not a continuous fora, because the sodel is
set up to use discrete Froude umber classes in determining the streaaline
depression associated with the particular curves shown in Figure 17. If
future refinements to the sodsl alloy a continuous depression algorithm, a
continuous form of the impact criteria will be appropriate.
TABLE 7. PLUME IMPACT CRITERIA BASED ON FIGURE 17
j-SHr — —
Froude l&raber
(Fr)
Fr < 0.4
0.4 <^Fr <_0.7
0.7 <^Fr < l.S
1.5 < Fr
< Plurae iepacts if
! H /a less than:
; 0.82
0.75
i 0.375
i assumed neutral
(no plmse impact)
!8.3 Application to the Atmosphere
! To apply this approximate model of stratified flow over a hill to the
atmosphere, the atmospheric stratification as described by the Froude nssaber
;Fr misr. be known. The Froude number is defined by:
H •£ and N
3z
(8-9)
jNote that a length scale, H, is incorporated into Fr. Ordinarily the
iatmospheric stratification is specified for routine air quality sodeling
'purposes by the Pasquill stability class, rather than by the Fronde number.
;The classification of stratification by stability class and the application !
jof the PGT Oy aad az curves for all stack heights are approximations that
jignore the variations with height of atmospheric stratification asd turbulent
diffusion. These approximations are not as good in the presence of a hill,
I because of the aew length scale that is introduced into the probiea. The
'prograa is written in such a way th/it the user must supply Fr if known, with
iH in Equation 8-9 corresponding to the hill height, a. If no Froude nussber
)is specified, the program assusses flow kinematics corresponding to neutral
:flow conditions. [Application of the Etodel at Widows Creek (Section 12)
'provides an example of the use of vertical temperature and velocity profiles
Jin defining Froude nrabers.j i
For routine application of the sodel using near-surface observations,
accurate Froude numbers are not available. Under these circumstances,
;default potential temperature gradients say be assumed throughout the over- j
'lying layer of the ataosphere influenced by the terrain feature. The tea- •
perature gradient could be specified for each of the neutral to stable j
classes in much the same way that the gradient is specified in
65
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TEXT ^ p
HERE nxycurrent stable $lume rise algorithms.
CENTER
OF PAGF;
-'' ll
p __,,. Similarly, the stability-dependent
jwind shear algorithms used to infer stack height wind speeds could also be
ji»?ed to infer a ssean elevated wind speed for use in calculating a Froude
••Eusaber. To the'extent that plisae rise, transport, and diffusion can be
jroughly characterized in this way, the Froude number-dependent streamline
'depression aay also be characterized. ' But such an approach should be fully
^snalyzed for sodel sensitivity to each assumption.
•j -Additional^3ppToaches"vill have-to be developed" for "cases" wheye~boH
Iplume and terrain are above a confined surface layer. This is the problem of
\a true two-layer flow. Over level terrain, the importance of such a condi-
jtion is reduced since ground-level impacts would obviously be small. In
cosrplex terrain, however, the model would be required to malce reasonable
.assumptions about plirae rise, transport velocities, plu&e spread, and Froude
number in order to calculate a. concentration on the elevated terrain surface.
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SECTION 9
COMPARISON WITH LABORATORY EXPERIMENTS—STRATIFIED FLOW
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r
9.1 Introduction
! The approach used to test the validity of the potential flow model
modified for stratification effects is the ssse as that used for neutral
flow. In the modified potential flow Bodel, calculations are performed using
Equations 5-20 through 5-^5 as in the neutral case, except that the plume
centerline trajectory is specified using Equations 8-2 through 8-8 to modify
the vertical displacement in neutral flow (Equation 8-1). In the absence j>f
t
-------
FIRST.
LiNEC-F
^•TYPWG GUttfE SHEET
CENTER
GE
_ l
TOP 0'
IMAGE
OnC
HE/
1000
500 -
A Experiment
Computed Using
Computed Using a'
Best Fit Curve (Snydsr)
.01
Source: Snyder 1977
Figure 19. Vertical concentration profile 50 cm downwind of a
9 en stack for stratified flow in flat terrain.
.OTTUV OF
'.'AGE rtREA
68
EPA-
'4-7 J
-------
L!i\E OF
TEXT
1000
500
100
50
10
5
<*
.1
.05
.01
GUIDE SHEET
567
Source: Srtyder 1977
CENTER
OF PAGE
TOP OF
^"AREA
A Experiment
© Computed Using a
a Computed Using o'
—- Best Fit Curve (Snyder)
9
Z(cm)
10
11
12
13
Figure 20. Vertical concentration profile 84.7 cm downwind of a
9 cm stack for stratified flow in flat terrain.
69
TTOM OF
AGE AREA,
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'0 ILLUS-
(Gin;)
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LINE OF
TtXT
TYPI.MG GUIDE SHEET
CtNTER
OF PAGE
TOP OF
HERE «49.3 Results in^Presence of Terrain Obstacle
DROPPED
HEAD;
BEGIN
SECTIONS
HERE
AREA
Vertical concentration profiles were not measured in the EPA experiments
on stratified flow. Instead, the ground-level concentrations were measured
along several lines from the crest of the hill, at various angles to the asean
flow. Figure 21a shows the measured ground-level concentrations along the ^_
on the surface going directly from the hill crest to the stack. In tfiTs
;y^^r7~T&e^nT~cT-esl^s~rp~c1it^ sfacTc~Base at
s « 84.7 on. The results of the model! computations using the originally
derived sigmas (circular symbols) and the boundary layer-enhanced sigmas
(square symbols) are also shown in Figure 21a. In the vicinity of the hill
(s <_20 cm), the concentration estimates based on the boundary layer-enhanced
dispersion parameter, o1, are within a factor of two of the experimental |
data. At the crest of the hill, the ground-level concentrations are 173% and!
208% of the observed concentrations using a and a ', respectively, while
close to the upwind edge .of the hemisphere,Concentrations are underestimated!
by nearly a factor of four. In interpreting these results, it should be
noted that the ground-level concentration varies exponentially with the
square of the distance between plume centerline and surface, and that the
•BSdei -calculations- are based ^m~a hemispherical-hill ^shape,"different frosr *"
the shape of the polynomial hill used in the laboratory experiments. The
hemisphere, for instance, meets the flat surface at s = 23 cm, while the
polynomial hill used in the experiments remains significantly above the flat
surface beyond s = 30 cm. -Therefore, the model underestimation with
increasing distance from the crest is directly related, in part, to the
differences in hill shape. Under these circumstances, the comparisons are
encouraging. ' j
The highest impacts occur at the crest. The predicted and the observed j
concentrations at the crest of the obstacle are shown in Table 8 for the 9 cmi
stack case. The terrain correction factor derived from the observations is j
0.183, and that,derived from the model; computations using a is 0.147. These;
are extremely low values, indicating that both the predicted and the observed
surface concentrations are much larger than those that would have been pre-
dicted by a terrain-following model, or by a partial height model using
terrain correction factors of 0.5 or 0.35. Concentrations predicted by each
of these three approaches are also compared in Table 8. It is seen that the
potential flow model offers considerable improvement in predicting the peak
concentration compared to these.other models. (Finally, if direct centerline
impingement is assumed, the predicted concentrations are 3 to 4 times larger
than the observed concentration.) I
BEG'N
LAST LINE
OF TEXT ^
i
!
\
BO i I Givi GF
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i 70 ;i
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. » . ,-,
*M\'0 iLLUS-
TRATlCiMS
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FIRST , TYPING GUIDE SHEET
LINECF CEf
TEXT GF
HERE gsj-
DRO°PED
HEAD,
D'EGiM
SECTIONS
\
(
MffiE »*-
i
70
60
l
= »
! .„ 8
"Ear g
, ,_-»--- .^^isi^K™.rs— -.-ff
JTER
3AGE >
.. — . - — - --
TOP OF'
^AREA
\
— i
* Experiment
,~ .- • Computed Using o
m Computed Using a'
S*.
1
^
p---»
•
5 10 15 20 25 20 35
| Distance Upwind along th« Ground from Hill Crest Jem)
i
Source: Snydar 1S73
;
;
i
i Figure 21a. Ground- level concentration for stratified flow as a
! function of distance upwind along the ground !
; from the hill crest for a 9 cm stack and 23cm hill.
( -
o_ j
r^T* S
'r. '"' ,- i
Or it i
1 ... '
__ i:7!- - JL
PAG?, i
EPA-267 (Cii.l
(4-76)
k
, X
L, .. N.
IHSTSSSMk- - . - ,~x~'> ' ••• '-j T - ••' - * ' • L ' ii- -'" - '
| HOUOM OF
IMAGE AhEA,
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DIMENSION
mp Tf.at cc
''":•:: V'AND iLLUS-
^1 ii j TRATICNS
ii 'MBER
lSt^VttiSilfnttit!ilif&a&t^ *.,<^..:.:^,,^
1
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1
1
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1
1
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•;
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,-v
3
*t
%
A
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FIRST "TYPING GUIDE SHEET
LINE OF
TEXT
HERE is
DROPPED
MEAD'
BEGIN
1_ TAB^ife 8. COMPARISON
CENTER
OF PAGE
TOP OF
> IMAGE
^""/vpf-iv
OF PREDICTED AND OBSERVED
CONCENTRATIONS AT HILL CREST F03
STACK TOW TANK EXPERIMENTS
I Normalized Surface
SECTIONS' • Model
MEKE 51
f~-
Potential Flow (o )
Potential Flow (a ')
Level Plume
Terrain Following
Partial Height (0.5)
Partial Height (0.35)
Predicted
63.4
76.9
125.0
1 x 10"25
1 x 10"5
0.11
THE 9 CM
Concentration at Crest
Observed
36
36
36
36
36
36
j " t
"Measuremer.ts and computations (using both sets of sigmas)"were arlso
[compared at ground level, outward from the crest at 90° to the flow. These i
•results are shown in Figure 21b. Again, the model is seen to work best in ;
predicting the maximum concentration close to the hill crest. Of£-hiil-crest I
.concentrations, though underpredicted, are less important in regulatory
japplications since these concentrations are an order of magnitude smaller
jthan those at the crest.. Other phenomena are active in the experiment,
jperhaps producing (by recirculation?) the secondary peak beyond the
kargin of the experimental hill. It is not clear to what extent concen-
jtrations closer to the hill are influenced by these phenomena.
j Overall, the approximations used to account for the effects of strati-
jfication in the potential flow model predict ground-level concentrations
jalong the downwind plume trajectory within a factor of two; but the results j
point to the need for further consideration of surface boundary layer effects j
land other hill shapes. Indeed, more experiments with the same hill configu- i
jration, but a wider range of stack heights, would aid the evaluation of the j
model's performance.
LAST LiNE
OF TEXT
EPA-2S7 (C-n.l
(4-76)
__ 72 il;
PAGE NUMSLR
BOTTOM OF
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j OUTSIDE
DIMENSION
FOR TABLES
VsAND ILI.US-
j TRATlOKiG
,~^~lm
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!^efS^m'f^^^^^^^!Sj^^'f^'^^'^^T:rr .j^.-j^^m'r.i^^-.^T.y-.j-?,*. .;.;
' F!o?r '.'"• ";TY>iNC GUIDE SHEET
' ' ' C E!
TEXT
HERE S»P ' A
r '
CROPPED ; j
HEAD; ( . . . . ,1
EECiN
SECriONa|_
HF.RE BH
)-.
1 80
1
70
\ 60
i
i
; 50
-< 1
1 1 ?
^ 40
c
3
I 2
! &
20
10
A
\
!
u
Vi
11
•\1
\l
f
88
- •!
H
fi!
tt
M
-1
*» »
•••• '• . •"'':••'.'' ' ••••:- •:•- . • • . . •.,
.rro TOP OF
SrF ' ^IMAGE
AGE „.„. ... ^ARFA
"j
/
A Experiment
e Computed Using o
a Computed Using a'
1
j
5 10 to 20 25 30 35 40 45
Crosawfod Distance along the Ground from Hill Crast (cm)
! Source: Snydar ti73
i
Figure 21b. Ground- level concentration for stratified flow as a
function of cross-wind distance along the ground
trom the hill crest for a 9 cm stack and 23 cm hill. i
,
P^CiN i
LAST 1 |
OF TE, §
— i
1 ......
BUI !UM Ot-
, IMAGE AREA:
j OUTSIDE
i
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DIMENSION
J FOR TARLE3
( ti *>••? vs :-.-:•:•:• '•'•'•'•- \ — — ~-
; JL 1~ . . iiii 73 ^ TRATIONS
EPA 737 (Cin.)
PAGE N'uMBER
1^^
—**^*'H -^**&-^^t'*^^*^^^^''^i[^r&k1rti^^
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V^j^'V^'ffiTfc'-^^ ^~v
BEGIN
FIRST
LINE OF
TEXT
HERE SB
TYPING GUIDE SHEET
CENTER
OF PAGE
DROPPED
HEAD;
BEGIN
SECTIONS
HERE
MODIFICATIONS FOR ARBITRARJK CROSSWIND ASPECT RATIO
I
10.1 Approach |
The treatment of potential flow ifa previous chapters deals with spheri-
cal or circular!ridge shaped hills. The model has been generalized to allow
for intermediate shapes by using an approximation technique based on an
interpolation of two-dimensional and three-dimensional flow field properties.
The parameter chosen to characterize the obstacle shape is the crosswind
aspect ratio, \, defined .as the ratio bf_h_alf_ of_ the crosswind^_breadth_pf_the
"8bstacTefT>, to^the obstacle height, aj. Shapes for"several different values*"
of X, where: I
BEGIN
LAST LiNE
OF TEXT *
SECTION 10
r^^tf'^^Farvpm**f?^w~7q^^
TOP OF
^JMAGE
AREA
X = b/a
(10-1)
9-1 '?:"
are illustrated^ in Figure 22. j
Because streamlines are not easiljr defined analytically for non-
axisyrametric shapes in three dimensions, an approximate procedure was
developed. Thi$ procedure uses the analytical description of the streamlines
for flows over a sphere and over a cylinder, as well as theoretical results
(J.C.R. frtait, personal communication to R. G. Isaacs, 20 July 1978) that |
describe the changes in velocity at the crest of the hill as the aspect ratio
is changed, and'experimental results that show the changes in the source
streamline above the crest as the aspect ratio is changed.
Changes inihill shape affect the flow field in two ways. First, the
shape of the plume centerline is altered and its form is found to be inter-
mediate betweenithe limiting two-dimensional and three-dimensional cases.
Second, the velocity along the plume trajectory is changed. The approach
used here to treat hill shapes intermediate between that of a circular ridge
and that of a sphere is to weight the flow fields of the two extreme cases toi
produce an approximation for intermediate cases.
10.2 Adjustments to Plume Centerline Trajectory Streamline
As described in Section 5.4.3, the height of the streamline,
specified by the streamline through the source, i|> , such that:
z, is
I (10-2)
where the particular functional dependence changes with the stream function,
u, determined by the shape of the obstacle. Two complete analytic solutions
-are available: I flow over a sphere and: flow over a cylinder. For a cylinder-
— i m 74
EPA-287 (Cin.l
(4-76)
PAGE NUMBER
BOTTOM OF
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, TR AT IONS
-------
Figure 22.
Definition sketch for aspect ratio Xib/a for hills of
spherical, intermediate, and cylindrical shapes.
p§j|>
~ CD
- o
g t~ > v.
c/> cr ^ o
in ^>
> CD
-------
I'Trl---"-'"" r-r—f-.-mpfWJlu" i...ftl"ICTJ'"--. n-r-T-^^^^rfr'^^'^Hy^^
BEGIN
F1RST TYPING GUIDE SHEET
i MCHC CENTF'R
L'NE °F or DA -c ^
TFXT . . OF PAuE >
HERE »i
DROPPED
HEAD;
BEGIN
SECTIONS
HERE ^
k I
i r 2 1
Tit .. - i
I *2"T
•and for a sphere (as in Equation 5-35)
,2 a3
j (x2+z2)3/2J
1
where z ij the height of the streamlin
As defined! above, the sphere corr
X = 1, and the cylinder (circular ridg
ratio, X = ». For a general aspect ra
and may be written as :
z =
i ,. < /">••
«2 1
I 1 (10-3)
s 2 2 l
V Hs
I2 1 * (10-4)
's * ,¥2 u2,3/2 U" J
|_ (VHs} J
2 at position x.
esponds to an aspect ratio of unity,
e) corresponds to an infinite aspect
tio the height will be a function of X
!(
-------
.^^^•M^v^ro^i^?^^
BEGIN •"..•!
FIRST TYPING GUIDE SHEET TOP OF 1
LINE OF C™™ .IMAGE-
n: PAHF xi»' i
TEYJ Ul MU .- -&ARFA !
HERE »»•
DROPPED
HEAD;
BEGIN
SECTIONS
10.3 Adjustmenls to Velocity Field
Changes in, the aspect ratio of the hill also. affect the speed of flow
along the streamline. An approximate scheme, which incorporates theoretical
results of Hunt] has been developed to account for this effect. One way to
- ,}
•j
-j
J
characterize th$ flow is by the so-called "speed-up factor," S, defined as__j
HERE j45Te ratio of the velocity at the crest) of the hill, ,U_, to the velocity, far ,
BEGIN
LAST LINE
OF TEXT »
upstream, U^:
S =
The speed-up factor (Hunt et al. 1978)
In particular, for X = X. = 1, (the sp
shows that
__ ^
U /U^ (10-3)
i
S will depend on the shape of the hi 111
lerical hill), potential flow theory
i c _ ori <\ - i c (10-9)
^OlMI — OIA..J — l.O \.*-U J J
SPH 1 '
and for X = X» -f « (;the.,circular ridge): -^
C
/'Vf C f\ "\
CYL = S(X_) •
For intermediate -"shapes, the theory (Hi
>• 2 (10-10)
mt et al. 1978) shows that:
i
S(X) = 2/[2 - B(X)] (10-11)
where
1
8(X) 1 + „
1 X -1
^ In IliV \^ 1 flf) I'M
i 9 Til") ln 1A* A L) LiU-lZJ
(X -l)1*'^
Some representative values of B(X) andiS (X) are tabulated in Table 9;
_,
•
note the asymptotic behavior as X-^l. These results apply only to the surface
velocity at the crest of the hill. To; use this result in approximating the
velocity field at other points, let the velocity at any point be considered
as an appropriately weighted average of the velocity corresponding to the
flow over a hill and that over a sphere:
U (x,?) = G^.W U-.- (xiz) + GCDU(X) Ucm, (.-,z) (10-13)
1 L.I L LI L i t>rri orrl
where the weighting functions G,-,. and
.G,,.,., are yet to be determined. These
functions are fc)und by using the theoretical expression for the speed-up
factor to find 1;he weighting functions at the crest of the hill, and by
assuming that the weights determined are applicable everywhere in the clow
field. In addition, the prope^ limiting forms for flow over a sphere and
over a cylinder are again required. "t'Js: P I^k'. ?f.
K
•A:_;C AritA;
v/ ^ i \_ u LJ c
- — DIMENSION
1 . 1 POD T/, D1 LC
I | 3/8" w W ' "rx'-x "YAND li-LUS- !
J J Si 77 ^iiii . TRATIONS ;
I • PAGE NUMBER i
I EPA-287 (Gin,) '
I (4-73) 5
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HERE
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SECTION? j,.
HERE
BEGIN
LAST LINE
OF TEXT £
EPA-237 (Cin.)
(4-76)
PAGE NUMBER
1YFIWU btHUi: bHttl
. . CENTER
OF PAGE ___^j$
^__ §
i
i— TABLE 9. REPRESENTATIVE
X B
VALUES OF SPEED-UP FACTOR S —
(X) S(X)
1 1.000 0.666...* 1.500* j
i !
