The multiple pressure tube rupture (MPTR) issue in RBMK safety technology

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Nuclear Engineering and Design 238 (2008) 1026–1061

The multiple pressure tube rupture (MPTR) issue in RBMK safety technology F. D’Auria a,∗ , B. Gabaraev b , O. Novoselsky b , V. Radkevich b , V.N. Filinov b , D. Mazzini a , F. Moretti a , F. Pierro a , A. Vigni a , L. Parafilo b , D. Kryuchkov c a

DIMNP, University of Pisa, Pisa, Italy b NIKIET, Moscow, Russia c PhEI, Obninsk, Russia

Received 22 September 2006; received in revised form 24 February 2007; accepted 1 March 2007

Abstract The RBMK core is constituted by more than one-thousand pressurized channels housed into stacked graphite blocks and connected at the bottom and at the top by small diameter (D) and long length (L) pipes (less than 0.01 and more than 10 m, respectively) that end up into headers and drum separators. Control valves are installed in the bottom lines. Due to the large L/D value and to the presence of valves and other geometric discontinuities along the lines connecting with the pressure channels, the Fuel Channel Blockage (FCB) event is possible and already occurred in two documented NPP events. Pressure tube rupture occurred in a third NPP event not originated by FCB. Previous investigations, have shown the relevance of these events for the safety technology, and the availability of proper computational technique for the analysis, see the first and the third companion paper in this journal issue, respectively. The occurrence of the FCB event remains undetected for a few tens of seconds because of the lack of full monitoring for the individual channels, fourth companion paper in this journal issue. Therefore, fission power continues to be produced in the absence of cooling. This brings in subsequent times to fuel rod overheating, pressure tube failure, damage of the neighbouring graphite brick and ejection of damaged fuel. Following the pressure tube rupture, reactor cavity pressurization, radioactivity release into the same area and change of fluid properties occur that allow the detection of the event and cause the reactor scram at a time of a few tens of seconds depending upon the channel working conditions and the severity of the blockage. Notwithstanding the [delayed] scram and the full capability of the reactor designed safety features to keep cooled the core, the multiple pressure tube rupture (MPTR) issue is raised. The question to be answered is whether the ‘explosion’ of the blocked pressure tube damages not only the neighbour graphite bricks but propagates to other channels causing the potential for several channel failure. In order to address the MPTR issue fuel channel thermal-hydraulics and three-dimensional (3D) neutron kinetics analyses have been performed, as well structural mechanics calculations for the graphite bricks and rings (graphite rings surround the pressure tube to accommodate for thermal and radiation induced expansions). The bases for the analysis and the results of the study are presented. The conclusion, not reported within a licensing based format, is that the MPTR consequences are not expected to be relevant for the safety of the RBMK installations. This is supported by the analysis of experiments performed at the TKR facility available at the EREC research Centre near Moscow. © 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

∗

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.2007.03.002

assembled in groups of 18 to constitute pressurized Fuel Channels (FC). A zirconium–niobium tube envelopes the channel to sustain the coolant pressure and is embedded into squarecross-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. Established fundamental principles, already valid in the 50s, are at the basis of the design of the reactor system that nowadays,

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following an experience of around 360 reactor-years, shows suitable operational and safety records with the noticeable exception of the Chernobyl unit 4 event in 1986. 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, also connected with the uses 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. The results of 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), allow to give an idea of RBMK current safety characteristics. 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,c,d, 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.,

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D’Auria et al. (2008a). The content of those papers can be summarized as follows with ‘qualification of computational tools’ constituting a common issue: • 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 3D neutron kinetics coupled with thermal-hydraulics in RBMK accident analysis (D’Auria et al., 2008d), • addressing the multiple pressure tube rupture (MPTR) issue, present paper, • 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, 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 where the innovation or modernisation feedbacks for the Smolensk-3 plant are not applicable. The configuration of the RBMK core with more than 1600 pressurized Fuel Channels (FC) make the designers aware of the problem connected with the rupture of one single tube. This may happen owing to a technological defect (even though the probability of such event could be negligible as discussed by D’Auria et al., 2008a), or due to the coolant blockage at the channel inlet, or due to power excursion (this event has been documented two times in existing reactors originated by coolant blockage, D’Auria et al., 2005, see also below). The consequences of the break of a single FC are handled by the overall protection system of the reactor with radiological consequences within the acceptance limits prescribed by the Regulatory Authority (see D’Auria et al., 2008a,b,c,d). However, in such conditions, i.e. after the FC break, (a) overheated fuel is ejected from the channel, and (b) the FC neighbouring the broken channel are loaded by hydraulic forces to an extent that can cause the failure thus triggering, through a domino type effect, the potential catastrophic failure of the core.

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The last item, commonly known with the terms multiple pressure tube rupture (MPTR), constitutes the main topic of this paper. The RBMK designers were aware of the issue and finalized the core design to prevent the MPTR occurrence. The recently available safety technology software and recent experiments, e.g., Medvedeva et al. (2004a), made it possible to substantiate the safety margins of the RBMK in relation to the MPTR according to the modern exigencies in the domain of nuclear reactor safety. The issue has been thoroughly studied in the past, e.g., NIKIET (1983, 1998) and constituted the subject of international conferences, e.g., Simonov et al. (1994), and of projects supported by the European Commission, e.g., Sureau et al. (1996) and TACIS (1996). Therefore, the objective of the present paper is two-fold: on the one hand to present the capabilities of computational tools and to outline the results of experiments dealing with the MPTR, on the other hand to show results from the application of those tools that bring (preliminary results have been obtained within the present framework that need further qualification) to the exclusion of the possibility of MPTR in currently operating RBMK NPP. 2. The boundary conditions for the MPTR issue 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 toward the accident scenario originated by the fuel channel blockage (FC-BLOCKAGE by D’Auria et al., 2008b,d) making reference to boundary conditions in the Smolensk-3 NPP unit. The key elements for achieving the objectives assigned for the paper can be found in chapters 4–6. Hereafter, chapters 2 and 3, the background for addressing the multidisciplinary problem arising from the FC-BLOCKAGE and the MPTR issues is introduced. This includes the presentation of following aspects: (a) sketches of components and zones of the RBMK core region to make clear the concerned accident scenario, (b) the characterization of the steady state operation of the reference RBMK boiling channel, (c) the experience from the pressure tube (PT) rupture events in RBMK NPP, (d) the phenomenological evolution of the transient, (e) the differences between the FC-BLOCKAGE and the FC-LOCA scenarios and (f) the licensing environment. 2.1. Elements of the RBMK core layout relevant to the MPTR The overall RBMK system, the primary loop, the confinement including the reactor cavity and the core region are described in the companion papers by D’Auria et al. (2008a,b,c,d), respectively. More details can be found in taken from the references Almenas et al. (1998), Uspuras and Kaliatka (2006) and D’Auria et al. (2005). A few elements are reported below that are relevant for the present study. 2.1.1. The overall core configuration Referring to the Smolensk-3 plant data the reactor core is composed by 2488 graphite columns or stacks, Fig. 1, of which:

Fig. 1. Radial cross-section of RBMK core (Smolensk-3 NPP). ‘White’ (or empty) squares are the (1570) fuel channels.

(a) 1570 fuel channel columns, Fig. 2, (b) 314 non-fuel channels columns (211 are control rods channels, part of the Control and Protection System, CPS, regularly distributed over the core lattice) and (c) 604 radial reflector channels. The following should be noted (relevant aspects for the present context): • ‘Hot’ and ‘cold’ graphite stacks are part of the core. A typical cell consisting of one CPS channel and of five fuel channels is illustrated in Fig. 3 (top). In the same figure (bottom) typical temperature values in one fuel channel ‘graphite cell’ during nominal core operation are reported (Parafilo et al., 2000). In all channels thermal power is generated in the graphite due to the neutron moderation process and is transferred to the central cooled channel (either FC or CPS channel, thick arrows in Fig. 3). Furthermore, graphite blocks enveloping FC are warmer than graphite blocks enveloping CPS channels, thus heat transfer occurs across gaps (narrow arrows in Fig. 3) as discussed by Uspuras and Kaliatka (2004). Coolant in the CPS is kept below the boiling point by suitable circulation flow. • Temperature of graphite is not only a function of the radial coordinates (above bullet) but also of the axial coordinate with lower average temperature at the bottom and at the top of the core (see results of steady-state analyses, for instance Fig. 18c in D’Auria et al., 2008b). Therefore, axial heat transfer occurs between ‘piled-up’ graphite blocks to a lower extent than radial heat transfer owing to smaller temperature differences. • The thickness of the gaps between adjacent graphite blocks, Fig. 3, depends upon temperature differences, not uniform all over the core, and upon neutron fluence: irradiation causes

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Fig. 2. Fuel channel and fuel rod of a RBMK.

•

•

•

•

Fig. 3. Graphite stacks in RBMK: (a) ‘module’ including five fuel channels and one CPS channel (red circle); arrows indicate the versus of the heat transfer; (b) typical graphite temperatures during nominal operation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

changes in the geometric dimensions of graphite blocks other than in material properties, e.g., IAEA (2000). Other gaps exist between pressure tubes and graphite rings and between graphite rings and graphite stacks (Fig. 4). The gap dimensions are largely a function of neutron fluence, pressure and temperature, e.g., operating conditions and core life. The gas, helium or nitrogen or a mixture helium–nitrogen, circulates inside the gaps among graphite stacks (see also the devoted paragraph below). Its main roles for the safety and operation of RBMK are: (a) detection of high radioactivity or humidity in the reactor cavity (irrelevant for the present context of analysis); (b) transferring thermal power from graphite to pressure tube; (c) transferring thermal power between adjacent graphite columns, i.e. heat transferred by the gas removal system is negligible compared with the heat passing from ‘hot’ stacks to ‘cold’ stacks. Mechanical, thermal and neutron related properties of materials constituting the core are largely a function of core life (neutron fluence) and of operating temperature, e.g., IAEA (2000). This must be considered in the analyses. The deformation characteristic of the fuel channels and associated graphite column depend upon the type of load (uniform, punctual, etc.) and upon the location. Furthermore, other than the pressure tube that constitutes the most resistant part of the ensemble, the graphite blocks, the fuel bundles and the central bar contribute to the overall stiffness.

2.1.2. The reactor cavity and the hydraulic connections Phenomena occurring in the confinement including the reactor cavity (RC), are discussed by D’Auria et al. (2008c). The sketch of the RC of the Smolensk-3 NPP with main hydraulic connections is given in Fig. 5. The connection of both the RC and the accident localisation system (ALS) with the environment should be noted.

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Fig. 4. Graphite block, graphite ring and pressure tube of the RBMK core and main geometric dimensions.

2.1.3. The ensemble of graphite columns, the enveloping tank and the structural constraints About 2500 graphite stacks constitute the core, with about 1500 fuel channels as described above. Each stack, composed of several blocks (one block shown in Fig. 4), is centred over a thick-walled, pressure resistant, zirconium (plus 2.5% niobium) tube. Each tube is constrained at the top and at the bottom in a complex way as given in Fig. 6a where possible constraint modelling is also shown. The ensemble of stacks is surrounded by a cylindrical steel tank (“KZh” structure in Fig. 6b; internal diameter 14.50 m, thickness 0.016 m and height 9.75 m), that together with the top and bottom metal structures (“E” and “OR” in Fig. 6b) forms the sealed region for the reactor cavity. In order to compensate for axial thermal expansion, the tank is provided with a bellows compensator. The tank is designed to resist to relatively small pressures (in the order of 0.6 MPa), and not to local loads due to the hard contact with bending columns. Nevertheless, in the case that a peripheral column is pushed against the tank, this

is expected to hinder further displacements of the columns and thus to play a role in mitigating the deformation of the involved stack ensemble. 2.1.4. The gas removal system The gas removal system has already been introduced in the paper by D’Auria et al. (2008c) because of its role in confinement analyses. The related sketch is given in Fig. 7. The main goal for the system design is to prevent graphite oxidation and to control pressure tubes sealed condition. Performing a best estimate analysis for this specific scenario, and for similar ones within the RBMK safety technology, may imply the consideration of the gas removal system. 2.2. The reference quantity values A variety of data is needed to calculate the complex scenario arising as a consequence of the fuel channel blockage. An idea of the parameters that characterize the transient performance

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Fig. 5. Sketch of the reactor cavity of the Smolensk-3 RBMK NPP with related main hydraulic connections.

of a fuel channel can be derived from Table 1. These include parameters relevant to: • thermal-hydraulics (related to primary system and confinement), • structural mechanics, • neutron kinetics.

