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NASA NTRS1932

On the theory of wing sections with particular reference to the lift distribution

This report gives a simple and exact method of calculating the lift distribution on thin wing sections. The most essential feature of the new theory is the introduction of an "ideal angle of attack," this angle being defined as that at which the flow enters the leading edge smoothly or, more precisely, as the angle of attack at which the lift at the leading edge equals zero. The lift distribution at this particular angle is shown to be a characteristic property of the section and has been termed the "basic distribution." it is shown that the lift of a wing section may always be considered to consist of (a) the basic distribution and (b) the additional distribution, where the latter is independent of the mean camber line and thus identical for all thin sections. The specific reason for the poor aerodynamic qualities of thin wing sections is pointed out as being due to the fact that the additional lift in potential flow becomes infinite at the leading edge. It is established that the essential parameter occurring in this analysis is the radius of curvature at the leading edge. It is further established that the actual slope of the lift curve is dependent on this parameter. The theoretical lift distribution is compared with the distribution obtained by direct measurement on a number of the more conventional wing sections. The new theory is of value in calculating the strength of wing sections.

Theodorsen, Theodore↗

NASA NTRS1935

Method for the determination of the spanwise lift distribution

The method for determination of the spanwise lift distribution is based on the Fourier series for the representation of the lift distribution. The lift distribution, as well as the angle of attack, is split up in four elementary distributions. The insertion of the angle-of-attack distribution in the Fourier series for the lift distribution gives a compound third series which is of particular advantage for the determination of the lift distribution. The method is illustrated in an example and supplemented by a graphical method. Lastly, the results of several comparative calculations with other methods are reported.

Lippisch, A↗

NASA NTRS1994

Velocity distributions among colliding asteroids

The probability distribution for impact velocities between two given asteroids is wide, non-Gaussian, and often contains spikes according to our new method of analysis in which each possible orbital geometry for collision is weighted according to its probability. An average value would give a good representation only if the distribution were smooth and narrow. Therefore, the complete velocity distribution we obtain for various asteroid populations differs significantly from published histograms of average velocities. For all pairs among the 682 asteroids in the main-belt with D greater than 50 km, we find that our computed velocity distribution is much wider than previously computed histograms of average velocities. In this case, the most probable impact velocity is approximately 4.4 km/sec, compared with the mean impact velocity of 5.3 km/sec. For cases of a single asteroid (e.g., Gaspra or Ida) relative to an impacting population, the distribution we find yields lower velocities than previously reported by others. The width of these velocity distributions implies that mean impact velocities must be used with caution when calculating asteroid collisional lifetimes or crater-size distributions. Since the most probable impact velocities are lower than the mean, disruption events may occur less frequently than previously estimated. However, this disruption rate may be balanced somewhat by an apparent increase in the frequency of high-velocity impacts between asteroids. These results have implications for issues such as asteroidal disruption rates, the amount/type of impact ejecta available for meteoritical delivery to the Earth, and the geology and evolution of specific asteroids like Gaspra.

Bottke, William F., Jr.↗

NASA NTRS1994

Internal velocity and mass distributions in simulated clusters of galaxies for a variety of cosmogonic models

The mass and velocity distributions in the outskirts (0.5-3.0/h Mpc) of simulated clusters of galaxies are examined for a suite of cosmogonic models (two Omega(sub 0) = 1 and two Omega(sub 0) = 0.2 models) utilizing large-scale particle-mesh (PM) simulations. Through a series of model computations, designed to isolate the different effects, we find that both Omega(sub 0) and P(sub k) (lambda less than or = 16/h Mpc) are important to the mass distributions in clusters of galaxies. There is a correlation between power, P(sub k), and density profiles of massive clusters; more power tends to point to the direction of a stronger correlation between alpha and M(r less than 1.5/h Mpc); i.e., massive clusters being relatively extended and small mass clusters being relatively concentrated. A lower Omega(sub 0) universe tends to produce relatively concentrated massive clusters and relatively extended small mass clusters compared to their counterparts in a higher Omega(sub 0) model with the same power. Models with little (initial) small-scale power, such as the hot dark matter (HDM) model, produce more extended mass distributions than the isothermal distribution for most of the mass clusters. But the cold dark matter (CDM) models show mass distributions of most of the clusters more concentrated than the isothermal distribution. X-ray and gravitational lensing observations are beginning providing useful information on the mass distribution in and around clusters; some interesting constraints on Omega(sub 0) and/or the (initial) power of the density fluctuations on scales lambda less than or = 16/h Mpc (where linear extrapolation is invalid) can be obtained when larger observational data sets, such as the Sloan Digital Sky Survey, become available.

