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NASA NTRS1992

Adaptive control of Space Station with control moment gyros

An adaptive approach to Space Station attitude control is investigated. The main components of the controller are the parameter identification scheme, the control gain calculation, and the control law. The control law is a full-state feedback space station baseline control law. The control gain calculation is based on linear-quadratic regulator theory with eigenvalues placement in a vertical strip. The parameter identification scheme is a recursive extended Kalman filter that estimates the inertias and also provides an estimate of the unmodeled disturbances due to the aerodynamic torques and to the nonlinear effects. An analysis of the inertia estimation problem suggests that it is possible to estimate Space Station inertias accurately during nominal control moment gyro operations. The closed-loop adaptive control law is shown to be capable of stabilizing the Space Station after large inertia changes. Results are presented for the pitch axis.

Bishop, Robert H.↗

NASA NTRS2010

Broken Ergodicity in MHD Turbulence

Ideal magnetohydrodynamic (MHD) turbulence may be represented by finite Fourier series, where the inherent periodic box serves as a surrogate for a bounded astrophysical plasma. Independent Fourier coefficients form a canonical ensemble described by a Gaussian probability density function containing a Hermitian covariance matrix with positive eigenvalues. The eigenvalues at lowest wave number can be very small, resulting in a large-scale coherent structure: a turbulent dynamo. This is seen in computations and a theoretical explanation in terms of 'broken ergodicity' contains Taylor s theory of force-free states. An important problem for future work is the case of real, i.e., dissipative flows. In real flows, broken ergodicity and coherent structure are still expected to occur in MHD turbulence at the largest scale, as suggested by low resolution simulations. One challenge is to incorporate coherent structure at the largest scale into the theory of turbulent fluctuations at smaller scales.

Shebalin, John V.↗

DOE OSTI2016

Solution of the Hot Zero Power BEAVRS Using a Pin-Cell Homogenized Model

The validation of a reactor physics code system is an essential part of the code development process. It allows for the evaluation of the code's ability to predict and model the complex physical processes that take place in a nuclear reactor under various operational conditions. Idaho National Laboratory (INL) has been developing a set of reactor physics analysis tools within the MOOSE framework. MAMMOTH is the main reactor physics application, which integrates other MOOSE applications to solve complex multiphysics problems. Results from this study demonstrate that the MOOSE based reactor physics tools, currently under development at INL, have the flexibility to model with high accuracy the HZP condition for a standard PWR. The DRAGON5-Rattlesnake full core pin-cell homogenized simulation produces eigenvalues and detector signals that are comparable to those generated with OpenMC and nTRACER. However, many improvements are necessary to achieve higher fidelity results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

A New CE TSUNAMI-3D Capability for Calculating Undersampling Metrics and Biases

This study investigates the viability of several statistical metrics for predicting the undersampling biases in continuous-energy (CE) Monte Carlo transport simulation tally estimates. Undersampling is a phenomenon in which a Monte Carlo simulation fails to use enough particles per generation to adequately sample fission points in all regions of a problem, resulting in biases in tally estimates that are much larger than the statistical uncertainties, potentially leading to erroneous conclusions regarding system performance and safety. Previous work found that biases due to undersampling could be as large as several hundred per cent mille (pcm) for eigenvalue estimates and up to tens or hundreds of percent for flux tally estimates. This paper documents the encapsulation of undersampling metrics within CE TSUNAMI-3D in the SCALE code system and examines the correlation between the various undersampling metric scores and the magnitude of various undersampling biases. Of the metrics examined, the RHW metric, the Tally Entropy metric, and the uncertainty in the scores for these metrics produce scores that correlated well with the fraction of the undersampling biases in various eigenvalue, flux, and energy-integrated reaction rate tallies in an infinitely reflected model of a PWR fuel assembly. The average number of nonzero scores per generation encountered by a tally was also found to show promise at predicting the magnitude of undersampling biases, and it also found use in detecting and filtering extremely undersampled tallies in the application of the other metrics. Future work will strengthen these conclusions by improving the degree of convergence for the examined tally and undersampling bias estimates, apply these metrics to a more broad variety of systems, and investigate variance reduction approaches for mitigating undersampling in Monte Carlo tally estimates. (authors)

