The three-dimensional neutron kinetics coupled with thermal-hydraulics in RBMK accident analysis

Available online at www.sciencedirect.com

Nuclear Engineering and Design 238 (2008) 1002–1025

The three-dimensional neutron kinetics coupled with thermal-hydraulics in RBMK accident analysis F. D’Auria a,∗ , S. Soloviev b , V. Malofeev c , K. Ivanov d , C. Parisi a a

DIMNP, University of Pisa, Pisa, Italy b NIKIET, Moscow, Russia c Kurchatov Institute, Moscow, Russia d Pennsylvania State University, PA, USA Received 22 September 2006; received in revised form 24 February 2007; accepted 1 March 2007

Abstract The RBMK core is a complex ensemble of high-pressure high-temperature tubes, graphite bricks, low-pressure low-temperature control rod tubes, graphite interstitial gas passages. An about 7 MPa boiling light water crosses the around 19 m long vertical tubes (7 m active length). The lattice consisting of graphite columns and hydraulic channels is bounded by the reactor cavity whose resistant elements are the metal cylindrical tank and thick circular top and bottom plates with proper holes for the passage of tubes. Related to a typical water cooled reactor, the peculiarities of the RBMK core can be summarized as follows: (a) large dimensions – the overall core volume is by far the largest for a nuclear power plant (NPP) producing electricity; (b) use of separate moderator and coolant constituted by graphite and light boiling water, respectively – the boiling water mostly absorbs neutrons in this environment leading to the (small) positive void reactivity coefficient; (c) presence of water channels very close to each other containing coolant at different temperatures (543–557 K and 350 K for fuel channels (FC) and control and protection system (CPS) channels, respectively); (d) presence of core-wide radial, core-wide axial and local temperature gradients in the graphite bricks with temperature values in the range 330–650 K with the high-temperature values justified by the neutron moderation and gamma-heating processes. Owing to the above peculiarities, the development and the use of a three-dimensional neutron kinetics code (3D NK) coupled with a onedimensional thermal-hydraulic (TH) code is essential in RBMK safety analyses. Two approaches have been used within the present context, i.e. use of coupled 3D NK-TH codes to support the accident analysis in the RBMK as discussed in the first of the companion papers in this journal volume: application of Korsar-Bars making use of the Unk code to derive ␭-matrices needed for Bars and of Relap5/3D-Nestle making use of the Helios code to derive the macroscopic cross-sections. Bounding transient analyses of accident scenarios including control rod withdrawal, various Loss of Coolant Accident (LOCA) and discharge of the control rod circuit, have been completed. In all of the analysed cases, starting from nominal operating conditions, modest fission power time gradients have been found, i.e. characterized by time derivative values for local and global power changes substantially smaller than current values accepted in safety analyses of light water reactors. © 2007 Elsevier B.V. All rights reserved.

1. Introduction The RBMK (Reactor Bolshoy Moshchnosty Kipyashiy) is a boiling light water cooled, graphite moderated thermal reactor. Slightly enriched uranium fuel is adopted for fuel rods that are assembled in two groups of 18 to constitute pressurized fuel channels (FC). A zirconium–niobium tube envelopes the

∗

Corresponding author. E-mail address: [email protected] (F. D’Auria).

0029-5493/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2007.03.003

channel to sustain the coolant pressure and is embedded into square-cross-section graphite blocks. More than 1600 graphite stacks with embedded fuel channel constitute the core that is bounded by a steel tank enclosed into a pressure resistant reactor cavity. The established fundamental principles, already valid in the 50s, are the basis of the design of the reactor system that nowadays, following an experience of around 360 reactoryears, shows suitable operational and progressing safety records with the noticeable exception of the Chernobyl unit 4 event in 1986.

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The detailed knowledge of the RBMK system configuration was not spread in the Western world till the 1986 event. Afterwards, “information batches” of RBMK technology became available and were unavoidably evaluated in the light of the Chernobyl event. This caused a search for and a characterization of inadequacies not counterbalanced by the identification of the acceptable safety features, ending-up in an overall negative judgement from the reactor safety viewpoint. The lack or the inadequacy of a comprehensive safety related documentation from the Soviet Union, connected with the utilization of the reactor, contributed to this judgement. Furthermore, geometric and material features of the reactor and primarily of the core, were not consistent with capabilities or with the validation domain of computational tools adopted in the Western world to assess the fulfilment of standard safety requirements, actually preventing a sound and (Russian) independent evaluation. A recently completed project sponsored by European Commission (EC), with the participation of RBMK designers in Russia and the supervision of the national utility and the regulatory authority, D’Auria et al., 2005, might be the basis for re-opening the discussion about the evaluation of safety and of the acceptability of those reactors. The project has been made possible owing to the availability of sophisticate computational tools developed and qualified in the last decade. These include powerful computers, advanced numerical solution methods, techniques for developing input decks and for proving the qualification level. The general subject of the project is the deterministic accident analysis where emphasis is given to the phenomena occurring during the expected transient scenarios rather than to the rigor needed within a nuclear reactor licensing process. Following the identification and the characterization of bounding scenarios assuming to envelope all accident conditions relevant to RBMK safety technology, two main chains of codes have been set-up and utilized to perform safety analyses. The main achievements from the project are critically reviewed in the set of six companion papers including the present one and are supported by recent literature documents, e.g. Sorokin et al., 2006 and Uspuras and Kaliatka, 2006. The objectives of the series of six papers can be summarized as follows: 1) To present numerical techniques and computational tools, including qualification levels and results from the applications, suitable for deterministic safety analysis of RBMK. 2) To demonstrate the results of computational analyses, which allow making conclusions about the current safety characteristics of the plants with RBMK reactors. The former objective is primarily pursued in the present paper and in the papers by D’Auria et al., 2008b–e (see also D’Auria et al., 2005) that constitute the support for the conclusions that are derived in the first paper of the series, e.g. D’Auria et al., 2008a. The content of those papers can be summarized as follows with ‘qualification of computational tools’ constituting a common issue:

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- overall perspective and status for deterministic accident analysis in RBMK, D’Auria et al., 2008a, - thermal-hydraulic performance of the primary system of RBMK following selected accidents, D’Auria et al., 2008b, - thermal-hydraulic performance of confinement system of RBMK, following selected accidents, D’Auria et al., 2008c, - the use and the relevance of three-dimensional neutron kinetics coupled with thermal-hydraulics in RBMK accident analysis, present paper, - addressing the multiple pressure tube rupture (MPTR) issue, D’Auria et al., 2008d, - the proposal for the individual channel monitoring (ICM) system to prevent pressure tube rupture following FC blockage, D’Auria et al., 2008e. The latter objective is pursued primarily in the paper by D’Auria et al., 2008a that makes use of results documented in the remaining five companion papers. The background and the rationale for achieving the selected objectives are also part of that paper. This also includes an arbitrarily defined list of topics derived from a spot-based investigation within the safety domain of water cooled reactors including RBMK. It must also be premised that well established probabilistic safety assessment (PSA) results have been used, Mankamo et al., 2000, but no investigation has been carried out to demonstrate the validity or the quality of those results. Data, analyses and conclusions in the six companion papers are related to the current configuration of the Smolensk-3 NPP (some reported analyses also relate to Ignalina-2 NPP) and no effort is made to provide any evaluation of safety for RBMK NPP where the innovation or modernisation feedbacks for the Smolensk-3 plant are not applicable. The objectives of the present paper are to demonstrate the qualification level of computational tools (codes and nodalizations, primarily) adopted for the coupled three-dimensional (3D) neutron kinetics (NK) and thermal-hydraulic (TH) accident analysis for RBMK core and to present key results from the application. Because of the peculiarities of the RBMK reactor, like large dimensions, separation between moderator and coolant, positive void coefficient, operation of control rods inside a nearly atmospheric pressure sub-cooled water refrigerated loop, the use of coupled 3D NK TH techniques constitutes an indispensable mean to establish the safety margins for this reactor in case of normal operation and accident conditions, as also recognized in a number of documents and papers available from the literature, e.g. IAEA, 2001, Fisher, 2000; Bubelis et al., 2003. 2. The boundary conditions for the coupled neutron kinetics thermal-hydraulic analysis The overall framework for the study can be found in D’Auria et al., 2008a, with more details given in D’Auria et al., 2005. In the present paper the attention is focused

