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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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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

A fast, high-order solver for the Grad–Shafranov equation

We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

An implicit logarithmic finite-difference technique for two dimensional coupled viscous Burgers’ equation

This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Application of Analytical Heat Transfer Models of Multi-layered Natural and Engineered Barriers in Potential High-Level Nuclear Waste Repositories - 12435

A combination of transient heat transfer analytical solutions for a finite line source, a series of point sources, and a series of parallel infinite line sources were combined with a quasi-steady-state multi-layered cylindrical solution to simulate the temperature response of a deep geologic radioactive waste repository with multi-layered natural and engineered barriers. This evaluation was performed to provide information to scientists and decision makers to compare candidate geologic media for a repository (crystalline rock [granite], clay, salt, and deep borehole), and to provide input for the future evaluation of the trade-off between pre-emplacement surface storage time, waste package size, and repository footprint. This approach was selected in favor of the finite element solution typically used to analyze the temperature response because it allowed rapid comparison of a large number of alternative disposal options and design configurations. More than 100 combinations of waste form, geologic environment, repository design configuration, and surface storage times were analyzed and compared. The analytical solution approach used to analyze the repository temperature response allowed rapid comparison of a large number of alternative disposal options and design configurations. More than 100 combinations of waste form, geologic environment, repository design configuration, and surface storage times were analyzed and compared. This approach allowed investigation of the sensitivity of the results to combinations of parameters that show that there is much flexibility to be gained in terms of spent fuel management options by varying a few key parameters. This initial analysis used representative design concepts and thermal constraints based on international design concepts, and it also included waste forms representing future fuel cycles with high burnup fuels. Unlike repository designs with large open tunnels and pre-closure ventilation, all of the disposal concepts analyzed in this study used enclosed emplacement modes, where the waste packages were in direct contact with encapsulating engineered or natural materials. The deep borehole repository concept limits the size of the SNF waste packages and may require rod consolidation to fit within the drill casing diameter. A single assembly waste package, assuming rod consolidation, was evaluated in the current analysis. Similar size restrictions apply for the HLW canisters. At this time no thermal constraints have been defined for the deep borehole repository concept. Representative EBS materials and properties were evaluated. However, changes in EBS design concepts and materials can also have significant effects on the maximum waste package surface temperature. Increased thermal conductivity of the buffer layer can be achieved by using an engineered buffer consisting of a mixture of graphite, sand, and bentonite [14]. One of the advantages of the analytical model is that it highlights the sensitivity of the results to the parameters that define the repository layout, including spacing between axial and lateral neighboring waste packages and drifts. It is clear that repository layout adjustments can be made to reduce the calculated peak temperatures. The results also show that significant reductions in required surface storage times can be achieved if higher thermal constraints can be justified Additional studies are planned to evaluate the trade-offs between surface storage times, repository layout parameters, and variations in EBS design concepts. Model validation and uncertainties will also be addressed. It is expected that shorter surface storage times and more optimized repository design configurations may be achieved. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2010

Polarization dynamics in nonlinear anisotropic fibers

We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincare sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincare sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi's functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Analytically solvable chaotic oscillator based on a first-order filter

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A three-dimensional laser ray-tracing methodology for radiation-hydrodynamics simulations

We report on a methodology for performing laser ray-tracing in three spatial dimensions for radiation-hydrodynamics simulation codes. Our method, which is an extension of that developed in Haines et al., Comput. Fluids 201, 104478 (2020), utilizes an automatically generated separate mesh for the laser ray-tracing from the radiation-hydrodynamics mesh. This enables the laser mesh to be tailored to minimize ray noise with significantly fewer rays than would be required when the ray-tracing is performed on the radiation-hydrodynamics mesh, primarily by allowing the use of high-aspect-ratio cells that are not suitable for hydrodynamics solvers. For a planar target, we show that our method provides a ≈ 100× reduction in computational expense to achieve a fixed level of ray noise relative to ray-tracing directly on the radiation-hydrodynamics mesh. The relatively low ray requirement also enables efficient computation of cross-beam energy transfer. Each cell in the logically cubic laser mesh is a non-convex dodecahedron with triangular sides, and numerical integration of the ray trajectories and inverse bremsstrahlung is performed by mapping each cell to the unit cube. We will describe our methodology in detail as well as its implementation in the xRAGE radiation-hydrodynamics code, discuss performance, and present the results from applying the methodology to test problems with analytic solutions for laser ray-tracing through a quadratic density gradient with an analytic solution as well as for a laser-driven heat front. In 3D radiation-hydrodynamics simulations of laser-driven experiments performed on the National Ignition Facility, laser ray-tracing with our methodology uses less than 1% of total computational time while introducing acceptably low levels of ray noise.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1985

