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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

HOTCFGM-1D: A Coupled Higher-Order Theory for Cylindrical Structural Components with Through-Thickness Functionally Graded Microstructures

The objective of this three-year project was to develop and deliver to NASA Lewis one-dimensional and two-dimensional higher-order theories, and related computer codes, for the analysis, optimization and design of cylindrical functionally graded materials/structural components for use in advanced aircraft engines (e.g., combustor linings, rotor disks, heat shields, blisk blades). To satisfy this objective, a quasi one-dimensional version of the higher-order theory, HOTCFGM-1D, and four computer codes based on this theory, for the analysis, design and optimization of cylindrical structural components functionally graded in the radial direction were developed. The theory is applicable to thin multi-phased composite shell/cylinders subjected to macroscopically axisymmetric thermomechanical and inertial loading applied uniformly along the axial direction such that the overall deformation is characterized by a constant average axial strain. The reinforcement phases are uniformly distributed in the axial and circumferential directions, and arbitrarily distributed in the radial direction, thereby allowing functional grading of the internal reinforcement in this direction.

Pindera, Marek-Jerzy↗
NASA NTRS1961

A Nonlinear Theory for Predicting the Effects of Unsteady Laminar, Turbulent, or Transitional Boundary Layers on the Attenuation of Shock Waves in a Shock Tube with Experimental Comparison

The linearized attenuation theory of NACA Technical Note 3375 is modified in the following manner: (a) an unsteady compressible local skin-friction coefficient is employed rather than the equivalent steady-flow incompressible coefficient; (b) a nonlinear approach is used to permit application of the theory to large attenuations; and (c) transition effects are considered. Curves are presented for predicting attenuation for a shock pressure ratio up to 20 and a range of shock-tube Reynolds numbers. Comparison of theory and experimental data for shock-wave strengths between 1.5 and 10 over a wide range of Reynolds numbers shows good agreement with the nonlinear theory evaluated for a transition Reynolds number of 2.5 X 10(exp 5).

Trimpi, Robert L.↗
NASA NTRS1998

A {3,2}-Order Bending Theory for Laminated Composite and Sandwich Beams

A higher-order bending theory is derived for laminated composite and sandwich beams thus extending the recent {1,2}-order theory to include third-order axial effect without introducing additional kinematic variables. The present theory is of order {3,2} and includes both transverse shear and transverse normal deformations. A closed-form solution to the cylindrical bending problem is derived and compared with the corresponding exact elasticity solution. The numerical comparisons are focused on the most challenging material systems and beam aspect ratios which include moderate-to-thick unsymmetric composite and sandwich laminates. Advantages and limitations of the theory are discussed.

Cook, Geoffrey M.↗
NASA NTRS1999

A Plasma Instability Theory of Gamma-Ray Burst Emission

A plasma instability theory is presented for the prompt radiation from gamma-ray bursts. In the theory, a highly relativistic shell interacts with the interstellar medium through the filamentation and the two-stream instabilities to convert bulk kinetic energy into electron thermal energy and magnetic field energy. The processes are not efficient enough to satisfy the Rankine-Hugoniot conditions, so a shock cannot form through this mechanism. Instead, the interstellar medium passes through the shell, with the electrons radiating during this passage. Gamma-rays are produced by synchrotron self-Compton emission. Prompt optical emission is also produced through this mechanism, while prompt radio emission is produced through synchrotron emission. The model timescales are consistent with the shortest burst timescales. To emit gamma-rays, the shell's bulk Lorentz factor must be $\simg 10(exp 3)$. For the radiative processes to be efficient, the interstellar medium density must satisfy a lower limit that is a function of the bulk Lorentz factor. Because the limits operate as selection effects, bursts that violate them constitute new classes. In particular, a class of optical and ultraviolet bursts with no gamma-ray emission should exist. The lower limit on the density of the interstellar medium is consistent with the requirements of the Compton attenuation theory, providing an explanation for why all burst spectra appear to be attenuated. Several tests of the theory are discussed, as are the next theoretical investigations that should be conducted.

