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Inverse Mapping of the Collision Kernel and Wall Flux Scaling in a Tall Convection‐Cloud Chamber Using Local Sensors and Knowledge‐Informed Deep Learning

Droplet collision–coalescence is a crucial process in cloud physics, but accurately representing this process under different dynamical conditions remains challenging. A proposed future convective‐cloud chamber aims to investigate this key process, but the method for observing it remains unclear, even though it is theoretically established that collision‐coalescence will occur. This study serves as a proof‐of‐concept demonstration of how knowledge‐informed deep learning, combined with measurement data from local sensors in the chamber, can be used to estimate the collision kernels, which determine how the droplet size distribution evolves during collision‐coalescence. In addition to estimating the collision kernel, we also address wall fluxes, another uncertain but important process that acts as a source of heat and moisture in the chamber. Ensemble runs of large‐eddy simulations are conducted by scaling the wall fluxes and the collision kernel, while the measured flow and cloud properties are used as inputs for a neural network. Results indicate that this approach successfully maps the scaling of wall fluxes and the collision kernel with biases of approximately 1% or less relative to the range of the target data. This proof‐of‐concept lays the groundwork for future applications; when the real measurements are available, real sensor data combined with the trained model presented in this work will enable estimation of the actual wall fluxes and collision kernel.

cloud chamber

Monte–Carlo ray-tracing studies of multiplexed prismatic graphite analyzers for the cold-neutron triple-axis spectrometer at the High Flux Isotope Reactor

A modern cold triple-axis spectrometer to study quantum condensed matter systems is planned for the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. Here, we describe the conceptual principles and design of a secondary spectrometer using a multiplexed, prismatic analyzer system relying on graphite crystals and inspired by the successful implementation of the Continuous Angle Multiple Energy Analysis (CAMEA) spectrometers at the Paul Scherrer Institute. This project is currently known as MANTA for Multi-Analyzer Neutron Triple-Axis. Here, we report Monte-Carlo ray-tracing simulations on a simple but realistic sample scattering kernel to further illustrate the prismatic analyzer concept’s workings, calibration, and performance. Then, we introduce a new statistical analysis approach based on the prismatic analyzer concept to improve the number of final energies measured on the spectrometer. We also study possible evolutions in the CAMEA design relevant for MANTA.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

On nonlocal problems with Neumann boundary conditions: scaling and convergence for nonlocal operators and solutions

Formulations of Neumann-type boundary conditions for boundary value problems in the nonlocal framework are beset with difficulties, some related to the choice of a proper scaling. Here we identify a space-dependent scaling for a nonlocal Neumann operator, for which we prove linear in δ (δ being the radius for the support for the kernel) convergence of the Neumann operator and $\mathcal{O}$(δ 2 ) convergence of solutions to their classical counterparts. The pointwise-like convergence of the nonlocal normal operator is cast as a new type of two-scale operator-point convergence, which we call condensated convergence . The results hold for general integrable kernels, a setting which is favored in numerical simulations. We support this analysis with numerical convergence studies using a piecewise linear discontinuous Galerkin discretization and show an $\mathcal{O}$(δ 2 ) rate of convergence of solutions, also exhibiting an $\mathcal{O}$(h 2 ) convergence, where h is the mesh size.

97 MATHEMATICS AND COMPUTING

"Source Term Modeling for Advanced Gas Micro-Reactors"

