Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21

Synchronized flash photolysis and pulse deposition in matrix isolation experiments

An apparatus is described which permits flash photolysis of a pulse-deposited gas mixture in a matrix isolation experiment. This technique obviates the limitations of in situ photolysis imposed by the cage effect and by secondary photolysis. The matrix is deposited in pulses at 30-s intervals and photolyzed sequentially by four synchronized flashlamps approximately 1 ms before the pulse strikes the cold surface. Pulsed deposition maintains adequate isolation and causes line narrowing, which enhances spectral sensitivity. The efficacy of flash photolysis combined with pulsed deposition for producing and trapping transient species was demonstrated by infrated detection of CF3 (from photolysis of CF3I/Ar mixtures) and of ClCO (from photolysis of Cl2/CO/Ar mixtures). The apparatus was used to study the photolytic decomposition of gaseous tricarbonylironcyclobutadiene, C4H4Fe(CO)3. The results indicate that the primary photolytic step is not elimination of C4H4, as suggested earlier, but rather of CO.

Allamandola, Louis J.↗

Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations

We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.

Barth, Timothy J.↗

Bound-free Spectra for Diatomic Molecules

It is now recognized that prediction of radiative heating of entering space craft requires explicit treatment of the radiation field from the infrared (IR) to the vacuum ultra violet (VUV). While at low temperatures and longer wavelengths, molecular radiation is well described by bound-bound transitions, in the short wavelength, high temperature regime, bound-free transitions can play an important role. In this work we describe first principles calculations we have carried out for bound-bound and bound-free transitions in N2, O2, C2, CO, CN, NO, and N2+. Compared to bound ]bound transitions, bound-free transitions have several particularities that make them different to deal with. These include more complicated line shapes and a dependence of emission intensity on both bound state diatomic and atomic concentrations. These will be discussed in detail below. The general procedure we used was the same for all species. The first step is to generate potential energy curves, transition moments, and coupling matrix elements by carrying out ab initio electronic structure calculations. These calculations are expensive, and thus approximations need to be made in order to make the calculations tractable. The only practical method we have to carry out these calculations is the internally contracted multi-reference configuration interaction (icMRCI) method as implemented in the program suite Molpro. This is a widely used method for these kinds of calculations, and is capable of generating very accurate results. With this method, we must first of choose which electrons to correlate, the one-electron basis to use, and then how to generate the molecular orbitals.

Schwenke, David W.↗

Electromagnetic Scattering by Discrete Random Media. III: The Vector Radiative Transfer Equation

A vector radiative transfer equation with an additional source term typical of dense media is obtained. The analysis includes (i) the derivation of an integral equation for the correlation matrix of the exciting field coefficients accounting for the correlation between the particles, (ii) the derivation of an integral representation for the specific coherency dyadicin terms of this matrix, and (iii) the simplification of the integral equation for the correlation matrix and of the integral representation for the specific coherency dyadic by employing a series of approximations which are characteristic of sparse media.

Adrian Doicu↗

A Numerical Method for Computing the State Transition Matrix Using Poincare Integral Invariants

The Poincare integral invariants describe the volumes of sets in Hamiltonian phase space. We use these invariants to derive a new numerical procedure for obtaining the state transition matrix (STM), which can be applied to both conservative and nonconservative systems. The method is analogous to a finite difference approximation of the STM, where perturbed states are numerically propagated along with the reference trajectory. We discuss the mathematical similarities between this new STM and existing methods, show numerical results for orbital motion and uncertainty propagation, and discuss new insights afforded by the Hamiltonian properties of phase flow.

state transition matrix↗

Refinement of the Robert-Bonamy Formalism: Considering Effects from the Line Coupling

