ML20151Z122
| ML20151Z122 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 08/13/1998 |
| From: | Fittante R, Gagnon A, Halac K WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML20138L015 | List: |
| References | |
| WCAP-14808-ERR, WCAP-14808-ERR-R05, WCAP-14808-ERR-R5, NUDOCS 9809210165 | |
| Download: ML20151Z122 (64) | |
Text
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WESTINGHOUSE NON-PROPRIETARY CLASS 3 WCAP-14808 Ov REVISION 5 NOTRUMP Final Validation Report for AP600 August 1998 R. L. Fittante A.F.Gagnon K. E. Halac 4
L E. Hochreiter J. Iyengar R. M. Kemper f D. A. Kester
, K. F. McNamee P. E. Meyer R. A. Osterrieder R. F. Wright M. Y. Young 9809210 PDR A hfo!03 PDR
- A Westinghouse Electric Company Energy Systems
, P.O. Box 355 Pittsburgh, PA 15230-0355 fV C 1998 Westinghouse Electric Company All Rights Reserved o:\4292w\4292w-fm.wpf:1b 081198
WESTINGHOUSE NON-PROPRIETARY CLASS 3
! WCAP-14808 l t/ REVISION 5 NOTRUMP Final Validation Report for AP600 Volume 2 ,
August 1998 R. L. Fittante A. F. Gagnon K. E. Halac '
L. E. Hochreiter J. Iyengar p R. M. Keinper V D. A. Kester K. F. McNamee P. E. Meyer R. A. Osterrieder R. F. Wright M. Y. Young Westinghouse Electric Company Energy Systems P.O. Box 355 Pittsburgh, PA 15230-0355 e C 1998 Westinghouse Electric Company All Rights Reserved o:\4292w\4292w-fm.wpf:1b@l198
l i
WESTINGHOUSE NON-PROPRIETARY CLASS 3 WCAP-14808 h i (V REVISION 5 1
NOTRUMP Final Validation .
l Report for AP600 l l
Volume 3 August 1998 I l
l R. L. Fittante A.F.Gagnon K. E. Halac L. E. Hochreiter J. Iyengar
,q R. M. Kemper V D. A. Kester K. F. McNamee P. E. Meyer R. A. Osterrieder R. F. Wright M. Y. Young Westinghouse Electric Company Energy Systems P.O. Box 355 Pittsburgh, PA 15230-0355
[)
N
@ 1998 Westinghouse Electric Company All Rights Reserved 0:\4292w\4292w-fm.wpf:1b 081198
._ _ _ . _ _ _ _ _. -_ _ _ . . _ _ . _ _ . _ _ . _ - _ _ _ _ . . _ _ _ _ _ . _ _ . ~ .
, s 1.7 Two Phase Flow Model .
To calculate the vapor and liquid flow rates, NOTRUMP solves a mixture momentum equation and uses constitutive relationships (referred to here as a " drift flux model") to separate the mixture into its vapor and liquid components.
1.7,1 Model Description a). Mixture momentum equation f The one-dimensional mixture momentum equation for a vertical pipe can be written (Reference 1-3):
BG u+1 BApuUu
+
1 BAp,U,' dP P,t, (j7-3)
=- - pug
& A dx A dx dx A i
where the subscript M denotes mixture, w denotes wall, U, denotes relative velocity (ft/sec), and:
a(l - a)p,p (1.7-2a)
P, =
Pu
- - Gu= puU, (1.7-2b) .
where the ' subscript v denotes the vapor region and I denotes the liquid region.
The second and third terms on the left-hand side are the momentum flux terms due to area change and mixture velocity and density gradients, including the effects of relative velocity between the phases.
In the NO' RUMP application to AP600, these momentum flux terms are ignored. His assumption is j evaluated in Section 1.7.5.
1 The w. don term in two-phase flow (second term on the right-hand side) for flow qualities up to j 3 90 peicent .. . valuated in NOTRUMP by assuming that the flow is all liquid, then applying a two- l phase fiction multiplier:
2
'dP' , P,t,.I't' G 2 (1.7-3)
,dz,, A 2,Da p, where f is the friction factor and D is the pipe diameter (ft.). De correlation used for two-phase l hydraulic loss is discussed in Section 1.9. For flow qualities above 90 percent, a linear transition is q assumed to all vapor flow (Section 2.16).
I' -
- July 1998 1
oM292wW292w.l.wpf:lb-081098 1,7 1 Rev.5 1.
With the above simplifications and after integrating over a flowlink length Ax, the NOTRUMP momentum equation becomes:
DGu , _ g p _ l 'gAx'_ 43 2
-P g Ax (I'7~4) 8t 2,D, p, I
A more convenient form of the momentum equation for numerical solution is in terms of volumetric flow. Consider the phasic mass conservation equations:
3GP, 1 BAap,U, , ,
Bt A 8x (1.7 Sa)
(1.7-5b)
B(1 - a)p, + 1 BA(1 - a)p,U, _ pu 8t A 8x Where F" is the vapor generation rate per unit volume (lb/ft.'/sec.).
Expand the phase conservation equations as follows:
da Sp, p, BAaU, Op, l
P 7 +G7+A dx ' 8x (1.7-6a)
O (1.7-6b) p'B(1dt
-a) + (18t- a)_p, ___
A
+dxp, BA(1 - a)U, + (1 - a)U, dxSp, = - F" l
l Then, dividing by vapor and liquid density respectively, noting that the da/dt's cancel, assuming that the rate of change of phase densities is small, and adding results in the volumetric flow equation:
1 l < ,
1 1 BA) , pu I _1 (1.7-7)
A dx , p, p,,
l I
The types of transients to which NOTRUMP is applied involve relatively slow depressurization transients, with insignificant vapor superheating, so that the assumption of nearly uniform phase density is reasonable. It can be seen from Equation 1.7-7 that, if the vapor generation rate is also small, the volumetric flow is insensitive to vapor fraction gradients, unlike the mass flow rate. This means that the volumetric flux at a node boundary remains constant, even though the density at the boundary may undergo a discontinuous change. It is therefore advantageous to solve the momentum equation in terms of volumetric flow (see Section 2.4 for coding details). The approach taken and assumptions made are discussed after introduction of the drift flux model in the next section.
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l b) Drift flux model Define the volumetric flux of vapor and liquid, j, and ji tft/sec.), and relative velocity U, in terms of the local velocities U, and Ui (ft/sec.):
j,=aU, (1.7-8a)
.i j, = (1 - a)U, (1.7-8b)
U, = U, - U, (1.7-8c) i l
i The vapor fraction a is the fraction of the local volume taken up by the vapor phase. i Also define the mixture volumetric flux j, as: l j = j, + j, (1.7-9) l Another relative quantity often used is the drift velocity, V,. This is defined as the velocity of the vapor U, relative to the volumetric flux j. It can be shown using the above equations that:
k V, = U, -j = (1 - a)U, (l.7 10)
- Rearrangement then gives the following basic equations of the drift flux model in terms of the drift j velocity:
j, = aj + aV, (1.7-I la) j, = (1 - a)j - uV, (1.7-11b)
The above equations are definitions that apply locally. To use these equations in real situations, they )
must be cast in forms that apply over the entire pipe. Variations in local vapor fraction and mixture velocity across the pipe now become important, and complicate the drift flux equations. How this averaging and separating is done depends to some extent on the flow regime being considered. For example, Equations 1.7-Ila and 1.7-1lb can be averaged as follows (Reference 1-4):
(j,) = (aj) + (aV,) (1.7-12a)
(j,) = ((1- a)j) -(nV,) (1.7-12b) i Define a distribution parameter C, as:
l C/
July 1998 OM292wW292w.l.wpf;lb 081098 1,73 Rev.5
C, = <"l> (1.7-13)
<cz><j >
Applying averaging to the second term of Equations 1.7-12a and 1.7-12b results in a weighted average drift velocity:
< 2 (1.7-14a)
<aV*> = <a> <a>
= <ax <Vy >
= <ax(1 - a)U,>
Introducing Equations 1.7-13 and 1.7-14c into Equations 1.7-12a and 1.7-12b gives:
<j,> = C,<a> <j> + <cr> <<Vy> (1.7-15a)
<j,> = (1 - C,<a>)<j> - <n> <<V,>> (1.7-1 Sb)
When the phases are highly separated, such as in annular flow, averaging across the pipe using l Equation 1.7-13 leads to C,=1.0. In these situations, it is sometimes more convenient to use an average drift velocity defined by:
<Vp = (1 - <a>)<U,> (1.7-16)
The corresponding drift flux equations are: )
<j,> = <a> <j> + <n> <Vp (1.7-17a) l l'
<jp = (1 - <a>)<j> - <a> <Vp (1.7 17b) l l "Ihe expression for mass velocity in the pipe becomes:
Gu= (p, - Ap<a>) <j> - Ap <a> <Vp (1.7-18)
In the following sections, it is useful to compare the various drift flux expressions on the same basis.