Fig. 6. Structural configuration of the RBMK core: (a) pressure tube constraints; (b) mechanically resistant elements.

Material properties and dependencies of some of the selected parameters upon temperature and fluence constitute additional sets of parameters needed for performing the analyses. 2.3. Experience from the occurred PT rupture events in RBMK NPP The individual channel flow blockage accidents happened and have been documented in the following RBMK NPP (year also reported): • Chernobyl-1 (1982), • Leningrad-3 (1992). A third pressure tube rupture event occurred in Leningrad1 (1975) and was initiated by local power excursion because the additional scram system (denominated ‘LAR-LAZ’), now installed in all RBMK NPP, was absent. During this event, although the mismatch between the flow rate and the increased power was experienced by more than one fuel channel, only one pressure tube failed.

Fig. 7. Sketch of the gas removal system from the RBMK reactor cavity.

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Table 1 Key quantities relevant for the analysis of the FC-BLOCKAGE scenario in RBMK No. 1

Item

Unit

Fuel generated power

Value

Notes

2.01

Typical value. Maximum allowed value is 1.6 times larger

MW 2 3 4

Power coming from graphite blocks Power removed by the gas cooling system per fuel bundle Fuel bundle active length

5 6 7 8

No. of fuel rods per bundle Diameter of the pressure tube Thickness of pressure tube Edge of the square graphite block

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

35 36 37

FC inlet flow-rate FC inlet sub-cooling FC inlet pressure FC outlet quality/void fraction FC total pressure drop Mass of coolant in one FC Ratio flow-rate/power Thickness of the gap between graphite blocks Young module of pressure tube Young module of central bar Young module of fuel bundle Young module of graphite stack Mass of UO2 in one FC Mass of zirconium in fuel assembly Mass of zirconium in FC wall Producible H2 in one FC Mass of graphite associated to FC Reactivity associated with the FC voiding Reactivity associated with the increase of 200 K for average fuel temperature in the bundle Pressure in reactor cavity Overpressure for scram in reactor cavity Average gas temperature in reactor cavity Fuel enrichment Burn-up (with above enrichment) Axial and radial temperature distribution for the graphite Beginning and end-of-life gas pressure in the fuel pin-hot condition Radioactivity in one FC, fuel Radioactivity in one FC, gap Yield stress for zirconium tube

38

Yield stress for graphite

28 29 30 31 32 33 34

0.12 <0.001 m

7.0

–

18 0.08 0.004 0.25

m

kg/s K MPa −/− MPa kg kg/MW m MPa × 103 at 300 ◦ C

kg

$

6.1 25 7.8 0.15/0.8 0.65 ∼8 ∼3 0.0015 75.4

145.0 141.8 29.2 53.0 0.95 and 1.7 743. +0.3 −0.44

K % MWd/t K

0.1 0.0075 823 2.0 and 2.4 10000 *

MPa

1.6 and 1.9

Ci

∼57000 ∼250 380–430

MPa

MPa

The first of the above listed events, Chernobyl-1 (1982), was a consequence of erroneous actions of the operator who, in adjusting the flow rates in the fuel channels, fully closed the control and isolation valve (CIV) of one FC. The designers responded to this event by equipping all CIV at all power units with restrainers of the CIV stem travel in order to prevent FC flow rate reduction during adjustment below the permissible minimum. The scenario for the second of the above listed events, Leningrad-3 NPP, is discussed below, see NIKIET (1992) and Fedosov et al. (1994). Status of the plant before the event: nominal operating conditions, 3150 MW. The blocked channel is characterized by the

See Fig. 1. Two fuel bundles are inserted into the channel

Equivalent cylinder radius (for modelling purposes) is 0.141 m Average value

Affected by irradiation and by thermal expansion 90.4 at 80 ◦ C 160.0 at 80 ◦ C

For fuel bundle and tube Assuming β = 0.007. Calculation by MCNP Assuming β = 0.007. Calculation by MCNP. In case of 300 K the value is −0.65 Nominal operation Case of Leningrad-3 NPP

Average value *See Fig. 3 above and Fig. 18c in D’Auria et al. (2008b)

See also Table 6 Typical range given, affected by temperature and fluence

6–9

coordinates 52-16, located in the left upper part of the reactor map. On 24 March 1992 at 2 h 34 min 45 s (event start), a pressure increase signal from the reactor cavity activated the fast acting emergency protection system and the reactor was scrammed by rod insertion within 2.5 s. This time (with an error of about 2 s) can be considered the time of the pressure tube rupture. Because of the time lag of 40 s between two recorded point from the flow-rate transducers the time of the flowrate reduction occurrence is known with an error of 40 s. A suitable number of withdrawn control rods was available for scram.

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The signal for shut-down system activation is triggered when the cavity pressure increases by 0.075 bar. Two seconds after the scram the relative pressure in the cavity reached 0.13 bar and subsequently decreased to the value of 0.1 bar after 5 s. Afterwards the pressure again started to rise with a slower rate and reached a peak of 0.19 bar 23–25 s after the event start. Then the cavity pressure steadily decreased. The cause for the accident was the flow decrease at the inlet originated by the failure of the control valve. In particular, a throttling device of the valve was partially destroyed and closed the flow area. The resulting abrupt flow rate decrease led to critical heat flux and then, subsequently, to fuel, clad and pressure tube overheating. The loss of strength of the pressure tube material caused the rupture. After the rupture flow reversal flow from the steam drum to the broken channel occurred causing the cooling of the upper part of the fuel channel and the further pressurization of the reactor cavity. About 14 h after the event, it was attempted to remove the broken channel. Only the hanger and a 0.54 m long part of the central supporting tube could be removed. The remaining part of the fuel assembly remained in the channel. Further investigation showed that the channel had ruptured in the upper part of the core approximately 6 m above the bottom. The graphite rings around the rupture location were partially destroyed and the graphite blocks were damaged. The fuel rods were mechanically bowed in the direction of the breach. On 28 March the extraction of the channel following the normal procedure began. Only the top part of the channel, with length of 4945 mm, was extracted. Based on the visual analysis of the broken channel the picture in Fig. 8 has been created. The graphite block and the fuel assembly were destroyed. However, the neighbouring fuel channels were not subject to any damages and were left in operation without any restrictions. Post accident examination (performed at Paul Scherrer Institute in Switzerland) showed that the pressure tube rupture occurred

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when the tube temperature was in the range 797–847 ◦ C (i.e. quite larger than the current licensing limit of 650 ◦ C). 2.4. The licensing environment The licensing environment for accident analysis in RBMK has been discussed in the companion papers (D’Auria et al., 2008a,b,c,d), pointing out aspects related to the overall system, to the confinement and to the fuel. Therefore the attention is focused here on the following key topics: • The consideration of the FC-BLOCKAGE within the licensing framework. • The pressure tube rupture curve. • The phenomena based list of scenarios relevant for RBMK safety analysis. 2.4.1. The FC-BLOCKAGE event and the licensing framework From the licensing point view, the following statements apply to the accident scenario in RBMK originated by blockage in one fuel channel: (a) The probability of occurrence, if one considers only the events documented in existing NPP, is of the order of 10−2 per reactor-year. Because of this, the event should be classified as design basis accident (DBA). (b) The event implies the severe damage of substantial amount of fuel, even though this is limited to one fuel channel therefore to an order of magnitude that is a fraction less than 1/1000 of the fuel mass in the core. Because of this the event should be classified as Beyond DBA (BDBA). (c) The event is not explicitly mentioned in the ‘list of events’ proposed by the IAEA (IAEA, 2005), that reflects the level of knowledge and agreement among specialists at the date,

Fig. 8. Leningrad-3 RBMK NPP: sketch of the damaged fuel channel following the 1992 accident.

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even though the event ‘break of a channel tube within the reactor cavity’ is a classified DBA (more details given in Section 3.2 below). (d) Following Uspuras (1999), the event ‘reduction or loss of flow in one fuel channel’ is ‘. . . one accidents initiated by equipment failure [that] should be also analysed . . .’ according to GAN (1987). (e) During the event, the DBA thresholds defined for RBMK accident analysis, e.g., fuel temperature below 1200 ◦ C, IAEA (2005) (see also D’Auria et al., 2008a,b), are overpassed. (f) The acronym Ultimate DBA (UDBA) is used for RBMK accident analysis, e.g., Lillington et al. (1997), but not in relation to the fuel channel blockage event. Therefore, if the fuel channel blockage event is not considered a DBA, a contradiction with item (a) might be envisaged. If the event is considered a DBA a contradiction raises in relation to item (e). In this case, the leakage of damaged nuclear fuel outside the pressure boundary brings an important difference between accident evolutions in RBMK related to other water cooled reactors as already pointed out by D’Auria et al. (2008a). The recommendation from the present study is to consider the flow blockage event in a RBMK fuel channel as a DBA and to offer measures capable to reduce probability of the event, for instance see D’Auria et al. (2008e). 2.4.2. The acceptability limits for pressure tube The pressure tube failure constitutes the most important occurrence during the event: on the one side it allows the detection of the event, on the other side it causes the release of radioactive material outside the pressure barrier, but also it brings to the possibility of cooling for the damaged channel and causes the potential for the MPTR. The failure of the pressure tube and of the associated graphite rings and graphite blocks is the result of a complex mechanical, thermo-hydraulic interaction process that is discussed into detail in chapter 3 below. Several quantities contribute to the process making the process itself a multidimensional problem. Combined criteria are strictly necessary to demonstrate the pressure tube rupture in a best estimate way, as discussed by Novoselsky and Filinov (1997a,b,c) (see also D’Auria et al., 2005). A synthesis (simplified and conservative) approach for the pressure tube rupture ‘continuous’ acceptability threshold is based on the diagram in Fig. 9. The pressure tube temperature at which the rupture is expected is reported as a function of the differential pressure across the tube walls. Any working condition below the dashed region is ‘safe’, while rupture is expected above the dashed region. The following should be noted: • CANDU and RBMK pressure tubes behave in a similar way. • The rupture is affected by the gradient of temperature rise and occurs ‘earlier’, i.e. at lower temperatures at low gradient compared with the higher gradient. • Graphite bounded tube have a slightly higher resistance than bare tubes.

Fig. 9. Simplified approach for establishing the acceptability thresholds for the integrity of pressure tubes of RBMK.

• The licensing rupture criterion, T < 650 ◦ C, is conservative, primarily at low differential pressures. 2.4.3. The FC-BLOCKAGE and the phenomena based list of relevant scenarios A phenomena based list of events has been proposed for the deterministic safety analysis of RBMK by D’Auria et al. (2005), also reported in D’Auria et al. (2008a). This is given in Table 2, where the FC-BLOCKAGE and its key role within the context of RBMK safety technology is underlined. Each of the letters ‘A’ to ‘F’ in the first column in Table 2, identifies classes of accidents characterized by bounding physical phenomena suitable to assess capabilities of computational tools. The class ‘D’, of concern within the present paper, deals with the class ‘FC rupture and MPTR’ and related phenomena are described in chapter 3 below. Key differences between the two scenarios in class ‘D’ (FC-BLOCKAGE and FC-LOCA) are also addressed in chapter 3. 3. The multidisciplinary problem associated with the FC-BLOCKAGE scenario An overview is given below of the phenomenological aspects associated with the scenario originated by the blockage of one fuel channel in the RBMK NPP (i.e. FC-BLOCKAGE event). To this aim, phenomena are identified that characterize the progression of the event together with differences between the concerned scenario and the FC-LOCA (Sections 3.1 and 3.2, respectively). The failure map for RBMK pressure tubes and the probable position for break elevation following FCBLOCKAGE are described in Section 3.3.

