J. Nucl. Eng., Volume 2, Issue 2 (June 2021) – 11 articles

Use of the quasistatic (k_eff) approximation for producing steady-state solutions for non-critical fission systems is known to result in an imbalance between energy release and deposition within the system. In this paper, we formally quantify this imbalance and present a self-consistent energy normalization technique that preserves nuclear energy release per reaction, as well as enforces energy balance between release and deposition mechanisms, regardless of the criticality state of the system. The proposed technique is straightforward to implement in any type of transport solver through the use of a simple energy rebalance factor. Theoretical and numerical results are presented that demonstrate the energy deposition bias for non-critical systems and the effectiveness of the proposed energy normalization technique. Full article

In this paper, the conceptual design and a preliminary study of the LUT Heating Experimental Reactor (LUTHER) for 2 MWth power are presented. Additionally, commercially sized designs for 24 MWth and 120 MWth powers are briefly discussed. LUTHER is a scalable light-water pressure-channel reactor designed to operate at low temperature, low pressure, and low core power density. The LUTHER core utilizes low enriched uranium (LEU) to produce low-temperature output, targeting the district heating demand in Finland. Nuclear power needs to contribute to the decarbonizing of the heating and cooling sector, which is a much more significant greenhouse gas emitter than electricity production in the Nordic countries. The main principle in the development of LUTHER is to simplify the core design and safety systems, which, along with using commercially available reactor components, would lead to lower fabrication costs and enhanced safety. LUTHER also features a unique design with movable individual fuel assembly for reactivity control and burnup compensation. Two-dimensional (2D) and three-dimensional (3D) fuel assemblies and reactor cores are modeled with the Serpent Monte Carlo reactor physics code. Different reactor design parameters and safety configurations are explored and assessed. The preliminary results show an optimal basic core design, a good neutronic performance, and the feasibility of controlling reactivity by moving fuel assemblies. Full article

Artificial neural networks (ANNs) for performing spectroscopic gamma-ray source identification have been previously introduced, primarily for applications in controlled laboratory settings. To understand the utility of these methods in scenarios and environments more relevant to nuclear safety and security, this work examines the use of ANNs for mobile detection, which involves highly variable gamma-ray background, low signal-to-noise ratio measurements, and low false alarm rates. Simulated data from a 2” × 4” × 16” NaI(Tl) detector are used in this work for demonstrating these concepts, and the minimum detectable activity (MDA) is used as a performance metric in assessing model performance.In addition to examining simultaneous detection and identification, binary spectral anomaly detection using autoencoders is introduced in this work, and benchmarked using detection methods based on Non-negative Matrix Factorization (NMF) and Principal Component Analysis (PCA). On average, the autoencoder provides a 12% and 23% improvement over NMF- and PCA-based detection methods, respectively. Additionally, source identification using ANNs is extended to leverage temporal dynamics by means of recurrent neural networks, and these time-dependent models outperform their time-independent counterparts by 17% for the analysis examined here. The paper concludes with a discussion on tradeoffs between the ANN-based approaches and the benchmark methods examined here. Full article

The spreading-solidification behaviour of the stratified molten metals was investigated. This is important in understanding the practical fuel debris distribution spread and solidified in the primary containment vessel (PCV) of Fukushima Daiichi Nuclear Power Plants (1F NPPs). In this study, the effect of outflow diameter on the material distribution before discharging was studied both experimentally and numerically. The two simulant metals were chosen so that the density ratio could be similar to the practical fuel and structure elements of the plant. They were arranged in a vessel and discharged on a receiving plate. The spreading experiments were performed using various outlet diameters with a density and reverse density stratification arrangement. After the experiment, X-ray analysis was performed to evaluate the material distribution in the solidified material. Moreover, a numerical analysis was performed to reveal the mechanisms that affect the material distribution after solidification. As a result, the low-density metal accumulated at the centre region regardless of the outlet diameters in the density stratification. In contrast, the outlet diameters affected the material distribution in the reverse density stratification because they affected the material outflow order. These findings may help increase our understanding of the fuel debris distribution in 1F NPPs. Full article

Functional expansion has been rigorously studied as a promising method in stochastic neutron transport and multi-physics coupling. It is a method to represent data specified on a desired domain as an expansion of basis set in a continuous manner. For convenience, the basis set for functional expansion is typically chosen to be orthogonal. In cylindrical PWR pin-cell simulations, the orthogonal Zernike polynomials have been used. The main advantage of using functional expansion in nuclear modeling is that it requires less memory to represent temperature and nuclide variations in fuel then using a fine discretization. Fewer variables are involved in the data storage and transfer process. Each nuclide can have its unique expansion order, which becomes very important for depletion problems. In a recent study, performance analysis was conducted on Zernike-based FETs on a 2D PWR geometry. For reaction rates like the absorption rate of U-238, however, many orders are needed with Zernike-based FETs to achieve a reasonable accuracy. This gap inspires the study in this paper on alternative basis set that can better capture the steep gradient with fewer orders. In this paper, a generalized functional expansion method is established. The basis set can be an arbitrary series of independent functions. To capture the self-shielding effect of U-238 absorption rate, an exponential basis set is chosen. The results show that the expansion order utilizing exponential basis can reduce by half of that from using orthogonal Zernike polynomials while achieving the same accuracy. The integrated reaction rate is also demonstrated to be preserved. This paper also shows that the generalized functional expansion could be a heuristic method for further investigation on continuous depletion problems. Full article