From Eqaations 1.7-15a/b and 1.7-17a/b, <V,> can be related to <<V,>> by:
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1.7.3 - Vertical Flow Models
,' Y a) Low vapor fraction concurrent flow For a variety of low void fraction conditions. it is found that the drift velocity is a simple function of
]
the phasic properties if the effects of variations in fluid conditions across the pipe are accounted for.
This is the case for a variety of flow regimes such as bubbly, slug, and churn turbulent flow (Reference 1-4). C, in Equation 1.7-13 varies from 1.1 to about 1.3, and <<Vg>> can be expressed by two equations, one of which applies in small diameter pipes in which slug flow can occur, and one in larger diameter pipes where churn turbulent flow is likely:
un ;
EApD
<<Vgp> = 0.35 (1.7-21a) )
Pi j l/4 U80E
<<V,p> = 1.53 (1.7-21b) j Pi 1
Several investigators have correlated vapor fraction in pools. For example, Sudo (Reference 1-5) p expressed vapor fraction as a function of several property groups and vapor volumetric flux to some ld power, assuming that the liquid volumetric flux was negligible in comparison to the vapor flux. He found that the assumption of negligible liquid flux is reasonable for values up to about I ftisec. He data range for this correlation is I to 100 atmospheres, and 0.2 to 1.5 ft. diameter. An earlier conelation, derived using similar assumptions, is the Yeh correlation (Reference 1-6), which is used in NOTRUMP. De Yeh correlation is based on rod bundle data, while the Sudo correlation is based l
primarily on pipes of various diameters. These correlations are compared in Figure 1.7-1. It can be l seen that the Yeh correlation agrees reasonably well at low to moderate vapor fractions with the more l recent Sudo model. He lower vapor fraction at low values of j, is expected due to the open nature i
of the tube bundle, allowing for larger bubbles and larger drift velocities. Although the Sudo l correlation database does not extend to diameters typical of some of the AP600 components, l extrapolation indicates lower vapor fraction for a given vapor flux, consistent with Yeh. The Sudo l model indicates a likely change in flow regime for void fractions exceeding about 0.6 (the flat portion
! of the curve). Above a volumetric flux of about 20 ft/sec., the Yeh correlation may overpredict the vapor fraction.
l l These void fraction corlelations, which are usually in the form a = Cjf, can be put in forms convenient for use in the drift flux model, as long as the vapor fraction is relatively low and the liquid flux is small compared to the vapor flux. Using Equation 1.7-17a, the following equation is obtained (Section 2.3 includes additional coding details):
i July 1998 eM292ww292w.l.wpf;1b 081098 1.7-6 Rev.5
<Vg> = Vg>> + (C, - 1)<j> (1.7-19)
In the following text, the brackets around the fluxes and the vapor fraction are removed. The brackets around the two forms of the drift velocity are retained.
From Equation 1.718, the rate of change of mass flow obtained through the momentum equation is recast in terms of the rate of change of volumetric flow (Section 2.4 contains additional coding details):
BApuU u _
BAj (1.7-20) at at where transient changes in drift velocity, vapor fraction, and phase density are assumed negligible compared to changes in volumetric flow. Note that these conditions should be approximately tme because the drift flux model relies on drift velocities derived from steady state tests.
1.7.2 Constitutive Relationships In the next subsections, the forms chosen for the drift velocity and C, are described. Since the drift flux model must be applied to upward and downward flow in vertical pipes, and also to flow in horizontal pipes, applicable correlations must be used.
In terms of geometry, there an: two distinct regians in which two-phase flow must be modeled in the AP600. Fitst, there are various pipes of both vertical and horizontal orientation, ranging from less than 1 in. in diameter to over 2 ft. Since these components contain the most significant hydraulic resistances, the highest mixture velocities are through these pipes.
Another group of components includes large diameter vessels in which pools of two-phase mixture reside. These are all at least several feet in diameter. Because the volumetric flow through the system is roughly conserved and is limited by the piping, fluid velocities in these regions are substantially l smaller, and phase separation is more extensive.
The objective of the following subsections is to describe the basis for the drift flux models used in NOTRUMP for flow in vertical and horizontal pipes. Several simple models are described that, though not used explicitly in the NOTRUMP application to AP600, serve to cladfy certain features and simplify assumptions of the drift flux model.
O July 1998 o:W292ww292w-l.wpf:Ib-081098 l,7 5 Rev.5
l 1
l l Qh ,
f,,p,U,2 2, (1.7-25a) f,p,U,2 (1.7-25b)
T' =
2 Wallis (Reference 1-9) developed an expression for the interfacial friction factor that is widely used in l these types of applications, and that visualizes an increasingly thick liquid film as equivalent to an l increasingly rough pipe-i f,= 0.005[1 + 75(1 - a)) (1.7 26)
A solution of Equation 1.7-24 to obtain the relative velocity was derived by Ishii (Reference 1-8).
He complete equations do not have a simple form, but Ishii simplified them to yield the following equation for <Vp:
<Vg> = I-G p EApD(1 - a) (1.7-27)
I S 0.015p, l a+ 4/p/p, C, can be defined for this flow regime so that Equation 1.7-27 can be put in a form consistent with Equations 1.7-15a/b. C, and <<Vp> for annular flow, using Equation 1.7-19 are:
I~"
C,, = 1 +
a+ 4/p/p, (l.7-28a) 1 -a gApD(1 -a) (1.7-28b)
<<V,p> =
0.015p, a+ 4/p/p, 3 While the annular C, and <<Vp> are obtained differently from the low void fraction form described by Equations 1.7-13 and 1.7-14c, these tenns are both describing the same thing: the slip of one phase relative to the other, in addition to the drift of vapor relative to the mixture as a whole.
De EPRI correlation fits functional forms of C, and <<Vp> to a wide range of data in the high j- vapor fraction range, so this model is the preferred approach and is used in NOTRUMP. However, the annular model above is used to highlight certain common features of high vapor fraction flow and is also used to justify certain simplifying assumptions.
i l
July 1998
- c
- W292wM292w.l.wpf;tt>.081098 },7 8 Rev.5
a<V,> = j, - aj (1.7-22a)
<vg> =(1 - a)j/a (1.7-22b)
. (I - G)""' (1.7-22c)
C "'
He EPRI model (Reference 1-7) uses the same basic form of the drift flux model expressed by Equation 1.7-13, but makes the variables <<V,>> and C, functions of the phase fluxes, fluid properties, and hydraulic diameter, and then uses these functions to fit a variety of data. Because of its applicability over a wide range of conditions, the EPRI model is used in modified form in NOTRUMP for nearly all the flow paths in AP600 except for large open areas such as the vessel and CMT. The modifications to the EPRI correlation are based on a review of the model and comparison with the simpler models discussed above and are explained further in a subsequent section.
b) High vapor fraction cocurrent flow At high vapor fractions, the annular flow regime is likely to exist. A model based on an annular film (Reference 1-8) can be used.
Assume an annular film flowing on the inside of a vertical tube. He simplified momentum equations for each phase are:
'dP t,P, (1.7-23a) y + Pv8
- Aa T.,P,3 t,P, (1.7-23b)
-'_dP + p,g' ,
,dx , = A(1 - a) A(1 - a)
Where P, is the interfacial area per unit length (ft.2/ft.), P., is the wall surface area in contact with the liquid (ft.2/ft.), t, is the interfacial shear stress (force per unit interfacial surface, Ibf/ft.') acting on the vapor,and t 3 is the wall shear stress acting on the liquid.
Subtracting one equation from the othe- eliminates the pressure gradient term and results in:
T=,P , t,Pi (1.7-24) 3pg. _ .
A(1 - a) Act(1 - a) t, can be expressed in a form similar to the wall shear stress, except that the relative velocity between the vapor and the liquid film is used:
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. . _ . _ . ~ _ _ _ _ _ _ _ - . - _ . _ _ . _ _ _ . . _ . --m- --_ _
l l i
l l i
, - c) Countercurrent flow I L
L. One of the most important flow regimes the drift flux mbdel must predict is the countercurrent regime. l r'
For situations where condensation is not significant, the most widely accepted flooding model, and that !
l which is used by Westinghouse in safety analysis codes such as NOTRUMP, is based on the Wallis flooding model. The original form of the equation, due to Wallis, is written in dimensionless form as:
j,"*+ m(-jd'8= C l
i (1.7-29a) j,*. b . l' i
! J ;
ApgD l
l $ P, (1.7-29b) 1
- ,., /P/P.ji, h J
l ApgD (1.7-29c)
$ P 1
1 D (1.7-29d) s P.
t O !
