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NASA NTRS2000

A Method for Calculating Transient Surface Temperatures and Surface Heating Rates for High-Speed Aircraft

This report describes a method that can calculate transient aerodynamic heating and transient surface temperatures at supersonic and hypersonic speeds. This method can rapidly calculate temperature and heating rate time-histories for complete flight trajectories. Semi-empirical theories are used to calculate laminar and turbulent heat transfer coefficients and a procedure for estimating boundary-layer transition is included. Results from this method are compared with flight data from the X-15 research vehicle, YF-12 airplane, and the Space Shuttle Orbiter. These comparisons show that the calculated values are in good agreement with the measured flight data.

Quinn, Robert D.↗

NASA NTRS2001

Calculation of the Scattering Amplitude Without Partial Wave Expansion

Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.

Shertzer, J.↗

NASA NTRS2001

Calculating Free Energies Using Average Force

A new, general formula that connects the derivatives of the free energy along the selected, generalized coordinates of the system with the instantaneous force acting on these coordinates is derived. The instantaneous force is defined as the force acting on the coordinate of interest so that when it is subtracted from the equations of motion the acceleration along this coordinate is zero. The formula applies to simulations in which the selected coordinates are either unconstrained or constrained to fixed values. It is shown that in the latter case the formula reduces to the expression previously derived by den Otter and Briels. If simulations are carried out without constraining the coordinates of interest, the formula leads to a new method for calculating the free energy changes along these coordinates. This method is tested in two examples - rotation around the C-C bond of 1,2-dichloroethane immersed in water and transfer of fluoromethane across the water-hexane interface. The calculated free energies are compared with those obtained by two commonly used methods. One of them relies on determining the probability density function of finding the system at different values of the selected coordinate and the other requires calculating the average force at discrete locations along this coordinate in a series of constrained simulations. The free energies calculated by these three methods are in excellent agreement. The relative advantages of each method are discussed.

Darve, Eric↗

NASA NTRS1994

Stress Calculations on Diamond Surfaces

Calculations were carried out to evaluate stresses for atoms located in the top several layers of (100)-(1x1), (100)-(2x1) and (111)-(1x1) surfaces of diamond. Only equilibrated surfaces were taken into consideration in this investigation. Stress values in the direction perpendicular to the exposed surface vanish. In lateral directions, however, stresses have non-vanishing values, in general. For the (100) surfaces calculated stress values are anisotropic. While the (2 x 1) reconstructed surface is under compression in both directions, calculations for the unreconstructed (1 x 1) plane, produced a compressive stress in one direction and a slight tension in the other. On the (111) surface, isotropic and relatively low compressive stress values were found. Present calculations indicate that atoms located only in a few top layers have lateral excess stresses which vanish very quickly for the atoms of interior layers as departing from the exposed surface.

Halicioglu, Timur↗

NASA NTRS1995

On the Calculation of Anisotropic Extinction Coefficients for Rigid Fibrous Ceramic Insulations

The specific anisotropic extinction coefficient e* couples the effective Radiative properties of a fibrous insulation into the radiation diffusion equation. This coefficient can be calculated using Mie scattering theory if fiber diameters, refractive indices and fiber orientation distributions are known. In general, fiber orientation distributions are not readily accessible and past calculations have considered fibers as either randomly distributed or normal to the heat flow direction. In certain rigid fibrous ceramic insulations neither of these cases apply well and a simple procedure is described for approximating e* from values calculated for the random and normal orientation cases. The intrinsic error associated with this scaling procedure is investigated. Numerical computations for several test structures and fiber materials show the average error to be less than 5% for net heat flux and radiation conductivity calculations.

Marshall, Jochen↗

NASA NTRS2001

Ab Initio and Improved Empirical Potentials for the Calculation of the Anharmonic Vibrational States and Intramolecular Mode Coupling of N-Methylacetamide

