ML19209C877
| 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) | |
Text
..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 in the analysis of accidents involving release of flammable compounds.
not 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 MM t'
y David Michlewicz cc: R Prados R Benedict R It 't1 J Costello D Michlewicz 3 "*"'
1176 115 e
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Loss ?reventiou and s
- L i
Safety Promotion iu L
,i the ?rocess Industries Preprints of the 1st International j
Loss Prevention Symposium,
}
the Hague / Delft, the Netherlands,
,. 28-30.\\tay I974
(
A s)mposium the Royal Institution of Engineers organizedby in the Netherlands (Kivi) and the Royal Netherlands Chemical Society (KNCV) and sponsored by the European Federation of Chemical Engineering (EFCE,137th event)
I C.H. Buschmann
<*,d b,
"$5Ei'$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
~ - - -
f.
9.2 b
t
, I.
d 221 h
I 4
ON THE SPREADIN3 CT A WAVY GAS REC-; A;ED NS AR THF. GkCt"tD
.d '
l 3
q A.P. VAN ULDEN c
Royal Netherlands Meteorological Institute t
De 311t I
The Netherlands e
h It is shown that the spreading of a heavy gas differs essentially from th 4
i spreading of a neutral gas.
gravity effects, whereas vertical spread is itmited. Horizontal spread is increased constderably by Q
e pared with experimental results.
Calculations are com-
.=
- 1. INThCDUCTION 3
.ti Cosmon atmospheric dispersion models, like o
the gaussian mooel f
are only practicable for As shown by Abbott 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 behaviour caf be expec-that c can be taken as approximately g
suggest ted, especJally when large smounts are re.
unity.
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 Itquid chlorine unmer pressure.ontaining small, the front advances with a distinct 9
an important fraction will evaporate instantaneously head or roller and relatively important mix-because of the heat capacity of the liquid ing might occur at the front.
.g T
Still, a phase.
Since the density of gaseous chlorine simple description with a vertical front, a
q ts about 2 5 times the censity of air, the velocity given by (1) and a horizontal front I.
ld as increasine area. chlorine will flow in all directions covering upper boundary gives satisfactory agreement with the experiments.
V
~
. Q *aere are a f'ew instances of this so-called j
density spread,
.j litterature.
wnich are treated in the
- 2. OEMSITY OPREAD OF A EATf GAS E
14 An example is the water front formed af ter a The density spread will be described of an
.l da-burs t.
This wa6er front has the appear-amount of a heavy gas which is released near
[
,y a:ce of a veritable wall of water advancing the ground instantaneously. The influence
.ith a certain velocity. Dimensional argu-of atmospheric turbulence and wind are
- ents suggest a
the form for such a front a velocity of neglected as a first approach. Later en this influence will be treated.
It is sup-posed that the volame of heavy gas can be c[f (1) l u s f
'1'$
appr ximated by a cylinder wita height h and shere c is an unknown constant, 4.
radius r, where h and r are the height of the rela-tive difference between the density 9 f ' surrounding fluid,
.a the heavy fluto and the density p2 t'h' the origin respectively. Mixing at the of thus a = (p3 p23/Pi In the case of a danburst p 3 )> p2 and a =1 E = 2n n h A dt dt W-i
_.3 where V is the volume of the cylinder, t the time and a an unknown constcnt.
CENSITY FRONT 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 P1 f
(4) f Uf P2 a( r) = (p f r)-p,)/p(r)
(5) g T
I where p(r) is
(
mixture and p the density of the heavy gas-i V
the density of air.
=
w a
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 h,r,4
{L;uye 1 o*
1176 il7 wM**
e 1,,
0 fT.tl i..
f 222 93 u. s,.
.n
~.
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.(u' i
7( r) /7
( r, r ' "
(6) i.
'tre1-
- . a
'.nu m
- e'il
.;.e e t.'e n e d.
- e.
8
( r/ r ) ~
(7)
- nte a:aa the tront Weity decreases h(r) / h
=
O
'1 grajaa.ly, there will to a moment that p V(r) u 2 lu., wnere it f
is anumed that p(rg.
O I #)
' * ( *,.p ) y
.hlu relatten characteri.es the trans *.cn O
3 0
from density spread to turbulent opread. As a result of turbulent mixing the height of s
g,y g j
I( g, c,
- o the cicud will increase.
7,/7(?) + ( (J -9)
-n3 t r3 3;;;.;n 13 not 33 2;enr;y notiefstle F
g a f J. 0 ". - Of time
. t 2
- ri.am al ;rm i t i n, r re : 4 ;.2, 3;.:e from o ju3 tion (N P d3
'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 g (0
-H' 7
a ce mller. tni the increase of the ra..:.s
{
g(r).f
[p' u
(10) of
.3, c;oud will be larger than in a ;Jrely 6
0 turbulent mixing process.
.k a /p The influence of wind on the movement ef the When mixing to not negli61ble, but ( p -o
}
a 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
~ #
u (r)%
'he cloud as a whole. yurthermore, strati.
l f
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
.,evertheless, a first a;proach is possible circumstances. yrom (10) it is easily a
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.
