A nonstiff solution for the stochastic neutron point kinetics equations

Introducing an approach that yields a nonstiff solution to solve the stochastic neutron point kinetics equations.

Title

A nonstiff solution for the stochastic neutron point kinetics equations

Author(s)

Milena Wollmann da Silva, Richard Vasques, Bardo E.J. Bodmann, Marco T. Vilhena

Publication

Annals of Nuclear Energy 97: 47-52

Description

We propose an approach to solve the stochastic neutron point kinetics equations using an adaptation of the diagonalization-decomposition method (DDM). This new approach (Double-DDM) yields a nonstiff solution for the stochastic formulation, allowing the calculation of the neutron and precursor densities at any time of interest without the need of using progressive time steps. We use Double-DDM to compute results for stochastic problems with constant, linear, and sinusoidal reactivities. We show that these results strongly agree with those obtained by other approaches established in the literature. We also compute and analyze the first four statistical moments of the solutions.

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Nonclassical particle transport in the 1-D diffusive limit

We provide computational results demonstrating for the first time that the solution of the nonclassical particle transport equation is well-approximated
by the solution of the nonclassical diffusion equation.

Title

Nonclassical particle transport in the 1-D diffusive limit

Author(s)

Richard Vasques, Rachel N. Slaybaugh, Kai Krycki

Publication

Transactions of the American Nuclear Society 114: 361-364

Description

In this paper, we investigate nonclassical particle transport taking place in a 1-D random periodic diffusive system. We provide computational results that validate the theoretical predictions, demonstrating for the first time that the solution of the nonclassical particle transport equation is well-approximated
by the solution of the nonclassical diffusion equation.

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NE 255: Numerical Simulation in Radiation Transport

http://www.nuc.berkeley.edu/courses/ne-255

Computational methods used to analyze nuclear reactor systems described by various differential, integral, and integro-differential equations. Numerical methods include finite difference, finite elements, discrete ordinates, and Monte Carlo. Examples from neutron and photon transport, heat transfer, and thermal hydraulics. An overview of optimization techniques for solving the resulting discrete equations on vector and parallel computer systems.

NE 250: Nuclear Reactor Theory

http://www.nuc.berkeley.edu/courses/ne-250

Computational methods used to analyze radiation transport described by various differential, integral, and integro-differential equations. Numerical methods include finite difference, finite elements, discrete ordinates, and Monte Carlo. Examples from neutron and photon transport; numerical solutions of neutron/photon diffusion and transport equations. Monte Carlo simulations of photon and neutron transport. An overview of optimization techniques for solving the resulting discrete equations on vector and parallel computer systems.

NE 155: Introduction to Numerical Simulations in Radiation Transport

http://www.nuc.berkeley.edu/courses/ne-155

Computational methods used to analyze radiation transport described by various differential, integral, and integro-differential equations. Numerical methods include finite difference, finite elements, discrete ordinates, and Monte Carlo. Examples from neutron and photon transport; numerical solutions of neutron/photon diffusion and transport equations. Monte Carlo simulations of photon and neutron transport. An overview of optimization techniques for solving the resulting discrete equations on vector and parallel computer systems.

NE 150: Introduction to Nuclear Reactor Theory

http://www.nuc.berkeley.edu/courses/ne-150

Neutron interactions, nuclear fission, and chain reacting systematics in thermal and fast nuclear reactors. Diffusion and slowing down of neutrons. Criticality condition and calculations of critical concentrations, mass and dimensions. Nuclear reactor dynamics and reactivity feedbacks. Production and transmutation of radionuclides in nuclear reactors.

