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No *
w-7405 -eng-26
REACTORDIVISION
PERIOD KEASUREKENTSON THE MOLTENSALT REACTOR EXPERIF!!l!T DURLMGFUEL CIRCULATION: TKEORYANI EXPERIIQNP
OAK RIDGE NATIONAL lLA.EORATORY Oak Ridge: Tennessee operacede by TJKION Cm&DE CORPORATIOM for the U.. ATOMIC EKERGY COHMISSIS~
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CONTENTS
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.ABSTRACT... INTRODUCTIOM
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Mwnericsl Grow-dwork
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ExFerirnentaS Resullt,s
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DISCUSSION OF RESULTS
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T h e o r e t i c a l Model Verifica,tion
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Recormendations fc;r t h e MSRE ACKNQWUDC-MENT REPEREE\rCES
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THEORY OF ZERO BOWER MIhETICS DURING FUEL C I R C b U T I O N RUI’CERECAL AXE EXPERIKENJ”AL WESULTS
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B. E . Prince
A s an a i d i n i n t e r p r e x l n g t h e zero-power k i n e t i c s e x p e r i n e n t s performed on t h e YGRE, a t h e o r y of p e r i o d dependence on t h e fuel c i r c u l a c i o n i s developed from t h e g e n e r a l space dependent reactor k i n e t i c s equations * A procedcre for evaluati n g t h e r e s u l t i n g inhow-type e ~ p ~ t by i ~machine n computazion i s presented, t o g e t h e r with numerical r e s u l t s r e l a t i n g t h e r e a c t i v i t y t o the observed asymptotic period, both with %he f u e l c i r c z r l a t i n g and with i z s t a t i o n a r y . Based on % h i s a n a l y s i s , t h e calcl;lated reac",vity d i f f e r e n c e between -the time independent f l u x c o n d l t i o n s f o r t h e nonclrculating and t h e circula-eing fuel s t a t e s i s i n c lose agreement with t h e value i n f e r r e d from t h e YSKX rod c a l i b r a t i o n experiments. Rod-b-m-p p e r i o d measurements made with $he f u e l c l r c u b a t i n g were conv e r t e d to d i f f e r e n t i a l rod worth by m e of t h i s model, These results a r e coqa-sed w i t h similar rod s e n s i t i v i t y meas-awrients made w i t h t h e f u e l sta-tionary. The rod s e n s i t i v i t i e s xeasured m d e r t h e s e two c o n d i t i o n s a g r e e favorably, w i t h i n t h e l i m i t s of p r e e l s i o n o f t h e p e r i o d m e a s n e x e n t s . Due t o t h e problem of maintaining adequate p r e c i s i o n , however: t n e period-rod s e n s i t i v i t y measurements provlde z less eonclasive t e s t of t h e t h e o r e t i c a l model t h a n t h e r e a c t l v i t y d i f f e r e n c e between the t i m e independent f l u c o n d i t i o n s , Suggestions are made f o r improving t h e precision of t h e experiments t o provide a more r i g i d test of t h e t h e o r e z i c a l model f o r t h e effects of c i r culation on the delayed neutron k i n e t i c s .
1. INTWQDUCTEON It i s w e l l recognized t h a t t h e c i r c u l a t i o n of fliel i n a Hiquid f u e l e d r e a c t o r i n t r o d u c e s some unique e f f e c t s i n t o i t s observabbe k i n e t i c behavior.
Foremost i n t h i s category i s t h e phenomenon of emission of"
delayed n e z t r o n s i n t h e p a s t of t h e c i r c u l s t i n g system e x t e r n a l t o t h e reac-Lor core where t h e y do not c o n t r i b u t e t o t h e chain r e a c t i o n .
The
b i t e r a t w e i n r e a c t o r k i n e t i c s c o n t a i n s s e v e r a l t h e o r e t i c a l s t u d i e s of ....
t n i s effect,'>
a but
there have been few o p p o r t u n i t i e s for p a r a l l e l
e x p e r i x e n t a l spludles.
The Molten Salt Beactor Experiment, h e r e a f t e r
2J
r e f e r r e 6 tc as thy hGREJ has p r e s e n t e d a uvliquc chance t o develop and
-,est soxe ar:alykizal rrodels f o r t k e zero power k i n e t i c s c f a c i r c u l a t i n g fuel r e c ' e c r
Thc e x p e r 4 a e c t a l measurements d i s c u s s e d Fn t h i s report
x e r e made as parz of an o w r a l L p ~ c ~ ; ~ tc a r ic e l i b r a t e the control rods
i n the MSRE. I n t h e i'irst s e r t i c n fcllvcice;J we dc;.tlop the t h e o r y dependence cn :%el
circ-illaticn.
The second
EF-ct?lcn
o j '
period
gives an account
o f t h e r e z : u l t s of a-pGLyirq thls theory t o t h e experimental measuremenTs me3e a u r i n g MSN R u n No, 3 .
F i n e l l y , in t b e third section, we
&~SCU.SE
t h e r e s d ' r s cf t k 5 s m r k i n teims of the general yroblem o f k i n e t i c s
analysis f o r c I r c - d a t i a ~ ;f u e l retwzcrp. by
Se-vera1 q w s t i o n s a r e left open
the present s-tu&-, adia these are diz.c;asced i n thak section.
s
r e p r e s e n t t h e MSWE c c r e , w i t h b o m d a r i e s corresponding pnysicaily t o t h e
channebleci r e g i o n of t h e actual c o r e . We have eombiied and extended t h e s e a n a l y s e s t o ixclude t h e c o n t r i b u t i o n t o t h e chaln 2 p e a c t i ~ ~o1f t h e delayed m u m o m e m i t t e d ~ h i l ethe f u e l i s in t h e plenums J u t shove and below t h e g r a p h i t e core, arid to f n c l u d e t h e case of t h e f l i z varying e x p o n e n t i a l l y witk a s t a b l e z s p p t o t i c perlod,
It w i l l be seen t h a t
8n
i d l o u r - t y p e equatior, r e s u l t s
which r e l a t e s the p e r i x l of a c i r c u l a t i n g fuel reactor- t o t h e s t a t i c r e a c t i v i t y of t h e saae r e a c t o r c o n f i g u r a t i o n , but i n which the f u e l i s
not circulating,
The s t a t i c r e a c t i v i t y , p c , i s d e f i n e d by t h e r e l a t i o n u
in which v is t h e p h y s i c a l , energy-averaged number of ceutrons e m i t t e d per f i s s i o n , and v
c
is t h e f i c t i t i o u s v a l u e f o r which t h e r e a c t o r w i t h
t h e s m e geometric and material c o n f f g u r a t i o n w m l d be c r i t i c a l w i t h the fuel stationary.
One f i n d s that 8 s a r e s u l t oâ‚Ź' z h l s d e f i n i t i o n , tne
r e a c t i v i t y for a c r i t i c a l , c i r c u l a t i n g f u e l c o n d i t f o n I s g r e a t e r Than z e r o ( h e r e , c r i t i c a l i t y de~otest-ne c o n d i t i o n of t i m e independence of t h e r,eu$ron and prec~rsorc o n c e n t r a t i o n s
e
ow ever, s i m e t h e s t a t i c
r e a c t i v ' l t y i s t h e q u a n t i t y norm&l%y o b t a i n e d En reactol- c a l c u l a t i o n p r o g r m s , it i s most convenient to reiate t h i s q u m t i t y directly to t h e ... ... b
asynpzotic period,
The t h e o r y following a s d-eveloped by beginning along g e n e r a l l i n e s
and d e l i n e a t i n g s p e c i a l a s s u a p t i o n s as t h e y are i n t r o d u c e d .
S e v e r a l of
t h e s e s i m p l i f y i n g approximations are s u i t a b l e f o r MSRE a n a l y s i s , b o t h i n t h e neutyonica model and t h e flow model f o r the c i r c d a t i n g f u e l . The s t a r t i n g p o i n t sf t h e ana%ysis i s t h e g e n e r a l t i m e dependent
rea,ctor equations, w r i t t e n
TO
i n c l u d e t h e t r a n s p o r t of delayed n e u t r o n
p r e e w s o r s by f u e l n o t i o n i n t h e a x i a l d i r e c t i o n :
4
!â‚ŹTie symbols Q and C r e p r e s e n t t h e neutron %lux and delayed neutron precursor d e r r s i t i e s .