42 ENGINEERING↗

DOE OSTI2017

MC 2 -3: Multigroup Cross Section Generation Code for Fast Reactor Analysis

This paper presents the methods and performance of the MC2 -3 code, which is a multigroup cross-section generation code for fast reactor analysis, developed to improve the resonance self-shielding and spectrum calculation methods of MC2 -2 and to simplify the current multistep schemes generating region-dependent broad-group cross sections. Using the basic neutron data from ENDF/B data files, MC2 -3 solves the consistent P1 multigroup transport equation to determine the fundamental mode spectra for use in generating multigroup neutron cross sections. A homogeneous medium or a heterogeneous slab or cylindrical unit cell problem is solved in ultrafine (2082) or hyperfine (~400 000) group levels. In the resolved resonance range, pointwise cross sections are reconstructed with Doppler broadening at specified temperatures. The pointwise cross sections are directly used in the hyperfine group calculation, whereas for the ultrafine group calculation, self-shielded cross sections are prepared by numerical integration of the pointwise cross sections based upon the narrow resonance approximation. For both the hyperfine and ultrafine group calculations, unresolved resonances are self-shielded using the analytic resonance integral method. The ultrafine group calculation can also be performed for a two-dimensional whole-core problem to generate region-dependent broad-group cross sections. Verification tests have been performed using the benchmark problems for various fast critical experiments including Los Alamos National Laboratory critical assemblies; Zero-Power Reactor, Zero-Power Physics Reactor, and Bundesamt für Strahlenschutz experiments; Monju start-up core; and Advanced Burner Test Reactor. Verification and validation results with ENDF/B-VII.0 data indicated that eigenvalues from MC2 -3/DIF3D agreed well with Monte Carlo N-Particle5 MCNP5 or VIM Monte Carlo solutions within 200 pcm and regionwise one-group fluxes were in good agreement with Monte Carlo solutions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1980

Modal methods in optimal control synthesis

Efficient algorithms for solving linear smoother-follower problems with quadratic criteria are presented. For time-invariant systems, the algorithm consists of one backward integration of a linear vector equation and one forward integration of another linear vector equation. Furthermore, the backward and forward Riccati matrices can be expressed in terms of the eigenvalues and eigenvectors of the Euler-Lagrange equations. Hence, the gains of the forward and backward Kalman-Bucy filters and of the optimal state-feedback regulator can be determined without integration of matrix Riccati equations. A computer program has been developed, based on this method of determining the gains, to synthesize the optimal time-invariant compensator in the presence of random disturbance inputs and random measurement errors. The program also computes the rms state and control variables of the optimal closed-loop system.

Bryson, A. E., Jr.↗

NASA NTRS1988

Reduced order models for nonlinear aerodynamics

Reduced order models are needed for reliable, efficient and accurate prediction of aerodynamic forces to analyze fluid structure interaction problems in turbomachinery, including propfans. Here, a finite difference, time marching Navier-Stokes code is validated for unsteady airfoil motion by comparing results with those from classical potential flow. The Navier-Stokes code is then analyzed for calculation of primitive and exact estimates of eigenvalues and eigenvectors associated with fluid-airfoil interaction. A variational formulation for the Euler equations and Navier-Stokes equations will be the basis for reduction of order through an eigenvector transformation.

Mahajan, Aparajit J.↗

NASA NTRS1988

System identification in the microcomputer environment

An implementation of an algorithm for system identification, the eigenvalue realization algorithm (ERA), on a microcomputer is reported. Test results are presented to show that accurate structural identification can be performed in a microcomputer environment. It is also shown that the memory limits (640 K) of small machines are generally adequate for solving large scale problems (e.g., Hankel matrices with 15,000 elements), with run times being on the order of several minutes.

Garcia, Ephrahim↗

DOE OSTI2016

A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearly degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non-conservative hyperbolic systems. •Inclusion of sub-structure and resolution of intermediate characteristic fields. •Well-balanced for single- and two-layer shallow water equations and multi-phase flows. •Euler equations with real equation of state, MHD equations, nonlinear elasticity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Exploiting a derivative discontinuity estimate for accurate G0W0 ionization potentials and electron affinities

Abstract The GW approximation has become an important tool for predicting charged excitations of isolated molecules and condensed systems. Its popularity can be attributed to many factors, including a favorable scaling and relatively good accuracy. In practical applications, the GW is often performed as a one-shot perturbation known as G 0 W 0 . Unfortunately, G 0 W 0 suffers from a strong starting point dependence and is often not as accurate as one would need. Self-consistent GW methodologies alleviate these problems but come with a marked increase in computational cost. In this manuscript, we propose the use of an estimate of the exchange-correlation derivative discontinuity to provide a remarkably good starting point for G 0 W 0 calculations, yielding ionization potentials and electron affinities with eigenvalue self-consistent GW quality at no additional cost. We assess the quality of the resulting methodology with the GW 100 benchmark set and compare its advantages over other similar methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1977