Maintaining the safety of the public, environment, and operating personnel is the most important factor in designing, operating, maintaining, and decommissioning nuclear reactors. In recent years, there has been a growing interest in the development of micro-reactors employing TRi-structural ISOtropic (TRISO)-coated particle fuel. In gas reactors, TRISO fuel plays an important role in the safety case for high temperature reactors because of the fission product retention properties of the fuel. This ability enables the use of a functional containment strategy for the reactor where multiple barriers are used to prevent fission product release to the environment. Part of the safety analysis of these advanced reactors is the assessment of radionuclide releases under normal and accident conditions through the multiple credited safety barriers. Using conservative assumptions, a mechanistic analysis can be performed to quantify these releases that combines the probabilistic assessment of failure with analytic solutions to radionuclide transport equations. Source term modeling for TRISO fuel has been performed for previous reactor designs; however, these models are outdated, in many cases proprietary, and need updates to be applied to the current state of TRISO fuel technology and alternative gas reactor core configurations [1]. Currently, the only publicly available source term assessment for gas reactors is an expert-based Monte Carlo simulation based on the effectiveness of the fuel kernel, coating layers, and graphite block in a modular high temperature gas reactor [2]. Thus, there is a need to develop a simple, versatile, and mechanistic model of fission product release and transport in gas reactor cores that could be applied to a variety of reactors through user inputs and reactor-specific radionuclide inventories. The release is calculated by the diffusion of the key safety important fission products through the kernel, silicon carbide (SiC), graphite for both intact and defective TRISO particles based on fuel and graphite temperatures in the reactor under normal operation. These releases from the fuel enter the coolant where they can plate-out on cooler surfaces. A clean-up model is included for designs with a coolant purification system to remove fission gases. This initial distribution of fission products in the reactor serves as an initial condition for potential releases under postulated accident conditions. The model then can calculate the fission product release for any transient temperature profile and fission product releases can then be used to assess radiological dose to the workers and the public using conventional dose tools. Data on the diffusion of fission products is based on historic German TRISO experiments and the more current Department of Energy (DOE) Advanced Gas Reactor (AGR) TRISO fuel development program. The model is coded in python with inputs and outputs in excel spreadsheets, as well as python plotting utilities to aid in the interpretation of the results. References: [1] INL, NGNP Mechanistic Source Term White Paper, INL-10-17997, July 2010. [2] David A. Petti, Richard R. Hobbins, Peter Lowry, Hans Gougar, “Representative Source Terms and The Influence of Reactor Attributes on Functional Containment in Modular High Temperature Gas-cooled Reactors,” Nuclear Technology, Vol. 184, p. 181-197, Nov. 2013.

07 ISOTOPE AND RADIATION SOURCES

Convolution-controlled rotation and scale invariance in optical correlation

A method is presented for evoking a controlled, continuously-variable degree of rotation- and scale-invariance in optical correlation; the method is suitable for off-line computation of filters, though not for real-time computation. While a closed-form solution for the blur kernels has thus far evaded solution, a digital approximation method has been presented. A simulated correlation run with real, frame-grabbed imagery has indicated the method's desired performance. These Gaussian blur kernels can be replaced with box-car kernels or other blur kernels suitable for the given correlation-task.

Juday, Richard D.

Assessment of buffer-IPyC thermomechanical debonding behavior using new experimental strength data in BISON

TRIstructural ISOtropic (TRISO) fuel is a nuclear fuel commonly used in High Temperature Gas-cooled Reactors (HTGRs). A single sub-millimeter-diameter TRISO fuel particle consists of a spherical fuel kernel surrounded by four coating layers: a low-density pyrocarbon buffer layer, an inner pyrolytic carbon (IPyC) layer, a silicon carbide (SiC) layer, and an outer pyrolytic carbon (OPyC) layer. The kernel is commonly made of UO2 or a mixture of uranium carbide and uranium oxide (UCO). During reactor operation, the TRISO coating layers are subjected to irradiation-induced dimensional changes and the associated thermomechanical behavior of each layer. One of the observed behaviors is gap formation between the buffer and IPyC layer due to the porous buffer’s irradiation-induced shrinkage exceeding that of the IPyC layer. Not all irradiated particles will experience buffer-IPyC gap formation. The debonding may be partial, or it may be nearly total. However, from post-irradiation examination of UCO TRISO fuels irradiated as part of the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program, it was concluded that partial buffer-IPyC debonding was the most common type of buffer-IPyC interaction. To predict TRISO thermomechanical performance, multi-physics models have been built that are being continually updated and refined. The BISON code is a finite element-based nuclear fuel performance code that may be used for 1D, 2D, and 3D TRISO particle simulations. This code is used to calculate fuel temperature, kernel swelling, buffer densification, thermal and irradiation creep, fracture, and fission gas production and release. One of the recent additions to the BISON code is the ability to model the process of layer debonding. This paper will focus on the simulation results of the improved BISON debonding model that will utilize updated strengths measured from irradiated AGR TRISO fuel particles. The new experimental strength data from micromechanical tests of irradiated TRISO fuel samples were exercised in the BISON simulations and compared to baseline strength data to assess their applicability in the models. This also includes updated buffer-IPyC bond strengths to simulate layer delamination. Based on current experimental observations it is noted that the buffer-IPyC separation occurs not exactly at the junction of these two layers, but more on the side of the buffer layer. That observation is also implemented in the TRISO interface debonding model. This improved modeling approach using experimental strength data to characterize buffer-IPyC debonding and its potential subsequent cracking will be presented in the paper along with comparisons to available experimental observations.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Improved Weld Residual Stress Modeling System in BlackBear

