FVY-81-164, Forwards Response to NRC Questions Re Fibwr Computer Code
| ML20038A867 | |
| Person / Time | |
|---|---|
| Site: | Vermont Yankee File:NorthStar Vermont Yankee icon.png |
| Issue date: | 11/16/1981 |
| From: | Rich Smith VERMONT YANKEE NUCLEAR POWER CORP. |
| To: | Ippolito T Office of Nuclear Reactor Regulation |
| References | |
| FVY-81-164, NUDOCS 8111240339 | |
| Download: ML20038A867 (33) | |
Text
>
VERMONT YAN KEE NUCLEAR POWER CORPORATION SEVENTY SEVEN GROVE STREET 2.C.2.1 RUTLAND.1/ERM O NT 05701 FVY P1-164 REPLY TO:
ENGINEERING OFFICE 1671 WORCESTER ROAD FRAMINGH AM. M ass ACH USETTS 017o1 TELEPHONE 6 6 7+8 7 2-8100 November 16, 1981 h
Y
'b f
CIT'\\!b) %
NLULt
~a i..
5 United States Nuclear Regulatory Commission
!g NOV2 31981* e Washington, D. C.
20555 u.s. ~ as w Mio*1 -Q comissoa Attention: Office of Nuclear Reactor Regulation Cf
?
Mr. T. A. Ippolito, Chief A
O Operating Reactors Branch #2 4
ifQa Division of Licensing
References:
a) License No. DPR-28 (Docket No. 50-271) b) Letter, VYNPC to USNRC, FVY 81-128, dated September 2, 1981 Proposed Change No. 98 c) Letter, USNRC to VYNPC, dated November 10, 1981
Subject:
Response to NRC Questions Regarding FIBWR Computer Code
Dear Sir:
The purpose of this letter is to provide the attached response to the questions transmitted by Reference (c).
We trust this information will enable the staff to complete their I
review of the subject code in a timely manner.
Should you have further l
questions, please contact us.
Very truly yours, VERMONT YANKEE NUCLEAR POWER CORPORATION
/b
$na l
l R. L. Smith l
Licensing Engineer D
sa 81'11240339 811116 "
PDR ADOCK 05000271 P
RESPONSES TO NUCLEAR REGULATORY COMMISSION'S QUESTIONS ON FIBWR COMPUTER CODE
s QUESTION 1: Equation 2-3, spatial acceleration pressure change in single phase unheated region, on Page 7 of the FIBWR topical (Reference 1) is not complete. Please specify the location where the flow area is used to calculate the mass velocity G.
RESPONSE
The mass velocity "G" in Equation 2-3 (Reference 1) is evaluated based on the final flow area. See Equation 4-28 of Reference 2.
a r
5 o
l l
l l
l I
a QUESTION 2: The single phase friction factor is calculated by the Blausius formula with constants A = 0.1892 and B = -0.2041.
This seems to assume a smooth surface in the flow path.
s.
What are the surface roughness and relative roughness of Vermont Yankee fuel cladding and other flow path surfaces?
b.
What are the friction factors using the Blausius correlation compared to those using the Moody correlation in the operating flow range?
c.
How do you justify the assumption of the smooth surface?
RESPONSE
a.
Several attempts were made to locate a reference document that contained the surface roughness or the relative roughness of Vermont Yankee fuel cladding or channel wall surfaces. It was found that this type of information was proprietary to the manufacturer and therefore was not made available to YAEC. However, during a telephone conversation, the manufacturer informally indicated that the surface roughness for these surfaces is in the range of 16-32 micro-inches.
b.
The friction factor
'f' given by the Blausius relationship is, B
f = ARe where A and B = input coefficients Re = single phase Reynolds number.
The values used as input to FIBWR for coefficients A and B are 0.1892 and -0.2041, respectively. In the normal operating range of BWR's the single phase Reynolds number is 5
of the order of 2 x 10,
Using the Blausius relationship, the frictioa factor
'f' will be,
-0.2041 5
f = 0.1892 (2 x 10 )
f = 0.0157 An estimate of the surface roughness that corresponds to a friction factor of 0.0157 can be made by using a fit to the Moody curves as given by Equation 4-15 in Reference 2.
A fit to the Moody curves is given by the well-known formula, h + 10 /Re)l/3]
(Eq. 4-15) 6 f = 0.0055 [1.0 + (20000 E/D Reference 2 where E = surface roughness, inches Dh = hydraulic diameter, inches Using the above equation with a friction factor f equal to 0.0157 and Dh equal to 0.5324 inches (hydraulic diameter of 8 x 8R type fuel channel) we have the surface roughness, E = 30 micro-inches or relative roughness E_ = 0.00005 Dh It can be seen that by using the Blausius relationship with A equal to 0.1892 and B equal to -0.2041, the corresponding surface roughness is within the range indicated by the manufacturer. -.
.,...x..
The justification for using the Blausius relationship for c.
calculating the friction factors is provided in response to Question 2b.
