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 Abstract Wind 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 I. INTRODUCllON dispersion downwind of the EBR-II complex. It is believed that the equations have general applicability A mathematical model of atmospheric dispersion of to wakes generated by most building complexes, but material released near thc ground from a building it is recognized that they have been derived from situated among other buildings is nccdcd in the safety one body of data for a single configuration under analysis of a nuclear power reactor. No such model essentially neutral stability conditions. Therefore, ad-has gained general acceptance, primarily because ditional research is nccded to study the significance experimental data for its development have been of the characteristic lengths that appear in the analy-lacking. sis, and to validate thc wake and 'diffusion models In 1967 the Environmental Sciences Scrvicc Admin- under conditions of low wind spccd and extremes of istration (ESSA)'onducted a I'ull-scale experiment atmospheric stability.

at the National Reactor Testing Station, Idaho Falls, Idaho (NRTS)t to obtain such data. The results of

2. PHYSICAL CONFIGURATION OF THE the study were first published in an ESSA semi-EBR.II COMPLEX annual report (Van der Hoven, ed., 1967) and a more extcndcd article appeared later in Nuclear Safety The general topography at INEL is shown in Fig.

(Dickson ei al., 1969). 1. The EBR-II complex lies near thc center of a wide, The data gathered in the 1967 experiment include fiat SW-NE valley. The valley wall northwest of the downwind concentrations of a tracer released near complex is broken by several NW-SE tributary val-the ground at the lee wall of thc EBR-II reactor build- "

leys.

ing, and mean wind speed and turbulence upwind and Fig. 2 is a plan view of the EBR-II buildings and downwind of the EBR-II building complex. The the instrumentation arrangement used in the field ex-published articles contain tables and graphs, of wind periment. The tests werc conducted in southwesterly turbulence parameters, non-dimcnsionalized con'cen- winds only. The meteorological towers were arranged tration isoplcths, and the standard deviations trand along a SW-NE line through the ccntcr ol'he reactor a, of the lateral and.vertical concentration distribu- building. The tracer was relcascd near thc ground at tions. An empirical expression for the growth of a the northeast side of thc containment structure. The 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

'f samplers werc deployed in arcs centered on the center the containment structure.

Figure 3 is a photograph of'he complex, looking model or to relate the observed data to thc geometry slightly north of casL Figs. 4a and 4b are photographs of the building complex. of a I:96 scale model of the complex'in thc Ncw The purpose of'his paper is to prcscnt thc factual York University air pollution wind tunnel (Halitsky inl'ormation gathcrcd in the EBR-II experiments, and ei al., 1963), oriented in the same wind direction as to offer a synthesis, of the observations in thc form in the 1967 field 'tests.

of equations for thc prediction of wake properties and The buildings in the,complex include the contain-mcnt structure (dome-capped cylinder), a power plant

'subsequently integrated into National Oceanic and building, two heat cxchangcr structures, a fuel cycle Atmospheric Administration (NOAA) t subsequently re-named Idaho National Enginccring ,facility and a number of smaller auxiliary buildings.

Laboratory (1NEL). The building heights range from'm to 29m, the 577 8609120405 860905 PDR ADOC< 05ppp41p A PDR

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highest being the containment structure (29m) and ,culatory flow, called a cavity,.immcdiatcly in the ice the power plant building (19 m). of the object, and a transition region extending some uncertain distance downwind in which the flow

3. DESCRIPTIOV OF WAKE FLOW properties approach those of the background flow.

Fig. 5 is a sketch of a vertical section through the This section is intended to provide the reader with wake of a solid cube resting on the ground. It shows a survey of some aspects of wake flow which will the background flow, the wake and its cavity, and be helpful in understanding the analysis of the EBR-II a displacement zone in which the background flow test data and the development of the dispersion is aocelcratcd around the cube without substantial model. Readers who may wish to become more change of turbulencc.

familiar with rcccnt developments in classical wake Thc cavity boundary-in Fig. 5 is a streamline that theory and experimentation as applied to buildings originates at the building edge (point,d) and ter-in a boundary layer may consult "Counihan et al. minates,at the downwind stagnation point (point h).

(1974) and Castro el al. (1975). In three-dimensional flow, the cavity boundary is a surface that contains all such streamlines. Strcamlincs 3.1 Definition of Terms that lie within the cavity boundary close upon them-A wake is generally understood to be a region of selves to create a toroidal circulatory flow, while the disturbed flow downwind of an object in a wind external streamlines continue downwind to re-create stream. It contains a highly turbulent region with cir- the background flow.

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%take and dispersion models Arc 5 Hi-votume oir sumpter locottons~

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er Cp to 0~

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0 (Source: Dickson et al., 1969)

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Slightly North of East (Source: Dickson et al.,

Fig. 3. Photograph of the EBR-II Complex, Looking, 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- When several buildings are arranged in a group, ary surface along which the magnitude of a character- each of the buildings will create a wake whose charac-istic wake property dcviates from that of the back- teristics are dependent on the local background flow ground flow at the same location by an arbitrarily for that building. The local background flow, in turn, small amount. In this paper, two properties will be may be the undisturbed background flow upwind of considered: mean velocity and r'ms turbulence. Each the group or it may contain flow disturbances created will provide its own boundary radius, designated Fh by upwind buildings. If the buildings are closely or r'orresponding to an arbitrarily small deficit of spaced, as in a building complex, it seems reasonable mean velocity or arbitrarily small excess of rms turbu- to expect that the individual building wakes will lence, respectively. merge into a composite wake which will be irregular Since object-generated disturbances decay with in shape and structure near the buildings, but will radial and downwind distance, the wake boundary acquire the characteristic closed wake boundary and as defined above will be a closed surface, perhaps asymptotically developing mean velocity and turbu-expanding initially as along dmno in Fig. 5, but even- lence distributions at greater downwind distances..

tually contracting and terminating. The existence of a composite cavity within the com-

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Background

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, Oitplocement Woke boundar y ztr er a b c le~ tt h>>

Bownwindl Cavity boundory i

Wake 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- It may seem unusual to employ equations that were ment of thc buildings, since thc individual cavities developed for the wakes of suspended flat plates to may terminate bcforc they merge. describe thc wake ol' group ol'uildings on the ground, since the two configurations differ in at least 3.2 IVakc Equaiions four essential respects. First,. the plates are two-The properties of wake flow that arc important to dimensional while the building complex is three-the development of thc dispersion model for thc dimensional. Second, the plates are solid while the EBR-II complex are the longitudinal and transverse building complex may be considered porous by'virtue variations of mean velocity and turbulencc, and the of separation of individual buildings. Third, the plates longitudinal variation of boundary radius. In the were tested in a unil'orm stream while the background absence of other data it is proposed to usc generalized flow'of thc complex is a ground surface boundary expressions that are approximations to data measured layer. Finally, transverse gusts are unimpeded as they by Cooper and Lutzky (1955) in the wake of rectangu- thc axis of the plate wake, but they are stopped 'ross lar flat plates suspcndcd normal to an airstream in by the ground surface in the complex wake.

a low turbulence (0.1%) wind tunnel. Table 1 shows It is, of course, possible to employ physical and the plate configurations. mathematical reasoning to estimate the effect ol'hese Table 1. Flat Plate Test Configurations Plate Dimensions R'haract.

