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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Numerical solution of singular Lyapunov equations

We consider the numerical solution of large scale singular (continuous-time) Lyapunov equations of the form AX + XA T + BB T = 0, where A is semistable, that is, its spectrum is contained in the left half plane, with the exception of a few semisimple eigenvalues at zero. We also consider the case of a few semisimple eigenvalues on the imaginary axis. We assume that we know these few eigenvalues (zero or imaginary), and that we have or can compute the corresponding invariant subspaces. We use this information to build an appropriate newly proposed subspace on which to project the Lyapunov equations, and then compute a low-rank approximation to the least squares solution. Selected illustrative numerical examples are provided.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1962

ELASTIC STABILITY OF SIMPLY SUPPORTED CORRUGATED CORE SANDWICH CYLINDERS

Theoretical buckling coefficients are obtained for the general instability of simply supported, corrugated core sandwich circular cylinders under combined loads with the core oriented parallel to the longitudinal axis of the cylinder. Buckling curves are presented for axial compression, external lateral pressure, torsion, and some typical interactions. The differential equations of equilibrium used to obtain the buckling equations were derived from the small deflection equations of Stein and Mayer which include the effect of deformation due to transverse shear. These equations are solved by Galerkin's equation. Remarks are made concerning the probable validity of the results of the small deflection theory for sandwich shells.

SHELL STABILITY↗
DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗
NASA NTRS1982

Pressure distributions and shock shapes for a bent-nose biconic at incidence

Initial results of a NASA study of the lift-drag characteristics of a 12.84/7 deg biconic model intended for airbraking during atmospheric entry of probes to Mars, Venus, Saturn, and Titan are reported. Pressure distributions and shock shapes were measured in the Langley 20 in. Mach 6 tunnel with the spherically blunted bent-nose model set at angles from 0-25 deg. Pressure distributions and shock shapes where computed using the STEIN flowfield code, which features a MacCormack scheme to integrate the three-dimensional Euler equations, the Rankine-Hugoniot jump conditions to model shock waves as discontinuities, and requires a supersonic condition at every step. A comparison was made between measured and predicted values. The leeward shock angle was found to be predictable to within 3% for all angles of attack, while parabolized Navier-Stokes equations are regarded as offering more accurate results than the STEIN code for surface pressure distributions.

Miller, C. G., III↗
DOE OSTI2020

The shock physics of giant impacts: Key requirements for the equations of state

We discuss major challenges in modeling giant impacts between planetary bodies, focusing on the equations of state (EOS). During the giant impact stage of planet formation, rocky planets are melted and partially vaporized. However, most EOS models fail to reproduce experimental constraints on the thermodynamic properties of the major minerals over the required phase space. Here, we present an updated version of the widely-used ANEOS model that includes a user-defined heat capacity limit in the thermal free energy term. Our revised model for forsterite (Mg 2 SiO 4 ), a common proxy for the mantles of rocky planets, provides a better fit to material data over most of the phase space of giant impacts. We discuss the limitations of this model and the Tillotson equation of state, a commonly used alternative model.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1999

Energy expenditure and balance during spaceflight on the space shuttle

The objectives of this study were as follows: 1) to measure human energy expenditure (EE) during spaceflight on a shuttle mission by using the doubly labeled water (DLW) method; 2) to determine whether the astronauts were in negative energy balance during spaceflight; 3) to use the comparison of change in body fat as measured by the intake DLW EE, 18O dilution, and dual energy X-ray absorptiometry (DEXA) to validate the DLW method for spaceflight; and 4) to compare EE during spaceflight against that found with bed rest. Two experiments were conducted: a flight experiment (n = 4) on the 16-day 1996 life and microgravity sciences shuttle mission and a 6 degrees head-down tilt bed rest study with controlled dietary intake (n = 8). The bed rest study was designed to simulate the flight experiment and included exercise. Two EE determinations were done before flight (bed rest), during flight (bed rest), and after flight (recovery). Energy intake and N balance were monitored for the entire period. Results were that body weight, water, fat, and energy balance were unchanged with bed rest. For the flight experiment, decreases in weight (2.6 +/- 0.4 kg, P < 0.05) and N retention (-2. 37 +/- 0.45 g N/day, P < 0.05) were found. Dietary intake for the four astronauts was reduced in flight (3,025 +/- 180 vs. 1,943 +/- 179 kcal/day, P < 0.05). EE in flight was 3,320 +/- 155 kcal/day, resulting in a negative energy balance of 1,355 +/- 80 kcal/day (-15. 7 +/- 1.0 kcal. kg-1. day-1, P < 0.05). This corresponded to a loss of 2.1 +/- 0.4 kg body fat, which was within experimental error of the fat loss determined by 18O dilution (-1.4 +/- 0.5 kg) and DEXA (-2.4 +/- 0.4 kg). All three methods showed no change in body fat with bed rest. In conclusion, 1) the DLW method for measuring EE during spaceflight is valid, 2) the astronauts were in severe negative energy balance and oxidized body fat, and 3) in-flight energy (E) requirements can be predicted from the equation: E = 1.40 x resting metabolic rate + exercise.

