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At least 1,225 records · Page 68
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Siegel, R.↗
NASA NTRS1996

A History of Aerospace Problems, Their Solutions, Their Lessons

The positive aspect of problem occurrences is the opportunity for learning and a challenge for innovation. The learning aspect is not restricted to the solution period of the problem occurrence, but can become the beacon for problem prevention on future programs. Problems/failures serve as a point of departure for scaling to new designs. To ensure that problems/failures and their solutions guide the future programs, a concerted effort has been expended to study these problems, their solutions, their derived lessons learned, and projections for future programs. This includes identification of technology thrusts, process changes, codes development, etc. However, they must not become an excuse for adding layers upon layers of standards, criteria, and requirements, but must serve as guidelines that assist instead of stifling engineers. This report is an extension of prior efforts to accomplish this task. Although these efforts only scratch the surface, it is a beginning that others must complete.

Ryan, R. S.↗
NASA NTRS1996

A Systematic Solution Approach for Neutron Transport Problems in Diffuse Regimes

A systematic solution approach for the neutron transport equation, based on a least-squares finite-element discretization, is presented. This approach includes the theory for the existence and uniqueness of the analytical as well as of the discrete solution, bounds for the discretization error, and guidance for the development of an efficient multigrid solver for the resulting discrete problem. To guarantee the accuracy of the discrete solution for diffusive regimes, a scaling transformation is applied to the transport operator prior to the discretization. The key result is the proof of the V-ellipticity and continuity of the scaled least-squares bilinear form with constants that are independent of the total cross section and the absorption cross section. For a variety of least-squares finite-element discretizations this leads to error bounds that remain valid in diffusive regimes. Moreover, for problems in slab geometry a full multigrid solver is presented with V(1, 1)-cycle convergence rates approximately equal to 0.1, independent of the size of the total cross section and the absorption cross section.

Manteuffel, T. A.↗
NASA NTRS1995

Comparison of Nonequilibrium Solution Algorithms Applied to Chemically Stiff Hypersonic Flows

Three solution algorithms, explicit under-relaxation, point implicit, and lower-upper symmetric Gauss-Seidel, are used to compute nonequilibrium flow around the Apollo 4 return capsule at the 62-km altitude point in its descent trajectory. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness.The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15 and 30, the lower-upper symmetric Gauss-Seidel method produces an eight order of magnitude drop in the energy residual in one-third to one-half the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 30 and above. At Mach 40 the performance of the lower-upper symmetric Gauss-Seidel algorithm deteriorates to the point that it is out performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.

Palmer, Grant↗
NASA NTRS1996

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Coirier, William J.↗
NASA NTRS1997

Dimerization in Highly Concentrated Solutions of Phosphoimidazolide Activated Mononucleotides

Phosphoimidazolide activated ribomononucleotides (*pN) are useful substrates for the non-enzymatic synthesis of polynucleotides. However, dilute neutral aqueous solutions of *pN typically yield small amounts of dimers and traces of polymers; most of *pN hydrolyzes to yield nucleoside 5'-monophosphate. Here we report the self-condensation of nucleoside 5'-phosphate 2- methylimidazolide (2-MeImpN with N = cytidine, uridine or guanosine) in the presence of Mg2(+) in concentrated solutions, such as might have been found in an evaporating lagoon on prebiotic Earth. The product distribution indicates that oligomerization is favored at the expense of hydrolysis. At 1.0 M, 2-MelmpU and 2-MelmpC produce about 65% of oligomers including 4% of the 3',5'-Iinked dimer. Examination of the product distribution of the three isomeric dimers in a self-condensation allows identification of reaction pathways that lead to dimer formation. Condensations in a concentrated mixture of all three nucleotides (U,C,G mixtures) is made possible by the enhanced solubility of 2-MeImpG in such mixtures. Although percent yield of intemucleotide linked dimers is enhanced as a function of initial monomer concentration, pyrophosphate dimer yields remain practically unchanged at about 20% for 2-MelmpU, 16% for 2-MeImpC and 25% of the total pyrophosphate in the U,C,G mixtures. The efficiency by which oligomers are produced in these concentrated solutions makes the evaporating lagoon scenario a potentially interesting medium for the prebiotic synthesis of dimers and short RNAs.

