Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Averages”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Approaches for averaging surface parameters and fluxes over heterogeneous terrain

Successful prediction of possible climate change depends on realistic parameterization of land surface processes in climate models. Such parameterizations must take appropriate account of the heterogeneities that are found in most earth surfaces. In this study, different averaging strategies for aggregating patch-scale heterogeneities to scales that are appropriate for mesoscale and climate model grids have been explored. A simple model for estimating area-average 'effective' surface flux parameters is evaluated. The model satisfies the energy balance equation and leads to a set of relationships between local and effective parameters in the governing equations for the surface energy balance. One outcome is that the resulting effective surface temperature is not a simple area-weighted average of component temperatures, but is a function of a specific combination of different resistances of the individual surface elements. A set of heterogeneous surfaces has been simulated to study the effective fluxes obtained using the described model. A comparison with results obtained by other investigators using different averaging methods is also performed.

Chehbouni, A.↗
NASA NTRS1995

Bounce-Averaged Hamiltonian for Charged Particles in an Axisymmetric but Nondipolar Model Magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M, J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. The L value of a field line is (by definition) inversely proportional to the flux enclosed by the corresponding magnetic shell of equatorial radius r(sub 0), and the L value at the neutral line (r(sub 0) = b) is denoted L*. The azimuthal coordinate phi measures magnetic local time. The best functional representation found for the normalized difference (L(exp 3)a(exp 3)/mu(sub E))(B(sub m) - B(sub 0)) between mirror-point field B(sub m) and equatorial field B(sub 0) along any field line is a 5-term expansion in powers (2/3 through 6/3) of the quantity X equivalent to (La/mu(sub E))(exp 1/2)K, where K equivalent to (J(exp 2)/8m(sub 0)M)(exp 1/2) is an adiabatically conserved quantity independent of particle energy, m(sub 0) is the rest mass of the particle, and a is the radius of the Earth. This functional form is motivated by results for limiting cases in which particles mirror very near and very far from the magnetic equator. Expansion coefficients corresponding to various powers of X are obtained from least squares fits to numerically computed results for X as a function of L and B(sub m). These are accurately expressible as fourth-order polynomials in (r(sub 0)/b)(exp 3), hence indirectly as functions of L/L* = 3La/2b. This representation, which leads (except for a manageably small region of parameter space) to better than 1% accuracy in the specification of B(sub m) as a function of K and L, allows bounce-averaged guiding center simulations to be performed without actually tracing the bounce motions of individual particles. Bounce-averaged drifts L' (meridional) and phi' (azimuthal) are proportional to derivatives of the Hamiltonian H (sum of kinetic and potential energies) with respect to phi and L, respectively. Our formulation thus provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗
NASA NTRS2003

A Theory of the von Weimarn Rules Governing the Average Size of Crystals Precipitated from a Supersaturated Solution

More than 75 years ago, von Weimarn summarized his observations of the dependence of the average crystal size on the initial relative concentration supersaturation prevailing in a solution from which crystals were growing. Since then, his empirically derived rules have become part of the lore of crystal growth. The first of these rules asserts that the average crystal size measured at the end of a crystallization increases as the initial value of the relative supersaturation decreases. The second rule states that for a given crystallization time, the average crystal size passes through a maximum as a function of the initial relative supersaturation. Using a theory of nucleation and growth due to Buyevich and Mansurov, we calculate the average crystal size as a function of the initial relative supersaturation. We confirm the von Weimarn rules for the case where the nucleation rate is proportional to the third power or higher of the relative supersaturation.