Since it was developed in 1979, the Robert-Bonamy (RB) formalism has been widely used in calculating pressure broadened half-widths and induced shifts for many molecular systems. However, this formalism contains several approximations whose applicability has not been thoroughly justified. One of them is that lines of interest are well isolated. When these authors developed the formalism, they have relied on this assumption twice. First, in calculating the spectral density F(ω), they have only considered the diagonal matrix elements of the relaxation operator. Due to this simplification, effects from the line mixing are ignored. Second, when they applied the linked cluster theorem to remove the cutoff, they have assumed the matrix elements of the operator exp(-iS(sub 1) - S(sub 2)) can be replaced by the exponential of the matrix elements of -iS(sub 1) - S(sub 2). With this replacement, effects from the line coupling are also ignored. Although both these two simplifications relied on the same approximation, their validity criteria are completely different and the latter is more stringent than the former. As a result, in many cases where the line mixing becomes negligible, significant effects from the line coupling have been completely missed. In the present study, we have developed a new method to evaluate the matrix elements of exp(-iS(sub 1) - S(sub 2)) and have refined the RB formalism such that line coupling can be taken into account. Our numerical calculations of the half-widths for Raman Q lines of the N(sub 2)-N(sub 2) pair have demonstrated that effects from the line coupling are important. In comparison with values derived from the RB formalism, new calculated values for these lines are significantly reduced. A recent study has shown that in comparison with the measurements and the most accurate close coupling calculations, the RB formalism overestimates the half-widths by a large amount. As a result, the refinement of the RB formalism goes in the right direction and these new calculated half-widths become closer to the "true" values.

spectra↗

Remote sensing of Earth Terrain

The Mueller matrix and polarization covariance matrix for polarimetric radar systems were studied. The clutter is modelled by a layer of random permittivity, described by a three dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model is applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. It is found that 8 out of 16 elements of the Mueller matrix are identically zero, corresponding to a covariance matrix with four zero elements. Theoretical predictions are matched with experimental data for vegetation fields. A general mixing formula is derived for discrete scatterers immersed in a host medium. The inclusion particles are assumed to be ellipsoidal. The electric field inside the scatterers is determined by quasistatic analysis, assuming the diameter of the inclusion particles to be much smaller than the wavelength. The results are applicable to general multiphase mixtures.

Kong, J. A.↗

Theoretical models for polarimetric radar clutter

The Mueller matrix and polarization covariance matrix are described for polarimetric radar systems. The clutter is modeled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model is applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. It is found that 8 out of 16 elements of the Mueller matrix are identically zero, corresponding to a covariance matrix with four zero elements. Theoretical predictions are matched with experimental data for vegetation fields.

Borgeaud, M.↗

Constituent-Based Life Models Being Developed for SiC/SiC Composites

For the successful utilization of ceramic matrix composites (CMC) as hot-section components in advanced aeropropulsion engines, the CMC constituents will need to be tailored and optimized to meet all the critical property demands of each component. Under the High-Speed Research (HSR) and Advanced High-Temperature Engine Materials Technology (HITEMP) Programs, the NASA Glenn Research Center at Lewis Field initiated research to develop mechanistic models for key CMC thermostructural properties. These models would describe the effects of different constituent factors (composition, geometry, and volume fraction) and of potential application conditions (stress, time, temperature, and environment) on these properties. Particular focus was placed on both analytical and numerical modeling of state-of-the-art SiC/SiC composites where the primary load-bearing constituents are stoichiometric SiC fibers in a complex multiphase SiC matrix produced by chemical vapor infiltration and melt infiltration. Recent studies have resulted in computer-based numerical models for the elastic modulus, thermal expansion, and thermal conductivity properties of the SiC/SiC system. Additional studies have generated analytical and empirical models for the time dependence of composite rupture strength at temperatures above 2200 F (1200 C), where CMC's have an important thermostructural advantage over current nickel-based superalloys. These life models utilize thermal activation theory and fiber stress-rupture results measured at Glenn to generate Larson-Miller (L M) plots of fiber rupture strength versus q, a single time- and temperature-dependent parameter. Assuming a worse case in which the SiC matrix is cracked, rupture is then controlled by the time-dependent fracture characteristics of the fiber bundles bridging the matrix cracks. With this as the controlling mechanism, one can then use simple composite theory and the fiber L M plots to predict CMC rupture strength versus the q parameter. The dashed line shows the predicted rupture strength of a SiC/SiC composite that is reinforced by a state-of-the-art stoichiometric SiC fiber. For the q parameter, time is in hours and temperature in degrees kelvin. To generate these predictions, a two-dimensional 0 /90 composite with approximately 16 percent fiber in the applied stress direction and an air test environment were assumed. As such, it is possible to compare the model predictions against limited stress-rupture data for this CMC as shown by the data points. The good agreement confirms the rupture model at least for the selected CMC and test conditions. Thus for this particular SiC/SiC composite, one can estimate a 1000-hr rupture strength of approximately 12 ksi at 2400 F (T = 1588 K and q = 39 700 K). At lower CMC application stresses, the SiC matrix is typically uncracked, so both the fiber and matrix constituents share the composite load. In this case, CMC rupture is controlled by the constituent with the longest rupture time based on the creep rate of the composite. Measured Monkman-Grant plots of rupture time versus creep rate for the two SiC constituents have been used to develop CMC life models for this important application condition. NASA and DOD are currently using this information to establish application and material goals for more advanced CMC's that can be used at even higher temperatures.