The characteristic velocity J (ft/sec.) is assumed to be a function of the tube diameter D. As the tube diameter increases, the liquid volumetric flux that can flow downward against a given upward flux of vapor increases. This type of behavior is usually called J' scaling. The constant C is found to range from 0.7 to 1.0, and the constant m from 0.8 to 1 (Reference 1-10).
Tests at larger scales show that the appropriate length scale for large tubes is not the tube diameter but the Taylor instability wave length:
0 A. (1.7-30)
S AP8 When the diameter length scale in J above is replaced by the Taylor length scale, the following characteristic velocity results:
nu K= CAPE (1.7-31) l 2
(- Pv i.
t L
This characteristic velocity is called the Kutateladze number, and the CCFL behavior under these
[p conditions is called K' scaling. 'Ihe nondimensional fluxes, obtained by replacing J with K in l
Jul 1998 c:W292wW292w.l.wpf:Ib-081098 1.7 9 ev. 5 I
1 1
Equation 1.7 29d. are described as k*. In this case, the liquid downward flux for a given vapor flux remains unchanged as tube diameter increases. For steam / water mixtures ranging from 15 to 1000 psia, K' scaling should apply for tubes larger than 'about 2 to 3 in, in diameter.
I The constant C changes with tube geomi:try at large scale. However, wide variations in geometry do not strongly affect the value of C. For flooding through holes in a plate, for example, tests by Bankoff (Reference 1-11) show that the value of C approaches two for large holes and thick plates typical of those in a PWR.
The constant m has been shown to be primarily a function of end conditions and to vary from 0.65 to 0.8 (Reference 1-11).
In summary, the CCFL data without condensation at small scales (pipe diameter less than 2 in.) can be adequately represented by the following equation and range of constants:
r niu jj8 + (0.8-> 1.0) $ (- j,)'8 = (0.7-+ 1.0) J in (l.7-32)
, P, ,
For large pipes and orifices typical of those in a reactor, the data can be represented by the following
! equation:
, ,iu l j,'8 + (0.7-+ 1.0) S (- j,)in = (l .5-+2.0)K in (l.7-33) t Pv, I When plotted on the (j,)in and (ji)'8 plane, the above equations are straight lines and define the boundary between permitted countercurrent flow and forbidden countercurrent flow. A two-phase flow computer model, be it drift flux or two fluid, should not predict countercurrent flow in the forbidden region.
Several approaches can be taken to derive a CCFL model applicable at all scales (Reference 1-12).
The NOTRUMP vertical CCFL model uses the [. ]" so that a transition takes place between J' and K' scaling as the pipe diameter increases. The constants m and C are 0.7, 1.0 (for small diameter), and 1.79 (for large diameter), respectively, based primarily on large pipe flooding data (Reference 1-13). Equations 1.7-32 and 1.7-33 are used to compare the NOTRUMP flooding predictions using simple pipe models of vanous diameters (Section 3.2).
In the following, the special forms of V e>> and C, are determined, which cause the drift flux model described by Equations 1.7-15a/b to sweep out the Wallis flooding curve as (x is varied, as shown in Figure 1.7-2. In this way, application of the drift flux model leads naturally to the correct limiting rates of countercurrent flow.
July 1998 oM292ww292w.t.wpf:Ib481098 1.7-10 Rev.5
l t
Starting with Equations 1.7-15a/b, and letting a'=uC, and auVp> = J,, eliminate j to yield:
l l (1 - n')j, - a'j,= J, (1.7-34)
!- Use Equation 1.7-33 to describe the flooding curve, and rewrite Equations 1.7-33 and 1.7-34 as:
i j)*+ (- MJ,)in - K/i2= 0 (1.7-35a)
(1 - a')j, - a'j, - J,= 0 (1.7-35b) where:
M,= (0.7)2 3p, (1.7-36a) 3 (1.7-36b) i K,= (l.79)2K
/
'( It is relatively straightforward to show (Reference 1-14) that for the drift flux lines to be tangent to the CCFL curve as a is varied, J, must have the form; a'(1 - a')K* (1.7-37)
J' =
a'+ M,(1 - n')
I A relationship must still be found between n' and a. It is observed (Reference 1-13) in large-scale flooding tests that the point of zero liquid downflow (j, = 0) is defined by a characterisuc vapor velocity and is independent of the vapor fraction (at high vapor fractions). 'Ihis characteristic velocity, l which also defines the constant K, in Equation 1.7-35a, is found to be:
r $ 1/4 K 8= 3.2 08 4 (1.7-38) 2 l 6 E' s i
i.
1 1
4 l
July 1998 oM292wW292w.l.wpf;lb-081098 1,7.] 1 Rev.5
Setting j, to zero in Equation 1.7-35b, and using Equation 1.7-37:
J* a'K* (1.7-39) j,(j,=0) = =
1 - n' a'+ M,(1 - n')
Since j, = aU,, and, at zero liquid penetration, U, = K,:
j,(j,= 0)= aK,= (l.7-40) n'+ M,(1 - a') ,
Thus:
a= (1.7-41) n'+ M,(1 - a')
A multiplier can be defined, called C.,. Using Equations 1.7-37 and 1.7-41:
a' = C,p (1.7-42a)
Me (1.7-42b)
=
C'#
1 + (M, - 1)a C ,K*
< < V ,,> > = (1.7-42c) 1 - C,p Equations 1.7-42b and 1.7-42c describe a drift flux model that sweeps out the CCFL curve as illustrated in Figure 1.7-2 and, at high vapor fraction, predicts a vapor velocity at the liquid holdup point consistent with the Kutateladze number. The C, defined by Equation 1.7-42b is derived in a manner different from those defined by Equation 1.7-13 or Equation 1.7-28a. Here, it is simply the form needed to obtain the proper asymptotic ochavior of the drift flux lines at the liquid hold up point.
Figure 1.7-3 compares C.,(Equation 1.7-28a) and C., as functions of vapor fraction. It can be seen that the behavior is t.imilar, even though C, applies to coeurrent flow. This similarity is taken advantage of when the overall model is summarized.
July 1998 oM292ww292w 1.wpf.lb-o81098 1.7-12 Rev.5
l l
d) Application of EPRI drift Gux model The EPRI drift flux model is used in modified form for 'all vertical pipes in the RCS, as described l below.
The drift velocity and distribution parameters derived from the EPRI correlation, [-
I
]" are compared to the flooding model values [ ]" from Equations 1.7-42b/c, and the [ minimums]" of each are taken. This forces the countercurrent flooding behavior to be bounded by the CCFL curve, as described by Equations 1.7-32 and 1.7-33. Although the EPRI l
l correlation has provision for calculating countercurrent flow, the approach is more complicated, and the CCFL curve is based only on flooding data through orifice plates. Examination of the drift flux i
l lines produced by the EPRI correlation indicates that a larger countercurrent region is permitted by the unmodified EPRI model. De modified model therefore tends to produce more liquid holdup. )
l l
l 1.7.4 Horizontal Flow Models a) Cocurrent flow l Several methods have been used to correct homogeneous flow theory for slip effects in horizontal two-phase flow, or high mass velocity cocurrent vertical flows. Rese methods usually involve flow
!t parameters or a slip ratio to relate flow variables such as flow ' quality or average volumetric flux to the l\ average vapor fraction. The slip ratio is defined as:
1
! < U,> (1 - <ot>)<j,>
S= , (3.7,43)
< U,> <ot><j,>
Thom (Reference 1-15) found that the slip ratio was basically a function of the vapor and liquid density ratio, over a wide range of conditions. The table below summarizes Thom's data.
Slip Ratio in Two-Phase Mixtures Determined by Thom Density Ratio (p, / p,) Slip Ratio 10 1.5 100 2.7 l
l 500 4.2 1000 5.5 t'
\
July 1998 oM292wu292w.l.wpf;1t>081098 1,7-13 Rev.5 i
(
Others (Reference 1-16) have used the flow parameter K, defined as:
a = K . ' .' (l.7-44)
J.+Ji Typical values of K are on the order of 0.8.
