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NASA NTRS1987

Probabilistic load model development and validation for composite load spectra for select space propulsion engines

A major task of the program to develop an expert system to predict the loads on selected components of a generic space propulsion engine is the design development and application of a probabilitic loads model. This model is being developed in order to account for the random nature of the loads and assess the variable load ranges' effect on the engine performance. A probabilistic model has been developed. The model is based primarily on simulation methods, but also has a Gaussian algebra method (if all variables are near normal), a fast probability integrator routine (for the calculation of low probability events), and a separate, stand alone program for performing barrier crossing calculations. Each of these probabilistic methods has been verified with theoretical calculations using assumed distributional forms.

Kurth, R.↗

NASA NTRS1993

Implementation of the block-Krylov boundary flexibility method of component synthesis

A method of dynamic substructuring is presented which utilizes a set of static Ritz vectors as a replacement for normal eigenvectors in component mode synthesis. This set of Ritz vectors is generated in a recurrence relationship, which has the form of a block-Krylov subspace. The initial seed to the recurrence algorithm is based on the boundary flexibility vectors of the component. This algorithm is not load-dependent, is applicable to both fixed and free-interface boundary components, and results in a general component model appropriate for any type of dynamic analysis. This methodology was implemented in the MSC/NASTRAN normal modes solution sequence using DMAP. The accuracy is found to be comparable to that of component synthesis based upon normal modes. The block-Krylov recurrence algorithm is a series of static solutions and so requires significantly less computation than solving the normal eigenspace problem.

Carney, Kelly S.↗

NASA NTRS1997

Environmental Assessment and Monitoring with ICAMS (Image Characterization and Modeling System) Using Multiscale Remote-Sensing Data

With the rapid increase in spatial data, especially in the NASA-EOS (Earth Observing System) era, it is necessary to develop efficient and innovative tools to handle and analyze these data so that environmental conditions can be assessed and monitored. A main difficulty facing geographers and environmental scientists in environmental assessment and measurement is that spatial analytical tools are not easily accessible. We have recently developed a remote sensing/GIS software module called Image Characterization and Modeling System (ICAMS) to provide specialized spatial analytical tools for the measurement and characterization of satellite and other forms of spatial data. ICAMS runs on both the Intergraph-MGE and Arc/info UNIX and Windows-NT platforms. The main techniques in ICAMS include fractal measurement methods, variogram analysis, spatial autocorrelation statistics, textural measures, aggregation techniques, normalized difference vegetation index (NDVI), and delineation of land/water and vegetated/non-vegetated boundaries. In this paper, we demonstrate the main applications of ICAMS on the Intergraph-MGE platform using Landsat Thematic Mapper images from the city of Lake Charles, Louisiana. While the utilities of ICAMS' spatial measurement methods (e.g., fractal indices) in assessing environmental conditions remain to be researched, making the software available to a wider scientific community can permit the techniques in ICAMS to be evaluated and used for a diversity of applications. The findings from these various studies should lead to improved algorithms and more reliable models for environmental assessment and monitoring.

Lam, N.↗

NASA NTRS2002

On Magnetic Spectra of Earth and Mars

The spectral method for distinguishing crustal from core-source magnetic fields is reexamined, modified, and applied to both a comprehensive geomagnetic field model and an altitude normalized magnetic map of Mars. The observational spectra are fairly fitted by theoretical forms expected from certain elementary classes of magnetic sources. For Earth we find fields from a core of radius 3512 +/- 64 km, in accord with the seismologic core radius of 3480 km, and a crust represented by a shell of random dipolar sources at radius 6367 +/- 14 km, near the planetary mean radius of 6371.2 km. For Mars we find no sign of a core-source field, only a field from a crust represented in same way, but at radius 3344 +/- 10 km, about 46 km below the planetary mean radius of 3389.5 km, and with sources about 9.6 +/- 3.2 times stronger.