Large-scale separation and hysteresis in cascades

An approach using a two-dimensional thin aerofoil, allied with the theory of viscous bluff-body separation, is used to study the initial cross-over from massive separation to an attached flow in a single-row unstaggered cascade. Analytic solutions are developed for the limit of small cascade-spacing. From the analytic solutions several interesting features of the cascade are examined, including multiple-solution branches and multiple regions of hysteresis. In addition, numerical results are presented for several selected aerofoils. Some of the aerofoils are found to contain markedly enlarged regions of hysteresis for certain critical cascade spacings.

Rothmayer, A. P.↗
DOE OSTI2010

SCALING LAWS AND TEMPERATURE PROFILES FOR SOLAR AND STELLAR CORONAL LOOPS WITH NON-UNIFORM HEATING

The bulk of solar coronal radiative loss consists of soft X-ray emission from quasi-static loops at the cores of active regions. In order to develop diagnostics for determining the heating mechanism of these loops from observations by coronal imaging instruments, I have developed analytical solutions for the temperature structure and scaling laws of loop strands for a set of temperature- and pressure-dependent heating functions that encompass heating concentrated at the footpoints, uniform heating, and heating concentrated at the loop apex. Key results are that the temperature profile depends only weakly on the heating distribution-not sufficiently to be of significant diagnostic value-and that the scaling laws survive for this wide range of heating distributions, but with the constant of proportionality in the Rosner-Tucker-Vaiana scaling law (P{sub 0} L {approx} T {sup 3}{sub max}) depending on the specific heating function. Furthermore, quasi-static solutions do not exist for an excessive concentration of heating near the loop footpoints, a result in agreement with recent numerical simulations. It is demonstrated that a generalization of the results to a set of solutions for strands with a functionally prescribed variable diameter leads to only relatively small correction factors in the scaling laws and temperature profiles for constant diameter loop strands. A quintet of leading theoretical coronal heating mechanisms is shown to be captured by the formalism of this paper, and the differences in thermal structure between them may be verified through observations. Preliminary results from full numerical simulations demonstrate that, despite the simplifying assumptions, the analytical solutions from this paper are accurate and stable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Ion-acoustic cnoidal waves in a quantum plasma

Nonlinear ion-acoustic cnoidal wave structures are studied in an unmagnetized quantum plasma. Using the reductive perturbation method, a Korteweg-de Vries equation is derived for appropriate boundary conditions and nonlinear periodic wave solutions are obtained. The corresponding analytical solution and numerical plots of the ion-acoustic cnoidal waves and solitons in the phase plane are presented using the Sagdeev pseudo-potential approach. The variations in the nonlinear potential of the ion-acoustic cnoidal waves are studied at different values of quantum parameter H{sub e} which is the ratio of electron plasmon energy to electron Fermi energy defined for degenerate electrons. It is found that both compressive and rarefactive ion-acoustic cnoidal wave structures are formed depending on the value of the quantum parameter. The dependence of the wavelength and frequency on nonlinear wave amplitude is also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Nonlinear galactic dynamos and the magnetic pitch angle

Pitch angles p of the large-scale magnetic fields B-bar of spiral galaxies have previously been inferred from observations to be systematically larger in magnitude than predicted by standard mean-field dynamo theory. This discrepancy is more pronounced if dynamo growth has saturated, which is reasonable to assume given that such fields are generally inferred to be close to energy equipartition with the interstellar turbulence. This “pitch angle problem” is explored using local numerical mean-field dynamo solutions as well as asymptotic analytical solutions. It is first shown that solutions in the saturated or kinematic regimes depend on only five dynamo parameters, two of which are tightly constrained by observations of galaxy rotation curves. The remaining three-dimensional (dimensionless) parameter space can be constrained to some extent using theoretical arguments. Predicted values of |p| can be as large as ∼40{sup ∘}, which is similar to the largest values inferred from observations, but only for a small and non-standard region of parameter space. We argue, based on independent evidence, that such non-standard parameter values are plausible. However, these values are located toward the boundary of the allowed parameter space, suggesting that additional physical effects may need to be incorporated. We therefore suggest possible directions for extending the basic model considered.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Particle motion around black hole in Horava-Lifshitz gravity