Both the slip ratio and the flow parameter can be expressed in terms of a horizontal C,3, defined below:
j,= C,pj (1.7-45a) j,= (1 - C,p)j (1.7-45b)
Substituting Equation 1.7-43 into Equation 1.7-45a:
(1 - a)C,pj (1.7-46) a(1 - C,p)j Rearranging, C, becomes:
S C**= (1.7-47) 1 + (S - 1)u From Equation 1.7-44, K = 1/Co...
The values of C ; nd C .,o calculated from nom's data and from the flow parameter K are plotted in Figure 1.7-4 and are :ompared with the low vapor fraction vertical flow form C , (C,, = 1.2 to 1.3) and the high vapor fraction form, C o.,(Equation 1.7-28a) at atmospheric pressure. It can be seen that the value of C, from the Bankoff model (1/K = 1.25) is similar to that obtained for low vapor fraction vertical flow, and the C,3 obtained from the nom data is similar to the annular flow model, C.,(and from Figure 1.7-3, also to the CCFL model, C.,).
This similarity suggests that both vertical and horizontal concurrent flows can be described with the same model for C,. For low vapor fraction flows, a constant value of 1.25 would apply; for annular or stratified flows, either C,., or C., would apply. When the pipe is in the vertical orientation, the same C, models can be used; only the applicable avg >> term needs to be added. This is what is done in the NOTRUMP code.
O: i July 1998 o W292wW292w.lawpf lb 081098 },7 14 Rev.5
l b) Stratified / countercurrent flow J
~ An important flow regime in horizontal channels is the s'tratified flow regime. In this flow regime, steam can flow countercurrent to the liquid, and there is little interaction between the phases. An j equally imponant aspect of these flows is the point at which the stratified flow regime transitions to a slug or bubbly regime. When the transition occurs, the interfacial drag between liquid and vapor i increases significantly, and the phases are forced to move concurrently.
i De flow regime transition from stratified to slug, or plug flow was investigated for square channels by Wallis and Dobson (Reference 1-17). ney proposed the following criterion:
jl= 0.5a 3 (l.7-48a) 3, ApgD (1.7-48b) s P.
A more complete model for transitions in horizontal flow in circular channels was developed by I Dukler and Taitel (Reference 1-18). An expression similar to that obtained by Wallis was developed for the stratified to intermittent boundary, with the constant replaced by a function of the stratified O water level.
i l
i As pointed out by Takeuchi (Reference 1-19), the stratified to intermittent boundary defined by the above equations is also equivalent to Wallis's solution to the problem of wave stability in horizontal channel flow (Reference 1-9). His solution defines a region of permissible concurrent or countercurrent stratified flow in the j,, ji plane in which waves on the water surface remain stable.
This region is illustrated in Figure 1.7-5. Outside this region, waves become unstable and cause the flow regime to change. Wallis's form of the equation for the wave stability problem is:
j,*n+j,*n,t (1.7-49)
For the Duckler-Taitel flow regime transition, the equation is similar in form, but with different exponents:
j,*n . j,*n, 3 (1.7-50) ne characteristic velocity is assumed to be a function of the cliannel diameter D and is equivalent to J in Equation 1.7-29d. In contrast to vertical flow, this relationship is expected to hold at both small and large scales. His is because interfacial disturbances on a horizontal interface are more stable than 4
on a vertical interface, dee to the additional stabilizing effect of gravity in the horizontal case.
l l
July 1998 l ov292ww292w.la.wpf:Ib-Oslo 9s 1.7-15 Rev.5 l
l l
For the Wallis-Dobson transition, the form is again similar but with different constants and exponents:
j,"+ j," = .707 (l .7-51)
Equations 1.7-49 to 1.7-51 can be used to represent the stratified flow regime transition boundary.
Since Equations 1.7-50 and 1.7-51 more accurately represent the data trends, these are used as benchmarks against which to compare predictions by the NOTRUMP code in Section 3.3.
It should be noted that the limits described by the above equations are stability limits, and as such should be viewed as upper limits to the stratified flow regime. The extent of countercuurrent flow is controlled primarily by the level gradients occurring in the pipe, as described below.
The driving force for horizontal countercurrent flow is assumed to be an initial liquid level difference in the channel, as illustrated in Figure 1.7-11. Positive flow is defined from left to right. The liquid experiences an additional force due to the level difference Ah, which is:
- AApgAh = - A(1 - a)ApgAh (1.7-52)
A balance is achieved when the interfacial drag is sufficient to offset this force. Integrating Equations 1.7-23a and 1.7-23b and assuming that wall shear is negligible results in:
t,P,Ax
-(AP + p,gAh) =
(l.7-53a) uA t'P,Ax (l.7-53b)
- ( AP + pyAh) = -
(1 - a)A This leads to:
t,P,Ax ApgAh = (1.7-54) ct(1 - a)A The interfacial perimeter P, (ft.) is approximately proportional to 4a(1-a)D, reaching a maximum I when the pipe is half full, and going to zero at each extreme. Using Equation 1.7-26 for the interfacial friction factor and rearranging leads to:
O oM292wW292w lawpf:Ib-081098 },7.{6 ey
- - - - - - . ~ . . - - .. .- . . -. ---
l l
O (1 - 00 x Apg(Ah/Ax)D (1 - <x)U' = - (1.7 55)
.04[l + 75(1 - a3], 3 p, For a wide range of vapot fractions at low pressure, the first term on the right hand side is approximately 0.6.
l The simple model developed above indicates that the countercurrent flow drift velocity is likely to be I substantially lower than the limit established by stability limits, unless the level gradient is on the order of 1.0.
As the mixture flow increases, wall shear is likely to become important. In this case, a slip component enters via C , whose form is similar to those obtained for annular flow. To simulate the overall behavior of horizontal flow, the following forms of V, and C, are used:
u (1.7-56a) i 1
r (1.7-56b) i where:
ca "
3 (1.7-57a)
(1.7-57b)
K cA =
APgWAx)D 3 p, As indicated in the previous subsection and demonstrated in Figures 1.7-2 and 1.7-3, the above expression for [ j" represents concurrent stratified and annular flows reasonably well, while the V, drift term accounts for countercurrent stratified flow at low mixture flow rates. 'Ihese forms also result in drift flux lines that sweep out a parabolic countercurrent flow boundary, consistent with the stability limits (although these boundaries are well below the limits defined by Equations 1.7-49, 1.7-50, and 1.7-51).
l July 1998 eM292wu292w-la.wpt:Ib.08109s 1.7 17 Rev.5
1.7.5 Effect of Neglecting Momentum Flux Terms his section provides detailed justification for not includ'mg momentum flux in the NOTRUMP models.
NOTRUMP does not include the second and third terms of Equation 1.7-1. He momentum flux I
terms arise from the acceleration imposed on the flow by density and area changes along the pipe.
Ris can more easily be seen by simplifying the momentum equation to consider steady, horizontal, ,
homogeneous equilibrium flow (the importance of drift or slip effects will be discussed later). The l
pressure gradient in this case is given by:
dP , _ fv, 1 d 1.7-58 dz 2D
' W'
- g _ A dz (W,u
,A, a
+ W ,u ,)
where P is the pressure, f is the friction factor, D is the pipe diameter, W is the mixture mass flow rate (subscripts f and g define the gas and liquid flows), A is the area, y,is the fluid specific volume (1/ density), & is the two phase multiplier, and u is the mixture velocity. Assuming homogeneous (u, = u,) conditions (the importance of drift or slip effects will be discussed later), the momentum equation becomes:
O dP fV, ' W 2 _ W du 1,7 59 E ,_2D ,A, A dz Since u = Wy/A, where v is the mixture specific volume, the velocity derivative can be replaced to
! yield:
l l
2
$dz = b2DG2 d -G28.Gv dz dA A dz, 1.7-60 1
Where G = W/A. The above equation separates the influence of changing specific volume, and changing flow area. In two phase flow, the mixture specific volume is given by:
y = v, + xv,,
where x is the steam quality. Since the phasic specific volumes are functions of pressure only, the i spatial derivative can be split into:
O l l
July 1998 0:W292wW292w.la.wpf:lb-o81098 } ,7.] 8 Rev.5 1
_ _ _ ._ _ . . .. _ _ _ _ . _ . . . ~._.__._ _ __ _ _ _ _ _ . . .
( dy r, dv dv, dP dx dx 1.7 61 o = _ +x _ + v'8 - = (xv, + (1 - x)v,,) _dP + v'8 _
l dz ,dP dP , dz dz 8 dz dz I
i.
