FAST: An advanced code system for fast reactor transient analysis

annals of NUCLEAR ENERGY Annals of Nuclear Energy 32 (2005) 1613–1631 www.elsevier.com/locate/anucene

FAST: An advanced code system for fast reactor transient analysis Konstantin Mikityuk *, Sandro Pelloni, Paul Coddington, Evaldas Bubelis, Rakesh Chawla 1 Laboratory for Reactor Physics and Systems Behaviour, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland Received 7 June 2005; accepted 16 June 2005

Abstract One of the main goals of the FAST project at PSI is to establish a unique analytical code capability for the core and safety analysis of advanced critical (and sub-critical) fast-spectrum systems for a wide range of different coolants. Both static and transient core physics, as well as the behaviour and safety of the power plant as a whole, are studied. The paper discusses the structure of the code system, including the organisation of the interfaces and data exchange. Examples of validation and application of the individual programs, as well as of the complete code system, are provided using studies carried out within the context of designs for experimental accelerator-driven, fast-spectrum systems. Ó 2005 Elsevier Ltd. All rights reserved.

1. Introduction FAST (Mikityuk et al., 2005) (Fast-spectrum Advanced Systems for power production and resource managemenT) is a PSI activity in the area of fast-spectrum core and safety analysis with emphasis on generic developments and Generation IV systems (GIF report, 2002). The main overall objective is to develop a general tool for core *

1

Corresponding author. Tel.: +41 056 310 23 85; fax: +41 056 310 23 27. E-mail address: [email protected] (K. Mikityuk). Co-affiliation: Ecole Polytechnique Fe´de´rale de Lausanne (EPFL), 1015 Lausanne, Switzerland.

0306-4549/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2005.06.002

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statics and dynamics behaviour of the whole reactor system, which is devoted to advanced fast-spectrum concepts in multi-domains including different coolants. A code system of this complexity is particularly attractive in the context of safety related studies aimed at establishing the basic feasibility of the advanced critical fast reactors being proposed by the Generation IV International Forum. Using this code system, it will be possible to analyse, in a systematic manner, a wide variety of transients, including those which may lead to asymmetric core conditions. Examples are the accidental withdrawal of control rods, the insertion of moderating material which may lead to a reactivity increase, e.g., water/steam in a gas-cooled core, the flow of gas bubbles in a liquid metal cooled core, local subassembly blockage, etc. In addition, through the modelling of the entire power plant, it will be possible to assess the complex phenomena which depend, not only on the core behaviour in the case of these novel reactor types, but also on the interaction between the primary and secondary systems. The driving force to achieve this goal lies in the fact that: (a) a unified system for the analysis of a broad range of hypothetical scenarios for advanced fast-spectrum reactors is not available currently, and (b) the stand-alone codes being foreseen as part of the package are state-of-the-art as regards a certain domain of applications, but are currently either not coupled together or adequately qualified and tested for advanced fast-spectrum system analysis. The present paper discusses the current status of the FAST code system in terms of its structure, including the organisation of the interfaces and data transfer (Section 2), the validation work which has been carried to date (Section 3), and specific illustrative applications (Section 4). The currently reported validation and application efforts relate mainly to studies which have been performed for fast-spectrum subcritical (accelerator-driven) systems. Thus, within the 5th European UnionÕs Framework Program (EU-FWP), the Preliminary Design Study of eXperimental Accelerator-Driven Systems (PDS-XADS) project was focused on the study of three different XADS design options, viz.: (1) one with a lead–bismuth eutectic (LBE) cooled 80 MWt core (Cinotti and Gherardi, 2002) (the ANSALDO design), (2) another with a helium-cooled 80 MWt core (Giraud, 2003) (the FRAMATOME design) and (3) a third with an LBE-cooled 50 MWt core (Abderrahim et al., 2000) (the MYRRHA design), all three subcritical cores being driven by a neutron spallation source corresponding to a proton accelerator beam impacting upon an LBE windowless target. One of the work packages of the PDS-XADS project was concerned with the assessment of the safety of the two 80 MWt designs (Coddington, 2002). A wide range of transients were analysed using the FAST code system in this context, results for some of which are reported in Section 4.

2. Structure of the FAST code system As indicated, the principal goal of the FAST project is to develop a general tool for the analysis of the core statics and the dynamic behaviour of advanced fast-spectrum reactor concepts, and to apply it to a selection of Generation IV reactors (GIF report,

