Results for “orientation distribution function” — Page 11

NASA NTRS1998

Evolution of Scientific and Technical Information Distribution

World Wide Web (WWW) and related information technologies are transforming the distribution of scientific and technical information (STI). We examine 11 recent, functioning digital libraries focusing on the distribution of STI publications, including journal articles, conference papers, and technical reports. We introduce 4 main categories of digital library projects: based on the architecture (distributed vs. centralized) and the contributor (traditional publisher vs. authoring individual/organization). Many digital library prototypes merely automate existing publishing practices or focus solely on the digitization of the publishing cycle output, not sampling and capturing elements of the input. Still others do not consider for distribution the large body of "gray literature." We address these deficiencies in the current model of STI exchange by suggesting methods for expanding the scope and target of digital libraries by focusing on a greater source of technical publications and using "buckets," an object-oriented construct for grouping logically related information objects, to include holdings other than technical publications.

Esler, Sandra↗

NASA NTRS2001

Photochemical Phenomenology Model for the New Millennium

The "Photochemical Phenomenology Model for the New Millennium" project tackles the issue of reengineering and extension of validated physics-based modeling capabilities ("legacy" computer codes) to application-oriented software for use in science and science-support activities. While the design and architecture layouts are in terms of general particle distributions involved in scattering, impact, and reactive interactions, initial Photochemical Phenomenology Modeling Tool (PPMT) implementations are aimed at construction and evaluation of photochemical transport models with rapid execution for use in remote sensing data analysis activities in distributed systems. Current focus is on the Composite Infrared Spectrometer (CIRS) data acquired during the CASSINI flyby of Jupiter. Overall, the project has stayed on the development track outlined in the Year 1 annual report and most Year 2 goals have been met. The issues that have required the most attention are: implementation of the core photochemistry algorithms; implementation of a functional Java Graphical User Interface; completion of a functional CORBA Component Model framework; and assessment of performance issues. Specific accomplishments and the difficulties encountered are summarized in this report. Work to be carried out in the next year center on: completion of testing of the initial operational implementation; its application to analysis of the CASSINI/CIRS Jovian flyby data; extension of the PPMT to incorporate additional phenomenology algorithms; and delivery of a mature operational implementation.

Bishop, James↗

NASA NTRS1992

Extracellular vesicles of calcifying turkey leg tendon characterized by immunocytochemistry and high voltage electron microscopic tomography and 3-D graphic image reconstruction

To gain insight into the structure and possible function of extracellular vesicles in certain calcifying vertebrate tissues, normally mineralizing leg tendons from the domestic turkey, Meleagris gallopavo, have been studied in two separate investigations, one concerning the electron microscopic immunolocalization of the 66 kDa phosphoprotein, osteopontin, and the other detailing the organization and distribution of mineral crystals associated with the vesicles as determined by high voltage microscopic tomography and 3-D graphic image reconstruction. Immunolabeling shows that osteopontin is related to extracellular vesicles of the tendon in the sense that its initial presence appears coincident with the development of mineral associated with the vesicle loci. By high voltage electron microscopy and 3-D imaging techniques, mineral crystals are found to consist of small irregularly shaped particles somewhat randomly oriented throughout individual vesicles sites. Their appearance is different from that found for the mineral observed within calcifying tendon collagen, and their 3-D disposition is not regularly ordered. Possible spatial and temporal relationships of vesicles, osteopontin, mineral, and collagen are being examined further by these approaches.

NASA Discipline Musculoskeletal↗

NASA NTRS1993

Effects of inversion on plastid position and gravitropism in Ceratodon protonemata

When dark-grown tip cells of protonemata of the moss Ceratodon purpureus are turned to the horizontal, plastids first sediment towards gravity in a specific zone and then the tip curves upward. To determine whether gravitropism and plastid sedimentation occur in other orientations, protonemata were reoriented to angles other than 90 degrees. Qualitative and quantitative light microscopic observations show that plastid sedimentation along the cell axis occurs in both upright and inverted cells. However, only some plastids fall and sedimentation is incomplete; plastids remain distributed throughout the length of the cell, and those plastids that sediment do not fall all the way to the bottom of the cell. Tip cells are gravitropic regardless of stimulation angle, and as in higher plants, the maximal rate of initial curvature is in response to a 120 degrees reorientation. Infrared videomicroscopy, time-lapse studies of living, inverted protonemata indicate that amyloplast sedimentation precedes upward curvature. Together, these data further support (i) the hypothesis that amyloplast sedimentation functions in gravitropic sensing in these cells, and (ii) the idea that gravity affected the evolution of cell organization.

