Stability criteria for n-th order, homogeneous linear differential equations
Stability criteria for n-th order homogeneous linear differential equations for real continuous functions obtained by Liapunov method
LIAPUNOV FUNCTION↗
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Results for “HOMOGENIZATION METHODS”
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.
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A parallel Jacobson-Oksman optimization algorithm
A gradient-dependent optimization technique which exploits the vector-streaming or parallel-computing capabilities of some modern computers is presented. The algorithm, derived by assuming that the function to be minimized is homogeneous, is a modification of the Jacobson-Oksman serial minimization method. In addition to describing the algorithm, conditions insuring the convergence of the iterates of the algorithm and the results of numerical experiments on a group of sample test functions are presented. The results of these experiments indicate that this algorithm will solve optimization problems in less computing time than conventional serial methods on machines having vector-streaming or parallel-computing capabilities.
Straeter, T. A.↗
The structure of evaporating and combusting sprays: Measurements and predictions
An apparatus was constructed to provide measurements in open sprays with no zones of recirculation, in order to provide well-defined conditions for use in evaluating spray models. Measurements were completed in a gas jet, in order to test experimental methods, and are currently in progress for nonevaporating sprays. A locally homogeneous flow (LHF) model where interphase transport rates are assumed to be infinitely fast; a separated flow (SF) model which allows for finite interphase transport rates but neglects effects of turbulent fluctuations on drop motion; and a stochastic SF model which considers effects of turbulent fluctuations on drop motion were evaluated using existing data on particle-laden jets. The LHF model generally overestimates rates of particle dispersion while the SF model underestimates dispersion rates. The stochastic SF flow yield satisfactory predictions except at high particle mass loadings where effects of turbulence modulation may have caused the model to overestimate turbulence levels.
Shuen, J. S.↗
Structure of Evaporating and Combusting Sprays: Measurements and Predictions
Complete measurements of the structure of nonevaporating, evaporating and combusting sprays for sufficiently well defined boundary conditions to allow evaluation of models of these processes were obtained. The development of rational design methods for aircraft combustion chambers and other devices involving spray combustion were investigated. Three methods for treating the discrete phase are being considered: a locally homogeneous flow (LHF) model, a deterministic separated flow (DSF) model, and a stochastic separated flow (SSF) model. The main properties of these models are summarized.
Shuen, J. S.↗
Two-phase flow
An experimental program to characterize the spray from candidate nozzles for icing-cloud simulation is discussed. One canidate nozzle, which is currently used for icing research, has been characterized for flow and drop size. The median-volume diameter (MVD) from this air-assist nozzle is compared with correlations in the literature. The new experimental spray facility is discussed, and the drop-size instruments are discussed in detail. Since there is no absolute standard for drop-size measurements and there are other limitations, such as drop -size range and velocity range, several instruments are used and results are compared. A two-phase model was developed at Pennsylvania State University. The model uses the k-epsilon model of turbulence in the continous phase. Three methods for treating the discrete phase are used: (1) a locally homogeneous flow (LHF) model, (2) a deterministic separated flow (DSF) model, and (3) a stochastic separated flow (SSF) model. In the LHF model both phases have the same velocity and temperature at each point. The DSF model provides interphase transport but ignores the effects of turbulent fluctuations. In the SSF model the drops interact with turbulent eddies whose properties are determined by the k-epsilon turbulence model. The two-phase flow model has been extended to include the effects of evaporation and combustion.
Tacina, Robert R.↗
Optimum structural sizing for gust induced response
The present paper describes an optimization capability for sizing airframe structures that are subjected to a combination of deterministic and random loads. Design constraints are implemented to prevent structural failure in fatigue and due to a single exceedance of the allowable stress. The random load is treated as a stationary, homogeneous process with a Gaussian probability distribution, and a frequency domain method is used for the computation of dynamic response parameters. An equal-probability-of-load-combination criterion is proposed in the formulation of strength constraints. This alleviates problems associated with the incomplete phase information available when using power spectral density methods. The optimization procedure is illustrated by examples using typical built-up structures.
Hajela, P.↗
The effects of compositional inhomogeneities and fractal dimension on the optical properties of astrophysical dust
Mathis and Whiffen (1989) have recently suggested that interstellar dust particles are fluffy aggregates of submicron-size particles composed of various astronomical minerals. These dust particles should exhibit optical properties that are quite different from standard dust, characterized by spherical particles of various homogeneous mineral composition. In this paper, the discrete dipole approximation (DDA) method is used to examine the effects of chemical inhomogeneities and spatial structure on the optical properties of interstellar Mathis-Whiffen-type dust particles. The spatial structure of the dust is represented by its fractal dimension, and the chemical inhomogeneities are simulated by randomly assigning the composition of the occupied sites in the structure to be either carbon or silicate. It is found that compositional inhomogeneities are the dominant parameter affecting the shape of the 9.7 and 18 micron silicate bands. Some bands-shape variations can be attributed to the fractal dimension of the dust. The results derived here can be used to explain or constrain variations in these parameters among various astronomical objects.