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2002). An appropriate, detailed 3D fast reactor dynamics code system has been assembled from existing codes which, where necessary, have been modified to simulate fast reactor features. This scheme is based upon the coupled reactor static/kinetics codes ERANOS (Doriath et al., 1993; Rimpault et al., 2002; Palmiotti et al., 1995) and PARCS (Joo et al., 1998), the thermal-hydraulics code TRAC/AAA (Spore et al., 2001) and the fuel rod thermal-mechanics code FRED (Mikityuk and Fomitchenko, 2000). The methods developed are aimed to be as generic as possible, since applicability to the different Generation IV fast reactor concepts is being sought. At the current stage, however, emphasis is being given to single-phase coolants, the gas-cooled fast reactor (GCFR) being of particular interest. The structure of the FAST transient code system is shown in Fig. 1, indicating the major components and the exchange of information. Two main options are available in the framework of this code structure, one based on point reactor kinetics and the other on spatial neutron kinetics. The main parts of the code system, as also the organisation of the interfaces between them, are briefly described below under the following headings: core neutronics data preparation, neutron kinetics, core and system thermal hydraulics, fuel and structure thermalmechanics, and coupling between different parts. Core neutronics data preparation for any burnup state: ERANOS

Steady-state fuel code

macro X-sections and their derivatives or reactivity coefficients ERANOSTOPARCS

for any burnup state fuel initial conditions: geometry, properties, etc

Re-calculation of reactivity (TRAC/AAA) or X-sections (PARCS)

modified macroscopic X-sections or reactivity coolant density via PVM

core height & radius, fuel temperatures via PVM

Neutron kinetics: TRAC/AAA (point) PARCS (3D)

power deposited infuel via PVM

power deposited in coolant via PVM Parallel Virtual Machine (PVM)

System thermalhydraulics: TRAC/AAA

coolant pressure & temperature

Fuel and structures thermal-mechanics: FRED

heat fluxes

Fig. 1. FAST code system structure (code modules are given in bold).

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2.1. Core neutronics data preparation This part of the code system (see Fig. 1) performs for any targeted reactor state as a function of the core burnup a pre-calculation of either: (1) the core power distribution, kinetics parameters and reactivity coefficients, in the case of point reactor kinetics, or (2) basic macroscopic cross-sections and their derivatives in the case of spatial neutron kinetics. In both cases, use is made of CEAÕs ERANOS (Version 2.0) code system (Doriath et al., 1993; Rimpault et al., 2002; Palmiotti et al., 1995), a deterministic methodology consisting of the newer generation of neutron and gamma transport modules developed within the European Fast Reactor collaboration. Among other capabilities, it performs core, shielding and fuel cycle calculations in conjunction with either non-adjusted or adjusted JEF-2.2 data and includes the most recent developments in calculational methods, e.g., the collision probability method in many groups and a 3D nodal transport theory variational method with perturbation theory and kinetics options. External neutron sources from MCNPX calculations can be input into ERANOS for accelerator-driven system (ADS) applications (Pelloni, 2003). 2.2. Neutron kinetics The neutron kinetics part of the code system performs a calculation at each time step of: (1) in the case of point reactor kinetics: reactor fission and decay heat power, concentration of the precursors of the delayed neutrons, using the TRAC/AAA code (see Fig. 1) and (2) in the case of spatial neutron kinetics: 3D fields of neutron fluxes, power, concentrations of precursors of delayed neutrons, etc., using the PARCS code (Joo et al., 1998), in its current version a 3D nodal-method, transient multi-group, neutron diffusion code for hexagonal and square geometries, having an interface with TRAC/AAA using the PVM system (Al Geist et al., 1994). The original cross-section parameterisation in PARCS was developed for light water reactor (LWR) applications, and this has been reviewed for fast-spectrum system analysis. In particular, the dominant reactivity feedback effects in LWR transients are the Doppler effect and the change in coolant (moderator) density or void, while in fast-spectrum systems, partly because of the relatively smaller magnitude of these, other feedback effects are of equal importance, e.g., fuel and core structure thermal expansion, which changes both the core dimensions and the effective fuel density, influencing the neutron leakage and core reactivity. As a consequence, two important aspects need to be considered:
First: all the important reactivity feedback effects have to be clearly identified.
Second: an appropriate functional form for parameterisation of cross-sections has to be implemented and verified, e.g., the adequacy of a formulation based on cross-section derivatives can only be verified via extensive comparisons with other codes using explicitly tabulated cross-sections as a function of suitable, independent state variables.

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The above is closely linked to the coupling of PARCS to the thermal-hydraulics (TRAC/AAA) and fuel behaviour (FRED) codes, since the derivatives of the crosssections need to be multiplied by values of the local state variables obtained from these codes, e.g., local fuel and coolant temperatures, fuel expansion effects, etc. The original (LWR) PARCS model uses the following procedure for re-calculating macroscopic cross-sections:

 pffiffiffiffi pffiffiffiffi oR oR p ffiffiffi ffi RðT F ; qM ; T M ; BÞ ¼ R0 þ ðZ  Z 0 Þ þ ð T F  T F0 Þ oZ Z 0 o T F T F0

 oR oR þ ðqM  qM0 Þ þ ðT M  T M0 Þ oqM qM0 oT M T M0
 oR ðB  B0 Þ; ð1Þ þ oB B0 where R is the macroscopic cross-section, Z the control rod position, TF the fuel temperature, qM the moderator density, TM the moderator temperature and B the boron concentration. The subscript ‘‘0’’ refers to reference conditions. A simple way to functionalize the cross-sections for fast-spectrum systems, in order to additionally take into account core expansion effects, is

