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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Ordinary planetary systems - Architecture and formation

Today we believe ordinary planetary systems to be an unremarkable consequence of star formation. The solar system, so far the only confidently known example in the universe of a planetary system, displays a set of striking structural regularities. These structural regularities provide fossil clues about the conditions and mechanisms that gave rise to the planets. The formation of our planetary system, as well as its general characteristics, resulted from the physical environment in the disk-shaped nebula that accompanied the birth of the sun. Observations of contemporary star formation indicate that the very conditions and mechanisms thought to have produced our own planetary system are widely associated with the birth of stars elsewhere. Consequently, it is reasonable to believe that planetary systems occur commonly, at least in association with single, sunlike stars. Moreover, it is reasonable to believe that many planetary systems have gross characteristics resembling those of our own solar system.

Levy, E. H.↗
NASA NTRS1992

An expert system for diagnosing environmentally induced spacecraft anomalies

A new rule-based, machine independent analytical tool was designed for diagnosing spacecraft anomalies using an expert system. Expert systems provide an effective method for saving knowledge, allow computers to sift through large amounts of data pinpointing significant parts, and most importantly, use heuristics in addition to algorithms, which allow approximate reasoning and inference and the ability to attack problems not rigidly defined. The knowledge base consists of over two-hundred (200) rules and provides links to historical and environmental databases. The environmental causes considered are bulk charging, single event upsets (SEU), surface charging, and total radiation dose. The system's driver translates forward chaining rules into a backward chaining sequence, prompting the user for information pertinent to the causes considered. The use of heuristics frees the user from searching through large amounts of irrelevant information and allows the user to input partial information (varying degrees of confidence in an answer) or 'unknown' to any question. The modularity of the expert system allows for easy updates and modifications. It not only provides scientists with needed risk analysis and confidence not found in algorithmic programs, but is also an effective learning tool, and the window implementation makes it very easy to use. The system currently runs on a Micro VAX II at Goddard Space Flight Center (GSFC). The inference engine used is NASA's C Language Integrated Production System (CLIPS).

Rolincik, Mark↗
NASA NTRS1991

Development of a calibrated software reliability model for flight and supporting ground software for avionic systems

The object of this project was to develop and calibrate quantitative models for predicting the quality of software. Reliable flight and supporting ground software is a highly important factor in the successful operation of the space shuttle program. The models used in the present study consisted of SMERFS (Statistical Modeling and Estimation of Reliability Functions for Software). There are ten models in SMERFS. For a first run, the results obtained in modeling the cumulative number of failures versus execution time showed fairly good results for our data. Plots of cumulative software failures versus calendar weeks were made and the model results were compared with the historical data on the same graph. If the model agrees with actual historical behavior for a set of data then there is confidence in future predictions for this data. Considering the quality of the data, the models have given some significant results, even at this early stage. With better care in data collection, data analysis, recording of the fixing of failures and CPU execution times, the models should prove extremely helpful in making predictions regarding the future pattern of failures, including an estimate of the number of errors remaining in the software and the additional testing time required for the software quality to reach acceptable levels. It appears that there is no one 'best' model for all cases. It is for this reason that the aim of this project was to test several models. One of the recommendations resulting from this study is that great care must be taken in the collection of data. When using a model, the data should satisfy the model assumptions.

Lawrence, Stella↗
NASA NTRS1995

Active galaxies observed during the Extreme Ultraviolet Explorer all-sky survey

We present observations of active galactic nuclei (AGNs) obtained with the Extreme Ultraviolet Explorer (EUVE) during the all-sky survey. A total of 13 sources were detected at a significance of 2.5 sigma or better: seven Seyfert galaxies, five BL Lac objects, and one quasar. The fraction of BL Lac objects is higher in our sample than in hard X-ray surveys but is consistent with the soft X-ray Einstein Slew Survey, indicating that the main reason for the large number of BL Lac objects in the extreme ulktraviolet (EUV) and soft X-ray bands is their steeper X-ray spectra. We show that the number of AGNs observed in both the EUVE and ROSAT Wide Field Camera surveys can readily be explained by modelling the EUV spectra with a simple power law in the case of BL Lac objects and with an additional EUV excess in the case of Seyferts and quasars. Allowing for cold matter absorption in Seyfert galaxy hosts drive up the inferred average continuum slope to 2.0 +/- 0.5 (at 90% confidence), compared to a slope of 1.0 usually found from soft X-ray data. If Seyfert galaxies without EUV excesses form a significant fraction of the population, then the average spectrum of those with bumps should be even steeper. We place a conservative limit on neutral gas in BL Lac objects: N(sub H) less than 10(exp 20)/sq cm.