Aspect Ratio Length Cavity Length Tested Range of x/L Source Shape (in) L (in)t xJL min max Fail el al. Rect. 5.00 x 5.00 1 5.0 2.96 0.6 4.g (1959) Rect. 3.54 x 7.07 '2 5.0 ?86 0.6 4.8 Rect. 2.24 x 11.20 5 5.0 ?46 0.6 4.8 Rect. 1.58 x 15.80 10 5.0" 2.26 0.6 4.8 Rect. 1.12 x 22.35 20 5.0 0.96 0.6 4.8 Rect 1.24 x co 2.82$ 0.6 4.8 Eq. Tri. side ~ 7.60 5.0 2.82 0.6 4,8 Circle dia. ~ 5.66 5.0 2.92, 0.6 4.8 Tabbed dia. ~ 6.00 4.3 3.04 0.6 4.8 Cooper & Rect. 0.2 x 0.2 1 0.20 21.0 683 Lutzky (1955) Rect.. 0.2 x 0.6 3 0.35 9.1 394 Rect. 0.2 x 1.0 5 0.45 6.9 302 Rect. 0.2 x 2.0 10 0.63 5.5 216 Circle dia ~ 0.2 0.18 26.4 771

'pan/chord.

't(area) '.

'$ x Jchord.

h JAMIs 1lALI'Isi' differences. but it is diAicult, if not impossible, to vali- h = Incan velocity defect ratio, Z = (Ii, u)/

date them with the EBR-ll field test data. Accord- (II, u,) or rms lurbulence excess ratio, E =

ingly, the equations will be used in the Aat plate form, (aa.)/(a a )

the only adjustmcnts being in the magnitudes of the subscripts constants which will be found by comparing the equa- o ~ background flow tions with the field test data.. a ~ on wake axis Cooper and Lutzky present their data as graphs ~

b = on wake boundary.

of non-dimensionalizcd Aow properties, but they do not gencralizc the data other than to conclude that Eqs. 2-5 and the Cooper and Lutzky data are the data are in agreement with the theory of axi-sym- shown in Fig. 6. The dependence on R in Eqs. 2-5 metric wakes in the following respects:. was sclccted to provide agrccment of Eqs. 2-5 with

1. The maximum values of mean velocity defect and the data at R = 1 and R = 10. The individual data rms turbulence vary as (downwind distance) 3/3. points in Fig. 6 were obtained froin Cooper and

2. The radius of the wake varies as (downwind dis-ILutzky's faired curves through the transverse distribu-tance)'". tions. The two upper sets of data points are the curve

3. The transverse distributions of mean velocity de-ordinates at r = 0. The two lower sets are the dis-fect and rms turbulence are universal functions of tances to the estimated extension of the faired curves (radius/wake radius). to zero mean velocity defect or zero rms turbulence The above predictions of wake theory are based excess. Some ambiguity may exist in the rms turbu-on an assumed turbulence-free background flow. lence curves because thc extrapolation to zero is a Cooper and Lutzky's air stream had small but finite matter of judgment.

turbulence, and they corrected their measurements by Eqs. 6a and 6b describe the transverse distribution subtracting the turbulent kinetic energy of the back- of both mean velocity deficit and rms turbulence excess. Fig. 7 shows those equations superimposed ground flow. Thus, the data in their paper represent excess turbulence rather than absolute turbulence. on the Cooper and Lutzky mean velocity defect data I have fitted curves to Cooper 'and Lutzky's data, for R = 3 and R = 5. The curves match the data at incorporating the above conclusions, and interpreting the upwind location (11 <x/L < 13), but do not

,the turbulence data as excess over background. The match at the downwind locations where the distribu-equations of the curves are: tion tends toward Gaussian at x/L > 220. Fig. 8 shows the same equations with the Cooper and Longitudinal Variations (uo u,)/uo = 0.32 (x/L) /3R'/ (2) Symbol R IO (aa)/u, = 025 (x/L) / R'/ (3) Ea.2/

IO rt/L ~ 1.35 (x/L)'+ R (4)

I>

rt/L 1.80(x/L)i/3 R-I/Io (5)

IO' IO t Transverse Variations /r Io

~ 5 d, 1.167 + 0.167 sin[7.121 (r/rt 0.221)], 3

~ I 0 S r/rt S OA41 (6a) b t 6~ 0.733 + 0.600 sin[n 5.622 (r/rt 0.162)], IO OA41 S r/rt S 1 (6b) Eq.3 IO s o

(note: argument is in radian mode) 3 I

where: t t S t t t IQI IQt lot u longitudinal mean velocity IO IO a= lo'ngitudinal rms turbulence R = plate aspect ratio = span/chord'=

t plate characteristic dimension = (chord) R IM x = downwind coordinate from plate lo 3 I

r ~ chordwisc coordinate from wake axis 5 lo IO' rt = wake boundary coordinate defined as the chordwisc.distance from the wake axis'to the point where the mean velocity defect u, u is Eq.5 t t t t t 10% of the maximum defect at that station ~ Iof IQt t'I, ~ wake boundary coordinate defined as the x/I chordwise'distance from the wake axis to the Fig. 6. Properties of Suspended Hat Plate IVakcs. Top to bottom: mean velocity defect, rms turbulence excess, point where the rms turbulence excess aa wake boundary based on mean velocity defect, wake is 10% of the maximum excess at that station boundary based on rms turbulence excess.

l I 1

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/o "/

1.2 0.9 Rote la+i(40(t)

I/

0.8 o 218 13 Q8 o 24.5 I I o 8I8 47 1.0 o 84,5 38 0.7 0 201.8 117 0.7 o 381.8 220 0.9 A 681.8 394 I O

0.6 0,8 Io 0.6

-Eq.6o Eq.6b Eq.6o Eq.6b 0.7

~+ o.s Io 0.5 I

06 >>o Q4 as o 0.3 0.4 0.3 0.3 0.2 0.2 0.2 0.1 0.1 O. I 0

0 0 0.5 I.O I.S 2.0 2.S O.S I.O I.S ~ 2.0 24

/(z I) /(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 istic of the EBR-II complex). Thus, the flat plate test profile is matched well by the equations in the entire range and the EBR-11 test range are coincident with tested range of 7 < x/L < 390. In both Figs. 7 and respect to turbulence excess only at the downwind 8, the tails of the distributions are not described by cnd of the field test range (x/L = 7).

the equations, which assume a wake boundary at Eqs. 2-6 represent measurements taken in the r/r>>z = 1.36. This is the location where the excess chordwise (parallel to short side) direction, normal or defect is 10% of the peak value or 13.3% of the to the plate axis. Measurements were not made in value at the axis. the spanwise direction. However, Fail e( al. (1955)

It may be noted here that the EBR-II tests were made complete travcrscs in the wakes of triangular, conducted in the range 0.6 < x/L < 6.9, which corre- circular, tabbed, and square plates in the range sponds to 50 <x < 600m when L= 87.5m. gl>is 0.66x/LS3.6 and found, that thc wakes had value of L is shown in a later section to be character- become axi-symmetric at x/L = 3.6. Rectangular z/zo z/z h 0 Q2 Q4 Q6 Qs IA) o a204 as as I.o 1.0 ~

I 1 R~3 I

1.4 1.3 IA)

P I RI5 Plotett 80IPII a9 1- Plotettt U, 80(

a9 0

h(,

"/b "/t.