Barlow, Douglas A.↗
NASA NTRS2012

Low Average Sidelobe Slot Array Antennas for Radiometer Applications

In radiometer applications, it is required to design antennas that meet low average sidelobe levels and low average return loss over a specified frequency bandwidth. It is a challenge to meet such specifications over a frequency range when one uses resonant elements such as waveguide feed slots. In addition to their inherent narrow frequency band performance, the problem is exacerbated due to modeling errors and manufacturing tolerances. There was a need to develop a design methodology to solve the problem. An iterative design procedure was developed by starting with an array architecture, lattice spacing, aperture distribution, waveguide dimensions, etc. The array was designed using Elliott s technique with appropriate values of the total slot conductance in each radiating waveguide, and the total resistance in each feed waveguide. Subsequently, the array performance was analyzed by the full wave method of moments solution to the pertinent integral equations. Monte Carlo simulations were also carried out to account for amplitude and phase errors introduced for the aperture distribution due to modeling errors as well as manufacturing tolerances. If the design margins for the average sidelobe level and the average return loss were not adequate, array architecture, lattice spacing, aperture distribution, and waveguide dimensions were varied in subsequent iterations. Once the design margins were found to be adequate, the iteration was stopped and a good design was achieved. A symmetric array architecture was found to meet the design specification with adequate margin. The specifications were near 40 dB for angular regions beyond 30 degrees from broadside. Separable Taylor distribution with nbar=4 and 35 dB sidelobe specification was chosen for each principal plane. A non-separable distribution obtained by the genetic algorithm was found to have similar characteristics. The element spacing was obtained to provide the required beamwidth and close to a null in the E-plane end-fire direction. Because of the alternating slot offsets, grating lobes called butterfly lobes are produced in non-principal planes close to the H-plane. An attempt to reduce the influence of such grating lobes resulted in a symmetric design.

Rengarajan, Sembiam↗
NASA NTRS2012

Biases in Long-term NO2 Averages Inferred from Satellite Observations Due to Cloud Selection Criteria

Retrievals of atmospheric trace gas column densities from space are compromised by the presence of clouds, requiring most studies to exclude observations with significant cloud fractions in the instrument's field of view. Using NO2 observations at three ground stations representing urban, suburban, and rural environments, and tropospheric vertical column densities measured by the Ozone Monitoring Instrument (OMI) over each site, we show that the observations from space represent monthly averaged ground-level pollutant conditions well (R=0.86) under relatively cloud-free conditions. However, by analyzing the ground-level data and applying the OMI cloud fraction as a filter, we show there is a significant bias in long-term averaged NO2 as a result of removing the data during cloudy conditions. For the ground-based sites considered in this study, excluding observations on days when OMI-derived cloud fractions were greater than 0.2 causes 12:00-14:00 mean summer mixing ratios to be underestimated by 12%+/-6%, 20%+/-7%, and 40%+/-10% on average (+/-1 standard deviation) at the urban, suburban, and rural sites respectively. This bias was investigated in particular at the rural site, a region where pollutant transport is the main source of NO2, and where longterm observations of NOy were also available. Evidence of changing photochemical conditions and a correlation between clear skies and the transport of cleaner air masses play key roles in explaining the bias. The magnitude of a bias is expected to vary from site to site depending on meteorology and proximity to NOx sources, and decreases when longer averaging times of ground station data (e.g. 24-h) are used for the comparison.

SEASONAL-VARIATIONS↗
NASA NTRS2016

Minimizing the Standard Deviation of Spatially Averaged Surface Cross-Sectional Data from the Dual-Frequency Precipitation Radar

For an airborne or spaceborne radar, the precipitation-induced path attenuation can be estimated from the measurements of the normalized surface cross section, sigma 0, in the presence and absence of precipitation. In one implementation, the mean rain-free estimate and its variability are found from a lookup table (LUT) derived from previously measured data. For the dual-frequency precipitation radar aboard the global precipitation measurement satellite, the nominal table consists of the statistics of the rain-free 0 over a 0.5 deg x 0.5 deg latitude-longitude grid using a three-month set of input data. However, a problem with the LUT is an insufficient number of samples in many cells. An alternative table is constructed by a stepwise procedure that begins with the statistics over a 0.25 deg x 0.25 deg grid. If the number of samples at a cell is too few, the area is expanded, cell by cell, choosing at each step that cell that minimizes the variance of the data. The question arises, however, as to whether the selected region corresponds to the smallest variance. To address this question, a second type of variable-averaging grid is constructed using all possible spatial configurations and computing the variance of the data within each region. Comparisons of the standard deviations for the fixed and variable-averaged grids are given as a function of incidence angle and surface type using a three-month set of data. The advantage of variable spatial averaging is that the average standard deviation can be reduced relative to the fixed grid while satisfying the minimum sample requirement.