1.0001 0.66675 1.50009
^ss. _ _ 1.001 0.6669 1.5003 \ »»-.
i
1.01 0.669 1.502
1.05 0.680 1.515
; 1.1 0.692 1.529
1.2 0.714 1.555
1.5 0.767 1.622
1 \
\ 2.0 0.826 1.703
3.0 0.891 1.803
5.0 0.944 1.894
10.0 0.980 1.961
20.0 0.993 1.986
100.0 0.99957 1.S9914
i
i
*Asymptotic value as X-^l
> I
I
; when V+-1, p-»- 2/3 (1+0(X-1))
i JU/0.- r r >
^ " | ilLzi_ &
TOP OF
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BOTTOM OF
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HERE *
TYPING GUIDE SHEET
CENTER
OF PAGE
DROPPED
HEAD;
BEGIN
SECTIONS
HERE
CYL " SSPH
Substituting S ' =1.5 and
I
2.0
herefore
where S(X) is determined from Equation? 10-11 and 10-12. This correction is
applied to each component of the velocity separately. Thus having modified
both the velocity field and the plume trajectory (streamline shape), the
program-proceeds- as prfevibissly- for -spherical-and-cytindrieal-hrils-. —Note— »
that because thfij speed-up factor for X=ilO is within 2% vf its value at Xsco,
the interpolation algoritha, for convenience, equates two dimensional flow
with all aspect ratios greater than or;equal to 10.
9-1/3"
EEGIN
LAST LINE
OF TEXT »
UCYL *
GSPH = 2
CYL
CYL
CYL " SSPH
(10-14)
results in
X7Xr*-M~[1
(S(X) - 1.5)
(2-S(X))
(10-15)
TOP OF
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AREA
I
3/8'
EPA-2S7 (Gin.)
(4-76)
iii. 79 Lul
PAGE NUMBER
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SECTIONS
HERE
SECTION 11
JC$I>
FLOW OVER HILLS OF HfTEMEDIATE ASPECT BATIO
11.1 Bsckgrousjd
I
Potential jflow Kcdel calculations! for hille of aspect ratios 1, 2, 3,
end 10 (effectively infinity) are cosspared to observed laboratory
bnd@r nsutral flow $?iadl tuisel conditions*
Th© wied ttaimel esperiaents wer® Conducted at the FKF (by W. H. Saydsr
U E. Britter). Results of that study ^sre isade eveilabl© to_^T_iQ_ehe
•^ersro"ff' sas in£gwsl 'data r*6|»6rt"(Snydesr" el" ®T. ~T97%)T
Model cc^utatieas retain the dis^isions ©Eployed in the data report,
eseept for the definition of the aspset ratio. As in the earlier
c©s$»arisoae for' the polyeoaial hill, linear vsrtieal sttd horigsatal spread
statistics near'.the hill location are developed fr^a the wied tunnel sata
obtaiffisd fcr the"'iio-terrain case (Say^ar et al. 1979a). This ^aouEts t©
opecifyicg dispersion rates present CFE Che laboratory eeale rather
to scale ds%m dispersion rates observed in the ateosptere.
TOP OF
IMAGE
'AREA
BEGIN
OF TEXT
11.2 Cospsrison of Hill Shapes
i
Four idealised hill sodele are ussd in the wind tunnel esperisasats.
All h^y« a trisagulsr longitudinal cro.sa-section. Hill 'C21 is a circular
corse, wit> surface slope of oa® half, j Hille "C4* aad *C6' are fabricated by
iaeertiag triangular ridge pieces bett^sen the origiaal cone halves, aad hill
'CX' is a giisple triangular ridge that; spans the width of the turaalo
DiffiKSsiiKis of thsse hills are sussasriged in Figure 23.
Snyder essd:Britter (1979b) define aspect ratios for thees hill shspas
to b@ the crosswiad length of the hill; between the two half-height point®,
divided by the hill height. In this report, however, the defiaitisa of the
aspect ratio ue@s &BK half the full erosswind hill dimension divided by the
hiil height (se« Pigxire 22). For the fcwo limiting hill shapes contained in
the aodel, the full crosssrfed dimension of the hill is either well defined
and sharp (sphere), or effectively infinity (cylinder).
In the esee of the sphere, the surface slope varies froa gero at the
crest to infinity at the base, sad so fehe crosewirad dimsssioa has distinct
end abrupt end points, fthea this idealised hill for® is used to represent
hill shapes wita coa@idsrebly smaller slope discontinuities at their basss,
eoas gsiaileg1 erejeswis^ disssssiea gSioald be selected that would insreaoe .the
similarity of the physical hill to the! spherical hill. For the wmd tmmel
esperisent® of Sayder and Britter, the! half hill height ert»8»iR«5 disensioa
LAST LINE .of_the cs®e coincides iileocieally with
3/8"
EPA-28? (Cin.l
(4-76)
the base of a spherical hill of equal-
iiii 80 ^
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D POPPED
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or PAGE
TOP Of
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'AREA
HIU.
L(cm)
Aspect Ratio
C2
0
46
1
C4
45
91
2
C8
^)
138
3
CX
Source: Sny&r et at.
3E
L/3
'JF
Figure 23. Details of hills use'd in EPA wind tunnel
81
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HERE »ff5f ight. There^r®, aspect ratioa foritlss hille studied by Srayto sad
Britts? are dsfiaed in this report to'be one-half the vstaa dsfiaed by
sad Britter. This d@fiEsitic»a iates tte losgittsdiasl bsse of 6ha
* hills to be the diseases !b®te®©a th« half hill haigtst pairaea
ratio to be the hill fe«igh£ divided by
-------
BEGIN
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LINE OF
TEXT
HERE Ss
TYPING GUIDE SHEET
CENTER
OF PAGE
DRGDPED
HEAD.
BEGIN
SECTION'S
HERE
TOP OF
(JMAGE
i ARF.A
f v©ff£lc®l pluaa spsreaf (OB) with downrind distsae© feoa
33 ea 6@ 293 ca suggeB&a etet its linear variation with s tar the regie*
ESS? s » ©4.7 da ess ba ede^isatftiy retina seated by the ersrad frea s • 33«0 esa
to a «• §4.7 ess. Curvature is es(x) ii v®ry saall over the range of
bast fit Gauesien ^igtaas derived fey Snyte et al.
.
A eeecad
isss
at plissss
ossful in
eser
height t
is the eeleulatieti of
£ the eurfac® ©tsd
the eeafcerlisia
set ra^cessarily
two
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HERt isfTl64 Coseparie^p for Pius® H®igSFEq«sJl to th® Obstacles
Hirai tsssKssaii ©sperisetat® for etsca height equal E® hill height (23.4 ca)
ere saal?§®d filrst beessss® eha ra»=hii| obeervseioae saggaeted that the plus®
at 23.J& ea is less affested |«y ehe surface bouradary iaf©r than is
the plUssa ?®leased at 11.7 eta (see Se^ticjs 11.3). Surface brnjEfctafy Isyer
as® ssoe ecasidarsd ia tha aofi^l* 6O feteir pE@Qerae® ®ay rsd«e@ the ~
s^-__.
11.4.1
I i « • * « # ifi**^>
CeacgtsEraEi^s asss ^sssursd at ttte hill crset vs B 84.7
tisss for caeh ^obatecle for®. A loEig4fc^^Ka^ section i® tokea at eto local
^h@ plux^ asi§» preduci^S eae oboervatioa of the surface
at ehs eirestj the eesoafi ©bservatioa is tekoa frcsa a ^ertieal
profiia at Eha er©st| sssd the third observation is takes in
cosjuaetiea ^i£ih a lateral profits at iereet height. All of tfesse vaisses are
by ^te@ factor ga^/Q triers ^ is the freestresa velocity in the
ceatissters par second (em/a)]f a ia the hill hei^s6? sad Q is
ofosanraEioaa elies? coasid@rsbl@ ee®fcEer ia surface
cmeetstra£ioa@ |at £b® hill er®@£s. Pejr eKcspl®,, multiple cbaainrseiosig at
the crest o£ hill C6 daritsg a vertical profile iseasOT-effieat sequeac
observctieas r^agisg fires Oo013 to 0.@79. ffiiea the eoapieee saries ©f
vertical profile points ia fsletted, ss^ average ^aiwe of 0.03 is ©fetaiaed
fros the ©feg@r¥^ eread. Sissilaff ®e@et@r is observed in the lateral eed
l©agitu
-------
BEGIM
FIRST
LINE OF
TEXT
HFRE B
DROPPED
HEAD;
BEGIN
TYPING GUIDE SHEET
to
CENTER
OF PAGE
T
to
emeratraticms befor® they e«J b@—
Ira both eyotewSp a norBalise^
eeaeestratiea ta wg«ds based ©a the s^al® Wa^/Q. The norsalisffid
CGSceBtrstieas 'r®p©?6ed by Sayfisr andJBritfer, aisd listed in Table 10, us®
400 es/s for Cfe sealing velocity. Ttiis is the free stream velocity in the
wisd tunnel. Tha raedsl eosputatiea® 488K33a £^® scaling velocity is eqwal to
sereaehiE® velocity at somre^ height, eensistemt with the OTMS!
ill TKeeeforei~Oia"~8caTihg
for the wissd £wm@l observations has tieea ehaaged BO that the scaling
ie that ©bservdd st seure® hei^it wit!| no obstacle in the ttnmel,
issw sarsalilsed eeacetstratioiss are listed in Table 11.
11. COJfPMISOM OP PREDICTED MB QBSEIVED
BEGIN
LAST LINE
OF TEXT
STACK HSIG3T EQUAL ifQ HILL BBIGH1g_
Hill! Crest
C©siceatrati0a j
Rill
2
3
5
10
O.J9103
o.bss
JK2S4 4-
0.037
0.015
0.008
0.003
0.034
0.019
0.015
TOP OF
IMAGE
AREA
*The observed vklusa ®rs Rormlised usiag the source hsight velocity
. coaceatraticaa predietad by the csaples terrain ssdel
iffleorporate verfeieal assd horisontal pl'ssas spread psr^astar® derived in
Seetiea 11.3, attd the aspect ratio weighting fuactioa derived in
Section 10. Cospatatiosaa are raade for; aspect ratios of 1, 2, 3, 5, sad
The results srej also listed in Table 1;1.
Comparing predicted and observed (value® shews that the hill crest
cos^utation ©verprediets by 40% at aapECt ratio equal to 1, ®sd quickly
undarpredicts fdr ®@pect ratio equal to or greater than 2. Over 5
the tasdel prediction is oaly 3.4% of tihe observed value, llhen the sassisEOTi
predicted conceatratioa for sny position ©a the hill is craspansd with the
observed concesieratioffl at the crest ia1 the wind tunnel, better agreesarat is
found at eost aspect ratios. OverpredictiKi® of 100% and 92 are foussd for
aspect ratios liand 2j uaderpredictieas of 25% asd BOX st aspect ratios of 3
and 10. Still the tresrf is evident! predicted grmiod-ievel ccaceatratiosss
fall off aich E$re rapidly with aspectj ratio than do the observed
gr©uBd-l@vsl c«aeeBtratisa3. This tresssl is visually appareat in Figure 24.
The potential flew ussdel comceKtrfltioaB may also be eospsred with
observatieas &rs& other modeling EsthcxSa using the terrain correctiea factor
(as in Section 7). Table 12 evs^stfissB surface cosjceatrations sss3 Js^lied
terrain correction factors forj the wihd tuoa@l ©b®eo?ationa| the potesatial
flow eodelf and'the surface esfjeentratiossg reeultirjg fr©a the half-height
tion raodelf the flat terrain aee^ption aodel (i.®.( esEraiffl-i
5 and the i level plus® asstreptioa ei>del (no eurfae® reflectioa
EPA-2S7 (Cin.)
(4-76!
85
PAGE NUMBER
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BEGIN
LIME o;
TEXT
HERE 36
CnOPFtED
HEMJ.
BEG'M
LAST LI
OF 7EX1
TYPING GIMDE SHEET
10
CENTER
OF PAGE
48
Aspect Ratio
Figure 24.
Predicted and observed concentrations for stack height
equal to hill height (23.4 cm).
TOP OF
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'AREA
86
30 1 I'OM OF
VAT-i-. AREA,
XITSIDE
OIMI-.NSIQN
FOR TABLES
AND ll.LUS-
TRATlON?.
EPA-2S7 (Cin.l
-------
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4* -• — — — •- • •
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i
TABLE 12. (SWMISOIf 0? STOFJiCE COKCETOATIOWS AT HILL CBEST - .-..,.
BETWEEN THE POTECHM. FLCW MODEL , THg HIHD TOSJ3^L OBSSWATIOK3,
THE H^LF-EEIGST ASSTCfflPTIOH, TSE TESMIE-FOttWIIKS fLIRffi
i- _ ASSSESPTIOWj &E53 TK3 iUT?BS» PLIS4S
ASSDMPTIOS TO! A STACK E3I6HT IC33.i 1
gjiniLJgSISffiLj..,
i
Aspect Surface Concentration ic Kill Great Terrain ^"""J0* F*c*^f ... ...,.,
Eatio Kodel Observed 1/2-Heisfot Ho Hill Laval Model Obs^^ed 1/2-Height Bo HiU. — Level
1 0.199 0.142 0.108 10"6 3.03 0.460
2 0.0103 0.034 0,108 . 10~S 3.03 0.629
3 O.C035 0.019 0.108 10~6 3.03 0.680
0.0005 0.015 0.108 10~6 3.03 0.764
0.483 0.5 1.0
0.567 0.5 1.0
0.598 0.5 1.0
0.610 0.5 1.0
0.0
0.0
0.0
0.0
T- — ' r~ Tl 03
ri; rn ~ = r~i
S 3 & S Q-
r^?~
i
i
SUar-n
(
1
;
«Th« tarr«i» ceyreceion factors asaociatad with the potential flos? faodel and eh« cbaervatieaa era
darivad feea tha ccffissntrstioos that sr« predietsd by tfea s»^el and observed in tha tunnel vsae ,
Equation 7-7). Thosa co??eceiea fsctoso for the etfeer appscadsas are S86use
J
" 0 O = =>
s
1
1
i
i
r
li
1
-»4
-^3
j£—
O
CD
r—
0
m
GO
X
^?.
%d
3 ^
i
!
-V
SsS
-------
''TffggSfwffiBMflffiraiyjffij;^^
TYPING GUIDE SHEET
CENTER
OF PAGE
BEGIN
FIRST
LIME OF
TEXT • ____. ________
HERE ^concentrations teo the terrain correcti
Uesived frsa tlia observations vary
crocsvind aspect ratio.
11.4.2 Otiher Pltssa Characteristics
HEAD;
BEGIN
SF.CTIONS
HERE
factors
Terrain correction
0.48 and 0.61 depsnding on the
BFolN
'.AST LINE
OF TEXT S
Th@ algetrdttaa used to predict plt^e ceaterlira® height at the hill cre««-
- • - • " •• • ' —° ve»iaclfi9M-«£-th«-««ataeliiM-
height with aspect ratio. Howsver, the lied ting cases, in which
ratio equals either 1 or 10, are cotspletely specified by Che theoretical
solution to potential flow ©v©r a sphere and over a cylinder. Therefore,
the overall tasgaitud® of ths predicts^ eenterline hei^it for these esses
Bust b® coshered to the observatieas Because only relative variations with
aspect ratio h£s bees fis®d» tfote thit pluae epresd statistics ar®
" " " determned by the spreading equations, by the theoretical
solutions for sphere and eflinder, and by the weighting for
position end velocities as|functions of aspect ratio.
Figures 23| end 26 eots^sre predicted with observed values of vertical
plume spread, dE, and plums centerline height, zg, over the crest. Two
o£ thes® represents a different interpretation of the vertical
profiles. ' I
The plsrae ieenterlica height raay be defined either as the height at
which the easinsss coaseatratioa occurs, or ss the height associated with the
centroid of ehe'&boerved vertical ccn^&titratiim distribution. Tliese two
height? ar® ahciwn in Figure 27 for th^ triangular ridge. The results of
these two possibilities yield the twojillustrated curves taarked "ceratroid"
atyi "msxiisam11 in the cosEpariscsa figures.
Similsrly^ o2 is sensitive to th4 centerline definition used. The
first choice (labeled as "Snyder et at." oa Figure 25) is derived by fitting
a reflected Gaussian curve to the vertical profile. The other two o~g
curves (lab@le^ by "ceatroid" and "saiifBuia") are calculated uaing s 2-point
reflected pl\m% equation sisiilsr to tliat used in Section 11-3. The surface
coaeentratiea se taken to be the average of the surface observations, ®a«i
the elevated concentration is taken eithsr near the centroid height, or at
the height of fsaxinassa conceotratioii. iln th® case of the centroid
calculation, ttte coacentratioa used i$ the average of the concentration at
the eeistroid height, end the Eiesieiaa concentration.
Th® resuloini curves show that t&e predicted behavior of the pluise
centerlins at Che hill crest is bounded by the interpretations of the
experimental data and, for aspect ratios larger than 2, the predicted
vertical sprea^ tends to fall below all of the values derived from the
observations. .The ehapa of the predicted zc curve begins to level off
quickly at aspect ratio 3 but, overall, the predictions of pltmsa centerline
bright above the crest are within 15% of the observed heights. The shape of
the predicted ojz curve only weakly echoes that of the observed curves,
For aspect ratios less than 3, the ao4®l overpredicts oz by aa auch ®s 50%
in the cass of \az CsaaKMsun), and oversredicte the corresponding eeraterline
hei^it by 50% as wall. j
However, £f the "eentroid" version of the observed oz is adopted fe-r
^aspect ratios iess thsa or equal to 2^ the predicted vertical plrais spread
~SXA the centerlins height agree with £hose observed to within """•'B
TOP OF
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AREA
I
3/8"
BOTTOM OF
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•OLTSIDE
DIMENSION
FOR TABLES
AND ILLUS-
TRATION'S
KPA-237 !Cin.)
(4-76)
PAGE NUMBER
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KGiM
OF TEXT
g .
o
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a
s e
ea
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ead Parametel
t
t- t
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LEGEND
= Predicted
= Observed
= Observed
= Ofaserved
•
— — *
_ .
-J-8
^w-(
•-••1
__f
4 6
Aspect Ratio
10
Figure 25. Vertical plume spread at hill crest for stack height
equal to hill height (23.4 cm).
_-L_~. -- „ _
1_ .„ 1_
(Cin.l
_. i . .
_ -'^ 89
PACK NUN
TOP OF
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AREA
1
:T70'/ OF j
IsGL AREA;:
jTSlDh !
FOflTAULfS ;
AUO iLLUS- j
!F;-MIONS
-------
BEGIN
FIRS;
L!M£ OF
TtV
t—
isL'RE }»<=•
TYPING GUIDE SHEET
ct'NTER
L
TOP OF
,IMAGE
*AREA
—•—i AKCA •
H 1
__!_..
A
E
O
V
CO
0
CJ
Q
>
O
JD
O
0)
C
C
A= Observed
flspect Rate
Predicted and observed plume height at hill crest for
stack height equal to hill height (23.4 cm).
10
TOM Q
GE ^R
'::;DE:
EN'S 10
TABU
) It.LU
-------
BtGIN
FIRST
LINE Or
TEXT _
HESt $4-
CHOPPED
HEAD,
TYPtNG GUJDt SHEET
EL1
u
N
CENTER
OF PAGt
TOP OF
IMAGE
'AREA
4Q _ Stack = 23.4 cm
Height of fsSaxsmum (23.4 cm)
.001
BEGIN r
LASTi I
O;:IE' Figure 27. Vertical concentration profiles over CX, the triangular ridge.
_ X.
F.PA-237 jCiii.i
(4-76)
ii 91 Jiii'
PAGE rjiJMBtR
BOTTOM OF
I MAG? ARL-A,
OUTSIDE
DIMENSION
=OR TAELk'S
'AND ILLUS-
1 RATIONS
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FIRST
LINE OF
TEXT
HERE S
DROPPED
HEAD;
9EGIN
SECTIONS
HERE fe
TYPING GUIDE SHEET
CENTER
OF PAGE
..—..4ratios of 3 and larg®^, the Eodsl predictions of 0g ere \
too aaall. Valets of vertical spread lara uiadarpredice&d by 271 at aspect
ratio 3S end by 57S at sspact ratio 1CJ. Therefore, sssg ©f ete
coBceatratioa uoderpredieticaa with increasing aspect ratio Esay be directly
related to qual^tstive esid quantitative differences in 02. !?©t@t for
£hat t|» observed vertical spread ©v@r the ridge (4.7 eaa) eseeed®
^assured ab the SESS doroswiad di^tsnee «wer flat terrains (4.0 ess)
TOPOF
r IMAGE
'AREA
BEGIN
LAST LINE
OF TEXT
iridge acts t© eospress
suit frcsa incr@@s@d «lisspfi?eioa in
from the horisoatal spread, o™.
potential fie?? pwr a
the vertical, this eshsiieed
the pz^seace efi the terrain
A simlar coaelusica
that the efcspss of
Thja overlap at aspect r
ri@@ at aspect pstio 2 is sissirag
ratio 3, £h® trtetsds again agree, bat tfhe predicted curve lies ebcs^t
below tbe observed. -Over the two-diEasnsional ridge the observed value
esesede the flat terrain valw® by 40%J Kota that the observed a,
are t&kea from the lateral profile in la horigostal plaae through ''the
in
io 1 is virtually e^actf toe the
the taodel reaalts.
