Search NASA⌕ Search

SEARCH · Search NASA

Results for “gradient calculation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Hybrid functional calculations of electronic structure and carrier densities in rare-earth monopnictides

The structural parameters and electronic structure of rare-earth pnictides are calculated using density functional theory (DFT) with the Heyd, Scuseria, and Ernzerhof (HSE06) screened hybrid functional. Specifically, we focus on RE-V compounds, with RE=La, Gd, Er, and Lu, and V=As, Sb, and Bi, and analyze the effects of spin-orbit coupling and treating the RE4$\textit{f}$ electrons as valence electrons in the projector augmented wave approach. The results of HSE06 calculations are compared with DFT within the generalized gradient approximation (DFT-GGA) and other previous calculations. We find that all these RE-V compounds are semimetals with electron pockets at the $\textit{X}$ point and hole pockets at Γ. Whereas in DFT-GGA the carrier density is significantly overestimated, the computed carrier densities using HSE06 is in good agreement with the available experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Transition to collapsed tetragonal phase in CaFe 2 As 2 single crystals as seen by 57 Fe Mössbauer spectroscopy

Temperature dependent measurements of 57 Fe Mössbauer spectra on CaFe 2 As 2 single crystals in the tetragonal and collapsed tetragonal phases are reported. Clear features in the temperature dependencies of the isomer shift, relative spectra area, and quadrupole splitting are observed at the transition from the tetragonal to the collapsed tetragonal phase. From the temperature dependent isomer shift and spectral area data, an average stiffening of the phonon modes in the collapsed tetragonal phase is inferred. The quadrupole splitting increases by ~25% on cooling from room temperature to ~100 K in the tetragonal phase and is only weakly temperature dependent at low temperatures in the collapsed tetragonal phase, in agreement with the anisotropic thermal expansion in this material. In order to gain microscopic insight about these measurements, we perform ab initio density functional theory calculations of the electric field gradient and the electron density of CaFe 2 As 2 in both phases. By comparing the experimental data with the calculations we are able to fully characterize the crystal structure of the samples in the collapsed-tetragonal phase through determination of the As z coordinate. Furthermore, based on the obtained temperature dependent structural data we are able to propose charge saturation of the Fe-As bond region as the mechanism behind the stabilization of the collapsed-tetragonal phase at ambient pressure.

36 MATERIALS SCIENCE↗

Spatial Patterns and Intensity of the Surface Storm Tracks in CMIP5 Models

To improve the understanding of storm tracks and western boundary current (WBC) interactions, surface storm tracks in 12 CMIP5 models are examined against ERA-Interim. All models capture an equatorward displacement toward the WBCs in the locations of the surface storm tracks’ maxima relative to those at 850 hPa. An estimated storm-track metric is developed to analyze the location of the surface storm track. It shows that the equatorward shift is influenced by both the lower-tropospheric instability and the baroclinicity. Basin-scale spatial correlations between models and ERA-Interim for the storm tracks, near-surface stability, SST gradient, and baroclinicity are calculated to test the ability of the GCMs’ match reanalysis. An intermodel comparison of the spatial correlations suggests that differences (relative to ERA-Interim) in the position of the storm track aloft have the strongest influence on differences in the surface storm-track position. However, in the North Atlantic, biases in the surface storm track north of the Gulf Stream are related to biases in the SST. An analysis of the strength of the storm tracks shows that most models generate a weaker storm track at the surface than 850 hPa, consistent with observations, although some outliers are found. A linear relationship exists among the models between storm-track amplitudes at 500 and 850 hPa, but not between 850 hPa and the surface. In total, the work reveals a dual role in forcing the surface storm track from aloft and from the ocean surface in CMIP5 models, with the atmosphere having the larger relative influence.

54 ENVIRONMENTAL SCIENCES↗

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 1: Summary report

The analysis uses a compressibility transformation and utilizes higher order closure rules to complete the transformation. By requiring that the momentum equations in differential form be satisfied at the wall and at the sublayer edge, correspondence rules are obtained which relate the variable property (VP) flow to a constant property (CP) flow in which mass transfer and pressure gradient occur simultaneously. A new CP formulation is developed and numerical results for a variety of cases are presented. Comparisons with earlier forms of the transformation and with experiment are included. For the zero pressure gradient case some differences between the various predictions are observed. For the several pressure gradient cases examined, the results are found to be essentially identical to those given by first order closure rules; i.e., by a form of transformation which relates the VP flow to a CP flow with pressure gradient but zero mass transfer.

