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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.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Three-dimensional unsteady flow calculations in an advanced gas generator turbine

This paper deals with the application of a three-dimensional, unsteady Navier-Stokes code for predicting the unsteady flow in a single stage of an advanced gas generator turbine. The numerical method solves the three-dimensional thin-layer Navier-Stokes equations, using a system of overlaid grids, which allow for relative motion between the rotor and stator airfoils. Results in the form of time averaged pressures and pressure amplitudes on the airfoil surfaces will be shown. In addition, instantaneous contours of pressure, Mach number, etc. will be presented in order to provide a greater understanding of the inviscid as well as the viscous aspects of the flowfield. Also, relevant secondary flow features such as cross-plane velocity vectors and total pressure contours will be presented. Prior work in two-dimensions has indicated that for the advanced designs, the unsteady interactions can play a significant role in turbine performance. These interactions affect not only the stage efficiency but can substantially alter the time-averaged features of the flow. This work is a natural extension of the work done in two-dimensions and hopes to address some of the issues raised by the two-dimensional calculations. These calculations are being performed as an integral part of an actual design process and demonstrate the value of unsteady rotor-stator interaction calculations in the design of turbomachines.

Rangwalla, Akil A.↗
NASA NTRS1997

Planar Doppler Velocimetry for Large-Scale Wind Tunnel Testing

Recently, Planar Doppler Velocimetry (PDV) has been shown by several laboratories to offer an attractive means for measuring three-dimensional velocity vectors everywhere in a light sheet placed in a flow. Unlike other optical means of measuring flow velocities, PDV is particularly attractive for use in large wind tunnels where distances to the sample region may be several meters, because it does not require the spatial resolution and tracking of individual scattering particles or the alignment of crossed beams at large distances. To date, demonstrations of PDV have been made either in low speed flows without quantitative comparison to other measurements, or in supersonic flows where the Doppler shift is large and its measurement is relatively insensitive to instrumental errors. Moreover, most reported applications have relied on the use of continuous-wave lasers, which limit the measurement to time-averaged velocity fields. This work summarizes the results of two previous studies of PDV in which the use of pulsed lasers to obtain instantaneous velocity vector fields is evaluated. The objective has been to quantitatively define and demonstrate PDV capabilities for applications in large-scale wind tunnels that are intended primarily for the production testing of subsonic aircraft. For such applications, the adequate resolution of low-speed flow fields requires accurate measurements of small Doppler shifts that are obtained at distances of several meters from the sample region. The use of pulsed lasers provides the unique capability to obtain not only time-averaged fields, but also their statistical fluctuation amplitudes and the spatial excursions of unsteady flow regions such as wakes and separations. To accomplish the objectives indicated, the PDV measurement process is first modeled and its performance evaluated computationally. The noise sources considered include those related to the optical and electronic properties of Charge-Coupled Device (CCD) arrays and to speckle effects associated with coherent illumination from pulsed lasers. The signal noise estimates are incorporated into the PDV signal analysis process and combined with computed scattering signals using a Mie scattering theory for polydisperse smoke particles. The relevant parameters incorporate a range of practical aerodynamic test conditions and facility sizes. The results define the optimum instrument configurations, show that the expected signal levels from a practical PDV system are sufficiently large to allow its useful application in large facilities, and show that the expected velocity measurement uncertainties are small compared to the mean velocities of interest for most subsonic, large-scale wind tunnel testing. Experimental studies using several experimental bench-top setups are then described that validate the physics of the PDV model and to calibrate its computed results. The validated model allows estimates of the uncertainties of PDV measurements and a complete definition of the PDV capabilities to be made with sufficient confidence to decide the viability of PDV for large-scale wind tunnel applications.