Brainerd, Jerome J.↗
NASA NTRS1999

Higher-Order Theory for Functionally Graded Materials

This paper presents the full generalization of the Cartesian coordinate-based higher-order theory for functionally graded materials developed by the authors during the past several years. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composite's functionally graded microstructure. The generalization outlined herein involves extension of the theoretical framework to enable the analysis of materials characterized by spatially variable microstructures in three directions. Specialization of the generalized theoretical framework to previously published versions of the higher-order theory for materials functionally graded in one and two directions is demonstrated. In the applications part of the paper we summarize the major findings obtained with the one-directional and two-directional versions of the higher-order theory. The results illustrate both the fundamental issues related to the influence of microstructure on microscopic and macroscopic quantities governing the response of composites and the technologically important applications. A major issue addressed herein is the applicability of the classical homogenization schemes in the analysis of functionally graded materials. The technologically important applications illustrate the utility of functionally graded microstructures in tailoring the response of structural components in a variety of applications involving uniform and gradient thermomechanical loading.

Aboudi, Jacob↗
NASA NTRS2001

Impact of Functionally Graded Cylinders: Theory

This final report summarizes the work funded under the Grant NAG3-2411 during the 04/05/2000-04/04/2001 period. The objective of this one-year project was to generalize the theoretical framework of the two-dimensional higher-order theory for the analysis of cylindrical functionally graded materials/structural components employed in advanced aircraft engines developed under past NASA Glenn funding. The completed generalization significantly broadens the theory's range of applicability through the incorporation of dynamic impact loading capability into its framework. Thus, it makes possible the assessment of the effect of damage due to fuel impurities, or the presence of submicron-level debris, on the life of functionally graded structural components. Applications involving advanced turbine blades and structural components for the reusable-launch vehicle (RLV) currently under development will benefit from the completed work. The theory's predictive capability is demonstrated through a numerical simulation of a one-dimensional wave propagation set up by an impulse load in a layered half-plane. Full benefit of the completed generalization of the higher-order theory described in this report will be realized upon the development of a related computer code.

Aboudi, Jacob↗
NASA NTRS2001

Flame-Vortex Interactions Imaged in Microgravity - To Assess the Theory Flame Stretch

The goals of this research are to: 1) Assess the Theory of Flame Stretch by operating a unique flame-vortex experiment under microgravity conditions in the NASA Glenn 2.2 Second Drop Tower (drops to identify operating conditions have been completed); 2) Obtain high speed shadowgraph images (500-1000 frames/s) using the drop rig (images were obtained at one-g, and the NASA Kodak RO camera is being mounted on the drop rig); 3) Obtain shadowgraph and PIV images at 1-g while varying the effects of buoyancy by controlling the Froude number (completed); 4) Numerically model the inwardly-propagating spherical flame that is observed in the experiment using full chemistry and the RUN 1DL code (completed); 5) Send images of the flame shape to Dr. G. Patniak at NRL who is numerically simulating the entire flame-vortex interaction of the present experiment (data transfer completed); and 6) Assess the feasibility of obtaining PIV velocity field images in the drop rig, which would be useful (but not required) for our assessment of the Theory of Flame Stretch (PIV images were obtained at one-g using same low laser power that is available from fiber optic cable in drop tower). The motivation for the work is to obtain novel measurement needed to develop a physically accurate model of turbulent combustion that can help in the control of engine pollutants. The unique experiment allows, for the first time, the detailed study of a negatively-curved (negatively stretched) flame, which is one of the five fundamental types of premixed flames. While there have been studies of flat flames, positively-curved (outwardly-propagating) cases and positively-strained (counterflow) cases, this is the first detailed study of a negatively-curved (inwardly-propagating) flame. The first set of drops in the 2.2 Second Drop Tower showed that microgravity provides more favorable conditions for achieving inwardly-propagating flames (IPFs) than 1-g. A vortex interacts with a flame and creates a spherical pocket, which burns inwardly. Shadowgraphs at 1000 frames/sec quantify the Markstein number and flame speed. A Low-Laser Power PIV System was developed and is being added to the drop package. Numerical computations were required to explain why the Markstein numbers measured for the inwardly-propagating flames differ from those of outward propagating flames; this is an important research issue in the assessment of the Theory of Flame Stretch. The RUN-1DL code (developed by Prof. B. Rogg) was run for IPF and OPFs with complex methane and propane chemistry. Results confirmed that Ma for the IPFs are larger than for OPFs as was observed experimentally. Physical reasons for these new findings about the Theory of Flame Stretch are being determined from the experiments and the computations. Several journal papers have been published; the drop package is described in the AIAA Journal, while the one-g results appear in three other journal papers.

