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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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At least 289 records · Page 16
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DOE OSTI2018

Cyber Network Design for Secondary Frequency Regulation: A Spectral Approach

We present a preliminary theoretical framework based on spectral graph theory that captures how the cyber topology of a distributed secondary frequency control scheme impacts the stability, optimality, and transient performance of our power system as a cyber-physical network. We show that a collection of polynomials defined in terms of the cyber and physical Laplacian eigenvalues encode information on the interplay between cyber and physical networks. It is demonstrated that to understand the impact of adding cyber connectivity, one should separate the low-damping and high-damping regimes. Although adding cyber connectivity always improves the performance for high-damping systems, it is not the case for low-damping scenarios. Based on the theoretical study, we discuss how a good cyber network should be designed. Our empirical study shows that for practical systems, the number of communication channels that is needed to achieve near-optimal performance is usually less than twice the number of buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Two-tier model reduction of viscoelastically damped finite element models

Transient simulations of linear viscoelastically damped structures necessitate critical computational resources to directly integrate the full-order finite element model with time-stepping algorithms. Traditional modal reduction techniques are not directly applicable to these systems since viscoelastic materials depend on time and frequency. A more appropriate reduction basis is obtained from the nonlinear, complex eigenvalue problem, whose eigenvectors capture the appropriate kinematics and enable frequency-based mode selection; unfortunately, the computational cost is prohibitive for computing these modes from large-scale engineering models. To address this shortcoming, this work proposes a novel two-tier reduction procedure to reduce the upfront cost of solving the complex, nonlinear eigenvalue problem. The first reduction step reduces the full-order model with real mode shapes linearized about various centering frequencies to capture the kinematics over a full range of viscoelastic material behavior (glassy, rubbery, and glass-transition zones). This tier-one reduction preserves time-temperature superposition and allows the equations to depend parametrically on operating temperature. The second-level reduction then solves the complex, nonlinear eigenmode solutions in the tier-one reduced space about a fixed temperature to further reduce the equations-of-motion. The method is demonstrated on a cantilevered sandwich plate to display its accuracy and efficiency in comparison to full-order model predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

NRC Multiphysics Analysis Capability Deployment FY2020 - Part 4

This report details progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Sup- port for Advanced Non-Light Water Reactors.” The tasks completed for this report are: • Task 3a: This task demonstrates the effectiveness of Griffin’s methods for interpolating cross sections and SPH correction factors as a function of control drum rotation. The Monte Carlo code Serpent is used to generate reference results. The accuracy of Griffin-calculated eigenvalues and reaction rates are studied as a function of control drum rotation for cross section and SPH factor libraries of varying fidelity. Higher-fidelity libraries require less interpolation and are therefore inherently more accurate; however, they require more computational resources to create. Overall, Griffin is able to accurately model eigenvalue and reaction rates over the full range of drum rotation using a library generated from three to five discrete drum rotations for a particular microreactor design. • Task 3c: This preliminary task successfully demonstrates the performance of a coupled neutron-photon transport calculation with Griffin using the spherical harmonics approximation. The Griffin solutions are compared to reference solutions from the continuous energy Monte Carlo codes MCNP and Serpent. Furthermore, this work also demonstrates how to prepare the neutron and photon libraries using NJOY, MCNP, and Serpent with the latest ENDF/B-VIII data for 235 U and graphite. The Griffin total energy deposition in the active core region is calculated within 0.3% of the reference, but it degrades in the reflector regions with a maximum difference of -1.5%. Overall, the results look promising and future analysis should use an improved data stream and focus on determining the potential cancellation of error within each energy group.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Towards Reconstruction of Complex Flow Fields Using Unit Flows

Many complex turbulent flows in nature and engineering can be qualitatively regarded as being constituted of multiple simpler unit flows. The objective of this work is to characterize the coherent structures in such complex flows as a combination of constituent unitary flow structures for the purpose of reduced-order representation. While turbulence is clearly a non-linear phenomenon, we aim to establish the degree to which the optimally weighted superposition of unitary flow structures can represent the complex flow structures. The rationale for investigating such superposition stems from the fact that the large-scale coherent structures are generated by underlying flow instabilities that may be reasonably described using linear analysis. Clearly, the degree of validity of superposition will depend on the flow under consideration. In this work, we take the first step toward establishing a procedure for investigating superposition. Experimental data of single and triple tandem jets in crossflow are used to demonstrate the procedure. A composite triple tandem jet flow field is generated from optimal superposition of single jet data and compared against ‘true’ triple jet data. Direct comparisons between the true and composite fields are made for spatial, temporal, and kinetic energy content. The large-scale features (obtained from proper orthogonal decomposition or POD) of true and composite tandem jet wakes exhibit nearly 70% agreement in terms of modal eigenvector correlation. Corresponding eigenvalues reveal that the kinetic energy of the flow is also emulated with only a slight overprediction. Temporal frequency features are also examined in an effort to completely characterize POD modes. The proposed method serves as a foundation for more rigorous and robust dimensional reduction in complex flows based on unit flow modes.