NASA Program Space Biology↗

NASA NTRS1987

Stochastic estimation of organized structures in turbulent channel flow

Linear stochastic estimation is used to approximate the conditional vector fields associated with high Reynolds stress producing events in numerically simulated turbulent channel flow. Joint probability density distributions of u-v are presented for y(+) between 1.35 and 180, and at each position the u-v values that make the greatest contributions to the average uv3 are used to define conditional ejection- and sweep-type events. In the y-z plane the conditional fields appear to be pairs of counter-rotating vortices. When the conditional event defined by the weighted probability density function is specified at a point close to the wall, the spacing and size of these eddies are consistent with the accepted wall streak spacing. As this point moves outwards, the eddy size increases significantly. An abrupt change in the flow angle occurs in the buffer layer and may indicate transition from streamwise oriented wall layer structures to hairpin vortices characterizing the outer layer.

Moin, P.↗

NASA NTRS2003

Development of a Dynamically Configurable, Object-Oriented Framework for Distributed, Multi-modal Computational Aerospace Systems Simulation: Second Year Progress Report

Mesh generation has long been recognized as a bottleneck in the CFD process. While much research on automating the volume mesh generation process have been relatively successful,these methods rely on appropriate initial surface triangulation to work properly. Surface discretization has been one of the least automated steps in computational simulation due to its dependence on implicitly defined CAD surfaces and curves. Differences in CAD peometry engines manifest themselves in discrepancies in their interpretation of the same entities. This lack of "good" geometry causes significant problems for mesh generators, requiring users to "repair" the CAD geometry before mesh generation. The problem is exacerbated when CAD geometry is translated to other forms (e.g., IGES )which do not include important topological and construction information in addition to entity geometry. One technique to avoid these problems is to access the CAD geometry directly from the mesh generating software, rather than through files. By accessing the geometry model (not a discretized version) in its native environment, t h s a proach avoids translation to a format which can deplete the model of topological information. Our approach to enable models developed in the Denali software environment to directly access CAD geometry and functions is through an Application Programming Interface (API) known as CAPRI. CAPRI provides a layer of indirection through which CAD-specific data may be accessed by an application program using CAD-system neutral C and FORTRAN language function calls. CAPRI supports a general set of CAD operations such as truth testing, geometry construction and entity queries.

Afjeh, Abdollah A.↗

NASA NTRSDate not supplied

Deflection of Solar Energetic Protons by an Ion Thruster

While Galactic Cosmic Rays (GCR) represent a long-term cancer risk to deep space human missions, Solar Energetic Particles (SEP) represent a significant acute radiation hazard to human spaceflight. This work investigates wave-particle interactions caused by the incidence of a beam of energetic protons, representing a notional SEP event, onto a cloud of ions representing a notional ion thruster plume. The resulting electromagnetic ion/ion instability is developed to investigate the degree to which energetic protons can be scattered out of the initial beam. This work includes investigations of deflection rate dependences on incident SEP energy and flux, ion thruster power and orientation relative to SEP incidence, plume ion species, and background plasma. Also investigated are the spectrum and angular distribution of electromagnetic radiation resulting from the wave-particle interactions. The primary objective of this investigation is to develop a technique for active mitigation of SEP radiation threats to spacecraft and crew, by exploring the wave-particle interaction of a SEP event with the plasma plume expelled from an ion thruster. Since the cost in expended fuel restricts this technique to intermittent use during interplanetary flights, effective prediction of when a SEP event might impact the mission is still important, and the observation of conditions that might lead to SEP events, human-in-the-loop space weather analyses, and development of SEP prediction models remain essential to crew safety, spacecraft function, and mission success.

Interplanetary Space Flight↗

NASA NTRS1989

Radiative transfer theory for active remote sensing of a forested canopy

A canopy is modeled as a two-layer medium above a rough interface. The upper layer stands for the forest crown, with the leaves modeled as randomly oriented and distributed disks and needles and the branches modeled as randomly oriented finite dielectric cylinders. The lower layer contains the tree trunks, modeled as randomly positioned vertical cylinders above the rough soil. Radiative-transfer theory is applied to calculate EM scattering from such a canopy, is expressed in terms of the scattering-amplitude tensors (SATs). For leaves, the generalized Rayleigh-Gans approximation is applied, whereas the branch and trunk SATs are obtained by estimating the inner field by fields inside a similar cylinder of infinite length. The Kirchhoff method is used to calculate the soil SAT. For a plane wave exciting the canopy, the radiative-transfer equations are solved by iteration to the first order in albedo of the leaves and the branches. Numerical results are illustrated as a function of the incidence angle.

