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NASA NTRSDate not supplied

Efficient Global Optimization with Gradient Finish for Design Under Uncertainty

The Efficient Global Optimization (EGO) algorithm is extended to include a gradient-descent-based finish upon reaching a threshold value of the expected improvement function. Emphasis is placed on efficient evaluation of local gradients using Kriging models during the gradient-based finish to enable application to design under uncertainty (DUU) problems. The modified algorithm is applied to both the well-known Rosenbrock function and a more challenging hypersonic inlet design under uncertainty problem. Results demonstrate improvement in locating the global optimum compared to the classical implementation of EGO, as well as a reduced number of true function evaluations compared to pure gradient-based algorithms. For the Rosenbrock function, a global optimum is returned using an average of 12% fewer function calls than a gradient-based optimizer with comparable tolerances. For the design under uncertainty problem, a global optimum is found using an average of 75% fewer function calls than a gradient-based optimizer. Global Pareto fronts of multiobjective DUU problems are obtained at little additional cost after a single optimization is complete.

Optimization↗
NASA NTRS2020

Experimental Setup and Parameters for Testing Uncoated and EBC-Coated CMCs under Thermal Gradients Induced by Laser Heating and Backside Air Cooling

An experimental setup to induce through thickness thermal gradients in ceramic matrix composite (CMC) specimens without and with an applied environmental barrier coating (EBC) is described in detail. Components of the experimental set up include a laser for the heat source on the front of the specimen, a cooling air nozzle on the back of the specimen with pyrometers to measure temperatures on both sides, and a full-field thermal image camera to ensure uniformity of the temperature distribution in the gage section of the specimen. Test specimen is loaded in a servohydraulic system, which can superimpose either static or dynamic loads on the specimen to investigate creep and fatigue behaviors of CMCs under through thickness thermal gradient conditions. Mechanical strains on the front and backsides of the test specimen were measured during the thermal gradient tests with superimposed mechanical loading using two contact extensometers. Selected through thickness thermal gradient test results generated with the experimental setup under different nominal front side temperatures and multiple constant laser power levels on uncoated and EBC coated CMCs and procedures used to generate those results are described in this report. Two examples of tests conducted using the test system on uncoated CMCs under creep and sustained-peak, low-cycle fatigue with through thickness thermal gradient conditions are provided.

ceramic matrix composite, environmental barrier co↗
NASA NTRSDate not supplied

Updates to Implicit Edge-Based Gradient Methods

In this paper, we report updates to the implicit edge-based gradient methods originally introduced in [H. Nishikawa, AIAA Paper 2020-3048, 2020]. First, we clarify the relationship between gradient accuracy and truncation error and show that the quadratic method involves a free parameter. Then, we provide a complete description and a simplified matrix form of the implicit gradient systems including a consistent boundary treatment, and derive a set of parameters for achieving fourth-order gradient accuracy on regular tetrahedral grids. A stability analysis is performed for a relaxation scheme used to solve the implicit gradient systems, and the result serves as a guide for choosing parameters. Numerical results are shown for accuracy verification and also for realistic inviscid flow problems in three dimensions, including flows with shock waves.

Weighted Least-Squares↗
NASA NTRS2024

Validation and Application of Satellite-Derived Sea Surface Temperature Gradients in the Bering Strait and Bering Sea

