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NASA NTRS1996

Self-Consistent Simulation of the Brownian Stage of Dust Growth

It is a widely accepted view that in proto-planetary accretion disks the collision and following sticking of dust particles embedded in the gas eventually leads to the formation of planetesimals (coagulation). For the smallest dust grains, Brownian motion is assumed to be the dominant source of their relative velocities leading to collisions between these dust grains. As the dust grains grow they eventually couple to the turbulent motion of the gas which then drives the coagulation much more efficiently. Many numerical coagulation simulations have been carried out to calculate the fractal dimension of the aggregates, which determines the duration of the ineffective Brownian stage of growth. Predominantly on-lattice and off-lattice methods were used. However, both methods require simplification of the astrophysical conditions. The aggregates found by those methods had a fractal dimension of approximately 2 which is equivalent to a constant, mass-independent friction time. If this value were valid for the conditions in an accretion disk, this would mean that the coagulation process would finally 'freeze out' and the growth of a planetesimal would be impossible within the lifetime of an accretion disk. In order to investigate whether this fractal dimension is model independent, we simulate self-consistently the Brownian stage of the coagulation by an N-particle code. This method has the advantage that no further assumptions about homogeneity of the dust have to be made. In our model, the dust grains are considered as aggregates built up of spheres. The equation of motion of the dust grains is based on the probability density for the diffusive transport within the gas atmosphere. Because of the very low number density of the dust grains, only 2-body-collisions have to be considered. As the Brownian stage of growth is very inefficient, the system is to be simulated over long periods of time. In order to find close particle pairs of the system which are most likely to undergo a collision, we use a particle-in-cell (PIC) method for the early stages of the simulation where the system is still very homogeneous and a tree method later when the particles are more clustered.

Kempf, S.↗
NASA NTRS1986

Estimation of vegetation cover at subpixel resolution using LANDSAT data

The present report summarizes the various approaches relevant to estimating canopy cover at subpixel resolution. The approaches are based on physical models of radiative transfer in non-homogeneous canopies and on empirical methods. The effects of vegetation shadows and topography are examined. Simple versions of the model are tested, using the Taos, New Mexico Study Area database. Emphasis has been placed on using relatively simple models requiring only one or two bands. Although most methods require some degree of ground truth, a two-band method is investigated whereby the percent cover can be estimated without ground truth by examining the limits of the data space. Future work is proposed which will incorporate additional surface parameters into the canopy cover algorithm, such as topography, leaf area, or shadows. The method involves deriving a probability density function for the percent canopy cover based on the joint probability density function of the observed radiances.

Jasinski, Michael F.↗
NASA NTRS1989

A class of high resolution explicit and implicit shock-capturing methods

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Yee, H. C.↗
NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗
NASA NTRS1995

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗
NASA NTRS2011

Broken Ergodicity in MHD Turbulence in a Spherical Domain

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

Shebalin, John V.↗
NASA NTRS2012

Formulation and Testing of Paraffin-Based Solid Fuels Containing Energetic Additives for Hybrid Rockets

Many approaches have been considered in an effort to improve the regression rate of solid fuels for hybrid rocket applications. One promising method is to use a fuel with a fast burning rate such as paraffin wax; however, additional performance increases to the fuel regression rate are necessary to make the fuel a viable candidate to replace current launch propulsion systems. The addition of energetic and/or nano-sized particles is one way to increase mass-burning rates of the solid fuels and increase the overall performance of the hybrid rocket motor.1,2 Several paraffin-based fuel grains with various energetic additives (e.g., lithium aluminum hydride (LiAlH4) have been cast in an attempt to improve regression rates. There are two major advantages to introducing LiAlH4 additive into the solid fuel matrix: 1) the increased characteristic velocity, 2) decreased dependency of Isp on oxidizer-to-fuel ratio. The testing and characterization of these solid-fuel grains have shown that continued work is necessary to eliminate unburned/unreacted fuel in downstream sections of the test apparatus.3 Changes to the fuel matrix include higher melting point wax and smaller energetic additive particles. The reduction in particle size through various methods can result in more homogeneous grain structure. The higher melting point wax can serve to reduce the melt-layer thickness, allowing the LiAlH4 particles to react closer to the burning surface, thus increasing the heat feedback rate and fuel regression rate. In addition to the formulation of LiAlH4 and paraffin wax solid-fuel grains, liquid additives of triethylaluminum and diisobutylaluminum hydride will be included in this study. Another promising fuel formulation consideration is to incorporate a small percentage of RDX as an additive to paraffin. A novel casting technique will be used by dissolving RDX in a solvent to crystallize the energetic additive. After dissolving the RDX in a solvent chosen for its compatibility with both paraffin and RDX, the mixture will be combined with the melted paraffin. With the melting point of the paraffin far below the decomposition temperature of the RDX, the solvent will be boiled off, leaving the crystallized RDX embedded in the paraffin. At low percentages of RDX additive and with crystallized RDX surrounded by paraffin, the fuel grains will remain inert, maintaining a key benefit of hybrids in the safety of the solid fuel.

