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At least 109 records · Page 6

Numerical aspects of computing high Reynolds number flows on unstructured meshes

An edge-data structure describing a mesh edge-wise given the vertices of each edge and neighboring cell information is used developing algorithms for the Navier-Stokes equations on triangular meshes. Edge formulas for the Galerkin and finite-element discretization of gradient, divergence, Hessian, and Laplacian operators are derived. A simple edge formula is derived for the discretization of the Laplacian operator, where precise theoretical conditions for a discrete maximum principle can be ascertained. Practical issues associated with solving the Navier-Stokes equations on unstructured meshes are addressed, along with issues concerning the generation of highly stretched triangular meshes and the modeling of turbulence on unstructured meshes. A turbulence modeling strategy is proposed, and numerical results for a high-Reynolds-number flow about single- and multielement airfoils are discussed.

Barth, Timothy J.↗

Autonomous Guidance of Agile Small-scale Rotorcraft

This report describes a guidance system for agile vehicles based on a hybrid closed-loop model of the vehicle dynamics. The hybrid model represents the vehicle dynamics through a combination of linear-time-invariant control modes and pre-programmed, finite-duration maneuvers. This particular hybrid structure can be realized through a control system that combines trim controllers and a maneuvering control logic. The former enable precise trajectory tracking, and the latter enables trajectories at the edge of the vehicle capabilities. The closed-loop model is much simpler than the full vehicle equations of motion, yet it can capture a broad range of dynamic behaviors. It also supports a consistent link between the physical layer and the decision-making layer. The trajectory generation was formulated as an optimization problem using mixed-integer-linear-programming. The optimization is solved in a receding horizon fashion. Several techniques to improve the computational tractability were investigate. Simulation experiments using NASA Ames 'R-50 model show that this approach fully exploits the vehicle's agility.

Mettler, Bernard↗

Finite Element Models for Electron Beam Freeform Fabrication Process

Electron beam freeform fabrication (EBF3) is a member of an emerging class of direct manufacturing processes known as solid freeform fabrication (SFF); another member of the class is the laser deposition process. Successful application of the EBF3 process requires precise control of a number of process parameters such as the EB power, speed, and metal feed rate in order to ensure thermal management; good fusion between the substrate and the first layer and between successive layers; minimize part distortion and residual stresses; and control the microstructure of the finished product. This is the only effort thus far that has addressed computer simulation of the EBF3 process. The models developed in this effort can assist in reducing the number of trials in the laboratory or on the shop floor while making high-quality parts. With some modifications, their use can be further extended to the simulation of laser, TIG (tungsten inert gas), and other deposition processes. A solid mechanics-based finite element code, ABAQUS, was chosen as the primary engine in developing these models whereas a computational fluid dynamics (CFD) code, Fluent, was used in a support role. Several innovative concepts were developed, some of which are highlighted below. These concepts were implemented in a number of new computer models either in the form of stand-alone programs or as user subroutines for ABAQUS and Fluent codes. A database of thermo-physical, mechanical, fluid, and metallurgical properties of stainless steel 304 was developed. Computing models for Gaussian and raster modes of the electron beam heat input were developed. Also, new schemes were devised to account for the heat sink effect during the deposition process. These innovations, and others, lead to improved models for thermal management and prediction of transient/residual stresses and distortions. Two approaches for the prediction of microstructure were pursued. The first was an empirical approach involving the computation of thermal gradient, solidification rate, and velocity (G,R,V) coupled with the use of a solidification map that should be known a priori. The second approach relies completely on computer simulation. For this purpose a criterion for the prediction of morphology was proposed, which was combined with three alternative models for the prediction of microstructure; one based on solidification kinetics, the second on phase diagram, and the third on differential scanning calorimetry data. The last was found to be the simplest and the most versatile; it can be used with multicomponent alloys and rapid solidification without any additional difficulty. For the purpose of (limited) experimental validation, finite element models developed in this effort were applied to three different shapes made of stainless steel 304 material, designed expressly for this effort with an increasing level of complexity. These finite element models require large computation time, especially when applied to deposits with multiple adjacent beads and layers. This problem can be overcome, to some extent, by the use of fast, multi-core computers. Also, due to their numerical nature coupled with the fact that solid mechanics- based models are being used to represent the material behavior in liquid and vapor phases as well, the models have some inherent approximations that become more pronounced when dealing with multi-bead and multi-layer deposits.

