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NASA NTRS2010

Probabilistic Structural Analysis Program

NASA/NESSUS 6.2c is a general-purpose, probabilistic analysis program that computes probability of failure and probabilistic sensitivity measures of engineered systems. Because NASA/NESSUS uses highly computationally efficient and accurate analysis techniques, probabilistic solutions can be obtained even for extremely large and complex models. Once the probabilistic response is quantified, the results can be used to support risk-informed decisions regarding reliability for safety-critical and one-of-a-kind systems, as well as for maintaining a level of quality while reducing manufacturing costs for larger-quantity products. NASA/NESSUS has been successfully applied to a diverse range of problems in aerospace, gas turbine engines, biomechanics, pipelines, defense, weaponry, and infrastructure. This program combines state-of-the-art probabilistic algorithms with general-purpose structural analysis and lifting methods to compute the probabilistic response and reliability of engineered structures. Uncertainties in load, material properties, geometry, boundary conditions, and initial conditions can be simulated. The structural analysis methods include non-linear finite-element methods, heat-transfer analysis, polymer/ceramic matrix composite analysis, monolithic (conventional metallic) materials life-prediction methodologies, boundary element methods, and user-written subroutines. Several probabilistic algorithms are available such as the advanced mean value method and the adaptive importance sampling method. NASA/NESSUS 6.2c is structured in a modular format with 15 elements.

Pai, Shantaram S.↗

DOE OSTI2020

Systematic over-estimation of lattice thermal conductivity in materials with electrically-resistive grain boundaries

Reducing the thermal conductivity κ of a material via nano-structuring to create small grain sizes is one of the most common strategies to improve thermoelectric materials. In such polycrystalline materials heat carrying phonons are scattered at the grain boundaries, which directly improves the thermoelectric quality factor and ultimately the figure-of-merit zT. In some cases, however, such as in Mg 3 Sb 2 , SnSe, and Mg 2 Si an opposite trend is found where higher lattice thermal conductivity reported in small grain polycrystalline material than in large grain or single crystal materials. This unphysical result indicates a problem with the conventional use of the Wiedemann–Franz law. Here, we trace this problematic finding to the electrical resistance at the grain boundaries, which leads to an overestimation of the phonon or lattice contribution of the thermal conductivity κ L . In materials with significant grain boundary electrical resistance, the estimated electronic contribution to the thermal conductivity LσT is low because the measured electrical conductivity σ is low. However within the grain electrons may still be transporting more heat than the total conductivity suggests, leading to an overestimation of κ L if the conventional κ L = κ – LσT is used with the measured values of κ and σ. Here, the overestimation of κL in small-grain samples is shown to be pervasive across a broad range of thermoelectric materials, including Mg 3 Sb 2 , Mg 2 Si, PbTe, PbSe, SnSe, (Hf,Zr)CoSb, CoSb 3 , and Bi 2 Te 3 alloys, and a correction is necessary to properly understand and predict their charge and heat transport.

36 MATERIALS SCIENCE↗

NASA NTRS1976

Effect of velocity gradients on measurements of turbulent shear stress

Experiments were carried out to evaluate the effects of normal velocity gradients on hot wire measurements in a subsonic boundary layer of the same size as the flow investigated by Johnson and Rose (1975). Both hot wire and film anemometers were used to measure the turbulent properties of the boundary layer. A special X-wire probe with one wire vertical and the other at an angle of about 40 deg to the flow was used to demonstrate the gradient effects. The results indicate that major errors are encountered when mean and turbulent velocity gradients exist along the length of hot wire sensors, the problem being more pronounced at high speeds. Although the split film sensor results show a significant improvement over the X-wire sensor, further reduction in the space resolution of sensors by roughly an order of magnitude would appear to be necessary to reduce the error to acceptable values near the wall.

Sandborn, V. A.↗

NASA NTRS1994

H2O-H2SO4 system in Venus' clouds and OCS, CO, and H2SO4 profiles in Venus' troposphere