The second-order Moller-Plesset ab initio electronic structure method is used to compute points for the anharmonic mode-coupled potential energy surface of N-methylacetamide (NMA) in the trans(sub ct) configuration, including all degrees of freedom. The vibrational states and the spectroscopy are directly computed from this potential surface using the Correlation Corrected Vibrational Self-Consistent Field (CC-VSCF) method. The results are compared with CC-VSCF calculations using both the standard and improved empirical Amber-like force fields and available low temperature experimental matrix data. Analysis of our calculated spectroscopic results show that: (1) The excellent agreement between the ab initio CC-VSCF calculated frequencies and the experimental data suggest that the computed anharmonic potentials for N-methylacetamide are of a very high quality; (2) For most transitions, the vibrational frequencies obtained from the ab initio CC-VSCF method are superior to those obtained using the empirical CC-VSCF methods, when compared with experimental data. However, the improved empirical force field yields better agreement with the experimental frequencies as compared with a standard AMBER-type force field; (3) The empirical force field in particular overestimates anharmonic couplings for the amide-2 mode, the methyl asymmetric bending modes, the out-of-plane methyl bending modes, and the methyl distortions; (4) Disagreement between the ab initio and empirical anharmonic couplings is greater than the disagreement between the frequencies, and thus the anharmonic part of the empirical potential seems to be less accurate than the harmonic contribution;and (5) Both the empirical and ab initio CC-VSCF calculations predict a negligible anharmonic coupling between the amide-1 and other internal modes. The implication of this is that the intramolecular energy flow between the amide-1 and the other internal modes may be smaller than anticipated. These results may have important implications for the anharmonic force fields of peptides, for which N-methylacetamide is a model.

Gregurick, Susan K.↗

NASA NTRS2003

Comparing Ultraviolet Spectra Against Calculations: First Results

The five-year goal of this effort is to calculate high fidelity mid-UV spectra for individual stars and stellar systems for a wide range of ages, abundances, and abundance ratios. In this first year, the emphasis was placed on revising the list of atomic line parameters used to calculate mid-UV spectra. First, new identifications of atomic lines and measurements of their transition probabilities were obtained for lines of the first and second ionization stages of iron-peak elements. Second, observed mid-UV and optical spectra for standard stars were re-analyzed and compared to new calculations, to refine the determination of transition probabilities and to estimate the identity of lines still missing from the laboratory lists. As evidenced by the figures, a dramatic improvement has resulted in the reproduction of the spectra of standard stars by the calculations.

Peterson, Ruth C.↗

NASA NTRS2001

Influence of Wake Models on Calculated Tiltrotor Aerodynamics

The tiltrotor aircraft configuration has the potential to revolutionize air transportation by providing an economical combination of vertical take-off and landing capability with efficient, high-speed cruise flight. To achieve this potential it is necessary to have validated analytical tools that will support future tiltrotor aircraft development. These analytical tools must calculate tiltrotor aeromechanical behavior, including performance, structural loads, vibration, and aeroelastic stability, with an accuracy established by correlation with measured tiltrotor data. The recent test of the Tilt Rotor Aeroacoustic Model (TRAM) with a single,l/4-scale V-22 rotor in the German-Dutch Wind Tunnel (DNW) provides an extensive set of aeroacoustic, performance, and structural loads data. This paper will examine the influence of wake models on calculated tiltrotor aerodynamics, comparing calculations of performance and airloads with TRAM DNW measurements. The calculations will be performed using the comprehensive analysis CAMRAD II.

Johnson, Wayne↗

NASA NTRS1997

Radiative heating of interstellar grains falling toward the solar nebula: 1-D diffusion calculations

As the dense molecular cloud that was the precursor of our Solar System was collapsing to form a protosun and the surrounding solar-nebula accretion disk, infalling interstellar grains were heated much more effectively by radiation from the forming protosun than by radiation from the disk's accretion shock. Accordingly, we have estimated the temperatures experienced by these infalling grains using radiative diffusion calculations whose sole energy source is radiation from the protosun. Although the calculations are 1-dimensional, they make use of 2-D, cylindrically symmetric models of the density structure of a collapsing, rotating cloud. The temperature calculations also utilize recent models for the composition and radiative properties of interstellar grains (Pollack et al. 1994. Astrophys. J. 421, 615-639), thereby allowing us to estimate which grain species might have survived, intact, to the disk accretion shock and what accretion rates and molecular-cloud rotation rates aid that survival. Not surprisingly, we find that the large uncertainties in the free parameter values allow a wide range of grain-survival results: (1) For physically plausible high accretion rates or low rotation rates (which produce small accretion disks), all of the infalling grain species, even the refractory silicates and iron, will vaporize in the protosun's radiation field before reaching the disk accretion shock. (2) For equally plausible low accretion rates or high rotation rates (which produce large accretion disks), all non-ice species, even volatile organics, will survive intact to the disk accretion shock. These grain-survival conclusions are subject to several limitations which need to be addressed by future, more sophisticated radiative-transfer models. Nevertheless, our results can serve as useful inputs to models of the processing that interstellar grains undergo at the solar nebula's accretion shock, and thus help address the broader question of interstellar inheritance in the solar nebula and present Solar System. These results may also help constrain the size of the accretion disk: for example, if we require that the calculations produce partial survival of organic grains into the solar nebula, we infer that some material entered the disk intact at distances comparable to or greater than a few AU. Intriguingly, this is comparable to the heliocentric distance that separates the C-rich outer parts of the current Solar System from the C-poor inner regions.