The Arctic is one of the most important regions in the world’s oceans for understanding the impacts of a changing climate. Yet, it is also difficult to measure because of extreme weather and ice conditions. In this work, we directly compare four datasets from the Group for High-Resolution Sea Surface Temperature (GHRSST) with a NASA Saildrone deployment along the Alaskan Coast and the Bering Sea and Bering Strait. The four datasets used are the Remote Sensing Systems Microwave Infrared Optimally Interpolated (MWIR) product, the Canadian Meteorological Center (CMC) product, the Daily Optimally Interpolated Product (DOISST), and the Operational Sea Surface Temperature and Ice Analysis (OSTIA) product. Spatial sea surface temperature (SST) gradients were derived for both the Saildrone deployment and GHRSST products, with the GHRSST products collocated with the Saildrone deployment. Overall, statistics indicate that the OSTIA product had a correlation of 0.79 and a root mean square difference of 0.11 °C/km when compared with Saildrone. CMC had the highest correlation of 0.81. Scatter plots indicate that OSTIA had the slope closest to one, thus best reproducing the magnitudes of the Saildrone gradients. Differences increased at latitudes > 65°N where sea ice would have a greater impact. A trend analysis was then performed on the gradient fields. Overall, positive trends in gradients occurred in areas along the coastal regions. A negative trend occurred at approximately 60°N. A major finding of this study is that future work needs to revolve around the impact of changing ice conditions on SST gradients. Another major finding is that a northward shift in the southern ice edge occurred after 2010 with a maxima at approximately 2019. This indicates that the shift of the southern ice edge is not gradual but has dramatically increased over the last decade. Future work needs to revolve around examining the possible causes for this northward shift.

Arctic↗
NASA NTRS1976

Temperature gradients and clear-air turbulence probabilities

In order to forecast clear-air turbulence (CAT) in jet aircraft flights, a study was conducted in which the data from a special-purpose instrument aboard a Boeing 747 jet airliner were compared with satellite-derived radiance gradients, conventional temperature gradients from analyzed maps, and temperature gradients obtained from a total air temperature sensor on the plane. The advantage of making use of satellite-derived data is that they are available worldwide without the need for radiosonde observations, which are scarce in many parts of the world. Major conclusions are that CAT probabilities are significantly higher over mountains than flat terrain, and that satellite radiance gradients appear to discriminate between CAT and no CAT better than conventional temperature gradients over flat lands, whereas the reverse is true over mountains, the differences between the two techniques being not large over mountains.

Bender, M. A.↗
NASA NTRS1979

The migration of fluid droplets and their interactions in a thermal gradient

When materials are processed in free fall, buoyant forces will be substantially reduced. Thus, the buoyant migration of droplets and bubbles which normally occurs on earth is expected to be overshadowed by migration due to other mechanisms in space processing. In particular, capillary forces on droplets due to the variation of interfacial tension around their periphery will play a significant role in governing their motion in space. While such interfacial tension gradients can be caused by thermal, compositional, and/or electrical gradients in the continuous phase, thermal gradients are convenient to use in controlled experimentation. On earth, due to interference from buoyant effects, it is difficult to study thermocapillary migration in sufficient detail. Also, the effects of a thermal gradient on the interactions among droplets are hard to study on Earth. Thus, an orbital facility for conducting experiments on the migration and interactions of fluid droplets in a continuous phase due to the action of a thermal gradient appears attractive.

Subramanian, R. S.↗
NASA NTRS1985

North-south asymmetry in activity on the Sun and cosmic ray density gradients

The marked N-S asymmetry in solar activity (with predominant activity in the Sun's Northern Hemisphere) during the 1960's could certainly account for a S-pointing cosmic ray gradient. It is also clear from the data that the response to this change in solar activity asymmetry, and the related change in the perpendicular cosmic ray density gradient, is different for cosmic ray telescopes in the Earth's Northern and Southern Hemispheres. Northern Hemisphere detectors see a S-pointing gradient in the 60's and a N-pointing gradient after 1971, while Southern Hemisphere telescopes see a S-pointing gradient both before and after the reversal.

Swinson, D. B.↗
NASA NTRS1985

Gradients and anisotropies of high energy cosmic rays in the outer heliosphere

Two cosmic rays which pass through the same point going in opposite directions will, in the absence of scattering and inhomogeneities in the magnetic field, trace helices about adjacent flux tubes, whose centerlines are separated by one gyrodiameter. A directional anisotropy at the point suggests a difference in the number of cosmic rays loading the two flux tubes; that is, a density gradient over the baseline of a gyrodiameter. Previous studies at lower energies have shown that the cosmic ray density gradients vary in time and space. It is suggested that the radial gradient associated with solar cycle modulation is supported largely by narrow barriers which encircle the sun and propagate outward with the solar wind. If so, the anisotropy is a desirable way to detect spatial gradients, because it can be associated with the local solar wind and magnetic field conditions. Anisotropic measurements made by Cerenkov detectors on Pioneers 10 and 11 were studied. It was found that local anisotropy varies greatly, but that the long term average is consistent with the global radial gradient measured between two spacecraft over a baseline of many AU.