Recent advances in aerodynamic energy concept for flutter suppression and gust alleviation using active controls

Control laws are derived, by using realizable transfer functions, which permit relaxation of the stability requirements of the aerodynamic energy concept. The resulting aerodynamic eigenvalues indicate that both the trailing edge and the leading edge-trailing edge control systems can be made more effective. These control laws permit the introduction of aerodynamic damping and stiffness terms in accordance with the requirements of any specific system. Flutter suppression and gust alleviation problems can now be treated by either a trailing edge control system or by a leading edge-trailing edge control system by using the aerodynamic energy concept. Results are applicable to a wide class of aircraft operating at subsonic Mach numbers.

Nissim, E.↗

NASA NTRS1989

Modified Chebyshev pseudospectral method with O(N exp -1) time step restriction

The extreme eigenvalues of the Chebyshev pseudospectral differentiation operator are O(N exp 2) where N is the number of grid points. As a result of this, the allowable time step in an explicit time marching algorithm is O(N exp -2) which, in many cases, is much below the time step dictated by the physics of the partial differential equation. A new set of interpolating points is introduced such that the eigenvalues of the differentiation operator are O(N) and the allowable time step is O(N exp -1). The properties of the new algorithm are similar to those of the Fourier method. The new algorithm also provides a highly accurate solution for non-periodic boundary value problems.

Kosloff, Dan↗

NASA NTRS1993

A modified Chebyshev pseudospectral method with an O(N exp -1) time step restriction

Kosloff, Dan↗

NASA NTRS1973

Optical potential approach to the electron-atom impact ionization threshold problem

The problem of the threshold law for electron-atom impact ionization is reconsidered as an extrapolation of inelastic cross sections through the ionization threshold. The cross sections are evaluated from a distorted wave matrix element, the final state of which describes the scattering from the Nth excited state of the target atom. The actual calculation is carried for the e-H system, and a model is introduced which is shown to preserve the essential properties of the problem while at the same time reducing the dimensionability of the Schrodinger equation. Nevertheless, the scattering equation is still very complex. It is dominated by the optical potential which is expanded in terms of eigen-spectrum of QHQ. It is shown by actual calculation that the lower eigenvalues of this spectrum descend below the relevant inelastic thresholds; it follows rigorously that the optical potential contains repulsive terms. Analytical solutions of the final state wave function are obtained with several approximations of the optical potential.

Temkin, A.↗

NASA NTRS1987

A combined stochastic feedforward and feedback control design methodology with application to autoland design

A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.

Halyo, Nesim↗

NASA NTRS1990

Bifurcations of relative equilibria

The characteristics of equivariant dynamical systems near relative equilibria (RE: group orbits which are invariant in the flow of an equivariant vector field) are investigated analytically, with a focus on the dynamics and bifurcation (B) behavior. The principles of Lie-group theory are reviewed; the decomposition of the vector field is explained; and particular attention is given to the Bs of RE occurring when an eigenvalue passes through zero, Hopf Bs of RE, the classification of generic secondary steady-state and Hopf Bs with symmetry group O(2), Bs of the zero solution of the Kuramoto-Shivashinsky equation, and possible generic steady-state Bs in the two-dimensional Benard problem. In the latter case, it is shown that the primary generic Bs are to two types of equilibria (hexagons and rolls), while the secondary Bs result in trajectories which are either equilibria or rotating waves.

Krupa, Martin↗

NASA NTRS1990

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 1

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. We present an implementation of a look-ahead version of the Lanczos algorithm which overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and is not restricted to steps of length 2, as earlier implementations are. Also, our implementation has the feature that it requires roughly the same number of inner products as the standard Lanczos process without look-ahead.

Freund, Roland W.↗

NASA NTRS1991

Adaptive control of Space Station during nominal operations with CMGs

An adaptive control approach is investigated for the Space Station. The main components of the adaptive controller are the parameter identification scheme, the control gain calculation, and the control law. The control law is the Space Station baseline control law. The control gain calculation is based on linear quadratic regulator theory with eigenvalue placement in a vertical strip. The parameter identification scheme is a real-time recursive extended Kalman filter which estimates the inertias and also provides an estimate of the unmodeled disturbances due to the aerodynamic torques and to the nonlinear effects. An analysis of the inertia estimation problem suggests that it is possible to compute accurate estimates of the Space Station inertias during nominal CMG (control moment gyro) operations. The closed-loop adaptive control law is shown to be capable of stabilizing the Space Station after large inertia changes. Results are presented for the pitch axis.

Bishop, R. H.↗