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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.

Mavriplis, Dimitri J.↗
NASA NTRS1995

Simultaneous concentration and purification through gradient deformation chromatography

Mobile-phase additives, commonly used to modulate absorbate retention in gradient elution chromatography, are usually assumed to be either linearly retained or unretained. Previous theoretical work from our laboratory has shown that these modulators, such as salts in ion-exchange and hydrophobic interaction chromatography and organic modifiers in reversed-phase chromatography, can absorb nonlinearly, giving rise to gradient deformation. Consequently, adsorbate peaks that elute in the vicinity of the head of the deformed gradient may exhibit unusual shapes, form shoulders, and/or be concentrated. These effects for a reversed-phase sorbent with aqueous acetonitrile (ACN) as the modulator are verified experimentally. Gradient deformation is demonstrated experimentally and agrees with simulations based on ACN isotherm parameters that are independently determined from batch equilibrium studies using the layer model. Unusual absorbate peak shapes were found experimentally for single-component injections of phenylalanine, similar to those calculated by the simulations. A binary mixture of tryptophan and phenylalanine is used to demonstrate simultaneous concentration and separation, again in agreement with simulations. The possibility of gradient deformation in ion-exchange and hydrophobic interaction chromatography is discussed.

NASA Discipline Number 93-10↗
NASA NTRS2004

Note on the Effect of Horizontal Gradients for Nadir-Viewing Microwave and Infrared Sounders

Passive microwave and infrared nadir sounders such as the Advanced Microwave Sounding Unit A (AMSU-A) and the Atmospheric InfraRed Sounder (AIRS), both flying on NASA s EOS Aqua satellite, provide information about vertical temperature and humidity structure that is used in data assimilation systems for numerical weather prediction and climate applications. These instruments scan cross track so that at the satellite swath edges, the satellite zenith angles can reach approx. 60 deg. The emission path through the atmosphere as observed by the satellite is therefore slanted with respect to the satellite footprint s zenith. Although radiative transfer codes currently in use at operational centers use the appropriate satellite zenith angle to compute brightness temperature, the input atmospheric fields are those from the vertical profile above the center of the satellite footprint. If horizontal gradients are present in the atmospheric fields, the use of a vertical atmospheric profile may produce an error. This note attempts to quantify the effects of horizontal gradients on AIRS and AMSU-A channels by computing brightness temperatures with accurate slanted atmospheric profiles. We use slanted temperature, water vapor, and ozone fields from data assimilation systems. We compare the calculated slanted and vertical brightness temperatures with AIRS and AMSU-A observations. We show that the effects of horizontal gradients on these sounders are generally small and below instrument noise. However, there are cases where the effects are greater than the instrument noise and may produce erroneous increments in an assimilation system. The majority of the affected channels have weighting functions that peak in the upper troposphere (water vapor sensitive channels) and above (temperature sensitive channels) and are unlikely t o significantly impact tropospheric numerical weather prediction. However, the errors could be significant for other applications such as stratospheric analysis. Gradients in ozone and tropospheric temperature appear to be well captured by the analyses. In contrast, gradients in upper stratospheric and mesospheric temperature as well as upper tropospheric humidity are less well captured. This is likely due in part to a lack of data to specify these fields accurately in the analyses. Advanced new sounders, like AIRS, may help to better specify these fields in the future.

Joiner, J.↗
NASA NTRS1997

A gradient in the duration of the G1 phase in the murine neocortical proliferative epithelium

