Search NASA⌕ Search

SEARCH · Search NASA

Results for “finite difference method”

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 1,495 records · Page 83

Time Scale Effects on the Temperature Coefficient of Reactivity

For a nuclear reactor, the temperature coefficient of reactivity (TCR) is of significance for both power control and safety analysis, but it is not always a constant. For example, the TCR may be dependent upon temperature due to Doppler broadening, and may be also dependent upon time scale due to heat transfer and thermal expansion. A fast burst reactor is a favorable nuclear facility to simulate the time scale effects on the TCR. Fast burst reactors are generally unmoderated research reactors of enriched uranium metal or uranium alloys. The neutrons are fast and the Doppler broadening effects can be neglected, and the TCR is mainly contributed by fuel thermal expansion. Fast burst reactors can operate on both steady state power mode and burst power mode. In steady state power mode, the systems are assumed to be in thermal equilibrium. In burst mode, the full width at half maximum (FWHM) of the power is from tens of microseconds to a few milliseconds, and the heat transfer is generally neglected. If FWHM is short enough, thermal expansion will have a time delay due to inertial effect. This paper is aimed to study the exact time scale effects on the TCR due to thermal expansion. The TCR contributed by the Doppler broadening effects was neglected, because it is relatively small (The k{sub eff} as a function of temperature was also calculated using the Monte Carlo particle transport code JMCT by our group, and no definite difference due to the temperature change was obtained near room temperature), and there is no method to evaluate the time scale dependence of the Doppler broadening effects yet. In the time scale from 1 x 10{sup -6} s to 1 x 10{sup 5} s, the TCR of a Godiva-like spherical fast burst reactor was calculated with perturbation theory. A Godiva-like spherical fast burst reactor was studied, the calculation of the time scale effects on TCR involved thermal conduction, thermoelasticity and reactivity variation analysis. Both the thermal and the thermoelastic problems were solved using ANSYS software. ANSYS is software implementation of finite element simulations, which is widely used in engineering field. The reactivity variation due to thermal expansion was calculated with perturbation theory.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Three-Dimensional Mathematical Model of Oxygen Transport Behavior in Electroslag Remelting Process

A transient three-dimensional model has been proposed to investigate the oxygen transport behavior in electroslag remelting process. The electromagnetism, heat transfer, multiphase flow, and species transport were calculated simultaneously by finite volume method. The volume of fluid approach was adopted to trace the metal–slag–air three-phase flow. Based on the necessary thermodynamics of oxygen transport behavior, a kinetic model was established to predict the mass source terms in species transport equation. The kinetic correction factor was proposed to account for the effect of the oxide scale formed on the electrode on the FeO content in slag. Finally, the effect of applied current on the oxygen transfer was studied. The predicted result agrees well with the measured data when the kinetic correction factor is set to be 0.5. The temperature distribution that affects the thermodynamics differs at the interfaces. The oxygen in air is absorbed into slag due to the oxidation at the slag/air interface. The Fe{sub 2}O{sub 3} in slag and the oxide scale contribute to the increase of FeO content in slag, and the latter one plays the leading role. The oxygen transfer from slag to metal mainly occurs during the formation of the droplet at the slag/metal droplet interface. With the current increasing from 1200 to 1800 A, the oxygen content increases from 76.4 to 89.8 ppm, and then slightly declines to 89.2 ppm when the current increases to 2100 A.