! i l where v' means the derivative of specific volume with respect to pressure. Combining the above !
i equations yields the following equation (similar to equation 2.44 of Reference 1-21:
1 l r m fv r 8 dx v dA G2 g $w +v,, g 1.7-62 p
__ = 6 7 s l dz e 1 + G 2 [xy, . (g _x)y,,j This equation shows that the momentum flux terms influence the pressure gradient locally (via the area and quality gradients in the numerator), and globally via the denominator.
l The area change term is accounted for in the NOTRUMP momentum equation by adding an overall ;
l loss factor K to the frictional term which calculates the overall loss in pressure across the area change.
Typically, area changes in the AP600 piping network are abrupt, and therefore introduce additional
! irrecoverable losses which must also be accounted for in the loss factor. Application of the
'%/
l momentum flux term shown above evaluates only the recoverable pressure change, and would not be accurate if applied without the additional or offsetting irrecoverable losses.
The quality gradient term is important where there is boiling due to heat transfer or flashing due to a pressure gradient. If the quality gradient is dominated by boiling from a surface, the energy equation gives:
W ' '8
=q r 1.7-63 dz l where h denotes fluid enthalpy and q'is the local linear heat rate (Btu /ft/s). Expanding the derivative (assuming pressure effects are small), the acceleration effect due to boiling becomes:
v'8 b = ."',8(9 '#A) 1.7-64 sz h, G The momentum flux term may be important during the natural circulation period, where mixture density differences drive the flow. Estimates using typical values indicate this term is comparable to July 1998 o.w292=w292w.itwpr.ib-ostoes 1,7 19 Rev.5
the friction term at low mass velocities in a boiling channel. In NOTRUMP, this component of the overall pressure drop is accounted for via the two phase multiplier correlation, which is derived from a data base which includes data in heated tubes (Reference' l 22, page 57).
NOTRUMP does not account for the increase in the overall pressure gradient resulting from the denominator in Equation 1.7-62. This term is examined in more detail below.
The increase in fluid quality can also be dominated by the pressure gradient. Across an orifice, for example, the fluid enthalpy can be assumed to be fairly constant, such that x = (h-h,)/hr, where h is constant. Therefore:
dx a h-h, dP V 1.7-65 v,, =v,e = r, (h,, + xh,,,) dP s
rs, rs The quality gradient term in this case appears in the denominator such that:
~ ~
dP .
dz 1 + G 2 [x(v', - v,, h', / h,,) + (1 - x)(v', - v,, h', / h,,)]
where as before the h' terms denote derivatives with respect to pressure. The value of the denominator is controlled by mass velocity. At high mass velocities, the denominator becomes less than one and the pressure gradient is increased. The denominator in fact is a measure of the degree to which the flow is approaching critical conditions.
Effect of uneaual phase velocity Equation 1.7-62 and 1.7-66 assume that the liquid and vapor move at the same velocity. Most flows will develop some difference in phasic velocity. 'Ihe effect of this relative velocity on the pressure gradient will be examined. Because the denominator is important at high mass velocities, and the slip ratio (u,/u,) is a more appropriate measure of the flow condition than the relative velocity (u,-u,), the effect of unequal phase velocities will be examined using the slip ratio. The mass velocity can be expressed as (Reference 1-21, Equation 3.17):
O July 1998 I ov292ww292w.tawpt:1b-osto9s 1.7-20 Rev.5
)
)
s A
i t'") r b +( T XIVr
,8 1.7-67 G=
U Ur ss s Let S = u,/ur . Then:
r '4
, r, ,4 1 XV u 1.7-68 G= s + (1 - x)v, = __r.
,U,r ,
S , c, e ,A I u l G= (xv, + S(1 - x)v,]4 = _.s 1 s
U,s c, l
1 a
Now evaluate the inertia term in Equation 1.7-58 assuming constant area and flow to simplify the i derivation, and use the equations above to get:
O l~
L'I 1d IW u + W,u,) = G2 d [xe + (1 - x)c,]
A dzs as dz 1.7-69 i
The expression in square brackets can be rearranged to give:
r 1.7-70 xe, + (1 - x)c, = xv, + (1 - x)v, + x(1 - x) -I v, + (S - 1)v,
.s Assuming the quality and slip ratio are independent of pressure, the denominator in Equation 1.7-62 is now:
r '
q 1 +G2 ye e
. (g _ x)y , x(i _ x) _g ys + (3 _ g)y , )
s 1.7 71
.s s .;
The effect of the additional terms in Equation 1.7-71 relative to the denominator in Equation 1.7-62
) will be examined below, i
Jul 1998 l o34292w\4292w.ltwpf:Ib 081098 },7-21 ev.5 j l
Calculated mass velocities in AP600 Figures 1.7-7 to 1.7-13 of Reference 120 show the vapor and liquid volumetric flux calculated by NOTRUMP in various components of the AP600. Rese figures indicate that mass velocities are generally quite low except in the ADS lines. It should be noted that the velocity shown for the ADS 4 i line is higher than actually calculated in NOTRUMP, because the area used to calculate the velocity l from the code output volumetric flow rate was about 20 percent smaller than was actually utilized in t' 10 TRUMP calculation. Nevertheless, fluid velocities are likely to be on the order of several ht. . .eds of feet per second in these lines. Since the mass velocity is likely to be highest in the ADS lines when the valves are open and critical flow exists at the valves, the importance of the denominator in determining the overall pressure drop will be examined at these locations. For simplicity, the compressibility terms in Equations 1.7-62 and 71 will be evaluated; sample calculations j indicate the quality terms in Equations 1.7-66 are smaller because of the relatively large value of hr,. l Table 1.7-2 lists fluid saturation properties at various pressures, from which the derivatives are obtained as shown. Table 1.7-3 evaluates the denominator at several pressures and qualities for ADSl-3, and Table 1.7 4 does the same for ADS 4 at the lower pressure. For each quality, the mass velocity in the piping approaching the valve is estimated by multiplying the critical mass velocity for the given pressure and quality (using the HEM model) by the area ratio of the valve to the upstream piping. These calculations indicate the following:
a) For ADSI-3, the pressure gradient leading up to the ADS valves could be underestimated by O l as much as 9 percent (the denominator ranges from .91 to .99). However, during the important period of low quality two phase flow, when the mixture level is at the top of the pressurizer, the error is substantially smaller. By itself, this difference is not sufficient to explain the differences between predicted and measured mass flow rates which are observed in some of the OSU tests (see response to RAI 440.721(c)).
b) For ADS 4, where two valves are assumed open, Table 1.7-5 indicates that the pressure gradient could be significantly underpredicted during the initial period just after the valves open, when the pressure is high enough that critical conditions exist. This is because the total valve area is comparable to the upstream piping area.
Figure 1.7-6 shows the effect on the denominator of assuming a slip ratio of 6, for the conditions shown in Table 1.7-4. It can be seen that phase slip increases the value of the denominator, and reduces the effect of acceleration on the pressure gradient. This is consistent with the observation that the Moody critical flow model, which assumes a large slip ratio, predicts a higher critical mass velocity than HEM (i.e., acceleration must be greater to produce large pressure gradients and choked conditions). Derefore, the conditions estimated in Tables 1.7-3 and 4 for homogeneous flow are the most severe to be expected.
July 1998 o.%292ww292w.la.wpf:lb.081098 1,7-22 Rev.5 l 1
N_QTRUMP model for ADS oicine and critical flow Figure 1.7-7 illustrates the noding used to model the ads piping and valves in AP600. The piping from the hot leg or pressurizer to the valve is simulated with a fluid node. A portion of the overall line resistance is allocated to the flow link connected to the pressurizer or hot leg. The local static pressure and enthalpy in the ADS piping node, P, and h , are used in the Henry Fauske and HEM critical flow models to calculate the critical mass velocity (Section 2.17 Reference 1-20). With this modeling, the frictional pressure drop in the piping leading to the ADS valve is accounted for. The HEM mo(* f N applied over the short remaining distance to the valve, where the effect of friction can be ignored. Swever, the NOTRUMP model contains two deficiencies:
a) The model does not account for acceleration effects in calculating the pressure distribution up to the ADS valve (previous sections),
b) The model does not account for the effect of significant upstream kinetic energy on the critical flow calculation.
As indicated in the previous section, lack of momentum flux terms in the momentum equation may result in an underprediction of the pressure drop to the ADS valves. In the next section, the effect of ignoring the kinetic energy terms in the calculation of critical flow is examined.