'%he o p e r a t o r L r e p r e s e n t s n e t neutron l o s s ( l e a k a g e ,
a b s o r p t i o n , and energy t r a n s f e r by s c a t t e r i n g ) , and P r e p r e s e n t s t h e produetion processes by fission. The e x p l i c i t r e p r e s e n t a t i o n of t'nese o p e r a t o r s depends on the model used i n a n a l y s i s .
If t h e s e processes
are given t h e i r rnost g e n e r a l r e p r e s e n t a t i o n i n terms o f t h e Bohtzman t r a r s p o r t equation, the neutron flux,
@
energy: d i r e c t f o n , and time v a r i a b l e s .
J
will be a f u n c t i o n
In order t o provide
position,
O f
8
framework
f o r d i s c u s s i o n which can ke d i r e c t l y r e l a t e d t o a p p l i c a t i o n , we s h a l l ~ S B U I T . thaF ~
t h e angular v a r i a b l e s have been i n t e g r a t e d from t h e equation,
i a e e jt h a t a, rrodel such as multigroup d i f f u s i o n t h e o r y o r i t s continuous eraesgy counterpart prcvides ax zdequate description of t h e neutron pspu-
Eation.
I n Eg. 3 , 8,bore: N i s taken as z e r o i n t h a t p a r t of t h e c i r -
c - d e t i n g l o o p which i s e x t e r n a l t o t h e chaFn r e a c t i n g regions. r e m i n i n g sjnbo%s i n Eqs
-
2 and
3 a r e (I - BTj,
%he
t h e f r a c t i o n of all.
n e ~ t r o n sf r s ~ f i s s i o n wkich a r e prompt, and f3, and hi? t h e production f r a c t i o n and decay c o n s t a n t f o r the i t h p r e c u r s o r group.
!â‚Źbe q u a n t i t i e s
- a r e energy s p e c t r m o p e r a t o r s which m u l t i p l y t h e t o t a l voluP and foi rretrpic p r s d u e t i ~ nL ' G P , ~ S of prompt and delayed neutrons to o b t a i n neutrons of s spec-iflc energy. Fi;r,ally, t h e syxbols v and V r e p r e s e n t the neutron f
v e l o c i t y and d i e Ifl-&%dv e l o c i t y , respeculveby A s ap9lded t o a. f l ~ ' , df u e l e d r e a c t o r wizh
such as t h e hEWE (-&ere
.... ...
8
keterogeneous s t r u c t u r e
t h e axial f u e l channels are l o c a t e d i n a m a t r i x
of solid g r s p h f t e n o d e r a t a r ) , ;he
u s u a l c e l l u l a r homogenization must be
azde en t h e neutron production and d e s t r u c t i o n r a t e s .
(1 -
BT) P@ =
X.1 C.1
T'nus, f o r exampbe
local r a t e of p r o d m t i o n of prompt fission neutrons, p e r -mit c e l l vol-me
= l o c a l F Z Z ~of production of i t h group of delayed
neutrons, per u n i t c e l l volUn;e.
If we assime t5at %he o p e r a t o r s
'6;
and P are time independent, corre-
poiidirig t o a f l x e d r"cd p o s i t i o n , we can i n v e s t i g a t e t h e c o n d i t i o n s mder
E
5 vhtck t h e f l u x a:ad
prec~rsord e n s i t i e s i n t h e r e a c t o r and -~,hee x t e r n a l wt
c i r c u l a t i n g system ~ a r yi n kime as e
Assuming s o l u t i o c s of E q s . 2
and 3 e x i s t of tlie form:
then 9
6
A s p r e v i o u s l y steted,
OUT
primary objectbve i s t o r e l a t e t h e observed
-1
s t a b l e reactor p e r i o d , w configuration.
t o the s t a t i c r e a c t i v i t y of t h e given r e a c t o r
Tbae s t e t i c r e a c t f v i t y deffned by Eq.
I is
t h e ahgebra-
i c a l l y largest eigenvalue of tlie equation :
where;
E.
Eather t h a n attexpting t o solve t h e r e a c t o r e q m t i o n s
6 and 7 d i r e c t l y ,
we w i l l make use of a procedure which i s o f t e n u s e f u l for spatial reactor k i n e t i c s problems.
S e v e r a l s o u r c e s give d e t a i l s o f similar a n a l y s e s f o r
s t a t i o n a r y f ~ e breactor systems (see, f o r example, R e f .
4).
we m l t i p l y
t h e ' r l o e ~ l "e q u a t i o n f o r the neutron popubatior?, by ari a p p r o p r i a t e weight-
i n g Function and i n t e g r a t e over t h e p o s i t i o n and energy variables of t h e
neutron popirlation i n order t o o b t a i n a. r e l a t i o n invoEving only " g l o b d "
or i n t e g r a l quantities. As seen bebow, 'by using the s t a t i c a d j o i n t flux, the s o l u t i o n of t h e a d j o i n t equa$ion corresponding t,a ~ q 8. as the
@i7
weight%ng f u n c t i o n , t h e r e s u l t i n g r e l a t i o n admits a d i r e c t physical interpretation.
Tfie a d j o i n t f l u , a l s o obtained i n most reactor physics calcu-
E ~ i t i ~ programs ia in cornon usage: is the solution sf
9
where L ana
(?PI
c
AT
o ~ ~ I - ~ ~aod Ij o- isn t to I,ana
FP
of ~ q 8. , ana p s
TS
the s m e algebraically l a r g e s t eigenvalue of ~ q .8. w i t h a p p r o p r i a t e l y prescribed boimdary coaditEons
32
t h e allowable f m c t i s n s on which these
ezpcrs,tars a r e d e f i n e d , the following r e l a t i o n ’ adjoint o p e r a t o r ;
++
can be used t o define t h e
Here A seprese~tsa b s t r a c t l y e i t h e r o f t h e o p e r a t o r s L and ?E’ and
(@i2 A$) de~otesthe scalar p r o d - x t , -t
gs asd
integratlm
Q V ~ Ft5e
i.e., t h e m u l t i p l i c a t i o n of Ag by
p o ~ i - e i ~and n energy variabEes of the rieutron
p a p a l a t ion O n forming the scaltir product o f Eq.
4-
6 with psJ we obtain
6
.......... ....... .:.
(12)
R
4
6 i=E
By makixg; use of Eq. 9; we nay yewrite tkis e q - u a t i x as
The f i r s t term on t h e Fight hand ~ i d eof E q ,
14 i s
s i m p l f f i e d i n appear-
axice if we make a convenkfonal type of definition of xhe p m x p t neutron
g e n e r a t i o n time;
We may a l s o note that :fie
second term con
ts?e r i g h t hand
side of Eq. E 4
appears as t h e diPferenee between t h e weighsed t o t a l p r o d w t i o n of de-
layed rie-utrsns and t h e weigkted pro&d@tionof delayed geutrens f r o m
.:.
precursor decay within the -
P~ECLOP.
__yl-____I_
cd
In
E I C C G ~ w ~ r~t h~ its C ~
definition
by Eqa. i and 8, t h e s t & , t t c I-eactivTty i s csmpletely determined by t h e geome',ric
and nateriz,b c o n f f g w a t i s n of t h e r e a c t o r : whether o r n o t the
fuel i s c i r c - d s - t f n g i n t h e actuaP r e a c t o r .
%e
r e l s t i o n s h i p between
and w expressed by Eq. a&, therefose,has an e x p l f e f t physical
Q
s
inter-
Fer example, i f the fuel composition 8,nd c o n t r o l r o d pcsitisn are such t h a t the f l u x i s time independent when t h e fuel. i s c i r c u l a t i n g , w = 0 in E q s . 6 and 7 . Eqaation 14 t h e 2 shows t h a t the s t a t i c r e a c t i v i t y pretation.
%os the j u s t criticel r e a c t o r is nm1eriezlby eqw,l t 3 t h e n e t d i f f e r e n c e
in t h e production o f del2yed neutrons described a'uovf?, ... ............