Fillius, W.↗
NASA NTRS1987

Latitudinal and radial gradients of anomalous and galactic cosmic rays in the outer heliosphere

Measurements from instruments on Voyagers 1 and 2 and Pioneer 10 are used to derive simultaneous radial and latitudinal gradients of anomalous cosmic-ray oxygen during the latter part of 1985. It is found that in the energy interval from 7.1-30.6 MeV/nucleon the latitudinal gradient is -3 to -4 percent/deg. The sign of the latitudinal gradient is opposite to that reported for the last solar cycle when the solar magnetic field polarity was reversed, as predicted by propagation models in which curvature and gradient drifts are significant. The ratios of the radial and latitudinal gradients of anomalous oxygen, anomalous helium, and galactic cosmic rays are similar, also in agreement with drift theory predictions. Based on drift theory, these observed ratios, which are near unity, lead to estimates of the perpendicular diffusion coefficient/particle velocity ratio in the range 3-8 x 10 to the 22nd sq cm/sec at 24.9 AU for particles with rigidities of about 2-3 GV.

Cummings, A. C.↗
NASA NTRS1989

Acoustic response of a rectangular waveguide with a strong transverse temperature gradient

An acoustic wave equation was developed for a perfect gas with spatially-variable temperature. The strong-gradient wave equation was used to analyze the response of a rectangular wave guide containing a thermally-stratified gas. It was assumed that the temperature gradient is constant, representing one-dimensional heat transfer with a constant coefficient of conductivity. The analysis of the waveguide shows that the resonant frequencies of the waveguide are shifted away from the values that would be expected from the average temperature of the waveguide. For small gradients, the frequency shift is proportional to the square of the gradient. The factor of proportionality is a quadratic function of the natural frequency of the waveguide with uniform temperature. An experiment is designed to verify the essential features of the strong-gradient theory.

Zorumski, William E.↗
NASA NTRS1993

Dense cores in dark clouds. VIII - Velocity gradients

An analysis of motions consistent with uniform rotation in dense cores is presented. Twenty-nine of the 43 cores studied have a statistically significant gradient. Some gradients are spatially continuous and are consistent with uniform rotation, but other apparent gradients are caused by clump-clump motion, or sharp localized gradients, within a map. The motions in L1495, B217, L1251, L43, B361, and L1551 are discussed in detail. In L1551, the residuals of the fit to the NH3 velocity field indicate an outflow from IRS5 in the same direction as the CO outflow. Gradient orientation appears to be preserved over a range of density, as evidenced by comparing results of NH3 to fits of (C-18)O and CS maps. The specific angular momentum is found to scale roughly as F exp 3/2, where R represents the diameter of the FWHM intensity contour in a map.

Goodman, A. A.↗
NASA NTRS1991

Modeling turbulent boundary layers in adverse pressure gradients

Many of the turbulent layers encountered in practical flows develop in adverse pressure gradients; hence, the dynamics of the thickening and possible separation of the boundary layer has important implications for design practices. What are the key physical processes that govern how a turbulent boundary layer responds to an adverse pressure gradient, and how should these processes be modeled? Despite the ubiquity of such flows in engineering and nature, these equations remain largely unanswered. The turbulence closure models presently used to describe these flows commonly use 'wall functions' that have ad hoc corrections for the effects of pressure gradients. There is, therefore, a practical and theoretical need to examine the effects of adverse pressure gradients on wall bounded turbulent flows in order to develop models based on sound physical principle. The evolution of a turbulent boundary layer on a flat wall with an externally imposed pressure gradient is studied.