McKenzie, Robert L.↗
NASA NTRS1995

Ionization nebulae surrounding CAL 83 and other supersoft X-ray sources

We present the results of an optical search for ionized gaseous nebulae surrounding luminous, 'supersoft' X-ray sources in the Large and Small Magellanic Clouds. This relatively new and mysterious X-ray class has characteristic luminosities approximately 10(exp 37)-10(exp 38) ergs/s with effective temperatures in the range of 2-6 x 10(exp 5) K. The presence of a large flux of UV and soft X-ray photons from these objects has led to predictions of bright optical emission lines from the local interstellar medium. One such object, CAL 83 in the LMC, was known to have an associated nebula, and we quantify here the asymmetry and luminosity of this remarkable nebula. Deep images were made using narowband filters to isolate the emission lines of H alpha and (O III) (lambda 5007). In these emission lines, the nebula is detected out to distances as far as 25 pc from the central object, and the integrated luminositu in each line is of order approximately 100 solar luminosity. Model calculations of such nebulae for chemical abundances characteristic of the LMC indicate that approximately 1% of the X-ray luminosity of the central source is reprocessed into the nebular H-alpha and (O III) lambda 5007 emission lines, from which we conclude that the time-averaged X-ray luminosity of the central source, CAL 83, is greater than 3 x 10(exp 37) ergs/s. The bright inner nebula contains approximately 150 solar mass within 7.5 pc of CAL 83, which clearly indicates that the nebular material has its origin in the interstelar medium. In sharp contrast, there were null detections for nebulae associated with nine other luminous, supersoft X-ray sources in the LMC and SMC, with upper limits for the (O III) luminosity that are a factor of approximately 10 below that for CAL 83. For eight of these latter sources, we conclude that either their time-averaged luminosity is substantially below that of CAL 83, or that the local interstellar medium is much less dense. The latter effect may be enhanced by expansion of the ionized nebula during the last several million years.

Remillard, R. A.↗
NASA NTRS1995

Ionization Nebulae Surrounding CAL 83 and Other Supersoft X-ray Sources

We present the results of an optical search for ionized gaseous nebulae surrounding luminous, "supersoft" X-ray sources in the Large and Small Magellanic Clouds. This relatively new and mysterious X-ray class has characteristic luminosities approximately 10(exp 37) - 10(exp 38) ergs/s with effective temperatures in the range of 2 - 6 x 10(exp 5) K. The presence of a large flux of UV and soft X-ray photons from these objects has led to predictions of bright optical emission lines from the local interstellar medium. One such object, CAL 83 in the LMC, was known to have an associated nebula, and we quantify here the asymmetry and luminosity of this remarkable nebula. Deep images were made using narrowband filters to isolate the emission lines of H.alpha and [O III] (lamda5007). In these emission lines, the nebula is detected out to distances as far as 25 pc from the central object, and the integrated luminosity in each line is of order approximately 100 solar luminosity. Model calculations of such nebulae for chemical abundances characteristic of the LMC indicate that approximately 1% of the X-ray luminosity of the central source is reprocessed into the nebular H.alpha and [O III] lamda5007 emission lines, from which we conclude that the time-averaged X-ray luminosity of the central source, CAL 83, is greater than 3 x 10(exp 37) ergs/s. The bright inner nebula contains approximately 150 solar mass within 7.5 pc of CAL 83, which clearly indicates that the nebular material has its origin in the interstellar medium. In sharp contrast, there were null detections for nebulae associated with nine other luminous, supersoft X-ray sources in the LMC and SMC, with upper limits for the [O III] luminosity that are a factor of approximately 10 below that for CAL 83. For eight of these latter sources, we conclude that either their time-averaged luminosity is substantially below that of CAL 83, or that the local interstellar medium is much less dense. The latter effect may be enhanced by expansion of the ionized nebula during the last several million years.

Remillard, R. A.↗
NASA NTRS2004

Towards a High Temporal Frequency Grass Canopy Thermal IR Model for Background Signatures

In this paper, we present our first results towards understanding high temporal frequency thermal infrared response from a dense plant canopy and compare the application of our model, driven both by slowly varying, time-averaged meteorological conditions and by high frequency measurements of local and within canopy profiles of relative humidity and wind speed, to high frequency thermal infrared observations. Previously, we have employed three-dimensional ray tracing to compute the intercepted and scattered radiation fluxes and for final scene rendering. For the turbulent fluxes, we employed simple resistance models for latent and sensible heat with one-dimensional profiles of relative humidity and wind speed. Our modeling approach has proven successful in capturing the directional and diurnal variation in background thermal infrared signatures. We hypothesize that at these scales, where the model is typically driven by time-averaged, local meteorological conditions, the primary source of thermal variance arises from the spatial distribution of sunlit and shaded foliage elements within the canopy and the associated radiative interactions. In recent experiments, we have begun to focus on the high temporal frequency response of plant canopies in the thermal infrared at 1 second to 5 minute intervals. At these scales, we hypothesize turbulent mixing plays a more dominant role. Our results indicate that in the high frequency domain, the vertical profile of temperature change is tightly coupled to the within canopy wind speed In the results reported here, the canopy cools from the top down with increased wind velocities and heats from the bottom up at low wind velocities. .

