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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 379 records · Page 21

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NASA NTRS1981

Two-dimensional integrating matrices on rectangular grids

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

Lakin, W. D.↗

DOE OSTI2024

Structure preserving and energy dissipative contact approaches for implicit dynamics

In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

42 ENGINEERING↗

DOE OSTI2021

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Multifidelity validation of digital surrogates using variable-density turbulent mixing models

In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable-density (Atwood = 0.22), compressible turbulent mixing. Though models of this kind (Reynolds averaged NavierStokes and large-eddy simulations) have been validated extensively with more canonical flows in previous studies, here the present approach offers novelty in the complexity of the geometry, the ensemble-based validation, and the uniformity of the computational framework on which the models are tested. Moreover, all experimental and computational tasks were completed by the authors which has led to a tightly coupled experimental configuration with its “digital twin.” The experimental divergent-shock-tube facility and its data acquisition methods are described and replicated in simulation space. A 2D Euler model which neglects the turbulent mixing at the interface is optimized to experimental data using a Gaussian process. This model then serves as the basis for both the 2D RANS and 3D LES studies that make comparisons to the mixing-layer data from the experiment. A relatively simple RANS model is shown to produce good agreement with experimental data only at late flow development times. The LES ensembles generally show good agreement with experimental data but display sensitivity to the characterization of initial conditions. Resolution-dependent behavior is also observed for certain higher-order statistics of interest. Overall, the LES model successfully captures the effects of divergent geometry, compressibility, and combined nonlinear instabilities inherent to the problem. The successful prediction of mixing width and its growth rate highlight the existence of three distinct regimes in the development of the instability, each with similarities to previously studied instabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Anti-Ultralocality and Plateau Models of Inflation

Anti-ultralocality refers to the growth of spatial gradient terms relative to velocity terms in the coupled Einstein--scalar field equations. It is a characteristic feature of decelerated expansion before the onset of inflation. Previous numerical relativity studies have shown that anti-ultralocality prevents the onset of inflation in models with power-law inflaton potentials. In this paper, we show that models with plateau-shaped inflaton potentials, which are considered to be the simplest way to generate a tensor-to-scalar ratio below current observational upper limits, are especially vulnerable to anti-ultralocality effects. The reasons are the flatness of the plateau and the energy density gap of $\sim 10$ orders of magnitude between the Planck density and the plateau potential energy. To study the problem, we develop a protocol for assessing the viability of inflationary models in general, and we apply it to a plateau potential using a previously validated numerical relativity code. We find that, starting from generic initial conditions, the growth of gradient terms in the Einstein equations relative to non-gradient terms either prevents inflation from lasting for enough $e$-folds or triggers a phase of quantum runaway. We show that the fine-tuning of initial conditions necessary to avoid these issues becomes more severe as the energy scale of inflation is made smaller, disfavoring common approaches for reducing the tensor-to-scalar ratio.

FOS: Physical sciences↗

NASA NTRS1975

Ride-quality testing under controlled flight conditions

As part of a NASA program to develop the technology of ride quality, a flight-test program has been conducted to obtain subjective reactions of a significant number of test passengers to a variety of controlled and repeatable flight conditions. For these experiments, the computer of a variable-stability research aircraft was programmed to precisely control the aircraft's in-flight motions as specified by motion command signals prerecorded on magnetic tape. Problems initially encountered derived primarily from the quality of the motion command signals and tape playback device, plus the aircraft motion response in degrees of freedom other than that desired. Problem solutions were obtained through the use of filtering and compensating networks. The variable-stability-system modifications, problems encountered, and their solutions are described. The test procedure is described and sample results are presented which illustrate the usefulness of this technique for ride-quality research.

Schoonover, W. E., Jr.↗

NASA NTRS1976

On the optimal minimum order observer-based compensator and the limited state variable feedback controller

Four design problems are considered: two on the optimal minimum order observer-based compensator design and two on the optimal limited state variable feedback controller. The problem of designing an optimal discrete time linear time-invariant observer-based compensator for the regulation of an n dimensional linear discrete time time-invariant plant with m independent outputs is considered. This is a stochastic design problem to the extent that the initial plant state is assumed to be a random vector with known first and second order statistics. The compensator parameters are obtained by minimizing the expectation, with respect to the initial conditions, of the standard cost, quadratic in the state and control vectors with the inclusion of cross terms.

Llorens-Ortiz, B.↗

NASA NTRS1983

Minimum-fuel turning climbout and descent guidance of transport jets

The complete flightpath optimization problem for minimum fuel consumption from takeoff to landing including the initial and final turns from and to the runway heading is solved. However, only the initial and final segments which contain the turns are treated, since the straight-line climbout, cruise, and descent problems have already been solved. The paths are derived by generating fields of extremals, using the necessary conditions of optimal control together with singular arcs and state constraints. Results show that the speed profiles for straight flight and turning flight are essentially identical except for the final horizontal accelerating or decelerating turns. The optimal turns require no abrupt maneuvers, and an approximation of the optimal turns could be easily integrated with present straight-line climb-cruise-descent fuel-optimization algorithms. Climbout at the optimal IAS rather than the 250-knot terminal-area speed limit would save 36 lb of fuel for the 727-100 aircraft.