Karam, M. A.↗

NASA NTRS1988

Integrated resource scheduling in a distributed scheduling environment

The Space Station era presents a highly-complex multi-mission planning and scheduling environment exercised over a highly distributed system. In order to automate the scheduling process, customers require a mechanism for communicating their scheduling requirements to NASA. A request language that a remotely-located customer can use to specify his scheduling requirements to a NASA scheduler, thus automating the customer-scheduler interface, is described. This notation, Flexible Envelope-Request Notation (FERN), allows the user to completely specify his scheduling requirements such as resource usage, temporal constraints, and scheduling preferences and options. The FERN also contains mechanisms for representing schedule and resource availability information, which are used in the inter-scheduler inconsistency resolution process. Additionally, a scheduler is described that can accept these requests, process them, generate schedules, and return schedule and resource availability information to the requester. The Request-Oriented Scheduling Engine (ROSE) was designed to function either as an independent scheduler or as a scheduling element in a network of schedulers. When used in a network of schedulers, each ROSE communicates schedule and resource usage information to other schedulers via the FERN notation, enabling inconsistencies to be resolved between schedulers. Individual ROSE schedules are created by viewing the problem as a constraint satisfaction problem with a heuristically guided search strategy.

Zoch, David↗

NASA NTRSDate not supplied

Overview of NASA's Ocean Color Instrument Solar Calibration Architecture, Pre-Launch Tests and Preliminary On-Orbit Results

Launched in February 2024, the PACE mission represents NASA’s next investment in ocean biology, clouds, and aerosol data records. A key feature of PACE is the inclusion of an advanced satellite radiometer known as the Ocean Color Instrument (OCI), a global mapping radiometer that combines multispectral and hyperspectral remote sensing. Like its predecessors, OCI will provide two day global coverage of TOA radiances. Unlike its predecessors, OCI will cover a spectral range from 340nm to 2260nm. Below 900nm, OCI will include two spectrometers that continuously span the ultraviolet to 600nm and 600nm to near-infrared spectral regions to provide hyperspectral radiances sampled every 2.5 nm, with a bandwidth of 5 nm for each channel. Wavelengths above 900nm are measured in seven discrete multispectral bands of varying bandwidths, six of which are at similar wavelengths to those on heritage missions to support both atmospheric and ocean color applications. Nominal spatial resolution is similar to the SeaWiFS instrument with 1050 m at nadir. As for SeaWiFS, the pixel size increases due to a ~20 degree tilt and as a function of scan angle. Variations in the radiometric sensitivity of each OCI channel over time will be monitored by solar diffuser measurements for short term instrument gain adjustments and independent lunar measurements for trend adjustments of long time periods, similar to the approach employed for the VIIRS instrument [4]. The OCI flight-unit was built at NASA’s Goddard Space Flight Center. At the time of this writing, OCI has completed on-orbit commissioning activities and normal science operations have begun. A key aspect of the OCI architecture is the capability to trend absolute and relative calibration changes over the course of mission life with solar calibration. Every 24 hours, the PACE spacecraft performs an inertial hold as the ground track nears the North Pole which orients a Quasi-Volume Diffuser (QVD) mounted on OCI towards the sun. By knowing the irradiance of the sun and the reflectivity of the target, the absolute radiance at the input to the OCI aperture can be computed as OCI scans the target. The allowable absolute uncertainty budget for each solar calibration measurement is 1.6% 1-sigma below 900nm at beginning of life (BOL) and the allowable relative uncertainty budget is ~0.26% 1-sigma. The Solar Calibration Assembly (SCA) consists of three targets selectable via a single mechanism which also opens a door. The targets consist of a Daily Bright Target (DBT), Monthly Bright Target (MBT), and Daily Dim Target (DDT). The bright targets are quartz QVDs with the monthly target being used to track the degradation of the daily target. The dim target is used to track CCD linearity using Progressive Time-Delay Integration (PTDI). A composite baffle is attached to the SCA housing aperture to block Earth shine and stray light from the spacecraft. The SCA assembly is mounted to a view port ~90° from OCI nadir. This paper provides an overview of driving solar calibration requirements, error-budgets and early trade studies which drove the solar calibration assembly (SCA) architecture and on-orbit maneuver. Measurements of the diffuser Bidirectional Reflectance Distribution Function (BRDF) at TNO, Netherlands and GSFC are briefly described. Optical modelling and test results at the sub-system and instrument level are included. Finally, preliminary measurements on-orbit are compared to pre-launch predictions.

