Text

Responds to 791011 Telcon.Forwards AP Van Ulden Article, Loss Prevention & Safety Promotion in Process Industries. Article Used in FSAR to Determine Area of Fluid Flowing Under Force of Gravity
	ML19209C877
Person / Time
Site:	Waterford
Issue date:	10/12/1979
From:	Michlewicz D; EBASCO SERVICES, INC.
To:	Read B; Office of Nuclear Reactor Regulation
References
	NUDOCS 7910180426
	Download: ML19209C877 (14)
	v • d • e

.

.g-EBASCO SERVICES INC0RPORATED UTILITY C O ;J S U L T AN T S - E N GINE E R S - CONSTRUCTORS TWO RECTOR STREET NEW YORK, N.Y.10006 c m. .oc ... . ...cor October 12, 1979 Jacques B J Read Accident Analysis Branch Division of Site Safety & Environmental Analysis US Nuclear Regulatory Commission Washington, DC 20555 Gentlemen:

In response to our conversation of October 11, 1979, I am sending you a copy of Van Ulden's article. Equation 11 in that article was used in Section 2.2.3.3 of the Waterford 3 FSAR to determine the area of a liquid flowing under the force of gravity. The equation was used o g in the analysis of accidents involving release of toxic chemicals, and not in the analysis of accidents involving release of flammable compounds.

In addition to the above article, I am enclosing an explicit derivation of Van Ulden's equation. This equation also appears in NUREG-0570.

Should you have any further questions regarding this matter, please call me at (212) 785-8796.

S1acerely yours, DM:no y MM t' David Michlewicz cc: R Prados R Benedict R It 't1 J Costello D Michlewicz 3 "*"'

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Loss ?reventiou and ; L i Safety Promotion iu -

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the ?rocess Industries Preprints of the 1st International j Loss Prevention Symposium,

} the Hague / Delft, the Netherlands,

,. 28-30.\tay I974

(

A s)mposium organizedby the Royal Institution of Engineers in the Netherlands (Kivi) and the Royal Netherlands Chemical Society (KNCV) and sponsored by the European Federation of Chemical Engineering (EFCE,137th event)

I

<*,d b, C.H. Buschmann

"$5Ei'$d.i f,@'50.h N PO 9 3..s 11/6 116 ELSEVIER SCIENTIFIC PUllLIS!!!NG CO\lPANY AMhlLRDAM - LONDON - NEW YORK D)N I

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, I. d 221 h I 4 l ON THE SPREADIN3 CT A WAVY GAS REC-; A;ED NS AR THF. GkCt"tD 3 .d '.

q A.P. VAN ULDEN c t Royal Netherlands Meteorological Institute De 311t I e #

The Netherlands ,

h

4 It is shown spreading that of a the gas.

neutral spreading of a heavy gas differs essentially from e th i gravity effects, whereas vertical spread is itmited. Horizontal spread is increased constderably Q* by pared with experimental results. Calculations are com- *

.=

1. INThCDUCTION 3

.t io Cosmon atmospheric dispersion models, like the gaussian mooel As shown by Abbott f are only practicable for the front velocity is gases with a density approximately equal to identical with the wave celerity in a quasi- .

the density of air. However, many gases uncoupled two-layer system, if the cogstant _

have considerably higher densities and a c is equal to unity. Experimental resulta different sispera n.t suggest behaviour caf be expec- unity. that c can be taken as approximately g ted, especJally when large smounts are re.

leased.

-,/

This signt occur for example af ter Another feature is shown by experiments.

" the failure of a storage tank c When the relative density difference is .e 9 Itquid chlorine unmer pressure.ontaining an important small, the front advances with a distinct

.g fraction will evaporate instantaneously head or roller and relatively important mix- ,

T because of the heat capacity of the liquid phase.

ing might occur at the front. Still, a Since the density of gaseous chlorine

q ts about 2 5 times the censity of air, the simple front description with a vertical front, a I.

l velocity given by (1) and a horizontal '

d as increasine area. chlorine will flow in all directions upper boundary gives satisfactory agreement covering

~

with the experiments. V

. Q *aere are a f'ew j density spread, instances of this so-called ',

.j litterature. wnich are treated in the 2. OEMSITY OPREAD OF A EATf GAS E 14

.l

An example is the water front formed af ter a da-burs t . The density spread will be described of an

