ML19339D012
ML19339D012 | |
Person / Time | |
---|---|
Site: | Vermont Yankee File:NorthStar Vermont Yankee icon.png |
Issue date: | 02/06/1981 |
From: | VERMONT YANKEE NUCLEAR POWER CORP. |
To: | |
Shared Package | |
ML19339D011 | List: |
References | |
YAEC-1234-ERR, NUDOCS 8102130097 | |
Download: ML19339D012 (26) | |
Text
. _ _ _ _ _ - . ___ _ _ _ _ - _ . - . _ _ _ . . - _ _ _ . - - _ _ _ _ _ _ - _-. .. ._ _ __
,s
- I ERRATA I Report,
- YAEC-1234, " Methods for the Analysis of Boiling Water Reactors, Steady State Core Flow Distribution Code (FIBWR)
I Change
Description:
The following enclosed pages should replace those in the originial report.
iI 5, 8, 13, 20, 22, 24, 25, 31, 37, 40, 41, 42, 43, 44, 51, 52 54, 58, 59, 89, 90, 91, 92, 105, 107.
(Solid lines on the right hand side of the pages show the approximate location of the changes.)
'I
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lh
- I I
lI E
k I
t l 810213000
4
- I i
I -
Top of Core l a j ZCH1 I a ZUHA ll' ,
a a lll i;9 i
\'
l .
m
_' In. .
li!!j NOTE: Bottom entry Peripheral Fuel ZHE.'
I lll l'[: i supports are welded into the core support plate. For these j' h bundles, path numbers 1, 2.
f Channel 5 and 7 do not exist.
y l o Spring Plug
' I P !
j li ZUHB i i I
'8 Core Support i h
- Lower i Tie 9
! ZGEO Plate #6 a
,f a
1 34 r n Bottom of core ZSTC y M_( C 7 j
" -- Shroud Fuel Support lb l Control Rod Guide I Core Length = ZCHI +
Fuel Length + ZGEO
? Tube
- 1. Control Rod Guide Tube - Fuel Support
- 2. Control Rod Guide Tube - Core Support I
Fuel Length = ZUHA +
~"
ZHET + ZUHB o 5 Plate 7 3. Core Support Plate - Incore Guide Control Rod Tube I Drive Housing 4.
5.
Core Support Plate - Shroud Control Rod Guide Tube - Drive Housing I 6.
7.
8.
Fuel Support - Lower Tie Plate Control Rod Drive Cooling Water Channel - Lower Tie Plate
- 9. Lower Tie Plate Holes
- 10. Spring Plug - Core Support Figure 1-2. Fuel Bundle Geometry and Various Leakage Flow Paths I
{
g . .
~,
y 2 2
Gfin31A final -O initial Ag=gtigi ('-4)
I, ,
Eacceleration
=
g +A c initial iUiti -
- - final where the momentum density, ; ,
is defined by 1 = <x)2 . (1 - <x>P' ,
(2 3)
II : o <a) ; (1 - <3>)
and
,I <x> = flow ouality
<a) = voi? fraction m = momentum density (lb/ft3)
I In heated recions, the flow area is assumed constant, and the fluid I acceleration is due :o density changes induced by the boiling process.
In this case, the formulation for the acceleration pressure change is q
. , c_ s 1
. (2-6)
"Pacceleration I
aC
" outlet " inlet _
The gravity or elevation nressure drop across a node is evaluated l
Fv
($~I) 1
' OD7 pay {gy
- - (I - b )) *
- gb) LU
- The frictional pressure losses are correlated in ter s of the sincle-l phase velocity head
,c LUC 2 2 (:-3)
- friction
- (- .
I D H 1'c'i f where f = sincle-nhase friction factor C' ' = the sincle phase velocity head 2Pe o.
I -p-
I At or near BWR conditions the Baroczy [8] correlation for the two-I 9 phase frictional multiplier, cio, is the default model in FIBWR_. Also availr.ble as user options are the Jones-Dight [9] fit to the Martinelli-
' Nelson curves, the homogeneous model, and a mass flux correction (10] to the Martinelli-Nelson curves.
