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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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49 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form is based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Development of tearing instability in a current sheet forming by sheared incompressible flow

Sweet–Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it forms. Formation can occur due to sheared, sub-Alfvénic incompressible flows which narrow the sheet. Standard tearing theory is not immediately applicable to such forming sheets for two reasons: first, because the flow introduces terms not present in the standard calculation; second, because the changing equilibrium introduces time dependence to terms which are constant in the standard calculation, complicating the formulation of an eigenvalue problem. This paper adapts standard tearing mode analysis to confront these challenges. In an initial phase when any perturbations are primarily governed by ideal magnetohydrodynamics, a coordinate transformation reveals that the flow compresses and stretches perturbations. Here, a multiple scale formulation describes how linear tearing mode theory can be applied to an equilibrium changing under flow, showing that the flow affects the separable exponential growth only implicitly, by making the standard scalings time dependent. In the nonlinear Rutherford stage, the coordinate transformation shows that standard theory can be adapted by adding to the stationary rates time dependence and an additional term due to the strengthening equilibrium magnetic field. Overall, this understanding supports the use of flow-free scalings with slight modifications to study tearing in a forming sheet.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Development of Tearing Instability in a Current Sheet Forming by Sheared Incompressible Flow

Sweet-Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it forms. Formation can occur due to sheared, sub-Alfvenic incompressible flows which narrow the sheet. Standard tearing theory (Furth et al. 1963; Coppi et al. 1976; Rutherford 1973) is not immediately applicable to such forming sheets for two reasons: first, because the flow introduces terms not present in the standard calculation; second, because the changing equilibrium introduces time dependence to terms which are constant in the standard calculation, complicating the formulation of an eigenvalue problem. This paper adapts standard tearing mode analysis to confront these challenges. In an initial phase when any perturbations are primarily governed by ideal MHD, a coordinate transformation reveals that the flow compresses and stretches perturbations. A multiple scale formulation describes how linear tearing mode theory (Furth et al. 1963; Coppi et al. 1976) can be applied to an equilibrium changing under flow, showing that tearing eigenfunctions grow slowly due to the flow and undergo exponential growth at a rate given by standard scalings with time dependence added. In the nonlinear Rutherford stage, the coordinate transformation shows that standard theory can be adapted by adding to the stationary rates time dependence and an additional term due to the strengthening equilibrium magnetic field. Overall, this understanding supports the use of flow-free scalings with slight modifications to study tearing in a forming sheet.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Robust Predictive Control for Modular Solid-State Transformer With Reduced DC Link and Parameter Mismatch

This paper presents the analysis and implementation of a predictive control method for dc-link regulation and voltage balance in a cascaded modular reduced dc-link solid-state transformer (SST). Passive components like bulky dc links limit the power density of power converters, especially medium-voltage (MV) SST. Reduced dc-link or low-inertia converters can dramatically reduce the size, cost, and weight by tolerating larger dc-link ripples and improve the reliability with electrolytic capacitor-less dc link. However, a small dc link leads to tight coupling between the input and the output stages, which is a challenge for control design. In stacked low-inertia converters (SLIC), the low-inertia converter modules are stacked for MV applications, resulting in coupling between the modules and making the control more challenging. A new model predictive control method which can achieve deadbeat regulation on the dc link without weighting factors has been proposed to address this novel problem. This paper focuses on analyzing the condition of the low-inertia dc link up to 80% ripple, the robustness of the control under parameter mismatches, high-order terms, and important implementation issues such as model-based sampling and computation delay compensation. Significantly, the high-order terms are introduced because of the large dc-link ripple. These high-order terms are unique to the SLIC and negligible in conventional high-inertia converters. A discrete-time large-signal model is built to capture the dc-link’s nonlinear dynamics, and the eigenvalues of a small-signal Jacobian matrix are analyzed with Floquet theory to evaluate stability, using the modular soft-switching solid-state transformer (M-S4T) as an example of the SLIC. Simulation and experimental results of an MVDC M-S4T verify the analysis and the predictive control method. Finally, the general application of the predictive control to low-inertia converters is compared against a conventional PI controller using a reduced dc-link active-front-end (AFE) rectifier as an example.