.(
The HEM critical flow model assumas frictionless adiabatic, steady flow and begins with the following simplified mass, energy and momentum conservation equations:
dW = 0 r 2' d h +."- =0
, 2, dP + pudu = 0 1.7-72 d
' dP +-u' 2
=0
, p 2, where h is the fluid enthalpy. Because the flow is assumed frictionless and adiabatic, the flow is isentropic. Therefore, either the momentum equation or the energy equation can be replaced by:
ds = 0
'O July 1998 oM292ww292w.itwpf:Ib Osl098 1,7 23 Rev.5
In the HEM, the energy and entropy equations are used. The differentials are expanded to give:
u,2 u'o l.7-73 h, +
=h+7 o s, = so where the subscript t represents the conditions at the throat, and the subscript 0 represents conditions at the location where the acceleration to the throat is assumed to begin. Usually this is taken as a location where the kinetic energy is negligible (uo is small). Given the stagnation enthalpy and entropy, the stagnation pressure and the conditions at the throat leading to the maximum mass velocity can be determined. In NOTRUMP, the Henry-Fauske and HEM models consist of a series of tables giving critical mass flux as a function of stagnation enthalpy, and stagnation pressure.
In the modeling of the ADS, the effect of a significant kinetic energy component at the start of the process must be examined. To determine what the appropriate stagnation pressure should be, retain the second form of the momentum equation, and expand the differential to yield:
2 2 dP u, -u o 1.7-74
{ P. ,g Jr. p 2 Assume that an average density can be defined such that:
P. dP , P, - Po 1.7-75 P V Then:
-2 -2 P"i puo 1.7-76 p' , p' .
2 2 This indicates that the " reservoir" pressure should include the recoverable portion of the fluid dynamic pressure at the point where acceleration is to begin.
O July 1998 oM292w\4292w.!a.wpf:lb-081098 },7 24 Rev.5
l l
l l The momentum equation can be written:
l l
djdP +-
u'2
=--
I dP ' dz (1.7.72a) p 2, p dz ,,
- where the term on th
- : right-hand side represents the pressure loss due to friction. His can be ;
approximated as: l i l l
, d P + P" 2 ' = $ ' dz t
, 2, dz,,
Assuming that a location can be found where the dynamic pressure is negligible (location where P =
Po .), then I
I
-- 2 dP (1.7 72b) p* . p2 u. , p** _ R , g (d3 2
The NOTRUMP procedure is to calculate the lo_tal Pressure just upstream of the valve (P, + P- u,)
2 from the hot leg or pressurizer (P,,, where dynamic pressure is negligible), then solve for the critical flow using the total pressure as the reservoir pressure.
Because of the energies and pressures involved, a significant velocity must exist at point 0 before significant error is introduced. For example, at 50 psia the enthalpy of steam is 1174 Btu /lb. For a 1 percent increase in the total enthalpy, the fluid velocity must be about 770 ft/s. His would indicate L that ignoring the kinetic energy terms, as is done in NOTRUMP, would result in negligible error.
To confirm this, an alternate flow calculation was performed on the ADS 4 piping system to compare with the NOTRUMP prediction (as noted previously, the effects of compressibility were determined to I' be most important for this component). For steam flow in a piping system, the effects of
- compressibility can be taken into account by the use of net expansion factors Y (Reference 1-23.
These factors are functions of the pressure difference through thm pipe, and the loss coefficient in the pipe (Figure 1.7-8). The flow rate through the pipe is calculated by the following equation (Equation 1-11, Reference 1-23:
July 1998 c:W292ww292w-la.wpf:Ib-081098 ],7 25 Rev.5
1 l
1 I l l 1 l
W, = 0.525Yd 2 (P n - P,) pmL 1.7-77 h
1 where d is the pipe diameter in inches. 'The calculated flow re.te through both valves assuming compressible conditions is compared with the incompressible result (Y=1) in Figure 1.7-9. To compare with the NOTRUMP AP600 predictions, vapor flow is plotted against hot leg pressure for the ADS 4 pipe in Figure 1.7-10. The NOTRUMP values are seen to remain below the calculated value assuming compressible conditions.
A model of the ADS 4 piping from the hot leg to the valves was developed. His modelincluded integration of the complete momentum and energy equations (assuming steady-state, homogeneous conditions). The NOTRUMP predictions were compared to this model (see response to RAI 440.796F, part (a)). NOTRUMP predicts similar flows through ADS 4 when the het leg pmssure is high enough to result in choked conditions at the valve. At lower pressures, the flow rate predicted by NOTRUMP was about 20 percent higher. His was attributed to underprediction of two-phase pressure drop in some fittings, such as elbows, and lack of acceleration terms, which is still relatively important. In terms of the total vapor released from the time of ADS 4 opening to IRWST injection, the effect was relatively small (about 5 percent).
Conclusion:
It is concluded that NOTRUMP has compensating errors in regions where the fluid acceleration is significant. These errors become significant only in the ADS 4 piping where both valves are open.
The overall effect, however, is to produce a reasonable estimate of the vapor flow through ADS 4 when compared with more detailed models.
O July 1998 c:W292wV292w.la.wpf:Ib-081098 },7 26 key. 5
l l
Table 1.71
- ' FIGURES DEPICTING RESULTS FROM VERTICAL AND HORIZONTAL FLOW MODELS 1
i Figure No. Title
- 1.7 1 Yeh Correlation versus Sudo Correlation l.7 2 CCFL Curve and Tangent Drift Flux Lines 1.7 3 Comparison of Various Forms of C for Vertical Flow Regime 1.7-4 Comparison of C, for Horizontal and Vertical Flow 1.7-5 Flow Regime Transitions in Horizontal Flow 1.7-6 Effect of Slip Ratio on Momentum Flux Equation Denominator 4
1.7 7 NOTRUMP Noding for ADS Valves 1.7-8 Effect of Compressibility on the Calculated 3:lowrate 7hrough a Piping System 1.7-9 Effect of Compressibility on ADS 4 Flow vs. Pressure i
1.7-10 NOTRUMP Predicted Vapor Flow Compared with Reference 123 Calculation l.7 11- Horizontal Stratified Flow with Level Gradient
[ 1.7-12 Flow Regimes in Hot Leg and Cold Leg (High Pressure, Prior to ADS Opening)
^
1.7 13 Flow Regimes in Hot Leg and Cold Leg (Intermediate Pre' :, Just After ADS Opening) 1.7 14 Flow Regimes in Hot Leg and Cold Leg (Low Pressure
, 1.7 15 Flow Regimes in Balance Line (High Pressure, Just Prior to ADS Opening) 1.7 16 Flow Regimes in Balance Line and Pressurizer Surge Line (Intermediate Pressure, Just After ADS Opening)
~
.l.7 17 Flow Regimes in Balance Iine and ADS-4 (Low Pressure) 1.7-18 Flow Regimes in Steam Generator Tubes (High Pressure, Just Prior to ADS Opening)
J 4
July 1998 eM292ww292w-la.wpf:Ib os109s 1.7-27 Rev.5 4
--v., ,., -
i I
Table 1.7 2 WATER SATURATION PROPERTIES AND DERIVATIVES )
PRESS TSAT VF VG VFG HF HG HFG VF VG 40 267.25 0.017151 10.496 10.47885 236.15 1169.8 933.65 0 0 45 274.44 0.017214 9.3988 9.381586 243.52 1172 928.48 1.26E-05 -0.21944 50 281.02 0.017274 8.514 8.496726 250.25 1174.1 923.85 1.2E-05 -0.17696 55 287.08 0.017329 7.785 7.767671 256.4 1175.9 919.5 1.lE-05 -0.1458 60 292.71 0.017383 7.1736 7.156217 262.2 1177.6 915.4 1.08E-05 -0.12228 90 320.28 0.017659 4.8953 4.877641 290.7 1185.3 894.6 0 0 95 324.13 0.0177 4.6514 4.6337 294.7 1186.2 891.5 8.2E-05 -0.04878 100 327.82 0.01774 4.431 4.41326 298.5 1187.2 888.7 8E-06 -0.M408 110 334.79 0.01782 4.0484 4.03058 305.8 1188.9 883.1 8E-06 -0.03826 120 341.27 0.01789 3.7275 3.70961 312.6 1190.4 877.8 7E-06 -0.03209 420 449.4 0.01942 1.1057 1.08628 429.6 1204.7 775.1 0 0
^
460 458.5 0.01959 1.0092 0.98961 439.8 1204.8 765 4.25E-06 -0.00241 500 467.01 0.01975 0.9276 0.90785 449.5 1204.7 755.2 4E-06 -0.00204 540 475.01 0.0199 0.8577 0.8378 458.7 12N.4 745.7 3.75E-06 -0.00175 580 482.57 0.02006 0.7971 0.77704 467.5 1203.9 736.4 4E-06 -0.00152 600 486.2 0.02013 0.76975 0.74962 471.7 1203.7 732 3.5E-06 -0.00137 620 489.74 0.02021 0.74408 0.72387 475.8 1203.4 727.6 4E-06 -0.00128 980 542.14 0.02152 0.4561 0.43458 539.5 1193.7 654.2 0 0 1020 546.99 0.02166 0.4362 0.41454 545.6 1192.2 646.6 3.5E-06 -0.0005 1000 544.58 0.02159 0.44596 0.42437 542.6 1192.9 650.3 3.5E-06 -0.00049 1060 551.7 0.02181 0.4177 0.39589 551.6 1190.7 639.1 3.75E-06 -0.00M6 1100 556.28 0.02195 0.4006 0.37865 557.5 1189.1 631.6 3.5E-06 -0.00043 O
July 1998 o:M292wW292w-Itwpf:lb-081098 1,7 28 Rev.5
1 l I l
I l
Table 1.7 3 l d ACCELERATION EFFECTS IN ADSI.3 PIPING (Note: See Table I.7 5 for nomenclature)
PRESS = 50 AVALVE - 0.324 APIPE = 0.6827 VF' = 1.2E-05 VFG = 8.4 % 726 VF= 0.017274 VG'= 0.176 % HFG = 923.85 SLIP = 6
'X GCRIT GRIPE V 1+G2V' STERM 1+G2V'S l 0.01 861 409 -0.00176 0.94 0.0015 0.99 I 0.1 283 134 -0.01769 0.93 0.0133 0.98 0.5 145 69 -0.08847 0.91 0.0369 0.95 0.9 110 52 -0.15926 0.91 0.0133 0.91 1
0.99 106 50 -0.17519 0.91 0.0015 0.91 i PRESS = 100 VF'= 8E.06 VFG = 4.41326 VF= 0.01774 VG' = -0.04408 HFG = 888.7 SLIP = 6 l
X CCRIT V GRIPE 1+G2V' STERM 1+G2V'S c ).