Belcher, Stephen E.↗
NASA NTRS1993

Thermoelastic response of metal matrix composites with large-diameter fibers subjected to thermal gradients

A new micromechanical theory is presented for the response of heterogeneous metal matrix composites subjected to thermal gradients. In contrast to existing micromechanical theories that utilize classical homogenization schemes in the course of calculating microscopic and macroscopic field quantities, in the present approach the actual microstructural details are explicitly coupled with the macrostructure of the composite. Examples are offered that illustrate limitations of the classical homogenization approach in predicting the response of thin-walled metal matrix composites with large-diameter fibers when subjected to thermal gradients. These examples include composites with a finite number of fibers in the thickness direction that may be uniformly or nonuniformly spaced, thus admitting so-called functionally gradient composites. The results illustrate that the classical approach of decoupling micromechanical and macromechanical analyses in the presence of a finite number of large-diameter fibers, finite dimensions of the composite, and temperature gradient may produce excessively conservative estimates for macroscopic field quantities, while both underestimating and overestimating the local fluctuations of the microscopic quantities in different regions of the composite. Also demonstrated is the usefulness of the present approach in generating favorable stress distributions in the presence of thermal gradients by appropriately tailoring the internal microstructure details of the composite.

Aboudi, Jacob↗
NASA NTRS1993

Simulation of sloshing dynamics induced forces and torques actuated on dewar container driven by gravity gradient and jitter accelerations in microgravity

Some experimental spacecraft use superconducting sensors for gyro read-out and so must be maintained at a very low temperature. The boil-off from the cryogenic liquid used to cool the sensors can also be used, as the Gravity Probe B (GP-B) spacecraft does, as propellant to maintain attitude control and drag-free operation of the spacecraft. The cryogenic liquid for such spacecraft is, however, susceptible to both slosh-like motion and non-axisymmetric configurations under the influence of various kinds of gravity jitter and gravity gradient accelerations. Hence, it is important to quantify the magnitude of the liquid-induced perturbations on the spacecraft. We use the example of the GP-B to investigate such perturbations by numerical simulations. For this spacecraft disturbances can be imposed on the liquid by atmospheric drag, spacecraft attitude control maneuvers, and the earth's gravity gradient. More generally, onboard machinery vibrations and crew motion can also create disturbances. Recent studies suggest that high frequency disturbances are relatively unimportant in causing liquid motions in comparison to low frequency ones. The results presented here confirm this conclusion. After an initial calibration period, the GP-B spacecraft rotates in orbit at 0.1 rpm about the tank symmetry axis. For this rotation rate, the equilibrium liquid free surface shape is a 'doughnut' configuration for all residual gravity levels of 10(exp -6) g(sub 0) or less, as shown by experiments and by numerical simulations; furthermore, the superfluid behavior of the 1.8 K liquid helium used in GP-B eliminates temperature gradients and therefore such effects as Marangoni convection do not have to be considered. Classical fluid dynamics theory is used as the basis of the numerical simulations here, since Mason's experiments show that the theory is applicable for cryogenic liquid helium in large containers. To study liquid responses to various disturbances, we investigate and simulate three levels of gravity jitter (10(exp -6), 10(exp -7), and 10(exp -8) g(sub 0)) each at three predominant frequencies (0.1, 1.0, and 10 Hz), combined with a gravity gradient appropriate for the GP-B orbit. Dynamical evolution of sloshing dynamics excited fluid forces and torque fluctuations exerted on the dewar container driven by the combined gravity gradient and jitter accelerations are also investigated and simulated.

Hung, R. J.↗
NASA NTRS1997

Effect of Temperature Gradient on Thick Film Selective Emitter Emittance

A temperature gradient across a thick (greater than or equal to .1 mm) film selective emitter will produce a significant reduction in the spectral emittance from the no temperature gradient case. Thick film selective emitters of rare earth doped host materials such as yttrium-aluminum-garnet (YAG) are examples where temperature gradient effects are important. In this paper a model is developed for the spectral emittance assuming a linear temperature gradient across the film. Results of the model indicate that temperature gradients will result in reductions the order of 20% or more in the spectral emittance.

