7th International Conference on Nuclear Engineering
Tokyo, Japan, April 19-23, 1999
ICONE-7447
INVESTIGATION OF SCDAP/RELAP5 HOT LEG MODELING FOR
SIMULATION OF COUNTERCURRENT NATURAL CIRCULATIONa
D. L. Knudson*
Idaho National Engineering and Environmental Laboratory
2525 North Fremont Avenue
Idaho Falls, ID 83415-3840
United States of America
E-mail: knu@inel.gov
Phone: 208-526-2899
Fax: 208-526-2930
and C. A. Dobbe
Idaho National Engineering and Environmental Laboratory
ABSTRACT
Natural circulation flows of superheated steam can develop during severe accidents in
pressurized water reactors (PWRs). Those flows are important because they can transfer decay
energy from the core to other parts of the reactor coolant system (RCS). The associated heatup
of RCS structures can lead to pressure boundary failures, including a potential for steam
generator tube rupture (SGTR). The potential for natural circulation induced SGTR was
studied extensively using SCDAP/RELAP5 because fission products could be released directly
to the environment through ruptured tubes. A two-pipe simulation of countercurrent natural
circulation in the hot leg of a PWR had to be used in the study because SCDAP/RELAP5
hydrodynamics are one-dimensional. An assessment of the two-pipe modeling approach was
needed because hot leg countercurrent natural circulation is an important contributor to
structural heating and an evaluation of the potential for SGTR would be incomplete without
establishing the validity of the model. The two-pipe model was assessed through
SCDAP/RELAP5 analyses that addressed the absence of circumferential conduction in the hot
leg wall and heat transfer between countercurrent flow streams. Results indicate that those
conjugate heat transfer effects reduce countercurrent flows and vapor temperatures, thereby
delaying the prediction of SGTR. Consequently, the two-pipe model was shown to be adequate
in providing a conservative evaluation of the potential for SGTR in PWRs.
Keywords: SCDAP/RELAP5, SGTR, severe accident modeling, natural circulation
a. Work supported by the United States Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, under
the United States Department of Energy Idaho Field Office Contract DE-AC07-94ID13223.
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1
INTRODUCTION
In-vessel, full-loop, and hot leg countercurrent natural circulation flows of superheated
steam can develop during severe accidents in pressurized water reactors (PWRs) with U-tube
steam generators (SGs). Those flows, which are characterized by the patterns illustrated in
Figure 1, are important because they can transfer decay energy from the core to other parts of
the reactor coolant system (RCS). The associated heatup of structures in the RCS can lead to
pressure boundary failures; with notable vulnerabilities in the pressurizer surge line, the hot leg
nozzles, and the SG tubes. The potential for a steam generator tube rupture (SGTR) is of
particular concern because, unlike other potential RCS pressure boundary failures, fission
products could bypass containment and be released directly to the environment through
ruptured tubes.
Steam
generator
Steam
generator
Pressurizer
In-vessel
natural
circulation
Hot leg
Hot leg
Cold leg
Cold leg
Steam
Water
Core
Full-loop
natural circulation
Hot leg countercurrent
natural circulation
Figure 1. Natural circulation flow patterns that can develop in PWRs with U-tube SGs.
The United States Nuclear Regulatory Commission (USNRC) developed a program to
address SG tube integrity issues in PWRs based on the possibility for environmental release.
An extensive effort to evaluate the potential for natural circulation induced SGTRs using
SCDAP/RELAP5 (Allison 1995) at the Idaho National Engineering and Environmental
Laboratory (INEEL) was directed as one part of the USNRC program (Knudson 1998).
Complete consideration of in-vessel, full-loop and hot leg countercurrent natural circulation
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modes was an integral part of the INEEL evaluation. However, a two-pipe model had to be
used to simulate countercurrent natural circulation flows in the hot leg because
SCDAP/RELAP5 hydrodynamics are one dimensional. The efforts taken to qualify use of the
two-pipe hot leg model are described in this report. This work was needed because hot leg
countercurrent natural circulation is an important contributor to RCS structural heating and an
assessment of the potential for SGTR in PWRs with U-tube SGs would be incomplete without
establishing the validity of the two-pipe modeling approach.
Relevant aspects of hot leg countercurrent natural circulation are discussed in Section 2. A
description of the SCDAP/RELAP5 two-pipe model used to evaluate the potential for SGTR in
PWRs with U-tube SGs is provided in Section 3. In addition, modifications used to assess the
validity of the SCDAP/RELAP5 model are also discussed. Results associated with this
assessment effort are presented in Section 4. And finally, pertinent conclusions are outlined in
Section 5. Section 6 contains a list of references.