Neuman, F.↗

NASA NTRS1990

Paired and interacting galaxies: Conference summary

The author gives a summary of the conference proceedings. The conference began with the presentation of the basic data sets on pairs, groups, and interacting galaxies with the latter being further discussed with respect to both global properties and properties of the galactic nuclei. Then followed the theory, modelling and interpretation using analytic techniques, simulations and general modelling for spirals and ellipticals, starbursts and active galactic nuclei. Before the conference the author wrote down the three questions concerning pairs, groups and interacting galaxies that he hoped would be answered at the meeting: (1) How do they form, including the role of initial conditions, the importance of subclustering, the evolution of groups to compact groups, and the fate of compact groups; (2) How do they evolve, including issues such as relevant timescales, the role of halos and the problem of overmerging, the triggering and enhancement of star formation and activity in the galactic nuclei, and the relative importance of dwarf versus giant encounters; and (3) Are they important, including the frequency of pairs and interactions, whether merging and interactions are very important aspects of the life of a normal galaxy at formation, during its evolution, in forming bars, shells, rings, bulges, etc., and in the formation and evolution of active galaxies? Where possible he focuses on these three central issues in the summary.

Norman, Colin A.↗

NASA NTRS1994

TOPEX/POSEIDON tides estimated using a global inverse model

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

Egbert, Gary D.↗

NASA NTRS1959

Three-Dimensional Lunar Mission Studies

Some three-dimensional lunar trajectories have been calculated by integration of the equations of motion of the classical restricted three-body problem of celestial mechanics. The calculations have been used for analysis of several aspects of lunar flight including requirements for achieving lunar impact and for establishment of a close lunar satellite. The allowable errors in initial conditions for lunar missions are strongly dependent on the values of the initial injection velocity and the injection angle. There can be large differences in results obtained from two-dimensional analyses (in which the vehicle trajectory is assumed to remain always in the earth-moon plane) and those obtained from three-dimensional analyses. Some of the accuracy tolerances can be fairly well estimated by use of a two-body analysis which considers the inclination of the plane of the vehicle trajectory to the earth-moon plane. Satisfactory orbits for a relatively close lunar satellite can be obtained with accuracies in the initial conditions approximately equal to those required for lunar impact.

Michael, William H., Jr.↗

NASA NTRS1976

Elliptic integral solutions to a class of space flight optimization problems

This paper is initially concerned with the minimum-time, exoatmospheric flight of a rocket with constant thrust acceleration magnitude, as in the cases of nuclear and solar electric propulsion. Gravitational acceleration is assumed to be a constant scalar multiple of the radius vector, plus a correction term which is a given function of time. The solution to the state equations is obtained in terms of elliptic integrals. A method is presented for the solution of the two-point boundary-condition problem associated with orbital transfer. At most, the latter method requires iteration upon final time, angle of injection, and two other parameters which are bounded. An example problem is provided which involves a rocket with very low thrust and a spiraling trajectory of many revolutions, but an altitude change of only several hundred miles above the earth. Finally, the original elliptic integral solution is extended to a larger class of low and intermediate thrust problems with constant thrust magnitude, mass decreasing with time, and an inverse square gravitational force.

Andrus, J. F.↗

DOE OSTI2023

Statistical Learning for Nonlinear Model Reduction from Local Simulations of Stochastic and Particle- and Agent-Based Systems

Stochastic physical systems across the sciences that have very high-dimensional state spaces, with a large number of fast degrees of freedom that force direct simulators to proceed by integration steps that are orders of magnitude smaller than events of interests (e.g., particle collisions). Examples range from molecular motion to dynamics of large populations of cells. A grand challenge in the simulation and understanding of such systems is the systematic construction of accurate, interpretable, reduced models, enabling faster simulations, revealing fundamental properties of the dynamics, and predicting phenomena of interest that the original simulator could not reached with sufficient accuracy or within a given computational budget. In this projected we developed novel statistical estimation/machine learning techniques for analyzing and building empirical reduced models for important families of high-dimensional stochastic systems, in particular: - we developed techniques for estimating interaction kernels in interacting particle- and agent-based systems, which are ubiquitous in Physics, Biology and many other sciences, given observed trajectories of the system; - we developed techniques for nonlinear model reduction for high-dimensional stochastic systems that have a small number of unknown, nonlinear slow variables, and a large number of fast modes, that are possibly of large magnitude, given observed short trajectories of the system in the form of bursts of trajectories from different initial conditions; - we developed novel techniques for estimating linear dynamical systems on graphs when both the dynamics and the underlying graph are unknown, and we have a sparse set of space-time observations; - we considered the problem of estimating an unknown nonlinear observation function of a standard process (e.g. Brownian motion), so that we can recognized if an observed dynamics is "just" a nonlinear version of a known dynamics; we also developed benchmarks for learning algorithms aimed at learning and classifying diffusion processes.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

The terminal area automated path generation problem

The automated terminal area path generation problem in the advanced Air Traffic Control System (ATC), has been studied. Definitions, input, output and the interrelationships with other ATC functions have been discussed. Alternatives in modeling the problem have been identified. Problem formulations and solution techniques are presented. In particular, the solution of a minimum effort path stretching problem (path generation on a given schedule) has been carried out using the Newton-Raphson trajectory optimization method. Discussions are presented on the effect of different delivery time, aircraft entry position, initial guess on the boundary conditions, etc. Recommendations are made on real-world implementations.