36 MATERIALS SCIENCE↗

Spatial density fluctuations and selection effects in galaxy redshift surveys

One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determining the shape of the correlation function, its possible evolution with redshift and the size and amplitude of large scale structures. Different selection effects, inevitably entering in any observation, introduce important constraints in the measurement of correlations. In the context of galaxy redshift surveys selection effects can be caused by observational techniques and strategies and by implicit assumptions used in the data analysis. Generally all these effects are taken into account by using pair-counting algorithms to measure two-point correlations. We review these methods stressing that they are based on the a-priori assumption that galaxy distribution is spatially homogeneous inside a given sample. We show that, when this assumption is not satisfied by the data, results of the correlation analysis are affected by finite size effects. In order to quantify these effects, we introduce a new method based on the computation of the gradient of galaxy counts along tiny cylinders. We show, by using artificial homogeneous and inhomogeneous point distributions, that this method identifies redshift dependent selection effects and disentangles them from the presence of large scale density fluctuations. We then apply this new method to several redshift catalogs and we find evidence that galaxy distribution, in those samples where selection effects are small enough, is characterized by power-law correlations with exponent γ=0.9 up to 20 Mpc/h followed by a change of slope that, in the range 20–100 Mpc/h, corresponds to a power-law exponent γ=0.25. Whether a crossover to spatial uniformity occurs at ∼ 100 Mpc/h or larger scales cannot be clarified by the present data.

79 ASTRONOMY AND ASTROPHYSICS↗

Efficient Distributed Optimization of Wind Farms Using Proximal Primal-Dual Algorithms: Preprint

This paper presents a distributed approach to perform real-time optimization of large wind farms. Wind turbines in a wind farm typically operate individually to maximize their own performance regardless of the impact of aerodynamic interactions on neighboring turbines. This paper optimizes the overall power produced by a wind farm by formulating and solving a nonconvex optimization problem where the yaw angles are optimized to allow some turbines to operate in misaligned conditions and shape the aerodynamic interactions in a favorable way. The solution of the nonconvex smooth problem is tackled using a proximal primal-dual gradient method, which provably identifies a first-order stationary solution in a global sublinear manner. By adding auxiliary optimization variables for every pair of turbines that are coupled aerodynamically and properly adding consensus constraints into the underlying problem, a distributed algorithm with turbine-to-turbine message passing is obtained; this allows for turbines to be optimized in parallel using local information rather than information from the whole wind farm. This algorithm is computationally light, as it involves closed-form updates. This approach is demonstrated on a large wind farm with 60 turbines. The results indicate that similar performance can be achieved as with finite-difference gradient-based optimization at a fraction of the computational time and thus approach real-time control/optimization.

17 WIND ENERGY↗

Efficient Distributed Optimization of Wind Farms Using Proximal Primal-Dual Algorithms

This paper presents a distributed approach to performing real-time optimization of large wind farms. Wind turbines in a wind farm typically operate individually to maximize their own performance regardless of the impact of aerodynamic interactions on neighboring turbines. This paper optimizes the overall power produced by a wind farm by formulating and solving a nonconvex optimization problem where the yaw angles are optimized to allow some turbines to operate in misaligned conditions and shape the aerodynamic interactions in a favorable way. The solution of the nonconvex smooth problem is tackled using a proximal primal-dual gradient method, which provably identifies a first-order stationary solution in a global sublinear manner. By adding auxiliary optimization variables for every pair of turbines that are coupled aerodynamically, and properly adding consensus constraints into the underlying problem, a distributed algorithm with turbine-to-turbine message passing is obtained; this allows for turbines to be optimized in parallel using local information rather than information from the whole wind farm. This algorithm is computationally light, as it involves closed-form updates. This approach is demonstrated on a large wind farm with 60 turbines. The results indicate that similar performance can be achieved as with finite-difference gradient-based optimization at a fraction of the computational time and thus approaching real-time control/optimization.

17 WIND ENERGY↗

Neutron Number Probability Distributions in a Subcritical System Using the Forward Master Equation