Chandra, Umesh↗

Thermodynamically consistent constitutive equations for nonisothermal large strain, elasto-plastic, creep behavior

The paper is concerned with the development of constitutive relations for large nonisothermal elastic-viscoplastic deformations for metals. The kinematics of elastic-plastic deformation, valid for finite strains and rotations, is presented. The resulting elastic-plastic uncoupled equations for the deformation rate combined with use of the incremental elasticity law permits a precise and purely deductive development of elastic-viscoplastic theory. It is shown that a phenomenological thermodynamic theory in which the elastic deformation and the temperature are state variables, including few internal variables, can be utilized to construct elastic-viscoplastic constitutive equations, which are appropriate for metals. The limiting case of inviscid plasticity is examined.

Riff, R.↗

Structural Analysis and Testing of an Erectable Truss for Precision Segmented Reflector Application

This paper describes analysis and test results obtained at Langley Research Center (LaRC) on a doubly curved testbed support truss for precision reflector applications. Descriptions of test procedures and experimental results that expand upon previous investigations are presented. A brief description of the truss is given, and finite-element-analysis models are described. Static-load and vibration test procedures are discussed, and experimental results are shown to be repeatable and in generally good agreement with linear finite-element predictions. Truss structural performance (as determined by static deflection and vibration testing) is shown to be predictable and very close to linear. Vibration test results presented herein confirm that an anomalous mode observed during initial testing was due to the flexibility of the truss support system. Photogrammetric surveys with two 131-in. reference scales show that the root-mean-square (rms) truss-surface accuracy is about 0.0025 in. Photogrammetric measurements also indicate that the truss coefficient of thermal expansion (CTE) is in good agreement with that predicted by analysis. A detailed description of the photogrammetric procedures is included as an appendix.

Collins, Timothy J.↗

On the Natural Structure of Amino Acid Patterns in Families of Protein Sequences

All known terrestrial proteins are coded as continuous strings of ≈20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the natural architectures of protein families. We present a method to search for patterns and groupings of patterns in protein sequences using a mathematically precise definition for “repetition”, an efficient algorithmic implementation and a robust scoring system with no adjustable parameters. We show that the sequence patterns can be well-separated into disjoint classes according to their recurrence in nested structures. The statistics of the occurrences of patterns indicate that short repetitions are sufficient to account for the differences between natural families and randomized groups of sequences by more than 10 standard deviations, while contiguous sequence patterns shorter than 5 residues are effectively random in their occurrences. A small subset of patterns is sufficient to account for a robust ”familiarity” definition between arbitrary sets of sequences.

Pablo Turjanski↗

Transmission media effects on precise Doppler tracking

The effects of the transmission media - the earth's troposphere and ionosphere, and the solar wind - on precise Doppler tracking are discussed. The charged particle effects can be largely removed by dual frequency observations; however there are limitations to these corrections (besides system noise and/or finite integration times) including the effects of magnetic fields, diffraction, and differential refraction, all of which must be carefully evaluated. The earth's troposphere can contribute an error of delta f/f approximately 10 to the minus 14th power.

Callahan, P. S.↗

Pressure data for four analytically defined arrow wings in supersonic flow

In order to provide experimental data for comparison with newly developed finite difference methods for computing supersonic flows over aircraft configurations, wind tunnel tests were conducted on four arrow wing models. The models were machined under numeric control to precisely duplicate analytically defined shapes. They were heavily instrumented with pressure orifices at several cross sections ahead of and in the region where there is a gap between the body and the wing trailing edge. The test Mach numbers were 2.36, 2.96, and 4.63. Tabulated pressure data for the complete test series are presented along with selected oil flow photographs. Comparisons of some preliminary numerical results at zero angle of attack show good to excellent agreement with the experimental pressure distributions.