. e
1E
the More gen-
e r a l case wcen -,he f l u x L s varying in t i m e aczariiigg t o a stable period,
8 t h e f i r s t term
QE
t h e r i g h t hard side of ~ q 14 . w i l l aiffer from zero,
and a l s o t h e e f f e c t i v e ebecrerrient in production sf delayed neutrons will
differ nmerrfcably from tke time independent case ( ci and J2 depend on w tkrsugl? E q s . CEUI
I X
-UX~
6 and 7'. 8
Equation
E4
i s an i n h o w type r e l a t i o n which
f o ~ a d ~ ~ t i ~an n 8,pprsximte d e t e r m i n a t i o n cs p 8 :
given an observed asymptotic p e r i o d , od
-1
One may observe t h a t it i n -
cludes the usuel iKilsur r e l a t i o n f o r t h e s t a t i o n a r y i%eE r e a c t o r as a s p e c i a l case, simply by s e t t i n g V = 0 i n Eq.
practical a s e of Eq.
14: we
7 . Before discussfrag t h e
can e x k i b i t the previous concepts i n an
e x p l i c i t algebraic xanner. From Eq. '9 we have,
Insertitig t h i s r e l a t i o n s h i p i n t o Ec,. E 4 g i v e s
/d
i=P
'i
9
6 (PO)
L= I T h i s equatiol? has t h e appearance o f t h e oydinary TRhoiLr r e l a t i o n i'or the
s t a t i o n a r y feel r e a c t o r , " except "that t h e e f f e c t i v e p r c a u c t i o c f r a c t i c i l s , B
-
i
wh.ich depecas on t h e c i r c u l a t i o n r a t e and i II?a d d i t i o n , the l a s t tern OK t h e r i g k t hand s5.de of' E q . 20
a r e r e d x e d by a qmnti.-Ly y
a l s c ~on w.
appears because t h e zero p o i n t of t h e s t a t i c react? corresponcx ts t i e c
t y was chosen to
positLon and geometry n t t h e j u s t - c r i t i c a l s t a t i o n a , r y
The u s u a l inhour relatlion f o r t,he s t a t i o n a r y f u e l reac%or
f w l react;or.
-
i s obtained by l e t t i n g V
0 amd y
-+
i
0 i n Eq. 20.
--+
Kltthudgk Eq. 20 :i.s
i n s t r u c t i v e i n d i s c u s s i n g t h e riet e f f e c t s c f e~elc i r c u l a t i c n , i t s s i r n -
-
piici.t;l. i s sonewhat deceptZve s i n c e y w,
through Ey.
7.
i
depends i n a complicated way or_
T h e r e f c r e , it w i l l 'be mcr'e convecicnt tc discuss t h e
use c? t h e inhour r e i a t i o c startixxg with t h e fcrm given in Eq.
14.
A t first appearaai.ce, iE o r d e r t o use Eq. 1 4 we tire required to
solve Eys. E q * lo f o r
6 and '7 f o r W , ci(x; a>, acd (b(2, E; w ) > arid a l s o to solve + Both a r e eigenvalue pro-slcriis i n wiiich (9 s and 4 s ( 2 , E; p s ) .
t i e algebraLcaLly l a r g e s t r e a l eiger.values, interest.
ana p
?
S'
are cc irrmctliate
Not only does Eq,. 111reduce tc an Id.eriti-t;y 3.f t1ii.s pr:icedurc
i s used., b a t it i s p r e c i s e l y t h e e x F l f . c i t s o l u t i o n QT ~ q s .6,and we w-ish t3 a v o i d .
T'ne g r e a t .
u
p,
4:
approximated by the s t a t i c f l u x distr?.'bution,
i s s u ' f i c l e n t l y we11
%
p o i n t , t h e va9i.di.ty o f t i i t s approximation i s a n e s s o f t h e delayed neutron f ' r a c t l c n , p
6s
end t h e observed s t a b l e
The b a s i c s i m p l i f i c a t f o n r e s u l t s from assuming t h a t t h e
shape of t h e asymptotic f l u x d i s t r i b u t i o n ,
ar_d
that
Yulr-,ess oi? ~ q 111 , is in i h e b a s i s i t pro-
v i d e s f o r approximating .the r e l a t i o ~bet wee^
period w - l .
7
i s s u b s t i t u t e d ?or
6
T'
e
Eron
B
CGl'lSeCpelice
physical. stand-
o?' t h e sna19.-
I_"t h i s approxirrialior: i s ~ a d e ,
i n E q . 7, t h i s equation e a be i n t e g r a t e d
a r o m d t h e c i r c u l a t i n g p a t h of t h e f 5 e l t,o o b t a i r , t k e distribT&ions of
delayed. precursors, c .
i
Before c o x p l e t i n g t h e a n a l y s i s , hcwevc;r, we
s k a i l n ; a k a seemi* apprmi.mat:i on t o siriplj f y the c o m p u t a t l x o
i c t e g r a l s occurring i n Eq.
2.4. It
the
can h e a s s u m d t h a t t h e correctiori
EO f o r the difference
ini
E ~ U T F B ~ appearirig S
i n Eq.
rate s"kep.
energy s p e c t r a f o r emisslon of prompt and delayed
14 can
b e cs;lculated approximately as a sepa-
is done by redl;cing
Tlr_:~
' C ~ Eage
for the ith group of de-
bayed neutrons f r s n k a t si? t h e prompt Eeutrors and modifying the s t a t i c delayed neutron f r a c t i o n s , f e c t o r s a p p r o p s i e x to
9
Bi,
by t h e r e l a t i v e non-leakage probability
b a r e r e a c t o r which approxirnates t h e a c t u a l c o r e .
S w h an apprexlmztisn c a also ~ b e J u s t i f i e d from an o b j e c t i v e sxandpoint,
since the correction f o r t h e d i f f e r i n g " e ~ e r g ye f f e c t i v e n e s s r ' of delayed n e u t m n s r e l a z l v e t o pro~ptneutrons is s m a l l compared t o t h e e f f e c t of
For ?;he IGRE,
t h e spa-eial t r s n s p o r t sf pl-ec-msors under c o n s i d e r a t i o n .
cd.cda,thons
6if
correction changes the e f r e c t h v e value of 0
0
3 . The net energy f o r T J % ~from ~ 0.006L t o
t h e former effect are given i n Ref.
T
00666
0
One f u r t h e r remark s x d d be Eade concerning Eq.
s t a t i c r e e c t i v i t y , p,
14,
A given
corres2o~dlngt o sone t i m e independenz reacisr
configuration %s also r e k t e d x i r o u g h Eq. l ! : ta e l l p h y s i c a l b j allowable ~
T r m s i e z x modes present i r t h e ce-Jtron f l u e f t e r t h e f i n a l r e a c t o r con-
In This study, we heve chosen t o
f l g a a t l s r ~has 5een eszabLished.
erilphasize s r ~ l yt h e rels,tim between tile c i r c u l a t i o n and t h e asymptotic
An spproxirrate ar2hys-Ls i n d f c a t e s c h a t t h e remaining eigenvalGes
rr.ode.
and eigenf~~:?cticne of' FQG. 6 a:d
d i f f e r I n c e r t a i n fu.nda,nen?;al r e s p e c t s
i ' r s m t - s s e csf ststisnery fie1 r e x t e r e , >E
S h Z l L EOL &$",lTpt
h i s topic
3::
a lzzer
L 4 dC:rLG2i5trZ;e Sect
tLliS.
For t h e purpose of t n i s report,
Except f o r
%,
brief retUsfi t o
we w i l l r e s t r g c t z . t t e n t i o n e n t i r e l y t o
$he analysis of the s i z b i e a s y x p t o t i c perfod measurenents Tke cGmpbetiO2 of' :he
of Eq.
7 arclbrd
reql.lllsed
E E ~ J S ~ cSo n s i s t s
;he sircul~tingp e t 5 of t h e f u e l ,
of' t h e i n t e g r ~ ~ t i ~ ~
BbviousHy, even if $
is replaced by 13 calculated fron Z q a 8 , fwther s i m p l i f i c a t i o n s i n t h e s
flow model a,re ~ c e s s a r ybeccre t h e problem becomes amenable t o practical csnptatisn.