Cen, Renyue↗

NASA NTRS1998

Performance Analysis of Distributed Object-Oriented Applications

The purpose of this research was to evaluate the efficiency of a distributed simulation architecture which creates individual modules which are made self-scheduling through the use of a message-based communication system used for requesting input data from another module which is the source of that data. To make the architecture as general as possible, the message-based communication architecture was implemented using standard remote object architectures (Common Object Request Broker Architecture (CORBA) and/or Distributed Component Object Model (DCOM)). A series of experiments were run in which different systems are distributed in a variety of ways across multiple computers and the performance evaluated. The experiments were duplicated in each case so that the overhead due to message communication and data transmission can be separated from the time required to actually perform the computational update of a module each iteration. The software used to distribute the modules across multiple computers was developed in the first year of the current grant and was modified considerably to add a message-based communication scheme supported by the DCOM distributed object architecture. The resulting performance was analyzed using a model created during the first year of this grant which predicts the overhead due to CORBA and DCOM remote procedure calls and includes the effects of data passed to and from the remote objects. A report covering the distributed simulation software and the results of the performance experiments has been submitted separately. The above report also discusses possible future work to apply the methodology to dynamically distribute the simulation modules so as to minimize overall computation time.

Schoeffler, James D.↗

NASA NTRS2000

The BATSE Gamma-Ray Burst E-Peak Distribution

Gamma-ray burst observed by BATSE are found to have approximately the same characteristic energy, denoted as E_p. We examine whether instrumental effects can give rise to this observation. We simulate the derivation of E-p and determine that the values in the BATSE sample are accurate and complete above a minimum fluence. We simulate the triggering of BATSE on gamma-ray bursts, deriving the efficiency of detecting bursts as a function of characteristic energy. From this simulation, we model the observed E_p distribution function expected when the intrinsic distribution function is a power-law. We find that this distribution produces poor fits to the observations. We find that a log-normal intrinsic distribution with a power-law tail gives a good fit to the data. From these fits, we conclude that instrumental effects cannot produce the observed E_p distribution, and that the observed distribution is a consequence of a narrow intrinsic distribution of E_p in gamma-ray bursts.

Brainerd, Jerome J.↗

NASA NTRS1999

Automatic Data Distribution for CFD Applications on Structured Grids

Development of HPF versions of NPB and ARC3D showed that HPF has potential to be a high level language for parallelization of CFD applications. The use of HPF requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement and data granularity. Since HPF hides data movement from the user even with this knowledge it is easy to overlook pieces of the code causing low performance of the application. In order to simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and partially implemented ADAPT (Automatic Data Distribution and Placement Tool). The ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level or inter application level. ADAPT is designed to annotate existing CFD FORTRAN application performing computations on single or multiple grids. On each grid the application can considered as a sequence of operators each applied to a set of variables defined in a particular grid domain. The operators can be classified as implicit, having data dependences, and explicit, without data dependences. In order to parallelize an explicit operator it is sufficient to create a template for the domain of the operator, align arrays used in the operator with the template, distribute the template, and declare the loops over the distributed dimensions as INDEPENDENT. In order to parallelize an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator then the loop which implements the operator can be declared as INDEPENDENT.