Economos, C.↗

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 3: Computer program manual

A computer program is described capable of determining the properties of a compressible turbulent boundary layer with pressure gradient and heat transfer. The program treats the two-dimensional problem assuming perfect gas and Crocco integral energy solution. A compressibility transformation is applied to the equation for the conservation of mass and momentum, which relates this flow to a low speed constant property flow with simultaneous mass transfer and pressure gradient. The resulting system of describing equations consists of eight ordinary differential equations which are solved numerically. For Part 1, see N72-12226; for Part 2, see N72-15264.

Schneider, J.↗

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 2: Constant property turbulent boundary layer flow with simultaneous mass transfer and pressure gradient

An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.

Boccio, J.↗

A Residuals Approach to Filtering, Smoothing and Identification for Static Distributed Systems

An approach for state estimation and identification of spatially distributed parameters embedded in static distributed (elliptic) system models is advanced. The method of maximum likelihood is used to find parameter values that maximize a likelihood functional for the system model, or equivalently, that minimize the negative logarithm of this functional. To find the minimum, a Newton-Raphson search is conducted that from an initial estimate generates a convergent sequence of parameter estimates. For simplicity, a Gauss-Markov approach is used to approximate the Hessian in terms of products of first derivatives. The gradient and approximate Hessian are computed by first arranging the negative log likelihood functional into a form based on the square root factorization of the predicted covariance of the measurement process. The resulting data processing approach, referred to here by the new term of predicted data covariance square root filtering, makes the gradient and approximate Hessian calculations very simple. A closely related set of state estimates is also produced by the maximum likelihood method: smoothed estimates that are optimal in a conditional mean sense and filtered estimates that emerge from the predicted data covariance square root filter.

Rodriguez, G.↗

Small-scale cyclones on the periphery of a Gulf Stream warm-core ring

Small-scale cyclones found around Gulf Stream warm-core ring 82B are investigated by using infrared satellite images and current information obtained with an acoustic-Doppler velocimeter. Currents in these cyclones reveal speeds ranging from 20 to 80 cm/s. One small cyclone or 'ringlet' found in June 1982 was studied extensively by removing the basic rotational velocities of 82B. The azimuthal velocity field for this ringlet was used with the gradient current equation to calculate the absolute dynamic topography at 100 dbar. It was found that the ringlet was 13 dyn-cm lower than its surroundings. In addition, neglect of the centrifugal term would have changed the dynamic topography of the ringlet by 30 percent. From a comparison with CTD data the absolute reference level was determined, and a vertical profile of horizontal currents was calculated for the ringlet. Other cyclones were found throughout the slope water region around warm-core ring 82B with observable lifetimes of 1 to 2 weeks. The northeast quadrant of 82B was a favored generation site for ringlets. Two cyclones were observed to form in this region and were advected anticyclonically around 82B. Typically, at any one time, six cyclones with diameters of approximately 40 to 50 km can be detected north of the Gulf Stream by using satellite images.

Kennelly, M. A.↗

Influence of disk leakage path on labyrinth seal inlet swirl ratio

The results of numerous investigators have shown the importance of labyrinth seal inlet swirl on the calculated dynamic stiffness of labyrinth seals. These results have not included any calculation of inlet leakage swirl as a function of geometry and sealing conditions of the given seal. This paper outlines a method of calculating the inlet swirl at a given seal by introducing a radial chamber to predict the gas swirl as it goes from the stage tip down to the seal location. For a centrifugal compressor, this amounts to including the flow path from the impeller discharge, down the back of the disk or front of the cover, then into the shaft seal or eye packing, respectively. The solution includes the friction factors of both the disk and stationary wall with account for mass flow rate and calculation of radial pressure gradients by a free vortex solution. The results of various configurations are discussed and comparisons made to other published results of disk swirl.

Kirk, R. Gordon↗

An experimental study of the turbulent boundary layer on a transport wing in subsonic and transonic flow

The upper surface boundary layer on a transport wing model was extensively surveyed with miniature yaw probes at a subsonic and a transonic cruise condition. Additional data were obtained at a second transonic test condition, for which a separated region was present at mid-semispan, aft of mid-chord. Significant variation in flow direction with distance from the surface was observed near the trailing edge except at the wing root and tip. The data collected at the transonic cruise condition show boundary layer growth associated with shock wave/boundary layer interaction, followed by recovery of the boundary layer downstream of the shock. Measurements of fluctuating surface pressure and wingtip acceleration were also obtained. The influence of flow field unsteadiness on the boundary layer data is discussed. Comparisons among the data and predictions from a variety of computational methods are presented. The computed predictions are in reasonable agreement with the experimental data in the outboard regions where 3-D effects are moderate and adverse pressure gradients are mild. In the more highly loaded mid-span region near the trailing edge, displacement thickness growth was significantly underpredicted, except when unrealistically severe adverse pressure gradients associated with inviscid calculations were used to perform boundary layer calculations.

