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Nuclear Technology
ISSN: 0029-5450 (Print) 1943-7471 (Online) Journal homepage:
On the Subcooled Critical Flow Model in RELAP5/
W. S. Yeung & J. Shirkov
To cite this article: W. S. Yeung & J. Shirkov (1996) On the Subcooled Critical Flow Model in
RELAP5/MOD3, Nuclear Technology, 114:1, 141-145, DOI: 10.13182/NT96-A35230
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Published online: 13 May 2017.
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Download by: [University of Florida]
Date: 25 October 2017, At: 21:41
W. S. YEUNG and J. SHIRKOV Yankee Atomic Electric Company
Bolton, Massachusetts 01740
choking, fluid flow
Downloaded by [University of Florida] at 21:41 25 October 2017
Received December 12, 1994
Accepted for Publication July 12, 1995
regions have been compared to data from separate effect
and integral test data. During the code development stage,
An analysis of an anomaly in the subcooled critical flow several deficiencies in the choking model have been identimodel in the RELAP5/MOD3 computer code is presented. fied. These deficiencies were subsequently corrected.3 One
Specifically, the code produces a discontinuity in going fromof the deficiencies concerns a discontinuity in single-phase
unchoked subcooled liquid flow (i.e., subsonic flow) to sub- steam critical flow rate due to incorrect throat density calcooled choked flow (i.e., sonic flow). The same anomaly has culation. However, no mention is made of the discontinubeen reported elsewhere. The root cause for this anomaly ity regarding unchoked and choked flow in the subcooled
has been analyzed, and it is found that the user-supplied region. One possible explanation is that almost all assessjunction loss coefficient and discharge coefficient play an ments are made against transient experiments in which subimportant role in the occurrence of this anomaly. The analy-cooled critical flow occurs at the start of the simulation, and
sis is verified by assessment against a test problem simulat- unchoked subcooled liquid flow is seldom simulated. It is
ing single-phase liquid flow through a convergent nozzle also for this reason that the observed discontinuity has no
with a fixed upstream pressure and a varying downstream impact on loss-of-coolant accident-type calculations using
pressure. A corrective measure to eliminate the discontinu- the RELAP5 series of codes.
ity is suggested.
The objective of this paper is to investigate the root
cause of this discontinuity. First, a test problem that reveals
the discontinuity is described. An analysis is then presented
for the root cause of the discontinuity. Results from actual
RELAP5/MOD3 calculations of the simple problem are
used to substantiate the analysis. Finally, a modification in
the subcooled choking criterion, which eliminates the disDuring the course of applying the RELAP5/MOD3
continuity, is suggested.
Version 3.1 computer code to calculate the steady-state flow
rate of subcooled liquid through a control valve, a disconII. DESCRIPTION OF TEST PROBLEM
tinuity in the mass flow rate was discovered. The discontinuity occurred as the flow went from unchoked to choked
flow as the downstream pressure was lowered. Other versions
Consider the ideal (i.e., frictionless) flow of subcooled
of the code (including a version of the RELAP5/MOD1
liquid through a converging nozzle as shown in Fig. 1. The
code) have been used, but the same discontinuity was calupstream conditions are fixed at Pup and T. The downstream
culated to exist for each version. It appears that this disconpressure is Pdaw„. As the downstream pressure decreases
tinuity exists in the RELAP5 code series.
from Pup, the liquid flow rate through the nozzle increases.
The increase continues until the local pressure at the nozThe same anomaly has been reported by Petelin et al.1
zle exit reaches a value Pvap, at which the liquid begins to
during their investigation of the International Standard
flash. The flow becomes choked, and further decrease of
Problem 27 (BETHSY small-break Test 9.1b). Those auPdown wiH not increase the flow rate through the nozzle.
thors suggested that the anomaly is closely connected with
The pressure Pvap, corresponding to the inception of the
the increase in the average junction liquid density and that
flashing, is usually less than the saturation pressure
this parameter may influence the choking criterion in a specorresponding to the liquid temperature T. Figure 2 depicts
cial way when the abrupt area change option is applied.
the steady-state flow rate as a function of Pdow„, as physiThe RELAP5 choking model has been well documented
in Vol. IV of the RELAP5/MOD3 code manual.2 The model cally expected.
has been extensively assessed by the RELAP5 user commuFigure 3 shows the nodalization of the test problem. The
nity and by the code developers. Calculated critical flow
nozzle is represented by a single volume (203), which is conrates in the subcooled, two-phase, and single-phase steam
nected on either side to a time-dependent volume (201 and
201 are fixed at Pup and T. The initial conditions for SV
203 are the same as those for TV 201. For TV 205, the conditions are specified at Pdown and X — 1.0. For each value
of Pdown. the problem is run until steady state is obtained.
The corresponding flow rate is recorded.