2 HOT LEG COUNTERCURRENT NATURAL CIRCULATION
A one-seventh scale model of a four-loop PWR was used in experiments conducted by
Westinghouse to study natural circulation phenomena (Stewart 1989 and Stewart 1992). The
model represented a half section of the PWR and therefore included a vessel to simulate an
equivalent portion of the reactor, two hot legs, and two SGs. The vessel contained structures to
represent the upper plenum internals and one half of the core fuel assemblies with radial and
axial flow resistance similar to the prototype. Core power was supplied through electrical
heaters. Experimental results indicated that hot leg countercurrent natural circulation in PWRs
with U-tube SGs consists of hot flow from the core to the SG outlet plenum through the top of
the hot leg and a fraction of the SG U-tubes as shown in Figure 1. Colder flow then returns to
the core through the remaining U-tubes and the bottom of the hot leg.
Initial experiments were conducted at low (atmospheric) pressure using water and sulfur
hexafluoride (SF6) as working fluids. Subsequent experiments were conducted at high pressure
(1.4 to 3.4 MPa) using SF6. (Experimental pressures of 1.4 to 3.4 MPa with SF6 are reported to
be equivalent to 15.2 to 16.5 MPa with steam in the prototype.) Both steady state and transient
tests were completed with variations in core power. In all cases, experimental results verified
that relatively-stable hot leg countercurrent natural circulation flow patterns will develop.
Stability is used as a descriptor in this context because countercurrent flows developed over a
wide range of experimental conditions, stratified flow patterns in the hot leg existed without
interaction between the hot and cold streams, and natural circulation flows were robust in that
they quickly re-established following major pertubations (like that introduced by pressurizer
relief valve cycling). Bulk mixing of hot flow in the top of the hot leg with the colder return
flow in the bottom of the hot leg was not observed.
3 SCDAP/RELAP5 MODELING
A SCDAP/RELAP5 (RCS loop) model typical of those used to evaluate the potential for
natural circulation induced SGTR is shown in Figure 2. Consistent with experimental
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observations, the model will allow development of natural circulation from the vessel to the
SG outlet plenum through top of the hot leg and a portion of the SG U-tubes with flow
returning to the vessel through the remaining tubes and the bottom of the hot leg. However, the
physical separation of hot and cold countercurrent flow streams that was imposed through the
use of two separate pipes to represent the hot leg is an important aspect of the model.
183
MSIV
158
SRVs
184
185
PORVs
186
187
SRVs
180
178
188
150
6
171
MFW
170-6
4
3
110
4
4
2
5
111
5
150
1
182
174
5
Steam generator
Pressurizer
160
172
5
4
3 3 6
3 6
2 2 7
2 7
1 1 8
1 8
176
157
PORVs
Containment
153
1
Reactor
vessel
2
153
3
105 106 107
155
114
156
582
Top of hot leg
100-1
2
3
4
100-5
581
Bottom of hot leg
101-5
4
3
2
101-1
502
Cold leg
122-4
3
2
122-1
116
1
118
RCP
2
Accumulator
190
116
5
4
RCP Seal Leak Path - 125
3
Figure 2. Typical SCDAP/RELAP5 nodalization using a two-pipe model for simulating hot
leg countercurrent natural circulation.
Sepa ration of hot leg c ountercurre nt f low streams was ne cessa ry beca us e
SCDAP/RELAP5 hydrodynamics are one-dimensional. The resulting two-pipe modeling
approach was adopted and appeared to be feasible only because experiments indicated that hot
and cold flow streams do not mix. In the absence of mixing, it was assumed that heat transfer
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from the fluid to the pipe wall was the most important process to address. Furthermore,
complete correlations for fluid-to-wall heat transfer are included in SCDAP/RELAP5.
Consequently, models as shown in Figure 2 were expected to be suitable for SGTR evaluation.
During peer reviews of the INEEL SGTR analyses, however, reviewers indicated that the
two-pipe modeling approach neglected potentials for circumferential conduction in the hot leg
wall and heat transfer between the hot fluid and the colder fluid. The potential for
circumferential conduction exists because the hot and cold countercurrent flow streams will
impose a temperature gradient in the hot leg. Although bulk mixing of the hot and cold flow
streams was not observed, a potential for radiation heat transfer across the fluid-to-fluid
interface could also develop. As discussed below, those additional heat transfer mechanisms
were incorporated in sensitivity analyses to assess the validity of the two-pipe modeling
approach.