The subject of this paper is the determination of the equilibrium probability distribution function (PDF) of the neutron population within a subcritical multiplying system in the presence of an intrinsic random source as a result of spontaneous fission (SF). Such systems are strongly stochastic and low order moments such as the mean and variance of the neutron number are not sufficient to characterize the true state of the neutron population. We base our work on the forward Master equation in a lumped model formulation for P{sub n} (t), n = 0, 1, 2,..., the probability of there existing η neutrons at time t and obtain solutions for the steady state distributions. The key parameters in this model, neutron lifetime and fission probability, are rigorously obtained by numerically solving the k-eigenvalue problem in a one-dimensional spherical system and using standard definitions of lumped parameters in terms of production and loss rates in finite systems. Previous work has examined single-chain PDFs (a single fission and the resulting progeny) for neutrons, uncoupled neutron-photon single-chain PDFs, both using a lumped backward Master equation formulation, as well as neutron PDFs in supercritical systems. In this paper, we analyze strictly subcritical systems, for which we compare analytically derived solutions with numerical computations for different multiplicity distribution models. For subcritical systems where the neutron population remains finite at steady state, we show that the forward Master equation can be very efficiently solved numerically to obtain the equilibrium distributions. Finally, this work is motivated by potential application to passive interrogation for detection of diverted nuclear materials as well to criticality safety. The equilibrium neutron number probability distribution in subcritical systems has been numerically investigated for several models of the induced and spontaneous fission multiplicity distribution. A well known approximate but closed form solution, namely the quadratic model, was shown to be unacceptably accurate for subcritical media. The matrix inversion and the recursion methods agree well and were benchmarked with the binary fission model, but the recursion formulation proves far more computationally efficient. A qualitative change in the shape of the neutron PDF is observed for increasing source strength, as expected, and a transition from a stochastic to a deterministic system is expected for a sufficiently strong source. We are currently extending this approach to obtain the equilibrium joint distribution of neutrons within the system and those that have leaked, to explicitly represent the neutron PDF as observed by an external detector. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Study of the electrical conductivity at finite temperature in 2D Si- MOSFETs

We investigate the low temperature density dependent conductivity of two dimensional electron systems in zero magnetic field for sample Si-15 MOSFETs. The first purpose of this paper is to establish that the knee of the conductivity σ{sub 0} (σ{sub 0} is the T = 0.3 conductivity obtained by linear extrapolation of the curves of σ (T) for different values of electron density, n{sub s}) as a function of the carrier densities n{sub s} for T = 0.3 K, observed by Lai et al. and Limouny et al. in previous work for two different samples, is independent of temperature. The second aim is the determination of the critical density, n{sub c}, of the metal-insulator transition. Many methods are used in this investigation of n{sub c} which have been already used for other samples. The motivation behind this last study is the observation of many values of n{sub c} that have been obtained from different methods and that are slightly different. We will use in this study three methods with the intention to infer which one is more appropriate to obtain n{sub c}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The Influence of Segregation of Mn on the Recrystallization Behavior of C-Mn Steels

The influence of Mn segregation that occurs during casting on recrystallization kinetics has been explored for a C-Mn automotive steel. A homogenization heat treatment was used to remove Mn segregation, while maintaining a similar initial austenite grain size to the segregated condition, to provide base-line comparison data. Deformation trials were carried out in a Gleeble thermomechanical simulator to 0.3 strains at 900 °C, and significant differences in both recrystallization times and final grain sizes were seen between the two conditions. The segregated sample incurred a longer recrystallization time and a wider recrystallized grain size distribution than the homogenized sample. A finite element model was used to predict the local deformation strains based on variations in material properties caused by segregation; the model used data from XRF elemental mapping of Mn to define the local mechanical properties based on differences in solid solution strengthening. Local strain variations ranging from 0.19 to 0.49 were predicted in the segregated sample for an overall applied 0.3 strain (compared to 0.26 to 0.35 in the homogenized sample); using these strains to predict the recrystallized grain sizes gave a much better prediction for the grain size distribution.

36 MATERIALS SCIENCE↗

Benchmarking NIMROD continuum kinetic formulations through the steady-state poloidal flow

In this work, continuum kinetic formulations are employed as a mechanism to include closure physics in an extended magnetohydrodynamics model. Two continuum kinetic approaches have been implemented in the plasma fluid code NIMROD [Sovinec et al., “Nonlinear magnetohydrodynamics with high-order finite elements,” J. Comput. Phys. 195, 355 (2004)] including a Chapman–Enskog-like (CEL) formulation and a more conventional df approach. Ion kinetic closure schemes are employed to describe the neoclassical flow properties in axisymmetric toroidal geometry. In particular, predictions for steady-state values of poloidal flow profiles in tokamak geometry are provided using both the df formulation and two different solution techniques for the CEL approach. These results are benchmarked against analytic theory predictions as well as results from the drift kinetic code DK4D. The continuum kinetic formulations employed here show agreement with both the analytic theory and DK4D results, and offer a novel velocity space representation involving higher-order finite elements in pitch angle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Pressure distribution along the AGS vacuum chambers with new types of pump out conduits