Frumkin, Michael↗

NASA NTRS2004

Pickup Ion Velocity Distributions at Titan: Effects of Spatial Gradients

The principle source of pickup ions at Titan is its neutral exosphere, extending well above the ionopause into the magnetosphere of Saturn or the solar wind, depending on the moon's orbital position. Thermal and nonthermal processes in the thermosphere generate the distribution of neutral atoms and molecules in the exosphere. The combination of these processes and the range of mass numbers, 1 to over 28, contribute to an exospheric source structure that produces pickup ions with gyroradii that are much larger or smaller than the corresponding scale heights of their neutral sources. The resulting phase space distributions are dependent on the spatial structure of the exosphere as well as that of the magnetic field and background plasma. When the pickup ion gyroradius is less than the source gas scale height, the pickup ion velocity distribution is characterized by a sharp cutoff near the maximum speed, which is twice that of the ambient plasma times the sine of the angle between the magnetic field and the flow velocity. This was the case for pickup H(sup +) ions identified during the Voyager 1 flyby. In contrast, as the gyroradius becomes much larger than the scale height, the peak of the velocity distribution in the source region recedes from the maximum speed. Iri addition, the amplitude of the distribution near the maximum speed decreases. These more beam like distributions of heavy ions were not observed from Voyager 1 , but should be observable by more sensitive instruments on future spacecraft, including Cassini. The finite gyroradius effects in the pickup ion velocity distributions are studied by including in the analysis the possible range of spatial structures in the neutral exosphere and background plasma.

Hartle, R. E.↗

NASA NTRS2008

Raindrop Size Distribution Measurements in Tropical Cyclones

Characteristics of the raindrop size distribution in seven tropical cyclones have been studied through impact-type disdrometer measurements at three different sites during the 2004-06 Atlantic hurricane seasons. One of the cyclones has been observed at two different sites. High concentrations of small and/or midsize drops were observed in the presence or absence of large drops. Even in the presence of large drops, the maximum drop diameter rarely exceeded 4 mm. These characteristics of raindrop size distribution were observed in all stages of tropical cyclones, unless the storm was in the extratropical stage where the tropical cyclone and a midlatitude frontal system had merged. The presence of relatively high concentrations of large drops in extratropical cyclones resembled the size distribution in continental thunderstorms. The integral rain parameters of drop concentration, liquid water content, and rain rate at fixed reflectivity were therefore lower in extratropical cyclones than in tropical cyclones. In tropical cyclones, at a disdrometercalculated reflectivity of 40 dBZ, the number concentration was 700 plus or minus 100 drops m(sup -3), while the liquid water content and rain rate were 0.90 plus or minus 0.05 g m(sup -3) and 18.5 plus or minus 0.5 mm h(sup -1), respectively. The mean mass diameter, on the other hand, was 1.67 plus or minus 0.3 mm. The comparison of raindrop size distributions between Atlantic tropical cyclones and storms that occurred in the central tropical Pacific island of Roi-Namur revealed that the number density is slightly shifted toward smaller drops, resulting in higher-integral rain parameters and lower mean mass and maximum drop diameters at the latter site. Considering parameterization of the raindrop size distribution in tropical cyclones, characteristics of the normalized gamma distribution parameters were examined with respect to reflectivity. The mean mass diameter increased rapidly with reflectivity, while the normalized intercept parameter had an increasing trend with reflectivity. The shape parameter, on the other hand, decreased in a reflectivity range from 10 to 20 dBZ and remained steady at higher reflectivities. Considering the repeatability of the characteristics of the raindrop size distribution, a second impact disdrometer that was located 5.3 km away from the primary site in Wallops Island, Virginia, had similar size spectra in selected tropical cyclones.

