In the last four decades, large efforts have been undertaken to provide reliable thermal-hydraulic system codes for the analyses of transients and accidents in nuclear power plants. Whereas the first system codes, developed at the beginning of the 1970s, utilized the homogenous equilibrium model with three balance equations to describe the two-phase flow, nowadays the more advanced system codes are based on the so-called “two-fluid model” with separation of the water and vapor phases, resulting in systems with at least six balance equations. The wide experimental campaign, constituted by the integral and separate effect tests, conducted under the umbrella of the OECD/CSNI was at the basis of the development and validation of the thermal-hydraulic system codes by which they have reached the present high degree of maturity. However, notwithstanding the huge amounts of financial and human resources invested, the results predicted by the code are still affected by errors whose origins can be attributed to several reasons as model deficiencies, approximations in the numerical solution, nodalization effects, and imperfect knowledge of boundary and initial conditions. In this context, the existence of qualified procedures for a consistent application of qualified thermal-hydraulic system code is necessary and implies the drawing up of specific criteria through which the code-user, the nodalization, and finally the transient results are qualified.
Evaluation of nuclear power
plants (NPPs) performances during accident conditions has been the main issue of
the research in nuclear fields during the last 40 years. Therefore, several
complex system thermal-hydraulic codes have been developed for simulating the
transient behavior of water-cooled reactors. In the early stage of the
development, the codes were primarily applied for the design of the engineered
safety systems. In 1978, the “appendix K requirements” [ safety analysis of accident scenarios; quantification of the conservative analyses margin; licensing purposes if the code is used together with a methodology
to evaluate uncertainties; probabilistic safety analysis (PSA); development and verification of accident management procedures; reactors design; analysis of operational events; core management investigation.
Best-estimate thermal-hydraulic codes (e.g., RELAP, TRAC, CATHARE, ATHLET,
Code development activities in more than three decades.
Due to the numerical
approximations and the empirical nature of the included models in the
thermal-hydraulic system codes, extensive activities related to validation of the codes have been pursued
during the years. The validation has been performed using experimental data
from specially designed scaled-down test facilities. In addition, transient data from real NPPs
were also considered due to the full scale and true geometry although those
data concern only conditions under fairly mild transients (operational
transients and start-up and commissioning tests). These activities have been
planned and carried out in national and international contexts in four levels,
mainly in the independent assessment area, involving the use of the following:
“fundamental” experiments [ separate effects test facilities (SETF) [ integral test facilities (ITF), including most of the international standard problems (ISP)
[ real plant data.
However,
notwithstanding the huge amounts of financial and human resources invested, the
results predicted by the code are still affected by errors whose origins can be attributed to several reasons as model deficiencies,
approximations in the numerical solution, nodalization effects, and imperfect knowledge
of boundary and initial conditions. In this context, the existence of qualified
procedures for a consistent application of qualified thermal-hydraulic system
code is necessary
and implies the drawing up of specific criteria through which the code-user, the
nodalization, and finally the transient results are qualified.
The current situation
related to the development, validation, and use of system codes can be
summarized as follows.
A state-of-the-art report in modeling LOCA (loss-of-coolant
accident) and non-LOCA transients and the compendium on ECCS (emergency core cooling
systems). Researches have been published in 1989 [ The CSAU (Code Scaling, Applicability and
Uncertainty), published in 1990, for example [ Code validation criteria and
detailed qualification programs exist, although not fully optimized or
internationally agreed on. In particular, the following hold. The integral test
facility CSNI code validation matrix (ITF-CCVM) report was initially published
in 1987 and extensively updated in 1996, [ As the last
expectation has proved unrealistic, a group of scientists was formed toward the
end of the 80s to set up the separate effect test facility CSNI code validation
matrix, SETF-CCVM, that was issued in 1994 [ The codes have reached an
acceptable degree of maturity although the reliable application is still
limited to the validation domain. The use of qualified codes is more
and more requested for assessing the safety of existing reactors, especially in
the former Soviet Union and in the Eastern countries, and for designing
advanced reactors. The codes availability is
increasingly growing especially in the countries belonging to the former Soviet Union, the Eastern countries,
Korea, China, and so forth. Special topics, like user [ A special attention from the scientific community has
always been given to the quantification of code uncertainty in predicting plant
transients. Methodologies to evaluate the
“uncertainty” have been proposed [
This paper reviews the
main features and limitations of the thermal-hydraulic system codes and the
procedures adopted for the qualification of computational tools, that is, not
only the codes, through the ITF and SETF validation matrixes, but also the
nodalization used to simulate the transient scenario in the NPP. Finally, taking
into account the multidisciplinary nature of reactor transients and
accidents (which include thermal-hydraulics, neutronics, structural, and
radiological aspects), the needs, the status of development, and the benefits
of code coupling are pointed out.
The system thermal-hydraulic codes are based upon the solution of six balance equations for liquid and steam that are supplemented by a suitable set of constitutive equations. The balance equations are coupled with conduction heat transfer equations and with neutron kinetics equations (typically point kinetics). The two-phase flow field is organized in a number of lumped volumes connected with junctions. Thermal-hydraulic components such as valves, pumps, separators, annulus, accumulators, and so forth, can be defined in order to represent the overall system configuration. In the following sections, main problematic aspects, from the point of view of the user, of a thermal-hydraulic system code are highlighted.