11.4.3 Mass Flrai
A Ecasure »f hos?
deecripticn i»'t?ie vslue of
plissa has unit ka®3 flus dsfiusd
jd sass flus.
by tte relatieas
to a
The ideal
CL
(11-3)
where both the velocity 0 and concesstratioa X @re eeratsrlise valises.
How wall tfcje wind tunnel esperisa^ra£s preserve a ease £lws of 1.0
suggests how wall the tsodel predictions may agree with the observations.
Threa curves ofi the observed Bortaaiis^d EJSSS flus are plotted in Figure 29.
The observed."S^yder et el." curve uses the os and ceneerlina
conceistratioa vkluea derived by Snyderj and Britter (1979b), ^hile the other
two curves are jbssed oa the og snd concentration KasisOTsa derived for the
ceatroid heig£it{ and the hei^it of maxitesaa conceiatrationo Overall, the
centre-id interpretation of the observe^ profiles yields the esasa flws
closest to unity. All three give tauehi the saae result for aspect ratio
greater than or| equal to 3. Figures 25 and 26 indicate that the ceatroid
interpretation isf the observaeioffls taadctes tt»a predicted valass of pi USES
depth aod height better than the other interpretations for sesll aspect
ratio. '
11.5 Coeparisoa for Plueas Height Equsl to Half the Obstacle
i
The cosples terrain siodel is EOS*
hill height stack. Predicted
-vertical aud hoirisoQt&l pica® spread
to
with the half
derived in
3/8"
EPA-7SV (Cin.)
(4-76)
i^ii 92 iii
PAGE NUMBER
BOTTOM OF I
IMAGE AREA;;
OUTSIDE i
11.3 ea<3 — DIMENSION j
f'-'RTAELES j
AND ILLUS- j
TRATIONS I
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LINE Of
TEXT .
HERE 3e
TVPING GUIDE SHEET
1...
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MEAD; ;
BEGIN !
SECTION
hERE
Cf."\iTER
Of PAGE
TOP OF
.IMAGE
A
6
O
V
o
e
m
L
0)
£
O
L
O
Q_
~O
O
0)
Q_
CO
0)
£
D
0
L
0>
Rspect RotLo
BEGIN
LAST LINE
Or TEXT «j
L
Figure 28.
Lateral plume spread at hill crest for stack height
equal to hill height (23.4 cm).
1
EPA-2S7
i4-7ui
93
Di'TOM CF
/IAGE AREA;
UTSiDE
1MENSION
rof": TABLES
AND ILLUS-
TRATIONS
-------
BEGIN
. , npsT WiWG GUIDE SHEET
>'-. LIM-Q^ CENTER
' TEXI ' OF PACE
HtRt y£- 1
\
DRCFPr.0 ' ••• "
^A-°- • u™__
BEGIN "
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I ^
X
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X
U
a
s
Normalized
> p
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ft 4 •
i
<
i
5 —
1
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/
/
I/
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/
/
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TOP OF
^1MAGE
___
LEGEND
D = Predicted
O = Observed
A = Observed
-t- = ObservedOnyder et al>
'<
'
< e
Aspect Ratio
to
3EGi\
LAST Li
Figure 29.
Predicted and observed Gaussian mass flux for stack
height equal to hill height (23.4 cm).
EPA-287 IC<».)
(4-7Si
IOVTOM OF
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LINE OF
TEXT
HERE
TYPING GUIDE SHEET
DROPPED
HEAD;
BEG'N
for aepscijr
"Table 13, rep
wall aa
HERE
13.
Hill
C2
C4
C6
cs
1
2
3
5
10
2.50
1.30
0.99
0.78
0.57
.»5jlnm^^...^^gT.y^^st^
CENTER
OF PAGE ^j
5 » land SO. The results, listed ira
•©dieted e@ae©a£rsticfiJ8 K©ar the eeest es
:he Mil er©st.
&HD pBiEWOT K0HMLIZS9 OTSF&CS
^I^UJ^ML TO ptMJ? KIM, Rszesf
sd CeaeOTtratira Observed
: 1 Hill KaHisusa Coacenferseios
2.61 2.09
1.43 1.25
1.18 1.18
0.97 —
0.73 0.9§
1 ^'»ffi*^;Aip^*,
TOP OF
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AREA
Observed ceneetstrstisaa mesetsred at Ehe hill crests,, aed corrected for
soarc® streaali'BS velocity, srs ares listed in Tsble 13. These values
raprsaeat the fi^erage ©f the obaer'at^ons taker.- frss irertiealj lateral^ @ad
loagitudiEal'profiles through the hil^ c^est. These emrfase ebssr^atioas
agree very «all (wiehia 5%). The ob@@s^?ed ecaeeatratiosss are easapsred
directly to ehsj prsdiet©^ cooeentrati^aa in Fisur® 30. Tina couples terraia
ratios b©e?i®@a 1 sad 2, aad smderpretSlets by as such as 422 at aspect
ratio 10. j j
Ualike the prS^ious experiment is ^sieh the stack hsight ^as eqssal to
th-s hill h@ighe (S^eioa 11.3), ^ertieal profiles of the pi«ass o^er the hill
shssssd virtually no elevated eKSsseeratratiOiS ^asiffisjEsa. App-areratly the
is eo greatly iafl«eac©d by the^boundary layer that the plasss
csaterlis® csaaot be readily ideatifi^ crver the crest. This ia esp®eially
the e®s« for the pr®fil@ &&&E the eona. At larger aspect ratios, a wsak
27).
predicted sad observed plras® spread statietieg £EBa©t be
compared directly (bsesua® the E«sdal as not dssigasd to eiraslata the physics
of the espsriEsait) it is iaetrtsctiw eo highlight the differences bet®a©ra
the
ceaterliee height evaluated at the cr^st. These ar@
fchrossgh 33. Figur© 31 ew^&r&s the predict®*
hill creets ag^int the height of the 1 centre id ©f the
predieted height lisa bst^een an absolute upper
r, the true ssurce etreamliisal in the wissd
Tha greaEffiEt ^oelitati^e
_SH!ELiiiS£_i?-^'0'^^--i.— £h@--^
ed ia Figures 31
height above the
observed wrtiea!
that the
the hill surface.
BEGIN
LAST LIN!
OF TEXT Ef-predicted_ md
, w 3/8"
EPA-287 (Cm.|
(4-76)
The
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....J
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rqsT TYPfMG GUIDE SHEET
-LINE OP C£NTER
TfxT OF PAGE •
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BEGIN ! 1Qi
SECTIONS ' u •
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O
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— >
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10"'
(
BEGUM
LAST L'NE
OF TEXT J
' 3 M -0"
L_ r: i.
tPA-?SV !Cn
(1-76)
k. •
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LC
D- PredLC
O = Obser-v<
A - Predlc
r~^*»~^
1
*=»»,
i
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1 . , ,
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'
..-.4- ^ 4
_- .
j
2 4 6 8 in
Rspect RotLo
— 'TO?/ OF
Predicted and observed concentrations for stack iGE A'sEA.
height equal to half the hill height (11.7 cm). rssDd
IEHSION
\ TABLES
i£vi % ^ . i TRAT.ONS
PAGE nuMER"
-------
. CEGIN
F|RST
LINE OF
.
TVPSWG GUIDE SHEET
HER£ He.
\
..L
HEAD, '
BEGIN
SECTION;
HERE 5
CENTER
OF PAGE
' TOP OF
IMAGE •
BEGIN
LAST LI is
OF TEXT
Figure 31.
4 6
fispect Ratio
Predicted sud observed plus© height at hill crest for
stack height equal to half the hill height (11.7 cm).
EPA-2E7 (Cm.)
(•S-761
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ruR TABLES
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Figure 32.
Vertical plume spread at hill crest for stack
equal to half the hill height (11.7 cm).
EPA-287 (C,r,.|
1 (4-76)
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- I
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BEGIN Figure 33. Lateral pluse spread at hill crest for st
LAST U equal to half the hill height (11.7 cm).
OF TEX'
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EPA-287 (Cin.)
(4-75) .
V
j^m^ ..-„,.,,,
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HERE S
tive'dieagzeeraene is $otrad~in the vertical pluasa"
This trena is siailaff to the os results in Seetiora 11.5, al thatch
sore procouaeea. &pfsar©s£lyj> iacresssd turbulene® levels in the wind
bsMEdsry layer jstrossgly affect plum® eispersioa E-ear
borna out by the turbulemea E®seur6Bea£s contests^ in the wiad
~ la eenjttneticm &ith their tracer
Mean }^@lociti@s syetssatieaily decrease at sll slevatic^s
increasing aspect ratio. V^ry close Co the siarfac® eh©
velocity is iffidspeadeat of t(he hill*® aspect ratio «d is gbout
1/4 4^ that in the usdioEurtjed bouadsry layer. The larger the
aspect ratio. Eh® greater is the hei^it to $?hieh the hill's
Baeeissa ©f the hills, longitudinal turbulence is decreased and
vertical turbulence is (considerably) iaereased very elo®e to the
surface. Surfee® turbulence increases systets-atically with
2)
longitudinal, is oboerved td 3 to 4 hill heights above the
surface, the increase bsing larger for the larger-aspect-ratio
hilld.
3) Negative Reynolds stresses, quite large in Esagnitud®, are ©bssrved
Lf the hill height. Although the scatter of the data is
large, it is apparent that the aagaittsde of the K
Reynolda stress increases with aspect ratio.
BEGIN
LAST LINE
' OF TEXT
Msasuressat® over the crest® of the hills
1)
la very erude teras, hills tfith aspect ratio of 2
si&iiav flew behavior, «feer4as the esae (C2) shews distinsetly
different behavior. For example, the speed-up factors are 1.15
for ehe eoaa aad 0.95 to 1.0 for the other hills. Yet the changes
are i|ot taoQotonic with aspect ratio.
layer
2) Chaages in turbulence relative to the unobstructed bouadary Is
iscressed with elevation anc! (in this case, systies&atieatly) wi
iracreasirag aspect ratio.
3) Very 'large negative EeynoldEi stresses sra observed? negative
are observed to one-half hill heists above the crests.
In es^sary, tha ©biservatioas indicate
surface upwind tof the hills increases
that vertical twrbulsae© sear the
considerably over the unobstrec£®<3
, inereasidg systematically with Aspect ratio. Lsrgs nagstiw leymold®
stresses associated with the increase*} turbuleraes are active up to one—half
the hill haighfi and, craiseqissatly, hsve a profound effect eras the developasaS
of vertical pl«sa spread over the hil^. Becau@© the turbulence iacresses
with aspect rafiio, os rises graphically as 8hcw*a in Figare 32. This
aspect ratio dependeaee of turbulence
3/8'
intensity is not accouated for ia the
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Cettelusioaa
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AR'EA
flew ees?j»l@s terrain wssfsl has batra cffi^arad tdLth
observations of flcs? ©ver four hill Efesp®® wi£h a®^@e!
£r©a 1 to 10 Ce££firig©as with surface coracentratioas issiffig
the level plwm^ aad terrain-foiloviug jpluaa as®«aptiona show that the level
pitesa approeeh ovesrpredicts observed doneentratiotts by t^o orders of
sagaituda, ergi [the terr^ira-follcwiEg jiluiae approach waderprediets by foar
orders of BSgnitads.
For aspscti ratios greater thas lt os is consistently
their flafc-terraia ^aiusa. FOP eKffiKpl@s the ratio ©S
over the rid§@ !(X » 10) to o« over fl4£ terraia is 1.45 for the
hal£-hill-tei$s!t etaek, eod 1.40 foz-'fihs full-hill-hei^Jt stack. The
.06 sad Kl®. Thee® eahsQeeEseacs ere aefc
observed ts ves'qlt froa flis? deforsat^eas. Such chaagas certainly eaoaat be
reproduced by potential flo& deforsaticas aloaso
Table 14 qo^ares observed to predicted 0y and 0S ratios for
fo«r aspect ratios end fesr bo£h stack jheigjhts. Als© iscluded in
are ratios of dbserpsd to prsdiet©^ @pee^-ap factor®. 'i!fe©s@ factors are
BEGIN
LAST LINE
OF TEXT
to be roughly inverse to the horis©at4l spread ratios. If the tssedel is to
eo^arg fsr^oral^ly ®i£h these wind ttimtel raeults9 the sa©ehanig®s centrolliag
th@ observed plu^e shape wist be bettsr «miersto©d.
I
I*!!
EPA-287 (Cin.)
(4-76)
Siii 101 ii
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CENTER
Ofl PAGF-
14. COMP&BISGH OF ©BSSCTED TO PP^BICTSD
OF FLTOH 8IZB Pt\R&mTESS AMD SPEED-UP
AS A wm&nsm ew ASPECT E&
Parameter
Stack » 0.5 Hill;
(oba.)
°s (Sayder et ai.)
a Cobs.)
S (pred.)
Stack « Hills
.)
q'a (ceatroid)
8 (oba.)
S'3/3"
y
E'A-287 (Gin.
14-76)
0.65
1.3
0.39
o (pred.) 0.99
et al.)
0.84
1.27
2.43
0.7S
1.33
1.21
1.21
0.78
A.
1.43
2.;
1.39
1.27
1.40
0.74
iii 102 ;:>>
PAGE NUMBER
1.40
3.19
0.70 0.69
i.:
1.53
1.53
0,73
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HERE V
SECTION 12
MODEL COMPARISON WITH FIELD OBSERVATIONS (WIDOWS CREEK DATA)
12.1 Background
Measured sulfur dioxide (802) concentrations near the Tennessee ** " '*"
Vallsy Authority (TVA) Widows Creek Steam Electric Power Plant in Alabama
are compared wi£h concentrations predicted by the potential flow cr"?aplex
terrain model. 'The routine laeteorological data from two towers, the
occasional temperature end velocity profiles, and the continuous S02
measurements at five monitors on a nearby ridge and one monitor on a nearby
^rnri -make th e~^rdc&%' Cteetr darts-bsee-'a- proms ittg -te sting- ground -for- ehe ^
complex terrain! modal. Comparison of the model predictions with the
observations at; Widows Creek tests the! model's ability to predict
concentrations on real terrain feature's under complex, uncontrolled
atmospheric floW conditions. j
o-yfc" j
12.2 The Widows Creek Steam Electric tower Plant
The 2,600 megawatt (Mw) coal-fired power plant operated by the WA at
Widows Creek, Alabama, is currently coksposed of eight individual boilers
three sain steeds. Boilers 1 though 61 feed a single 304.8-meter (ra) stack;
boilers 7 snd 8, each feed a 152.4-m stack. The 304.8-ra stack has been in
use for all six boilers since early 1978. Prior to this titse, boilera 1
through 6 fed separate 82-m stacks that were subject to frequent dowawash
events. To avoid the complicating effects of dowzswash and multiple plusae
interactions, only data commencing in January 1973 is ueed.
Figure 34 displays the topography; of the area. The terrain feature of
greatest interest is the bluff located to the southeast of the plant. Its
face rises 840 feet (255 m) in a distance of 0.9 kilometers (km), yielding a
nearly unifona slope of about 1:4 (^16°). At the top of the rise, roughly
2.6 km from the) plant, the terrain levels at the plateau called
Sand Mountain, 275 m above the power plant elevation. Atop this plateau,
five §02 monitors are positioned in an arc with a rosais distance of 3.5 km
from the plant.! The two monitors closest to the crest are 3.2 km frora the
plant, and that at the center of the arc is 4 tea away. Two meteorological
towers are identified in Figure 34. One is near power plant elevation on
the valley floor, and the other is nedr the central monitor of the plateau
sespling arc. |
Other terrjain features are located to the northwaat of the power
plant. Two of these—Suasaerhouse Mountain and Cumberland Plateau—have
BEGIN single S©2 tsoni'tore at their crests. lOnly SuEasrhouse Mountain (275 sa) is
LAST LINE.isolated enough] to be considered a second suitable terrain feature for —
OF TEXT g^eoaroaring predicted and observed cone@nt:ratj.gn_8_.
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3/8"
EPA-287 (Cin.)
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ilS 103 ill
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'34. • The Widows Creek 'steaa electric po-*er plant and
surrounding^features. _*;.,>.
104
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^^__ The Saad Mountain ridge is shmra Jin cross-sectian'in""Figure 35.
"Spplicstisa of tlse eossples terrain aodpl to this feature requires selecting"
an appropriate circular cylinder and placing it at aa spproprise® dietsraee
ssureel The selection as®tJ® in this report ia compared to the
terrain in Figure 35. The height, or radius, of the circular-
cylinder is tak^ra to b© 275 sa, rad its center is placed 3.2 to froa the
-scarce. This source—to-creat distance! places the eodei crest receptor at —
BEGIN
LAST LINE
OF TEXT
ere, alttoeragh traa actual ridge crest lies as close eo the sourc® as 2.6 too
In effect, the ridg® is modeled as if jit curved through the easplitsg arc.
If the setusl geometry had been preserved, the isodel crest would coincide
with the true crast, ead the monitors i^ould li© on the downwind side of the
circular cyliedibr. I
Applicatioii of the ssedel to SuassteThouse Mountain follows in sim-leir
fashion. For thia cotspsrison, the hill crest is set a distance of 8.7 ka
fros the Widows I Creek facility. Tne hjeight is the ssma as that used at
San.d ^santsin, 275 ci. Rovsver, the crbsswind shsp® lies between that of a
simple sphere end cylisder. The sppro-Kisaate crosswind distance through the
from one 0.5 hill-hei^it pointj to the other is 2.2 tea. The aspect
by the height of the hill. Therefore the erossuind aspect ratio for the
sodal hill is set at 4.
12.3 Case Selection for Model Comparisons
9-1'8"
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'AREA j
12.3.1 Analysis of the Tennessee
Monitor Bata
Valley Authority Sulfwr Dioxide
Bigitized S02 coacentratioas and pateorologieal data (teEperature and
wind® at 10 a afid 61 a) collected at the TVA Widows Creek Steam Electric
Poser Plant Ksre supplied by the TVA far Quality Braach, Mussels Shoals,
ia. The ebaptster tape contained,! in part, hourly S02 coacentratioas
the five sapnitors oa Sand Mownfcai^j and the single aoaitor on
Mountain for the period January 1, 1978, to September 30, 1978.
This is the period of Eioet interest as! the last of boilers 1-6 was tied into
the new 304.8-m stack in late December), 1977.
The first ptep in selecting the hburs best suited for model cos^arisons
w&a to search for those hours with at jleaat one monitor reporting an S02
concentration gireater Ehaa or equal td 0.10 parts psr raillion (ppa) or
570 Mg/a^. A total of 73 hours %*as identified for ridge impacts (Sassd
Mountain), and k& hours for tssouod isapects (Su^nerhows® tfeuntain).
West, hours with unstable stability classifications ware rwled oat.
The stability w?s§ assessed primarily from the temperature gradients between
10 m aad 61 a at the tower atop the ridge. Because the layer between 61 sad
10 m say not bei entirely representative of conditions at stack heights of
150 and 3®) a, the cut-off value for tesperature differences was sat at
1.5 tijses the dry adiabatic lapse rate:, or -0.75°C/51 a <-1.35°F/51 a).
This criterion redsiced the nws&er of eoHparisora cases to 27 houra of ridge
ispsct, aad 15 hours of saouad ispact. | For ataost all of these hours, the
souree-reeeptorj trajectory corresponded readily with the wind direction
recorded by the, 61-a sensor on the ri«£ge. Table 15 snd 16 list the selected^
sod corresponding S02 concentrations for Sand Mountain
m 105 ji^;
PAGE NUMBER
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c&OuKS SiSIu
A7 sSAMB
i
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Hr>d
MSI ON
'ABLES
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•or-js
-Z37 (Cm
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TOTLS 16. SOTS SELECTED TOE &SGDBL COSfPABISSES AT
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Yesr
802
Borar
(10
.-3
M 15
IS
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78
73
78
78
78
78
78
78
78
78
78
78
78
78
78
4 -
4
24
143
143
166
166
167
220
222
223
258
260
260
262
2000
21GO
1000
660
700
2300
2400
100
660
2400
100
900
2300
2460
200
100
450
130
140
120
120
140
140
190
150
ISO
170
240
260
100
I
EPA-287 (Gin.)
