ML17055C374

Wake & Dispersion Models for EBR-II Bldg Complex

ML17055C374
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Site:	Nine Mile Point
Issue date:	10/31/1976
From:	Halitsky J JAMES HALITSKY
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ATTACHMENT 2 WAKE AND DISPERSION MODELS FOR THE EBR-II BUILDING COMPLEX JAhfES HALIlsKY Consultant in Environmental Meteorology, 122 North Highland Place, Croton-on-Hudson, N.Y. 10520, U.S.A.

(First received November 1975 and in revised form October 1976)

P AbstractWind properties measured downwind of the reactor containment structure at the EBR-11 complex were found to be in agreement with predictions made with a mathematical wake model that was derived from measurcmcnts in thc wakes of suspended tlat plates in a wind tunnel and modified for the presence of thc ground boundary. Simultaneous concentration measurements of a tracer released, in thc lce of the reactor containmcnt structure were found to be in agreement with the predictions of a mathematical dispersion model that incorporated thc wake model in conjunction with atmospheric turbulence properties. Thc analysis provides insights into the nature and properties of building wakes in the atmosphere, and their inliuence on dispersion of released material.

N dispersion downwind of the EBR-II complex. It is believed that the equations have general applicability to wakes generated by most building complexes, but it is recognized that they have been derived from one body of data for a single configuration under essentially neutral stability conditions. Therefore, ad-ditional research is nccded to study the significance of the characteristic lengths that appear in the analy-sis, and to validate thc wake and 'diffusion models under conditions of low wind spccd and extremes of atmospheric stability.

I. INTRODUCllON A mathematical model of atmospheric dispersion of material released near thc ground from a building situated among other buildings is nccdcd in the safety analysis of a nuclear power reactor. No such model has gained general acceptance, primarily because experimental data for its development have been lacking.

In 1967 the Environmental Sciences Scrvicc Admin-istration (ESSA)'onducted a I'ull-scale experiment at the National Reactor Testing Station, Idaho Falls, Idaho (NRTS)t to obtain such data. The results of the study were first published in an ESSA semi-annual report (Van der Hoven, ed., 1967) and a more extcndcd article appeared later in Nuclear Safety (Dickson ei al., 1969).

The data gathered in the 1967 experiment include downwind concentrations of a tracer released near the ground at the lee wall of thc EBR-II reactor build-ing, and mean wind speed and turbulence upwind and downwind of the EBR-II building complex.

The published articles contain tables and graphs, of wind turbulence parameters, non-dimcnsionalized con'cen-tration isoplcths, and the standard deviations trand a, of the lateral and.vertical concentration distribu-tions. An empirical expression for the growth of a with downwind distance and rms fluctuation of hori-

,zontal wind ange is proposed.

The articles contain no mention of attempts to crcatc a wake dispersion model or to relate the observed data to thc geometry of the building complex.

The purpose of'his paper is to prcscnt thc factual inl'ormation gathcrcd in the EBR-II experiments, and to offer a synthesis, of the observations in thc form ofequations for thc prediction of wake properties and

'subsequently integrated into National Oceanic and Atmospheric Administration (NOAA) t subsequently re-named Idaho National Enginccring Laboratory (1NEL).

2. PHYSICAL CONFIGURATION OF THE EBR.II COMPLEX The general topography at INEL is shown in Fig.

1. The EBR-II complex lies near thc center of a wide, fiat SW-NE valley. The valley wall northwest of the complex is broken by several NW-SE tributary val-

" leys.

Fig. 2 is a plan view of the EBR-II buildings and the instrumentation arrangement used in the field ex-periment. The tests werc conducted in southwesterly winds only. The meteorological towers were arranged along a SW-NE line through the ccntcr ol'he reactor building. The tracer was relcascd near thc ground at the northeast side of thc containment structure. The samplers werc deployed in arcs centered on the center

'fthe containment structure.

Figure 3 is a photograph of'he complex, looking slightly north of casL Figs. 4a and 4b are photographs of a I:96 scale model of the complex'in thc Ncw York University air pollution wind tunnel (Halitsky ei al., 1963), oriented in the same wind direction as in the 1967 field 'tests.

The buildings in the,complex include the contain-mcnt structure (dome-capped cylinder), a power plant building, two heat cxchangcr structures, a fuel cycle

,facility and a number of smaller auxiliary buildings.

The building heights range from'm to 29m, the 577 8609120405 860905 PDR ADOC< 05ppp41p A

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1. Terrain at the Idaho Natiorlal Engineering Laboratory (Source: Van dcr Hoven, cd.,

1968).

highest being the containment structure (29m) and the power plant building (19 m).

3. DESCRIPTIOV OF WAKE FLOW This section is intended to provide the reader with a survey of some aspects of wake flow which will be helpful in understanding the analysis of the EBR-II test data and the development of the dispersion model.

Readers who may wish to become more familiar with rcccnt developments in classical wake theory and experimentation as applied to buildings in a boundary layer may consult "Counihan et al.

(1974) and Castro el al. (1975).

3.1 Definition of Terms A wake is generally understood to be a region of disturbed flow downwind of an object in a wind stream. It contains a highly turbulent region with cir-

,culatory flow, called a cavity,.immcdiatcly in the ice of the object, and a transition region extending some uncertain distance downwind in which the flow properties approach those of the background flow.

Fig. 5 is a sketch of a vertical section through the wake of a solid cube resting on the ground. It shows the background flow, the wake and its cavity, and a displacement zone in which the background flow is aocelcratcd around the cube without substantial change of turbulencc.

Thc cavity boundary-in Fig. 5 is a streamline that originates at the building edge (point,d) and ter-minates,at the downwind stagnation point (point h).

In three-dimensional flow, the cavity boundary is a surface that contains all such streamlines. Strcamlincs that lie within the cavity boundary close upon them-selves to create a toroidal circulatory flow, while the external streamlines continue downwind to re-create the background flow.

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~9enerotor Tower 2 ver Cp to 0~

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~74-m Tower Fig. 2. Instrument Locations at the EBR-II Complex (Source: Dickson et al., 1969) r

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Fig. 3. Photograph of the EBR-II Complex, Looking,Slightly North of East (Source: Dickson et al.,

1969).

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Fig. 4. Photographs of a Model of the EBR-II Complex in the Wind Tunnel. Upper: Looking NE.

Lower: Looking SW. Floor markings are 80 ft (24;4 m) squares centered on the containment structure.

(Source: Halitsky er al., 1963).

The wake boundary may be defined as the'imagin-ary surface along which the magnitude of a character-istic wake property dcviates from that of the back-ground flow at the same location by an arbitrarily small amount. In this paper, two properties will be considered:

mean velocity and r'ms turbulence.

Each will provide its own boundary radius, designated Fh or r'orresponding to an arbitrarily small deficit of mean velocity or arbitrarily small excess of rms turbu-lence, respectively.

Since object-generated disturbances decay with radial and downwind distance, the wake boundary as defined above will be a closed

surface, perhaps expanding initiallyas along dmno in Fig. 5, but even-tually contracting and terminating.

When several buildings are arranged in a group, each of the buildings willcreate a wake whose charac-teristics are dependent on the local background flow for that building. The local background flow, in turn, may be the undisturbed background flow upwind of the group or it may contain flow disturbances created by upwind buildings. If the buildings are closely spaced, as in a building complex, it seems reasonable to expect that the individual building wakes will merge into a composite wake which will be irregular in shape and structure near the buildings, but will acquire the characteristic closed wake boundary and asymptotically developing mean velocity and turbu-lence distributions at greater downwind distances..

The existence of a composite cavity within the com-

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4 Background

liow

, Oitplocement ztr er c le~

0 Woke boundar y Cavity boundory Wake a

b tt h>>

i Bownwindl stagnation 3

point 4

Mean velocity prof I f~e Fig, 5. Sketch of Flow Zones Around a Cube on thc Ground (Source: Slade, ed, 1968).

positc wake is probably dcpcndcnt upon the arrange-ment of thc buildings, since thc individual cavities may terminate bcforc they merge.