All major existing light water reactor (LWR) safety thermal-hydraulics system codes follow the concept of a “free nodalization,” that is, the code user has to build up a detailed noding diagram which maps the whole system to be calculated into the frame of a one-dimensional thermal-hydraulic network. To do this, the codes offer a number of basic elements like single volumes, pipes, branches, junctions, heat structures, and so forth. This approach provides not only a large flexibility with respect to different reactor designs, but also allows predicting separate effect and integral test facilities which might deviate considerably from the full-size reactor.
As a consequence of this rather “open strategy,” a large responsibility is passed to the user of the code in order to develop an adequate nodalization scheme which makes best use of the various modules and the prediction capabilities of the specific code. Due to the existing code limitations and to economic constraints, the development of such a nodalization represents always a compromise between the desired degree of resolution and an acceptable computational effort. It is not possible here to cover all the aspects of the development of an adequate nodalization diagram, however, two crucial problems will be briefly mentioned which illustrate the basic problem.
As has been quite often
misunderstood, a continuous refinement of the spatial resolution (e.g., a
reduction of the cell sizes) does not automatically improve the accuracy of the
prediction. There are two major reasons for this behavior:
the large number of empirical
constitutive relations used in the codes has been developed on the basis of a
fixed (in general coarse) nodalization; the numerical schemes used in
the codes generally include a sufficient amount of artificial viscosity which
is needed in order to provide stable numerical results. A reduction of the cell
sizes below a certain threshold value might result in severe nonphysical
instabilities.
From those considerations, it can be concluded that no a priori optimal approach for the
nodalization scheme exists.
Multidimensional effects, especially with respect to flow splitting and flow merging processes (e.g., the connection of the main coolant pipe to the pressure vessel), exist also in relatively small scale integral test facilities. The problem might become even more complicated due to the presence of additional bypass flows and a large redistribution of flow during the transient. It is left to the code user to determine how to map these flow conditions within the frame of a one-dimensional code, using the existing elements like branch components, multiple junction connections, or cross-flow junctions. These two examples show how the limitations in the physical modeling and the numerical method in the codes have to be compensated by an “engineering judgment” of the code user which, at best, is based on results of detailed sensitivity of assessment studies. However, in many cases, due to lack of time or lack of appropriate experimental data, the user is forced to make ad hoc decisions.
Even though the number
of user options has been largely reduced in the advanced codes, various
possibilities exist about how the code can physically model specific phenomena.
Some examples are as follows.
Choice between engineering type models for choking or use of code
implicit calculation of critical two-phase flow conditions. Flow multipliers for subcooled or saturated choked flow. The efficiency of separators. Two-phase flow characteristics of main coolant pumps. Pressure loss coefficient for pipes, pipe connections, valves, branches, and so forth.
Since in many cases direct measured data are not available or, at least, not complete, the user is
left to his engineering judgment to specify those parameters.
The assessment of LWR safety codes is mainly performed on the basis of experimental data coming from scaled integral or separate effect test facilities. Typically in these scaled-down facilities, specific effects, which might be small or even negligible for the full-size reactor case, can become as important as the major phenomena to be investigated. Examples are the release of the heat from the structures to the coolant, heat losses to the environment, or small bypass flows. Often, the quality of the prediction depends largely on the correct description of those effects which needs a very detailed representation of the structural materials and a good approximation of the local distribution of the heat losses. However, many times the importance of those effects is largely underestimated, and consequently, wrong conclusions are drawn from results based on incomplete representation of a small-scale test facility.
The general thermal-hydraulic system behavior is described in the codes by the major code modules based on a one-dimensional formulation of the mass, momentum, and energy equations for the separated phases. However, for a number of system components, this approach is not adequate and consequently additional, mainly empirical models have to be introduced, for example, for pumps, valves, separators, and so forth. In general, these models require a large amount of additional code input data, which are often not known since they are largely scaling dependent.
A typical example is the input data needed for the homologous curves which describe the pump behavior under single and two-phase flow conditions which in general are known only for a few small-scale pumps. In all these cases, the code user has to extrapolate from existing data obtained for different designs and scaling factors which introduces a further uncertainty to the prediction.
Most of the existing codes do not provide a steady-state option. In these cases pseudo-steady-state runs have to be performed using more or less artificial control systems in order to drive the code towards the specified initial conditions. The specification of stable initial and boundary conditions and the setting of related controllers require great care and detailed checking. If this is not done correctly, a large risk, that even small imbalances in the initial data will overwrite the following transient, exists especially for slow transients and small break LOCA calculations.
The calculation of state and transport properties is usually done implicitly by the code. However, in some cases, for example, in RELAP5, the code user can define the range of reference points for property tables, and therefore, can influence the accuracy of the prediction. This might be of importance especially in more “difficult regions,” for example, close to the critical point or at conditions near atmospheric pressure. Another example is constituted by the fuel materials property data: the specification of fuel rod gap conductance (and thickness) is an important parameter, affecting core dryout and rewet occurrences that must be selected by the user.
