Modelling of Nuclear Reactor Multiphysics: From Local Balance Equations to Macroscopic Models in Neutronics and Thermal-Hydraulics is an accessible guide to the advanced methods used to model nuclear reactor systems. The book addresses the frontier discipline of neutronic/thermal-hydraulic modelling of nuclear reactor cores, presenting the main techniques in a generic manner and for practical reactor calculations.The modelling of nuclear reactor systems is one of the most challenging tasks in complex system modelling, due to the many different scales and intertwined physical phenomena involved. The nuclear industry as well as the research institutes and universities heavily rely on the use of complex numerical codes. All the commercial codes are based on using different numerical tools for resolving the various physical fields, and to some extent the different scales, whereas the latest research platforms attempt to adopt a more integrated approach in resolving multiple scales and fields of physics. The book presents the main algorithms used in such codes for neutronic and thermal-hydraulic modelling, providing the details of the underlying methods, together with their assumptions and limitations. Because of the rapidly expanding use of coupled calculations for performing safety analyses, the analysists should be equally knowledgeable in all fields (i.e. neutron transport, fluid dynamics, heat transfer).The first chapter introduces the book’s subject matter and explains how to use its digital resources and interactive features. The following chapter derives the governing equations for neutron transport, fluid transport, and heat transfer, so that readers not familiar with any of these fields can comprehend the book without difficulty. The book thereafter examines the peculiarities of nuclear reactor systems and provides an overview of the relevant modelling strategies. Computational methods for neutron transport, first at the cell and assembly levels, then at the core level, and for one-/two-phase flow transport and heat transfer are treated in depth in respective chapters. The coupling between neutron transport solvers and thermal-hydraulic solvers for coarse mesh macroscopic models is given particular attention in a dedicated chapter. The final chapter summarizes the main techniques presented in the book and their interrelation, then explores beyond state-of-the-art modelling techniques relying on more integrated approaches.
1. 1. Introduction - p. 1 2. 2. Transport phenomena in nuclear reactors - p. 13 3. 2.1. Nuclear reactors as multi-physics and multi-scale systems - p. 13 4. 2.2. Neutron transport - p. 25 5. 2.3. Fluid dynamics - p. 43 6. 2.4. Heat transfer - p. 50 7. 2.5. Overview of the modelling strategies - p. 57 8. 2.6. Deterministic and macroscopic modelling of nuclear systems - p. 60 9. 2.7. Conclusions - p. 69 10. 3. Neutron transport calculations at the cell and assembly levels - p. 73 11. 3.1. Representation of the energy dependence - p. 73 12. 3.2. Treatment of resonances - p. 81 13. 3.3. Resolving the energy dependence - p. 108 14. 3.4. One-dimensional micro-group pin cell calculations - p. 118 15. 3.5. Two-dimensional macro-group lattice calculations - p. 138 16. 3.6. Criticality spectrum calculations - p. 164 17. 3.7. Cross-section homogenization and condensation - p. 175 18. 3.8. Depletion calculations - p. 178 19. 3.9. Cross-section preparation for core calculations - p. 184 20. 3.10. Conclusions - p. 189 21. 4. Neutron transport calculations at the core level - p. 193 22. 4.1. Angular discretization of the neutron transport equation - p. 193 23. 4.2. Spatial discretization of the neutron transport equation - p. 218 24. 4.3. Determination of the steady-state core-wise solution - p. 231 25. 4.4. Determination of the non-steady-state core-wise solution - p. 237 26. 4.5. Conclusions - p. 248 27. 5. One-/two-phase flow transport and heat transfer - p. 251 28. 5.1. Tools required for flow transport modelling - p. 251 29. 5.2. Derivation of the space- and time-averaged conservation equations for flow transport - p. 258 30. 5.3. Flow models - p. 277 31. 5.4. Spatial and temporal discretizations of the flow models - p. 289 32. 5.5. Modelling of heat conduction in solid structures - p. 300 33. 5.6. Conclusions - p. 307 34. 6. Neutronic/thermal-hydraulic coupling - p. 311 35. 7. Conclusions - p. 337 36. Index - p. 345
