Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “eigenvalue analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

CSPlib - A Software Toolkit for the Analysis of Dynamical Systems and Chemical Kinetic Models

CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems. The software provides support for: General ODE models (gODE model class) for computing source terms and Jacobians for a generic ODE system; TChem model (ChemElemODETChem model class) for computing source term, Jacobian, other necessary chemical reaction data, as well as the rates of progress for a homogenous batch reactor using an elementary step detailed chemical kinetic reaction mechanism. This class relies on the TChem [2] library; A set of functions to compute essential elements of CSP analysis (Kernel class). This includes computations of the eigensolution of the Jacobian matrix, CSP basis vectors and co-vectors, time scales (reciprocals of the magnitudes of the Jacobian eigenvalues), mode amplitudes, CSP pointers, and the number of exhausted modes. This class relies on the Tines library; A set of functions to compute the eigensolution of the Jacobian matrix using Tines library GPU eigensolver; A set of functions to compute CSP indices (Index Class). This includes participation indices and both slow and fast importance indices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improved Cross Section Generation Capability of Griffin in FY22

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of deterministic steady-state transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication as well as transient solvers for spatial dynamics with the improved quasi-static method. Griffin uses cross section data in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. In recent years, the MC 2 -3 modules have been added to Griffin for fast reactor cross section generation, and the self-shielding application programming interface (SSAPI) was implemented in the ISOXML module for thermal reactor cross section generation. The on-the-fly slowing down method and double-heterogeneity treatment have been implemented to SSAPI and verified against particulate fuel-bearing graphite-moderated thermal reactor problems with high accuracy. This year, work has been focused on improving the cross section generation capability of ISOXML and streamlining the cross section generation procedures. In addition, the form function data were added to ISOXML in order to support the pin power reconstruction capability that was newly implemented in Griffin in this fiscal year. To facilitate the cross section generation using MC 2 -3 and SSAPI in Griffin, the cross section generation workflows have been set up for both fast and thermal spectrum reactors. The MOOSE action system tool was devised for fast spectrum problems, and the MOOSE stochastic tool was adopted to the branch calculation procedure for thermal spectrum problems. Meanwhile, to ensure the accuracy of group-constants, the thermal up-scattering kernel calculator accounting for resonance scattering was implemented in ISOXML, demonstrating the accurate computation of a Doppler-broadened scattering kernel of any Legendre order within a reasonable timescale. Other aspects of ISOXML, such as deletion solver and data, documentation, ISOXML file management, and the interface for Mixture, were improved as well.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1971

Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

Rosenbaum, J. S.↗
NASA NTRS1987

An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

Cohn, Stephen E.↗
NASA NTRS1989

An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

Cohn, Stephen E.↗
NASA NTRS1981

On the propagation of long waves in acoustically treated, curved ducts

A two dimensional study is presented on the behavior of long waves in lined, curved ducts. The analysis includes a comparison between the propagation in curved and straight lined ducts. A parametric study was conducted over a range of wall admittance and duct wall separation. The complex eigenvalues of the characteristic equation, which in the case of a curved duct are also the angular wavenumbers, were obtained by successive approximations.

Rostafinski, W.↗
NASA NTRS1981

On the propagation of long waves in acoustically treated, curved ducts

A two-dimensional, detailed study is presented on the behavior of long waves in lined, curved ducts. The analysis includes a comparison between the propagation in curved and straight lined ducts. A parametric study was conducted over a range of wall admittance and duct wall separation. The complex eigenvalues of the characteristic equation, which in the case of a curved duct are also the angular wavenumbers, have been obtained by successive approximations.

Rostafinski, W.↗
NASA NTRS1990

On the instabilities of supersonic mixing layers - A high-Mach-number asymptotic theory

The stability of a family of tanh mixing layers is studied at large Mach numbers using perturbation methods. It is found that the eigenfunction develops a multilayered structure, and the eigenvalue is obtained by solving a simplified version of the Rayleigh equation (with homogeneous boundary conditions) in one of these layers which lies in either of the external streams. This analysis leads to a simple hypersonic similarity law which explains how spatial and temporal phase speeds and growth rates scale with Mach number and temperature ratio. Comparisons are made with numerical results, and it is found that this similarity law provides a good qualitative guide for the behavior of the instability at high Mach numbers. In addition to this asymptotic theory, some fully numerical results are also presented (with no limitation on the Mach number) in order to explain the origin of the hypersonic modes (through mode splitting) and to discuss the role of oblique modes over a very wide range of Mach number and temperature ratio.