Tokay, Ali↗

NASA NTRS2010

Analyzing Distributed Functions in an Integrated Hazard Analysis

Large scale integration of today's aerospace systems is achievable through the use of distributed systems. Validating the safety of distributed systems is significantly more difficult as compared to centralized systems because of the complexity of the interactions between simultaneously active components. Integrated hazard analysis (IHA), a process used to identify unacceptable risks and to provide a means of controlling them, can be applied to either centralized or distributed systems. IHA, though, must be tailored to fit the particular system being analyzed. Distributed systems, for instance, must be analyzed for hazards in terms of the functions that rely on them. This paper will describe systems-oriented IHA techniques (as opposed to traditional failure-event or reliability techniques) that should be employed for distributed systems in aerospace environments. Special considerations will be addressed when dealing with specific distributed systems such as active thermal control, electrical power, command and data handling, and software systems (including the interaction with fault management systems). Because of the significance of second-order effects in large scale distributed systems, the paper will also describe how to analyze secondary functions to secondary functions through the use of channelization.

Morris, A. Terry↗

NASA NTRS2010

Distributed Propulsion Vehicles

Since the introduction of large jet-powered transport aircraft, the majority of these vehicles have been designed by placing thrust-generating engines either under the wings or on the fuselage to minimize aerodynamic interactions on the vehicle operation. However, advances in computational and experimental tools along with new technologies in materials, structures, and aircraft controls, etc. are enabling a high degree of integration of the airframe and propulsion system in aircraft design. The National Aeronautics and Space Administration (NASA) has been investigating a number of revolutionary distributed propulsion vehicle concepts to increase aircraft performance. The concept of distributed propulsion is to fully integrate a propulsion system within an airframe such that the aircraft takes full synergistic benefits of coupling of airframe aerodynamics and the propulsion thrust stream by distributing thrust using many propulsors on the airframe. Some of the concepts are based on the use of distributed jet flaps, distributed small multiple engines, gas-driven multi-fans, mechanically driven multifans, cross-flow fans, and electric fans driven by turboelectric generators. This paper describes some early concepts of the distributed propulsion vehicles and the current turboelectric distributed propulsion (TeDP) vehicle concepts being studied under the NASA s Subsonic Fixed Wing (SFW) Project to drastically reduce aircraft-related fuel burn, emissions, and noise by the year 2030 to 2035.

Kim, Hyun Dae↗

NASA NTRS2011

Distribution Functions of Sizes and Fluxes Determined from Supra-Arcade Downflows

The frequency distributions of sizes and fluxes of supra-arcade downflows (SADs) provide information about the process of their creation. For example, a fractal creation process may be expected to yield a power-law distribution of sizes and/or fluxes. We examine 120 cross-sectional areas and magnetic flux estimates found by Savage & McKenzie for SADs, and find that (1) the areas are consistent with a log-normal distribution and (2) the fluxes are consistent with both a log-normal and an exponential distribution. Neither set of measurements is compatible with a power-law distribution nor a normal distribution. As a demonstration of the applicability of these findings to improved understanding of reconnection, we consider a simple SAD growth scenario with minimal assumptions, capable of producing a log-normal distribution.

McKenzie, D.↗

NASA NTRS2012

Inferred Lunar Boulder Distributions at Decimeter Scales

Block size distributions of impact deposits on the Moon are diagnostic of the impact process and environmental effects, such as target lithology and weathering. Block size distributions are also important factors in trafficability, habitability, and possibly the identification of indigenous resources. Lunar block sizes have been investigated for many years for many purposes [e.g., 1-3]. An unresolved issue is the extent to which lunar block size distributions can be extrapolated to scales smaller than limits of resolution of direct measurement. This would seem to be a straightforward statistical application, but it is complicated by two issues. First, the cumulative size frequency distribution of observable boulders rolls over due to resolution limitations at the small end. Second, statistical regression provides the best fit only around the centroid of the data [4]. Confidence and prediction limits splay away from the best fit at the endpoints resulting in inferences in the boulder density at the CPR scale that can differ by many orders of magnitude [4]. These issues were originally investigated by Cintala and McBride [2] using Surveyor data. The objective of this study was to determine whether the measured block size distributions from Lunar Reconnaissance Orbiter Camera - Narrow Angle Camera (LROC-NAC) images (m-scale resolution) can be used to infer the block size distribution at length scales comparable to Mini-RF Circular Polarization Ratio (CPR) scales, nominally taken as 10 cm. This would set the stage for assessing correlations of inferred block size distributions with CPR returns [6].