Figure 4 shows the calculated results for the following
input data: Aup = 0.1 m 2 , AT = 0.001 m 2 , L = \m,Pup =
6.0 MPa, T = 500 K. The abrupt area option is used for the
valve junction, with zero user input loss coefficient. As can
be seen, the flow increases gradually as Pdown decreases. At
- 2 . 3 MPa, the flow becomes choked, and the flow rate suddenly jumps to a larger value and remains there for Pdown <
2.3 MPa. The cause for this discontinuity is discussed in
Sec. III.
Fig. 1. Flow of subcooled liquid through nozzle.
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The theoretical aspects of the RELAP5 choking model
have been given elsewhere.2 Here we shall focus on singlephase subcooled liquid. In essence, a critical choking velocity Vc is calculated at the throat based on the Bernoulli
equation and an empirical correlation for Pvap. The result
is given by
2 (PUn Pvap)
' c= V
' up+'
where Vup is the upstream velocity and p is the liquid density, which is assumed constant in this study. From
KpAup = VCAT .
Hence, Eq. (1) can be rewritten as
Fig. 2. Variation of steady-state flow rate with downstream
TV 201
SV 203
Pup, T
Fig. 3. Nodalization of test problem.
2 ( ^up
p[ 1 -
where Pvap is evaluated from the Jones-Alamgir-Lienhard
correlation 4 and is a function of Vc. Equation (3) therefore
represents an implicit equation in Vc and can be solved by
iteration. If a discharge coefficient CD is specified, Eq. (3)
will be modified to
V} =
2 ( Pup Pvap) Co
p[\ - (Ar/Aup)2]
If the flow is not choked, the junction velocity will be given
by the Bernoulli equation applied across the junction. Refer to the nodalization diagram, Fig. 3, and apply the Bernoulli equation from volume 203 to volume 205:
Pup + iPVlp - Pdown + \pVdown + K\pVj
From continuity, Vup= VjAT/Aup and Vdown =
Hence Eq. (5) becomes
. (5)
2 (Pup ^down
Vf =
205). The nozzle exit is modeled by a trip valve junction
(204), and the nozzle inlet is modeled by a single junction
(202). The flow area for TV 201, SJ 202, and SV 203 is the
same and is denoted by Aup, the exit area is denoted by Ar,
and the area for TV 205 is denoted by Adow„. The choking
option is specified at the valve junction only. Wall friction
is deactivated for frictionless flow. The conditions for TV
K + (AT/Adown)2 -
In Eq. (6), K is the junction loss coefficient, either internally
calculated (if the abrupt area option is used) or user specified, or both.
The choking criterion is applied as follows. At each time
step, the junction velocity from Eq. (6) is compared to the
critical velocity from Eq. (4). If Vj < Vc, the flow is not
choked, and the junction velocity will be given by Eq. (6)
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Downstream Pressure (MPa)
Fig. 4. Variation of steady-state flow rate against downstream pressure.
and is a function of the downstream pressure. If Vj > Vc,
the flow is choked, and the junction velocity will be set equal
to Vc regardless of the downstream pressure. At the point
of choking, therefore, Vj = Vc. Thus, equating Eqs. (4) and
(6), one could solve for the downstream pressure necessary
to choke the flow as
Keff Cp ( PUp ~ Pvap)
Pdown Pup
where Ke/f is defined as
\A ) •
III.A. Nature of Discontinuity
The cause of the observed discontinuity in the subcooled
liquid region can be best explained with Eq. (7), and depends
on its solution. Define a parameter such that
Z =
that the solution of Pdow„ significantly impacts the choking
logic and hence the steady-state flow rate response.
To illustrate the effect of Z on the steady-state flow rate,
the test problem was run with various combinations of K
and CD. The geometrical and boundary conditions were the
same as before. The smooth area option was used with user
input K values. Figure 5 summarizes the results for various
Z. Each data point represents a steady-state run. Each mass
flow rate result was normalized with respect to CDmcrit,
where m cril is the critical flow rate corresponding to unit
discharge coefficient. The effect of Z is evident. For Z > 1,
the steady-state flow rate is discontinuous across the choked
point. For Z < 1, the flow rate is generally smooth across
the choked point. The following explanation is put forth.
1. Z < 1: Because Pup is always >Pvap, Eq. (10) indicates that the downstream pressure for choking is >P v a p .
The steady-state flow rate is continuous across the choked
point, as it should be. Note that for small values of Z, the
choking downstream pressure can be relatively high. Indeed,
if Z = 0, Pdown = Pup for choking, which is not physical. It
may be concluded that Z cannot be zero for this test
2. Z > 1: For this case, Pdown will be <Pvap for choking.
values of Z, Pdovm may be significantly less than Pvap
Pdown ~ Pvap = (1 — 2)(Pup — Pvap) •
(10) and may even become negative. According to our analysis,
the steady-state flow rate should still be continuous, as long
Depending on the values of Z, the downstream pressure for
as Pd0wn remains positive. In addition, if Pdown is negative
choking may be greater or less than Pvap. It will be shown
Equation (7) can then be rewritten as
Yeung and shirkov
I ill
1 0.6
•o 0.5
Downloaded by [University of Florida] at 21:41 25 October 2017
Fig. 5. Variation of steady-state flow rate against downstream pressure for various Z.
according to Eq. (10), then the flow should not be choked
at all. However, the code does not behave in this manner.