A coupled problem of diffusion and condensation is solved for the H2SO4-H2O system in Venus' cloud layer. The position of the lower cloud boundary and profiles of the H2O and H2SO4 vapor mixing ratios and of the H2O/H2SO4 ratio of sulfuric acid aerosol and its flux are calculated as functions of the column photochemical production rate of sulfuric acid, Phi(sub H2SO4). Variations of the lower cloud boundary are considered. Our basic model, which is constrained to yield f(sub H2O) (30 km) = 30 ppm (Pollack et al. 1993), predicts the position of the lower cloud boundary at 48.4 km coinciding with the mean Pioneer Venus value, the peak H2SO4 mixing ratio of 5.4 ppm, and the H2SO4 production rate Phi(sub H2SO4) = 2.2 x 10(exp 12)/sq cm/s. The sulfur to sulfuric acid mass flux ratio in the clouds is 1:27 in this model, and the mass loading ratio may be larger than this value if sulfur particles are smaller than those of sulfuric acid. The model suggests that the extinction coefficient of sulfuric acid particles with radius 3.7 micrometers (mode 3) is equal to 0.3/km in the middle cloud layer. The downward flux of CO is equal to 1.7 x 10(exp 12)/sq cm/s in this model. Our second model, which is constrained to yield f(sub H2O) = 10 ppm at the lower cloud boundary, close to the value measured by the Magellan radiooccultations, predicts the position of this boundary to be at 46.5 km, which agrees with the Magellan data; f(sub H2O) (30 km) = 90 ppm, close to the data of Moroz et al. (1983) at this altitude; Phi(sub H2SO4) = 6.4 x 10(exp 12)/sq cm/s; and Phi(sub co) = 4.2 x 10(exp 12)/sq cm/s. The S/H2SO4 flux mass ratio is 1:18, and the extinction coefficient of the mode 3 sulfuric acid particles is equal to 0.9 km in the middle cloud layer. A strong gradient of the H2SO4 vapor mixing ratio near the bottom of the cloud layer drives a large upward flux of H2SO4, which condenses and forms the excessive downward flux of liquid sulfuric acid, which is larger by a factor of 4-7 than the flux in the middle cloud layer. This is the mechanism of formation of the lower cloud layer. Variations of the lower cloud layer are discussed. Our modeling of the OCS and CO profiles in the lower atmosphere measured by Pollack et al. (1993) provides a reasonable explanation of these data and shows that the rate coefficient of the reaction SO3 + CO yields CO2 + SO2 is equal to 10(exp -11) exp(-(13,100 +/- 1000)/T) cc/s. The main channel of the reaction between SO3 and OCS is CO2 + (SO)2, and its rate coefficient is equal to 10(exp -11) exp(-(8900 +/- 500)/T) cc/s. In the conditions of Venus' lower atmosphere, (SO)2 is removed by the reaction (SO)2 + OCS yields CO + S2 + SO2. The model predicts an OCS mixing ratio of 28 ppm near the surface.

Krasnopolsky, V. A.↗

NASA NTRS1995

Bidirectional reflectance of oceanic waters: A comparison of modeled and measured upward radiance fields

The bidirectional reflectance of oceanic waters is conveniently described in a normalized way by forming the ratio of the upwelling irradiance E(sub u) to any upwelling radiance L(sub u)(theta prime, phi). This ratio, Q (theta prime, theta(sub 0), (phi(sub 0) - phi), where theta prime, phi are the nadir and azimuth angles for the upward radiance and theta(sub 0), phi(sub 0) are the zenith and azimuth angles of the Sun, has been determined from measurements at sea and computed via Monte Carlo simulations using the inherent optical properties measured in the field and appropriate boundary conditions (clear sky, no wind, varying Sun angle). Experimental ad computed Q values are in excellent agreement. This successful comparison confirms the importance of the bidirectional character of ocean reflectance, already pointed out from a purely numerical approach without field validation, and corroborates the extended range of the Q variations. The later point is of importance when interpreting the marine signals detected by an ocean color satellite-borne sensor. The validation is extended by considering the historical data for the radiance distributions in Lake Pend Oreille determined at various depths. The closure issue in ocean optics is examined by solving the direct problem of radiative transfer and through a model-data comparison in terms of radiance field.

Morel, Andre↗

NASA NTRS1979

The interaction between giant gaseous protoplanets and the primitive solar nebula

The manner in which a giant gaseous protoplanet becomes embedded in the primitive solar nebula determines surface boundary conditions which must be used in studying the evolution of such objects. On the one hand, if the system resembles a contact binary system, then the envelope of the protoplanet should approach the entropy of the surrounding nebula. On the other hand angular momentum transfer by resonance and tidal effects between the nebula and the protoplanet may cause the nebula to exhibit a zone of avoidance near the protoplanet, thus inhibiting exchange of material. This problem has been studied with a computer program developed by D. N. C. Lin which simulates disk hydrodynamics by particle motions with dissipation. These studies suggest that for expected values of the protoplanet/protosun mass ratios, significant inhibition of mass exchange is likely, so that it is a reasonable next step to undertake protoplanet evolution studies with the imposition of minimum protoplanet surface temperatures.

Cameron, A. G. W.↗

NASA NTRS1990

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.

Bodonyi, R. J.↗

NASA NTRS1992

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

Bodonyi, R. J.↗

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

Cohn, Stephen E.↗

NASA NTRS1966

Calculated blade response at high tip-speed ratios

This paper presents the initial results of a digital computer study of helicopter rotor-blade-motion stability for a broad range of forward speeds encompassing proposed conventional and compound helicopter designs. The analysis treats the general case of nonlinear, coupled flapping and lagging motions of hinged rigid blades. The results of the study to date indicate that blade-motion stability boundaries cannot be specified for a given blade design in terms of a fixed value of rotor tip-speed ratio. The stability boundaries can shift significantly within the desired operational speed range, with the stability limits depending upon the rotor loading, the magnitude of the disturbance encountered by the blade, and the blade position at the instant the external disturbance is encountered. The sample methods suggested for improving blade-motion stability include increasing the effective hinge spring restraint by incorporating pitch-flap coupling or by using hingeless or teetering rotor systems. Reducing rotor loading also has a beneficial effect on the blade-motion stability. The results indicate that methods used to deal with the blade-motion stability problem can be expected to diminish the overall vibration levels of the helicopter rotor system across the entire design speed range.

