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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 1,279 records · Page 71
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Calculating Flows In Turbomachine Channels

Noniterative integral-entrainment method yields good approximations. Method of approximate calculation of flow in channel of turbomachine based on interaction of viscous flow in boundary layers with inviscid flow in core layer. Faster and more robust than other approximate methods of same type. Suitable for use in preliminary calculations for design and for off-design operation of turbomachinery. Flows in conical diffuser channels represented by two-dimensional boundary-layer and one-dimensional core flows described by equations of new method.

Schumann, Lawrence F.↗
NASA NTRS1974

Secondary vorticity in axial compressor blade rows

A theoretical investigation of secondary flow in compressor blade rows is presented. Formulas for calculating secondary flows in annular cascade blade passages are derived. The influence of the relative rotation vector on secondary velocity perturbations, using recent developments in shear-flow theory, is examined. A method of calculating the flow through successive blade rows is given and a comparison is made with experimental results.

Dixon, S. L.↗
NASA NTRS1978

Theoretical evaluation of high speed aerodynamics for arrow wing configurations

A limited study in the use of theoretical methods to calculate the high speed aerodynamics of arrow wing supersonic cruise configurations was conducted. The study consisted of correlations with existing wind tunnel data at Mach numbers from 0.8 to 2.7, using theoretical methods to extrapolate the wind tunnel data to full scale flight conditions, and presentation of a typical supersonic data package for an advanced supersonic transport application prepared using the theoretical methods. A brief description of the methods and their application was given. In general, all three methods had excellent correlation with wind tunnel data at supersonic speeds for drag and lift characteristics and fair to poor agreement with pitching moment characteristics. The VORLAX program had excellent correlation with wind tunnel data at subsonic speeds for lift and pitching moment characteristics and fair agreement in drag characteristics.

Dollyhigh, S. M.↗
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), https://doi.org/10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. Here, we examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 x 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), doi:10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. We examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 × 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Markov information sources

A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.

Massey, J. L.↗
NASA NTRS1971

Calculation of trajectories using constant and slowly varying functions

A method is presented for calculating trajectories for the restricted problem of three bodies which utilizes conic propagation of the state vector with frequency correction of position and velocity by means of a constant or slowly varying function. This method of calculating trajectories was applied to the planar circular restricted three body problem, the planar elliptic restricted problem, and the ephemeral restricted problem. Two methods (the refined method and the straight forward method) of determining the direction of the position correction are presented for the circular restricted problem and the elliptic restricted problem of three bodies. Only the straight forward method was used with the ephemeral restricted problem. The earth, the moon, and a space vehicle comprise the restricted three body model that is used.

Culpepper, B. K.↗
NASA NTRS2002

Ceramic Inclusions In Powder Metallurgy Disk Alloys: Characterization and Modeling

Powder metallurgy alloys are increasingly used in gas turbine engines, especially as the material chosen for turbine disks. Although powder metallurgy materials have many advantages over conventionally cast and wrought alloys (higher strength, higher temperature capability, etc.), they suffer from the rare occurrence of ceramic defects (inclusions) that arise from the powder atomization process. These inclusions can have potentially large detrimental effect on the durability of individual components. An inclusion in a high stress location can act as a site for premature crack initiation and thereby considerably reduce the fatigue life. Because these inclusions are exceedingly rare, they usually don't reveal themselves in the process of characterizing the material for a particular application (the cumulative volume of the test bars in a fatigue life characterization is typically on the order of a single actual component). Ceramic inclusions have, however, been found to be the root cause of a number of catastrophic engine failures. To investigate the effect of these inclusions in detail, we have undertaken a study where a known population of ceramic particles, whose composition and morphology are designed to mimic the 'natural' inclusions, are added to the precursor powder. Surface connected inclusions have been found to have a particularly large detrimental effect on fatigue life, therefore the volume of ceramic 'seeds' added is calculated to ensure that a minimum number will occur on the surface of the fatigue test bars. Because the ceramic inclusions are irregularly shaped and have a tendency to break up in the process of extrusion and forging, a method of calculating the probability of occurrence and expected intercepted surface and embedded cross-sectional areas were needed. We have developed a Monte Carlo simulation to determine the distributions of these parameters and have verified the simulated results with observations of ceramic inclusions found in macro slices from extrusions and forgings. The ultimate goal of this study will be to use probabilistic methods to determine the reliability detriment that can be attributed to these ceramic inclusions.