Larson, Daniel B.↗
NASA NTRS1980

Note on the eigensolution of a homogeneous equation with semi-infinite domain

The 'variation-iteration' method using Green's functions to find the eigenvalues and the corresponding eigenfunctions of a homogeneous Fredholm integral equation is employed for the stability analysis of fluid hydromechanics problems with a semiinfinite (infinite) domain of application. The objective of the study is to develop a suitable numerical approach to the solution of such equations in order to better understand the full set of equations for 'real-world' flow models. The study involves a search for a suitable value of the length of the domain which is a fair finite approximation to infinity, which makes the eigensolution an approximation dependent on the length of the interval chosen. In the examples investigated y = 1 = a seems to be the best approximation of infinity; for y greater than unity this method fails due to the polynomial nature of Green's functions.

Wadia, A. R.↗
NASA NTRS1980

Sample processor for the automatic extraction of families of compounds from liquid samples and/or homogenized solid samples suspended in a liquid

A sample processor and method for the automatic extraction of families of compounds, known as extracts, from liquid and/or homogenized solid samples are disclosed. The sample processor includes a tube support structure which supports a plurality of extraction tubes, each containing a sample from which families of compounds are to be extracted. The support structure is moveable automatically with respect to one or more extraction stations, so that as each tube is at each station a solvent system, consisting of a solvent and reagents, is introduced therein. As a result an extract is automatically extracted from the tube. The sample processor includes an arrangement for directing the different extracts from each tube to different containers, or to direct similar extracts from different tubes to the same utilization device.

Jahnsen, Vilhelm J.↗
NASA NTRS2012

Macro Scale Independently Homogenized Subcells for Modeling Braided Composites

An analytical method has been developed to analyze the impact response of triaxially braided carbon fiber composites, including the penetration velocity and impact damage patterns. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. Currently, each shell element is considered to be a smeared homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. To determine the stiffness and strength properties required for the constitutive model, a top-down approach for determining the strength properties is merged with a bottom-up approach for determining the stiffness properties. The top-down portion uses global strengths obtained from macro-scale coupon level testing to characterize the material strengths for each subcell. The bottom-up portion uses micro-scale fiber and matrix stiffness properties to characterize the material stiffness for each subcell. Simulations of quasi-static coupon level tests for several representative composites are conducted along with impact simulations.

Blinzler, Brina J.↗
NASA NTRS2002

High-Fidelity Generalization Method of Cells for Inelastic Periodic Multiphase Materials

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress said inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model, and with finite-element results for transverse loading.

Aboudi, Jacob↗
NASA NTRS2011

A Groundmass Composition for EET 79001A Using a Novel Microprobe Technique for Estimating Bulk Compositions. Lithology A as an Impact Melt?

Petrologic investigation of the shergottites has been hampered by the fact that most of these meteorites are partial cumulates. Two lines of inquiry have been used to evaluate the compositions of parental liquids: (i) perform melting experiments at different pressures and temperatures until the compositions of cumulate crystal cores are reproduced [e.g., 1]; and (ii) use point-counting techniques to reconstruct the compositions of intercumulus liquids [e.g., 2]. The second of these methods is hampered by the approximate nature of the technique. In effect, element maps are used to construct mineral modes; and average mineral compositions are then converted into bulk compositions. This method works well when the mineral phases are homogeneous [3]. However, when minerals are zoned, with narrow rims contributing disproportionately to the mineral volume, this method becomes problematic. Decisions need to be made about the average composition of the various zones within crystals. And, further, the proportions of those zones also need to be defined. We have developed a new microprobe technique to see whether the point-count method of determining intercumulus liquid composition is realistic. In our technique, the approximating decisions of earlier methods are unnecessary because each pixel of our x-ray maps is turned into a complete eleven-element quantitative analysis. The success or failure of our technique can then be determined by experimentation. As discussed earlier, experiments on our point-count composition can then be used to see whether experimental liquidus phases successfully reproduce natural mineral compositions. Regardless of our ultimate outcome in retrieving shergottite parent liquids, we believe our pixel-bypixel analysis technique represents a giant step forward in documenting thin-section modes and compositions. For a third time, we have analyzed the groundmass composition of EET 79001, 68 [Eg]. The first estimate of Eg was made by [4] and later modified by [5], to take phase diagram considerations into account. The Eg composition of [4] was too olivine normative to be the true Eg composition, because the ,68 groundmass contains no forsteritic olivine. A later mapping by [2] basically reconfirmed the modifications of [5]. However, even the modified composition of [5] has olivine on the liquidus for ~50 C before low-Ca pyroxene appears [6].

