Results for “Operator approximation” — Page 76

NASA NTRS1995

Hubble Space Telescope nickel-hydrogen battery testing: An update

The Marshall Space Flight Center (MSFC) began testing the HST Ni-H2 Six Battery Test and the 'Flight Spare Battery' Tests approximately one year before the launch of the HST. These tests are operated and reported on by the MSFC, but are managed and funded by Goddard Space Flight Center in direct support of the HST program. The HST Ni-H2 batteries are built from Eagle Picher RNH-90-3 cells. The HST EPS (electrical power system) is a direct energy transfer power system. The HST Ni-H2 Six Battery Test is a breadboard of the HST EPS. The batteries in the test are composed of test module cells and packaged into three battery modules identical to the flight modules. This test is the HST EPS testbed. The 'Flight Spare Battery' Test is a simulation of one of the six battery channels on the HST. The cells in the test are from the flight spare lot of cells, which are the same lot of cells that three of the six HST flight batteries are made from. This test is the battery life test for the HST program.

Whitt, Thomas H.↗

NASA NTRS1996

Analysis, design and testing of high pressure waterjet nozzles

The Hydroblast Research Cell at MSFC is both a research and a processing facility. The cell is used to investigate fundamental phenomena associated with waterjets as well as to clean hardware for various NASA and contractor projects. In the area of research, investigations are made regarding the use of high pressure waterjets to strip paint, grease, adhesive and thermal spray coatings from various substrates. Current industrial methods of cleaning often use ozone depleting chemicals (ODC) such as chlorinated solvents, and high pressure waterjet cleaning has proven to be a viable alternative. Standard methods of waterjet cleaning use hand held or robotically controlled nozzles. The nozzles used can be single-stream or multijet nozzles, and the multijet nozzles may be mounted in a rotating head or arranged in a fan-type shape. We consider in this paper the use of a rotating, multijet, high pressure water nozzle which is robotically controlled. This method enables rapid cleaning of a large area, but problems such as incomplete coverage (e.g. the formation of 'islands' of material not cleaned) and damage to the substrate from the waterjet have been observed. In addition, current stripping operations require the nozzle to be placed at a standoff distance of approximately 2 inches in order to achieve adequate performance. This close proximity of the nozzle to the target to be cleaned poses risks to the nozzle and the target in the event of robot error or the striking of unanticipated extrusions on the target surface as the nozzle sweeps past. Two key motivations of this research are to eliminate the formation of 'coating islands' and to increase the allowable standoff distance of the nozzle.

Mazzoleni, Andre P.↗

NASA NTRS1996

Implicity restarted Arnoldi/Lanczos methods for large scale eigenvalue calculations

Eigenvalues and eigenfunctions of linear operators are important to many areas of applied mathematics. The ability to approximate these quantities numerically is becoming increasingly important in a wide variety of applications. This increasing demand has fueled interest in the development of new methods and software for the numerical solution of large-scale algebraic eigenvalue problems. In turn, the existence of these new methods and software, along with the dramatically increased computational capabilities now available, has enabled the solution of problems that would not even have been posed five or ten years ago. Until very recently, software for large-scale nonsymmetric problems was virtually non-existent. Fortunately, the situation is improving rapidly. The purpose of this article is to provide an overview of the numerical solution of large-scale algebraic eigenvalue problems. The focus will be on a class of methods called Krylov subspace projection methods. The well-known Lanczos method is the premier member of this class. The Arnoldi method generalizes the Lanczos method to the nonsymmetric case. A recently developed variant of the Arnoldi/Lanczos scheme called the Implicitly Restarted Arnoldi Method is presented here in some depth. This method is highlighted because of its suitability as a basis for software development.