3.2 IVakc Equaiions The properties of wake flow that arc important to the development of thc dispersion model for thc EBR-II complex are the longitudinal and transverse variations of mean velocity and turbulencc, and the longitudinal variation of boundary radius.

In the absence of other data it is proposed to usc generalized expressions that are approximations to data measured by Cooper and Lutzky (1955) in the wake of rectangu-lar flat plates suspcndcd normal to an airstream in a low turbulence (0.1%) wind tunnel. Table 1 shows the plate configurations.

It may seem unusual to employ equations that were developed for the wakes of suspended flat plates to describe thc wake ol' group ol'uildings on the ground, since the two configurations differ in at least four essential respects.

First,. the plates are two-dimensional while the building complex is three-dimensional.

Second, the plates are solid while the building complex may be considered porous by'virtue of separation ofindividual buildings. Third, the plates were tested in a unil'orm stream while the background flow'of thc complex is a ground surface boundary layer. Finally, transverse gusts are unimpeded as they

'ross thc axis of the plate wake, but they are stopped by the ground surface in the complex wake.

It is, of course, possible to employ physical and mathematical reasoning to estimate the effect ol'hese Table

1. Flat Plate Test Configurations Source Plate Shape Dimensions (in)

Aspect RatioR'haract.

Cavity Tested Range Length Length of x/L L (in)t xJL min max Fail el al.

(1959)

Cooper &

Lutzky (1955)

Rect.

Rect.

Rect.

Rect.

Rect.

Rect Eq. Tri.

Circle Tabbed Rect.

Rect..

Rect.

Rect.

Circle 5.00 x 5.00 3.54 x 7.07 2.24 x 11.20 1.58 x 15.80 1.12 x 22.35 1.24 x co side ~ 7.60 dia. ~ 5.66 dia. ~ 6.00 0.2 x 0.2 0.2 x 0.6 0.2 x 1.0 0.2 x 2.0 dia ~ 0.2 1'2 5

10 20 1

3 5

10 5.0 5.0 5.0 5.0" 5.0 5.0 5.0 4.3 0.20 0.35 0.45 0.63 0.18 2.96

?86

?46 2.26 0.96 2.82$

2.82 2.92, 3.04 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 21.0 9.1 6.9 5.5 26.4 4.g 4.8 4.8 4.8 4.8 4.8 4,8 4.8 4.8 683 394 302 216 771

'pan/chord.

't(area) '.

'$ xJchord.

h

JAMIs 1lALI'Isi' Longitudinal Variations (uo u,)/uo = 0.32 (x/L)

/3R'/

(aa)/u, = 025 (x/L)

/ R'/

rt/L~ 1.35 (x/L)'+R rt/L 1.80(x/L)i/3 R-I/Io Transverse Variations (2)

(3)

(4)

(5) d, ~ 1.167 + 0.167 sin[7.121 (r/rt 0.221)],

0 S r/rt S OA41 (6a) 6 ~ 0.733 + 0.600 sin[n 5.622 (r/rt 0.162)],

OA41 S r/rt S 1

(6b)

(note: argument is in radian mode) where:

u longitudinal mean velocity a= lo'ngitudinal rms turbulence R = plate aspect ratio =

span/chord'=

plate characteristic dimension = (chord) R x = downwind coordinate from plate r ~ chordwisc coordinate from wake axis rt = wake boundary coordinate defined as the chordwisc.distance from the wake axis'to the point where the mean velocity defect u, u is 10% of the maximum defect at that station t'I, ~ wake boundary coordinate defined as the chordwise'distance from the wake axis to the point where the rms turbulence excess aa is 10% of the maximum excess at that station differences. but it is diAicult,ifnot impossible, to vali-date them with the EBR-ll field test data. Accord-ingly, the equations will be used in the Aat plate form, the only adjustmcnts being in the magnitudes of the constants which willbe found by comparing the equa-tions with the field test data..

Cooper and Lutzky present their data as graphs of non-dimensionalizcd Aow properties, but they do not gencralizc the data other than to conclude that the data are in agreement with the theory of axi-sym-metric wakes in the following respects:.

1. The maximum values of mean velocity defect and rms turbulence vary as (downwind distance) 3/3.

2. The radius of the wake varies as (downwind dis-tance)'".

3. The transverse distributions of mean velocity de-fect and rms turbulence are universal functions of (radius/wake radius).

The above predictions of wake theory are based on an assumed turbulence-free background flow.

Cooper and Lutzky's air stream had small but finite turbulence, and they corrected their measurements by

" subtracting the turbulent kinetic energy of the back-ground flow. Thus, the data in their paper represent excess turbulence rather than absolute turbulence.

I have fitted curves to Cooper 'and Lutzky's data, incorporating the above conclusions, and interpreting

,the turbulence data as excess over background. The equations of the curves are:

IO IO'

~

b t

Ea.2/

Symbol R

IO

/rIo 5

3 I

I>

IO t IO Eq.3 IO s

o 3

I IO t

t IQI t

S IQt t

t lot IO t

IM lo I35lo IO' Eq.5 t

~

Iof t

t IQt t

t x/I Fig. 6. Properties of Suspended Hat Plate IVakcs. Top to bottom: mean velocity defect, rms turbulence

excess, wake boundary based on mean velocity defect, wake boundary based on rms turbulence excess.

h = Incan velocity defect

ratio, Z = (Ii, u)/

(II, u,) or rms lurbulence excess ratio, E =

(aa.)/(a a

)

subscripts o ~ background flow a ~ on wake axis

~b = on wake boundary.

Eqs.

2-5 and the Cooper and Lutzky data are shown in Fig. 6. The dependence on R in Eqs. 2-5 was sclccted to provide agrccment of Eqs. 2-5 with the data at R =

1 and R = 10. The individual data points in Fig. 6 were obtained froin Cooper and ILutzky's faired curves through the transverse distribu-tions. The two upper sets of data points are the curve ordinates at r = 0. The two lower sets are the dis-tances to the estimated extension of the faired curves to zero mean velocity defect or zero rms turbulence excess.

Some ambiguity may exist in the rms turbu-lence curves because thc extrapolation to zero is a matter ofjudgment.

Eqs. 6a and 6b describe the transverse distribution of both mean velocity deficit and rms turbulence excess.

Fig. 7 shows those equations superimposed on the Cooper and Lutzky mean velocity defect data for R = 3 and R = 5. The curves match the data at the upwind location (11 <x/L < 13), but do not match at the downwind locations where the distribu-tion tends toward Gaussian at x/L > 220.

Fig.

8 shows the same equations with the Cooper and

l I

1

tahe and dtspetstoit ttu>u:Ix 5}(3 z/E, 0 0204 OS 0.8 1.0 z/) ~

0 Q2 OA 0$ 0.8 IA)

I.o I

1

~

i'j' R ~ 3 Q9,,

Rote tt uoil40(

1,4 1.2 I.o 0.9 R 5 Rote la+i(40(t) 0.8 0.7 0.6

~+ o.s Q4 0.3 0.2 0.1

-Eq.6o Eq.6b 00

/o

"/

o 218 13 o

8I8 47 0 201.8 117 o 381.8 220 A 681.8 394 1.0 0.9 I

O 0,8 Io 0.7 Io I

06

>>o as o 0.4 0.3 0.2 O. I Q8 0.7 0.6 0.5 0.3 0.2 0.1 Eq.6o Eq.6b I/

o 24.5 I I o 84,5 38 0

0.5 I.O I.S 2.0 2.S

/(z I)

O.S I.O I.S

~

2.0 24

/(z~)

Fig. 7. Normalized Mean Velocity Defect for Suspended Flat Plate Wakes. Left: Aspect ratio ~ 3.

