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At least 379 records · Page 21

Fiber shape effects on metal matrix composite behavior

The effects of different fiber shapes on the behavior of metal matrix composites is computationally simulated. A three-dimensional finite element model consisting of a group of nine unidirectional fibers in a three by three unit cell array of a SiC/Ti-15-3 metal matrix composite is used in the analysis. The model is employed to represent five fiber shapes that include a circle, an ellipse, a kidney, and two different cross shapes. The distribution of stresses and the composite material properties, such as moduli, coefficients of thermal expansion, and Poisson's ratios, are obtained from the finite element analysis using the various fiber shapes. Comparisons of these results are used to determine the sensitivity of the composite behavior to the different fiber shapes. In general, fiber dominated properties are not affected by fiber geometry and matrix dominated properties are only moderately affected.

Brown, H. C.↗

Summation by parts, projections, and stability

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Olsson, Pelle↗

Prebuckling and Postbuckling Response of Tailored Composite Stiffened Panels with Axial-Shear Coupling

Results of a numerical parametric study of the prebuckling and postbuckling response of tailored composite stiffened panels with axial-shear coupling are presented. In the stiffened panels, axial-shear stiffness coupling is created by rotating the stiffener orientation and tailoring the skin laminate anisotropy. The panels are loaded in axial compression and the effects of stiffener orientation and skin anisotropy on the panel stiffness, buckling parameters, and axial-shear coupling response are described. Results are obtained from a nonlinear general shell finite element analysis computer code. The prebuckling and postbuckling responses can be affected by both the stiffener orientation and skin laminate anisotropy, and the effects are different and load dependent. The results help identify different mechanisms for axial-shear coupling, and show that a load-dependent structural response can be controlled by selecting appropriate stiffener and skin parameters.

Young, Richard D.↗

Vlasov simulations of electron-ion collision effects on damping of electron plasma waves

Collisional effects can play an essential role in the dynamics of plasma waves by setting a minimum damping rate and by interfering with wave-particle resonances. Kinetic simulations of the effects of electron-ion pitch angle scattering on Electron Plasma Waves (EPWs) are presented here. In particular, the effects of such collisions on the frequency and damping of small-amplitude EPWs for a range of collision rates and wave phase velocities are computed and compared with theory. Both the Vlasov simulations and linear kinetic theory find the direct contribution of electron-ion collisions to wave damping significantly reduced from that obtained through linearized fluid theory. To our knowledge, this simple result has not been published before. Simulations have been carried out using a grid-based (Vlasov) approach, based on a high-order conservative finite difference method for discretizing the Fokker-Planck equation describing the evolution of the electron distribution function. Details of the implementation of the collision operator within this framework are presented. Such a grid-based approach, which is not subject to numerical noise, is of particular interest for the accurate measurements of the wave damping rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Language Model Combination and Adaptation Using Weighted Finite State Transducers

In speech recognition systems language model (LMs) are often constructed by training and combining multiple n-gram models. They can be either used to represent different genres or tasks found in diverse text sources, or capture stochastic properties of different linguistic symbol sequences, for example, syllables and words. Unsupervised LM adaption may also be used to further improve robustness to varying styles or tasks. When using these techniques, extensive software changes are often required. In this paper an alternative and more general approach based on weighted finite state transducers (WFSTs) is investigated for LM combination and adaptation. As it is entirely based on well-defined WFST operations, minimum change to decoding tools is needed. A wide range of LM combination configurations can be flexibly supported. An efficient on-the-fly WFST decoding algorithm is also proposed. Significant error rate gains of 7.3% relative were obtained on a state-of-the-art broadcast audio recognition task using a history dependently adapted multi-level LM modelling both syllable and word sequences