3.1
Circumferential Conduction in the Hot Leg Wall
Circumferential conduction in the hot leg wall was simulated by calculating the heat that
could be conducted between top and bottom halves of each section of each hot leg during each
time step, as would occur without the separation imposed by the two-pipe model. The
parameters needed to complete this simulation are shown in Figure 3. Specifically, each
calculation was based on the volume-averaged temperatures of the pipe halves (Tp,h and Tp,c)
as reported by SCDAP/RELAP5. The difference between the volume-averaged temperatures
was used as the conduction driving potential and the “average” volume-averaged temperature
was used to determine the thermal conductivity (k) of the stainless steel pipe wall. A
conduction path length equal to a quarter of the wall centerline circumference (πrc/2) was used
since the volume-averaged temperatures were assumed to approximate wall temperatures half
way between the top/bottom of the pipe and the intersection of the pipe halves. Heat transfer
surface areas were twice the product of the wall thickness (t) and length of each pipe section
(L), given that conduction will develop symmetrically on both sides of the hot leg. The
calculated conduction of heat for each section of each hot leg, Qc as given by Equation 1, was
then added to the bottom half and subtracted from the top half of each section of each hot leg
during each time step.
t
Tp,h
circumferential
conduction path
Tp,h
ro
L
ri
rc
Tp,c
Tp,c
Figure 3. Parameters for simulating circumferential conduction in the two-pipe hot leg model.
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k ( 2Lt )
Q c = ------------------- ( Tp, h – T p, c )
( πr c ⁄ 2 )
(1)
where
k
= thermal conductivity of the hot leg evaluated at (Tp,h + Tp,c)/2,
2Lt
= area for circumferential heat conduction consisting of a length, L, times
the wall thickness, t, for both interfacing surfaces of the hot leg,
πrc/2 = circumferential conduction path length (at the centerline radius of the
hot leg as shown in Figure 3),
Tp,h = volume-averaged temperature of the pipe representing the top (hot) half
of the hot leg, and
Tp,c = volume-averaged temperature of the pipe representing the bottom
(cold) half of the hot leg.
3.2
Fluid-to-Fluid Heat Transfer
Radiation was assumed to be the primary mechanism for fluid-to-fluid heat transfer in the
hot leg because mixing of countercurrent flow streams was not experimentally observed. For
modeling convenience, convective processes were used to represent the assumed radiation heat
transfer as follows.
Very thin rectangular structures were effectively placed between hot and cold
countercurrent flow streams in each section of each hot leg. The width of each structure was
set at the hot leg inside diameter (2r i ) with a length corresponding to the length of the
applicable hot leg section (L). Each structure was assigned a very high thermal conductivity
and a very low heat capacity. A very high (constant) convective heat transfer coefficient was
then applied to the side of each structure in contact with the hot fluid. Consequently, each
rectangular structure was effectively held at a uniform temperature equal to the temperature of
the associated hot flow stream (T f,h ). Radiation heat transfer (Q r ), and the equivalent
convective heat transfer, from each rectangular structure to the applicable cold stream (at the
temperature Tf,c) was then calculated using Equation 2, given black body assumptions and the
fact that the structure temperature was equal to hot stream temperature (Tf,h).
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4
Q r = σ ( 2ri L ) ( T f, h – T f, c ) = h e ( 2r i L ) ( T f, h – T f, c )
(2)
where
σ
= Stefan-Boltzmann constant,
2riL = area for radiation and convection heat transfer at the interface between
the hot and cold flow streams,
Tf,h = temperature of the fluid in the pipe representing the top (hot) half of the
hot leg,
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Tf,c = temperature of the fluid in the pipe representing the bottom (cold) half
of the hot leg, and
he
= convection heat transfer coefficient for simulating an equivalent level
of radiation heat transfer.
Equation 2 can be simplified, as given by Equation 3, to yield an expression for a
convective heat transfer coefficient (he) that is equivalent to the black body radiation potential.
The resulting equivalent convective heat transfer coefficient for each rectangular structure at
each time step was then applied to the side of the structure in contact with the cooler flow
stream.
2
2
h e = σ ( T f, h + T f, c ) ( T f, h + T f, c )
(3)
4
RESULTS
SCDAP/RELAP5 analyses using the two-pipe model with and without conjugate heat
transfer effects (as discussed above) were completed for a station blackout accident in a typical
PWR. A station blackout accident was assumed because those accidents are considered to be
one of the more likely scenarios leading to natural circulation flows at temperatures and
pressures that could threaten SG tube integrity (as well as the integrity of other vulnerable RCS
pressure boundaries). A comparison of results from the analyses can be used to determine if
the two-pipe model without circumferential conduction and fluid-to-fluid heat transfer is
appropriate for use in evaluating the potential for SGTR in PWRs.