Sorensen, Danny C.↗

NASA NTRS1996

A CFD Study of Turbojet and Single-Throat Ramjet Ejector Interaction

Supersonic ejector-diffuse systems have application in driving an advanced airbreathing propulsion system, consisting of turbojet engines acting as the primary and a single throat ramjet acting as the secondary. The turbojet engines are integrated into the single throat ramjet to minimize variable geometry and eliminate redundant propulsion components. The result is a simple, lightweight system that is operable from takeoff to high Mach numbers. At this high Mach number (approximately Mach 3.0), the turbojets are turned off and the high speed ramjet/scramjet take over and drive the vehicle to Mach 6.0. The turbojet-ejector-ramjet system consists of nonafterburning turbojet engines with ducting canted at 20 degrees to supply supersonic flow (downstream of CD nozzle) to the horizontal ramjet duct at a supply total pressure and temperature. Two conditions were modelled by a 2-D full Navier Stokes code at Mach 2.0. The code modelled the Fabri choke as well as the non-Fabri non critical case, using a computational throat to supply the back pressure. The results, which primarily predict the secondary mass flow rate and the mixed conditions at the ejector exit were in reasonable agreement with the 1-D cycle code (TBCC).

Chang, Ing↗

NASA NTRS1961

Exploratory Environmental Tests of Several Heat Shields

Exploratory tests have been conducted with several conceptual radiative heat shields of composite construction. Measured transient temperature distributions were obtained for a graphite heat shield without insulation and with three types of insulating materials, and for a metal multipost heat shield, at surface temperatures of approximately 2,000 F and 1,450 F, respectively, by use of a radiant-heat facility. The graphite configurations suffered loss of surface material under repeated irradiation. Temperature distribution calculated for the metal heat shield by a numerical procedure was in good agreement with measured data. Environmental survival tests of the graphite heat shield without insulation, an insulated multipost heat shield, and a stainless-steel-tile heat shield were made at temperatures of 2,000 F and dynamic pressures of approximately 6,000 lb/sq ft, provided by an ethylene-heated jet operating at a Mach number of 2.0 and sea-level conditions. The graphite heat shield survived the simulated aerodynamic heating and pressure loading. A problem area exists in the design and materials for heat-resistant fasteners between the graphite shield and the base structure. The insulated multipost heat shield was found to be superior to the stainless-steel-tile heat shield in retarding heat flow. Over-lapped face-plate joints and surface smoothness of the insulated multi- post heat shield were not adversely affected by the test environment. The graphite heat shield without insulation survived tests made in the acoustic environment of a large air jet. This acoustic environment is random in frequency and has an overall noise level of 160 decibels.

Goodman, George P.↗

NASA NTRS1999

Large-Scale Parallel Viscous Flow Computations using an Unstructured Multigrid Algorithm

The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS (Full Approximation Scheme) approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors.

Mavriplis, Dimitri J.↗

NASA NTRS2000

Far Ultraviolet Imaging from the Image Spacecraft: Wideband FUV Imaging - 2

The Far Ultraviolet Wideband Imaging Camera (WIC) complements the magnetospheric images taken by the IMAGE satellite instruments with simultaneous global maps of the terrestrial aurora. Thus, a primary requirement of WIC is to image the total intensity of the aurora in wavelength regions most representative of the aurora] source and least contaminated by dayglow, have sufficient field of view to cover the entire polar region from spacecraft apogee and have resolution that is Sufficient to resolve auroras on a scale of 1 to 2 latitude degrees, The instrument is sensitive in the spectral region from 140- 190 nm. The WIC is mounted on the rotating, IMAGE spacecraft viewing radially outward and has a field of view of 17 deg in the direction parallel to the spacecraft spin axis. Its field of view is 30 deg in the direction perpendicular to the spin axis, although only a 17 deg x 17 deg image of the Earth is recorded. The optics was an all-reflective, inverted Cassegrain Burch camera using concentric optics with a small convex primary and a large concave secondary mirror. The mirrors were coated by a special multi-layer coating, which has low reflectivity in the visible and near UV region, The detector consists of a MCP-Intensified CCD. The MCP is curved to accommodate the focal surface of the concentric optics. Tile phosphor of the image intensifier is deposited on a concave fiberoptic window, which is then Coupled to the CCD with a fiberoptic taper. The camera head operates in a fast frame transfer mode with the CCD being read approximately 30 full frames (512 by 256 pixel) per second with an exposure time of 0.033 s. The image motion (file to the satellite spin is minimal during such a short exposure. Each image is electronically distortion corrected using the look up table scheme. An offset is added to each memory address that is proportional to the image shift due to satellite rotation, and the charge signal is digitally summed in memory. On orbit, approximately 300 frames will be added to produce one WIC image in memory. The advantage of the electronic motion compensation and distortion correction is that it is extremely flexible, permitting several kinds of corrections including motions parallel and perpendicular to the predicted axis of rotation. File instrument was calibrated by applying ultraviolet light through a vacuum monochromator and measuring the absolute responsivity of the instrument. To obtain the data for the distortion look up table the camera was turned through various angles and the input angles corresponding to a pixel matrix were recorded. It was found that the spectral response peaked at 150 nm and fell off in either direction. The equivalent aperture of the camera, including mirror reflectivities and effective photocathode quantum efficiency, is about 0.04 sq cm. Thus, a 100 Rayleigh LBH aurora is expected to produce 23 equivalent counts per pixel per 10 s exposure at the peak of instrument response.