1.2 o (55 x/o '/L7 15.8 9 1.1 0.8 75.8 44I 75.5 34 o 195.8 113I Io 4 375.8 217 o 195'7 4375.5 168 07 ~

o 675.8 390 a9 ~ Q7 A675.5 302 b

08 Q6 I Eq.6o 'q.sb~ 4.6o 4.6b

'8 0.5 Q5 f'.4 o.s b I

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0 0.5 1.0 IS 2.0 2.5 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 The Richardson Number was calculated for each found to produce wakes that exhibited essentially the test by same characteristic. The EBR-II complex has an effec- Ri = (g/T)(dT/d: + i )(dft/dc)" z (7) tive equivalent flat plate in the shape of a rectangle where of aspect ratio 3.6 (see later). Accordingly, it does not g = gravitational constant = 9.8 m-sec z

seem unreasonable to assume that Eqs. 2-6 would T = 295 K (assumed) be equally valid in the spanwise direction at and dT/dc = (T Tz)/72K-m beyond the center of the test range. I' 0.010 R-m 'adiabatic lapse rate).

4. %1ND MEASOREMENTS The value of (dft(dc)6 was obtained by assuming a power law for wind speed and taking the derivative 4.1 Approach Wind Characteristics at 6m, giving (dtt/dc),= nu/6. Values of the ex-Meteorological data taken during the field tests are ponent n were assumed to bc 0.5 for inversion and given in Table 2, which is rcproduccd from Dickson 0.25 for lapse temperature gradients. Calculated et ai. (1969). The first line of data for each test gives values of Ri are shown in Table 2. Thirteen of the the approach wind condition. All tests were reported fifteen tests had -0.006 S Ri 6 +0.004, indicating to have been conducted in southwesterly winds. The near-neutrality. Test 2 was most unstable with individual mean wind directions werc not reported, Ri = -0.012, Test 15 was most stable with but the diffusion data in Figs. 3 and 4 of the reference Ri = +0.018. Even these departures from neutrality indicate an average wind direction of about 217'. are not large.

Table 2. Meteorological Data for EBR-II Site Obtained from 30-min Samples Taken at 6-m Height IVind direction hT, temp.

standard deviation, difference. 'C deg u, wind 2-74-m 0.5-2-m Rich.

Test alai speed, levels al levels at Number No. Date Time Tower location horizontal vertical m/sec 400.m arc S.m arc Ri 2 3.1.67 1401-1431 600m upwind 5.7 3.6 5.1 50 m downwind 57.0 16.9 1.8 100 m downwind 30.5 14.6 2.8 -0.34'0.012 200 m downwind 8.9 8.3 4.8 400 m downwind 6.2 5.5 4.8 1.9 600 m downwind 5.8 3;5 5.0 3 3.7.67 1734-1803 600 m upwind 8.9 4.2 6.0 50m downwind 21.6 11.8 2.0 -0.45 100 m downwind 14.2 10.1 4.1 200 m downwind 10.9 7.6 5.1 400 m downwind 9.1 4.5 6.1 -0.84 -0.001 600m downwind 9.0 4.1 6.1 4 3.7.67 2005-2035 600 m upwind 11.3 3.2 5.8 50 m downwind 37.1 13.9 3.3 -0.50 100 m downwind 26.6 13.7 3.9 200 m downwind 15.2 7.5 4.6 400 m downwind 1 1.8 3.8 5.5 +0.94 +0.003 600 m downwind 11.1 3.4 5.7 5 3,8.67 1836-1906 600m upwind 7.3 3.7 6.0 50 m downwind '2.9 10.8 3.5 ,0.39 100 m downwind 16.4 10.3 4.3 200 m downwind 1 1.1 7.4 5.4 400 m downwind 7.3 4.5 6.1 -0.1 7 600 m downwind 7.2 3.8 6.2 6 3.8.67 2001-2032 600 m upwind 9A 3.9 5.7 50 m downwind 53.5 14.4 2.8 -0.11 100 m downwind 27.9 13.3 3.5 200 m downwind 1 1.0 6.0 5.2 400 m downwind 9.4 4.6 5.5 -0.1 1 600 m downwind 9.3 4.0 5.6 7 3.&.67 2129-2159 600m upwind 5.9 3.5 8.0 50 m downwind 35.0 .16.8 3.7 -0.22 100 m downwind 17.6 15.1 5.5 200 m downwind 11.4 7.5 5.8 400 m downwind 7.2 5.3 7.2 +0.50 +0.001 600 m downwind 6.0 3.5 8.0 ,

I QaLe and dLspvtyu>r: mnu'tv 5}5 Table 2~ontiuu<<d IVind direction hT. temp.

standard deviation, diA'crence, 'C deg tl, wind 2-74.m 0.5-2-m Rich.