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Table 2 Phenomena based list of accident scenarios suitable for deterministic accident analysis in RBMK (D’Auria et al., 2008a) Identification No.a

Acronym explanation

A1

LOCA-PH-FIGDH: LOCA in pressure header with failure to isolate GDH

A2

LOCA-SL: LOCA originated by a break in steam line LOOP-ATWS: loss of on site power with the ATWS condition

A3

A4

Codes adopted for achieving results documented in the present paper

Largest primary system break with single failure. Challenging core cooling and the ECCS design Highest depressurization rate. Challenging core cooling and the ECCS design Challenging core cooling and the neutron kinetics model of the thermal-hydraulic system codes Check of the capability of the ‘ECCS bypass’ to cool the core Challenging the venting capability of the reactor cavity (part of the confinement)

Relap5

B2

GDH-BLOCKAGE: full blockage of the GDH GDH-BLOCKAGE-SA: Full blockage of the GDH with the ‘Severe Accident’ assumption of no bypass line available LOCA-PH-FIGDH: see A1

B3

LOCA-SL: see A2

Contain

C1

FC-BLOCKAGE: full blockage of one fuel channel GDH-BLOCKAGE: see A4

Relap53D©/Nestle

Korsar-Bars

C4 D1

CR-G-WITHDRAWAL: continued withdrawal of a CR bank (or group) CPS-LOCA: voiding (or LOCA) of the CPS FC-BLOCKAGE: see C1

D2b

FC-LOCA: rupture of one FC

Contain & Relap5 Fluent-Ansys Korsar-Rapta

E1

FC-BLOCKAGE: see C1

Cocosys Melcor

E2

GDH-BLOCKAGE-SA: see B1

B1

C2 C3

F1 a b

FC-BLOCKAGE: see C1

Cocosys & Relap5

Contain & Relap5

Challenging the ALS (part of the confinement) structural resistance (same as A1) Challenging the reactor building (part of the confinement) venting capability (same as A2) Challenging the calculation of the local fission power generation (same as D1) To assess and to understand the local core response (same as A4) Challenging RIA (Reactivity Initiated Accident) scenario for core integrity

Relap5-3D©/Nestle Relap5-Ansys Katran-U Stack

Relap5

Reasons for the selection

Driving accident for the study. Challenging various phenomenological areas and codes To assess the ballooning model in the fuel pin mechanics area To assess the hydrogen and the fission products source term and transport (same as D1) To assess the hydrogen and the fission products source term and transport in one extreme conditions (same as B1) To formulate the ICM proposal (same as D1)

See Table 3 in D’Auria et al. (2008a). In particular, ‘A’ to ‘F’ identify classes of accidents characterized by bounding phenomena. The class of accidents ‘D’, of concern for the present paper, deals with ‘FC rupture and MPTR’.

The multidisciplinary nature and the demonstration of complexity for the concerned scenario constitute important outcomes from the description. 3.1. Expected phenomena The main phenomena expected following the FCBLOCKAGE event and the qualitative time succession can be derived from the diagram in Fig. 10, main arrow at the top. Other horizontal arrows in the diagram indicate technological subjects relevant during the concerned time frame. The two vertical arrows indicate: (1) The potential role of the individual channel monitoring (ICM) system in preventing the progression of the accident (see D’Auria et al., 2008e).

(2) The assessed role of the tank (see chapter 5) in contributing to limit the possibility of MPTR. Thermal-hydraulic phenomena are relevant at the beginning of the transient, like dry-out, and counter-current flow limitation at the outlet of the channel that prevents water from the stem drum to enter the blocked channel. Neutron kinetics phenomena are also relevant since the beginning because of the reactivity coefficient associated with coolant void formation and (consequent) temperature increase of the fuel. Phenomena associated with fuel performance become important because of the unavoidable high temperatures and consequent metal water reaction, clad collapse and substantial rod deformation. Radiation heat transfer is also relevant at this point in time. Break of the pressure tube and of the neighbouring graphite blocks occur by ductile and fragile mechanisms, respectively. At

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Fig. 10. Main phenomena and qualitative time evolution expected following the FC-BLOCKAGE event in RBMK NPP.

(nearly) the same time of the pressure tube rupture event, twophase critical flow occurs at the break together with flow reversal at channel top and ejection of damaged fuel and possible chemical reactions between the damaged fuel and the surrounding graphite. The ejection of fuel is caused by hydraulic forces at the break caused by pressure wave propagation at first (tenths of a second time-scale) and to the high fluid speed later on. Pressurization of reactor cavity occurs as well as mixing of steam and non-condensable gas, therefore confinement thermalhydraulics is relevant. Mechanical stresses are generated occur upon neighbouring graphite stacks causing elastic and plastic and deformation for the associated fuel channels (potential precursor phenomena for the MPTR). The rupture of pressure tubes causes heavily damaged fuel to enter the reactor cavity, thus making relevant the area of fission products transport. A detailed list of phenomena is provided in Table 3 , where codes suitable for the evaluation of those phenomena are identified, too. The codes have been used within the project described by D’Auria et al. (2005). In the case a quality proof is available to the authors in relation to the concerned phenomenon, the letter is added to in the fourth column of Table 3. 3.2. The difference between FC-BLOCKAGE and FC-LOCA In order to better focus on selected important phenomena, differences between FC-LOCA and FC-BLOCKAGE, e.g., scenarios D1 and D2 in Table 2, are discussed hereafter. The discussion should also aim at presenting the FC-LOCA scenario even though with a level of detail lower than the FC-BLOCKAGE (same level of detail would also cause an un-necessary longer paper).

By FC-LOCA the scenario is meant here originated by the sudden break of one pressure tube inside the graphite stacks. Therefore, the FC-LOCA acronym is not an indication of: • A break in the pressure tube inside the reactor cavity in the region outside the graphite blocks (i.e. inside the free space of the reactor cavity). • A break in the pipelines connecting the pressure tube with the Group Distribution Header (channel inlet region) of the steam drum (channel outlet region). Both of these set of events are relevant in the safety assessment of RBMK and are part of the list of DBA according to IAEA (2005) (see also D’Auria et al., 2008a). In the above cases scram is generated early during the transient with a situation of undamaged fuel and good cooling conditions can be kept, by the existing emergency safety features during the entire course of the transient (i.e. till the full recovery of the NPP). The origin of a FC-LOCA is typically a defect of the pressure tube in the active region. The related probability has been estimated as negligible in the recent paper by Lee et al. (2006) (see also D’Auria et al., 2008a), but it should be investigated as a DBA according to the document at reference IAEA (2005). The similarity between FC-LOCA and FC-BLOCKAGE lies in the fact that in both cases a pressure tube is broken, thus implying the damage of the graphite block(s) close to the rupture region. The following differences exist between FC-LOCA and FC-BLOCKAGE: • In the case of FC-LOCA the scram occurs at a time when the fuel is not overheated (originated by the same signal as in

Table 3 List of expected phenomena following the FC-BLOCKAGE event in RBMK NPP and suitable codes for the evaluation No. 1 2 3

Event

Blockage at channel inlet

4 5

Dry-out

Over-passing the threshold for clad integrity

14 15 16

Codesa

Notes

Flow-rate decrease Void increase in the FC Change in pressure drop distribution along the FC axis Flooding (and possible CCFL) at FC outlet Neutron kinetics feedback due to loss of coolant

Korsar & Relap5

The blockage may be partial or total

Bars & Nestle

Coolant is an absorber, see Fig. 17 in D’Auria et al. (2008d)

Rod surface temperature excursion Steam superheating generation and transport Neutron kinetics feedback due to Doppler effect Flooding (and possible CCFL) at FC outlet Change in fission power generation Clad collapse Releases of gaseous FP Change of bundle geometry and of cooling characteristics Radiation heat transfer Clad damage

Korsar & Relap5 Bars & Nestle Korsar & Relap5 Bars & Nestle Rapta & Frap Refp & Melcor Relap5 Relap5 Rapta & Frap Melcor

Over-passing the threshold for significant H2 production 17 18 19 20 21 22

Rupture of the PT

23 24 25 26 27 28 29 30 31

Pressurization of reactor cavity and scram occurrence

Fuel bundle damage (loss of geometric integrity) Temperature increase in PT Creep of the PT Mechanical interaction of PT with graphite rings and with graphite blocks in the region of creep Flow-rate (reversal) from steam drum established Cooling of the bundle region at an elevation higher than the break Simultaneous break of PT, graphite rings and blocks in the creeping region TPCF at the break and at a top location of the affected FC Hydraulic loads on thermally damaged fuel bundle Loss of damaged fuel from the break Chemical interaction between molten-damaged fuel and graphite Continuous H2 generation Pressurization of the RC Cooling (quench) of both halves of fuel bundles separated by the break Heat transfer through graphite gaps

Korsar & Relap5 U Stackb & Ansys

Relevant to ICM design See Fig. 17 in D’Auria et al. (this issue-d) Phenomena at rows 2 and 3 also apply Owing to phenomena at rows 5 and 8 Loss of integrity expected for the fuel rod Minor effect Relevant during later phases, too Phenomena associated with ‘severe accidents’ start in the fuel region (e.g., candling corium oxidation, etc.)

Owing to the phenomenon at the row above Axial location of the creeping region depending upon BIC like % of FC blockage

Korsar & Relap5 Owing to the phenomenon at the row above U Stack & Ansys

Ductile and fragile mechanisms for PT and graphite, respectively

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6 7 8 9 10 11 12 13

Key phenomena

Korsar & Relap5 Fluent Fluent & Melcor – Korsar & Relap5 Cocosys & Relap5 Korsar & Relap5 Cocosys & Relap5

Large radioactivity release to RC High temperature chemical interactions not investigated From claddings and possibly from PT walls Because of the high pressure in the reactor cavity Liquid penetration possible owing to the stop of power generation. Stop of H2 production Relevant during later phases, too 1037

Key phenomena

Codesa

Notes

Ansys & U Stack

Limited by the displacement associated with the creep deformation before rupture for the broken PT Situation of no propagation of the rupture (no MPTR) Negligible in case of superheated steam in the FC

36

Mechanical load due to displacement of the broken blocks Dynamic forces associated to the pressure wave propagation Dynamic forces associated with flashing Differential pressurization of the graphite gaps on opposite faces of neighboring graphite blocks Elasto-plastic deformation of several FC

37

Touching of fuel stacks and tank

38

Transport of H2 from broken FC to graphite gaps and to RC free space Transport of FP from broken FC to graphite gaps and to RC free space

Relap5 & Melcor

Cooling (including quench) of graphite blocks by water coming from the break and flooding of RC

U Stack & Relap5

No.