Driscoll, James F.↗
NASA NTRS1994

A Comparison of Density Functional Theory with Ab initio Approaches for Systems Involving First Transition Row Metals

Density functional theory (DFT) is found to give a better description of the geometries and vibrational frequencies of FeL and FeL(sup +) systems than second order Moller Plesset perturbation theory (MP2). Namely, the DFT correctly predicts the shift in the CO vibrational frequency between free CO and the Sigma(sup -) state of FeCO and yields a good result for the Fe-C distance in the quartet states of FeCH4(+) 4 These are properties where the MP2 results are unsatisfactory. Thus DFT appears to be an excellent approach for optimizing the geometries and computing the zero-point energies of systems containing first transition row atoms. Because the DFT approach is biased in favor of the 3d(exp 7) occupation, whereas the more traditional approaches are biased in favor of the 3d(exp 6) occupation, differences are found in the relative ordering of states. It is shown that if the dissociation is computed to the most appropriate atomic asymptote and corrected to the ground state asymptote using the experimental separations, the DFT results are in good agreement with high levels of theory. The energetics at the DFT level are much superior to the MP2 and in most cases in good agreement with high levels of theory.

Ricca, Alessandra↗
NASA NTRS2002

Efficient Reformulation of the Thermoelastic Higher-order Theory for Fgms

Functionally graded materials (FGMs) are characterized by spatially variable microstructures which are introduced to satisfy given performance requirements. The microstructural gradation gives rise to continuously or discretely changing material properties which complicate FGM analysis. Various techniques have been developed during the past several decades for analyzing traditional composites and many of these have been adapted for the analysis of FGMs. Most of the available techniques use the so-called uncoupled approach in order to analyze graded structures. These techniques ignore the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. The higher-order theory for functionally graded materials (HOTFGM) is a coupled approach developed by Aboudi et al. (1999) which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the original higher-order theory for two-dimensional elastic problems is developed and validated. The use of the local-global conductivity and local-global stiffness matrix approach is made in order to reduce the number of equations involved. In this approach, surface-averaged quantities are the primary variables which replace volume-averaged quantities employed in the original formulation. The reformulation decreases the size of the global conductivity and stiffness matrices by approximately sixty percent. Various thermal, mechanical, and combined thermomechanical problems are analyzed in order to validate the accuracy of the reformulated theory through comparison with analytical and finite-element solutions. The presented results illustrate the efficiency of the reformulation and its advantages in analyzing functionally graded materials.

Bansal, Yogesh↗
NASA NTRS2003

Applicability of Markets to Global Scheduling in Grids: Critical Examination of General Equilibrium Theory and Market Folklore

Markets are often considered superior to other global scheduling mechanisms for distributed computing systems. This claim is supported by: a casual observation from our every-day life that markets successfully equilibrate supply and demand, and the features of markets which originate in the general equilibrium theory, e.g., efficiency and the lack of necessity of 2 central controller. This paper describes why such beliefs in markets are not warranted. It does so by examining the general equilibrium theory, in terms of scope, abstraction, and interpretation. Not only does the general equilibrium theory fail to provide a satisfactory explanation of actual economies, including a computing-resource economy, it also falls short of supplying theoretical foundations for commonly held views of market desirability. This paper also points out that the argument for the desirability of markets involves circular reasoning and that the desirability can be established only vis-a-vis a scheduling goal. Finally, recasting the conclusion of Arrow's Impossibility Theorem as that for global scheduling, we conclude that there exists no market-based scheduler that is rational (in the sense defined in microeconomic theory), takes into account utility of more than one user, and yet yields a Pareto-optimal outcome for arbitrary user utility functions.