spaceborne meteorological radar↗
NASA NTRS2017

Background and Lunar Neutron Populations Detected by LEND and Average Concentration of Near-Surface Hydrogen near the Moon's Poles

Neutron flux measurements by the Lunar Exploration Neutron Detector (LEND) on the Lunar Reconnaissance Orbiter (LRO) enable quantifying hydrogen-bearing volatiles in the lunar surface from orbit. Accurately determining hydrogen abundance requires discriminating between the instrument background detection rate and the population of lunar-sourced neutrons that are sensitive to surficial hydrogen. We have investigated the detection rate for lunar and non-lunar (spacecraft-sourced) neutrons in LEND by modeling maps of measured count rate in three LEND detector systems using linear combinations of maps compiled from LEND detectors and from the Lunar Prospector Neutron Spectrometer. We find that 30% of the global-average 24.926 +/- 0.020 neutron counts per second (cps) detected by the LEND STN3 thermal-energy neutron sensor are lunar-sourced neutrons in the thermal energy range (E < 0.4 eV), 65% are lunar-sourced neutrons in the epithermal and fast energy range (E > 0.4 eV), and 5% are from spacecraft-sourced background signal. In the SETN epithermal neutron detector, 90% of the 10.622 +/- 0.002 neutron detections per second are consistent with a lunar source of epithermal and fast neutrons combined (E > 0.4 eV), with 3% due to lunar-sourced thermal neutron leakage into the detector (E < 0.4 eV), and background signal accounting for 7% of total detections. Background signal due to spacecraft-derived neutrons is substantial in the CSETN collimated detector system, accounting for 57% of the global average detection rate of 5.082 +/- 0.001 cps, greater than the 48% estimated from cruise-phase data. Lunar-sourced epithermal and fast neutrons account for 43% of detected neutrons, including neutrons in collimation as well as neutrons that penetrate the collimator wall to reach the detector. We estimate a lower limit of 17% of lunar-sourced neutrons detected by CSETN are epithermal neutrons in collimation (0.37 cps), with an upper limit estimate of 54 +/- 11% of lunar-sourced neutrons received in collimation, or 1.2 +/- 0.2 cps global average. The pole-to-equator contrast ratio in epithermal and high-energy epithermal neutron flux indicates that the average concentration of hydrogen in the polar regolith above 80deg north or south latitude is ∼105 ppmw (parts per million by weight), or 0.095 +/- 0.01 wt% water-equivalent hydrogen. Above 88deg north or south, the concentration increases to ∼140 ppmw, or 0.13 +/- 0.02 wt% water-equivalent hydrogen. The similar pattern of neutron flux suppression at both poles suggests that hydrogen concentration generally increases nearer the pole and is not closely associated with a specific feature such as Shackleton Crater at the lunar south pole that has no northern counterpart. Epithermal neutron flux decreases with increasing latitude outside the polar regions, consistent with surface hydration that increases with latitude if that hydration extends to ∼13-40 cm into the surface.