(4-7C)
I
S^l 107 .^
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-* r^ ^n GO
i % ™ 3 1
O 2
it"
(m)
O
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m
rn
> -1
S 3
Figure 35.
Comparison of the idealized cross-section of Sand ^fountain
to the southeast of Widows Creek power plant with the
circular cylinder assumed in the complex terrain model.
;d
j.. ^ ^
9, ~- c
y
v» O
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@eeh of these feetars the T7A Air Quality Branch £ss«ieft@»I ell
t©sgperature, sssd velocity profiles, md hourly eaiesicas data.
12.3.2 A&alysis of Selected Esaissicaa estd Mraoepheric Data
Dp
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«
. . 1
Tmi& 17. CASES OF 8IGRI7ICABT KPACT TMT E&VB ASWCIATTO
-. WmC4U FtCFII^S ©F
\
\ Ridge Impact lours
i Profit® Ofee«rTOti©«8 Ti^
j
1 Julisa Bay Month Day tear T©^p>®r®eur® ^eleeity
: 3 13 1300 1227 1332
40 29 1300 1228 1312
^ IfO 79 OS©0 0841 07WJ
226 8 14 1200 1247 1140
230 8 IS 1000 0920 0925
230 8 18 1300 1223 1395
232 8 20 14-1500 1225*163S 1430
Maura! IsspseE Hours
Prefil© Obg©rv®£icn Tiss
Jrali^i Bay Msatb Bsy H©ssc Te^serafturss V®l@ei£y
4 14 2Q-21G0 2030 2355
166 6 15 2400 0005 2340
222 8 10 2400 W04 2322
i
i
f
* 1 '
1
r~ ! ~~
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Jj -,,,,., ! ,.,. . ' -.-•.-. "YAN>Q ILLUS-
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EPA-28V (Cin.
(4-76)
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TVPIMG GUIDE SHEET
. . CENTER
OF PAGE ^
ttatendned SOT |aeh g&fcaefe ez&&, with fefag caceptioa of eh© staefe ra^i«ss»
S^p@ssS ®a ft&e individual !boil@r loada per ©seh hour. toiler load® for esete — '
sissit sad tour esday sCwdy we listed ia Tsbl® 10.
J
T&B1S 1®. HOUSE
ifaiiass t
Y GIOSS wm &
Bait ~~
lae© Month 'Day Honr 12345678
3 01 03 1300 100 73
40 02 69 1300 46 60
WO 07 09 0900 123 123
226 08 14 1200 111 Off
230 OS 18 1000 112 59
230 08 IS 1300 112 61
232 OS 20 1400 Off 59
.SI32 OS- -4 -20 6-11530— -0£i- -40-
4 01 04 2000 94 90
4 01 04 2100 96 88
166 06 q.,/815 2400 101 57
222 0§ 10 2409 82 Off
114 103 104 106 Off 311
47 55 51 53 Off 344
130 125 129 123 Off 456
129 131 128 123 524 Off
Off 130 122 128 271 281
Off 133 132 130 290 281
129 133 132 127 4SO Off
- 130— 130 — 130 — U7 — 4©&- 4tf- 9*
110 '90 93 101 398, Off
110 90 108 104 413 Off
90 89 59 69 Off 241
88 64 84 51 244 297
i
^relira.eas'V ealeulatieae Cor £h@ tall stack indiesEs tfa&t tfee
ia^oct of emissieaa fstRa this stack Ajferiag £ha hsmr® wader s£«
. ;*
I
•J
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fa Table 18 £fel«® li®if;tee ia the @ta ©f t
rise Ah.
»
TftHJS IS
Julies Ray K
3
40
190
226
. FinM, 1S1GHTS
10115 WITH £BD TJITflO
stiith Bay lowr
1 3 13G0
2 9 1300
7 9 0900
to ataek height e&& the iiE®l plass
OF EMISSION FROM EOILSSS 7 AHD §
JT FULL S0j> SST5UBSIKG " —
Scrabbsd Pits®
Pltrae Hei^st (is) Height (a)
Jait 7 Unit 8 Halt 7 Prait 8
445 - 422
432 - 4Q9
325 - 307
8 14 1200 k,085 - 855
«^3© 1.8— 6-1/218 1960 3SO -345 319- -§2®-pa=
230
232
4 9-1
1@S
222
Of the aeve
oaly Sowf K®re
day 40 hour 1301
heists daring
other thre© hen
eseeed tsd.es th
The three h
(Sts^erhTOise KB
Te^sratar®
(aft@r eeresaiE
The dasted lies
8 18 1300
8 20 14-1500
,\. 4 20-2100
6 15 2400
1
833 802 73S 733
600 - 533
309 - 289
335 - 317
i
8 10 2400 ! 3S8 374 335 352
i
j tiotsrs identified for impact ess the ridg@ (SasuS Mauntain)
selected for eo^arisoa, with tlse a©d@ls day 3 hoar 1300,
Ss, day 190 hour 0900, esd day 23Q feosar 1000. PIufflQ
£tsae@ bowrs varied from 325 E@E©rs to 445 a. For the
ps 5 pl«s^ hgigtits ^sri^ feet6»sezs SCO IB and 1^085 BS ^iieh
§ height of the ridgs.
«urs idesti£i®fi for iapset oa the isolated jmswisd
«sa£aira) s@w slailar fis^l pl«ffis heights (309 to 375 a).
| profiles for each of the genera ease hoara reEsaiaing
g for pl«ase riae) are presented in Figures 36 thr®«gh 42.
8 ideatify th© s^sa t@s@pfflrs£OT@ gra«!ien£ wssd ia the piusa
rieg cslcalatioa, end tha horizontal lime is the resultant final plwaea
height frea the
place entirely
The S£>2 esi
hourly boiler 1
eseh unit, wti&
' 152.4-ia stacks. la ell e@e@s pltos® rise is s©sm to 6@ke
Within tte layers describes by the indicated mean
*§ * dSTIl ^ £9 !
531U6H.B » 1
iaiesi rates froa each fejsiler unit ss®re cslcule£ed frora
0^8, weskly ewlfwr eraieEt aud hc«t ralue of Ehe coal for
ssartly averagea of the gross energy oatptat of' the
facility p©r he^t input as fuel. The isulfur coaKeat had been adjusted by
WA to reflect
•>
R O /o "
fOJ conversion of the s^lfwr coatent to g02« To eosiput®
1
|
i '
__.
^",:.;,. >
„
TOP OF
3/8"
EPA-237 (Cin.)
(4-76)
BOTTOM OF
IMAGE AREA;
OUTSIDE
DIMENSION
._ FOR TABLES
yAND ILLUS-
TRATKJI^S
PAGE NUMBER
-------
BEGIN
FIRST
LINE OF
TEXT'
HERE %>
TYPiNG GUIDE SHfTET
TOO
550
I 400
250
200
160
100
SO
0
CENTER'
or PAGE
5.3 m/s
finsl Plume Height
\
Profite Obsssvstion: 1227 LT
Vetocity ProfiSa Observation: 1332 LT
I I !
-3 -2
Temperatura (°C)
-1
TOP OF
IMAGE
AREA
3 m/s
Figure 36. Temperature profile used to calculate plume rise and
Froude nuraber on day 3, hour 1300, 1978.
'JL
EPA-287
(4-76)
„___!.
(Cii.)
iiii "3 .-:;
PAGE NUMBtR
OF
AGE AREA;
JTSIDE
WENSION
R TABLES
ID ILLUS-
IKATIOi^JS
-------
BEGIN :
FIRST
LINE OF
TEXT
HERE H
DROPPED
HEAD;
BEGIN
SECTIONS
HERE B
TYPING GUiDE SHEET
CENTER
OF PAGE
750
TOO
550
450
<=»
150
100
50
0
2.0 m/s
Rnal Pfurne Height
3.2 m/s
1.6 m/s
3.3 m/s
Temperature Profile Observation: 1228 LT
Vetocrty Profile Obssrvation: 1312 LT
I I
1
BEGIN'
LAST I
Of TE>
Figure 37.
Tetaperature profile used to calculate plume rise and
Froude number on day 40, hour 1300, 1978.
EPA-237 (Cin.J
I4-7G)
TOP OF
IMAGE
^
AREA
BOTTOM OF
I IMAGE AREA;
! OUTSIDE
DIMFNSIOM
FOR TABLES
AND ILLUS-
, TRATIOMS
-------
fTjtTE-ss??
FIRST
LINE OF
TEXT
Ht'RE
DRfl
BEG
SEQ
HEIJ
^ Y
-------
?£?'Si^ < -?'"'•'''• VT~lL~nS'*?"^, •
.."':"'• ' TVPING GUIDE SHEET ' .
HERF
DROPPED
HEAD,
BEGIM
SECTIONS
HERE «
BEGIN s
LAST 1
/ i
t — i
Temperature Profile Observation: 0320 LT
Velocity Profile Observation: 0325 LT
I
24
Temperatuf® (°C)
Figure 39. Temperature profile used to calculate plume rise and
Froude number on day 230, hour 1000, 1978.
116
TOP OF
, IMAGE
nor. OM OF
IMAGf AREA;
OUTSIDE
Dlf/ENClON
FOR TAELFG
Af.;0 !LLUS-
TRA1ION5
-------
4.3 m/s
7 = 0.0011 (°C/ml
AZ /
Temperature Profile Observation: 2030 LT
Velocity Profile Observation: 2355 LT
I I
6 7
Temperature (°C)
8
LAST' 1
OF TB R
Figure 40. Temperature profile used to calculate piume rise and
Froude number on day 4, hour 2100, 1978.
117 _i;
EF6-237 (Cin.)
(4-7-SI
TOP OF
IMAGF.
AREA
-------
HR.T.T
TYPING GUIDE SHEET
CENTIK
OP PAGE:
TOP OF
I MAGE -]
750
700
650
600
550
500
450
M. 400
300
250
200
150
100
50
8.4 m/s
6.9 m/s
Rnal Plums Heigfrt
2.4 m/s
AT
AZ
1.3 m/s
Temperature Profile Observation: QQQ5 LT
Velocity Profite Observation: 2340 LT
I
I
20
21
22 23
Temperature (°C)
24
25
Figure 41.
Temperature profile used to calculate plume rise and
Froude number on day 166, hour 2400, 1978.
118
-------
WING GU'DE SS-ltET
CRMTFfi
OF FAGt
550
500
450
1 400
**
JE
G>
a 350
300
250
200
150
100
SO
7.4 m/s
5m/s
Final Plume Height
AT - -O.OOS5(°C/m)
1.9 m/s
Temperature Profile Observation: 0QQ4 LT
Velocity Profite Observation: 2322 LT
1.0 m/s
18
19
20
21
22
23
Figure 42.
Temperature profile used to calculate plume rise and
Froude number on day 222, hour 2400, 1978.
EPA-«.'37 (Cin.)
(4-76)
TOP OF
BOTTOM OF
IMAGE AREA;
OUTSIDE
D.PENSION
FOP. TABLES
-f Au'D ILLUS-
, TRATION3
-------
BEGIN
FIRST
LINE OF
; TEXT
HErtE 5*1
DROPPED
HEAD-
BEGIN
SECTIONS
HERE Si
j
BEGIN
LAST L'Nt
OF TEXT if
TVPiNG GUIDE SHEET
CENTER
cr- PAGE ,.
n „ r - . j^S
•the hourly ©Eissiea rate, the aulfwr and heat coateat ssffletsrerassit® K&de
oa ea^plea tskea oac@ & week at each boiler srer®
-------
BEGIN
FIRST TYPING GUIDE SHEET
^y»!*«^»q!^r^r^^
LIME OF CENTER TOP OF
TEXT OF PAGE ^1MAGE
HEHE »
DROPPED
HEAD;
BEGIN
SECTIONS
HERE JS
BEGIN
1 A^T 1 IMP
a isfrfee height of the hill i
—— * m • *i_tt i
T is itQA fiwerag® tssparatrar?
29/3s is fths petsatiel ten^eratt;
g is Ithe seealeratieai due ta
i j
Kaffl3fl©%® of the tea^sratur© pro file i
-©rust-Vaisaia $r@qo®aey, sad the free-
(a),
(°K)
re laps® rat© (°K/a), and
gravity, 9.8 ®/5^«
lone allosro £te calcralatioss o£ H, the
streeia velocity say fea de&srEdaad frsar
MntM
if the available wisd profiles sr® not repraeeffitaeive of the ea@@ hour. Tfee i
particular velcieities chosea srere stib;
rfflrage of 3SO tcj 400 ta. Table 21 pr®e<
those gevca hc-^rs selected for e©dsl 4
actively selected witbia ete height
fflts the Froude nssaSjer remits for
os^arisoa. For all three ftmsrs
shoeing significant impacts on Sussierftouae Ko«Btaisj (mouad), flow cotidjtioaa
era closest Eo jneutral flew; two of tbe four hours shfwiesg sigaificaat
iffipaeta oa SasS Kowataia (ridge) are C
TABT^ 21 j OF RESULTS OB
Julian Day Hour U(Q/S)
.eadiag to stable stratification.
f G&LOJlAfWSS
39/32 (°KAa) Fr
^ ^ - e-i/->- J
40 1300 3^1
190 0900 2.6*
230 1000 2.5
q.l /S"
4r 2100 7.0
166 2400 4.5
222 2400 5.0
*Estrapoiated from towsr dats.
Disp@r@iOiS stability claase® for
0.5932 OT91 ^
0.6034 1.02
0.0196 0.37
0.0093 0.52
0.0109 1.30
0.0053 1.24
0.0033 1.73
tteese heurs are root directly
^sasured. Thejtmser dsts give stability elsss estimates f&s the layer b@l®s?
the stacks b@s@d ca the 6es?parst«re gt
appropriat® So 'the el@^®tica of the p1
profiles, eud Stability class csa be «
radiest (Tsfele 22) . Data fssre
.«ESS cea be takeia frsa fife® fceasperatrar®
iaeenaiaed agaia fir-«aa the ££.s^c«ratore
gradient. Keither of these Esstheds, however , tskes aceoaat of Efee ®iad
speed, or the influetBce of u^mizd tertsin features.
I [
TABIS 22. STABILIT? CL&$SXFICATIOH SYSTEM
|
Stability Bascrigtica Stability C
Estreaaly Casteble 1 or A
Modarately teeEable 2 or B
Sli^itly Uastafele 3 or C
Heutral 4 or D
Sli^tly StabW 5 or E
Moderately Stable 6 or F
Eatresaly Stsbie 7 or G
OF TEXT »f-
I 4
§3/8 | -xv:.:
J JL_ ^j 1
Teaperatere asogs
with Height
lass (OC/100 a)
< -1.9
-1.9 to -1.7
-1.7 to -1.5
-1.5 to -0.5
-0.5 to +1.5
+1.5 to +4.0
> +4.0
BOTTOM OF
IMAGE AREA;
OUTSIDE
DIMENSION
FOR TAEtES
•.;.;. ""YAKD ILLUS-
21 J: TRATIONS
PAGE NUMBER
EPA-287 (Cm.)
(4-76)
i
-------
BEGIN
FIRST
LINE OF
TEXT ^
HERE
DROPPED
HEAD;
BEGIN
TYPING GUIDE SHEET
CENTER
OF PAGE
TOP OF
.IMAGE
AREA
ffl@si£ 'lesa 8te!b>l®* class. Th® csee period @ra
md 40 ©r® bothih@wr 1300 with low wia$! epeeda. Usadsr these esaditicB®,
digpsrslou elssS ®sy fall betwea the {inferred class (0) @a«3 tfoe messt less
stsble elss® (C). The oth©r two perieiSe, h©0r Q9QQ on day 190 end hrnsr 1000
OB day 2S9, hs^e such sors stable temperature gradients sad slightly
SECTIONS mss^ sp«eds>9 e©j the inferred stabilieyj class Cl) say fee
HERE
All Sfere© feowsd impact cases
that ^orasspeffid to etabilitijss betroea class 0 aad E at night
(tistsr 21C^ or 2^09). &sc®«8® of tha ^firnd spesde and terr®£fa rotsghaesSj
stability els&iss'B eay ha acre approjMfifetej both class 1 eaS class D
cas® hours.
®ade. Table 23 suasarizes these chcsices for the
23.J R^SGES OF DISPS1S10H STABILIT? CLASS CSSIGHATIOHS
TO
EASED OH
I
TIKS 0? DAY
Bay
Profile AT
Raaga. Mofeled
13
40
1300
2SO
!
166
222
C-D
C-D
D-E
B-E
D-B
D-E
D-E
BEGIN
LAST LINE
OF TEXT S
The cemplea terraia esdal ^as risni fcr 28 cases 5 four runs for e©dri of
the e@v@a ease tetsrs. Th@ four TUBS per case hossr arise froa elss four
possible eeimisiEatiess of two pUiae heights arad two stability classes. (Hue
"scsubbsd" sad ftsnscrwbbed" sEaek parsssters give different elusee rises.)
Predicted eoacetitr©ticas are aorssalized by the quantity Q/5JaS where Q is
the eaissioo ra^e, 0 ths steck top velbeity, aad a the hill height.
Table 24 Hat® ph@ resujlta of the Eodel ctJspwtstions for £fee fonsr ridge
caees; sfed Table 25 the results! for the three ssouad is^sact eaee®.
In efee two! cases chsractsrised by, very low Froude nusi&ers (days 190
emd 2^), grouad-le^el eoraeeatratieas zncreaBe with plisss height. This
effect i@ spariosasi it results froa tssisg the ®Kpirieally-c!eri¥eii
PAGE NUMBER
BOTTOM OF
IMAGE AREA;
OUTSIDE
DIMENSION
FOR TABLED
AND ILLUS-
I THAT !OWS
-------
1
*""
Q Juiien
• - Day R
•
f 3
r 3
/
I-
40
1 40
2 K 40
c w
g 4Q
^
190
190
190
190
230
230
230
230
Pilrill
v 5 - 2 -
TAILS 24. RESULTS
IMPACT 013 THE
sipht (a)
445
445
422
422
432
432
409
409
325
325
307
307
347
347
322
322
- . . . , -i • . . . -_ .-•
OF JOTS!
BK&tBY S"
, CA
EBCT
LCTLATIOWS S
(SA1ID MOOKI
Stability Ficowda {formalised
Class Ksffijfber Concentration
4(D)
3(C)
4
3
4
3
4
3
4
5(E)
4
5
4
5
4
5
. .
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1 -W
.91
.91
.91
.91
.02
.02
.02
.02
.37
.37
.37
.37
.52
.52
.52
.52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.0003
.1497
.0017
.1656
.0009
.1514
.0018
.1671
.4663
.1459
.4371
.1248
.1951
.0182
.1814
0.0133'
poa HOOIS
fAIM)
8HC*™
T '-n CT TT 5
m rp ^ rn ^! ~r — < r— -T
f^j 1^ k; > y fn {J 2 5
CO
m ;
O.i-
Inferred Terrain Infasred Piisiaa
Corrsction Fscfior Path C«3€ffici©®6 ..'
0.597
0.5S3
0.593
0
0
0
0
0
c
0
0
0
0
.599
.611
.613
.617
.618
.344
.344
.372
.372
.412
0.412
0
.452
0.452
0.349
0.349
0.383
0.333
0.390
0.390
0.430
0.430
0.225
0.225
0.299
0.299
0.258
0.25S
0.358
0.35S
-
i> ^; — t
5 5- 0
in > ~a
> Ci 0
mO
j - -
1 ' s
!
-;
\
I
i
1
;
I
: . 5
s
'1
Si
-------
rn ' 3:
x r~
$ ™
-^•j— -
Julian
Day
4
4
4
4
166
166
166
166
222
222
222
222
!
390|§
5< 1 ^ £ 3
J2 ;? rn > '~
CO rv o
^H -?• m is
Plmsa
Height (a)
309
309
289
289
335
335
317
317
370
370
344
344
XraSSdE 25 • iiS!