Baloga, S. M.↗

NASA NTRS2012

Longitudinal Differences of Ionospheric Vertical Density Distribution and Equatorial Electrodynamics

Accurate estimation of global vertical distribution of ionospheric and plasmaspheric density as a function of local time, season, and magnetic activity is required to improve the operation of space-based navigation and communication systems. The vertical density distribution, especially at low and equatorial latitudes, is governed by the equatorial electrodynamics that produces a vertical driving force. The vertical structure of the equatorial density distribution can be observed by using tomographic reconstruction techniques on ground-based global positioning system (GPS) total electron content (TEC). Similarly, the vertical drift, which is one of the driving mechanisms that govern equatorial electrodynamics and strongly affect the structure and dynamics of the ionosphere in the low/midlatitude region, can be estimated using ground magnetometer observations. We present tomographically reconstructed density distribution and the corresponding vertical drifts at two different longitudes: the East African and west South American sectors. Chains of GPS stations in the east African and west South American longitudinal sectors, covering the equatorial anomaly region of meridian approx. 37 deg and 290 deg E, respectively, are used to reconstruct the vertical density distribution. Similarly, magnetometer sites of African Meridian B-field Education and Research (AMBER) and INTERMAGNET for the east African sector and South American Meridional B-field Array (SAMBA) and Low Latitude Ionospheric Sensor Network (LISN) are used to estimate the vertical drift velocity at two distinct longitudes. The comparison between the reconstructed and Jicamarca Incoherent Scatter Radar (ISR) measured density profiles shows excellent agreement, demonstrating the usefulness of tomographic reconstruction technique in providing the vertical density distribution at different longitudes. Similarly, the comparison between magnetometer estimated vertical drift and other independent drift observation, such as from VEFI onboard Communication/Navigation Outage Forecasting System (C/NOFS) satellite and JULIA radar, is equally promising. The observations at different longitudes suggest that the vertical drift velocities and the vertical density distribution have significant longitudinal differences; especially the equatorial anomaly peaks expand to higher latitudes more in American sector than the African sector, indicating that the vertical drift in the American sector is stronger than the African sector.

total electron content↗

NASA NTRS2017

The Velocity and Density Distribution of Earth-Intersecting Meteoroids: Implications for Environment Models

Meteoroids are known to damage spacecraft: they can crater or puncture components, disturb a spacecraft's attitude, and potentially create secondary electrical effects. Because the damage done depends on the speed, size, density, and direction of the impactor, accurate environment models are critical for mitigating meteoroid-related risks. Yet because meteoroid properties are derived from indirect observations such as meteors and impact craters, many characteristics of the meteoroid environment are uncertain. In this work, we present recent improvements to the meteoroid speed and density distributions. Our speed distribution is derived from observations made by the Canadian Meteor Orbit Radar. These observations are de-biased using modern descriptions of the ionization efficiency. Our approach yields a slower meteoroid population than previous analyses (see Fig. 1 for an example) and we compute the uncertainties associated with our derived distribution. We adopt a higher fidelity density distribution than that used by many older models. In our distribution, meteoroids with TJ less than 2 are assigned to a low-density population, while those with TJ greater than 2 have higher densities (see Fig. 2). This division and the distributions themselves are derived from the densities reported by Kikwaya et al. These changes have implications for the environment: for instance, the helion/antihelion sporadic sources have lower speeds than the apex and toroidal sources and originate from high-T(sub J) parent bodies. Our on-average slower and denser distributions thus imply that the helion and antihelion sources dominate the meteoroid environment even more completely than previously thought. Finally, for a given near-Earth meteoroid cratering rate, a slower meteoroid population produces a comparatively higher rate of satellite attitude disturbances.