Test tre. speed, levels at levels at Number No. Date Time Tower location horizontal vertical m/sec 400-m arc 50.m arc Ri 8 4.5.67 2027-2057 600m upwind S.I 3.9 6.1 50m downwind 17.2 13.2 3.7 -0.28 100m downwind 14.7 12.0 4.3 200 m downwind 5.1 M.I M'.3 400 m downwind 5.7 +0.45 +0.002 600 m downwind 8.0 4.0 6.0 9 4.5.67 2201-2131 600 m upwind 8.6 4.4 42 50 m downwind 17.6 I 1.7 2.2 -0.39 100 m downwind 13.9 9.2 2.7 200 m downwind M'.5 M'.1 3.1 400 m downwind 3,8 +0.28 600 m downwind 8.7 4.5 4.0 10 4.5.67 2332-0002 600 m upwind 6.9 4.3 5.9 50 m downwind 15.8 I I.l 3.7 -0.34 100 m downwind 11.6 9.5 4,3 200m downwind M~ 5.0 400m dov nwind 6.6 4.2 5.6 +0.39 +0.002 600 m downwind 6,9 ~ 4.2 4.8 11 4.13.67 1447-1517 600 m upwind 11.9 4.0 9.7 50 m downwind 30.9 13.2 5.4 -0.78 100 m downwind 19.7 10.9 6.5 200 m downwind 11.8 6.7 7.9 400 m downwind 10.6 4.0 9.0 -0.28t 600 m downwind 12.1 4.0 9.6 12 4.13.67 1559-1628 600 m upwind 10.8 4.1 9.8 50 m downwind 33.0 I" 9 4.7 -0.50 100 m downwind 21.9 I I.O 6.2 200 m dowmvind I 1.4 6.5 8.0 400 m downwind 10.9 3.7 9.4 -2.39 -0.005 600 m downwind 10.9 4.1 9.7 13 4.13.67 1700-1730 600m upwind I IA 3.6 10.5 50m downwind 29.7 13.2 5.5 -0.39 100 m downwind 19.8 9.4 6.9 200 m downwind 11.0 6.0 8.6 400 m downwind 11.5 4.0 9.3 -2.11 -0.003 600 m downwind I 1.5 3.7 10.4 14 4.13.67 IS05-1835 600 m upwind 9.3 4.1 10.3 50 m downwind 25.2 I 1.9 5.0 -0.39 100 m downwind I 1.3 8.2 6.6 200 m downwind 9.4 4.4 7.7 400 m downwind 10.2 4.8 7.6 -1.67 -0.002 600 m downwind 9A 42 10.2 15 4.13.67 2016-2046 600m upwind 16.6 2.7 4.0 50 m downwind 24.7 12.6 1.7 0.0 100 m downwind 20.0 7.9 2.2 200m downwind 16.7 5.4 2.7 400 m downwind 19.8 3.8 3.4 +3.72 +0.018 600 m downwind 16.7 2.8 3.9 16 4.14.67 1953-2024 600m upwind 4.6 4.0 6.5 50m downwind 31.2 15.3 2.1 -0.39 100 m downwind 18.2 12.4 3.2 200 m downwind 9.1 7.6 3.6 400 m downwind 6.0 3.6 4.9 +0.56 s +0.002 600 m downwind 4.6 3.9 6.4

'ata missing.

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

I E Jesus IIAIIIS>;1 v I- v Lopse points are connected to the downwind data by dot-(o) dash lines. Ilorizontal lines extending upwind from

- F.P'~

C Inversion 600U and dosvnwind from about 1.000 arc intended to reprcscnt the undisturbed atmosphere, since the E wind properties are assumed homogeneous upwind b of Ihc complex, and are assumed to be asymptotic Io thc same values dowriwind of the complex.

(r rF ----- EBR-11 Thc ordinate of Fig. 10a is labeled tr because that Open terroin 0 grid ill Eq 35 is thc notation used by Dickson. It should bc remem-bered, howcvcr, that spccd was mcasurcd with a cup ipl 10 io anemometer which responds to horizontal winds from Distonce downwind(m) 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-(b) Lopse duces continuous wind movement.

The mean speed variation in the lee of the complex r rlnversion I

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 Cr rrr 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, E with an average of 049. The probable existence of F

EBR-II Open terroin 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 prid

~

111 Eq 36 average ol'0.99, indicating that mean speed recovery was substantially complete by 600m in all tests.

IO to io Thc'teral turbulence intensity a,Jir, as ap-Distance downwind tm) proximated by thc rms horizontal gust angle a~., is Fig. 9. Concentration Standard Deviations at the EBR-11 highest at 50 m, and thc largest obscrvcd value is 57'n Complex. Top: Lateral. Bottom: Vertical. (Source: Dick- Test 2. The slopes of the curves bctwccn 50m and son er ai., 1969) 100m indicate thc probability of higher values at shorter distances. A theoretical maximum value of

'he only unusual item in the approach wind data 360/$ 12 = 104'or a>. can occur at the downwind is the extremely large value of a> = 16.6'n Test 15 cnd of a cavity where the distribution of horizontal under strong inversion conditions. This apparently is wind angles may approach uniformity. Thus, the a characteristic of the site, as indicated in Fig. 9a observed variation ol'<. is consistent with the hy-by thc large values ol' in E and F stabilities pothesis of a short cavity (<50m in length).

measured in open terrain west of thc EBR-II complex The vertical turbulence intensity awJu, as approxi-(at Grid III in Fig. I). A similar enlargement of a, mated by the rms vertical gust angle a., behaves does not occur (sce Fig, 9b). A possible source of in a similar manner to ap., with ambient cut-offs at such large pcrturbations may be density currents somewhat larger downwin'd distances because the ver-created by radiational cooling ol'he tranverse valley tical component of ambient turbulence is smaller than walls northwest ol'the site, and discharged in a south- the horizontal component.

east direction into thc main valley where the primary The wake boundary cannot be determined from the flow is from the southwest. observed data because no spanwise or vertical distri-butions of wind angle were measured.

4.2 Wake Characteristics

5. 51ATIIEAIATICALDESCRIPTIO."I OF TIIE EOR.II The test data ol'able 2 arc graphed in Fig. 10. COMPLEX VVAKE The portions of thc graphs bctwccn x = 50m and 600m are drawn to correct logarithmic scale. Test S.l Fitting of IVake Equations ra Observed Data data are connected by solid lines. The three dashed Numerical values of L and R for the EBR-II com-lines in-the oz and.a~ curves between 100m and plex were found by replacing the complex by an 400m indicate that 'data arc missing at 200m for equiva)ent flat plate implanted in the ground with Tests 8, 9 and 10. Upwind conditions are plotted at ils ccntcr al ground elevation at thc tracer release the abscissa location marked 600U, and these data point, its short cdgcs vertical, and its long edges nor-

Wake and dispersion mode)s Cq Eq. 8 for gest l3 (a) test ovg fest 15 7

7, g 2 I.S 600V 50 100 200 400600 4

O b 50 (b) 4l Test no.

Eq. I3 20 C7 0

~

Io E

O 5

0IV I I O

600U 50 IOO 200 400 600 40 bB (c) fq. I4 20 C7 C 9 IO IO 3 C7 I2el4 I I, I 6 8

O 1

2 600V 50 IOO 200 400600

~4 Longitudinol distonce, x (m)

Fig. 10. Wind Properties Along the Line of Towers 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 from which IV= 166m. Substitution of these values on thc complex in Fig. 11. of L and R into Eqs. 2-5 yielded the following down-The exposed half of the plate has height H and wind equations of an equivalent fiat plate wake for

'width IV. Therefore chord = 2ff, L = (2HlV) and the EBR-II complex:

R = IV/2H. Elimination of IV from thc above yields L 2ff Ro.s Ir, ~(1 8.16x r

)I7, (8)

A'numerical value of' was selected on physical

d. = 6.37x u, (9) grounds. and a value of' was selected to provide the best agreement of Eqs. 2 and 3 with observed rr, = 23.4 x "3 (10) wind measurements. Thc plate width then followed = 31.2x "3 rs (11) from above.

