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NASA NTRS1978

Reynolds number criticality in dynamic tests

To extrapolate from subscale wind tunnel tests to full-scale flight is a well-recognized problem. It becomes especially critical for present day high performance missiles and aircraft which operate at high angles of attack where separated flow effects often dominate the vehicle aerodynamics. The dynamic effects of flow separation can usually not be simulated at subscale Reynolds numbers. This is illustrated by examples of tests with slender vehicles and high performance aircraft. It is shown how analytic means can be developed establishing theoretical relationships between dynamic and static aerodynamic characteristics and how such means make it possible to extrapolate analytically from subscale tests to full-scale flight. The roll of future high Reynolds number facilities in establishing such 'analytic extrapolation' tools is discussed.

Ericsson, L. E.↗

NASA NTRS1979

Structural analysis of cylindrical thrust chambers, volume 1

Life predictions of regeneratively cooled rocket thrust chambers are normally derived from classical material fatigue principles. The failures observed in experimental thrust chambers do not appear to be due entirely to material fatigue. The chamber coolant walls in the failed areas exhibit progressive bulging and thinning during cyclic firings until the wall stress finally exceeds the material rupture stress and failure occurs. A preliminary analysis of an oxygen free high conductivity (OFHC) copper cylindrical thrust chamber demonstrated that the inclusion of cumulative cyclic plastic effects enables the observed coolant wall thinout to be predicted. The thinout curve constructed from the referent analysis of 10 firing cycles was extrapolated from the tenth cycle to the 200th cycle. The preliminary OFHC copper chamber 10-cycle analysis was extended so that the extrapolated thinout curve could be established by performing cyclic analysis of deformed configurations at 100 and 200 cycles. Thus the original range of extrapolation was reduced and the thinout curve was adjusted by using calculated thinout rates at 100 and 100 cycles. An analysis of the same underformed chamber model constructed of half-hard Amzirc to study the effect of material properties on the thinout curve is included.

Armstrong, W. H.↗

NASA NTRS1988

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

Sidi, Avram↗

NASA NTRS1988

Ozone profile measurements at McMurdo Station Antarctica during the spring of 1987

During the Antarctic spring of 1986, 33 ozone soundings were conducted from McMurdo Station. These data indicated that the springtime decrease in ozone occurred rapidly between the altitudes of 12 and 20 km. During 1987, these measurements were repeated with 50 soundings between 29 August and 9 November. Digital conversions of standard electrochemical cell ozonesondes were again employed. The ozonesonde pumps were individually calibrated for flow rate as the high altitude performance of these pumps have been in question. While these uncertainties are not large in the region of the ozone hole, they are significant at high altitude and apparently resulted in an underestimate of total ozone of about 7 percent (average) as compared to the Total Ozone Mapping Spectrometer (TOMS) in 1986, when the flow rate recommended by the manufacturer was used. At the upper altitudes (approx. 30 km) the flow rate may be overestimated by as much as 15 percent using recommended values (see Harder et al., The UW Digital Ozonesonde: Characteristics and Flow Rate Calibration, poster paper, this workshop). These upper level values are used in the extrapolation, at constant mixing ratio, required to complete the sounding for total ozone. The first sounding was on 29 August, prior to major ozone depletion, when 274 DU total ozone (25 DU extrapolated) was observed. By early October total ozone had decreased to the 150 DU range; it then increased during mid-October owing to motion of the vortex and returned to a value of 148 DU (29 DU extrapolated) on 27 October.

Hofmann, D. J.↗

NASA NTRS1990

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Sidi, Avram↗

NASA NTRS1990

A comparison of surface sensible and latent heat fluxes from aircraft and surface measurements in FIFE 1987

Surface fluxes of sensible and latent heat over a tall-grass prairie in central Kansas, as measured by 22 surface stations during FIFE 1987, are compared with values gained indirectly by linear extrapolation of aircraft-measured flux profiles to the surface. The results of 33 such comparisons covering the period 26 June to 13 October 1987 indicate that the sensible heat flux profiles were generally more linear with less scatter in the measurements at each level than were the latent heat flux profiles, the profile extrapolations of sensible heat flux in general underestimate the surface averages by about 30 percent, with slightly better agreement during periods of small flux, and the profile extrapolations of latent heat flux in general underestimate the surface averages by about 15 percent, with overestimates during periods of small fluxes (dry conditions) and overestimates during periods of large fluxes (moist conditions). Possible origins of the differences between the two sets of measurements are discussed, as directions for further research.