Voorhies, C. V.↗

NASA NTRS1991

A simple method for quantitating the propensity for calcium oxalate crystallization in urine

To assess the propensity for spontaneous crystallization of calcium oxalate in urine, the permissible increment in oxalate is calculated. The previous method required visual observation of crystallization with the addition of oxalate, this warranted the need for a large volume of urine and a sacrifice in accuracy in defining differences between small incremental changes of added oxalate. Therefore, this method has been miniaturized and spontaneous crystallization is detected from the depletion of radioactive oxalate. The new "micro" method demonstrated a marked decrease (p < 0.001) in the permissible increment in oxalate in urine of stone formers versus normal subjects. Moreover, crystallization inhibitors added to urine, in vitro (heparin or diphosphonate) or in vivo (potassium citrate administration), substantially increased the permissible increment in oxalate. Thus, the "micro" method has proven reliable and accurate in discriminating stone forming from control urine and in distinguishing changes of inhibitory activity.

NASA Discipline Regulatory Physiology↗

NASA NTRS1991

Fourier functional analysis for unsteady aerodynamic modeling

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Lan, C. Edward↗

NASA NTRS1991

Fourier functional analysis for unsteady aerodynamic modeling

Chin, Suei↗

NASA NTRS2003

Estimation and Simulation of Slow Crack Growth Parameters from Constant Stress Rate Data

Closed form, approximate functions for estimating the variances and degrees-of-freedom associated with the slow crack growth parameters n, D, B, and A(sup *) as measured using constant stress rate ('dynamic fatigue') testing were derived by using propagation of errors. Estimates made with the resulting functions and slow crack growth data for a sapphire window were compared to the results of Monte Carlo simulations. The functions for estimation of the variances of the parameters were derived both with and without logarithmic transformation of the initial slow crack growth equations. The transformation was performed to make the functions both more linear and more normal. Comparison of the Monte Carlo results and the closed form expressions derived with propagation of errors indicated that linearization is not required for good estimates of the variances of parameters n and D by the propagation of errors method. However, good estimates variances of the parameters B and A(sup *) could only be made when the starting slow crack growth equation was transformed and the coefficients of variation of the input parameters were not too large. This was partially a result of the skewered distributions of B and A(sup *). Parametric variation of the input parameters was used to determine an acceptable range for using closed form approximate equations derived from propagation of errors.

Salem, Jonathan A.↗

NASA NTRS1992

Hierarchical tapered bar elements undergoing axial deformation

A method is described to model the dynamics of tapered axial bars of various cross sections based on the well-known Craig/Bampton component mode synthesis technique. This element is formed in terms of the static constraint modes and interface restrained normal modes. This is in contrast with the finite elements as implemented in NASTRAN where the interface restrained normal modes are neglected. These normal modes are in terms of Bessel functions. Restoration of a few of these modes leads to higher accuracy with fewer generalized coordinates. The proposed models are hierarchical so that all lower order element matrices are embedded in higher order element matrices. The advantages of this formulation compared to standard NASTRAN truss element formulation are demonstrated through simple numerical examples.

Ganesan, N.↗

DOE OSTI2023

LHC hadronic jet generation using convolutional variational autoencoders with normalizing flows

Abstract In high energy physics, one of the most important processes for collider data analysis is the comparison of collected and simulated data. Nowadays the state-of-the-art for data generation is in the form of Monte Carlo (MC) generators. However, because of the upcoming high-luminosity upgrade of the Large Hadron Collider (LHC), there will not be enough computational power or time to match the amount of needed simulated data using MC methods. An alternative approach under study is the usage of machine learning generative methods to fulfill that task. Since the most common final-state objects of high-energy proton collisions are hadronic jets, which are collections of particles collimated in a given region of space, this work aims to develop a convolutional variational autoencoder (ConVAE) for the generation of particle-based LHC hadronic jets. Given the ConVAE’s limitations, a normalizing flow (NF) network is coupled to it in a two-step training process, which shows improvements on the results for the generated jets. The ConVAE+NF network is capable of generating a jet in 18.30 ± 0.04 μ s , making it one of the fastest methods for this task up to now.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Mechanistic verification of empirical UO 2 fuel fracture models

