Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Homogenization theory”

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

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

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Thermal inertias in the upper millimeters of the Martian surface derived using Phobos' shadow

The first thermal images of Phobos' shadow on the surface of Mars, in addition to simultaneous visible images, were obtained by the Phobos'88 Termoskan instrument. The best observed shadow occurrence was on the flanks of Arsia Mons. For this occurrence, we combined the observed decrease in visible illumination of the surface with the observed decrease in brightness temperature to calculate thermal inertias of the Martian surface. The most realistic of our three models of eclipse cooling improves upon our preliminary model by including nonisothermal initial conditions and downward atmospheric flux. Most of our derived inertias fall within the range 38 to 59 J/(sq m s(exp 1/2) K), (0.9 to 1.4 x 10(exp -3) cal/(sq cm s(exp 1/2) K)) corresponding to dust-sized particles (for a homogeneous surface), consistent with previous theories of Tharsis as a current area of dust deposition. Viking infrared thermal mapper (IRTM) inertias are diurnally derived and are sensitive to centimeter depths, whereas the shadow-derived inertias sample the upper tenths of a millimeter of the surface. The shadow-derived inertias are lower than those derived from Viking IRTM measurements (84 to 147), however, uncertainties in both sets of derived inertias make conclusions about layering tenuous. Thus, near-surface millimeter versus centimeter layering may exist in this region, but if it does, it is likely not very significant. Both eclipse and diurnal inertias appear to increase near the eastern end of the shadow occurrence. We also analyzed a shadow occurrence near the crater Herschel that showed no observed cooling. This analysis was limited by cool morning temperatures and instrument sensitivity, but yielded a lower bound of 80 on eclipse inertias in that region. Based upon our results, we strongly recommend future spacecraft thermal observations of Phobos' shadow, and suggest that they will be most useful if they improve upon Terinoskan's geographic and temporal coverage and its accuracy.

Betts, Bruce H.↗
NASA NTRS1974

Cloud base levels for Jupiter and Venus and the heteromolecular nucleation theory

For purified binary gas mixtures like NH3-H2O or HCl-H2O, partial pressures appreciably greater than the two saturation partial pressures are needed to condense the gas mixture into small solution droplets (homogeneous heteromolecular nucleation). Thus without foreign nuclei, clouds are not as easily formed as in the theories of Lewis; the latter should be valid only if large condensation nuclei are available. We calculate here from classical homogeneous heteromolecular nucleation theory the threshold partial pressures necessary to achieve droplet nucleation for the gas mixtures NH3-H2O (Jupiter), HCl-H2O (Venus), H2SO4-H2O (Venus), and C2H5OH-H2O (laboratory).

Stauffer, D.↗
NASA NTRS1977

Scale-covariant theory of gravitation and astrophysical applications

A scale-covariant theory of gravitation is presented which is characterized by a set of equations that are complete only after a choice of the scale function is made. Special attention is given to gauge conditions and units which allow gravitational phenomena to be described in atomic units. The generalized gravitational-field equations are derived by performing a direct scale transformation, by extending Riemannian geometry to Weyl geometry through the introduction of the notion of cotensors, and from a variation principle. Modified conservation laws are provided, a set of dynamical equations is obtained, and astrophysical consequences are considered. The theory is applied to examine certain homogeneous cosmological solutions, perihelion shifts, light deflections, secular variations of planetary orbital elements, stellar structure equations for a star in quasi-static equilibrium, and the past thermal history of earth. The possible relation of the scale-covariant theory to gauge field theories and their predictions of cosmological constants is discussed.

Canuto, V.↗
NASA NTRS1991

The surface and through crack problems in layered orthotropic plates

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Erdogan, Fazil↗
NASA NTRS1985

Whistler damping at oblique propagation - Laminar shock precursors

This paper addresses the collisionless damping of whistlers observed as precursors standing upstream of oblique, low-Mach number terrestrial bow shocks. The linear theory of electromagnetic waves in a homogeneous Vlasov plasma with Maxwellian distribution functions and a magnetic field is considered. Numerical solutions of the full dispersion equation are presented for whistlers propagating at an arbitrary angle with respect to the magnetic field. It is demonstrated that electron Landau damping attenuates oblique whistlers and that the parameter which determines this damping is beta-e. In a well-defined range of parameters, this theory provides damping lengths which are the same order of magnitude as those observed. Thus electron Landau damping is a plausible process in the dissipation of upstream whistlers. Nonlinear plasma processes which may contribute to precursor damping are also discussed, and criteria for distinguishing among these are described.