Kelly, Robert D.↗

NASA NTRS1989

Low temperature measurement of the vapor pressures of planetary molecules

Interpretation of planetary observations and proper modeling of planetary atmospheres are critically upon accurate laboratory data for the chemical and physical properties of the constitutes of the atmospheres. It is important that these data are taken over the appropriate range of parameters such as temperature, pressure, and composition. Availability of accurate, laboratory data for vapor pressures and equilibrium constants of condensed species at low temperatures is essential for photochemical and cloud models of the atmospheres of the outer planets. In the absence of such data, modelers have no choice but to assume values based on an educated guess. In those cases where higher temperature data are available, a standard procedure is to extrapolate these points to the lower temperatures using the Clausius-Clapeyron equation. Last summer the vapor pressures of acetylene (C2H2) hydrogen cyanide (HCN), and cyanoacetylene (HC3N) was measured using two different methods. At the higher temperatures 1 torr and 10 torr capacitance manometers were used. To measure very low pressures, a technique was used which is based on the infrared absorption of thin film (TFIR). This summer the vapor pressure of acetylene was measured the TFIR method. The vapor pressure of hydrogen sulfide (H2S) was measured using capacitance manometers. Results for H2O agree with literature data over the common range of temperature. At the lower temperatures the data lie slightly below the values predicted by extrapolation of the Clausius-Clapeyron equation. Thin film infrared (TFIR) data for acetylene lie significantly below the values predicted by extrapolation. It is hoped to bridge the gap between the low end of the CM data and the upper end of the TFIR data in the future using a new spinning rotor gauge.

Kraus, George F.↗

NASA NTRS1992

Siderophile elements and the earth's formation

Two comments on a work by Murthy (1991) concerning the abundances of siderophile elements in the earth's mantle are presented. In the first comment it is asserted that the basis of Murthy's extrapolation is the assumption that the Gibbs free energy change for the partitioning reaction is independent of temperature, and as this is generally not a valid assumption thermodynamically, and as this is contradicted by most experimental data, the issue of mantle siderophile elements remains unresolved. In the second comment it is asserted that the extrapolation method used by Murthy does not appear to be valid thermodynamically, and that an extrapolation based on generally accepted thermodynamic assumptions yields different results. In a reply, Murthy takes issue with the comments.

Jones, J. H.↗

NASA NTRS1992

Solution of the Schroedinger equation for a double minimum potential

We apply Richardson's extrapolation to zero mesh size to calculate the dissociation energies and wavefunctions of a double minimum potential curve for the E,F1Sigma(+)g state of H2. We demonstrate that a double minimum potential presents no difficulties and that this extrapolation method is to be preferred over a quadratic extrapolation or the use of a basis expansion.

Goorvitch, D.↗

NASA NTRS1992

A comparison of surface sensible and latent heat fluxes from aircraft and surface measurements in FIFE 1987

Kelly, Robert D.↗

NASA NTRS1993

Metal-silicate thermochemistry at high temperature - Magma oceans and the 'excess siderophile element' problem of the earth's upper mantle

Low-temperature metal-silicate partition coefficients are extrapolated to magma ocean temperatures. If the low-temperature chemistry data is found to be applicable at high temperatures, an important assumption, then the results indicate that high temperature alone cannot account for the excess siderophile element problem of the upper mantle. For most elements, a rise in temperature will result in a modest increase in siderophile behavior if an iron-wuestite redox buffer is paralleled. However, long-range extrapolation of experimental data is hazardous when the data contains even modest experimental errors. For a given element, extrapolated high-temperature partition coefficients can differ by orders of magnitude, even when data from independent studies is consistent within quoted errors. In order to accurately assess siderophile element behavior in a magma ocean, it will be necessary to obtain direct experimental measurements for at least some of the siderophile elements.

