Search NASA⌕ Search

SEARCH · Search NASA

Results for “growth law”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Temporal Variation of Aerosol Properties at a Rural Continental Site and Study of Aerosol Evolution through Growth Law Analysis

Aerosol size distributions were measured by a Scanning Mobility Particle Sizer (SMPS) onboard the CIRPAS Twin Otter aircraft during 16 flights at the Southern Great Plains (SGP) site in northern central Oklahoma as part of the Aerosol Intensive Operation period in May, 2003. During the same period a second SMPS was deployed at a surface station and provided continuous measurements. Combined with trace gas measurements at the SGP site and back-trajectory analysis, the aerosol size distributions provided insights into the sources of aerosols observed at the SGP site. High particle concentrations, observed mostly during daytime, were well correlated with the sulfur dioxide (SO2) mixing ratios, suggesting nucleation involving sulfuric acid is likely the main source of newly formed particles at the SGP. Aerosols within plumes originating from wildfires in Central America were measured at the surface site. Vertically compact aerosol layers, which can be traced back to forest fires in East Asia, were intercepted at altitudes over 3000 meters. Analyses of size dependent particle growth rates for four periods during which high cloud coverage was observed indicate growth dominated by volume controlled reactions. Sulfate accounts for 50% to 72% of the increase in aerosol volume concentration; the rest of the volume concentration increase was likely due to secondary organic species. The growth law analyses and meteorological conditions indicate that the sulfate was produced mainly through aqueous oxidation of SO2 in clouds droplets and hydrated aerosol particles.

Wang, Jian↗
NASA NTRS1990

Time development of a perturbed-spherical nucleus in a pure supercooled liquid. I - Power-law growth of morphological instabilities. II - Nonlinear development

The linear growth stage of the morphological instabilities developing at the liquid-solid interface during crystal growth from an axisymmetric spherical nucleus is analyzed. The corresponding growth rate parameters are calculated numerically, and it is shown that morphological instabilities for free growth evolve according to a power law in agreement with WKB results and contrary to an exponential law found in a quasi-stationary approximation. The time evolution of an arbitrary perturbed liquid-solid interface from a linear into the nonlinear stage is studied. The initial perturbations include the eigenfunctions for the linear problem, localized perturbations of the grain-boundary type, and a stochastic noise. It is shown that the perturbations grow and spread in a wavelike manner. The formation of a predendritic growth stage is characterized by establishment of constant values of tip radius and velocity.

Pines, V.↗
NASA NTRS1985

Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

Two coupled, nonlinear differential equations are proposed for the modeling of the elastic and rate (time) dependent inelastic behavior of structural metals in the absence of recovery and aging. The structure of the model is close to the unified theories but contains essential differences. It is shown that the model reproduces almost elastic regions upon initial loading and in the unloading regions of the hysteresis loop. Under loading, unloading and reloading in strain control the model simulated the experimentally observed sharp transition from nearly elastic to inelastic behavior. When a formulation akin to existing unified theories is adopted the almost elastic regions reduce the points and the transition upon reloading is very gradual. For different formulations the behavior under sudden in(de)creases of the strain rate by two orders of magnitude is simulated by numerical experiments and differences are noted. The model represents cyclically neutral behavior and contains three constants and two positive, decreasing functions. The determination of constants and functions from monotonic loading with strain rate changes and relaxation periods is described.

Krempl, E.↗
NASA NTRS1986

Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

Two coupled, nonlinear differential equations are proposed for the modeling of the elastic and rate (time) dependent inelastic behavior of structural metals in the absence of recovery and aging. The structure of the model is close to the unified theories but contains essential differences. It is shown that the model reproduces almost elastic regions upon initial loading and in the unloading regions of the hysteresis loop. Under loading, unloading and reloading in strain control the model simulated the experimentally observed sharp transition from nearly elastic to inelastic behavior. When a formulation akin to existing unified theories is adopted the almost elastic regions reduce the points and the transition upon reloading is very gradual. For different formulations the behavior under sudden in(de)creases of the strain rate by two orders of magnitude is simulated by numerical experiments and differences are noted. The model represents cyclically neutral behavior and contains three constants and two positive, decreasing functions. The determination of constants and functions from monotonic loading with strain rate changes and relaxation periods is described.