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on the thermal-hydraulic and neutron kinetics performance of the RBMK core making reference to the Smolensk-3 NPP unit. The key elements for achieving the objectives assigned to the paper can be found in Chapters 3 and 4. Hereafter, the background for performing the thermal-hydraulic accident analysis is given and includes four aspects: (a) description of components and zones of the core to make clear the accident scenarios, (b) outline of the licensing environment for the application of coupled 3D NK TH techniques, (c) current status and relevance for the coupled 3D NK-TH analyses, (d) derivation of input data for three-dimensional neutron kinetics computer codes. The information related to margins to critical heat flux available in RBMK fuel channels and to natural circulation performance of the core, already given by D’Auria et al., 2008b, is also relevant for the current subject. 2.1. Elements of the layout of the core of RBMK Selected elements, i.e. sketches, zones and components, of the RBMK core region that are relevant to the description of transient scenarios considered in the present paper, are reported in Figs. 1–9 (taken from the refs. Uspuras and Kaliatka, 2006 and D’Auria et al., 2005), with short description in the paragraphs below. Referring to the Smolensk-3 plant data, see also Clemente et al., 1997, the reactor core is composed by 2488 graphite columns or stacks, of which - 1570 fuel channel columns (see Section 2.1.1), - 314 non-fuel channels columns, - 604 radial reflector channels. The non-fuel channel columns (314) are subdivided as follows: - 211 control and protection system (CPS) channels (see Section 2.1.2), - 12 axial detector channels, - 90 additional absorbers, - 1 water column. The additional absorbers (in the number of 90) are located symmetrically around the core midline in order to increase the operative reactivity margin. Regular and cluster type absorbers shall be distinguished, characterized, respectively, by an annular absorbing section and by the presence of sixteen 4.1 mm boron carbide filled tubes. 2.1.1. The fuel element A fuel assembly consists, Fig. 1, of an upper and a lower fuel bundle, symmetrically placed around the core middle plane. Each section is formed by 18 active rods and a central steel rod that ensures structural rigidity together with 11 spacer grids equally distributed along the section.

Each fuel rod has a zirconium alloy (Zr + 1% Nb) clad that protects the fuel pellets, see Fig. 1. The fuel rod geometric dimensions (i.e. clad and pellet radius, gap etc.) and material composition, other than the zirconium alloys above mentioned, are similar to those adopted for other types of water cooled reactors. However, a 2 mm diameter central hole is present in the fuel pellets. The top, the central and the bottom segments of a typical reactor fuel channel are shown in the lower part of Fig. 1. The central segment usually called pressure tube (PT) is made of a zirconium–niobium alloy (Zr + 2.5% Nb). The top and bottom segments (numbers 3 and 11 in the lower sketch of Fig. 1, respectively) are stainless steel pipes. 2.1.2. The CPS and the control rods A flow diagram of the control and protection system can be found in Fig. 2. This is a ‘nearly’ atmospheric pressure loop, fully independent from the main cooling circuit (MCC) of the RBMK core, with water cooling needed to prevent overheating of control rods. The same CPS is used to cool the additional absorbers and the reflector channels. There are three types of control rods (set of 211): - 32 short control rods, - 24 safety or fast scram control rods, - 155 manual control rods. The manual control rods move upward from the bottom of the core when inserted, all others move downward from the core top. A cross-section view of the safety control rods can be found in Fig. 3. 2.1.3. The cross-section map of the core and reference sketches for the analysis The complexity of the material and geometric configuration of the RBMK reactor core appear from the above discussion. A better idea can be derived from the cross-section map in Fig. 4. This figure, considering the daily re-fueling strategy for the core, shows the need to refer to a specific reactor core working situation in order to perform meaningful safety (and licensing) analyses. Therefore, the reference situation for the present study is constituted by the configuration on ‘October 16, 1996’ of the Smolensk-3 NPP, Fig. 5. Starting from the configuration in Fig. 5, the boundary conditions needed for a realistic 3D NK TH analysis, other than the MCC and the CPS thermal-hydraulic conditions, include suitable maps for: • Inlet flow rates in individual fuel channels (a guess value for the ratio inlet flow rate/power is also needed for each channel to be confirmed at the end of the steady-state calculation). • Burn-up for each fuel channel (possibly with an assigned axial shape). • Axial position of each control rod. • Fluence for each graphite stack (thermal properties of graphite are affected by the irradiation, possibly with an assigned axial shape).

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Fig. 1. Details for the fuel element of the RBMK.

• Consistent (with thermal-hydraulic data, namely heat transfer to MCC and CPS channels) radial and axial temperature profiles in the graphite stacks. Furthermore, a special procedure for allowing the best reconstruction of the axial and the radial power profile is needed. Support sketches are needed to characterize the 3D NK TH accident analyses for RBMK core. In the present case, these are given together with nodalization sketches (Chapter 3) or making use of the diagram in Fig. 5. The position of the group of control rods considered for the CR-G-WITHDRAWAL accident scenario is given in Fig. 6.

2.2. The licensing environment for the use of coupled 3D NK TH techniques in accident analysis The licensing environment for deterministic safety analyses for RBMK can be found in D’Auria et al., 2008a (see also D’Auria et al., 2005). Three key elements relevant to the accident analysis framework are constituted by: a) The list of design basis accidents (DBA). b) The list of acceptable criteria for the primary circuit. c) The requirements for the quality of the codes, including the ‘certification’ process proposed by the Russian Regulatory Authority.

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Fig. 2. Sketch of the control and protection system (CPS) for a RBMK NPP.

A DBA list applicable for Safety Analysis Reports of RBMK, item (a), is given in Table 1, derived from the ref. IAEA, 2005. A variety of accident scenarios from the list has been analysed within the context of the present study (D’Auria et al., 2005) with key results outlined in the companion papers D’Auria et al., 2008a–c. It can be seen from Table 1 that proper attention is devoted to neutron kinetics related scenarios, e.g. reactivity initiated accident (RIA) and anticipated transient without scram (ATWS), rows 6 and 8.

Fig. 3. Cross-section view of a typical RBMK safety control rods (dimensions are in cm).

Fig. 4. Cross-section view of the core of the RBMK (acronyms CR, FSR and SCR are for ‘control rod’, ‘fast scram rod’ and ‘short control rod’).

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Fig. 5. Core configuration for the Smolensk 3 RBMK NPP on 16.10.1996.