1 -
2.3.2 Pressure Drop Because of Local Losses The FIBWR code has three models for the two phase local loss multiplier. The default model is the modified homogeneous expression:
" l* L/;g - 1) (2-15)
- )20 cal .
where S is an empirical constant. If 5 = 1.0, this reduces to the ho=ogeneous expression. FIBWR also contains the Janssen codel as :odified by Weis=an [11] and the Ro=le codel [24] as options.
2.4 Leakage Flow Models 2.4.1 Bypa ss Region Due to the low flow velocity, the pressure drop in the bypass region a bov e the core support plate is essentially all elevation head. Thus, the sum of the core support plate dif ferential pressure and the bypass region elevation head is equal to the core dif ferential pressure.
The flow through the bypass flow paths is expressed by the form:
C, 3 V=C &PI73 + C2aP * + C 3aP' . (2-16; l
E The leakage paths to the bypass for a typical BWR geocetry are shown data at low qualities must be that flow quality does not equal equilibrium quality. More i=portantly, it appears that the two qualities are equal above 5 percent qua l i ty . Thus, flow cuality is known only for equilibriu:
~ qualities above 5 percent, where the two qualities are equal, and verification of the void quality codels can be done only for equilibriun qualities above 5 percent. Section 3.3 will discuss verification of the q
=
co=bined subcooled boiling and void-quality models for equilibrium qualities G I below 5 percent. g
.9 rp I Figures 3-5 and 3-6 coepare both the EPRI and Dix models to data 1 1
f rom the FRIGG Loop. As may be seen, the Dix odel tends to underpredict I the da ta, especially at higher qualities, while the EPRI model catches the ?
5 data very well. Apparently, rod bundle flow conditions are core hotogeneous )
(lower slip ratio) than the tube flow conditions upon which the Dix g correlation is based. Possibly the spacer grids contribute to mixing of g r
the vapor and liquid , =aking the flow more hocogeneous. Note that the local effect of spacer grids is ignored both in the =odels and in the experi= ental 2 I
data (as void fraction measurements were made as far as possible from spacer j 7
locations). e O
3.3 subcooled Boiline Moc'el s I The second aspect of void fraction prediction involves the so-called subcooled boiling models. These models must relate flow cuality to equilibriun quality so that the void fraction may be cceputed as a functie-of the predicted flow quality. As shown earlier, flow cuality varies significantly from equilibrium quality only at c ua l i t i e s l owe r t ha n approximately 5 percent at nor=al Bk'R opera t ing condi t ions .
I I
I Since flow quality is not available experimentally, the only comparisons to data which are possible are void fraction comparisons. Note that since the void quality models are not verified at low qualities, a given data comparison can verify only the predictions of the combined subcooled boiling and void quality models.
It was decided to compare the EPRI and the Saha-Zuber subcooled boiling models to FRIGG Loop data. The exponential profile was chosen for the Saha-Zuber model since that was in the original data comparisons of Saha and Zuber. The hyperbolic tangent profile was used in conjunction with the EPRI subcooled boiling model, as suggested by its developers.
The Dix void quality model was used with the Saha-Zuber subcooled model and the EPRI void quality model was used in conjunction with EPRI's subcooled boiling model.
Figures 3-7, 3-8 and 3-9 display void fraction versus axial location for several FRIGG Loop runs. Predictions of the EPRI model and the Saha-Zuber model with Dix void quality are also indicated. It can be seen that both Saha-Zuber and EPRI do a good job of predicting the location of zero void fraction. Both are certainly within the error band of the experiments; and, in fact, they agree with each other quite well.
I 3.4 Two-Phase Frictional Pressure Gradient I Of the models for the two phase frictional multiplier which are available in FIBWR, only the Baroczy model is based on steam / water data I I
I I TABLE 3-1 I Geometric Data for FRIGG Loop Test Section FT-36c 36 Number of Heated Rods Heated Length 4365 mm (171.8 in)
Nonunifom Radial Heat Flux Distribution I Rel.itf ve Radial 6 Inner Rods Heat Flux Distribution 12 Interadjacent Rods 18 Peripheral Rods 0.854 0.926 1.097 Nonunif o m*
I Axial Heat Flux Distribution Heated Rod, OD Unheated Center Rod, OD 13.8 mm (0.534 in) 20.0 mm (0.787 in) 159.5 mm (6.28 in)
Shroud, ID I Wetted Hydraulic Diameter
,.ated Hydraulic Diameter 26.9 mm (1.06 in) 36.6 mm (1.441 in) 8 Number of Spacers Variable Operating Pressure Variable Inlet Subcooling Inlet Throttling, Velocity IIeads Variable HO Coolant 2
- See Figure 3-1.