'Sl?e approx'matisns
we have used i n r e p r e s e n t i n g t h e circu-
laL%ng l o o p of t h e $ERE are sliown s c h e x a t i c a l l y i n ?Tgo 1. Tkae model c o n s i s t s of a Zhree r e g r z n a p p r o x i n a t i o n t o %he actual core, r e p r e s e n t i n g t h e lower cr e i t r i i n c e pEemrn, Lke g r a p h i t e moderated r e g i s n , and t n e -~;pper,o r e x i t pbe:;im,
respectLuely.
Tle core I s r e p r e s e n t e d as
2.
right
cylinder with volurr_es ,n t h e upper and lower plenums e q u a l t o tkose of
z=H : z
H,
IM'T
7 C 3 N T H 3 L H06
--CONTI701 ROD TPIKBLE (TYDICAL) CHANNELEC REGION
ST GRAPHITE
((I)
MSRE CORE GEOMETRY (SCHEMCTIC!
!=O
(6:
MODEL FOR N E a T R O N
CS CALCU:
AT'ONS
Fig. 1. Geometry of' MSRE Care and Three Region Corc Modei Used in Physics Calculations.
.. .... . _.... ...... =/
the
actual
of that
NEm.3 ccxe. used
Fluid that
in
a
velocity
@OilStEUlt
OV&T
region
upper
plenum,
flow
distribution
between
the
is
wheye
is
k
of
the
prec~~sox
the
linear
axial
fluid densities
aepencl
,!LIct.hough importance assigr: 5 c:iz
a
-KTl tf;
ay;
the
determined
the
kth
fluid
region. of
plerrm
in
velocity
to
physecai
st.at-uIpo~l~t~
this t3
neilkrcc
-fl?lr
in
flow
these
botto-m flow
In
the
head
the
direction region.
velocity
in
flow),
with
each the
it
(external
loop)
low
neutron
relatively
allowable,
rather
was considered
region
the
flux regions.
of
are
region
and
*
moderated
neutron
a region
t.re8.t;
the the
(plug
zero
se I-87-71 >-.. C..& approximations
a. lir-ear
radius
reg ion,
time
is
QCCUX
by
It
regions
very
and t k is the r-es iaence wi.11 be seen later t-hat tine
kth
residence
lower
so that
awl-age
velocity
the
in in
the
t o be constant
In the
OrL,?T 03 the
assumed
plenum
of
outer
graphite
is
velocities
the
reversal
indicated
region
whereas
and the
we have
1er.gtl-i
in
near
due tcl the
study, lower
of the
E
time
the
and
version
have
Kiglies
coxe.
Haminar,
downcomer
present
except
magnitude
complex
peripheral
12 the
nearly
mockup
moderated
the
axis
a sinrphified
computatfons.T
TP&~?..core
of
core
is
physics
graphite
part
tke
flow
the
the
large
abQut
the
with
within 3,
n?odeb Is
MS?E core
studies
fxel
small
region
al% previous
dynamics
the
12e&XlJr
fsr
Tlrkis thxee-region
importance
as
more
"'well
a
(adjaint
than realistic
stirred
flux)
tanlk"
assigned
to
. 0 14; Withi;. spatis tke
~sszmed
the
eztixe
aver
the
of
velocity
flow,
profile
to
be flat
rates radial
ass-~2ing and s&joint coordinate,
neglected the
and
consider
neutrons
in
the
radial product
and axial
fluxes.
primary
radial
of
axial
to
across the
neutron
in
Eq,
l)i.
of
the
neutron
we preaverage the
the
we have
direction
averaging
separability
only
in
approximation,
integrals
Thus 9 if
difference can be expected
As a first
the
scalar
radial.
the
and delayed
salt
ratesimplledin to
region,
fuel
coxe 2 and have
equfvalent
yoduetion
moderated of prompt
direction
prod-uction is
graphite
distributions
be is
the
the
(z>
the
This
fluxes
dependence
of P@
8
i n the i n t e g r a t i o n of E q .
7, the problem reduces e n i i r e l y t o a
one-dimensional c a l c u l a t i o n ( l i n e model).
*
With t h e s e s i n p l i f i c a t i o n s , t5e reqLired i m e g r a t i o n of Eq. now b e completed.
7 can
A s w r i t t e n i n t h e preceeding formulas, the p r e c u r s o r
d e n s i t i e s and nectron r e a c t i o n rates are t h e homogenized v a l u e s , i . e . , normalized to a u n i t c e l l v o E u e of t h e r e a c t o r .
To i n t e g r a t e Eq. 7 ,
a c c o m t must be t a k e n of t h e v a r i a t i o n i n t h e f l u i d volume f r a c t i o n over khe path of flow tlirough t h e r e a c t o r ,
I f ak is tlie l ~ o l m ef r a c t i o n of
f u e l i n the k t h r e g i o n and s u p e r s c r i p t
(01
i s used t o i n d i c a t e t h e gre-
c u r s o r d e n s i t i e s 2nd prompt neutron production r a t e i n the f u e l ;
The v a l u e s of a used far numerical c a l c u l e t i o n s w i t h :he: model of t h e
MSRE core shown i n Fig. lb were 8.225 f o r t h e g r a p h i t e moderated r e g i o n ,
and 1.Q and 0.91 f o r t h e t o p and b o t t o n p l e n ~ m s , r e s p e c t i v e l y . e x p l i c i t forms of Eq.
The
7 for t n e v a r i o u s r e g i o n s become:
a> Graphite moderated r e g i o n
b)
Top p l e n m
c)
External piping
~
*ICne
~
v a l i d i t y of *his approximation i s n o t imuiediately obvious; how eve^, it appears t o be adequate i n the l i g h t of resczlts p r e s e n t e d
later
d)
In
Bottom
the
above
B-EC is
of
region lb).
a well
(as
Ia is the
tank regions.
the
loweT
average
the
upper the
above,
heig‘nt
fission
plenum,
external the
approximation, Pn Eq.
of
the
and L-H pi?ing
lower
contrast
27,7 tQ is
the
production
rate
is
moderated the
and heat
plenum
in
graphite
effective
is
to
plug
average for
Length
exchanger
region the
region,
treated
by means
flow
residence es&
(see
model time
and
element
of
fluid
the
precursor
plenum,
!Tbe boundary concentrations As applied
the
representing
mixed
remaining
Bc is of
As described
the
in
eq-z&ions,
tk-,e thickness
of the Fig.
p%enum
to
conditions in
the
salt,
for each region cl i' p: are continuous
Eq.
24,
these
conditiors
reqluire along
are;
qt =tl,) = qz = 3) 1
that
-the path
of
flow.
for
The last ~f t h e eqixations given above r e s u l t s frsm averaging he precursor
c o n c e n t r a t i o n obtained from solving Eq.
27 over the ~ e s i d e ~ ct ei m e t
4" By lise of t h e csntinuity c o c d i t i o n s for t h e e n t r a n c e and e x i t c o n c e n t r a t i o n s i n each region, the above equatLons may be sed z o solve l"sr ci0 ( 0 ) m e result is:
-
where t h e following d e f i n i t i o n s of the residence t i m e s have been used:
e
a6 H
The computational p l - ~ ~ e 6 ~ 1developed -e i n t h 5 s s e c t i o n iriay be summm-feed as f o l l o w s :
CalciLz.te appraxlma$locs to t h e s t a t i c flux and a d j o i n t f l u
:o
a x i a l d i s t y i b u t i o n s k y s t a n d a r d teckxiques of core p h y s i c s a,nalysis,. n
From a" specified asynp-cotic inverse p e r i o d , w, and tile static
C.
"?,:
flux uis:sibution, 0 c, ( 0 ; ~usfng )
-
Eq-
35
e
corresponding to t h e same r e a c t o r state, c a l c u l a t e Note = h a t t h e a b s o l u t e n o r m a l i z a t i o n of t h e f l u x
i s ar';3itrary s i n c e Ea_. 1 b i s icdependent of t h e f l u x n o r m a l i z a t i o n .
3.
CaEeuHste t h e a x i a l distribution of precursor d e n s i t i e s in the 0
s a l t , c _ . ( z ; w ) , by means cf I
~C)~~TU% 30 ~ Lt Sh r m g h
34.