Furthermore, the overall delta P calculated by FIBWR, using these models, has compared favorably well with the measured plant data over a wide range of power and flow operating conditions as documented in Section 5.2 of Reference 1.
i l
I l
l
- QUESTION 3: The FIBWR topical indicates that a modified Baroczy two phase friction multiplier is recommended for Vermont Yankee design analysis. Please specify the numerical expression of the modified Baroczy correlation including the mass flux correction factor as functions of property index. How does the two phase multiplier prediction compare to the Baroczy correlation?
RESPONSE
The modified Baroczy correlation incorporated in FIBWR has been taken from RETRAN computer code (Reference 5). A description of the modified Baroczy correlation was taken from Reference 5 and is provided in Appendix A.
It should be pointed out that this modified Baroczy correlation is also used in widely accepted codes such as RELAP4.
4 l
1 I
l _. _..
m QUESTION 4: In local pressure drop calculations, a modified homogeneous two-phase local loss multiplier is used:
Is the empirical constant $ equal to 1.2 used in the design a.
analysis as the value is used in the comparison with the FRIGG Loop data shown in Figures 3-117 b.
In Figures 3-11, the comparison is made only for the bulk boiling region.
In the two-phase multiplier also used in the subcooled boiling region? How does it compare with data?
Why are the homogeneous void relationship and two phase local c.
loss multiplier used in the water tube flow calculation?
The value of the empirical constant % equel to 1.0 was used
RESPONSE
a.
in Vermont Yankee design analysis, strictly as a matter of convenience. This empirical constant is used for determining the two phase form loss multipliers associated with the spacer grids and the upper tie plate. The approach taken in the design analysis was to adjust the "K's" (with $=1.0) associated with the spacer grids and upper tie plate till the calculated pressure drop was equal to the measured pressure drop for Vermont Yankee.
b.
The two-phase multiplier is calculated as a function of flow quality; therefore, it is also used in the subcooled boiling region. In a BWR channel, the subcooled boiling occurs within approximately two feet from the bottom of the heated length assuming normal subcooled inlet conditions. Further, there is only one spacer (out of seven spacers) that is located within the subcooled region for which a local loss multiplier needs to be calculated for determining the local pressure drop. The local two-phase multiplier calculated for this spacer is approximately equal to 1.0 due to small flow quality (see sample problem in Reference 2).
The corresponding local pressure drop associated with this spacer is 2 0.3 psi. Even a 20% change in the local loss multiplier will not have a significant impact on the calculated local w.. _.
. ~..
pressure drop for this spacer. Furthermore, the total pressure drop across a BWR core (for full power / flow conditions) is in the range of 20 - 25 psi; therefore, the impact of local pressure drop associated with the spacer located in the subcooled region would be insignificant.
During normal operation of BWR's, boiling is not expected to c.
occur in the water tubes. If there is any boiling, very low flow qualities would be expected. At these low flow qualities, the effect of different void models on Ap would be insignificant. lherefore, the homogeneous void model was chosen because it provides calculational simplicity. The homogeneous two-phase local loss multiplier model is incorporated to account for two-phase losses in the event that boiling does occur.
a QUESTION 5: A simplified EPRI void fraction model is used but not explicitly described in the FlBWR topical. However, the model is described in the EPRI-FIBWR (Reference 2) report.
a.
Describe how the Equation 4-2 (Reference 2) is derived to calculate the coolant temperature, Tdeparture, at which the subcooled boiling begins.
b.
Does the v.oid departure temperature correspond to the onset of wall voidage or detached voidage?
c.
How do you prove the correctness of the EPRI model prediction of the onset of subcooled boiling since no data is presented?
RESPONSE
a.
The formula for the liquid temperature at the point of net vapor generation is a simplification of the more detailed mechanistic model of Lellouche and Zolotar (Reference 6).
According to the mechanistic model, the vapor generation rate is the sum of three terms representing: 1) wall heating, 2) bulk boiling due to the direct deposition of energy, and 3) flashing or condensation due to transient pressure effects.
The point of initiation of subcooled boiling in steady state is derived by neglecting all but the wall heating term, and then setting the vapor generation rate to zero. This leads to:
9 wall " 9" liquid + h (T, - T )
(1)
~
A y
where:
q" wall
- wall heat flux q" liquid
- heat flux directly to liquid frcm the wall T
- liquid temperature y
h
- Hancox-Nicol heat transfer A
coefficient for condensation T,
- saturation temperature o-Equation (1) simply states that all the wall heat flux goes to the liquid, either directly or through the condensation of vapor.
The total wall heat flux at any point in a heated channel according to the Le11ouche and Zolotar (Reference 6) model is,
+ h (Iw - T )
(2) 9"v,11 = h (3r - T,)
D 1
B P
630 where:
hB" l
e
- Thom nucleate boiling
(.7 2)2 heat transfer coefficient h - Dittus-Boelter convective heat transfer D
coefficient T, - Wall surface temperature The wall heat transferred directly to the liquid is given by Lellouche and Zolotar (Reference 6) as, liquid = h (T* - T )
~
9 D
1 9~11guid "
h D(Ty + T, - 2 T )
(3) 1 where:
T* - vapor film temperature Equations (1), (2) and (3) may be combined to eliminate Ty and q"lig id, yielding an expression for T, the 1
The departure temperature where subcooled boiling begins.
details are algebraic manipulations, and are not reproduced here. The result is Equation 4-2 in the FIBWR report giving the liquiri temperature at the departure point.
b.