IMPACT OTI THE I
Stability
4(D)
5(E)
4
5
4
5
4
5
4
5
4
5
JOLTS OP KC
EOLATSD HO
frowda
Knsabar
1.30
1.30
1.30
1.30
1.24
1.24
1.24
1.24
1.73
1.73
1.73
1.73
-C v> cn
SoS
rn — i -^
Q "~
1 1^ S
>BEL CALCTLATIOKS F01 HOUB3 SHOWING
SJ10 (8WSMSR1C08B MOWTAIW)
KorEsaliEcd Inferred Terrain lafar
CoaceatraEicm CorrscEion Psc£©r Faeb C
0.1040 0.638
0.0200 0.653 (
0.1195 0.6S8
0.0296 0.66S i
0.0896 0.64S 1
0.0116 0.649 (
0.0982 0.655 (
0.0170 0.655 (
0.0429 0.703 «
0.0016 0.70S C
0.0558 0.715 (
0.0034 0.715 C
\ "
3T. CD ' J
SI O ^x fn ~ ^ m *
- • m r" ""' *T -I 5 '
^LJ, «
-fl ./..,^
? ":
?@d P1SS5S > :
ssf ficicHBt £ • :
o '
C • '"*"
).616 n "v
n • . i
3.616 H 1
: f
0.651 ; J
3.651 j J
5.571 t
3.571 . 1
3.602 : "
).602 ;
1.607 .
>.6©7 1
).643 1
J.643 |
i
Uv i
1 ij p- 4
|| B ,1
5 o ^ • ^
m T1 J
:-|
-------
BEGIN
FIRST
LINE OF
TEXT
HERE »
TYPING GUIDE SHEET
CENTER
OF PAGE
TOP OF
12.4.2
firon
The eessesdtraticus predicted ©S tfill ers; £
ia £h@ eeaeeratratioa
fiaetor.
e^Lssioa rates end «?iss3 ^p€®ds, sad the resultant nctnsaliEstioa
factors for each of the sev&a £®s£ cage hours are sisaaarised ia Table 26.
The tt®rssligsti'ca factors ecavere rasdgl eosieentracioas t© units
Only £ts© £®o 1^2-a stacks (boiler wni£3 7 emd 8) are iseladed because the
iapect froa tha 304-sa stsck is asal!. j Hote that aorsalization
gives £©r ismsoiitrolled eaiesioas onlyj The WA Air Qaality Braaeh
that BO serubbiJBg ocewrred ©a unit 7 oaring these tours, arad either
quarters or ful,l scrubbing (80% resov^l efficiency) occurred on Unit 8. 1m
@ligli£ly different gross Io4d values (@@l) wsre reported for both
^^saits^&iEiag- ttesa fee^ra-. _JSaia_iaf©r^atioa_iiaa_bei2E_ia£agEate«S Hitb_ the—^
previous data, land revised esassioaa for units 7 sad 8 ©re pressaEed in
Table 27 along yith the new Eormalissfiicm faetors.
plus® risa ce^utatis4s have besn E^de for £h© seven case
hours usisg a gultiple-lsyer plisss rise exteasion of the stable Erigga j
rise equatiotfs'i CHblzworth 1978). For |hoars tdten wraie 7 dc@3 not op@rat<
the scrubbed pitse rise height is caismlatedf for all other hours,
pluigs height is calculated] Khea both units 7 and 8 sre
©psrstiEg, the 'higher plessa elevatiea jcorresponding £© unit 7 is used
SO2 codeeatrstioas of this unscirubbed unit 7 plssie are rassre ehass
twice those of .the scrubbed trait 8 plema. The rasltileyer pl«sas
with the sitjgle layer pluses feeigtjts in Tables 28® and 2!
give aesrly the eeas val«as £0r days 3, 4, ©r«d 46. The greatest difference
occurs for dsy ,166, where the na^ pisses rise esceesds £he previews valua by
55 a. Conceatxlsticas predicted using!the sailtilayer plta^ heists ®re also
ared with eh® observed values. ;
For the hours of isspaet ©a the ridge (Ssad Koastain) the taadel caa
BEGIN
LAST LINE
OF TEXT
AREA
in all eases.
diepsrsiesn rate scaewtser® befiweea
class C e®& el^ss D is required to match the observed eoaeentratioa. The
class D c©spBt«kion overprediets by 1^8%. On day 408 however, the class C
result overprediets by less fh&n 201, jaad say therefore be coasidered e.
mstch.
-------
j* > f-«£3>-
; — M I rj_,
^ --J ••-.
; _ co
j ° '
5
;
i UBS-
: I
\
r
1 1 m
f: fl' f '.
i
(« j
f
1 ~-i >
i: £|
r OF
2 p
,. C/3 l —
CO
O^"CD zn<->-oc^^:^
m~1;? "1=i^O^S5
>-- r- ^ o ^n m
"'5 ^ 2 b H
S .'n % '••-> _ jf.
?! .1 . - . .. ,j 51 t f
' A 1
r t ], i
i
TABLE 26. OKCOSTOOLLED SOj COKCHfEATION KOTMALIUTIOH "' '
FACTOSS FOI TEST CCS5PASISOJ8 HOWS t
SO. Emisaioas, . ,' :
Julia.- Terrein Haigbt Unit 7 S 8 Stack Top „ _ L .-
Day o(a) Q (g/s) Velocity 0 (sa/e) Normalisation Factor » Q/OTT (p^/a ) '
3 2~1 1984 2.0 13,117
40 275 1756 2.5 9,288 ;
190 275 3442 1.2 37,928 '
— 230 275 4265 1.5 37 , 598 |~
4 275 2536 3.0 11,178
166 275 1672 4.5 4,913 ,
222 275 4054 1.4 38,574
j
i
I
f
I
1 f |
"--,1
1~n -,;
j
J C7 .1
o j
m .j
m .'|
m
-•;
"/
o 3- ;;-1
"" 1
•;:
I
_:i
']
fc -^
^SU -i
SigfS 5f 5S :•:>*
33 S. _( > — ' m J> -D
-i 5 <2 ^ o >oo"''^
>'uo D m < m -n . -."«!
" 5 m S 3 ' -".-f-t
S 2 5 ^ _^
-------
O r~ en
- £ S
— 1 j —
X 1™
— 1 =;
$ m
i
O
CO
3
—
hs£ -
1
' I
X lr> OT X 0 • -)5
5 o S S5 o S S 5 3 *
"•ri-^c^ S><^eEc|
^^—l—JL -"^
^ ' i •'''•
TABLE 27. RSVISBD SO, EMISSIOH RATES FOR TOITS 7 AHD 8 1
2
AKD COMBITOD COKCEWTMTIOM BOEMM.IS^TIOH FACTORS , ' -r ;
L Taffl 1KCLTO2 SCRUBBER OPE!lft,TIOK3
Juliem 014 Eaiesicas (g/s) Baw load/Old Lo£<3 Unie 8
Osy Unit 7 Unit 8 Bisit 7 Emit 8 Scrubbing Factor*
3 0 1,934 - 0.987 0.4
>
t'TV
^rf
40 0 1,756 - 1.027 0.4
190 0 3,442 - 0.991 0.2
1 230 2,094 2,171 1.036 1.C41 0.4
4 2.53S 0 0.995
i 166 0 1,672 - 1.C4S 0.2
222 1,842 2,242 1.220 0.990 .4
t, ^i Scrubbing factor « 1 - scrubber ueiHsatiea x scrubber efficiency.
C3 I
•m r. •.-.•-•
!
j/
i
— < > "^ O O ^ or
33 -- O — r- ^- C
> ft 3 =i ZJ > -H
-< ^J . m £o (D — i
0 F J> i 5 m §
£ C ^ 0 m S o
(
Rev EajissioTis (g/a) Honsalis-seion "
Unie 7 ttatt 8 Factor ((j^/a3) ;
0 783 5,177
0 721 3,314
0 £82 7,515
2169 904 27,090
2,523 0 11,121 :
0 350 1,028 -.r . •. 1,1- i
*
' '' ' )•
I
i
-
1 i 1
-*':;i
-;, ;{
"** '-'a
s; • :|
CD, .1
6-> j
li
a; ]
rri ^
' ;-:|
'i
.j
-i
' - \
O o '"'I
" m '.|
ri rn ' '«
^ -30 1
•'
"5
-•- J
./j
i
•1
t:i
•-5
" '1
V - --"I
. . , ._!_ ...^^ j
p Ci "° '' ^
m TI '-J
• " ' •'<;
&'*&v&e^^&jf£HUE&ii&
-------
FF
r
tS
_ r_ _ --.a
O r CT -r en cs -!- O -A
-n ;> JJJ rri n-- rn rn :;t:) x — * ' — ~n ca -•:'
^ i i o . " o ~* z/-i
fef nn (g (/> _^_, ^ ;
L^*5f">»« .
~ fe' 1 c~*
t ^
1 Q
b
^
^
cc
r|- - - - - - - . - -^ p j'
I
j
^
~» ' ^
: S - 3 'J
| TABLE 28s. COMPARISON OF PREDICTED AHD OBSERVED SO. COMCEWTSATIOHS (pg/m3) AT WIDOWS CEEEK j .^ % 1
[
f
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'
TABLE 28b. COMPARISON OF
.
PEEBICTED AKD OBSERVED SO 9 COKCS
.2 5 ^
•••---- • - - [ | i r i
1 1 .• 1
•NTMTIOBJS (pg/ffl3).AT HIlKf^S CIEHK
Julian Crouds Pluao Observed Half-Height Aasumpticn Predictions Level Plum Kodel PretSictloae
Day Musber HaiuJit (ra) Concentration Stability C Stability 0 Stability B Stability C Stability D Stability E
i
E
'i
i.
-^4
r,
3 0.91 422 393
40 1.02 402 550
190 0.37 320 576
230 0.52 370 603
r "
4 1.30 301 1,179
166 1.24 373 367
222 1.73 392 393
i
~^ O O ^ c3
O — <— -- O
33 ^ _| > — (
Eidge ImpeoC
654 1 -
574 3
362 5
, - 136 0
r
H9und Isspact
1,887 864
67 6
1,459 70
t
O ^
Tl ^
" -'&
i m |
i i 5 J g : ' ™ ° '-I
£ c - o m S o "1
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TAHLE 29. COMPARISON OF OBSERVED
AT WIDOWS CREEK AHD PREDICTED
OU THE POTENTIAL FLOW KOrEL WITH
Ifeiltilayer
Julian Plusae Height
Pay (ta)
Observed
Concestratioa
Terrain Model Predictions
Stability C Stability Q Stability E
422
402
320
393
550
576
603
Ridge Impact
932
729
270
157
4,599
12,038
3,354
7,711
Mound Impact
4
166
222
301
373
392
1,179
367
393
1,529
99
2,123
531
16
246
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FveTTTrotreennfat ions1 ."and eKe~ earee's1
"overpredietsd before are EOW even further off.
Additional perspective on the rao
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HER£ B
; Given the j£rreducible rajeer taint ites in the Emissions and the
ataoapheric datfi at plv«e hei^it, moral detailed corapariscns of the predicted"
and observed concentrations for theee seven cases are not warranted.
i
12. * Stsssiary akd Conclusions
Jlusse interactions with two terrain features aear the Widows Creek —
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terrain model. ; Meteorological conditions used in the model correspond to
soven hours selected from nine Booths 'of hourly §02 and meteorological
data collected by the TVA Air Quality iBranch. The hours selected for
comparison were, derived by Batching hours of high measured S02
concentrations 'oa the two terrain features with neutral-to-stable
atmospheric conditions. In addition, ;only those hours with nearly
coincident vertical temperature and velocity profiles were considered. Of
the seven hours^ finally selected, four are associated with impacts oa the
ridge, and three are associated with impacts on the isolated raound. The
highest saeasured S02 concentration on the ridge during the 9-asosth period
was 0.85C pps (2,227 pg/ra^) observed on day 226, and that oa the sound BBS
•«4fc»450 -p-ps- (1-j 1-7*9 -ng/si-*)''observed- oa-day -4» — — — — —- -— —
The hour associated with the greatest ridge impact ms not selected for |
saodel analysis because no suitable velocity and temperature profiles exist j
] for that period. Consequently, the aodel's ability to simulate £h® greatest !
observed impact on the ridge is not known. The case hour of greatest impact j
on the mound (day 4, hour 2100) was simulated! cae choice of predicted
concentration was nearly equal to that observed.
A partial heij^t model using a plwae path coefficient of 0.5 perronaad
about as well aa the potential flow sodel for all Froude ntMabers greater
than 0.6. For lower Froisde nussbers a path coefficient of 0.35 produced
results sisilar to potential flow sodsl. The level plusae jaocSel greatly
overpredicted sost of the tiase, and Hatched observed coneentratiois for the
one hour in which the other tsodels markedly ut^erpredicted,
Uncertainties is the aeteorological conditions at plssee height, sad ia
the emssiotis froa the facility, cloud the comparison of ssdei predictions
with observations. Given the range of data, reasonable combinations of
assumptions can produce good correspondence beteeea the concentrations in
six of the seven cases. This dees not, however, constitute an adequate
evaluation of the Eodel because of thQ uncertainties underlying these
assumptions. The three greatest uncertainties lie in the specification of
the dispersion parameters, the final plusae height, and the actual emission
rate. Data are not available for more accurate estiaates of diffusion rates
and plume elevation. i
nonetheless, the prelirainary coasparison for the hour of greatest impact
on SuaBserhouse Mountain is encouraging and the bracketing of observed
concentrations ;(in many of the other eases) suggests that better
observations may «ell iaprove raodel perforsaance.
i t
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HERE 9
T
ASMS, 1963. Recosgseaded Guife for the Prediction of the Dispersion of
Airborae Effluents. M. §sath, e<3. Hf« York, BY.
Briggs, G. A. 1975. 'Plws® Rise Prediction. Leetttres on Air Pollution amd
Eavircnggntal Impact Analysts, Aserican Meteorological Society,
pp. 80-34.;
Briggs, G. A. 1973. Diffusion Estimation for Saall Emissions,
Ateospheric Turbulence and Diffusion Laboratory Contribution File
Ho. 79« ,
Briggs, G. A. 1969. Pltcsa Rise, Critical levies (TIB-25075). Atoaic
Energy Ccsgaission, Division of Technical Information, Oak Ridge, TH.
Britter, S. E.,1 J. C. R. Hunt, sad J. 'S. Pwttock.
Pollratioa Concentrations Kear Buildings and Hills. ProeaedJBgs of
Ccmfareace oa gyetSBa aad Hodel8in Air and Water Polluti&a. last.
Meas. and Control, Louden,
Csbe, D. B. et al. 1977. Application of the Gaussian Dispersion Model to
Predicting Masiat^ Pltsse Concentrations ij^Abrtiptl^ Sis ing Terrain.
Mr Pollution~Coatrol~A8sociation (APCA) Paper Ko. 77-58.2.
)
Cramer, H. B., B. V. G«arys esd J. F. Bowers. 1975. Mffusion-ffiodel
CalCTElaSleaa of Long—Tern and ghort-Tera Growre!-Level gQg
Coaeeatraticas in AllssfeCTy
Peimsylveaia. SPA 903/9-75-018.
BEGIN
LAST LIKE
OF TEXT S
Prepared for U.S. Isviron^satal Protection Ageaey, Eegion III,
Philadelphia, PA. j
Csanady, G. T. 1973. Turbulent Hffusion in the BnviroitBsnt_. Boston:
D. Seidal. >
Egan, B. A. 1975. Turbulent Diffusion in Cosiplez Terrain. Proceediaga of
Workshop on Air Pollatica Meteorology aad Enwiroametiital AsBeas^ent.
American Meteorological Society, Boston, MA, Ssp£e^?er SO-Qctober 3.
i j
Eg en, B. A. and A. Bass. 1976. Air Quality Modeling of Effluent Pltases in
Sough Terrain. Proceediafga o£ Tfoird Syisposiisa on^Atgosptsggic_
Turbaleace, Diffusion and Air Quality. Mericaa Meteorological
Society, Raleigh, KG, October, 19-22.
AREA
EPA-267 (C-n.)
(4-761
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OF PAGE
B. A., RtjI^'S^i-60* sm^ c« Vaudo. 1979. AessassiEg Air Qgaliey
in Effigies®; of Hsrotaismss Terrai^.
Pifftasiea jsad Air PoHafcion.
TOP OF
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AREA
Society, Eaao, m, J«usry 15-18.1
SPA 1978.
Protection Ageaey, j
. 1PA-450/2-78-027. U.S.
of M
Hiads, W. T. 1970. Diffusion O^er Coastal Ktoustaies of
Atessphagie BaviroEg'sat 4sl@7-124.
Eoffosgle, G. w.t B. A. Egs0s snd 3, i[. Grains. 1977. Appileatio®
Models £H Ceraplex fesraia,, *mcdino£ JoiatCpngeremea
^^^ ,_
Meteorological Seei@ty, Bsseoa, MA.
i i
Holzworth, G. C. 1978. Estimated Effective Chiaaey H®£^»£s Bssed en
Essriesoade' Observatieas at Seleceed Sites ia Eh® te&ited States.
BEGIN
LAST LINE
OF TEX] Js
j J. C. R. aad 1. J. Msslheara. 1973. Ttarfeialeae© Bispersioa from
Sources Wear Ti?0-DiaEasi©Qal Obstacles. Joaraal o£ Fluid
Macbamies 61! 245-274 .
Hunt, J. C. R.j J. S. Puttock, end W. te. Saydsr. 1979. Turbulent
frca a Point Smsree in Stratified satd Heatral Fls$?s Arowad a
?Br@e—DiEsasirassl Hill* Fart I •* Diffsasioa Siquatioffl toaly®is.
Ateospheric Era'gdgi^aeit^ 13; 1227-1239.
i ' !
Hunt, J. C. R. and W. H. Sayd^r. 197S. Plow Strwetwre snd Turbulent
Diffusion Armmd a Thre®-Bia©a@ieaal Hill. Fart II - Surface
to Upstreesa
Hunt, J. C. R.?! Wo H. Stiyderp and a. E. LawsoiSj Jr. 1978. Flo^y
aad TogbMlent Dif f«@ica ArmiRd a !°rhreg-Bigga@ieaal Hill. Flusid
®a Effect® of Stratiflcatica? Part 1, Flow
EPA-6TO/4-78-041 . U.S. Ea^irosigsatal Proteetioa Ageacy, Research
Park, HC.
iay J. S. 1979. ScheEe for EstiE^tii8% Dispegsion ParsKst©ra as a
Fuaetioa of Sslease. _lfoi^it. EPA-6CO/4-79-OS2. U.S.
. _
Proteetioa Agmey, Research Triaagl® Park, EIC.
1 i
Leahey, S. M. 1974. Ofesanratiojsal SSadies of Atraospheric Diffusion
Processsa cw©r Irregular Terrsia. Proceedings e£ the 67th liaetiag
the Mr Pollutioa Coaerol Association, Dawfei'j CO, J«a@. 9-13.
§3/8" Y
1 1_
TRATIONS
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-^e«hey, D.
J. Bssiitdky. 1973.
Low
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Related Diffusion Estimates froa a Site Located in the ItsdsOT River
Valley. AfeBqfjgherie EB^irorosat 17849-61.
P. B>9 L. B. Babeolal, and JP. B.
41 of ft over Cffinplsa T@sr®iQ«
Pollutiea.
1974. Diffusion
J!-g_ igQg
"
Miller, C. W.
for Rough
Milras~The®9©a, t. M.
. AtiBpsphegie tovigenasot
I
1960. Theoretical
Tos&t
la Pltaae
Pesqwiil, F. 1978.
SP4-6DO/4-78-021. U.S. Envirssaaatai FroEeseioa ^gsney, Esssarch
Park. KC.
^-- 1970v
ieEV P-*r As- sa^ L.
Sttsdy (IAPPBS.) .
1-4. Kstioosl Air Pollution Control
Adsiaistrafcicss Pablicaticm Kos. 70-2, 0589.
• i
Sb@e?e?t B. L.»'D. a. Miao££, atsd G. R. Hilat. 1977.
Cos gf ieient8fog
^ _^_ .
Prepared for the 0.S. EEsrgy Sssearcli
EY-76-C-02-4
..
A&aiaieEratioa.
Snyder, H. H. 1977. Safes Report. Projects Hnrat Hill Study. Part?