Bonacuse, Pete↗
NASA NTRS2001

Ceramic Inclusions in Powder Metallurgy Disk Alloys: Characterization and Modeling

Powder metallurgy alloys are increasingly used in gas turbine engines, especially in turbine disk applications. Although powder metallurgy materials have many advantages over conventionally cast and wrought alloys (higher strength, higher temperature capability, etc.), they suffer from the rare occurrence of ceramic defects (inclusions) that are inherent to the powder atomization process. These inclusions can have a potentially large detrimental effect on the durability of individual components. An inclusion in a high stress location can act as a site for premature crack initiation and thereby considerably reduce the fatigue life. Because these inclusions are exceedingly rare, they typically do not reveal themselves in the process of characterizing the material for a particular application (the cumulative volume of the test bars in a fatigue life characterization is typically on the order of a single actual component). Ceramic inclusions have, however, been found to be the root cause of a number of catastrophic engine failures. To investigate the effect of these inclusions in detail, we have undertaken a study where known populations of ceramic particles, whose composition and morphology are designed to mimic the "natural" inclusions, are added to the precursor powder. Surface-connected inclusions have been found to have a particularly large detrimental effect on fatigue life; therefore, the quantity of ceramic "seeds" added is calculated to ensure that a minimum number will intersect the surface of the fatigue test bars. Because the ceramic inclusions are irregularly shaped and have a tendency to break up in the process of extrusion and forging, a method of calculating the probability of occurrence and expected intercepted surface area was needed. We have developed a Monte Carlo simulation to determine the distributions of these parameters and have verified the simulated results with observations of ceramic inclusions found in macroscopic slices from extrusions and forgings. Fatigue specimens have been machined from Udimet 720 (a powder metallurgy superalloy) forgings, to determine the effects of the inclusions on fatigue life. The ultimate goal of this study will be to use probabilistic methods to determine the reliability detriment that can be attributed to these ceramic inclusions. This work has been supported by the Ultra Safe and Ultra- Efficient Engine Technologies programs.

Bonacuse, Peter J.↗
NASA NTRS1974

Thermodynamic properties derived from the free volume model of liquids

An equation of state and expressions for the isothermal compressibility, thermal expansion coefficient, heat capacity, and entropy of liquids have been derived from the free volume model partition function suggested by Turnbull. The simple definition of the free volume is used, and it is assumed that the specific volume is directly related to the cube of the intermolecular separation by a proportionality factor which is found to be a function of temperature and pressure as well as specific volume. When values of the proportionality factor are calculated from experimental data for real liquids, it is found to be approximately constant over ranges of temperature and pressure which correspond to the dense liquid phase. This result provides a single-parameter method for calculating dense liquid thermodynamic properties and is consistent with the fact that the free volume model is designed to describe liquids near the solidification point.

Miller, R. I.↗
NASA NTRS1980

On the barrier to crystal nucleation in lunar glasses

The paper describes an analytical method for calculating in detail the size distributions of small crystallites and nuclei in supercooled liquids as they are being quenched to form a glass and subsequently reheated above the glass transition to produce crystallization. This method is applied to experiments performed using differential thermal analysis (DTA) to estimate the barriers to crystal nucleation and the cooling rates required to form glasses or bodies with various degrees of crystallinity. DTA data and derived nucleation barriers are reported for anorthite and for the following lunar compositions: 15498, 15418, matrix and intrusion compositions of breccia 15286, Apollo 15 green glass, Luna 24 highland basalt, and 65016.

Yinnon, H.↗
NASA NTRS1998

Global Surface Ultraviolet Radiation Climatology from TOMS and ERBE Data

The overall goal of this project has been to develop a method for calculating the distribution of solar ultraviolet radiation (UVR) over most of the earth's surface using NASA's Total Ozone Mapping Spectrometer (TOMS) and Earth Radiation Budget Experiment (ERBE) data, and to use this method to develop a UVR climatology that is useful in the context of the global ozone depletion issue. The research carried out with this support has resulted the following accomplishments: (1) a radioactive transfer method. based on the delta-Eddington approximation, was successfully developed; (2) the method was applied to the five years of overlapping TOMS and ERBE Monthly-Hourly data to examine the impact of global variability in cloud cover on trends in surface UVR; (3) a presentation was made on effects of stratospheric ozone depletion; (4) the radioactive transfer model was finally applied to all daylight hours to make a through study of the global effect of cloud cover;and (6) a five-year global climatology of surface UVR based on all of the research has been prepared for general distribution.

