Chapter 2 – OVERVIEW OF 3D-NK-TH COUPLED CODES
METHODOLOGY
2.1.
COUPLED CODES APPROACH
Recent developments in numerical methods and computational resources combined with the accumulated experience in power plant operation has made possible a more in-depth investigation of complex phenomena in nuclear reactor technology. Nowadays, the use of coupled codes in a wide range of engineering problems are extensively used, as processing time is reduced and more complete results are achieved.
In this chapter, an overview of the coupling methodology of TH and NK codes for transient evaluation in NPP will be briefly described. More detailed information can be found in References [2] and [19].
The incorporation of 3D analysis of the reactor core for transient calculations, motivated by enlargement of computational resources, is at present time worldwide spread and tends to replace the former 2D or 1D evaluations. The reason of its extensive use is that it may allow gaining margins by predicting a more realistic core behaviour during accident than the former calculations tools.
The trend nowadays tends to be more directed to performing the analyses with a best-estimate (BE) approach, meaning that the TH phenomena are simulated as accurately as possible. In TH analyses core power distributions are usually explicitly specified, for instance by providing time-dependent functions. It can also be obtained from simplified kinetics models simulating in most cases only the transient overall core reactivity feedback responses (considering the core as a “point” or point kinetics or “0-D”) or from a one-dimensional kinetics approach. Consequently, by employing these methodologies, the simulation of a detailed core power distribution is not possible and an approach using static power factors has been established.
However, this practice requires the application of additional conservatisms when specifying those power factors, as they also have to include uncertainties due to the loss in resolution of the transient true spatial power distribution. Thus conservative and unfavourable core power distributions are applied in the TH analysis to ensure the fuel rods will experience more severe
As another branch, separate from the basic TH system analysis area, advanced computer codes have been developed for the transient 3D simulation of nuclear kinetics responses of a nuclear reactor core exposed to various reactivity perturbations. These perturbations can have their origin in control rod movements or changes in the TH conditions of the core coolant, including changes in the concentration of soluble boron in the liquid phase. The associated power variations can include both global core-wide changes but also local changes restricted to only a few fuel assemblies. The original core power level and operational history (burn-up) have profound influences on the power responses.
The codes use nuclear cross-section tables evaluated on a detailed level, providing neutron energy dependent probabilities for specific nuclear reactions to occur. Those tables are used as a basis for determining the core state which includes allowances for burnable absorbers and for flux heterogeneities at fuel assembly borders and core outer regions (reflector sections). The needed core TH conditions have mostly been obtained from quite simple internal TH models simulating only the conditions in the core itself, with the need for adequately specified boundary conditions at core inlet and outlet sides, or at best from simple models simulating the RPV internal flow paths.
Normally, the TH and NK codes were developed to accomplish different tasks in nuclear design and safety analysis. Nevertheless, with recent computer developments resulting in the availability of powerful computation capabilities at reasonable costs, the interconnection between the two disciplines has become possible. This type of detailed NK-TH overall simulation capability of transients in LWR NPP may provide a more complete evaluation of the safety margins found in previous (licensing) TH simulations in which a point kinetics model or a 1-D model was used. This re-evaluation of the safety margins, from a more realistic (BE) point of view, may bring incentives to more efficiently utilise the fuel and obtain cost benefits in the operation of the nuclear power plants while still preserving – and possibly even improving – nuclear safety [3].
2.2.
FIELDS OF APPLICATION
The 3D-NK-TH technique is particularly suitable for simulating transients which involve core spatial asymmetric phenomena and strong feedback effects between core neutronics and reactor loop thermal-hydraulics.
Relevant PWR transients for coupled 3D-NK-TH analyses are briefly described below and consideration has been given to the recently issued IAEA guidelines [8].
• MSLB - Accident originated by the double-ended guillotine break of one SL. Positive reactivity is caused by the cooling of the primary water following depressurisation of the SG. The “plug” of cold water typically reaches the core a few seconds after the break occurs in the steam line. A regional core power increase may occur due to partial mixing in the RPV downcomer of cold water from the affected SG with hot water from the intact SG. The potential regional nature of the transient and the amount of positive reactivity introduced justify the coupled analysis. HZP and FP initial conditions can be investigated at BOC and EOC conditions.
