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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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NASA NTRS1994

A rapid-pressure correlation representation consistent with the Taylor-Proudman theorem materially-frame-indifferent in the 2D limit

A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.

Ristorcelli, J. R.↗

NASA NTRS2009

Extending Newtonian Dynamics to Include Stochastic Processes

A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.

Zak, Michail↗

NASA NTRS1986

Quasistatic evolution of magnetostatic coronal structures

Four separate but related studies of coronal magnetostatic equilibria under a variety of boundary conditions and distributions of coronal current are reviewed. Physically, all four studies assume an axisymmetric corona whose radial magnetic field at the coronal base is dipolar. Electric currents in the model coronas are assumed to flow in the azimuthal direction, giving rise to Lorentz forces that must be balanced by pressure gradients and gravity. Mathematically, such coronas are described by the equation of magnetostatic force balance and Ampere's law. Although highly idealized, the axisymmetric magnetostatic models described provide insights into the behavior of a variety of coronal structures. The models show how more realistic current sheet boundary conditions and coronal density variations may be modeled.

Wolfson, Richard↗

NASA NTRS1983

Composition of the Venus atmosphere

After giving an historical account of the development of Venus atmospheric composition explorations and the various instrumental techniques used in them, attention is given to recommended values for the mixing ratios of gases at altitudes below 100 km. Together with the various constituent groups of gases, their observations, and related processes and models, the mathematical background for current one-dimensional photochemical and transport models is given. Excited species are then discussed, and references to upper limits for the abundances of unobserved gases are listed. Available data on isotopic abundances are assessed, and questions pertinent to the further investigation of the Venus atmosphere's origin and evolution are formulated.

Von Zahn, U.↗

NASA NTRSDate not supplied

CFD Predictions of Boiling Regime Transitions during Line Chilldown validated against a 1G LN2 Experiment

Introduction Before filling a propellant tank on the ground or in Space, the transfer line between the donor and receiver tanks must be cooled down preferably by sacrificing a minimum amount of the cryogenic fluid. The cryogenic line chill-down process involves a transition between different flow boiling regimes, namely, film boiling, transition film boiling, and nucleate boiling which are complex and may be quite gravity-dependent. Capturing these boiling phenomena and predicting the transition between them in a CFD framework is new and challenging both for 1g and microgravity applications. Materials & Methods The present work addresses this challenge by employing a two-phase Eulerian approach in the context of a homogeneous fluid mixture together with the Lee phase change model to capture the film boiling regime of the chill-down process using ANSYS Fluent®. The nucleate boiling regime is predicted by incorporating an in-house developed sub-grid model that accounts for bubble nucleation, bubble growth, bubble departure diameter, and their shedding frequency. The sub-grid model is encoded and implemented into Fluent via a user-defined function for the wall-fluid heat flux calculations. The mathematical formulation and numerical implementation of the CFD model are described in detail. The coupled CFD-Subgrid model is validated against published experimental data for liquid nitrogen chill-down of a heated stainless-steel pipe in 1g. Results Numerical simulation results show good agreements between the CFD predictions of the wall temperature evolution, rewetting temperature, and transition between film and nucleate boiling, with the experimental measurements published by Darr et al [2] for several different LN2 flowrates in the vertical pipe orientation. The CFD predictions for the wall temperature distribution indicate a rapid quenching of the wall at two upstream and downstream temperature sensing locations as compared to the experimental measurement. The only tuning parameter in the CFD model is the Lee mass transfer coefficient. The CFD Model predicts the Liedenfrost rewetting temperature in close agreement with the experiment. This marks a transition between stable and transitionary flow boiling regimes. The CFD-predicted boiling curve for the downstream sensor location is also compared against its experimental counterpart and indicates that the model is able to predict all the key temperature and heat flux parameters during the transitions from stable to transitionary film boiling to nucleate boiling in close agreement with the experiment. A sequence of predicted volume fraction, and temperature contours depicting these transitions will be presented.

Evaporation Condensation↗

NASA NTRS1984

Galactic chemical evolution and nucleocosmochronology - Standard model with terminated infall

Some exactly soluble families of models for the chemical evolution of the Galaxy are presented. The parameters considered include gas mass, the age-metallicity relation, the star mass vs. metallicity, the age distribution, and the mean age of dwarfs. A short BASIC program for calculating these parameters is given. The calculation of metallicity gradients, nuclear cosmochronology, and extinct radioactivities is addressed. An especially simple, mathematically linear model is recommended as a standard model of galaxies with truncated infall due to its internal consistency and compact display of the physical effects of the parameters.