The EPRI void model predicts the onset of experimentally observable void fractions. This location is often referred
.-~
n-,
,--,.,--.,..,.c,n..
w,,
n,.-,,-,,.--,.w.
nns-,--,.m,,,
.g
i to as the point of void departure or detachment. For i
further details the reader is referred to the Appendix D of Reference 6.
c.
See response to Question 9.
i l
4 4
i f
f i
i i
a I
F QUESTION 6: In the EPRI void qu> 1ity model, the distribution parameter, C,,
is calculated by the modified Bankoff-Jones correlation.
a.
Provide a figure showing the distribution p.arameter as a function of void fraction and pressure.
- b.
How does the modified Bankoff-Jones model compare to the Bankoff-Jones and Dix models?
c.
Is there an error in the expression of L n Pages 4-6 of N
Reference 2?
RESPONSE
a.
Figure I shows the distribution parameter, C, as a o
function of void fraction,<a>, and pressure.
b.
Figure 2 shows a comparison of C, as a function of void fraction, <a>, as predicted by Bankoff, Dix, and EPRI void models at 1000.0 psia.
c.
There is no error in the expression for L n Pages 4-6 of N
Reference 2.
Ihe distribution parameter, C, goes to zero o
as void fraction,<a>, approaches zero. In order to avoid division by zero in the Fortran expression, L is set N
equal to one when void fraction equals zero. This does not af fect the void fraction calculation because <a> is zero by definition.
- The staff verified that the intent of this question was to provide a figure showing a comparison of C as a function of void fraction as predicted by the EPRI, Bankoff, and die void models.
e-QUESTION 7: In the EPRI void model, the drift velocity, Vgj, is expressed by Equation 4-8, Reference 2.
i Provide a figure showing the drift velocity as a function of s.
pressure and void fraction.
1 b.
How does the result compare to the terminal rise velocity with the coefficient K3 = 2.97 Figure 3 shows the drift velocity, Vgj, as a function of
RESPONSE
a.
pressure and void fraction as predicted by the EPRI void model.
b.
The expression for terminal rise velocity, U, as given in t
Reference 2, Equation 4-6, is, 0.25 Ut=K3 (0, - og) o ggc_
Sin 0, pZg where O = surface tension, lb /ft f
2 g = gravitational constant, 32.174 ft/sec gc = 32.174 lbm - ft e
lbf - cec K3 = experimental c6nstant 0- angle with the horizontal.
l For vertical flow it is often assumed that the drift velocity is proportional to the terminal rise velocity.
The term: aal rise velocity with K3 = 2.9 at various pressure is tabulated below,. _.-..
-. -- - -..., -..... ~.
,... ~....
9 Uc Pressure (psia) 1.284 500 1.188 900 1.165 1000 1.143 1100 1.120 1200 It can be seen from Figure 3 that Vgj predicted by the EPRI roid model varies as a function of void fraction and approaches the correct limit of zero when void fraction approaches unity. On the other hand, the terminal rise velocity, U, with K3 = 2.9 t
is not a function of void fraction.
4 I
{
l l
l l
t -
t
s.
..-._._ =.....-.
QUESTION 8: Paga 20 of Reference 1 states that, based on Figures 3-4 showing void fraction as a function of equilibrium quality from FRIGG Ioop data, "it appears that the two qualities (flow and equilibrium qualities) are equal above 5% quality".
Justify this statement about thermal equilibrium above 5% quality.
RESPONSE
The statement that flow quality approximately equals equilibrium quality above 5% was merely an observation on an " eyeball" review of the FRIGG data. The FIBWR methodology does not make any such assumption based upon the above observation.
QUNSTIW 9: The EPRI void model is only verified against FRIGG Loop dite above 5% quality. It has not been verified for the subcooled boiling region. How do you justify the validity of the model?
RESPONSE
The EPRI void model has been verified against data obtained from FRIGG Loop and CISE as outlined in References 3 and 6.
This data includes both the subcooled and the saturated region. The degree of agreement is well demonstrated by examining Figures 4,5,6, 7,8,9 and Table 1 presented in Reference 3.
I i
l l l l
l
[
..._.._m._...
... ~ _.
..y..
QUESTION 10:
In the FIBWR and COBRA IIIC comparison, the same conservation equations and constitutive equations are used. With the only difference being the steam tables, explain why the pressure drops predicted by the two codes can be different by as much as 10%. If the difference is solely due to the difference in water property calculations, is there any proof that the water property program used in FIBWR is correct?
RESPONSE
In order to understand the possible effect of steam table differences between COBRA IIIC and FIBWR, one must understand how each code obtains fluid properties. In FIBWR, steam tables taken from RELAP4/RETRAN of fluid properties as a function of pressure and temperature are used; while in COBRA, a user input file of saturation properties only are used. Thus, if COBRA desires the value of a iluid property for subcooled water, an interpolation is made in the user input table to obtain the saturated fluid property at the temperature desired. Ihus, COBRA values of fluid properties for subcooled conditions will always be approximate since only saturated fluid properties are used.