Nakai, Junko↗
NASA NTRS2003

High-Pressure Transport Properties Of Fluids: Theory And Data From Levitated Drops At Combustion-Relevant Temperatures

Although the high pressure multicomponent fluid conservation equations have already been derived and approximately validated for binary mixtures by this PI, the validation of the multicomponent theory is hampered by the lack of existing mixing rules for property calculations. Classical gas dynamics theory can provide property mixing-rules at low pressures exclusively. While thermal conductivity and viscosity high-pressure mixing rules have been documented in the literature, there is no such equivalent for the diffusion coefficients and the thermal diffusion factors. The primary goal of this investigation is to extend the low pressure mixing rule theory to high pressures and validate the new theory with experimental data from levitated single drops. The two properties that will be addressed are the diffusion coefficients and the thermal diffusion factors. To validate/determine the property calculations, ground-based experiments from levitated drops are being conducted.

Bellan, Josette↗
NASA NTRS1949

Boundary Layer Theory: Laminar Flows - Part 1

The purpose of this presentation is to give you a survey of a field of aerodynamics which has for a number of years been attracting an ever growing interest. The subject is the theory of flows with friction, and, within that field, particularly the theory of friction layers, or boundary layers. As you know, a great many considerations of aerodynamics are based on the so-called ideal fluid, that is, the frictionless incompressible fluid. By neglect of compressibility and friction the extensive mathematical theory of the ideal fluid (potential theory) has been made possible.

Schlichting, H.↗
NASA NTRS2003

Vortex Loops at the Superfluid Lambda Transition: An Exact Theory?

A vortex-loop theory of the superfluid lambda transition has been developed over the last decade, with many results in agreement with experiments. It is a very simple theory, consisting of just three basic equations. When it was first proposed the main uncertainty in the theory was the use Flory scaling to find the fractal dimension of the random-walking vortex loops. Recent developments in high-resolution Monte Carlo simulations have now made it possible to verify the accuracy of this Flory-scaling assumption. Although the loop theory is not yet rigorously proven to be exact, the Monte Carlo results show at the least that it is an extremely good approximation. Recent loop calculations of the critical Casimir effect in helium films in the superfluid phase T < Tc will be compared with similar perturbative RG calculations in the normal phase T > Tc; the two calculations are found to match very nicely right at Tc.

Williams, Gary A.↗
NASA NTRS2005

Second-order multiple-scattering theory associated with backscattering enhancement for a millimeter wavelength weather radar with a finite beam width

Effects of multiple scattering on reflectivity are studied for millimeter wavelength weather radars. A time-independent vector theory, including up to second-order scattering, is derived for a single layer of hydrometeors of a uniform density and a uniform diameter. In this theory, spherical waves with a Gaussian antenna pattern are used to calculate ladder and cross terms in the analytical scattering theory. The former terms represent the conventional multiple scattering, while the latter terms cause backscattering enhancement in both the copolarized and cross-polarized components. As the optical thickness of the hydrometeor layer increases, the differences from the conventional plane wave theory become more significant, and essentially, the reflectivity of multiple scattering depends on the ratio of mean free path to radar footprint radius. These results must be taken into account when analyzing radar reflectivity for use in remote sensing.

radar reflectivity↗
NASA NTRS2006

The Curious Events Leading to the Theory of Shock Waves

We review the history of the development of the modern theory of shock waves. Several attempts at an early-theory quickly collapsed for lack of foundations in mathematics and thermodynamics. It is not until the works of Rankine and later Hugoniot that a full theory is established. Rankine is the first to show that within the shock a non-adiabatic process must occur. Hugoniot showed that in the absence of viscosity and heat conduction conservation of energy implies conservation of entropy in smooth regions and a jump in entropy across a shock. Even after the theory is fully developed, old notions continue to pervade the literature well into the early part of the 20th Century.