The AGS HEBT and ring vacuum system is monitored by the discharge current of the magnet ion pumps, which is proportional to the pressure at the inlet port of these ion pumps. The discharge current is measured and suitably calibrated to indicate the ion pump pressure. In order to calculate the vacuum chamber pressure from the ion pump pressure, a detailed analysis is essential to compute their difference in different scenarios. Such analysis has been carried out numerically in the past for the system with the older type of pump out conduits, and similar analysis using FEM in ANSYS is presented in this paper with the newer type of pump out conduit.

43 PARTICLE ACCELERATORS↗

Directing the far-from-equilibrium assembly of nanoparticles in confined liquid crystals by hydrodynamic fields

The assembly of nematic colloids relies on long-range elastic interactions that can be manipulated through external stimuli. Confinement and the presence of a hydrodynamic field alter the defect structures and the energetic interactions between the particles. Here, the assembly landscape of nanoparticles embedded in a nematic liquid crystal confined in a nanochannel under a pressure-driven flow is determined. The dynamics of the liquid crystal tensor alignment field is determined through a Poisson-Bracket framework, namely the Stark–Lubensky equations, coupled with the zero-Reynolds momentum equations and the liquid crystal Landau-de Gennes free energy functional. A second order semi-implicit time integration and a three-dimensional Galerkin finite element method are used to resolve flow and nematic fields under several conditions. In general, the zero Reynolds flow displaces the defects around the particles in the upstream direction and renders the surface anchoring ineffective when the flow strength dominates over the nematic elasticity. More importantly, the potential of mean force for particle assembly is non-monotonic independent of surface anchoring. Our results show that the confinement length scale determines the repulsion/attraction transition between colloids, while the flow strength modifies the static defect structure surrounding the particles and determines the magnitude of the energetic barrier for successful assembly. In the attractive regime, the particles move at different rates through the nematic until one particle eventually catches up with the other. This process occurs against or along the direction of flow depending on the flow strength. Ultimately, these results provide a template for engineering and controlling the transport and assembly of nanoparticles under far-from equilibrium conditions in anisotropic media.

36 MATERIALS SCIENCE↗

Unconventional fermionic pairing states in a monochromatically tilted optical lattice

We study the one-dimensional attractive fermionic Hubbard model under the influence of periodic driving with the time-dependent density matrix renormalization group method. We show that the system can be driven into an unconventional pairing state characterized by a condensate made of Cooper pairs with a finite center-of-mass momentum similar to a Fulde-Ferrell state. We obtain results both in the laboratory and the rotating reference frames demonstrating that the momentum of the condensate can be finely tuned by changing the ratio between the amplitude and the frequency of the driving. In particular, by quenching this ratio to the value corresponding to suppression of the tunneling and the Coulomb interaction strength to zero, we are able to “freeze” the condensate. We finally study the effects of different initial conditions and compare our numerical results to those obtained from a time-independent Floquet theory in the large frequency regime. Lastly, our work offers the possibility of engineering and controlling unconventional pairing states in fermionic condensates.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Performance analysis and implementation details of the Energy Conserving Semi-Implicit Method code (ECsim)

We present in this work the implementation of the Energy Conserving Semi-Implicit Method in a parallel code called ECsim. This new code is a three-dimensional, fully electromagnetic particle in cell (PIC) code. It is written in C/C++ and uses MPI to allow massive parallelization. ECsim is unconditionally stable in time, eliminates the finite grid instability, and has the same cycle scheme as the explicit code with a computational cost comparable to other semi-implicit PIC codes. All these features make it a very valuable tool to address situations which have not been possible to analyze until now with other PIC codes. In this work, we show the details of the algorithm implementation and we study its performance in different systems. ECsim is compared with another semi-implicit PIC code with different time and spectral resolution, showing its ability to address situations where other codes fail.