Related to the activity documented in the present paper, the analyses have been performed considering phenomena-based list of events bounding expected 3D NK TH conditions for the RBMK core (see Tables 3 and 4 in the paper by D’Auria et al., 2008a). The accident is discussed within the present paper, whose results are given in Chapter 4 and are listed in Table 2. The cross-connection has also been made in the last two columns of Table 2 with the list in Table 1 The list of acceptable criteria for the present analysis, item (b), is the same applicable for the evaluation of the ECCS already given by D’Auria et al., 2008b and reported here as Table 3 for the

sake of completeness. The criteria nos. 2 and 9 are specifically applicable for the present context. Additional requirements (not reported here) are provided for the reactivity associated to each control rod as well as for the insertion strategies of control rods. The Regulatory Authority in Russia Rostehnadzor (previously Gosatomnadzor, GAN) has issued regulatory documents containing requirements for the certification of numerical codes used in safety analyses of nuclear installations, refs. GAN, 2000, 2001, item (c). A ‘frozen’ version of the code is needed to get the certification together with a ‘verification report’ including the methods, the model and the applications needed to prove

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Fig. 6. Support sketch for the radial position of the group of control rods considered for the withdrawal accident scenario in the Smolensk-3 NPP core.

the reliability of a given code. The Korsar and the Relap5 codes adopted within the present framework got the certification for use in water cooled reactor accident analysis. Nowadays, no Regulatory Authority of any Country has issued mandatory requirements for the use of coupled 3D NK TH techniques to the deterministic accident analysis of any NPP and no requirement is issued by GAN in relation to licensing analyses performed by coupled 3D NK TH codes in RBMK. However, the importance of such analyses is worldwide recognized with special reference to RBMK reactors in IAEA, 2005 (related to RIA “. . . a meaningful analysis is only possible using 3-D neutronic codes.”). 2.3. Present status for coupled 3D NK TH analyses and relevance for RBMK

Fig. 7. Flow chart for the application of the Unk code, to produce input for the Bars 3D neutron kinetics code.

The beginning of development of coupled 3D NK TH techniques can be identified in the early 90s when both system thermal-hydraulic codes and 3D neutron kinetics codes, separately, achieved a suitable level of maturity for NPP applications. However, applications of industrial interest (e.g. scoping-

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Fig. 8. Details of the thermal-hydraulic Smolensk-3 RBMK nodalization developed for the coupled Relap5/3D-Nestle codes.

Table 1 Class of events considered in RBMK deterministic safety analysis with identification of the DBA, IAEA, 2005 No

Event group

Accident scenarios

Class

1 2 3 4 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 6.1 6.2 6.3 6.4 6.5 7 8 9

Anomalies of core coolant temperature Anomalies of system pressure Anomalies of core coolant flow rate Increase of core coolant inventory

–

Transient (T)

LOCA

RIA

‘Critical’ LOCA ATWS Fuel handling accidents

Guillotine break of GDH Guillotine break of down-comer Break in inlet pipeline of FC Break in outlet pipeline of FC Break of FC inside RC Break of the main feed-water pipeline Break of the main steam line Failure to close of the main steam valve Break of a small diameter pipeline outside the ALS Inadvertent safety/relief valve opening Main steam valve stuck open Rupture of water communication line Rupture of a pressure line inside the reactor cavity Rupture of a pipeline in the blow-down and cooling system Voiding of the CPS cooling circuit Erroneous refuelling Prolonged withdrawal of CR at both full and low power CR drop including the absorber part of short rods falling out of the core Nitrogen ingress into reactor coolant system after actuation of ECCS –

DBA

BDBA

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Fig. 9. Details of the coupling map for Smolensk-3 RBMK nodalization developed for the coupled Korsar-Bars codes: (a) left core side; (b) right core side.

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Table 2 Selected bounding events to evaluate the 3D NK TH response of the RBMK core and connection with the licensing list of accidents Identification No.

Acronym explanation

Codes adopted for achieving results documented in the present paper

1

FC-BLOCKAGE: full blockage of one fuel channel.

Relap53D©/Nestle

2

GDH-BLOCKAGE: full blockage of the GDH. CR-G-WITHDRAWAL: continued withdrawal of a CR bank (or group). CPS-LOCA: voiding (or LOCA) of the CPS.

3 4

Korsar-Bars Relap5-3D©/Nestle

scientific investigations, safety analyses support to licensing of NPP) for the coupled codes were available toward the end of the same decade. A variety of publications testifies of the status of advancement and of the applicability to NPP for the coupled 3D NK TH techniques, e.g. Aragones et al., 1996; Ivanov and Baratta, 1999; Langenbuch, 1999; and Holmes et al., 2000. Remarkable activities recently completed at the international level include: a) The series of three benchmarks proposed by Nuclear Science Committee of the Organization for Economic Cooperation and Development (OECD) including the main steam line break in PWR, the steam line closure in BWR and the main coolant pump restart in VVER-1000 as discussed by Ivanov et al., 1999; Solis et al., 2001 and Ivanov et al., 2003, respectively. b) The European Commission CRISSUE Project, D’Auria et al., 2004, dealing with the state of the art in the use of coupled 3D NK TH techniques. Thresholds of acceptability for calculations and uncertainty predictions for coupled analyses are discussed, together with criteria to set-up and qualify coupled input decks. In the area of RBMK safety analysis, the already mentioned works by Bubelis et al., 2003, Clemente et al., 1997; Fisher,

Reasons for the selection

Class and no. in Table 1

Challenging the calculation of the local fission power generation. To assess and to understand the local core response. Challenging reactivity initiated accident (RIA) scenario for core integrity.

[Equivalent for some aspects to] DBA – 5.5 – DBA – 6.3 DBA – 6.1

2000, and IAEA, 2001 give an idea of the current status and of the relevance of coupled 3D NK TH techniques. Namely, the heterogeneous and non-symmetric configuration of the RBMK core, as depicted in Section 2.1, and its dimensions are at the origin of the specific interest toward those techniques in safety technology. The key outcomes from the overview of the mentioned literature relevant to the present framework can be summarized as follows: - Coupled 3D NK TH techniques have achieved a suitable level of maturity and are ready for applications in the domain of safety and licensing of NPP. This also includes the specific capability “best estimate plus uncertainty evaluation”, e.g. Bousbia Salah et al., 2006. The use of those techniques for the evaluation of safety margins is highly recommended for current and future analyses. - Nuclear systems like BWR, CANDU and RBMK characterized by large geometric dimensions and material heterogeneity in the core including the presence of steam and liquid and the separation between moderator and coolant, may take the largest benefit from the use of the above techniques. However, coolant non-homogeneities caused by imperfect mixing make the techniques relevant for all generic accident situations in water cooled nuclear reactors.

Table 3 Selected RBMK acceptance criteria for design basis accident, IAEA, 2005 No.

Parameter

Acceptance criterion

1 2 3 4 5 6

Fuel pellet temperature Fuel pellet average enthalpy increase Fuel clad temperature Fuel clad thickness oxidation Core-wide H2 generation Fuel channel pressure tube temperature

7 8 9

MCC pressure Radiation doses in the early phase of the accident Fission power

<2800 ◦ C <710 kJ/kg <1200 ◦ C* <18% <1% <350 ◦ C at 13.4 MPa <650 ◦ C at 8 MPa or below <10.4 MPa < 0.5 cSv whole body <5 cSv for the thyroid <110% nominal

◦ Added *

to the original list. Fuel clad collapse occurs at 700 ◦ C.

Notes

Same criteria are applicable to LWR

Scram occurrence◦

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Table 4 Results from the qualification of Unk and Helios codes against MCNP code results related to the infinite multiplication factor ‘k∞ ’ and the void reactivity coefficient ‘αv ’ in situation typical of RBMK fuel ‘k∞ ’ (temperature 300 K, fresh fuel) No.