 oR oR RðT F ; qC ; R; H Þ ¼ R0 þ ðZ  Z 0 Þ þ ðln T F  ln T F0 Þ oZ Z 0 o ln T F T F0


 oR oR oR þ ðq  qC0 Þ þ ðR  R0 Þ þ ðH  H 0 Þ; oqC qC0 C oR R0 oH H 0 ð2Þ where qC is the coolant density, R the average core radius and H the average core height. Eq. (2) represents the current status of cross-section parameterisation in the FAST code system. Other reactivity feedbacks which may need to be given due consideration in the parameterisation for specific future applications include: the relative movement of the fuel with respect to the control rods, removal of structural materials from the core, change of coolant composition, e.g., the inclusion of moderating material, as well as design specific phenomena such as core ‘‘flowering’’, where depending upon the core restraint, there is a differential radial expansion between the top and the bottom of the core. 2.3. Core and system thermal hydraulics The thermal-hydraulics part of the code system calculates, using the TRAC/AAA code (Spore et al., 2001), the coolant temperatures, velocities, pressure, etc., in the core and reactor plant, at each time step. The TRAC/AAA code is based on the USNRC LWR transient (safety) analysis code TRAC-M and includes a 3D (hydraulic) vessel component, a generalised heat structure component to model fuel rods,

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heat exchangers, environmental heat losses, etc., as well as models for all the ‘‘normal’’ reactor plant components, e.g., pumps, valves, separators and turbines. In addition to containing these standard elements, the AAA version was updated at the US Los Alamos National Laboratory to simulate: (1) additional working fluids (including liquid metals and helium), (2) the deposition of power in the working fluid, (3) the tracking of trace material that flows with the fluid, and (4) the heat conduction within the working fluid which is particularly important for liquid metal coolants. Additional updates have been made to the TRAC/AAA code at PSI, including those necessary: (1) to improve the simulation of gas/heavy-metal two-phase flow, (2) to restructure the code output, (3) to improve the wall heat transfer for gascooled systems and (4) for ADS applications, to account for changes of the external neutron source strength. Furthermore, an important modification of the TRAC/ AAA code is represented by its present linking to the FRED fuel rod model, which has significantly improved the simulation of the fuel rod performance under transient conditions (see the following section). Since, for the Generation IV fast reactor concepts currently under investigation (e.g., the GCFR), the coolant remains single-phase, no work has been done to validate or modify the interfacial relations. The one exception to this is the case of gaslift-pump driven liquid-metal coolant flow, as used in the Ansaldo LBE XADS design. For this particular phenomenon, assessment against experimental data and corresponding code improvements have been carried out (see Section 3.3). 2.4. Fuels and structures thermal mechanics The fuel and structure thermal-mechanics part of the code system performs, at each time step, a calculation of temperatures, stresses and strains in the fuel and structures (i.e., fuel pin, core diagrid, heat exchanger tubing, reactor vessel, etc.). This is done using either the FRED thermal-mechanical code (Mikityuk and Fomitchenko, 2000) or the TRAC/AAA heat structure model, the choice made depending upon the nature of the structure and the level of detail required. The Ôon-lineÕ modelling of thermal-mechanical fuel behaviour during transients is an important feature of the FAST code system, both for the accounting of reactivity effects (due to core thermal expansion) and for estimation of the fuel failure probability. Because of the tight coupling between the fuel rod and core structure behaviour, and the importance of corresponding reactivity feedback in fast systems, it is more crucial to establish such implicit coupling (see Fig. 1) between the reactor kinetics (PARCS), thermal-hydraulics (TRAC/AAA) and fuel thermal-mechanics (FRED) than it is in the case of LWR applications. 2.5. Coupling between different parts A special interface code, ERANOSTOPARCS, has been developed at PSI to convert, for any reactor state, ERANOS cross-sections produced with the cell code ECCO, as well as dedicated delayed neutron data, into a form suitable for use in PARCS,

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including the aforementioned cross-section derivatives. ERANOSTOPARCS, in terms of the generated parameters, was validated on the basis of extensive comparisons between: (a) statics calculations performed using the PARCS code and the VARIANT module of ERANOS, equivalent options being employed thereby, and (b) TRAC/ PARCS dynamics calculations and results obtained using KIN3D, the kinetics module of ERANOS which was originally developed at CEA and FZK. In the latter case, feedback effects, such as fuel Doppler, coolant density and thermal expansion, have currently been accounted for in an approximate manner, viz., by introducing channel-averaged parameter values from TRAC into KIN3D at selected time points. Some results of this study are presented in Section 3.2. As stated above, an advantage of using PARCS and TRAC/AAA as components of the FAST code system is that the interface software is supplied as part of the PARCS code package, and this has been implemented and tested at PSI. The coupled TRAC/PARCS system has been extensively used for LWR applications by the code developers. The FRED fuel rod behaviour modelling code has been included in the TRAC/ AAA code as a subroutine (Mikityuk, 2003). FRED includes its own internal time integration scheme and has the option to divide the TRAC/AAA time-step into sub-steps if convergence is not obtained. Representative heat structures are specified in both the TRAC/AAA and FRED input decks. At each time step, TRAC/AAA performs thermal-hydraulic and power calculations using the temperature distribution in the fuel rods, or other structures, obtained from FRED at the previous time step and returns to FRED the axial distribution of the clad-to-coolant heat flux and power distribution (obtained from PARCS). With this data, FRED then calculates fuel rod properties and temperatures for the same time step and returns to TRAC/ AAA the temperature distribution. Temperatures in the heat structures calculated by TRAC/AAA are overwritten by these FRED data. The main ongoing task in the area of coupling the code modules together is the extension of the interface to include all the additional feedback variables that are important for the change in the transient reactivity for fast-spectrum systems. This work is being performed in parallel with the cross-section parameterisation described earlier. For a treatment of fast-spectrum systems in many energy groups, further work may be required to optimize the overall convergence procedure.