This report presents enhancements to the MOOSE-based BlackBear application aimed at improving its capability to simulate welding and other thermo-mechanical manufacturing processes. Two primary avenues of improvement are pursued. First, to enhance user accessibility, we introduce a centralized default block restriction mechanism that ensures coverage checks are performed within user-specified default blocks. This default setting is applied consistently to all block-describable objects, such as variables, kernels, and more. In addition, we develop a modular action for moving heat source simulations, which integrates path file parsing, subdomain modification, and heat source kernel enforcement into a single, streamlined configuration. Second, to improve solver robustness, we implement an alternative method for assigning initial conditions to the updated active domain during the simulation, thereby enhancing convergence behavior. To validate the framework, we design and conduct several benchmark simulations, including heat conduction with progressive material addition, linear elasticity with time-dependent material deposition, and viscoplasticity model with isotropic hardening under similar conditions. Finally, we demonstrate the effectiveness of the proposed framework through large-scale thermo-mechanical welding simulations in both two and three dimensions.

42 ENGINEERING

Accelerating magnonic simulations with the pseudospectral Landau-Lifshitz equation

The pseudospectral Landau-Lifshitz (PS-LL) model can describe atomic-scale magnetic exchange interactions within a continuum framework. This is achieved by employing a convolution kernel that models the nonlocal interaction in a grid-independent manner. Even though the PS-LL was originally introduced to address atomic exchange, any nonlocal kernel can be modeled. In the field of magnonics, the dipole field is fundamental to describe the dispersion relation of magnons, the quasiparticle representation of angular momentum. Because dipole-dipole interactions are long-range, numerical approaches typically rely on convolutions. Here, we demonstrate that the PS-LL model can be used to perform magnonic simulations with a single convolution kernel derived from analytical solutions. We demonstrate a twofold increase in computational speed compared with the full dipole calculation. This approach is valid insofar as the excitations are linear, which is typically the case for magnons. Our results have the potential to accelerate magnonic research, particularly for the inverse design method, where several simulations must be performed to achieve the desired outcome.

Mathematics and computing

Radiation effects induced in pin photodiodes by 40- and 85-MeV protons

PIN photodiodes were bombarded with 40- and 85-MeV protons to a fluence of 1.5 x 10 to the 11th power p/sq cm, and the resulting change in spectral response in the near infrared was determined. The photocurrent, dark current and pulse amplitude were measured as a function of proton fluence. Changes in these three measured properties are discussed in terms of changes in the diode's spectral response, minority carrier diffusion length and depletion width. A simple model of induced radiation effects is presented which is in good agreement with the experimental results. The model assumes that incident protons produce charged defects within the depletion region simulating donor type impurities.

Becher, J.

Optimal focal-plane restoration

Image restoration can be implemented efficiently by calculating the convolution of the digital image and a small kernel during image acquisition. Processing the image in the focal-plane in this way requires less computation than traditional Fourier-transform-based techniques such as the Wiener filter and constrained least-squares filter. Here, the values of the convolution kernel that yield the restoration with minimum expected mean-square error are determined using a frequency analysis of the end-to-end imaging system. This development accounts for constraints on the size and shape of the spatial kernel and all the components of the imaging system. Simulation results indicate the technique is effective and efficient.

Reichenbach, Stephen E.

Scheduling message processing for reducing rollback propagation

Traditional checkpointing and rollback recovery techniques for parallel systems have typically assumed the communication pattern is specified by program behavior. In this paper we exploit the property that the communication pattern can often be changed at run-time without affecting program correctness. A scheduling algorithm for message processing and its implementation for reducing rollback propagation are described. The algorithm incorporates a user-transparent prioritized scheme based upon the run-time communication and checkpointing history. Communication trace-driven simulation for several parallel programs written in the Chare Kernel language demonstrates that the probability of rollback propagation can be reduced at the cost of slight additional performance degradation.