NASA Center ARC↗

NASA NTRS1996

Molecular Dynamics Calculations

The development of thermodynamics and statistical mechanics is very important in the history of physics, and it underlines the difficulty in dealing with systems involving many bodies, even if those bodies are identical. Macroscopic systems of atoms typically contain so many particles that it would be virtually impossible to follow the behavior of all of the particles involved. Therefore, the behavior of a complete system can only be described or predicted in statistical ways. Under a grant to the NASA Lewis Research Center, scientists at the Case Western Reserve University have been examining the use of modern computing techniques that may be able to investigate and find the behavior of complete systems that have a large number of particles by tracking each particle individually. This is the study of molecular dynamics. In contrast to Monte Carlo techniques, which incorporate uncertainty from the outset, molecular dynamics calculations are fully deterministic. Although it is still impossible to track, even on high-speed computers, each particle in a system of a trillion trillion particles, it has been found that such systems can be well simulated by calculating the trajectories of a few thousand particles. Modern computers and efficient computing strategies have been used to calculate the behavior of a few physical systems and are now being employed to study important problems such as supersonic flows in the laboratory and in space. In particular, an animated video (available in mpeg format--4.4 MB) was produced by Dr. M.J. Woo, now a National Research Council fellow at Lewis, and the G-VIS laboratory at Lewis. This video shows the behavior of supersonic shocks produced by pistons in enclosed cylinders by following exactly the behavior of thousands of particles. The major assumptions made were that the particles involved were hard spheres and that all collisions with the walls and with other particles were fully elastic. The animated video was voted one of two winning videos in a competition held at the meeting of the American Physical Society's Division of Fluid Dynamics, held in Atlanta, Georgia, in November 1994. Of great interest was the result that in every shock there were a few high-speed precursor particles racing ahead of the shock, carrying information about its impending arrival. Most recently, Dr. Woo has been applying molecular dynamics techniques to the problem of determining the drag produced by the space station truss structure as it flies through the thin residual atmosphere of low-Earth orbit. This problem is made difficult by the complex structure of the truss and by the extreme supersonic nature of the flow. A fully filled section of the truss has already been examined, and drag predictions have been made. Molecular dynamics techniques promise to make realistic drag calculations possible even for very complex partially filled truss segments flying at arbitrary angles.

Source record↗

NASA NTRS2004

Comparing Ultraviolet Spectra against Calculations: Year 2 Results

The five-year goal of this effort is to calculate high fidelity mid-W spectra for individual stars and stellar systems for a wide range of ages, abundances, and abundance ratios. In this second year, the comparison of our calculations against observed high-resolution mid- W spectra was extended to stars as metal-rich as the Sun, and to hotter and cooler stars, further improving the list of atomic line parameters used in the calculations. We also published the application of our calculations based on the earlier list of line parameters to the observed mid-UV and optical spectra of a mildly metal-poor globular cluster in the nearby Andromeda galaxy, Messier 3 1.

Peterson, Ruth C.↗

NASA NTRS2006

Representation of the Geosynchronous Plasma Environment in Spacecraft Charging Calculations

Historically, our ability to predict and postdict spacecraft surface charging has been limited by the characterization of the plasma environment. One difficulty lies in the common practice of fitting the plasma data to a Maxwellian or Double Maxwellian distribution function, which may not represent the data well for charging purposes. We use electron and ion flux spectra measured by the Los Alamos National Laboratory (LANL) Magnetospheric Plasma Analyzer (MPA) to examine how the use of different spectral representations of the charged particle environment in computations of spacecraft potentials during magnetospheric substorms affects the accuracy of the results. We calculate the spacecraft potential using both the measured fluxes and several different fits to these fluxes. These measured fluxes have been corrected for the difference between the measured and calculated potential. The potential computed using the measured fluxes and the best available material properties of graphite carbon, with a secondary electron escape fraction of 81%, is within a factor of three of the measured potential for 87% of the data. Potentials calculated using a Kappa function fit to the incident electron flux distribution function and a Maxwellian function fit to the incident ion flux distribution function agree with measured potentials nearly as well as do potentials calculated using the measured fluxes. Alternative spectral representations gave less accurate estimates of potential. The use of all the components of the net flux, along with spacecraft specific average material properties, gives a better estimate of the spacecraft potential than the high energy flux alone.