Moorhead, A. V.↗

NASA NTRS2020

Model-Reference Adaptive Control of Distributed Lagrangian Infinite-Dimensional Systems Using Hamilton’s Principle

This paper presents a Hamilton's principle for distributed control of infinite-dimensional systems modeled by a distributed form of the Euler-Lagrange method. The distributed systems are governed by a system of linear partial differential equations in space and time. A generalized potential energy expression is developed that can capture most physical systems including those systems that have no spatial distribution. The Hamilton's principle is applied to derive distributed feedback control methods without resorting to the standard weak-form discretization approach to convert an infinite-dimensional systems to a finite-dimensional systems. It can be shown by the principle of least action that the distributed control synthesized by the Hamilton's principle is a minimum-norm control. A model-reference adaptive control framework is developed for distributed Lagrangian systems in the presence of uncertainty. The theory is demonstrated by an application of adaptive flutter suppression control of a flexible aircraft wing.

Nguyen, Nhan T.↗

DOE OSTI2021

Influence of Ink Formulation and Drying Conditions on Ionomer Distribution in High-Performance Roll-to-Roll-Coated Gas-Diffusion Electrodes

To enable mass production of fuel cell membrane electrode assemblies (MEAs) catalyst layers production will require continuous roll-to-roll (R2R) coating processes. Gas diffusion electrodes (GDEs) are advantageous for mass production because the catalyst layer can be directely coated on the microporous layer of the gas diffusion media without the need for a decal-transfer process. It is known that the water-to-alcohol ratio in the catalyst ink influences the interactions of the ionomer with the catalyst leading to different distributions of ionomer in spray-coated catalyst layers. It is also known that during drying of colloidal mixtures, like fuel cell inks, factors such as drying rate, particle size, and agglomeration influence how the materials distribute themselves throughout the thickness of the dired film. Thus far there have only been limited studies to understand how process conditions such as ink formulation and drying temperature influence the distribution of ionomer and catalyst coated using scalable methods. This understanding is especially important for GDEs since it is known that having a sufficient amount of ionomer at the catalyst layer-membrane interface is critical for high performance. In this study we have focused on determining how the ratio of water to 1-propanol in the catalyst ink ink and drying temperature influence the distribution of ionomer throughout the thickness of the catalyst layer. Using a combination of Kelvin probe and x-ray photoelectron spectroscopy we show that an ionomer-rich surface is promoted by a higher drying rate and a water-rich catalyst ink. In contrast, a 1-propanol catalyst ink leads to a lower concentration of ionomer on the top surface. Using x-ray computed tomography, we are able to characterize the ionomer distribution throughout the thickness of the layer. We find that, in addition to promoting an ionomer-rich top surface, water-rich inks lead to a more homogenous distribution of ionomer, whereas a 1-propanol-rich ink leads to a more irregular distribution. It is found that MEA performance is improved by selecting conditions and ink formulations that promote ionomer enrichment at the top surface to facilitate a good interface with the membrane. MEAs prepared with a 75 wt% water catalyst ink with a 0.9 I/C have equivalent performance to spray-coated GDEs. Critically, these R2R-coated GDEs do not need an additional ionomer overlayer like the spray-coated GDEs do, reducing the number of processing steps in a manufacturing setting. This work shows that with the appropriate selection of materials, ink formulation, and processing conditions gas-diffusion electrodes are a viable pathway for fuel cell manufacturing.

ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION↗

DOE OSTI2022

Coordinated voltage control and reactive power regulation between transmission and distribution systems

Systems and methods are described for coordinating volt-var control between sub-transmission and distribution systems. Distributed energy resources of a distribution system are aggregated into virtual power plants from which reactive power can optimally be dispatched to the sub-transmission system. A sub-transmission controller executes a volt-var AC optimal power flow optimisation function to minimize voltage fluctuations that might otherwise occur when coordinating with a distribution system having distributed energy resources. The distribution system can use a sensitivity matrix for regulating voltage at distribution feeders while fulfilling a transmission or sub-transmission system's demand requests.

Samaan, Nader A.↗