Introduction
Controlled fission power has been utilized for electricity production world-
wide in the nuclear power plants based on the light water reactor technology
for several decades. It has proven its efficiency and safety during these years
and has shown itself to be a reliable and durable energy source, [27] [29] [28].
The foundation pillar in the non-military utilization of fission nuclear
power has always been the strong emphasis on safety. Safety has been
achieved by continuously pursuing in-depth reviews and re-evaluation of
safety-related issues incorporating findings from ongoing nuclear safety re-
search activities worldwide. Specific requirements have been deployed at
the design and in the permissible conditions, thus preventing the occurrence
of accidents. It is realized that as new findings and analysis capabilities
become available safety will be increased and in addition it is possible that
the safety margins presently employed will eventually be relieved (decreased)
without compromising the actual safety. Prevention and mitigation measure,
however, must be properly balanced with cost-reduction needs. A thorough
knowledge of fundamental issues allows the pursuit of the goal of ensuring
safety at reasonable costs.
The advancements in numerical methods and computer technology cou-
pled with the continuing increase in operational experience has been moving
in the last few years toward the investigation of best estimate simulations
of complex scenarios in nuclear power plants. Nowadays, the coupled code
methods are used extensively, since they allow reducing CPU time and pro-
vide a global vision of the system behavior.
The activity carried out is part of a broader one ongoing at Pisa Univer-
sity and dealing with various software couplings, suitable for safety analysis
in nuclear technology: coupling between 3D neutron kinetics and thermal-
hydraulics, between thermal-hydraulics and structural mechanics, between
plant system and containment. Such activity improves the common under-
standing of safety issues and design/operating conditions and, in brief, puts
the basis for a technology advancement.
xiii
Chapter 1
State-of-the-art BE Coupled
Techniques
Topics connected with the interaction between thermal-hydraulics and neu-
tronics still challenge the design and the operation of Light Water nuclear
Reactors (LWR). The lack of full understanding of such complex mechanisms
imposed the adoption of conservative safety limits. Those safety margins put
restrictions to the optimal exploitation of the plants, causing increase in the
economic profit of the plant. The recent availability of powerful computer
and computational techniques, together with the continuing increase in op-
erational experience, imposes the revisiting of those areas and eventually the
identification of design/safety requirements that can be relaxed.
During the last decades safety analyses were performed using a variety
of simplified and conservative models. Generally, computational tools were
developed in parallel ways, and only few connections between them exist,
as for neutronic codes, where a simplified thermal-hydraulic model is usu-
ally used. On the other hand, thermal-hydraulic system codes use point or
one dimensional kinetic approach. Also, channel codes, even though their
multi-channel model, use imposed boundary conditions. Nowadays, with
the reduced cost of computers and also the availability of higher proces-
sor speeds, the code application domain has been correspondingly enlarged.
Therefore, it becomes feasible to perform Best-Estimate simulations through
the incorporation of three-dimensional modeling of reactor core into system
codes [59], [60]. Benefits of such technology are expected for the industry,
regulatory and licensing topics. These issues include, for example, the design
of new reactors, relaxation of the safety margins, allowing higher operating
power, and extending the fuel cycles (increased burn-up) [61].
Nowadays, several international activities have been completed or are in
progress aimed at characterizing the capabilities of the coupled code calcula-
tions in simulating realistically complex transients in Nuclear Power Plants
(NPP). These activities include the OECD/NEA Benchmarks as the PWR
1
CHAPTER 1. STATE-OF-THE-ART BE COUPLED TECHNIQUES 2
Main Steam Line Break (MSLB) in TMI-1 [30], the BWR Turbine Trip (TT)
in Peach Bottom [12], the VVER-1000 coolant transient [21] and the PWR
MOX fuel.
The University of Pisa has so far experienced and participated in several
activities in the field of coupled code calculations using 3D neutron kinetic,
structural mechanics, containment, and thermal-hydraulic system codes [13]
[36]. For this purpose, various versions of RELAP5 [7] and 3D neutronic
codes PARCS [42] [25], NESTLE [56], and QUABBOX [49] have been used.