Capobianco, Christopher J.↗

NASA NTRS1993

Collisional and dynamical history of Gaspra

Interpretation of the impact record on Gaspra requires understanding of the effects of collisions on a target body of Gaspra's size and shape, recognition of impact features that may have different morphologies from craters on larger planets, and models of the geological processes that erase and modify impact features. Crater counts on the 140 sq km of Gaspra imaged at highest resolution by the Galileo spacecraft show a steep size-frequency distribution (cumulative power-law index near -3.5) from the smallest resolvable size (150 m diameter) up through the large feature (1.5 km diameter crater) of familiar crater-like morphology. In addition, there appear to be as many as eight roughly circular concavities with diameters greater than 3 km visible on the asteroid. If we restrict our crater counts to features with traditionally recognized crater morphologies, these concavities would not be included. However, if we define craters to include any concave structures that may represent local or regional damage at an impact size, then the larger features on Gaspra are candidates for consideration. Acceptance of the multi-km features as craters has been cautious for several reasons. First, scaling laws (the physically plausible algorithms for extrapolating from experimental data) indicate that Gaspra could not have sustained such large-crater-forming impacts without being disrupted; second, aside from concavity, the larger structures have no other features (e.g. rims) that can be identified with known impact craters; and third, extrapolation of the power-law size distribution for smaller craters predicts no craters larger than 3 km over the entire surface. On the other hand, recent hydrocode modeling of impacts shows that for given impact (albeit into a sphere), the crater size is much larger than given by scaling laws. Gaspra-size bodies can sustain formation of up to 8-km craters without disruption. Besides allowing larger impact craters, this result doubles the lifetime since the last catastrophic fragmentation event up to one billion years. Events that create multi-km craters also globally damage the material structure, such that regolith is produced, whether or not Gaspra 'initially' had a regolith, contrary to other models in which initial regolith is required in order to allow current regolith. Because the globally destructive shock wave precedes basin formation, crater size is closer to the large size extrapolated from gravity-scaling rather than the strength-scaling that had earlier been assumed for such small bodies. This mechanism may also help explain the existence of Stickney on Phobos. Moreover, rejection of the large concavities as craters based on unfamiliar morphology would be premature, because (aside from Stickney) we have no other data on such large impact structures on such a small, irregular body. The eight candidate concavities cover an area greater than that counted for smaller craters, because they are most apparent where small craters cannot be seen: on low resolution images and at the limb on high resolution images. We estimate that there are at least two with diameter greater than 4 km per 140 sq km, which would have to be accounted for in any model that claims these are impact craters.

Greenberg, R.↗

NASA NTRS1994

High speed civil transport: Sonic boom softening and aerodynamic optimization

An improvement in sonic boom extrapolation techniques has been the desire of aerospace designers for years. This is because the linear acoustic theory developed in the 60's is incapable of predicting the nonlinear phenomenon of shock wave propagation. On the other hand, CFD techniques are too computationally expensive to employ on sonic boom problems. Therefore, this research focused on the development of a fast and accurate sonic boom extrapolation method that solves the Euler equations for axisymmetric flow. This new technique has brought the sonic boom extrapolation techniques up to the standards of the 90's. Parallel computing is a fast growing subject in the field of computer science because of its promising speed. A new optimizer (IIOWA) for the parallel computing environment has been developed and tested for aerodynamic drag minimization. This is a promising method for CFD optimization making use of the computational resources of workstations, which unlike supercomputers can spend most of their time idle. Finally, the OAW concept is attractive because of its overall theoretical performance. In order to fully understand the concept, a wind-tunnel model was built and is currently being tested at NASA Ames Research Center. The CFD calculations performed under this cooperative agreement helped to identify the problem of the flow separation, and also aided the design by optimizing the wing deflection for roll trim.

