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
Structure of the RRT / MACD group
• 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)
Method Development
• 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
Code system development
•
•
•
•
Expansion of research reactor and power reactor capabilities
International use of code system
Coupling toward multi-physics capability
Next generation system development
OSCAR-4
• Overall System for the CAlculation of Reactors, v4
• International usage in research reactor modelling
• Research platform for university partnerships
Fission systems
CONTROL THE FISSION CHAIN REACTION
Your first simulation…
# neutrons in one generation
k  multiplica tion factor 
# neutrons in preceeding generation
• 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…
140 neutrons
leak
1040
neutrons
N0
Fast Fission

1000
neutrons
Fast Nonleakage
900 neutrons
Lf
Resonance
Escape
k 1
p
k    L f  p  Lt  f 
1000
neutrons
Reproduction
620 neutrons

495 neutrons
180 absorbed
by resonance
peaks
Thermal
Utilization
f
720 neutrons
Thermal
Non-leakage
Lt
100 neutrons
leak
In reality…
1 
ˆ . + t ( r , E )  ( r , E ,
ˆ ,t )

v t
-


ˆ  dE s (E  E,
ˆ 
ˆ )  (r , E,
ˆ , t )
d

4
 (E)
4
0

4

ˆ  dE (E) f (r , E)  (r , E,
ˆ , t )
d

0
Flux solution needed in 7 dimensional space... A tough problem
Deterministic Solution methods
and/or
Stochastic solution methods
What is OSCAR-4?
Neutronic reactor calculational system
• 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
Characteristics
• 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
Links
• 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)
Methodology and Theory (1)
DETERMINISTIC CALCULATIONAL PATH
PROBLEM SIZE
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
ENERGY and SPATIAL DETAIL
Nodal Diffusion
Theory
• Full 3D core
• Few Energy Groups
(2-10)
Two specific projects from MACD
Dr. Francois van Heerden
• A Coarse Grained Particle Transport Solver
Designed Specifically for Graphics Processing
Units
Dr. Pavel Bokov
• In-Core Fuel Management Optimization
(ICFMO)
Example Project 2:
In-Core Fuel Management
Optimization (ICFMO)
Pavel M. Bokov, Evert B. Schlünz
Radiation and Reactor Theory
Problem description
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
fuel assembly (SAFARI-1)
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)
grid plate of an empty reactor core
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
ICFMO as a Multiobjective Problem
Diverse utilization goals may be pursued during a typical operational cycle
•
objectives may be in conflict
•
objectives may vary from one cycle to another
Other utilization and safety
goals and constraints
Optimize neutron intensity in
the neutron beams located in
exterior of the core
Maximise production of the
radioisotope Molybdenum-99
Maximise silicon doping
capacity of the reactor
14
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
•
•
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)
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)
ICFMO: Problem characteristics
•
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)
≈ 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
reactor
reactor model
reactor modelling tool
Pareto solution of the multiobjective
optimization problem
optimization methods
• Adapted metaheuristic algorithms
– Harmony search
– Cross entropy method
• Versions of algorithms
–
Single-objective with Chebyshev
scalarization
– Truly multiobjective
• Other multiobjective algorithms
(under investigation)
Solution Approaches
reactor
reactor model
reactor modelling tool
Pareto solution of the multiobjective
optimization problem
artificial neural network
(ANN) metamodel of reactor
responses
optimization methods
• Adapted metaheuristic algorithms
– Harmony search
– Cross entropy method
• Versions of algorithms
–
Single-objective with Chebyshev
scalarization
– Truly multiobjective
• Other multiobjective algorithms
(under investigation)
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)
THANK YOU