Marshall, H. L.↗
NASA NTRS2011

Non-Nuclear Testing of Compact Reactor Technologies at NASA MSFC

Safe, reliable, compact, autonomous, long-life fission systems have numerous potential applications, both terrestrially and in space. Technologies and facilities developed in support of these systems could be useful to a variety of concepts. At moderate power levels, fission systems can be designed to operate for decades without the need for refueling. In addition, fast neutron damage to cladding and structural materials can be maintained at an acceptable level. Nuclear design codes have advanced to the stage where high confidence in the behavior and performance of a system can be achieved prior to initial testing. To help ensure reactor affordability, an optimal strategy must be devised for development and qualification. That strategy typically involves a combination of non-nuclear and nuclear testing. Non-nuclear testing is particularly useful for concepts in which nuclear operating characteristics are well understood and nuclear effects such as burnup and radiation damage are not likely to be significant. To be mass efficient, a SFPS must operate at higher coolant temperatures and use different types of power conversion than typical terrestrial reactors. The primary reason is the difficulty in rejecting excess heat to space. Although many options exist, NASA s current reference SFPS uses a fast spectrum, pumped-NaK cooled reactor coupled to a Stirling power conversion subsystem. The reference system uses technology with significant terrestrial heritage while still providing excellent performance. In addition, technologies from the SFPS system could be applicable to compact terrestrial systems. Recent non-nuclear testing at NASA s Early Flight Fission Test Facility (EFF-TF) has helped assess the viability of the reference SFPS and evaluate methods for system integration. In July, 2011 an Annular Linear Induction Pump (ALIP) provided by Idaho National Laboratory was tested at the EFF-TF to assess performance and verify suitability for use in a10 kWe technology demonstration unit (TDU). In November, 2011 testing of a 37-pin core simulator (designed in conjunction with Los Alamos National Laboratory) for use with the TDU will occur. Previous testing at the EFFTF has included the thermal and mechanical coupling of a pumped NaK loop to Stirling engines (provided by GRC). Testing related to heat pipe cooled systems, gas cooled systems, heat exchangers, and other technologies has also been performed. Integrated TDU testing will begin at GRC in 2013. Thermal simulators developed at the EFF-TF are capable of operating over the temperature and power range typically of interest to compact reactors. Small and large diameter simulators have been developed, and simulators (coupled with the facility) are able to closely match the axial and radial power profile of all potential systems of interest. A photograph of the TDU core simulator during assembly is provided in Figure 2.

Houts, Michael G.↗
NASA NTRS1998

Re-Observing the First Hours of Supernova 1987A

This project was designed to use archival data from the International Ultraviolet Explorer (IUE) to measure the flux from the shock breakout from SN 1987A, emitted in the first few hours of the event, reflected from neighboring dust clouds in the form of a light echo. Such hot flux from the initial moments of a SN had never been observed before, and this offers a unique opportunity to measure it in reflection. Gilmozzi (1991, in "SN 1987A and Other Supernova") had reported such a detection of using IUE from observations made in 1988 and 1989. Our analysis of these data showed that this detection was very weak, and subject to changes comparable to the size of the signal according to various reasonable means of extracting the spectra. In fact, the features reported by Gilmozzi (1998 in "Ultraviolet Astrophysics Beyond IUE") are not found in a conventional NEWSIPS extraction or extended-source extraction of these data. The 1995 and 1996 IUE data collected for Crotts and Gilmozzi shows a more robust signal (about 20sigma,) from a cloud that echoes brighter in the optical than the 1988 feature. This shows a well-detected signal of about 5 x 10(exp -16) ergs per s/sq cm/Angstroms/arc sq sec at 1300 Angstroms, with a declining slope to redder wavelengths. This surface brightness, while detected with confidence in both large and small SVVT apertures, is still fainter than the reflected flux expected for most models of shock breakout. We have also taken the opportunity to recover the echo signal from exposures taken on Astro-1 and Astro-2 flights of the Ultraviolet Imaging Telescope (UIT) while pointed towards SN 1987A. These data yield a complementary result on the reflected flux, an upper limit of about 5 x 10(exp -17) ergs per s/sq cm/Angstroms/arc sq sec, spread over fainter optically echoing clouds, and over the same band where the signal was detected by IUE. While this appears in contradiction with the IUE result, it is made consistent by the corresponding strengths of the echoes in the optical.