Jones, John H.↗
NASA NTRS2009

Cast Aluminum Alloys for High Temperature Applications Using Nanoparticles Al2O3 and Al3-X Compounds (X = Ti, V, Zr)

In this paper, the effect of nanoparticles Al2O3 and Al3-X compounds (X = Ti, V, Zr) on the improvement of mechanical properties of aluminum alloys for elevated temperature applications is presented. These nanoparticles were selected based on their low cost, chemical stability and low diffusions rates in aluminum at high temperatures. The strengthening mechanism at high temperature for aluminum alloy is based on the mechanical blocking of dislocation movements by these nanoparticles. For Al2O3 nanoparticles, the test samples were prepared from special Al2O3 preforms, which were produced using ceramic injection molding process and then pressure infiltrated by molten aluminum. In another method, Al2O3 nanoparticles can also be homogeneously mixed with fine aluminum powder and consolidated into test samples through hot pressing and sintering. With the Al3-X nanoparticles, the test samples are produced as precipitates from in-situ reactions with molten aluminum using conventional permanent mold or die casting techniques. It is found that cast aluminum alloy using nanoparticles Al3-X is the most cost effective method to produce high strength aluminum alloys for high temperature applications in comparison to nanoparticles Al2O3. Furthermore, significant mechanical properties retention in high temperature environment could be achieved with Al3-X nanoparticles, resulting in tensile strength of nearly 3 times higher than most 300- series conventional cast aluminum alloys tested at 600 F.

Lee, Jonathan A.↗
NASA NTRS1992

Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

The basic objective of this research is to extend the capabilities of Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the computational analyses of high speed reacting flows. In the efforts related to LES, we were primarily involved with assessing the performance of the various modern methods based on the Probability Density Function (PDF) methods for providing closures for treating the subgrid fluctuation correlations of scalar quantities in reacting turbulent flows. In the work on DNS, we concentrated on understanding some of the relevant physics of compressible reacting flows by means of statistical analysis of the data generated by DNS of such flows. In the research conducted in the second year of this program, our efforts focused on the modeling of homogeneous compressible turbulent flows by PDF methods, and on DNS of non-equilibrium reacting high speed mixing layers. Some preliminary work is also in progress on PDF modeling of shear flows, and also on LES of such flows.

Givi, P.↗
NASA NTRS1992

LAI inversion from optical reflectance using a neural network trained with a multiple scattering model

The inversion of the leaf area index (LAI) canopy parameter from optical spectral reflectance measurements is obtained using a backpropagation artificial neural network trained using input-output pairs generated by a multiple scattering reflectance model. The problem of LAI estimation over sparse canopies (LAI < 1.0) with varying soil reflectance backgrounds is particularly difficult. Standard multiple regression methods applied to canopies within a single homogeneous soil type yield good results but perform unacceptably when applied across soil boundaries, resulting in absolute percentage errors of >1000 percent for low LAI. Minimization methods applied to merit functions constructed from differences between measured reflectances and predicted reflectances using multiple-scattering models are unacceptably sensitive to a good initial guess for the desired parameter. In contrast, the neural network reported generally yields absolute percentage errors of <30 percent when weighting coefficients trained on one soil type were applied to predicted canopy reflectance at a different soil background.

Smith, James A.↗
NASA NTRSDate not supplied

Active Thermography Based on Tensor Rank Decomposition

Principal Component Thermography applies Singular Value Decomposition (SVD) to post-process data that are derived from active thermographic inspections. SVD provides useful compression of the data and allows for better understanding of substructure and indications of potential damage. In the standard approach, SVD is applied to a certain reshaping of a three-dimensional data stack into a two-dimensional array. This work applies the CANDECOMP-PARAFAC (CP) tensor rank decomposition directly to the three-dimensional data to avoid the initial reshaping step in order to begin to develop an inspection method that can more accurately detect defects in non-homogeneous and anisotropic materials. Tests against simulated data that compare the CP decomposition method with traditional Principal Component Thermography based on SVD are described. Finally, the method of Proper Generalized Decomposition (PGD) is used to derive the CP decomposition, and its performance against other algorithms is also discussed.

Thermography↗
NASA NTRS1974

Buckling of cylindrical shells with random imperfections

Buckling of long cylindrical shells with random imperfections subjected to axial loads is treated using the method of truncated hierarchy. A system of homogeneous variational equations is set up to examine the existence of bifurcation in the neighborhood of the equilibrium state. These equations are linear and involve stationary random coefficients. The truncated-hierarchy method is applied, and characteristic equations are obtained. Various exponential cosine correlation functions associated with asymmetric imperfections are examined numerically. Qualitatively, the results obtained are as anticipated.

Fersht, R. S.↗