,y This wa6er front has the appear- amount of a heavy gas which is released near [

a:ce of a veritable wall of water advancing the ground instantaneously. The influence

.." .ith asuggest

ents certain velocity. Dimensional argu- of atmospheric turbulence and wind are ,

.'. a the form u s f

for such a front a velocity of l

c[f (1) neglected as a first approach. Later en this influence will be treated. It is sup-posed that the volame of heavy gas can be appr ximated by a cylinder wita height h and

'1'$' shere c is an unknown constant, 4. the rela- radius r, where h and r are the height of

.a * " *" # ""#*

tive difference between the density 9 of the origin respectively. Mixing at the f ' surrounding the heavy fluto andfluid, the density p2 t'h' '" *

thus a = (p3 p23/Pi In **#

the case of a danburst p 3 )> p2 and a =1 E dt = 2n n h dt A W-

_.3 i

where V is the volume of the cylinder, t the CENSITY FRONT time and a an unknown constcnt. ,

p1) p 2 The following quantities can now be written ,

as funettons of spreaaing radius r:

. V(r) = 2 h(r) r (3) u(r)=c[t(r)gh(r)'

f (4)

Uf f

[f g

P1

P2 a ( r) = (p f r)-p,)/p(r) (5) ;

T I where p(r) is

( #

i w

V mixture and p the a

density of the heavy gas-the density of air.

=

u.a . .vuw.wa e ' ,

The values of 7(r), h(r), r, p(r) and A(c) at time t:0 ara lonoted by 7

{L;uye 1 o* h,r,4 1176 il7 wM**

e f

_ . _ _ . _ 1,, 0 fT.tl i.. .

222 u . s, . , ,. ,

.n ~. 93 Equations (2)-(5) can be solved and we find: mi n:M will ' o mvl ec t a d ; levity aprod is

,, *he tosin it in.: rrocesa and e;uattens te i .(u' 7( r) /7 m ( r, r ' " (6) i. 'tre1-

. a '.nu ,

. ' ; e'il .;.e e t.'e n e d . ;e. 8 h(r) / h * = ( r/ rO ) ~ (7) : nte a:aa the tront Weity decreases -

'1 grajaa.ly, there will to a moment that p V(r) u 2 lu., wnere it is anumed that p(rg. '

' f O I #) * ' *

( *,

O

.p3 ) y0 .hlu relatten characteri.es the trans *.cn '

from density spread to turbulent opread. As g ,y g s a result of turbulent mixing the height of j I( g , c,F - o the cicud will increase.

7,/7(?) + ( (Jg -9) -n3 t r3 3;;; .;n 13 not 33 2;enr;y notiefstle

. t 2 :ri.am al ;rm i t i n, r re : 4 ;.2, 3; .:e from o ju3 tion (N P d3 a f J. 0 ". - Of time 'e . . ty J: [ad in : turclient Jfre31 'etn'*. .

can te obtained, bec " e J 4 - . crea;' tl2 ra.iiua of

he cicud.

!wo cre:ic.1 c:y "3 ~- --

. c uae to a cerfgun extent the e f fe ct .'

'When Sixing at the f ront ic ne.;.y;ble we n -; re tread remaina af ter the transit'::,

get .

, tne incresce o f t he he:-ht of the cic;d will a - g (0 -H' 7 ce mller. tni the increase of the ra..:.s

{ u g(r).f [p' (10) of .3, c;oud will be larger than in a ;Jrely 6 0 turbulent mixing process. .

.k

When mixing to not negli61ble, but ( p -o a} /p a The influence of wind on the movement ef the is fairly small, we Cet el ud is ceeplicated, because tne wind ;ro-file and concentratica distribution are gl P -P*)V ' ~ #

$(p .p ),

needed to calculate the average velocity cf uf (r)% 'he cloud as a whole. yurthermore, strati.

l r xp r sp fication effects have to be taken into account, which will decrease the cloud velo.

l More generally it can be stated that eq.(1C) city.

in a reasonably approxi=ative formula in all circumstances. yrom (10) it is easily .,evertheless, a a first a;proach is possible

! derived that the relation between time and if stratificattor. effects are neglected. -

l spreading radius is given by The wind profile is assumed to be logarith.

g mic. If the vertic 1 cenean ration distr:.2 g (p ,p ) y' tion is ta<en to be uniform during the densi.

