SEARCH · Engineering Papers

Results for “computable general equilibrium”

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.

SourceResearch connectionFrom yearThrough year

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

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

NASA NTRS1991

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Stoll, Frederick↗

NASA NTRS1980

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Kamat, M. P.↗

NASA NTRS1998

Elemental Fractionation During Rapid Accretion of the Moon Triggered by a Giant Impact

Recently, Ida et al. made an N-body simulation of lunar accretion from a protolunar disk formed by a giant impact. One of their important conclusions is that the accretion time of the Moon is as short as one month. Such rapid accretion is a necessary consequence of the high surface density of a lunar mass disk accreting just beyond the Roche limit (about 3Re); the Safronov accretion time (a few days) is even shorter. The energy of accretion always exceeds the gravitational binding energy of newly arriving matter. Hence, without an energy sink, the accreting body is thermally unstable. For the Earth and other planets, radiation acts as the sink. However, in such a short accretion time, the Moon cannot radiate the accretional energy. Even radiating at a silicate cloudtop temperature of roughly 2000 K, it would take more than 100 yr to radiatively cool the Moon. The plausible alternative heat sinks are heat capacity, latent heat of vaporization, and thermal escape of the gas to space (i.e., hydrodynamic blowoff). The latter becomes plausible for the Moon because the scale height at 2000 K (about 300 km) is a significant fraction of the lunar radius. The early stages of lunar (or "lunatesimal") growth release relatively little energy and can occur simply by heating the material, especially if the accreting material is originally cold. However, the material is unlikely to be cold, because the disk itself is hot and cooling time is long, while the lunar accretion time iss very short. Therefore, the moon is likely to accrete condensed material just after it condenses. Accordingly, the newly accreted material will be on the verge of vaporization and will have very little heat capacity to spare. The immediate heat sink is the latent heat of vaporization. Most of the vapor will escape from the moon, because the thermal energy in the gas can be used to drive escape. However, vaporization is generally incomplete. the latent heat of vaporization exceeds the energy of accretion. Viewed globally, the accretional energy is about half the energy required to vaporize the entire Moon. Thus to first approximation, half of the Moon-forming material can be vaporized and lost during accretion. During this process, we would expect preferential loss of relatively volatile elements. Escape will retard the rate of accretion. To test these ideas, we computed detailed models of the thermal state of the Moon during accretion. We pay special attention to the structure of the silicate atmosphere and its loss rate by calculating the chemical species at equilibrium. We used the PHEQ program which includes 12 elements (H,O,C,Mg,Si,Fe,Ca, Al, Na,Ti, and N.) and 272 compounds (including ionic compounds). Because of the large heats of vaporization and ionization, the adiabatic atmosphere is nearly isothermal and massive escape is expected. The pressure of the atmosphere is determined by the balance between vaporization of a accreting material and escape. If the accretion time is one month, a 0.3 bar atmosphere is expected. Elemental fractionation depends strongly on the temperature of the accreting material. The initial temperature of the material can be estimated from the condition of gravitational instability in the protolunar disk. As shown by Ida et al, accretion starts when gravitational instability occurs when more than 99% of the material condenses. At this point, all of Ca, Al, Si, Mg, and Fe, and 95% of Na (probably K also), are in condensed phases. If the moon is formed from the accretion of such material, volatile elements such as Na, and K are retained by the moon only early in accretion. At later times, K and Na are lost and a fraction of the MG, Si and Fe is lost. However, refractory elements such as Ca and Al are retained and so achieve a mild degree (factor 2) of superabundance.

Abe, Y.↗

NASA NTRS2003

A Generalized Multi-Phase Framework for Modeling Cavitation in Cryogenic Fluids

A generalized multi-phase formulation for cavitation in fluids operating at temperatures elevated relative to their critical temperatures is presented. The thermal effects and the accompanying property variations due to phase change are modeled rigorously. Thermal equilibrium is assumed and fluid thermodynamic properties are specified along the saturation line using the NIST-12 databank. Fundamental changes in the physical characteristics of the cavity when thermal effects become pronounced are identified; the cavity becomes more porous, the interface less distinct, and has increased entrainment when temperature variations are present. Quantitative estimates of temperature and pressure depressions in both liquid nitrogen and liquid hydrogen were computed and compared with experimental data of Hord for hydrofoils. Excellent estimates of the leading edge temperature and pressure depression were obtained while the comparisons in the cavity closure region were reasonable. Liquid nitrogen cavities were consistently found to be in thermal equilibrium while liquid hydrogen cavities exhibited small, but distinct, non-equilibrium effects.