• LOFW-ATWS - Blockage of FW pumps also originated by partial station blackout causes LOFW. Primary loop temperature increase and moderator and Doppler neutron feedbacks contribute to power decrease. The ATWS analysis is deemed necessary considering the (relatively high) accident frequency. The accident scenario originated by the MSIV closure, again with the ATWS condition (i.e. MSIV closure-ATWS) could be studied with similar assumptions (apart from the initiating event) as the LOFW-ATWS;
• CR ejection - Local reactivity increase is expected following CR ejection. This justifies the application of the 3D coupled techniques. The highest worth CR should be considered. HZP and HFP initial conditions can be investigated at BOC and EOC conditions. Ejection of CR banks or of a group of CR can be of interest. The CR ejection is connected with an SBLOCA due to the damage of the holding mechanism for the ejected rod;
• LBLOCA-DBA - The accident is originated by the double-ended guillotine break of one CL at a location between the RPV and the MCP. The accident constitutes a pillar in the safety demonstration and in the licensing of any LWR, with main reference to the evaluation of the ECCS design and thus is part of the official NPP FSAR. The proposal for 3D neutron kinetics/thermal-hydraulic analysis is mainly linked to the need to quantify the conservatism introduced by the highly conservative peak factors for linear power that cause high values for PCT. The use of advanced coupled neutron kinetics/thermal-hydraulic techniques engenders the removal of that
RIA occurs in the case of positive moderator temperature coefficient, which is possible in principle at BOC with a high boron concentration;
• Boron Dilution - The inactive loop is assumed to have de-borated water in the loop seal having a volume consistent with the system geometry. This transient is representative of transients originated by the presence of boron in the primary loop;
• MSLB-ATWS - The MSLB constitutes a DBA transient (see description above). The ATWS feature is not justified by any PSA study. Rather, the recommendation for the 3D coupled analysis derives from the bounding nature that this transient might have (i.e. in terms of input reactivity for the core) and from the consideration that core integrity can be predicted for such an extreme situation.
• SBLOCA-ATWS - This is a TMI-type accident originated by a small loss of integrity in the primary loop. The relatively high frequency of occurrence justifies the ATWS condition. Positive reactivity insertion can be assumed to come from de-borated water coming from any ECCS. The amount of fresh water injection should be in accordance with the individual plant’s features and maintenance programmes.
2.3.
COUPLED COMPUTATIONAL TOOLS REQUIRED
Complex codes are required for the following three steps in the application of 3D coupled Techniques [3]:
• Code for deriving suitable neutron kinetics cross-sections (CSC); • Thermal-hydraulic system code (THSC); and
• Neutron kinetics codes (NKC).
The cross-section data are modeled by averaging the microscopic cross sections, obtained from various libraries which contain microscopic cross sections for various reactions, absorption, fission, transport, and scattering, as a function of neutron energies, over neutron energy spectrum and over spatial dependence of the flux in a unit fuel cell in order to account for heterogeneous effects.
The energy groups are concentrated around the neutron thermal energy for which more than 50 % of the groups are related to the resonance energies of U235, Pu239, and Pu240. The libraries also contain yields and decay constants for the various fission products. Cross section calculations are generally performed through lattice physics code as CASMO, and HELIOS [3]. Generally, a 2-D
boundaries. As input, they require a number of densities characterizing the materials of the fuel assembly, the coolant and moderator densities, temperatures, and fuel temperatures (data provided from a thermal-hydraulic code, while the fuel density and fission product densities are provided by a depletion code).
Cross section group constants are generated for each region of the core in which the composition is different (according to their fuel types, fuel assembly shroud, water gap, control rods and burn-up quantities).
Regarding THSC Codes, a safety key parameter of the evaluation and assessment of NPP is closely related to the ability of determining the time-space thermal-hydraulic conditions throughout the reactor coolant system and especially in the core region. The established method to evaluate those complex conditions is carried out by the so-called BE THSC codes, e.g. RELAP5, TRAC, ATHLET, and CATHARE. They are generally based on non-homogeneous, non-equilibrium two-phase flow governing equations.