Right: Aspect Ratio ~ 5. (Source: Cooper and Lutzky, 1955).

Lutzky rms turbulence excess data. The turbulence profile is matched well by the equations in the entire tested range of 7 < x/L < 390. In both Figs. 7 and 8, the tails of the distributions are not described by the equations, which assume a wake boundary at r/r>>z = 1.36. This is the location where the excess or defect is 10% of the peak value or 13.3% of the value at the axis.

It may be noted here that the EBR-II tests were conducted in the range 0.6 < x/L< 6.9, which corre-sponds to 50 <x < 600m when L= 87.5m. gl>is value of L is shown in a later section to be character-istic of the EBR-II complex). Thus, the flat plate test range and the EBR-11 test range are coincident with respect to turbulence excess only at the downwind cnd of the field test range (x/L = 7).

Eqs.

2-6 represent measurements taken in the chordwise (parallel to short side) direction, normal to the plate axis. Measurements were not made in the spanwise direction. However, Fail e( al. (1955) made complete travcrscs in the wakes of triangular,

circular, tabbed, and square plates in the range 0.66x/LS3.6 and found, that thc wakes had become axi-symmetric at x/L = 3.6.

Rectangular z/zo 0 Q2 Q4 Q6 Qs IA) 1.4 z/z h o a204 as as I.o 1.0~

I a9 0.8 07 ~

I Eq.6o 'q.sb~

'8 0.5 f'.4 I

I 1

R~3 Plotett h(, 80IPII

"/b

"/t.

0 15.8 9

75.8 44I o 195.8 113I 4 375.8 217 o 675.8 390 1.3 1.2 IA)P a9 1-1.1 Io a9

~

Q7 b

08 Q6 Q5 o.s b

O.S I) o.4

<1 a3 4.6o I

RI5 Plotettt U, 80(

x/o '/L o

(55 7

75.5 34 o 195'7 4375.5 168 A675.5 302 4.6b Q2 ai o

oo 0.2 0.1 Q2 0.1 oo 0

0.5 1.0 IS 2.0 2.5 0

0 Qs l.o I.s 2.0 2.S

'/(t ),

/(zI)t Fig. 8. Normalized R. M. S. Turbulence Excess for Suspended Flat Plate Wakes. Left: Aspect ratio ~ 3.

Right: Aspect ratio ~ 5. (Source: Cooper and Lutzky, 1955).

I I

JAWING HALIIS&i plates having aspect ratios between 1 and IO were found to produce wakes that exhibited essentially the same characteristic. The EBR-II complex has an effec-tive equivalent flat plate in the shape of a rectangle of aspect ratio 3.6 (see later). Accordingly, it does not seem unreasonable to assume that Eqs. 2-6 would be equally valid in the spanwise direction at and beyond the center of the test range.

4. %1ND MEASOREMENTS 4.1 Approach Wind Characteristics Meteorological data taken during the field tests are given in Table 2, which is rcproduccd from Dickson et ai. (1969). The first line of data for each test gives the approach wind condition. All tests were reported to have been conducted in southwesterly winds. The individual mean wind directions werc not reported, but the diffusion data in Figs. 3 and 4 of the reference indicate an average wind direction of about 217'.

The Richardson Number was calculated for each test by Ri = (g/T)(dT/d: + i )(dft/dc)" z (7) where g = gravitational constant = 9.8 m-sec z

T = 295 K (assumed) dT/dc = (T Tz)/72K-m I'

0.010 R-m 'adiabatic lapse rate).

The value of (dft(dc)6 was obtained by assuming a power law for wind speed and taking the derivative at 6m, giving (dtt/dc),= nu/6.

Values of the ex-ponent n were assumed to bc 0.5 for inversion and 0.25 for lapse temperature gradients.

Calculated values of Ri are shown in Table 2. Thirteen of the fifteen tests had

-0.006 S Ri 6 +0.004, indicating near-neutrality.

Test 2

was most unstable with Ri = -0.012, Test 15 was most stable with Ri = +0.018. Even these departures from neutrality are not large.

Table 2. Meteorological Data for EBR-II Site Obtained from 30-min Samples Taken at 6-m Height Test No.

Date Time Tower location IVind direction standard deviation, deg alai horizontal vertical u, wind

speed, m/sec hT, temp.

difference. 'C 2-74-m 0.5-2-m levels al levels at 400.m arc S.m arc Rich.

Number Ri 2

3.1.67 1401-1431 600m upwind 50 m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 5.7 57.0 30.5 8.9 6.2 5.8 3.6 5.1 16.9 1.8 14.6 2.8 8.3 4.8 5.5 4.8 1.9 3;5 5.0

-0.34'0.012 3

3.7.67 1734-1803 4

3.7.67 2005-2035 600 m upwind 50m downwind 100 m downwind 200 m downwind 400 m downwind 600m downwind 600 m upwind 50 m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 8.9 21.6 14.2 10.9 9.1 9.0 11.3 37.1 26.6 15.2 1 1.8 11.1 4.2 11.8 10.1 7.6 4.5 4.1 3.2 13.9 13.7 7.5 3.8 3.4 6.0 2.0 4.1 5.1 6.1 6.1 5.8 3.3 3.9 4.6 5.5 5.7

-0.84

+0.94

-0.45

-0.50

-0.001

+0.003 5

3,8.67 1836-1906 6

3.8.67 2001-2032 7

3.&.67 2129-2159 600m upwind 50 m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 600 m upwind 50 m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 600m upwind 50 m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 7.3

'2.9 16.4 1 1.1 7.3 7.2 9A 53.5 27.9 1 1.0 9.4 9.3 5.9 35.0 17.6 11.4 7.2 6.0 3.7 6.0 10.8 3.5 10.3 4.3 7.4 5.4 4.5 6.1

-0.1 7 3.8 6.2

+0.50 3.9 5.7 14.4 2.8 13.3 3.5 6.0 5.2 4.6 5.5

-0.1 1 4.0 5.6 3.5 8.0

.16.8 3.7 15.1 5.5 7.5 5.8 5.3 7.2 3.5 8.0,

,0.39

-0.11

-0.22

+0.001

I

QaLe and dLspvtyu>r: mnu'tv 5}5 Test No.

Date Time Tower location Table 2~ontiuu<<d IVind direction standard deviation, deg tre.

horizontal vertical tl, wind

speed, m/sec hT. temp.

diA'crence, 'C 2-74.m 0.5-2-m levels at levels at 400-m arc 50.m arc Rich.

Number Ri 8

4.5.67 2027-2057 9

4.5.67 2201-2131 10 4.5.67 2332-0002 11 4.13.67 1447-1517 12 4.13.67 1559-1628 13 4.13.67 1700-1730 14 4.13.67 IS05-1835 15 4.13.67 2016-2046 16 4.14.67 1953-2024 600m upwind 50m downwind 100m downwind 200 m downwind 400 m downwind 600 m downwind 600 m upwind 50 m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 600 m upwind 50 m downwind 100 m downwind 200m downwind 400m dov nwind 600 m downwind 600 m upwind 50 m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 600 m upwind 50 m downwind 100 m downwind 200 m dowmvind 400 m downwind 600 m downwind 600m upwind 50m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 600 m upwind 50 m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind 600m upwind 50 m downwind 100 m downwind 200m downwind 400 m downwind 600 m downwind 600m upwind 50m downwind 100 m downwind 200 m downwind 400 m downwind 600 m downwind S.I 17.2 14.7 M.I 8.0 8.6 17.6 13.9 M'.5 8.7 6.9 15.8 11.6 6.6 6,9 11.9 30.9 19.7 11.8 10.6 12.1 10.8 33.0 21.9 I 1.4 10.9 10.9 I IA 29.7 19.8 11.0 11.5 I 1.5 9.3 25.2 I 1.3 9.4 10.2 9A 16.6 24.7 20.0 16.7 19.8 16.7 4.6 31.2 18.2 9.1 6.0 4.6 3.9 13.2 12.0 M'.3 4.0 4.4 I 1.7 9.2 M'.1 4.5 4.3 II.l 9.5 M~