(V 0.01 1565 743 -0.00043 0.95 0.0004 0.99 l l
0.1 539 256 -0.0044 0.94 0.0033 0.98 0.5 282 134 -0.02204 0.91 0.0092 0.0 0.9 216 103 -0.03 % 7 0.91 0.0033 0.92 0.99 207 98 -0.04364 0.91 0.0004 0.91 PRESS = 600 VF= 3.5E-06 VFG = ' O.74 % 2 VF = 0.02013 VG' = -0.00137 HFG = 732 SLIP = 6 X GCRIT GRIPE V 1+G2V' STERM 1+G2V'S J
0.01 6284 2982 lE-05 0.98 0.0000 1.00 1 0.1 2661 1263 -0.00013 0.95 0.0001 0.99 O.5 1599 759 -0.00068 0.92 0.0003 0.95 j 0.9 1254 595 -0.00123 0.91 0.0001 0.91 '
O.99 1204 571 -0.00135 0.90 0.0000 0.91 i
PRESS = 1000 )
f3 VF' = 3.5E-06 VFG = 0.42437 VF = 0.02159 l
l !
l July 1998 eM292ww292w.la.wpcib.osio9s 1,7 29 Rev.5
Table 1.7 3 (cont.)
ACCELERATION EFFECTS IN ADSI 3 PIPING (Note: See Table 1.7 5 for nomenclature)
VG' = -0.00049 HFG = 650.3 SLIP = 6 X GCRIT GRIPE V 1+G2V' STERM 1+G2V3 0.01 8633 4097 1.4E-06 0.99 4.2E-06 1.01 0.1 4177 1983 -4.6E-05 0.96 3.82E-05 0.99 0.5 2639 1252 -0.00024 0.92 0.0001 % 0.95 0.9 2101 997 -0.00044 0.91 3.82E-05 0.91 0.99 2021 959 -0.00048 0.90 4.2E-06 0.91 O
l l
l l
l l
t l
e July 1998 0:M292wW292w-lawpf:lt>M1098 1.7-30 Rev.5
._. . . _ _ _ . . . . _ _ _ - -_ _ _ - - - . . . ~ - - . - - . . . - . . . . - - -_-
l
!h Table 1.7 4 f\
ACCELERATION EFFECTS IN ADSI 3 PIPING (Note: See Table 1.7 5 for nomenclature) i
! VF= 3.5E-06 VFG = 0.42437 VF = 0.02159 VG' = -0.00049 HFG = 650.3 SLIP = 6 l
X GCRIT GRIPE V 1+G2V' STERM 1+G2VS 0.01 8633 4097 -1.4E-06 0.99 4.3E-M 1.01 0.1 4177 i983 -4.6E-05 0.96 3.82E-05 0.99 0.5 2639 1252 -0.00024 0.92 0.0001 % 0.95 1
0.9 2101 997 -0.00044 0.91 3.82E-05 0.91 0.9 2101 997 -0.00044 0.91 3.82E-05 0.91 0.99 2021 959 -0.00048 0.90 4.3E-06 0.91 iO July 1998 o.u292ww292w lawpf:1t>.081098 1,7-31 Rev.5
Table 1.7 5 ACCELERATION EFFECTS IN ADS 4 PIPING PRESS = 50 AVALVE 0.527 APIPE = 0.559 VF' = 1.2E-05 VFG = 8.496726 VF = 0.017274 VG' = 0.17696 HFG = 923.85 SLIP = 6 4
X GCRIT GRIPE V 1+G2V' STERM 1 +G2V'S 0.01 861 812 -0.00176 0.75 0.0015 0.96 0.1 283 267 -0.01769 0.73 0.0133 0.93 0.5 145 136 -0.08847 0.64 0.0369 0.79 0.9 110 104 -0.15926 0.63 0.0133 0.66 0.99 1% 50 -0.17519 0.63 0.0015 0.63 Nomenclature:
GCRIT = critical mass flux at ADS valve GRIPE = mass flux upstream of the valve = GCRIT*AVALVE/APIPE V' = x vg' + (1-x) y,'
2 1+G V' = denominator in equation 440.721(h) - 5 STERM = last term in equation 440.721(h) - 13 1+G2 VS = equation 440.721(h)-14 O
July 1998 oM292ww292w la.wpf:tMe1098 1,7 32 Rev.5
l I
l 1.7.6 Conclusion O
I l
To determine whether the NOTRUMP drift flux model is being applied within its range of applicability, flow regime maps were generated using the models of Taitel and Dukler (References 1-18 and 1-24). On these maps were placed calculated liquid and vapor volumetric fluxes from selected components from a NOTRUMP calculation of the AP600 2-in. cold leg break. The results are shown in Figures 1.7-11 to 1.7-18. It can be seen that in general, horizontal pipes are always stratified, while vertical pipes traverse several of the flow regimes discussed in this section. De pressurizer surge line is a special case because it is a slanted, curved pipe. Tests in inclined pipes (Reference 1-25) indicate that the stratified flow j i regime cannot be maintained in slightly inclined pipes, reverting instead to flow regimes more typical of l vertical pipes. De surge line flowlink is therefore modeled as a vertical flowlink, and phasic flows are l placed on the vertical flow regime map (see Figure 1.7-16). It can be seen that the expected flow regime is annular in the surge line. Because of the special geometry of the surge line, the NOTRUMP drift flux model may have difficulty predicting the correct phasic flows in this component.
It is concluded that the NOTRUMP drift flux model is applicable in both vertical and horizontal pipes.
l The surge line may present problems to the model due to its unique geometry. There are also indications that the model predicts excessive liquid holdup (i.e., a restrictive CCFL) relative to data in vertical pipes.