Kanavarioti, Anastassia↗
NASA NTRS1959

Details of Exact Low Prandtl Number Boundary-Layer Solutions for Forced and For Free Convection

A detailed report is given of exact (numerical) solutions of the laminar-boundary-layer equations for the Prandtl number range appropriate to liquid metals (0.003 to 0.03). Consideration is given to the following situations: (1) forced convection over a flat plate for the conditions of uniform wall temperature and uniform wall heat flux, and (2) free convection over an isothermal vertical plate. Tabulations of the new solutions are given in detail. Results are presented for the heat-transfer and shear-stress characteristics; temperature and velocity distributions are also shown. The heat-transfer results are correlated in terms of dimensionless parameters that vary only slightly over the entire liquid-metal range. Previous analytical and experimental work on low Prandtl number boundary layers is surveyed and compared with the new exact solutions.

Sparrow, E. M.↗
NASA NTRS1959

Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

Mirels, Harold↗
NASA NTRS1998

Investigation of Solution Polymerizations in Microgravity and 1 G

The in-situ dielectric spectra for the solution polymerization of polydiacetylene has been successfully measured. The results show a distinct difference between the response for the bulk solution and surface polymerization. It also shows a low frequency peak in the dissipation factor which is present in both the bulk and surface polymerizations. These features may prove to be significant indicators for important polymerization processes. Future studies will investigate the mechanisms responsible for these dielectric responses. This technique will eventually be used to monitor microgravity polymerizations and provide in-situ data on how microgravity affects solution polymerization.

Kennedy, Alvin P.↗
NASA NTRS1998

Photonic and Opto-Electronic Applications of Polydiacetylene Films Photodeposited from Solution and Polydiacetylene Copolymer Networks

Polydiacetylenes (PDAS) are attractive materials for both electronic and photonic applications because of their highly conjugated electronic structures. They have been investigated for applications as both one-dimensional (linear chain) conductors and nonlinear optical (NLO) materials. One of the chief limitations to the use of PDAs has been the inability to readily process them into useful forms such as films and fibers. In our laboratory we have developed a novel process for obtaining amorphous films of a PDA derived from 2-methyl4-nitroaniline using photodeposition with Ultraviolet (UV) light from monomer solutions onto transparent substrates. Photodeposition from solution provides a simple technique for obtaining PDA films in any desired pattern with good optical quality. This technique has been used to produce PDA films that show potential for optical applications such as holographic memory storage and optical limiting, as well as third-order NLO applications such as all-optical refractive index modulation, phase modulation and switching. Additionally, copolymerization of diacetylenes with other monomers such as methacrylates provides a means to obtain materials with good processibility. Such copolymers can be spin cast to form films, or drawn by either melt or solution extrusion into fibers. These films or fibers can then be irradiated with UV to photopolymerize the diacetylene units to form a highly stable cross-linked PDA-copolymer network. If such films are electrically poled while being irradiated, they can achieve the asymmetry necessary for second-order NLO applications such as electro-optic switching. On Earth, formation of PDAs by the above mentioned techniques suffers from defects and inhomogeneities caused by convective flows that can arise during processing. By studying the formation of these materials in the reduced-convection, diffusion-controlled environment of space we hope to better understand the factors that affect their processing, and thereby, their nature and properties. Ultimately it may even be feasible to conduct space processing of PDAs for technological applications.

Paley, Mark S.↗
NASA NTRS1999

Magnetic Damping of Solid Solution Semiconductor Alloys

The objective of this study is to: (1) experimentally test the validity of the modeling predictions applicable to the magnetic damping of convective flows in electrically conductive melts as this applies to the bulk growth of solid solution semiconducting materials; and (2) assess the effectiveness of steady magnetic fields in reducing the fluid flows occurring in these materials during processing. To achieve the objectives of this investigation, we are carrying out a comprehensive program in the Bridgman and floating-zone configurations using the solid solution alloy system Ge-Si. This alloy system has been studied extensively in environments that have not simultaneously included both low gravity and an applied magnetic field. Also, all compositions have a high electrical conductivity, and the materials parameters permit reasonable growth rates. An important supporting investigation is determining the role, if any, that thermoelectromagnetic convection (TEMC) plays during growth of these materials in a magnetic field. TEMC has significant implications for the deployment of a Magnetic Damping Furnace in space. This effect will be especially important in solid solutions where the growth interface is, in general, neither isothermal nor isoconcentrational. It could be important in single melting point materials, also, if faceting takes place producing a non-isothermal interface. In conclusion, magnetic fields up to 5 Tesla are sufficient to eliminate time-dependent convection in silicon floating zones and possibly Bridgman growth of Ge-Si alloys. In both cases, steady convection appears to be more significant for mass transport than diffusion, even at 5 Tesla in the geometries used here. These results are corroborated in both growth configurations by calculations.