Balsa, Thomas F.↗
NASA NTRS1986

Implementation of the Lanczos method for structural vibration analysis on a parallel computer

The use of the Lanczos method in a parallel environment is investigated by implementing the algorithm for structural vibration problems on a parallel computer. It is shown that introducing shifts, assigning each processor a different region in the eigenvalue spectrum, and implementing the Lanczos method in parallel is an effective strategy for speeding up calculations. Test problem results include examples of the 'Lanczos phenomenon' where roundoff error in the vector orthogonalization can result in spurious eigenvalues which must be identified and discarded. The calculation strategy described here permits straightforward determination of these spurious eigenvalues. It is demonstrated that significant speedups in calculation time can be realized over traditional sequential methods.

Bostic, S. W.↗
NASA NTRS1984

A numerical analysis of transient planetary waves and the vertical structure in a meso-strato-troposphere model, part 1.4A

The structure of unstable planetary waves is computed by a quasi-geostrophic model extending from the surface up to 80 km by means of eigenvalue-eigenfunction techniques in spherical coordinates. Three kinds of unstable modes of distinct phase speeds and vertical structures are identified in the winter climate state: (1) the deep Green mode with its maximum amplitude in the stratosphere; (2) the deep Charney mode with its maximum amplitude in the troposphere: and (3) the shallow Charney mode which is largely confined to the troposphere. Both the Green mode and the deep Charney mode are characterized by very slow phase speeds. They are mainly supported by upward wave energy fluxes, but the local baroclinic energy conversion within the stratosphere also contributes in supporting these deep modes. The mesosphere and the troposphere are dynamically independent in the summer season decoupled by the deep stratospheric easterly. The summer mesosphere supports the easterly unstable waves 1-4. Waves 3 and 4 are identified with the observed mesospheric 2-day wave and 1.7-day wave, respectively.

Zhang, K. S.↗
NASA NTRS1977

On the launch vehicle payload interface response

A method has been developed by which an estimate of the launch vehicle/payload interface response is derived from the interface responses obtained from missions with the identical launch vehicle but different payloads. This method requires knowledge of the launch vehicle eigenvalues, interface modal displacements, and the dynamic characteristics of the payloads. No other launch vehicle information is required. The organization responsible for the payload is able to perform loads and responses analysis resulting from a payload change without interfacing with the launch vehicle organization.

Chen, J. C.↗
NASA NTRS1982

Eigenspace techniques for active flutter suppression

Mathematical models to be used in the control system design were developed. A computer program, which takes aerodynamic and structural data for the ARW-2 aircraft and converts these data into state space models suitable for use in modern control synthesis procedures, was developed. Reduced order models of inboard and outboard control surface actuator dynamics and a second order vertical wind gust model were developed. An analysis of the rigid body motion of the ARW-2 was conducted. The deletion of the aerodynamic lag states in the rigid body modes resulted in more accurate values for the eigenvalues associated with the plunge and pitch modes than were obtainable if the lag states were retained.

Garrard, W. L.↗
DOE OSTI2021

Planetary normal mode computation: Parallel algorithms, performance and reproducibility

This report is an extension of work entitled “Computing planetary interior normal modes with a highly parallel polynomial filtering eigensolver.” by Shi et al., [1] originally presented at the SC18 conference. A highly parallel polynomial filtered eigensolver was developed and exploited to calculate the planetary normal modes. The proposed method is ideally suited for computing interior eigenpairs for large-scale eigenvalue problems as it greatly enhances memory and computational efficiency. In this article, the second-order finite element method is used to further improve the accuracy as only the first-order finite element method was deployed in the previous work. The parallel algorithm, its parallel performance up to 20k processors, and the great computational accuracy are illustrated. The reproducibility of the previous work was successfully performed on the Student Cluster Competition at the SC19 conference by several participant teams using a completely different Mars-model dataset on different clusters. Both weak and strong scaling performances of the reproducibility by the participant teams were impressive and encouraging. The analysis and reflection of their results are demonstrated and future direction is discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A posteriori superlinear convergence bounds for block conjugate gradient