Krempl, E.↗
DOE OSTI2020

A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytic solutions to the simplified model equations corresponding to each instability are derived separately, which are then used to calibrate the model coefficients to predict specific values of the mixing layer growth parameters and exponents. The buoyancy-shear–drag equations for the bubble and spike mixing layer widths are then solved numerically, and a turbulent diffusivity (or viscosity) is constructed dimensionally as the product of the mixing layer width, h, and its time-derivative, dh/dt. Surrogate turbulent fields are then constructed by multiplying a presumed, approximate self-similar spatial profile by appropriate functions of h and dh/dt. Using several simplifying approximations, the turbulent diffusion equations satisfied by the mean mass fraction and mean shear velocity are solved analytically in a reference frame moving with the mean advection velocity, and it is shown that the mean fields evolve in space and time as expected. The explicit modeling and solution of turbulent transport equations (e.g., for the turbulent kinetic energy and its dissipation rate or a lengthscale) are not required. By using separate equations for the bubble and spike evolution, the model naturally captures the asymmetry induced by an increasing density contrast between the heavy and light fluids. The model also includes molecular dissipation and diffusion, and therefore, can describe transition to fully-developed turbulence if the initial turbulent diffusivity/viscosity is much smaller than the molecular diffusivity/viscosity. This model is applied to constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and variable-density Kelvin–Helmholtz mixing layers to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results. This relatively simple model can be implemented numerically, and is expected to be useful for fundamental as well as astrophysical and inertial confinement fusion applications.

42 ENGINEERING↗
NASA NTRS1990

Chemical reaction of atomic oxygen with evaporated films of copper, part 4

Evaporated copper films were exposed to an atomic oxygen flux of 1.4 x 10(exp 17) atoms/sq cm per sec at temperatures in the range 285 to 375 F (140 to 191 C) for time intervals between 2 and 50 minutes. Rutherford backscattering spectroscopy (RBS) was used to determine the thickness of the oxide layers formed and the ratio of the number of copper to oxygen atoms in the layers. Oxide film thicknesses ranged from 50 to 3000 A (0.005 to 0.3 microns, or equivalently, 5 x 10(exp -9) to 3 x 10(exp -7); it was determined that the primary oxide phase was Cu2O. The growth law was found to be parabolic (L(t) varies as t(exp 1/2)), in which the oxide thickness L(t) increases as the square root of the exposure time t. The analysis of the data is consistent with either of the two parabolic growth laws. (The thin-film parabolic growth law is based on the assumption that the process is diffusion controlled, with the space charge within the growing oxide layer being negligible. The thick-film parabolic growth law is also based on a diffusion controlled process, but space-charge neutrality prevails locally within very thick oxides.) In the absence of a voltage measurement across the growing oxide, a distinction between the two mechanisms cannot be made, nor can growth by the diffusion of neutral atomic oxygen be entirely ruled out. The activation energy for the reaction is on the order of 1.1 eV (1.76 x 10(exp -19) joule, or equivalently, 25.3 kcal/mole).