T A Livengood↗
NASA NTRS2018

Background and Lunar Neutron Populations Detected by LEND and Average Concentration of Near-Surface Hydrogen near the Moon's Poles

Neutron flux measurements by the Lunar Exploration Neutron Detector (LEND) on the Lunar Reconnaissance Orbiter (LRO) enable quantifying hydrogen-bearing volatiles in the lunar surface from orbit. Accurately determining hydrogen abundance requires discriminating between the instrument background detection rate and the population of lunar-sourced neutrons that are sensitive to surficial hydrogen. We have investigated the detection rate for lunar and non-lunar (spacecraft-sourced) neutrons in LEND by modeling maps of measured count rate in three LEND detector systems using linear combinations of maps compiled from LEND detectors and from the Lunar Prospector Neutron Spectrometer. We find that 30% of the global-average 24.926 0.020 neutron counts per second (cps) detected by the LEND STN3 thermal-energy neutron sensor are lunar-sourced neutrons in the thermal energy range (E < 0.4 eV), 65% are lunar-sourced neutrons in the epithermal and fast energy range (E > 0.4 eV), and 5% are from spacecraft-sourced background signal. In the SETN epithermal neutron detector, 90% of the 10.622 0.002 neutron detections per second are consistent with a lunar source of epithermal and fast neutrons combined (E > 0.4 eV), with 3% due to lunar-sourced thermal neutron leakage into the detector (E < 0.4 eV), and background signal accounting for 7% of total detections. Background signal due to spacecraft-derived neutrons is substantial in the CSETN collimated detector system, accounting for 57% of the global average detection rate of 5.082 0.001 cps, greater than the 48% estimated from cruise-phase data. Lunar-sourced epithermal and fast neutrons account for 43% of detected neutrons, including neutrons in collimation as well as neutrons that penetrate the collimator wall to reach the detector. We estimate a lower limit of 17% of lunar-sourced neutrons detected by CSETN are epithermal neutrons in collimation (0.37 cps), with an upper limit estimate of 54 11% of lunar-sourced neutrons received in collimation, or 1.2 0.2 cps global average. The pole-to-equator contrast ratio inepithermal and high-energy epithermal neutron flux indicates that the average concentration of hydrogen in the polar regolith above 80 north or south latitude is ~105 ppmw (parts per million by weight), or 0.095 0.01 wt% water-equivalent hydrogen. Above 88 north or south, the concentration increases to ~140 ppmw, or 0.13 0.02 wt% water-equivalent hydrogen. The similar pattern of neutron flux suppression at both poles suggests that hydrogen concentration generally increases nearer the pole and is not closely associated with a specific feature such as Shackleton Crater at the lunar south pole that has no northern counterpart. Epithermal neutron flux decreases with increasing latitude outside the polar regions, consistent with surface hydration that increases with latitude if that hydration extends to ~13-40 cm into the surface.

Livengood, Timothy A.↗
NASA NTRS2019

Weighted Least-Squares Cell-Average Gradient Construction Methods for the VULCAN-CFD Second-Order Accurate Unstructured-Grid Cell-Centered Finite-Volume Solver

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches to augment the number of cells participating in the stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cell-average gradients is described and investigated. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 8 turbulent flow of air around a blunt wedge is computed to demonstrate the robustness and convergence behavior of the new method for constructing stencils of use in a weighted linear least-squares gradient method for a hypersonic flow.

White, Jeffery A.↗
NASA NTRS2021

Evaluation of Higher-order Quadrature Schemes in Improving Computational Efficiency for Orientation-averaged Single-Scattering Properties of Nonspherical Ice Particles