2 '

ty spread and gaussian during the turca;ent

,k r -r o

= 2c t (11) ap spread, the average cloud velocity can be

' ,~

calculated.

Thus the area covered by density spread i.4 a A pras.tical =ethod to esti= ate cencentra.

linear function of time. tions at large distances from the source is -

I Jo the front velocity depends eni; ..e the following:

= ass surplus put into the atmosphe.e by the (a) Calculate the radius r uand height h u instantaneous release and on the spreading for which uf = 2 u.

I ## **

(b) Calculate the positicn of the cloud.

3. TE INF1.UDICE Cy /JHC3pK4RIC CC::DITICNS (c) Use an area-source gaussian model with -

, , r uand h to y calculate downwind conces.

g The description given in the last paragraph trations or dosages.

, is not complete, because wind and turbulence

' The third eteorological factor which shoalt

' l are nearly always aresent in the atmosphere.

be taken into account is solar radiatien. <

1 Vertical turbulent ^ mixing thougn, will be ,'

early all the heat received from solar radi.

l.- inhibited by the density jump as long as this ation will be kept in the cloud of heavy gas, jump is sufficiently large. In order to get

,' a first estimate of the relative i=portance because the stable accer surf ace acts as an effective lid. 2ecaNe the thickness of it, I of vertical turbulent sixing, the available g turtalent enerry can be compared with the cloud is much smaller than the thickness of g average potentral energy difference between the atmespher:c boundary layer during day. -'

time, the cloud will be heated much mere the heavy gas layer and the surrounding air. rapidly than the surrot nding air. Therefere

The for ser is approximately equal to 2 p, uf the relative density dif ference will decresce where u. is the friction velocity , wnile the more rapidly during daytime and the effect of (-

! latter is given by i( p(r)-;s,) g h(r) = density spread will be less. , , _

I l i P(r) uf . Cf course the preceding calculations are .

As long as the turbulent energy is relatively only valid if the terraie. is absoluuly flat. i

-t small, which means that 2u. a u , vertical f

Cn a slope dravity forces will let t:te heavy o

, gas float downwards.

1176 118 . . -

e w 0 .

h.'

~ 0' c

,.,----f.- %_

$c.

y , .* y r

. . ..e.s,.-.

..s ,

4,,

. s .w . . ,. ., ...

[ *; :

. .- - . . . . ... . . . . . .- :s,w.1 ' . ...~.

+"

.,.2.. .

-e- v *. -. - w., ,L c_ .t w c. x _

.39 . . -_ - _, . . _

.- .- u ,a

)r .*. ['s J. I < *

g .y n t .3 .

v,w.' . 223 Vis*. 7. ' 0:l TC 7,PRT.,ADI iG CF A EAVY Ga3 a 1.J. AIL Ni.;AR TIC %CUna x >

1 specially in stable atmospheric conditions t(y) = y3/2 -y o 3/2 ( 9/8 g .,,. A )-i .

. townwini transport can be inhibited by obsta- o o

' cles, because the heavy gas will stay near _/ d, ,2 * *

%, ftte ground. It is even possible that a x(y)=u(y -y[/]A (9/8 g 3, a,))

y peat part of a cloud of he2vy cas remains '

, at the sa e location during the wnole night 2/3 i and is :t dispersed until an hour or so y = -- (9/3 g 0o ao)37) +y o I

- > sfter sunrise, when the cloud is nested by u f 9 solar radiation. $J o o we take y, a 2u;_

we a M ve at

[ . s_(.* 4. CD3!!I Ol' READ GCM A OC:iTI:iUCU3 000 ROT ,

t. . The problem of the density spread from a 2/3 continuous source can be solved by a space-y/y o

= 1. ,,1 x/y o

+ 1 (13) y

. trae transformation. In stationary condt-

. tic:s sooner or. ,ater the nesvy gas will be wn..ich is ,,the .,ormula given by Larsen and

. c, traes;crted by the =ean wind, so the .,.,ux of aorensen.

,his for=ula was anplied to the J.. density spreat of waste water.

,k heavy gas through a vertical plane on right 5

syles to the 2irection of the wind is equal 5. A*3 :,XFr...a MEN,,

f .- to the s:arce strength. .he area o., this g

aross-section of tne cluee is denotad by [

.he vertica;. source area is .n

. order to *est the ef fect of density

F, ,. s Zhy.

