1. Third LEADER International Workshop “Analysis and design issues of LFR reactor concept: ALFRED” Pisa-Bologna, 4-7 September 2012 Introduction to physical problems and design of LFR systems cores: open questions S. Dulla Politecnico di Torino, Torino, Italy

2. 3rd LEADER International Workshop 2 Sandra Dulla, PhD  Assistant professor in Reactor Physics at Politecnico di Torino (since 2007)  Research activity in the field of: Methods for neutron transport Neutron kinetics Innovative reactor neutronics (ADS, MSR) Dynamics of Lead-Cooled Reactors … the reason why I am here talking today …

3. 3rd LEADER International Workshop 3 Dynamics of LFR  Joint activity of the Reactor Physics and Thermal-hydraulics research groups at POLITO Combine the different expertise Collaboration work to develop models and methods for the analysis of LFR by means of coupled neutronic-thermalhydraulic simulations  … but I am not here (only) to advertise our work !  Let’s try to understand why it seems like our work is useful …

4. 3rd LEADER International Workshop 4 Design of LFR - I  Design of LFR Behavior in operational conditions Optimization of fuel utilization Stability to small perturbations Response to accidental conditions …  Most of these aspect require time- dependent evaluations of the system, taking into consideration the interaction of different physical phenomena and components constituting the core

5. 3rd LEADER International Workshop 5 Design of LFR - II  Focusing on the reactor core Neutron behaviour Thermal-hydraulics of the coolant Material behavior (chemical stability, effects under irradiation, mechanical stresses, …) …  These aspects will be treated with different level of detail during the rest of the workshop  I will be focusing on some aspects to be considered, with special regards to neutronics and thermal-hydraulics

6. 3rd LEADER International Workshop 6 Neutronics of LFR - I  Fast system … differences to thermal LWR ? High energy neutrons  Longer mean free paths  Reduced optical dimension of the system  Possible increased anisotropy in the interaction of neutrons with the medium  Which model is used to study the neutronics of LWR ? At core level  diffusion  In this case, are the hypotheses of diffusion satisfied ? NO  Transport may seem more adequate Huge computational effort Still complicated to perform full-core coupled calculations in trasport The use of diffusion needs to be verified  qualification step in the code development

7. 3rd LEADER International Workshop 7 Neutronic models - I transport diffusion Anisotropy treatment Larger # of unknowns Isotropy Hp Reduced # of unknowns Diffusive Fick’s law

8. 3rd LEADER International Workshop 8 Neutronic models - II  We may choose diffusion or transport, in both cases some approximations are required Spatial discretization of the equations  Possible distortion of the geometry  Possible reduced heterogeneity of the materials

9. 3rd LEADER International Workshop 9 A side note on homogenization…  In some sense, fast systems can be nicer  Starting from the statement (to be discussed) that is not possible to resolve at the pin-level for a full-core, it can be noticed that High energy  Longer free path Small heterogeneities may be less important The spatial homogenization may even work better than for LWR

10. 3rd LEADER International Workshop 10 Neutronic models - III Angle discretization (for transport)  S N approach  Ray effects  P N approach  Reduced capability to treat anisotropy

11. 3rd LEADER International Workshop 11 Neutronic models - IV  Energy discretization Generation of multigroup cross-sections Constraints based on the type of application  Cell calculation  high number of groups  Full-core  # of groups have to be reduced !  What is the “correct” number of groups ? Hard to distinguish characteristics energy More energy groups than in the LWR case are required  I am not even talking about MC … we may discuss why …

12. 3rd LEADER International Workshop 12 Neutronics of LFR  Full-core neutron analysis Diffusion is still the feasible choice, especially when coupled calculations are concerned Some approximations are then in order  Solve the heterogeneity of the system  spatial homogenization  Reduce the energy detail  Energy groups collapsing Are all these steps straightforward? Some examples …

13. 3rd LEADER International Workshop 13 Once upon a time… the cross section issue  Our research activity on the full-core neutronics of LFR started in the frame of the ELSY project  At that stage, we were working only on the neutronic part Full-core solver in multigroup diffusion Nodal approach in square geometry at the assembly level  As a consequence, cross sections had to be generated: Homogeneous in the assembly With a reduced number of energy groups

14. 3rd LEADER International Workshop 14 The cross section issue  Let’s focus on the energy group collapsing  Cross sections were generated by ENEA with the cell code ECCO (part of ERANOS) on a 66-group discretization  In order to perform fast full-core calculations, a reduced number of group was at order In LWR, 2-group have been proved to be enough What about LFR ?