In this paper, we extend to the block case the a posteriori bound showing superlinear convergence of the conjugate gradient method developed by van der Vorst and Vuik in [J. Comput. Applied Math., 48 (1993), pp. 327–341]. That is, we obtain similar bounds but now for the block conjugate gradient method. We also present a series of computational experiments, illustrating the validity of the bound developed here as well as the bound by Simoncini and Szyld from [SIAM Review, 47 (2005), pp. 247–272] using angles between subspaces. Using these bounds, we make some observations on the onset of superlinearity and how this onset depends on the eigenvalue distribution and the block size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

ANS Winter 2024 Summary: MCCAFE: The Monte Carlo Constructor for ATR Fuel Elements

The Irradiation Experiment Neutronics Analysis Department at Idaho National Laboratory (INL) has implemented a new analysis workflow for experiments in the Advanced Test Reactor (ATR). One key piece of this workflow is the Monte Carlo Constructor for ATR Fuel Elements, or MCCAFE. For each ATR operating cycle, the Reactor and Nuclear Safety Engineering (RNSE) Department first solves the core in eigenvalue mode and depletes the driver fuel materials. In a separate calculation, neutronics analysts model and deplete the materials of one or more irradiation experiments, usually in a series of fixed-source Monte Carlo N-Particle (MCNP) models of the ATR for neutron transport calculations. It was desirable to use the results of the former calculations to inform the models of the latter. MCCAFE is a Python program developed using American Society of Mechanical Engineers Nuclear Quality Assurance-1 procedures at INL. Its purpose is to take the calculated results from the RNSE depletion solutions and the measured or projected operating parameters from the Nuclear Data Management and Analysis System (NDMAS) to generate fixed-source models of the ATR core at given points in time across one or more cycles.

99 - GENERAL AND MISCELLANEOUS↗
NASA NTRS1982

Application of the reduced basis method to nonlinear transient thermal analysis

An effort to apply the reduced basis method to nonlinear transient thermal analysis is described. The method combines the classical Rayleigh-Ritz and modal superposition techniques with contemporary finite element methods to retain modeling versatility as the degrees of freedom in a problem are reduced. The essence of the method is to use a few thermal modes from eigenvalue analyses as basis vectors to represent the temperature response for a given thermal problem similar to the use of vibration modes to represent displacements in a dynamic response problem. Approximate temperature distributions were obtained using the reduced basis method for a small section of the Shuttle Orbiter lower wing undergoing reentry heating. Good agreement was obtained between the reduced basis method solutions and full system solutions with reductions in the degrees of freedom of up to a factor of four. The good agreement indicates the reduced basis method has the potential for significant reduction in computing effort for thermal analysis; however, considerable work remains to determine techniques for selecting the type and number of basis vectors needed for approximate solutions to more complex transient thermal problems.

Shore, C. P.↗
DOE OSTI2023

New Cross Section Measurements and Evaluations of Zirconium Isotopes [Slides]

This presentation gives a look to new cross section measurements and evaluations of Zirconium (Zr) isotopes. This lecture includes highlights of accomplishments made in 2022. Additionally, it explains the motivation for investigation, new measurements, and re-evaluation of the Zr isotopes. This presentation concludes with a preliminary evaluation result from RPI 90 Zr evaluation and preliminary results from Eigenvalue sensitivity study on Zr sensitive critical benchmark experiments.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS1975

Ellipsometer measurements of epitaxial GaAs layers: A concept

Report discusses analysis involving Maxwell's equations formed in a 6-by-6 matrix. By applying boundary conditions at proper points in sample, equation for propagation of light through anisotropic medium is reduced to eigenvalue problem resulting in 4-by-4 matrix.

Desmet, D. J.↗