The selection of H was based on assuming a plate Eq:8 is shown by the heavy lines in Fig. 10a. The height which was effectively equal to thc average solid line rePrescnts an average of u, = II6ppv =

wake height at the center of the complex. Such a wake 6.6m-scc '. The two dashed lines correspond to the follows thc contour of the containment vessel dome highest and lowest observed values of I7epptr, or 10.5 and lies somewhat higher than the roofs of the and 4.0 m-sec ', respectively.

various other buildings. I chose an average value of Eq. 9 can bc compared to the data in Fig. 10b H = 23 m, which lies betwccn the power plant height if the assumption is made that the longitudinal and of 19 m and the dome height of 29 m. lateral turbulcncc intensities are approximately equal, A trial and error proccdurc, using Eqs. 2 and 3 in which case, and the observations of Fig. 10 led to the selection of L= 87.5m, therefore 'R ~ (87.5/2 x 23)' 3.618, rrJu, ~ rr.../u, = rres/57.3. (12)

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

2. 50 5

Equivalent flail

~~(57. 3

'/

e closs a/8)'tability 2&'Q'5% Io/

W.(88 (b) Wake contours in vertical center plane zsby Eq.18 2.5' 25~20~ 10' 8 "Ci 5~

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 data, it is proposed that thc factor of'0.52 be applied 'o Eqs. 10 and 11 to yield ass 365 (x" 8.16) '.

(13)'he, horizontal wake boundary heavy line in Fig. 10b is Eq. 13. Thc predicted y, ~ 23.4 x'" (15) values are generally higher than the observations at all distances, but the agreement is better at the longer ys = 31.2x'ls (16) distances. vertical wake boundary Fig. 10c includes a hcavy curve that corresponds to thc equation zs ~ 12.2x'" (17)

= 052 aez (l4) z,' 16.2x'" (18) aes where the factor 0.52 ig the ratio a,/ar obtained from 5.2 The. EBR-Il II'ake in a Turbulent Arniosphere Figs. 9a and 9b at a distance of 300m in D stability, Figurc I I shows thc calculated wake boundary and and ace is given by Eq. 13. Thc rationale for Eq. 14 various longitudinal turbulence intensity contours is that vertical wind Auctuations are suppressed by expressed as thc angle (57.3 a Ju)', at the ground the ground, whereas longitudinal ones are not. Thcre- plane and in the vertical centerplane, superimposed forc the approximation analogous to Eq. 12, but lor on plan and clcvation views of the complex.

the vertical direction is ae. = aJir < aJii, and thc Thc wake properties in the ground plane in Fig.'la factor 0.52 is an estimate ol'he reduction. Thc 300m werc calculated by Eqs. 6a, 6b, 8, 9, and 16. By distance and D stability werc chosen as an average using Eq. 16 rather than Eq. IS thc.wake boundary location and an average stability for thc EBR-II tests. was defined in terms of turbulence excess rather than The suppression of vertical turbulcncc by thc mean velocity 'deficit, thcrcby creating a broader ground indicates that the real wake is not axi-sym- wake. One simplification was introduced to facilitate metric as in the case of the suspended Aat plate. It the computation. The argument in Eqs. 6a and 6b may be inferred, therefore, that thc vertical wake was taken as:/:> in thc calculation of both /),'or boundary'is also suppressed. In the abscncc of other turbulence excess and Z for mean velocity deficit.

K

~ ~

s 5'akv and <b~petsivn madel~

An exact c:ilculation of d would llavc rcqllircd the atmospheric and wake turbulent energies combine. a argument to be =/=This simplification reduced the subject which needs considerable investigation.

local mean velocities somewhat, thereby increasing The lobed shape of the curves in Fig. 11 is thc the turbulence intensities and broadening the turbu- result of a peaking of'turbulent intensity at r/r', =

lence intensity contours. 0.40 0.45. This peak is produced by thc rolling up

. The wake properties in the vertical centerplanc, of vortex sheets generated at the periphery of the Fig. lib, were calculated by Eqs. 6a, 6b, 8, 9 and complex (or at the edges of its equivalent flat plate).

18, with the same simplification as used in the ground It seems to be a permanent feature of the wake, as plane. may be inferred from Fig. 8. This behavior is mark-The wake as depicted in Fig. 11 is to be interpreted edly different from that of the peak mean velocity as the wake that would exist at the EBR-II complex delcct, which occurs at about the same radial distance if the background flow turbulence were the same as in the EBR-II test range, but progresses inward in the flat plate wind tunnel test airstream, and if towar'd the axis with increasing distance downwind, the turbulence along the wake boundary were in according to Fig, 7.

excess of this by some small variable amount. Thc The curves have not been extended to x/L = 0 turbulencc intensity along the wake boundary may because the 'equations do not predict realistic values at short distances. Such deviations may be attributed be found bycombining Eqs 2,3,6b, 8.and 9 to obtain (o ju)> = 0.85(x~'~ 1.09) '19)

P 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 This yields values of (a Ju)i, = 0.042, 0.019 and 0.012 at x = 100, 300 and 600 m, rcspcctively. Therefore, ~ standing alone would cxtcnd to 2.3 diameters or 56m at the ccntcr of the EBR-II test range the equivalent from the center of the vessel (Frame 14, Fig. 5.23, liat plate boundary turbulence would be about 2% Slade, ed. (1968). This corresponds to x 43m from and thc background turbulence would bc about 0.1% the release point in the complex. It seems possible In the atmosphere, thc turbulence intensity is larger that flow re-organization in the lee of thc containment than in the wind tunnel because friction and tempera- vessel cavity could account for much of thc deviation ture differences within the atmosphere generate turbu- between predicted and observed characteristics at lent eddies whose behavior is customarily categorized short distances, with the remainder due to flow dis-by Pasquill stability classes. Slade, ed (1968) suggests turbances created by thc adjacent buildings.

i that the standard deviation of horizontal wind angle An important aspect of Fig. 11 is thc illustration fluctuations, a~ may be taken as an indicator of that wakes arc finite in extent, and their lengths vary atmospheric stability. Table 3 contains Slade's values inversely as the stability (short for unstable, long for of aii and the corresponding Pasquill stability classes. stable). Thc wake of the EBR-11 complex in neutral If the approximation ol'q. 12 is used, it may be stability (Pasquill D), is about 300m long at the axis scen that turbulence intensity in the atmosphere is and about 450m long at thc cnd ol'he lobe. At the not only larger than in the wind tunnel, but it is also extremes ol'he stability range, thc axial lengths larger than at the wake boundary. would bc about 110 m for Pasquill 8 and 19 I 0 m long Thc curves marked (57.3 atu)'n Fig. 11 may be for Pasquill F, according to the model equations.

taken.as contours of aa, if Eq. 12 is valid. They may Confirmation of'model predictions in other than Pas-also be viewed as wake boundaries for the specified quill D stability is lacking, but the above estimates stability classes when such a boundary is defined as should be qualitatively correct, at the least.

the surface enclosing a region in which the wake tur-bulence intensity exceeds atmospheric turbulence in- 6. DlSPERSION tensity'. This is a crude definition, but it is a useful one for estimating wake boundaries. A more refined 6.1 General Properties of Nake Plumes definition requires knowledge of the manner in which A plume will be dcfincd as the region containing non-zero concentrations of dispersed material. The Table 3. Atmospheric Dispersion Constants at ihc EBR-11 plume boundary is the curved surface that encloses Site all of thc released material.