Townsend, J. C.↗

Computing Vibration-Mode Matrices From Finite-Element Output

Postprocessing algorithms devised to facilitate vibrational-mode analyses of dynamics of complicated structures. Yields inertia matrices and elastic/rigid-coupling matrices. Such analyses important in simulation and control in active suppression of vibrations in large building or in precise aiming of large antenna.

Levy, Roy↗

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Quarteroni, Alfio↗

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 2: Solutions and numerical results

This paper discusses an incremental-iterative nonlinear solution technique for solving the nonlinear finite element equations of the superconducting state of a superconductor. The untreated equations are highly ill-conditioned and are impossible to solve within the typical 16-place double precision supplied by most computers. A combination of matrix scaling and mesh grading techniques is used to reduce the condition number of the tangent stiffness matrix and increase the accuracy of the current carrying boundary layer representation. Numerical results for a one-dimensional model of a time-independent superconductor treated by the Ginzburg-Landau model are presented and discussed. The computed solutions clearly display the Meissner effect of magnetic field expulsion from the central region of the superconductor. These results are compared to the physics of a low-viscosity fluid problem. From this analogy, a physical argument is advanced about the macroscopic behavior of superconductors.

Schuler, James J.↗

Fused Bead Analysis of Diogenite Meteorites

Bulk rock chemistry is an essential dataset in meteoritics and planetary science [1]. A common method used to obtain the bulk chemistry of meteorites is ICP-MS. While the accuracy, precision and low detection limits of this process are advantageous [2], the sample size used for analysis (approx.70 mg) can be a problem in a field where small and finite samples are the norm. Fused bead analysis is another bulk rock analytical technique that has been used in meteoritics [3]. This technique involves forming a glass bead from ~10 mg of sample and measuring its chemistry using a defocused beam on a microprobe. Though the ICP-MS has lower detection limits than the microprobe, the fused bead method destroys a much smaller sample of the meteorite. Fused bead analysis was initially designed for samples with near-eutectic compositions and low viscosities. Melts generated of this type homogenize at relatively low temperatures and produce primary melts near the sample s bulk composition [3]. The application of fused bead analysis to samples with noneutectic melt compositions has not been validated. The purpose of this study is to test if fused bead analysis can accurately determine the bulk rock chemistry of non-eutectic melt composition meteorites. To determine this, we conduct two examinations of the fused bead. First, we compare ICP-MS and fused bead results of the same samples using statistical analysis. Secondly, we inspect the beads for the presence of crystals and chemical heterogeneity. The presence of either of these would indicate incomplete melting and quenching of the bead.

Mittlefehldt, D.W.↗

Coherent Mode Decomposition for Kolmogorov Optical Turbulence in a Finite Aperture

An analysis of the coherent mode decomposition of an optical field after propagation through atmospheric turbulence is presented. The coherent modes represent an ideal basis by which to decompose the field for design of mode-limited optical systems. Due to rotational symmetry of the Fredholm integral operator for Kolmogorov optical turbulence, the coherent modes exhibit separable solutions classified by a radial and azimuthal mode index. The study of the coherent modes is then reduced to that of the radial functions determined by the coherence ratio and obscuration ratio. Analysis of the spectrum of eigenvalues yields sharp bounds on the efficiency of receivers using incoherent or coherent combining with mode-limited photonic devices in the presence of Kolmogorov turbulence. The effective number of modes needed to represent Kolmogorov optical turbulence is studied via the von Neumann entropy, purity, and largest eigenvalue, and the differences in the different definitions is discussed. The similarity of the coherent modes to linearly polarized (LP) fiber modes is quantified yielding a precise characterization of the maximum gain that can be achieved in mode-limited systems via mode shaping techniques. As a final application, a mode sorting technique is presented for optimally splitting power from atmospherically degraded light into a finite number of modes simultaneously maximizing total coupling efficiency and minimizing the difference in average power between channels.

free-space optical communication↗

Coherent Mode Decomposition for Kolmogorov Optical Turbulence in a Finite Aperture