Analytical solutions of Maxwell equations around a black hole immersed in an external uniform magnetic field in the background of the Kehagias-Sfetsos (KS) asymptotically flat black hole solution of Horava-Lifshitz gravity have been found. The influence of a magnetic field on the effective potential of the radial motion of a charged test particle around a black hole immersed in an external magnetic field in Horava-Lifshitz gravity has been investigated by using the Hamilton-Jacobi method. An exact analytical solution for dependence of the minimal radius of the circular orbits r{sub mc} from KS parameter {omega} for motion of a test particle around a spherical symmetric black hole in Horava-Lifshitz gravity has been derived. The critical values of the particle's angular momentum for captured particles by a black hole in Horava-Lifshitz gravity have been obtained numerically. The comparison of the obtained numerical results with the astrophysical observational data on the radii of the innermost stable circular orbits gives us the estimation of the parameter as {omega}{approx_equal}3.6{center_dot}10{sup -24} cm{sup -2}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Analysis of gas membrane ultra-high purification of small quantities of mono-isotopic silane

A small quantity of high-value, crude, mono-isotopic silane is a prospective gas for a small-scale, high-recovery, ultra-high membrane purification process. This is an unusual application of gas membrane separation for which we provide a comprehensive analysis of a simple purification model. The goal is to develop direct analytic expressions for estimating the feasibility and efficiency of the method, and guide process design; this is only possible for binary mixtures of silane in the dilute limit which is a somewhat realistic case. In addition, analytic solutions are invaluable to verify numerical solutions obtained from computer-aided methods. Hence, in this paper we provide new analytic solutions for the purification loops proposed. Among the common impurities in crude silane, methane poses a special membrane separation challenge since it is chemically similar to silane. Other potential problematic compounds are: ethylene, diborane and ethane (in this order). Nevertheless, we demonstrate, theoretically, that a carefully designed membrane system may be able to purify mono-isotopic, crude silane to electronics-grade level in a reasonable amount of time and expenses. We advocate a combination of membrane materials that preferentially reject heavy impurities based on mobility selectivity, and light impurities based on solubility selectivity. We provide estimates for the purification of significant contaminants of interest. In this study, we suggest cellulose acetate and polydimethylsiloxane as examples of membrane materials on the basis of limited permeability data found in the open literature. We provide estimates on the membrane area needed and priming volume of the cell enclosure for fabrication purposes when using the suggested membrane materials. These estimates are largely theoretical in view of the absence of reliable experimental data for the permeability of silane. And finally, future extension of this work to the non-dilute limit may apply to the recovery of silane from rejected streams of natural silicon semi-conductor processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Space-charge-limited currents for cathodes with electric field enhanced geometry

This paper presents the approximate analytic solutions of current density for annulus and circle cathodes. The current densities of annulus and circle cathodes are derived approximately from first principles, which are in agreement with simulation results. The large scaling laws can predict current densities of high current vacuum diodes including annulus and circle cathodes in practical applications. In order to discuss the relationship between current density and electric field on cathode surface, the existing analytical solutions of currents for concentric cylinder and sphere diodes are fitted from existing solutions relating with electric field enhancement factors. It is found that the space-charge-limited current density for the cathode with electric-field enhanced geometry can be written in a general form of J = g(β{sub E}){sup 2}J{sub 0}, where J{sub 0} is the classical (1D) Child-Langmuir current density, β{sub E} is the electric field enhancement factor, and g is the geometrical correction factor depending on the cathode geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Kinetic simulations and reduced modeling of longitudinal sideband instabilities in non-linear electron plasma waves