Crotts, Arlin P. S.↗
NASA NTRS1996

Studies of Two-Phase Flow Dynamics and Heat Transfer at Reduced Gravity Conditions

The ability to predict gas-liquid flow patterns is crucial to the design and operation of two-phase flow systems in the microgravity environment. Flow pattern maps have been developed in this study which show the occurrence of flow patterns as a function of gas and liquid superficial velocities as well as tube diameter, liquid viscosity and surface tension. The results have demonstrated that the location of the bubble-slug transition is affected by the tube diameter for air-water systems and by surface tension, suggesting that turbulence-induced bubble fluctuations and coalescence mechanisms play a role in this transition. The location of the slug-annular transition on the flow pattern maps is largely unaffected by tube diameter, liquid viscosity or surface tension in the ranges tested. Void fraction-based transition criteria were developed which separate the flow patterns on the flow pattern maps with reasonable accuracy. Weber number transition criteria also show promise but further work is needed to improve these models. For annular gas-liquid flows of air-water and air- 50 percent glycerine under reduced gravity conditions, the pressure gradient agrees fairly well with a version of the Lockhart-Martinelli correlation but the measured film thickness deviates from published correlations at lower Reynolds numbers. Nusselt numbers, based on a film thickness obtained from standard normal-gravity correlations, follow the relation, Nu = A Re(sup n) Pr(exp l/3), but more experimental data in a reduced gravity environment are needed to increase the confidence in the estimated constants, A and n. In the slug flow regime, experimental pressure gradient does not correlate well with either the Lockhart-Martinelli or a homogeneous formulation, but does correlate nicely with a formulation based on a two-phase Reynolds number. Comparison with ground-based correlations implies that the heat transfer coefficients are lower at reduced gravity than at normal gravity under the same flow conditions. Nusselt numbers can be correlated in a fashion similar to Chu and Jones.

Witte, Larry C.↗
NASA NTRS2006

Sensor Data Qualification for Autonomous Operation of Space Systems

NASA's new Exploration initiative for both robotic and manned missions will require higher levels of reliability, autonomy and reconfiguration capability to make the missions safe, successful and affordable. Future systems will require diagnostic reasoning to assess the health of the system in order to maintain the system s functionality. The diagnostic reasoning and assessment will involve data qualification, fault detection, fault isolation and remediation control. A team of researchers at the NASA Glenn Research Center is currently working on a Sensor Data Qualification (SDQ) system that will support these critical evaluation processes, for both automated and human-in-the-loop applications. Data qualification is required as a first step so that critical safety and operational decisions are based on good data. The SDQ system would monitor a network of related sensors to determine the health of individual sensors within that network. Various diagnostic systems such as the Caution and Warning System would then use the sensor health information with confidence. The proposed SDQ technology will be demonstrated on a variety of subsystems that are relevant to NASA s Exploration systems, which currently include an electrical power system and a cryogenic fluid management system. The focus of this paper is the development and demonstration of a SDQ application for a prototype power distribution unit that is representative of a Crew Exploration Vehicle electrical power system; this provides a unique and relevant environment in which to demonstrate the feasibility of the SDQ technology.