Kristo, Paul J.↗
DOE OSTI2023

3D full core BEAVRS using OpenMOC with transport equivalence

Using an optimized implementation of the three-dimension method of characteristics for neutron transport, as well as a novel equivalence method for transport calculations de- signed to recover self-shielding errors from neglecting the angular dependence of reso- nant group absorption, a 3D full core light water reactor hybrid stochastic-deterministic eigenvalue calculation was achieved. This paper presents the optimizations developed and compares the transport solutions obtained. It realizes a runtime near 6,000 CPU hours for the statepoint, an improvement of an order of magnitude on previous works, with less than 1% error on pin fission/U-238 capture ratios and a few dozen pcms on the eigenvalue.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints

Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.

PDE-constrained optimization↗
DOE OSTI2018

Design and convergence analysis of the conforming virtual element method for polyharmonic problems

In the recent years, there has been a tremendous interest to numerical methods that approximate partial differential equations (PDEs) on computational meshes with arbitrarily-shaped polygonal/polyhedral (polytopal, for short) elements. A nonexhaustive list of such methods include the Mimetic Finite Difference method [4, 9, 21, 24, 28, 33, 35, 62, 64–67], the Polygonal Finite Element Method [68, 73, 74], the polygonal Discontinuous Galerkin Finite Element Methods [5, 7, 8, 10, 13–15, 18, 36, 38, 39, 41, 50], the Hybridizable Discontinuous Galerkin and Hybrid High-Order Methods [46–48, 51], the Gradient Discretization method [49, 53, 54], the Finite Volume Method [52], and the BEM-based FEM [71]. An alternative approach that also proved to be very successful is provided by the Virtual Element method (VEM), which was originally proposed in [19] for the numerical treatment of second-order elliptic problems [43, 44], and readily extended to linear and nonlinear elasticity [22, 25, 56], plate bending problems [37], Cahn-Hilliard equation [3], Stokes equations [2], Laplace-Beltrami equation [55], Darcy-Brinkam equation [76], discrete topology optimization problems [6], fracture networks problems [29], eigenvalue problems [59, 75]. The mixed virtual element formulation was proposed in [20, 34]; the nonconforming Virtual element formulations was proposed for second-order elliptic problems in [16], and later extended to general advection-reaction-diffusion problems, Stokes equation, the biharmonic problems, the iegenvalue problem, and the Schrodinger equation in [11, 30, 42, 45, 58, 80]. The p- and hp-version of the VEM were developed in [26, 27] and efficient multigrid methods for the resulting linear system of equations in [12]. A posteriori error estimates can be found in [40].

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The structure and propagation of laminar flames under autoignitive conditions