An important fluid property for friction pressure drop calculations is the liquid viscosity. A comparison of the COBRA IIIC input table to a printout of FIBWR fluid properties shows that the COBRA value of saturated liquid viscos'ity at 1039 psia is 4% less than the corresponding FIBWR value. Since friction pressure drop is linearly dependent upon fluid viscosity, this translates directly into a 4% pressure drop error. The fluid property errors will be even greater for subcooled conditions for reasons discussed above.
To quantify the effect of the saturated steam table differences, an input entry was added to COBRA at 1039 psia with fluid properties identical to those of FIBWR. With this change in COBRA input, the two codes will have identical satutsted fluid properties at 1039 psia, but COBRA will still use approximate subcooled fluid properties.
The FIBWR to COBRA IIIC comparisons for a BWR fuel assembly as 1
illustrated on Figures 4-4 and 4-5 (Reference 1) were then recalculated with the new COBRA steam table. It was discovered during this investigation that the previous COBRA IIIC to FIBWR comparisons for this fuel assembly had slightly different axial power distributions, and that only 10 axial nodes were used in COBRA IIIC while 24 were used in FIBWR. These differences in the COBRA IIIC model were corrected such that the two codes now have identical axial power profiles, and both use 24 axial nodes.
The BWR fuel assembly was simulated by both codes for a range of inlet mass fluxes. Table 1 lists representative results from both COBRA IIIC and FIBWR. It is seen that the agreement between the two codes is now quite excellent. Figure 4 is a plot of the axial dependence of void fraction for two of the cases on Table 1.
TABLE 1 Fredictions of Pressure Drop and Void Fraction for a BWR Fuel Assembly with Zero Local Losses Mass Heat Pressure Drop Exit Void Fraction Case Flux Flux COBRA IIIC FIBWR COBRA IIIC FIBWR 6lb 6 Btu 10 2
10 2
psi psi hr f t hr f t 1
1.22 0.11 5.03 5.05
.623
.621 2
0.20 0.11 1.44 1.53
.974
.974 3
4.00 0.11 12.4 12.5
.013
.030 I -_
Elli t illllIlllil ill[Illilll t i[Illlilili j ll e llilli jilli t t ill jililililllIllillllllIllli t illlIllillllE O 00 G
-f
=
1.90 E-
==
=
-5
=
1.80 5-E E
AT 1200 N IA j
L AT 1100 PGIA E
1.70 E
AT 1000 PGIA J
E, AT 900 PGIA E
3 'g
=
E
-5
=
1.50 5-
=
E
=
E 1.40 E-
==
=
-E
=
1.30 E-
==
=
5
=
1.20 5-c.10
/h
~N.
1 5
O E
.?
/
E_
1.00 ~r
.' j E_
-5 90 E-
=
=
-5
=
.50 E-
=
E
=
E
-E
.70 E-E E
E E 5 s=
.m e-
=
=
-5
=
.50 :
==
=
-5
=
40 2
=
E
-@=
.30
=
E
-5=
.10 I''Il''''i'I''i''''I''Ii''''II''i'''IfIIIIf'''=
c O.00
.10
.20 30 40 50 00
.70 50 90 1.00 0.00
< ALPHA >
Figure 1. Distribtuion parameter, C, as a function of void fraction,
<a>, and pressure as predScted by EPRI void model.
2.0 E18 318 8 8 ll13 613 3 3 3 3 l13 3 3 3 3 3 3 ll18111113 ll1813 8 3 311ll1111113 8 lI 3181313 3 ll 113 31311ll 18 3 3 311l l18 3 3 I1 I II
=
=
1.90 E-
-3
=
=
=
=
1.50 m-
=
E AT 1000 PGIA E
=
1.70 E-
-a
=
=
DIX
,j 1.53
=-
E SANCFF
=
=
EPRI E
1.50 E-
=
=
=
=
1.40 E-
-e
=
=
=
1.30 E-
-E
=
=
=
1.20 m-
-E-E c.10
~
/
E
, _._ h 1
-e O
=
=
=
5 1.00 R*
p
/
=
=
=
.90 E-
/
-e E
/
=
90 E~
/
E
/
5
.70 's-
/
-E 5
/
5
.M &
f 4
E
/
E
.50
/
=
.=
40 E/
-E E/
E
.30 E-
-e
=
l
=
=
l
.20 E-
=
=
=
=
.10 i-
-E
=
=
f lit tillllIlt lit t ilit tfilit t llillit tli lllll t lltl111111tlll111111lt ll11tliitilli t t iili tiliit tlit tE 0.00 O.00
.10 30 30 40 50 00
.70
.50 90 1.00
< ALPHA >
l Figure 2. Distribution parameter, C. as a function of void fraction, o
<a>, as predicted by BANK 0FF, DIX, and EPRI void model at 1000.0 psia. ___ -- -
1 00 n o n n i n o n i n g i n n u n i n i n u n i n n u i n i n i n u n g n i n u n g o n i n u i n o n n i g n u n n3
=
90 E
-3_
E
AT 1200 PE!A E
AT 1100 Pe!A
=
=
AT 1000 PelA
- 80
=
AT 900 PWIA
=
3 AT 900 PEIA 3
E E
8
.70 E-
-3_
o o
=
=
=
=
a
=
5.ao
-3
=
N.g,
_=
3
=
>.so E
-E
=
_=
=
b 3%v.'