O l
i l
i i
l I
l July 1998
! o:W292wW292w la.wpf:lt481098 },7 33 Rev.5 l
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s h Comparison of Yeh to Sudo Void Fraction Correlation; Atmospheric Pressure P t 4,
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Figure 1.7 2 CCFL Curve and Tangent Drift Flux Lines July 1998 oM292ww292w.itwpf;1bes109s 1.7 35 Rev.5
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EFFECT OF SUP RATIO ON DENOMINATOR 1 00 0 90 0 80 -
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Figure 1.7 6 Effect of Slip Ratio on Momentum Flux Equation Denominator
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July 1998 oM292wW292w la.wpf.lb 081098 1.7-39 Rev.5
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Figure 1.7 7 NOTRUMP Noding for ADS Valves July 1998 oM292ww292w la.wpf:Ib 081098 1,7 40 Rev.5
- n v
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Threveh Pipe to e Larger Mew Aree ir = 1.3 i a l
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l Figure 1.7-8 Effect of Compressibility on the Calculated Flowrate Through a Piping System '
July 1998 o:W292ww292w.la.wpf:!b48tM8 1.7-41 Rev.5 i N-
O A084 FLOW VS PRES 8URE USING COMPRESSIBILITY FACTOR 80.000 -
70 000 -
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Figure 1.7-9 Effect of Compressibility on ADS 4 Flow vs. Pressure e i July 1998 oM292ww292w-la.wpf;tb-081098 1.7-42 Rev.5
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AP600 2lNBREAK IN FNODE 49 12 node core Wess Flow Rote (ibm /s)
A WCFL 185 0 0 ADS 4A VAP0ut flow Wass Flos Rote (Inm/s) - '
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O Figure 1.7-10 NOTRUMP Predicted Vapor Flow Compared with Reference 123 Calculation 19 c:W292ww292w la.wpf;lb 081098 1.7-43 Julgp.985
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July 1998 o:w292ww292w la.wpf;1bO81098 1.7-50 Rev.5
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1.17 Key Features of the AP600 Analysis Methodology The application of NOTRUMP as an Appendix K evaluation model to the AP600 must take into
, account the findings from the assessment described in this report. First, the following conservative features required by Appendix K are applied:
i a) Appendix K requirements 2
ANS 71 + 20 percent core decay heat j Application of this model increases the core power by nearly 25 percent compared with the j more recent 1979 ANS standard for decay heat, during the time period of most interest near i
the point of ADS-4 actuation. Since the mass inventory and system pressure is in large part determined by the steam generation rate, application of this model leads to significant conservatism.
3 1
Moody critical flow model at the break and break spectrum 3 Application of the Moody model results in overprediction of the break flow by about 20 percent relative to data. The integral effects tests confirm that larger breaks tend to reduce system mass to a greater extent than smaller breaks. This model therefore is also considered to include additional conservatism, when combined with the required analysis of a spectrum of breaks.
b) Additional Conservatisms to Account for Plant Geometry Uncertainties The resistances in the DVI, IRWST, CMT, and accumulator lines are set at design upper bound values to reduce the flow rate from the passive components into the RCS. In addition, the minimum effectise critical flow area is used in the ADS critical flow calculation, and maximum resistances are used in the ADS flow paths.
Minimum containment pressure (14.7 psia) is assumed.
O V
July 1998 a:W292ww292w-ld.wpf.It>481098 1,17 1 Rev.5
i 1
c) Additional Confirmatory Checks and Assumptions to Account for Model Deficiencies J Table 1.171 summarizes the highly ranked component phenomena from the PIRT (Table 1.3-1) and the results of the assessment performed in this report. In several areas, model deficiencies in NOTRUMP resulted in minimal agreement with the data. The reasons for the minimal agreement are also given. For each area where agreement was minimal, the actions taken into account for the deficiency in the AP600 analysis are also given. The three specific actions to be taken are:
- 1. De flow velocity through the PRHR primary will be confirmed to be less than 1.5 ft/sec in all AP600 simulations. In addition, the PRHR is removed from the model after ADS 1-3 actuation to further reduce the depressurization rate.
- 2. If the flow through the PRHR is higher than 1.5 ft/sec. for any significant period of time, the calculation for the limiting case (minimum mass or highest PCT) is repeated with the PRHR heat transfer surface area reduced by 50 percent to account for the potential overprediction of heat transfer.
- 3. The IRWST flow will be delayed to account for potential nonconservatism in the prediction of system pressure after ADS-4 actuation. His will be accomplished by reducing the IRWST level by 6 feet. The basis for this value is described in the response to RAI 440.721(g).
in summary, the differences between predicted and actual integral test results can be attributed to one or more of the identified model deficiencies discussed in this report. For those areas where the Ol agreement was found to be minimal, specific steps have been taken to address the deficiency in the AP600 analysis.
l l
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l
. 1 1
0 July 1998 o.M292wu292w-Id.wpf:1t>.081098 1,17 2 Rev.5 l l
_ _ . _ . . _ . . m .
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{g TABLE 1.17-1 ASSESSMENT
SUMMARY
?
E Component Phenomenon Assessment Results How Treated in AP600 Analysis Comments d
p ADS 1-3:
13
@ Critical flow Reasonable; provided correct Minimum critical flow areas ADSl-3 inlet quality too high reservoir conditions are because PRZR level swell is ;
calculated underpmdicted; result is under prediction of ADSI-3 flow Two-Phase Pressure drop Reasonable Upper bound loss coefficients Lack of momentum flux terms 1 in ADS 1-3 tesults in small error Valve loss coefficients N/A Upper bound loss coefficients
[ obtained from valve tests a
D ADS 4:
Two-phase pressure drop Minimal; due to lack of Apply IRWST level penalty' Flow out ADS 4 is momentum flux terms, Upper bound loss coefficients overpredicted, resulting in early underpredicted pressure drop PRZR drain and IRWST initiation BREAK:
Critical flow Reasonable; provided reservoir Moody model used. Low-level swell results in lower quality is correctly predicted Break size, location ranged 2 quality flow at break; total system mass is under predicted
' Level penalty is indirect correction for most significant deficiency, lack of momentum flux in ADS 4. All SAR cases run with increasel ADS 4 resistance to confirm level penalty approach.
5 Additional studies ranging CD for break.
?- '
ss uw
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M TABLE 1.17-1 V
b ASSESSMENT
SUMMARY
(Cont.)
8 e
Assessment Results How Treated in AP600 Analysis Comments i Component Phenomenon t
3 ACCUMULATORS:
Upper bound loss coefficients h.
. Injection flow Reasonable Maximum water temperature 3
COLD LEGS:
Minimal, but conservative No change Balance line refilling delays CMT Phase separation at tees drain VESSEUCORE:
Decay heat N/A 1971 +20% ANS used.
Natural circulation flow Reasonable No change
[
w Mixture level Conservative if core uncovers No change Mixture level underpredicted in l A i boil-off experiments -
CMT:
Circulation Excellent No change Hermal Stratification Minimal, but conservative No change Lack of model increases CMT exit temperature, reduces core subcooling Draining Reasonable No change Some evidence of delayed flashing (non-equilibrium) in 1/2 inch break; judged no important c
- e-0~%.
u.
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5 I: TABLE I.17-1 5 ASSESSMENT
SUMMARY
(Cont.)
?
is: Component Phenomenon A____x,t Results How Treated in AP600 Analysis Conaments 4
2 DOWNCOMER:
Level Minimal for DEDVI Apply IRWST level penalty Range CD for Downcomer model does not predict 3 break to assure limiting case found 2-D temperatures. Excess condensation during IRWST.
HOT LEGS:
Stratifications, phase separation Minimal due to ad hoc model; Apply IRWST level penalty Liquid flow out ADS 4 is controlled at tecs impact is small by constant system inventory, inlet flows, self correcting system IRWST:
_ Gravity draining Feasonable Use upper bound line resistance High IRWST flow in OSU due to Maximum water temperature PRZ draining, downcomer h condensation 6
PRESSURIZER AND SURGE LINE:
CCFL Minimal but conservative No change; gi"en correct or high vapor flow, Rapid draining through surge line provided vapor flow is correct CCFL is conservative caused by low vapor flow due to low pressure drop through ADS 4 Entrainment (above mixture Reasonable No change Low ADSI-3 mass flow is due to level) low level swell, not entrainment ,
above the mixture level Level Swell Minimal non-conservative during Apply IRWST level penalty Rapid draining due to poor ADS 4 draining pressure drop prediction; confirmed by studies with increased ADS 4 resistance l'$
ss w
l o
7 TABLE 1.171 ASSESSMENT
SUMMARY
(Cont.)
r Component Phenomenen As== ment Results How Treated in AP600 Analysis Commsents g
i
} STEAM GENERATOR:
Natural circulation Reasonable No change
~
Minimal No change Underprediction in PRHR, CMT l Heat transfer increases SG heat transfer l
Tube draining Reasonable No change PRHR:
i Minimal, conservative if primary Remove PRilR after ADS 3, check Heat transfer not overpredicted as Heat transfer flow is low PRHR flow long as primary side is limiting Minimal, conservative if primary Remove PRHR after ADS 3, check Under predicted flow reduces
- Recirculation flow G flow is low PRHR flow PRHR heat transfer UPPER HEADflPPER PLENUM:
Mixture level Reasonable No change i
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