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I O 100 120 140 160 180 O 20 40 60 80 Channel Length, inches I Void fraction versus axial heizht for FRIGG Loop run with Figure 3 7 .
low inlet subcoolinc,.
l
\
1
- 9 -
(4-5)
I 2
E C #Iocal .
aPlocal = ,
- g ~
c L _,
where
- s I
2
- local = two-phase local loss multiplier
' ~
G = mass flux (lbm/hr-ft2)
Z = axial distance (ft)
Lg = heated length (ft)
E
- spacer single-phase loss coefficient lE
'E ~~
9
= two-phase frictional loss multiplier 7
o c = density (lbm/ft3) f = single-phase friction factor
- g = hydraulic diameter (ft) lE Dg 1
q' = monentum density = , ,
E <X>- . (1-<X>)-
lg O g<27 f;(1-<2>)
p = gravitational constant (ft/sec ) ,
constant relating force and acceleration (1bn-ft/lbf-sec~)
g_ =
lE
- W Each of the above teres will be directly integrated, but first models for void fraction <i(Z)> and flow cuality <X> as a function of elevation axial heat E are needed. For si=nlicity, thermal ecuilibrium and unifor 1
3 Thus, <X> is zero un until the boiling boundary defined i
flux are assumed.
by an energy balance as, p3 x, C Ax -sih sub lg iW PH C I
I where
>= subcooled boiling initiation location (ft)
- g ,
-lE Ax -s
= correctional flow area (ft-)
h = inlet subcoolinP (enthalpy) (Btu /lbr) sub I
I u = vapor velocity (ft/see) j = mixture volunetric flow velocity (ft/sec) l '
l It may be seen from these definitions that as flow quality approaches unity, C, must approach unity, and } ) must approach zero. M s is because at this extreme, <a) is uniformly equal to unity across the pipe (recuirine and the vapor velocity (u p) becomes equal to j (rect. iring C, to ecual 1.0);
V to ecual 0.0). Thus, to assume constant values of C, and Vg3 other than 1.0 and 0.0 respectively, will give the incorrect limit on void f! action as cuality aporoaches 1.0. In fact, the Zuber-Findlay relationship will always credict void fraction less than one for cuality ecual to one if Co > 1.0 or Vgj > 0.0.
,I In order to avoid physically unrealistic values of void fraction
,I in this analysis, the void fraction will be set ecual to unity whenever flow cuality ecuals one.
Ecuations (4-2) throuch (4-4) may now be integrated up the channel. BeginninF with the acceleration pressure drop 1
G- 1 ~
Mace = (; ) ; (0)
I ._
il - G (L..))]2 n
<X(LH )>2 _ _1
(;.79) o {2 ,
I a
(3(L ;> c, ace = g (1 - (3(;H p; ; ;R t c -
The elevation pressure drop integral will be broken into two parts, representine tSe sincle pbare and the two-phase regions.
I " ,'
Fravity
.n 7CC t' *7 C p L.H - d "'
~
Using the definition of density [o = O g - (O. -O g)a];
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I L 1 Z~I2 g (0, ~O f.Pgravitv " I
- O t
flH -)) ~
F ' g) ; y,,;+7
~
Ec Fc e s
_6
'a'ith the aid of intecral tables, this may be integrated to yield ,
I 5L H"E6_
~# In I h ~ (# 1
- 8) H~A )
APgravity F5 F 3A +F6-CA F2
\ -
5 I
- r, F
S T
H'6
+T l
(4-21)
- - - In _
r
,I F
.z _$4 +r 6_
~
i
)
In order to evaluate the frictional pressure loss, a model for 3
, is, I
ti,'- is recuired. A simple fit to the Martinelli-Nelson model for : ,
' I*L\ -1 <X>0.824 - 1.0 (4-22) 1.2 2-
=J I r. ~g I
f L.