Characteristic a> A wake plume is a plume whose source lies within Pasquill According to a wake. Thc boundary of a wake plume may take Stability Slade cithcr of two 1'orms, depending upon the location of Class (deg) (rad) apa, p, the source within the wake. If the source lies within 0.436 the cavity, material will disperse rapidly to the cavity A 25 8 20 0.349 boundary by cavity circulation and diffusion, then it C 15 . 0.262 0.284 0.90 0.064 0.99 will disperse to the wake boundary by wake turbu-D 10 0.175 0.488 0.72 0.120 0.86 lence outside of the cavity, and finally, it will disperse E 5 0.087 0.300 0.85 0.403 0.53 by atmospheric turbulcncc beyond the wake bound-F 2.5 0.044 ary. The plume boundary 1'or a source in thc cavity aq (rad) = a Ju, a~ ~ a~ x~, a, a, x~. 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 infinity downivind vessel. Thc sampling grid is shown in Fig. 2. Thc x and will have a radial dimension which is larger than axis extended to the northeast, thc ccntcrs of thc the wake boundary radius and increases monotoni- sampling arcs were at the center of the containment cally with distance downwind at a rate that is solely vessel, and the arcs intersected the.v axis at distances dependent on atmospheric turbulence. The latter of 30, 100, 200. 400 and 600 m from the release point.

characteristic is a consequence of the 'definition of a The release and sampling points were at an elevation wake boundary as the surface beyond which the tur- of 1 m above ground, and the release and sampling bulcncc is atmospheric. periods were 30 min.

If the source lies within the wake downwind of the Thirteen tests provided usable data'for dispersion cavity. material will disperse by wake turbulence to analysis. These were Tests 2-13 and Test 16 in Table the wake boundary and then by atmospheric turbu- 2. Seven tests werc conducted under lapse conditions lence beyond the wake boundary. The plume bound- and six under inversion conditions; however, the sta-ary for such a source will extend from the source bility was essentially neutral for 'all except, perhaps, to infinity downwind, and will have a radial dimen- Test 2, because of the high wind speeds.

sion that grows monotonically with distance down- Discrete concentration measuremcnts are not given wind from the source at a variable rate depending in Dickson er ai (1969). The data arc prescntcd as on the local intensity of wake or atmospheric turbu- isoplcths of the concentration coeflicient K, and lence at the plume boundary. graphs of the longitudinal and vertical standard devi-In the classical approach to diffusion, one usually ations of concentration distribution aand a, and specilies the spatial distribution of diffusivity and center)ine concentration X, vs downwind distance.'he mean velocity, and then proceeds to a solution of non-dimensional concentration coeAicicnt K is the differential equation of dilTusion, either in closed defined by form or by numerical approximation. When the diffu- K = Xf(,AQ (20) sivity is constant in a transverse plane, the mathema-where tical solution is a Gaussian distribution of concen-

. tration. While the Gaussian distribution is quite rea- X = local concentration (g m" s) listic for most of the plume region, it is not realistic ((, = mean velocity of background'flow, assumed to near the boundary because it predicts that material bc ((pppU in Table 1 (m sec ')

will be found cverywhcrc out to infinity in a radial Q = release rate (g sec ')

direction. In order to overcome this physical impossi- A = a characteristic area for wake dispersion analy-bility, it is conventionally assu(ned that the Gaussian sis. The Nuclear Regulatory Commission custo-distribution is valid to some nominal radial distance, marily sets A equal to thc area of thc isolated after which thc concentration is zero. Fr'cquently, this containment vessel projected onto thc distance is taken to be r ~ 2.5 aat which point the plane. For the EBR-II reactor, A = 665m'.

concentration is 4.39% of the axial concentration, and This was the area used by Dickson er al.

the material enclosed within the boundary of a bi-In presenting the data, Dickson et ai. grouped thc Gaussian plume is 0.987 or 97.4% of the released tests according to temperature gradient, i.e., lapse (7 amount.

tests) or inversion (6 tests). Isopleths of K~., K In wake diffusion, the diffusivity is not constant and K iwerc given for each gradient group. The in a transverse section: therefore the Gaussian distri-bution is not a good rcprcsentation, even at interior K isopleths are reproduced herein as Figs. 12 (lapse) and 13 (inversion). The solid curves are the locations. Until adequate experiments are performed test observations.

to establish thc spatial distribution of di!Tusivity in The lateral standard deviation of concentration ar wakes, it would seem to be morc prudent to employ divas computed from thc concentration distribution in the plume boundary as a basic parameter in conjunc-each arc. Two methods, not explained in detail, were tion with concentration distributions that seem used. The first, apparently, was the conventional sta-rcasonablc on physical grounds and agree reasonably tistical treatment of a group of mmsuremcnts. The well with measurements.

second is said to be based on Xe and the crosswind Accordingly, thc approach that was used in deve-integrated concentration CIC Fig. 11 ol'he reference loping thc dispersion model for thc EBR-II complex gives thc formula was to combine realistic radial concentration distribu-tions, plume boundaries and mean velocity distribu- ar ~ (CIC)(2n) '(~(Xr) (21) tions in an equation that satisfied mass continuity where and predicted the observed decay ol'oncentration X~ ~ peak concentration along an arc along the plume axis.

6.2 Dispersion Measurements CIC= f Xdy Dispersion was measured at the EBR-11 complex (Note: in reference Fig. 11, Xr is shown under the by sampling concentrations of uranine dye released *square root sign but this is bclicvcd to be a drawing adjacent to the downwind surface of the containment error).

II l',

II

Nui e ana d";wriml n Jr<< Cu I Plume ondrwoke axis I

Calculated K 0 O. I 0.2

/

Wake bounda'ry o

/

/

~

0.2 Ou

'observed K Q4 /

l.o / /

// /

/ /

/" ~ 600m

/ag ss loam Wind Stability:

Release point: Bottom downwind SW. 7.6mps Lapse 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 The observed variation of ccntcrline concentration measured, but was computed from the lateral distri- with downwind distance for all tests is given in Fig.

bution of.concentration, using thc assumption that 10 of Dickson et al. Howcvcr, the source strength thc vertical distribution of concentration was Gaus- is not given; therefore the ordinates cannot be con-

'22) verted to values of F. Dickson et al. stated that the sian. Presumably, a, is given by

\ power law relationship X~ x fits the data quite

a. = Q(CIC) '(2n) well for both lapse and inversion conditions. The exponent -0.6 is approxilnately the linear slope of App. A contains derivations of Eqs. 21 and 22. the X~ vs x curves on thc log-log plot of Fig. 10.

Thc observed variation of mean aand a, vs x but a correction is needed for the difference in for the two temperature gradient classes is shown in ordinate and abscissa scales. The corrected exponent Fig. 9. would be -1.34.

I O. I Wake boundary 0 io / I Plume ond wake axis

// I Calculated K 0 O.l

/, /

I I

/i Obse/vedK

/

0.2

/ r

//

//

0.4 I.O 600m 400m rr Oom st lOOm 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 II 6.3 Dispersian i'lfodel of P = 0,75 was selected to provide a boundar> half.