,k 2
r -r
= 2c t
(11) ty spread and gaussian during the turca;ent o
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 and height h u
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 and h to calculate downwind conces.
u y
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 because the stable accer surf ace acts as an a first estimate of the relative i=portance effective lid.
2ecaNe the thickness of it, I
of vertical turbulent sixing, the available cloud is much smaller than the thickness of g
turtalent enerry can be compared with the the atmespher:c boundary layer during day.
g average potentral energy difference between 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.
l i P(r) uf.
Cf course the preceding calculations are I
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 Cn a slope dravity forces will let t:te heavy o
f gas float downwards.
1176 118 w
e 0.
h.'
~
0' c
,.,----f.-
$c.....s,.-.
..s.e y,.* y r 4,,
. s.w.
.- :s,w.1 '....~.
[ *; :
+"
.,.2..
-e-v w.,
,L
.t w
c.
x _
- .39 c_
.-.- u
,a
).* ['s J.
I < *
- r. g.y n t.3.
v,w.'.
223 V.
- 7. '
0:l TC 7,PRT.,ADI iG CF A EAVY Ga3 a 1.J. AIL Ni.;AR TIC %CUna is*
x
-y
( 9/8 g.,,. A )-i y /2 3/2 3
1 specially in stable atmospheric conditions t(y) =
. townwini transport can be inhibited by obsta-o 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
- - > sfter sunrise, when the cloud is nested by (9/3 g 0 a )37) i and is :t dispersed until an hour or so y = -
+y I
o o o
u f 9 solar radiation.
$J o o we a M ve at
[. s_(.* 4. CD3!!I Ol' READ GCM A OC:iTI:iUCU3 000 ROT we take y, a 2u; 2/3
- t.. The problem of the density spread from a y/y
+ 1 (13)
- 1.,,1 x/y
=
y continuous source can be solved by a space-o o
- . trae transformation. In stationary condt-
. tic:s sooner or,ater the nesvy gas will be wn..ich is,,the.,ormula given by Larsen and
. c, aorensen.
,his for=ula was anplied to the J..
traes;crted by the =ean wind, so the
.,.,ux of density spreat of waste water.
,k heavy gas through a vertical plane on right syles to the 2irection of the wind is equal 5
- 5. A*3 :,XFr...
MEN,,
a f.- to the s:arce strength.
.he area o., this g
aross-section of tne cluee is denotad by
[
.n order to *est the ef fect of density
- F,
,. s Zhy.
.he vertica;. source area is spread on the dispersion o f a heavy gas jan 5 a 2h y.
.,e magnitude o.,o0 1$ a.eter-o oo
~
experiment was carried out in he.ethe.'-
- "p. air.ed by the source s,t,,rength Wo (m's 1) and s
s 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 3 2.
Initial mix;ng is neglected.
ed, description of the experiment is g;ven 3
in'.
The location was a large area of re-la the sa:e way as in paragraph 2 we get:
covered land some 33 km west of Rotter am.
3(y)/3 = (y/y )*
(12) as a harmless substitute for chlorine DIC:(-
0
- 2 was used, whi:h has a density of 4.2 (y/y ?
(13) times the density of air. An amount of *000 h(y!/h
=
0 0
'q freen 12 was eva; crated quasi-instanta-p 3
neously. Condensati:n of water vapour este l
(f/y )
(14) the cload visible te:aase of the low toiling a(y)
=
1 +
0 o". a temperature of freon 2, wnich is -5 0.
j c
7 i
- urinc *he first few sec nds expansi n 9
9g3
- aused intensive mixing with air, wa en f.
u(y) =d (13) resulted after,acoat 3 s in a freon-air mix-S d
ture of 2+00 m' with a density of 1.25 :::es 6 (3(yj + p.
c a
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 the so.rce.
Lne C nunuoas read;ng.as i
y
'v' 3 Vail 2Cle 3: " -. 5 fra the source.
d
=
(%)
tsy) 247
/
ind- ~nd tema rstu re crofiles ap to *: -
y C and relative hat;21ty.ere measared 2t s:te 115 tan 0e from the source. During the exper.
Ira.slation by the mean sind during this
- gs, is inent net r1diat; n was zero, the surf 2
- e layer was exactly neutral and tua wind pro-y ny) c' file leg =r;thr.;c with 1 13 wind no
- d o f
= u
/
~
3 TJ' he T025an*Ss len?th and fri:*ian utv')
velocity,were esti stej to be 0.05 mand l
3 c-r-
. mly.
11t. :ns ( ')
Wd t*
){l
- 'r 1 *
.:d
, 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) 5 :t, Vs with be g nning coniitienst t =
= 1.25 q, r = 12 and h
- 5. b.
\\
2400 m
,p
/
\\
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 = 22.=
0.5 -ts f
f
'I is valid at a time t = 80 s.
At this ti e
}
l I
th*
1 "d h 2rrid ^t 53 ' fr " th' l
1000 m g{g I
scarce and has a calculated radius of 7o,.