40
=
=
=
=
=
_=
=
30 5" i
=
=
=
.20 9
{
=
=
=
_=
=
.iG E-
=
=
=_
p
=
=
in i n n i l u o n n i h n u n n l i n u n n i n n i n n b n n n n li n u n n i n n n i n i n i n n7itrnmui o,oo 0.00
.iG
.ao
.mo 4o
.so
.co
.70
.so
.no 1.0o
<M. FHA >
Drift Velocity, V j, as a function of void fraction,
<a>,
Figure 3.
g and pressure as predicted by EPRI void model.. -.. _. -. _. _ -
Q - FIBWR X - COBRA 3C O
(D 120
( >
/g 100 80 4
4 Axial Q
g Distance g
g (in.)
60 6
44 4
7 40 o
4 4
20 0
20 40 60 80 100 VOID FRACTION FIGURE 4: Cornparison of FIBWR and COBRA 3C Predictions of Void Fraction for a BWR 7 x 7 Fuel Assgmbly, Heat Flux 6
Equals 0.11 x 10 BTU /hr-ft - - - _ - _ _ - _ - _ - _ _ _ _ _ - _ - _ _ _ _
\\
REFERENCES
- 1) Ansari, A.F., " Methods for the Analysis of Boiling Water Reactors, Steady-State Core Flow Distribution Code", YAEC-1234, December 1980.
- 2) "FIBWR: A Steady-State Core Flow Distribution Code for Boiling Water Reactors", Computer Code User's Manual, EPRI NP-1924-CCM, July 1981.
- 3) 1411ouche, C.S., B.A. Zolotar, "A Mechanistic Model for Predicting Two-Phase Void Fraction for' Water in Vertical Tubes, Channels, and Rod Bundles", EPRI, 1980.
- 4) Baroczy, C.J., "A Systematic Correlation for Two-Phase Pressure Drop",
NAA-S R-MEM0-11858, 1966.
- 5) "RETRAN - A Program for One-Dimensional Transient Thermal-Hydraulic Analysis of Complex Fluid Flow System", EPRI-CCM-5, Volume 1, December 1978.
- 6) Lellouche, G.S., B.A. Zolotar, "A Mechanistic Model for Predicting Two-Phase Void Fraction for Water in Vertical Tubes, Channels and Rod Bundles", EPRI, 1981. (Update to Reference 3).
s.
~.
n a
m at 5
1 e
l l
}
APPENDIX A i
5 r=-e
= * * -w-s--*
a+-%_m.g,a m,-e g
_e,e e,,_,=e_
e 1.1.2 Baroczy Correlation The correlation of Baroczy[III.1-6,111.1-7] incorporates a mass flux correction factor for the friction mul'tiplier. The Baroczy correlation is made up of two The first set of curves consists of the friction sets of curves as follows.
0 2
The multi-multiplier, $ p, at a reference mass flux of I x 10 lb,/hr-ft.
2 plier is given as a function of a physical property index 7
30.2 r = (b b,
(III.1-19)
Pts gs, The mass flux correction with the thermodynamic quality, x, as a parameter.
factor, F, is also expressed as a function of r with quality as a parameter.
g 6
s The correction factors were obtained for mass flux values of 0.25 x 10,
')
6 6
6 2
0.50 x 10 2.0 x 10, and 3.0 x 10 lb,/hr-ft.
The Baroczy correlation included in RETRAN has been modified in the following The physical property parameter, r of Equation 111.1-19, has been manner.
converted to an equivalent pressure for the saturated steam-saturated ifquid The numerical values of the friction multiplier at the reference water case.
mass flux G = 1.0 x 10 lb,/hr-f t have been changed from the original values 6
6 2
2 at G = 1.0 x 10 lb,/hr-f t which are used given by Baroczy. The values of $ p in RETRAN are given in Table 111.1-1. The values of the mass flux correction j
6 6
6 6
j factor, F, for G = 0.25 x 10, 0.50 x 10, 2.0 x 10, and 3.0 x 10 k are given in Tables III.1-2 through III.1-5, respectively. Linear lb,/hr-f t 6
extrapolation is used for values of the mass flux le'ss than 0.25 x 10 lb,/hr-6 and and linear interpolation is used for mars flux values between 0.25 x 10 2
ft 6