These equations are generally formulated in term of spatial and time averaged conservations of mass, momentum, and energy with allowances for soluble component in the liquid phase and non-condensable components in the vapor phase. The constitutive relationships are used to describe wall friction, heat transfer and inter-phase drag and mass transfer between phases through interfacial area based on the rather static flow regime maps. These codes are essentially 1D, although most codes have various capabilities to at least in an approximate way to be able to simulate basic 3D flow field conditions. Thus the multi-dimensionality of the flow field can only be approximated. Due to the numerical approximations and of the empirical nature of included models in the thermal-hydraulic system codes extensive activities related to validation of the code models have been pursued during the years.
The validation has partly been done using experimental data from specially designed scaled down test facilities. These ones have the possibility to simulate major parts of a complete reactor system. They are also devoted to investigate specific thermal-hydraulic phenomena or the behaviour of single components (pumps, valves, tees, etc.), and provide additional validation information.
On the other hand, the NKC constitute the heart of the neutronic calculations since they allow to determine the flux and power distribution in the core as well as the core multiplication factor.
Generally, to solve neutron diffusion equation numerically, the reactor core is discretized in nodes where the nuclear properties are supposed to be constant. This constitutes the basic idea for
flux for each of these cells is calculated. The corresponding cross sections are also homogenized at the level of the fuel assembly. Different kinds of methods have been used to solve numerically the neutron diffusion equation as finite difference methods, synthesis methods, finite elements methods and nodal methods.
The consistent application of CSC, THSC and NKC is required to perform a full 3D coupled neutron kinetics/thermal-hydraulic calculation. However, the CSC can be used independently and THSC and NKC must be coupled and should interact at each time step.
2.4.
COUPLING PROCESSES
Two different approaches are generally used to couple TH system codes with 3D neutron kinetics models: serial integration and parallel processing coupling. The serial integration approach (e.g. RELAP5/3D-NESTLE) includes modification of the codes, usually by implementing a neutronic subroutine into the TH system code [3]. In the parallel processing approach (e.g. RELAP5/3.3-PARCS) the TH system and 3D neutronic kinetics codes are executed separately and exchange needed data during the calculation.
In the first case, substantial programming effort is needed to properly achieve the integration, while in the latter case only minor modifications are made to already existing codes. In the latter case it is crucial to provide the data exchange between the two codes in carefully and properly selected time sequences; thus, great attention must be paid to the process of data transfer and the associated time control of the execution processes of the two codes. An obvious advantage of this methodology is that the codes are isolated and can independently be updated and maintained. The kinetics model receives TH data from the TH system code, such as fuel temperatures, coolant void fraction, moderator density and temperature, and boron concentration, and returns the fuel power back to the TH system code.
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 significantly reduced, especially when modelling large BWR cores.
Coupled codes RELAP5/PARCS and TRACE/PARCS are examples of this parallel coupling approach using “message passing” data transfer, in this case on a calculational mesh cell or node level, using data communication routines from the Parallel Virtual machine (PVM) package [14].
corresponding averaged channel/fuel rod model. In most codes the point kinetics can be related to several parallel coolant channels and corresponding fuel rod models describing parts of the reactor core. The 3D neutron kinetics models for core analysis have been expanded to full reactor core models, which comprise complete models of the TH in the core region. The coupling can be achieved in two ways – internal and external, as presented in Fig. 2.1.
Figure 2.1 – Exchange of parameters for different ways of coupling
With internal coupling, the 3D nodal neutron kinetics model is integrated into the core TH model of the system code. Each neutron kinetic node is coupled directly to a core thermal-hydraulic cell in the system code and is solved with each TH iteration. Though this method requires the exchange of a significant amount of information between the two codes. One major disadvantage of this method is that it involves significant modifications in both codes.
In external coupling the neutron kinetics code is combined with a separate core TH model. It is then coupled to the full TH system code by passing boundary conditions at the top and bottom of the core. Only a few parameters need to be exchanged between the two codes. This method improves the coupling procedure because it requires little or no modification of the TH or neutron kinetics codes to be performed. However, there are certain problems with the external coupling
numerical instabilities and slow convergence. A scheme of coupling codes in an external approach is presented in Fig. 2.2.