3. Validation of the FAST code system In addition to the development of the code system, it is important to benchmark and/or validate the individual components, as well as the code system as a whole. In this respect, as indicated earlier, advantage has been taken of the fact that ‘‘well developed’’ components were available in several cases. However, their envisaged use will often be at the limits of their original development window. Thus, for example, the application of the planned code system to the doubly heterogeneous, advanced fuel concepts proposed for the gas-cooled fast reactor, or to heavy-metal

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coolant thermal hydraulics, will require significant further development and validation. In the current phase, emphasis has been placed on the validation of the separate parts of the code system. The examples of such validation presented here are: testing of ERANOS against results pertaining to the ADS-related MUSE-4 critical and subcritical experiments (Soule and Gonzalez, 2000), TRAC/PARCS benchmarking against ERANOS and KIN3D calculations for a model of the CAPRA-CADRA critical gas-cooled core (Murgatroyd, 2002), and TRAC/AAA validation against experimental data for two-phase liquid-metal/nitrogen flow (Mikityuk et al., 2004), as well as against transient tests in the TALL lead–bismuth loop (Sehgal et al., 2004). Additionally, TRAC/AAA verification against other codes in the frame of the OECD/WPPT ADS beam-trip benchmark (DÕAngelo, 2004) is presented in Section 4. 3.1. MUSE-4 benchmark The ERANOS code system has been extensively verified in the past against data for critical sodium-cooled fast-spectrum systems. Recently, PSI participated with the ERANOS code in the MUSE-4 benchmark (Soule and Gonzalez, 2000), an international exercise related to the simulation of ADS-representative experimental configurations in the MASURCA facility, providing a new verification basis for ERANOS application to advanced fast reactor systems. A total of 16 participants provided a total of 34 solutions employing various combinations of Monte Carlo and deterministic codes with data libraries based on JEF-2.2, ENDF/B-6 and JENDL3.2 evaluations. The most widely used code was MCNP, in different versions and with various options. On the other hand, ERANOS was the most widely used deterministic code. This work included the analysis of two different fast critical configurations and one subcritical system. The first critical core (COSMO) was characterised by a MOX fuel zone surrounded by a steel/sodium reflector. The second critical configuration (M4CRIT) was composed of the same fuel and reflector, but with the presence of an accelerator tube and a central lead region, while the third (subcritical) model (M4SC2) was constructed by replacing some of the fuel elements in M4CRIT by reflector assemblies. PSI provided results obtained with both ERANOS and the stochastic code MCNP, each associated with different nuclear data libraries. The deviation of the ERANOS results from experimental values was found to be of the same order as that for MCNP, as also for results averaged over all solutions. In brief, the different MUSE-4 related PSI investigations have led to an increased confidence in the use of ERANOS for accurate prediction of fast-spectrum core characteristics such as spectral indices and keff (Plaschy, 2004). 3.2. Benchmarking of TRAC/PARCS against ERANOS and KIN3D for a gas-cooled core For neutronics calculations, the PARCS code was benchmarked earlier against ERANOS for both LBE and gas-cooled XADS systems. It was shown thereby that

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Table 1 Comparison of ERANOS and TRAC/PARCS predictions of reactivity coefficients for the CAPRACADRA gas-cooled core Reactivity coefficients

ERANOS

TRAC/PARCS

Doppler constant (pcm) Coolant density (pcm/°C) Core radial expansion (pcm/°C) Core axial expansion (pcm/°C)