Liu, X.↗

Free-field propagation of high intensity noise

Research on high intensity (finite amplitude) acoustic waves shows that nonlinear distortion effects generally result in a shift of energy to higher frequencies. The higher intensities associated with supersonic jets would therefore indicate that high frequency enhancement of the spectrum should occur, resulting in the differences observed between subsonic and supersonic jets. A 10,000 acoustic watt source installed in an anechoic chamber generates sound levels such that acoustic shocks are readily observable. Dual frequency excitation of the source produces a strong parametric effect with a difference frequency comparable in level to the primary frequency. The test set up and recording equipment being used to determine the finite amplitude noise representative of an actual supersonic jet are described as well as the development of a computer program based on Burger's equation. The spectra of 1/2 octave band, 1 kHz sine wave, and dual frequency input and output are presented in graphs along with waveforms at Z = .025, 0.1, and 1.0.

Mcdaniel, O. H.↗

Component-adaptive grid embedding

One of the major problems related to transonic flow prediction about realistic aircraft configuration is the generation of a suitable grid which encompasses such configurations. In general, each aircraft component (wing, fuselage, nacelle) requires a grid system that is usually incompatible with the grid systems of the other components; thus, the implementation of finite-difference methods for such geometrically-complex configurations is a difficult task. An approach was developed to treat such a problem. The basic idea is to generate different grid systems, each suited for a particular component. Thus, the flow field domain is divided into overlapping subdomains of different topology. These grid systems are then interfaced with each other in such a way that stability, convergence speed and accuracy are maintained.

Atta, E. H.↗

Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers

Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used.

Wong, Yau Shu↗

Finite-element-analysis model and preliminary ground testing of controls-structures interaction evolutionary model reflector

Results of two different nonlinear finite element analyses and preliminary test results for the final design of the Controls-Structures Interaction Evolutionary Model are presented. Load-deflection data bases are generalized from analysis and testing of the 16-foot diameter, dish shaped reflector. Natural frequencies and mode shapes are obtained from vibrational analysis. Experimental and analytical results show similar trends; however, future test hardware modifications and finite element model refinement would be necessary to obtain better correlation. The two nonlinear analysis procedures are both adequate techniques for the analysis of prestressed structures with complex geometries.

Reaves, Mercedes C.↗

Aeroelasticity of wing and wing-body configurations on parallel computers

The objective of this research is to develop computationally efficient methods for solving aeroelasticity problems on parallel computers. Both uncoupled and coupled methods are studied in this research. For the uncoupled approach, the conventional U-g method is used to determine the flutter boundary. The generalized aerodynamic forces required are obtained by the pulse transfer-function analysis method. For the coupled approach, the fluid-structure interaction is obtained by directly coupling finite difference Euler/Navier-Stokes equations for fluids and finite element dynamics equations for structures. This capability will significantly impact many aerospace projects of national importance such as Advanced Subsonic Civil Transport (ASCT), where the structural stability margin becomes very critical at the transonic region. This research effort will have direct impact on the High Performance Computing and Communication (HPCC) Program of NASA in the area of parallel computing.