15.  The questions are: How many groups are suitable ? Which are the cut-off energies ?  Cross section generation is a kind of an art, and requires a deep understanding of the existing physical phenomena, in order to be able to preserve relevant quantities when the energy detail is reduced 3rd LEADER International Workshop 15 The cross section issue

16. 3rd LEADER International Workshop 16 Digression on a different subject  To confirm that performing a full-core coupled NE-TH calculations is not a trivial task, we may recall the CASL project HUGE project involving various Labs and Universities in the USA (25M$/year) Objective: high performance computing for LWR Some aspects deserve our attention… Consortium for Advanced Simulation of Light Water Reactors (CASL)

17. 3rd LEADER International Workshop 17 The CASL project  Focus is on LWR Well-assessed technology  Objective is to integrate existing computational tools Mixed diffusion-transport solvers CFD calculations Chemistry and material behavior  Still, the perspective of such simulator is not so close in time… and we are talking about “old”, well- known reactors  Moreover, I have not been talking about TRANSIENT BEHAVIOR…

18. 3rd LEADER International Workshop 18 Trying to summarize  The solution of the neutronic problem for LFR poses various questions/problems, associated to the different physics and the necessity to validate/qualify the computational tools  The use of computationally-heavy solver (deterministic transport and MC) can be adopted at some stages of the design process, but stability and parametric studies require more flexible and fast computational tools  The situation becomes even more complicated when we recall that We need to perform time-dependent calculations The core behavior is to be described by the interaction of neutronics and thermal-hydraulics, al least

19. 3rd LEADER International Workshop 19 Time-dependent neutronics  Inversion of the full problem  high computational cost  Approach that has been adopted in many codes: Point Kinetics (PK) All spatial and spectral effects neglected (all system behaves as a point) Has been proved to work properly in various situations, for LWR, depending on the coupling of the system Its use for innovative systems is questionable, and in fact currenct activities are in the direction of performing spatial kinetics

20. 3rd LEADER International Workshop 20 Limits of the “pure” neutronic approach  It may be considered “easy”, since the equations are linear ( well, easy is something different to me … )  It neglects any effect of change of temperature Change of density of coolant Impact on cross sections …  In general, this affects both the steady- state and transient calculations

21. 3rd LEADER International Workshop 21 Thermal feedback  How can the thermal feedback term be introduced into the neutronic model ?  Option 1: use of temperature coefficients Global parameters  easy to deal with Evaluated through k eff, static calculations  are they really the correct ones to be used in time- dependent situations ? Global parameters  how can they be interfaced with spatial neutronics ?

22. 3rd LEADER International Workshop 22 Use of Temp coefficients  If we consider a PK model, the coupling is straightforward: External perturbation Derivative of keff vs. temperature

23. 3rd LEADER International Workshop 23 Use of temperature coefficients Analytical relations based on the results of simulations

24. 3rd LEADER International Workshop 24 Use of temperature coefficients  The use of temperature coefficients is consistent with a PK approach The effect of the temperature change is related to a single, characteristic temperature of the whole fuel/coolant The reactivity effect is introduced into the neutronic model as an integral parameter, smeared over the whole core and directly affecting the power Localized effects (CR extraction, flow pattern modifications, …) cannot be described

25. 3rd LEADER International Workshop 25 Coupled NE-TH models for LFR  There are various codes approaching the coupled problem of a reactor core, with different hypotheses and approximations  Most of them were originally developed for application to LWR, and are now extending their capabilities to treat other neutron spectra and coolant characteristics  An overview (not exaustive) of these codes has been carried out by the PhD student working with us on this subject …

26. 3rd LEADER International Workshop 26 Coupled NE-TH models for LFR Important point: the different parts need to be consistent It is useless (and a waste of time !) to perform a very detailed CFD calculation and then couple it with a PK neutronics !

27. 3rd LEADER International Workshop 27 A NE-TH coupled model @ POLITO  Different fluid wrt water  Properties not totally assessed (some activities are under way for the validation of the TH model against experimental data from ENEA-Brasimone)  Possible approaches E.g., CFD on single channel  hard to extend to the full-core level (this approach will be discussed during these days)  Would require a very detailed NE model as well

28. 3rd LEADER International Workshop 28 A NE-TH coupled model @ POLITO  Possible approaches, e.g. Our approach  exploit the similar characteristics of the LWR fuel assembly to a TH problem of interest in fusion application: superconducting cables  Coupling with a NE model at the «same level» of detail: nodal solution at the hexagonal assembly level Good compromise and consistency of the NE and TH approaches

29. 3rd LEADER International Workshop 29 A NE-TH coupled model @ POLITO  Joint effort in the field of reactor physics and thermal-hydraulics  Objective: develop a code to be used for parametric studies, stability studies adn time- dependent simulation Some approximations on the detail to be treated need to be introduced The consistency in the characteristics of the NE and TH modules is preserved The expertise in a different field (superconducting cables for fusion applications) is exploited

