Nuclear Systems Juan Antonio Blanco 9 th April 2019 Director: Pablo - PowerPoint PPT Presentation

Neutronic-Thermohydraulic-Thermomechanic Coupling for the Modeling of Accidents in Nuclear Systems Juan Antonio Blanco 9 th April 2019 Director: Pablo Rubiolo (CNRS) Co-director: Eric Dumonteil (IRSN) Grenoble, France

Outline 1. Criticality and Basics of Nuclear Physics 2. Thesis Subject 3. Multi-Physics Coupling 4. Results 5. Conclusions 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 2

1. Criticality Accidents A criticality accident is an involuntary and uncontrolled fission chain reaction It can occur in nuclear systems involving very different • Geometric configurations • Phases • Phenomena Recent accidents: Tokaï-Mura (Japan 1999, 3 deads), etc. The “Tickling the Tail of the Dragon” accident (Los Alamos, 1945) – Source Atomic Heritage Foundation 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 3

1. Nuclear Physics: Basic concepts 𝑙 𝑞 ≡ 𝑸𝒔𝒑𝒏𝒒𝒖 𝑁𝑣𝑚𝑢𝑗𝑞𝑚𝑗𝑑𝑏𝑢𝑗𝑝𝑜 𝐺𝑏𝑑𝑢𝑝𝑠 ≡ 𝑂𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝒒𝒔𝒑𝒏𝒒𝒖 𝑜𝑓𝑣𝑢𝑠𝑝𝑜𝑡 𝑗𝑜 𝑝𝑜𝑓 𝑕𝑓𝑜𝑓𝑠𝑏𝑢𝑗𝑝𝑜 𝑂𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑜𝑓𝑣𝑢𝑠𝑝𝑜𝑡 𝑗𝑜 𝑝𝑜𝑓 𝑕𝑓𝑜𝑓𝑠𝑏𝑢𝑗𝑝𝑜 𝜍 ≡ 𝑆𝑓𝑏𝑑𝑢𝑗𝑤𝑗𝑢𝑧 ≡ 𝑙 − 1 𝑙 ≡ 𝑁𝑣𝑚𝑢𝑗𝑞𝑚𝑗𝑑𝑏𝑢𝑗𝑝𝑜 𝐺𝑏𝑑𝑢𝑝𝑠 ≡ 𝑂𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑜𝑓𝑣𝑢𝑠𝑝𝑜𝑡 𝑗𝑜 𝑞𝑠𝑓𝑑𝑓𝑒𝑗𝑜𝑕 𝑕𝑓𝑜𝑓𝑠𝑏𝑢𝑗𝑝𝑜 𝑂𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑜𝑓𝑣𝑢𝑠𝑝𝑜𝑡 𝑗𝑜 𝑞𝑠𝑓𝑑𝑓𝑒𝑗𝑜𝑕 𝑕𝑓𝑜𝑓𝑠𝑏𝑢𝑗𝑝𝑜 𝑙 𝒍 < 𝟐 𝝇 < 𝟏 𝒕𝒗𝒄𝒅𝒔𝒋𝒖𝒋𝒅𝒃𝒎 𝒍 = 𝟐 𝝇 = 𝟏 𝒅𝒔𝒋𝒖𝒋𝒅𝒃𝒎 𝑫𝒑𝒏𝒒𝒑𝒗𝒐𝒆 𝒐𝒗𝒅𝒎𝒇𝒗𝒕 𝒋𝒕 𝒈𝒑𝒔𝒏𝒇𝒆 𝒍 > 𝟐 𝝇 > 𝟏 𝒕𝒗𝒒𝒇𝒔𝒅𝒔𝒋𝒖𝒋𝒅𝒃𝒎 𝝃 = 𝟑 − 𝟒 𝒐𝒇𝒗𝒖𝒔𝒑𝒐𝒕 𝒃𝒔𝒇 𝒔𝒇𝒎𝒇𝒃𝒕𝒇𝒆 𝑸𝒃𝒔𝒖𝒋𝒅𝒗𝒎𝒃𝒔 𝑫𝒃𝒕𝒇 𝑱𝒐𝒅𝒋𝒆𝒇𝒐𝒖 𝑶𝒇𝒗𝒖𝒔𝒑𝒐 𝒇𝒚𝒅𝒋𝒖𝒇𝒕 𝑮𝒋𝒕𝒕𝒋𝒎𝒇 𝑶𝒗𝒅𝒎𝒇𝒗𝒕 𝜍 > 𝛾 𝑡𝑣𝑞𝑓𝑠 𝑞𝑠𝑝𝑛𝑞𝑢 𝑑𝑠𝑗𝑢𝑗𝑑𝑏𝑚 𝜸 = 𝑮𝒔𝒃𝒅𝒖𝒋𝒑𝒐 𝒑𝒈 𝒆𝒇𝒎𝒃𝒛𝒇𝒆 𝒐𝒇𝒗𝒖𝒔𝒑𝒐𝒕 𝑮𝒋𝒕𝒕𝒋𝒑𝒐 𝒅𝒊𝒃𝒋𝒐 𝒋𝒕 𝒕𝒗𝒕𝒖𝒃𝒋𝒐𝒇𝒆 𝟐 − 𝜸 𝝃 𝒒𝒔𝒑𝒏𝒒𝒖 𝒐𝒇𝒗𝒖𝒔𝒑𝒐𝒕 𝒑𝒐𝒎𝒛 𝒙𝒋𝒖𝒊 𝒒𝒔𝒑𝒏𝒒𝒖 𝒐𝒇𝒗𝒖𝒔𝒑𝒐𝒕 𝜸𝝃 𝒆𝒇𝒎𝒃𝒛𝒇𝒆 𝒐𝒇𝒗𝒖𝒔𝒑𝒐𝒕 𝑻𝒗𝒒𝒇𝒔𝒅𝒔𝒋𝒖𝒋𝒅𝒃𝒎 𝑢~0.1 𝑡 𝑢~10 −6 𝑡 𝑻𝒗𝒒𝒇𝒔 𝑸𝒔𝒑𝒏𝒒𝒖 𝑫𝒔𝒋𝒖𝒋𝒅𝒃𝒎 Fission Chain Reaction Juan Antonio Blanco - CNRS-IRSN 09/4/2019 4