Byun, Chansup↗

Stereo Imaging Velocimetry of Mixing Driven by Buoyancy Induced Flow Fields

Mixing of two fluids generated by steady and particularly g-jitter acceleration is fundamental towards the understanding of transport phenomena in a microgravity environment. We propose to carry out flight and ground-based experiments to quantify flow fields due to g-jitter type of accelerations using Stereo Imaging Velocimetry (SIV), and measure the concentration field using laser fluorescence. The understanding of the effects of g-jitter on transport phenomena is of great practical interest to the microgravity community and impacts the design of experiments for the Space Shuttle as well as the International Space Station. The aim of our proposed research is to provide quantitative data to the community on the effects of g-jitter on flow fields due to mixing induced by buoyancy forces. The fundamental phenomenon of mixing occurs in a broad range of materials processing encompassing the growth of opto-electronic materials and semiconductors, (by directional freezing and physical vapor transport), to solution and protein crystal growth. In materials processing of these systems, crystal homogeneity, which is affected by the solutal field distribution, is one of the major issues. The understanding of fluid mixing driven by buoyancy forces, besides its importance as a topic in fundamental science, can contribute towards the understanding of how solutal fields behave under various body forces. The body forces of interest are steady acceleration and g-jitter acceleration as in a Space Shuttle environment or the International Space Station. Since control of the body force is important, the flight experiment will be carried out on a tunable microgravity vibration isolation mount, which will permit us to precisely input the desired forcing function to simulate a range of body forces. To that end, we propose to design a flight experiment that can only be carried out under microgravity conditions to fully exploit the effects of various body forces on fluid mixing. Recent flight experiments, by the P.I. through collaboration with the Canadian Space Agency (STS-85, August 1997), aimed at determining the stability of the interface between two miscible liquids inside an enclosure show that a long liquid column (5 cm) under microgravity isolation conditions can be stable, i.e. the interface remains sharp and vertical over a short time scale; thus transport occurs by molecular mass diffusion. On the other hand, when the two liquids were excited from a controlled vibration source (Microgravity Vibration Isolation Mount) two to four mode large amplitude quasi-stationary waves were observed. The data was limited to CCD recording of the dynamics of the interface between the two fluids. We propose to carry out flight experiments to quantify the dynamics of the flow field using Stereo Imaging Velocimetry and measure the concentration field using laser fluorescence. The results will serve as a basis to understand effects of g-jitter on transport phenomena, in this case mass diffusion. As the measurement of the kinematics of the flow field will shed light on the instability mechanism. The research will allow measurement of the flow field in microgravity environment to prove two hypotheses: (1) Maxwell's hypothesis: finite convection always exists in diffusing systems, and (2) Quasi-stationary waves inside a bounded enclosure in a microgravity environment is generated by Kelvin-Helmholtz instability; resonance of the interface which produces incipient mixing is due to Rayleigh-Taylor instability. The first hypothesis can be used as a benchmark experiment to illustrate diffusive mixing. The second hypothesis will lead to the understanding of g-jitter effects on buoyancy driven flow fields which occur in many situations involving materials processing, and other basic fluid physics phenomena. In addition, the second hypothesis will also provide insight in how Rayleigh-Taylor and Kelvin-Helmholtz instabilities propagate concentration fronts during mixing. Measurement of the flow field using SIV is important because it is the flow field which causes instability at the interface between the two fluids. Mixing driven by buoyancy induced flow fields will be addressed both experimentally and computationally. The experimental effort will address the kinematics of mixing: stretching, transport and chaos. Quantification of the mechanisms of mixing will consists of measuring the flow field using the SIV system at Glenn and capturing the dynamics of the interface, to measure mass transport, using a CCD camera. These experiments will be carried out within the framework of Earth's gravity and g-jitter microgravity acceleration as in a Space Shuttle environment or the International Space Station. The g-jitter will be induced and controlled using a tunable vibration isolation platform to isolate against vibration as well as input periodic and random vibration to the system. The parametric range of the microgravity experiment will be extended from the experiments on STS-85 to investigate higher mode quasi-stationary waves (8 to 12), as well as resonance regions which leads to chaos and turbulence. Ground-based experiments will focus on effects of vibration on stably stratified fluid layers in order to scale for possible scenarios in a microgravity environment. These vibrations will be subjected perpendicular to the concentration field on the ground since the parallel case can only be carried out in a microgravity environment. The concept of dynamical similarity will be applied to tune the experiments as closely as possible to a Space Shuttle environment or the International Space Station. The computational effort will take advantage of the Computational Laboratory at Glenn to corroborate the experimental findings with predictions of the dynamics of the flow field using the codes FLUENT (finite difference based) and FIDAP (finite element based). We will investigate two important cases, single-fluid model to address dilute systems with negligible jump in viscosity and the more general two-fluid model which accounts for finite jump in viscosity. Apart from its microgravity relevance, this experiment is well suited to study dynamics in nonlinear systems.