Joseph J Knuble↗

NASA NTRSDate not supplied

Overview of NASA's Ocean Color Instrument Solar Calibration Architecture, Pre-Launch Tests and Preliminary On-Orbit Results

Launched in February 2024, the PACE mission represents NASA’s next investment in ocean biology, clouds, and aerosol data records. A key feature of PACE is the inclusion of an advanced satellite radiometer known as the Ocean Color Instrument (OCI), a global mapping radiometer that combines multispectral and hyperspectral remote sensing. Like its predecessors, OCI will provide two day global coverage of TOA radiances. Unlike its predecessors, OCI will cover a spectral range from 340nm to 2260nm. Below 900nm, OCI will include two spectrometers that continuously span the ultraviolet to 600nm and 600nm to near-infrared spectral regions to provide hyperspectral radiances sampled every 2.5 nm, with a bandwidth of 5 nm for each channel. Wavelengths above 900nm are measured in seven discrete multispectral bands of varying bandwidths, six of which are at similar wavelengths to those on heritage missions to support both atmospheric and ocean color applications. Nominal spatial resolution is similar to the SeaWiFS instrument with 1050 m at nadir. As for SeaWiFS, the pixel size increases due to a ~20 degree tilt and as a function of scan angle. Variations in the radiometric sensitivity of each OCI channel over time will be monitored by solar diffuser measurements for short term instrument gain adjustments and independent lunar measurements for trend adjustments of long time periods, similar to the approach employed for the VIIRS instrument [4]. The OCI flight-unit was built at NASA’s Goddard Space Flight Center. At the time of this writing, OCI has completed on-orbit commissioning activities and normal science operations have begun. A key aspect of the OCI architecture is the capability to trend absolute and relative calibration changes over the course of mission life with solar calibration. Every 24 hours, the PACE spacecraft performs an inertial hold as the ground track nears the North Pole which orients a Quasi-Volume Diffuser (QVD) mounted on OCI towards the sun. By knowing the irradiance of the sun and the reflectivity of the target, the absolute radiance at the input to the OCI aperture can be computed as OCI scans the target. The allowable absolute uncertainty budget for each solar calibration measurement is 1.6% 1-sigma below 900nm at beginning of life (BOL) and the allowable relative uncertainty budget is ~0.26% 1-sigma. The Solar Calibration Assembly (SCA) consists of three targets selectable via a single mechanism which also opens a door. The targets consist of a Daily Bright Target (DBT), Monthly Bright Target (MBT), and Daily Dim Target (DDT). The bright targets are quartz QVDs with the monthly target being used to track the degradation of the daily target. The dim target is used to track CCD linearity using Progressive Time-Delay Integration (PTDI). A composite baffle is attached to the SCA housing aperture to block Earth shine and stray light from the spacecraft. The SCA assembly is mounted to a view port ~90° from OCI nadir. This paper provides an overview of driving solar calibration requirements, error-budgets and early trade studies which drove the solar calibration assembly (SCA) architecture and on-orbit maneuver. Measurements of the diffuser Bidirectional Reflectance Distribution Function (BRDF) at TNO, Netherlands and GSFC are briefly described. Optical modelling and test results at the sub-system and instrument level are included. Finally, preliminary measurements on-orbit are compared to pre-launch predictions.

ocean color↗

NASA NTRS2004

Advanced Optical Diagnostic Methods for Describing Fuel Injection and Combustion Flowfield Phenomena