E i t h e r a nuqerical
i_?tcgratisnprsceciuse or an~byticalapproximations f o r i 3 evaluaziing t n e i n t e g - e l s e de^ c r i b e d in
4.
Tr-e fsrmer method
the f'olbowirg s e c t i c n
ZakJiate p
6
WBS
gs( z >
can b e used
used in the work
e
by p e r f o n i ~ gthe i n t e g r a t i o c s ix Ea_. L4*
: 1 is obvious tnet the m%ymeans of practical c a l c u l a t i o n w i t h t h i s ~ck?en;ei s the d i g i t s 1 c o ~ p u t e s . A c a l c u l a t i o n program based on thts scheme
w a s w 5 t t e n f o r the 1B.i-7390. S p e c i f i c d e t a i l s concerning t h e n m x r i c a l ~ e s ~ l l - t sand ,
the appbica;ion
given i n Sectiovi 3 .
of t h i s analysls to t h e MSRE experiments %re
Our i n t e n t i o n i n t h i s secLion Ls t o a p p l y Eq. 1 4 t o t h e ar;alysis of a s e r i e s of r o d bump-stable p e r i o d rneasurernents made with t h e MSRE curing f u e l c i r c u l a t i o n .
TP%,eserreaswements were t a k e n a t v a r i o u s con-
t r o l r o d i n s e r t i o n s during the c o u s e of enriclment of t h e f u e l s a l t i n
R u n KO* 3 .
It has been seer frore t h e a n a l y s i s p r e s e n t e d i n S e c t i o n 2
t h a t t h e q u a n t i t i e s r e q u i r e d t o r e l a t e t h e measured a s y x p t o t i c v e r i o d
t o r e a c t i v i t y are t h e s t a t i c d i s t r i b u t i o n s of the p r e c u r s o r c o n s e n t r a t i o n and t h e f i s s i o n prsd-dction rate t o g e t h e r w i t h t h e a s s s c i a t e d a d j o i n t f l u x
We have alreedy intl-ochced s e v e r a l approximations i n order
distribution,
to s i x p l i Y y c a l c u l a t i o n s w i t h Eg. 1 4 .
We now make e x p k i c f z use of t h e
group d i f f u s i o n model f o r t h e neutron fluxes.
The f l u x d i s t r i b x t i o n s we
s h a l l use were o b t a i n e d from s t a n d a r d core p h j r s i c s a n a l y s i s w i t h onedimensional multigroup and two-dimensional,
for t h e neutron:@ b e h a v i o r .
few group d i f f u s i o n models
I n performing a "first
pound" a n a l y s i s of
the experimental rr,easurements, t h e attempt w a s made to m i n t a i n as much computational s i m p l i c i t y as p o s s i b l e withoat d i s c a r d i n g t h e e s s e n t i a l f e a t u r e s of t h e r e a c t o r and f ~ e hc i r c u l a t i o n models.
It has been shown t k a t t h e s t a t i c d i s t r i b u t i o n P i n Eq.
l4 are
r)
6 s ancl 0,s
those appropriate t o t h e a s p p t o t i c state, :.e.,
reactor-rod configuration d u r i n g t h e period measureiKent
cjzc-x-ring
the
However
the
t h r e e control rods i n the MSRE are i c a highPy l o c a l i z e d c l u s t e r about t h e c e n t e r of t h e core ( F i g . 2 ) > m d t h e i n s e r t i o n of a s i n g l e rod
produces a p e r t u r b a t i o n i n t h e thermal fbux d i s t r i b u t i o n which Ls f a i r l y
well localized
ila
t h e radial d i r e c t i o n .
Some calculational results i n
support of t h i s conclusion are s:iown i n F i g . 3 .
These are p l o t s of tl?e
r a d i a l variation of the thermal flux, t a k e n at sn azimuthal a n g l e h a l f way between c o n t r o l r o d s 2 and 3.
The c a l c u l a t i o n s were made w i t h t h e
two dimensional d i f f u s i o n program EXT.EBNPNATOR,G a s i n g an R-Q model of t h e M3RE c o r e geometry.
Tne p e r t u r b e d fluxes w i t h r o d No. 2 i n s e r t e d
a r d w i t h a l l t h r e e r o d s i n s e r t e d are cmpared with the fluxes when a l l ................ .. ww ../
k--I
2
--
I
TYPICAL FUEL PASSAGE
REACTOR CENTERLINE
Fig. 2 .
Lattice Rrrangenect o f NS3X C o n t r o l Rods
e
r
19
: CALCULATIONS
I
I
10
20
I 30
40 RADIUS (crn)
50
66
70
80
Fig. 3 . Radial Distribution of Thermal F l u in MSRE Core (Calcul a t e d ~ u r v e )s
rods ere f u l l y w i t h d r B m * * I n a l l c a s e s , the fluxes al-e normalized to
a core power level of" EO Nw.
It may be s e e n t h a t t h e shape of t h e f l m
is relatively undisturbed over a barge f r a c t i o n of t h e radial c r o s s section of t h e c o r e .
One xay a l s o m t e t h a t t h e t o t a l neutron production rates i n t h e numer-
14 are
a t o r and denominatsr of' Eq. r e u t r e n papoau-ction.
m u l t i p l i e d by t h e energy spectrums of
ela ace, when performing t h e i n t e g r a t i o n
energy
i n evalu&ting the scalar products i n Eq. 14, only t h e h i g h energy p o r t i o n (whel-e ?(E)
f 0) c o n t r i b u t e s
approximate :he
t~ t n e r e s u l t .
fast g r o q e d j o i x t
flzlx
We t h e r e f o r e need only
distribution*
Based on the p r e c e e d i ~ go b s e r v a t i o n s , as a final set of" simplifying approximations we have used only -,he u r p e r t u ~ b e dd i s t r i b u t i o n s of I'ission production and fas-c adjoic-, f'lu, corresponding t o t h e case of t h e rods
Tcis s i i n p E i f l e a t i s n i s c o n s i s t e n t with t h e n e g l e c t oi' t h e r a d i a l vzr1atLons of' f l u and precursor c o n c e n t r a t i o n s over the core wh'lch LES dLscussed in Section 2* f d l y w i t h d r e w ~from the care
e
The calculated ulapez.tu,,rbed axicE d i s t r i b u t i o n s o f f i s s i o n p r o a m t i o n
rates and f s s t adjoin:
;'lux a r e given in Pig.
4. These
were used f o r
t h e c a l c u l a t i o n of the zxia2 6 i s ~ ~ i b u t i o nofs The s i x delayed neirtron
p r e c u r s o r grougs, in accardaiice w i t h t h e scheme developed En SectjoP, 2. 0
The Pndi\Ti&Uai p r e c u r s o r c c n c e n t r a t i o n s , c I( 2 ) were mflc.ltipbied by hi acci sumed t o aktain the total Escal rate of emission o r delqyed ne-d~rona ~
along tr,e flaw p z t h thro-:gh tributions
the r e a x t o r c o r e .
re s t m n h F4g- $,
:or
!These r e s u l t i n g t o t e l a s -
t5e particular cases of w = 0 1
( c i r c d a t i n g c r H t i c a 1 ) and
~4
=
0-1s e e - (10 see stable period), and a l s o
f o r the c z s e when the P ~ e li s n c t c i r c u l a t i n g .
A l l chree d i s t r i b u t i o n s
are i o r n a ~ i z e i it o t h e s m e t o t s 1 production rate:
pegs.
m e botzom
plen7m i s amftted frcm E g ; . 5 s i n c e t h e w e l l s t i r r e d t a c k mo&eE w a s used to r e p r e s e n t The dePayed neutron production i n t h i s reglon.
Based on these s m e unpertur3ed f l - z e s t h e r e l a t z o n s h i p between the stabEe irverse p e r i o d , w
-1
correspandicg XItile rsdi
a ~ tdh e increment i n s t a t i c r e a c t i v i t y S I
shown in p i g .
6. For
C Q I T I ~ Z ~ ~ ~ O ; ~
*The "dip" i n the ta:erxah f l u x wher, the three pods a r e f - d b y w f t h d r a m i s ca;~sed by the presecce of the IIT5R-8 rod thimbles.