Clayton, D. D.↗

NASA NTRS2002

Stagnation Flow in Streamer Boundaries

It is possible for flow tubes adjacent to closed magnetic field lines on the boundaries of streamers to have spreading factors that change rapidly according to height. Mathematical models in this thin layer are prone to uncertainties. In this paper we use an analytical model of magnetically closed and adjacent open regions to calculate the spreading factor close to the closed field lines and near the flow on the open field lines. We recovered the shape of the closed field region, or helmet, and show the evolution of the helmet under increasing temperature. We also show why and when stagnation flow can occur in the area of the cusp at the top of the helmet.

Suess, S. T.↗

NASA NTRS1998

A Compendium of Wind Statistics and Models for the NASA Space Shuttle and Other Aerospace Vehicle Programs

The wind profile with all of its variations with respect to altitude has been, is now, and will continue to be important for aerospace vehicle design and operations. Wind profile databases and models are used for the vehicle ascent flight design for structural wind loading, flight control systems, performance analysis, and launch operations. This report presents the evolution of wind statistics and wind models from the empirical scalar wind profile model established for the Saturn Program through the development of the vector wind profile model used for the Space Shuttle design to the variations of this wind modeling concept for the X-33 program. Because wind is a vector quantity, the vector wind models use the rigorous mathematical probability properties of the multivariate normal probability distribution. When the vehicle ascent steering commands (ascent guidance) are wind biased to the wind profile measured on the day-of-launch, ascent structural wind loads are reduced and launch probability is increased. This wind load alleviation technique is recommended in the initial phase of vehicle development. The vehicle must fly through the largest load allowable versus altitude to achieve its mission. The Gumbel extreme value probability distribution is used to obtain the probability of exceeding (or not exceeding) the load allowable. The time conditional probability function is derived from the Gumbel bivariate extreme value distribution. This time conditional function is used for calculation of wind loads persistence increments using 3.5-hour Jimsphere wind pairs. These increments are used to protect the commit-to-launch decision. Other topics presented include the Shuttle Shuttle load-response to smoothed wind profiles, a new gust model, and advancements in wind profile measuring systems. From the lessons learned and knowledge gained from past vehicle programs, the development of future launch vehicles can be accelerated. However, new vehicle programs by their very nature will require specialized support for new databases and analyses for wind, atmospheric parameters (pressure, temperature, and density versus altitude), and weather. It is for this reason that project managers are encouraged to collaborate with natural environment specialists early in the conceptual design phase. Such action will give the lead time necessary to meet the natural environment design and operational requirements, and thus, reduce development costs.

Smith, O. E.↗

NASA NTRS1983

A mathematical model for crop spectral-temporal trajectories based on a plant growth model

The Kubelka-Munk radiative transfer model is combined with an approximation of Kauth-Thomas greeness and brightness transforms to derive approximate closed form expressions for crop greeness and brightness surrogates in terms of canopy biomass. The greeness relation derived resembles an existing empirical relation between leaf area index and greeness. A simple growth model based on interception and utilization of photosynthetically active radiation is developed and used to describe the time evolution of greeness and brightness. The model developed does not yet yield definitive profile calculations but suggests a conceptual framework which may be found useful for further profile analysis.

Woolford, T. L.↗

NASA NTRS1978

Global crop production forecasting data system analysis

The author has identified the following significant results. Findings led to the development of a theory of radiometric discrimination employing the mathematical framework of the theory of discrimination between scintillating radar targets. The theory indicated that the functions which drive accuracy of discrimination are the contrast ratio between targets, and the number of samples, or pixels, observed. Theoretical results led to three primary consequences, as regards the data system: (1) agricultural targets must be imaged at correctly chosen times, when the relative evolution of the crop's development is such as to maximize their contrast; (2) under these favorable conditions, the number of observed pixels can be significantly reduced with respect to wall-to-wall measurements; and (3) remotely sensed radiometric data must be suitably mixed with other auxiliary data, derived from external sources.

Castruccio, P. A.↗

NASA NTRS1996

Controlled Quantum Packets

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

DeMartino, Salvatore↗

NASA NTRS1992

A first-order global model of Late Cenozoic climatic change: Orbital forcing as a pacemaker of the ice ages