Event

32 33 34 34

40

U Stack & Relap5 Ansys & U Stack

Melcor

This constitutes a constraint to the propagation of the PT rupture Possible. The tank may contribute to increase the constraint to the propagation of the PT rupture Risk of deflagration negligible in case of functioning of the gas cooling system Various chemical and physical processes relevant. H2 (see above) and FP may enter the pool and finish into the ALS Potential interaction with dissociated O2 not investigated

ALS = accident localisation system (part of the RBMK confinement), BIC = boundary and initial conditions, CCFL = counter current flow limitation, FC = fuel channel, FP = fission products, ICM = individual channel monitoring, PT = pressure tube, = qualification evaluated within the present context, RC = reactor cavity and TPCF = two phase critical flow-rate. a Adopted codes within the present framework, D’Auria et al. (2008a), see also D’Auria et al. (2005). b Katran code is embedded into U Stack. Fig. 11. Differences between FC-LOCA and FC-BLOCKAGE scenarios: (a) clad radius calculated by Korsar-Rapta; (b) gap size calculated by Relap5-Frap.

the case of FC-BLOCKAGE, i.e. over-pressurization of the reactor cavity). • In the case of FC-LOCA after the break occurrence, the fuel is immediately cooled by high velocity fluid coming from the bottom and the top of the channel (only flow reversal from channel top is available in the case of FC-BLOCKAGE). • Because of the above, no dry-out condition is expected in FCLOCA after the break occurrence: despite their increase the clad surface temperatures of the fuel rods remain well below the stated safety limit. • In the case of significant delay in scram signal, overheating of fuel clad is expected after the pressure tube rupture event. The mechanism for clad damage is the ‘ballooning’ in the case of FC-LOCA, and is the ‘collapse’ in the case of the FC-BLOCKAGE and occurs before the pressure tube rupture event. This is illustrated in Fig. 11, where results from two couples of [coupled] codes are shown: (a) the increase in clad radius versus time (500 s is the transient start time) calculated by Korsar-Rapta code is given in Fig. 11a and is caused by the increasing pressure difference across the clad (rod internal pressure nearly constant and decreasing external pressure); (b) the decrease in gap size versus time (100 s is the transient start time) calculated by Relap5/Frap code is given in Fig. 11b and

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Deformation of neighboring graphite stacks

Relap5

1038

Table 3 (Continued)

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is caused by the increasing clad temperature (with pressure differential across the clad remaining nearly constant during the calculated transient period). The fuel rods can be damaged by hydraulic loads caused by the high speed flow at the break. Accordingly, radioactivity source term inside the reactor cavity can be larger in case of FC-LOCA compared with FC-BLOCKAGE. • The break flow is greater in the case of FC-LOCA compared with FLOW-BLOCKAGE. Energy outflow from the break can also be greater in the former case: this difference has been found to have a negligible effect in case of evaluations for possible MPTR. 3.3. The failure-map and the break location for RBMK channels Once the fuel channel blockage event triggers, the following system parameters or occurrences are relevant for determining the scenario: (a) nominal operating power of the affected channel, (b) axial power shape and/or linear power peaking factor of the affected channel, (c) percentage of the blockage, (d) axial and azimuthal position of the break, (e) area of the break. The nominal channel power and the percentage of blockage values are linked by the ‘FC failure map’ and the axial power shape and the power peak factor contribute to the calculation of the break axial position, both of these discussed below. The azimuthal position of the break has a role in the estimation of the possibility of MPTR, but it is a statistic quantity with uniform distribution (i.e. as a function of the angle identified by the break axis in the horizontal plane and any reference radius in the same plane centred on the axis of the fuel bundle).

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The area of the break has been found to have a minor role upon the long term overall scenario progression, provided it is (much) larger than the flow area associated with the minimum cross-section at the top of the fuel channel. In this case, critical flow establishes at the top of the affected fuel channel and rupture area is irrelevant for the mass and energy release from the break. However, break area is relevant for the estimation of ‘prompt’ hydraulic loads upon the fuel bundle and the neighbouring channels and related graphite stacks. The ‘prompt’ hydraulic loads including pressure wave propagation vanishes in tenths of a second. All the parameters (a) to (e) are considered in the analyses discussed in chapter 5 In addition, both the RBMK channel failure map and the characterization of the axial break position following FC-BLOCKAGE constitute significant results (see chapter 5) from the application of the computational tools presented in chapter 4. These are discussed hereafter in advance, in order to complete the phenomenological picture of the fuel channel blockage scenario. 3.3.1. The failure map for RBMK fuel channels A fuel channel failure map has been derived as a significant by-product of the analysis conducted in relation to the FC-BLOCKAGE (D’Auria et al., 2005). The FC failure map is given in Fig. 12 and shows the boundaries for pressure tube and clad damage. The following should be noted: • The map is derived based on the results from ‘discrete’ calculations of pressure tube failure in the domain fuel channel initial power versus the percentage of blockage of the channel inlet pipe. The percentage of blockage is defined in terms of % blocked free flow area. • Overheating of the clad is a prerequisite for the occurrence of the pressure tube failure, but not in all cases fuel rod overheating implies pressure tube rupture.

Fig. 12. Failure map for RBMK fuel channels following the FC-BLOCKAGE event (D’Auria et al., 2005).

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• The blue region represents the space of un-failed nonoverheated rods. Three different colours are used to characterize the damage area for rods only (all three regions) or for pressure tube and rods (the two regions on the extreme right of the diagram). • Oxidation is the reason for failure in the extreme right region of the map, oxidation and collapse occur in the central damage region and collapse occurs in the left region of the damage area. In addition, hydraulic loads are at the origin of further pin failure (or of the ‘increase’ in the fuel pin damage level) in the two right regions of the damage area. The map has been derived by a dozen code runs. Therefore the boundaries among the various zones are approximate. More valuable is the procedure adopted to derive the map and the embedded qualitative information. 3.3.2. The characterization of the elevation of the break along the fuel channel axis The full channel blockage causes a fast voiding in the channel, i.e. the order of magnitude for the channel emptying times is one second. Therefore, all zones of the fuel bundle remain early in the transient without cooling and fuel and rod surface temperature growths are faster where linear power is higher. This typically happens in the central region of the bundle along the axis. High rod temperatures imply high temperatures for pressure tube owing to radiation and contact heat transfer and consequent trigger of creep mechanism for tube rupture. Partial channel blockage is expected to cause dry-out owing to liquid film depletion earlier in the upper region of the bundle with bottom region partially cooled. In this situation, high temperatures with rods and, subsequently, tube wall damage occur in the upper part of the bundle. The overall phenomenological picture related to the possible elevation of the break along the fuel channel axis and the discussion above are summarized in the sketch of Fig. 13.

Fig. 13. Sketch to illustrate the parameters affecting the break location along the fuel channel axis.

4. The computational tools and the qualification level to calculate the FC-BLOCKAGE The variety of computational tools necessary to calculate the scenario consequent to the blockage of one RBMK fuel channel can be derived from the previous chapter. In particular, the numerical codes that have been adopted within the present context are listed in Table 3. An outline of the main features of adopted codes and nodalizations is given below. Additional details related to codes can be found in D’Auria et al. (2005). 4.1. The codes The numerical codes adopted within the present framework (Table 3) are distinguished in Table 4 according to the technological areas discussed by D’Auria et al. (2008a) and a short

Table 4 Classification of codes adopted for the analysis of the FC-BLOCKAGE scenario in RBMK according to technological areas relevant in nuclear reactor safety No.

Technological safety area

1

Codes

Notes

Primary System

Relap5, Korsar

Also includes H2 generation and transport

Fuel Confinement

Frap, Rapta Cocosys, Relap5 Fluent Katran, Ansys (U Stack)a

System Thermal-Hydraulics 2 3 4 5

Computational Fluid Dynamics Structural Mechanics

6

Neutron Kinetics

7 8 9

Fission Products a

Generation of average parameters (e.g., macroscopic cross-sections or ‘λ-functions’) 3D transient neutron flux Generation Transport

U Stack code has capabilities to handle technological safety areas 1, 2, 3 and 5.

Njoy, Unk, Helios

Bars, Nestle Refp, Melcor Cocosys, Melcor

The MPTR issue is addressed by the U Stack code and by a procedure (given in chapter 6)

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description is provided hereafter in relation to codes not discussed in companion papers (D’Auria et al., 2008a,b,c,d). It shall be noted that all technological areas identified as characterizing the deterministic analysis sector within the nuclear reactor safety are relevant for evaluating the consequences of the fuel channel blockage scenario in RBMK. 4.1.1. System Thermal-Hydraulics: primary system Relap5 and Korsar codes are adopted to calculate the thermalhydraulic parameters following the FC-BLOCKAGE event in the Main Coolant Circuit of the RBMK. Relap5 is the widely known and diffused code developed by Idaho National Laboratory in the US already available since the end of 70s. Korsar is based on the same principles and equations at the basis of Relap5 and was developed and qualified in the last few years at the St Petersburg Institute NITI in Russia. Information can be found in D’Auria et al. (2008b). 4.1.2. System Thermal-Hydraulics: fuel Rapta and Frap codes are adopted to calculate the fuel performance parameters including rod deformation following the FC-BLOCKAGE event in the RBMK fuel bundle. The code Rapta, includes basic models of processes and phenomena inherent to behaviour of fuel rods with oxide fuel and cladding made of zirconium alloy in various transient and emergency regimes of RBMK reactor. Thermo-mechanical modules were developed making reference to one single-equivalent (i.e. the most loaded in terms of thermal power) fuel rod. The code is qualified against experimental data, e.g., Goncharov et al. (2005). The code Frap is a well established international code developed at Pacific Northwest National Laboratory in the US aiming at the evaluation of fuel rod performance. Two main modules are part of the code: Frapcon, e.g., Lanning et al. (1997), and Fraptran e.g., Cunningham et al. (2003), that calculate the steady state and the transient performance, respectively. The qualification level can be recognized from the references of the above documents. The code is embedded into the Relap5 code. 4.1.3. System Thermal-Hydraulics: confinement Cocosys and Relap5 codes are adopted to calculate the thermal-hydraulic parameters in the RBMK confinement following the FC-BLOCKAGE event. Relap5 code has already been mentioned above. Cocosys code has been developed and qualified in the last few years at the GRS in Germany. Information about the codes and their qualification level in the concerned area can be found in D’Auria et al. (2008c) (information about Cocosys as a fission product transport code is also given below). 4.1.4. Computational fluid dynamics Fluent code has been adopted to calculate hydraulic loads acting upon the fuel rods following the rupture of the pressure tube occurring during the FC-BLOCKAGE event. Fluent is a commercial ‘finite volume’ based code, e.g., Fluent Inc. (2003), for modelling fluid flow and heat transfer in complex systems. It can be used for (not an exhaustive list) the analysis of: (a)

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incompressible or compressible, steady-state or transient, inviscid, laminar, and turbulent flows; (b) flows with Newtonian as well as non-Newtonian rheology; (c) convective, natural and forced, coupled conduction-convective-radiation heat transfer; (d) moving reference frames, including sliding mesh interfaces and mixing planes; (e) flows of chemical species, mixing and reaction, including combustion and surface deposition reactions; (f) flows with arbitrary volumetric sources of heat, mass, momentum and turbulence; (g) two-phase flows, including cavitation. 4.1.5. Neutron kinetics: generation of average parameters Njoy code is used to extract information from material related libraries for microscopic cross-sections functions of energy (e.g., ENDF). Helios and Unk codes are used to derive macroscopic cross-sections or ‘␭-matrices’, respectively that are used as input by 3D neutron kinetics codes (see below). Information about Njoy, Helios and Unk codes can be found in D’Auria et al. (2008c). 4.1.6. Neutron kinetics: 3D transient neutron flux Nestle and Bars codes respectively coupled to Relap5 and Korsar codes are adopted to calculate the neutron kinetics parameters in the individual fuel channel and associated graphite stack following the FC-BLOCKAGE event. Both Nestle and Bars are widely used and qualified codes within US and Russia, respectively, in the area of their application, i.e. the transient neutron kinetics in water cooled nuclear reactors. Information can be found in D’Auria et al. (2008c). 4.1.7. Structural mechanics and the MPTR issue Katran and Ansys codes have been adopted to calculate stresses and strains in the pressure tube and in the graphite blocks following the rupture of the pressure tube occurring during the FC-BLOCKAGE event. Katran is a special code developed within the RBMK design technology, e.g., Parafilo et al. (2000) and Soloviev et al. (2003). The code models a spatial axis symmetric problem of viscousplastic deformation of the pressure tube loaded with internal pressure that is uniform along the azimuthal angle and variable together with temperature along the height. Anisotropy of the tube material properties is taken into account. Calculation of deformations is made for any axial section according to the profile of temperature. At a certain stage of the deformation process, the interaction of a pressure tube with the graphite column is taken into account. After the occurrence of extended contact between a tube and the graphite, the blocks of graphite column are loaded with internal pressure minus the “resistant reaction” of the tube. The occurrence of a critical pressure for the graphite block causes the formation of cracks under the simultaneous occurrence of pressure tube ballooning. The full loss of integrity for the graphite blocks occurs when the cracks cover the entire cross-section. After the destruction of graphite blocks the further deformation of a tube before break is calculated. The estimation of the integrity of pressure tubes is carried out by considering temperatures, deformations, force and power failure criteria.