In addition an uncertainty methodology has been developed in order to re-
alize an assessment of the code calculations errors.
1.1 Field of application of coupled techniques
Coupled code calculation approach constitutes the normal evolution of an-
alytical simulation methods applied for performing safety analysis of NPPs.
Until recent years most of the safety analyses, at least for PWR, were
done with codes which model the neutronics only with point kinetics. For
BWR, transient analyses have been carried out traditionally with axially
one-dimensional models since the coupling between neutronics and thermal
hydraulics is very strong. The advantage of using coupled 3D THSC/NKC
is more evident in the analysis of strongly asymmetric neutron/thermal-
hydraulic transients for which simple point kinetic and one-dimensional ther-
malhydraulic models are not able to provide an acceptable physical repre-
sentation of the phenomena that occur in the core.
The need for coupled 3D neutronics calculation is greatest in cases where
strong feedback between the core kinetic and the coolant loop as well as in
situations where power excursion is important and its distribution changes
during the transient. Also a reactor core is never uniform (even if it was
initially constructed with uniform repartition of fuel assemblies) as a conse-
quence of non uniform consumption. The accuracy of the analyses can be
improved significantly by modeling directly the interaction of the neutron
kinetics and the fluid-dynamics using the coupled codes calculations. This
is particularly true for a number of transients for which simple point kinetic
and one-dimensional thermalhydraulic models are not able to provide an
acceptable physical representation of the phenomena that occur in the core:
• almost all Reactivity Initiated Accidents (RIA) and especially
if the reactivity increases are induced by thermal-hydraulic effects.
In such cases strong interactions between core kinetics and coolant loop
thermal-hydraulics exist.
if the perturbation is asymmetric in the core. Typical examples of a
Design Basis Accident (DBA), which cannot easily be calculated with-
out a three-dimensional core model, are the Main Steam Line Break
CHAPTER 1. STATE-OF-THE-ART BE COUPLED TECHNIQUES 3
(see chapter 6) and Control Rod Ejection (CRE) accidents. In this
latter case considerable deformation of the radial and axial power dis-
tributions occur in the core.
if there are possibilities for re-criticality in the later phase of the
transient during the cool down phase. This is particularly emphasized
for high values of moderator temperature coefficient, for increased high
burn-up fuel (see appendix 8.2.1), or for extended use of MOX fuel.
the local boron dilution accident in PWR and VVER. The boron
concentration is often non uniformly transported into and through the
reactor core causing a reactivity transient that could be severe (see
chapter 8).
all Anticipated Transients Without Scram (ATWS) and other Be-
yond Design Basis Accidents (BDBA) need more sophisticated calcula-
tions to eliminate any uncertainty due to spatial effects. In fact, using
fewer dimensions in the core modeling did in some cases change the
whole accident scenario.
• the BWR stability issues in plant conditions and beyond the stability
threshold
• nuclear power improvement programs which generate the demand for
reducing uncertainties.
1.2 SOA Codes
Three main typologies of complex codes are required for the application of
3D coupled techniques:
• code for deriving suitable neutron kinetics cross-sections (CSC = cross
section code), such as CASMO-3, CASMO-4, PHOENIX, HELIOS,
CPM-3, APOLLO2 and TRASLAT;
• thermal-hydraulic system code (THSC), such as ATHLET, RELAP5-
3D, CATHARE-2, TRAC-PF1, TRAC-M (TRACE), TRAC-BF1 and
POLCA-T;
• neutron kinetics code (NKC), such as DYN3D, QUABOX, NESTLE,
PARCS and NEM.
CSC can be used out of the line while THSC and NKC must be coupled
and interact at each time step. In the frame of this thesis, cross-sections
have been generated with CASMO-4 and transients have been simulated
with RELAP5-3D, which constitutes a serial integration between RELAP5
THSC and NESTLE NKC (see fig. 1.1).
CHAPTER 1. STATE-OF-THE-ART BE COUPLED TECHNIQUES 4
Figure 1.1: RELAP5-3D domain
1.3 Coupling
There are certain requirements to the coupling of thermal-hydraulic system
codes and neutron-kinetics codes that ought to be considered, [48] [43] [47]
[41].