All the existing codes are using automatic procedures for the selection of time step sizes in order to provide convergence and accuracy of the prediction. Experience shows, however, that these procedures do not always guarantee stable numerical results, and therefore, the user might often force the code to take very small time steps in order to pass through trouble spots. In some cases, if this action is not taken, very large numerical errors can be introduced in the evolution of any transient scenario and are not always checked by the code user.
In order to prepare a complete input data deck for a large system, the code user has to provide a huge number of parameters (approx., 15 to 20 thousand values for an NPP nodalization) which he has to type one by one. Even if all the codes provided consistency checks, the probability for code input errors is relatively high and can be reduced only by extreme care following clear quality assurance guidelines.
A key feature of the activities performed in nuclear reactor safety technology is constituted by the necessity to demonstrate the qualification level of each tool adopted within an assigned process and of each step of the concerned process. Computational tools include (numerical) codes, nodalizations, and procedures. Furthermore, the users of those computational tools are part of the process and need suitable demonstration of qualification.
A consistent application (development, qualification, and application) of a thermal-hydraulic system code is
depicted in Figure
A consistent application (development, qualification and application) of a thermalhydraulic system code.
The code constitutes the main tool for
investigating the NPP behavior or for evaluating the efficacy of systems or
special procedures during accident transient scenarios. The following
constitutes the main requisites for a qualified use of the code [ Capability of the code to reproduce the relevant phenomena occurring for the selected spectrum of accidents. Capability to reproduce the peculiarities of the reference plant/facility. Capability to produce suitable results for a comparison with the acceptable criteria. Availability of qualified users. The NPP and the accident conditions: all the
relevant zones, systems, procedure, and related actuation logic is to be
included in the calculation. This item also includes any external event,
boundary and initial condition necessary to identify the plant but also the
selected accident. The phenomena occurring (expected) during the accident. Development phase: several models are
created, developed, and improved by the code development team; many checks are
necessary to qualify each model and the global architecture of the code. Independent assessment phase: the code is ready to be used but qualified calculations performed by organizations independent from the code-development team are needed to check independently
the declared capabilities of the code.
Essentially the code must be able to reproduce two fundamental aspects [
In order to ensure those capabilities, the code qualification process is needed and the following two phases can be identified.
It is relevant to note that in the development phase the code models can be changed and the code is not available to the final user. In the independent assessment phase, the final version of the code is
distributed and the user is generally forbidden to change any element of the
code models apart from the normal available options as described in the user
manual.
The activities performed during the development
phase are (Figure qualification of the nodalization; qualification of the user; definitions of procedures for the use of the code; evaluation of the accuracy from a qualitative and quantitative point of view.
The
The above items are connected with the application of the code to experimental tests performed in ITF. The procedure
for the qualification of the nodalization is described with more details in the
Section
Internal and external (independent) code assessment.
Besides the demonstration of the code capability in reproducing an experiment performed in a test facility, the code
must be checked also in performing NPP calculation. This constitutes the final
step of the independent code assessment (Figure
Code independent assessment.
The contemporaneous acceptability of
the accuracy (step of the process connected with experiments in ITF) and of the
similarity analysis (step of the process connected with NPP) constitutes the positive
demonstration of the code capability and the end of the code assessment. The
calculated accuracy is possibly included in the data base suitable for
uncertainty evaluation (block 6 in Figure
As consequence, new revision or new version of
the code can be produced during the development phase: a new revision contains
a new physical modeling whereas a new version may contain new numerical
methods, new modules, new submodules, new preprocessing or post-processing or a
new code architecture. The steps
typically performed during the qualification process of a new revision or of a new
version of the code are depicted in Figure Analytical experiments, with separate effect tests and component tests,
are used for the development and the validation of closure laws. System tests or integral tests used to validate the general consistency
of the revision. Successive revisions of constitutive laws are implemented in
successive versions of the code and assessed.
Constitutive relationships are developed and assessed following a general methodology hereafter summarized.
Qualification process of a new revision or a new version of the code.
Analytical experiments, including separate effect tests and component tests, are performed and analyzed. Separate effect tests investigate a physical process such as the interfacial friction, the wall heat transfer. Component tests investigate physical processes which are specific to a reactor component, such as the phase separation in a Tee junction.
Development of a complete
Qualification calculations of the analytical tests are used in order to validate each closure relationship.
Verification calculations of system tests or integral tests are used in order to validate the general consistency of the revision.
Delivery of the code version and revision is fully assessed (qualified and verified) and documented (description documents and assessment reports).
A new revision of constitutive laws is developed using some general principles.
Data are first compared with existing models; if necessary, original
models are developed. When and where data are missing, simple extrapolations of existing
qualified models are used. No mechanistic model is developed without the
experimental evidence of its relevance. In a prequalification phase, some tests of each experiment of the
qualification matrix are calculated. A systematic qualification of the frozen revision is then performed. All
tests of the qualification matrix are calculated and qualification reports are
written. The qualification program has to cover the whole range of accidental transients
in LWR. As examples, the following accidents have to be considered for a PWR: large
break loss of coolant accidents (LBLOCA); small break loss of coolant accidents
(SBLOCA); steam generator tube ruptures (SGTR); loss of feed water (LOFW); main
stream line break (MSLB); loss of residual heat removal (RHR) system. The code has to be fully portable on all machines, so that a unique code
version is released to all the users. No code options for physical models, or as few as possible, have to be
proposed to the user. The users guidelines should be as precise as possible and take full
benefit of the experience gained from the code-development team.