Maul, William A.↗
NASA NTRS2018

Quantification of Dynamic Model Validation Metrics Using Uncertainty Propagation from Requirements

The Space Launch System, NASA's new large launch vehicle for long range space exploration, is presently in the final design and construction phases, with the first launch scheduled for 2019. A dynamic model of the system has been created and is critical for calculation of interface loads and natural frequencies and mode shapes for guidance, navigation, and control (GNC). Because of the program and schedule constraints, a single modal test of the SLS will be performed while bolted down to the Mobile Launch Pad just before the first launch. A Monte Carlo and optimization scheme will be performed to create thousands of possible models based on given dispersions in model properties and to determine which model best fits the natural frequencies and mode shapes from modal test. However, the question still remains as to whether this model is acceptable for the loads and GNC requirements. An uncertainty propagation and quantification (UP and UQ) technique to develop a quantitative set of validation metrics that is based on the flight requirements has therefore been developed and is discussed in this paper. There has been considerable research on UQ and UP and validation in the literature, but very little on propagating the uncertainties from requirements, so most validation metrics are "rules-of-thumb;" this research seeks to come up with more reason-based metrics. One of the main assumptions used to achieve this task is that the uncertainty in the modeling of the fixed boundary condition is accurate, so therefore that same uncertainty can be used in propagating the fixed-test configuration to the free-free actual configuration. The second main technique applied here is the usage of the limit-state formulation to quantify the final probabilistic parameters and to compare them with the requirements. These techniques are explored with a simple lumped spring-mass system and a simplified SLS model. When completed, it is anticipated that this requirements-based validation metric will provide a quantified confidence and probability of success for the final SLS dynamics model, which will be critical for a successful launch program, and can be applied in the many other industries where an accurate dynamic model is required.

Brown, Andrew M.↗
NASA NTRS2009

Using Satellite Data to Evaluate Linkages Between Land Cover/Land Use and Hypertension in a National Cohort

Coincident with global expansion of urban areas has been an increase in hypertension. It is unclear how much the urban environment contributes as a risk factor for blood pressure differences, and how much is due to a variety of environmental, lifestyle, and demographic correlates of urbanization. Objectives/Purpose: The purpose of this study is to examine the relationship between living environment (defined as urban, suburban, or rural) and hypertension in selected regions from the REasons for Geographic And Racial Differences in Stroke (REGARDS) cohort. Methods: REGARDS is a national cohort of 30,228 participants from the 48 contiguous United States. We used data from 4 metropolitan regions (Philadelphia, Atlanta, Minneapolis and Chicago) for this study (n=3928). We used Land Cover/Land Use (LCLU) information from the 30-meter National Land Cover Data. Results: Overall, 1996 (61%) of the participants were hypertensive. We characterized participants into urban, suburban or rural living environments using the LCLU data. In univariate models, we found that living environment is associated with hypertension, but that after adjustment for known hypertension risk factors, the relationship was no longer present at the 95% confidence level. Conclusions: LCLU data can be utilized to characterize the living environment, which in turn can be applied to studies of public health outcomes. Further study regarding the relationship between hypertension and living environment should focus on additional characteristics of the associated environment.

McClure, Leslie↗
NASA NTRS2011

Ares I-X First Stage Internal Aft Skirt Re-Entry Heating Data and Modeling

The CLVSTATE engineering code is being used to predict Ares-I launch vehicle first stage reentry aerodynamic heating. An engineering analysis is developed which yields reasonable predictions for the timing of the first stage aft skirt thermal curtain failure and the resulting internal gas temperatures. The analysis is based on correlations of the Ares I-X internal aft skirt gas temperatures and has been implemented into CLVSTATE. Validation of the thermal curtain opening models has been accomplished using additional Ares I-X thermocouple, calorimeter and pressure flight data. In addition, a technique which accounts for radiation losses at high altitudes has been developed which improves the gas temperature measurements obtained by the gas temperature probes (GTP). Updates to the CLVSTATE models are shown to improve the accuracy of the internal aft skirt heating predictions which will result in increased confidence in future vehicle designs