4.2

~ 4.2 4.0 13.2 10.9 6.7 4.0 4.0 4.1 I"9 I I.O 6.5 3.7 4.1 3.6 13.2 9.4 6.0 4.0 3.7 4.1 I 1.9 8.2 4.4 4.8 42 2.7 12.6 7.9 5.4 3.8 2.8 4.0 15.3 12.4 7.6 3.6 3.9 6.1 3.7 4.3 5.1 5.7 6.0 42 2.2 2.7 3.1 3,8 4.0 5.9 3.7 4,3 5.0 5.6 4.8 9.7 5.4 6.5 7.9 9.0 9.6 9.8 4.7 6.2 8.0 9.4 9.7 10.5 5.5 6.9 8.6 9.3 10.4 10.3 5.0 6.6 7.7 7.6 10.2 4.0 1.7 2.2 2.7 3.4 3.9 6.5 2.1 3.2 3.6 4.9 6.4

+0.45

+0.28

+0.39

-0.28t

-2.39

-2.11

-1.67

+3.72

+0.56

-0.28

-0.39

-0.34

-0.78

-0.50

-0.39

-0.39 0.0

-0.39

+0.002

+0.002

-0.005

-0.003

-0.002

+0.018 s +0.002

'ata missing.

t -2.78 according to Van der Hoven, ed. (1967).

I E

Jesus IIAIIIS>;1 v I- (o) v Lopse C

- F.P'~

Inversion (r r EBR-11 F ----- Open terroin grid ill 0

Eq 35 E

b ipl 10 io Distonce downwind(m)

(b)

Lopse r rlnversion I

rr Cr r E

F EBR-II

- -- Open terroin prid 111

~Eq 36 IO to io Distance downwind tm)

Fig. 9. Concentration Standard Deviations at the EBR-11 Complex. Top: Lateral. Bottom: Vertical. (Source: Dick-son er ai., 1969) 4.2 Wake Characteristics The test data ol'able 2 arc graphed in Fig.

10.

The portions of thc graphs bctwccn x = 50m and 600m are drawn to correct logarithmic scale.

Test data are connected by solid lines. The three dashed lines in-the oz and.a~

curves between 100m and 400m indicate that 'data arc missing at 200m for Tests 8, 9 and

10. Upwind conditions are plotted at the abscissa location marked 600U, and these data

'he only unusual item in the approach wind data is the extremely large value of a> = 16.6'n Test 15 under strong inversion conditions. This apparently is a characteristic of the site, as indicated in Fig. 9a by thc large values ol' in E and F stabilities measured in open terrain west of thc EBR-II complex (at Grid III in Fig. I). A similar enlargement of a, does not occur (sce Fig, 9b). A possible source of such large pcrturbations may be density currents created by radiational cooling ol'he tranverse valley walls northwest ol'the site, and discharged in a south-east direction into thc main valley where the primary flow is from the southwest.

points are connected to the downwind data by dot-dash lines. Ilorizontal lines extending upwind from 600U and dosvnwind from about 1.000 arc intended to reprcscnt the undisturbed atmosphere, since the wind properties are assumed homogeneous upwind of Ihc complex, and are assumed to be asymptotic Io thc same values dowriwind of the complex.

Thc ordinate of Fig. 10a is labeled tr because that is thc notation used by Dickson. It should bc remem-bered, howcvcr, that spccd was mcasurcd with a cup anemometer which responds to horizontal winds from any direction. At the downwind cnd of a wake cavity, where the mean horizontal (vector) velocity is very small, thc mean horizontal speed may be appreciably higher bemuse thc fluctuatin nature of the flow pro-duces continuous wind movement.

The mean speed variation in the lee of the complex is quite similar to that observed downwind of flat plates beyond thc cavity region, i.e., low near the cavity and increasing asymptotically'to the approach wind value with increasing distance downwind. The minimum recorded speeds occurred at 50 m, at which location the ratio usp/u6ppv ranged from 0.32-0.63, with an average of 049. The probable existence of smaller speeds upwind of 50m is indicated by the slopes of the curves. This suggests that a cavity, if one existed, was shorter than 50m in length. The ratio ll6pp/trppptr ranged from 0.95 to 1.03 with an average ol'0.99, indicating that mean speed recovery was substantially complete by 600m in all tests.

Thc'teral turbulence intensity a,Jir, as ap-proximated by thc rms horizontal gust angle a~., is highest at 50 m, and thc largest obscrvcd value is 57'n Test 2. The slopes of the curves bctwccn 50m and 100m indicate thc probability of higher values at shorter distances.

A theoretical maximum value of 360/$ 12 = 104'or a>. can occur at the downwind cnd of a cavity where the distribution of horizontal wind angles may approach uniformity. Thus, the observed variation ol'<. is consistent with the hy-pothesis of a short cavity (<50m in length).

The vertical turbulence intensity awJu, as approxi-mated by the rms vertical gust angle a., behaves in a similar manner to ap., with ambient cut-offs at somewhat larger downwin'd distances because the ver-tical component ofambient turbulence is smaller than the horizontal component.

The wake boundary cannot be determined from the observed data because no spanwise or vertical distri-butions of wind angle were measured.

5. 51ATIIEAIATICALDESCRIPTIO."I OF TIIE EOR.II COMPLEX VVAKE S.l Fitting of IVake Equations ra Observed Data Numerical values of L and R for the EBR-II com-plex were found by replacing the complex by an equiva)ent flat plate implanted in the ground with ils ccntcr al ground elevation at thc tracer release point, its short cdgcs vertical, and its long edges nor-

Wake and dispersion mode)s Cq 7,

g 2

I.S 4

O b

50 4l 20 C7

~0 Io E

Eq. 8 for gest l3 test ovg fest 15 600V 50 100 200 400600 Eq. I3 (a) 7 (b)

Test no.

O 5

0 IV IOI 600U 50 IOO 200 400 600 40 bB 20 C7 C

IO C7 8

O 1

2 fq. I4 9

IO 3

I2el4 II, I6

~4 600V 50 IOO 200 400600 Longitudinol distonce, x (m)

(c)

Fig. 10. Wind Properties Along the Line ofTowers at the EBR-11 Complex. Top: Mean speed. Center:

llorizonta) gust angle. Bottom: Vcrtica) gust angle.

mal to the wind. The plate is shown superimposed on thc complex in Fig. 11.

The exposed half of the plate has height H and

'width IV. Therefore chord = 2ff, L = (2HlV) and R = IV/2H. Elimination of IV from thc above yields L

2ff Ro.s A'numerical value of' was selected on physical grounds. and a value of' was selected to provide the best agreement of Eqs.

2 and 3 with observed wind measurements.

Thc plate width then followed from above.

The selection of H was based on assuming a plate height which was effectively equal to thc average wake height at the center of the complex. Such a wake follows thc contour of the containment vessel dome and lies somewhat higher than the roofs of the various other buildings. I chose an average value of H = 23 m, which lies betwccn the power plant height of 19 m and the dome height of 29 m.

A trial and error proccdurc, using Eqs.

2 and 3

and the observations of Fig. 10 led to the selection of L= 87.5m, therefore 'R ~ (87.5/2 x 23)'

3.618, from which IV= 166m. Substitution of these values of L and R into Eqs. 2-5 yielded the following down-wind equations of an equivalent fiat plate wake for the EBR-II complex:

Ir, ~(1 8.16x r )I7,

d. = 6.37x u,

rr, = 23.4 x "3 rs = 31.2x "3 (8)

(9)

(10)

(11) rrJu, ~ rr.../u, = rres/57.3.