Some other additional remarks about the qualification process of the code are as follows.
The validation against experimental data is essential in the process of system codes development and
improvement as it has been discussed in the previous section. The models implemented and used in a code are
generally developed based on experimental tests performed in specific facilities. It is possible to distinguish among.
Basic facilities: In these facilities the fundamental phenomena are
reproduces; the results are used to improve the equations of the single model
or to derive empirically the relation between the relevant parameters; this
kind of facilities are designed with goal to reproduce the specific phenomenon
to be investigate. Separate effect facilities: in these facilities some relevant zones of
the NPP are reproduced by a suitable scaling law to investigate the local
occurrence of a phenomenon; the results of the experiments performed in these
facilities are used to create and to validate the (several) models to be included
in a code. Integral tests facilities: these facilities are simulators of reference
NPP. All the relevant parts and systems of an NPP are reproduced by a suitable
scaling law. The whole plant is reproduced and the global plant response is obtained
as results. The results are used to realize and improve the models and to check
the code capabilities.
It will be noted that also the data from NPP
can be used, if available. However, in an NPP the data obtained are the one
recorded by the system of control of the plant while, typically, the facilities
are equipped with a large number of sensors and many detailed data are generated
making the instrumentation of the facilities more suitable for code validation.
Huge effort was done by the
OECD/NEA/CSNI from 1991 to 1997 in the construction of the separate effects
test facility code validation matrix (SETF-CCVM, published in 1994) for thermal-hydraulic
system codes [
By the validation matrices, the best sets of openly available experimental data for code validation, assessment, and improvement were collected in a systematic way. Quantitative code assessment with respect to the quantification of uncertainties in the modeling of individual phenomena by the codes is also an outcome of the matrix development. In addition, the construction of such matrices is an attempt to record information of the experimental work which has been generated around the world over the last years in the LWR safety thermal-hydraulics field. 187 facilities covering 67 relevant phenomena for LOCA and non-LOCA transient applications of PWRs and BWRs within a large range of useful parameters were identified and about 2094 tests were included in the SETF-CCVM matrix. The majority of these phenomena are also relevant to advanced water-cooled reactors. The major elements of the SETF-CCVM have been already integrated into the validation matrices of the major best-estimate thermal-hydraulic system codes, for example, RELAP5, CATHARE, TRACE, and ATHLET.
A total number of 177 PWR and BWR integral tests have
been selected as potential source for thermal-hydraulic code validation in the
ITF-CCVM report. Counter-part tests, similar tests and OECD ISP
tests were introduced in the report. Counter-part tests and similar tests in
differently scaled facilities are considered highly important for code
validation and therefore they were included in the tables of ITF selected
experiments. Moreover, over the last
twenty-nine years, CSNI has promoted 48 ISPs [
The reason why this section has been included
in the paper directly derives from the fact that the scaling analysis is the
needed link between the experiments performed in ITF and SETF and their
utilization in the code validation process. The flow diagram in Figure
Role of the scaling analysis in the code assessment process.
An NPP is characterized by high power (up to
thousands of MW), high pressure (tens of MPa), and large geometry (hundreds of
m3), thus it is well understandable the impossibility to perform
experiments preserving all these three quantities. The term scaling is in
general understood in a broad sense covering all differences existing between a
real full size plant and a corresponding experimental facility. An experimental
facility may be characterized by geometrical dimension and shape, arrangements,
and availability of components, or by the mode of operation (e.g., nuclear versus
electrical heating). All these differences have the potential to distort an
experimental observation precluding its direct application for the design or
operation of the reference plant. Distortion can be defined as a partial or
total suppression of physical phenomena caused by only changing the size
(geometric dimension) or the shape (arrangement of components) of the facility
[
Three main objectives can be
associated to the scaling analysis as follows:
the design of a test facility; the code validation, that is, the demonstration that the code accuracy is
scale independent; the extrapolation of experimental data (obtained into an ITF) to predict
the NPP behavior. Time-reducing scaling:
rigorous reduction of any linear dimension of the test rig would result in a
direct proportional reduction in time scaling. This is considered to be of
advantage only for cases where body forces due to gravity acceleration are
negligible compared to the local pressure differentials. Time preserving scale: based on a scale reduction of the volume of the loop system combined with a direct proportional scaling of energy sources and sinks (keeping constant the core power to system
volume ratio). Idealized time preserving modeling procedures: based on the equivalency of the mathematical representation of the full size plant and of the test rig. It is deduced from a separated treatment of the conservation equations for all involved volume modes and flow paths assuming homogeneous fluid.
For the test facility design, three types of scaling principles can be adopted as follows.
Integral test facilities are normally designed to preserve geometrical similarity with the reference reactor system. Generally all main components (e.g., rector pressure vessel, downcomer, rod bundle, loop
piping, etc.) and the engineered safety system (HPIS, LPIS, accumulators,
auxiliary feed water, etc.) are represented. ITF are used to investigate, by
direct simulation, the behavior of an NPP in case of off-normal or accident
conditions. The geometrical similarity of the hardware of the loop systems has
been abandoned in favor of a preservation of geometric elevations, which are
decisive parameters for gravity dominated scenarios (e.g., in case of natural
circulation processes). Thus the reduction of the primary system volume is
largely achieved by an equivalent reduction in vertical flow cross sections.