1. Nuclear Physics: Basic concepts ➢ Dependence of neutron cross sections on the relative velocity between neutron and nucleus ➢ Target nuclei are in continual motion 𝑈 1 < 𝑈 2 < 𝑈 3 due to their thermal energy 𝑈 ➢ With increasing temperature the nuclei 1 𝜏(𝐹, 𝑈) vibrate more rapidly within their lattice structures 𝑈 2 𝑈 3 ➢ Broadening of the energy range of neutrons that may be resonantly absorbed in the fissile 𝐹 0 𝐹 Doppler Broadening Other Feedbacks exists like density change and geometry expansion (Leakage) Juan Antonio Blanco - CNRS-IRSN 09/4/2019 5

1. Criticality Accidents and Experiments ➢ Variety of accidents and experiments were reviewed ➢ Goal: select cases to cover a wide range of phenomena Available Data Heterogeneous Solid Media: Liquid Media: • • Media (Solid-Liquid) GODIVA I, II, III, IV SILENE • • • Spent Fuels Pools Flattop CRAC (diphasic) • • CABRI Passed accidents (Tokai-mura …) 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 6

2.Thesis Subject 2.1 State of Art  Current numerical models used by the safety authority limited for criticality accidents in:  Geometry modelling  Transient simulated time 2.2 Objective  Develop a more general transient multi-physics multiscale tool with:  Detailed phenomena modelling  Higher space/time scale flexibility  Best-estimate (Not conservative) 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 7

3. Transient Multi-physics Multiscale Tool Power Distribution Thermal- Neutronics hydraulics Density and Doppler effects Precursors Advection Thermal- mechanics Why Multiphysics Model?  Mechanistic model  Account for all relevant phenomena  High time/space scale flexibility 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 8

3. Multi-physics Tool: the Bricks/Codes  OpenFOAM is an open source software based in C++ for CFD C++ Library numerical resolution of the continuum mechanics including CFD  Serpent 2 is a 3D continue in energy Monte Carlo code for Monte Carlo Code (Serpent) reactor physics and irradiation calculus (burnup) Juan Antonio Blanco - CNRS-IRSN 09/4/2019 9

Multi-physics Coupling Godiva Experiment • Neutronics • Thermomechanics • Juan Antonio Blanco - CNRS-IRSN 09/4/2019 10

3. Multi-physics Coupling Godiva Experiment  Experiment description:  Geometry: sphere  Size: ~8.85 cm radius  Fuel: enriched Uranium (95%)  Mass: ~54 𝑙𝑕  Reactivity control mechanisms: none  only neutronics feedback effects 𝑆𝑓𝑚𝑏𝑢𝑗𝑤𝑓 𝐵𝑛𝑞𝑚𝑗𝑢𝑣𝑒𝑓  Key phenomena to be modeled:  Super prompt critical transient ( ρ > β )  Thermal expansion (density and leakage feedback)  Doppler effect (temperature feedback ) 𝑢 − 𝑢 𝑛 𝑄𝑓𝑠𝑗𝑝𝑒 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 11

3. Multi-physics Coupling Phenomena of Interest Power Distribution Thermal- Neutronics hydraulics Density and Doppler effects Precursors Advection Monte-Carlo (SERPENT) SPN Method Thermal- mechanics Stress-Strain Analysis Dynamic Mesh Models for thermal expansion 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 12