(12)

Eq:8 is shown by the heavy lines in Fig. 10a. The solid line rePrescnts an average of u, = II6ppv =

6.6m-scc

'. The two dashed lines correspond to the highest and lowest observed values of I7epptr, or 10.5 and 4.0 m-sec ', respectively.

Eq. 9 can bc compared to the data in Fig. 10b if the assumption is made that the longitudinal and lateral turbulcncc intensities are approximately equal, in which case,

JAMlk I(ill.risks (o) Woke contours m qround plane zs by Eq.I6 Equivalent flail e

2&'Q'5%

Io/

W.(88

'/

2. 50 5

~~(57. 3 a/8)'tabilitycloss (b) Wake contours in vertical center plane zsby Eq.18 2.5' 25~20~

i5~

8 "C 10' 2H046 0

IOO 200 300 400 500 600 700 Distance tram releose point, x, (m) 0 I

2 3

4 6

6 r

8 Normalized dislonce.

x/L Fig.

I I. Calculated Wake Boundaries and Turbulence Intensity Contours. Top: In ground plane.

Bottom: In vertical ccntcrp)anc.

Combining Eqs. 8, 9 and 12 then yields ass 365 (x" 8.16) '.

(13)'he, heavy line in Fig. 10b is Eq.

13. Thc predicted values are generally higher than the observations at all distances, but the agreement is better at the longer distances.

Fig. 10c includes a hcavy curve that corresponds to thc equation horizontal wake boundary y, ~ 23.4 x'"

ys = 31.2x'ls vertical wake boundary zs ~ 12.2x'"

(15)

(16)

(17) data, it is proposed that thc factor of'0.52 be applied

'o Eqs. 10 and 11 to yield aes = 052 aez (l4) z,'

16.2x'"

(18) where the factor 0.52 igthe ratio a,/ar obtained from Figs. 9a and 9b at a distance of 300m in D stability, and ace is given by Eq.

13. Thc rationale for Eq. 14 is that vertical wind Auctuations are suppressed by the ground, whereas longitudinal ones are not. Thcre-forc the approximation analogous to Eq. 12, but lor the vertical direction is ae. = aJir < aJii, and thc factor 0.52 is an estimate ol'he reduction. Thc 300m distance and D stability werc chosen as an average location and an average stability for thc EBR-II tests.

The suppression of vertical turbulcncc by thc ground indicates that the real wake is not axi-sym-metric as in the case of the suspended Aat plate. It may be inferred, therefore, that thc vertical wake boundary'is also suppressed.

In the abscncc of other 5.2 The. EBR-Il II'ake in a Turbulent Arniosphere Figurc I I shows thc calculated wake boundary and various longitudinal turbulence intensity contours expressed as thc angle (57.3 aJu)',

at the ground plane and in the vertical centerplane, superimposed on plan and clcvation views of the complex.

Thc wake properties in the ground plane in Fig.'la werc calculated by Eqs. 6a, 6b, 8, 9, and

16. By using Eq. 16 rather than Eq. IS thc.wake boundary was defined in terms of turbulence excess rather than mean velocity 'deficit, thcrcby creating a

broader wake. One simplification was introduced to facilitate the computation. The argument in Eqs.

6a and 6b was taken as:/:> in thc calculation of both /),'or turbulence excess and Z for mean velocity deficit.

K

~

~

s 5'akv and <b~petsivn madel~

i Table 3. Atmospheric Dispersion Constants at ihc EBR-11 Site Characteristic a>

Pasquill According to Stability Slade Class (deg)

(rad)

apa, p,

A 8

C D

E F

25 0.436 20 0.349 15 0.262 0.284 0.90 0.064 0.99 10 0.175 0.488 0.72 0.120 0.86 5

0.087 0.300 0.85 0.403 0.53 2.5 0.044 aq (rad) = a Ju, a~ ~ a~ x~, a, a, x~.

An exact c:ilculation of d would llavc rcqllircd the argument to be =/=This simplification reduced the local mean velocities somewhat, thereby increasing the turbulence intensities and broadening the turbu-lence intensity contours.

. The wake properties in the vertical centerplanc, Fig. lib, were calculated by Eqs.

6a, 6b, 8, 9 and 18, with the same simplification as used in the ground plane.

The wake as depicted in Fig. 11 is to be interpreted as the wake that would exist at the EBR-II complex if the background flow turbulence were the same as in the flat plate wind tunnel test airstream, and if the turbulence along the wake boundary were in excess of this by some small variable amount. Thc turbulencc intensity along the wake boundary may be found bycombining Eqs 2,3,6b, 8.and 9 to obtain (oju)> = 0.85(x~'~ 1.09) '19)

P This yields values of (aJu)i, = 0.042, 0.019 and 0.012 at x = 100, 300 and 600 m, rcspcctively. Therefore,

~

at the ccntcr of the EBR-II test range the equivalent liat plate boundary turbulence would be about 2%

and thc background turbulence would bc about 0.1%

In the atmosphere, thc turbulence intensity is larger than in the wind tunnel because friction and tempera-ture differences within the atmosphere generate turbu-lent eddies whose behavior is customarily categorized by Pasquill stability classes.

Slade, ed (1968) suggests that the standard deviation of horizontal wind angle fluctuations, a~ may be taken as an indicator of atmospheric stability. Table 3 contains Slade's values of aii and the corresponding Pasquill stability classes.

If the approximation ol'q.

12 is used, it may be scen that turbulence intensity in the atmosphere is not only larger than in the wind tunnel, but it is also larger than at the wake boundary.

Thc curves marked (57.3 atu)'n Fig.

11 may be taken.as contours of aa, if Eq. 12 is valid. They may also be viewed as wake boundaries for the specified stability classes when such a boundary is defined as the surface enclosing a region in which the wake tur-bulence intensity exceeds atmospheric turbulence in-tensity'. This is a crude definition, but it is a useful one for estimating wake boundaries.

A more refined definition requires knowledge of the manner in which atmospheric and wake turbulent energies combine. a subject which needs considerable investigation.

The lobed shape of the curves in Fig.

11 is thc result of a peaking of'turbulent intensity at r/r', =

0.40 0.45. This peak is produced by thc rolling up of vortex sheets generated at the periphery of the complex (or at the edges of its equivalent flat plate).

It seems to be a permanent feature of the wake, as may be inferred from Fig. 8. This behavior is mark-edly different from that of the peak mean velocity delcct, which occurs at about the same radial distance in the EBR-II test

range, but progresses inward towar'd the axis with increasing distance downwind, according to Fig, 7.

The curves have not been extended to x/L = 0 because the 'equations do not predict realistic values at short distances.

Such deviations may be attributed to thc presence of building cavities and, possibly, of a continuous'cavity ol'he entire complex. It may be noted that the cavity of the containment vessel when standing alone would cxtcnd to 2.3 diameters or 56m from the center of the vessel (Frame 14, Fig. 5.23, Slade, ed. (1968). This corresponds to x 43m from the release point in the complex. It seems possible that flow re-organization in the lee ofthc containment vessel cavity could account for much of thc deviation between predicted and observed characteristics at short distances, with the remainder due to flow dis-turbances created by thc adjacent buildings.

An important aspect of Fig.

11 is thc illustration that wakes arc finite in extent, and their lengths vary inversely as the stability (short for unstable, long for stable). Thc wake of the EBR-11 complex in neutral stability (Pasquill D), is about 300m long at the axis and about 450m long at thc cnd ol'he lobe. At the extremes ol'he stability range, thc axial lengths would bc about 110 m for Pasquill 8 and 19 I0 m long for Pasquill F, according to the model equations.

Confirmation of'model predictions in other than Pas-quill D stability is lacking, but the above estimates should be qualitatively correct, at the least.

6. DlSPERSION 6.1 General Properties of Nake Plumes A plume will be dcfincd as the region containing non-zero concentrations of dispersed material. The plume boundary is the curved surface that encloses all of thc released material.