DiCarlo, James A.↗

On the use of the consistent mass matrix in flexible multibody systems

Two different methods are used in finite element structural analysis to define element mass distribution: consistent and lumped mass approximations. The lumped mass method is currently favored in multibody dynamics software packages because of its computational efficiency. This paper, however, presents a multibody dynamics formulation based on the consistent mass approach which should prove to be as computationally efficient as the lumped mass approach. It is shown that when component flexibility is modelled using modal coordinates, the equations of motion, as formulated by these two methods, are very similar in appearance, thereby facilitating their comparison. It is also shown, through simulation of a simple multibody system, that a system formulated with the lumped mass approximation will often require more finite elements and smaller integration step sizes than the corresponding consistent mass system.

Anthony, Tobin C.↗

Advances in dual algorithms and convex approximation methods

A new algorithm for solving the duals of separable convex optimization problems is presented. The algorithm is based on an active set strategy in conjunction with a variable metric method. This first order algorithm is more reliable than Newton's method used in DUAL-2 because it does not break down when the Hessian matrix becomes singular or nearly singular. A perturbation technique is introduced in order to remove the nondifferentiability of the dual function which arises when linear constraints are present in the approximate problem.

Smaoui, H.↗

Heating distribution comparison between asymmetric and symmetric blunt cones

An experiment was performed to compare the heating distribution between symmetric and asymmetric large-angle blunt cones, with cone angles of 100, 120, and 140 deg. These hot-wall data were obtained from models made from typical thermal protection insulation for proposed aeroassisted orbital transfer vehicles. Experimental data are compared with predictions using a boundary-layer integral matrix procedure with kinetics to determine how well the heating distribution over an asymmetric cone could be approximated using axisymmetric solutions for a cone and spherical segment. In addition, a relationship between the stagnation-point heat-transfer rate and the bow-shock standoff distance for these cones is discussed. The heat-distribution data from the symmetric and asymmetric cones were very similar. Numerical results compared well with the measured wall temperatures at the stagnation point but slightly underpredicted them over the conical portion of the models.

Stewart, D. A.↗

1200 to 1400 K slow strain rate compressive behavior of small grain size NiAl/Ni2AlTi alloys and NiAl/Ni2AlTi-TiB2 composites

In order to impart ductility into NiAl-Ni2AlTi alloys, small grain size single (Ni-45Al-5Ti) and two (Ni-40Al-10Ti) phase intermetallics are fabricated by a process which yields fine microstructures in NiAl. The results of a study of elevated temperature compressive properties of two small grain size NiAl-Ni2AlTi alloys are then described. In addition, the behavior of the Ti-modified nickel aluminides with 20 vol pct TiB2 particles of approximately 1 micron in diameter is also investigated, since these compositions have the potential for being the matrix material in high temperature particulate-strengthened composites.

Whittenberger, J. Daniel↗

An efficient solution technique for shockwave-boundary layer interactions with flow separation and slot suction effects

An efficient method for computing two-dimensional compressible Navier-Stokes flow fields is presented. The solution algorithm is a fully-implicit approximate factorization technique based on an unsymmetric line Gauss-Seidel splitting of the equation system Jacobian matrix. Convergence characteristics are improved by the addition of acceleration techniques based on Shamanskii's method for nonlinear equations and Broyden's quasi-Newton update. Characteristic-based differencing of the equations is provided by means of Van Leer's flux vector splitting. In this investigation, emphasis is placed on the fast and accurate computation of shock-wave-boundary layer interactions with and without slot suction effects. In the latter context, a set of numerical boundary conditions for simulating the transpiration flow in an open slot is devised. Both laminar and turbulent cases are considered, with turbulent closure provided by a modified Cebeci-Smith algebraic model. Comparisons with computational and experimental data sets are presented for a variety of interactions, and a fully-coupled simulation of a plenum chamber/inlet flowfield with shock interaction and suction is also shown and discussed.