Mende, S. B.↗

NASA NTRS2001

Buffer Gas Acquisition and Storage

The acquisition and storage of buffer gases (primarily argon and nitrogen) from the Mars atmosphere provides a valuable resource for blanketing and pressurizing fuel tanks and as a buffer gas for breathing air for manned missions. During the acquisition of carbon dioxide (CO2), whether by sorption bed or cryo-freezer, the accompanying buffer gases build up in the carbon dioxide acquisition system, reduce the flow of CO2 to the bed, and lower system efficiency. It is this build up of buffer gases that provide a convenient source, which must be removed, for efficient capture Of CO2 Removal of this buffer gas barrier greatly improves the charging rate of the CO2 acquisition bed and, thereby, maintains the fuel production rates required for a successful mission. Consequently, the acquisition, purification, and storage of these buffer gases are important goals of ISRU plans. Purity of the buffer gases is a concern e.g., if the CO, freezer operates at 140 K, the composition of the inert gas would be approximately 21 percent CO2, 50 percent nitrogen, and 29 percent argon. Although there are several approaches that could be used, this effort focused on a hollow-fiber membrane (HFM) separation method. This study measured the permeation rates of CO2, nitrogen (ND, and argon (Ar) through a multiple-membrane system and the individual membranes from room temperature to 193K and 10 kpa to 300 kPa. Concentrations were measured with a gas chromatograph that used a thermoconductivity (TCD) detector with helium (He) as the carrier gas. The general trend as the temperature was lowered was for the membranes to become more selective, In addition, the relative permeation rates between the three gases changed with temperature. The end result was to provide design parameters that could be used to separate CO2 from N2 and Ar.

Parrish, Clyde F.↗

NASA NTRS2004

As-Fabricated Reinforced Carbon/Carbon Characterized

Reinforced carbon/carbon (RCC) is a critical material for the space shuttle orbiter. It is used on the wing leading edge and the nose cap, where maximum temperatures are reached on reentry. The existing leading-edge system is a single-plate RCC composite construction with a wall thickness of approximately 1/4 in., making it a prime reliant protection scheme for vehicle operation.

Jacobson, Nathan S.↗

NASA NTRS2005

Studying Star and Planet Formation with the Submillimeter Probe of the Evolution of Cosmic Structure

The Submillimeter Probe of the Evolution of Cosmic Structure (SPECS) is a far- infrared/submillimeter (40-640 micrometers) spaceborne interferometry concept, studied through the NASA Vision Missions program. SPECS is envisioned as a 1-km baseline Michelson interferometer with two 4- meter collecting mirrors. To maximize science return, SPECS will have three operational modes: a photometric imaging mode, an intermediate spectral resolution mode (R approximately equal to 1000-3000), and a high spectral resolution mode (R approximately equal to 3 x 10(exp 5)). The first two of these modes will provide information on all sources within a 1 arcminute field-of-view (FOV), while the the third will include sources in a small (approximately equal to 5 arcsec) FOV. With this design, SPECS will have angular resolution comparable to the Hubble Space Telescope (50 mas) and sensitivity more than two orders of magnitude better than Spitzer (5sigma in 10ks of approximately equal to 3 x 10(exp 7) Jy Hz). We present here some of the results of the recently-completed Vision Mission Study for SPECS, and discuss the application of this mission to future studies of star and planet formation.