TIP SPEED↗

NASA NTRS1996

A New Higher-Order Composite Theory for Analysis and Design of High Speed Tilt-Rotor Blades

A higher-order theory is developed to model composite box beams with arbitrary wall thicknesses. The theory, based on a refined displacement field, represents a three-dimensional model which approximates the elasticity solution. Therefore, the cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are automatically included in the formulation. The model accurately captures the transverse shear stresses through the thickness of each wall while satisfying all stress-free boundary conditions. Several numerical results are presented to validate the present theory. The developed theory is then used to model the load carrying member of a tilt-rotor blade which has thick-walled sections. The composite structural analysis is coupled with an aerodynamic analysis to compute the aeroelastic stability of the blade. Finally, a multidisciplinary optimization procedure is developed to improve the aerodynamic, structural and aeroelastic performance of the tilt-rotor aircraft. The Kreisselmeier-Steinhauser function is used to formulate the multiobjective function problem and a hybrid approximate analysis is used to reduce the computational effort. The optimum results are compared with the baseline values and show significant improvements in the overall performance of the tilt-rotor blade.

McCarthy, Thomas Robert↗

NASA NTRS1982

Finite analytic numerical solution of axisymmetric Navier-Stokes and energy equations

Convective heat transfer for steady state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature and heat transfer coefficients for flow with Reynolds number of 5.0, 100.0, 1000.0, and 2000.0, and Prandtl number of 0.1, 1.0, and 10.0 with uniform grid sizes are reported for axisymmetric pipe with sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic solution is stable, converges rapidly, and simulates the convection of fluid flow accurately since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values thereby minimizing the false numerical diffusion.

Chen, C.-J.↗

NASA NTRS2011

Space-Time Data Fusion

Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.

Greenhouse Gases Observing Satellite (GOSAT)↗

DOE OSTI2025

Information theory optimization of signals from small-angle scattering measurements

Small-angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions is resolution limited, and through an inverse Fourier transform, the measured SAXS intensities directly relate to the physical space occupied by the particles via the P (r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible, provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment, suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P (r)-distribution. The hybrid score utilizes the Akaike information criteria and Durbin-Watson statistic that considers parameter-model complexity, i.e., degrees of freedom, and the randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best parameter model appropriately representing the observed scattering data.

Rambo, Robert P. [Science and Technology Facilitie↗

DOE OSTI2021

Lattice determination of 𝐼=0 and 2 𝜋⁢𝜋 scattering phase shifts with a physical pion mass

Phase shifts for 𝑠-wave 𝜋⁢𝜋 scattering in both the 𝐼 =0 and 𝐼 =2 channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of 32 3 ×64. These results support our recent 2021 study of direct 𝐶⁢𝑃 violation in 𝐾 → 𝜋⁢𝜋 decay, improving our earlier 2015 calculation. The phase shifts are determined for both stationary and moving 𝜋⁢𝜋 systems, at three (𝐼 = 0) and four (𝐼 = 2) different total momenta. We implement several 𝜋⁢𝜋 interpolating operators including a scalar bilinear “𝜎” operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1983

Spherical accretion onto quasars

The problem of time-steady accretion of gas irradiated by a self-consistently generated quasar-like continuum is investigated. A controversy in the literature is resolved by a careful distinction between the existence of solutions and their stability. Specific criteria are found for when thermal instabilities may disrupt single-phase steady flow. As a function of initial temperature (1,000,000-100,000,000 K), the boundaries of stable flow in the luminosity are determined relative to the Eddington (L/LE)-efficiency plane. The thermal and dynamical history of these steady flows is analyzed. The observational data that define quasars and type I Seyfert galaxies are matched to find values of efficiency and L/LE required for consistent spherically symmetric steady-flow models. The efficiency is constrained to be less than 1/100, and L/LE resides between several times 1/1000-1/100.

Krolik, J. H.↗

NASA NTRS1996

Kinetics of Diffusional Droplet Growth in a Liquid/Liquid Two-Phase System

We address the problem of diffusional interactions in a finite sized cluster of spherical particles for volume fractions, V(sub v) in the range 0-0.01. We determined the quasi-static monopole diffusion solution for n particles distributed at random in a continuous matrix. A global mass conservation condition is employed, obviating the need for any external boundary condition. The numerical results provide the instantaneous (snapshot) growth or shrinkage rate of each particle, precluding the need for extensive time-dependent computations. The close connection between these snapshot results and the coarsegrained kinetic constants are discussed. A square-root dependence of the deviations of the rate constants from their zero volume fraction value is found for the higher V(sub v) investigated. This behavior is consistent with predictions from diffusion Debye-Huckel screening theory. By contrast, a cube-root dependence, reported in earlier numerical studies, is found for the lower V(sub v) investigated. The roll-over region of the volume fraction where the two asymptotics merge depends on the number of particles, n, alone. A theoretical estimate for the roll-over point predicts that the corresponding V(sub v) varies as n(sup -2), in good agreement with the numerical results.

Glicksman, M. E.↗