Schmitz, Craig P.↗
NASA NTRS2000

Airborne Measurements of Nitric Oxide, Nitrogen Dioxide, Ozone, and Total Reactive Nitrogen During the NASA Global Tropospheric Experiment

Fabrication of the University of Michigan Multichannel Chemiluminescence Instrument (UMMCI) was completed in early 1996 and the instrument participated in test flights on the NASA P3B at Wallops Island prior to integration and deployment for the PEM- Tropics A Mission. The UMMCI consists of 4 channels for simultaneous measurements of ozone and NO with the option for measurements of NO2 and NOy (total reactive nitrogen) when converters are placed upstream of the NO channels. Each NO channel consists of a zeroing volume and reaction vessel, while the ozone channel consists of an ozone catalyst (or scrubber) trap that is not in line with the reaction vessel. The detectors in all for channels are Hamamatsu photomultiplier tubes, which are followed by pulse amplifier discriminators on the NO channels and an electrometer on the ozone channel. Schematics of the Detector Module and NOx/03 Probe Insert and Diagrams of the Control and Data System, the Power and Ground System, the Gas Flow System, and the Calibration System Flow are attached. Intercomparisons were conducted with G. Gregory, NASA/Langley, during the test flights (following prior calibration of the ozone generator/calibrators at the Wallops Long-Path Absorption facility). Initial test results appeared to be reasonable, and instrument characterization studies proceeded for the ozone channel and the 3 NO channels until deployment for integration for the PEM-Tropics Mission. Ozone data was obtained for Flights #4, and 6-2 1, and finalized data was submitted to the PEM-Tropics Data Archive and to the Science Team during the April 1997 Data Workshop. Although it initially appeared that the instrument sensitivity varied, subsequent tests showed that this was the fault of a leak in the ozone calibrator. In fact; the instrument sensitivity has not been observed to vary in a large number of tests over the years since the PEM-Tropics mission. We have, therefore, a very high degree of confidence in the O3 data that we submitted. NO data was obtained for all flights except the mission out of Christmas Island and the subsequent return to Hawaii, during which time the NO channels were contaminated with back-flushing pure NO from the O3 channel. The NO channels were found to suffer from a varying artifact (7 - 22 pptv) which made the instrument's results unreliable for the marine boundary layer portions of the missions (where conditions were extremely clean with NO typically < 2 pptv and O3 only 8 ppbv). Nonetheless, the NO values were an upper limit and were quite useful in identifying pollution layers and outflow from the Latin American Continent. NO data was submitted to the archive for all flights during which data was obtained. Ozone data from the P3B was among the results presented in several peer-reviewed publications. Notably, the ozone data supported the first published finding of evidence for the occurrence of aerosol nucleation in the marine boundary layer. As well, the ozone data was utilized in a treatment of the wavenumber spectra of winds, temperature and trace gases and to demonstrate the occurrence of layering as observed by the P3B during PEM-Tropics A . O3 and NO data were used in an assessment of the impact of southern hemispheric biomass burning, and in the role of NOx and O3 in HOx photochemistry during the PEM Tropics A mission. These data, along with other species measured during PEM-Tropics A, have also been employed in the generation of climatologies for tropospheric ozone and its precursors by the PI's research group.

Carroll, Mary Anne↗
NASA NTRS2003

PEM-INST-001: Instructions for Plastic Encapsulated Microcircuit (PEM) Selection, Screening, and Qualification