30. 3rd LEADER International Workshop 30 The TH model - I  Analogies with the Toroidal field superconducting coils Prevailing convection along the direction of the coolant (Pb/liquid He) flow Conductive term across fuel elements/coils develops on longer time scales These aspects allow a similar treatment of the fluid- dynamic problem, adopting a 1D+2D scheme

31. 3rd LEADER International Workshop 31 The TH model - II 1D axial analysis along each closed assembly (z): mass/momentum/energy conservation equations in,, + transient heat conduction 2D inter-channel (xy) coupling (weak)

32. 3rd LEADER International Workshop 32 The TH model - III  Some comments on the model characteristics One fuel and coolant temperature for each fuel element at different elevation (discretization along z) The detail of the single fuel pin is lost  this is not a CFD calculation This aspect will affect the possible transients that can be simulated (e.g. counterflow in natural convection), but the resulting computational time is largely reduced How is the corresponding neutronics ?

33. 3rd LEADER International Workshop 33 The NE model Multigroup diffusion approximation of the transport equation 33 Temperature dependent  TH Coarse mesh approach: 2D conformal mapping applied to hexagonal geometry z direction: Introduced buckling term to account for axial neutron losses Imposed a sine shape on the flux along the axis, such that: computed in a 2D hexagon

34. 3rd LEADER International Workshop 34 The coupling strategy TISC  platform TH module internal time-stepping NE module internal time-stepping Temp. maps Power map Explicit coupling at τ ~ shortest TH time scales NE time scales TH time scales τ xy : heat diff. time through wrapper τ pin : heat diffusion time inside a pin τ z : transit time along channel τ Pb-pin : coolant-pin heat transfer time τ prompt : prompt neutron lifetime Flux shape scale (depends on transient ) τ delayed : delayed neutron precursor lifetime τ [s]

35. 3rd LEADER International Workshop 35 Domain definition 35/18 Boundaries of computational domain Reflector neglected (at present) for the sake of simplicity Input from ELFR available data BC (x and y):  NE: no incoming current  TH: adiabatic BC (z):  TH: T in, p in, p out (hydraulic parallel) x y z

36. 3rd LEADER International Workshop 36 Some tests performed …  Verification of the thermal coupling Red channels: T in = 900 K White channels: T in = 673 K ► Case 1: dm/dt nom  τ xy >> τ z ► Case 2: reduced dm/dt (loss of flow, flow blockage)  τ xy ~ τ z

37. 3rd LEADER International Workshop 37 Some tests performed …  Verification of the thermal coupling Steady state profiles Case 1: 2D coupling  negligible effect Case 2 (simulation of natural circulation): 2D coupling  T peaks smoothing

38. 3rd LEADER International Workshop 38 Some tests performed …  Criticality search test Compute NE flux shape (power distribution) Compute temperature distribution Has the temperature reached a steady state value |T new -T old |/T new < tol? Cross section homogenized data Initial temperature distribution in the system Start End Update the cross section with the new temperature profile YES NO Define a new reference condition dividing ν∑ f by k eff T 0 = T in = 673 K v Pb ~ 1 m/s Temperature feedback: ∑ f (T fuel,T Pb ), ∑ r (T fuel,T Pb ) (homogenized data from a liquid metal cooled system with hexagonal fuel element and MOX fuel … want to see the database ?)

39. 3rd LEADER International Workshop 39 Some tests performed …  Criticality search test k eff ↓ while T ↑  negative feedback k eff < 1, as k eff = 1 is imposed in the “cold reactor” condition Characteristic time ~ τ z because τ xy is negligible at (dm/dt) nom

40. 3rd LEADER International Workshop 40 Some tests performed …  Criticality search test

41. The importance of validation  To confirm the appropriateness of the approximations at the bases of a model/code, a validation process is required  For example, a first step to validate the TH model in the code FRENETIC against experimental data from the ENEA Integral Circulation Experiment (ICE) is under way and has already given some results 3rd LEADER International Workshop 41

42. Integral Circulation Experiment  Not really the best person to describe this facility …  The Integral Circulation Experiment (ICE) is performed in the CIRCE large scale facility at the ENEA Brasimone Research Centre. Cylindrical main vessel filled with about 70 tons of molten Lead-Bismuth Eutectic (LBE) LBE heating and cooling system Suitable geometry to be represented with the TH code in FRENETIC 3rd LEADER International Workshop 42

43. Result of the first step of validation Computed vs. experimental outlet temperatures during the full power characterization test 3rd LEADER International Workshop 43

44. An attempt of a summary  LFR design poses challenges in the various physical aspects (neutronics, thermal- hydraulics, …) affecting the core behavior  The problem can be tackled with different approaches (MC, full-core diffusion, coupled codes, cell calculations in transport, …), but some guidelines should be considered Internal consistency of the computational tools adopted Consistency of the tool with the desired outcome Validation of the newly developed tools with experiments (when available) Critical analysis of the extent of the results that can be obtained 3rd LEADER International Workshop 44