The objective of these requirements is to provide accurate solutions in
a reasonable amount of CPU time in coupled simulations of detailed opera-
tional transient and accident scenarios. These requirements are met by the
development and implementation of six basic components of the coupling
methodologies:
• Coupling approach
• Ways of coupling - internal or external coupling
• Spatial mesh overlays
• Coupled Time-Step Algorithms
• Coupling Numerics - Explicit, Semi-Implicit and Implicit Schemes
• Coupled Convergence Schemes
These requirements have been analyzed in the frame of the CRISSUE-S
Project, [59] [60] [61].
Some details related to the coupling approaches are here provided.
CHAPTER 1. STATE-OF-THE-ART BE COUPLED TECHNIQUES 5
1.3.1 Integration algorithm or parallel processing
Two different approaches are generally utilized to couple 3-D kinetics models
with system codes: serial integration coupling and parallel processing cou-
pling (fig. 1.2). Serial integration requires modifications of the codes usually
performed by implementing a neutronics subroutine into the TH system
code. Parallel processing allows the codes to be run separately and exchange
data during the calculation. The data exchange is usually performed using
Parallel Virtual Machine (PVM) environment. PVM is a powerful tool for
coupling large stand-alone codes and performs calculations on multiple pro-
cessors. PVM environment requires development of interface routine and
modification of the stand-alone codes and inputs for use with PVM.
Figure 1.2: Exchange or parameters for different ways of coupling
When the thermal-hydraulic model is built using parallel TH channels
there is also a possibility that the different channels are processed on different
processors. In this way the calculation time could be reduced significantly,
especially when modeling large BWR cores.
RELAP5-3D uses the serial integration coupling (see paragraph 3.1.2).
1.4 Need for uncertainty
Uncertainty and the need for uncertainty evaluation are linked to the use
of BE codes as opposed to conservative codes or assumptions in the code
application. The application of coupled 3D NK / THS codes implies the
CHAPTER 1. STATE-OF-THE-ART BE COUPLED TECHNIQUES 6
choice of the BE approach. Some consideration is provided in relation to the
need for BE, the difference between the BE and conservative approaches,
the origin of uncertainties and the current status of uncertainty evaluation.
Additional details can be found in refs [4], [11].
The selection of a BE analysis instead of a conservative one depends upon
a number of conditions that are independent of the analysis itself. These
include the available computational tools and expertise, the availability of
suitable NPP data, or the requests from regulatory bodies. In addition,
conservative analyses are still widely used to avoid the need for developing
realistic models based on experimental data, a task that may prove to be
unrealistic in the case of BDBA, or simply to avoid the burden of changing
an approved code or the approaches or procedures to obtain the licensing.
The demonstration of plant operational and safety margins is usually
given by means of conservative codes, whose use hides huge margins without
the possibility of explicitly quantifying them. Using best estimate state of the
art computer codes and methods permits full quantification of safety mar-
gins, optimization of plant systems and provides more cost-effective and safe
plants. As a result, the best estimate approach may allow for the elimination
of unnecessary conservatism in the analysis and could permit the regulatory
body and plant operating organization to establish a more consistent bal-
ance for a wide range of acceptance criteria. A conservative approach does
not give any indication about actual plant behavior including time scale
for preparation of emergency operating procedures, or for use in accident
management and preparation of operation manuals for abnormal operating
conditions.
Although the acceptability of the approach to be used for an accident
analysis needs to be defined by the regulatory body, the use of totally con-
servative approaches (conservative models, input data and plant conditions)
is unwarranted nowadays, given the broad acceptance of best estimate meth-
ods (e.g. mature best estimate codes are widely available around the world,
an extensive database exists for nearly all power reactor designs and best
estimate plant calculations are well documented). The use of totally best es-
timate approach implies the issue of quantifying code uncertainties for every
phenomenon and for every accident sequence.