Neuronogenesis in the neocortical pseudostratified ventricular epithelium (PVE) is initiated rostrolaterally and progresses caudo-medially as development progresses. Here we have measured the cytokinetic parameters and the fractional neuronal output parameter, Q, of laterally located early-maturing regions over the principal embryonic days (E12-E15) of neocortical neuronogenesis in the mouse. These measures are compared with ones previously made of a medial, late-maturing portion of the PVE. Laterally, as medially, the duration of the neuronogenetic interval is 6 days and comprises 11 integer cell cycles. Also, in both lateral and medial areas the length of G1 phase (TG1) increases nearly 4-fold and is the only cell cycle parameter to change. Q progresses essentially identically laterally and medially with respect to the succession of integer cell cycles. Most importantly, from E12 to E13 there is a steeply declining lateral to medial gradient in TG1. The gradient is due both to the lateral to medial graded stage of neuronogenesis and to the stepwise increase in TG1 with each integer cycle during the neuronogenetic interval. To our knowledge this gradient in TG1 of the cerebral PVE is the first cell biological gradient to be demonstrated experimentally in such an extensive proliferative epithelial sheet. We suggest that this gradient in TG1 is the cellular mechanism for positionally encoding a protomap of the neocortex within the PVE.

Non-NASA Center↗
NASA NTRS2006

Experiments on the Motion of Drops on a Horizontal Solid Surface due to a Wettability Gradient

Results from experiments performed on the motion of drops of tetraethylene glycol in a wettability gradient present on a silicon surface are reported and compared with predictions from a recently developed theoretical model. The gradient in wettability was formed by exposing strips cut from a silicon wafer to decyltrichlorosiland vapors. Video images of the drops captured during the experiments were subsequently analyzed for drop size and velocity as functions of position along the gradient. In separate experiments on the same strips, the static contact angle formed by small drops was measured and used to obtain the local wettability gradient to which a drop is subjected. The velocity of the drops was found to be a strong function of position along the gradient. A quasi-steady theoretical model that balances the local hydrodynamic resistance with the local driving force generally describes the observations; possible reasons for the remaining discrepancies are discussed. It is shown that a model in which the driving force is reduced to accomodate the hysteresis effect inferred from the data is able to remove most of the discrepancy between the observed and predicted velocities.

Moumen, Nadjoua↗
NASA NTRS2007

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

The scattering of rotor noise is an area that has received little attention over the years, yet the limited work that has been done has shown that both the directivity and intensity of the acoustic field may be significantly modified by the presence of scattering bodies. One of the inputs needed to compute the scattered acoustic field is the acoustic pressure gradient on a scattering surface. Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. These formulations are presented in this paper. The first formulation is derived by taking the gradient of Farassat's retarded-time Formulation 1A. Although this formulation is relatively simple, it requires numerical time differentiation of the acoustic integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. The acoustic pressure gradient predicted by these new formulations is validated through comparison with the acoustic pressure gradient determined by a purely numerical approach for two model rotors. The agreement between analytic formulations and numerical method is excellent for both stationary and moving observers case.

Lee, Seongkyu↗
NASA NTRS2008

Integrating the Gradient of the Thin Wire Kernel

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

Champagne, Nathan J.↗
NASA NTRSDate not supplied

A 3-D Nodal-Averaged Gradient Approach for Unstructured-Grid Cell-Centered Finite-Volume Methods for Application to Turbulent Hypersonic Flow

A 2-D nodal weighted least-squares gradient method and a related face-averaged nodal gradient approach that were developed for use with triangular grids are extended to 3-D for use with tetrahedral grids. In addition, a method, developed in 2-D, to stabilize the iterative convergence of these methods on quadrilateral cells is described and extended to 3-D and remedies are investigated to determine the nodal gradient averaging approach most suitable for use with grids made up of hexahedral, prismatic, pyramidal and tetrahedral cells. Moreover, due to an interest in hypersonic flow, a robust multidimensional gradient limiter procedure that is consistent with the stencil used to construct the nodal gradients is described. Finally, we demonstrate that the resulting 3-D methods are sufficiently robust for use in scramjet computations through the solution of three canonical turbulent hypersonic flow problems as well as a physically realistic 3-D scramjet inlet geometry.