2 3.0 x 10 lb,/hr-ft. For mass fluxes greater than 3 x 10 lb,/hr-ft, the mass 6
2 flux correction is given by 44 e
III-6
v e
b TA8tE 111.1-1 RETRAN VALUES OF THE MODIFIED BAROCZY TWO-PHASE FRICTION MULTIPLIER 6
2 AT G = 1.0 x 10 lb,/hr-ft Prop Index{gjy Thermodynamic Quality r 0.001 0.010 0.020 0.050 0.10 0.15 0.20 0.30 0.40 8.50 0.60 0.70 ' O.90 1.00 0.001 2.11 8.8 15.0 33.5 68 108 150 233 330 500 690 880 1080 1000 0.002 2.09 8.5 14.2 29.5 50 73 96 141 190 276 360 470 560 500 0.003 2,02 8.1 13.2 26.2 41 58 73 105 138 195 255 322 390 333 0.005 1.97 7.1 11.2 22 31 43 53 72 01 125 160 202 243 200 0.007 1.83
- 5. 9 9.1 17.2 25 35 42 56 68 93 116-148 172 143 0.008 1.77 5.5 8.2 15.7 23 32 39 51 62 83 102 130 152 125 0.009 1.69 5.1 7.6 14 21 29.5 35.7 46.5 56 75 93 117 136 111 0.010 1.60 4.7 7.0 12.8 19.2 27.5 33 43 51.5 69 84 106 121 100 0.020 1.24
- 2. 5 3.6 6.6 11 15.8 19 25 29.5 38 44 54 57.5 50 7'
3.03 1.14 1.88 2.55 4.6
- 7. 6 11 13.2 17.8 20.5 27 30 35.5 38 33.3 3.05 1.10 1.50 1.89 3.15 4.6 6.6 8.2 11 13 15.3 18.5 21 22.2 20 l
0,07 1.08 1.35 1.68 2.55 3.6 4.8 5.8 7.8 9.3 12 13.3 15 15.7 14.3 0.08 1.08 1.31 1.60 2.4 3.25 4.2 5.1 6.8 8.1 10.5 11.8 13 13.6 12.5 0.09 1.07 1.28 1.55 2.25 3.05 3.85 4.5 6.1 7.2 9.4 10.4 11.3 12.0 11.1 0.10 1.07 1.26 1.51 2.12 2.82 3.55 4.2 5.5 6.6 8.5 9.4 10.2 10.8 10.0 0.20 1.04 1.15 1.31 1.61 1.95 2.23 2.55 3.0 3.34 4.2 4.8 5.1 5.25
- 5. 0 0.3 1.02 1.10 1.21 1.40 1.63 1.8 1.92 2.2 2.5 2.9 3.2 3.35 3.42 3.33 0.5 1.02 1.06 1.11 1.20 1.31 1.40 1.45 1.55 1.64 1.82 1.93
- 2. 0 2.02 2.0 0.7 1.01 1.03 1.05 1.10 1.15 1.20 1.22 1.24 1.28 1.34 1.40 1.42 1.43 1.43 0.8 1.01 1.02 1.03 1.06 1.10 1.12 1.13 1.14 1.15 1.20 1.22 1.24 - 1.25 1.25 0.9 1.00 1.01 1.01 1.02 1.04 1.05 1.06 1.07 1.07 1.08 1.09 1.11 1.11 1.11 l
0.2 i-I ).. Property Index, F = ( $8) 35 p
p where p = dynamic viscosity P
gs ts p = density 1 = liquid g = gas s = saturation h
s f
f a
p..-
TABLE III.1-2 RETRAN VALUES OF THE BAROCZY MASS FLUX CORRECTION FAC 6
2 AT G = 0.25 x 10 lb,/hr-ft Thermodynamic Quality Inde c 0.001 0.010 0.050 0.10 0.20 0.40 0.60 0.80 1.00__
Proper *.y 0.001 1.40 1.40 1.30 1.493 1.493 1.36 1.255 1.13 1.0 0.002 1.268 1.268 1.15 1.457 1.457 1.306 1.197 1.114 1.0 0.003 1.19 1.19 1.061 1.435 1.435 1.274 1.162 1.106 1.0 0.005 1.168 1.168 1.037 1.41 1.41 1.24 1.140 1.098 1.0 0.007 1.173 1.173 1.082 1.392 1.392 1.253 1.142 1.091 1.0 0.008 1.177 1.178 1.101 1.388 1.388 1.26 1.143 1.09.
1.0 0.009 1.179 1.184 1.120 1.382 1.382 1.264 1.144 1.09 1.0 0.010 1.181 1.191 1.135 1.379 1.379 1.268 1.145 1.089 1.0 0.020 1.193 1.236 1.235 1.363 1.363 1.295 1.151 1.087 1.0 0.03 1.201 1.262 1.293 1.371 1.371 1.31 1.153 1.084 1.0 1.212 1.295 1.369 1.41 1.41 1.33 1,16 1.081 1.0 0
0.07 1.20 1.283 1.417 1.18 1.48 1.35 1.165 1.08 1.0 0.08 1.19 1.268 1.435 1.516 1.516 1.36,
1.17 1.08 1.0 O.05 0.09 1.181 1.25 1.452 1.55 1.55 1.37 1.174 1.08 1.0 0.10 1.172 1.238 1.469 1.582 1.582 1.379 1.179 1.079 1.0 0.20 1.120 1.151 1.540 1.77 1.77 1.416 1.189 1.07 1.0 0.3 1.091 1.113 1.40 1.59 1.59 1.309 1.15 1.053 1.0 0.5 1.054 1.067 1.232 1.34 1.34 1.179 1.087 1.031 1.0 0.7 1.03 1.034 1.12 1.178 1.178 1.092 1.045 1.017 1.0 0.8 1.02 1.021 1.077 1.113 1.113 1.059 1.029 1.01 1.0 0.9 1.31 1.011 1.038 1.055 1.055 1.029 1.014 1.005 120 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 t
j...