389 0.85 1.23 0.385

448 0.80 1.22 0.388

transport effects are relatively unimportant for LBE systems while, for gas-cooled systems, because of the significant voided volume in the core, neutron transport effects can contribute up to 2000 pcm in the calculation of keff (Pelloni, 2005). As one of the first applications of the coupled PARCS and TRAC/AAA codes to a fast-spectrum system, a modified model of the CAPRA-CADRA gas-cooled core (Murgatroyd, 2002) has been used for test calculations of steady-state and transient behaviour, comparison being made with the ERANOS and KIN3D codes. One of the main aims of this study has been to check the preparation of the basic cross-sections and their derivatives with respect to fuel temperature, coolant density and core thermal expansion. In order to allow consistent comparisons to be made with PARCS predictions, the diffusion option was used in both ERANOS and KIN3D. Results for the Doppler constant (Waltar and Reynolds, 1981) and for other reactivity coefficients calculated by TRAC/PARCS and ERANOS based upon the use of a consistent group structure are presented in Table 1. The differences between the two calculations result from the different numerical solution schemes of the diffusion equation used in ERANOS and PARCS. In addition the fuel temperature distribution assumed in the ERANOS calculation is flat over the whole core, ‘‘making plausible’’ the somewhat larger discrepancy of the Doppler constant. Comparison of the relative power evolution in a test calculation of an unprotected control rod ejection transient using KIN3D and TRAC/PARCS is shown in Fig. 2. Both types of 3.5

TRAC/PARCS Relative power

3.0

KIN3D

2.5 2.0 1.5 1.0 0.0

0.2

0.4

0.6

0.8

1.0

Time,s Fig. 2. Comparison of relative power evolution in test calculations of an unprotected control rod ejection transient for the CAPRA-CADRA gas-cooled core using KIN3D and TRAC/PARCS.

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comparisons demonstrate the reliability of the currently developed procedure for preparing the basic cross-sections and their derivatives with respect to fuel temperature, coolant density and core thermal expansion. 3.3. TRAC/AAA validation against two-phase liquid-metal/nitrogen flow data A gas lift pump concept based on the bubbling of inert gas in liquid metal to enhance the natural circulation of the primary coolant is currently being considered in a number of LBE-cooled reactor projects. In particular, the gas lift pump is used in the LBE XADS design (Cinotti and Gherardi, 2002). Thus, verification of the twophase heavy-metal/gas flow model in the FAST code system has been an important issue. The TRAC/AAA analysis was accordingly carried out of four sets of experiments with two-phase heavy-metal/nitrogen flow, corresponding to different geometries (pool-type and loop-type), coolants (water, LBE, gallium, Woods metal), flowrates and void fraction ranges (Mikityuk et al., 2004). Some of the experiments analysed had been performed with both water and liquid metals using essentially the same test-section configuration and measurement technique. This enabled the accuracy of TRAC/AAA predictions to be tested on the basis of the water data before analysis of the liquid metal experiments. The predictions of the code versus the test data for various void fractions are presented for water and liquid metals in Fig. 3(a) and (b), respectively. The TRAC/AAA bubble drag model was modified by reducing the bubble drag coefficient by a factor of 2, in order to obtain the good agreement indicated. 3.4. TRAC/AAA validation against TALL LBE test data To provide an additional validation basis for application of the FAST code to analysis of the LBE XADS design (Cinotti and Gherardi, 2002), TRAC/AAA simulation has been carried out of transient tests performed on the Thermal-hydraulic ADS Lead-bismuth Loop (TALL) facility at the Royal Institute of Technology,

0.5 0.4 0.3 0.2 0.1 0.0 0.0

a

0.5 pool-type test loop-type test

Calculated void fraction

Calculated void fraction

0.6

0.1

0.2

0.3

0.4

Measured void fraction

0.5

0.4 0.3 0.2

0.0 0.0

0.6

b

pool-type test (LBE) pool-type test (Ga) loop-type test (LBE) loop-type test (Woods)

0.1

0.1

0.2

0.3

0.4

0.5

Measured void fraction

Fig. 3. Comparison of TRAC/AAA void fraction predictions with test data for: (a) water and (b) liquid metals.

500

500

450

450

Temperature, ºC

Temperature, ºC

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400 core tank outlet HX inlet HX outlet core tank inlet

350 300 250 200

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400 core tank outlet HX inlet HX outlet core tank inlet

350 300 250 200

150

150

0

1000

2000

3000

4000

Time, s

a

0

1000

2000

3000

4000

Time, s

b

Fig. 4. Results of: (a) measurements and (b) TRAC/AAA calculations for a LOF test at the TALL facility.

500 core tank outlet HX inlet HX outlet core tank inlet

450 400 350 300

Temperature, ºC

Temperature, ºC

500

250

400 350 300 250

200

200 0

a

core tank outlet HX inlet HX outlet core tank inlet

450

2000

4000

6000

8000

10000

Time, s

0

b

2000

4000

6000

8000

10000

Time, s

Fig. 5. Results of: (a) measurements and (b) TRAC/AAA calculations for a LOHS test at the TALL facility.

Stockholm (Sehgal et al., 2004). As support for ADS-related technologies, this facility was designed and constructed for investigating the heat transfer performance of different types of heat exchangers, as also the thermal-hydraulic characteristics of natural circulation and forced circulation flow under steady-state and transient conditions. The LBE loop is of 6.8 m height and has been scaled to provide a prototypic power/volume ratio in representing the main components of the LBE XADS system. The loop essentially consists of a heater, pump, heat exchanger and piping. Glycerol is used as secondary fluid. Results of measurements at the TALL facility and post-calculations, using the TRAC/AAA code, are presented in Figs. 4 and 5 for loss of flow (LOF) and loss of heat sink accidents (LOHS), respectively. Good agreement is seen to be obtained, in each case, between the predictions and the experimental results.