Jeffery A White↗
NASA NTRSDate not supplied

Crucial Role of Thermal Gradients in MMS Fluxgate In-Flight Calibration

To meet the science goals of the Magnetospheric Multiscale (MMS) mission, the Fluxgate Magnetometer (FGM) must measure the ambient magnetic field with an accuracy of 0.1 nT. On a typical MMS orbit, the offsets (or zero levels) of the 3-axis FGM can vary by ~0.5 nT (exclusive of periods in Earth shadow). Previous studies have shown that these variations can be characterized as functions of sensor temperature, TS, and can thus be corrected to within 0.2 nT in the spin plane using in-flight calibration techniques (Bromund, et al., 2016, https://ntrs.nasa.gov/citations/20160014711). In that presentation, we noted two significant observations: A distinct function of TS must be used to characterize offsets during shadow: offsets at a given TScan differ by as much as 2 nT in shadow vs sunlight. Offsets change after maneuvers, without a commensurate change in TS . These changes can be as large as 2 nT. We now note a third, related observation: Offsets increase with proximity to the earth even when TS is constant, resulting in variations of ~0.2 nT at 4-5 Earth radii (RE) These effects are evidence that offsets are a multivariate function of TS and another factor, namely: thermal gradients. Due to the spacecraft spin, the Earth and the Sun each provide a relatively constant thermal input onto one instrument face while the opposite face remains in shadow, thus giving rise to thermal gradients. The thermal gradient depend on the orientation of the spin axis relative to the Earth or Sun. We observe that offsets vary by as much as 0.17 nT/degree as a function of the tilt of the spin axis towards the Sun. Thermal input from the Earth is dominated by Outgoing Longwave Radiation (OLR). Due to the proximity to Earth, the inverse proportion of the distance squared is a significant factor in the thermal gradient attributed to Earth OLR. We find that offsets can be corrected to <0.05 nT accuracy near perigee when accounting for these factors using empirically determined constants of proportionality that account for differences in emissivity of the top and bottom faces of the sensor to OLR (as well as other thermal effects). The changes in offset associated with thermal gradient are of the same order of magnitude as effects that were formerly attributed to sensor temperature alone, and thus both parameters are necessary to characterize the FGM offsets.

Kenneth R Bromund↗
NASA NTRS1971

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.↗
NASA NTRS1973

Interplanetary radial gradients of galactic cosmic ray protons and helium nuclei - Pioneer 8 and 9 measurements from 0.75 to 1.10 AU.

We report measurements of the radial interplanetary cosmic ray gradient made with cosmic ray instruments aboard the Pioneer 8 and 9 spacecraft. The time period covered in these studies is from January 1968 to June 1969. During this time, the radial separation of these two spacecraft varied from 0.75 to 1.10 AU from the sun. This study includes detailed measurements of the differential spectra and gradients of protons and helium nuclei from 2 to 1200 Mev/nucleon. The differential gradient for each species is observed to go through a broad maximum of about 50%/AU at energies corresponding to about 1 BV rigidity, decreasing at both lower and higher rigidities. The proton and helium nuclei gradients are small down to the lowest energies we measure.-

Webber, W. R.↗
NASA NTRS1976

Gradient optimization and nonlinear control

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

Hasdorff, L.↗
NASA NTRS1976

Further evidence of a latitude gradient in the solar wind velocity

Simultaneous Mariner and Explorer data are used in the present paper to show that the large-scale gradient in the bulk velocity of the solar wind observed by Coles (1972) is a heliographic latitude gradient. A value of roughly 15 km/sec/deg for the gradient is derived by a correlation technique employed by Coleman and Rosenberg (1971). A simple model of the velocity/latitude dependence is developed and is shown to be consistent with a direct comparison of the observed Mariner and Explorer velocities. The gradient inferred from the Mariner and Explorer data is compared with values obtained from corresponding analyses of Vela and IPS data.