Szofran, Frank R.↗
NASA NTRS1999

Application of the Space-Time Conservation Element and Solution Element Method to One-Dimensional Advection-Diffusion Problems

Test problems are used to examine the performance of several one-dimensional numerical schemes based on the space-time conservation and solution element (CE/SE) method. Investigated in this paper are the CE/SE schemes constructed previously for solving the linear unsteady advection-diffusion equation and the schemes derived here for solving the nonlinear viscous and inviscid Burgers equations. In comparison with the numerical solutions obtained using several traditional finite-difference schemes with similar accuracy, the CE/SE solutions display much lower numerical dissipation and dispersion errors.

Wang, Xiao-Yen↗
NASA NTRS1997

Liquid-Liquid Phase Separation in Supersaturated Lysozyme Solutions and Associated Precipitate Formation/Crystallization

Using cloud point determinations, the phase boundaries (binodals) for metastable liquid-liquid (L-L) separation in supersaturated hen egg white lysozyme solutions with 3%, 5%, and 7% (wlv) NaCl at pH= 4.5 and protein concentrations c between 40 and 400 mg/ml were determined. The critical temperature for the binodal increased approximately linearly with salt concentration. The coexisting liquid phases both remained supersaturated but differed widely in protein concentration. No salt repartitioning was observed between the initial and the two separated liquid phases. After the L-L separation, due to the presence of the high protein concentration phase, crystallization occurred much more rapidly than in the initial solution. At high initial protein concentrations, a metastable gel phase formed at temperatures above the liquid binodal. Both crystal nucleation and gel formation were accelerated in samples that had been cycled through the binodal. Solutions in the gel and L-L regions yielded various types of precipitates. Based on theoretical considerations, previous observations with other proteins, and our experimental results with lysozyme, a generic phase diagram for globular proteins is put forth. A limited region in the (T,c) plane favorable for the growth of protein single crystals is delineated.

Muschol, Martin↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1998

Magnetic Damping of Solid Solution Semiconductor Alloys

The objective of this study is to conduct the Earth-based research sufficient to successfully propose a flight experiment (1) to experimentally test the validity of the modeling predictions applicable to the magnetic damping of convective flows in conductive melts as this applies to the bulk growth of solid solution semiconducting materials in the reduced gravitational levels available in low Earth orbit and (2) to assess the effectiveness of steady magnetic fields in reducing the fluid flows occurring in these materials during space processing. To achieve the objectives of this investigation, we are carrying out a comprehensive program in the Bridgman and floating-zone configurations using the solid solution alloy system Ge-Si. This alloy system was chosen because it has been studied extensively in environments that have not simultaneously included both low gravity and an applied magnetic field. Also, all compositions have a high electrical conductivity, and the materials parameters permit high growth rates compared to many other commonly studied alloy semiconductors. An important supporting investigation is determining the role, if any, that thermoelectromagnetic convection (TEMC) plays during growth of these materials in a magnetic field. Some compositional anomalies observed by us in magnetic grown crystals can only be explained by TEMC; this has significant implications for the deployment of a Magnetic Damping Furnace in space. This effect will be especially important in solid solutions where the growth interface is, in general, neither isothermal nor isoconcentrational. It could be important in single melting point materials, also, if faceting takes place producing a non-isothermal interface.

Szofran, Frank R.↗
NASA NTRS1998

The Effect of Solution Parameters on Lysozyme Nucleation Rates and Crystal Quality

In the pursuit of strongly diffracting high quality macromolecule crystals of suitable volume, this study investigates how the formation of macromolecules in solution and their growth characteristics effect crystal volume and diffracting quality. We systematically investigated the effect of solution conditions on lysozyme nucleation rates and the volume of crystals produced. Batch crystallization plates were used in combination with a video microscope system to measure nucleation rates and crystal volume. As expected from classical nucleation theory, crystal numbers were found to increase with increases in temperature and supersaturation. Small changes in solution pH, at constant supersaturation values were found, however, to dramatically effect the number of crystals nucleated in the wells varying from 1000s to 10s in the pH range 4.0 to 5.2. Having optimized the conditions required to produce an appropriate number of crystals of a suitable volume for X-ray analysis, a large number of uniform crystals were produced under exactly the same conditions. In the X-ray analysis of more than 50 such crystals there was found a wide variation in crystal lattice parameters and data quality. The variation in X-ray quality crystal samples is thought to be related to the growth rate variation caused by growth rate dispersion seen in lysozyme crystal growth experiments.

Judge, R. A.↗
NASA NTRS1999

A Spherical Earth Solution for TOA Lightning Location Retrieval

The problem of retrieving ligntning, ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered, It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (e.g., minimization). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A summary of a quasi-analytic extension of the spherical Earth solution to an oblate spheroid Earth geometry is also provided.

Koshak, W. J.↗