Cheung, Samson↗

NASA NTRS1995

Turbulance boundary conditions for shear flow analysis, using the DTNS flow solver

The effects of different turbulence boundary conditions were examined for two classical flows: a turbulent plane free shear layer and a flat plate turbulent boundary layer with zero pressure gradient. The flow solver used was DTNS, an incompressible Reynolds averaged Navier-Stokes solver with k-epsilon turbulence modeling, developed at the U.S. Navy David Taylor Research Center. Six different combinations of turbulence boundary conditions at the inflow boundary were investigated: In case 1, 'exact' k and epsilon profiles were used; in case 2, the 'exact' k profile was used, and epsilon was extrapolated upstream; in case 3, both k and epsilon were extrapolated; in case 4, the turbulence intensity (I) was 1 percent, and the turbulent viscosity (mu(sub t)) was equal to the laminar viscosity; in case 5, the 'exact' k profile was used and mu(sub t) was equal to the laminar viscosity; in case 6, the I was 1 percent, and epsilon was extrapolated. Comparisons were made with experimental data, direct numerical simulation results, or theoretical predictions as applicable. Results obtained with DTNS showed that turbulence boundary conditions can have significant impacts on the solutions, especially for the free shear layer.

Mizukami, M.↗

NASA NTRS1994

Toward unbiased determination of the redshift evolution of Lyman-alpha forest clouds

The possibility of using D(sub A), the mean depression of a quasar spectrum due to Ly-alpha forest absorption, to study the number density evolution of the Ly-alpha forest clouds is examined in some detail. Current D(sub A) measurements are made against a continuum that is a power-law extrapolation from the continuum longward of Ly-alpha emission. Compared to the line-counting approach, the D(sub A)-method has the advantage that the D(sub A) measurements are not affected by line-blending effects. However, we find using low-redshift quasar spectra obtained with the Hubble Space Telescope (HST), where the true continuum in the Ly-alpha forest can be estimated fairly reliably because of the much lower density of the Ly-alpha forest lines, that the extrapolated continuum often deviates systematically from the true continuum in the forest region. Such systematic continuum errors introduce large errors in the D(sub A) measurements. The current D(sub A) measurements may also be significantly biased by the possible presence of the Gunn-Peterson absorption. We propose a modification to the existing D(sub A)-method, namely, to measure D(sub A) against a locally established continuum in the Ly-alpha forest. Under conditions that the quasar spectrum has good resolution and S/N to allow for a reliable estimate of the local continuum in the Ly-alpha forest, the modified D(sub A) measurements should be largely free of the systematic uncertainties suffered by the existing D(sub A) measurements. We also introduce a formalism based on the work of Zuo (1993) to simplify the application of the D(sub A)-method(s) to real data. We discuss the merits and limitations of the modified D(sub A)-method, and conclude that it is a useful alternative. Our findings that the extrapolated continuum from longward of Ly-alpha emission often deviates systematically from the true continuum in the Ly-alpha forest present a major problem in the study of the Gunn-Peterson absorption.

Lu, Limin↗

NASA NTRS1996

Chlorine Deactivation in the Lower Stratospheric Polar Regions during late Winter: Results from UARS