Ballard, Jerrell R., Jr.↗
NASA NTRS1977

Finite element analysis of aeroacoustic jet-flap flows

A computational analysis was performed on the steady, turbulent aerodynamic flowfields associated with a jet-blown flap. For regions devoid of flow separation, a parabolic approximation to the governing time-averaged Navier-Stokes equations was applied. Numerical results are presented for the symmetry plane flow of a slot-nozzle planar jet flap geometry, including prediction of flowfield evolution within the secondary mixing region immediately downstream of the trailing edge. Using a two equation turbulence kinetic energy closure model, rapid generation and decay of large spatial gradients in mean and correlated fluctuating velocity components within the immediate wake region were predicted. Modifications to the turbulent flow structure, as induced by porous surface treatment of the flap, were evaluated. The recirculating flow within a representative discrete slot in the surface was evaluated, using the two dimensional, time-averaged Navier-Stokes equations.

Baker, A. J.↗
NASA NTRS1974

Laser velocimeter measurements of the helicopter rotor-induced flow field

The use of a two-color laser velocimeter to measure the flow velocities in the wake of a helicopter rotor is discussed, including methods for obtaining two components of both instantaneous and time-averaged velocities. Results are presented from an experiment using a 2.13 m diameter model helicopter rotor operating at a tip speed ratio of 0.18 in a wind tunnel. The location of the tip vortex from the preceding blade was determined on the advancing side, and the diameter of the vortex core was found to be 15 percent of the blade chord (1.5 percent of the radius). The effects of the airfoil's bound vorticity were observed in the velocity distributions vry near the blade. These effects suggest that the laser velocimeter may be used to determine the aerodynamic loading (circulation) at a spanwise station on the blade. Also, the structure and boundary of the time-averaged wake were investigated.

Biggers, J. C.↗
NASA NTRS1981

Flame structure in a swirl stabilized combustor inferred by radiant emission measurements

Results of measurements of time-averaged chemiluminescent emissions from CH, OH, and CO2 and of Na tracer emissions along lateral lines-of-sight through a cylindrical premixed, swirl-stabilized combustor are reported. Assuming axial symmetry and small optical depth, raw data are inverted to obtain local emission levels from these species as a function of radius. The chemiluminescent emissions are interpreted as signatures of chemical reaction and used in determining the regions of reactions and heat release in the combustor. The data are compared with composition and velocity data obtained in the combustor for identical operating conditions. The results demonstrate that reaction occurs in a relatively narrow, turbulent flame-like combustion zone which begins upstream of the time-averaged location of the swirl-induced recirculation zone and propagates around and laterally away from the recirculation zone into the unburned gas.

Beyler, C. L.↗
NASA NTRS2012

Space Weathering Investigations Enabled by NASA's Virtual Heliophysical Observatories

Structural and chemical impact of the heliospheric space environment on exposed planetary surfaces and interplanetary dust grains may be generally defined as space weathering . In the inner solar system, from the asteroid belt inwards towards the Sun, the surface regolith structures of airless bodies are primarily determined by cumulative meteoritic impacts over billions of years, but the molecular composition to meters in depth can be substantially modified by irradiation effects. Plasma ions at eV to keV energies may both erode uppermost surfaces by sputtering, and implant or locally produce exogenic material, e.g. He-3 and H2O, while more energetic ions drive molecular change through electronic ionization. Galactic cosmic ray ions and more energetic solar ions can impact chemistry to meters in depth. High energy cosmic ray interactions produce showers of secondary particles and energetic photons that present hazards for robotic and human exploration missions but also enable detection of potentially useable resources such as water ice, oxygen, and many other elements. Surface sputtering also makes ejected elemental and molecular species accessible for in-situ compositional analysis by spacecraft with ion and neutral mass spectrometers. Modeling of relative impacts for these various space weathering processes requires knowledge of the incident species-resolved ion flux spectra at plasma to cosmic ray energies and as integrated over varying time scales. Although the main drivers for investigations of these processes come from NASA's planetary science and human exploration programs, the NASA heliophysics program provides the requisite data measurement and modeling resources to enable specification of the field & plasma and energetic particle irradiation environments for application to space weather and surface weathering investigations. The Virtual Heliospheric Observatory (VHO), Virtual Energetic Particle Observatory (VEPO), Lunar Solar Origins Exploration (LunaSOX), and Space Physics Data Facility (SPDF) services now provide a wide range of inner heliospheric spacecraft data that can be applied to space weathering of potential exploration destinations including the Moon, asteroids, and the moons of Mars, as well to radiation hazard assessment for the spacecraft and human explorers. For example, the new VEPO service for time-averaging of multi-source ion flux spectra enables the specification of composite flux spectra from a variety of ongoing and legacy missions for applications to surface interaction modeling. Apollo to Artemis data resources of LunaSOX enable specific space weathering investigations for the Moon, while VHO more generally covers the space field and plasma environments of the inner and outer solar system from the sunward-most perihelia of the twin Helios spacecraft to the ongoing heliosheath passages of the twin Voyagers. Composite multi-source spectra from VEPO can also be applied to the continuing compilation of accumulated 1-AU fluence spectra, mostly contributed by solar wind plasma and energetic particle events, for determination of time-averaged particle compositional and kinetic energy output from the Sun and for modeling of long-term irradiation impacts on planetary surfaces.