Results from the SCDAP/RELAP5 analyses indicated that the hot leg vapor ∆T (i.e., the
difference between the temperature of the hot vapor in the top half of the hot leg and the
temperature of the cooler vapor in the bottom half of the hot leg) was reduced as a result of
circumferential conduction and fluid-to-fluid heat transfer in the hot leg as indicated in
Figure 4. (Temperature oscillations shown in the figure are due to pressurizer relief valve
cycling.) The reduction in hot leg vapor ∆T led to a reduction in hot leg countercurrent flow
and a corresponding general reduction in the heat transferred to RCS structures. With less
energy transferred to most loop structures, more energy was stored in core and more energy
had to be rejected through pressurizer relief valve cycling. Consequently, creep rupture failure
of the pressurizer surge line was predicted 150 s earlier with conjugate heat transfer effects
than in the base case (without those effects) as indicated in Table 1.
Vapor temperatures entering the SG tubes were also reduced as a result of conjugate heat
transfer effects in the two-pipe hot leg model as indicated in Figure 5. The reduced vapor
temperatures entering the SG tubes resulted in lower SG tube temperatures, which delayed
prediction of SGTR. Specifically, the results indicate that the addition of circumferential
conduction in the hot leg wall and fluid-to-fluid heat transfer could delay SG tube failure
relative to surge line failure by 280 s (see Table 1).
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Vapor temperature difference (K)
1000.0
base case
with conjugate heat transfer
800.0
600.0
400.0
200.0
0.0
9000.0
11000.0
13000.0
15000.0
Time (s)
Figure 4. Differences between vapor temperatures in the top and bottom halves of the hot leg
with and without conjugate heat transfer effects.
Table 1. RCS pressure boundary failure times (in s after station blackout initiation) based on a
two-pipe SCDAP/RELAP5 hot leg model with and without conjugate heat transfer effects.
Component
Base Case
With Conjugate Heat Transfer Effects
(without conjugate heat transfer effects)
Surge line
13,730
13,580
SG U-tube
14,960
15,090
5
CONCLUSIONS
A two-pipe model for simulating hot leg countercurrent natural circulation was assessed
through SCDAP/RELAP5 analyses that addressed the absence of circumferential conduction
in the hot leg wall and fluid-to-fluid heat transfer between countercurrent flow streams. Results
indicate that those conjugate heat transfer effects reduce the difference between the
temperature of the hot vapor in the top half of the hot leg and the temperature of the cooler
vapor in the bottom half of the hot leg. That differential temperature reduction led to reduced
hot leg countercurrent flows and reduced vapor temperatures in the SGs. As a result, SG
U-tube temperatures were reduced and the prediction of SGTR was delayed, indicating that
consideration of conjugate heat transfer effects in the hot leg will decrease the calculated
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Vapor temperature (K)
1400.0
1200.0
base case
with conjugate heat transfer
1000.0
800.0
600.0
9000.0
11000.0
13000.0
15000.0
Time (s)
Figure 5. Vapor temperatures entering the SG U-tubes with and without conjugate heat
transfer effects.
potential for SGTR. These are important conclusions because they indicate that a degree of
conservatism exists in earlier SCDAP/RELAP5 analyses that used the two-pipe model to
evaluate the potential for SGTR. Furthermore, they indicate that modeling complications
associated with circumferential conduction and fluid-to-fluid heat transfer between hot leg
countercurrent flow streams do not need to be considered in future analyses.
6 REFERENCES
Allison, C. M., et al.: SCDAP/RELAP5/MOD3.1 Code Manuals, NUREG/CR-6150, (1995).
Knudson, D. L., et al.: SCDAP/RELAP5 Evaluation of the Potential for Steam Generator Tube
Rupture as a Result of Severe Accidents in Operating Pressurized Water Reactors,
INEEL/EXT-98-00286, Revision 1, (1998).
Stewart, W. A., et al.: Natural Circulation Experiments for PWR Degraded Core Accidents,
Electric Power Research Institute Project NP-6324-D Report, (1989).
Stewart, W. A., et al.: Natural Circulation Experiments for PWR High Pressure Accidents,
Electric Power Research Institute Project RP2177-5 Report, (1992).
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