Rinehart, Stephen A.↗

NASA NTRS2003

Quantum detection of coherent-state signals in the presence of noise

A general method for solving an important class of quantum detection problems will be presented and evaluated. The quantum theory for detecting pure states for communications purposes has been developed over two decades ago, however the mixed state problem representing signal plus noise states has received little attention due to its great complexity. Here we develop a practical model for solving the mixed-state problem using a discrete approximation to the coherent-state representation of signal plus noise density operators.

Quantum communication quantum detection↗

NASA NTRS2006

Lower-cost architectures for large arays of small antennas

Future plans for NASA's Deep Space Network (DSN) call for the construction of arrays of small antennas to compliment and eventually replace the existing network of large single antennas. The motivation for this transformation is the need to support much higher downlink data rates in the future, along with the realization that the most cost-effective way to do this is though a large increase in total collecting area on the ground. As currently designed, the DSN arrays will consist of approximately four hundred 12-m diameter antennas at each of three longitudes, operating at X and Ka bands (8 and 32 GHz).

small antennas↗

NASA NTRS1962

Unitary Wind Tunnel Tests of 30-Degree Conical Ribbon Parachute and a Rotofoil Parachute Towed in the Wake of a Conical Nosed Cylindrical Body

Multiple wind tunnel test trials were conducted on a 30 degree conical ribbon parachute with porosities of 30, 27, and 24 percent. Variables were Mach number, dynamic pressure, towline length, and coefficient of drag. A Rotofoil parachute having a porosity of approximately 24 percent was tested, but failed after about 30 seconds of operation at a Mach number of 1.8 All of the parachutes had a nominal diameter and shroud line length of 10 inches. Drag coefficients were based on the area of a circle having a diameter two-thirds of the nominal parachute diameter.

WIND TUNNEL TESTS↗

NASA NTRS2008

Gusev Crater on Mars: Wet and Dry

The Mars Exploration Rover Spirit has traversed over 7.5 km in 1470 sols of operations at the Gusev Crater landing site. Chemical and mineralogical evidence from approximately 200 in-situ samples indicate various degrees of exposure to liquid water, from wet and saturated to dry and unaltered. (1) Six samples with concentrations of amorphous silica between 60 and 95 wt% were discovered in a small valley less than 50 meters in length. Associated enrichments in titanium oxide, relatively insoluble at low pH, suggest that these silica deposits formed as a result of acidic leaching processes. Liquid water interactions with these surface materials were necessary to remove cations solubilized in the low pH environment or to concentrate silica in solution prior to precipitation. (2) Hydrated ferric sulfates are found in subsurface deposits which have the unmistakable chemical signatures of nearby rocks. The movement of hydrothermal fluids and/or fumarolic vapors through local rocks prior to precipitation of these materials is suggested by these observations. (3) Goethite (alpha-FeOOH), a mineral phase which requires water to form, represents 20% to 35% of the iron in numerous rock samples (Clovis Class) on the West Spur of the Columbia Hills. Alteration of iron under aqueous conditions is clearly indicated by this presence of goethite. (4) Nearly isochemical signatures are found in elemental analyses of over ten distinct samples (Wishstone/Watchtower class rocks), yet the ratio of ferric iron to total iron varies from 0.4 to 0.95. Small quantities of water, insufficient to flush cations from the samples, were likely responsible for this weathering. (5) Bromine, a trace element readily mobilized by water, is found in high concentrations in certain rock interiors and is enhanced in subsurface soils, consistent with transport to localized cold traps by water thin-films. (6) Also relevant to the characterizing the role of liquid water is the discovery of an areally extensive ultramafic sequence of rocks where over 70% of the iron is in unaltered olivine and the ferric to total iron ratio is 0.1. This result indicates that certain materials at the martian surface have been protected from aqueous alteration.