Rhodes, E. J., Jr.↗
NASA NTRS1977

Turbulence measurements in axisymmetric supersonic boundary layer flow in adverse pressure gradients

Mean flow and turbulence measurements are presented for adiabatic compressible turbulent boundary layer flow in adverse pressure gradients. The gradients were induced on the wall of an axially symmetric wind tunnel by contoured centerbodies mounted on the wind tunnel centerline. The boundary layer turbulence downstream of a boundary layer bleed section in a zero pressure gradient was also examined. The measurements were obtained using a constant temperature hot-wire anemometer. The adverse pressure gradients were found to significantly alter the turbulence properties of the boundary layer. With flow through the bleed holes there was a measureable decrease in the rms longitudinal velocity fluctuations near the wall and the turbulent shear stress in the boundary layer was reduced.

Gootzait, E.↗
NASA NTRS1978

Lognormality of gradients of advected scalars

The gradient of an advected scalar in turbulent flow is treated in a coordinate system moving with a fluid particle. This Lagrangian coordinate system is chosen to be rotating such that the gradient vector lies along the 1-axis at all times; the final results are independent of this particular coordinate system. In the absence of diffusion, the magnitude of the gradient at the position of the fluid particle is shown to be a lognormal random process. The action of diffusion is to reduce the probability density for the largest values of the gradient.

Hill, R. J.↗
NASA NTRS1978

Effects of solid-propellant temperature gradients on the internal ballistics of the Space Shuttle

The internal ballistic effects of combined radial and circumferential grain temperature gradients are evaluated theoretically for the Space Shuttle solid rocket motors (SRMs). A simplified approach is devised for representing with closed-form mathematical expressions the temperature distribution resulting from the anticipated thermal history prior to launch. The internal ballistic effects of the gradients are established by use of a mathematical model which permits the propellant burning rate to vary circumferentially. Comparative results are presented for uniform and axisymmetric temperature distributions and the anticipated gradients based on an earlier two-dimensional analysis of the center SRM segment. The thrust imbalance potential of the booster stage is also assessed based on the difference in the thermal loading of the individual SRMs of the motor pair which may be encountered in both summer and winter environments at the launch site. Results indicate that grain temperature gradients could cause the thrust imbalance to be approximately 10% higher in the Space Shuttle than the imbalance caused by SRM manufacturing and propellant physical property variability alone.

Sforzini, R. H.↗
NASA NTRS1980

Stability of several oxide dispersion strengthened alloys and a directionally solidified gamma/gamma prime-alpha eutectic alloy in a thermal gradient

Thermal gradient testing of three oxide dispersion strengthened alloys (two Ni-base alloys, MA 754 and MA 6000 E, and the Fe-base MA 956) and the directionally solidified eutectic alloy, gamma/gamma prime-alpha, have been conducted. Experiments were carried out with maximum temperatures up to 1200 C and thermal gradients on the order of 100 C/mm. The oxide dispersion strengthened alloys were difficult to test because the thermal stresses promoted crack nucleation and growth; thus the ability of these alloys to maintain a thermal gradient may be limited. The stability of individual fibers in gamma/gamma prime-alpha was excellent; however, microstructural changes were observed in the vicinity of grain boundaries. Similar structures were also observed in isothermally annealed material; therefore thermal gradients do not affect the microstructure of gamma/gamma prime-alpha in any significant manner.

Staniek, G.↗
NASA NTRS1980

Experimental analysis of the boundary layer transition with zero and positive pressure gradient

The influence of a positive pressure gradient on the boundary layer transition is studied. The mean velocity and turbulence profiles of four cases are examined. As the intensity of the pressure gradient is increased, the Reynolds number of the transition onset and the length of the transition region are reduced. The Tollmein-Schlichting waves disturb the laminar regime; the amplification of these waves is in good agreement with the stability theory. The three dimensional deformation of the waves leads finally to the appearance of turbulence. In the case of zero pressure gradient, the properties of the turbulent spots are studied by conditional sampling of the hot-wire signal; in the case of positive pressure gradient, the turbulence appears in a progressive manner and the turbulent spots are much more difficult to characterize.

Arnal, D.↗