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NEUP Proposed Graduate Study

My field of interest lies in computational modeling of multiphysics processes. In nuclear

science and engineering, the coupling of nuclear, fluid dynamics, chemical, andmechanical processes is of the utmost importance to ensure safe operation of nuclear

reactors. Due to the inherently multidisciplinary nature of such problems and thecomplexity of coupling fundamentally different processes, current multiphysics analysis

of nuclear reactors has been limited to simplified physical representations. Most currentmultiphysics simulations decouple processes through order split methods to reduce the

complexity in modeling coupled systems, but at the risk of losing accuracy. Thedevelopment of efficient methods to tackle fully coupled multiphysics problems using

high-fidelity models is still very much needed.

In approaching these types of problems, my interests lie in four areas: 1) Developing

mathematical models for fully coupling neutronic and thermomechanical processes, 2)developing strategies to solve these two processes in parallel through distributed memory

parallel programming, 3) writing an integrated software application that incorporatesmodules for these coupled processes in simple nuclear fuel assembly geometries, and 4)

developing rich and informative visualizations of these complex processes occurring inmaterials. As a first step, I plan to create a model for the coupled neutronic and

thermomechanical processes occurring in a spherical fast burst reactor. The simplifiedgeometry will allow me to focus on the important mathematical aspects of the problem

and design of the algorithmic implementation. Furthermore, it will serve as a startingpoint to extend the model to more complex systems.

The main challenge in coupling neutronic and thermomechanical processes is that theyare often described by nonlinear equations (e.g. neutron transport equation, Navier-

Stokes equation). From a mathematics standpoint, coupled nonlinear processes are solved

numerically using Newtons method. Oftentimes, nonlinear processes are simplifiedusing first order linear approximations (e.g. diffusion equation, linear elastic waveequation) and subsequently coupled [1]; or the nonlinear forms are kept intact, but the

processes are loosely coupled using operator split methods. Operator split methods areconvenient since computational tools for legacy single physics codes are widely available

and highly optimized, but there are some drawbacks to this approach. In strongly coupledprocesses, such as the neutronics and thermomechanics in a fast burst reactor, the

feedback mechanisms that are crucial to reactor safety are poorly described [2]. Clearly,fully coupled multiphysics simulations are needed, which makes my generalized

approach even more useful.

The computational complexity of a fully coupled multiphysics model also requires muchconsideration. Solving the seven-dimensional Boltzmann neutron transport equationrequires massive computing resources to converge neutron fluxes at each temporal step.

Adding solution variables for other physical processes increases the compute time foreach iteration and the memory footprint. The Multiphysics Object Oriented Simulation

Environment (MOOSE) framework tackles this issue by using a Jacobian-free Newton-Krylov scheme so only the matrix-vector product is needed and not the full matrix.

Through a similar approach, or perhaps by leveraging the MOOSE framework, solution

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algorithms for other multiphysics processes can be developed.

The system I plan to study for my masters project is the spherical fast burst reactor. This

reactor operates by oscillating between a supercritical, condensed state and a subcritical,expanded state with an oscillation period of ~50 microseconds. The rapid expansion and

contraction of the fuel is caused by energy deposition from fission. The energy depositionis accompanied by thermal expansion and mechanical stresses ranging from 1-300 MPa

[2]. The neutronics and materials processes alone are well understood and can bemodeled independently with high fidelity in many situations. However, the processes in

this system are tightly coupled, have similar time constants, and experience largedeviations. Numerous researchers have suggested or implemented loosely coupled

hydrodynamics models of the material behavior [1,2]. Using a hydrodynamics model, thematerial is assumed to have fluid-like behavior. The advantage of this approach is that

the nonlinear behavior could be treated without making any approximations orassumptions. Since the thermomechanical behavior of the material is highly nonlinear

and affects the criticality and safety of the system, it is important to understand how theseprocesses provide feedback and to use simulations to assess safety limits.

With this project I hope to gain an understanding of how to construct and implement highperformance simulations of complex processes occurring in nuclear materials. By the

time I finish this project, I will have taken coursework in nuclear reactor physics andalgorithm design that will allow me to leverage my accumulated knowledge and

experience to approach more complex geometries and other multiphysics processesoccurring in nuclear materials. Furthermore, my masters project is structured to validate

the coupled hydrodynamics and thermomechanics model and not necessarily delve deepinto studying the fast burst reactor. Instead of branching off to other systems, one other

potential route is to perform a more rigorous analysis of the spherical fast burst reactorunder other transient situations. These and other paths will be considered as I progress on

my masters project.

Computational analysis of fully coupled multiphysics systems promises to further our

knowledge of the coupled processes occurring in nuclear fuels. I believe my approach ofdemonstrating an extensible, scalable code on a small, simple geometry can provide

important insights for approaching larger problems and in delving deeper intomultiphysics simulations in all geometries. These simulations are crucial to

demonstrating the safety of nuclear reactors and by keeping intact the fundamentalequations that describe processes, we can accurately model material behavior.

References

[1] S. Y. Kadioglu, D. A. Knoll, and C. de Oliveira, "Multiphysics Analysis of Spherical

Fast Burst Reactors,"Nuclear Science and Engineering, vol. 163, pp. 132-143, Oct 2009.[2] R. Kimpland, Preliminary Results of Godiva-IV Prompt Burst Modeling, LA-UR-

96-1498, Los Alamos National Laboratory, May 1996.