Chubb, Donald L.↗
NASA NTRS1996

Solidification Interface Shape and Location During Processing in High Gradient Furnace with Quench

High Gradient Furnace with Quench (HGFQ) is being developed to facilitate metals processing experiments aboard the International Space Station. The sample is centered in an annular furnace and is held fixed during processing. The furnace itself is made to translate over the sample. Once in process, heat will flow through the sample from the Heater Zone to the Chill Zone. If operating conditions are correct, the solidification interface will stand in the gradient zone. Objectives of the HGFQ process are to provide a high gradient for the solidification with the solidification interface properly positioned in the gradient zone. At the recent RDR for HGFQ, one of the panelists raised the question about the suitability of HGFQ for potential future PIs. Specifically, it was stated by the design team at RDR that the present HGFQ design would provide a radius of curvature of the solidification interface of at least one sample diameter. The RDR panel argued that this was too small, and that most investigators would need a radius of curvature larger than this. The requirements established by the current PIs are shown. These requirements do not contain any specification about the interface shape. However, these requirements do define the envelope of operational parameters for HGFQ. The objectives of the present investigation are to 1) determine a suitable means of quantifying the interface shape, and 2) investigate the interface shape and how it is affected by processing parameters. The processing parameters to be considered are 1) sample material, 2) sample diameter, and 3) gradient zone length.

Woodbury, Keith A.↗
NASA NTRS2000

Influence of the Latitudinal Temperature Gradient on Soil Dust Concentration and Deposition in Greenland

To investigate the effects of changes in the latitudinal temperature gradient and the global mean temperature on dust concentration in the Northern Hemisphere, experiments with the GISS GCM (Goddard Institute for Space Studies General Circulation Model) are performed. The dust concentration over Greenland is calculated from sources in central and eastern Asia, which are integrated on-line in the model. The results show that an increase in the latitudinal temperature gradient increases both the Asian dust source strength and the concentration over Greenland. The source increase is the result of increased surface winds, and to a minor extent, the increase in Greenland dust is also associated with increased northward transport. Cooling the climate in addition to this increased gradient leads to a decrease in precipitation scavenging, which helps produce a further (slight) increase in Greenland dust in this experiment. Reducing the latitudinal gradient reduces the surface wind and hence the dust source, with a subsequent reduction in Greenland dust concentrations. Warming the climate in addition to this reduced gradient leads to a further reduction in Greenland dust due to enhanced precipitation scavenging. These results can be used to evaluate the relationship of Greenland ice core temperature changes to changes in the latitudinal and global temperatures.

Tegen, Ina↗
NASA NTRS2000

Influence of the Latitudinal Temperature Gradient on Soil Dust Concentration and Deposition in Greenland

To investigate the effects of changes in the latitudinal temperature gradient and the global mean temperature on dust concentration in the Northern Hemisphere, experiments with the Goddard Institute for Space Studies General Circulation Model (GISS GCM) are performed. The dust concentration over Greenland is calculated from sources in central and eastern Asia, which are integrated on-line in the model. The results show that an increase in the latitudinal temperature gradient increases both the Asian dust source strength and the concentration over Greenland. The source increase is the result of increased surface winds, and to a minor extent, the increase in Greenland dust is also associated with increased northward transport. Cooling the climate in addition to this increased gradient leads to a decrease in precipitation scavenging, which helps produce a further (slight) increase in Greenland dust in this experiment. Reducing the latitudinal gradient reduces the surface wind and hence the dust source, with a subsequent reduction in Greenland dust concentrations. Warming the climate in addition to this reduced gradient leads to a further reduction in Greenland dust due to enhanced precipitation scavenging. These results can be used to evaluate the relationship of Greenland ice core temperature changes to changes in the latitudinal and global temperatures.

Tegen, Ina↗