Choosing proper spatial mesh overlays or mappings between nodes of the core models in the TH system and the 3D-NK codes for a given transient is a difficult task. Careful consideration has to be given to expected possible asymmetric and local core behaviour conditions, as the nodalizations of the core in the two models and their relationship have a great influence in determining the local core parameters and hence the power distribution during the simulated transient.
Core transients revealing pronounced 3D asymmetric characteristics constitute a basis for verifying the overall performance of the coupled code systems. The main objective in such calculations is to predict the core 3D local TH conditions and associated power distribution as accurately as possible.
The available THSC have the option to model the core by means of several parallel channels, with possible additions of cross-flow radial connections (exemplified by the RELAP5 code), or by using a 3D-TH component, included for instance in the RELAP5/3D, TRAC-PF1 and TRACE codes.
When mapping neutronic assemblies to TH channels, different requirements have to be fulfilled. For example one obvious requirement would be to map similar neutronic assemblies in terms of their design to one TH channel. However, there are also other characteristics of the assemblies that must be considered in the mapping process, such as relative power, coolant flow, void distribution, type of bundle inlet throttling (orificing), type of fuel (enrichment), burn-up, etc. Other requirements relate to retaining core symmetry and characteristics. In addition, any expected transient asymmetric core TH inlet conditions affecting certain assemblies more than others have to be taken into account when the mapping is being performed.
In practical terms the detailed mapping not only relates specific neutronic assembly nodes to given TH channel nodes or cells but also provides the weights between the two meshes. These weights, ranging between 0 and 1 inclusive, determine both the amount of neutronic power to the TH and heat structure components as well as the associated TH feedback to the neutronic nodes.
Figure 2.2 – Scheme of 3D-NK-TH coupling
2.5.
NEUTRON
KINETICS
AND
THERMAL-HYDRAULIC
NODALIZATION REQUIREMENTS
Computer codes require the preparation of a mathematical model that can adequately simulate all or part of a nuclear power plant. This mathematical model consists of the computer code itself, and a set of input data grouped in a file (or files) that substantially describe the plant (or facility) within the boundaries and assumptions of the code models. Preparation of such a model is not only the source of the largest number of errors, but also of uncertainties that affect the use of best-estimate codes. Comprehensive knowledge of the computer code models is not sufficient for the error-free preparation of the nodalization [22].
A major issue in the use of mathematical models or codes is the model’s actual capability to reproduce plant (or facility) behaviour under steady-state and transient conditions. Model verification and qualification are concerned by this question.
Regarding TH nodalization (input deck) development, each portion of the plant that is of interest for the analyses is divided into discrete components (nodes). The model is developed
of a complex system such as a LWR plant can be undertaken in a number of ways. The simplest subdivision of a plant model would be into a set of control volumes or nodes that are equally sized, but for a successful analysis solution a number of factors must be addressed: numerical stability, run time and spatial convergence. Modelling LWR systems requires not only the simulation of the fluid stream tubes, but also the modelling of solid structures (slabs) that store heat or contain heat sources. Thus, discretization of the structures is also necessary.
To a great extent, engineering judgment is used to develop an input deck. The importance of establishing a procedure for the nodalization set-up and qualification is a consequence of employing such judgement. The procedure can be split into the following steps: a) gathering of a verified set of NPP data, b) set-up of the plant nodalization (input deck for nominal steady-state conditions) and c) qualification of the nodalization.
In order to achieve a NK nodalization a much smaller number of code-user decisions and choices is needed in comparison with thermal-hydraulic nodalization. This can easily be understood by considering that only the core is concerned and makes the process of developing a 3D neutron kinetics nodalization more straightforward.
A first group of requirements (nodalization development) includes the identification of the core array matrix and reflector materials, the variety of fuel elements or FA that constitute the core, the variety of fuel rods that constitute each FA (burnable poisons, etc.) and the relative position of CR.
The ranges of validity of the parameters, namely of cross-sections, should be compared with the ranges of variations expected during the transient calculation. Thermal-hydraulic input parameters (required by the stand-alone 3D neutron kinetics codes) should be properly identified and consistently fixed. User choices, including ADF, xenon consideration, etc., shall be properly justified, along with the selected value of the time step. Reproduction of reference code runs is recommended before any use of the code [2].