Potential users of plastic encapsulated microcircuits (PEMs) need to be reminded that unlike the military system of producing robust high-reliability microcircuits that are designed to perform acceptably in a variety of harsh environments, PEMs are primarily designed for use in benign environments where equipment is easily accessed for repair or replacement. The methods of analysis applied to military products to demonstrate high reliability cannot always be applied to PEMs. This makes it difficult for users to characterize PEMs for two reasons: 1. Due to the major differences in design and construction, the standard test practices used to ensure that military devices are robust and have high reliability often cannot be applied to PEMs that have a smaller operating temperature range and are typically more frail and susceptible to moisture absorption. In contrast, high-reliability military microcircuits usually utilize large, robust, high-temperature packages that are hermetically sealed. 2. Unlike the military high-reliability system, users of PEMs have little visibility into commercial manufacturers proprietary design, materials, die traceability, and production processes and procedures. There is no central authority that monitors PEM commercial product for quality, and there are no controls in place that can be imposed across all commercial manufacturers to provide confidence to high-reliability users that a common acceptable level of quality exists for all PEMs manufacturers. Consequently, there is no guaranteed control over the type of reliability that is built into commercial product, and there is no guarantee that different lots from the same manufacturer are equally acceptable. And regarding application, there is no guarantee that commercial products intended for use in benign environments will provide acceptable performance and reliability in harsh space environments. The qualification and screening processes contained in this document are intended to detect poor-quality lots and screen out early random failures from use in space flight hardware. However, since it cannot be guaranteed that quality was designed and built into PEMs that are appropriate for space applications, users cannot screen in quality that may not exist. It must be understood that due to the variety of materials, processes, and technologies used to design and produce PEMs, this test process may not accelerate and detect all failure mechanisms. While the tests herein will increase user confidence that PEMs with otherwise unknown reliability can be used in space environments, such testing may not guarantee the same level of reliability offered by military microcircuits. PEMs should only be used where due to performance needs there are no alternatives in the military high-reliability market, and projects are willing to accept higher risk.

Teverovsky, Alexander↗
NASA NTRS2012

An Initial Examination for Verifying Separation Algorithms by Simulation

An open question in algorithms for aircraft is what can be validated by simulation where the simulation shows that the probability of undesirable events is below some given level at some confidence level. The problem is including enough realism to be convincing while retaining enough efficiency to run the large number of trials needed for high confidence. The paper first proposes a goal based on the number of flights per year in several regions. The paper examines the probabilistic interpretation of this goal and computes the number of trials needed to establish it at an equivalent confidence level. Since any simulation is likely to consider the algorithms for only one type of event and there are several types of events, the paper examines under what conditions this separate consideration is valid. This paper is an initial effort, and as such, it considers separation maneuvers, which are elementary but include numerous aspects of aircraft behavior. The scenario includes decisions under uncertainty since the position of each aircraft is only known to the other by broadcasting where GPS believes each aircraft to be (ADS-B). Each aircraft operates under feedback control with perturbations. It is shown that a scenario three or four orders of magnitude more complex is feasible. The question of what can be validated by simulation remains open, but there is reason to be optimistic.

White, Allan L.↗
NASA NTRS2017

Verification Testing: Meet User Needs Figure of Merit

Verification is the process through which Modeling and Simulation(M&S) software goes to ensure that it has been rigorously tested and debugged for its intended use. Validation confirms that said software accurately models and represents the real world system. Credibility gives an assessment of the development and testing effort that the software has gone through as well as how accurate and reliable test results are. Together, these three components form Verification, Validation, and Credibility(VV&C), the process by which all NASA modeling software is to be tested to ensure that it is ready for implementation. NASA created this process following the CAIB (Columbia Accident Investigation Board) report seeking to understand the reasons the Columbia space shuttle failed during reentry. The reports conclusion was that the accident was fully avoidable, however, among other issues, the necessary data to make an informed decision was not there and the result was complete loss of the shuttle and crew. In an effort to mitigate this problem, NASA put out their Standard for Models and Simulations, currently in version NASA-STD-7009A, in which they detailed their recommendations, requirements and rationale for the different components of VV&C. They did this with the intention that it would allow for people receiving MS software to clearly understand and have data from the past development effort. This in turn would allow the people who had not worked with the MS software before to move forward with greater confidence and efficiency in their work. This particular project looks to perform Verification on several MATLAB (Registered Trademark)(The MathWorks, Inc.) scripts that will be later implemented in a website interface. It seeks to take note and define the limits of operation, the units and significance, and the expected datatype and format of the inputs and outputs of each of the scripts. This is intended to prevent the code from attempting to make incorrect or impossible calculations. Additionally, this project will look at the coding generally and note inconsistencies, redundancies, and other aspects that may become problematic or slow down the codes run time. Certain scripts lacking in documentation also will be commented and cataloged.

