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NASA NTRS1987

Infrared properties of an anisotropically stirred fluid

A renormalization group is developed for the Navier-Stokes equations driven by an anisotropically correlated random stirring force. The stirring force generates homogeneous turbulence with a preferred direction. The force correlation is the sum of a small anisotropic perturbation and an isotropic correlation chosen, so that the fixed point of renormalization group has a k exp -5/3 energy spectrum. Fixed points for the anisotropic correlation are found near this isotropic fixed point. Two types of anisotropy are analyzed. when the additional stirring is in the plane perpendicular to the preferred direction, the renormalized viscosity is increased. When it is aligned with the preferred direction, the viscosity is decreased. A possible connection with the inverse energy cascade of two-dimensional turbulence is discussed.

Rubinstein, Robert↗

NASA NTRS1988

A hybrid-stress finite element for linear anisotropic elasticity

Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.

Fly, Gerald W.↗

NASA NTRS1991

Anisotropic elliptic optical fibers

The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

Kang, Soon Ahm↗

NASA NTRS1992

Mechanics of anisotropic plates and shells - A new look at an old subject

A number of aspects of the mechanics of anisotropic plates and shells are discussed. The topics covered include computational models of anisotropic plates and shells, consequences of anisotropy on deformation couplings, symmetry types, stress concentrations and edge effects, and importance of transverse shear deformation; recent applications and recent advances in the modeling and analysis of anisotropic plates and shells; and new research directions.

Noor, A. K.↗

NASA NTRS1992

Polarimetric emission from anisotropic media for passive remote sensing of sea ice

The polarimetric emission from an anisotropic medium with applications to the passive microwave remote sensing of sea ice is investigated. Based on the fluctuation-dissipation theory, the Stokes vector is obtained for the thermally exicted electromagnetic radiation from an anisotropic object. By modeling sea ice as a layered anisotropic medium, the Stokes vector representing the polarimetric emission is illustrated for various geophysical conditions. It is found that the difference in the brightness temperatures measured at two surface temperatures is correlated with the thickness of the sea ice. For cases where the c-axis of sea ice is aligned or not random in the horizontal plane, the calculated brightness temperatures show a periodic variation when plotted as a function of the azimuthal angle of the observation direction, indicating that the polarimetric Stokes parameters can be used to detect the direction of c-axes in sea ice.

Yueh, S. H.↗

NASA NTRS1994

Method of determining load in anisotropic non-crystalline materials using energy flux deviation

An ultrasonic wave is applied to an anisotropic sample material in an initial direction and the intensity of the ultrasonic wave is measured on an opposite surface of the sample material by two adjacent receiving points located in an array of receiving points. A ratio is determined between the measured intensities of two adjacent receiving points, the ratio being indicative of an angle of flux deviation from the initial direction caused by an unknown applied load. This determined ratio is then compared to a plurality of ratios of a similarly tested, similar anisotropic reference material under a plurality of respective, known load conditions, whereby the load applied to the particular anisotropic sample material is determined. A related method is disclosed for determining the fiber orientation from known loads and a determined flux shift.

Prosser, William H.↗

NASA NTRS1995

Emission line signatures of anisotropic turbulence in accretion disks

We investigate observable effects of anisotropic turbulence on the velocity profiles and eclipse behavior of emission lines from accretion disks. Turbulence expands the local line broadening profile, enhancing the surface brightness of saturated emission lines. Anisotropic turbulence produces anisotropic emission in such lines. The effects become observable when the turbulence exceeds the thermal velocity. Each term in the velocity-velocity correlation matrix produces a distinctive azimuthal pattern of enhanced emission-line surface brightness on the face of the accretion disk. These patterns express themselves as changes in the observable shapes of the disk's emission lines. The best place to look for turbulence effects is in saturated emission lines of heavy elements such as Ca, Mg, and Fe, which have a smaller thermal velocity at a given sound speed and at moderate inclination (60-70 degrees), since the Keplerian shear broadening dominates at higher inclinations.

Horne, Keith↗

NASA NTRS1994

Extension of the quasistatic far-wing line shape theory to multicomponent anisotropic potentials

The formalism developed previously for the calculation of the far-wing line shape function and the corresponding absorption coefficient using a single-component anisotropic interaction term and the binary collision and quasistatic approximations is generalized to multicomponent anisotropic potential functions. Explicit expressions are presented for several common cases, including the long-range dipole-dipole plus dipole-quadrupole interaction and a linear molecule interacting with a perturber atom. After determining the multicomponent functional representation for the interaction between the CO2 and Ar from previously published data, we calculate the theoretical line shape function and the corresponding absorption due to the nu(sub 3) band of CO2 in the frequency range 2400-2580 cm(exp -1) and compare our results with previous calculations carried out using a single-component anisotropic interaction, and with the results obtained assuming Lorentzian line shapes. The principal uncertainties in the present results, possible refinements of the theoretical formalism, and the applicability to other systems are discussed briefly.