! / J where C is the mass flux correction f actor of Jones [9), given by, 6
1 .36 + .0005p + 0.1 G/106 _ ,gng713p of;g 6
for G < 0.7 10 I
f i
1.2A - 0004p + 0.110 id /G + .00028p 10 /G 6 for G > 0.7+10 6 I
j vhere o is in psia and G is in ID" l ft -br l
l The above model for 07a. ;
is convenient because it is a function only I
t 1
of cuality, which may readily be integrated.
Performing the intecration,
~ -
L fc 2 ,
pH 2 d2 nfriction - 2n e n o ,L,
. t:
- a ,
,- : } Ly' d:
f C' Ly' + 1.2 -.l. - 1 *
(F i z - F;)
~P 2Pch!# l /
1
- .1 -
u.1-1 l l l
^ C 2 3
<xo.H u .824 . (4-23)
AP bH + 1.2 C D#H t 1.824 F1 friction " 28c (Og ) _
The local losses may be evaluated using the modified homogeneous
- multiplier model of ifocal' 9 I y I l + 6 !.3.<x> .
(4-24) oplocal " vc j
28co L ( '
= 1+B (Ft Z - F2 . (4-25) aplocal
{28c* L
- f _
.)
I where the summation is over the number of spacers present, and S is the 2
parameter used to modify the homogeneous =odel for clocal*
Each of the components of the pipe pressure drop, acceleration, friction, gravity, and local are now known as a function of the given input l
parameters. That is, the ap components of Equation (4-1) are given in turn Note the analytical by Equations (4-20), (4-23), (4-21), and (4-25).
expressions above are valid only if it is assumed that the densities and enthalpies of both the liquid and vapor, the applied heat flux, and the In addition, the parameters Co and V gj do not change with axial location.
models assume equilibrium two-phase flow with pure liquid inlet conditions and two-phase exit conditions.
The analytical model has been extended to han'dle unheated regions both above and below the heated length. This extension of the analysis useful since it also permits subcooled or superheated exit conditicns is most which were not allowed in the above analysis.
lI The analytical model described above was used to predict the pressure Btu drop in a vertical, uniformly heated tube with subcooled (20 lba I I
subcooling) liquid untor at ths inlet at 1020 psia. The void distribution pars =eter, C o
, was set equal to unity; and the vapor drif t velocity, "g3, was set equal to :ero. The =ars flux was varied .iuch that the exit flow I .
quality varied fro: unity to :ero. There were no local losses =odeled.
The analytically calculated values of pressure drop for the above case are plotted as functions of = ass flux on Figure 4-1.
I *he FI3k'R code was used to si=ulate the sa=e physi al si:uation In the FIBb'R run, for which the above analytical predictions were =ade.
the op-tons of ho=ogeneous void-quality model, equilibrium subcooled boiling I model, and Martinelli-Nelson friction multiplier with the Jones = ass flow correction were selected. Thus, the FI3k'R :odels =atched :he analytical
=edel in every respect except that FI3k'R computes liquid density as a function of temperature at the i= posed pressure instead of assu=ing constan:
liquid density as the analytical model. Twenty-four axial nodes were used I in the F!3k'R prediction.
Figure 4-1 displays the FIBb'R predictions of the total pipe pressure drop and of each pressure drop co=ponent, and co= pares the= to the analytical solution. It is observed that FI3b'R and the analytical solution agree :o f
within a few percent at every point except for the calculation of acceleration pressure drop at high = ass flux, where the pipe exit condi:icns were single-phase liquid. The analytical model assu=es constant liquid density, and thus incorrectly predicts :ero acceleration pressure drop wher the exit conditions are pure liquid, while FISWR correctly varies the liquid l
i density with te=perature and predicts nonzero liquid acceleration.
I lI ,I l
I 4.2 Oualification Versus COBRA IIIC The FIBk'R momentum and energy equations and their numerical solutions may be verified by comparing the FIBb'R predictions to those of an existing,
~ fully verified computer code, COBRA IIIC [14], for some sample problems in which the two codes solve exactly the sa=e equations using identical constitutive models. COBRA IIIC and FIBb7 solve precisely the sa=e continuity, energy, and axial mo=entum equations, so long as the transverse flow in COBRA is zero. Of course, COBRA IIIC does not have the capability of handling the detailed Bk2 geo=etry that FIBb'R allows, nor will COBRA IIIC predict bypass or water tube flows. However, for simple heated, parallel channels with no local losses, COBRA IIIC and FIBk2 can be made to solve exactly the same equations if consistent models are selected in I the two codes.