An analysis of the coherent mode decomposition of an optical field after propagation through atmospheric turbulence is presented. The coherent modes represent an ideal basis by which to decompose the field for design of mode-limited optical systems. Using the rotational symmetry of the Fredholm integral operator for Kolmogorov optical turbulence, it is shown that the coherent modes exhibit separable solutions classified by radial and azimuthal quantum numbers. The study of the coherent modes is then reduced that of the radial functions determined by the aperture-coherence diameter ratio and obscuration ratio. Analysis of the spectrum of eigenvalues yields sharp bounds on the efficiency of receivers using incoherent or coherent combining with mode-limited photonic devices in the presence of Kolmogorov turbulence. The effective number of modes needed to represent Kolmogorov optical turbulence is studied via the von Neumann entropy, purity, and largest eigenvalue, and the differences in the different definitions is discussed. The similarity of the coherent modes to linearly polarized (LP) fiber modes is quantified yielding a precise characterization of the maximum gain that can be achieved in mode-limited systems via mode shaping techniques. As a final application, a mode sorting technique is presented for optimally splitting power from atmospherically degraded light into a finite number of modes simultaneously maximizing total coupling efficiency and minimizing the average and instantaneous power ratio between channels.

free-space optical communication↗

The NANOGrav 12.5 yr Data Set: The Frequency Dependence of Pulse Jitter in Precision Millisecond Pulsars

Low-frequency gravitational-wave experiments require the highest timing precision from an array of the moststable millisecond pulsars. Several known sources of noise on short timescales in single radio pulsar observationsare well described by a simple model of three components: template fitting from a finite signal-to-noise ratio, pulsephase/amplitude jitter from single-pulse stochasticity, and scintillation errors from short-timescale interstellarscattering variations. Currently template-fitting errors dominate, but as radio telescopes push toward higher signalto-noise ratios, jitter becomes the next dominant term for most millisecond pulsars. Understanding the statistics ofjitter becomes crucial for properly characterizing arrival time uncertainties. We characterize the radio frequencydependence of jitter using data on 48 pulsars in the North American Nanohertz Observatory for GravitationalWaves timing program. We detect significant jitter in 43 of the pulsars and test several functional forms for itsfrequency dependence; we find significant frequency dependence for 30 pulsars. We find moderate correlations ofrms jitter with pulse width (R = 0.62) and number of profile components (R = 0.40); the single-pulse rms jitter istypically 1% of pulse phase. The average frequency dependence for all pulsars using a power-law model hasindex 0.42. We investigate the jitter variations for the interpulse of PSR B1937+21 and find no significantdeviations from the main pulse rms jitter. We also test the time variation of jitter in two pulsars and find thatsystematics likely bias the results for high-precision pulsars. Pulsar timing array analyses must properly modeljitter as a significant component of the noise within the detector.

Lam, M. T.↗

GPS time transfer with implementation of selective availability

The international community of time metrology is facing a major challenge with the Selective Availability (SA) degradation of GPS satellite signals. At present there are 6 Block 1 satellites and 8 Block 2 satellites operating. According to the policy of the U.S. Department of Defence the Block 1 satellite signals will not be degraded, but these satellites are old with a finite life. The Block 2 satellites, which have all been launched since 1988, were subject to Selective Availability from March 25, 1990. The effect of SA should be to limit precision to about 100 meters for navigation and 167 ns for timing. A study was conducted in order to understand the nature of the actual introduced degradation, and to elaborate the means of removing the effects of this degradation on time transfer. This study concerns the time extraction from GPS satellites at NIST, USNO and Paris Observatory, and the comparison of atomic clocks between these laboratories by common view approach. The results show that when using the data taken over several days the time extraction can be achieved with uncertainty of a few tens of nanoseconds, while strict common-view has removed entirely the effects of SA during the periods under study.

Allan, David W.↗

Interactive grid generation for turbomachinery flow field simulations

The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids for turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.

Choo, Yung K.↗

Interactive grid generation for turbomachinery flow field simulations

The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids of turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.

Choo, Yung K.↗