4. Application of the FAST code system As indicated in Section 1, the currently reported validation and application efforts for the FAST code system relate mainly to studies which have been performed within

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the 5th EU-FWPÕs project Preliminary Design Study of eXperimental AcceleratorDriven Systems (PDS-XADS). Three different XADS design options were considered thereby, viz., the ANSALDO LBE-cooled 80 MWt core (Cinotti and Gherardi, 2002), the FRAMATOME helium-cooled 80 MWt design (Giraud, 2003) and the MYRRHA LBE-cooled 50 MWt core (Abderrahim et al., 2000). The PSI contribution to the PDS-XADS project was mainly in the work package concerned with the assessment of the safety of the two 80 MWt designs (Coddington, 2002). A wide range of transients were analysed using the FAST code system in this context, viz., protected and unprotected transient overpower, spurious beam trip, loss of flow, loss of heat sink, loss of coolant, overcooling, etc. This section presents results from three specific analyses carried out: (a) calculation of the OECD/WPPT transient benchmark simulating a beam interruption in an LBE-cooled and MOX-fuelled accelerator-driven system (DÕAngelo, 2004), (b) a comparison of the transient behaviour of the LBE and gas-cooled XADSs under protected and unprotected loss of flow conditions (PLOF, ULOF), and (c) fuel behaviour during a beam overpower transient in the LBE-cooled XADS, the latter serving to demonstrate the successful integration of the different fuel modules into the FAST code system. 4.1. OECD/WPPT beam-trip benchmark The calculational transient benchmark ‘‘Beam interruption in a lead–bismuth cooled and MOX fuelled accelerator-driven system’’ (DÕAngelo, 2004) was aimed at study of the behaviour of LBE-cooled XADS (Cinotti and Gherardi, 2002) and MYRRHA-type (Abderrahim et al., 2000) systems during beam interruptions of various durations, using pre-defined physical parameters. The main differences between the XADS and MYRRHA core designs are in the fuel pin linear power levels (80 W/ cm and 320 W/cm on average, respectively) and core heights (0.9 and 0.6 m, respectively). These differences determine the significantly different fuel temperature levels in the two systems. Nine institutions participated in the analysis, providing 10 solutions obtained with 10 different codes. One of the sets of the results was obtained at PSI with the TRAC/AAA code. Relative reactor power and peak fuel centreline temperature history calculated by TRAC/AAA for the 6-s beam trip benchmark for XADS and MYRRHA are shown in Fig. 6. The calculated decrease of the fuel peak temperature for each ADS, for beam trips durations of 1 and 6 s, are given in Table 2 as averaged values over all solutions, together with the maximum difference between the individual results. Discrepancies between the different code predictions are seen to be relatively minor, being highest at about 8% in the case of the MYRRHA peak-power pin. The excellent agreement between the individual solutions is largely a consequence of the nature of the current phase of the benchmark, which has deliberately been kept very simple in its formulation. Confirmation has nevertheless been achieved that TRAC/AAA is able to simulate, using point kinetics, transients in a subcritical source-driven reactor system.

K. Mikityuk et al. / Annals of Nuclear Energy 32 (2005) 1613–1631 1.2

2500

1100

1.0

2250

1000

0.8 0.6

800

0.4

700 600 0

5

10

15

20

Temperature, K

900

Rel. power

Temperature, K

Fuel centreline temperature

1.0

2000

0.8 Fuel centreline temperature

1750

0.6

1500

0.4

0.2

1250

0.2

0.0

1000

25

0.0 0

5

Time, s

10

15

20

25

Time, s

XADS

a

1.2

Relative reactor power

Relative reactor power

Rel. power

1200

1625

MYRRHA

b

Fig. 6. Relative reactor power and peak fuel centreline temperature calculated by TRAC/AAA for the 6-s beam trip benchmark for the two LBE-cooled ADS designs: (a) XADS and (b) MYRRHA.

Table 2 Decrease of fuel peak temperature in the beam trip benchmark, °C System

Pin power level (W/cm)

Beam interruption (s) 1

XADS XADS MYRRHA MYRRHA

6 a

80 (average) 115 (peak) 220 (average) 320 (peak)

63 ± 2 89 ± 4 190 ± 13 825 ± 58

270 ± 2 390 ± 18 260 ± 21 1220 ± 98

a 63 ± 2 means that the decrease averaged over all solutions is 63 °C and the maximum difference between the solutions is 2 °C.

4.2. PLOF, ULOF transients in the LBE and gas-cooled XADSs As an illustration of the PSI transient analysis of the two XADS designs (Coddington, 2002), the TRAC/AAA calculational results for the core power, flowrate and temperatures during a protected loss of flow accident (PLOF) are shown in Figs. 7 and 8 for the two cases (parts a and b, respectively).