AXIAL %ISTAN:;E
FROM BOTTOM OF GRAPHITE [cm)
Fig. 4 e Axial Distributions of Fissicjn Cerssitg in F u c l S a l t and Fast Groups A d j o i n t Flux (CalcuLated Curves).
e,.&
............
L 6
22
QRNL-DWG 65-48654R
_____
0
20
40 60 80 (80 120 i40 16.0 DISTANCE FROM BOTTOM OF GRAPHITE ( c m )
180
200
e
23
I 2
1
Fig. 6 . CurYes ) 0
E
R e a c t i v i t y vs S t a b l e I n v e r s e Period of IGRE ( C a l c u l a t e d
p ~ ~ p o s e aa? calculated curve i s also given for t h e standerd inhour rela-
tisn47"when t h e f u e l i s s t a t i o n a r y in the c o r e . . A l l of t h e s e c a l c u l a t i o n s are baaed on the static values of pi and hi and t h e f u e l r e s i d e n c e times given in Table E .
Table I S t a . t i c Delayed Neutron P ~ ~ C W S Q T C h a r a c t e r i s t i c s and Fuel Residence Times used L n C a l c u l a t i o n s
4
3
13.07
26.28
5 7.66
6 2.86
Fcae 1
As t x curves
ir_
Ti&#
2
i i l u s t r a t e , beeause t h e rr4argin between t 4 e p?omp-L
a ~ deldiyed d n e u t r o n s o u c ~ has ~ s been i n c r e a s e d by t h e spctiak trarsport
of t h e
~ ~ ~ C U ~ S Ot h F eS sace ,
static reactivity increment prodwes a f a s t e r
r a t e of"rise of' b a t h x u t r o n and precursor d e m i t l e s .
The calculated.
c - a ~ e sexxend sorevhat beyond t n e r e g i o n of p r a c t i c a l i n t e r e s t i n experl-
mental messweanents of che sta-ske p e r l o d . -,he p x p o s e s of i l l u s t r a t i o n .
They m e p r e s e n t e d mainly f o r
Plz acalyzing the experimental daza, it
proved t o be most expedient to c a r r y out machine calc-iAations of t h e
r e a c t i v i t y increments corresponding t o each observed s t a b l e p e r i o d .
Exxxrimental R e s u l t s I n t h e chronology of t h e MSRE zero power experlments, t h e masurements of I n t e r e s t i n t h i s study began a t t h e p o i n t o f reaching t h e mini-
mum
235
U c o n c e n t r a t l o n r e q u i r e d f o r c r i t i c a l i t y w i t h c l r c u l a t i o n s topped
and a l l c o n t r o l rods f u l b y w i t h d r a m .
A summary of' t h e z e r o power e x p e r i -
ments i s g i v e n elsewhere,aQ and we consider only t h o s e d e t a i l s perLinent t o t h e t o p i c of t h i s r e p o r t . Once t h i s f i r s t basepoLnt 236U c o n c e n t r a t i o n had keen reacned, the c o n c e n t r a t i o n w a s f u r t h e r i n c r e a s e d by t h e e d d i t l s n of capsules of enr i c h e d f u e l s a l t con%a,inir_g approximately
85g mounts of
a3sU.
me
m o u n t of c o n t r o l rod i n s e r t i o n r e q u i r e d t o coapensate for t h e s e e d d i t i o n s w a s measured, and p e r i o d measurements about t h e s e x w c r i t i c z l rod p o s i -
t i o n s were made.
Csre w a s t a k e n to determine t h e minimum e x t r a a d d i t i o n
of 235U r e q u i r e d t o reach c r i t i c a l i t y w i t h t h e f u e l c i r c i i h a t i n g and &I-
rods f u l l y withdrawn,
Ozce t h i s second b a s e p o i n t w m reached, t h e
c r i t i c a l r o d p o s i t i o n and p e r l o d measurements were made f i r s t w i t h t h e pmp stopped t h e n wizli t h e f u e l c i r c u l a t i n g .
The measurements w e r e
t e r m i n a t e d when enough p 3 5 U had been added 50 c a l i b r a t e one rod over i t s e n t i r e l e n g t h of' t r a v e l .
Most of t h e p e r i o d measureaects were made 2n p a i r s .
The rod whose
s e n s i t i v i t y w8s t o be measzlred was f i r s t a d j u s t e d t o make t n e r e a c t o r c r i t i c a l a t about
lo
watts.
%her: it
wzs pulled a p r e s c r i b e d d i s t a c e e
and h e l d t h e r e u n t i l the p o w e r nsd i n c r e a s e d by about t w o decades.
The
rod was t h e n imserteed t o b r i n g the power back t o EO warts and- t h e neaswe-
ment wa,s r e p e a t e d at a somewhat s h o r t e r s t a b l e p e r i o d .
Two f i s s i o l ? c h m -
b e r s d r i v i n g l o g - c o u n t - r a t e meters and a two-pen r e c o r d e r were used t o
measure the p e r i o d .
The s t 8 b l e p e r i o d w a s determined by averaging t h e
s l o p e s of t h e two curves (which u s u a l l y agreed w i t h i n about 2$)*
Periods
observed w e r e g e n e r d l y i n t h e range o f 30 t o l$O s e e . P r i o r t o p u l l i n g t h e rod for each period measurement: the a-ctempt
wzs made t o h o l d t h e power l e v e l a t 1 0 w a t t s f o r a t l e a s t 3 minutes, i n an e f f o r c t o asswe i n i t i a l equilibriun of t h e delayed neutron p r e c u r s o r s . GenerPalky, however, it w a s d i f f i c u l t t o prevent a s E f g h t i n i t i a l d r i f t
f.n t h e power l e v e l as observed on a l i n e a r r e c o r d e r , and c o r r e c t i o n s were
t h e r e f o r e introduced f o r t h i s i n i t i a l p e r i o d .
The d i f f e r e n c e between
%L.,er e a c c i v i t y dcring t h e t r a n s i e n t and the initial r e a c t i v i t y , as cornputed from t h e in-hour r e l a t i o n , w a s d l v i d e d by t h e r o d movement and
this s e n s t t i v i t y w a s a s c r i b e d to t h e sod a t t h e m ~ a np o s i t i o n . The results of The rod s e n s i t i v i t y measuremats made w i t h t h e Yael s t a t i o n a r y are --
7.
shown i n E g .
Sirace t h e rod r e a c t i v i t y wsr-ch i s
a f f e c t e d by the %asu c o n c e n t r a t i o n , t h e o r e t i c a l c o r r e c t k m s have been a p p l i e d t o t h e raw data t o a c c o m t for t h e f a c t t h a t t h e 2351J
mss w a s
c a n t i n - m l l y being i n c r e a s e 0 dwil(lg cke course of t'nese experiments. 1-06secsitivities shovn Ln F i g .
7 have
%he
been normalized to a single a s s U
c o n c e n t r a t i o n , t h e t a t t h e beginning of the c a l i b r a t i o n measurements.
Tiie c a l i b r a t i o n curve in Fig. '7 c o n s t i t u t e s a convenient refereslce from which the sta"kc r e a c c i v i t y e q u i v a l e n t of t h e a 3 5 U a d d i t i o n s can be determined, simply by r e l a t i n g t h e l n t e g r a l under t h e curve between t h e f d b y witklr6ram p o s i t i o n and t h e e r d t i c a l r o d position 'vo %he a 3 s U mass.
By '3.pplyHng % k l s equivalence t o t h e rr,inimlxn % 3 ยง U increment between c r i - t i c a l i t y w i t h the f u e l sxationary and w i t h it c i r c u l a t i n g , one o b t a i n s an
experimental determ5na"Yon of the r e a c t i v i t y l o s s increment due t~ c i r -
culation. In addition, t h e curve i n Fig.
a convenient comparison
d a t a taken while t h e f u e l was c i r c u l a t i n g .
curve far t h e rod sensltivl:y
En the f i r s t sf :he
7 is
two zbove cases, t h e reactivity increment
cbtsined f r o x e x p e r f r x n t was 0.212 & 0.004$ 6k/k.
Thfs was f o m d t o
co~perew i t k 9.222$ c e l c u b a t e d directly froln Eq. 14, with w = 0 .