Water in channel

Fuel enrichment (%)

MCNP

Unk

ε % (Unk)

Helios

ε % (Helios)

1 2 3 4 5 6

+ + + − − −

2.0 2.4 2.6 + Erbium 2.6 + Erbium 2.0 2.4

1.27332 1.33144 1.23610 1.24825 1.32256 1.36991

1.27257 1.33013 – – 1.31888 1.36856

−0.06 −0.10 – – −0.28 −0.10

1.27838 1.33594 1.24440 1.24572 1.31549 1.36475

0.40 0.34 0.67 −0.20 −0.53 −0.38

‘αv ’

7 8 9

Fuel enrichment (%)

MCNP

2.0 2.4 2.6 + Erbium

0.04924 0.03847 0.01215

2.4. Derivation of input data for three-dimensional neutron kinetics analyses Suitable 3D neutron kinetics computer codes are based upon the solution of the diffusion equations, discussed in Chapter 3 below, and require as input properly averaged values of parameters connected with the interactions between neutrons and material constituting the core, primarily fuel, moderator, coolant and absorbers (including control rods). The origin of these parameter values is constituted by datasets or libraries for microscopic cross-sections of individual materials or compounds, e.g. the “ENDF” or a derived dataset as by Little, 1998, where the neutron energy is the independent variable typically ranging over several orders of magnitude (i.e. from hundredths of eV to tens of MeV). Special computer codes are used to process the above datasets to derive results in the form needed for the use by 3D neutron kinetics codes. In the present case the ‘end-user’ of averaged parameters are constituted by the 3D NK codes Bars and Nestle, refs. Avvakumov and Malofeev, 1997 and Turinsky et al., 1995, as discussed in Chapter 3. The specialized Unk code, ref. Belousov et al., 1998, and the Helios code, ref. Studsvik, 2000, both reading the Njoy code output (see below), are used to produce the input data for Bars and Nestle codes, respectively. The Njoy is a modular computer code used for converting evaluated nuclear data from the “ENDF” format into libraries useful for application calculations, refs. MacFarlane, 1993 and MacFarlane and Muir, 1994. It can serve applications ranging from continuous-energy Monte Carlo, through deterministic transport codes, to reactor lattice physics codes, see below. Njoy handles a wide variety of nuclear effects, including resonances, Doppler broadening, heating, radiation damage, thermal scattering, gas production, neutrons and charged particles, photo-atomic interactions, self shielding, probability tables, photon production, and high-energy interactions (up to 150 MeV).

Unk 0.04631 0.03843 –

ε % (Unk)

Helios

ε % (Helios)

−5.9 −0.1 –

0.03711 0.02881 0.00132

−24.6 −25.1 >100

The Monte Carlo transport code MCNP, e.g. see Briesmiester, 1997, constitutes an advanced powerful tool to perform transport calculation for the detailed geometric configuration of the core of any reactor and it was used in the present framework to validate Helios and Unk results. However, computational resources limitations prevent so far the extensive application of such code and restrict its practical usefulness. 2.4.1. The Unk code approach The flow chart for the application of the Unk code, Belousov et al., 1998, focused to the use of the Bars code, is given in Fig. 7. The Unk output is constituted by ‘␭-function’ or ‘Matrices’ to be used by Bars 3D neutron kinetics code. Unk is a lattice physics code that solves 1D or 2D multi-group neutron transport equation by the collision probability method allowing for detailed structure of cross-sections. A proof of the qualification of the Unk code in situations typical for RBMK can be found in Table 4 where results for the multiplication factor ‘k∞ ’ and for the void reactivity coefficient ‘αv ’ are compared with results obtained by MCNP and Helios. The reported errors are related to the results of the MNCP code that was used as reference for the present qualification analysis, D’Auria et al., 2005. 2.4.2. The Helios code approach Helios is a neutron and gamma transport code for lattice burn-up, in general two-dimensional geometry. It was developed by StudsvikTM ScandPower since the 1993, Studsvik, 2000. The code version ‘1.6’ has been used in the present study. Helios is composed by several modules. In particular, AURORA and ZENITH are the input and the output processor code modules. HERMES is the database for the code that is also obtained by the application of the above mentioned Njoy code. Helios is a well established international software qualified by independent users, e.g. Kriangchaiporn et al., 2002, even in the specific RBMK area, e.g. Jasiulevicius and Sehgal, 2002. The validation activity performed within the context of the present

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study, Table 4, shows a large error in predicting the void coefficient in the comparison with the ‘reliable’ MCNP code result. However, errors were specifically found in the case of the use of Erbium doped nuclear fuel, row 9 in Table 4, that was not of main interest for the present application. The errors at rows 7 and 8 of Table 4 indicate the need for deeper investigation on their origin. Notwithstanding this, they were considered acceptable within the present context in view of the fact that Unk-Bars codes were also used (other than Helios–Nestle). The output of Helios is constituted by sets of parameterized macroscopic cross-sections that need to be interpolated and processed before their implementation in the Nestle code. 3. The coupled computational tools The wording “coupled computational tools” in the area of 3D NK TH applications implies the presence and the availability of: (a) (b) (c) (d) (e)

Thermal-hydraulic system code. Neutron kinetics (3D NK) code. Coupling strategy and a related coupling software. Nodalizations for each of the TH and the 3D NK code. Input deck for the interface between thermal-hydraulics and neutron kinetics.

Within the present context, two TH codes and two 3D NK codes are considered and have been applied to situations of interest to RBMK. Namely, Korsar-Bars and Relap5/3D-Nestle constitute the coupled codes. The Smolensk-3 NPP core in the configuration of 16.10.96 provides the necessary data for the nodalizations and input decks. Making reference to the items (a)–(e) above: • The system thermal-hydraulics codes Korsar and Relap5/3D, item (a), have been extensively used and qualified for RBMK conditions as also discussed by D’Auria et al., 2008b and related references. Namely, extended demonstrations of applicability of Relap5/3D and Korsar to RBMK conditions can be found in D’Auria et al., 2005. • The three-dimensional neutron kinetics Nestle, Turinsky et al., 1995, and Bars, Avvakumov and Malofeev, 1997, codes have been extensively qualified in a variety of conditions related primarily to pressurized water reactors, item (b). • The coupling strategy and the possible related software are analyzed within the CRISSUE S project, D’Auria et al., 2004, item (c). A detailed discussion of the topic at item (c) goes beyond the scope of the present set of papers. Here it is sufficient to mention that in both considered cases, i.e. Korsar-Bars and Relap5/3D-Nestle, a full integration of codes has been achieved and information-feedback from one code to the other occurs at each time step (typically in the range 10−1 –10−3 s). Thermal-hydraulic conditions like pressures, temperatures (in the coolant and in the fuel), heat transfer coefficients and densities are calculated by the TH code and fission power (including decay heat) is calculated by the 3D NK code from the solution of neutron kinetics diffusion equations. Geometric cells over which the numerical integration processes are