A wake plume is a plume whose source lies within a wake. Thc boundary of a wake plume may take cithcr of two 1'orms, depending upon the location of the source within the wake. If the source lies within the cavity, material will disperse rapidly to the cavity boundary by cavity circulation and diffusion, then it will disperse to the wake boundary by wake turbu-lence outside of the cavity, and finally, it will disperse by atmospheric turbulcncc beyond the wake bound-ary. The plume boundary 1'or a source in thc cavity will extend from thc most upwind end of the wake

s((i(

JAM!5 HALI(slav (point d in Fig, 5. for cx:implc) to infinitydownivind and will have a radial dimension which is larger than the wake boundary radius and increases monotoni-cally with distance downwind at a rate that is solely dependent on atmospheric turbulence.

The latter characteristic is a consequence of the 'definition of a wake boundary as the surface beyond which the tur-bulcncc is atmospheric.

Ifthe source lies within the wake downwind of the cavity. material will disperse by wake turbulence to the wake boundary and then by atmospheric turbu-lence beyond the wake boundary. The plume bound-ary for such a source will extend from the source to infinity downwind, and will have a radial dimen-sion that grows monotonically with distance down-wind from the source at a variable rate depending on the local intensity of wake or atmospheric turbu-lence at the plume boundary.

In the classical approach to diffusion, one usually specilies the spatial distribution of diffusivity and mean velocity, and then proceeds to a solution of the differential equation of dilTusion, either in closed form or by numerical approximation. When the diffu-sivity is constant in a transverse plane, the mathema-tical solution is a Gaussian distribution of concen-

. tration. While the Gaussian distribution is quite rea-listic for most of the plume region, it is not realistic near the boundary because it predicts that material will be found cverywhcrc out to infinity in a radial direction. In order to overcome this physical impossi-bility,it is conventionally assu(ned that the Gaussian distribution is valid to some nominal radial distance, after which thc concentration is zero. Fr'cquently, this distance is taken to be r ~ 2.5 aat which point the concentration is 4.39% of the axial concentration, and the material enclosed within the boundary of a bi-Gaussian plume is 0.987 or 97.4% of the released amount.

In wake diffusion, the diffusivity is not constant in a transverse section: therefore the Gaussian distri-bution is not a good rcprcsentation, even at interior locations. Until adequate experiments are performed to establish thc spatial distribution of di!Tusivity in wakes, it would seem to be morc prudent to employ the plume boundary as a basic parameter in conjunc-tion with concentration distributions that seem rcasonablc on physical grounds and agree reasonably well with measurements.

Accordingly, thc approach that was used in deve-loping thc dispersion model for thc EBR-II complex was to combine realistic radial concentration distribu-tions, plume boundaries and mean velocity distribu-tions in an equation that satisfied mass continuity and predicted the observed decay ol'oncentration along the plume axis.

6.2 Dispersion Measurements Dispersion was measured at the EBR-11 complex by sampling concentrations of uranine dye released adjacent to the downwind surface of the containment vessel. Thc sampling grid is shown in Fig. 2. Thc x axis extended to the northeast, thc ccntcrs of thc sampling arcs were at the center of the containment vessel, and the arcs intersected the.v axis at distances of 30, 100, 200. 400 and 600 m from the release point.

The release and sampling points were at an elevation of 1 m above ground, and the release and sampling periods were 30 min.

Thirteen tests provided usable data'for dispersion analysis. These were Tests 2-13 and Test 16 in Table

2. Seven tests werc conducted under lapse conditions and six under inversion conditions; however, the sta-bility was essentially neutral for 'all except, perhaps, Test 2, because of the high wind speeds.

Discrete concentration measuremcnts are not given in Dickson er ai (1969). The data arc prescntcd as isoplcths of the concentration coeflicient K, and graphs of the longitudinal and vertical standard devi-ations of concentration distribution aand a, and center)ine concentration X, vs downwind distance.'he non-dimensional concentration coeAicicnt K is defined by where K = Xf(,AQ (20)

X = local concentration (g m"s)

((, = mean velocity of background'flow, assumed to bc ((pppU in Table 1 (m sec ')

Q = release rate (g sec ')

A = a characteristic area for wake dispersion analy-sis. The Nuclear Regulatory Commission custo-marily sets A equal to thc area of thc isolated containment vessel projected onto thc plane.

For the EBR-II reactor, A = 665m'.

This was the area used by Dickson er al.

In presenting the data, Dickson et ai. grouped thc tests according to temperature

gradient, i.e., lapse (7 tests) or inversion (6 tests). Isopleths of K~., K and K iwerc given for each gradient group. The K isopleths are reproduced herein as Figs.

12 (lapse) and 13 (inversion). The solid curves are the test observations.

The lateral standard deviation of concentration ar divas computed from thc concentration distribution in each arc. Two methods, not explained in detail, were used. The first, apparently, was the conventional sta-tistical treatment of a group of mmsuremcnts.

The second is said to be based on Xe and the crosswind integrated concentration CIC Fig. 11 ol'he reference gives thc formula ar ~ (CIC)(2n) '(~(Xr)

(21) where X~ ~ peak concentration along an arc CIC= f Xdy (Note: in reference Fig.

11, Xr is shown under the

• square root sign but this is bclicvcd to be a drawing error).

II II l',

Nui e ana d";wriml n Jr<<

Cu I Plume ondrwoke axis I

Wake bounda'ry o Ou Calculated K

0

/

/

'observed K

O. I 0.2 0.2

/

~

Q4

/

l.o

/

/

/

/

/

/

/

/"

~

/ag ss loam Wind ': SW. 7.6mps Release point: Bottom downwind Stability: Lapse 600m Fig. 12. K-Isopleths in the Ground Plane as Observed (Mean of Lapse Tests) and Calculated for Neutral Stability (Source: Dickson el al., 1969).

The vertical standard deviation a,

was not

measured, but was computed from the lateral distri-bution of.concentration, using thc assumption that thc vertical distribution of concentration was Gaus-sian. Presumably, a, is given by

\\

a. = Q(CIC) '(2n) '22)

App. A contains derivations of Eqs. 21 and 22.

Thc observed variation of mean aand a, vs x for the two temperature gradient classes is shown in Fig. 9.

The observed variation of ccntcrline concentration with downwind distance for all tests is given in Fig.

10 of Dickson et al. Howcvcr, the source strength is not given; therefore the ordinates cannot be con-verted to values of F. Dickson et al. stated that the power law relationship X~

x fits the data quite well for both lapse and inversion conditions. The exponent -0.6 is approxilnately the linear slope of the X~ vs x curves on thc log-log plot of Fig.

10.

but a

correction is needed for the difference in ordinate and abscissa scales. The corrected exponent would be -1.34.

I io Wake boundary 0 Calculated K 0

/,

O.l 0.2 0.4 I.O O. I

/ I Plume ond wake axis

//

I I

Obse/vedK I

/ /i

/

r

/

/

///

400m 600m rr Oom lOOm st Release point: Bottom downwind.

Wmd

SW,6.3mps Stability:Inversion tF Fig. 13. K-Isopleths in thc Ground Plane as Observed (Mean of Inversion Tests) and Calculated for Neutral Stability (Source: Dickson el al., 1969).

~

~

592

)hMI.S 14l,ltsVi 6.3 Dispersian i'lfodel Thc mathematical dispersion model that provided the best fit to thc observation v as of thc following form:

X = 2FQ (aa, u) '(y) g(z)

(23)

II of P = 0,75 was selected to provide a boundar>

half.

ividth at x = 0 that would be consistent with the observed values of aat x > 0 in neutral stability.

as given in Fig. 9a.

The constants ap. a, and p, were found by fitting the expression where a = axr (27)

I

-X = concentration at point x, y, z Q ~ release rate of source at ground level a= standard deviation ol'oncentration distri-bution in y direction a, = standard deviation of concentration distri-bution in z direction u = local mean velocity at distance x, constant over >

." plane f(y) = distribution function in y direction g(z) = distribution function in z direction 2 ~ ground reflection factor F= mass balance constant.