Gary, S. P.↗
NASA NTRS1984

Analysis and testing for rotordynamic coefficients of turbulent annular seals with different, directionally homogeneous surface-roughness treatment for rotor and stator elements

A theory is presented, based on a simple modification of Hirs' turbulent lubrication equations, to account for different but directionally-homogeneous surface roughness treatments for the rotor and stator of annular seals. The theoretical results agree with von Pragenau's predictions that a damper seal which uses a smooth rotor and a rough stator yields more net damping than a conventional seal which has the same roughness for both the rotor and stator. Experimental results for four stators confirm that properly-designed roughened stators yield higher net damping values and substantially less leakage than seals with smooth surfaces. The best seal from both damping and leakage viewpoints uses a round-hole-pattern stator. Initial results for this stator suggest that, within limits, seals can be designed to yield specified ratios of stiffness to damping.

Childs, D. W.↗
NASA NTRS1974

Remarks on the decay of homogeneous turbulence from a given state

A previous theory which did not require a usual closure assumption required three or more initial spectra. By allowing a simple physical assumption (a modification of Kovasznay's (1948) hypothesis), the required number of spectra is reduced to two. Agreement with experiment is good.

Deissler, R. G.↗
NASA NTRS1992

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Tsang, Leung↗
NASA NTRS2011

Broken Ergodicity in MHD Turbulence in a Spherical Domain

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

Shebalin, John V.↗
NASA NTRS1999

Modeling the Dynamics of Ensemble-Averaged Linear Disturbances in Homogeneous Shear Flow

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. The calibration is based on homogeneous shear flow where disturbances can be described by rapid distortion theory (RDT). The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined. Key words: transition/turbulence modeling, homogeneous shear, rapid distortion theory.

Thacker, W. D.↗
NASA NTRS1996

Transient Creep of a Composite Lower Crust: Constitutive Theory - 1

A composite model is proposed to describe the time-dependent response of the Earth's lower crust. The motivation for such it model is twofold: First, new observations of widespread postseismic deformation indicate that the deep continental crust responds viscoelastically, having both long-and short-term decay times. Second, by any number of observationally based rationales, the lower crust is compositionally and structurally heterogeneous over many length scales. For heterogeneities that have much smaller characteristic lengths than the minimum deformation wavelength of interest, the aggregate rheology can be described by composite media theory. For wavelengths of the order of the thickness of the lower crust (approx. = 25-40 km) and larger, composite theory may be applied to heterogeneities that are smaller than about several hundred meters, or equivalent to the vertical extent of a thick lower crustal mylonitic shear zone. The composite media theory developed here is constructed using both Eshelhy-Mori-Tanaka theory for aligned generalized spheroidal inclusions and a generalized self-consistent method. The inclusions and matrix are considered to be Maxwellian viscoelastic: a rheology that is consistent with past homogeneous models of postseismic stress relaxation. The composite theory presented here introduces a transient response to a suddenly imposed stress field which does not appear in homogeneous Maxwell models. Analytic expressions for the amplitude and duration of the transient and for the effective long-and short-term viscosities of the composite are given which describe the sensitivity to inclusion concentration (phi), to shape, and to ratio of inclusion-to-matrix viscosity (R).

Ivins, Erik R.↗
NASA NTRS1983

Determining the alpha dynamo parameter in incompressible homogeneous magnetohydrodynamic turbulence

Alpha, an important parameter in dynamo theory, is proportional to either the kinetic, current, magnetic, or velocity helicity of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first order smoothed equations that describe the alpha effect. In two cases, when alpha is proportional to either the magnetic helicity or velocity helicity, alpha is determined experimentally from two point measurements of the fluctuating fields in incompressible, homogeneous turbulence having arbitrary symmetry. For the other two possibilities, alpha is determined if the turbulence is isotropic.

Matthaeus, W. H.↗
NASA NTRS1975

Electromagnetic and hydromagnetic waves in a cold magnetoplasma

The basis of the theory of waves in a cold homogeneous magnetoplasma is reviewed. The radio approximation (associated with Appleton) applies when the wave-frequency is large compared with the geometric mean of the electronic and ionic gyrofrequencies. The hydromagnetic approximation (associated with Alfven) corresponds to infinite conductivity along the lines of flux of the imposed magnetic field and applies when the wave-frequency is small compared with the plasma-frequency. The rich variety of dispersion phenomena existing in a magnetoplasma is illustrated by polar diagrams showing both the variation of group-velocity with beam-direction and the direction in which the antenna must be pointed to aim a beam in a particular direction.

Booker, H. G.↗
NASA NTRS1977

Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions

It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.