MCN 3 According to this transition conditica the
~
l density spread should te dcminant at least w
c.
)
f during the 40 s the cloud was visible, h
\\
/
figure 3 the calculatc3 and measured spread-CENTER
- ng radius are compared.
\\
j OF N
N CLOUD sP~'~
/-
6[1 HORIZONTAL SPREAD 1
MEASURED j
o
.~~'s l'" U N * * ' / /-
i+
EDG.-t 3
CLOUD
/'
\\pWIND d 40 ",
\\ / X SENT Y
J; o
OF -
o i
l
,/, /
PRE t
/
g a
l
,' }
MODEL
{
o 7.
s\\
o 500m i
$20 MEASURED I
(L ATE R AL )
I 9
O
.,i O
<t i
b e
'{
yE
- . ~
o,/
'-)
Y,h i ct
/
w //
t
/
s
'N
'/
0 10 20 30 I.05 C j
TIME ia a
o
?
-7 's
.v.
5)
,i CONTINUOU Ii8"#' 3 100m 'j grM
?
READ 1NG 1,,
,tu,,n,1 r,,i,,
(,1,,g,t,,)
i, 3
somewhat larger, and the lateral radius s
33mi.; #
somewhat smaller than the calculated one.
""~ F p The calculated and observed covered areas.
',fis ARCH 1 d
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
i.I height of the cloud can now be used to find t
)
a value for the constant s.
This value
[
does not seem to differ significantly from s
Figure 2 ero, as is shown in figure 4, wnere the 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,
stretched a little along wind.
This is affect our result, we shall neglect it and v
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
- l i.
~
i
.% L' & 'l / t-f'I A m
~
~
~ ~ '
a
[. :
4 U.,'
0:3 THE 3F?nDING OF A HLVT GAO hEII.i.3.:D NC..R THE CacCND 225 i
e h'
[.
VERTICAL SPREAD VERTICAL SPREAD
,.='
{,
t.0 -
,.=,
i
"..
e c
i D6 3
O I
'.=.e a I, e i i
o 30.
\\
o j i MEASURED 3
.=== "= MCCEL m
cAusslAN i
i 1
u MC I
I
$20-4
': 2;i PRESENT I
6 1
MODEL G
=
C I
\\
G MEASURED 10,="
g.
l s
4 o
,,_ _ _ -- -e
~ ~
0, v 'y e
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, m l HORIZONTAL SPREAD t
store the received dosage is one tenth of the tasage received in the centre of the cloud.
200 I
, e,e j
"s a gnassian listrib2 tion this :s the equi.
i PRESENT
/
ralent of 2.1+ ti: es the standard leviatio:t.
/,/,
1 MCCEL
) Treo the total doca.se wnich 160 $
r' passed tnreuch W
as arch and tne cloud veloc;ty the neight of c
A--ME ASURE D the cl:ud was calculated.
"'hese calculations S
/
speed pite -ell wit the 1 : ted erofile y 120 j
/
f 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-2 *0
..="."
/
n:.' y.. t c ne rren : ei r2ns;t.:n time of C
[
="",s="',,==""
N s.
men a f aassian no ul is used..;tneut a:
1
\\
!.0 #
a Tr:;er : rre;*.cn.;r.ensity arr+2.8 O AUS $l AN ne
- a..
- 0. ve: 2:a1 : reai :s far t:0 la:
s.
s.=",=
MCCEL
.: 1 m:n,
- =.' m :- expa: -
.s=*,,
- r:n e:re :e.
n--
s a ra-g..
...., =.~. e 3~
~ --
-~~
m.
.a 0
Z0 Go W
Boo e
- ,resse : -
a serted 'jer.:al stread after t.e tra".s z ti:n sf.0'.. i ce noted. Oensi.
CISTANCE FROM SOURCE I
tf effe:ts reca n cresent daring a..;ng time et12r:21en:e is say:ressed to a level that c li :e fe;nd in 3
- re :- t;e at.osphere.
e.;ure 6
's*f:e. 31.0
. c e t r :... :r. cf. u r c ul ::t-ce ts *ne horizont11 nrnd wi..
b e-. nited l
86**.
. e r 't.: i r:1 1 :? - l 1; i 371-
, 12..
."LT J W.1
^
g.
t I' 1
'I$
I T TI gr'.
.3
't*.
t' '.
re
.' ; 1 3l
,t,
,y, s
. 531 l
.V
' 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 g
the o 1 el"
'. nnow thn moael cannot ce aced for hea'ty (a. tea, with-j out a proper correction for densit. 3pread.
i q
l gjj'jj"g[
As a racult of tensity spread E cencen-trations over larcer areas shoald be expec-I 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
- en;
- c.
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
]
of this study is greatly appreciated.
2 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 (j
dispersten estimates. e.3. Oepartment of Health, Education and Welfare, Cincin-v nati, Ohio, Revised (1969).
i 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 t
No. 5 ' (1961).
i
)
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 1 "b) ')
/ U l
L 2
t peu l
4W j
' t.
i f
. )
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