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Ansys is a commercial ‘finite element’ based code, e.g., Ansys Inc. (2002), for performing static and dynamic analyses of linear and non-linear problems (due to materials properties, geometry, contact between surfaces, etc.) in many fields of application (structural, thermal, electromagnetic, fluid-dynamic, etc.). It is possible to solve coupled problems in the areas of fluid-structure and thermal–mechanical interactions. The MPTR related analysis is performed (as mentioned in Table 4) by the U-Stack code and, independently, by a procedure making use of different codes as described in chapter 6. The 3D U Stack code, Baldin et al. (2004) and Parafilo et al. (2004), developed by PhEI and NIKIET Institutions in Russia, is an integrated computational tool used for the simulation of processes taking place in the graphite stack, the reactor cavity, the gas circuit and the main circulation circuit of a RBMK in case of a pressure tube leakage. The capabilities of Katran as well as of a thermal-hydraulic system code like Relap 5 are embedded into the U Stack. This code is capable of assessing the venting system efficiency of the reactor cavity in dealing with small leakages. In case of large breaks of pressure tubes with coolant discharge leading to graphite stack deformation, the code allows the evaluation of the stack deformation and the assessment of the possibility of propagation of the rupture top intact fuel channels. 4.1.8. Fission products: generation Refp code is used to calculate the source term associated with the operation of a fuel channel of the RBMK, i.e. the amount of radioactivity that is released during the progression of the FC-BLOCKAGE event. The program simulate the behaviour of five isotopes of radioiodine, two isotopes of caesium and five noble gases. It provides a step by step calculations of: (a) the releases from fuel and coolant including the sub-division between gaseous and liquid volumes inside the confinement, (b) the changes of chemistry and of physical form of iodine, (c) the removal from the confinement atmosphere and the absorption on the walls and (d) the revolatilization and adsorption of iodine and leakage outside the confinement (Moskalev and Jankowski, 2004). However, the last capabilities of the code are not exploited within the present framework and related analyses are carried out by Cocosys and Melcor, as described in the next paragraph. 4.1.9. Fission products: transport Cocosys and Melcor codes are used to calculate the transport of the fission products generated as a consequence of the melting and the damage of a RBMK fuel bundle during the progression of the FC-BLOCKAGE event. Fission products are transported inside the primary circuit and, to the largest extent, from the break region to the reactor cavity, to the pool, to the Accident Localization System and to the environment (flow paths discussed in D’Auria et al., 2008c). Cocosys and Melcor, developed and qualified at GRS in Germany (already mentioned) and at Sandia National Laboratory in US, respectively, are well established codes widely used by the international community. The qualification level in the area of interest is demonstrated in the papers by Ahrens et al. (2003) and by Nagasaka et al. (1998), for Cocosys and Melcor codes, respectively.

4.2. The nodalisations Nodalizations or input decks have been developed and qualified (as far as possible) for each of the code listed in Table 4. In some cases different input decks for the same code were prepared to address specific objectives of the analysis (e.g., the mechanical resistance of the bare pressure tube, of the pressure tube plus the graphite rings and graphite blocks, with different assumptions for the constraints, etc.). At the end, more than 20 input decks were prepared and used to obtain a comprehensive view of the FC-BLOCKAGE scenario. A detailed description of all of these can be found in D’Auria et al. (2005) and is far beyond the scope of the journal paper. However, selected sketches representative of input decks developed in relation to the areas mentioned in Section 4.1 are outlined hereafter. Approximate dimensions of nodalizations, e.g., number of nodes or of elements for the various cases, are given in D’Auria et al. (2008a) and are not repeated here. Notes about the qualification level of the nodalizations are given below not in a systematic way. 4.2.1. The TH input decks covering the areas ‘System Thermal-Hydraulics: Primary System And Confinement’ The thermal-hydraulic nodalization for the overall RBMK system, main coolant circuit and confinement are discussed by D’Auria et al. (2008b,c), respectively. The fuel channel nodalization with the connected portion of the reactor cavity is given in Fig. 14. The same level of qualification applicable for the overall core model, i.e. above papers, is valid here. Several valves are part of the input deck and are ‘installed’ perpendicular to the channel axis. Each valve opening control takes input from the pressure difference across the tube walls and from the wall temperature in the region where the valve is installed. The curve in Fig. 9 is modelled and the (simplified) approach described in Section 2.4 is used to determine the conditions for valve opening. Once opened the valve does never close. The implemented logic is such to allow the calculation of the break location (location of the valve along the axis) and the break area (number of valves open). Several studies have been done to optimize the input deck also aimed at identifying the best value for the individual valve area. The two ‘columns’ on the left of the figure represent the reactor cavity gaps. Namely, the gap around the affected channel and the overall gap area (and volume) associated with eight neighbouring channels, as shown in the sketch on the top right of the figure, are simulated. This allows the calculation of the differential pressure across the neighbouring channel stack. The first column on the left represents the remaining space in the reactor cavity and allows, together with the simulated upper, lower and side cavity free volume, the calculation of the absolute pressure in the cavity. 4.2.2. The FU input decks covering the area ‘System Thermal-Hydraulics: Fuel’ The fuel in RBMK does not differ from the fuel in other types of water cooled reactors, including the material properties of interest. Therefore, ‘well established’ (limited independent

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Fig. 14. The TH input deck covering the areas ‘System Thermal-Hydraulics, Primary System and Confinement’ to model the FC-BLOCKAGE in RBMK: Relap5 code used to model the affected channel and two rows of neighbouring graphite stacks in the confinement.

Fig. 15. The FU input deck covering the area ‘System Thermal-Hydraulics, Fuel’ to model the FC-BLOCKAGE in RBMK: Rapta and Frap codes nodalizations (left and right, respectively) of the fuel rod.

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4.2.4. The NK input decks covering the areas ‘Neutron Kinetics: Generation of Average Parameters and 3D Transient Neutron Flux’ The neutron kinetics nodalizations suitable for the generation of macroscopic cross-section and ‘λ-functions’ (needed for Nestle and Bars code) and for performing transient coupled 3D neutron kinetics thermal-hydraulic analyses (by Relap5/3DNestle and Korsar-Bars) are described by D’Auria et al. (2008d). The NK nodalization is used, as described in the abovementioned paper, to calculate the actual fission power in the bundle affected by the FC-BLOCKAGE event considering the counterfeiting effect of voiding (positive reactivity) and of Doppler (negative reactivity). 4.2.5. The SM input deck covering the area ‘Structural Mechanics’ As in the case of the FU input deck discussed above, a ‘well established’ (limited independent qualification needed) nodalization with suitable level of detail has been developed suitable for the Ansys code. The input deck includes the pressure tube and the associated graphite ring and bricks, as shown in Fig. 17. Extensive validation was conducted and documented in the mentioned report mainly in relation to the creep model and to the

Fig. 16. The CFD input deck covering the area ‘Computational Fluid Dynamics’ to model the FC-BLOCKAGE in RBMK: Fluent model of affected region of the pressure tube to calculate hydraulic loads acting upon the fuel bundle.

qualification needed) nodalizations with suitable level of detail are used for Rapta and Frap as shown in the sketches of Fig. 15. The nodalizations are used to determine temperature and pressure (for the internal gas) transients inside the fuel rods and the deformation of the clad till the possible rupture event. The timing of such occurrences are also calculated. Results obtained by Rapta have already been shown in Fig. 11. 4.2.3. The CFD input deck covering the area ‘Computational Fluid Dynamics’ A region of the fuel bundle of the RBMK fuel channel enclosed by two horizontal planes (orthogonal to the channel axis) has been modelled for the application of the Fluent code, including a simplified form for the break (consequence of the FC-BLOCKAGE event). The sketch of the nodalization is given in Fig. 16. Convergence analyses were carried out for the number of nodes as well as sensitivity studies related to the choice of the turbulence model and the assumed free area for the break. Single phase flow (gas) is used to simulated the superheated steam exiting the break. The gas speed causes forces (nearly) perpendicular to the rod axis and resulting hydraulic forces. These are applied to the individual rods in the bundle and, based upon the related constraints (i.e. grids), the material properties and the actual temperature values, the conditions are calculated for rod disruption (caused by hydraulic loads).

Fig. 17. The SM input deck covering the area ‘Structural Mechanics’ to model the FC-BLOCKAGE in RBMK: Ansys model of the break region of the pressure tube plus graphite ring plus graphite block.

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optimum number of meshes. Sensitivity studies were performed in relation to the effects of fluence, gap thicknesses (across the graphite ring), graphite average temperature, heating rate and hardening of the pressure tube. The nodalization was used to determine the loads (primarily internal pressure for the zirconium tube) and the conditions (primarily wall temperature for the pressure tube) under which the compound formed by the pressure tube, the ring and the graphite brick fail. Information about the azimuthal location of the break could also be attained. 4.2.6. The MPTR input deck covering the area ‘MPTR’ In order to address the MPTR issue, two independent ways have been pursued as already mentioned: (1) use of a procedure based on the application of nodalizations described above; (2) use of the U Stack code. The procedure at item (1) is discussed in chapter 6 and the U Stack nodalization, item (2), is outlined below. The geometric arrangement of the core, the thermal-hydraulic conditions of the primary loop and of the confinement, the configuration of the constraints and the material properties constitute the main input dataset necessary to develop a suitable U-Stack nodalization. A simplified sketch is given in Fig. 18.

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Typical relevant aspects of the MPTR scenario that are considered in the nodalization, giving an idea of the complexity of the problem are: • Translational movements of graphite bricks affected by: (a) inertia of the brick, pressure on lateral edges, (b) contact forces from neighbouring stacks, (c) deformation of the pressure tube and (d) friction in the contact between adjacent bricks. • Rotational movements of graphite bricks affected by: (a) moment of inertia, (b) torque caused by non-uniform pressure distribution and (c) torque from contact and friction forces. • Various cases of contact between pressure tube and graphite stack include: (a) no contact, (b) one contact region, (c) two or three contact regions and (d) contact along the entire surface of the tube. The U-Stack nodalization could benefit of the qualification based on the experiments performed in various versions of the TKR facility installed at Electrogorsk (Ru), e.g., Medvedeva et al. (2004b). The qualification domain for the U Stack code and nodalization also included the simulation of the event in Leningrad-3 NPP described above, NIKIET and PhEI (2006). 4.2.7. The FP input decks covering the areas ‘Fission Products: Generation and Transport’ The main path for the fission product release, including the phenomena of generation and transport, is inside the confinement. Therefore, the adopted input decks are those outlined in D’Auria et al. (2008c) specifically related to Cocosys and Relap5. In addition, the developed Melcor nodalization for the RBMK NPP includes features that are similar to the Cocosys nodalization. The FP nodalizations are used to calculate the fission product transport throughout the confinement and the source term to the environment. The main output is constituted by the radioactivity amount in each region of the confinement and in the environment. The source term to environment is characterized by timing and elevation of the release and is suitable for providing input to the environmental impact codes. 5. The FC-BLOCKAGE predicted scenario Results related to the FC-BLOCKAGE scenario, according to the information available from Table 2 has been given by D’Auria et al. (2008a,b,c,d) with all transients outlined in the former case and with focus put on 3D neutron kinetics in the latter case. Hereafter a complete picture of the scenario is given, considering the technological safety areas already defined and adopted in chapter 4. 5.1.1. Boundary and initial conditions

Fig. 18. The MPTR input deck covering the area ‘MPTR’ to model the FCBLOCKAGE in RBMK: U-Stack model of a portion of the core. ‘Crack propagation valves’ can be seen in the upper diagram and arrow indicating flow paths across graphite stacks in the lower diagram.

The nominal operating conditions for Smolensk-3 RBMK are assumed (see D’Auria et al., 2008a) as boundary and initial conditions for the analysis. The considered blocked channel has vertical and horizontal coordinates 27–32 e.g., Fig. 10 in D’Auria et al. (2008d), with axial power distribution assumed

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as the core average power distribution, Fig. 11 of the same paper. The channel is characterized by an initial power of 2.1 MWth and by a ‘flow-rate/power’ ratio equal to 3 kg/MW s. Other input data, namely, inlet and outlet pressure, inlet sub-cooling, pressure of the reactor cavity, axial and radial distribution for the graphite temperature are given in Table 1. As an exception, the results for the area ‘System ThermalHydraulics, Confinement’, obtained by the U Stack and Cocosys codes relate, respectively: • to the blocked channel with coordinates 52–16 of the Leningrad-3 core where the initial power is 2.0 MWth and the ‘flow-rate/power’ ratio is to 3.8 kg/MW-s; in this case the flow-blockage event brings the core inlet flow-rate from 7.5 to 0.25 kg/s.