Modal expansions based on k-eigenvalues and α-eigenvalues are commonly used in order to investigate the reactor behaviour, each with a distinct point of view: the former is related to fission generations, whereas the latter is related to time. Well-known Monte Carlo methods exist to compute the direct k or α fundamental eigenmodes, based on variants of the power iteration. The possibility of computing adjoint eigenfunctions in continuous-energy transport has been recently implemented and tested in the development version of TRIPOLI-4^®, using a modified version of the Iterated Fission Probability (IFP) method for the adjoint α calculation. In this work we present a preliminary comparison of direct and adjoint k and α eigenmodes by Monte Carlo methods, for small deviations from criticality. When the reactor is exactly critical, i.e., for k₀ = 1 or equivalently α₀ = 0, the fundamental modes of both eigenfunction bases coincide, as expected on physical grounds. However, for non-critical systems the fundamental k and α eigenmodes show significant discrepancies. Full article

The thermal scattering law (TSL), i.e., S(α,β), represents the momentum and energy exchange phase space for a material. The incoherent and coherent components of the TSL correlate an atom’s trajectory with itself and/or with other atoms in the lattice structure. This structural information is especially important for low energies where the wavelength of neutrons is on the order of the lattice interatomic spacing. Both thermal neutron scattering as well as low energy resonance broadening involve processes where incoming neutron responses are lattice dependent. Traditionally, Doppler broadening for absorption resonances approximates these interactions by assuming a Maxwell–Boltzmann distribution for the neutron velocity. For high energies and high temperatures, this approximation is reasonable. However, for low temperatures or low energies, the lattice structure binding effects will influence the velocity distribution. Using the TSL to determine the Doppler broadening directly introduces the material structure into the calculation to most accurately capture the momentum and energy space. Typically, the TSL is derived assuming cubic lattice symmetry. This approximation collapses the directional lattice information, including the polarization vectors and associated energies, into an energy-dependent function called the density of states. The cubic approximation, while valid for highly symmetric and uniformly bonded materials, is insufficient to capture the true structure. In this work, generalized formulation for the exact, lattice-dependent TSL is implemented within the Full Law Analysis Scattering System Hub (FLASSH) using polarization vectors and associated energies as fundamental input. These capabilities are utilized to perform the generalized structure Doppler broadening analysis for UO₂. Full article

This paper illustrates the relative importance of the largest first- and second-order sensitivities of the leakage response of an OECD/NEA reactor physics benchmark (a polyethylene-reflected plutonium sphere) to the benchmark’s underlying total cross sections. It will be shown that numerous 2nd-order sensitivities of the leakage response with respect to the total cross sections are significantly larger than the largest corresponding 1st-order sensitivities. In particular, the contributions of the 2nd-order sensitivities cause the mean (expected) value of the response to differ appreciably from its computed value and also cause the response distribution to be skewed towards positive values relative to the mean. Neglecting these large 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response’s variance and expected value. The results presented in this paper also underscore the need for obtaining reliable cross section covariance data, which are currently unavailable. Finally, comparing the CPU-times needed for computations, this paper demonstrates that the Second-Order Adjoint Sensitivity Analysis Methodology is the only practical method for computing 2nd-order sensitivities exactly, without introducing methodological errors, for large-scale systems characterized by many uncertain parameters. Full article

Zirconium hydride (ZrH_x) is a moderator material used in TRIGA and other reactors that may exist in multiple phases with varying stoichiometry, which include the $\delta$ phase and the $ϵ$ phase. Current ENDF/B-VIII.0 ZrH_x thermal scattering law (TSL) evaluations do not distinguish between phases. These sub-libraries were generated with the LEAPR module of NJOY using historic phonon spectra derived from a central force model and assume incoherent elastic scattering for both bound hydrogen and zirconium, which neglects the effects of crystal structures important for scattering from zirconium bound in ZrH_x. In this work, the TSLs for hydrogen and zirconium bound in $\delta$-ZrH_x and $ϵ$-ZrH₂ were generated from phonon spectra derived from modern ab initio lattice dynamics methods and ab initio molecular dynamics. Subsequently, TSLs for hydrogen and zirconium in ZrH_x and ZrH₂ were generated using the Full Law Analysis Scattering System Hub (FLASSH) code. The built-in generalized coherent elastic routine was used to generate the previously neglected elastic contribution from zirconium for this material. The present TSLs provide both a re-evaluation of the current ZrH sub-libraries and expansion of the set of TSLs available for the examination of neutrons in systems with zirconium hydride, permitting explicit treatment of $\delta$ and $ϵ$ phases. Full article

A study was performed to determine which transport events should be used to initiate a weight window lookup to achieve the best variance reduction performance. A weight window lookup potentially triggers particle splitting (in important regions of phase space) or rouletting (in unimportant regions), thereby optimizing computational effort. Potential initiating transport events include collisions (both pre- and post-collision), geometry surface crossings, traversing a mean-free path, and streaming across a weight window boundary. Permutations of these initiating events were tested on an urban model with background radiation sources and a spent fuel cask with a neutron dose mesh tally. Generally, all methods perform better with finer weight window meshes. Tracking on weight windows performs well for coarse weight window meshes, while a combination of splitting each mean-free path, geometric surface crossing, and before collisions performs well for fine weight window meshes. Full article