14 SOLAR ENERGY↗
DOE OSTI2024

Geometric Interpretation of a Non-Linear Extension of Quantum Mechanics

We recently introduced a particular non-linear generalization of quantum mechanics that has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. In this paper, we suggest that the two components of the wave function represent the system described by the Hamiltonian H in two different asymptotic regions of spacetime and we show that the non-linear terms can be viewed as giving rise to gravitational effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Quantization of the Electromagnetic Field in Three-Dimensional Photonic Structures on the Basis of the Scattering Matrix Formalism (S Quantization)

A technique for quantization of the electromagnetic field in photonic nanostructures with three-dimensional modulation of the dielectric constant is developed on the basis of the scattering matrix formalism (S quantization in the three-dimensional case). Quantization is based on equating the eigenvalues of the scattering matrix to unity, which is equivalent to equating each other the sets of Fourier expansions for the fields of the waves incident on the structure and propagating away from the structure. The spatial distribution of electromagnetic fields of the modes in a photonic nanostructure is calculated on the basis of the R and T matrices describing the reflection and transmission of the Fourier components by the structure. To calculate the reflection and transmission coefficients of individual real-space and Fourier-space components, the structure is divided into parallel layers within which the dielectric constant varies as a function of two-dimensional coordinates. Using the Fourier transform, Maxwell’s equations are written in the form of a matrix connecting the Fourier components of the electric field at the boundaries of neighboring layers. Based on the calculated reflection and transmission vectors for all polarizations and Fourier components, the scattering matrix for the entire structure is formed and quantization is carried out by equating the eigenvalues of the scattering matrix to unity. The developed method makes it possible to obtain the spatial profiles of eigenmodes without solving a system of nonlinear integro-differential equations and significantly reduces the computational resources required for calculating the probability of spontaneous emission in three-dimensional systems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Insights on the Effects of Magnetic Forces on the Efficiency of Vibration Energy Harvesting Absorbers in Controlling Dynamical Systems

This study investigates the effects of magnetic constraints on a piezoelectric energy harvesting absorber while simultaneously controlling a primary structure and harnessing energy. An accurate forcing representation of the magnetic force is investigated and developed. A reduced-order model is derived using the Euler–Lagrange principle, and the impact of the magnetic force is evaluated on the absorber’s static position and coupled natural frequency of the energy harvesting absorber and the coupled primary absorber system. The results show that attractive magnet configurations cannot improve the system substantially before pull-in occurs. A rigorous eigenvalue problem analysis is performed on the absorber’s substrate thickness and tip mass to effectively design an energy harvesting absorber for multiple initial gap sizes for the repulsive configurations. Then, the effects of the forcing amplitude on the primary structure absorber are studied and characterized by determining an effective design of the system for a simultaneous reduction in the primary structure’s motion and improvement in the harvester’s efficiency.

42 ENGINEERING↗
DOE OSTI2023

Drude weights in one-dimensional systems with a single defect

Ballistic transport of a quantum system can be characterized by Drude weight, which quantifies the response of the system to a uniform electric field in the infinitely long timescale. The Drude weight is often discussed in terms of the Kohn formula, which gives the Drude weight by the derivative of the energy eigenvalue of a finite-size system with the periodic boundary condition in terms of the Aharonov-Bohm flux. Recently, the Kohn formula is generalized to nonlinear responses. However, the nonlinear Drude weight determined by the Kohn formula often diverges in the thermodynamic limit. In order to elucidate the issue, in this work we examine a simple example of a one-dimensional tight-binding model in the presence of a single defect at zero temperature. We find that its linear and nonlinear Drude weights given by the Kohn formula (i) depend on the Aharonov-Bohm flux and (ii) diverge proportionally to a power of the system size. Here, we argue that the problem can be attributed to different order of limits. The Drude weight according to the Kohn formula (“Kohn-Drude weight”) indicates the response of a finite-size system to an adiabatic insertion of the Aharonov-Bohm flux. While it is a well-defined physical quantity for a finite-size system, its thermodynamic limit does not always describe the ballistic transport of the bulk. The latter should be rather characterized by a “bulk Drude weight” defined by taking the thermodynamic limit first before the zero-frequency limit. While the potential issue of the order of limits has been sometimes discussed within the linear response, the discrepancy between the two limits is amplified in nonlinear Drude weights. We demonstrate the importance of the low-energy excitations of O(1/L), which are excluded from the Kohn-Drude weight, in regularizing the bulk Drude weight.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

A FLEXIBLE NONLINEAR DIFFUSION ACCELERATION METHOD FOR THE FIRST ORDER EIGENVALUE SN EQUATIONS DISCRETIZED WITH DISCONTINUOUS FEM