• to the maximum power channel of Smolensk-3 characterized by an initial power of 2.9 MWth. Boundary and initial condition values for quantities not reported in the above two dashed items coincide with the values described in the previous paragraph. 6. Results The resulting sequence of main events (Smolensk-3 channel with coordinates 27–32) is given in Table 5. Reference is made to the safety technology area identified below and to the phenomena listed in Table 3. It shall be noted that for some events or related quantities, like evaluation of hydraulic loads acting upon the fuel rods following the break of the pressure

Table 5 Resulting sequence of main events and related key-quantities values for the FC-BLOCKAGE scenario considering the various technological areas relevant for the safety analysis No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 a

Event

Time (s)a

Notes

Full blockage occurrence Full blockage completed Dry-out occurrence 10 K superheated steam appears at the channel outlet Fission power attains 90% of its initial value Only steam present in the channel Clad surface temperature achieves 700 ◦ C

0 0.1 1–40 3

Range given for the various axial locations Relevant to ICM design (D’Auria et al., 2008e)

Pressure tube heating rate before break (K/s) The pressure tube temperature achieves 700 ◦ C ‘Prompt’ radioactivity release to MCC (Ci) Clad achieves 1204 ◦ C Occurrence of the ‘first’ break Elevation of the first break (m) Overall break area (m2 ) Break opening time Flow reversal occurs at channel outlet Time of maximum load acting upon neighboring graphite stack Value of the maximum load on neighboring graphite stack (t) Scram occurrence Quench of wall temperatures above break axis Max pressurization rate in gas-gap (MPa/s) Pressurization rate in reactor cavity (MPa/s) Maximum hydraulic load acting upon (still) intact rods (kN) Maximum stress in graphite before crack propagation (MPa) Value of fission power before the scram (%) Quantity of damaged fuel (%) due to thermal loads and hydraulic loads Maximum pressure in the reactor cavity (MPa) Quantity of H2 produced (kg) Radioactivity in the reactor cavity 200 s after the break occurrence (Ci/kg) Radioactivity in the ALS 200 s after the break occurrence (Ci/kg) Radioactivity to the environment 200 s after the break occurrence (Ci) Quench of wall temperatures below break axis Or value of the specified quantity.

∼10 12 20–70 10–12 71 250 65 74 (tB ) 5 ** 0.05 tB + 0.5 tB + 2

3D coupled NK TH analysis Clad collapse occurs, Fig. 11b. Range given for the various axial locations Relevant for calculating tube rupture time Start of creep mechanism Fission gases release Start of significant H2 production Starting from the bottom of the active fuel **Value > > than flow area of outlet pipe Based on creep analysis

22

Including dynamic load. See also Fig. 34b

tB + 2.2 tB + 5 ∼0.6 0.04 2.8

Pressure increase in RC = 0.075 MPa

6.6 ∼85 ∼40 <0.13 0.06 4.1e3/5.7e−3 2.9e3/5e−3 1.0 ∼tB + 300

Average value for 5 s after the break start This causes rupture of eventually intact rods at the location of break occurrence The value largely depends on parameters like fluence % of initial value. % of initial value at 5 s after scram. This corresponds to about 50 kg Free space region During the predicted transient duration Radioactivity values are derived from radioisotopes masses. H2 to the environment has not been calculated.

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Fig. 19. FC-BLOCKAGE scenario, area ‘System Thermal-Hydraulics, Primary System’, Relap5 results for the affected channel, short term: (a) flow-rates at the inlet and at the outlet; (b) pressure in different positions along the axis; (c) flow-rates across the ‘break’ simulation valves.

tube, the ‘nearly’ steady-state assumption has been made. Therefore, timing is related to the connected event that is the result of the ‘dynamic’ calculation (in this case the rupture opening time). 6.1.1. Area ‘System Thermal-Hydraulics, Primary System’ Results for quantities related to the area ‘System ThermalHydraulics, Primary System’ obtained by the application of the Relap5 code are given in Figs. 19–21.

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Fig. 20. FC-BLOCKAGE scenario, area ‘System Thermal-Hydraulics, Primary System’, Relap5 temperature results for the affected channel, long term: (a) rod surface; (b) fluid; (c) pressure tube.

In the channel inlet region, Fig. 19a, the flow-rate vanishes at the transient start owing to the blockage. Immediately after, following the vaporization of the existing coolant mass in the channel, flow-rate at the channel outlet also vanishes. However, flow reversal occurs after the rupture occurrence in the upper part of the channel as identified by the horizontal part of the break. The pressure in the channel changes two times during the transient, Fig. 19b: (1) soon after the blockage, pressure drop redistribution occurs; (2) after the tube rupture occurrence pressure in the lower part of the channel and in the region of the break achieve the reactor cavity pressure (or very close to it) and pres-

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Fig. 21. FC-BLOCKAGE scenario, area ‘System Thermal-Hydraulics, Primary System’, Relap5 results for the affected channel: (a) overall channel power and void fraction along the axis; (b) trajectory (bold dotted line) to determine the pressure tube rupture time.

sure in the upper region is determined by pressure drops along the flow path from the steam drum (where pressure remains at the initial value) and the break. The opening of three break simulators can be seen in Fig. 19c. The result show that conditions for channel rupture are reached simultaneously in different parts of the channel along the axis. However, the rupture at one level immediately releases the pressure at other levels and the overall break area calculated in this way is consistent with the experimental values (Baldin et al., 2004; Medvedeva et al., 2004b) and with the values measured in post-accident examination of Chernobyl-1 (1982) and Leningrad-3 (1992) events, e.g., NIKIET (1983, 1992), respectively. In particular, the predicted value for the ‘equivalent break length’ along the channel axis is 0.7 m approximately and the break area is roughly 10 times the value of the cross-section area

of the fuel channel outlet pipeline. Therefore, the overall mass flow-rate is only affected by the cross-section of the channel outlet pipeline (i.e. not by the break area itself). The horizontal break axis is centred around the elevation of 5 m starting from the bottom of the active fuel. The sum of the flows though the breaks in Fig. 19c equals the amount of flow reversal in Fig. 19a. Rod surface, fluid and pressure tube temperatures at different axial elevations are reported in Fig. 20a–c. The following should be noted (see also Table 5): • Dry-out phenomenon and superheated steam at the channel outlet are calculated immediately after the blockage event. • In a few tens of seconds, after the blockage event, temperatures for rod damage (clad collapse mechanism), pressure

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tube damage (break opening) and significant H2 production occur. • The occurrence of the break event causes, in about one second, ‘turnaround’ of all temperatures in the channel region above the break axis. • After the break occurrence, quenching of metal temperatures in the region above the break axis is completed in a few seconds, while quenching of the bottom part of the channel is completed in a few hundreds seconds. The time for channel emptying can be derived from Fig. 21a, as well as the “assigned” power curve. The curve can be distinguished into three periods: (a) the steady state nominal imposed value for the channel, i.e. till t = 0 s, (b) the transient till the scram, determined by the coupled 3D neutron kinetics thermalhydraulic analysis derived from results in D’Auria et al. (2008d) and (c) the decay power period, fixed after the estimation of the scram time. The graphical support for estimating the break occurrence time can be found in Fig. 21b. For the considered scenario, a nearly vertical trajectory is calculated (pressure difference across the tube wall remains constant with increasing temperature) that ‘hits’ the available threshold curve when break time is predicted. 6.1.2. Area ‘System Thermal-Hydraulics, Fuel’ Results for quantities related to the area ‘System ThermalHydraulics, Fuel’ obtained by the application of the Relap5/Frap code are similar to results already discussed in relation to Fig. 11b: the clad rupture is caused by the collapse mechanism with constant overpressure acting across the clad wall and increasing rod surface temperature (thus, decreasing material strength conditions). In performing the fuel performance analysis including the mechanical deformation of the clad by the Frap code, it has been ensured that the thermal transient (e.g., rod surface data provided in Fig. 20a and fuel pellet temperatures) during the ‘period of un-deformed rod’, produced the same results by Relap5 and Frap codes (documentation available in D’Auria et al., 2005).

Fig. 22. FC-BLOCKAGE scenario, area ‘System Thermal-Hydraulics, Confinement’, U Stack results for pressure evolutions in the reactor cavity: (a) along the axis of the affected channel including ‘free-space’; (b) in different gas-gaps at 6.4 m elevation.

The pressure peak of the open space of the cavity (needed to assess the integrity of the cavity walls) remains below 0.16 MPa. The difference between pressures in Fig. 22b give are needed to calculate the mechanical load acting upon the neighbouring channels (i.e. to estimate the MPTR possibility).

6.1.3. Area ‘System Thermal-Hydraulics, Confinement’ Results for quantities related to the area ‘System ThermalHydraulics, Confinement’, obtained by the application of the U Stack and Cocosys codes are given in Figs. 22 and 23, respectively. In relation to both the analyses, time ‘t = 0 s’ corresponds to the rupture opening time. Pressure evolutions in different positions along the axis are given in Fig. 22a including the ‘open’ region of the reactor cavity and pressure evolutions at same elevation in different radial positions (i.e. in different gas-graphite gaps) are given in Fig. 22b. The following can be observed: A ‘quasi-static’ pressure peak as high as 0.6 MPa is calculated in the gas graphite gap adjacent top the broken channel.

Fig. 23. FC-BLOCKAGE scenario, area ‘System Thermal-Hydraulics, Confinement’, Cocosys results for pressure evolutions in affected confinement regions.

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The pressure time trends of the various involved zones of the confinement can be derived from Fig. 23 for the long-term transient evolution. The reference nodalization is presented in Fig. 4 of D’Auria et al. (2008c). An average pressure is calculated for the affected channel (gas) gap region in this case, red curve in Fig. 23. In the long term period of the transient, i.e. after about 2 h since the transient start, the predicted pressure increase is less than 0.03 MPa.

6.1.4. Area ‘Computational Fluid Dynamics’ Results for quantities related to the area ‘Computational Fluid Dynamics’ obtained by the application of the Fluent code are given in Fig. 24. By adopting the input deck outlined in Fig. 16, the velocity and the pressure fields are derived at first, following the break occurrence. Then, three constraint assumptions are considered to model the spacer grids (schemes A, B and C

Fig. 24. FC-BLOCKAGE scenario, area ‘Computational Fluid Dynamics’, Fluent results for mechanical loads acting on fuel rods in the neighborhoods of the break axis.

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in Fig. 24). This allowed the evaluation of the hydraulic load acting upon the selected region of the rod. Allowable load (or ‘critical load’, last row of the table in Fig. 24), was determined independently considering geometry and material properties. The result is given in the bottom part of Fig. 24, related to the overall bundle section: hydraulic loads are such to cause the rupture of at least 5 (over 18) rods, whereas nine rods appear ‘safe’ and the status of four remaining rods needs more accurate specification of boundary and initial conditions in order to be evaluated. The documented one is the result of a ‘static’ analysis with constant fluid speed, set at the maximum value corresponding to the critical flow that establishes at the break. The allowable load is connected with the actual temperatures of the fuel rods thus allowing the connection with the ‘dynamic’ transient calculation documented in the previous paragraphs. 6.1.5. Area ‘Neutron Kinetics, 3D Transient Neutron Flux’ The key result from the area ‘Neutron Kinetics, 3D Transient Neutron Flux’, obtained by the 3D coupled code Relap5/3DNestle, has already been given in Fig. 20a, initial 74 s of the transient. Besides, it is shown that the fission power produced in the affected channel decreases following the blockage event:

Fig. 25. FC-BLOCKAGE scenario, area ‘Neutron Kinetics, 3D Transient Neutron Flux’, Relap5/3D-Nestle results for non-dimensional fission power: (a) selected axial regions of the affected fuel channel; (b) axial distribution at different times.