1.0

1.0 core power 0.8

Rel. units

Rel. units

0.8 0.6 0.4 core flowrate

0.6 0.4

0.2

0.2

0.0

0.0

core flowrate

core power 0

20

40

60

80

100

0

Time, s

a

LBE-cooled XADS

20

40

60

80

Time, s

b

He-cooled XADS

Fig. 7. Relative core power and flowrate during protected loss of flow in the two XADSs.

100

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2000

1500

1500

Temperature, oC

Temperature,oC

peak fuel temperature

peak fuel temperature 1000 peak clad temp 500

1000 peak clad temp 500

core outlet coolant temperature

0 0

20

0

40

60

80

100

core outlet coolant temperature 0

20

40

Time, s

a

60

80

100

Time, s

b

LBE-cooled XADS

He-cooled XADS

Fig. 8. Temperatures during protected loss of flow in the two XADSs.

For the LBE system, the LOF accident was simulated by stopping the argon supply to the gas lift pumps. For the He system, the accident was modelled by stopping the primary blower with the subsequent actuation of 2 of 3 shutdown cooling system (SCS) units. The beam trip in the He-cooled XADS (Fig. 7(b)) occurs, at the beginning of the transient, using the ‘‘main blower status’’ as a trip signal. For this reason, all temperatures decrease in the gas system (Fig. 8(b)), while in the LBE case, there is some temperature increase, viz., 70 °C for fuel and 150 °C for cladding (Fig. 8(a)) until the coolant outlet temperature reaches 420 °C, generating the beam trip signal (Fig. 7(a)). Note that in the LBE system the decay heat is removed completely by natural circulation of the heavy-metal coolant which finally stabilizes at about 20% of the nominal value, while the coolant flowrate in the gas-cooled core is provided by the SCS blowers at the level of about 30%. In the unprotected case (Figs. 9 and 10), the core power changes insignificantly (Fig. 9), but the temperature increase in the gas system is much higher than in the LBE case. The natural circulation level of LBE coolant is very high, viz., more than 40% of the nominal value (Fig. 9(a)), and the peak temperatures stabilize at 1120 °C in fuel and at 640 °C in cladding (Fig. 10(a)). For the gas system, two units of the 1.0

1.0

core power

core power 0.8

Rel. units

Rel. units

0.8 0.6 core flowrate 0.4

0.4

core flowrate

0.2

0.2 0.0

0.0 0

20

40

60

80

100

0

Time, s

a

0.6

LBE-cooled XADS

20

40

60

80

Time, s

b

He-cooled XADS

Fig. 9. Relative core power and flowrate during unprotected loss of flow in the two XADSs.

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1500

Temperature, oC

Temperature,oC

2000

peak fuel temperature 1000 peak clad temperature 500

core outlet coolant temperature

0

peak fuel temperature

1500 peak clad temperature 1000 core outlet coolant temperature 500

0 0

20

40

60

80

100

0

20

40

Time, s

a

1627

LBE-cooled XADS

60

80

100

Time, s

b

He-cooled XADS

Fig. 10. Temperatures during unprotected loss of flow in the two XADSs.

safety cooling system provide a flow rate of about 30% of the nominal value (Fig. 9(b)) and the peak temperatures stabilize at 2000 °C in fuel and at 1220 °C in cladding (Fig. 10(b)). This comparative analysis is just one example from the wide range of hypothetical accidents considered in the comprehensive PDS-XADS safety study (Coddington, 2002). Even just this one type of transient, however, clearly brings out the main differences between the two systems: (1) extremely high difference in coolant density and, as a consequence, significantly higher thermal inertia and natural circulation potential in the LBE XADS, and (2) different fuel design (viz., fuel diameter) and, as a consequence, significantly higher fuel temperatures in the gas-cooled XADS. In summary, the results obtained show that the LBE-cooled XADS exhibits a very wide safety margin (for both protected and unprotected transients) as a consequence of very favourable safety characteristics. The latter include excellent heat transfer properties and high boiling point of the coolant, favourable in-vessel and secondary system coolant natural circulation flow characteristics, and the large thermal inertia within the primary system as a result of the large coolant mass (pool design). For the gas-cooled XADS, the results bring out the importance of the core heat transfer, show the adequacy of the decay heat removal system for protected depressurization and loss of flow transients, and provide appropriate definition of the time window for backup proton beam shutdown systems in the event of an unprotected transient. 4.3. Fuel behaviour during beam overpower in the LBE-XADS Appropriate accounting for the fuel behaviour during beam overpower in the LBE-cooled XADS is the analysis which has been chosen to demonstrate the successful integration of the fuel module into the FAST code system. For the transient considered, a linear increase of the external source power to six times the nominal value is assumed over a 10-s period, this power being kept constant until 80 s into the accident before the external source is switched off. Although the scenario is not realistic (too severe), it is quite suitable for checking the coupling of the thermal, hydraulic and mechanical modules, in particular from the viewpoints of gap closure effects and cladding plastic deformation.