Cooper, John F.↗
NASA NTRS1997

Measurement Capabilities of Planar Doppler Velocimetry in Large-Scale Wind Tunnels

Over the past few years, Planar Doppler Velocimetry (PDT) has been shown by several laboratories to offer an attractive means for measuring three-dimensional velocity vectors everywhere in a light sheet placed in a flow. Unlike some other optical means of measuring flow velocities, PDT is particularly attractive for use in large wind tunnels where distances to the sample region may be several meters, because it does not require the spatial resolution and tracking of individual scattering particles or the alignment of crossed beams at large distances. To date, demonstrations of PDT (also called Doppler Global Velocimetry by some authors) have been made either in low speed flows without quantitative comparison to other measurements, or in supersonic flows where the Doppler shift is large and its measurement is relatively insensitive to instrumental errors. Moreover, most reported applications have relied on the use of continuous-wave lasers, which limit the measurement to time-averaged velocity fields. This work summarizes the results of two previous studies of PDT in which the use of pulsed lasers to obtain instantaneous velocity vector fields is evaluated. The objective has been to quantitatively define and demonstrate PDT capabilities for applications in large-scale wind tunnels that are intended primarily for the testing of rotorcraft and subsonic aircraft at speeds typically less than 100 m/s. For such applications, the adequate resolution of low-speed flow fields requires accurate measurements of small Doppler shifts that are obtained at distances of several meters from the sample region and with a field of view that is sufficient to encompass the entire region of interest. The use of pulsed lasers provides the unique capability to obtain not only time-averaged fields, but also their statistical fluctuation amplitudes and the spatial excursions of unsteady flow regions such as wakes, separations, and rotor-tip vortices. To accomplish the objectives of these studies, the PDT measurement process was first modeled and its performance evaluated computationally. The noise sources considered included those related to the optical and electronic properties of Charge-Coupled Device (CCD) arrays and to speckle effects associated with the coherent illumination of aerosols from pulsed lasers. The signal noise estimates were incorporated into the PDT signal analysis process and combined with computed scattering signals using a Mae scattering theory for a distributed range of aerosol particle sizes. The results are used to define the necessary instrument configuration, to show that the expected signal levels from a practical PDT system are sufficiently large to allow its useful application in large facilities, and to show that the expected velocity measurement uncertainties are small compared to the mean velocities of interest for most subsonic, large-scale wind tunnel testing, Experimental studies using several bench-top setups are then described that validate the physics of the PDT model and demonstrate the ability to obtain accurate PDT measurements using procedures that are compatible with large-scale wind tunnel operations. The PDT measurement capabilities found in this study lead to the conclusion that PDT offers significant advantages compared to other means of measuring velocity fields in large-scale wind tunnels, including those operating at low speeds.

McKenzie, Robert L.↗
NASA NTRS1987

Turbomachinery

The discipline research in turbomachinery, which is directed toward building the tools needed to understand such a complex flow phenomenon, is based on the fact that flow in turbomachinery is fundamentally unsteady or time dependent. Success in building a reliable inventory of analytic and experimental tools will depend on how the time and time-averages are treated, as well as on who the space and space-averages are treated. The raw tools at disposal (both experimentally and computational) are truly powerful and their numbers are growing at a staggering pace. As a result of this power, a case can be made that a situation exists where information is outstripping understanding. The challenge is to develop a set of computational and experimental tools which genuinely increase understanding of the fluid flow and heat transfer in a turbomachine. Viewgraphs outline a philosophy based on working on a stairstep hierarchy of mathematical and experimental complexity to build a system of tools, which enable one to aggressively design the turbomachinery of the next century. Examples of the types of computational and experimental tools under current development at Lewis, with progress to date, are examined. The examples include work in both the time-resolved and time-averaged domains. Finally, an attempt is made to identify the proper place for Lewis in this continuum of research.

Simoneau, Robert J.↗
NASA NTRS2005

Summary of Simplified Two Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydrogen/Oxygen

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (greater than l x 10(exp -20)) moles per cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T(sub 4)). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/Air fuel and for H2/O2. A similar correlation is also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T(sub 4)) as a function of overall fuel/air ratio, pressure and initial temperature (T(sub 3)). High values of the regression coefficient R squared are obtained.