Davis, V. A.↗

NASA NTRS2006

Quiet High Speed Fan (QHSF) Flutter Calculations Using the TURBO Code

A scale model of the NASA/Honeywell Engines Quiet High Speed Fan (QHSF) encountered flutter wind tunnel testing. This report documents aeroelastic calculations done for the QHSF scale model using the blade vibration capability of the TURBO code. Calculations at design speed were used to quantify the effect of numerical parameters on the aerodynamic damping predictions. This numerical study allowed the selection of appropriate values of these parameters, and also allowed an assessment of the variability in the calculated aerodynamic damping. Calculations were also done at 90 percent of design speed. The predicted trends in aerodynamic damping corresponded to those observed during testing.

Bakhle, Milind A.↗

NASA NTRS2006

Calculation of Radiation Protection Quantities and Analysis of Astronaut Orientation Dependence

Health risk to astronauts due to exposure to ionizing radiation is a primary concern for exploration missions and may become the limiting factor for long duration missions. Methodologies for evaluating this risk in terms of radiation protection quantities such as dose, dose equivalent, gray equivalent, and effective dose are described. Environment models (galactic cosmic ray and solar particle event), vehicle/habitat geometry models, human geometry models, and transport codes are discussed and sample calculations for possible lunar and Mars missions are used as demonstrations. The dependence of astronaut health risk, in terms of dosimetric quantities, on astronaut orientation within a habitat is also examined. Previous work using a space station type module exposed to a proton spectrum modeling the October 1989 solar particle event showed that reorienting the astronaut within the module could change the calculated dose equivalent by a factor of two or more. Here the dose equivalent to various body tissues and the whole body effective dose due to both galactic cosmic rays and a solar particle event are calculated for a male astronaut in two different orientations, vertical and horizontal, in a representative lunar habitat. These calculations also show that the dose equivalent at some body locations resulting from a solar particle event can vary by a factor of two or more, but that the dose equivalent due to galactic cosmic rays has a much smaller (<15%) dependence on astronaut orientation.

Clowdsley, Martha S.↗

NASA NTRS2010

Monte-Carlo Simulation of Radiation Track Structure and Calculation of Dose Deposition in Nanovolumes

INTRODUCTION: The radiation track structure is of crucial importance to understand radiation damage to molecules and subsequent biological effects. Of a particular importance in radiobiology is the induction of double-strand breaks (DSBs) by ionizing radiation, which are caused by clusters of lesions in DNA, and oxidative damage to cellular constituents leading to aberrant signaling cascades. DSB can be visualized within cell nuclei with gamma-H2AX experiments. MATERIAL AND METHODS: In DSB induction models, the DSB probability is usually calculated by the local dose obtained from a radial dose profile of HZE tracks. In this work, the local dose imparted by HZE ions is calculated directly from the 3D Monte-Carlo simulation code RITRACKS. A cubic volume of 5 micron edge (Figure 1) is irradiated by a (Fe26+)-56 ion of 1 GeV/amu (LET approx.150 keV/micron) and by a fluence of 450 H+ ions, 300 MeV/amu (LET approx. 0.3 keV/micron). In both cases, the dose deposited in the volume is approx.1 Gy. The dose is then calculated into each 3D pixels (voxels) of 20 nm edge and visualized in 3D. RESULTS AND DISCUSSION: The dose is deposited uniformly in the volume by the H+ ions. The voxels which receive a high dose (orange) corresponds to electron track ends. The dose is deposited differently by the 56Fe26+ ion. Very high dose (red) is deposited in voxels with direct ion traversal. Voxels with electron track ends (orange) are also found distributed around the path of the track. In both cases, the appearance of the dose distribution looks very similar to DSBs seen in gammaH2AX experiments, particularly when the visualization threshold is applied. CONCLUSION: The refinement of the dose calculation to the nanometer scale has revealed important differences in the energy deposition between high- and low-LET ions. Voxels of very high dose are only found in the path of high-LET ions. Interestingly, experiments have shown that DSB induced by high-LET radiation are more difficult to repair. Therefore, this new approach may be useful to understand the nature of DSB and oxidative damage induced by ionizing radiation.