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

the best fit to thc observation v as of thc following as given in Fig. 9a.

form:

The constants ap. a, and p, were found by fitting X = 2FQ (aa, u) '(y) g(z) (23) the expression where a = axr (27)

-X = concentration at point x, y, z to the C, D, E and F stability curves in open terrain Q ~ release rate of source at ground level in Fig. 9a, at x = 200 and 600(n. Numerical values a= standard deviation ol'oncentration distri- ol'hc constants are given in Table 3. The factor ol'.5 bution in y direction in Eqs. 25 and.26 implies that dispersion in an a, = standard deviation of concentration distri- undisturbed atmosphcrc terminates at 2.5 a.

bution in z direction Thc combination of initial expansion due to build-u = local mean velocity at distance x, constant ing ivake plus subsequent growth by atmospheric tur-over > ." plane bulence, as given by Eqs. 25 and 26, is believed to f(y) = distribution function in y direction adequately rcprescnt the actual plume boundary g(z) = distribution function in z direction growth since the plume boundary lies near or outside 2 ~ ground reflection factor ol'he wake boundary (scc Figs. 12 and 13).

F= mass balance constant.

6.3.2 Distribution Firnctions Explicit forms for a~ au, f(y) and g(z) were de-Equations 1'or the growth of aand a, with x can rived 1'rom the observations and introduced into Eq. il'hc be found from the plume boundary equations 23, and equation g i;~

was then found from the mass balance, form of the distribution functions f(y) and g(z) is known.

The lateral distribution function f(y) was derived I

= Xi(dydz (24) by measuring the lateral displacement ol'he K iso-Q pleths from the plume centerline in Figs. 12 and 13 6.3.1 Plume Boundaries at various downwind distances, and plotting them in non-dimensional 1'orm K/K, vs y/y, as in Fig. 14. Thc In order to fmd a,. a f(y) and g( ) it was necessary plume axis was assumed to be the (curved) line join-to assume a form for the plume boundaries y, and ing the ends of the K isoplcth loops. The traverscs Zy were located at the ends of the isopleth loops. The Since the material was released in the cavity of thc small circles in Fig, 14 are the averages of left and containment vessel, a form was needed to provide in-right displacements. Thc values ol'(, used in normali-itial dispersion to the cavity boundary at x = 0 and zation were calculated from Eq. 25 in D stability.

subsequent growth by atmospheric turbulence at The hcavy curves in Fig. 14 arc a Gaussian distri-x) 0. The sclcctcd lateral and vertical boundary bution and a parabolic distribution having the follow-equations were ing equations:

y, = PIV/2+ 2.5arx~

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

Gaussian:

K/K, ~ exp[ y /2a] with a~ 0.4y~ (28) where Parabolic:

distance from plume axis to plume y( z(

boundary K/K, ~ [I y/y(,] . (29)

IV equivalent fiat plate width (166m) The observed distribution is clearly not Gaussian, and H equivalent liat plate height above ground the parabolic form is a representative average fit to (23 m) both sets ol'ata.

constants for parabolic boundary expan- The value of a for the parabolic distribution is sion found by building separation factor (0.75).

So((K/K,) (y/yq) d(y/yq)

The terms PIV/2 and H provide an initial plume So(K/Kd d(y/y>)

boundary expansion due to cavity mixing. In thc ver-tical direction, thc expansion is allowed to go to thc Substitution of K/K, from Eq. 29 into Eq. 30 yields

.- 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 ar ~ yJ+10 (parabolic distribution).

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 (31)

'K 0

II

I 4 tt all 'lnd dlvp"(<Ion (il )0o and thc slandard deviations became (o) Lapse ax = 19.69+ ax~ (35) ae 80 (rr = 9.20 + a, x"'. (36) 9( IOI Ois(ance, x(m) The local mean velocity (( was assumed to be that 06 hC 72 at thc plate axis. given by Eq. 8, or

'Y 6 8.16x l97 ((/((, = (1 2(s). (8) a4 Introduction of Eqs. 8 and 33-36 into Eqs. 23 and 24 yielded 0.2 F = 3/2$ 20n. (37)

For convenicncc in comparing thc model predic-0 0.2 '('7 0.4 i 0.6 0.8 I tions with observations. Eq. 23 was normalized IO

.according to Eq. 20 to >ield the dispersion equation OL8 9

8(

l6 (b) Inversion K=

AXu, =

Q 251 68 ((re u/((,) '(y) 0(:) (38)

Ois(ance, x(m) 0 0.6 6.4 Comparison with Obseroations l4 l8 bC 53 Isoplcths of K in the ground plane, calculated by a4 398 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.

0 0.2 0.4 0.6 0.8 (,0 Dispersion is controlled by wake turbulence for dis-

)(( 70 tances up to about 400m and by atmospheric turbu-Fig. 14. Lateral Distribution of Normalized Concentration lence thcrcafter. This suggests that thc parabolic dis-CocAicienL Top: Mean of Lapse tests. Bottom: Mean of inversion Tests. tribution used for f(y) in thc wake region should bc gradually replaced by the asymptotic Gaussian form at larger distances.

observations. The C and E curves are higher, follow- The variation of K along the plume axis is shown ing the site characteristics. in Fig. 15. The lapse and inversion data points were 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 a Wind tunnel interruptions caused by building separation in the horizontal direction are not present in a vertical 0 lo'I hC direction. Therefore a, is given by ~tnversibn 0

0 a, =:(/2.5 (Gaussian distribution). (32) Lapse 4t O

Values of a, calculated by Eqs. 26 and 32 are plot- 100 cO ted in Fig. 9b. The calculated values are higher than the observed values. However it should be remem- o bered that thc observed values were, in fact, not c O

observed but calculated 1'rom an assumed Gaussian cO Calcu(a(ed V lor distribution, and therefore do not provide a clear test o stability of Eq. 32. X Id 6.3.3 Dispersion Equation In view of the above, the distributions used in Eq.

23 became lat R 4 l(P" 4 4 (04 Downwind distance, x(rn) f(y) (1 (33)

Fig. 15. Variation of Concentration Coctlicient with Dis-

- expt'.->

y/410(rr)'(z)

/2ar'5 (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 to' curves marked C, D and E werc calculated,by Eq.

"38. The D (neutral stability) curve is a good fit to s thc data for x > 80m. Some scatter in the observa- 4 tions occurs in the mngc 30 < x < 80m. Eq. 38 C

,Ol e Colculoted tor XI debates markedly from the observations at x < 30 m. 0 stability This is a consequence of thc assumed u/u, variation OI

, ~NRC model which goes to zero at x = 23.3m and produces in- C O o

. finite F, at thc same distance.