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this constitutes an input for the analysis performed within the framework of the present paper. The decrease in power production is of the order of 10% of the initial power and occurs mostly in the initial 5 s of the transient, caused by the Doppler effect. Compared with the case of constant power, the consideration of the actual power brings to a delay of about 25 s in the prediction of the occurrence for pressure tube rupture. Additional results related to the application of the coupled 3D neutron kinetics code to the FC-BLOCKAGE scenario can be found in the companion paper by D’Auria et al. (2008d), including the background for the derivation of the mentioned result (e.g., cross-section derivation, power in neighbouring channels, etc.). The power change in non-dimensional form associated to each individual axial node of the affected channel is reported in Fig. 25 together with the axial power distribution at different times. As expected, in some regions, e.g., bottom regions, the power increases after the blockages event. However, the overall effect for the overall bundle is a decrease in generated fission power.

Fig. 26. FC-BLOCKAGE scenario, area ‘Structural Mechanics’, KatranU Stack results for pressure tube quantities, related to a tube close to the broken one, along the axis, at the time 23 s after the rupture: (a) bend stresses; (b) deformation of tube surface.

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The neutron kinetics response associated with geometry change are not considered in the present study. In the course of an accident, these are expected to occur on the first time, when the threshold for clad damage (collapse in this case) is overpassed. Thereafter (i.e. with the predicted event progression), possibly, rods bowing, contact(s) with pressure tube, violent oxidization connected with the H2 production and, possibly clad and/or rods disruption due to thermal and hydraulic loads occur. Each of these event can be associated with change in neutron properties, i.e. ‘λ-matrices’ or macroscopic cross-sections, and create an additional feedback upon fission power. The available coupled 3D neutron kinetics thermal-hydraulic computational tools, namely Korsar-Bars, are ready to account for geometry

changes (D’Auria et al., 2005). However, such feedback was not considered within the present framework. 6.1.6. Area ‘Structural Mechanics’ Results for quantities related to the area ‘Structural Mechanics’ obtained by the application of the U-Stack and Ansys codes are given in Figs. 26 and 27. The use of those codes implies neglecting (case of Ansys) the consideration of the tube rupture criterion given in Fig. 9 (see also Fig. 21b for its application) and the use of more sophisticate criteria (case of Katran-U Stack) or of the material properties (case of Ansys). In the case of application of these codes, a relevant the input is constituted by

Fig. 27. FC-BLOCKAGE scenario, area ‘Structural Mechanics’, Ansys results: (a) sensitivity of maximum principal stress to fluence and temperature of graphite; (b) sensitivity of maximum principal stress to pressure tube temperature increase rate; (c) plane distribution of maximum principal stress before crack propagation.

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the temperatures predicted by the thermal-hydraulic code, e.g., pressure tube and graphite, and the output are the stresses and the strains for the system under consideration as a function of time, i.e. the zirconium tube, the graphite ring and the graphite stack. The rupture location and the occurring time is also an output from the analysis (and may differ from the result shown in Fig. 21b). The Katran-U Stack (Katran can be classified as onedimensional code) coupled code is capable of calculating, among the other things, the deformation and the shape change of pressure tube along the axis as a function of time. The axial distribution of bend stresses and of deformation after the break event for a tube close to the broken one, is given in Fig. 26. The break occurrence causes a bend deformation (in the reported case, maximum at around 5.5 m from the bottom of active fuel) for about 14 cm, Fig. 26b (see also the right sketch in Fig. 6a). This implies the displacement and/or the break of at least two graphite blocks, to accommodate for the movement of the metal pressure tube (see chapter 6). The use of the Ansys code implies (in addition to what mentioned above): (a) The need to model with suitable level of detail (i.e. by finite elements) each of the three components of the system under consideration. Convergence should be demonstrated when decreasing the mesh size. (b) The knowledge from the user or the user assumption in relation to parameters like friction between adjacent components (e.g., ‘zirconium tube versus graphite rings’, or ‘graphite brick versus graphite brick’), gap thicknesses and local material properties, both affected by the life in the core and by the fluence. (c) The need to perform a variety of sensitivity studies. These included: ‘graphite ring-graphite brick’ thickness, fluence and related hardening for graphite and pressure tube, average graphite temperature, pressure tube heating rate and number of meshes. Sample Ansys results, given in Fig. 27, relate to sensitivity studies (Fig. 27a and b) and to the spatial distribution of maximum principal stress in a horizontal plane, Fig. 27c at a time just before the crack propagation start. As expected, the rate of temperature increase of the pressure tube has a large influence upon the time of the break occurrence, Fig. 27a (Relap5 calculated values for such parameter are given in Table 5). The smaller is the heating rate, the greater is the delay before the onset of contact. In the case of gap equal to 0.7 mm and fluence equal to 22 × 1021 n/cm2 , the contact always occurs when the pressure tube temperature reaches about 1050 K, so the mentioned delay is inversely proportional to the heating rate (consistently with the information provided by the diagram in Fig. 9). One effect of irradiation on the graphite is the decrease of the thermal conductivity that leads to an increase of the graphite operating temperature. The effect of such increase on the time history of the maximum principal stress, assuming an initial gap completely closed and two different fluence values can be seen

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Fig. 28. FC-BLOCKAGE scenario, area ‘Fission Products, Generation and Transport’, Melcor result for H2 transport in the primary system and in the confinement.

from Fig. 27b. As the graphite temperature increases, the actual gap to be filled by the creeping pressure tube becomes larger due to the increased graphite thermal deformation. The effect is the same as having a larger initial cold gap. The stress intensification phenomenon at the edge of the graphite ring causes in the location of the contact with the graphite brick the most probable point for the propagation of the crack, the inside the graphite brick, as evidenced in Fig. 27c (red ellipse in the bottom diagram). 6.1.7. Area ‘Fission Products, Generation and Transport’ Within the safety technology area ‘Fission Products, Generation and Transport’ the H2 transport is considered at first hereafter, even though this is a possible (typical) output of the areas ‘System Thermal-Hydraulics, Primary System and Confinement’. The amount of H2 produced and transported inside the primary system (MCC in the figure) and in the confinement, reactor cavity and accident localisation system (RC and ALS in the fig-

Table 6 Refp calculation of the fission product inventory in one Smolensk-3 RBMK NPP fuel channel with average burn-up of approximately of 7500 MWd/t Nuclide

131 I 132 I 133 I 134 I 135 I 85m Kr 87 Kr 88 Kr 133 Xe 135 Xe 134 Cs 137 Cs

Activity in the lower fuel element (Ci)

Activity in the upper fuel element (Ci)

Fuel

Gap

Fuel

Gap

2163 3051 4370 5297 4178 938 1678 2339 4537 713 25.6 88.4

21.2 38.3 15.4 7.2 7.6 1.8 1.6 2.1 30.4 3.2 0.87 3.1

2037 2874 4120 4992 3936 887 1587 2211 4274 671 24.4 83.5

18.4 33.2 13.4 6.3 6.6 1.6 1.4 1.8 26.4 2.8 0.76 2.7

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ure, respectively) can be seen in Fig. 28, as calculated by the Melcor code. The following should be observed: • Time 100 s is the start of the FC-BLOCKAGE event and, as expected, H2 production starts immediately after the event.

• The total amount of H2 produced and transported is much lower than the amount theoretically producible in one fuel channel, i.e. of the order of 1%, see Table 1. • The break occurrence time is predicted at about 50 s instead of 74 s as given in Fig. 21. This is due to the consideration of constant full power in the period before the pressure tube

Fig. 29. FC-BLOCKAGE scenario, area ‘Fission Products, Generation and Transport’, Cocosys results for fission products transport in the confinement: (a) release of xenon; (b) deposition of iodine mass at 3 h after the rupture and (c) release of Cesium aerosol in the form CSOH.

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Fig. 30. Sketch dealing with the MPTR issue. One broken channel may cause failure of adjacent channels. In the right side, the worst conditions for rupture propagation are given.

rupture (e.g., the power decrease calculated by the coupled 3D neutron kinetics analysis was not taken into account in the present study). The amount of fission products leaving the rupture and transported inside various zones of the confinement and to the environment (confinement zones and flow-path to the environment given in Fig. 5, more details available by D’Auria et al., 2008c) can be seen in Fig. 29 as calculated by the Cocosys code. The following should be observed: • The total amount of fission products ‘stored’ in one fuel channel is given in Table 6 as calculated by the Refp code. Based on the performed investigation, all radioactivity in the gap (third and fifth columns in Table 6) is released to the main cooling circuit and primarily to the confinement at the time of the rupture opening. • Time 0 s in the Fig. 29a and c is the opening time of the pressure tube rupture. • Releases to the environment occur more than 1 h after the FC-BLOCKAGE event start. • The amount of releases to the environment constitutes a fraction for around 4–8 orders of magnitude lower than the overall release in terms of mass of the isotopes (more details, including a comprehensive list of released isotopes is available from D’Auria et al., 2005). • The release of fission products is assumed to be caused only by thermal damage of the fuel. Releases caused by hydraulic loads including the impact of already thermal damaged pieces of fuel with solid surfaces (e.g., graphite bricks) is neglected. • Based on the post-accident examination of the events in Chernobyl-1 (1982) and Leningrad-3 (1992) (NIKIET, 1983, 1992) and the supporting analyses performed within the present framework, it can be estimated that about 50 kg of fuel looses its integrity and its design configuration following the FC-BLOCKAGE event.

7. The MPTR related results The consequences of the FC-BLOCKAGE event for the affected blocked channel and for the confinement and the environment have been evaluated and discussed in the previous chapter. The problem here is to estimate the possibility that the rupture of one channel (unavoidable for the considered event) triggers a domino effect including the rupture of other channels (i.e. dealing with the MPTR issue). The MPTR scenario can be triggered by events other than the FC-BLOCKAGE, like the fuel channel Loss of Coolant Accident, or the group distribution header blockage (e.g., FC-LOCA and GDH-BLOCKAGE, see the list in Table 2), or a variety of Anticipated Transient Without Scram (ATWS) and/or Reactivity

Fig. 31. FC-BLOCKAGE scenario, area ‘MPTR’: directions of spatial decomposition for graphite block motion considered by U Stack code.

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Initiated Accidents (RIA), other than the notorious Chernobyl4 event (1986). Although the Probabilistic Safety Assessment (PSA) has not been part of the present investigation, as already mentioned, and although MPTR analyses have been conducted for transients other than the individual fuel channel blockage, e.g., Novoselsky and Filinov (2000), the present investigation shows that the only “realistic” origin of MPTR to be considered in Safety Analysis Report is the FC-BLOCKAGE event. Two independent studies have been conducted within the present framework, using the U-Stack code and a MPTR procedure detailed in the following. For both cases, the sketch in Fig. 30 applies, with assumptions adopted for the procedure given in the right side. The results discussed in chapter 5 constituted the basis for deriving the conclusion about the MPTR issue.

8. Results from U Stack Considering the ‘initial failure location’ as shown in Fig. 30, the U Stack uses the ‘spatial decomposition method’ to calculate the motion of graphite blocks along the axes X, Y and Z as depicted in Fig. 31 and the rotation around the axes X, Y and Z. The key results from the application of the U-Stack code are given in Fig. 32 in a pictorial form and are supported by the diagrams in Figs. 22 and 26. Furthermore, nodalization sketches in Figs. 6 and 18 and related description should be considered (together with sketches in Figs. 30 and 31 above mentioned). A comprehensive documentation of the results can be found in NIKIET (2004) (see also D’Auria et al., 2005). The following aspects are relevant:

Fig. 32. FC-BLOCKAGE scenario, area ‘MPTR’, U Stack results related to the Leningrad-3 (1992) NPP event: (a) tube deformation process after the blockage event; (b) ‘stabilized’ situation at the end of the analysis.