Hill. EPA| Fluid Modeling Facility (isnpu1blisto@sl aaaascript).
i
' i
Snyder, W. H. 1978. Data Report. Project! Huat Bill gtudy. Part:
Chaessl - PolyEBsial Hill. EPA Fluid Modeling Facility (unpublished
tsana script).
i
Sayder, U. H. sad R. B. Britter. 1979®. Saadsprsy Bouodary Layer
Coar^terisation (SSBL4). Onpiblished EPA data report.
! I
Snyder, W. H. ssd 1. I. Britter. 197fb. Aspect Ratio Study (&S2AT).
Snyder, W. H. aad G. L. Mar@h. 1977. ZSat® Report. Projects Hunt Hill
Study. Parts Wiad Tttmsel - Polynomial Hill. U.S
Agency Fluid Modeling Facility (umpssfelished
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HERE Bfc'Start» G. E., f|. R. licks, ®®d C. R. ^icksoa. 1976. Efflweat
Terraio.
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BEGIN
SECTIONS
HERE »
Meteorological g^siefcy, EsleigJ»,i EC, ©eeefe®? 19-22.
i i
Start, 6* 1., 0. M. Bicfessffa, etsd L. L
S«ttosif 0. G.
, B. B. 11970. Workshop of Ate&spberic Bispersiea Estimates
of Health, Itoc®ti«m m& ¥@lf©re. Fublie Health
599-AP-2S, 88 pp. i
U.S.
, M. Di 1977.
in Repgrt_to fch.8EPA of
__ _ _
' Coafereaea oa efee BL-'AHo4eliKg^GuIdenBe, pT 210.
Wilson, S. B. 4e al. 1976. DifftBgiea Under
Atsassfharie ^saanistratica,
Tecfeaical Hsaoraadna 1SL
Ii'iE _
»?s?wwj™«
' fl
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APPENDIX A
PROGRAM DESCRIPTION - CMPLX MODEL
137
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PROGRAM DESCRIPT
-A
- CMPLX MODEL
Al. Introduction
This section susaarizes the essential operating features of the com-
puter model CMFLX developed during the:initial phase of this work. Because
of the research inature of this computer code, it is expected that signi-
ficant revisions may evolve based on subsequent experiiaeiital and theoretical
developments. Therefore, no attempt has been made to produce coasprehensive
KP8?8™ documentation at this_time,_particularly_with_respee_t Jt0 .£he_.speci-.s_
fled input/output format chosen. Howe¥er, the overview presented her® will
enable the potential user to become thoroughly familiar with the fundamental
programing aspects of the code and orient him to its use.
The CMPLX program is a Gaussian point-source diffusion model applicable
to isolated terrain obstacles of arbitrary crosswind aspect ratio in the
flow field downwind froa the source. |The plume is assumed to be easbedded
in a potential flow field determined by the specific source/obstacle con-
figuration involved. This geometry determines: (1) the pluiae trajectory
above the surface, and (2) the kinematic constraints on pluse dispersion
imposed by the spatial dependence of the velocity field. The theoretical
aspects incorporated within the code have been previously described (Section
5) and will be feferenced by equation number. Since the formalism adopted
has been pursue4 rigorously only for neutral flows and the limiting aspect
ratio cases of a three-dimensional axisyrazaetric hill and a two-dimensional j
circular ridge, certain approximations have been incorporated to extend the i
model to a broader class of potential field situations, including the effects!
of stratification and intermediate aspect ratios. These features are dis- j
cussed in Sections 8 and 10, respectively, and will not be repeated here.
The code in its present form consists of a main program, four sub-
routines s and two function subroutines. In the course of the discussion to
follow, reference will be made to the program flowchart (Appendix B) by
FORTRAN statement numbers in parentheses and flowchart page number and to
the computer program listing (Appendix C) by compiler line number (at the
far right of each printed record). Cement cards have been used extensively
in the listing, and essential data presented there will not be repeated.
Variable and subroutine names are capitalized by convention. A sample
output listing is illustrated in Appendix D.
A2. Main Program
A flowchart of the main program (Appendix B, p. 148) illustrates the
features of the calculations performed for each case.
' ___ iili 138 _j __ _____
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read Input values for a particular situation (XS, HS, HA, XL,
ALAM,|DELICT, RKST, FROUDE),
specify necessary constants,
relevant nondiffiensionkl parameters,
© streamline and velocity field aspect ratio weighting —
factoys for neutral f ICM (A)'
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specify two- and three-dimeniional streamline for neutral flow and
weight for given aspect ratio (B),
compute empirical streamline!lowering for stable stratification
effects (C),
perform along-streamline line integrals (D), and
compute dispersion coefficients, centerline and ground-level
concentrations; print out results (E)
i i
(Program elements followed by capital letters are explained in the following j
| _ 6-1 "2 •
T
BEG!,.;
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A2.1 Aspect Ratio Weighting Factors (A)
! i
As described in Section 10, the effects on a flow field of a hill with
intermediate aspect ratio ALAM, falling between the two- and three-
diEensionai limits, ALAM = 10.0, ALAM = 1.0, are defined by streamline (WZ)
and velocity field (WV2, WV3) weighting factors. If the specified value of
ALAM is less than or equal to unity (601) a three-dimensional computation is
made (WV2 = O.OJ WZ, WV3 = 1.0). Conversely, all aspect ratios greater than
or equal to 10.0 are assumed to characterize two-dimensional situations
(602), and the values (W2 = 1.0; WZ, OT3 = 0.0) are assigned. If neither
condition is satisfied, a general weighting of streamline height based on
one set of wind,tunnel experiments is adopted:
! I
lj?Z = l.O/ALAM**!.!
while velocity fields are defined based on the speed-up factor SUP (Equation
10-13), and weights are given by (Equation 10-17):
I
WV2 * 2.0 * (SUP - 1.5)
WV3 = 2.0 * (2.0 - SUP) |
| I
1 <
A2.2 Neutral Streamline Evaluation (B)
1 i
Beginning with statement 603 (Appendix B, p. 150), two- and three-
dimensional streamlines are evaluated through the source as (XX,ZZ) pairs
assuming the obstacle to be one of these limiting cases. The code sequence
to statement 60S i:; performed twice: once for ND = 2 tatd once for KD = 3.
"The value of the stream function through the source PSIP, determined by
\parameters XS, HS, HA, is first computed by calling function subroutines
V|[.-JP_SIP2D or PSIP3D. Since this value must remain constant along the trajectory,,
'"'streamline Equation 5-28 is solved for each ZZ value to yield a unique
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value defining the streamline (see aiscussion in Section 5.4.3). Only _
positive XX values are computed, since! the stresaaline is symmetric about the
origin at the obstacle center.
The upper and lower limits to possible ZZ values are given by the
height of tli© streaalirae HI above the {rrest 1C (at XX*=0.0) and that at
XX = 100.0 (tak^ra as infinity), respectively. Appropriate ZZ values are _
gjSelected within ; this range at two_ £ggo|"tioiB_. A total of NINC values are
~
HI
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rang
<_ 22 <_ (ZC+KS)/2.0
and NINCMI («NI?C-INC2) values such that:
(ZC+KS)/2.0 < ZZ <_ ZC
Dual resolution's adopted since the streamline becomes relatively flat in
the region determined by INC2. Nominal values of NINC « 550 and INC2 « 150
have been selected to provide adequate j resolution in each region. Thus a
total of 550 (XX, ZZ) pairs are computed.
Computed (XX72Z) pairs~are~stored['{lilie~8ri*ppendlx"B,~~151) and" indexeiT'i
by an integer v^lue from 1 to NINC in arrays (FITX(ND,II), FITZ(HD, II)), j
respectively. They are placed in common with subroutine ZITRPL (Appendix B, j
p. 163 ), which 'provides a z-value for; any given x-value by linear inter- j
polation. Once. -the two- and three -dissfensional streamlines are evaluated, j
the aspect ratio '"streamline weighting factor (WZ) is used to corapute a
weighted neutral streamline stored as j(FITX(l, II), FITZ(1, II)). The
x-resolutioa chosen is that of the three-dimensional streamline (i.e.,
FITX(1, II) = F|TX(3, II)) necessitating a call to ZITRPL to find the height
of the two-disse^sioraal streamline ZEE2,, corresponding to each new x-value
(two- and three-tdisensional streamlines have different (x,z) resolutions).
The weighted z-value is given by:
FITZ(}, II) = (1.0-WZ)*ZEE2*tfZ*FITZ(3, II)
! i
This sequence terminates on statement 605.
A2.3 Streamline Lowering Because of Stable Stratification Effects (C)
1 I
As previously discussed (Section 8), the predominant effect of stable
stratification is assumed to be a lowering of the streamline below the value
it would attain at the crest of the obstacle in neutral flow. The magnitude
of the effect is based on experiment for the three-dimensional case and
assumed to extead proportionally to the general case. This aspect of the
calculation (statements 605 to 610) isj illustrated in the flowchart in
Appendix B, p. 152. i
If PGT stability class (KST) of 4!or less (A = 1, B = 2, C = 3, D = 4)
is specified, no stability effect is coaputed. For stably stratified
cases, a correction is applied to the neutral streamline with a maximum
depression at tfe© crest (XX = 0.0), decreasing linearly with increasing
|XX| to no depression for all |XX| >_ 2.0*HA. For each KST, a value of the
-s-treamline height above the crest ZCF f.s computed as a function of HS and
±MO Jiill. heights...
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streamline Depression DELTAS and fractional streamline depression FMC3__
are evaluated wjlth respect to the neutral three-dimensional streaaline.
Although data is available only for thje three-dimensional effect, it is
assumed that a similar depression is applicable to two-diiaensional and
aspect ratio weighted stresalines. For the two-dimensional cas®, a frac-
tional weighting FRAC2 appropriate to {each two-dimensional XX value (=FIYX(2,
sspTT)) is evaluated. Finally, each streamline value is multiplied by the
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FITZ(1, II)
FITZ(2, II)
FITZQ5, II)
FITZ(1, II) I* FRAC3
FITZ(2, II) j* FRAC2
FITZ(3, II) I* FRACZ
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(Note: it is necessary to retain and weight the two- snd three-dimensional
streamlines at this point since they are used in TKER to compute the filial
velocity fields!)
A2.4 Along Streamline Line Integrals (D)
**• ~The"line Integrals'3* ~ahd"T"(se~e Sectton~5r~Equatibns 5^117 5-127
5-23, 5-24) determining the magnitude pf crosswind and noraal dispersion are
evaluated by the coding between statements 610 and 101 (See Appendix B, pp.
153 to 155 for flowchart.)
The values1 of these integrals PHID and TEED, respectively, are stored
in arrays indexed by integer values JJ corresponding to a given position
along the x-axis, S2(JJ), and downwind, distance from the source, DDW(JJ).
These are related by DDW (JJ) = S2(JJ) - XS. Since these integrals are
continuous functions of along streamline distance, s, it was decided to
sample their values at a discrete number of points determined by a user-
specific dimensional resolution, DELINT (nondimensionally, DEL). The total
number of values sampled, JF, is restricted only by the total array size
(dimension) of the affected variables within the region of interest along
the x-axis:
JF - AINT((XL-XS)/DEL)
I
where XS is the stack position from obstacle center and XL is an arbitrary
point chosen downwind of the obstacle.; (These arrays are currently
subscripted for 50 values.) j
The integration is performed by Simpson's rule along streamline
segments with upper limit BB and lower; limit AA corresponding to one DEL
interval. The fine resolution within each segment is selected by specifying
NN. The integration mesh size is then;
H = (SB-AA)/FN = DEL/FN
(FN is the floating point value of NN.)
When JJ * 1, the lower limit is set as XS; the source position and the j >c7iO" >
IMAGE Apr A
OUTSIDL
DEL i S Diy':NS!-:'
~3~t~~•-.-- \Ar,
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TYPING GUIDE SHEET
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HERE »^subsequent iterations,"the upper ii|ait~is chosen as:
* DEL
DROPPED
HE4D;
BEGIN
SECTIONS
HERE *
BEGIN
LAST UNI
OF TEXT ?4~
= SS = AINT(XS) + JJ
and lower limitf
AA •»
- DEL
For each JJ, the values of the md T integrals for the specified DEL
interval are computed as follows:
PINT
TINT
AA
P dx
BB
/ Tdx
AA
^ejrespective kernels P, T are evaluated at each grid point x by calling_
a sequence of two subroutines TKER andj D1D2 (see Appendix B, pp. 158, 159,
i61>.J-o.' .Returned values from those subroutines include the P and T
feesmeiSI along $treasjline velocity UUU and slope M and the diffusivities
in each direction Dl, D2. (Subroutines will be described in more detail
in the following,section.) The segment of the integrals for each JJ value
are summed iteratively in arrays PHI(JJ), TEE(JJ):
I
PHI(JJ) = PINT «• PHI(JJ-l)
TEE(JJ) = TINT + TEE(JJ-l)
These arrays are the line integral values along the streamline from the
source XS to the position S2(JJ) along! the x-axis without multiplication
by the diffusivities Dl, D2. As described earlier (Section 5.5, Equa-
tions 5-6 and 54-17), effective diffusivities are defined at each downwind
distance (or constant values are prescribed, Cl, C2). The and T integrals
at distance S2(JJ) along the x-axis are given by:
PHID(JJ) = PHI(JJ) * Dl
TEED(JJ) = TEE(JJ) * D2
This procedure continues for JF iterations and proceeds along the x-axis to
a position of S2(JF) = AINT(XS) + JF*D£L. By choosing an appropriate value
of XL (say, one hill height along the positive x-axis), calculations are
performed alonglthe windward trajectory and terminate after passing the
obstacle crest to the leeward side. I
A3.5 Compute Sigmas, Centerline and Ground-Level Concentrations (E)
Beginning 6n line 101, parallel calculations are begun to compute
dispersion coefficient estimates and centerline and ground-level concentra-
tions as a function of downwind distance from the source for two cases:
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TRAT10NS
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i. HERE
TYPING GUIDE SHEET
CENTER
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a flat terrain situation, with the given stack parameters and —
stability class (left branch in flowchart, Appendix B, p. 156 and
157 ) and
2) the analogous situation with
" "" = -XS (righ
distance DDW(JJ)
the obstacle centered at downwind
t branch).
p;£iH2i enfcs-used -ere-the--
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PGT "flat" terrain values evaluated asi SIGZM(JJ) and SIGYNH(JJ), respec-
tively, while centerline and ground-lej/el concentrations are computed using
the Gaussian solution (Equations 5-7 apd 5-20) with height above the surface
taken as a constant value given by the! effective stack height MS.
To evaluatfe the functions in the presence of the obstacle. Equations
5--20 through S-{25 are used with the dispersion coefficients SIGZH(JJ) and
SIGYH(JJ) given, in terms of the $ and IT integrals and along streamline
velocity, US(JJ). Centerline concentrations, CCLH(JJ), are the coefficients
of the exponential term in the Gaussian solution and ground-level values are
cosputed by multiplying the centerline; values by a factor equal to 2.0 times
the exponential'tena using the appropriate SIGZH(JJ) and height of plume
^fnteriiue above surface, ANS(JJ>-.-~~This -height—is-det«minsd by -subroutine^
SURF, which computes the distance from! the surface along the normal to the j
streamline at a given x-value. This subroutine will be described further in !
the next section. f i
After printing out the required tables of the values described above, j
(see test cas'e,-,Appendix D), the program computes off-axis, ground-level
concentrations CGL(JJ,K) by multiplying centerline concentrations by a
crosswind exponential expressed in fractional increments of SIGYJi(JJ) up to |
two standard deviations off-axis. An integer flag, IY, is set to facilitate j
this additional'calculation if required.
If new data is encountered by the; read statement 555, the entire
sequence is repeated commencing at start. Otherwise, the program proceeds
to line 999 where the job ends (EGJ means end of job).
A3. Subroutines
i
This section briefly describes
SURF, and ZITRPL.
!
A3.1 Subroutine D1D2
subroutines D1D2, PSI2D, PSI3D, TKER,
BEGIN
LAST LINE
OF TEXT B
This subroutine computes the required values of along-streamline
diffusivities in the vertical (Dl) and! crosswind (D2) directions. Basic
features of D1D2 are schematically presented in the flowchart on pp. 158
and 159 of Appendix B. It consists of a number of branches that perform
the following functions:
|
e If thfe branching parameter IFLAG = 0, the calculations are per-
formed fcv constant diffusivity values (statement 80) specified as j
Cl and C2, for the normal and crosswind diffusivities, respec-
tively.
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FOR TABLES
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If a &ffusivity is sought f^r the "flat" case, such as in
Section E of the main prograi (see Section A.2.5 above), the value
of th$ parameter H is set:
H = 0.0
s parameter
and dispersion coefficients pre read directly from the PGT curves
as a function of stability class KST for a given downwind distance"!
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If IFLAG $ 0 and H j< 0.0, thfc calculation continues, and the
distance along the streamline PS and the advection time PT are
computed by D1D2 using a Tay
Si
il+1
or series of the form:
each time D1D2 is called during the Simpson's rule integration
schema {Section A72T4). Forj each ^JJ interval, it "is necessary "to1-"
keep Count of the integration loop counter I. When both JJ and I
are zero (at point -XS), diffusivities are set identically equal
to ze^o (statement 75). For each subsequent 1=0, the initial
valv.es of PS,PT are set equal to the values PSA(JJ-l), PTA(JJ-l)
from the previous DEL interval integration. Note that calls to
D1D2 are arranged to increase the x-argument linearly from -XS to
BB (the upper limit for any integration segment.) Therefore, when
XX = IjIB (statement 97), i.e., the upper limit for a particular DEL
integration limit is reached, the value of PS and PT are, respec-
tively, the along-streamline distance and time. The PS value is
dimensional!zed and used at the downwind distance x (statement 98)
to evaluate dimensional vertical and horizontal dispersion
coefficients for the flat case using the PGT prescription for a
specified KST. Dimensional diffusivities are then computed
(beginning at statement 71) using the dimensional advection time
PI. These are non-dimensional!zed for return to the main program
(statement 90).
In this manner the diffusivities from D1D2 are returned as functions of
downwind distance at a resolution equivalent to DEL, scaled with respect to
the "flat" PGT values. j
1 I
\3.2 StatementiFunctions: PSI2D, PSI3D
i
For given diraensionless x- and z-arguments, the statement functions
PSI2D and PSI3D (see Appendix B, p. 160 ) return the dimensionless values of '
the two- and three-dimensional stream functions for flow over a half cylinder
and an axisynsmetric hemisphere, respectively.
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I
I
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,4-76)
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HERE S4-A3.3
TYPING GUIDE SHEET
CENTER
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HEAD.
BEGIN
SECTIONS
HERE . B
Subrouting TKER
• i
This subroutine computes the aspejct ratio weighted velocity field
CUU.W), which is used to evaluate slope (M), along streamline velocity
(UUU), and the P and T kernels for a given x-value. It is called repeatedly
during the Simpson's rule integration 'scheme described in the previous
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section.
162
The following steps are followed (see Appendix B, p. 161 and
I
« Velocity components for two-dimensional flow (U2,V2) are computed
from an analytical expression derived from the two-dimensional
streams function for given x ^nd z. (Subroutine ZITRPL is called
by setting argv^aent ND = 2 to obtain the appropriate z-value along
the two-dimensional streamline).
9 An analogous computation is performed for the components of the
corresponding three-dimensional velocity field, first calling
ZITRPL (X, NINC, 3, Z) to provide the height along the three-
dimensional streamline.
-« The aspect ratio "weighted velocity field is" computed" from weighting;
factors KV2, WV3 (see Section 5.2.1):
UU = WV2 * U2 «• WV3 * U3
VV = WV2 * V2 + WV3 * V3
9-1 •„• I
I I
• Slope M:
y = w/uu
o Finally, the kernels P and T! are computed for each x within the
integration, in addition to along-streamline velocity.
I
A3.4 Subroutine SURF )
i
SURF is called during evaluation of ground-level concentrations to
compute the distance between the plume centerline given by the streamline
equation for a given x-value and the surface. This distance is defined as
the length of the line segment normal to the streamline at point (S3, ZEE)
and intersecting the surface. The point of intersection with the surface
may fall into oae of two regions: j
, I
(1) before the windward and after the leeward edge of the obstacle
(AXINT > 1.0); i.e., in the flat part of the topography; or
1
(2) on the obstacle AXINT < 1.0 |
; !