j wi s
g
..,s' TABLE III.1-3 RETRAN VALUES OF THE BAROCZY MASS FLUX CORRECTION FACTOR 0
2 AT G = 0.50 x 10 lb,/hr-f t Property Thermodynamic Quality i
Index r 0.001 0.010 0.050 0.10 0.20 0.40 0.60 0.80 1.00 0.001 1.205 1.288 1.205 1.28 1.27 1.20 1.155 1.088 1.0 0.002 1.17 1.269 1.17 1.276 1.249 1.176 1.13 1.08 1.0 0.003 1.149 1.259 1.149 1.271 1.237 1.161 1.118 1.074 1.0 0.005 1.13 1.245 1.13 1.263 1.23 1.157 1.109 1.07 1.0 0.007 1.127 1.234 1.137 1.258 1.23 1.168 1.11 1.071 1.0 0.008 1.124 1.229 1.14 1.254 1.23 1.171 1.11 1.071 1.0 0.009 1.122 1.224 1.146 1.251 1.231 1.176 1.11 1.071 1.0 O.010 1.12 1.22 1.15 1.25 1.231 1.18 1.11 1.072 1.0 O.020 1.112 1.191 1.175 1.237 1.236 1.202 1.15 1.076 1.0 i
ll 0.03 1.107 1.176 1.19 1.229 1.239 1.216 1.2 1.079 1.0 7
0.05 1.100 1.154 1.21 1.22 1.246 1.235 1.27 1.08 1.0 0.07 1.092 1.141 1.23 1.254 1.3 1.245 1.32 1.078 1.0 0.08 1.09 1.134 1.24 1.277 1.337 1.253 1.36 1.075 1.0 0.9 1.088 1.128 1.25 1.297 1.369 1.262 1.4 1.073 1.0 0.10 1.085 1.121 1.259 1.314 1.398 1.27 1.42 1.07 1.0 0.20 1.07 1.085 1.31 1.427 1.56 1.31 1.6 1.059 1.0 0.2 1.06 1.063 1.231 1.33 1.422 1.231 1.2 1.043 1.0 0.5 1.037 1.037 1.133 1.188 1.242 1.133 1.07 1.025 1.0 0.7 1.019 1.019 1.069 1.096 1.123 1.069 1.035 1.012 1.0 1
0.8 1.01 1.01 1.042 1.06 1.078 1.042 1.021 1.007 1.0 0.9 1.004 1.004 1.021 1.029 1.037 1.021 1.01 1.003 1.0 i
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 j.g 4 *..g k
h
,+
r.". g'. :
^
. s a.... ;..,ld$, e.5G i..c.,,....'..$ U.M.9......
,,..a.-.-..
, - - ~,
TABLE 111.1-4 RETRAN VALUES OF,THE BAROCZY MASS FLUX CORRECTION FACTOR 6
2 AT G = 2.0 x 10 lb,/hr-ft Thermodynamic Quality Index r 0.001 0.010 0.050 0.10 0.20 0.40 0.60 0.80 1.00 _
Property 0.001 0.810 0.700 0.720 0.732 0.740 0.790 0.838 0.920 1.0 0.002 0.835 0.687 0.704 0.728 0.748 0.799 0.848 0.923 1.0 0.003 0.850 0.680 0.697 0.725 0.751 0.804 0.855 0.928 1.0 0.005 0.863 0.690 0.700 0.728 0.755 0.800 0.848 0.919 1.0 0.007 0.870 0.715 0.715 0.738 0.758 0.789 0.830 0.902 1.0 0.008 0.872 0.825 0.720 0.742 0.759 0.782 0.821 0.898-1.0 0.010 0.874 0.741 0.730 0.750 0.760 0.775 0.810 0.888 1.0 0.020 0.885 0.792 0.758 0.773 0.768 0.750 0.770 0.858 1.0 0.03 0.891 0.822 0.773 0.787 0.770 0.731 0.748 0.840 1.0 0.05 0.900 0.860 0.794 0.803 0.775 0.710 0.720 0.816 1.0 7
0.07 0.913 0.880 0.795 0.795 0.750 0.700 0.700 0.795 1.0 0.08 0.920 0.884 0.792 0.785 0.735 0.685 0.685 0.785 1.0 0.09 0.925 0.889 0.790 0.778 0.722 0.670 0.670 0.778 1.0 g
0.10 0.929
-0.891 0.788 0.770 0.710 0.660 0.660 0.770 1.0 O.20 0.960 0.911 0.770 0.720 0.640 0.585 0.585 0.720 1.0 0.3 0.969 0.933 0.830 0.787 0.728 0.687 0.687 0.787 1.0 O.4 0.975 0.950 0.870 0.840 0.792 0.760 0.760 0.840 1.0 l
0.6 0.987 0.971 0.928 0.910 0.883 0.868 0.868 0.910 1.0 0.8 0.993 0.989 0.968 0.961 0.948 0.942 0.942 0.961 1.0 0.9 0.997 0.995
-0.983 0.980 0.975 0.974 0.974 0.980 1.0
[
1.0 1.0 1.0 1.0 1.0
. 1. 0 1.0 1.0 1.0 1.0 e.
l 3
.e l
i s
3 o
u.-
,e
" " ' ~
TA8tE 111.1-5 RETRAN VALUES OF THE BAROCZY MASS FLUX CORRECTION FACTOR 6
2 AT G = 3.0 x 10 lb,/hr-f t The - dynamic Quality Property Index r 0.001 0.010 0.050 0.10 0.20 0.40 0.60 0.80 1.00 0.001 0.710 0.550 0.570 0.613 0.600 0.680 0.751.