Lubin, Dan↗
NASA NTRS1999

A Simple Method for Nucleon-Nucleon Cross Sections in a Nucleus

A simple reliable formalism is presented for obtaining nucleon-nucleon cross sections within a nucleus in nuclear collisions for a given projectile and target nucleus combination at a given energy for use in transport, Monte Carlo, and other calculations. The method relies on extraction of these values from experiments and has been tested and found to give excellent results.

Tripathi, R. K.↗
NASA NTRS1983

Compliance and stress sensitivity of spur gear teeth

The magnitude and variation of tooth pair compliance with load position affects the dynamics and loading significantly, and the tooth root stressing per load varies significantly with load position. Therefore, the recently developed time history, interactive, closed form solution for the dynamic tooth loads for both low and high contact ratio spur gears was expanded to include improved and simplified methods for calculating the compliance and stress sensitivity for three involute tooth forms as a function of load position. The compliance analysis has an improved fillet/foundation. The stress sensitivity analysis is a modified version of the Heywood method but with an improvement in the magnitude and location of the peak stress in the fillet. These improved compliance and stress sensitivity analyses are presented along with their evaluation using test, finite element, and analytic transformation results, which showed good agreement.

Cornell, R. W.↗
NASA NTRS1986

Finite strain calculations of continental deformation. I - Method and general results for convergent zones. II - Comparison with the India-Asia collision zone

The present investigation has the objective to perform numerical experiments on a rheologically simple continuum model for the continental lithosphere. It is attempted to obtain a better understanding of the dynamics of continental deformation. Calculations are presented of crustal thickness distributions, stress, strain, strain rate fields, latitudinal displacements, and finite rotations, taking into account as basis a model for continental collision which treats the litoshphere as a thin viscous layer subject to indenting boundary conditions. The results of this paper support the conclusions of England and McKenzie (1982) regarding the role of gravity in governing the deformation of a thin viscous layer subject to indenting boundary conditions. The results of the experiments are compared with observations of topography, stress and strain rate fields, and palaeomagnetic latitudinal displacements in Asia.

Houseman, G.↗
DOE OSTI2022

Comparing machine learning and interpolation methods for loop-level calculations

The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a process requires the evaluation of computationally intensive integrals. A wide variety of methods in machine learning have been used to tackle this problem, but often the motivation of using one method over another is lacking. Comparing these methods is typically highly dependent on the problem at hand, so we specify to the case where we can evaluate the function a large number of times, after which quick and accurate evaluation can take place. We consider four interpolation and three machine learning techniques and compare their performance on three toy functions, the four-point scalar Passarino-Veltman D_0 D 0 function, and the two-loop self-energy master integral M. We find that in low dimensions (d = 3), traditional interpolation techniques like the Radial Basis Function perform very well, but in higher dimensions (d=5, 6, 9) we find that multi-layer perceptrons (a.k.a neural networks) do not suffer as much from the curse of dimensionality and provide the fastest and most accurate predictions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Computer programs for plotting curves with various dashed-line sequences

Two FORTRAN-callable subprograms have been written to draw a smooth curve through a set of input points as a solid line or as a general sequence of long and short dashes. Subroutine LINSEQ draws conventional curves whereas subroutine CONSEQ draws smooth closed curves (contours). The subprograms are based on an approximate calculation of the arc length along the curve and spline interpolation along the arc length. Options are provided for smoothing of the input data and for offsetting the plotted curve from the input data points. The method of calculation of the arc length and the generation of the line sequence are described.Usage descriptions of the main subprograms, sample calling programs illustrating the various features of the subprograms, and sample plots are given. The subroutines should be readily adaptable to almost any computer-driven incremental plotter.

Desmarais, R. N.↗
NASA NTRS1972

The electromagnetic structure of interplanetary space

A method to calculate the three-dimensional structure of the interplanetary magnetic field is presented. The integrations are based on magnetograph recordings of longitudinal magnetic fields in the solar photosphere. The program by Altschuler and Newkirk is used to calculate the radial component of the magnetic field on the source surface, situated at r = 2.6r. This determines the inner boundary conditions for the integration outwards of the interplanetary field equations by means of the method that is described. Computer-drawn plots of the interplanetary field lines out to the earth's orbit are presented for the periods around the total solar eclipses of November 12, 1966, and March 7, 1970. During the former period the interplanetary field exhibited a clean, dipole-type structure, while during the latter period the field was more complicated and had four sectors in the equatorial plane. A movie was presented, showing how the interplanetary field structure rotates as seen by a magnetometer in the sun's equatorial plane.

Stenflo, J. O.↗