Recovery from enhanced chlorine conditions in the lower stratospheric polar regions of both hemispheres is investigated using data from the Upper Atmosphere Research Satellite (UARS). Microwave Limb Sounder (MLS) measurements of ClO within the polar vortices are used to infer ClO(sub x) (ClO + 2Cl202) abundances that are then correlated with simultaneous Cryogenic Limb Array Etalon Spectrometer (CLAES) measurements of ClON02 and Halogen Occultation Experiment (HALOE) measurements of HCl obtained starting within 5 days of the end of the MLS and CLAES high-latitude observing periods in each hemisphere. Time series of vortex-averaged mixing ratios are calculated on two potential temperature surfaces (585 K and 465 K) in the lower stratosphere for approximately month-long intervals during late winter: August 17 - September 17, 1992, in the southern hemisphere and February 12 - March 16, 1993, in the northern hemisphere. The observed mixing ratios are adjusted for the effects of vertical transport using diabatic vertical velocities estimated from CLAES tracer data. In the northern hemisphere, the decrease in ClO, is balanced on both surfaces by an increase in ClON02- In the southern hemisphere, continuing polar stratospheric cloud activity prevents ClO from undergoing sustained decline until about September 3. In contrast to the northern hemisphere, there is no significant chemical change in vortex-averaged ClON02 at 465 K, and there is an apparent decrease in ClON02 at 585 K, even after the enhanced ClO abundances have started to recede. Results from the SLIMCAT chemical transport model initialized with UARS data and run with OH + ClO yields HCl + 02 as an 8% channel suggest that the primary recovery product in the south during this time period is not ClON02, but HCl. HALOE HCl mixing ratios are extrapolated back to the time of the MLS and CLAES data. At 585 K, the chlorine budget can be made to balance by extrapolating HCl back to a value of 0.6 parts per billion by volume (ppbv) at the beginning of the study period; at 465 K, the contribution from extrapolated HCl is not sufficient to offset the loss in ClOx, and there is a slight imbalance between the decrease in reactive chlorine and the change in chlorine reservoirs. The difficulty in closing the chlorine budget in the southern hemisphere may arise from complications caused by ongoing activation, incomplete photochemical assumptions, and/or inadequate data quality.

Santee, M. L.↗

NASA NTRS1999

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

Siclari, Michael J.↗

NASA NTRS2001

Searching for the Beginning of the Ozone Turnaround Using a 22-Year Merged Satellite Data Set

We have used the data from six satellite instruments that measure the total column amount of ozone to construct a consistent merged data set extending from late 1978 into 2000. The keys to constructing a merged data set are to minimize potential drift of individual instruments and to accurately establish instrument-to-instrument offsets. We have used the short-wavelength D-pair measurements (306nm-313nm) of the SBUV and SBUV/2 instruments near the equator to establish a relatively drift-free record for these instruments. We have then used their overlap with the Nimbus 7 and EP TOMS instruments to establish the relative calibration of the various instruments. We have evaluated the drift uncertainty in our merged ozone data (MOD) set by examining both the individual instrument drift uncertainty and the uncertainty in establishing the instrument- to-instrument differences. We conclude that the instrumental drift uncertainty over the 22-year data record is 0.9 %/decade (2-sigma). We have compared our MOD record with 37 ground stations that have a continuous record over that time period. We have a mean drift with respect to the stations of +0.3 %/decade which is within 1-sigma of our uncertainty estimate. Using the satellite record as a transfer standard, we can estimate the capability of the ground instruments to establish satellite calibration. Adding the statistical variability of the station drifts with respect to the satellite to an estimate of the overall drift uncertainty of the world standard instrument, we conclude that the stations should be able to be used to establish the drift of the satellite data record to within and uncertainty of 0.6 %/decade (2-sigma). Adding to this an uncertainty due to the-incomplete global coverage of the stations, we conclude that the station data should be able to establish the global trend with an uncertainty of about 0.7 %/decade, slightly better than for the satellite record. We conclude that merging the two records together gives only a slight improvement in the uncertainty. Keeping them separate gives the greater confidence of two independent measures of the ozone trend and potential recovery. We fit the trend in our MOD record through May of 1991 and then extrapolated forward to see if the data at the end of the record was above the statistical model as a measure of ozone recovery as was done in the last WMO/UNEP assessment report. Because our data set drifts with respect to the ground-stations through May of 1991, we calculated a smaller global trend (-1.1 %/decade) than in the WMO/UNEP report. Our data in 1998 and 1999 was, on average 2 DU above the extrapolated statistical model with a 2-sigma uncertainty of 6 DU. For the combined mid-latitudes of the northern and southern hemispheres, the data was 5 DU above the extrapolated statistical model with a 2-sigma uncertainty of 10 DU. These may be signs of recovery, but they are still statistically insignificant.

Stolarski, Richard S.↗