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performed by the two codes must be consistent but do not necessarily coincide with cells typically smaller in the case of the 3D NK code. Consistency is achieved by ensuring that one cell of the TH code bounds different cells, typically around 10, of the 3D NK code. • Nodalizations and input decks including those related to the interface between TH and 3D NK have been developed and qualified as far as possible within the present framework, items (d) and (e). • In relation to the coupled Relap5/3D-Nestle code, qualification proofs exist for RBMK that are independent from the present application, e.g. Fisher, 2000 and Bubelis et al., 2003. • A pioneering effort has been made in relation to the application of Korsar-Bars to RBMK core transient analyses. Therefore, in the following sections emphasis is given to the short description of 3D NK codes, 2nd bullet above, and to the nodalizations and input decks, 4th bullet above; results from the applications of the coupled codes are discussed in Chapter 4 (last two bullets). 3.1. The three-dimensional neutron kinetics codes and their applicability to RBMK 3.1.1. The Bars code, Avvakumov and Malofeev, 1997 The Bars code (see also Avvakumov et al., 2000) was developed based on the method of heterogeneous reactor theory, e.g. Galanin, 1971 and Duderstadt and Hamilton, 1976. The heterogeneous method is based on the analytical representation of the neutron flux distribution in the form of Green’s functions superposition, e.g. Stakgold, 1998. The method allows to take into account the detailed material and geometric structure of the core by explicit representation of components like fuel pins, control rods, moderator, coolant. The Green’s function is derived from the solution of a few groups diffusion equation for an infinite uniform media with a singular source at the cell axis. The intensities of the singular sources are determined in such a way that relationships between neutron flux and current at the boundaries of each reactor cell coincide with those obtained from the transport calculation for a single cell. The latter relationship is defined by means of a boundary condition matrix, -Matrix. This is determined as the result of a set of neutron transport calculations for the cell with varying neutron currents at the cell boundary, Kwaratzhehy and Kochurov, 1985. In comparison with few groups neutron cross-sections, -Matrices provide for the same accuracy of the reactor calculation by smaller number of energy groups. An axial dependence of the neutron flux is found by Fourier series expansion. As a result of the solution of the original differential equations, a set of linear algebraic equations is obtained. These general heterogeneous equations connect all pairs of the reactor cells. This leads to unresolved problem because of the needed computational resources. Therefore, a difference approximation of Green’s function is introduced to produce equations ‘connecting’ only neighbouring cells, Kochurov and Malofeev, 1977.

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To calculate fast transients, the heterogeneous method uses ‘time absorption’ matrices instead of the traditional neutron velocities, Avvakumov and Malofeev, 1991. The spatial time neutron flux distribution within a time step is represented in a form of a product of a time dependent amplitude function and a spatial dependent form function. A comprehensive demonstration of validation for the Bars code in situation typical of pressurized water reactor is provided by Avvakumov et al., 2000. Demonstration of validation for the RBMK conditions is provided by Avvakumov et al., 1994. 3.1.2. The Nestle code, Turinsky et al., 1995 Nestle is a multi-dimensional neutron kinetics code developed at the North Carolina State University which solves the two- or four-group neutron diffusion equations in either Cartesian or hexagonal geometry using the nodal expansion method and the non-linear iteration technique. An advantage of the nonlinear iterative strategy is that Nestle can be utilized to solve either the nodal or the finite difference method representation of the few groups neutron diffusion equation. The steady-state eigenvalue and the time dependent neutron flux can be solved. Three-, two-, or one-dimensional models may be used. Several different core symmetry options are available including quarter, half and full core options for Cartesian geometry and 1/6, 1/3 and full core options for hexagonal geometry. Zero flux, non-re-entrant current, reflective and cyclic boundary conditions are available. The ‘border profiled lower upper’ matrix solver is used to efficiently solve sparse linear systems of the form AX = B. This matrix is designed to take advantage of pipelines, vector hardware and shared-memory parallel architecture to run fast. The matrix is most efficient for solving systems that correspond to networks, such as pipes, but is efficient for any system that it can permute into border-banded form. Speed-ups over the default solver are achieved in Relap5/3D running with the above matrix on multi-dimensional problems, for which it was intended. A neutron cross-section model has been implemented that allows the neutron cross-sections to be parameterized as a function of the Relap5/3D heat structure temperatures, fluid void fraction or fluid density, soluble poison concentration and fluid temperatures. An example of the validation of Nestle for water cooled nuclear reactor condition can be found in the paper by Judd et al., 1994. Validation for RBMK conditions of the code coupled with Relap5/3D can be found in already mentioned documents, e.g. Bubelis et al., 2003. 3.2. The coupled nodalizations and the validation Two nodalizations for the analysis of 3D NK TH phenomena in Smolensk-3 RBMK NPP have been developed for Relap5/3DNestle and Korsar-Bars codes. The development of those two nodalizations implied development of two input decks for each

Table 5 Details of the thermal-hydraulic Smolensk-3 RBMK nodalization developed for the coupled Korsar-Bars codes FC group

No. of FC

FC identification in Fig. 9

1 2 3 4 5 6 7 –

1 5 6 11 13 739 795 1570

804 (left half) 801 . . . 803, 840, 841 (left half) 797 . . . 800, 838, 839 (left half) 790 . . . 796, 834 . . . 837 (left half) 782 . . . 789, 829 . . . 833 (left half) Remaining FC of the left half FC of the right half TOTAL (fuel rod bundles at rows 1 and 2 in the table at the bottom of Fig. 5)

of the TH system codes, the 3D NK codes and the related interfaces, as already mentioned. Details will be provided below, separately for the thermal-hydraulic nodalizations and for the neutron kinetics nodalization together with the interface input decks. 3.2.1. Thermal-hydraulic nodalizations (for Korsar and Relap5/3D) The TH nodalizations were derived from those discussed by D’Auria et al., 2008b, used for primary circuit transient analysis. In order to optimize the computer resources, basically to include more nodes in the core region, the original input decks were made detailed for the core region and simplified for the rest of the loop. In relation to the Korsar nodalization the following information applies, supplemented by the data given in Table 5: - Two halves of the loop are simulated. Pipelines of the three main coolant pumps are lumped in each half and one additional path simulates the piping with the pump in stand-by conditions. - The two steam drums of each half are represented by one equivalent node. - Steam lines of each half are modelled by one equivalent pipeline till the turbine stop valves. - The right half of the reactor core is modelled by one equivalent channel. - The left half channels are lumped into four to six equivalent channels depending upon the scenario. - One group distribution header is simulated in the left half and the remaining ones (for left and right parts) are lumped in one equivalent Korsar component. - Graphite blocks are modelled by a cylinder of equivalent volume with conditions of thermal insulation on the external border (this is acceptable considering the ‘short’ duration of the analyzed transients). - Ten axial nodes are used for each individual modelled channel. In relation to the Relap5/3D nodalization the following information applies, supplemented by the data given in Fig. 8:

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Fig. 10. Details of the map for Smolensk-3 RBMK nodalization developed for the coupled Relap5/3D-Nestle codes.

- The reactor core is composed by 2488 channels (see the table at the bottom of Fig. 5). Namely, 1570 fuel channels, 314 non-fuel channels (control rods, axial detectors, additional absorber and water column) and 604 radial reflector channels are considered, as already mentioned. - Fifty-six thermal-hydraulic ‘model-channels’ are distinguished: the left part of the core is modelled by eight fuel channels and fed by one equivalent group distribution header; the right part is modelled by 45 fuel channels fed by 22 group distribution headers i.e. the actual number in the Smolensk3 NPP. Other ‘model-channels’ are included to simulate the external reflector and the CPS (see below). - Graphite columns and gas gaps are simulated for each core channel part of the model. - The three types of control rods (manual, shortened and safety) and the axial detectors are modelled by one equivalent channel (model-channel 54); the additional absorber and the water column channels constitute the model-channel 55 and the radial reflectors constitute the model-channel 1 (see below). - Twenty-four plus two axial nodes are used for each individual thermal-hydraulic modelled channel (see below). 3.2.2. Neutron kinetics and ‘interface’ nodalizations (for Bars, Nestle and coupled codes) In the case of Bars, the core is simulated by a 48 × 48 3D NK nodalization. Every individual fuel channel, split into 10 equal length cells along the axis, is distinguished. The macro constants (or -Matrices) describing the neutron-physical properties of the medium, reported as a function of burn-up, average temperature of fuel, average temperature of graphite, and coolant