Bazell, David↗
Interpretation of DTA experiments used for crystal nucleation rate determinations
An analysis is presented of two schemes which have been proposed for the determination of the temperature dependence of homogeneous crystal nucleation rates in glasses via DTA measurements. The first method is based upon the postulate that the inverse of the temperature at which the DTA crystallization rate is maximum, will increase monotonically as the number density of nucleated particles increases. The secone method is based on the observation that the intensity at T(p) (peak height) increases as T(p) grows. The validity of both of these methods is assessed for inorganic glasses for two specific crystal growth models.
Weinberg, Michael C.↗
PDF turbulence modeling and DNS
The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.
Hsu, A. T.↗
A mapping closure for turbulent scalar mixing using a time-evolving reference field
A general mapping-closure approach for modeling scalar mixing in homogeneous turbulence is developed. This approach is different from the previous methods in that the reference field also evolves according to the same equations as the physical scalar field. The use of a time-evolving Gaussian reference field results in a model that is similar to the mapping closure model of Pope (1991), which is based on the methodology of Chen et al. (1989). Both models yield identical relationships between the scalar variance and higher-order moments, which are in good agreement with heat conduction simulation data and can be consistent with any type of epsilon(phi) evolution. The present methodology can be extended to any reference field whose behavior is known. The possibility of a beta-pdf reference field is explored. The shortcomings of the mapping closure methods are discussed, and the limit at which the mapping becomes invalid is identified.
Girimaji, Sharath S.↗
Stationary turbulent closure via the Hopf functional equation
Explicit solutions of the stationary Hopf equation are discussed and their computational possibilities are explored. The motivation is to circumvent the infinite hierarchy of coupled equations for the velocity moments and obtain an exact closure of the steady-state 3D Navier-Stokes equations, without modeling assumptions or truncation. The Hopf formulation of the Navier-Stokes equation is reviewed. A stationary homogeneous solution for 2D flow is displayed and discussed. It is shown how depletion of nonlinearity may arise for 3D forced homogeneous flow. The general 3D forced case is considered and a method for closing the 3D unforced equations with arbitrary boundary conditions is derived.
Shen, Hubert H.↗
Induced nucleation of carbon dust in red giant stars
This study quantitatively tests the proposed model of induced nucleation of carbonaceous grains in carbon-rich red giant stars. Induced nucleation is the process of grain growth initiated by the presence of reactive surfaces provided by seed particles. The numerical study was performed using a deailed chemical kinetic model of carbon deposition, grain coagulation, and homogeneous nucleation of polycyclic aromatic hydrocarbons (PAHs). The model uses a method of moments to keep track of developing grain population in the forming dust shell. We test the efficiency of grain formation for large ranges of dust shell parameters typical for carbon stars. Our model is capable of producing a range of optically thick and thin dust shells in carbon stars. Results are in accord with (IRAS) spectral classes of carbon stars. The resulting composite grains produced are consistent with those recently found in ancient meteorites. This model also provides a realistic explanation for high abundances of (PAHs) in the interstellar medium and some planetary nebulae.
Cadwell, Brian J.↗
The Effect of Fiber Strength Stochastics and Local Fiber Volume Fraction on Multiscale Progressive Failure of Composites
Continuous fiber unidirectional polymer matrix composites (PMCs) can exhibit significant local variations in fiber volume fraction as a result of processing conditions that can lead to further local differences in material properties and failure behavior. In this work, the coupled effects of both local variations in fiber volume fraction and the empirically-based statistical distribution of fiber strengths on the predicted longitudinal modulus and local tensile strength of a unidirectional AS4 carbon fiber/ Hercules 3502 epoxy composite were investigated using the special purpose NASA Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC); local effective composite properties were obtained by homogenizing the material behavior over repeating units cells (RUCs). The predicted effective longitudinal modulus was relatively insensitive to small (~8%) variations in local fiber volume fraction. The composite tensile strength, however, was highly dependent on the local distribution in fiber strengths. The RUC-averaged constitutive response can be used to characterize lower length scale material behavior within a multiscale analysis framework that couples the NASA code FEAMAC and the ABAQUS finite element solver. Such an approach can be effectively used to analyze the progressive failure of PMC structures whose failure initiates at the RUC level. Consideration of the effect of local variations in constituent properties and morphologies on progressive failure of PMCs is a central aspect of the application of Integrated Computational Materials Engineering (ICME) principles for composite materials.