Spaid, Frank W.↗

Applications of interferometrically derived terrain slopes: Normalization of SAR backscatter and the interferometric correlation coefficient

Terrain slopes, which can be measured with Synthetic Aperture Radar (SAR) interferometry either from a height map or from the interferometric phase gradient, were used to calculate the local incidence angle and the correct pixel area. Both are required for correct thematic interpretation of SAR data. The interferometric correlation depends on the pixel area projected on a plane perpendicular to the look vector and requires correction for slope effects. Methods for normalization of the backscatter and interferometric correlation for ERS-1 SAR are presented.

Werner, Charles L.↗

Post-optimality analysis in aerospace vehicle design

This analysis pertains to the applicability of optimal sensitivity information to aerospace vehicle design. The present analysis demonstrates that post-optimality information generated through first-order computations can be used to accurately predict file effect of constraint and parameter perturbations on the optimal solution. This assessment is based on the solution of an aircraft design problem in which the post-optimality estimates are shown to be within a few percent of the true solution over the practical range of constraint and parameter variations. Through solution of a reusable, single-stage-to-orbit, launch vehicle design problem, this optimal sensitivity information is also shown to improve the efficiency of the design process. For a hierarchically decomposed problem, this computational efficiency is realizable by estimating the main-problem objective gradient through optimal sensitivity calculations. By reducing the need for finite differentiation of a re-optimized subproblem, a significant decrease in the number of objective function evaluations required to reach the optimal solution is obtained.

Braun, Robert D.↗

A CFD Approach to Modeling Spacecraft Fuel Slosh

Energy dissipation and resonant coupling from sloshing fuel in spacecraft fuel tanks is a problem that occurs in the design of many spacecraft. In the case of a spin stabilized spacecraft, this energy dissipation can cause a growth in the spacecrafts' nutation (wobble) that may lead to disastrous consequences for the mission. Even in non-spinning spacecraft, coupling between the spacecraft or upper stage flight control system and an unanticipated slosh resonance can result in catastrophe. By using a Computational Fluid Dynamics (CFD) solver such as Fluent, a model for this fuel slosh can be created. The accuracy of the model must be tested by comparing its results to an experimental test case. Such a model will allow for the variation of many different parameters such as fluid viscosity and gravitational field, yielding a deeper understanding of spacecraft slosh dynamics. In order to gain a better understanding of the dynamics behind sloshing fluids, the Launch Services Program (LSP) at the NASA Kennedy Space Center (KSC) is interested in finding ways to better model this behavior. Thanks to past research, a state-of-the-art fuel slosh research facility was designed and fabricated at Embry Riddle Aeronautical University (ERAU). This test facility has produced interesting results and a fairly reliable parameter estimation process to predict the necessary values that accurately characterize a mechanical pendulum analog model. The current study at ERAU uses a different approach to model the free surface sloshing of liquid in a spherical tank using Computational Fluid Dynamics (CFD) methods. Using a software package called Fluent, a model was created to simulate the sloshing motion of the propellant. This finite volume program uses a technique called the Volume of Fluid (VOF) method to model the interaction between two fluids [4]. For the case of free surface slosh, the two fluids are the propellant and air. As the fuel sloshes around in the tank, it naturally displaces the air. Using the conservation of mass, momentum, and energy equations, as well as the VOF equations, one can predict the behavior of the sloshing fluid and calculate the forces, pressure gradients, and velocity field for the entire liquid as a function of time.

Marsell, Brandon↗

Combined Structural Analysis of Core and Image Log of TGH 76-31 South East of Mt Baker, Washington State

Despite active volcanism, few geothermal energy resources have been developed in the Cascades Range. Temperature Gradient Hole 76-31 was drilled to ~440 m measured depth to probe for zones where fractures provide fluid conduits that transport deep volcanic heat to shallow depths that could support baseload, carbon neutral electrical generation. These zones were predicted by a Play Fairway assessment (PFA) of resource potential along a zone 11 km west-southwest of the summit of Mount Baker Volcano. Rock core, temperature logs, and an acoustic image log were obtained. By comparison to outcrops, the core has been initially interpreted as the Chilliwack group comprised of partially metamorphosed basaltic to andesitic volcanics. Core mapping reveals complex, steeply dipping networks of fractures and brecciation along slickensided strike slip faults; clay alteration is common in many of these structures. The majority of fractures are thoroughly healed by layers of chlorite and calcite; preservation of pyrite indicates anoxic conditions. The majority of fracture porosity resides in very dense fractures a few centimeters or less in length. The image log provides good insights into attitude of fractures that fully transect the core, but generally underestimates fracture density. The combination of complex, non-planar fracture zones containing many short fractures and healing promote misinterpretation of natural fracture attitude and density in the image log. The healing and anoxic minerals are consistent with the conductive temperature gradient measured in the well below a shallow isothermal zone, although, several fractures are open or only partially healed and resulted in fluid entries into the well. Here, the equilibrated measured temperature gradient of 64ºC/km and calculated heat flow of 145 mW/m2 is more than twice the regional average, indicating local influence of the Mt Baker magmatic system at the Little Park Creek TGH site.