.,e magnitude o.,o0 1$ a.eter-spread on the dispersion o f a heavy gas jan 5 a 2h y .

s o oo ~

experiment was carried out in he s .ethe.'-

"p . air.ed by the source s,t,,rength Wo (m's 1) and lands in Cetober 1973. un ier the sapervision

. t'.e cean wtad speed u. 2nd is given by of the Ministry of 'oeial A f f airs. ; detail-

_. , . W, a 33 2. Initial mix;ng is neglected. ed, description of the experiment is g;ven la the sa:e way as in paragraph 2 we get: in'. The location was a large area of re-covered land some 33 km west of Rotter am.

3(y)/3* = (y/y0)* (12) as a harmless substitute for chlorine DIC:(- .

2 was used, whi:h has a density of 4.2 h(y!/h 0 = (y/y0 ? (13) times the density of air. An amount of *000

. 'q freen 12 was eva; crated quasi-instanta-p 3 neously. Condensati:n of water vapour este l a(y) = 1 + (f/y ) (14) the cload visible te:aase of the low toiling c

o". a temperature of freon 2, wnich is -5 0 0.

j 7 i

urinc *he first few sec nds expansi n 9 9g3: aused intensive mixing with air, wa en

f. u(y) =d S (13) resulted after,acoat 3 s in a freon-air mix-c d a ture of 2+00 m' with a density of 1.25 :::es 6 (3(yj + p . the dansity o f air.

- o l

n order to measure the imensions and :ath l

a(y? is nere the lateral velocity of the e , . 3, ;m3 3 7; r,, 33, ;;73 y;3tn;, _(3g,,

travy its particles, the front Ltself is films and :nctocra ns were 2 sed. Losage j i stati nnry. Seasurements aero 2.e at threa 2 renes at I ne t;:e needed for a spread from y, to y .1 stances of -;; . : , m 'a.s M O m fre is y the so.rce. Lne C nunuoas read;ng .as i d

'v' 3 Vail 2Cle 3: " -. 5 fra the source.

tsy) =

(%)

y 247 /

ind- ~nd tema rstu re crofiles ap to *: - .

C and relative hat;21ty .ere measared 2t s:te

Ira .slation by the mean sind during this 115 tan 0e from the source. During the exper.

gs, is inent net r1diat; n was zero, the surf 2: e y layer was exactly neutral and tua wind pro-c' file leg =r;thr.;c with 1 13 wind no

d o f ny)

= u ','

utv')~

3 TJ'

he T025an*Ss len?th and fri:*ian

/3 velocity,were esti stej to be 0.05 mand l

. c- r- . mly .

'r 1 * .:d ){l '

11t . :ns ( ') Wd t*

, g ., ! ,3- 3 ', ,

l "J $ ~^n ..r- .. 'A 1!3 en j no"; 't-

i. es-

r

_ .' .r . d.

.. 3: e J ; .1 '. me ta. e: uti . :f *txtnc p, ,, , ,

3,. ;, , y ,, ,

r .e :.e 2.ec t e 1 er a - .. wt a=- we o

, . , , J \

, o a*

ltvo a

-- ~' '~

.i 224 92

' . . r. '

. ; LL .

chear.

Calculuttens are made with e.tuation (10) with be g nning coniitienst t = 5 :t , Vs

/ \ 2400 m ,p = 1.25 q , r = 12 and h 5. b.

\ The con -- tin t c la then as Jnity.

f \

/

.. f:nd ug 4 r and t a r- lu + 3

\ -1

/

\ The transition condition u = f 22.= 0.5 -ts f

l 'I is valid at a time t = 80 s. At this ti e }

l I th* 1 "d h 2rrid ^t 53 ' fr " th' 1000 m I scarce and has a calculated radius of 7o, .

g{g

~ -

MCN 3 According to this transition conditica the

c. l density spread should te dcminant at least w

) f during the 40 s the cloud was visible, h

\ / figure 3 the calculatc3 and measured spread- .

\ . CENTER :ng radius are compared.