In t h e
secocd c a s e , t h e roC s e n s l t i v i t i e s determrned from p e r i o d measurerrents 6uricg c b r c u l a t f o n and Eo_. l b are shown i n F i g . 8. curves i n Ffgures
7 and 6 ere
ider,tical.
Kote t h a t t h e s o l i d
The experimental p0int.s were
foirnd to be distributed fairly c%cseky absilt> ;he
r e f e r e n c e curve, but the
s c a t t e r of' p o i n t s r e l a t i v e ts t h i s curve i s somewhat larger t h a n observed w i t h t h e data p o i n t s o f F i g . s m r c e s of t h i s sca$uter,
7.
Suggestions concerning t h e possfble
snd methods f o r i a p r o v h g t h e precisLon of t h e s e
aeasurenents are ir_c%udedi n -the f o l l o w i n g s e c t l ~ n .
27
ROD POSITION (in.)
Fig. 7 . D i f f e r e n t i a l Wo~t:?of IGRE C o n t r o l Rod No. 1, Measured with Fuel Stationary. (Normalized to i n i t i a l . c r i t i c a l 23 'U l o a d i n g ) .
CRNL-DWG 65-IC657
0.07
__
4.
DISCUSSION QF RESULTS
T h e o r e t i c a l Model V e r i f i c a t i o n I n keeping w i t h -,he order of p r e s e n t a t i o n of t h e preceedlng p r t of t h i s memoran&rm, we snzll f i r s t d i s c u s s t h o s e a s p e c t s of t h e results which r e b a t e d i r e c t l y t o t h e t h e o r e t i c a l model,
Following t h i s , some
s u g g e s t i o n s concerning t h e MSRE experiments w i l l be made.
As a t e s t of t h e t h e o r e t i c a l model f o r d e t e r n i n i n g t h e e f f e c t s of fuel c i r c u l a t i o n on t h e delayed n e d r o n p r e c u r s o r s , q u i t e s a t i s f a c k o r y r e s u l t s were o b t a i m d f o r t h e r e a c t i v i t y rfncrement between tile J u s t c r i t i c a l states w i t h t h e pump stopped 2nd w i t h t h e i ' u e l In s t e a d y c i r c u lation.
Mere, t h e p r i n c i p a l d i f f e r e n c e i n our model and an e a r l i e r
c a l c d a t i o n by Haubenreich3 i s t h e s p e c r f i c ineHusioE of t h e t o p and bottom r e a c t o r plenums 8 s a d d i k i o n a l so2arces of delayed neutron emission which c o n t r i b u t e t o t h e chaln r e a c t i o n .
A s w a s shown i n F i g .
5,
the
combined e f f e c t of f u e l flow and r a d i o a c t i v e decay of t h e p r e c u r s o r s i s t o "skew" t h e d i s t r i b u t i o n of" delayed emission toward t h e upper core and t h e t o p plenum.
It' i s i x p o r t a n t t o n o t i c e tha-c t h i s r e l a t i v e i n c r e a s e
i n emission of &hayed neki;rons i n t h e t o p p l e n m i s f u r t h e r a c c e m u a t e d by t h e much l a r g e r f u e l vobme f r a c t i o n i n t h i s r e g i o n ( t h e e f f e c t i v e neutron production i s t h e product of t k e t h e fuel volume f r a c t i o n )
S Q U C ~
i n t h e fuel s e l t t i m e s
Because Maubenreich's model accounted for
the ultimate contributLon to f i s s i o n of o n l y t h o s e delayed neutrons
emitted I n the channelled r e g i o n of t h e c o r e ? he o b t a i n e d
8
somewhat
largel- e f f e c t i v e l o s s i n delayed neutrons due t o c i r c u l a t i o n . Although t h e s e r e s u l t s seem t o cons-eitute an adequate t e s t of the model f o r t h e s t e a d y s t a t e c o n d i t l o n , we cannot extend t h i s claim t o t n e s t a b l e asymptotic p e r i o d s measured over t h e e n t i r e range of r o d t r a v e l , due p r i m a r i l y to the l a c k of p r e c i s i o n i n t h e p e r i o d measurements.
Bow-
ever, u n t i l more p r e c i s e measurements can be made, t h i s c a l c u l a t i o n a l model appears t o b e an adequate d e s c r i p t i o n oP the delayed neutron p r e c u r s o r t r a n s p o r t due t o c i r c u l a t i o n . More g e n e r a l l y : one may pose t h e qiies-tion of t h e need f o r s e n s i t i v e
t e s t s and models of t h e delayed n e u t r s n kinetiics & z i n g flue% c i r c u l a t i o n
a t zero power.
For t h e 1-06c a l i b r a t i o n work, It i s alwrys p o s s i b l e t o
s t o p the f u e l p u m ~ , p e r f o r n ;he ~ e s t sw i t h t h e f u e l s t a t i o n a r y - i n t h e core, and use simpEer, t;elE developed methods f o r t h e a n a l y s i s of s t a b l e
periods. ALso, -;he q u e s t i o z s of ultin;a$e safety and s t a h i % i t y of t h e r e a c t o r g e n e r C l g i n v o l v e l a r g e r e a c t i v i z y a d d i t i o n s which take p l a c e on 8
timi? scale &srt compzred t o t h e core t r a n s i t time, and greatly in-
faiaence t h e k i n e t i c s of -,he prompt neutron generacion.
These q u e s t i o n s
a l s o involve n o n l i x e a r i x L e r a c t i s n e f f e c t s w i t h temperature a t high
.
pQTE!P.
En a d d f t i o n t o t h e tneoretisal i n t e r e s t , t h e r e are several contrib u t i o n s a good u d e r s t a n E 3 c g of tke e f f e c t of c i r c u l a t i o n on t h e delayed neutron k i c e t i c s c m make from t h e viewpoint of r e a c t o r o p e r a t i o n .
For
example: $he observed d i f f e r e n c e s between t h e f u e l s t a t i o n a r y and c i r c u Eating c r i t i c a l c o n d i t i o n s can c o n s t i t u t e a s e n s i t i v e method of deterrnin-
i r g Pile% c i r c u l a t i o n ra,te, cmo11;2t of c i r c a l a t i n g gas bubbles, o r any s p e c i a l c h a r a t e r i s t i c dLe t o -,he circula;ion.
PJecessasy control systen;
s e n s i t i v i t i e s and response t i m s f o r norxnab o p e r a t i o n can b e s p e c i f i e d wizh l e s s u n c e r t e i n i t y i n t h e desigr of ozher ~ o l - c e ns a l t reactors. Mtliough xusk of t h i s study o v e r l a p s t k e t of e a r l i e r work, it I s
u s e f u l t o re-exphasize h e r e that the k i n e t i c s of c i r c u l a t i n g fuel syscems
belong to a mtklematical category w3ich is f m k n e n t a l h y d i f f e r e n t rron: tbat of s t e t i s n a r y f ~ e i e dr e a c t o r s
T h i s I s ~ a r t i c u l a r b yimportant i n
t h e descriptioc sf r e a c t o r t r m s i e n t s o c c u r r i s e on parable with ;he
EL
t i m e scale con-
fuel ;rarsi-b tlrres-, I s i s a p p r o p r i a t e Lo r e f e r t o t h e
c ; r c u h ~ i n g fuel s y s t ~ l x sas ";,ime-lag" d i f f e r e n t i d equations for
7,he
systenas, g o x x n e d bj? p a r t l a 1
delayed e n i t t e r c o n c e m r a t l o m
t h a n by o r d b a r y d i f f e r e n t i a l eq;atLons.
rcther
For rnmy purposes, approximate
r e d u e t i o m of t h e equz,ticns t o a f o m sirnila- t o t h e k h e t i c s e q u a t i o x
cf t h e stationary t'ue%ed systems are adequate (e.&;., t h e replecement of eff the i n d i v i d u a l delayed f'rac-,,ons, pi, by e f ' f e c t i v e r e d m e d values, Pi i n the conventionel reactor k i n e t i c s ecpatiolas 9
dses mt seem transient,
-LO be f l ~ E l yj u s + , i f i e d
e
his r e d a c t i o n , however,
for TIE anaEysis of an a r b i t r a r y
I n t h i s s t u d y , the only- conditiofis w e have f u l l y examined are
t k e Just critlcab s t a t e and tke s z e l ~ eof f l u a n changing wi%
asymptotic p e r i o d ,
a stable
For a complete t h e o r e t i c a l understanding oâ‚Ź $lie
coupling of t h e c i r c u l a t i o n with t h e delayed neutron k i n e t i c s , w e need a l s o t o analyze t h e "cansient delayed neutron aodes, mentioned b r i e f l y i n Section 2.