Dorney, Dan↗

NASA NTRS1973

Linear convective modes and the energy transport in stellar convection zones.

Model stars whose convection zones had been prepared in accordance with the standard mixing-length theory were used as a basis for the computation of unstable convective modes. It was found that no superposition of statistically independent, nonviscous, adiabatic, convective modes can reproduce the radial dependence of the convective flux of the model. This implies that the representation of a stellar convection zone as a superposition of unstable adiabatic linear modes is inconsistent with the mixing-length theory, and that conclusions based upon such a representation should be regarded with caution. It is also shown that if the linear scale of convective motions is greater than (or of the same order as) the pressure scale height, then the fractional deviation of the pressure from equilibrium will generally not be negligible, as assumed in the mixing-length theory, but will be at least of the same order as the fractional deviation of the density from equilibrium.

Hart, M. H.↗

NASA NTRS1993

A comparison of the predictive capabilities of several turbulence models using upwind and central-difference computer codes

Four turbulence models are described and evaluated for transonic flows using the upwind code CFL3D and the central-difference code TLNS3D. In particular, the effects of recent modifications to the half-equation model of Johnson-King are explored in detail, and different versions of the model are compared. This model can obtain good results for both two-dimensional (2D) and three-dimensional (3D) separated flows. The one-equation models of Baldwin-Barth and Spalart-Allmaras perform well for separated airfoil flows, but can predict the shock too far forward at the outboard stations of a separated wing. The equilibrium model of Baldwin-Lomax predicts the shock location too far aft for both 2D and 3D separated flows, as expected. In general, all models perform well for attached or mildly separated flows.

Rumsey, Christopher L.↗

NASA NTRS1993

A Comparison of the Predictive Capabilities of Several Turbulence Models using Upwind and Central-Difference Computer Codes

Rumsey, Christopher L.↗

NASA NTRS2013

radEq Add-On Module for CFD Solver Loci-CHEM

Loci-CHEM to be applied to flow velocities where surface radiation due to heating from compression and friction becomes significant. The module adds a radiation equilibrium boundary condition to the computational fluid dynamics (CFD) code to produce accurate results. The module expanded the upper limit for accurate CFD solutions of Loci-CHEM from Mach 4 to Mach 10 based on Space Shuttle Orbiter Re-Entry trajectories. Loci-CHEM already has a very promising architecture and performance, but absence of radiation equilibrium boundary condition limited the application of Loci-CHEM to below Mach 4. The immediate advantage of the add-on module is that it allows Loci-CHEM to work with supersonic flows up to Mach 10. This transformed Loci-CHEM from a rocket engine- heritage CFD code with general subsonic and low-supersonic applications, to an aeroheating code with hypersonic applications. The follow-on advantage of the module is that it is a building block for additional add-on modules that will solve for the heating generated at Mach numbers higher than 10.

McCloud, Peter↗

NASA NTRS2017

Electromagnetic Scattering and Emission by a Fixed Multi-Particle Object in Local Thermal Equilibrium: General Formalism

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering emission problem for a fixed object, and derive such fundamental corollaries as the scattering emission volume integral equation, the Lippmann Schwinger equation for the dyadic transition operator, the multi-particle scattering emission equations, and the far-field limit. We show that in the framework of fluctuational electrodynamics, the computation of the self-emitted component of the total field is completely separated from that of the elastically scattered field. The same is true of the computation of the emitted and elastically scattered components of quadratic linear forms in the total electromagnetic field. These results pave the way to the practical computation of relevant optical observables.