In the first case, the intersection point XINT obeys the equation of
the line normal to the streamline at point (S3, ZEE) (i.e., has the negative
reciprocal slope SLO) and has a zero z-value. For the second case, the
intersection point XT,ZT obeys the equation of the same line and also the
.,£- equation of the circle defining the surface in the x,z plane. For both
OF TEXT "^teases, the value ZNS is calculated from the basic geometric relationship for
j~the"~dlstance between~two~points i ^
, %'^" 7
BEGIN
LAST LI
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(-3-76)
'^ 145
PAGF. f'ji
ahi'fe-'ifoiii^ifilrrf1* -'^-^'"''^""•sJ"
-------
'. BEGIN
FIRST
LINE OF
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HFRE
TYPING GUIDE SHEET
CENTER
OF PAGE
DROPPED
HEAD;
BEGIN
SECTIONS
HERE
5 Subrouting ZITRPL
This is a sample linear interpolation routine that returns the z-value
(ZEE) for any given x-value (SX) within the range defined by arrays FITX(MD, j
II), FITZ(ND, II) of NINC discrete, x-iand z-values, respectively, defining j
the ND-dimensional streamline C^D equals 1 is the aspect ratio weighted j
^Streamline). Since only positive definite values are stored in these arrays J
of the argument is taken. A DO loop searches down the FITX(ND,II) array in
order of descending x-magnitude by incrementing the argument until the
[condition: i i
FITX(ND, KP1) £XX <_ FITX(ND.K) j
!is met at which point control passes to statement 2 and the DO loop is j
[terminated. At this point, a linear interpolation for the appropriate z- \
|value ZEE is performed, and ZEE is returned to the calling program. j
i
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EPA-287 \Cm.
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APPENDIX B
PROGRAM FLOW CHART
147
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'•'. TYPING iSU IDE SHEET
Read Input Values
XS. HS, HA. XL, ALAM,
DELICT, KKST. FROUDE
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TYPING GUIDE SHtET
CENTER
OF PAGF.
A. Compute Streartilirts and Velocity Field Aspect
Weighting Factors for fSSeutrsl Flow.
t
a
Enter vj Tast for 20/30
fcnter >&| Umitir,g Cases
Streamline Weighting
WZ-1.0/ALAM"1.1
Velosity Weighting
Compute BETA
Compute SUP
= 2.0' (SUP -1.5)
WV3 = 2.0* (2.0 - SUP)
149
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iLu'JS-
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TT**- •^:?g''^V^*W^^?B-'^''ff'V*fl'^j^^
FIRST TYPING GLHDE SHEET
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TEXT r _ '..
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I LASTLir.EL
I OF TE/,1 ^"*~
CEWTER
OF PAGE
Bl. Spscify Both 20 & 3D Streamline through Source for Neutral
Flow; Weight by Aspect Ratio
Compute Value of
Stream Function through
PSIP2D (XS, HS, U, A)
PSJP3D {XS, HS, U, A)
Compute ZC:Z VaSue
of Maximum Streamline
Deflection sbov® Crest
at XX = 0.0
Compute H1:Z Vaiue
of Streamline at
XX =100.0
Solve Streamlirta Eqn:
XX = XX (ZZ. PSiPJ
Using NINC Values of 2Z
« With INC2 Values:
H1 < ZZ < (ZC + HS)/2.0
« NIESSCMI Values:
(ZC + HS)/2.0 < ZZ < ZC
150
"Z]
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LINE OF
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HERE as
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B£G!N
SECTIOM-
HERE !*?*-
BEGIM
LAST LI I if I _
OP TEXT &**•
TYPING GUIDE SHEET
;__ x_ .
EPA 267
CEMTER
OF-PAG.?
82. (Continued)
Values in FiTX.Z
F!TZ«2,
FITXJ3. !
FITZ(3,
FITX(2or3.
= 0.0
Weight f^sutrsl Streamline
by Aspect Rstio
, II)
Call Subroutine ZITRPL
Find Z Value ol 2D S.F. ZEE2
Corresponding U> FITXd, li)
^Return
WEIGHT 2D/3D Z Values
ZZ = (1.0-WZ) * ZEE2 + WZ ' FITZJ3.II)
Store Weighted S.L.
FITX(!,H) = XX
151
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FOH TABLES
ILLUS-
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""BEGIN
FIRST ,
LINC ~
, /^ \^^j^^~i^~-''~^vfv^>if'^v^^f^w^yKif',^fM* 'j-|^»Tu*'."'^y"J/yr|y>?gj^JfTiyy'y!~i^p^' I^-M^T"! •> 'n'jm •
TYPING GUIDE SHEET
C. Compute Empirics! StraamBna Depasssfon Due to Stability
^
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BEGIN i
SECT1G
HFRE i
BEGIN
LAST L
Oc TEX
Weight S.L. Depression
by Froisc'a dumber
Compute Frouds #
Corrected Z at
Crest Based on
Fit to Empirical
Data : ZCF
Compute Depression
at Other XX
Compute Fractional
Depression at
XX : FRAC3
Assume Same
Fractional! Depression
for 2D and
Aspect Ratio
Weighted S.L.
FITZ'(3, II) l
1 FRAC3
FITZ(2.II)-
FITZ{2, II) * FRAC2
FiTZ(i.ii)=
FITZ(1, II) ' FRAC3
FOR TAPLFS
Af'JD ILLUS-
(4-70
-------
BEGIN
FIRST
LINE OF
TEXT .
HERE S
DROPPED
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BEGIN
SECTION
HCrlh
BCGIM
LASTLINF|_
OF TEXT 3fi-
TYPING GUIDE SHEET
01. Perform along Streamline Line Integrals
EPA-2&7 (&
(4-761
Set Up Intention Parameters:
D5EL= Nondtmensional Resolution
of Output
JF = # of integrations Given by
Region of fnterest from
Source {at XS) to Downwind
Position (XL)
FN = # of Resolution Points within
Each DEL interval
Begin Integration (JJ = 1, JF)
Upper Limit on X Axis
B = AINT(XS)
Lower Limit
AA=XS
Lower Limit
BB-DEL
Integration Interval
Zero Summation
Variables
SUM 5 = 0.0 ; SUMS = 0.0
SU!Vi8 = 0.0 ; SUSV89 = 0.0
Initialize Loop
Counter
1 = 0
„•:; 153 ;,
f: -,!- r,',"•.'',.'-.'•<
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ARC A
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TEXT ^
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UROPPED
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BEGIN
'SECTIONS
H[FiE i5
TVPJNG GUIDE SHEET
D2. (Continued)
Evaluate Integral
Kerne! Values at
Lower Limit AA
...,••*-
Give X Its Starting
Value for Loop
X = AA + H
^
Continue
*
XPH = X + H
*
Evaluate integral
Kernel Veiues at
X. XPH :
PX, TX, PXPH, TXPH
£
SUMS = SUMS + PX
SUMS = SU?^S + PXPH
SUM8 = SUft^B H- TX
SUM9 = SUMS -6- TXPH
s
/I - /EM •3\\___- ^^ !»
^N°
1 = 1+2
X=X+2«H
D2
'Call
Subroutine
TKER
Kernels : P,T
Velocity : U
Slops : M
j Return
I Call
Subroutine
D1D2
Diffusivities :
D1, D2
Along S.L
Integretion
Return
Evaluate Integral
Kernel Vslues at
08-H,
Compute Final
Integrals
PINT, TINT
154
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J.
UOTTOM OF
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^D ILLUC-
[RATIONS
-'•I
(4-7&J
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FIRST
LINE OF
TEXT
HERE £s
DROPPED
HEAD;
BEGIN
so:nor«;s[__
HERE Stp-
TVPiNG GUIDE SHEE
BEGIN
LAST LIKE
OF TE:XT 3
4 3/a-
_ JL_
EPft-287 (Cin.
(is,yr)
D3. (Continue
TE!
(Q2J—& jg
F
T
J
CENTER
OF PAGE
. _. >
~
4)
Ad$ Previous Iteration
:{JJ)"TINT + TEE(JJ-
IUJ)-PINT
E(jJ)»TINT
4? 4>
Multiply by Effective
Diffusivity :
•HIDIJJt-PHKJJ) "01
EEDUJ) - TEE(JJ) * D
^
VuJosity at JJ = USJJJ)
Slops stJJ = S LOPE (JJ
A
Xu=jX^
^No
05
V
p. 01
!
I
t
1QC
.„.___ „
-1)
', ^
2
)
mi)
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BOTTOM OF
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OUTolDE
DIMEiJSION
TOR TABLES
f-AND ILLUS-
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HERE
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HERE
,^^
TYPING GUIDE SHEET
^TZrrnT&f r~e-rr-- tr_-~-f
CENTER
OF PAGE
El. Compute Sigmas, Centerline,. and Ground-Level Concentrations
Do Loop for Concentrations
Set Up fJecesssry Parametsrs
for Each Downwind Distance:
DDW(JJ) ;JJ = t,JF
No Obstacis
Evaluate Diffusivities:
Ca!IDtD2
Compute 0 and T
Integrals W hen
No Obsts:!© Present
Compute Crosswind
and Normal
Dispersion Coefficients
Compute Centerline
Concentration
Obstacle
Compyte Distance from
Surface to S.L. at S2JJ
Call Subroutine ZITRPL
Call Subroutine SURF
Compute Crosswind and
Normal Dispersion Coefficients
Compute Centerline
Concentration
TOP OF
Compute Ground-Level
Concentration
EPA-237 iCin.i
(4-76)
Print Out Results
ifl
Compute Ground-Level
Concentration
^ 156 „
'TOM OF
,GE AREA,
rsiDE
IENSION
! TAELLS
ILLUS-
7MAT IONS
-------
?'
'BEGiN
FIRST
LINE OF
HERE »P~
!
DROPPFD j
HEAD, !
BcGIN |
SECTIONS j__
HERE
T-
LAST LM\!"L
OF TEXT ?i-
"''!:'~^^ •r*r^m
• •:<•.•-'.•••'• •- .-; •• .- • •-.'• \ ' , ,-• ,--
TVPiNG GUiDE SHEET
OF PAGE
Compute Sigmas. Centerlin©, and Ground-Level Concentrations (Continued)
¥
Compute Off-Axis
Ground Level
Concentrations
Print Out
Off-Axis
Concentrations
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T 'AREA
LOT TOM OF
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OUTSIDE
-—I DIMENSION
' 1-09 TABLGS
AND ILI.US-
TRATIOi-iS
-------
FIRST
L)NE OF Subroutine D1D2 (KST, U, XX, 01. 02, XS. IFLAG, C1. C2. M, H. JJ, I. BB, HA. DO)
TEXT
HERS
•POP
DROPPED :
HEAD; '
BEGi.'vl ;
SECTIONS
HERE a
Data Statements
for Dispersion
Coefficients
Constant Diffustvitiss
Dt = C1/(HA * U0»
= C2/
-------
TYPiMG QUIDS'SHEET""•"
Subroutine D1D2 (Continued)
Dimensionatize X:
X = X * HA
Go to (10. 20, 30,40, 50, 60), KST
Compute PGT Sigmas:
For Appropriate Class
SZ = S2«KST, X)
SY = SY(KST, X)
Convert M to KM
SZ = SZ/1000.
SY = SY/1000.
Dimensionaiize PT
P1 = PT ' HA/UO
Compute Dimensional
Diffusivities D1, D2
Nondimertsionalize
Diffus'^ities
•^ Return^)
;L 159
-------
TYPING GU'DE SHEET
TO? OF
, IMAGE
Statement Function PSI2D (X. 2. U. A)
-A2/(X2
ReturnJ
Statement Function PS13D (X, 2, U, A)
( Enter
160
'.i G
MO
,ti J
LU
\5
-------
BEGIN
.F.RST
LINE •>
TEXT
TYPING GUIDE SHEET
Subroutine TKER (X. Z, A, Y. P. T, RX2, UUU. M. WZ2, WZ3, WV2, WV3)
Evaluate Z{X) along 2D
Streamline:
CallZITRPUX. NINC.2.Z)
Evaluate (U2, V2) Components
of 20 VeEocity FieSd
Given Z(X)
Evaluate 2(X) along 3D
Streamlirss:
Call ZITRPL (X. NINC. 3, Z)
Evaluate JUS, V3) Ccsmponents
of 3D Velocity Field
Given Z(X)
Weight Velocity Fields
According to Aspect Ratio
UU| = IU2 U3\ |WV2|
til \V2 V3f 1WV3|
Slops M = W/UU
RX2 = W2 ' BX2 + t -
Evaluate Kernels1
M* VV) •
Along S.L Velocity:
UUU = SQRTJUU °* 2 + VV ** 2)
Call
zi;
fzF
TOP OF
161
-------
BEGIN
FiKSf
. Lir'JE OF
G GUIDE SHEET
Subroutine SURF (S3. ZEE. SLD. A. ZMS)
Enter
Evaluate X Value of
Intercept of Line 1 to
S.LatXVAL =S3:
X!NT
Solve for Point (XT, ZT):
Interaction of i to S.L
and Circular Surface
ZNS = SORT ((XVAL - XT»"2
+ (ZEE-ZT)«*2)
Doss not Intercept
Surface of Obstacle
= SQRT(ZEE**2
(S3-XINT)"2
TOP OF
Return^
-ACT Lirj£i_
OF TEXT XV-
^ 162
r1 / , - d ; '-1- '•..''
-------
BEGIN
FIRST
LINE CF
TYPING GUIDF SHEE1
TOP OF
, IMAGE
H Subroutine ZiTRPL (SX. NIWC. ND, ZEE)
CF TTX"1"
XX = ABS (SX)
NINCMt
= ^ssNc-
1
001 K=1,N!fSSCM1
KP1 = K
+ 1
FITX«ND, KP1> < XX < FITX(MD.
XD = (FITXtND. K)-XX)/
(FITX(ND. K» -
F!TX«ND, KP1»)
ZEE= FITZ(ND, K) +
XD*(FITZ(ND. KP1)
FITZ(ND, KU
Z2
\/
"\
163
EPA-237 'C-.r.!
-------
APPBJDIX C
SOURCE PROGRAM LISTING
164
-------
BEGIN
F'PST
LINE-OP
TLXT ''
TYPi^G GUIDE SHEET
CEflTER
TOP OF
/ / KSQLEVEL«-1, CLASSES. TI ME»20
/•ROUTE PRINT RMT22
// EXEC FTG1CLG. REGION. GO100K, TIME. G0<=20, PARN-'NOSOURCE, NOMAP'
//FORT. SYSIN DD *
C
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**»»» ERT MODEL "CPSPLX" :
*****
VERSION UPDATE 2. 1 JAWARY
GAUSSIAN DIFFUSION MODEL.
TERRAIN.
1980
COMPLEX****
THIS PROGRAM COMPUTES THE POTENTIAL FLOW PARAMETERS OF AN OSSTACL
OF ARBITRARY ASPECT RATIO IMBEDDED IN A MEAN FLOW OF VELOCITY UO
WITH GIVEN STABILITY CLASSi KST.
A TURBULENT PLUME IS IMBEDDED IN THE POTENTIAL FLOW (HUNT AND
MULNERN.1973)
R. C. ISAACS, ERT,INC.
1978
MODIFICATIONS ACCOUNT FOR WIND TUNNEL DATA FOR INTERMEDIATE
ASPECT RATIOS BETWEEN SPH£RE(CONE> AND CYLINDER (TRIANGULAR
RIDGF).
D. C. STRIMAITIS, ERT INC. 1979
INPUT PARAMETERS REQUIRED
XS - DISTANCE OF SOURCE UPWIWD OF THE CENTER OF THE OBSTACLE
HS = PLUME HEIGHT (KM)
HA = HEIGHT OF OBSTACLE (KM)
XL * UPWIND DISTANCE OF RECEPTOR FROM CENTER OF f>l>jTACLE (K«>
ALAM = OBSTACLE ASPECT RATIO
DELINT= DOWNWIND RESOLUTION (KM)
NOTE: L(XL-XS)/DELINT3. LE. 50
PKST - PGT STABILITY CLASS (REAL)
FROUDE= FROUDE NUMBER (U/NH)
OTHER DEFINITIONS
UO = FREE STREAM VELOCITY
ND = DIMENSION (2 OR 3)
YS = DISTANCE OF SOURCE DISPLACEMENT FROM AXIS Oc SYMMETRY
PSIP *• VALUE OF STREAM FUNCTION AT SOURCE
PSI = STREAM FUNCTION FOR OBSTACLE (PSI2D OR PSI3D)
1FLAG = SWITCH CONTROLLING DIFFUS I VI TY CALCULATION
IFLAG " 1 . DIFFUSIVITY VARIES W/ X; =• 0 : CONSTANT
Dl - DIFFUSION COEFFICIENT IN 'N' DIRECTION (COMPUTED)
D2 » DIFFUSION COEFFICIENT IN 'GAMMA' DIRECTION (COMPUTED)
Cl = DIFFUSION COEFFICIENT IN 'N' DIRECTION (CONSTANT)
C2 = DIFFUSION COEFFICIENT IN 'GAMMA' DIRECTION (CONSTANT)
IY o SWITCH FOR OFF AXIS CALCULATION; =0( NOT COMPUTED) ; =1 (COMPU
CALL ERRSET(£08, 400, -1, 1 )
SPECIFICATION STATEMENTS
COMMON FITX(3, 600),FITZ(3, 600)
COMMON NINC
COMMON ZC, XS
DIMENSION PHI (50), TEE (50) , US( 50) , R2S( 50)
DIMENSION PHID(50), TEEIK50)
DIMENSION S2-'50>, DDW(50), ANS( 50) , SIGZNH( 50 ) . SIGVNH( 50) , CCLNH( 50),
1CGLNH(50),SIGZH(50),SIGYH(50),CCLH(50), CGLH(50), FNH( 50 > , FH(50)
DIMtNSION FLUXNH(SO), FLUXH(50>, TFACNH<50>, TFACH(50)
DIMENSION R(20>
DIMENSION SLOPE (50)
DIMENSION YD( 11), CGH50, 11 ). YYD( 11)
DIMENSION A0(7>- Al <7>, A2(7>, ZCFl7>
165
TTOM OF
5.GE AREA;
TS IDE
iltlvSION
R TABLES
:D H.LUS-
VflONS
C
-------
BEGIN
FIRST
l.iNE OF
VEXT
HtRF JB
DIlOPFED
HEAD
flEG'M
JECTiONS
HERL SB
TYPING GUIDE SHEET
. TOP OF
REAL MX.MXPH.MA.M3.MBKH
DATA AO/-0. 070.-0. 040,-0. 042,-0. 052. -0 040,-0. 533. -0 476/
DATA Al/0. 189. 0. 105, 0. 105, 0. 103, 0. 052, I 047, 0. 924/
DATA A2/0. 174, 0. IBS, 0. 142, 0. 141, 0. 173, -0. 418, -0. «09/
C "•i~ "• ~ ••—™* —— ———————••"••—•»«••••.—-—••———.-»...»_______ ——_——__•_»_____________ _,^_
C FORMAT STATEMENTS
200 FORMAT(SFIO. 3)
201 FORMATdOX,8dPE12. 3))
202 FQRMATdOX. 13, 4(1PE12 3, 5X»
203 FORMAT(2(1PE12. 3»
204 FORMAT dKO, 3X. 'COEFFS. = ', 1P10E11. 4, /. JOX, 1P10E11. 4, /)
205 FDRMATdOX.2dPE12. 5»
206 FQRMAT(Il)
207 FORHATdOX. 1PE12. S>
208 FOSMATOOX. 12)
209 FORMAT('l')
210 FORMAT(49X. 'DIFFUSION EQUATION SOLUTIONS',/, 15X, 'SIGMA Z, SIGMA Y
1PLUME CENTERLIf^E AND GROUND LEVEL CONCENTRATIONS', /. 1SX,
2'FOR AN OBSTACLE OF ARBITRARY ASPECT RATIO',////)
211 FORMATdOX, 'FLOW PARAMETERS './/.T15, 'OBSTACLE HEIGHT =',F5. 1.T38,
1'WIND SPEED - ',F3. 1,T60, 'SOURCE HEIGHT = ',F4. 2,T97, 'CROSSWIWD DI
2SP=',F3. 1.//.T15, 'DIST. SOURCE FROM OBSTACLE CENTER='-F6. 1, T60,
3'DIST. OF FINAL RECPTR*» ',F3. 1.T97, 'ASPECT RATIO', ' = '.F4 1.//T15,
4'VERTICAL DIFFUSIVITY •= ', 1PE10. 3, T&O, "CROSSWIND DIFFUSIVITY - ',
51PE10.3,T97.'KST « ',13,///)
212 FORMAT(T1O, 'DISTANCE', T25, 'DISTANCE', T40, 'DISPLACEMENT', T55,
1'SIGMA Z',T70, 'SIGMA Z'-T85, 'SIGMA Y'.TIOO, 'SIGMA Y',T115, 'WIND SP
2EED'. /.