density are obtained per each cell by the Unk code, as already mentioned. The Bars noding is coupled with the Korsar code according to the map in Fig. 9 (see also Table 5). In the case of Nestle code a 56 × 56 3D NK nodalization was developed and coupled to the Relap5/3D code consistently with the sketch in Fig. 10. The following shall be added: - The core (i.e. each channel of the 56 × 56 matrix) is subdivided into 12 axial cells. The first and the twelfth planes have an axial dimension of 0.3 m (i.e. corresponding to the graphite bottom and top reflectors) and planes from 2 to 11 have an axial length of 0.7 m. It may be noted that this is the same sub-division adopted in Bars nodalization where proper boundary conditions are supplied for the axial reflector (the sane note also applies to the radial reflector). - The adopted core compositions are: a) the 2.0% enriched fuel (with different burn-up, 12 compositions); b) the 2.4% enriched fuel (with different burn-up, 49 compositions); c) the axial detector (1 composition); d) the control rods (3 compositions, one per each manual, shortened and safety control rod); e) the additional absorber (1 composition); f) the water column (1 composition); g) the radial reflector (3 compositions). - There are two thermal-hydraulic mesh points for each neutron kinetics mesh point. Instead the dimension of the thermalhydraulic node for the bottom and top reflector is the same as for the neutron kinetics node.

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- Total numbers of neutron kinetics, conduction heat transfer and hydraulic meshes are around 30000, 32000 and 5000, respectively (utilized computer resources). 3.2.3. Validation of the coupled nodalizations The qualification level discussed for thermal-hydraulic nodalizations in D’Auria et al., 2008b is also applicable in the present cases. The qualification process for the coupled nodalizations requires a different step process with a number of acceptability thresholds as outlined by D’Auria et al., 2004. Selected results from the RBMK coupled nodalization validation process are reported by D’Auria et al., 2005. The above process also implied the achievement of a stable steady state and the comparison between key output parameters obtained by the two coupled nodalizations. The demonstration of steady state was achieved for the key thermal-hydraulic (e.g. flow rates and void fractions in each FC) and neutron kinetics (e.g. primarily ‘keff ’ and fission power) parameters. Additional checks included the demonstration of: • Stability for temperature profile in the graphite at different axial levels (see also D’Auria et al., 2008b). • Correctness of decay power in the fuel. • Correctness of power generated in the graphite and of decay power in the graphite (this last quantity independent upon the decay power in the fuel). • Correctness of the value of various control rod worth available from NPP measurements. • Correctness of selected reactivity feedbacks, e.g. void (integral values valid for the whole core are available from elaborations of NPP measurements). Hereafter, a few sample results from the nodalization validation process are given in Figs. 11 and 12 applicable to both Korsar-Bars and Relap5/3D-Nestle nodalizations and only to the Relap5/3D-Nestle nodalization, respectively. A ‘suitable reproduction’ of measured data can be observed. A typical result related to the coupled 3D TH NK steadystate calculation achieved at the end of the qualification process is given in Fig. 13. Typical disuniformities in generated power

Fig. 11. Nodalization qualification process for the coupled Korsar-Bars and Relap5/3D-Nestle nodalizations: core averaged axial power distribution.

Fig. 12. Nodalization qualification process for the coupled Relap5/3D-Nestle nodalization, axial power distribution in selected channels (see Fig. 10): (a) coordinates 50-17; (b) coordinates 40-47.

between neighbouring rows of channels due to the presence of different number of non active fuel channels (control rods additional absorbers, etc.) can be observed in Fig. 13a with difference values ranging up to 40% of the nominal power. The data in Fig. 13 emphasize the need for coupled analyses. 4. The accident performance of the RBMK core The overview of accident scenarios in Table 2 and the related key results (typically associated with rod surface temperature and core power) have already been given in the companion paper by D’Auria et al., 2008a. The purpose here is to substantiate the results by providing the background for the analysis (as done in Chapters 2 and 3) and to provide complementary information to characterize the core performance during the selected transient scenarios. The level of description for NPP details, for boundary conditions including the fuel status, for logics of ECCS actuation, etc., is such to prevent the classification of the documented study as ‘licensing analysis’. Rather, results from best-estimate calculations not supported by uncertainty evaluation are documented here and shall be considered as relevant for the safety evaluation of the RBMK core neutron kinetics and thermal-hydraulic performance and suitable for the objective of this paper. The considered scenarios are those listed in Table 2 and the concerned RBMK is the Smolensk-3 NPP. Selected boundary and initial conditions (BIC) are those discussed in Chapter 3 (e.g. Fig. 5) and in the above mentioned companion paper. Additional

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Table 6 Additional boundary conditions adopted for the Korsar-Bars analysis

Fig. 13. Steady-state values achieved for normalized power in the Smolensk-3 NPP for the configuration of 16.10.96: (a) distribution along the diameter (27 horizontal in Fig. 10); (b) core-wide distribution.

BIC values, specifically related to the core configuration can be found in Tables 6 and 7 and in Fig. 14. These data give a deeper idea of the complexity of the analyses, including the control logics for the CPS operation (Fig. 14). More details can be found in D’Auria et al., 2005.

Parameter

Value

Reactor power (MWt) Power of the left half of reactor (MWt) Power of the right half of reactor (MWt) Coolant flow rate in FC group 1 (Table 5) (kg/s) Coolant flow rate in FC group 2 (Table 5), kg/s Coolant flow rate in FC group 3 (Table 5), kg/s Coolant flow rate in FC group 4 (Table 5), kg/s Coolant flow rate in FC group 5 (Table 5), kg/s Coolant flow rate in FC group 6 (Table 5), kg/s Coolant flow rate in FC group 7 (Table 5), kg/s Maximum channel power (MWt) Radial power peaking factor

3159.2 1354.9 1804.3 5.697 32.98 32.84 63.27 61.44 3884.0 5433.6 3.18 1.62

Fig. 14. Boundary conditions for the Korsar-Bars analysis related to the withdrawal of a control rod group (rods 179, 194 and 196) and the subsequent system reaction (scram) with the automatic insertion of rods 153 and 165 (see Figs. 20 and 21).

Results of the transients listed in Table 2 as well as of additional ones have been obtained by both Korsar-Bars and Relap5/3D-Nestle coupled codes, with the exception of the CPS-LOCA only calculated by Relap5/3D-Nestle. Hereafter, results for transients nos. 1, 2 and 4 in Table 2 (namely FC-

Table 7 Typical characterization of insertion depths of selected individual control rods adopted in coupled nodalizations Korsar-Bars and Relap5/3D-Nestle (see also Fig. 4 for location) CR #

Insert. depth, (cm)

CR type

CR #

Insert. depth, (cm)

1 2 3 4 5

30 220 60 30 −240

CR CR CR CR SCR

55 56 57 58 59

30 30 30 30 30

45 46 47 48 49

−280 660 −230 30 30

SCR CR SCR FSR CR

99 100 101 102 103

30 700 30 150 30

CR type

CR #

Insert. depth, (cm)

CR type

FSR CR FSR CR CR

109 110 111 112 113

30 30 610 30 30

FSR CR CR CR CR

Interrupted table CR 153 30 CR 154 20 FSR 155 30 CR 156 680 FSR 157 30

FSR CR FSR CR CR

CR #

Insert. depth, (cm)

CR type

163 164 165 166 167

20 −270 30 −290 30

CR SCR CR SCR CR

207 208 209 210 211

30 30 20 110 30

CR CR CR CR CR

Nomenclature: CR, FSR and SCR are for ‘(manual) control rod’, ‘fast scram rod’ and ‘short control rod’, respectively. Insertion depth for CR and FSR is measured from the upper edge of the top reflector. Insertion depth for SCR is measured from bottom of reactor core (negative values because SCR are bottom to top inserted).