Several sources of uncertainties threaten the accuracy of safety analy-
sis of complex thermal hydraulic systems: the simplified or approximated
models implemented in the code, incomplete and approximate knowledge of
plant data, possible errors introduced into the model by the user, limited
number of volumes, junctions and mesh points of the adopted nodalisation,
error propagation and numerical diffusion. Scaling studies to quantify the
influence of scaling variations between experiments and the actual plant en-
vironment are included in this definition. These concepts are applicable to
any of the CSC, NKC and THSC. The approaches pursued for uncertainty
evaluation can be distinguished in two main categories, i.e. propagation of
CHAPTER 1. STATE-OF-THE-ART BE COUPLED TECHNIQUES 7
code-input and of code-output uncertainties, respectively.
The uncertainty methodology proposed by University of Pisa (UMAE)
appears having achieved a reasonable maturity level, [34].
The idea of Internal Assessment of Uncertainty came to light in 1996
and was realized by the CIAU method that utilizes the basic approach of
the UMAE at the University of Pisa, [35].
The CIAU (Code with capability of Internal Assessment of Uncertainty)
allows the achievement of continuous uncertainty bands simultaneously with
the BE calculation, thus avoiding the uncertainty-methodology-user effect
and the need of resources for uncertainty prediction. However, a suitable
error-database must be made available to pursue the CIAU approach. In
a joint effort between University of Pisa and PSU the CIAU method has
been recently extended to the evaluation of uncertainty from coupled 3D
neutronics thermal-hydraulics calculations. Sample results are shown in fig.
1.3, taken from [18].
The full implementation and use of the procedure requires a database
of errors not available at the moment. However, the data reported in fig.
1.3 give an idea of the errors expected from the application of the present
computational tool to problems of practical interest.
CHAPTER 1. STATE-OF-THE-ART BE COUPLED TECHNIQUES 8
Figure 1.3: Results from a sample application of CIAU to a coupled 3D
NKC-THSC calculation
Chapter 2
Scope of the Activity
As outlined in chapter 1, many physical phenomena occurring within nuclear
systems cannot be properly described with simplified neutron kinetic models
(i.e. point kinetics) and require detailed thermal-hydraulic models coupled
with 3-D neutron kinetic codes. Local power excursions (e.g. CRE), asym-
metric cool downs, boron dilutions, axial offset shifts are examples of these
phenomena. Coupled 3D thermal hydraulic / 3D neutron kinetics codes and
methods, which have been developed in order to specifically address these
transients, presently constitute an advanced tool, whose use allows gaining
detailed results associated with largely reduced uncertainties (see chapter 1).
The coupled codes and methods capacity of accurately describing the
physical phenomena occurring in NPPs make their use advisable even for
the analysis of those transients that are not characterized by asymmetric
phenomena, such as the LBLOCA (see 9.
The inclusion of 3-D neutron kinetic core models in the safety analyses
allows the execution of Best Estimate (BE) assessments of the interactions
between core and loops, which in turn allow precisely quantifying safety
margins and optimizing plant systems, providing safer and more economic
NPP designs (see par. 1.4).
The purpose of the activity carried out is to address the application of
TH/3D-NK codes to safety analyses of PWRs, [13]. The code used for the
analyses is RELAP5-3D, developed by INEEL. Three main NPP types have
been selected, in order to cover a wide range of characteristics and problem-
atics of the present and future generations of PWRs: Westinghouse AP1000
(passive PWR, 3400 MWth, 2 loop, U-SGs, 157 square W FA 17x17), TMI-
1 (BW PWR, 2772 MWth, 2 loop, 2 OTSGs, 177 B&W square FA 15x15)
and VVER1000 (3000 MWth, 4 loop, horizontal SG, 163 hexagonal FA).
The NSSS models of these NPPs, set up and qualified in the first part of
the activity, have been used to analyze the selected reference transients:
• AP1000 DECLG LOCA
• AP1000 Small LOCA
9
CHAPTER 2. SCOPE OF THE ACTIVITY 10
• AP1000 Station Blackout
• AP1000 LTCC
• AP1000 MSLB
• VVER-1000 MCP3 Insertion
• TMI-1 B&W PWR LBLOCA
• TMI-1 Boron Dilution
• TMI-1 RTC after SCRAM due to Low Moderator Temperature
• TMI-1 SBLOCA with Loop Deboration and RCP Restart
The activity focused on two main topics: the development and qualifica-
tion of an analysis procedure, which allows performing adequate coupled 3D
NKC-THSC calculations capable of gaining reliable results, and the assess-
ment and characterization of the reactivity feedbacks due boron concentration
changes in the primary reactor coolant system (RCS).