Cascades↗

Density functional based methods for light harvesting molecules

The goal of the proposal was to computationally study the photoinduced charge transfer excited states of organic molecules. The systems of interest are the large organic supramolecules that have potential for photovoltaic applications. The simulation of the charge transfer excited states in large supramolecular assemblies require quantum mechanical methods that can be applied to systems with hundreds of atoms. Through this project we have implemented a perturbative delta-self-consistent field method that can easily describe the charge transfer excited states with regular density functionals without range separation. The cost of the calculations of an excited state is similar to that of the ground state. The method also allows for calculation of the energy gradients of the excited state. The developed method was applied to study a number of different supramolecular systems containing hundreds of atoms with excellent agreement with experiment. The absorption characteristics and the influence of density functional approximations were also examined. These led to several studies on the variety of organic electron donor and acceptor molecules. Apart from these developments through this project we also improved the code capabilities by implementing new meta-GGA functionals. This was a major step since the code is purely density functional and earlier the functional capabilities were limited only to generalized gradient approximations. A total of 23 peer-reviewed publications in top chemical physics journals resulted from this grant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fragmentation Prediction for a Brittle Ceramic: An Integrated Two-Scale Model Approach

A new implementation of a multi-scale fragmentation model is introduced that combines existing independent macro and micro-scale models into a single material model within the Library of Advanced Materials for Engineering (LAME) that can be used directly by the finite element structural mechanics code SIERRA/SM, developed at Sandia National Laboratories. The implementation not only joins existing independent fragmentation models into a single framework, but also enables further development by virtue of being integrated into SIERRA/SM. Integration with a finite element structural mechanics code for a true two-way coupling of the fragmentation models that were previously independent. Hereafter, the prior implementation will be referred to as the sequentially applied fragmentation model. In contrast, the newly developed model will be called the integrated two-scale model. The sequentially applied fragmentation model consists of two independent models applied sequentially to account for the macro-scale and microscale fragmentation. The macro-scale fragmentation behavior is calculated using an elastic gradient damage explicit material model developed to model fracture in brittle materials. The micro-scale fragmentation model is an implementation of the 1D cohesive-zone model developed by Zhou, et al. The micro-scale model is implemented by post-processing the macro-scale data that provides initial conditions for the 1D analysis. The micro-scale model is necessary to predict the resulting fragment size distribution at length scales inaccessible to the finite element based macro-scale model. The full range of fragmentation behavior is then predicted by combining the results from the two independent models. The sequentially applied fragmentation model was used to predict the fragments that result from impact loading of a brittle material, which in that case was a ceramic cylinder of commercial UO{sub 2} nuclear fuel. Understanding the fragmentation behavior of such materials is important for evaluating the risk of airborne particulate release under impact loading scenarios. This work will verify the implementation of the integrated two-scale model using the same experiment modeled by the existing sequentially applied model. The purpose of this manuscript is to introduce the new integrated two-scale fragmentation model and validate the implementation against the existing sequentially applied model for a specific case of impact loading of a brittle material. This validation case will not fully utilize the benefits of having the model integrated into the finite element code as a material model. Rather, this study will demonstrate consistency between the two fragmentation models to ensure that the success of the sequentially applied model will be duplicated by the integrated two-scale approach. Once validated, further development of the model can be made by utilizing the integration into the finite element code to create a fully two-way coupled fragmentation model that will be extended to include higher fidelity models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Investigation on Microsegregation of IN718 Alloy During Additive Manufacturing via Integrated Phase-Field and Finite-Element Modeling

In this work, we apply a multi-scale model combining finite-element method (FEM) and phase-field model (PFM) to simulate the evolution of solidification microstructures at different locations within a molten pool of an additively manufactured IN718 alloy. Specifically, the FEM is used to calculate the shape of molten pool and the relative thermal gradient G at the macroscale. Then, the calculated thermal information is input into PFM for microstructure simulation. Finally, the morphology of solidification structures and formation of Laves phase at different sites are studied and compared. We found that the solidification site with a large angle between the temperature gradient and the preferred crystalline orientation could build up a high niobium (Nb) concentration in the liquid during solidification but has less possibility of forming continuous long chain morphology of Laves phase particles. This finding provides an understanding of the microstructure evolution inside the molten pool of IN718 alloy during solidification. Further, the finding indicates that the site with a large misorientation angle will have a good hot cracking resistance after solidification.

36 MATERIALS SCIENCE↗