Fromhold, A. T.↗
NASA NTRS2018

A Dual Spring Modeling Approach for Static and Fatigue Failure Assessments of Carbon/Epoxy Composite Sub-Elements

A dual spring model is developed for the static and fatigue damage predictions of laminates interface in composite structures. Stress concentrations can be induced by the defects formed in the fabrication or service process. A conventional S-N based fatigue damage model may not be accurate to predict the fatigue life of a structure with high stress concentration. With the dual spring model, static delamination failure can be simulated using springs of cohesive type material model while fatigue delamination development can be predicted using linear springs, where the crack driving force is computed based on virtual crack closure technique (VCCT). A Paris law type fatigue growth law with its mode mixity is applied for fatigue crack growth prediction. After verified using benchmark examples, including Double Cantilever Beam (DCB), End-Notched Flexure (ENF) and Mix-Mode Bending (MMB), the proposed dual spring model is applied in the static and fatigue damage prediction of NASA/Boeing sub-elements and UTC sub-elements.

Cui, Xiaodong↗
NASA NTRS1984

Hidden-Line Computer Code

New, efficient solution minimizes run time. Approach based on approved theorem provides formal basis for assuring generality and rapid execution. Theorem does not directly address nuisance of square law growth. Analysis of algorithm shows it tends to avoid square-law growth, and rigorous testing verified algorithm tends to enjoy almost linear growth.

Hedgley, D. R., Jr.↗
NASA NTRSDate not supplied

Validation of Delamination Growth Predictions under Fatigue Loading using the Single Leg Bending Specimen

The Single Leg Bending Specimen (SLB) was chosen for a study to compare experimentally determined delamination growth with analysis predictions. First, fatigue tests were performed on SLB specimens with several different starter delamination lengths. Specimens were cycled in load control and delamination length increase was continuously recorded with increasing number of cycles. Test results from different load levels were combined to capture the entire delamination growth law (Paris Law) over a wide range of energy release rates. Second, a recently developed interpolation scheme was used to predict the Paris Law associated with the SLB specimen. This interpolation scheme allows the calculation of the growth rates for a given mixed-mode ratio from known single-mode growth laws. Third, finite element analyses were performed using two-dimensional models of the SLB specimen. New Virtual Crack Closure Technique based analysis tools for automated delamination growth analysis under cyclic loading in Abaqus were used for growth predictions. Fourth, the predictions from analyses were compared to experimental fatigue data. Remaining analysis shortcomings were highlighted.

Ronald Krueger↗
NASA NTRS1998

Subparabolic Oxidation Behavior of Silicon Carbide at 1300 C

The phenomenon of subparabolic oxide growth rate, more the rule than the exception in the oxidation of silica formers, is examined in light of data sets acquired in SiC oxidation experiments at 1300 C. Negative deviation from parabolic kinetics is shown to correlate with oxide crystallinity. The data sets were analyzed to ascertain the predominant and contributing growth laws, and tested with models that describe the overall kinetics as combinations of the familiar growth laws.

Ogbuji, Linjus U. J. T.↗
NASA NTRS1976

Equivalent constant-amplitude concept for crack growth under spectrum loading

To simplify crack-growth calculations, an equivalent constant-amplitude concept is developed based on the crack-closure phenomenon and on results of pilot tests that showed that the crack-opening load remained essentially constant while cracks grew under repeating random-load sequences containing several thousand load peaks. An equation of crack growth equivalence resulting from derivations based on the crack closure crack growth law is obtained and used to determine a relationship between an equivalent number of cycles of constant-amplitude loading and the distribution of the random loads, the exponent in the crack growth law, and the ratio of the crack-opening load to the maximum load. The validity of the concept is tested experimentally on six different random-load sequences. Good agreement is found between experimental results and theoretical predictions.

Elber, W.↗
NASA NTRS1996

Growth and Morphology of Phase Separating Supercritical Fluids

The scientific objective is to study the relation between the morphology and the growth kinetics of domains during phase separation. We know from previous experiments performed near the critical point of pure fluids and binary liquids that there are two simple growth laws at late times. The 'fast' growth appears when the volumes of the phases are nearly equal and the droplet pattern is interconnected. In this case the size of the droplets grows linearly in time. The 'slow' growth appears when the pattern of droplets embedded in the majority phase is disconnected. In this case the size of the droplets increases in proportion to time to the power 1/3. The volume fraction of the minority phase is a good candidate to determine this change of behavior. All previous attempts to vary the volume fraction in a single experimental cell have failed because of the extreme experimental difficulties.