Non-NASA Center↗
NASA NTRS1982

An experimental investigation of hypersonic flow over biconics at incidence and comparison to prediction

Pressure distributions, aerodynamic coefficients, shock shapes, and oil-flow patterns were measured on spherically blunted, 12.84 deg/7 deg on-axis and bent biconics at Mach 6 in air. The angle of attack, referenced to the axis of the aft-cone, was varied from -10 to 40 deg in nominal 5 deg increments. Predictions from an inviscid flowfield computer code referred to as STEIN and codes which solve the three-dimensional parabolized Navier Stokes (PNS) equations were compared with measurement. Three PNS codes were found which provided accurate predictions of windward and leeward pressure distributions for angles of attack to 25 deg.

Miller, C. G.↗
NASA NTRS1972

Theoretical study of the ionospheric G factor

A derivation from kinetic theory of the energy balance equation used in wave interaction work is reviewed. Then G is defined and two models for G are presented: one, a model based on Gerjuoy-Stein cross sections for both O2 and N2; the other based on a more recent model for O2 cross sections. The two models differ considerably in their temperature dependence. The limits of applicability of the useful energy balance equation (hence of the concept of G) are discussed and it is found that no difficulty arises unless the transmitter power is more than 1000 times that now employed at the present operating frequency.

Hagenbuch, K. M.↗
NASA NTRS1978

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

Stein, M.↗
NASA NTRS1985

Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing

Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.

Stein, M.↗
NASA NTRS1947

Critical stress of thin-walled cylinders in axial compression

Empirical design curves are presented for the critical stress of thin-wall cylinders loaded in axial compression. These curves are plotted in terms of the nondimensional parameters of small-deflection theory and are compared with theoretical curves derived for the buckling of cylinders with simply supported and clamped edges. An empirical equation is given for the buckling of cylinders having a length-radius ratio greater than about 0.75.

Batdorf, S B↗
NASA NTRS1988

Laser pyrometry

A method of determining the emissivity of a hot target from a laser-based reflectance measurement which is conducted simultaneously with a measurement of the target radiance is described. Once the correct radiance and emissivity are determined, one calculates the true target temperature from these parameters via the Planck equations. The design and performance of a laser pyrometer is described. The accuracy of laser pyrometry and the effect of ambient radiance are addressed.

Stein, Alexander↗
NASA NTRS1993

Advances in time-scale algorithms

The term clock is usually used to refer to a device that counts a nearly periodic signal. A group of clocks, called an ensemble, is often used for time keeping in mission critical applications that cannot tolerate loss of time due to the failure of a single clock. The time generated by the ensemble of clocks is called a time scale. The question arises how to combine the times of the individual clocks to form the time scale. One might naively be tempted to suggest the expedient of averaging the times of the individual clocks, but a simple thought experiment demonstrates the inadequacy of this approach. Suppose a time scale is composed of two noiseless clocks having equal and opposite frequencies. The mean time scale has zero frequency. However if either clock fails, the time-scale frequency immediately changes to the frequency of the remaining clock. This performance is generally unacceptable and simple mean time scales are not used. First, previous time-scale developments are reviewed and then some new methods that result in enhanced performance are presented. The historical perspective is based upon several time scales: the AT1 and TA time scales of the National Institute of Standards and Technology (NIST), the A.1(MEAN) time scale of the US Naval observatory (USNO), the TAI time scale of the Bureau International des Poids et Measures (BIPM), and the KAS-1 time scale of the Naval Research laboratory (NRL). The new method was incorporated in the KAS-2 time scale recently developed by Timing Solutions Corporation. The goal is to present time-scale concepts in a nonmathematical form with as few equations as possible. Many other papers and texts discuss the details of the optimal estimation techniques that may be used to implement these concepts.

Stein, S. R.↗