Ma, Q.↗

NASA NTRS1995

Anisotropic microturbulence near the Sun

Interplanetary scintillation observations which sample the spatial spectrum of electron density at scales between 10 and 100 km show power-law spectra which are flatter than the Kolmogorov spectra observed at larger scales by spacecraft and also, indirectly, by phase scintillation of coherent radio signals. Furthermore, angular broadening observations of compact radio sources have shown that the microscale density fluctuations are field-aligned and become more anisotropic as R decreases inside 10 solar radius. We present angular broadening observations taken in October of 1992 which were recorded nearly simultaneously on the VLA and VLBA arrays. The VLA samples structure at scales between 3 and 30 km, whereas the VLBA samples scales between 200 and 4000 km. The small scale VLA measurements of the south polar source 1246-075 showed lower turbulence than those of the equatorial source 1256-057, consistent with previous work showing that the density delta N(exp 2)(sub e) is a factor of 10-15 lower in coronal holes. The VLA observations inside of 10 solar radius were anisotropic, as expected. We were not able to measure the equatorial source with the VLBA inside of 10 solar radius because the scattering was too strong, however we did observe the polar source just inside this distance with both the VLA and the VLBA. Significant anisotropy was seen on the smaller scales, but the larger scales were essentially isotropic. This suggests that the process responsible for the anisotropic microturbulence is distinct from the larger scale isotropic turbulence.

Coles, William A.↗

NASA NTRS1999

Predicting Buoyant Shear Flows Using Anisotropic Dissipation Rate Models

This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated-, the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered: one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of' the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows. pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.

So, R. M. C.↗

NASA NTRS2000

Anisotropic Nanomechanics of Boron Nitride Nanotubes: Nanostructured "Skin" Effect

The stiffness and plasticity of boron nitride nanotubes are investigated using generalized tight-binding molecular dynamics and ab-initio total energy methods. Due to boron-nitride BN bond buckling effects, compressed zigzag BN nanotubes are found to undergo novel anisotropic strain release followed by anisotropic plastic buckling. The strain is preferentially released towards N atoms in the rotated BN bonds. The tubes buckle anisotropically towards only one end when uniaxially compressed from both. A "skin-effect" model of smart nanocomposite materials is proposed which will localize the structural damage towards the 'skin' or surface side of the material.

Srivastava, Deepak↗

NASA NTRS2004

Subsurface Stress Fields in FCC Single Crystal Anisotropic Contacts

Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and non-crystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis (FEA). Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single crystal contact problems require extremely refined three-dimensional (3-D) finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses (RSS) on the principal slip planes also involves considerable post-processing work. For these reasons it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

Arakere, Nagaraj K.↗

NASA NTRS2005

The features of self-assembling organic bilayers important to the formation of anisotropic inorganic materials in microgravity conditions

Materials with directional properties are opening new horizons in a variety of applications including chemistry, electronics, and optics. Structural, optical, and electrical properties can be greatly augmented by the fabrication of composite materials with anisotropic microstructures or with anisotropic particles uniformly dispersed in an isotropic matrix. Examples include structural composites, magnetic and optical recording media, photographic film, certain metal and ceramic alloys, and display technologies including flat panel displays. The new applications and the need for model particles in scientific investigations are rapidly out-distancing the ability to synthesize anisotropic particles with specific chemistries and narrowly distributed physical characteristics (e.g. size distribution, shape, and aspect ratio).