NN ,

j OF ...

s - CLOUD

. P~'~ /- ! HORIZONTAL SPREAD -

6[1 1

o MEASURED j :-

/-

EDG.-t i+

OF - '

o .~~'s 3 o l'" U N * * ' / '

J; /' \pWIND d 40 ", Y t

CLOUD

/ ' ' i g a l \/X

,/, / SENT PRE

{ o 500m

7. s\

i o l ,', } MODEL . :<

$20 , MEASURED I : '

I b

.,i 9O O

<t (L ATE R AL )

i -

e , , ,

Y,h i yE :. ~

'{

t

'-)

/

w //

ct

,/ .

s

/ o j

'N # '/ 0 10 20 TIME 30 I.05 C '"

a

!' o ia

?

,i

-7 's .v.

5) Ii8"#' 3

?

CONTINUOU READ 1NG 100m 'j grM ,, 1,, ,tu,,n,1 r,,i,, (,1,,g ,t,,) i,

< s 3 somewhat larger, and the lateral radius ,

33mi.; # somewhat smaller than the calculated one. *,

$ ""~ F p The calculated and observed covered areas.

d '

',fis ARCH 1 owever, show a very good fit. This is an ,

ndicatien that e can be taken as unity in-

i '

SOURCE deed. Furthermore, the measure =ents of the i

) ,

height of the cloud can now be used to find t i .I a value for the constant s. This value .

[

does not seem to differ significantly from ero, as is shown in figure 4, wnere the s Figure 2

3 calculation with aa O is compared with the ,

i The cloud was visible with distinct bounda- easurements.

ries during about 40 s or up to 30 m from it must be said, however, that the best fit .

the source. Durin6 this time the visible is obtained with = 0.05 an.1 that the 1 boundary is taken as the edge of the cloud. neasurements are not very accurate, so t.5at ,

The measurements showed that the cloud had a some mixing at the front certainly may j

more or less cylindrical shape, but was occur. As this mixing does not essentially h, v

stretched a little along wind. This is affect our result, we shall neglect it and '

partly due to the fact that the source was conclude that equation (10) may be used ~

s, only quasi-instantaneous, partly to wind with a constant c = 1. .

e g

b i .

1176 120 i e

i. ;l ~

i

.% L' & 'l / t- f'I A

_ _ . . _ _ _ . . m .

~

' ~ ~ ~ '

a

[. :

4 ;

U . ,' 225 0:3 THE 3F?nDING OF A HLVT GAO hEII.i.3.:D NC..R THE CacCND !';.

.. i e

h'

[. VERTICAL SPREAD VERTICAL SPREAD ,.='

{,

. i t.0 - ,.=, . .

c e 3 i ="..= D6.

O I o '.=.e\

a I, e i i m 30. cAusslAN "

o j i MEASURED 3 .=== "= MCCEL i

i 1 u MC I %.

I $20- .." 4

I PRESENT ." .

': 2;i 6 1 C

\ MODEL G =

I G "

g. l s : 10 ,=" MEASURED 4,,_ _ _ -- -e -

~ ~ o-0, - . - .

ve 'y ,

a . '>.

0 10 20 30 t.0 S o 200 4co eco eco toca m .' .

TIME DISTANCE FRCM SOURCE

t .' 4 Figure 4 Fisure 5 2 1

'It larger dist ances turbulent transport is it;ortant. for It difrases t!.e bounsar:es of .

t?.e cloud, and we have to define the tosition l of there boundaries. .e accept the convent- '

j ist. t?.at the boundaries of ine cloud li, store the received dosage is one tenth of the m l HORIZONTAL SPREAD t $

tasage received in the centre of the cloud. 200 I , e ,e "s a gnassian listrib2 tion this :s the equi.

ralent of 2.1+ ti: es the standard leviatio:t.

i 1

PRESENT MCCEL

/,/,

/ .

j

) Treo the total doca.se passedwnich tnreuch 160 $

, W r' as arch and tne cloud veloc;ty the neight of c A--ME ASURE D

, the cl:ud was calculated. "'hese calculations S ! /

f speed pite -ell wit the 1 : ted erofile y 120 j satsare:ents (Josage near the ;round ans at *

/

j .

t.) t) . It is found that the he14-ht of tne o r

c's.it decreased during tne first 60 s and in:reasti .if t e rwards. This screes reac n-n:.' y .. t c ne rren : ei r2ns;t.:n time of 2 *0 C

/

..="."