Edwards, Jack R.↗

Investigation of a geodesy coexperiment to the Gravity Probe B relativity gyroscope program

Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus. Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is miniscule, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques. The GP-B system offers two main possibilities for geodesy. One is as a drag-free satellite to be used in trajectory-based estimates of the Earth's gravity field. We described calculations involving that approach in our previous reports, including comparison of laser only, GPS only, and combined tracking and a preliminary estimate of the possibility of estimating relativistic effects on the orbit. The second possibility is gradiometry. This technique has received a more cursory examination in previous reports, so we concentrate on it here. We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data. The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainty of all coefficients between degrees 5 and 50 is reduced by factors of up to 30 over current satellite-only estimates and up to 7 over estimates which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive.

Everitt, C. W. F.↗

Heterogeneous plagioclase compositions in the Maralinga CK4 chondrite

One of the characteristic features of CK chondrites is the wide compositional range displayed by feldspar grains in matrix relative to the narrow range of compositions exhibited by the highly equilibrated olivines and pyroxenes. Recently, it was suggested that these heterogeneous feldspar compositions may have been strongly influenced by shock metamorphisms. It is shown that the apparent range of feldspar compositions in Maralinga probably results from annealing during parent body thermal metamorphism rather than shock. The majority of matrix feldspars in Maralinga are typically 50 microns in size and are compositionally zoned, with oligoclase cores (approximately An40) and bytownite rims (approximately An80). The contact between core and rim is sharp and abrupt and is readily observed in backscattered scanning electron microscopy (SEM) images.

Keller, Lindsay P.↗

Melt rock components in KREEPy breccia 15205: Petrography and mineral chemistry of KREEP basalts and quartz-normative mare basalts

Many current models for the origin of lunar highland rocks feature as an essential component the assimilation of KREEPy material by primitive magmas parental to the Mg-rich suite and alkali suite plutonic rocks. Similar models have also been proposed for the origin of various mare basalt suites. However, any model which considers assimilation of KREEP an important petrologic process must sooner-or-later deal with the question: what is KREEP? Because pristine KREEP basalts are rare, and most known samples are small (e.g., 15382/15386), the geochemical variability of KREEP basalts is poorly known. Other KREEP compositions which are commonly used in these models include the hypothetical 'high-K KREEP' component of Warren and Wasson, which is derived from Apollo 14 soil data, and the 'superKREEP' quartz-monzodiorite 15405. Lunar breccia 15205 is a polymict regolith breccia that consists of approximately 20% KREEP basalt clasts and 20% quartz-normative basalt clasts in a KREEP-rich matrix. Bulk rock mixing calculations show that this sample comprises about 84% KREEP. The clasts range up to 1 cm in size, but most are considerably smaller. The primary aim is to characterize pristine KREEP basalts petrographically, to establish the range in chemical compositions of KREEP basalts, and to test models that were proposed for their origin. In addition, we may be able to extend the compositional range recognized in the quartz-normative basalt suite and cast some light on its origin as well. Preliminary whole rock geochemical data on the KREEP basalts are presented in a companion paper by M.M. Lindstrom and co-workers. Concentration is on petrography and mineral chemistry of these clasts, and the implications these data have for the origin of the different melt rock suites.

Shervais, John W.↗

Observation of Intralaminar Cracking in the Edge Crack Torsion Specimen

The edge crack torsion (ECT) test is evaluated to determine its suitability for measuring fracture toughness associated with mode III delamination growth onset. A series of ECT specimens with preimplanted inserts with different lengths is tested and examined using nondestructive and destructive techniques. Ultrasonic inspection of all tested specimens reveals that delamination growth occurs at one interface ply beneath the intended midplane interface. Sectioning and optical microscopy suggest that the observed delamination growth results from coalescence of angled intralaminar matrix cracks that form and extend across the midplane plies. The relative orientation of these cracks is approximately 45 deg with respect to the midplane, suggesting their formation is caused by resolved principal tensile stresses arising due to the global mode-III shear loading. Examination of ECT specimens tested to loads below the level corresponding to delamination growth onset reveals that initiation of intralaminar cracking approximately coincides with the onset of nonlinearity in the specimen's force-displacement response. The existence of intralaminar cracking prior to delamination growth onset and the resulting delamination extension at an unintended interface render the ECT test, in its current form, unsuitable for characterization of mode III delamination growth onset. The broader implications of the mechanisms observed in this study are also discussed with respect to the current understanding of shear-driven delamination in tape-laminate composites.

Czabaj, Michael W.↗