Duval, W. M. B.↗

Technique for Calculating Solution Derivatives With Respect to Geometry Parameters in a CFD Code

A solution has been developed to the challenges of computation of derivatives with respect to geometry, which is not straightforward because these are not typically direct inputs to the computational fluid dynamics (CFD) solver. To overcome these issues, a procedure has been devised that can be used without having access to the mesh generator, while still being applicable to all types of meshes. The basic approach is inspired by the mesh motion algorithms used to deform the interior mesh nodes in a smooth manner when the surface nodes, for example, are in a fluid structure interaction problem. The general idea is to model the mesh edges and nodes as constituting a spring-mass system. Changes to boundary node locations are propagated to interior nodes by allowing them to assume their new equilibrium positions, for instance, one where the forces on each node are in balance. The main advantage of the technique is that it is independent of the volumetric mesh generator, and can be applied to structured, unstructured, single- and multi-block meshes. It essentially reduces the problem down to defining the surface mesh node derivatives with respect to the geometry parameters of interest. For analytical geometries, this is quite straightforward. In the more general case, one would need to be able to interrogate the underlying parametric CAD (computer aided design) model and to evaluate the derivatives either analytically, or by a finite difference technique. Because the technique is based on a partial differential equation (PDE), it is applicable not only to forward mode problems (where derivatives of all the output quantities are computed with respect to a single input), but it could also be extended to the adjoint problem, either by using an analytical adjoint of the PDE or a discrete analog.

Mathur, Sanjay↗

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗

Numerical similarity solution for a variable coefficient K(m, n) equation

A technique for finding numerical similarity solutions to an initial boundary value problem (IBVP) for generalized K(m, n) equations is described. The equation under consideration is nonlinear and has variable coefficients. The original problem is transformed with the aid of Lie symmetries to an initial value problem (IVP) for a nonlinear third-order ordinary differential equation. The existence and uniqueness of the solution are examined, and the problem is consequently solved with the aid of a finite-difference scheme for various values of the governing parameters. In lieu of an exact symbolic solution, the scheme is validated by comparing the numerical solutions with the approximate analytic solutions obtained with the aid of the method of successive approximations in their region of validity. The accuracy, efficiency, and consistency of the scheme are demonstrated. Numerical solutions to the original initial boundary value problem are constructed for selected parameter values with the aid of the transforms. The qualitative behavior of the solutions as a function of the governing parameters is analyzed, and it is found that the examined IBVPs for generalized K(m, n) equations with variable coefficients that are functions of time, do not admit solitary wave or compacton solutions.

97 MATHEMATICS AND COMPUTING↗

High Order Difference Method for Low Mach Number Aeroacoustics

A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved analytically using separation of variables.

Mueller, B.↗

On the nonlinear interfacial instability of rotating core-annular flow

The interfacial stability of rotating core-annular flows is investigated. The linear and nonlinear effects are considered for the case when the annular region is very thin. Both asymptotic and numerical methods are used to solve the flow in the core and film regions which are coupled by a difference in viscosity and density. The long-term behavior of the fluid-fluid interface is determined by deriving its nonlinear evolution in the form of a modified Kuramoto-Sivashinsky equation. We obtain a generalization of this equation to three dimensions. The flows considered are applicable to a wide array of physical problems where liquid films are used to lubricate higher or lower viscosity core fluids, for which a concentric arrangement is desired. Linearized solutions show that the effects of density and viscosity stratification are crucial to the stability of the interface. Rotation generally destabilizes non-axisymmetric disturbances to the interface, whereas the centripetal forces tend to stabilize flows in which the film contains the heavier fluid. Nonlinear affects allow finite amplitude helically travelling waves to exist when the fluids have different viscosities.

Coward, Aidrian V.↗

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, we derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.

54 ENVIRONMENTAL SCIENCES↗