This t r a n s i e n 5 cou-pkirg d e t e r n i n e s t h e e f f e c 5 i v e t i n e t o
e s t a b l i s h t h e asymptotic p e r i o d , and should also provide a basis f o r approximations made i n t h e e n a l y s i s of a r b i t r a r y t r a a s i e r t s
I
S o r e pre-
l i m i n a r y work has been done en t h i s problem, and w e hope t o make t k i s t h e s u b j e c t of a future anemorsndu~n, Wecormendations f o r t.he YSRE
One reason f o r t h e leek, of p r e c i s i o n of z;?e rod Fw-p-period measurement of c o n t r o l r a d s e n s i t i v i t y i s t h e t t h e Hat,r,er i s t h e r a t i o o f two snrthl q u a n t i z i e s
For best ~ e s u E t s ,t n i s r e q u i r e s t n e experimenter
""0
maintain h i g h p r e c i s i o n i n both t h e rneasilreinent o f t h e increment i n r o d
positlsn and tr,e s l o p e cf t h e l o g n vs t i m e cu.rve.
FhrEy i n t h e course
of t h e s e e x p e r i x e n t s it w a s decided t h a t only t h e r e g u l a r r e a c t o r i n s t r ~ mentation would be used f o r t h e rod s e c s i t i v i t y measurenents,
Beterml-
n a t i o n of t h e p e r i o d i n ea& measurernent involved l a y i n g a s t r s i g h t - e d g e
along t h e pen l i n e r e c c r d en she Hog n c h a r t and reading t h e zinc i n t e r v a l g r a p h i c a l l y along t h e h o r i z o n t a l scale which corresponded to a. change of s e v e r a l decades i n t h e neutron l e v e l .
Since these c h a r t s , t o g e t h e r w i t h
t h e pen speeds, aye su'cJect t o v a r i z t i s n s , t h i s i s e r r o r i n t h e rod s e i s i t i v i t y measurements. e ~ " r o probably ~> less important Q
i n the rod p o s i t i o n s ?
8,
probzble source of
A second p o s s i b l e source of
l i e s in the measuremxt o f the Tncrements
It, has Seen seen t h a t
the s c a c t e r i n t h e experi-
mental points was larger for t h e s e n s i t i v i t y memuremerits made during circulation
a
This i s expected, s i n c e s i n i l a r increnaents i n r e d with-
tkrawal r e s u l t i n a s h o r t e r staaBe p e r i o d ucder t h e s e condLtfons. Although a c o q l e t e e r r o r a n a l y s i s h a s not been c a r r i e d out, t h e s e
considerations would seem t o b e obvious s t s , r t i E g p o i n t s i n any f u t u r e attempt t o obtain more p r e c i s e measmements of t h e r o d s e n s i t i v i t i e s .
At t h e t i m e t h e s e experiments wes'e p e r f o m e d ,
t h e bEWE o n - l i n e computer
w a s u n a v a i l a b l e f o r t h e automatic r e c o r d i n g of experimental d a t a .
It
would be useful, during f u t u r e MSRE operat%on, t o r e p e a t some o f t h e p e r i o d measuernents while a t zero power, using t h e coxputes i n the d a t a
h
Hogging shim
mode to
eutomatieally
record
csuEd
be adjusted
to vary
reds
regubatirr,g
rod
for
precise
experiments
bration
obtained
judged
the is from
adequate
for
'%he coc~eration cperatir-g is
sta-??
gratef-Lily
of the
in
not the
Data t3
great,
the
since
measurements
further
n and time
irritial
critical
intervals.
The
position
of the
The immediate the
with
precision the
fuel
of
need the
for
rod
stationary
more cabi-
is
operation.
of J,
W. Ergel
per? orxicg
the i?Jso,
Proecssi.ng
implement
log
measurements,
aekEci:rILedged.
Central
cornputatiocs
period
the
tkc
and various experiments 55e
Facility ana9ysj.s.
author for
members and aid,lng is
of the in
indebted
grogramming
to the
MSm
analysis $,
L.
machine
Lucius
33 REFERENCES 1. 5. k, Fleck, Jr., Theory o f Low Pcwer K i n e t l c s o f C i r c L l b t i n p FueL Reactors Wtth Sc\veraS Groups of Delayed Xeutrons, USMC Repcrt ~ ~ ~ - (3~ -35 4 ' i ) , Brookhaven Maiional L a b c r a t o r y , 1955
5.
B. Friedvan,
9
Chapter 1, J c
c
'I,
P. N. Hau5enreic-h e t al., MSRE Design ar,d Opyrations Report, P a r t 111; Nuclear A n a l y e i s , USAEC 3 e p o r t ORlK8-T%l-730,Cak Ridge N a t i o n a l Laborator& February 3, 1964.
se
S, Glasstone and M u C . E:ilczrid, Thc ELernects of Nuc;ear TherJry, Chapter 18, Van Nostra
Reactor
INTERPU'AL BISTRIBUTION
1. R. K . 2 * S . J. 3 . W. P. 4. 3 . F. 5. s. E . w. I,. L. 7. E. S . /-
8.
9. 10.
4E. E.
13. lk. 15.
16.
17. 18. 19. 2029. 22. 23.
24. 25.
~6~ 27. 28.
29. 30.
34*
y2. 33. 34. 35.
Admis Ball Bartncld Balman
Bcall
Bennett Bettie F. F. Blankrnship R. B l m b e r g C. 6. Bcrkowsaf R. B. B r i g g s G. M. Burger S. Cantor €3. S. C a r l s n i t h 8. D. Chevcrton C . W. Craven, Jr. J. L. Crowley F. L. C u l l e r J. G . Bclene S. J . D i t t o G. E. Ediscn J. R. Engel E. P. Epler W. K. Ergen D. E. F e r g u s m T. E , Fowler A. P. F r a a s B. IT. F r y C . H. G a b h a r d 8 . B. G a l l a h e r E , H. Gift w. R. GriIXs R. 1%. G u p o n P. 2. Harley P. N. Haubenreich
36. V. B.
Halt
37. 38. 39.
T. L. Hudson L. Sung P. R. Kasten 40. R. S . Ked1 41. M. 6. K e l l y Lt2. T. W. K c r l i n 43. H. T. Kerr + b e S. S. K i r s l i s
$5.
S. I. Krakoviak
46. R. B. Lindauer 47.
J. L. L ~ c i u s
M. I. E.m-din R. R. Ly-on K . G. MacPherson R. E. MacPhei; on C . B. Martin K. E. McCoy €I. C. McCardy 9.:. F. McDuffie A. J. M i l l e r R. E. Moore E . A. Nephew M, R. Fayne A. M. P e r r y II. E. P i p e r E'. H. Pi',katnen C. M. Podeweltz C . A. F r e s k i t t . B. E. P r i n c e J. I,. Redford M. Richardson R. C . Robertssl-, K. c. R o l l e r M. I;. R c s e r t h a l A. ide Savolaicen D. S c c t t 7'
M. J. Skinner 0 , E. Smith F. G. Smit.h I . Bpiewak R. C . S t e f f y J. R . Ta,llackson R. E. Tlrorrra W. E. Thomas M. E. Tobias B. E. Trauger M, E. Tsagaris
w. c.
Ulrieh
D. R. Vondy E. E* Webster A. M. Weinberg F. G. Welfare G. D. Whitman J, V. Wilson Centra1 Research L i b r a r y Docment Reference Section La5 c r a t o r y Records La4boratary Records (LRD-RC )
108-=2. E i v l s i o n 3f Technical In%rx!ation Extension (DTPE) 123. Research and DeveSopnent. Division, OR0 l.24-E5 8ea.ctor Slivfsion, OR0 a