OI Calculoted for The vend tunnel test data points merge smoothly C 0 stability wtth with the field data points in the region of overlap. OI II o U~ Bo This lends credibility to the wind tunnel values at short downwind distances. Evidently a cavity diffu- ,0 IE IO 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 iOI e s tOO e values will be reduced by a factor ol'.84. Similarly, distance, x(mi e'ownwind

\

il'he Gaussian form of 0(=) is replaced by the para- Fig. 17. Comparison of Dispersion Models.

bolic form, the multiplying factor for K is 1.19. If u is held constant and equal to tt the factor changes for the EBR-II complex. The model is very good with distance, as shown in Fig. 17. at close range but overcslimates concentrations for It is also of some interest to compare Eq. 38 with 80 < x < 600m. The latter occurs because insuAi-the dispersion model ol'.S.A.E.G (1974) for calculat- cient weight is given to initial broadening of the ing concentrations downwind of a leak in a contain- plume by the combined wake of all the buildings in ment structure. The governing equation lor ccntcrlinc the complex. At larger distances, initial building concentration at ground level is effects become less significant, and the diffcrcnces bctwcen thc N R C and equivalent tlat plate models X/litJQ [try'> + cj- i (39) remains essentially in thc lateral distribution function where c = 0.5 and the other terms are as previously j(y). As noted previously an asymptotic transforma-defined, together with the restriction that F, may tion to the Gaussian form is to bc expected on physi-not be smaller than one-third of the value obtained cal grounds. Experimental data are nccded to deter-by Eq. 39 with c ~0. Fig. 17 shows this model mine the rate at which this transformation should be introduced.

Release point: Bottom downwind Wind  : SW, t.ym/sec Stability: Neutral 7. SU51MARY The mean velocity and turbulence measured along 0.7 a longitudinal axis dowmvind of the EBR-II reactor containment structure can be modeled by equations that were dcrivcd from mcasurcmcnts along the longi-et tudinal axis of a suspended flat plate, with a modi-e 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 50 III 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 K-lsoplcths in the Ground Plane as Observed in and error, and sccms to be physically reasonable in Fig. 16.

Wind Tunnel Model Tests. retrospect.

l~y "I'hi ground lioundar) cflcct ii;is>>itioduccd b) makiiig prclimniary csiini;iten of thc parameters in multiplying the vertical component of turbulence in- other applications.

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 REfERENCES range in Pasquill D stability.

If the wake boundary is delined as the imaginary Castro. I. P. and A. G. Robins (1975): The effect of a thick surface enclosing thc region in which turbulence in- incident boundary layer on ihe low around a small sur-face mounted cube. Central Electricity Generating tensity is greater than atmospheric, then real wakes Board, Marchwood Laboratories Report R/M/N795, are finite in length, width and height, and the dimen- Marchwood, England.

sions are inversely proportional to thc atmospheric Cooper R, D.. and M. Lutzky (1955): Exploratory investi-turbulence intensity components in the respective di- gation of turbulent wakes behind bluff bodies, U.S, Navy rections. The EBR-11 complex wake was about 400 m Dept. David Taylor Model Basin Rep. No. DTMB-963.

Counihan, J.. J. C. R. Hunt and P. S. Jackson (1974):

long. 270m wide and 70m high, according to model Wakes behind iwo-dimensional surface obstacles in tur-predictions, under the neutral stability conditions that bulent boundary layers. L Fluid hfech. 3 564, pp existed during the field tests. 529-563.

Thc cxistcnce of a xvake cavity at the EBR-11 com- Dickson, C R., G. E. Start and E. H. Markee, Jr. (1969):

Aerod>adamic erects of the EBR-II reactor complex on plex was indicated by the decrease of mean velocity eflluent concentrations. Nuclear Safety, 10, No. 3 May-and increase of turbulencc intensity along the wake June.

axis, with decreasing longitudinal distance. Extrapola- Fail, R., J. A. Lawford and R. C. W. Eyre (1957): Low tion of this trend to zero mean velocity at x = 23 m speed experiments on the wake characteristics of flat plates normal to an air stream. Aer. Rcs. Council R and suggests thc termination of a cavity near that point.

M 3120. London.

This is shorter than the cavity of'hc isolated EBR-II Haliisky J., J. Go! den, P. Ilalpcrn, and P. Wu (1963): Wind containmcnt structure, and it indicates that flow irre- tunnel tests of gas dilTusion from a leak in the shell gularities created by wind passage bc(ween buildings of a nuclear power reactor and from a nearby stack.,

may perturb individual building cavities. New York University Dept, of Met. and Ocean. GSL Rep. No. 63<<2 (Contract Cwb-10321 with U.S. Weather The merging of individual cavities into a single Bureau Environmental Meteorological Research Pro-composite cavity for the complex is indicated by thc ject).

rapid initial dispersion of material to thc lateral boun- Sladc. D. H.. cd. (1968): Meteorology and Atomic Energy, daries of the wake. However, insuflicient information U,S. Atomic Energy Commission Div. of Tech. Inf.

is available to define the shape of such a cavity or CFSTI Doc. TID.24190, U.S.A.F C. (1974): Regulatory Guide 1.4, Rcv. 2, Assunip-its internal flow dynamics. tions Used for Emluating ihe Potential Radiological A dispersion model was developed that included .Consequences of a Loss of Coolant Accident for Boiling initial plume expansion governed by the equivalent Water Reactors.

flat plate dimensions, variation of mean velocity along Van der Hovcn I., ed, (1967): Atmospheric Transport and Diffusion in the Planetary Boundary Layer. U.S. Dept.

thc plume axis, parabolic distribution of'material in of Commcrce, ESSA Air Resources Laboratories Tech.

the horizontal and Gaussian distribution in the verti- Mem. RLTM-ARL3. Dec. 1967.

cal. The model was in good agreement with the field Van der Hoven I., ed. (1968): Atmospheric Transport and observations beyond a distance of 30m, but it over- Diffusion in the Planetary Boundary Layer, U.S. Dept.

prcdictcd at shorter distances. Thc failure of the of Commerce, ESSA Air Resources Laboratories Tech.

Mcm. ERLTM-ARL 5. May 1968.

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 APPENDIX A maximum of 19% because flow reorganization after Derioation of Gaussian CIC equations termination ol'he wake will eventually create a Gaus-sian, rather than parabolic, lateral distribution of con- To obtain as centration. The model can be modified to incorporate Let this transition, but information as to the rate of tran-sition is lacking. X,p ~ Q(nba,6) 'xp {-y (2') ) AI The dispersion model was tuned to the obscrvcd Then 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-CIC ~ X< p dy ~ Q(naa,u) '(2n)'x A.2

'.4 bution for lateral dispersion. It should be possible 'o and formulate techniques for calculating these par-ameters from the geometry of thc complex, but ad- Xe ~ Xx a p Q(na a,u) ditional tests in other confiigurations arc ncedcd to A.2 and A.3 io obtain: 'ombine provide the requisite data base. Meanwhile, the results ol'his investigation may serve as a guide for a(CIC) (2n) '" X,

l' To obtain a, (CIC) (2r)' a, A.6 Lct Then Q ~, XUdydc A.S a, Q(CIC) '(2tt) "~ A.7

0