I As a first effort, a sa ple problem in the Battelle report [25]
describing COBRA IIIC was solved for a variety of = ass flow rates using both COBRA IIIC and FIBb'R. This problem involves a one-twelfth section of sy==etry of a 19-rod bundle. This pie-shaped section is divided into five subchannels as illustrated in Figure 4-2.
In order for COBRA IIIC and FIBb'R to solve precisely identical problems, it was necessary to " turn off" the transverse flow in COBRA IIIC and to select identical void-quality and subcooled boiling models in bot!'
codes. Since both COBRA IIIC and FIBb3 allow the use of the homogeneous void quality relation and Levy's subcooled boiling model, these options were chosen for use in the sample probles.
In order to eliminate subchannel-to-subchannel mass transfer in I
I I
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I
.I
/ .
- > /
!g l 2
/ f/ 3 sueenannet designaten
//4V I '
4}W I //
fod designation
!I l
Figure 4-2. One-twel f th section of symmetry from a 19-rod bundle divi:et into 5 subchannels.
lI II I
-v.
!I I _
il 1
6 6 4 6 4 6
!I
.'lE
! 3.0 -
Subchannel 1 Subchannel4 -
Subchannel 2 Pressure l
5 Drop, psi A
O
- g 2.0 -
- g A
ig
'E Legend
- A FIBWR lB O COBRA IllC I , , , , , , i i 1.0 t ' ' ' '
.6 .7.8.91 2 3 4 5 6 7 89 10
!l EN Mass Flow,10- 2 (Ibm /hr)
Figure 4-3. Pressure drop versus subchannel mass flow comparison of FIS'n'R and COBRA IIIC for one-twelfth section of symmetry from a 19-rod bundle.
I
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4 . .
I
, , , . . . i 6
~
Legend ~
I -
140 -
Pressure =
Mass flux =
1,000 psia 0.5 106lbm/hr.ft2 2>
~
130 - Heat flux = 1.5 106 BTU /hr- ft2
~
120 -
I 110 - ja
~
~
100 -
90 -
I Axial
~
Distance, I inches 70 -
~
60 - 0 -
~
50 -
3 o
~
40 lI b
l -
30 -
Legend l
l 2 0 0 FIBWR _
20 -
A COBRA filC l 10 -
! 0 0
i
.1 e
.2 i
.3 4 1 -
.5 i
.6 i
.7 .8 r
.9 Void Fraction, lW Figure 4-5. Void fraction versus height predictions of FIBWR and COEPA IIIC I for a Quad Cities fuel assembly.
I K = 6.44 d (5-4) l w2 Reference (15] gives the orifice plus lower tie plate pressure drop as a function of the active flow. Knowing the active flow, an estimate I of the total flow entering the orifice was made by assuming that the total bypass flow was 10.0 percent of the active flow going through the central region assemblies at full power / flow conditions. According to Reference
[18), 65 percent of the total bypass flow enters the orifice and 35 percent Therefore, for an leaks through channel independent bypass flow paths.
active flow of 1.2 x 105 lb/hr, the flow entering the orifice equals 5 lb/hr. Using Equation 1.2 x 105 + (1.2 x 0.1 x 0.65), or 1.278 x 10 (5-4) and the orifice plus lower tie place pressure drop (for for the central assemblies which has the orifice diameter of 2.222 inches) an active flow of 1.2 x 10 lb/hr [15), we have, 5
(5-5)
K * = 6.44 x 9. 2 _
CENTRAL ORIF + LTP t
(1.278)2 i
or K = 37.14 CE M A Knowing the total 'K', Idel'Chik [19] was used to estimate the ratio E LTP p
kTP , he ra & M g was found to be equal to 0.2558. Using this
( g ORIF
' ORIF ratio and the total 'K', the form loss coefficients for the orifice and lower tie plate were determined as follows:
(5-6)
LTP = 0. 2 558 I'ORIF I From Equation (5-5) and Equation (5-6),
lI -
K *
- OR17 I and I .