The discontinuity is a manifestation of choking being predicted earlier than our simple analysis would indicate. For
instance, consider the Z = 2.62 curve. The RELAP5/MOD3
code predicted choking even though the junction flow rate
from the normal momentum solution is - 3 0 % lower than
the critical flow rate. It is possible that during the transient
calculation, the junction is found choked due to numerical
oscillations (particularly at the first time step). Once the
junction is choked, the unchoking test is not sufficient to unchoke the junction. As a result, the junction remains choked
as steady state is approached, even though the junction velocity is less than the subcooled critical velocity. This explanation forms the basis for a proposed modification, to be
discussed in Sec. IV, to eliminate the discontinuity.
The discontinuity is therefore seen as a result of the combined effect of code logic, the manner in which steady-state
solution is reached (which depends on specification of boundary conditions), and user input data (i.e., the Z parameter).
In particular, unphysical results may arise if inconsistent
user input K factors, flow areas, and discharge coefficients
are specified. For instance, if Z is specified such that Pdow„
is negative, then our analysis shows that the flow will never
be choked. This is unphysical and is because of the inappropriate user input data.
A modification has been suggested in Ref. 1. Here, we
suggest another corrective measure to eliminate the discontinuity for any value of Z, based on the present analytical
study. Since the discontinuity may not exist if realistic input data are used for the break junction, this modification
is suggested for the sake of numerical smoothness.
The root cause for the discontinuity is related to the inability of the unchoking test to unchoke the junction, which
renders the flag CHOKE in subroutine JCHOKE being always true once it is set. In the subcooled choking test logic,
the junction is choked if either the flag CHOKE is true or
the junction velocity Vj is greater than or equal to the critical velocity Vc. The modification therefore removes the
test on the flag CHOKE in the logic and bases the choking
decision solely on Vj > Vc. Thus, the condition Vj > Vc
serves as both choking and unchoking test for the junction.
With this modification, the code will behave exactly the
same way as the simple analysis of Sec. Ill indicates.
Results for several cases of Z > 1 have been obtained
using the modified code version. Figure 6 shows the steadystate flow rate against the downstream pressure. No discontinuity is calculated. In addition, the calculated flow is never
choked for the entire range of Pdown. The impact of this
modification on the code prediction of separate effect and
integral tests must be investigated before adaptation.
Downloaded by [University of Florida] at 21:41 25 October 2017
Fig. 6. Variation of steady-state flow rate against downstream pressure with code modification.
A root cause analysis of an observed discontinuity in the
subcooled choked/unchoked flow has been presented. It has
been found that the user input junction loss coefficient and
discharge coefficient affect the occurrence of the discontinuity. The root cause is traced to the inability of the code
to unchoke a junction even though the junction velocity is
well below the critical velocity for the specified flow conditions. By modifying the choking test to be based only on the
relative magnitudes of the junction and critical velocity, the
discontinuity is eliminated. Recently, code developers at
Idaho National Engineering Laboratory have completed
modifying the unchoking tests to eliminate this anomaly. 5
The corresponding code updates will be available in the next
code release, Version 3.2.
1. S. PETELIN, O. GORTNAR, and B. MAVKO, "RELAP5 Subcooled Critical Flow Model Verification," Trans. Am. Nucl. Soc.,
69, 546 (1993).
2. K. E. CARLSON et al., "RELAP5/MOD3 Code Manual,"
NUREG/CR-5535, EGG-2596, Vol. 4, EG&G Idaho (June 1990).
3. W. L. WEAVER, "Improvements to the RELAP5/MOD3
Choking Model," EGG-EAST-8822, Idaho National Engineering
Laboratory (Dec. 1989).
4. O. C. JONES, Jr., "Flashing Inception in Flowing Liquids," J.
Heat Transfer, 102 (1980).
5. P. MURRAY, Idaho National Engineering Laboratory, Personal Communication (July 28, 1994).
W. S. Yeung (BS, mechanical engineering, University of Lowell, 1976; PhD, mechanical engineering, University of California, 1979) is a principal engineer at Yankee
Atomic Electric Company (YAEC). His current technical interest is in thermalhydraulic analysis using RELAP5/MOD3 and water hammer fluid transient analysis.
J. Shirkov (MS, Moscow Institute of Energetics, 1987) is a nuclear engineer at
YAEC. His current interests include computational methods in thermal hydraulics and
heat exchanger analysis.
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