The laminar flame speed s l is an important reference quantity for characterising and modelling combustion. Experimental measurements of laminar flame speed require the residence time of the fuel/air mixture (τ f ) to be shorter than the autoignition delay time (τ). This presents a considerable challenge for conditions where autoignition occurs rapidly, such as in compression ignition engines. As a result, experimental measurements in typical compression ignition engine conditions do not exist. Simulations of freely propagating premixed flames, where the burning velocity is found as an eigenvalue of the solution, are also not well posed in such conditions, since the mixture ahead of the flame can autoignite, leading to the so called “cold boundary problem”. In this paper, a numerical method for estimating a reference flame speed, s R , is proposed that is valid for laminar flame propagation at autoignitive conditions. Two isomer fuels are considered to test this method: ethanol, which in the considered conditions is a single-stage ignition fuel; and dimethyl ether, which has a temperature-dependent single- or two-stage ignition and a negative temperature coefficient regime for τ. Calculations are performed for the flame position in a one-dimensional computational domain with inflow-outflow boundary conditions, as a function of the inlet velocity U I and for stoichiometric fuel–air premixtures. The response of the flame position, L F , to U I shows distinct stabilisation regimes. For single-stage ignition fuels, at low U I the flame speed exceeds U I and the flame becomes attached to the inlet. Above a critical U I value, the flame detaches from the inlet and L f becomes extremely sensitive to U I until, for sufficiently high U I , the sensitivity decreases and L f corresponds to the location expected from a purely autoignition stabilised flame. The transition from the attached to the autoignition regimes has a corresponding peak dL f /dU I value which is proposed to be a unique reference flame speed s R for single-stage ignition fuels. For two-stage ignition fuels, there is an additional stable regime where a high-temperature flame propagates into a pool of combustion intermediates generated by the first stage of autoignition. This results in two peaks in dL f /dU I and therefore two reference flame speed values. The lower value corresponds to the definition of s R for single-stage ignition fuels, while the higher value exists only for two-stage ignition fuels and corresponds to a high temperature flame propagating into the first stage of autoignition and is denoted s R ' . Finally, a transport budget analysis for low- and high-temperature radical species is also performed, which confirms that the flame structures at U I = s R and U I = s R ' do indeed correspond to premixed flames (deflagrations), as opposed to spontaneous ignition fronts which do not have a unique propagation speed.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Three-Dimensional Full-Core BEAVRS Using OpenMOC with Transport Equivalence

Using an optimized implementation of the three-dimensional (3D) method of characteristics for neutron transport, along with a novel equivalence method for transport calculations that was designed to correct self-shielding errors from neglecting the angular dependence of resonant group absorption, a 3D full-core light water reactor hybrid stochastic-deterministic eigenvalue calculation was achieved. This paper presents the optimizations developed and compares the transport solutions obtained. For the statepoint, run times near 10 000 CPU hours are achieved—improving on previous works by an order of magnitude—with near 1% error on pin fission to 238 U capture ratios and a few dozen pcms on the eigenvalue.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

A Note on the Probability of Initiation Problem

The purpose of this note is to draw attention to Pál for his derivation of the Pál-Bell equation which is used by LLNL and LANL to model Probability of Initiation (POI) problems. Both laboratories credit the equation to Bell and Lee. Although the equation formulated by Bell and Lee and the equation derived by Pál appear to be the same, the equation by Bell and Lee is flawed. Scattering, which was absent in Bell’s original formulation of a POI problem, was later introduced by Bell and Lee by replacing a fission term with a scattering term. Such a replacement, however, leads to an incorrect average number $\overline{v}$ of neutrons that is produced in a fission event. By approaching a POI problem from probabilistic point of view, Pál formulates the problem as a branching process that i) describes the growth of a population of neutrons in a fissile medium, and ii) predicts $\overline{v}$ correctly. There are five reasons for writing this report. The first is to clarify the failing in Bell and Lee’s derivation. The second is to establish the origin of the equation used by the laboratories. The third is to elucidate the fixed point technique formulated by Mokhtar-Kharroubi to solve the Pál-Bell equation. The fourth is to derive the α eigenvalue that is associated with a super-critical situation. The fifth is to describe in the Appendix a second order positivity preserving technique that accelerates the convergence of the first order fixed point method developed by Mokhtar-Kharroubi.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion

This paper presents a novel homogenization equivalence technique aiming to simultaneously leveragethe simplicity of the Super Homogenization (SPH) method to reproduce reference reaction rates andthe ability to preserve reference leakage rates at desired surfaces through Discontinuity Factors (DF).The need for this new class of methods arises from the inability of the current state-of-the-art SPH technology to properly reproduce the reactor multiplication factor for problems with significant leakage. This work shows that this defect lies in the use of normalization factors in the SPH algorithm: while they are necessary with purely reflecting problems to ensure uniqueness of the solution, they introduce homogenization inconsistencies if at least one vacuum boundary condition is present. Two solutions to this problem are presented in this work: (i) to simply remove the normalization factor or (ii) to introduce additional degrees of freedom in the form of DFs in such a way that the normalization factors can still constrain the problem. While the former clearly offers unrivaled simplicity and can lead to very satisfactory results for leakage-dominated cores or if spatial restriction of the SPH regions is applied – as demonstrated for the High Temperature Test Reactor, the latter is more robust and does not require to scale the fission terms with the reference eigenvalue.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Advanced Quantum Poisson Solver in the NISQ era

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental results, and discuss the sources of errors. Finally, we conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.