Kt7p = 7.56 Similarly, Reference (15] was used to determine the values of the form loss coefficient 'K' based upon Equation (5-4) for the peripheral assemblies in the Vermont Yankee core which has an orifice diameter of 1.488 inches. In this case, an estimate of the total flow entering the orifice was made by assuming that the total bypass flow was 5.0 percent of the active flow going through the peripheral region assemblies at full power / flow conditions. Therefore, from Reference (15] for an active flow of 0.7 x 105 lb/hr and Equation (5-4), we have,
=K +K LTP
= 6.44 x 13.946 (5-7) bERIPHERAL ORIF
((.7) + (.7 x 0.05 x .65)]2 I or I K = 171.94 I Since the lower tie plate design for the central and peripheral assemblies is the same, the form loss coefficient KLTP f r the central and periptural region assemblies should be equal.
I Therefore, g (peripheral) = KLTP (central) = 7.56 I From Equation (5-7),
I K ORIF (peripheral) = 171.94 - 7.56 = 164.38
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1 m = -J .:
=
w-
- u .
- r. -l .
4 e
I i .: =
s ._
i = -. x n
a
= + - -.
i e d' - ..
~
e _
. 2 I
c.
t e
3
=
I
_ z w I = .
' _ - z =
= z :
J . -
I . -;
I
. -6 .
w 0 .,=
i -
- > - u i
, c
_. u. .
's .
u.
s x . :c . _-
s -
?.:
N -
N - I2 I -
. =
I N
\
e s-l m ?J . e s
l ' l a
lI ! ! ! ! ! ! l t l I l f ! ! I i l t l I l f l l l l l l *-
ee e x e m = =c e e m = :c
= .
-- -n -
mm m mm - - - - -
e e m (Tsd) do20 GJnssa;d l anidaTJ, Ja so 1 9 aaI Jiao
6.0 CONCLUSION
S 6.1 The accuracy of the FIBWR coding has been verified by cosparisons t - ,
to an analytical solution and with COBRA IIIC results.
6.2 The void-quality relationships and the pressure drop calculations using the recommended models give good agreement with experimental j
data.
6.3 FIBWR predictions of Vermont Yankee flow distributions, pressure drops and bypass flow are in good agreement with plant data and process computer predictions.
' 6.4 The FIBWR code, with the recommended models, will provide an accurate prediction of core flow distribution and pressure drops for use in core reload design and licensing calculations. The recommendet models lg E are:
o Baroczy for the 2 phase friction multiplier.
o Blausius relationship for the friction factor 'f' with constants i
A = 0.1892 and B = -0.2041.
!I o Modified homoganeous model for the 2 phase form loss multiplier.
l
!E o EPRI-701D model for the void quality relationship.
i
" o EPRI-VOID model for the initiation of subcooled boiling.
l l
I
-105-l
I " Core Design and Operating Data for Cycle 1 of Hatch 1", EPRI-NP-562, (15)
I January *979.
(16) Exxon Nuclear Co., "Results of Leak Test on General Electric Type Finger Springs and Bypass Flow Holes", 1980.
. (17) Letter from L.H. Heider (YAEC) to USNRC, " Additional Information with to Vermont Yankee Bypass Void Analysis", dated December 12, I Respect 1973.
(18) General Electric Co., "BWR Fuel Channel Mechanical Design and I Deflection", NEDO-21354, GE Licensing Topical Report, September 1976.
1.E. Idel'Chik, " Handbook of Hydraulic Resistance, Coefficients of (19)
Local Resistance and of Friction", USAEC-TR-6630, 1960.
(20) General Electric Co., " Plant Modifications to Eliminate Significant Incore Vibrations", NEDO-21091, November 1975, pages 4-7.
(21) J.P. Waggener, " Friction Factors for Pressure Drop Calculations",
Nucleonics, Vol. 19, No. 11, 1961.
(22) " Core Pressure Drop Measurements" as given in the Startup Test Calculations for Vermont Yankee, Table I-5, September 4, 1970 (Spec.
No. 22A2218, Revision 0, Sheet No. I-19).
(23) Memo from M.J. Hebert to A.A. Farooq Ansari, " Energy Deposition Analysis Methods", YAEC, dated November 5, 1980.
(24) P.A. Lottes, " Nuclear Science and Engineering", 9, 26 (1961).
(25) D.S. Rowe, " Cross Flow Mixing Between Parallel Flow Channels During Boiling (COBRA)", BNWL-371 PT1, 1967.
i l
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t f
-107-