Standard UO 2 fuel pellets used in light-water reactors fracture during irradiation due to the large thermal gradient in the radial direction. Over the decades, numerous researchers have explored fuel cracking from experimental and modeling points of view. To date, there have been both empirical and mechanistic approaches to predict the number of fragments that form in UO 2 . The empirical models only consider maximum power and burnup as inputs. Existing mechanistic approaches for normal operation have not accounted for irradiation effects. Here, this work employs a mechanistic fuel cracking model using the extended finite element method to explore radial crack formation while including a sensitivity analysis that accounts for the randomization of tensile strength within the fuel, the strength randomization criteria (uniform or volume-weighted Weibull), power ramping rates, computational mesh density, maximum power level, and irradiation (burnup) effects. The results indicate that the uncertainty in this mechanistic modeling approach envelopes the predicted values from three different empirical correlations in almost all cases. This means that, for computationally intensive analyses involving UO 2 fragmentation, the empirical correlations can be used. However, since the mechanistic calculations bound those of the empirical correlations, there is confidence in the applicability of the mechanistic approach developed in this work to generate a correlation for fuel types where limited data exists (e.g., doped-UO 2 , U 3 Si 2 ).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Follow the power—pathways to steady-state tokamak reactors

Abstract Diagramming pathways of dimensionless power is a potent method for extrapolating between operating points on present-day tokamaks and future burning plasma devices. The heat transport power, current drive power, H-mode threshold power and other ‘plasma physics’ powers can be expressed in dimensionally correct (or normalized) form as Pa 3/4 , where P is the power and a is the plasma minor radius, with the relative gyroradius ( ρ * ) dependence ranging from gyro-Bohm-like for transport ( P a 3 / 4 ∝ ρ * − 3 / 2 ), Bohm-like for current drive ( P a 3 / 4 ∝ ρ * − 5 / 2 ) and worse than Bohm-like for H-mode threshold ( P a 3 / 4 ∝ ρ * − 3 ). The D–T fusion power cannot be normalized in the same fashion since it is governed by nuclear physics, but at fixed B T it scales like P a 3 / 4 ∝ ρ * − 9 / 2 . Other ‘mixed physics’ powers can be incorporated into the dimensionless power framework by holding B T fixed in the same manner. Diagramming these dimensionless powers vs ρ * shows how the pathway to a steady-state reactor can be optimized relative to various operational boundaries. Using a steady-state hybrid discharge with β N = 3.2 from DIII-D as the starting point, a multi-parameter optimization finds an attractive pathway to steady-state operation on ITER using 76 MW of current drive power (fusion gain of Q fus = 8), along with a pathway to Q fus = 20 in a JET-sized steady-state reactor with B T = 10 T.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1972

Hydrodynamic water impact

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Kettleborough, C. F.↗

NASA NTRS1978

Numerical inverse Laplace transformation for determining the system response of linear systems in the time domain

An algorithm is described that is based on the method of breaking the Laplace transform down into partial fractions which are then inverse-transformed separately. The sum of the resulting partial functions is the wanted time function. Any problems caused by equation system forms are largely limited by appropriate normalization using an auxiliary parameter. The practical limits of program application are reached when the degree of the denominator of the Laplace transform is seven to eight.

Friedrich, R.↗

NASA NTRS1985

Test method for telescopes using a point source at a finite distance

A test method for telescopes that makes use of a focused ring formed by an annular aperture when using a point source at a finite distance is evaluated theoretically and experimentally. The results show that the concept can be applied to near-normal, as well as grazing incidence. It is particularly suited for X-ray telescopes because of their intrinsically narrow annular apertures, and because of the largely reduced diffraction effects.