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• The blockage event causes pressure tube overheating and creep deformation as shown in the upper right part of Fig. 32 related to the affected tube. • The deformation of the tube can be observed in the upper left part of Fig. 32 where the profile of the tube is reported at different times before the break. • The time of break occurrence and the axial location of the break can also be deducted from the upper left diagram in Fig. 32. • After the break opening, graphite gaps are pressurized and a full map of the pressure in the gaps is calculated by the code, e.g., Fig. 22. • The strongly asymmetric radial and axial pressure distribution, with pressure peaks in the break region, constitutes the main source of load for neighbouring fuel channels with additional contribution given by dynamic loads in the vicinity of the break. • Hydraulic loads produce deformation and stresses in individual pressure tubes and graphite stacks as depicted in Fig. 26 in relation to pressure tubes. • Actual deformation and stresses for pressure tube and graphite bricks are compared with (limit) allowable values. • The final result is given in the bottom part of the Fig. 32: five graphite bricks are predicted to be damaged and several bricks are displaced from their original position. A few channels around the broken one are calculated to have undergone plastic deformation. Definitely, the rupture causes displacement of stacks neighbouring the broken channel, but no propagation of the rupture is calculated. This is in accordance with the evidence from the NPP event (NIKIET, 1992) and from recent experiments performed in the TKR full size (related to a group of individual channels) experimental facility, e.g., Medvedeva et al. (2004b). 8.1. Results from the procedure The proposed MPTR procedure basically reflects the architecture of the U-Stack code, as described into detail by D’Auria et al. (2005). The procedure is based on the adoption of different codes and different assumptions. The following three elements of the procedure are distinguished: I. Calculation of admissible loads: structural analyses are performed with the aim of determining the maximum admissible loads on the columns surrounding the initiating failure, depending on the failure location over the reactor core. An elasto-static model, based on the Ansys finite element code, was developed to perform such analyses. II. Calculation of applicable (or actual) loads: thermalhydraulic analyses are performed by means of the Relap5 code, with the aim of estimating the actual loads acting on the columns surrounding a failed channel. III. Comparison between admissible and applicable loads: the results of the previous two steps are compared so as to identify those initiating failure locations, which could determine a rupture propagation.

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Fig. 33. FC-BLOCKAGE scenario, area ‘MPTR’: characterization of break location inside the cross-section map of the RBMK core needed for the MPTR procedure (the blue triangle shows ‘cold fuel elements).

The key approximations adopted in the procedure are: (a) no feedback is considered between structural mechanics and thermal-hydraulics calculations; (b) no consideration is given to plasticity in any place; (c) no explicit dynamic analysis is performed involving the consideration of vibrations, pressure waves and fluid-structure interaction (see the third step below). The first step for applying the procedure consists in the geometric characterization of the break location that includes (the break area has minor influence as already discussed): • The position of the affected fuel channel in the horizontal cross-section map of the RBMK core (Fig. 33). • The axial location of the break, calculated according to the discussion provided in relation to Fig. 13. • The azimuthal location of the break, corner-wise or side-wise, right side of Fig. 30. Only side-wise breaks are considered, though the probability of occurrence of side-wise break is low: once a break is predicted at a given axial location there is a probability around 10−2 that the azimuthal break axis coincide with the centred orthogonal axis of neighbouring channels. In this situation, a lower number of stacks constitute an active constraint for the propagation of the rupture, assuming no friction among sliding graphite bricks. The side-wise break position constitutes a conservative assumption. • The distance from the tank of the affected row of channels and the number of ‘cold’ channels between the broken channel and the tanks wall, see the sketch in Fig. 33. In facts the Young module of ‘cold’ channels is about 1.2 times larger than the Young module of ‘hot’ channels. The second step for applying the procedure addresses the element ‘I.’ above. A map of admissible loads for each fuel channel of the concerned RBMK core is created according to: (a)

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the number of stacks that separate the concerned stack from the tank, also including the number of ‘cold’ stacks, (b) the distance of the last stack from the tank and (c) the axial elevation of the break.

The third step for applying the procedure addresses the element ‘II.’ above. The differential pressure distribution acting along the axis of the closest stack is calculated as a function of time following the break occurrence.

Fig. 34. FC-BLOCKAGE scenario, area ‘MPTR’, results from the special procedure related to the Smolensk-3 calculation: (a) second step, allowable loads; (b) third step actual load; (c) fourth step channels prone to rupture propagation.

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The fourth step for applying the procedure addresses the element ‘III.’ above and allows the ‘straightforward’ identification in the map of the fuel channels that are prone to the propagation of the rupture. The results from the second to the fourth step are given in Fig. 34. The following should be noted: • The red colour in Fig. 34a identifies the weakest fuel channels. Various maps have been derived in D’Auria et al. (2005), depending upon the load axial distribution, i.e. concentrated, uniform and peaked, and upon the consideration or not of the tank as resistant element. The data shown in the figure relate to the peaked load and to the presence of the tank. • The diagram in Fig. 34b is the result of ‘static’ pressure difference acting upon the opposite sides of the concerned fuel stack. The consideration along the axis of time evolutions like those shown in Fig. 22 (in the present case obtained by Relap5, see also D’Auria et al., 2008c) allows the achievement of the diagram in Fig. 34b. The integral under the curve is the load that has the ‘peaked shape’ already considered for the results in Fig. 34a. The dynamic loads expected at the beginning of the transient (e.g., pressure wave and jet forces acting during a few seconds after the break occurrence) are added to the loads in the form of ‘static’ pressure difference. The sum constitutes the ‘actual’ load considered for the fourth step. • The diagram in Fig. 34c shows the fuel channels that are prone to the propagation of the rupture: for those channels, the actual load is larger than the ‘resistant’ force and the channels may get plastic condition as a consequence of a rupture occurring in the neighbouring position. The obtained results show that about 2% of the RBMK core channels, in the case of the Smolensk-3 NPP, may reach limiting condition, i.e. beginning of plastic deformation. However, two key conservative assumptions have been considered: (1) side-wise break configuration when calculating the ‘actual’ load (even in such condition the ‘actual’ load is slightly larger than the ‘admissible’ load); (2) no plasticity when calculating the ‘admissible’ loads. It is concluded that the MPTR issue is irrelevant for the safety of the RBMK in the case of the FC-BLOCKAGE scenario, in accordance with the conclusions achieved in section 6.1 by the application of the U-Stack code. 8.2. Conclusions Results from best-estimate, coupled 3D structural mechanics, CFD, thermal-hydraulics and neutron kinetics calculations for RBMK core performance following the blockage of one channel are discussed in the paper. The study requested also the use of ‘severe-accident’ computational tools for the prediction of hydrogen and fission products transport inside the confinement and to the environment. The analyses are not supported by uncertainty evaluation and should not be considered to the level of a licensing study. The main achieved purposes were to demonstrate that no unacceptable situation is predicted during the considered accident

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evolutions (e.g., radioactivity release to the environment below the threshold of acceptability) and to demonstrate the availability and the suitability of sophisticate coupled computational tools. The adopted coupled thermal-hydraulic neutron kinetics codes, namely Relap5/3D-Nestle and Korsar-Bars, were coupled with structural mechanics codes, e.g., Ansys and KatranU Stack and with the codes suitable for predicting fission product transport, e.g., Melcor and Cocosys, respectively. The main conclusions from the analysis of the FCBLOCKAGE scenario can be summarized as follows: • The scenario puts an enormous challenge to the codes: all key technological areas relevant to the deterministic reactor safety are involved. About 40 phenomena have been identified as characterizing the scenario and related computational tools have been evaluated. • The key output data from the analysis are (the Smolensk-3 RBMK NPP is considered): • Affected bundle power decreases soon after the blockage event owing to Doppler effect (negative) typically larger than the positive reactivity effect induced by the channel voiding. • One fuel bundle destroyed (composed of two parts). • About 50 kg of irradiated fuel loose their geometric and structural integrity and (potentially) escape the pressure boundary of the Main Cooling Circuit, but are collected inside the reactor cavity. • No challenge put to the structural integrity of the reactor cavity or to any other region of the confinement. • No danger predicted that is originated by H2 deflagration. • The amount of radioactivity release to the environment, starting about one hour after the event occurrence, is within the regulatory allowed limits. • A few graphite bricks belonging to the affected fuel channel are damaged with bricks of surrounding column remaining intact. • The possibility for the occurrence of the multiple pressure tube rupture (MPTR) was excluded. The qualification level of the U-Stack code in addressing the MPTR issue as well as of an independent procedure based on the use of different computational tools has been demonstrated and brought to the conclusion at the last bullet above. It seems to be expedient to consider the offer related to a monitoring system to prevent the pressure tube rupture of the affected channel, see D’Auria et al. (2008e). 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.

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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 the Commission is responsible for the use which might be made of the information in the paper and the views expressed are the sole responsibility of the authors and not necessarily reflect the views of EC. References Ahrens, G., Fischer, K., Kanzleiter, T., K¨uhnel, A., Poss, G., Funke, F., Greger, G.U., Hesse, F., Allelein, H.J., Weber, G., Schwarz, S., 2003. The ThAI Facility and Program. Thermal-hydraulic and iodine experiments for Cocosys validation: an overview”—PHEBUS FP project. In: Proceedings of the Meeting of Circuit and Containment Aerosols Interpretation Circle (CACIC) Group, Bergen (Nl) March 27, 2003. Almenas, K., Kaliatka, A., Uspuras, E., 1998. Ignalina RBMK-1500. A Source Book Extended and Updated Version. Lithuanian Energy Institute, Kaunas (LT), ISBN 9986-492-35-1, pp. 1–198. Ansys Inc., 2002. Ansys User’s Manual (Version 6.0). Ansys Inc., Canonsburg (US). Baldin, V.D., Zhukov, I.V., Novoselsky, O., Safonov, V., Filinov, V., Kryuchkov, D.V., Parafilo, L.M., Soloviev, S., Osokin, M., 2004. Processes taking place in the reactor cavity and accident localization system of RBMK in case of pressure tube or primary pipeline ruptures. In: Proceedings of the International Conference Pressure Tube Reactors: Problems and Solutions, Moscow (Ru), October 19–20, 2004. Cunningham, M.E., Beyer, C.E., Medvedev, P.G., Berna, G.A., 2003. Fraptran: A Computer Code for the Transient Analysis of Oxide Fuel Rods, vol. 1. US NRC NUREG/CR-6739, Washington (US). D’Auria, F. (Ed.), Soloviev, S., Novoselsky, O., Moskalev, A., Radkevitch, V., Malofeev, V., Parisi, C., Cherubini, M., Pierro, F., Moretti, F., 2005. Deterministic Safety Technology in RBMK, EC TACIS Project R2.03/97. Software Development for Accident Analysis of VVER and RBMK Reactors in Russia, Final Technical Report, Part B University of Pisa, ISBN 88-902189-0-8, pp. 1–838. D’Auria, F., Gabaraev, B., Soloviev, S., Novoselsky, O., Moskalev, A., Uspuras, E., Galassi, G.M., Parisi, C., Petrov, A., Radkevich, V., Parafilo, L., Kryuchkov, D., 2008a. Deterministic Accident Analysis for RBMK’. J. Nucl. Eng. Des. 238 (4), 975–1001. D’Auria, F., Gabaraev, B., Radkevich, V., Moskalev, A., Uspuras, E., Kaliatka, A., Parisi, C., Cherubini, M., Pierro, F., 2008b. Thermal-hydraulic Performance of Primary System of RBMK in case of Accidents. J. Nucl. Eng. Des. 238 (4), 904–924. D’Auria, F., Novoselsky, O., Safonov, V., Uspuras, E., Galassi, G.M., Cherubini, M., Giannotti, W., 2008c. Thermal-hydraulic performance of confinement system of RBMK in case of accidents. J. Nucl. Eng. Des. 238 (4), 925–939. D’Auria, F., Soloviev, S., Malofeev, V., Ivanov, K., Parisi, C., 2008d. The threedimensional neutron kinetics coupled with thermal-hydraulics in RBMK accident analysis. J. Nucl. Eng. Des. 238 (4), 1002–1025. D’Auria, F., Cherubini, M., Pierro, F., Giannotti, W., 2008e. The individual channel monitoring (ICM) proposal to improve safety performance of RBMK. J. Nucl. Eng. Des. 238 (4), 1062–1079. Fedosov, A., Fjodorov, V., Krayushkin, A., Mileschin, A., Donderer, R., Von Ehrenstein, D., Liermann, R., Ziggel, H., 1994. Single Channel Flow-Rate Decrease Analyses in RBMK Reactors Thermal Reactor Safety Assessment. BNES, London (UK).

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