Hsin, C.-C.↗

NASA NTRS1986

Senstitivity analysis of horizontal heat and vapor transfer coefficients for a cloud-topped marine boundary layer during cold-air outbreaks

The effects of external parameters on the surface heat and vapor fluxes into the marine atmospheric boundary layer (MABL) during cold-air outbreaks are investigated using the numerical model of Stage and Businger (1981a). These fluxes are nondimensionalized using the horizontal heat (g1) and vapor (g2) transfer coefficient method first suggested by Chou and Atlas (1982) and further formulated by Stage (1983a). In order to simplify the problem, the boundary layer is assumed to be well mixed and horizontally homogeneous, and to have linear shoreline soundings of equivalent potential temperature and mixing ratio. Modifications of initial surface flux estimates, time step limitation, and termination conditions are made to the MABL model to obtain accurate computations. The dependence of g1 and g2 in the cloud topped boundary layer on the external parameters (wind speed, divergence, sea surface temperature, radiative sky temperature, cloud top radiation cooling, and initial shoreline soundings of temperature, and mixing ratio) is studied by a sensitivity analysis, which shows that the uncertainties of horizontal transfer coefficients caused by changes in the parameters are reasonably small.

Chang, Y. V.↗

NASA NTRS1989

Goertler vortices in supersonic and hypersonic boundary layers

The problem of Goertler vortices in compressible boundary layers over concave walls is considered. At O(1) wavelengths, the instability is governed by parabolic partial differential equations that are solved numerically to determine the effect of various initial conditions on the development of Goertler vortex instability in compressible boundary layers. The results show that both the velocity and temperature fluctuations may lead to a Goertler vortex. The vortex growth rates determined from the present method are found to differ somewhat from those given by a normal mode solution. At both the supersonic and hypersonic Mach numbers, cooling has a small destabilizing effect. In addition, the most unstable disturbances shift toward lower wavelengths because of thinning of the boundary layer. The results also show that compressibility has a stabilizing effect on the Goertler instability, while the effect of an adverse pressure gradient is found to be destabilizing. The behavior of the Goertler vortex structure with Mach number is also examined. At hypersonic Mach numbers, vortices are located near the edge of the boundary layer for adiabatic wall conditions. However, the entire boundary layer is affected when the wall is cooled.

Spall, R. E.↗

NASA NTRS2007

Automated Knowledge Discovery From Simulators

A computational method, SimLearn, has been devised to facilitate efficient knowledge discovery from simulators. Simulators are complex computer programs used in science and engineering to model diverse phenomena such as fluid flow, gravitational interactions, coupled mechanical systems, and nuclear, chemical, and biological processes. SimLearn uses active-learning techniques to efficiently address the "landscape characterization problem." In particular, SimLearn tries to determine which regions in "input space" lead to a given output from the simulator, where "input space" refers to an abstraction of all the variables going into the simulator, e.g., initial conditions, parameters, and interaction equations. Landscape characterization can be viewed as an attempt to invert the forward mapping of the simulator and recover the inputs that produce a particular output. Given that a single simulation run can take days or weeks to complete even on a large computing cluster, SimLearn attempts to reduce costs by reducing the number of simulations needed to effect discoveries. Unlike conventional data-mining methods that are applied to static predefined datasets, SimLearn involves an iterative process in which a most informative dataset is constructed dynamically by using the simulator as an oracle. On each iteration, the algorithm models the knowledge it has gained through previous simulation trials and then chooses which simulation trials to run next. Running these trials through the simulator produces new data in the form of input-output pairs. The overall process is embodied in an algorithm that combines support vector machines (SVMs) with active learning. SVMs use learning from examples (the examples are the input-output pairs generated by running the simulator) and a principle called maximum margin to derive predictors that generalize well to new inputs. In SimLearn, the SVM plays the role of modeling the knowledge that has been gained through previous simulation trials. Active learning is used to determine which new input points would be most informative if their output were known. The selected input points are run through the simulator to generate new information that can be used to refine the SVM. The process is then repeated. SimLearn carefully balances exploration (semi-randomly searching around the input space) versus exploitation (using the current state of knowledge to conduct a tightly focused search). During each iteration, SimLearn uses not one, but an ensemble of SVMs. Each SVM in the ensemble is characterized by different hyper-parameters that control various aspects of the learned predictor - for example, whether the predictor is constrained to be very smooth (nearby points in input space lead to similar output predictions) or whether the predictor is allowed to be "bumpy." The various SVMs will have different preferences about which input points they would like to run through the simulator next. SimLearn includes a formal mechanism for balancing the ensemble SVM preferences so that a single choice can be made for the next set of trials.

Burl, Michael↗

DOE OSTI2021

Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion

SUMMARY Full-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

58 GEOSCIENCES↗