Griner, D. B.↗

NASA NTRS2004

Crustal Magnetic Spectra from Correlated Sources on Mars

The spectral method for distinguishing crustal from core-source magnetic fields has been re-examined, modified and applied to both a comprehensive geomagnetic field model and an altitude normalized magnetic map of Mars. These observational spectra are fairly fitted by theoretical forms expected from certain elementary classes of magnetic sources. For Earth we found fields from a core radius 3512 +/- 64 km and a crust represented by a shell of random dipolar sources at radius 6367 +/- 14 km. For Mars we found only a field from a crust represented in the same way, but 46 +/- 10 km below the planetary menu radius. More realistic theoretical spectra, allowing for crustal thickness, oblateness and magnetization by a planet centered dipole, were derived and discussed, as were spectral effects of laterally correlated sources. The main effect of laterally correlated sources is to soften the spectrum at high degrees. We tend to over-estimate source shell depth when this is omitted. To include this effect simply size and magnetization distribution functions for extended sources are recast as a characteristic diameter and mean square magnetization amplitude for an ensemble of vertically magnetized spherical caps on a shell. For small caps, and at moderated degrees, the practical derivatives of the log-theoretical spectrum with respect to amplitude, shell radius, and cap diameter are approximately proportional to l, n, and -n **2, respectively. Separation of diameter from amplitude from layer thickness. Results from applications to observational spectra are discussed, noting that there are now several fine field models for Mars; moreover, the terrestrial magnetic spectrum at high degrees, as revised, updated with high precision Oerstad data, and upgrade with high resolution Champ data, appears softer than before.

Voorhies, Coerte V.↗

NASA NTRS2005

More on Magnetic Spectra from Correlated Crustal Sources on Mars

The spectral method for distinguishing crustal from core-source magnetic fields has been re-examined, modified and applied to both a comprehensive geomagnetic field model and an altitude normalized magnetic map of Mars. These observational spectra are fairly fitted by theoretical forms expected from certain elementary classes of magnetic sources. For Earth we found fields from a core of radius 3512 plus or minus 64 km, in accord with the 3480 km seismologic radius, and a crust represented by a shell of random dipolar sources at radius 6367 plus or minus 14 km, just beneath the 6371.0 km mean radius. For Mars we found only a field from a crust represented in same way, but 46 plus or minus 10 km below the planetary mean radius of 3389.5 km, and with sources about 9.6 plus or minus 3.2 times stronger than Earth's. It is remarkable that the same simple theoretical form should fairly fit crustal magnetic spectra for both worlds and return crustal-source depth estimates of plausible magnitude. Evidently, the idea of an ensemble of compact, quasi-independent, magnetized regions within these planetary crusts has some merit. Yet such estimates, at best a kind of average, depend upon both the observational spectrum fitted and the physical basis of the theoretical spectrum.

Voorhies, C. V.↗

NASA NTRS1994

The Flux-integral Method for Multidimensional Convection and Diffusion

The flux-integral method is a procedure for constructing an explicit, single-step, forward-in-time, conservative, control volume update of the unsteady, multidimensional convection-diffusion equation. The convective plus diffusive flux at each face of a control-volume cell is estimated by integrating the transported variable and its face-normal derivative over the volume swept out by the convecting velocity field. This yields a unique description of the fluxes, whereas other conservative methods rely on nonunique, arbitrary pseudoflux-difference splitting procedures. The accuracy of the resulting scheme depends on the form of the subcell interpolation assumed, given cell-average data. Cellwise constant behavior results in a (very artificially diffusive) first-order convection scheme. Second-order convection-diffusion schemes correspond to cellwise linear (or bilinear) subcell interpolation. Cellwise quadratic subcell interpolants generate a highly accurate convection-diffusion scheme with excellent phase accuracy. Under constant-coefficient conditions, this is a uniformly third-order polynomial interpolation algorithm (UTOPIA).

Leonard, B. P.↗