Hegseth, John↗
NASA NTRS1985

Impacts in Ice: Commissions of Solar System Crater Populations

The classical phases of cratering are compression, excavation, and modification. Recent theory, however, supports and alternative sequence of physical events: (1) coupling - energy and momentum are transferred, and the cratering flow field is set up; (2) power-law-growth the flow field expands, with transient cavity dimensions expressible as a simple power law function of time; and (3) late phase - some combination of gravity, strength, and viscosity limits cavity growth, initially causing a deviation from power-law behavior and eventually determining the size and shape of the final (transient) crater. The dominant mechanism that limits cavity growth defines a cratering regime and a single variable, the coupling parameter, determines the scaling laws in the various regimes. The coupling parameter is intermediate in dimensionality between energy and momentum and its exact form is determined. For simple materials with rate and scale independent strength, the transition crater diameter between the strength and gravity regimes is, within reasonable bounds, independent of velocity. Even the smallest craters observed by Voyager appear to be gravity dominated.

Mckinnon, W. B.↗
NASA NTRS2002

COSP for Windows: Strategies for Rapid Analyses of Cyclic Oxidation Behavior

COSP is a publicly available computer program that models the cyclic oxidation weight gain and spallation process. Inputs to the model include the selection of an oxidation growth law and a spalling geometry, plus oxide phase, growth rate, spall constant, and cycle duration parameters. Output includes weight change, the amounts of retained and spalled oxide, the total oxygen and metal consumed, and the terminal rates of weight loss and metal consumption. The present version is Windows based and can accordingly be operated conveniently while other applications remain open for importing experimental weight change data, storing model output data, or plotting model curves. Point-and-click operating features include multiple drop-down menus for input parameters, data importing, and quick, on-screen plots showing one selection of the six output parameters for up to 10 models. A run summary text lists various characteristic parameters that are helpful in describing cyclic behavior, such as the maximum weight change, the number of cycles to reach the maximum weight gain or zero weight change, the ratio of these, and the final rate of weight loss. The program includes save and print options as well as a help file. Families of model curves readily show the sensitivity to various input parameters. The cyclic behaviors of nickel aluminide (NiAl) and a complex superalloy are shown to be properly fitted by model curves. However, caution is always advised regarding the uniqueness claimed for any specific set of input parameters,

Smialek, James L.↗
NASA NTRS2004

Windows(Registered Trademark)-Based Software Models Cyclic Oxidation Behavior

Oxidation of high-temperature aerospace materials is a universal issue for combustion-path components in turbine or rocket engines. In addition to the question of the consumption of material due to growth of protective scale at use temperatures, there is also the question of cyclic effects and spallation of scale on cooldown. The spallation results in the removal of part of the protective oxide in a discontinuous step and thereby opens the way for more rapid oxidation upon reheating. In experiments, cyclic oxidation behavior is most commonly characterized by measuring changes in weight during extended time intervals that include hundreds or thousands of heating and cooling cycles. Weight gains occurring during isothermal scale-growth processes have been well characterized as being parabolic or nearly parabolic functions of time because diffusion controls reaction rates. In contrast, the net weight change in cyclic oxidation is the sum of the effects of the growth and spallation of scale. Typically, the net weight gain in cyclic oxidation is determined only empirically (that is, by measurement), with no unique or straightforward mathematical connection to either the rate of growth or the amount of metal consumed. Thus, there is a need for mathematical modeling to infer spallation mechanisms. COSP is a computer program that models the growth and spallation processes of cyclic oxidation on the basis of a few elementary assumptions that were discussed in COSP: A Computer Model of Cyclic Oxidation, Oxidation of Metals, vol. 36, numbers 1 and 2, 1991, pages 81-112. Inputs to the model include the selection of an oxidation-growth law and a spalling geometry, plus oxide-phase, growth-rate, cycle-duration, and spall-constant parameters. (The spalling fraction is often shown to be a constant factor times the existing amount of scale.) The output of COSP includes the net change in weight, the amounts of retained and spalled oxide, the total amounts of oxygen and metal consumed, and the terminal rates of weight loss and metal consumption.