This work describes a Nonlinear Diffusion Acceleration (NDA) method for the first order SN equations that discretizes both the transport equation and the associated diffusion system using discontinuous finite elements; the diffusion system is solved on a potentially coarser mesh and with a coarser energy group structure than the SN equations. The developed method differs from current methods by allowing the SN and diffusion system to be discretized with arbitrary FEM bases and by using an additive update of the SN system. The benefit of this capability is extension of the stability region to optically thicker mesh cells and stability without the necessity to underrelax the iterative algorithm. The presented method introduces the notion of consistency of the SN and diffusion solutions and derives suitable definitions of the cross sections, drift vectors, and element face closures. The NDA equations are solved using a Picard iteration scheme. Numerical results are presented for the C5G7 benchmark problem highlighting the effectiveness of the methods when deployed with the diffusion system discretized on the same mesh as the SN system. Additional results are presented for cases where the diffusion system features a coarser mesh, coarser energy group structure, or both, demonstrating its stability and effectiveness in these cases. It is observed that the effectiveness of the NDA method reduces when reducing the resolution of the associated diffusion system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An entropy-based debiasing approach to quantifying experimental coverage for novel applications of interest in the nuclear community

This manuscript proposes a novel information-theoretic approach to the quantification of experimental relevance, i.e., coverage, to achieve optimal data assimilation results for nuclear engineering applications. Specifically, this work posits the need for a new metric, called coverage (q C ) of an application’s quantity of interest, i.e., eigenvalue or power peaking for an advanced reactor concept, defined herein as the theoretically maximum achievable reduction in the quantity’s uncertainty given measurements from a pool of experiments in a manner that is independent of the data assimilation procedure employed. Currently, reduction in a quantity’s uncertainty is strongly biased by the underlying assumptions of the assimilation procedure to account for the under-determined nature of such problems and the similarity criterion employed to identify relevant experiments. To address this challenge, this work has developed a coverage metric, q C , based on mutual information, which establishes a new conceptual framework for assessing coverage, one that is independent of the model parameters and responses degree of variations in both the experimental and application domains, i.e., linear vs non-linear, and their prior uncertainty distributions, i.e., Gaussian vs. non-Gaussian. The q C is an entropic measure capable of addressing coverage for general nonlinear problems with non-Gaussian uncertainties and inclusive of the measurement uncertainties from multiple experiments. Numerical experiments from manufactured analytical problems as well as a set of benchmarks from the ICSBEP handbook are employed to demonstrate its theoretical and practical performance as compared to the c k -based experiment selection methodology, commonly employed in the neutronic community. The manuscript then employs other well-known adaptations to existing data assimilation methodologies for nonlinear and non-Gaussian problems capable of achieving the coverage posited by q C .

Bayesian data assimilation↗
DOE OSTI2024

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

Masud, Arif↗
DOE OSTI2017

Proposed Semi-Analytic Benchmark for Coupled Neutronics/Thermal-Hydraulics Feedback in Multiphysics Simulations

The past decade has seen considerable advancements in multiscale and multiphysics simulations that account for nonlinear effects of feedback between different physical processes within a single calculation. One area of particular interest has been multiphysics simulations that include both neutronics and thermal-hydraulics effects to accurately model the thermal feedback effects present in nuclear reactors. During this time, many groups have successfully modeled thermal feedback effects by coupling a variety of different types of neutron transport and thermal-hydraulic solvers together. However, formal verification and validation of these coupled code systems has proven challenging due to a lack of benchmark problems with well-characterized reference solutions. One approach is to confirm gross energy balance using bulk coolant properties (outlet temperature/enthalpy) for code verification purposes. Alternatively, code-to-code comparisons of results for a predefined reference/challenge problem have been used to establish reasonability of local results (neutron flux, heating, enthalpy rise) for various implementations, for example the VERA Core Physics Progression Problems. While community solutions are valuable for assessing the relative performance and fidelity of different implementations, they are not guaranteed to provide a measure of the absolute accuracy of a given implementation. In fact, these code-to-code comparisons can give a false sense of confidence by masking the effects of errors or approximations that are common to all of the solution methods tested. This is a particular concern when many methods derive from a common approach, such as Picard iteration. To this end, an analytical benchmark would be very valuable for verifying individual coupled physics implementations, as well as for providing a formal assessment of algorithm accuracy and sensitivity to model approximations such as mesh size and number of convergence iterations. However, creation of an analytical benchmark is difficult due to the complex nature of the eigenvalue form of the neutron transport equation (which does not permit a simple analytical solution for non-trivial cases) as well as the variety of different empirical closure relationships used in thermal-hydraulic modeling. In this paper we propose a benchmark for coupled neutronics/thermal-hydraulics simulations. The proposed benchmark overcomes the challenges associated with a multiphysics benchmark problem by using a fixed-source (rather than eigenvalue) formulation of the neutron transport equation and limiting fluid properties to the single-phase regime where the density and temperature of the coolant are related to enthalpy by a known relationship, while still preserving significant nuclear/thermal feedback effects within the simplified problem. The new benchmark is easy to simulate using existing coupled physics implementations, and allows for a direct comparison with a reference solution, as provided in this summary.

42 ENGINEERING↗