Due to the impossibility to perform relevant
experiment at full scale (i.e., in an NPP), the use of ITF or SETF is unavoidable.
In order to address the scaling issue, different approaches have been proposed
and are available from literature. However, a comprehensive solution has not
yet been achieved and moreover, it is evident that the attempt to scale up all thermal-hydraulic phenomena that occur during an assigned transient results in a myriad
of factors which have counterfeiting values [
Schematic representation of a two-phase flow condition in a reactor pressure vessel of a facility during an SBLOCA.
As a consequence, the only way to solve the
scaling problem is to consider only those phenomena and parameters that have a
real impact on the whole problem under investigation. The focusing on a single
phenomenon which occurs during a limited time (compared with the entire
duration of the problem) should be avoided because it is governed by factors
that are not scalable. Therefore a
hierarchy in the definition of the scaling factors is necessary and a global
strategy is needed [ developing a system code; qualifying the code against experimental data; demonstrating that the code-accuracy (i.e., discrepancy
between measured and calculated trends) only depends upon boundary initial conditions
(BIC) values (within the assigned variation ranges) and is not affected by the
scale of concerned ITF; applying such code to predict the same
relevant phenomena that are expected to find in a same experiment (or
transient) performed at different scale; performing NPP Kv-scaled calculation and
explaining the discrepancies (if any) between NPP Kv-scaled calculation and
measured trends in ITF considering only BIC values and hardware differences
(i.e., distortions).
Assuming the availability of a qualified code and of a qualified user, it is necessary to define a procedure to qualify the nodalization in order to obtain qualified (i.e., reliable) calculation results. In this section a procedure for the nodalization qualification is discussed.
A major issue in the use of mathematical models is constituted by the model capability to reproduce the plant or facility behavior under steady-state and transient conditions. These aspects constitute two main checks for which acceptability criteria have to be defined and satisfied during the nodalization-qualification process. The first of them is related to the geometrical fidelity of the nodalization of the reference plant; the second one is related to the capability of the code nodalization to reproduce the expected transient scenario.
The checks about the nodalization are necessary
to take into account the effect of many different sources of approximations,
like the following.
The data of the reference plant available to the user are typically non exhaustive to reproduce a perfect “schematization” of the reference plant. From the available data, the user derives an approximated nodalization of the plant reducing the level of detail. The code capability to reproduce the hardware, the plant systems and the actuation logic of the systems reduce further the level of detail of the nodalization. the code options must be adequate; the nodalization solutions must be adequate; some systems components can be tested only during transient conditions (e.g., ECCS that are not involved in the normal operation).
The reasons for the checks about the capability
of the code nodalization to perform the transient analysis deriving from
following considerations:
A simplified scheme of a procedure that can be adopted for the qualification of the nodalization is depicted in Figure
Flow sheet of nodalization qualification procedure.
This step is related to the information available by the user manual and
by the guidelines for the use of the code. This type of information takes into
account the specific limits and assumptions of the code (specific of the code
adopted for the analysis) and some guidelines deriving from the best practices for
realizing the nodalization. From a generic point of view, the following aspects
should be carefully adopted:
homogeneous nodalizations; strict observation of the user guidelines; standard use of the code options.
User experience and developers recommendations are useful to set up particular procedure to be applied for a better nodalization. These special procedures are related to the specific code adopted for the analysis. An example is constituted by the “slice nodalization” technique adopted with the RELAP5 code to improve the capability of the code to reproduce transients involving natural circulation phenomena.
The realization of the nodalization depends on several aspects:
available data, user capability and experience, code capability. The
nodalization must reproduce all the relevant parts of the reference plant; this
includes geometrical and materials fidelity and reproduction of the systems and
related logics. From a generic point of view, the following recommendations can
be done.
Data must be qualified or in other words, data has to derive from
qualified data facility (if the analysis is performed for a facility); qualified test design; qualified test data. The data base for the realization of the nodalization should be derived from
official document and traceability of each reference should be maintained.
However three different types of data can be identified as follows:
qualified data, from official sources; data deriving from nonofficial sources; these types of data can be derived from
similar plant data, or other qualified nodalization for the same type of plant; the use of these data can introduces potential errors and the effect on the calculation results must be carefully evaluated; data assumed by the user; these data constitute some assumptions of the user (on the base of the experience or by similitude with other similar plants). The use of this type of data should be avoided. Any special assumptions adopted by the user or special solutions in the nodalization must be recorded and documented.
The “steady-state” qualification level includes different checks: one is related to the evaluation of the geometrical data and of numerical values implemented in the nodalization; the other one is related to the capability of the nodalization to reproduce the steady-state qualified conditions. The first check should be performed by a user different from the user has developed the nodalization. In the second check a “steady-state” calculation is performed. This activity depends on the different code peculiarities. As an example, for RELAP5, the steady-state calculation is constituted by a “null-transient” calculation (i.e., the “transient” option is selected and no variation of relevant parameters occurs during the calculation).