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BLOCKAGE, GDH-BLOCKAGE and CPS-LOCA) are derived from Relap5/3D-Nestle calculations and results for transient No 3 in Table 2 (namely CR-G-WITHDRAWAL) are derived from Korsar-Bars calculation. 4.1. The full blockage of one FC The key issue for the FC-BLOCKAGE scenario from the point of view of neutron kinetics is the prediction of fission power for the affected FC power. Channel voiding caused by evaporation introduces positive local reactivity affected by burn-up and fuel composition, operating conditions (e.g. flowto-power ratio) and channel location in the core. The same voiding unavoidably causes dry-out and average fuel temperature increase with consequent local negative reactivity source by the Doppler effect. The timing of events like the start of significant metal water reaction, the deformation of the fuel rods and of the rod bundle, the UO2 melting and the rupture of the clad and of the pressure tube, including for the last event the rupture area and the location, as well as the possibility ‘to control’ the event by the individual channel monitoring system (D’Auria et al., 2008e), are affected by the prediction of the transient fission power after the blockage. Furthermore, the blockage of one FC causes a flow perturbation in the remaining FC fed by the same GDH and a neutron kinetics perturbation in the neighbouring FC that require a 3D NK TH coupled calculation and a detailed noding scheme around the affected FC. The channel with vertical and horizontal coordinates 27-29 in Fig. 10 is selected as affected element characterized by an initial power of 2.4 MWth. The results of the coupled Relap5/3DNestle codes calculation are given in Figs. 15 and 16, related to the blocked channels and to the remaining core parts, respectively. The following can be observed: - the blockage event starts at t = 0 s time and at t = 1 s the fuel channel inlet flow rate vanishes, Fig. 15a, - no scram is foreseen because no signal is actuated before the break of the pressure tube (see also below), - in a couple of seconds (timing applicable to the 2.4 thermal MW FC) the dry-out event happens and the clad surface temperatures start rising at all elevation achieving the clad collapse condition a few seconds later and the threshold for significant hydrogen production at about 10 s, Fig. 15b, - the power in the blocked FC decreases for an amount of 10–15% following the event with a sharp decrease in the initial 5 s of the transient. This is due to the Doppler effect, i.e. negative reactivity insertion, (with the boundary conditions considered for the present analysis including the selection of the affected FC location in the core) that is larger than the positive reactivity insertion caused by voiding, Fig. 15c. It shall be noted that the power prediction is meaningless after the pressure tube rupture (i.e. starting from about 40 s into the transient, D’Auria et al., 2008d) due to fuel ejection from the channel.

Fig. 15. Smolensk-3 FC-BLOCKAGE 3D NK TH coupled calculation by Relap5/3D-Nestle code, affected FC performance: (a) inlet flow rate; (b) rod surface temperatures at various elevations; (c) generated power.

- The fission power generated in neighbouring FC remains practically constant in a few tens of seconds after the event. However, a small decrease can be observed due to slight flow rate increase in the channels fed by the same GDH, Fig. 16a. - The overall core power is almost unaffected by the event. The slight decrease is primarily the consequence of the effects mentioned above (power decrease in the affected channel and in the channels belonging to the same GDH), Fig. 16b. A series of steady-state calculations were performed by the MNCP code, Parisi, 2007, in relation to an infinite RBMK type lattice with the characteristics of the selected Smolensk-3 fuel bundle (burn-up conditions, distance from absorbers, etc.). The

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4.2. The full blockage of the group distribution header (GDH) The scenario GDH-BLOCKAGE has been discussed at the level of primary system performance in the companion paper D’Auria et al., 2008b, related to the Smolensk-3 NPP. An outline of the same event has also been given by D’Auria et al., 2008a, related to Ignalina-2 at the level of primary system performance and related to Smolensk-3 in relation to the result for overall core power. In the present paper the attention is focused toward the 3D NK performance of the Smolensk-3 RBMK NPP core (configuration 16.10.96). The following additional information is relevant:

Fig. 16. Smolensk-3 FC-BLOCKAGE 3D NK TH coupled calculation by Relap5/3D-Nestle code, overall core performance: (a) power of neighbouring channels; (b) overall core power.

average fuel temperature and the void fractions were selected from the Relap5/3D-Nestle presented analysis (i.e. average void fraction and fuel temperature were ‘consistent’ in each calculation). In this way the data from the series of MNCP steady-state calculations could be graphically reported as a function of time. The curves in Fig. 17 show that the Doppler becomes larger than the void coefficient at about 5 s into the transient. Several tens (or hundreds) of such calculations should be conducted to characterize the actual core performance in a variety of fuel loading and burn-up conditions.

- The GDH-BLOCKAGE event from the point of view of phenomena occurring in the affected channels involves the consideration of aspects similar to the FC-BLOCKAGE event discussed in Section 4.1. This is particularly true for the channel (partial) voiding when the ECCS Pressure Header-GDH bypass line opens and, related to the Doppler effect, when dry-out phenomena occur. - The concerned fuel channels are characterized by dark colours in Fig. 10 and typically disposed along a radius of the core, thus inducing a power perturbation to the overall core. - The ECCS bypass line ensures a ‘partial’ cooling to the affected fuel channels, see also D’Auria et al., 2008b. - Thus, the main purpose of the coupled analysis is the evaluation of the local and overall fission power. Therefore, the thermal-hydraulic stability of the channels and the evaluation of the timing of the possible channel rupture (see D’Auria et al., 2008a,b) do not constitute a topic for the analysis. - Owing to the above, no results are presented in this analysis for the pressure tube temperature, neither related to the achievement of conditions for rupture. Selected time evolutions relevant for the assessment of the coupled thermal-hydraulic neutron kinetic performance of the core can be found in Figs. 18 and 19 (the overall system performance can be derived from Table 9 and Figs. 25 and 26 by D’Auria et al., 2008b). The data in Fig. 18 confirm the thermal-hydraulic performance of the affected channels already described in the mentioned papers, with main reference to the occurrence of thermal-hydraulic instabilities and associated dry-out. The data in Fig. 19a show the decrease in power predicted for any of the channels belonging to the blocked GDH and to selected groups of channels bounding the previous ones. Also core power is predicted to decrease for about 2% of the nominal value owing to the occurrence of the event, Fig. 19b. The value is outside the sensitivity ranges of neutron power instruments and therefore no scram is expected before the break of one or more pressure tubes. 4.3. The withdrawal of a group of control rods

Fig. 17. Smolensk-3 FC-BLOCKAGE, results from MNCP steady-state calculations (average fuel temperature and void calculated by Relap5/3D-Nestle code at each time).