Marek, C. John↗
NASA NTRS2005

Simplified Two-Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydorgen/Oxygen

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two-time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (> 1 x 10(exp -20) moles/cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T4). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/air fuel and for the H2/O2. A similar correlation is also developed using data from NASA s Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T4) as a function of overall fuel/air ratio, pressure and initial temperature (T3). High values of the regression coefficient R2 are obtained.

Molnar, Melissa↗
NASA NTRS1999

Aerodynamic Analysis of Multistage Turbomachinery Flows in Support of Aerodynamic Design

This paper summarizes the state of 3D CFD based models of the time average flow field within axial flow multistage turbomachines. Emphasis is placed on models which are compatible with the industrial design environment and those models which offer the potential of providing credible results at both design and off-design operating conditions. The need to develop models which are free of aerodynamic input from semi-empirical design systems is stressed. The accuracy of such models is shown to be dependent upon their ability to account for the unsteady flow environment in multistage turbomachinery. The relevant flow physics associated with some of the unsteady flow processes present in axial flow multistage machinery are presented along with procedures which can be used to account for them in 3D CFD simulations. Sample results are presented for both axial flow compressors and axial flow turbines which help to illustrate the enhanced predictive capabilities afforded by including these procedures in 3D CFD simulations. Finally, suggestions are given for future work on the development of time average flow models.

Adamczyk, John J.↗
NASA NTRS1975

Optical and X-ray observations of the PSR 1913 + 16 field

We have obtained medium-resolution spectra in the yellow of seven stars in the error box of the binary radio pulsar PSR 1913 + 16, using the image-tube scanner at the Lick 3-m telescope. None of the objects is spectroscopically abnormal and thus a strong candidate for membership in the system. The data are used to establish the extinction in the field, which is modest for this low galactic latitude. For three of the stars, limits of the order V exceeding 23 mag on optical pulsations with the frequency of the radio pulsar are derived. X-ray observations of the field have been obtained in the 2.5-7.5 keV band, using the UCL experiment aboard OAO Copernicus. No source is detected, with a 2 sigma upper limit on the time-averaged flux of 1.0 times 10 to the -10th power ergs per sq cm per sec.

Davidsen, A.↗
NASA NTRS1980

A microprocessor based high speed packet switch for satellite communications

The architectures of a single processor, a three processor, and a multiple processor system are described. The hardware circuits, and software routines required for implementing the three and multiple processor designs are presented. A bit-slice microprocessor was designed and microprogrammed. Maximum throughput was calculated for all three designs. Queue theoretic models for these three designs were developed and utilized to obtain analytical expressions for the average waiting times, overall average response times and average queue sizes. From these expressions, graphs were obtained showing the effect on the system performance of a number of design parameters.

Arozullah, M.↗
NASA NTRS1982

Surface wind analyses for Seasat

During the 99 days of Seasat operation, two large-scale experiments were conducted which established the satellite sensors' wind measuring capabilities: (1) the Gulf of Alaska Experiment (GOASEX), and (2) the Joint Air Sea Interaction Experiment (JASIN), which unlike GOASEX was independent of the Seasat program and undertook comprehensive air and sea investigations which furnished excellent comparison data for Seasat. Qualitative comparison windfields were also provided by several storms. The point measurements in GOASEX and JASIN were averaged in conjunction with Seasat scatterometer regions and, on the basis of comparisons between several anemometers on buoys and meteorological ships and the calculation of various averaging times, a 20-min average yields a scatterometer scale windfield accuracy of up to + or 1 m/sec and + or - 10 deg in well-behaved windfields.

Brown, R. A.↗
NASA NTRS1984

User's Guide for ERB 7 Matrix. Volume 1: Experiment Description and Quality Control Report for Year 1

The Nimbus 7 ERB MATRIX Tape is a computer program in which radiances and irradiances are converted into fluxes which are used to compute the basic scientific output parameters, emitted flux, albedo, and net radiation. They are spatially averaged and presented as time averages over one-day, six-day, and monthly periods. MATRIX data for the period November 16, 1978 through October 31, 1979 are presented. Described are the Earth Radiation Budget experiment, the Science Quality Control Report, Items checked by the MATRIX Science Quality Control Program, and Science Quality Control Data Analysis Report. Additional material from the detailed scientific quality control of the tapes which may be very useful to a user of the MATRIX tapes is included. Known errors and data problems and some suggestions on how to use the data for further climatologic and atmospheric physics studies are also discussed.

Tighe, R. J.↗