3T10. 'FROM OBSTACLE'.T25, 'FRCOT SOURCE'. T40, 'ABOVE SUSP. '.T55, '(K>0 0
4BSTACLE)', T70, '(OBSTACLE)',T85. '(NO OBSTACLE)'. T100.
5'(OBSTACLE) ',/>
213 FORMATdX, 1P08S15. 3)
214 FORMAT(//, TiO. 'DISTANCE'.T25, 'DISTANCE'. T40, 'DISPLACEMENT'. T3S,
l'CENTERLINE'.T70, 'CEMTERLINE'-T85, 'GROUNDLEVEL',T100, 'GROUMDLEVEL
3T10, 'FROM OBSTACLE',T25, 'FROM SOURCE', T40, 'ABOVE SURF. ', T55.
4'COWCEPJTRATION'. T70, 'CONCENTRATION', T85, 'CONCENTRATION', T100,
5'CONCENTRATION', /, T5S, '(NO OBSTACLE)', T7O, '(OBSTACLE)',
6T85, '
220 FORMAT(/,T2, 'DOWMWIND', T60, 'OFF AXIS DISTANCE'./.
1T2, 'DISTANCE'.T12, 1P11E10. 2-/>
221 FORMAT(2X, 1P12E10. 2)
222 FOf»MATX, 'IY=', 12, //>
223 FOHMAT(//,3X,'PLUME IMPACTS HILL AND DOES NOT GO OVER TOP'./)
224 FORfAT
231 FORMAT(6X. 'XS'.SX. 'HS'.8X. HA'.BX, 'XL'.VX, 'ALAM'.&X. 'DlINT',
16X, 'Rt
-------
BEGIN
FIRST
LINE 01
TYPING GUIDE SHEET
CENTER
HERt'T'
C
C
555
C
c
c
c
c
c
c
c
c
c
c
c
601
602
603
C
C
C
SPECIFY CONSTANTS
PI»3. 14159
Cl«2. OE-3
C2-S.OE-3
YS=0. 0
ROOT=0. 0
AA=0. 0
BB"0. 0
A-1.0
IFLAG=1
IY-1
ASSLiME DIKENSIQNLESS VALUE FOR BOTH FREE STREAM VELOCITY UO
AND HO8IZOMTA!- WIND SPEED U
UO-1.0
U»l. 0
READ(5, 200, END*>999) XS,HS,HA,XL, ALAM, DELINT, RKST, FROUDE
W«ITE(6, 230)
WHITE(6.231)
WRIT£<6.2OO) XS.HS,HA,XL, ALAM, DELINT, RKST, FROUDE
KST»RKST
IF(FROUDE. EG. 0. 0) KST«-4
IF
-------
FIRST TYPING GUIDE SHEET '
LINE OF-"~7'--- •—~™ JOPOF
l':Xl '"'* 1'Vjt
hFRc S»J C PSIP3D" VALUE OF STREAMFUNCTION ALON8 STREAMLINE IN 3D FLOW ^A
> C STREAMLINE EQUATION IN EACH CASE EVALUATED BY SOLVING:
C PSI2D(X,Z) » PSIP2D OR
I C PSI3D(X. Z) «> PSIP3D
fspi'JPr1|"'0 t ^ _-._
U( VJi '--' J \» — ' — — — --———— — — — — — — — — — — — — — — — — — -• — -• — — — .•.—• — — .•.— —....-.....— ..____.«.______.._____
HP.VJ C NEUTRAL STREAMLINE STORED AS:
gFCIN c x " F1TX(ND. II)
SfCT'OHsf C 2 FITZ4ND, II)
Hn,r' ^ C ND » 3 08 3 (2D OR 3D)
DO 604 N0=2.3
c
C DEFINE STREAM FUNCTION. VALUE THROUGH SOURCE, AND B
IF(ND.QT.2) ©0 TO 1
PSIP=PSI2D(XS. HS, U. A)
B=PSIPXU
GO TO 2
1 PSIP»PSI3D(XS. HS. U, A)
B=2. 0*PSIP/U
2 WRITE(6, 203) B.PSIP
c
C COMPUTE ZC " Z DISPLACEMENT OF SOURCE STREAMLINE OVER CREST OF HI
IF(ND. QT. 2) GO TO 3
60 TO 4
C SOLVE CUBIC EON FOR 3D ZC
3 RADCL*--<*«!. 5»/3.
2C=EM*COS(THTA)
C SECOND AND THIRD SOLNS LESS THAN ZERO
ROOT>---1.
GO TO 4
32O ZC=1.5874*A
ROOT-0.
GO TO 4
330 AA= <. 5»A*»3*SQRT(RADCL » *» <1. /3. )
BB=(. 5*A*»3-SGf?T(RADCL) )**
j ZINC2^(HLFPT-H1>/INC2 ,
\ ZINC1-/NINCMI T1OM OF 5
j WRITE(6,201> PSIP.B,ROOT,AA- DB, ZC,BETA, HI
r-c.-j.v i NINC=NINC + 1
L^,:r'l p,(-| DO 100 1 = 1, NINC
„/-.'"(• IF(I. GT. INC2) GO TO 9
or i L < f s*
i .•? - ":
]__ | "'"_ __ | __. _.^.168 ~_ —i
EPA-^87 (CiM.) / ' |
("3-7&I ; ^
-------
DROPPED
HEAD.'
TYPING GUIDE SHEET
TOP OF
-IMAGE
ZZ«H1+J«ZINC2
CO TO 10
J=I-INC2-1
ZZ-HLFPT+J«ZINC1
CONTINUE
IF(ND. GT. 2) GO TO 5
1FCZZ. EG. HI) GO TO 61
ARG»» ( )
GO TO 6
IF(ZZ. EQ. HI) CO TO 61
ARG=> < (A«»3/(i. 0-B/ZZ**2) )»*(2. 0/3. O>-ZZ»«2>
IF(ARG. LT. 0. 0) GO TO 7
XX«SGRT(ARG)
GO TO 8
XX <• 100. TAKEN AS EFFECTIVE INFINITY
XX=100.
GO TO 8
XX=0. 0
ZZ-ZC
CONTINUE
11 = 1
FITZCND, 1I)=ZZ
FITX(ND, II)=XX
FITX(ND, NINC>=0. 00
CONTINUE
CONTINUE
»*•«• B-fr-t
WRITE<6, 218)
THIS LOOP (DO 605) WEIGHTS THE NEUTRAL STREAMLINE WITH
ASPECT RATIO USING WZ
DO 605 II=1,NINC
XX=FITX(3, II)
FITXd, II)=XX
ZITRPL= SUBROUTINE PROVIDES Z INTERPOLATION FOR ANY X VALUE
GIVEN STREAMLINE IN FITX (ND. 1 1 ) . FITZ IFR=1
IF(Ff»nuDE. GE. 1. 10. AND. FROUDE. LT. 1 50) IFR=^2
IFCFROUDE. GE. 0. 92. AND. FROUDE. LT. 1. 10) IFR=3
IF (FROUDE. GE. 0. 83. AND. FROUDE. LT 0 9
IFR=4
IFR-5
IF'FRQUDE. GE. 0. 40. AND. FROUDE. LT. 0. 70) IFR=6
)
IF t FROUDE. GE. 0. 70. AND. FROUDE LT. 0. 83)
) WRITE(6,:
1 WRirfc<6,223>
IF((-ROl«PE. LT 0. 40
Ih"( IFR. I.E. 5. AND HS. LT 0. 3VS
IF< IFR. EQ. 6 AND. HS. i.T 0. 75
IF ( IFR. EQ. 7. AND HS LT. 0. 82
URIIE'6.224> IFR
CALCULATE THE TOW-TANK ZC AND CHFCK THAT IT EXCEEDS THf HILL HcIGHl
ZCF< IFfy ) = 1 -KAO( IFRl+Al ( IFR )»HS+A2< IFR)tftS**2)
IF(Zi'.F( 1FW). LT. 1. ) ZCF(IFR) = 1. 001
DELMAx=FITZ(3.NINC>-ZCF(IFR)
DO 60cv 11 = 1 , NINC
169
-------
"p!RST •"'"?•.?"•,.',.«"
HN^OF-
TEXT
HErtE S
i
DROPPED !
HEAD. ;
f-IGIN :
$-CTIOJ*
KHE 3
60S
606
610
C
C
C
C
609
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
fiff-'lV
USUiME C
Cf TEXT J
; j ~~^~, - -U— -
EPA-zy
l-t-7CI
TTTf HTCjnaVJllJC "Oncer-"""'-- •» • T -tr«-— i^"-- ^T-TTT- — »T7 ^:.-":"™--'i"--'-—?-«--~i> -^..r^.,,,,-,^,. ,_^___,-.-. „,,_,„_-„„-
CENTER ' " - " " '•• '
~ . _
XX»FITX(3, ID
IF. LT. (DEL/2. 0» SS»>0. 0
S2(JJ)=SS
INTEGRATE FOR EFFECTIVE SIGMA Y AND Z SQUARED
NUMERICAL INTEGRATION BY SIMPSONS RULE
ADAPTED FROM DQRW AMD KCCRACKEN 1972
SET UP INTEGRATION PARAMETERS
NN=100
FN=NN
AA=SS-DEL
IF(JJ EG. 1) AA=*XS
H=(BB-AA)/FN
TWOH^2. 0*H
SUM5-0. 0
SUM6=-O 0
SUM8=--0. 0
SUM9-0. 0
1=0
CALL TKER(AA, ZA, A, Y, PA- TA, RA, UA, MA. HZ. WV2, WV3 )
CALL D1D2
-------
^^^fmWG-GUnre sHttr-
EG;N
:TIONJ
o n
o7 LI
F TEXT
CENTER
C
29
C
28
92
93
21
101
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
INITIALIZE LOOP COUNTER
1-1
BEGIN INTEGRATION
CONTINUE
XPH-X+H
CALL TKER
TEE < J J ) =T I NT-t-TEE ( J J- 1 )
TEED ( J J ) =TEE ( J J ) «D2
PHID( JJ)*>PHI ( JJ)*D1
GO TO 93
TEE(JJ)=TINT
PHK JJ)=PINT
PHID( JJ)=PHI ( JJ)*D1
TEED ( JJ ) =TEE < JJ ) *D2
CONTINUE
US( JJ)=UB»U
R2S(JJ)=RB
SLOPE (JJ>=MB
CONTINUE
CONTINUE
#**« fr*«t»»»«»»***9»«»*fl.«»»**«-»*»**»*6****«-«-*««»»»«**«a «•***«••»»«•*»*
COMPUTE SIGMAS, CE.%!TERLINE AND GROUND LEVEL CONCENTRATIONS
WITH THE OBSTACLE AND WITHOUT THE OBSTACLE AS A FUNCTION OF
DOWNWIND DISTANCE
FLAT TERRAIN VALUES
DDW = DOWNWIND DISTANCE FROM SOURCE
SIGZNH= NORMAL DISPERSION COEFFICIENT (NO OBSTACLE)
SIGYNH= CROSSWIND DISPERSION COEFFICIENT (NO OBSTACLE)
CCLNH = CONCENTRATION . CENTERLINE
-------
SHEET"
LINE OF —
CENTER
Hhf!E
HEAD'
DO 102 JJ-l.JF
DDWtJJ>=B2-XS
C EVALUATION : NO OBSTACLE (NH)
P-PHID(JJ)
T-TEED(JJ)
U1»US(JJ)
R2=R2S
CALL D1D2
TEENH»D2»DDW < JJ)/< U»HS»«2)
SIGZNH-= SQRT<2. 0*HS»*2*TEENH>
CCLNH=<1. 0/(4. 0*PI ) >
ARC3=HS*«2/(2. 0***2)
IF(ARG3. GE. 179.5 > GO TO 70
CGLNH(JJ)=CCLNH
SIGYH
IFCS3 EQ. 0.0) GO TO 17
C CORRECTION FOR FIT MADE OVER HILL BY INTERPOLATING FROM EXACT S. F
IF(ABS
ANS=?. 0»CGLH(JJ>
GO TO 73
77 CGLH(JJ)=1 1E-78
73 CONTINUE
FNH(JJ)=CGLNH(JJ)/CCLKH(JJ>
FH(JJ>=CGLH(JJ)/CCLNH(JJ)
IF(FH(JJ). LT. 3 OE-76) FH(JJ)=3. OE-7^
IF(FMH(JJ) LT. 3. OE-76) FNHfJJ>=3 OE--~'6
FLUXNH(JJ>=U*SIGZNH(JJ>«SIGYNH*CCLNH(JJ>
FLUXH(JJ)=US(JJ)*SI&ZH(JJ)*SIGYH'JJ»«CCLH(J.')
172
_TOP OF
IMAGE
AREA
-------
•JNtOF
TEXT _
CENTER
yi 1.1.'j
-,Cf- TEXT
102
C
904
903
906
999
TFACNH> )/Hb
CONTINUE
~-—"~ — — — «• -- — — «—•—— — — .— •-.-.-..— ___.-._____.M.___ __ _ ____ __ _» — —«._ ___ __ ___ _ — — ___ ___
PRINT OUT RESULTANT ARRAYS OF SIGMAS AND CONCENTRATIONS
WRITE<6. 209)
WRITE<6, 210)
WRITE<6, 21 1 ) HA, IK). HS, YS, XS, XL, ALAM, Dl, D2, KST
WRITE<6, 2S2)
i4RITE<6, 213) ,ANS,SIGZNH,SIGZH,
1SIGYNH. JJ=1, JF)
WRITEC6. 214)
WRITE<6. 216) (S2(JJ), DDW( JJ) . ANS( JJ), CCLNH( JJ), CCLH< JJ),
ICGLNH(JJ), CGLH(JJ), JJ«1,JF )
WRITE<6, 215)
WRITE<6, 216) (S2«=YYD
CGL(JJ, K)=CGLH< JJ)*EXP<-0. 5*YD(K)**2)
CONTINUE
CONTINUE
WRITE (6, 220) (YYD(K), K=l, 11)
DO 9O6 JJ=1, JF
WRITE (6, 223 ) (DDW( JJ), (CGL( JJ, K), K=l, 11 ))
CONTINUE
GO TO 555
STOP
END
SUBROUTINE D1D2(KST, U, XX, Dl, D2, XS, ITLAG,C1, 02, M, H, JJ, I.BB.HA, UO)
THIS SUBROUTINE EVALUATES THE DIMENSJDNLESS DIFFUPIVITIES Dl AND
D2 IN THE Z AND Y DIRECTIONS .RESPECTIVELY
REAL M
DIMENSION PSA(SO). PTA(50)
DIMENSION KD(5), AD(6), BD(6)
DIMENSION XA<7>, XB<2), XE<8). XF(9), AA(8), DA(8), ABO), Bl<3),
1AE(9), BE(9>, AF(10),BF(10)
DATA XA/.5, .4, .3. 25, . 2, . 15, I/
XB/. 4, . 2/
XD/30. , 10. , 3. , 1 . , . 3/
XE/40. , 20. , 10. , 4. , 2. , 1. . . 3, .
XF/60. , 30. , 15. , 7. , 3. . 2
DATA
DATA
DATA
DATA
I/
1. , . 7, . 2/
DATA AAX 453. 85, 346. 75, 258. 89, 217. 41, 179 52, 170. 22, 158. O8, 122. 8/
DATA BA/2. 1166, 1. 7283, 1. 4094, 1. 2644, 1. 1262. 1. 0932, 1. 0542, . 9447.'
DATA AB/109. 30, 98. 483, 90. 673/
DATA Bl /I. 0971,0. 98332, 0. 93198/
DATA AD/44. 053, 36. 650, 33. 504, 32. 093, 32. 093, 34. 459/
DATA BD/0. 51 179, 0. 56589, 0. 60486, 0. 64403, 0 81066, 0. 86974X
DATA AE/47. 618, 35. 420, 26. 970, 24. 703, 2?. 534, 21 628, 21. 628. 23. 331,
1 2*. 26/
DATA BE/0.29592,0.37615,0.46713,0.50527.0 S71 54, 0. 63077, 0 7b66C>,
1 0. 81936, 0. S366/
DATA AK/34 219,27.074,22.651,17.836,16.187,14 823,
1 14 457, 15. 209/
DATA BF/0. 21716. 0. 27436, 0. 32661. O. 41507, 0 46
-------
BEGIN
FIRST
LINE OF
TEXT
HERE S&
DHOPPED
HEAD,
BcGiN
SECTION
TYPING GUIOt SHEET
TOP OF
93
96
97
98
99
101
C
10
11
12
C
20
CONTINUE
IF
00 TO 93
IF *H/U
GO TO 96
PS-=PSA,KST
STABILITY A
TH»(24. 167-2. 5334«ALOQ GO TO 69
DO 11 ID"*!. 7
IF»8
SZ=AA(ID>*X»«BA(ID)
GO TO 71
STABILITV B
TH=( 18. 333-1. 8096»ALQ9(X) )/57. 2958
IF(X. QT. 35. ) GO TO &9
DO 21 1D°>1.2
IF(X. GE. XB(ID» GO TO 22
21
i
22
i- 1 c
: so
;
' C
40
• 41
f j
42
C
'JO
I
j
51
52
• C
': 60
; BEGIN
! LAST L;ric ,
OF TEXT ^T____^r "l
I
f 3/*' __ J
, — — — "
EPA-?3? (Cin.l
I4-7C.1
^^gfi^iSS^^^^^^^^**^
CONTINUE
ID=3
SZ-AB(ID)«X*»S1(ID)
GO TO 70
STABILITY C
TH=(12. 5-1. OS37&ALOO<8»/57. 2958
SZ=61. 141»X*«K>. 91465
60 TO 70
STABILITY D (NEUTRAL)
TH=<8. 3333-0. 72382«ALOG ( X ) )/57. 2959
DO 41 ID=1.S
IF SO TO 52
CONTINUE
SZ-AE(ID)«X«-*BE
GO TO 70
STABILITY F
TH<=(«. 1667-0. 36191»ALOe
-------
BEGIN
HRST
LINE OF
TEXT
HERE
DROPPED
HEAD;
BEMN
EEf,TiOr-:c[..,
HERt f^-l
LAST LI;:C
OF iEXT 3
TYPING GUIDE SHEET
62
69
70
71
75
80
C
102
90
C
C
C
C
C
C
C
CBiTER
1D-10
SZ-AF ( ID)«Xt»BF< ID)
SO TO 70
6Z»500O.
SO TO 71
IF(SZ. GT. 3OOO. ) 8Z""5000.
SYMOOQ. «X*SSN >
TOP OF
IMAGE
"iREA
SV«SY/SOOO.
Dl«SZ»*a/<2. 0*P1
D2«SY»»a/<2.
D2-D2/
CONTINUE
RETURN
END
FUWTICN PS!2D(K. Z.U, A)
2D STREAM FUNCTION FOR FLOW OVER CIRCULAR RIDGE
PSI2D «*U*Z«<1. 0-(A««2/ )>
RETURN
END
FUNCTION PSI3D
REAL M
COflHON NINC
SUBROUTINE WEISHTS VELOCITY FIELD BY ASPECT RATIO
20 VELOCITY FIELD
U2 - VELOCITY IN X DIRECTION
V2 » VELOCITY IW Z DIRECTION
CALL ZITRPL
R = (X2+Z2>«*. 5O
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WEIGHTED V€LDC2TIE8
UU - VELOCITY IN K DIRECTION
W - VELOCITY IN Y DIRECTION
H • SLOPE
RX2 » D58TAf«E FROM AXIS OF SYFOTETRY TO STREAMLINE
UUU » M.0^9 STREA«.IfS VELOCITY
P • KERt^EL Of PH! LIKS INTEGRAL
T - KERKEL OF T LINS INTESSAL
M«W/UU
RETURN
SUiROUTINS BUaF«S3, ZEE. BLQ. A.
THI8 SUEROUTEMS COf^UTES T(« DISTANCE OF THE STREiiWLIMS FROM
TH£ SURFACE CF T(=£ SPHERE (OR -PLAfiEJ
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