Explicit forms for a~ au, f(y) and g(z) were de-rived 1'rom the observations and introduced into Eq.

23, and g was then found from the mass

balance, equation i;~

Q =

Xi(dydz (24) 6.3.1 Plume Boundaries In order to fmd a,. af(y) and g( ) it was necessary to assume a form for the plume boundaries y, and Zy Since the material was released in the cavity of thc containment vessel, a form was needed to provide in-itial dispersion to the cavity boundary at x = 0 and subsequent growth by atmospheric turbulence at x) 0. The sclcctcd lateral and vertical boundary equations were y, = PIV/2+ 2.5arx~

(25) z(, = H + 2.5 a,xr'26) where y( z(

IV H

distance from plume axis to plume boundary equivalent fiat plate width (166m) equivalent liat plate height above ground (23 m) constants for parabolic boundary expan-sion building separation factor (0.75).

The terms PIV/2 and H provide an initial plume boundary expansion due to cavity mixing. In thc ver-tical direction, thc expansion is allowed to go to thc top cdgc of thc equivalent Aat plate. In the lateral direction, thc constant P restricts thc mixing to some fraction of the plate width. Thc physical rationale for P is to provide for interruption of cavity mixing by air seepage between buildings. The numerical value to the C, D, E and F stability curves in open terrain in Fig. 9a, at x = 200 and 600(n. Numerical values ol'hc constants are given in Table 3. The factor ol'.5 in Eqs. 25 and.26 implies that dispersion in an undisturbed atmosphcrc terminates at 2.5 a.

Thc combination of initial expansion due to build-ing ivake plus subsequent growth by atmospheric tur-bulence, as given by Eqs. 25 and 26, is believed to adequately rcprescnt the actual plume boundary growth since the plume boundary lies near or outside ol'he wake boundary (scc Figs. 12 and 13).

6.3.2 Distribution Firnctions Equations 1'or the growth of aand a, with x can be found from the plume boundary equations il'hc form of the distribution functions f(y) and g(z) is known.

The lateral distribution function f(y) was derived by measuring the lateral displacement ol'he K iso-pleths from the plume centerline in Figs.

12 and 13 at various downwind distances, and plotting them in non-dimensional 1'orm K/K, vs y/y, as in Fig. 14. Thc plume axis was assumed to be the (curved) line join-ing the ends of the K isoplcth loops. The traverscs were located at the ends of the isopleth loops. The small circles in Fig, 14 are the averages of left and right displacements. Thc values ol'(, used in normali-zation were calculated from Eq. 25 in D stability.

The hcavy curves in Fig. 14 arc a Gaussian distri-bution and a parabolic distribution having the follow-ing equations:

Gaussian:

K/K,~ exp[ y /2a] with a~ 0.4y~

(28)

Parabolic:

K/K,~ [I y/y(,].

(29)

The observed distribution is clearly not Gaussian, and the parabolic form is a representative average fit to both sets ol'ata.

The value of a for the parabolic distribution is found by So((K/K,)(y/yq) d(y/yq)

So(K/Kd d(y/y>)

Substitution of K/K, from Eq. 29 into Eq. 30 yields ar ~ yJ+10 (parabolic distribution).

(31)

Values of acalculated by Eqs. (25) and (31) for C, D and E stability are plotted in Fig. 9a. The D curve is seen to lie between thc lapse and inversion

'K 0

II

I 4 tt all 'lnd dlvp"(<Ion (il

)0o ae 06 hC

'Y a4 0.2 80 9(

IOI 6

l97 72 (o) Lapse Ois(ance, x(m) and thc slandard deviations became ax = 19.69+ ax~

(35)

(rr = 9.20 + a, x"'.

(36)

The local mean velocity (( was assumed to be that at thc plate axis. given by Eq. 8, or

((/((, = (1 8.16x 2(s).

(8)

Introduction of Eqs. 8 and 33-36 into Eqs. 23 and 24 yielded F = 3/2$20n.

(37) 0 IO 0.2 0.4 i 0.6 0.8 I

'('7 For convenicncc in comparing thc model predic-tions with observations.

Eq.

23 was normalized

.according to Eq. 20 to >ield the dispersion equation OL8 8(

9 l6 (b) Inversion

AXu, K =

= 251 68 ((re u/((,) '(y)0(:)

(38)

Q 0.6 0

l4 bC a4 53 398 l8 Ois(ance, x(m) observations. The C and E curves are higher, follow-ing the site characteristics.

It is not possible to perform a similar analysis in the vertical since no data were taken in this direction.

A Gaussian distribution was assumed because flow interruptions caused by building separation in the horizontal direction are not present in a vertical direction. Therefore a, is given by a, =:(/2.5 (Gaussian distribution).

(32)

Values of a, calculated by Eqs. 26 and 32 are plot-ted in Fig. 9b. The calculated values are higher than the observed values. However it should be remem-bered that thc observed values were, in fact, not observed but calculated 1'rom an assumed Gaussian distribution, and therefore do not provide a clear test of Eq. 32.

0 0.2 0.4 0.6 0.8

(,0

)(( 70 Fig. 14. Lateral Distribution of Normalized Concentration CocAicienL Top: Mean of Lapse tests. Bottom: Mean of inversion Tests.

a Wind tunnel 0

hC lo'I 4tO c

100 O

o c

OcOV o

X Id Lapse

~tnversibn 0

0 Calcu(a(ed lor stability 6.4 Comparison with Obseroations Isoplcths of K in the ground plane, calculated by Eq. 38, are shown in Figs.

12 and

13. Thc isopleths were made symmetrical about the curved plume axis. The wake boundary in D stability is also shown for rel'ercncc.

Agreement bctwcen calculated and observed K isoplcths is good. There appears to be little difference between thc lapse and inversion tests.

Dispersion is controlled by wake turbulence for dis-tances up to about 400m and by atmospheric turbu-lence thcrcafter. This suggests that thc parabolic dis-tribution used forf(y) in thc wake region should bc gradually replaced by the asymptotic Gaussian form at larger distances.

The variation of K along the plume axis is shown in Fig. 15. The lapse and inversion data points were 6.3.3 Dispersion Equation In view of the above, the distributions used in Eq.

23 became f(y)

(1 y/410(rr)'(z)

- expt'.-> /2ar'5 lat R

4 l(P" 4

4 (04 Downwind distance, x(rn)

(33)

Fig. 15. Variation of Concentration Coctlicient with Dis-(34) tance along Plume Axis.

JnMI 'I lint lt'It >

me;toured at thc ends of the K isoplcth loops in Fig~.

12 and

13. The wind tunnel data poinls were measured in a similar nninncr from Fig.

16. The curves marked C, D and E werc calculated,by Eq.

"38. The D (neutral stability) curve is a good fit to thc data for x > 80m. Some scatter in the observa-tions occurs in the mngc 30 < x < 80m.

Eq.

38 debates markedly from the observations at x < 30 m.

This is a consequence of thc assumed u/u, variation which goes to zero at x = 23.3m and produces in-

. finite F, at thc same distance.

The vend tunnel test data points merge smoothly with the field data points in the region of overlap.

This lends credibility to the wind tunnel values at short downwind distances.

Evidently a cavity diffu-sion model is needed to predict the observed values at short distances on physical grounds. Such a model is beyond the scope of this paper.

It is of some intcrcst to assess thc sensitivity of Eq. 38 to perturbations of the parameters. If tr tr, and u are unchanged, but f(y) is changed from the parabolic to the Gaussian I'orm, the calculated R

values will be reduced by a factor ol'.84. Similarly, il'he Gaussian form of 0(=) is replaced by the para-bolic form, the multiplying factor for K is 1.19. If u is held constant and equal to tt the factor changes with distance, as shown in Fig. 17.