Over the past decade advanced optical diagnostic techniques have evolved and matured to a point where they are now widely applied in the interrogation of high pressure combusting flows. At NASA Glenn Research Center (GRC), imaging techniques have been used successfully in on-going work to develop the next generation of commercial aircraft gas turbine combustors. This work has centered on providing a means by which researchers and designers can obtain direct visual observation and measurements of the fuel injection/mixing/combustion processes and combustor flowfield in two- and three-dimensional views at actual operational conditions. Obtaining a thorough understanding of the chemical and physical processes at the extreme operating conditions of the next generation of combustors is critical to reducing emissions and increasing fuel efficiency. To accomplish this and other tasks, the diagnostic team at GRC has designed and constructed optically accessible, high pressurer high temperature flame tubes and sectar rigs capable of optically probing the 20-60 atm flowfields of these aero-combustors. Among the techniques employed at GRC are planar laser-induced fluorescence (PLIF) for imaging molecular species as well as liquid and gaseous fuel; planar light scattering (PLS) for imaging fuel sprays and droplets; and spontaneous Raman scattering for species and temperature measurement. Using these techniques, optical measurements never before possible have been made in the actual environments of liquid fueled gas turbines. 2-D mapping of such parameters as species (e.g. OH-, NO and kerosene-based jet fuel) distribution, injector spray angle, and fuel/air distribution are just some of the measurements that are now routinely made. Optical imaging has also provided prompt feedback to researchers regarding the effects of changes in the fuel injector configuration on both combustor performance and flowfield character. Several injector design modifications and improvements have resulted from this feedback. Alternate diagnostic methods are constantly being evaluated as to their suitability as a diagnostic tool in these environments. A new method currently under examination is background oriented Schlieren (BOS) for examining the fuel/air mixing processes. While ratioing the Stokes and anti-Stokes nitrogen lines obtained from spontaneous Raman is being refined for temperature measurement. While the primary focus of the GRC diagnostic work remains optical species measurement and flow stream characterization, an increased emphasis has been placed on our involvement in flame code validation efforts. A functional combustor code should shorten and streamline future combustor design. Quantitative measurements of flow parameters such as temperature, species concentration, drop size and velocity using such methods as Raman and phase Doppler anemometry will provide data necessary in this effort.

Locke, Randy J.↗

NASA NTRS2017

Evolution of NASA's Earth Science Digital Object Identifier Registration System

NASA's Earth Science Data and Information System (ESDIS) Project has implemented a fully automated system for assigning Digital Object Identifiers (DOIs) to Earth Science data products being managed by its network of 12 distributed active archive centers (DAACs). A key factor in the successful evolution of the DOI registration system over last 7 years has been the incorporation of community input from three focus groups under the NASA's Earth Science Data System Working Group (ESDSWG). These groups were largely composed of DOI submitters and data curators from the 12 data centers serving the user communities of various science disciplines. The suggestions from these groups were formulated into recommendations for ESDIS consideration and implementation. The ESDIS DOI registration system has evolved to be fully functional with over 5,000 publicly accessible DOIs and over 200 DOIs being held in reserve status until the information required for registration is obtained. The goal is to assign DOIs to the entire 8000+ data collections under ESDIS management via its network of discipline-oriented data centers. DOIs make it easier for researchers to discover and use earth science data and they enable users to provide valid citations for the data they use in research. Also for the researcher wishing to reproduce the results presented in science publications, the DOI can be used to locate the exact data or data products being cited.

DOI; digital object identifier; mappin↗

NASA NTRS2005

International Space Station Electric Power System Performance Code-SPACE

The System Power Analysis for Capability Evaluation (SPACE) software analyzes and predicts the minute-by-minute state of the International Space Station (ISS) electrical power system (EPS) for upcoming missions as well as EPS power generation capacity as a function of ISS configuration and orbital conditions. In order to complete the Certification of Flight Readiness (CoFR) process in which the mission is certified for flight each ISS System must thoroughly assess every proposed mission to verify that the system will support the planned mission operations; SPACE is the sole tool used to conduct these assessments for the power system capability. SPACE is an integrated power system model that incorporates a variety of modules tied together with integration routines and graphical output. The modules include orbit mechanics, solar array pointing/shadowing/thermal and electrical, battery performance, and power management and distribution performance. These modules are tightly integrated within a flexible architecture featuring data-file-driven configurations, source- or load-driven operation, and event scripting. SPACE also predicts the amount of power available for a given system configuration, spacecraft orientation, solar-array-pointing conditions, orbit, and the like. In the source-driven mode, the model must assure that energy balance is achieved, meaning that energy removed from the batteries must be restored (or balanced) each and every orbit. This entails an optimization scheme to ensure that energy balance is maintained without violating any other constraints.