Kim, H.↗
NASA NTRS2026

Reliability Models and Demonstration of a Fault-Tolerant Motor Concept for Vertical Takeoff and Landing Vehicles

This report documents the completion of the Revolutionary Vertical Lift Technology Project Annual Performance Indicator 24-3.2.4.1: “Apply and document reliability prediction for high reliability motor concept.” Two modeling tools were completed for calculation of reliability of fault-tolerant (FT) motors, and key FT operations of a modular FT motor were demonstrated experimentally. The two models are complementary tools for the stakeholder and user community. Both models employ Markov chain theory. The first model is a time-homogeneous Markov chain model, and the second is a time-inhomogeneous Markov-Weibull model. This report’s main sections are as follows: 1.0 Introduction, 2.0 Theory, 3.0 Motor Reliability Models, 4.0 Validation of FT Operation by Hardware Demonstration, and 5.0 Concluding Remarks. Novel contributions to the field include development of a modular FT motor concept for electrified vertical takeoff and landing (eVTOL) application, solution methods to solve the reliability calculations, development of figures of merit, and the introduction of “linked chains” to formulate a building-block approach for time-inhomogeneous Markov-Weibull modeling of motor reliability. Example case studies have been completed, and results are provided and discussed herein. A four-module FT motor concept was developed to a preliminary-design level of detail. This eVTOL FT motor concept was designed for galvanic, magnetic, and thermal isolation of stator winding faults. The reliability of the concept motor was calculated using a time-inhomogeneous Markov chain model. Employing average failure rate as a metric, 570 times greater reliability was achieved as compared to a baseline motor without fault tolerance. A demonstrator motor was built and tested. The testing demonstrated the key features of FT operation and validated the essential premises of the FT motor concepts presented herein. The experiments included successful demonstration of the feasibility of the following four key FT features: (1) terminal open-circuit operation, (2) thermal isolation after fault, (3) terminal short-circuit operation, and (4) internal short-circuit operation. These works indicate that FT modular motor drives offer promise for addressing the daunting reliability gap that electric aircraft propulsor drives are facing relative to the best conventional motor drive technology that is available today.

Electric Motor↗
NASA NTRS1992

Grain size reduction in granular flows of spheres - The effects of critical impact energy

Methods employed to derive recent kinetic theories for rapid noncomminuting granular flows are extended to homogeneous flows in which a fraction of the repeated collisions produce tiny fractures on the particles' peripheries and gradually reduce their effective diameters. The theory consists of balance equations for mass, momentum, and energy, as well as constitutive relations for the presence tensor and collisional rates of mass and energy lost. The work of Richman and Chou (1989) is improved by incorporating into the constitutive theory the critical impact energy below which no mass loss occurs in a binary collision. The theory is applied to granular shear flows and, for fixed shear rates, predicts the time variations of the solid fraction granular temperature, and induced stresses, as well as their extreme sensitivities to small changes in the critical impact energy.

Richman, M. W.↗
NASA NTRS1986

Fiber Composite Sandwich Thermostructural Behavior: Computational Simulation

Several computational levels of progressive sophistication/simplification are described to computationally simulate composite sandwich hygral, thermal, and structural behavior. The computational levels of sophistication include: (1) three-dimensional detailed finite element modeling of the honeycomb, the adhesive and the composite faces; (2) three-dimensional finite element modeling of the honeycomb assumed to be an equivalent continuous, homogeneous medium, the adhesive and the composite faces; (3) laminate theory simulation where the honeycomb (metal or composite) is assumed to consist of plies with equivalent properties; and (4) derivations of approximate, simplified equations for thermal and mechanical properties by simulating the honeycomb as an equivalent homogeneous medium. The approximate equations are combined with composite hygrothermomechanical and laminate theories to provide a simple and effective computational procedure for simulating the thermomechanical/thermostructural behavior of fiber composite sandwich structures.

Chamis, C. C.↗
NASA NTRS1994

Hot proton anisotropies and cool proton temperatures in the outer magnetosphere

The hot protons of the outer magnetosphere typically exhibit a temperature anistropy such that T(sub perp)/T(sub parallel) greater than 1, where perpendicular and parallel symbols denote directions relative to the background magnetic field. If this anisotrpy is sufficiently large, the electomagneitc proton cyclotron anistropy instability may be excited. This instability is studied using linear Vlasov theory and one-dimensional hybrid simulations for a homogeneous plasma model representative of conditions in the outer magnetosphere with a hot anisotropic proton component (denoted by subscript h) and a cool, initially isotropic proton component (subscript c). Linear theory yields an instability threshold condition on the hot proton temperature anistropy where as the simulations imply an upper bound on T(sub perp h)/T(sub parallel h); both the threshold and the upper bound have similar scaling with the maximum growth rate gamma (sub m), the parallel beta of the hot component, beta(sub parallel h), and the relative density of the hot component n(sub h)/n(sub e). An anlysis of plasma observations from the Los Alamos magnetospheric plasma analyzer (MPA) in geosynchronous orbits finds that the maximum value of the hot proton temperature anisotropy approximately satisfies the predicted scaling with beta(sub parallel h) and nu(sub h)/n(sub e) and yields the proportionality factor that quantifies this upper bound. The simulations are also used to examine the heating of the cool proton cyclotron instability. The simulations yield a scaling for the dimensionless late-time cool proton average temperature T(sub c)/T(sub parallel h) as (n(sub h)/n(sub e))/beta(sub parallel h exp 0.5). Analysis of MPA data shows that the observed values of T(sub c)/T(sub parallel h) have similar scaling and again yield the proportionality factor which quantifies this relationship.

Gary, S. Peter↗