Ehud Greenspan Bio

Dr. Greenspan is a Professor of the Graduate School since summer 2014. He has over 50 years of research experience in a wide variety of nuclear reactor physics, methods development and advanced reactor design related activities. In recent years his research interests are conception, design and analysis of advanced (primarily, Generation-IV) nuclear reactors and advanced nuclear fuel cycles. Specific objectives of his research are: Improving the sustainability of nuclear energy by increasing the utilization of the uranium and thorium fuel resources; minimizing the amount and radiotoxicity of the nuclear waste; improving proliferation resistance of nuclear energy along with improving the safety and economics of nuclear reactors. Over the past 15 years he has been the PI of 9 DOE funded (NERI; NEUP) multi-year projects most of which explored the feasibility of innovative core design and fuel cycles. His presently favorite reactor concept is “breed-and-burn” (B&B) fast reactors. A B&B reactor is a breeder reactor that converts into fissile fuel a significant fraction of the fertile feed fuel and then fissions a significant fraction of the bred fissile fuel without fuel reprocessing. B&B reactors can offer uranium utilization that is between 50 to 120 times that of LWRs. The amount of electricity that could be generated in B&B fast reactors using the presently available depleted uranium stockpiles (nuclear “waste”) is the equivalent of between 8 to 20 centuries of the total present US demand of electricity. Unfortunately, in order to achieve a B&B mode of operation the fuel will have to withstand nearly 2.5 times higher fast neutron induced radiation damage that has been proven acceptable. To alleviate this problem we recently proposed “seed-and-blanket” sodium cooled fast reactor (SFR) cores made of a critical seed and a subcritical B&B blanket. Specifically, we are searching for best ways to make beneficial use of the large fraction (up to 30%) of the fission neutrons that leak out from a seed designed to effectively transmute trans-uranium elements (TRU) from LWR used nuclear fuel to drive a B&B thorium fueled blanket to generate as large a fraction of the core power as possible without exceeding the presently acceptable radiation damage level of the fuel cladding material – 200 displacements-per-atom (DPA). Results obtained so far are highly promising – the reactivity increase with burnup of the B&B blanket greatly improves the performance of the TRU transmuting seed while the excess seed neutrons enable to generate close to 50% of the core power from the blanket while fissioning 7% of the thorium without the need for reprocessing the thorium fuel. He has over 500 publications with his students and other collaborating researchers.

The nonclassical diffusion approximation to the nonclassical linear Boltzmann equation

Showing that the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium.

Title

The nonclassical diffusion approximation to the nonclassical linear Boltzmann equation

Author(s)

Richard Vasques*

Publication

Applied Mathematics Letters 53: 63–68

Description

We show that, by correctly selecting the probability distribution function for a particle’s distance-to-collision, the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of probability distribution function preserves the true mean-squared free path of the system.

Link to Publication

MocDown

Jeffrey Seifried (alumnus)

MocDown (http://jeffseif.github.io/MocDown/) is an efficient tool which loosely couples simulations for neutron transport, isotopic transmutation, thermo-fluids, and the equilibrium core composition search within advanced nuclear reactor cores. The development of MocDown focused on facilitating both fast runtime (by employing concurrent threading and efficient regex parsing when possible) and fast post-processing (with simple and consistent hierarchical storage of result files). MocDown also employs object-oriented programming in Python 3 for flexible modification with external libraries.

To do so, MocDown couples three models for self-consistent simulations: thermo-fluids, neutron transport, and transmutation and recycling. The MocDown accelerated recycling scheme efficiently finds the equilibrium cycle, whose isotopic composition matches that of its successor. Using these techniques, MocDown has been successfully used to simulate the RBWR-Th design, a fuel-self-sustaining nuclear reactor core design which operates with only thorium as its charge.

Adjoint-based uncertainty quantification in multiphysics reactor modeling

Manuele Aufiero, Michael Martin, Massimiliano Fratoni

Coupled neutronics-thermal/hydraulics simulations are of great interest for the analysis and design of nuclear reactors. Ongoing studies of advanced and GEN-IV reactors call for the adoption of accurate modeling tools that are based on Monte Carlo neutron transport and CFD-based T/H solutions. In this framework, the capability to propagate uncertainties in the input data through the coupled simulation is highly desirable.

Recently, Generalized Perturbation Theory (GPT) methods have been implemented in continuous energy Monte Carlo codes, broadly expanding their capabilities. Some of these methods (e.g., available in the Serpent code) are suitable to be adopted in combination with Open Source finite-volume libraries for continuum mechanics solvers (e.g., the OpenFOAM C++ multiphysics toolkit).

The present project involves the projection of the input uncertainties and the reactor generalized responses onto sets of orthogonal basis functions, along with the adoption of extended GPT methods for the calculation of sensitivities in the coupled problems. The comparison of nuclear data uncertainty propagation results against standard methods in simple benchmark cases shows that the new approach might provide a reliable and efficient option for Uncertainty Quantification in multiphysics problems.