0.835 1.0 t
0.002
.0.742 0.520 0.540 0.600 0.610 0.690 0.768 0.835 1.0 0.003 0.762 0.502 0.520 0.590 0.614 0.696 0.776 0.870 1.0 0.005 0.788 0.514 0.523 0.600 0.619 0.686 0.755 0.852 1.0 0.007 0.798 0.554 0.546 0.612 0.620 0.667 0.727 0.830 1.0 0.008 0.801 0.570 0.554 0.620 0.621 0.660 0.715 0.820 1.0 0.009 0.806 0.582 0.562 0.622 0.622 0.650 0.704 0.811 1.0 0.010 0.810 0.595 0.570 0.626 0.623 0.645 0.695 0.803 1.0 0.020 0.832 0.677 0.617 0.654 0.630 0.603 0.635 0.753 1.0
/l 0.03 0.848 0.725 0.644 0.670 0.634 0.580 0.600 0.725 1.0 7
0.05 0.868 0.787 0.680 0.691 0.640 0.550 0.556 0.690 1.0
[*
0.07 0.887 0.818 0.690 0.690 0.620 0.530 0.530 0.663 1.0 0.08 0.894 0.827 0.690 0.685 0.610 0.520 0.520 0.654 1.0 0.09 0.900 0.833 0.690 0.680 0.600 0.515 0.515 0.648 1.0
.i 6
0.10 0.906 0.840 0.690 0.675 0.593 0.510 0.510 0.640 1.0 i
0.20 0.945 0.882 0.690 0.650 0.560 0.475 0.475 0.603 1.0 1
0.3 0.960 0.913 0.770 0.740 0.670 0.610 0.610 0.702 1.0 0.4 0.970 0.935 0.825 0.800 0.750 0.700 0.700 0.773 1.0 0.5 0.978 0.950 0.868 0.850 0.810 0.775 0.775 0.830 1.0 0.7 0.989 0.973 0.931 0.924 0.900 0.885 0.885 0.910 1.0 i
0.8 0.992 0.983 0.957 0.952 0.940 0.928 0.928 0.945 1.0 0.9 0.996 0.991 0.979 0.975 0.975 0.968 0.968 0.975 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
.-..v i'
.Eh
at G = 3 x 10 )(G/106 - 2) 6 g
(G/106 > 3). (111.1-20)
(F Ig*
6 (G/106, 3)
,7 (F at G = 2 x 10 )
g
- i One other modification is incorporated into the RETRAN version of the Baroczy 6
Instead of multiplying the two-phase moltiplier for G = 1 x 10 correlation.
by the mass flux correction, the following equation is used.
2 lb,/hr-ft
'2tp,k
- I *
'2
- 1.0 F
(III.1-21) 6 g.
tp,k @lx10 The original Baroczy model is given by
@.g 2
F
'2tp,k
'tp,k G=1x10 6
g g
Comparing Equation III.1-22 with Eqt.atton III.1-21 and examining the basic multipifers given in Table III.1-1 shows the effect of using Equation III.1-22 The modifications which have been incorporated instead of Equation 111.1-21.
l tion have been developed with into the RETRAN version of the Baroczy corre a experimental data in References III.1-8 through III.1-13.
?
4 J
/
......,5...),* % a t**s e
d w
REFERENCES TO APPENDIX A III.1-6 Baroczy, C. J., "A Systematic Correlation for Two-Phase Pressure drop," Chem. Engng. Prog. Symp. Series, g,
232-249, 1966.
III.1-7 Baroczy, C.
J., "A Systematic Correlation for TVo-Phase Pressure Drop," NAA-SR-Memo - 11858, 1966.
a III.1-8 Isbin, H.
S., Moen, R.
H., Wickey, R.
O., Mosher, D. R.
and Larson, H.
C., "Two-Phase Steam-Water Pressure Drops,"
Chem. Eng. Symp. Series No. 23, M, 75-84, 1959.
111.1-9 Berkowitz, L., et al., "Results of Wet Steam Cooling Experiments: Pressure Drop, Heat Transfer, and Burnout Measurements with Round Tubes," CISE R27, 1960.
111.1-10 Adorin, N., et al., " Measurements in Annular Tubes with Internal and Bilateral Heating," CISE R31, 1961.
111.1-11 Adorin, N., et al., " Design and Construction of Facility for Hest Transfer Experiments with Wet Steam," CISE R23, 1960.
III.1-12
- Nylund, 0., et al., " Measurements of Hydrodynamic Characteristics, Instability Thresholds, and Burnout Limits for 6-Rod Clusters in Natural and Forced Circulation." FRIGG-1, 1967.
III.1-13
- Nylund, O., et al., " Hydrodynamics and Heat Transfer Measurements on a Full-Scale Simulated 36-Rod Marviken Fuel Element with Uniform Heat Flux Distribution," FRIGG-2, 1968.