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The exercise was performed by applying three different modelling schemes:
First, use was made simply of the original TRAC/AAA fuel rod model.
Second, the reactivity feedback due to fuel axial expansion was also taken into account.
Finally, both the more detailed FRED fuel rod model and reactivity feedback due to fuel axial expansion were used.

5

2800

4

2400 Temperature (K)

Relative power (-)

The calculational results are presented in Figs. 11 and 12. Fig. 11(a) shows the time history of the relative power calculated by the TRAC/AAA point kinetics model in conjunction with the three different schemes. The lower power levels in the second and third calculations are explained by the negative reactivity effect

3 1 2 3

2 1

2000 1600

1 2 3

1200 800 400

0 0

20

a

40 60 Time (s)

80

0

100

20

40 60 Time (s)

b

80

100

Fig. 11. Relative power and peak fuel temperature during beam overpower in the LBE-XADS for the three different fuel rod modeling schemes: 1, original TRAC/AAA fuel rod model; 2, TRAC/AAA fuel rod model with reactivity feedback due to fuel axial expansion; 3, FRED fuel rod model with reactivity feedback due to fuel axial expansion.

Hoop stress (MPa)

Radius (mm)

3.62 3.61 3.60 pellet outer radius clad inner radius

3.59

40

1.8

stress deformation

20

1.2

0

0.6

-20

3.58 0

a

2.4

20

40 60 Time (s)

80

0.0 0

100

b

Hoop plastic defromation (%)

60

3.63

20

40

60

80

100

Time (s)

Fig. 12. Results from the TRAC/FRED modelling of the LBE-XADS beam overpower transient, in terms of: (a) fuel pellet and clad inner radii, and (b) hoop stress and hoop plastic strain on cladding inner surface.

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due to the fuel axial expansion. The time history of the peak fuel temperature is shown in Fig. 11(b). The fuel temperature in the third calculation is seen to be significantly (about 200 °C) lower because the FRED model accounts for a contact component in the fuel-to-clad heat conductance. For this reason, the Doppler and fuel expansion effects are smaller and the power level is slightly higher (Fig. 11(a)) in the third case as compared to the second calculation. Changes of fuel pellet radius and clad inner radius, evaluated in the third calculation, are presented in Fig. 12(a). The corresponding hoop stress and hoop plastic deformation on the cladding inner surface are shown in Fig. 12(b). In the open gap regime, the hoop stress is negative due to the temperature difference across the cladding. After gap closure, the stress quickly grows and reaches a yield point at about 32 s. The resulting hoop plastic deformation on the clad inner surface is about 1.3%. No plastic deformation is predicted on the clad outer surface. Although the chosen transient, with its factor of six increase in external source power, is somewhat arbitrary, the exercise has demonstrated the operability of the modified TRAC/AAA code, including the integration of the FRED fuel rod model for effective simulation in different regimes. It has also shown that, under closed gap conditions, a more detailed fuel rod modelling can lead to significantly more accurate predictions of fuel temperature and power. The above examples from the comprehensive PDS-XADS safety assessment study carried out at PSI serve to demonstrate the ability of the FAST code system to simulate the transient behaviour of advanced fast-spectrum reactors in a general manner, i.e., systems having several circuits with different coolants, multiple heat structures, various types of system components, etc.

5. Conclusions The FAST project is a PSI activity in the area of fast-spectrum systems with emphasis on generic developments, a principal goal being to develop a unique code capability for the core and safety analysis of advanced critical (and sub-critical) fast reactors. The paper has presented the structure of the code system, the organisation of the interfaces between the individual modules and data exchange, along with examples of the validation and application of the individual codes and the system as a whole. In the current phase of this activity, emphasis has been placed on the validation of the separate parts of the code system for advanced fast reactor designs and related phenomena. The examples given of such validation include: benchmarking of ERANOS against MUSE-4 experiments, TRAC/PARCS benchmarking against ERANOS and KIN3D, TRAC/AAA validation against two-phase liquid-metal/ nitrogen flow data and against transient tests in the TALL lead–bismuth loop, as also verification of TRAC/AAA against other codes in the frame of OECD/WPPT beam-trip benchmark. The FAST code system has been successfully applied to the safety assessment of LBE and gas-cooled experimental accelerator-driven systems (XADSs) as part of the

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5th EU-FWPÕs PDS-XADS project. Examples have been given of comparative transient analyses of the two different XADS designs, as also of the effectiveness of the integration of the individual modules into the FAST code system. To summarise, the following are the main conclusions concerning the current status of the new code system: (i) the validation results demonstrate the reliability of the developed procedure for preparing the basic cross-sections and their derivatives with respect to fuel temperature, coolant density and core thermal expansion, (ii) the predictions of individual components of the FAST code system are, in general, in good agreement with test data, as also with calculational results from other similar codes, and (iii) the FAST code system has been successfully used for LBE and gas-cooled XADS transient analysis.

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