It is also of some interest to compare Eq. 38 with the dispersion model ol'.S.A.E.G (1974) for calculat-ing concentrations downwind of a leak in a contain-ment structure. The governing equation lor ccntcrlinc concentration at ground level is X/litJQ

[try'>+ cj-i (39) where c = 0.5 and the other terms are as previously defined, together with the restriction that F, may not be smaller than one-third of the value obtained by Eq. 39 with c ~0.

Fig.

17 shows this model Release point: Bottom downwind Wind

SW, t.ym/sec Stability: Neutral to' s

4C

,Ol XI e

OI CO O

I C

OIIIo Colculoted tor 0 stability

, ~NRC model o

Calculoted for 0 stability wtth U ~ Bo

,0 IE IO iOI e

s tOO e

e'ownwind

distance, x(mi

\\

Fig. 17. Comparison of Dispersion Models.

7. SU51MARY for the EBR-II complex. The model is very good at close range but overcslimates concentrations for 80 < x < 600m. The latter occurs because insuAi-cient weight is given to initial broadening of the plume by the combined wake of all the buildings in the complex.

At larger distances, initial building effects become less significant, and the diffcrcnces bctwcen thc N R C and equivalent tlat plate models remains essentially in thc lateral distribution function j(y). As noted previously an asymptotic transforma-tion to the Gaussian form is to bc expected on physi-cal grounds. Experimental data are nccded to deter-mine the rate at which this transformation should be introduced.

0.7 et e

50 III Fig. 16. K-lsoplcths in the Ground Plane as Observed in Wind Tunnel Model Tests.

The mean velocity and turbulence measured along a longitudinal axis dowmvind of the EBR-II reactor containment structure can be modeled by equations that were dcrivcd from mcasurcmcnts along the longi-tudinal axis of a suspended flat plate, with a modi-fication to incorporate the effect of a solid ground boundary.

The paramctcr that is ncedcd to quantify thc model for the EBR-II complex is thc size and shape of an equivalent flat plate to replace thc assortment of buildings in the complex. It ivas found that 'a rec-tangular plate of height 46m and width 166m, half-imbedded in thc ground at the lec surface of the con-tainment vcsscl, ivas appropriate. The height dimen-sion was selcctcd as a visual average of the building heights. Thc width dimension was arrived at by trial and error, and sccms to be physically reasonable in retrospect.

l~y

"I'hi ground lioundar) cflcct ii;is>>itioduccd b) multiplying the vertical component of turbulence in-tensity and the vertical height of thc wake boundary by a factor of 0.52, which is the average value of a,/a for point source dispersion over thc test distance range in Pasquill D stability.

If the wake boundary is delined as the imaginary surface enclosing thc region in which turbulence in-tensity is greater than atmospheric, then real wakes are finite in length, width and height, and the dimen-sions are inversely proportional to thc atmospheric turbulence intensity components in the respective di-rections. The EBR-11 complex wake was about 400 m long. 270m wide and 70m high, according to model predictions, under the neutral stability conditions that existed during the field tests.

Thc cxistcnce of a xvake cavity at the EBR-11 com-plex was indicated by the decrease of mean velocity and increase of turbulencc intensity along the wake axis, with decreasing longitudinal distance. Extrapola-tion of this trend to zero mean velocity at x = 23 m suggests thc termination of a cavity near that point.

This is shorter than the cavity of'hc isolated EBR-II containmcnt structure, and it indicates that flow irre-gularities created by wind passage bc(ween buildings may perturb individual building cavities.

The merging of individual cavities into a single composite cavity for the complex is indicated by thc rapid initial dispersion of material to thc lateral boun-daries of the wake. However, insuflicient information is available to define the shape of such a cavity or its internal flow dynamics.

A dispersion model was developed that included initial plume expansion governed by the equivalent flat plate dimensions, variation of mean velocity along thc plume axis, parabolic distribution of'material in the horizontal and Gaussian distribution in the verti-cal. The model was in good agreement with the field observations beyond a distance of 30m, but it over-prcdictcd at shorter distances.

Thc failure of the model at short distances is due to inapplicability in a wake cavity region.

At distances longer than

600m, the model is expected to overpredict axial concentrations, by a maximum of 19% because flow reorganization after termination ol'he wake willeventually create a Gaus-sian, rather than parabolic, lateral distribution of con-centration. The model can be modified to incorporate this transition, but information as to the rate of tran-sition is lacking.

The dispersion model was tuned to the obscrvcd data in thc following rcspccts: sclcction ol'hc equiv-alent flat platcwidth IV, sclcction of the building sep-aration I'actor P, and selection of the panbolic distri-bution for lateral dispersion. It should be possible

'o formulate techniques for calculating these par-ameters from the geometry of thc complex, but ad-ditional tests in other confiigurations arc ncedcd to provide the requisite data base.

Meanwhile, the results ol'his investigation may serve as a guide for makiiig prclimniary csiini;iten of thc parameters in other applications.

REfERENCES Castro. I. P. and A. G. Robins (1975): The effect of a thick incident boundary layer on ihe low around a small sur-face mounted cube.

Central Electricity Generating

Board, Marchwood Laboratories Report R/M/N795, Marchwood, England.

Cooper R, D.. and M. Lutzky (1955): Exploratory investi-gation of turbulent wakes behind bluffbodies, U.S, Navy Dept. David Taylor Model Basin Rep. No. DTMB-963.

Counihan, J.. J. C.

R. Hunt and P.

S. Jackson (1974):

Wakes behind iwo-dimensional surface obstacles in tur-bulent boundary layers. L Fluid hfech.

3

564, pp 529-563.

Dickson, C R., G. E. Start and E. H. Markee, Jr. (1969):

Aerod>adamic erects of the EBR-II reactor complex on eflluent concentrations. Nuclear Safety, 10, No. 3 May-June.

Fail, R., J. A. Lawford and R. C. W. Eyre (1957): Low speed experiments on the wake characteristics of flat plates normal to an air stream. Aer. Rcs. Council R and M 3120. London.

Haliisky J., J. Go!den, P. Ilalpcrn, and P. Wu (1963): Wind tunnel tests of gas dilTusion from a leak in the shell of a nuclear power reactor and from a nearby stack.,

New York University Dept, of Met. and Ocean. GSL Rep. No. 63<<2 (Contract Cwb-10321 with U.S. Weather Bureau Environmental Meteorological Research Pro-ject).

Sladc. D. H.. cd. (1968): Meteorology and Atomic Energy, U,S. Atomic Energy Commission Div. of Tech.

Inf.

CFSTI Doc. TID.24190, U.S.A.F C. (1974): Regulatory Guide 1.4, Rcv. 2, Assunip-tions Used for Emluating ihe Potential Radiological

.Consequences of a Loss of Coolant Accident for Boiling Water Reactors.

Van der Hovcn I., ed, (1967): Atmospheric Transport and Diffusion in the Planetary Boundary Layer. U.S. Dept.

of Commcrce, ESSA Air Resources Laboratories Tech.

Mem. RLTM-ARL3. Dec. 1967.

Van der Hoven I., ed. (1968): Atmospheric Transport and Diffusion in the Planetary Boundary Layer, U.S. Dept.

of Commerce, ESSA Air Resources Laboratories Tech.

Mcm. ERLTM-ARL5. May 1968.

Then CIC ~

X<

p dy ~ Q(naa,u) '(2n)'x A.2 and Xe ~ Xx a

p Q(na a,u)

'ombine A.2 and A.3 io obtain:

a(CIC) (2n) '"X,'.4 APPENDIX A Derioation of Gaussian CIC equations To obtain as Let X,p ~ Q(nba,6) 'xp {-y(2')

)

A I

l'

To obtain a, Lct Q ~,

XUdydc A.S Then (CIC)(2r)'

a, a,

Q(CIC) '(2tt) "~

A.6 A.7

0