Salas, Manuel D.↗
NASA NTRS2007

Nonlinear Theory and Breakdown

The main points of recent theoretical and computational studies on boundary-layer transition and turbulence are to be highlighted. The work is based on high Reynolds numbers and attention is drawn to nonlinear interactions, breakdowns and scales. The research focuses in particular on truly nonlinear theories, i.e. those for which the mean-flow profile is completely altered from its original state. There appear to be three such theories dealing with unsteady nonlinear pressure-displacement interactions (I), with vortex/wave interactions (II), and with Euler-scale flows (III). Specific recent findings noted for these three, and in quantitative agreement with experiments, are the following. Nonlinear finite-time break-ups occur in I, leading to sublayer eruption and vortex formation; here the theory agrees with experiments (Nishioka) regarding the first spike. II gives rise to finite-distance blowup of displacement thickness, then interaction and break-up as above; this theory agrees with experiments (Klebanoff, Nishioka) on the formation of three-dimensional streets. III leads to the prediction of turbulent boundary-layer micro-scale, displacement-and stress-sublayer-thicknesses.

Smith, Frank↗
NASA NTRS2009

A Finite Element Theory for Predicting the Attenuation of Extended-Reacting Liners

A non-modal finite element theory for predicting the attenuation of an extended-reacting liner containing a porous facesheet and located in a no-flow duct is presented. The mathematical approach is to solve separate wave equations in the liner and duct airway and to couple these two solutions by invoking kinematic constraints at the facesheet that are consistent with a continuum theory of fluid motion. Given the liner intrinsic properties, a weak Galerkin finite element formulation with cubic polynomial basis functions is used as the basis for generating a discrete system of acoustic equations that are solved to obtain the coupled acoustic field. A state-of-the-art, asymmetric, parallel, sparse equation solver is implemented that allows tens of thousands of grid points to be analyzed. A grid refinement study is presented to show that the predicted attenuation converges. Excellent comparison of the numerically predicted attenuation to that of a mode theory (using a Haynes 25 metal foam liner) is used to validate the computational approach. Simulations are also presented for fifteen porous plate, extended-reacting liners. The construction of some of the porous plate liners suggest that they should behave as resonant liners while the construction of others suggest that they should behave as broadband attenuators. In each case the finite element theory is observed to predict the proper attenuation trend.

Watson, W. R.↗
NASA NTRS2009

Further Development of Ko Displacement Theory for Deformed Shape Predictions of Nonuniform Aerospace Structures

The Ko displacement theory previously formulated for deformed shape predictions of nonuniform beam structures is further developed mathematically. The further-developed displacement equations are expressed explicitly in terms of geometrical parameters of the beam and bending strains at equally spaced strain-sensing stations along the multiplexed fiber-optic sensor line installed on the bottom surface of the beam. The bending strain data can then be input into the displacement equations for calculations of local slopes, deflections, and cross-sectional twist angles for generating the overall deformed shapes of the nonuniform beam. The further-developed displacement theory can also be applied to the deformed shape predictions of nonuniform two-point supported beams, nonuniform panels, nonuniform aircraft wings and fuselages, and so forth. The high degree of accuracy of the further-developed displacement theory for nonuniform beams is validated by finite-element analysis of various nonuniform beam structures. Such structures include tapered tubular beams, depth-tapered unswept and swept wing boxes, width-tapered wing boxes, and double-tapered wing boxes, all under combined bending and torsional loads. The Ko displacement theory, combined with the fiber-optic strain-sensing system, provide a powerful tool for in-flight deformed shape monitoring of unmanned aerospace vehicles by ground-based pilots to maintain safe flights.

Ko, William L.↗