Method and Code development activities in the RRT section Rian Prinsloo, Francois van Heerden, Pavel Bokov September 2015 Overview of the OSCAR-4 code system Necsa / Wits workshop

Outline Necsa background The development team Some reactor theory The OSCAR-4 system Example project: Next generation development: Coarse grained particle transport method Example project: An in-core fuel optimisation method

Necsa

MACD group and OSCAR-4 7 members (3-4 PhD, 3-4 MSc, 1-2 Bsc.H and 2-3 students) Typical background in physics, applied mathematics, nuclear engineering and computer science Method Development (research platform) and Code system development (industry linkage) Structure of the RRT / MACD group Development of modelling approaches to various physical phenomenon in reactor environment Focus on efficient, high fidelity solution schemes for neutronic, thermal-hydraulic and material distribution in and around reactor Method Development Expansion of research reactor and power reactor capabilities International use of code system Coupling toward multi-physics capability Next generation system development Code system development Overall System for the CAlculation of Reactors, v4 International usage in research reactor modelling Research platform for university partnerships OSCAR-4

CONTROL THE FISSION CHAIN REACTION Fission systems

If k=1 : no change in neutron population and system in time independent  Critical System If k<1 : number of neutron decrease from one gen to the next and dies out  Sub-Critical System If k>1 : number of neutrons grow without bound, each gen larger than the previous  Super-Critical System Your first simulation…

Fast Non- leakage Resonance Escape Thermal Non-leakage Thermal Utilization Reproduction Fast Fission 1000 neutrons 1040 neutrons 900 neutrons 140 neutrons leak 180 absorbed by resonance peaks 720 neutrons 100 neutrons leak 620 neutrons 495 neutrons 1000 neutrons Your first simulation…

Flux solution needed in 7 dimensional space... A tough problem Deterministic Solution methods and/or Stochastic solution methods In reality…

What is OSCAR-4? Nodal diffusion code utilizing neutron transport and neutron diffusion theory to predict spatial and spectral neutron distribution in reactor core Performs depletion of reactor core components to predict isotopic distribution Neutronic reactor calculational system Multi-group nodal diffusion solver for core solution (very fast) Steady state, point kinetic and spatial kinetic options Extensive pre- and post processor capabilities for automated core-follow, reload, optimization and equilibrium analysis Expansive set of theory and user manuals as well as tutorials Characteristics Thermal-hydraulic modules for feedback for single channel to sub-channel analyses (such as COBRA-TF) Coupled to external lattice codes for cross-section generation (such as SERPENT) Number density export options for detailed Monte Carlo analyses (such as MCNP) Links

Methodology and Theory (1) Transport Theory 2D Single / Multi Assembly or full core Fine or continuous Energy Groups Span state space Cross-section representation Continuous fit through point-wise data Multi-dimensional model Nodal Diffusion Theory Full 3D core Few Energy Groups (2-10) PROBLEM SIZE ENERGY and SPATIAL DETAIL DETERMINISTIC CALCULATIONAL PATH

Two specific projects from MACD A Coarse Grained Particle Transport Solver Designed Specifically for Graphics Processing Units Dr. Francois van Heerden In-Core Fuel Management Optimization (ICFMO) Dr. Pavel Bokov

Example Project 2: In-Core Fuel Management Optimization (ICFMO) Pavel M. Bokov, Evert B. Schlünz Radiation and Reactor Theory

A fuel reloading operation is periodically executed in nuclear reactors and a part of the least reactive fuel (called bunt or depleted) is replaced with a fresh one The following may occur between two operational cycles: 1.Depleted fuel assemblies (FAs) are discharged from a reactor core 2.Fresh FAs may be loaded into the core 3.FAs already in the core may be exchanged with spare FAs kept in a pool (not fresh) 4.The placement of FAs in the core may be changed, resulting in a fuel reconfiguration (or shuffle) The in-core fuel management optimization (ICFMO) problem refers to the problem of finding an optimal fuel reload configuration for a nuclear reactor core 13 Problem description fuel assembly ( SAFARI-1 ) grid plate of an empty reactor core