Plante, I.↗

NASA NTRS2010

Calculation of Dose Deposition in 3D Voxels by Heavy Ions

The biological response to high-LET radiation is very different from low-LET radiation, and can be partly attributed to the energy deposition by the radiation. Several experiments, notably detection of gamma-H2AX foci by immunofluorescence, has revealed important differences in the nature and in the spatial distribution of double-strand breaks (DSB) induced by low- and high-LET radiations. Many calculations, most of which are based on amorphous track models with radial dose, have been combined with chromosome models to calculate the number and distribution of DSB within nuclei and chromosome aberrations. In this work, the Monte-Carlo track structure simulation code RITRACKS have been used to calculate directly the energy deposition in voxels (3D pixels). A cubic volume of 5 micrometers of side was irradiated by 1) 450 (1)H+ ions of 300 MeV (LET is approximately 0.3 keV/micrometer) and 2) by 1 (56)Fe26+ ion of 1 GeV/amu (LET is approximately 150 keV/micrometer). In both cases, the dose deposited in the volume is approximately 1 Gy. All energy deposition events are recorded and dose is calculated in voxels of 20 micrometers of side. The voxels are then visualized in 3D by using a color scale to represent the intensity of the dose in a voxel. This simple approach has revealed several important points which may help understand experimental observations. In both simulations, voxels which receive low dose are the most numerous, and those corresponding to electron track ends received a dose which is in the higher range. The dose voxels are distributed randomly and scattered uniformly within the volume irradiated by low-LET radiation. The distribution of the voxels shows major differences for the (56)Fe26+ ion. The track structure can still be seen, and voxels with much higher dose are found in the region corresponding to the track "core". These high-dose voxels are not found in the low-LET irradiation simulation and may be responsible for DSB that are more difficult to repair. By applying a threshold on the dose visualization, voxels corresponding to electron track ends are evidenced and the spatial distribution of voxels is very similar to the distribution of DSB observed in gamma H2AX experiments, even if no chromosomes have been included in the simulation. Furthermore, this work has shown that a significant dose is deposited in voxels corresponding to electron track ends. Since some delta-rays from iron ion can travel several millimeters, they may also be of radiobiological importance.

Plante, Ianik↗

NASA NTRS2010

On Calculating the Zero-Gravity Surface Figure of a Mirror

An analysis of the classical method of calculating the zero-gravity surface figure of a mirror from surface-figure measurements in the presence of gravity has led to improved understanding of conditions under which the calculations are valid. In this method, one measures the surface figure in two or more gravity- reversed configurations, then calculates the zero-gravity surface figure as the average of the surface figures determined from these measurements. It is now understood that gravity reversal is not, by itself, sufficient to ensure validity of the calculations: It is also necessary to reverse mounting forces, for which purpose one must ensure that mountingfixture/ mirror contacts are located either at the same places or else sufficiently close to the same places in both gravity-reversed configurations. It is usually not practical to locate the contacts at the same places, raising the question of how close is sufficiently close. The criterion for sufficient closeness is embodied in the St. Venant principle, which, in the present context, translates to a requirement that the distance between corresponding gravity-reversed mounting positions be small in comparison to their distances to the optical surface of the mirror. The necessity of reversing mount forces is apparent in the behavior of the equations familiar from finite element analysis (FEA) that govern deformation of the mirror.

Bloemhof, Eric E.↗

NASA NTRS2010

Uncertainties Associated with Theoretically Calculated N2-Broadened Half-Widths of H2O Lines

With different choices of the cut-offs used in theoretical calculations, we have carried out extensive numerical calculations of the N2-broadend Lorentzian half-widths of the H2O lines using the modified Robert-Bonamy formalism. Based on these results, we are able to thoroughly check for convergence. We find that, with the low-order cut-offs commonly used in the literature, one is able to obtain converged values only for lines with large half-widths. Conversely, for lines with small half-widths, much higher cut-offs are necessary to guarantee convergence. We also analyse the uncertainties associated with calculated half-widths, and these are correlated as above. In general, the smaller the half-widths, the poorer the convergence and the larger the uncertainty associated with them. For convenience, one can divide all H2O lines into three categories, large, intermediate, and small, according to their half-width values. One can use this division to judge whether the calculated half-widths are converged or not, based on the cut-offs used, and also to estimate how large their uncertainties are. We conclude that with the current Robert- Bonamy formalism, for lines in category lone can achieve the accuracy requirement set by HITRAN, whereas for lines in category 3, it 'is impossible to meet this goal.

Ma, Q.↗