The development of a theory of the evolution of the climate of the earth over millions of years can be subdivided into three fundamental, nested, problems: (1) to establish by equilibrium climate models (e.g., general circulation models) the diagnostic relations, valid at any time, between the fast-response climate variables (i.e., the 'weather statistics') and both the prescribed external radiative forcing and the prescribed distribution of the slow response variables (e.g., the ice sheets and shelves, the deep ocean state, and the atmospheric CO2 concentration); (2) to construct, by an essentially inductive process, a model of the time-dependent evolution of the slow-response climatic variables over time scales longer than the damping times of these variables but shorter than the time scale of tectonic changes in the boundary conditions (e.g., altered geography and elevation of the continents, slow outgassing, and weathering) and ultra-slow astronomical changes such as in the solar radiative output; and (3) to determine the nature of these ultra-slow processes and their effects on the evolution of the equilibrium state of the climatic system about which the above time-dependent variations occur. All three problems are discussed in the context of the theory of the Quaternary climate, which will be incomplete unless it is embedded in a more general theory for the fuller Cenozoic that can accommodate the onset of the ice-age fluctuations. We construct a simple mathematical model for the Late Cenozoic climatic changes based on the hypothesis that forced and free variations of the concentration of atmospheric greenhouse gases (notably CO2), coupled with changes in the deep ocean state and ice mass, under the additional 'pacemaking' influence of earth-orbital forcing, are primary determinants of the climate state over this period. Our goal is to illustrate how a single model governing both very long term variations and higher frequency oscillatory variations in the Pleistocene can be formulated with relatively few adjustable parameters.

Saltzman, Barry↗

NASA NTRS1990

Zodiacal dust bands - Their relation to asteroid families

The zodiacal dust band phenomenon is presently reproduced by a mathematical model of orbitally evolved collisional debris spatial distributions whose torus exhibits particle-density maxima at heliocentric latitudes near its constituent particles' mean proper orbital inclinations, as well as near the loci of the particle orbits' perihelia and aphelia. Models of dust toruses for seven asteroid families are generated and compared with observations of the principal dust bands. Nonequilibrium models of dust band production and evolution furnish a framework within which all dust band observations can be understood.

Sykes, Mark V.↗

NASA NTRS2014

Numerical Modeling of Ocular Dysfunction in Space

Upon introduction to microgravity, the near-loss of hydrostatic pressure causes a marked cephalic (headward) shift of fluid in an astronaut's body. The fluid shift, along with other factors of spaceflight, induces a cascade of interdependent physiological responses which occur at varying time scales. Long-duration missions carry an increased risk for the development of the Visual Impairment and Intracranial Pressure (VIIP) syndrome, a spectrum of ophthalmic changes including posterior globe flattening, choroidal folds, distension of the optic nerve sheath, kinking of the optic nerve and potentially permanent degradation of visual function. In the cases of VIIP found to date, the initial onset of symptoms occurred after several weeks to several months of spaceflight, by which time the gross bodily fluid distribution is well established. We are developing a suite of numerical models to simulate the effects of fluid shift on the cardiovascular, central nervous and ocular systems. These models calculate the modified mean volumes, flow rates and pressures that are characteristic of the altered quasi-homeostatic state in microgravity, including intracranial and intraocular pressures. The results of the lumped models provide initial and boundary data to a 3D finite element biomechanics simulation of the globe, optic nerve head and retrobulbar subarachnoid space. The integrated set of models will be used to investigate the evolution of the biomechanical stress state in the ocular tissues due to long-term exposure to microgravity.

intraocular pressure↗

NASA NTRS1993

A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence

The turbulent mass flux, or equivalently the fluctuating Favre velocity mean, appears in the first and second moment equations of compressible kappa-epsilon and Reynolds stress closures. Mathematically it is the difference between the unweighted and density-weighted averages of the velocity field and is therefore a measure of the effects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the effects of the mean density gradients, in the same way the anisotropy tensor characterizes the effects of the mean velocity gradients. An evolution equation for the turbulent mass flux is derived. A truncation of this equation produces an algebraic expression for the mass flux. The mass flux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results.

Ristorcelli, J. R.↗

NASA NTRS2001

The Use of Non-Standard Devices in Finite Element Analysis

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Schur, Willi W.↗

NASA NTRS1977

Orbit-orbit resonances among natural satellites

A qualitative physical description of the orbital resonance mechanism based on a previously published (Greenberg et al. 1972; Greenberg, 1973) mathematical analysis is presented. The fundamental principles of the resonance mechanism are illustrated by an examination of the Titan-Hyperion case. More complex resonances, including Enceladus-Dione, Mimas-Tethys are considered. Resonance phenomena involving the rings of Saturn, the inner three satellites of Uranus, and the inner three Galilean satellites of Jupiter are also discussed. The role of analyses of resonance phenomena in developing theories of satellite formation and evolution is examined.

Greenberg, R.↗

NASA NTRS2010

Better Modeling of Electrostatic Discharge in an Insulator

An improved mathematical model has been developed of the time dependence of buildup or decay of electric charge in a high-resistivity (nominally insulating) material. The model is intended primarily for use in extracting the DC electrical resistivity of such a material from voltage -vs.- current measurements performed repeatedly on a sample of the material over a time comparable to the longest characteristic times (typically of the order of months) that govern the evolution of relevant properties of the material. This model is an alternative to a prior simplistic macroscopic model that yields results differing from the results of the time-dependent measurements by two to three orders of magnitude.

Pekov, Mihail↗