A spurious signal is assumed at the origin of the event denominated withdrawal of a group of control rods. In the considered

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Fig. 18. Smolensk-3 GDH-BLOCKAGE 3D NK TH coupled calculation by Relap5/3D-Nestle code, performance of the affected channels: (a) total flow rate through the ECCS bypass line; (b) flow rate in selected channels; (c) rod surface temperatures in selected channels.

scenario, three rods belong to one group and are located in the bottom of the core as shown in Fig. 6. The withdrawal speed is assigned as well as the automatic counter-reaction logic, Fig. 14, i.e. the scram caused by high power. Location of the rods in the core and withdrawal speed constitute key input parameters for the analysis. The core power change rate and the time for the possible achievement of set-point for

scram, fixed at 110% of nominal power, are the main output parameters. The main results are shown in Figs. 20 and 21, with reference to selected neutron kinetics and thermal-hydraulic parameters, respectively. The power increase is different in each group of channels and larger in the code lumped channels embedding the failed

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Fig. 19. Smolensk-3 GDH-BLOCKAGE 3D NK TH coupled calculation by Relap5/3D-Nestle code, evaluation of fission power: (a) in selected channels of the affected and ‘neighbour’ GDH; (b) overall core.

rods, Fig. 20b. The overall core power increase is such to cause the scram at around 5 s after the start of the control rod group withdrawal event, Fig. 20a. The change in the axial power profile can be observed in Fig. 20c: the “decay” power profile, function of the individual channel burn-up, can be derived from the curves that relate to a timing into the transient larger than about 7 s. The thermal-hydraulic results show the decrease in void fraction in each lumped channel (Fig. 21a), expected because of the power decrease with flow rates remaining almost unchanged (Fig. 21b) (with changes caused by the re-balanced pressure drop in the core after scram). 4.4. The LOCA in the control and protection system (CPS) loop The analysis of the scenario LOCA in the control and protection system of the RBMK core (CPS-LOCA) requires a detailed modelling of the concerned system including the safety technological areas of (CPS) devoted macroscopic neutron cross-sections derivation, the 3D neutron kinetics (CPS) modelling and the (CPS) thermal-hydraulic modelling, the last one making reference to the sketch given in Fig. 2. The loss of cooling of the ‘nearly’ atmospheric pressure circuit of the CPS loop can be originated by a leakage in the bottom

Fig. 20. Smolensk-3 CR-G-WITHDRAWAL 3D NK TH coupled calculation by Korsar-Bars code, evaluation of fission power: (a) in each core half; (b) in each group of channels; (c) axial profile in each group of channels.

of the core region (a break in the upper part of the core does not cause draining of the coolant). Furthermore, a) any detected leakage can be stopped by proper actuation of valves by the operators, b) lost water can be easily reintegrated in the low-pressure environment of the CPS, c) the maximum leakage rate and the consequent ‘small’ level decrease rate in the CPS channels is connected with the maximum free flow area of maximum piping in the bottom of the core,

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Fig. 21. Smolensk-3 CR-G-WITHDRAWAL 3D NK TH coupled calculation by Korsar-Bars code, selected thermal-hydraulic parameters in each group of channels: (a) void fraction at the outlet; (b) inlet flow rate.

d) the positive reactivity insertion following CPS voiding has qualitatively the same root cause as the (positive) void coefficient for the coolant, but is different from the quantitative point of view owing to different densities variations (i.e. from full to empty for a given region) of the fluid and for the different material locally affected by the voiding (primarily control rods in the present case and fuel bundles in the case of loss of coolant). The main results are shown in Figs. 22 and 23, with reference to selected thermal-hydraulic and neutron kinetics related parameters, respectively. Key events with comments, as needed, are provided below: - start of the accident, t = 0 s, - scram occurrence, t = 25 s (Fig. 23b), due to over-passing the threshold of 110% for fission power, - full voiding of the channels, t = 45 s (Fig. 22a), - time when flow rates and clad temperatures in the fuel channels attain a stable value consistent with the reactor scram event, t = 70 s (Figs. 22b and c), - end of the calculation, t = 300 s.

Fig. 22. Smolensk-3 CPS-LOCA 3D NK TH coupled calculation by Relap5/3DNestle code, selected thermal-hydraulic parameters: (a) void fraction in the CPS channels; (b) flow rates in selected fuel channels; (c) rod surface temperatures in selected fuel channels.

Two additional aspects are relevant in this transient, constituted by the aluminium cladding of some control rods and by the Wigner energy release from the graphite-followers part of selected rods. Related to the first issue, it has been found that control rod surface temperature exceed the aluminium melting temperature. In this case deformation may prevent the full insertion of those rods. However, in upgraded RBMK NPP the aluminium is not supposed to be used any more. Therefore, the issue is not relevant within the present context. No specific analysis has been made related to the second topic that is originated by a well characterized physical phenomenon. However, the Wigner energy release from control rod followers is not expected to affect the conclusions achieved here.

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respect to other water cooled reactors that can be at the origin of unpredictable or unacceptable accident evolutions. b) Rather, time variations for neutron flux and associated fission power are characterized by longer time constants in RBMK compared with other types of water cooled reactors in the case of assigned accidents (e.g. control rod ejection versus control rod withdrawal). Differences are originated by the large inertia associated with the ‘large’ masses of coolant and of moderator and by the large dimensions: the low power density, watts per cubic meter of core is one measure of such differences. c) The low-pressure circuit (or the environment for the operation) of the CPS constitutes a relevant intrinsic safety feature of the RBMK core not available in other types of water cooled reactors with the significant exception of the CANDU: control rods are inserted into atmospheric pressure loop and independent types of mechanisms are available to move the rods, i.e. not subject to the common mode failure. d) A full capability has been demonstrated for threedimensional coupled thermal-hydraulic neutron kinetics techniques for predicting the local performance of RBMK core. Those techniques may reveal essential for the demonstration of safety margins of these reactors. Fig. 23. Smolensk-3 CPS-LOCA 3D NK TH coupled calculation by Relap5/3DNestle code, power: (a) in selected lumped channels; (b) for the entire core.

5. Conclusions Results from best-estimate, coupled three-dimensional thermal-hydraulics neutron kinetics calculations for RBMK core performance in case of accidents are discussed in the paper. The analyses are not supported by uncertainty evaluation and should not be considered a licensing study. The main achieved purposes were to demonstrate that no unacceptable situation is predicted during the considered accident evolutions and to demonstrate the availability and the suitability of sophisticate coupled 3D NK TH techniques. The adopted coupled codes, namely Relap5/3D-Nestle and Korsar-Bars, that take benefit from input data generated by Helios and Unk codes, together with related input decks of Smolensk-3, are qualified according to state-of-the-art procedures and thresholds of acceptability (not discussed within the present framework, see also recommendations below) for the analysis of the three-dimensional performance of the RBMK core. The mentioned procedures involved the detailed identification and characterization of phenomena and of variation ranges for key connected parameters. Results from different code qualification processes are documented in the listed references. Main conclusions relevant to the accident analysis can be summarized as follows: a) The thermal-hydraulic and neutron kinetics design features of the RBMK core and the nominal operation conditions, in the area of accident analysis, do not cause differences with

The achievement of the described results requires broad range analyses where several databases are needed like fuel crosssections, burn-up data, NPP construction and operational data, logics for the actuation of various systems and different sophisticate software (i.e. codes). Proper qualification of each step of the analysis, beyond what has been done in the present study with consideration of available NPP measurements is recommended to make a full use of the techniques here presented. It is also recommended for Regulatory Authority to request the use of the coupled thermal-hydraulics neutron kinetics techniques for substantiating the safety of RBMK NPP. Acknowledgements The present paper is devoted to the memory of the eminent Russian researcher and technologist Dr. Yuri Cherkashov who passed away in May 2006. He contributed to the crucial effort of designing the fuel channel of the RBMK and was decorated and granted a State award for his services. Around fifty researchers at NIKIET and University of Pisa took part in the EC (European Commission) Project activities that were at the origin of the present one plus five companion papers in this journal issue. Most of their names appear as co-authors of the papers or of the references. Their contribution is gratefully acknowledged. A number of persons provided a managerial support to the activities; among them, we wish to recall V. Shandra and C. Sollima. The work would not have been possible without the contribution and the willingness of the Russian Beneficiary Institution Rosenergoatom to cooperate and to supervise the activities. Special thanks are due to Dr. E. Hicken and Dr. R.B. Duffey who took the charge of evaluating all this material and to Profs. M. Mazzini and G. Petrangeli for their continuous supervision of the activities. Neither the EC nor any person acting on behalf of

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