97 MATHEMATICS AND COMPUTING↗

A unified radiative magnetohydrodynamics code for lightning-like discharge simulations

A two-dimensional Eulerian finite difference code is developed for solving the non-ideal magnetohydrodynamic (MHD) equations including the effects of self-consistent magnetic field, thermal conduction, resistivity, gravity, and radiation transfer, which when combined with specified pulse current models and plasma equations of state, can be used as a unified lightning return stroke solver. The differential equations are written in the covariant form in the cylindrical geometry and kept in the conservative form which enables some high-accuracy shock capturing schemes to be equipped in the lightning channel configuration naturally. In this code, the 5-order weighted essentially non-oscillatory scheme combined with Lax-Friedrichs flux splitting method is introduced for computing the convection terms of the MHD equations. The 3-order total variation diminishing Runge-Kutta integral operator is also equipped to keep the time-space accuracy of consistency. The numerical algorithms for non-ideal terms, e.g., artificial viscosity, resistivity, and thermal conduction, are introduced in the code via operator splitting method. This code assumes the radiation is in local thermodynamic equilibrium with plasma components and the flux limited diffusion algorithm with grey opacities is implemented for computing the radiation transfer. The transport coefficients and equation of state in this code are obtained from detailed particle population distribution calculation, which makes the numerical model is self-consistent. This code is systematically validated via the Sedov blast solutions and then used for lightning return stroke simulations with the peak current being 20 kA, 30 kA, and 40 kA, respectively. The results show that this numerical model consistent with observations and previous numerical results. The population distribution evolution and energy conservation problems are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Different approaches to modeling the LANSCE H{sup −} ion source filament performance

An overview of different approaches to modeling of hot tungsten filament performance in the Los Alamos Neutron Science Center (LANSCE) H{sup −} surface converter ion source is presented. The most critical components in this negative ion source are two specially shaped wire filaments heated up to the working temperature range of 2600 K–2700 K during normal beam production. In order to prevent catastrophic filament failures (creation of hot spots, wire breaking, excessive filament deflection towards source body, etc.) and to improve understanding of the material erosion processes, we have simulated the filament performance using three different models: a semi-empirical model, a thermal finite-element analysis model, and an analytical model. Results of all three models were compared with data taken during LANSCE beam production. The models were used to support the recent successful transition from the beam pulse repetition rate of 60 Hz–120 Hz.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Experimental Characterization and Numerical Modeling of the Interaction Between Carbon Fiber Composite Prepregs During a Preforming Process

We report carbon fiber reinforced composites have received growing attention because of their superior performance and high potential for lightweight systems. An economic method to manufacture the parts made of these composites is a sequence of forming followed by a compression molding. The first step in this sequence is called preforming that forms the prepreg, which is the fabric impregnated with the uncured resin, to the product geometry, while the molding process cures the resin. Slip between different prepreg layers is observed in the preforming step, and it is believed to have a non-negligible impact on the resulting geometry. This paper reports a method to characterize the interaction between different prepreg layers, which should be valuable for future predictive modeling and design optimization. An experimental device was built to evaluate the interactions with respect to various industrial production conditions. The experimental results were analyzed for an in-depth understanding about how temperature, relative sliding speed, and fiber orientation affect the tangential interaction between two prepreg layers. Moreover, a hydro-lubricant model was introduced to study the relative motion mechanism of this fabric-resin-fabric system, and the results agreed well with the experiment data. Lastly, the interaction factors obtained from this research will be implemented in a preforming process finite element simulation model.

36 MATERIALS SCIENCE↗

Stabilization of numerical interchange in spectral-element magnetohydrodynamics

In this study, auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C 0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. Lastly, the projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355-386], provided that the projections introduce numerical dissipation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The phase diagram of quantum chromodynamics in one dimension on a quantum computer

The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behaviour of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce colour-neutrality constraints. This work pioneers the quantum simulation of QCD at finite density and temperature for two and three colours, laying the foundation to explore QCD phenomena on quantum platforms.

Quantum information↗