3. Multi-physics Coupling Neutronics  Neutron population described by Boltzmann equation and a balance of precursors with an advection term is used (in case of liquid fuels) 𝐻 𝑒 𝜓 𝑒 𝐹 𝑠, Ω, 𝐹, 𝑢 = −ℒ − 𝒰 + 𝒯 + 𝜓 𝑞 𝐹 1 𝜖𝜔 Ԧ 1 − 𝛾 𝐺 𝜔 Ԧ 𝑠, Ω, 𝐹, 𝑢 + ෍ 𝜇 𝑒 𝐷 𝑒 Ԧ 𝑠, 𝑢 𝑤 𝐹 𝜖𝑢 4𝜌 4𝜌 𝑒=1 Delayed Rate of change Streaming + Disappearance + Scattering + Fissions Neutrons source 𝜖𝐷 𝑒 𝑠, 𝑢 + 𝐸 𝑒 𝛼 2 𝐷 𝑒 Ԧ 𝑠, 𝑢 = 𝛾 𝑒 𝐺𝜔 Ԧ Ԧ 𝑠, Ω, 𝐹, 𝑢 − 𝜇 𝑒 𝐷 𝑒 Ԧ 𝑠, 𝑢 − 𝑣 ∙ 𝛼𝐷 𝑒 Ԧ 𝑠, 𝑢 for 𝑒 = 1 𝑢𝑝 𝐻 𝑒 𝜖𝑢 Local rate Production Destruction Convection Diffusion of change Liquid Media Neutronics Juan Antonio Blanco - CNRS-IRSN 09/4/2019 13

3. Multi-physics Coupling Neutronics methods and strategy Diffusion Simplified PN PN/ SN /Pij Monte Carlo • Fick’s Law • Flux and Scattering • Spherical Harmonics • Continuous in angle 𝐵𝑜𝑕𝑚𝑓 (Ω) Cross Section Numerical • Ԧ 𝐾 = −𝐸𝛼𝜚 Legendre Polynomials Quadrature expansion Point Kinetics Quasi-Static Method Direct Calculation • Fundamental Mode • Time resolution strategy in • Direct discretization of time 𝑈𝑗𝑛𝑓 (𝑢) Simple ODE larger time steps derivative • One-group Multi-Group Continuous 𝐹𝑜𝑓𝑠𝑕𝑧 (𝐹) Neutronics Juan Antonio Blanco - CNRS-IRSN 09/4/2019 14

3. Multi-physics Coupling Neutronics: A) the Simplified PN  The transient multigroup SP3 equations consist in a set of two coupled PDEs  The order 0 is identical to diffusion approximation equation  The order 2 takes into account anisotropies in the scattering cross section with a Legendre Polynomial Expansion 𝜖෡ 1 𝜚 0 1 𝐺 𝜚 0 − 2𝜚 2 + 2Σ 0 𝜚 2 + 2 𝜖𝜚 2 −1 𝛼 ෠ 𝜚 0 − Σ 0 ෠ ෠ order 0 𝜖𝑢 = 𝛼 3 Σ 1 𝜚 0 + 𝜖𝑢 + 𝑇 𝑒 𝑊 𝑙 𝑊 𝜖෡ 3 𝜖𝜚 2 3 5 4 2 𝐺 𝜚 0 − 2𝜚 2 + 2 2 𝜚 0 2 ෠ 3 Σ 0 ෠ −1 𝛼𝜚 2 − order 2 𝜖𝑢 = 𝛼 7 Σ 3 3 Σ 2 + 3 Σ 0 𝜚 2 − 𝜚 0 + 𝜖𝑢 − 3 𝑇 𝑒 𝑊 3 𝑙 3𝑊 Neutronics 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 15

3. Multi-physics Coupling Neutronics: B) the Quasi-Static Method 𝜔 Ԧ 𝑠, Ω, 𝐹, 𝑢 Key hypothesis: 𝑜 𝑢 𝜔 Ԧ 𝑠, Ω, 𝐹, 𝑢 = 𝑜 𝑢 𝜚 Ԧ 𝑠, Ω, 𝐹, 𝑢 1 𝜚 Ԧ 𝑠, Ω, 𝐹, 𝑢 𝑊 𝐹 𝜚 Ԧ 𝑠, 𝛻, 𝐹, 𝑢 𝑋 0 Ԧ 𝑠, 𝛻, 𝐹 = 𝑑𝑝𝑜𝑡𝑢𝑏𝑜𝑢 t  First hypothesis : separation of the neutron angular flux into an amplitude function 𝑜 𝑢 and a shape function 𝜚 Ԧ 𝑠, Ω, 𝐹, 𝑢  Second hypothesis : makes the two separated functions unique Neutronics 09/4/2019 Juan Antonio Blanco - CNRS-IRSN 16