Electromagnetic scattering; Thermal emission; Fluc↗

NASA NTRS1985

Vibration/Libration Interaction Dynamics During the Orbiter Based Deployment of Flexible Members

Essential features of a general formulation for studying librational dynamics of a large class of spacecraft during deployment of flexible members are reviewed. The formulation is applicable to a variety of missions ranging from deployment of antennas, booms and solar panels to manufacturing of trusses for space platforms using the space shuttle. The governing nonlinear, non-autonomous and coupled equations of motion are extremely difficult to solve even with the help of a computer, not to mention the cost involved. To get some appreciation as to the complex interactions between flexibility, deployment and attitude dynamics as well as to help pursue stability and control analysis, the equations are linearized about their nominal deflected equilibrium configuration. The procedure is applied to the Space Shuttle based deployment of boom and plate-like members. Results suggest substantial influence of the inertia parameter, flexural rigidity of the appendages, orbit eccentricity, deployment velocity, initial conditions, etc. on the system response. The results should prove useful in planning of the Orbiter based experiments aimed at assessing effectiveness of procedures for studying dynamics and control of flexible orbiting members.

Modi, V. J.↗

NASA NTRS1992

On explicit algebraic stress models for complex turbulent flows

Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

Gatski, T. B.↗

NASA NTRS1976

Statistical equilibrium calculations for silicon in early-type model stellar atmospheres

Line profiles of 36 multiplets of silicon (Si) II, III, and IV were computed for a grid of model atmospheres covering the range from 15,000 to 35,000 K in effective temperature and 2.5 to 4.5 in log (gravity). The computations involved simultaneous solution of the steady-state statistical equilibrium equations for the populations and of the equation of radiative transfer in the lines. The variables were linearized, and successive corrections were computed until a minimal accuracy of 1/1000 in the line intensities was reached. The common assumption of local thermodynamic equilibrium (LTE) was dropped. The model atmospheres used also were computed by non-LTE methods. Some effects that were incorporated into the calculations were the depression of the continuum by free electrons, hydrogen and ionized helium line blocking, and auto-ionization and dielectronic recombination, which later were found to be insignificant. Use of radiation damping and detailed electron (quadratic Stark) damping constants had small but significant effects on the strong resonance lines of Si III and IV. For weak and intermediate-strength lines, large differences with respect to LTE computations, the results of which are also presented, were found in line shapes and strengths. For the strong lines the differences are generally small, except for the models at the hot, low-gravity extreme of our range. These computations should be useful in the interpretation of the spectra of stars in the spectral range B0-B5, luminosity classes III, IV, and V.

Kamp, L. W.↗

NASA NTRS1989

Grains charges in interstellar clouds

The charge of cosmic grains could play an important role in many astrophysical phenomena. It probably has an influence on the coagulation of grains and more generally on grain-grain collisions, and on interaction between charged particles and grains which could lead to the formation of large grains or large molecules. The electrostatic charge of grains depends mainly on the nature of constitutive material of the grain and on the physical properties of its environment: it results from a delicate balance between the plasma particle collection and the photoelectron emission, both of them depending on each other. The charge of the grain is obtained in two steps: (1) using the numerical model the characteristics of the environment of the grain are computed; (2) the charge of a grain which is embedded in this environment is determined. The profile of the equilibrium charge of some typical grains through different types of interstellar clouds is obtained as a function of the depth of the cloud. It is shown that the grain charge can reach high values not only in hot diffuse clouds, but also in clouds with higher densities. The results are very sensitive to the mean UV interstellar radiation field. Three parameters appear to be essential but with different levels of sensitivity of the charge: the gas density, the temperature, and the total thickness of the cloud.

Bel, N.↗

NASA NTRS1994

Dynamics of binary-disk interaction. 1: Resonances and disk gap sizes

We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.

Artymowicz, Pawel↗

NASA NTRS2017

High-order Accurate Finite-Volume Formulations for the Pressure Gradient Force in Layered Ocean Models

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates andor terrain-following representations.

pressure gradient force↗

NASA NTRS1994

Accurate interlaminar stress recovery from finite element analysis

The accuracy and robustness of a two-dimensional smoothing methodology is examined for the problem of recovering accurate interlaminar shear stress distributions in laminated composite and sandwich plates. The smoothing methodology is based on a variational formulation which combines discrete least-squares and penalty-constraint functionals in a single variational form. The smoothing analysis utilizes optimal strains computed at discrete locations in a finite element analysis. These discrete strain data are smoothed with a smoothing element discretization, producing superior accuracy strains and their first gradients. The approach enables the resulting smooth strain field to be practically C1-continuous throughout the domain of smoothing, exhibiting superconvergent properties of the smoothed quantity. The continuous strain gradients are also obtained directly from the solution. The recovered strain gradients are subsequently employed in the integration o equilibrium equations to obtain accurate interlaminar shear stresses. The problem is a simply-supported rectangular plate under a doubly sinusoidal load. The problem has an exact analytic solution which serves as a measure of goodness of the recovered interlaminar shear stresses. The method has the versatility of being applicable to the analysis of rather general and complex structures built of distinct components and materials, such as found in aircraft design. For these types of structures, the smoothing is achieved with 'patches', each patch covering the domain in which the smoothed quantity is physically continuous.