Kinetic Vlasov simulations of one-dimensional finite amplitude Electron Plasma Waves are performed in a multi-wavelength long system. A systematic study of the most unstable linear sideband mode, in particular its growth rate γ and quasi- wavenumber δk, is carried out by scanning the amplitude and wavenumber of the initial wave. Simulation results are successfully compared against numerical and analytical solutions to the reduced model by Kruer et al. [Phys. Rev. Lett. 23, 838 (1969)] for the Trapped Particle Instability (TPI). A model recently suggested by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)], which in addition to the TPI accounts for the so-called Negative Mass Instability because of a more detailed representation of the trapped particle dynamics, is also studied and compared with simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1999

A Spherical Earth Solution for TOA Lightning Location Retrieval

The problem of retrieving ligntning, ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered, It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (e.g., minimization). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A summary of a quasi-analytic extension of the spherical Earth solution to an oblate spheroid Earth geometry is also provided.

Koshak, W. J.↗
DOE OSTI2012

Solving non-Markovian open quantum systems with multi-channel reservoir coupling

We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically. - Highlights: Black-Right-Pointing-Pointer The concept of multi-channel vs. single-channel reservoir coupling is rigorously defined. Black-Right-Pointing-Pointer The non-Markovian quantum state diffusion equation for arbitrary multi-channel reservoir coupling is derived. Black-Right-Pointing-Pointer An exact time-local master equation is derived under certain conditions. Black-Right-Pointing-Pointer The analytical solution to the three-level system in a vee-type configuration is found. Black-Right-Pointing-Pointer The evolution of the three-level system under generalized Ornstein-Uhlenbeck noise is plotted for many parameter regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Vertically stratified two-phase flow in a curved channel: Insights from a domain perturbation analysis

In this work, we investigate the fully developed flow field of two vertically stratified fluids (one phase flowing above the other) in a curved channel of rectangular cross section. The domain perturbation technique is applied to obtain an analytical solution in the asymptotic limit of low Reynolds numbers and small curvature ratios (the ratio of the width of the channel to its radius of curvature). The accuracy of this solution is verified by comparison with numerical simulations of the nonlinear equations. The flow is characterized by helical vortices within each fluid, which are driven by centrifugal forces. The number of vortices and their direction of circulation varies with the parameters of the system (the volume fraction, viscosity ratio, and Reynolds numbers). We identify nine distinct flow patterns and organize the parameter space into corresponding flow regimes. We show that the fully developed interface between the fluids is not horizontal, in general, but is deformed by normal stresses associated with the circulatory flow. The results are especially significant for flows in microchannels, where the Reynolds numbers are small. The mathematical results in this paper include an analytical solution to two coupled biharmonic partial differential equations; these equations arise in two-phase, two-dimensional Stokes flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

EFFECT OF FINITE LARMOR RADIUS ON COSMIC-RAY PENETRATION INTO AN INTERPLANETARY MAGNETIC FLUX ROPE

We discuss a mechanism for cosmic-ray penetration into an interplanetary magnetic flux rope, particularly the effect of the finite Larmor radius and magnetic field irregularities. First, we derive analytical solutions for cosmic-ray behavior inside a magnetic flux rope, on the basis of the Newton-Lorentz equation of a particle, to investigate how cosmic rays penetrate magnetic flux ropes under an assumption of there being no scattering by small-scale magnetic field irregularities. The results show that the behavior of a particle is determined by only one parameter f{sub 0}, that is, the ratio of the Larmor radius at the flux rope axis to the flux rope radius. The analytical solutions show that cosmic rays cannot penetrate into the inner region of a flux rope by only gyration and gradient-curvature drift in the case of small f{sub 0}. Next, we perform a numerical simulation of a cosmic-ray penetration into an interplanetary magnetic flux rope by adding small-scale magnetic field irregularities. The results show that cosmic rays can penetrate into a magnetic flux rope even in the case of small f{sub 0} because of the effect of small-scale magnetic field irregularities. This simulation also shows that a cosmic-ray density distribution is greatly different from that deduced from a guiding center approximation because of the effect of the finite Larmor radius and magnetic field irregularities for the case of a moderate to large Larmor radius compared to the flux rope radius.

79 ASTRONOMY AND ASTROPHYSICS↗