We evaluate several high-order quadrature schemes for accuracy and efficacy in obtaining orientation-averaged single-scattering properties (SSPs). We use the highly efficient MIDAS to perform electromagnetic scattering calculations to evaluate the gain in efficiency from these schemes. MIDAS is shown to be superior to DDSCAT, a popular discrete dipole approximation (DDA) method. This study is motivated by the fact that quality physical precipitation retrievals rely on using accurate orientation-averaged SSPs derived from realistic hydrometeors as input to radiative transfer Models (RTMs). The DDA has been a popular choice for single-scattering calculations, due to its versatility with respect to target geometry. However, being iterative-solver-based (ISB), the most used DDA codes, e.g. DDSCAT and ADDA, must solve the scattering problem for each orientation of the target separately. As the size parameter and geometric anisotropy of the hydrometeor increase, the number of orientations needed to obtain accurate orientation-averages can increase drastically and so does the computation cost incurred by the ISB-DDA methods. MIDAS is a Direct-Solver-Based (DSB) code, its decomposition of the original large matrix with a high rank into multiple more manageable smaller matrices of lower ranks makes it much more computationally efficient while maintaining excellent accuracy. In addition, direct solvers consider all requested orientations at once, giving MIDAS further advantage over popular ISB-DDA methods. MIDAS, when combined with high-order quadrature for orientation averaging, can be greater than three orders of magnitude more efficient in obtaining RTM-ready SSPs of complex-shaped hydrometeors than existing ISB-DDA methods, with the native quadrature schemes they offer.

Ines Fenni↗
NASA NTRS2021

SHARPEN: A Scheme to Restore the Distribution of Averaged Precipitation Fields

A key strategy in obtaining complete global coverage of high-resolution precipitation is to combine observations from multiple fields, such as the intermittent passive microwave observations, precipitation propagated in time using motion vectors, and geosynchronous infrared observations. These separate precipitation fields can be combined through weighted averaging, which produces estimates that are generally superior to the individual parent fields. However, the process of averaging changes the distribution of the precipitation values, leading to an increase in precipitating area and a decrease in the values of high precipitation rates, a phenomenon observed in IMERG. To mitigate this issue, we introduce a new scheme called SHARPEN (Scheme for Histogram Adjustment with Ranked Precipitation Estimates in the Neighborhood), which recovers the distribution of the averaged precipitation field based on the idea of quantile mapping applied to the local environment. When implemented in IMERG, precipitation estimates from SHARPEN exhibit a distribution that resembles that of the original instantaneous observations, with matching precipitating area and peak precipitation rates. Case studies demonstrate its improved ability in bridging between the parent precipitation fields. Evaluation against ground observations reveals a distinct improvement in precipitation detection skill, but also a slightly reduced correlation likely because of a sharper precipitation field. The increased computational demand of SHARPEN can be mitigated by striding over multiple grid boxes, which has only marginal impacts on the accuracy of the estimates. SHARPEN can be applied to any precipitation algorithm that produces an average from multiple input precipitation fields and is being considered for implementation in IMERG V07.

Jackson Tan↗
NASA NTRS1962

Theoretical estimates of the average surface temperature on mars

Estimates of the average surface temperature on Mars are derived from radiative equilibrium considerations. A minimum possible surface temperature is estimated by computing the radiative equilibrium temperature that the Martian surface would have if the planet had no atmosphere. An estimate of the maximum possible value of the average surface temperature is obtained by computing the surface temperature that would result from a maximum greenhouse model. The computations indicate that the average surface temperature is in the range 219K to 233K. Comparisons of the theoretical computations with indications of surface temperature obtained from thermal emission observations are found to be in reasonable agreement.

Surface temperature↗
NASA NTRS1972

Numerical averaging in orbit prediction.

This paper is a presentation of some useful aspects of a numerical averaging technique that has been applied with considerable success to the orbit prediction problem for artificial satellites. The method has been tested in a variety of situations wherein the satellite is subjected to combinations of perturbations for which adequate analytic theories are practically impossible. The technique provides many of the advantages of analytic averaging while retaining the ability to simulate the effects of any kind of small force that can be deterministically modeled. The theoretical basis for the method is straightforward but the details of its implementation are somewhat confusing and need some explanation. A particularly useful set of averaged equations is presented along with a description of an efficient algorithm for their solution. Examples of the advantages to be obtained by use of the method are included.