The relevant geometrical values and the relevant thermal-hydraulic parameters of the steady-state conditions are identified. The selected geometrical values and the selected relevant parameters are derived, respectively, from the input deck of the nodalization and from the steady-state calculation for performing the comparison with the hardware values and the experimental parameters.
This is the step where the adopted acceptability criteria are applied to
evaluate the comparison between hardware and implemented geometrical values in
the nodalization (e.g., volumes, heat transfer area, etc.) and between the experimental
and calculated steady-state parameters (e.g., pressures, temperatures, mass
flow rates, etc.). Some comments can be added as follows.
The experimental data are typically available with error bands which
must be considered in the comparison with the calculated values and parameters. The steadiness of the steady-state calculation must be checked.
If one or more than one of the checks in the step “f” are not fulfilled,
a review of the nodalization (step “c”) must be performed. This process can
request more detailed data, improvement in the development of the nodalization,
different user choices. The path “g” must be repeated till all acceptability
criteria are satisfied. A list of the geometrical values and of the
thermal-hydraulic parameters to be checked is given in Table
Parameters and acceptable errors for the nodalization qualification at “steady-state” level.
Quantity | Acceptable error ( | |
---|---|---|
1 | Primary circuit volume | 1% |
2 | Secondary circuit volume | 2% |
3 | Nonactive structure heat transfer area (overall) | 10% |
4 | Active structure heat transfer area (overall) | 0.1% |
5 | Non-active structure heat transfer volume (overall) | 14% |
6 | Active structure heat transfer volume (overall) | 0.2% |
7 | Volume versus height curve (i.e., “local” primary and secondary circuit volume) | 10% |
8 | Component relative elevation | 0.01 m |
9 | Axial and radial power distribution ( | 1% |
10 | Flow area of components like valves, pumps orifices | 1% |
11 | Generic flow area | 10% |
(*) | ||
12 | Primary circuit power balance | 2% |
13 | Secondary circuit power balance | 2% |
14 | Absolute pressure (PRZ, SG, ACC) | 0.1% |
15 | Fluid temperature | 0.5% (**) |
16 | Rod surface temperature | 10 K |
17 | Pump velocity | 1% |
18 | Heat losses | 10% |
19 | Local pressure drops | 10% ( |
20 | Mass inventory in primary circuit | 2% ( |
21 | Mass inventory in secondary circuit | 5% ( |
22 | Flow rates (primary and secondary circuit) | 2% |
23 | Bypass mass flow rates | 10% |
24 | Pressurizer level (collapsed) | 0.05 m |
25 | Secondary side or downcomer level | 0.1 m ( |
°The % error is defined as the ratio (reference or measured value—calculated value).
The “dimensional error” is the numerator of the above expression.
*With reference to each of the quantities below, following a one-hundred-second “null-transient” calculation, the solution must be stable with an inherent drift <1%/100 second.
**And consistent with power error.
⋀ Of the difference between the maximum and minimum pressure in the loop.
⋀ ⋀ And consistent with other errors.
This step constitutes the “On Transient” level qualification. This
activity is necessary to demonstrate the capability of the code nodalization to
reproduce the relevant thermal-hydraulic phenomena expected during the
transient. This step also permits to verify the correctness of some systems
that are in operation only during transient events. Criteria, both qualitative
and quantitative, are established to express the acceptability of the transient
calculation. Two different aspects can be identified as follows.
The code input deck concerns with the nodalization of an ITF. In this case the code calculation is used for the
code assessment. Checks include the code options selected by the user, the
solutions adopted for the development of the ITF nodalization, the logic of
some systems (e.g., ECCS). Typically many experimental results are available,
thus a similar test can be adopted for performing the “On Transient” level
qualification. The objective of the code
calculation is constituted by the analysis of a transient in an NPP. In this
case, it is necessary to check the nodalization capability to reproduce the
expected thermal-hydraulic phenomena occurring during the transient, the
selected code options, the adopted solutions for the development of the NPP
nodalization, and the logic of the systems not involved in the steady-state
calculation. Typically no data exist for the transients performed in the NPP. For
this reason, data from experiments carried out in ITF can be used for
performing the so-called “Kv-scaled” calculation. The Kv-scaled calculation
consists in using the developed NPP nodalization for predicting an experimental
transient (whose kind is similar to the one under investigation in the NPP)
performed in an ITF. The NPP nodalization is prepared for the Kv-scaled
calculation by properly scaling the BICs characterizing the selected transient
in the ITF. In other words, power, mass flow rates and ECCS capacity are scaled
adopting as scaling factor the ratio between the volume of the facility and the
volume of the NPP. The capability of the nodalization to reproduce the same
transient evolution and the thermal-hydraulic relevant phenomena is the needed
request for satisfying the “On Transient” qualification level.
In this step the relevant thermal-hydraulic phenomena and parameters
are selected and a comparison between the calculated and experimental data is
performed. The selection of the phenomena derives from the following sources:
experimental data analysis (engineering judgment is request); CSNI phenomena identification; use of Relevant Thermal-hydraulic Aspects (RTA, engineering judgment is request).