Tessler, Alexander↗

NASA NTRS1998

Locations of Halide Ions in Tetragonal Lysozyme Crystals

Anions play an important role in the crystallization of lysozyme, and are known to bind to the crystalline protein. Previous studies employing X-ray crystallography had found one chloride ion binding site in the tetragonal crystal form of the protein and four nitrate ion binding sites in the monoclinic form. Studies using other approaches have reported more chloride ion binding sites, but their locations were not known. Knowing the precise location of these anions is also useful in determining the correct electrostatic fields surrounding the protein. In the first part of this study the anion positions in the tetragonal form were determined from the difference Fourier map obtained from the lysozyme crystals grown in bromide and chloride solutions under identical conditions. The anion locations were then obtained from standard crystallographic methods and five possible anion binding sites were found in this manner. The sole chloride ion binding site found in previous studies was confirmed. The remaining four sites were new ones for tetragonal lysozyme crystals. However, three of these new sites and the previously found one corresponded to the four unique binding sites found for nitrate ions in monoclinic crystals. This suggests that most of the anion binding sites in lysozyme remain unchanged, even when different anions and different crystal forms of lysozyme are employed. It is unlikely that there are many more anions in the tetragonal lysozyme crystal structure. Assuming osmotic equilibrium it can be shown that there are at most three more anions in the crystal channels. Some of the new anion binding sites found in this study were, as expected, in pockets containing basic residues. However, some of them were near neutral, but polar, residues. Thus, the study also showed the importance of uncharged, but polar groups, on the protein surface in determining its electrostatic field. This was important for the second part of this study where the electrostatic field surrounding the protein was accurately determined. This was achieved by solving the linearized version of the Poisson-Boltzmann equation for the protein in solution. The solution was computed employing the commercial code Delphi which uses a finite difference technique. This has recently become available as a module in the general protein visualization code Insight II. Partial charges were assigned to the polar groups of lysozyme for the calculations done here. The calculations showed the complexity of the electrostatic field surrounding the protein. Although most of the region near the protein surface had a positive field strength, the active site cleft was negatively charged and this was projected a considerable distance. This might explain the occurrence of "head-to-side" interactions in the formation of lysozyme aggregates in solution. Pockets of high positive field strength were also found in the vicinity of the anion locations obtained from the crystallographic part of this study, confirming the validity of these calculations. This study clearly shows not only the importance of determining the counterion locations in protein crystals and the electrostatic fields surrounding the protein, but also the advantage of performing them together.

Lim, Kap↗

NASA NTRS2005

Updated Chemical Kinetics and Sensitivity Analysis Code

An updated version of the General Chemical Kinetics and Sensitivity Analysis (LSENS) computer code has become available. A prior version of LSENS was described in "Program Helps to Determine Chemical-Reaction Mechanisms" (LEW-15758), NASA Tech Briefs, Vol. 19, No. 5 (May 1995), page 66. To recapitulate: LSENS solves complex, homogeneous, gas-phase, chemical-kinetics problems (e.g., combustion of fuels) that are represented by sets of many coupled, nonlinear, first-order ordinary differential equations. LSENS has been designed for flexibility, convenience, and computational efficiency. The present version of LSENS incorporates mathematical models for (1) a static system; (2) steady, one-dimensional inviscid flow; (3) reaction behind an incident shock wave, including boundary layer correction; (4) a perfectly stirred reactor; and (5) a perfectly stirred reactor followed by a plug-flow reactor. In addition, LSENS can compute equilibrium properties for the following assigned states: enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. For static and one-dimensional-flow problems, including those behind an incident shock wave and following a perfectly stirred reactor calculation, LSENS can compute sensitivity coefficients of dependent variables and their derivatives, with respect to the initial values of dependent variables and/or the rate-coefficient parameters of the chemical reactions.

Radhakrishnan, Krishnan↗