Robson, Walter↗
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 OSTI2021

Error Bounds for Dynamical Spectral Estimation

Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data. Although the approach has been widely applied in biomolecular simulations, its error properties remain poorly understood. Here we analyze the error of a dynamical spectral estimation method called “the variational approach to conformational dynamics" (VAC). We bound the approximation error and estimation error for VAC estimates. Our analysis establishes VAC's convergence properties and suggests new strategies for tuning VAC to improve accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Properties of coupled-cluster equations originating in excitation sub-algebras

In this paper we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of nilpotent sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending concepts behind actives-spaces and seniority numbers to provide more accurate description of electron correlation effects. Moreover, new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for though cases defined by the presence of strong static and dynamic correlation effects. We will also explore invariance properties associated with the nilpotent sub-algebras to define a new class of CC approximations referred in this paper to as the nilpotent-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.

Kowalski, Karol↗
DOE OSTI2025

Temperature sensitivity of the equilibrium neutronics and accident analysis of the HTR-10

Pebble-Bed High-Temperature Gas-cooled Reactors (PB-HTGR) are moderated by the graphite in the fuel pebbles and the graphite reflector surrounding the pebble-bed. Because graphite is by far the most abundant material in PB-HTGRs and the primary moderator, accurate modeling of the graphite material, including density, impurities, and temperatures, is crucial for accurate computational modeling and simulation of these reactors. While main characteristics of the graphite components are often known, the local temperature is less well known and often averaged over all components. Here, this work studies the impact of considering accurate temperature profiles in the graphite material on the generation of a small PB-HTGR model at the state of equilibrium operation and on short-term accident progression. The fuel compositions for the PB-HTGR were determined using a jump-in equilibrium modeling method, the Axial Radial Zone Equilibrium Modeling (AR-ZEM) method. In contrast to previous work, the AR-ZEM method was used considering thermal-hydraulic feedback from the MELCOR code to determine temperatures of the fuel pebbles and the surrounding graphite reflector. The consideration of an axial and radial temperature profile in the core and reflector, as opposed to uniform material temperatures, had an impact of almost 1,300 pcm on the equilibrium core eigenvalue and caused significant differences in the discharged plutonium fuel inventory with up to 4.9% and 11.0% for Pu-239 and Pu-242, respectively. To assess the impact on short-term accident progression, two Anticipated Transient Without SCRAM (ATWS) events, a Pressurized Loss of Forced Coolant (PLOFC) and a Control Rod Withdrawal (CRW) with loss of flow, were simulated with MELCOR. The use of temperature profiles in the equilibrium core models did not reveal a significant impact on the temperature, power, or reactivity responses during the transients. In conclusion, a need for consideration of accurate temperature profiles, in particular for the graphite reflector, was found for the generation of equilibrium PB-HTGRs core models using jump-in methods, but detailed temperature profiles may not be necessary when performing conservative transient analysis.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. DMMs using deep neural networks to parametrize the transition of Markov probability distributions have recently been shown to provide more expressiveness in modeling sequential data and dynamical system responses. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a rigorous analytical method to prove the necessary and sufficient conditions of DMM's stochastic stability. This task is achieved by spectral analysis of the efficiently computed Jacobians of probabilistic maps modeled by deep neural networks. We make theoretical connections between the eigenvalues of neural network's weights and the different activation function types used on the stability and overall dynamic behavior of DMMs with Gaussian distributions. We empirically substantiate our theoretical results on stochastic stability and eigenvalue spectra via several numerical experiments. Formal stability guarantees of DMMs can substantially improve their robustness and trustworthiness, necessary for reliable use in safety-critical real-world applications.

Drgona, Jan↗
DOE OSTI2023

Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian

Here simulations of laser-induced electron dynamics in a molecular system are performed using time-dependent (TD) equation-of-motion (EOM) coupled-cluster (CC) theory. The target system has been chosen to highlight potential shortcomings of truncated TD-EOM-CC methods [represented in this work by TD-EOM-CC with single and double excitations (TD-EOM-CCSD)], where unphysical spectroscopic features can emerge. Specifically, we explore driven resonant electronic excitations in magnesium fluoride in the proximity of an avoided crossing. Near the avoided crossing, the CCSD similarity-transformed Hamiltonian is defective, meaning that it has complex eigenvalues, and oscillator strengths may take on negative values. When an external field is applied to drive transitions to states exhibiting these traits, unphysical dynamics are observed. For example, the stationary states that make up the time-dependent state acquire populations that can be negative, exceed one, or even complex-valued.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