This is the step where checks are performed to evaluate the acceptability of the
calculation both from qualitative and from quantitative point of view. For the
qualitative evaluation the following aspects are involved:
Visual observation. This means that a visual comparison is performed
between experimental and calculated relevant parameters time trends; Sequence of the resulting events. This means that the list of the
calculated significant events together with their timing of occurrence is compared
with the experimental events; Use of the CSNI phenomena. The relevant phenomena suitable for the code
assessment and their relevance in the selected facility and in the selected
test are identified. A judgment can be express taking into account the
characteristics of the facility, the test peculiarities and the code results; Use of the RTAs. RTAs are typically identified inside the
phenomenological windows (i.e., time windows where a unique relevant phenomenon
is occurring) and are characterized by special parameters. These parameters can
be time values, single values, integral values, gradient values and
nondimensional values.
An example of a table containing RTAs is given in Table
Quantitative checks
are carried out by using the Fast Fourier Transform Based Method (FFTBM). This
special tool performs the comparison between experimental and calculated time
trends in the frequency domain for a list of selected parameters and
calculates, for each of them, a numerical value by which the accuracy is
quantitatively evaluated (no engineering judgment is involved in this process).
The FFTBM makes also possible to obtain a numerical judgment of the overall
results of the calculation. Criteria based on the values attained by FFTBM had
been selected for accepting the transient calculation. A description of the
FFTBM can be found in [
UNIT | EXP | UNIPI 91BN1OLPSI | CEA c2m4_lcea | Judgment UNIPI/CEA | ||
---|---|---|---|---|---|---|
RTA: pressurizer emptying | ||||||
TSE | Emptying time* | s | 131 | 46 | — | R/- |
Scram time | s | 41 | 38 | 41 | R/E | |
RTA: steam generators secondary side behaviour | ||||||
TSE | Main feed water off, turbine bypass | s | 59 | 55 | 42 | E/R |
SVP | Difference between PS and SG 1 SS pressure at 100 s | MPa | 0.42 | 0.33 | 0.37 | R/R |
SVP | SG 1 mass | Kg/(s) | ||||
at the end of subcooled blowdown | 774/(82) | 781/(75) | 761/(82) | E/E | ||
when PS pressure equals SG 1 SS pressure | 869/(618) | 938/(408) | 847/(463) | R/R | ||
when ACC starts | 804/(2955) | 802/(3019) | 788/(3075) | E/R | ||
when LPIS starts | 938/(5176) | 1126/(6529) | 956/(5474) | R/R | ||
SYP | SG 1 pressure | MPa | ||||
at the end of subcooled blowdown | 7.15 | 7.10 | 7.05 | E/E | ||
when PS pressure equals SS pressure | 6.95 | 7.04 | 7.03 | R/R | ||
when ACC starts | 4.11 | 3.95 | 4.00 | R/E | ||
when LPIS starts | 0.88 | 0.83 | 0.83 | E/E | ||
RTA: subcooled blowdown | ||||||
TSE | Upper plenum in sat conditions | s | 83 | 100 | 110 | R/R |
IPA | Break flow up to 100 s | kg | 152 | 161 | 162 | R/R |
RTA: first dryout occurrence | ||||||
TSE | Time of dryout | s | 2237 | 2299 | 2444 | E/R |
Range of dryout occurrence at various core levels | s | 2237 | 2299 | 2444 | R/R |
This path is actuated if any of the checks (qualitative and quantitative) is not fulfilled. The nodalization is improved by adopting different noding solutions, changing code options or increasing the level of detail using, if available, more precise data. Every time the nodalization is modified a new qualification process will be performed through the loop “c-d-e-f-h-i-j-c.”
This is the last step of the procedure. The obtained nodalization is used for the selected transient and the selected facility or plant. Any subsequent modification of the nodalization (e.g., necessary to better reproduce the experimental results) requires a new qualification process both at “steady-state” and “on transient” level.
Complex computer codes are used for the
analysis of the performance of NPPs. They include many types of codes that can
be grouped in different categories [
Historically, these codes have been developed independently, but have been mainly used in combination with system thermal-hydraulic codes. By increasing the capacity of computation technology, safety experts thought of coupling these codes in order to reduce uncertainties or errors associated with the transfer of interface data and to improve the accuracy of calculation. The coupling of primary system thermal-hydraulics with neutronics is a typical example of code coupling; other cases include coupling of primary system thermal-hydraulics with structural mechanics, fission product chemistry, computational fluid dynamics, nuclear fuel behavior and containment behavior. Problems that need to be addressed in the development and use of coupled codes include ensuring adequate computer capacity and efficient coupling procedures, validation of coupled codes and evaluation of uncertainties, and consequently the applicability of coupled codes for safety analyses.
The major purposes of the development of
coupled code are to be capable of representing the results of interactions
between different physical phenomena in more detail. Since the calculation
method of each code is not changed, reduction of computational time or necessary
computer memory volume is not expected. Nevertheless, many additive benefits
are expected as follows.