Wang, Yi-Min

Comparison of Clouds and Cloud Feedback between AMIP5 and AMIP6

We examine the changes in clouds and cloud feedback between Phase 5 (AMIP5) and Phase 6 (AMIP6) of the Atmospheric Model Intercomparison Project. Each model is perturbed by uniformly increasing the sea surface temperature by 4 K. The simulated cloud fraction, the perturbed states and cloud radiative kernels are used to derive cloud feedback in the shortwave (SW), longwave (LW) and their sum (Net). Compared to AMIP5, the cloud fraction in AMIP6 increases by 9.1%, while the perturbation leads to a 0.25% decrease. The Net cloud feedback at the top of the atmosphere (TOA) is almost double (174%). Statistical tests support that this change is mainly due to an increase in the surface SW cloud feedback caused by optically thick, middle and low clouds. The contribution of the atmospheric Net component (12%) stems from the increase in the atmospheric LW cloud feedback, likely to play a role in weakening (strengthening) the northward (southward) meridional atmospheric energy transport, while the opposite is true for the surface LW and Net cloud feedback in the meridional oceanic energy transport. The substantial increase in cloud feedback at the TOA primarily contributes to the higher climate sensitivity. The cloud feedback spread in AMIP6 is comparable to that in AMIP5.

Clouds

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING

GPU Accelerated Sparse Cholesky Factorization

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a Cholesky factorization of the coefficient matrix is performed using a right-looking approach and the resulting triangular factors are used to compute the solution. Sparse Cholesky factorization is compute intensive. In this work we investigate techniques for reducing the factorization time in sparse Cholesky factorization by offloading some of the dense matrix operations on a GPU. We will describe the techniques we have considered. We achieved up to 4x speedup compared to the CPU-only version.

Karsavuran, M Ozan

Nonparametric probability density estimation by optimization theoretic techniques

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

Scott, D. W.

Liquid–Vapor Phase Equilibrium in Molten Aluminum Chloride (AlCl 3 ) Enabled by Machine Learning Interatomic Potentials

Molten salts are promising candidates in numerous clean energy applications, where knowledge of thermophysical properties and vapor pressure across their operating temperature ranges is critical for safe operations. Due to challenges in evaluating these properties using experimental methods, fast and scalable molecular simulations are essential to complement the experimental data. In this study, we developed machine learning interatomic potentials (MLIP) to study the AlCl 3 molten salt across varied thermodynamic conditions (T = 473–613 K and P = 2.7–23.4 bar), which allowed us to predict temperature-surface tension correlations and liquid–vapor phase diagram from direct simulations of two-phase coexistence in this molten salt. Two MLIP architectures, a Kernel-based potential and neural network interatomic potential (NNIP), were considered to benchmark their performance for AlCl 3 molten salt using experimental structure and density values. The NNIP potential employed in two-phase equilibrium simulations yields the critical temperature and critical density of AlCl 3 that are within 10 K (∼3%) and 0.03 g/cm 3 (∼7%) of the reported experimental values. An accurate correlation between temperature and viscosities is obtained as well. In doing so, we report that the inclusion of low-density configurations in their training is critical to more accurately represent the AlCl 3 system across a wide phase-space. The MLIP trained using PBE-D3 functional in the ab initio molecular dynamics (AIMD) simulations (120 atoms) also showed close agreement with experimentally determined molten salt structure comprising Al 2 Cl 6 dimers, as validated using Raman spectra and neutron structure factor. Furthermore, the PBE-D3 as well as its trained MLIP showed better liquid density and temperature correlation for AlCl 3 system when compared to several other density functionals explored in this work. Overall, the demonstrated approach to predict temperature correlations for liquid and vapor densities in this study can be employed to screen nuclear reactors-relevant compositions, helping to mitigate safety concerns.

Ab initio molecular dynamics

Shock Hugoniot calculations using on-the-fly machine learned force fields with ab initio accuracy

We present a framework for computing the shock Hugoniot using on-the-fly machine learned force field (MLFF) molecular dynamics simulations. In particular, we employ an MLFF model based on the kernel method and Bayesian linear regression to compute the free energy, atomic forces, and pressure, in conjunction with a linear regression model between the internal and free energies to compute the internal energy, with all training data generated from Kohn–Sham density functional theory (DFT). We verify the accuracy of the formalism by comparing the Hugoniot for carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that Kohn–Sham calculations for the Hugoniot can be accelerated by up to two orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the Hugoniots of 14 materials in the FPEOS database, comprising 9 single elements and 5 compounds, between temperatures of 10 kK and 2 MK. We find good agreement with first principles results in the literature while providing tighter error bars. In addition, we confirm that the inter-element interaction in compounds decreases with temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Simulations of classical three-body thermalization in one dimension

One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V ij ∝ 1/|x i –x j | n or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ 2 ⁢T$\frac{1}{2}$ – $\frac{1}{n}$, where ρ is the number density. Furthermore, the corresponding proportionality constant decreases with increasing n.

1-dimensional systems