Talham, Daniel R.↗

NASA NTRS2010

Active Damping Using Distributed Anisotropic Actuators

A helicopter structure experiences substantial high-frequency mechanical excitation from powertrain components such as gearboxes and drive shafts. The resulting structure-borne vibration excites the windows which then radiate sound into the passenger cabin. In many cases the radiated sound power can be reduced by adding damping. This can be accomplished using passive or active approaches. Passive treatments such as constrained layer damping tend to reduce window transparency. Therefore this paper focuses on an active approach utilizing compact decentralized control units distributed around the perimeter of the window. Each control unit consists of a triangularly shaped piezoelectric actuator, a miniature accelerometer, and analog electronics. Earlier work has shown that this type of system can increase damping up to approximately 1 kHz. However at higher frequencies the mismatch between the distributed actuator and the point sensor caused control spillover. This paper describes new anisotropic actuators that can be used to improve the bandwidth of the control system. The anisotropic actuators are composed of piezoelectric material sandwiched between interdigitated electrodes, which enables the application of the electric field in a preferred in-plane direction. When shaped correctly the anisotropic actuators outperform traditional isotropic actuators by reducing the mismatch between the distributed actuator and point sensor at high frequencies. Testing performed on a Plexiglas panel, representative of a helicopter window, shows that the control units can increase damping at low frequencies. However high frequency performance was still limited due to the flexible boundary conditions present on the test structure.

Schiller, Noah H.↗

NASA NTRS2013

Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws

Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software

Nemeth, Noel↗

NASA NTRS2019

Adjoint-Based Anisotropic Mesh Adaptation for a Stabilized Finite-Element Flow Solver

An adjoint solver is implemented in the FUN3D stabilized finite-element flow solver. The adjoint solution is used to generate anisotropic, adapted meshes to control error in scalar out- put functionals, such as lift or drag coefficient. The inviscid and turbulent adjoints are verified with a finite-difference derivative approximation and can be used in design optimization in addition to mesh adaptation. The adjoint capability represents an extension of previous research using the FUN3D stabilized finite-element capability with metric-based mesh adaptation and interpolation-based error estimates to generate highly anisotropic adapted meshes for turbulent flows. In the present work, a metric-based approach is again utilized, where the adjoint and the primal solutions both contribute to the generation of a metric tensor field that is subsequently used to produce the required anisotropic mesh for each adaptation cycle. Adaptive results are then shown for an inviscid supersonic flow over a diamond airfoil, inviscid transonic flow over the ONERA M6 wing, and viscous laminar flow over the NACA 0012 airfoil, all using drag force as the output functional. Adjoint-based adaptation is compared with a multiscale solution-based approach that controls the L norm of Mach number interpolation error to demonstrate the effectiveness and effciency of the adjoint-based adaptive mesh technology.

Balan, Aravind↗

NASA NTRSDate not supplied

Verification of Viscous Goal-Based Anisotropic Mesh Adaptation

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics. A key ingredient for the broader acceptance of unstructured mesh adaptation is the verification of these implementations. Anisotropic metric construction methods are evaluated with analytically defined primal fields and the corresponding entropy variables as adjoint fields. This allows the comparison of different metric formulations and different implementations of the same formulation without the complications of a flow and adjoint solution method. The convergence of the output associated with the entropy variable adjoint is studied for mesh adaptation to these fields and a manufactured solution. Mesh adapted drag output is studied for two simple wings in compressible laminar flow to show fine-mesh convergence of multiple metric construction methods to less than a single drag count. The documentation of these verification exercises helps to prepare these goal-based methods for routine use in more complex simulations for production workflows.

mesh adaptation↗

DOE OSTI2020

CHARACTERIZATION ON ANISOTROPIC THERMAL CONDUCTIVITY FOR BIG AREA ADDITIVE MANUFACTURING WITH POLYMERS

Additive manufacturing with polymers has been used mainly for prototyping. A recent development of Big Area Additive Manufacturing (BAAM) at Oak Ridge National Laboratory has opened its applications in the mold and die industry. A numerical simulation and prediction for a mold heating performance requires accurate anisotropic thermal properties of the printed material, which are challenging to obtain, and often requires the use of multiple techniques. The transient plane source (TPS) technique has been widely used due to its ability to measure the thermal properties of an extensive range of materials (solids, liquids, powder). Despite the capability to characterize thermal conductivity k of isotropic and anisotropic materials, the measurements of latter materials are limited to the cases, where the samples have the same thermal conductivity k along x- and y-axis that form the radial plane. In this work, the method for a characterization of k in all three dimensions is developed, and the application of TPS is extended to the determination of thermal properties along the x-, y-, and z-axis individually. The materials are represented by additively manufactured polymers including polylactic acid (PLA) and styrene maleic anhydride (SMA). The developed method consists of (1) a determination of the heat capacity of the polymers by means of TPS in combination with the developed in this work data analysis procedure, (2) a machining three types of cylindrical samples from the same material, with the height corresponding either to x-, y-, or z-direction of printing, and (3) a determination of axial thermal conductivity employing anisotropic model and using previously determined heat capacity

Trofimov, Artem↗