14 Diverse utilization goals may be pursued during a typical operational cycle objectives may be in conflict objectives may vary from one cycle to another Maximise production of the radioisotope Molybdenum-99 ICFMO as a Multiobjective Problem Maximise silicon doping capacity of the reactor Other utilization and safety goals and constraints Optimize neutron intensity in the neutron beams located in exterior of the core

Nonlinear assignment problem (fuel assemblies to loading positions) Large disjoint feasible decision space (discrete variables) Multiple nonlinear objectives and constraints (multi-objective optimization) Computationally expensive (requires a reactor modelling tool, i.e. core simulator for objective function and constraint values evaluations) ICFMO: Problem characteristics

Nonlinear assignment problem (fuel assemblies to loading positions) Large disjoint feasible decision space (discrete variables) Multiple nonlinear objectives and constraints (multi-objective optimization) Computationally expensive (requires a reactor modelling tool, i.e. core simulator for objective function and constraint values evaluations) ICFMO: Problem characteristics e.g. loading SAFARI-1 core (26 positions) with 26 fuel assemblies yields 26! ≈ 4×10 26 combinations (≈ number of atoms in 36 litres of water) e.g. loading SAFARI-1 core (26 positions) with 26 fuel assemblies yields 26! ≈ 4×10 26 combinations (≈ number of atoms in 36 litres of water)

Nonlinear assignment problem (fuel assemblies to loading positions) Large disjoint feasible decision space (discrete variables) Multiple nonlinear objectives and constraints (multiobjective optimization) Computationally expensive (requires a reactor modelling tool, i.e. core simulator for objective function and constraint values evaluations) ICFMO: Problem characteristics

Nonlinear assignment problem (fuel assemblies to loading positions) Large disjoint feasible decision space (discrete variables) Multiple nonlinear objectives and constraints (multi-objective optimization) Computationally expensive (requires a reactor modelling tool, for objective function and constraint value evaluations) ICFMO: Problem characteristics ≈ 4 min required in OSCAR-4 to evaluate a single reload configuration on PC ≈ 1000 configurations evaluated in 3 days ≈ 4 min required in OSCAR-4 to evaluate a single reload configuration on PC ≈ 1000 configurations evaluated in 3 days This is a difficult, ill-structured problem to solve

Solution Approaches Adapted metaheuristic algorithms –Harmony search –Cross entropy method Versions of algorithms – Single-objective with Chebyshev scalarization –Truly multiobjective Other multiobjective algorithms (under investigation) Adapted metaheuristic algorithms –Harmony search –Cross entropy method Versions of algorithms – Single-objective with Chebyshev scalarization –Truly multiobjective Other multiobjective algorithms (under investigation) reactorreactor modelreactor modelling tool optimization methods Pareto solution of the multiobjective optimization problem

Solution Approaches Adapted metaheuristic algorithms –Harmony search –Cross entropy method Versions of algorithms – Single-objective with Chebyshev scalarization –Truly multiobjective Other multiobjective algorithms (under investigation) Adapted metaheuristic algorithms –Harmony search –Cross entropy method Versions of algorithms – Single-objective with Chebyshev scalarization –Truly multiobjective Other multiobjective algorithms (under investigation) reactorreactor modelreactor modelling toolartificial neural network (ANN) metamodel of reactor responses optimization methods Pareto solution of the multiobjective optimization problem

Status and Future Plans 1 PhD and 2 BEng projects (Stellenbosch University) in progress Harmony Search with scalarization incorporated to OSCAR-4 Several alternative multiobjective algorithms are under investigation The optimization feature has been applied to SAFARI-1 and HOR research reactors Extension of methodology to multicycle problems, allow non-fuel components to be loadable Adapt/apply our methods and tools to power rectors Develop loading pattern optimization / reactor design tool Metamodels based on artificial neural networks is a promising tool for various applications (not only optimization)

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