validation↗
NASA NTRSDate not supplied

Computational Fluid Dynamics Models of the NASA White Sands Test Facility Particle Impact Test Nozzles

The particle impact ignition mechanism is considered to be the most effective means for igniting metals in gaseous oxygen environments and is a concern for every oxygen system. For this reason, the National Aeronautics and Space Administration (NASA) commits a large amount of resources attempting to understand and defend against this phenomenon. The most practical means of accomplishing this is through extensive of testing. To this end, over the years NASA has developed and built a facility and various apparatuses to test material or component vulnerability to a particle impact ignition. In testing materials, NASA uses sub-sonic and supersonic nozzles to replicate the conditions that a material is expected to experience in service. However, challenges include obtaining an understanding of the gas dynamics and of the particle behavior through and up to the point of impact at the material under test. One means of addressing these challenges is the use of computational fluid dynamics (CFD). If a CFD model can be built and validated, the model can then be used to confidently interrogate changes to inlet conditions and particle geometries, as well as changes to nozzle geometries to better simulate a material’s in-situ conditions and greatly reduce or eliminate trial-and-error approaches in testing. This paper will show NASA’s approach to and results of using CFD to better understand their particle impact nozzles.

Computational Fluid Dynamics↗
NASA NTRS1993

Improving the chi-squared approximation for bivariate normal tolerance regions

Let X be a two-dimensional random variable distributed according to N2(mu,Sigma) and let bar-X and S be the respective sample mean and covariance matrix calculated from N observations of X. Given a containment probability beta and a level of confidence gamma, we seek a number c, depending only on N, beta, and gamma such that the ellipsoid R = (x: (x - bar-X)'S(exp -1) (x - bar-X) less than or = c) is a tolerance region of content beta and level gamma; i.e., R has probability gamma of containing at least 100 beta percent of the distribution of X. Various approximations for c exist in the literature, but one of the simplest to compute -- a multiple of the ratio of certain chi-squared percentage points -- is badly biased for small N. For the bivariate normal case, most of the bias can be removed by simple adjustment using a factor A which depends on beta and gamma. This paper provides values of A for various beta and gamma so that the simple approximation for c can be made viable for any reasonable sample size. The methodology provides an illustrative example of how a combination of Monte-Carlo simulation and simple regression modelling can be used to improve an existing approximation.

Feiveson, Alan H.↗
NASA NTRS1990

The application of CFD to rotary wing flow problems

Rotorcraft aerodynamics is especially rich in unsolved problems, and for this reason the need for independent computational and experimental studies is great. Three-dimensional unsteady, nonlinear potential methods are becoming fast enough to enable their use in parametric design studies. At present, combined CAMRAD/FPR analyses for a complete trimmed rotor soltution can be performed in about an hour on a CRAY Y-MP (or ten minutes, with multiple processors). These computational speeds indicate that in the near future many of the large CFD problems will no longer require a supercomputer. The ability to convect circulation is routine for integral methods, but only recently was it discovered how to do the same with differential methods. It is clear that the differential CFD rotor analyses are poised to enter the engineering workplace. Integral methods already constitute a mainstay. Ultimately, it is the users who will integrate CFD into the entire engineering process and provide a new measure of confidence in design and analysis. It should be recognized that the above classes of analyses do not include several major limiting phenomena which will continue to require empirical treatment because of computational time constraints and limited physical understanding. Such empirical treatment should be included, however, into the developing CFD, engineering level analyses. It is likely that properly constructed flow models containing corrections from physical testing will be able to fill in unavoidable gaps in the experimental data base, both for basic studies and for specific configuration testing. For these kinds of applications, computational cost is not an issue. Finally, it should be recognized that although rotorcraft are probably the most complex of aircraft, the rotorcraft engineering community is very small compared to the fixed-wing community. Likewise, rotorcraft CFD resources can never achieve fixed-wing proportions and must be used wisely. Therefore the fixed-wing work must be gleaned for many of the basic methods.

Caradonna, F. X.↗