Since the interface data are easily, automatically and frequently exchanged between codes, the results of
calculation would be obtained faster than the combination of individual codes
and also be more reliable. Since the development works are limited to
the interface part, the cost and time for development can be minimized. Since the interface data between each code would be adjusted to meet the specifications (e.g., noding of the system or time increment of calculation) of each code at the development stage, additional assumptions or data averaging and reductions are not required when performing the calculation. Those that have the knowledge of the
existing codes are not necessary to study the coupled code from the beginning,
because the existing knowledge is applicable to the coupled code. improvement of the understanding of the phenomena of interest for safety; better assessment/demonstration of the conservatisms (versus historical approaches such as the use of point kinetics or evaluation models); extension of the capabilities of the codes for safety analysis and training/simulators; better assessment of uncertainties associated with the use of best estimate couplet codes. Faster turnaround of calculation allows the users to perform more precise analysis and more sensitivity or case studies. This would contribute in more detail to understand the features of the plant, systems or components. More accurate calculation would contribute to remove unnecessary uncertainties and to identify margins available to use for the plant. Uncertainties due to user effects would be minimized because the existing knowledge of individual codes is applicable to the coupled codes. design the coupling so that auditing is easy and feasible; provide guidelines to minimize user effects; allow provisions for reasonable conservatisms; structure the code so that coupling is easy and feasible; standardize the coupling procedures; integrate as much as possible the existing approved calculation methodologies.
It is expected that those benefits can contribute to the improvement of activities carried out by both licensing
authorities and industries. Expectations for licensing authorities can mainly
be derived from the features of coupled codes such as more accurate calculation
than the combination of individual codes. These are summarized as follows:
Many benefits are expected with the use of coupled codes for industries. These are as follows.
The request to use qualified tools in licensing calculations constitutes one of the main problems to be addressed in the
development of coupled computer codes and it is caused by the limited
availability of data, which can be obtained from operating plants. To reduce
the effort for the qualification of the coupled codes, code developers are
requested to use only validated revisions of codes. In addition, the code
developers are requested to
A noticeable progress in the capabilities of system codes has been observed in the past decades. From the design and safety engineering point of view, thermal-hydraulic system codes are considered to have reached an acceptable level of maturity. Most of the problems and questions that come up a couple of decades ago have been solved or an answer has been proposed. In other words, there is more need to synthesize the work done in the international ground than to identify new problems. For instance, if corresponding measured and calculated trends are given, possible research should be focused on answering whether the discrepancy is acceptable and less on minimizing the discrepancy itself (e.g., through an improved model). It is evident that all the progress has been made in the recent past is a consequence of experimental researches. After 30 years of validation through basic, separate and integral effect tests facilities and after code improvements, system codes are able to predict main phenomena of PWR & BWR transients with reasonable accuracy. Nowadays the attention should be focused more on developing procedures for a consistent application of a thermal-hydraulic system code. This need has been highlighted in the paper and implies the drawing up of specific criteria through which the code-user, the nodalization and finally the calculated transient results can be qualified.
The full exploitation of “advanced” best-estimate system codes (e.g.,
TRAC, RELAP, ATHLET, CATHARE), which are strictly based on two-fluid
representation of two-phase flow and a “best-estimate” description (in contrast
with the evaluation models which used many conservative assumptions) of complex flow and heat transfer
conditions, implies mainly their acceptability by the licensing authorities. In
fact, notwithstanding the important achievements and progresses made in the
recent years, the predictions of advanced best-estimate computer codes are not
exact but remain uncertain because of the following.
The assessment process depends upon data almost always
measured in small scaled facilities and not in the full power reactors. The models and the solution methods in the codes are
approximate: in some cases, fundamental laws of the physics are not considered.
Consequently, the results of the best estimate code calculations may not be applicable to
give “exact” information on the behavior of an NPP during postulated accident
scenarios. Therefore, best-estimate analysis must be supplemented by proper
uncertainty evaluations in order to be meaningful and conditions for their
application should be made clear for accepting the available uncertainty
methods in the licensing process.
In conclusion, the present status, of system codes development, assessment, and related uncertainty evaluation, is adequate as far as the largest majority of design and safety problems of current water-cooled reactors are concerned. Anyway, new scientific goals must be achieved. To this aim, projects and programmes based on the development of system codes with multidimensional and multifluid capability and with “open” interfaces for an easy coupling with other codes in areas like neutronics (for implementing presently available 3D codes), CFD, structural mechanics (e.g., for pressurized thermal-shock studies), and containment constitute the new frontier of the scientific and engineering community in this field. However, taking into account that the development of such codes with measurable increased improvements in their capabilities may need several decades, it is an evident consequence that the existing system thermal-hydraulic codes are going to be used for one or two decades in their present configuration.
One-dimensional, three-dimensional
Best estimate
Best-estimate methods-uncertainty and sensitivity evaluation
Boundary initial conditions
Boiling water reactor
CSNI code validation matrix
Computational fluid dynamic
Code scaling applicability and uncertainty
Committee on the safety of nuclear installations
Emergency core cooling systems
Fast fourier transform based method
Homogeneous equilibrium model
High pressure injection system
International standard problem
Integral test facility
Large break loss of coolant accidents
Loss of coolant accident
Loss of feed water
Low pressure injection system
Light water reactor
Main steam line break
Nuclear power plants
Organization for cooperation and development
Probabilistic safety analysis
Pressurized water reactor
Residual heat removal
Relevant thermal-hydraulic aspect
Small break loss of coolant accidents
Separate effect test facility
Steam generator tube ruptures
Software quality assurance
Two-phase flow condition
Uncertainty method study