Hojnicki, Jeffrey↗

NASA NTRS1990

Building distributed rule-based systems using the AI Bus

The AI Bus software architecture was designed to support the construction of large-scale, production-quality applications in areas of high technology flux, running heterogeneous distributed environments, utilizing a mix of knowledge-based and conventional components. These goals led to its current development as a layered, object-oriented library for cooperative systems. This paper describes the concepts and design of the AI Bus and its implementation status as a library of reusable and customizable objects, structured by layers from operating system interfaces up to high-level knowledge-based agents. Each agent is a semi-autonomous process with specialized expertise, and consists of a number of knowledge sources (a knowledge base and inference engine). Inter-agent communication mechanisms are based on blackboards and Actors-style acquaintances. As a conservative first implementation, we used C++ on top of Unix, and wrapped an embedded Clips with methods for the knowledge source class. This involved designing standard protocols for communication and functions which use these protocols in rules. Embedding several CLIPS objects within a single process was an unexpected problem because of global variables, whose solution involved constructing and recompiling a C++ version of CLIPS. We are currently working on a more radical approach to incorporating CLIPS, by separating out its pattern matcher, rule and fact representations and other components as true object oriented modules.

Schultz, Roger D.↗

NASA NTRS1982

Design and calibration of a coherent lidar for measurement of atmospheric backscatter

This paper discusses the background requirements for, and the design and calibration of a coherent Doppler lidar which is oriented specifically toward the measurement of low values of atmospheric backscatter at a wavelength of 10.6 microns. The lidar is a compact, continuous wave system which can operate in two modes, multiple particle scattering and single particle scattering. In the multiple scattering mode, the lidar employs an extended focal volume and utilizes a technique similar to Dicke switching to achieve measurement of the volume backscatter. In the single scattering mode, the focal volume is reduced to ensure a high probability of single particle scattering. Measurement of the single particle backscatter as a function of time leads to the formation of signal histogram from which the volume backscatter can be inferred. In addition to providing the atmospheric backscatter value, appropriate data processing algorithms and focal volume calibration allow the single particle mode to yield information on the atmospheric aerosol scattering cross-section distribution.

Jones, W. D.↗

NASA NTRS1994

The Effects of Sensor Field-of-View on the Geometrical Characteristics of Sea Ice Leads and Implications for Large-Area Heat Flux Estimates

The release of heat from sea ice fractures ('leads') is an important component of the heat budget in the Arctic, but their impact on regional scale climate is difficult to assess without more information on their distribution in both space and time. Remote sensing of leads using satellite data, specifically AVHRR thermal and Landsat visible-band imagery, is examined empirically with respect to lead width, orientation, and area fraction. The geometrical aspects of the sensor are simulated so that the effect of sensor field-of-view on retrieved lead width statistics can be assessed. This is done using Landsat data and simulated lead networks degraded to AVHRR pixel sizes. The analyses illustrate how leads of sufficiently high contrast tend to 'grow' with increasing pixel size and how small or low contrast leads disappear. The relationship between lead contrast and the width/field-of-view ratio is also examined in order to determine the limits of lead detectability, and illustrates the multivalued nature of the problem of lead width retrieval. To help quantify the importance of changes in lead statistics, turbulent heat flux is calculated as a function of lead width and lead fraction. It is shown that pixel size has a substantial effect on estimates of turbulent heat transfer from leads to the atmosphere.

Key, J.↗

NASA NTRS1959

Longitudinal Laminar Flow Between Cylinders Arranged in Regular Array

The increasing complexity of heat transfer and process situations which involve fluid flow has demanded the frequent use of flow passages of unusual geometrical configuration. The present investigation is concerned with one such novel configuration, namely the longitudinal flow between solid cylindrical rods which are arranged in regular array. A schematic diagram of the situation under study. The rods may be located either in triangular or square array. The flow will be taken to be laminar and fully developed. The aim of this analysis is to determine the pressure drop, shear stress, and velocity-distribution characteristics of the system. The starting point of this study is the basic law of momentum conservation. The resulting differential equation has been solved in an approximate, but almost exact, manner by the use of truncated trigonometric series. Results are obtained over a wide range of porosity values for both the triangular and square arrays. Heat transfer has not been considered. The configuration under investigation has potential application in compact heat exchangers for nuclear reactors and other situations. Further the results should also be of interest in the theory of flow through unconsolidated porous beds (ia, 9a). The only related analytical work known to the authors is that of Emersleben (S), who considered only the square array. His rather involved solution, based on complex zeta functions, appears to be valid only at high porosities. Experiments covering a porosity range of 0.093 to 0.984 have been made by Sullivan (4) using parallel-oriented fibers, most of the tests being for fibers in random array. These previous investigations will be compared with the present theory in a later section.

Sparrow, E. M.↗