Yen, Albert↗

NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

Allgood, Daniel C.↗

NASA NTRS2009

Dual Cryogenic Capacitive Density Sensor

A dual cryogenic capacitive density sensor has been developed. The device contains capacitive sensors that monitor two-phase cryogenic flow density to within 1% accuracy, which, if temperature were known, could be used to determine the ratio of liquid to gas in the line. Two of these density sensors, located a known distance apart, comprise the sensor, providing some information on the velocity of the flow. This sensor was constructed as a proposed mass flowmeter with high data acquisition rates. Without moving parts, this device is capable of detecting the density change within a two-phase cryogenic flow more than 100 times a second. Detection is enabled by a series of two sets of five parallel plates with stainless steel, cryogenically rated tubing. The parallel plates form the two capacitive sensors, which are measured by electrically isolated digital electronics. These capacitors monitor the dielectric of the flow essentially the density of the flow and can be used to determine (along with temperature) the ratio of cryogenic liquid to gas. Combining this information with the velocity of the flow can, with care, be used to approximate the total two-phase mass flow. The sensor can be operated at moderately high pressures and can be lowered into a cryogenic bath. The electronics have been substantially improved over the older sensors, incorporating a better microprocessor, elaborate ground loop protection and noise limiting circuitry, and reduced temperature sensitivity. At the time of this writing, this design has been bench tested at room temperature, but actual cryogenic tests are pending

Youngquist, Robert↗

NASA NTRS2010

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively.

Allgood, Daniel C.↗

NASA NTRS2010

Modeling of LEO Orbital Debris Populations in Centimeter and Millimeter Size Regimes

The building of the NASA Orbital Debris Engineering Model, whether ORDEM2000 or its recently updated version ORDEM2010, uses as its foundation a number of model debris populations, each truncated at a minimum object-size ranging from 10 micron to 1 m. This paper discusses the development of the ORDEM2010 model debris populations in LEO (low Earth orbit), focusing on centimeter (smaller than 10 cm) and millimeter size regimes. Primary data sets used in the statistical derivation of the cm- and mm-size model populations are from the Haystack radar operated in a staring mode. Unlike cataloged objects of sizes greater than approximately 10 cm, ground-based radars monitor smaller-size debris only in a statistical manner instead of tracking every piece. The mono-static Haystack radar can detect debris as small as approximately 5 mm at moderate LEO altitudes. Estimation of millimeter debris populations (for objects smaller than approximately 6 mm) rests largely on Goldstone radar measurements. The bi-static Goldstone radar can detect 2- to 3-mm objects. The modeling of the cm- and mm-debris populations follows the general approach to developing other ORDEM2010-required model populations for various components and types of debris. It relies on appropriate reference populations to provide necessary prior information on the orbital structures and other important characteristics of the debris objects. NASA's LEO-to-GEO Environment Debris (LEGEND) model is capable of furnishing such reference populations in the desired size range. A Bayesian statistical inference process, commonly adopted in ORDEM2010 model-population derivations, changes a priori distribution into a posteriori distribution and thus refines the reference populations in terms of data. This paper describes key elements and major steps in the statistical derivations of the cm- and mm-size debris populations and presents results. Due to lack of data for near 1-mm sizes, the model populations of 1- to 3.16-mm objects are an empirical extension from larger debris. The extension takes into account the results of micro-debris (from 10 micron to 1 mm) population modeling that is based on shuttle impact data, in the hope of making a smooth transition between micron and millimeter size regimes. This paper also includes a brief discussion on issues and potential future work concerning the analysis and interpretation of Goldstone radar data.

Xu, Y.-L.↗