Uphoff, C.↗
NASA NTRS1973

The average chemical composition of the lunar surface

The available analytical data from twelve locations on the moon are used to estimate the average amounts of the principal chemical elements (O, Na, Mg, Al, Si, Ca, Ti, and Fe) in the mare, the terra, and the average lunar surface regolith. These chemical elements comprise about 99% of the atoms on the lunar surface. The relatively small variability in the amounts of these elements at different mare (or terra) sites, and the evidence from the orbital measurements of Apollo 15 and 16, suggest that the lunar surface is much more homogeneous than the surface of the earth. The average chemical composition of the lunar surface may now be known as well as, if not better than, that of the solid part of the earth's surface.

Turkevich, A. L.↗
NASA NTRS1952

Experimental Investigation of Average Heat-Transfer and Friction Coefficients for Air Flowing in Circular Tubes Having Square-Thread-Type Roughness

An investigation of forced-convection heat transfer and associated pressure drops was conducted with air flowing through electrically heated Inconel tubes having various degrees of square-thread-type roughness, an inside diameter of 1/2 inch, and a length of 24 inches. were obtained for tubes having conventional roughness ratios (height of thread/radius of tube) of 0 (smooth tube), 0.016, 0.025, and 0.037 over ranges of bulk Reynolds numbers up to 350,000, average inside-tube-wall temperatures up to 1950deg R, and heat-flux densities up to 115,000 Btu per hour per square foot. Data The experimental data showed that both heat transfer and friction increased with increase in surface roughness, becoming more pronounced with increase in Reynolds number; for a given roughness, both heat transfer and friction were also influenced by the tube wall-to-bulk temperature ratio. Good correlation of the heat-transfer data for all the tubes investigated was obtained by use of a modification of the conventional Nusselt correlation parameters wherein the mass velocity in the Reynolds number was replaced by the product of air density evaluated at the average film temperature and the so-called friction velocity; in addition, the physical properties of air were evaluated at the average film temperature. The isothermal friction data for the rough tubes, when plotted in the conventional manner, resulted in curves similar to those obtained by other investigators; that is, the curve for a given roughness breaks away from the Blasius line (representing turbulent flow in smooth tubes) at some value of Reynolds number, which decreases with increase in surface roughness, and then becomes a horizontal line (friction coefficient independent of Reynolds number). A comparison of the friction data for the rough tubes used herein indicated that the conventional roughness ratio is not an adequate measure of relative roughness for tubes having a square-thread-type element. The present data, as well as those of other investigators, were used to isolate the influence of ratios of thread height to width, thread spacing to width, and the conventional roughness ratio on the friction coefficient. A fair correlation of the friction data was obtained for each tube with heat addition when the friction coefficient and Reynolds number were defined on the basis of film properties; however, the data for each tube retained the curve characteristic of that particular roughness. The friction data for all the rough tubes could be represented by a single line for the complete turbulence region by incorporating a roughness parameter in the film correlation. No correlation was obtained for the region of incomplete turbulence.

Sams, E. W.↗
NASA NTRS1975

Averaged initial Cartesian coordinates for long lifetime satellite studies

A set of initial Cartesian coordinates, which are free of ambiguities and resonance singularities, is developed to study satellite mission requirements and dispersions over long lifetimes. The method outlined herein possesses two distinct advantages over most other averaging procedures. First, the averaging is carried out numerically using Gaussian quadratures, thus avoiding tedious expansions and the resulting resonances for critical inclinations, etc. Secondly, by using the initial rectangular Cartesian coordinates, conventional, existing acceleration perturbation routines can be absorbed into the program without further modifications, thus making the method easily adaptable to the addition of new perturbation effects. The averaged nonlinear differential equations are integrated by means of a Runge Kutta method. A typical step size of several orbits permits rapid integration of long lifetime orbits in a short computing time.

Pines, S.↗
NASA NTRS1975

A time-averaged cosmic ray propagation theory

An argument is presented, which casts doubt on our ability to choose an appropriate magnetic field ensemble for computing the average behavior of cosmic ray particles. An alternate procedure, using time-averages rather than ensemble-averages, is presented.

Klimas, A. J.↗