[

N s. men a f aassian no ul is used. .;tneut a Tr:;er : rre;*.cn .;r .ensity arr+2.8 ne a:

!.0 #

1

="",s="',,=="" \

O AUS $l AN

a.. 0. ve: 2:a1 : reai :s far t:0 la: s. s.=",= MCCEL

.: 1 m:n, ::=.' m :- expa: - .s=*,,

r:n e:re :e . n--

...., =.~ .m.es a ra-

, .. ..,. . . g.. .

. . , .a 3~ ~ -- -~~ --

,resse : -

a serted 'jer .:al stread 0 Z0 Go W Boo e after t .e tra".s z ti:n sf.0'.. i ce noted. Oensi. CISTANCE FROM SOURCE I tf effe:ts reca n cresent daring a ..;ng time et12r:21en:e is say:ressed to a level that c li :e fe;nd in 3 :re :- t;e at.osphere.

' e.;ure 6

's*f:e. 31.0 . c e t r : . . . :r. cf . u r c ul ::t-ce ts *ne horizont11 nrnd wi.. b e- . nited l 86**. . e r 't .: i r:1 1 :? - l 1; i 371-

!. , 12 . .

. ."LT J W.1 .

^

g.

. . t I'

. 1

'I$ : - I T TI

.3 s 't*. !

gr'..

.. t' re

. 531 l .V .' ; 1 , . , 3l ,t, ,y,

' L . ;'l l' t

.11* c i . . .i c i . .

11* ., 4.,*

,lar , - :t7.. .

s.

'C 1. .

\ 'v*

l&*e f ..ty '

li ~ > r e T T p i 1. , *

.in

e 226 A.P. 7,. ! iLD:::3

. :c:; wJh ;. *

. tr of .

the o 1 el" '. nnow thn . '

g moael cannot ce aced for hea'ty (a. tea, with-j out a proper correction for densit. 3pread.

, i q l

As a racult of tensity spread E trations over larcer areas shoald be expec-cencen- ;

I gjj'jj"g[ ,

I ted.

I Strong winds anj isolation reduce the effact of density sprea.i. On the et er hand, ions-ity rrread darin.; the nie-St c- Le very lar- aver very f.:* te: i It a :t be f.ot;:ed

hat : c.

en; ao :t the wind la .tiely te .. cur. .,n up-s treu po .;1t;:n need not .. anfc.

.JK3CULID3:2;25!3 The contr:bu tion of Or. :i. .. ,.braham, Oelft Hydrolics Laboratory, and nr. 3. Sood, Technical University of Delft, to the set-up

2

] of this study is greatly appreciated. .

The permission of the Institutiens and 00=-

panies which organi:ed the experiment, and ,

of Or. M.U.F. Ochregardus. Director-in-Chief j of the Royal Netherlands Feteorclogical 1

Institute, to publish this study is grate-

,f fully acknowledged.

.f RITERINOIS

1. 0.3. Turner Workoook for atmospheric dispersten estimates. e.3. Oepartment of (j Health, Education and Welfare, Cincin- v i nati, Ohio, Revised (1969).

j D.H. 3 lade . Meteorology and Ato:ic

Energy.1.3. Atomic ner;y Con 31ssion No. TID-24190, National 2ureau of 3 and-ards, 'J.3. Department of Co :merce,

) 3pr;*.gfield, Virginia ( *969) . .

-; 2. M.3. Abbott

Cn the spreading of one

? fluid ever another. La Houille 31anche i

t No. 5 ' (1961). *

)

. 3. N. tienji and J.. 3usin er . 3tatility i dependence of tem:erature, hu=i:ity and vertical wind velocity variances in the atnespheric surface layer. J. Met. Soc.

J ran, ser. II, Vol. 50 (1972).

4 I. Larsen and T. 33rensen 3acyancy

] spread of waste water in coastal re-ions.

I Froceedings *

th Conference on Coastal

, Engineering (1963) .

5. Experiments with Freon-12 and Ohiorine.

,' The Ministry of Occial Affairs, The Netherlands. To be published. ~/ 4

/U 1l "b)L ')

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^^* ^ " ^ ^ "^^

EBASCO SERYlCES INCORPORATED gyh bIbb! bN[2-CAT: l0/Ilf71 NEW YORK gggg7 l g, [

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