Both topics have been addressed using the infrastructure developed, in
terms of methods, qualified nodalization, neutron kinetic and system codes.
2.1 Activity on the analysis procedure
This activity was aimed at rationalizing and improving the analysis proce-
dure adopted to carry out coupled 3D NKC/THSC calculations. Taking a
reference the classical procedure usually adopted (and which has been ob-
served during the international cooperations performed) some intermediate
steps have been added, essentially in the phase of validation of the coupling
and qualification of the cross section set. In particular, in order to improve
the assessment of the real valued added by the adoption of coupled codes
and techniques, three standard exercises were defined, which allow the align-
ment between the 0D NK and the 3D NK models, in terms of reactivity
feedbacks due to moderator density, doppler effect and boron concentration
(see chapter 5).
2.2 Activity on boron
The issue of control of recriticality following SBLOCA in PWRs [55] was
identified following a request for reconsideration of the safety priority ranking
of GSI-22, Inadvertent Boron Dilution Events, based on new information on
high burn-up fuel and new calculations provided by B&W. Reactivity inser-
tion event tests indicated that high burn-up fuel may be more susceptible to
reactivity events than previously expected, and fuel failure may occur at fuel
CHAPTER 2. SCOPE OF THE ACTIVITY 11
enthalpy values that were previously judged acceptable (see chapter 8.2.1).
In addition, B&W calculations predicted prompt criticality with significant
heat generation under conditions that may result from small-break (SB) LO-
CAs. If a B&W-designed NSSS spends some time in a boiling/condensing
mode following a SBLOCA, a substantial amount of deborated water may
accumulate in the RCP suction piping. Restart of natural circulation can be
a mechanism for causing deborated water to flow into the core, and possibly
resulting in criticality. Displacement of deborated water could potentially
cause a prompt-critical condition due to insertion of several dollars of excess
reactivity.
In addition, many PWRs have no positive means of detecting boron
dilution during cold shutdown. At the time this issue was evaluated by
USNRC, there had been more than 25 reported instances of inadvertent
boron dilution during maintenance and refueling, [50].
Although none of these events resulted in an inadvertent criticality, the
safety concern is the possibility of such an event. If the boron is sufficiently
diluted and the reactor core is near the beginning of the cycle (BOC), it is
possible to bring the reactor to criticality with all of the control rods already
inserted into the core. The only way to shut down the core again in such
circumstances would be to re-borate the moderator, an action that could
take considerable time. The reported events had occurred with sufficient
frequency to raise the question as to whether, considering their possible
consequences, the degree of protection was appropriate.
Within this context, the objective of the activity carried out on boron
is to develop a tool that allows to account properly for boron concentration
effects on reactivity and to assess the capability of the RELAP5-3D plant
code to perform a BE analysis of a boron dilution RIA. The reference plant
for the boron activity has been the TMI-1 B&W PWR. A procedure for
the calculation of boron reactivity coefficients was developed and qualified.
After the execution of some preliminary and academic calculations, aimed at
checking the model, several runs were performed representing realistic and
extreme scenarios. The outcome of this analysis was the derivation of curves
that provide the maximum energy deposition to the fuel as a function of
the amount of deborated water accumulated in the primary RCS. Finally,
RELAP5-3D capability of modeling in full transient mode the deboration
phenomenon following a SBLOCA has been assessed.
2.3 Activity on the coupling with the containment
As a bypass result of the activity, a quite detailed investigation on the op-
portunity and possibility of including a thermal hydraulic model of the con-
tainment system in the safety analysis of the NSSS was performed, [36]. An
analysis methodology was developed, which is based on off line calculations
CHAPTER 2. SCOPE OF THE ACTIVITY 12
and separate effect models.
This provides a very smooth and realistic containment model behavior
and allows a proper description of the thermal hydraulic behavior of the com-
plex system composed of the primary and secondary reactor cooling systems
and the containment.