multiscale analysis↗
Supported Organoiridium-Pincer Catalysts for the Nonoxidative Dehydrogenation of High-Density Polyethylene
The iridium-pincer complex {p-OP( t Bu) 2 -C 6 H 2 -2,6-OP( t Bu) 2 ] 2 }Ir(C 2 H 4 ) ( P [Ir]) has been reported as a stable and active catalyst toward alkane dehydrogenation in homogeneous and supported heterogeneous systems. Dehydrogenation has been shown as a practical method toward functional polyolefins, with dehydrogenated high-density polyethylene (deHDPE) demonstrated as a valuable synthon for upcycling, as orthogonal C-H strategies are key to end-of-life upcycling. The heterogenization of P [Ir] on oxides (SiO 2 , Al 2 O 3 , and TiO 2 ; P [Ir]/E y O x ) yields a mixture of organometallic Ir-fragments whose catalytic nonoxidative dehydrogenation activity is modulated by the binding modes of the active metal on the surface. The binding mode was elucidated by a combination of solid-state NMR and XAFS analyses and supported by DFT calculations. Surface binding through the ligand enables active organoiridium that catalyzes internal olefination of deHDPE up to 1.23 mol % at 200 °C under dynamic vacuum. Alternatively, when the organoiridium is bonded though the metal center (Ir-O SiO ), catalyst activity is negligible. Furthermore, the catalytic activity of P [Ir]/SiO 2 showed comparable reactivity with the homogeneous analogue under the same catalytic conditions, and the heterogenized catalyst can be reused up to three cycles. In conclusion, this work highlights the importance of understanding how organometallic precursors react with hydroxylated metal oxide surfaces to establish structure-property relationships.
Hunt, Samuel B. [Argonne National Laboratory (ANL)↗
Aeroelastic stability of coupled flap-lag motion of hingeless helicopter blades at arbitrary advance ratios
Equations for large amplitude coupled flap-lag motion of a hingeless elastic helicopter blade in forward flight are derived. Only a torsionally rigid blade excited by quasi-steady aerodynamic loads is considered. The effects of reversed flow together with some new terms due to radial flow are included. Using Galerkin's method the spatial dependence is eliminated and the equations are linearized about a suitable equilibrium position. The resulting system of homogeneous periodic equations is solved using multivariable Floquet-Liapunov theory, and the transition matrix at the end of the period is evaluated by two separate methods. Computational efficiency of the two numerical methods is compared. Results illustrating the effects of forward flight and various important blade parameters on the stability boundaries are presented.
Friedmann, P.↗
Copper carbon composite wire with a uniform carbon dispersion made by friction extrusion
Copper-carbon composites are a group of materials with excellent mechanical, electrical, thermal, and tribological properties. However, bulk size copper-carbon composites made by the traditional manufacturing processes, like rolling or extrusion, fall short of reaching some of these properties predicted by theory or demonstrated only by samples at centimeter scale or smaller. The two main challenges to the successful scaling-up are: 1) to uniformly disperse carbon in the metal matrix; 2) to avoid degradation due to oxidation or reaction from overheating. In this work, we first demonstrate friction extrusion as a new method to make bulk-size void-free copper-carbon composite wires with homogenized carbon dispersion. Three different carbon varieties, graphite powder, graphene nanopowder, and carbon nanotubes, were added to the copper matrix with the concentration ranging from 0.5 wt% to 15 wt%. Special tooling, processing parameters, and procedures were developed, especially for high carbon content samples. Ten-fold reductions of both copper grain size and carbon particle size were achieved and attributed to the high shear deformation. Energy dispersive X-ray spectrometry indicates the carbon powder was refined to a sub-micron level and uniformly dispersed in the copper matrix. Compared with that of pure copper, the thermal capacity of the composite wire increases by 30 % while density reduces by 29 %.
Friction extrusion, Metal matrix composite, Graphe↗
Sub-tesla On-Chip Nanomagnetic Metamaterial Platform for Angle-Resolved Photoemission Spectroscopy
Magnetically controlled states in quantum materials are central to their unique electronic and magnetic properties. However, direct momentum-resolved visualization of these states via angle-resolved photoemission spectroscopy (ARPES) has been hindered by the disruptive effect of magnetic fields on photoelectron trajectories. Here, we introduce an in situ method that is, in principle, capable of applying magnetic fields up to 1 T. This method uses substrates composed of nanomagnetic metamaterial arrays with alternating polarity. Such substrates can generate strong, homogeneous, and spatially confined fields applicable to samples with thicknesses up to the micron scale, enabling ARPES measurements under magnetic fields with minimal photoelectron trajectory distortion. Here, we demonstrate this minimal distortion with ARPES data taken on monolayer graphene. Our method paves the way for probing magnetic field-dependent electronic structures and studying field-tunable quantum phases with state-of-the-art energy-momentum resolutions.
Magnetic properties↗
Extraction of high-purity medium-chain-length polyhydroxyalkanoates via combined mechanical treatment and mild oxidation
Polyhydroxyalkanoates (PHAs) are a class of polyester polymers of microbial origin and considered biodegradable alternatives to conventional plastics. To make PHAs cost-competitive with synthetic plastics, their production cost, including extraction cost, should be significantly reduced. Herein, this study aimed to develop an effective extraction method based on combined mechanical disruption and chemical treatment for the recovery of high-purity medium-chain-length PHAs (mcl-PHAs) at a lower cost. mcl-PHAs-accumulating Pseudomonas strains were used for PHA extraction via high-pressure homogenization (HPH) coupled with surfactant treatment and mild alkaline hydrogen peroxide oxidation. The mechanical-chemical method was found to have strong synergy for PHA extraction while minimizing PHA depolymerization. The optimized condition resulted in nearly 90 % mcl-PHA recovery with high purity (>91 %). The extracted high-purity PHAs exhibited thermal and mechanical properties suitable for downstream applications entailing flexible and elastomeric materials.
42 ENGINEERING↗