Smialek, J. L.↗
DOE OSTI2022

Multilayer interface tracking model of pure tungsten oxidation

Here, we present a numerical model to predict oxide scale growth on tungsten surfaces under exposure to oxygen at high temperatures. The model captures the formation of four thermodynamically-compatible oxide sublayers, WO 2 , WO 2.72 , WO 2.9 , and WO 3 , on top of the metal substrate. Oxide layer growth is simulated by tracking the oxide/oxide and oxide/metal interfaces using a sharp-interface Stefan model coupled to diffusion kinetics. The model is parameterized using selected experimental measurements and electronic structure calculations of the diffusivities of all the oxide subphases involved. We simulate oxide growth at temperatures of 600°C and above, extracting the power law growth exponents in each case, which we find to deviate from classical parabolic growth in several cases. We conduct a comparison of the model predictions with an extensive experimental data set, with reasonable agreement at most temperatures. While many gaps in our understanding still exist, this work is a first attempt at embedding the thermodynamic and kinetic complexity of tungsten oxide growth into a comprehensive mesoscale kinetic model that attempts to capture the essential features of tungsten oxidation to fill existing knowledge gaps and guide and enhance future tungsten oxidation models.

36 MATERIALS SCIENCE↗
NASA NTRS2000

Gravity Effects in Diffusive Coarsening of Bubble Lattices: von Neumann's Law

von Neumann modelled the evolution of two-dimensional soap froths as a purely diffusive phenomenon; the area growth of a given cell was found to depend only on the geometry of the bubble lattice. In the model, hexagons are stable, pentagons shrink and heptagons grow. The simplest equivalent to the area growth law is / approximately t(sub beta). The result depends on assuming (1) an incompressible gas; (2) bubble walls which meet at 120 deg and (3) constant wall thickness and curvature. Each assumption is borne out in experiments except the last one: bubble wall thickness between connecting cells varies in unit gravity because of gravity drainage. The bottom part of the soap membrane is thickened, the top part is thinned, such that gas diffusion across the membrane shows a complex dependence on gravity. As a result, experimental tests of von Neumann's law have been influenced by effects of gravity; fluid behavior along cell borders can give non-uniform wall thicknesses and thus alter the effective area and gas diffusion rates between adjacent bubbles. For area plotted as a function of time, Glazier (J.A. Glazier, S.P. Gross, and I. Stavans, Phys. Rev. A. 36, 306 (1987); J. Stavans, J.A, Glazier, Phys. Rev. Lett. 62, 1318 (1989).) suggest that in some cases their failure to observe von Neumann's predicted growth exponent ((sup beta)theor(sup =1; beta)exp(sup =0.70 + 0.10)) may have been the result of such "fluid drainage onto the lower glass plate". Additional experiments which varied plate spacing gave different beta exponents in a fashion consistent with this suggestion. During preliminary long duration experiments (approximately 100 h) aboard Spacelab-J, a low-gravity test of froth coarsening has examined (1) power law scaling of von Neumann's law (beta values) in the appropriate diffusive limits; (2) new bubble lattice dynamics such as greater fluid wetting behavior on froth membranes in low gravity; and (3) explicit relations for the gravity dependence of the second moment (or disorder parameter) governing the geometric spread in cell-sidedness around the mean of perfect hexagonal filling. By reducing the gravity-induced distortion in lattice wall thickness, the diffusion-limited regime of bubble coarsening becomes available for performing critical tests of network dynamics.

Noever, David A.↗