Modelling of Nuclear Reactor Multiphysics: From Local Balance Equations to Macroscopic Models in Neutronics and Thermal-Hydraulics is an accessible guide to the advanced methods used to model nuclear reactor systems. The book addresses the frontier discipline of neutronic/thermal-hydraulic modelling of nuclear reactor cores, presenting the main techniques in a generic manner and for practical reactor calculations.The modelling of nuclear reactor systems is one of the most challenging tasks in complex system modelling, due to the many different scales and intertwined physical phenomena involved. The nuclear industry as well as the research institutes and universities heavily rely on the use of complex numerical codes. All the commercial codes are based on using different numerical tools for resolving the various physical fields, and to some extent the different scales, whereas the latest research platforms attempt to adopt a more integrated approach in resolving multiple scales and fields of physics. The book presents the main algorithms used in such codes for neutronic and thermal-hydraulic modelling, providing the details of the underlying methods, together with their assumptions and limitations. Because of the rapidly expanding use of coupled calculations for performing safety analyses, the analysists should be equally knowledgeable in all fields (i.e. neutron transport, fluid dynamics, heat transfer).The first chapter introduces the book’s subject matter and explains how to use its digital resources and interactive features. The following chapter derives the governing equations for neutron transport, fluid transport, and heat transfer, so that readers not familiar with any of these fields can comprehend the book without difficulty. The book thereafter examines the peculiarities of nuclear reactor systems and provides an overview of the relevant modelling strategies. Computational methods for neutron transport, first at the cell and assembly levels, then at the core level, and for one-/two-phase flow transport and heat transfer are treated in depth in respective chapters. The coupling between neutron transport solvers and thermal-hydraulic solvers for coarse mesh macroscopic models is given particular attention in a dedicated chapter. The final chapter summarizes the main techniques presented in the book and their interrelation, then explores beyond state-of-the-art modelling techniques relying on more integrated approaches.
1. 1. Introduction - p. 1 2. 2. Transport phenomena in nuclear reactors - p. 13 3. 2.1. Nuclear reactors as multi-physics and multi-scale systems - p. 13 4. 2.2. Neutron transport - p. 25 5. 2.3. Fluid dynamics - p. 43 6. 2.4. Heat transfer - p. 50 7. 2.5. Overview of the modelling strategies - p. 57 8. 2.6. Deterministic and macroscopic modelling of nuclear systems - p. 60 9. 2.7. Conclusions - p. 69 10. 3. Neutron transport calculations at the cell and assembly levels - p. 73 11. 3.1. Representation of the energy dependence - p. 73 12. 3.2. Treatment of resonances - p. 81 13. 3.3. Resolving the energy dependence - p. 108 14. 3.4. One-dimensional micro-group pin cell calculations - p. 118 15. 3.5. Two-dimensional macro-group lattice calculations - p. 138 16. 3.6. Criticality spectrum calculations - p. 164 17. 3.7. Cross-section homogenization and condensation - p. 175 18. 3.8. Depletion calculations - p. 178 19. 3.9. Cross-section preparation for core calculations - p. 184 20. 3.10. Conclusions - p. 189 21. 4. Neutron transport calculations at the core level - p. 193 22. 4.1. Angular discretization of the neutron transport equation - p. 193 23. 4.2. Spatial discretization of the neutron transport equation - p. 218 24. 4.3. Determination of the steady-state core-wise solution - p. 231 25. 4.4. Determination of the non-steady-state core-wise solution - p. 237 26. 4.5. Conclusions - p. 248 27. 5. One-/two-phase flow transport and heat transfer - p. 251 28. 5.1. Tools required for flow transport modelling - p. 251 29. 5.2. Derivation of the space- and time-averaged conservation equations for flow transport - p. 258 30. 5.3. Flow models - p. 277 31. 5.4. Spatial and temporal discretizations of the flow models - p. 289 32. 5.5. Modelling of heat conduction in solid structures - p. 300 33. 5.6. Conclusions - p. 307 34. 6. Neutronic/thermal-hydraulic coupling - p. 311 35. 7. Conclusions - p. 337 36. Index - p. 345
