Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Diffusion equations”

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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Light-trapping and recycling for extraordinary power conversion in ultra-thin gallium-arsenide solar cells

Here, we demonstrate nearly 30% power conversion efficiency in ultra-thin (~200 nm) gallium arsenide photonic crystal solar cells by numerical solution of the coupled electromagnetic Maxwell and semiconductor drift-diffusion equations. Our architecture enables wave-interference-induced solar light trapping in the wavelength range from 300-865 nm, leading to absorption of almost 90% of incoming sunlight. Our optimized design for 200 nm equivalent bulk thickness of GaAs, is a square-lattice, slanted conical-pore photonic crystal (lattice constant 550 nm, pore diameter 600 nm, and pore depth 290 nm), passivated with AlGaAs, deposited on a silver back-reflector, with ITO upper contact and encapsulated with SiO 2 . Our model includes both radiative and non-radiative recombination of photo-generated charge carriers. When all light from radiative recombination is assumed to escape the structure, a maximum achievable photocurrent density (MAPD) of 27.6 mA/cm 2 is obtained from normally incident AM 1.5 sunlight. For a surface non-radiative recombination velocity of 10 3 cm/s, this corresponds to a solar power conversion efficiency of 28.3%. When all light from radiative recombination is trapped and reabsorbed (complete photon recycling) the power conversion efficiency increases to 29%. If the surface recombination velocity is reduced to 10 cm/sec, photon recycling is much more effective and the power conversion efficiency reaches 30.6%.

14 SOLAR ENERGY↗
DOE OSTI2016

Axisymmetric flows from fluid injection into a confined porous medium

In this work, we study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M , the viscosity ratio of displaced fluid relative to injected fluid, and Γ , which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R 2 /T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid ( Γ $\ll$ 1 and M < 1) where we identify a self-similar solution that indicates a parabolic interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity ( Γ $\ll$ 1 and M = 1), where we find a self-similar solution that predicts a distinct parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid ( Γ $\ll$ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow ( Γ $\gg$ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. “Axisymmetric gravity currents in a porous medium,” J. Fluid Mech. 543, 293–302 (2005)]. The various axisymmetric flows are summarized in a Γ - M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime. The implications of the regime diagram are discussed using practical engineering projects of geological CO 2 sequestration, enhanced oil recovery, and underground waste disposal.

42 ENGINEERING↗
DOE OSTI2017

Inferring morphology and strength of magnetic fields from proton radiographs

Proton radiography is an important diagnostic method for laser plasma experiments and is particularly important in the analysis of magnetized plasmas. The theory of radiographic image analysis has heretofore only permitted somewhat limited analysis of the radiographs of such plasmas. We furnish here a theory that remedies this deficiency. We show that to linear order in magnetic field gradients, proton radiographs are projection images of the MHD current along the proton trajectories. We demonstrate that in the linear regime (i.e., the small image contrast regime), the full structure of the projected perpendicular magnetic field can be reconstructed by solving a steady-state inhomogeneous 2-dimensional diffusion equation sourced by the radiograph fluence contrast data. Here, we explore the validity of the scheme with increasing image contrast, as well as limitations of the inversion method due to the Poisson noise, discretization errors, radiograph edge effects, and obstruction by laser target structures. We also provide a separate analysis that is suited to the inference of isotropic-homogeneous magnetic turbulence spectra. Finally, we discuss extension of these results to the nonlinear regime (i.e., the order unity image contrast regime).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Calculating RF current condensation with consistent ray-tracing and island heating

Finally, by exploiting the nonlinear amplification of the power deposition of RF waves, current condensation promises new pathways to the stabilization of magnetic islands. We present a numerical analysis of current condensation, coupling a geometrical optics treatment of wave propagation and damping to a thermal diffusion equation solver in the island. Taking into account the island geometry and relativistic damping, previous analytical theory can be made more precise and specific scenarios can be realistically predicted. With this more precise description, bifurcations and associated hysteresis effects could be obtained in an ITER-like scenario at realistic parameter values. Moreover, it is shown that dynamically varying the RF wave launching angles can lead to hysteresis and help to avoid the nonlinear shadowing effect.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Wide bandwidth frequency-domain thermoreflectance: Volumetric heat capacity, anisotropic thermal conductivity, and thickness measurements

A frequency-domain thermoreflectance (FDTR) system with a frequency range of 1 Hz to 75 MHz is presented. The wide bandwidth of pump modulation frequency enables enhanced simultaneous thermophysical property characterization of bulk and thin-film materials. The wide bandwidth FDTR system is demonstrated with simultaneous measurements of in-plane and cross-plane thermal conductivities of sapphire and muscovite mica, thickness and thermal conductivity of gold/titanium thin films, and isotropic thermal conductivity and volumetric heat capacity of lithium niobate and silicon. Thermophysical properties measured with FDTR are compared to literature values or independent measurements for verification. Finally, at low frequencies, a negligible error was achieved in the numerical integration of the heat diffusion equation with a Gauss–Legendre quadrature method solved with 400 integration points and an upper integration limit of 16weff, where weff is the effective pump–probe 1/e2 radius.

Ziade, Elbara (ORCID:0000000249020497)↗
DOE OSTI2022

Thermal model for time-domain thermoreflectance experiments in a laser-flash geometry

Time-domain thermoreflectance (TDTR) is a well-established pump–probe method for measuring thermal conductivity and interface conductance of multilayers. Interpreting signals in a TDTR experiment requires a thermal model. In standard front/front TDTR experiments, both pump and probe beams typically irradiate the surface of a multilayer. As a result, existing thermal models for interpreting thermoreflectance experiments assume that the pump and probe beams both interact with the surface layer. Here, we present a frequency-domain solution to the heat-diffusion equation of a multilayer in response to nonhomogeneous laser heating. This model allows analysis of experiments where the pump and probe beams irradiate opposite sides of a multilayer. We call such a geometry a front/back experiment to differentiate such experiments from standard TDTR experiments. As an example, we consider a 60nm amorphous Si film. We consider how signals differ in a front/front vs front/back geometry and compare thermal model predictions to experimental data.

Peng, Wanyue↗
DOE OSTI2014

Hot electromagnetic outflows. III. Displaced fireball in a strong magnetic field

The evolution of a dilute electron-positron fireball is calculated in the regime of strong magnetization and high compactness (ℓ ∼ 10{sup 3}-10{sup 8}). Heating is applied at a low effective temperature (<25 keV), appropriate to breakout from a confining medium, so that relaxation to a blackbody is inhibited by pair annihilation. The diffusion equation for Compton scattering by thermal pairs is coupled to a trans-relativistic cyclo-synchrotron source. We find that the photon spectrum develops a quasi-thermal peak at energy ∼0.1 m{sub e}c {sup 2} in the comoving frame, with a power-law slope below it that is characteristic of gamma-ray bursts (GRBs; F{sub ω} ∼ const). The formation of a thermal high-energy spectrum is checked using the full kinetic equations. Calculations for a baryon-dominated photosphere reveal a lower spectral peak energy, and a harder low-energy spectrum, unless ion rest mass carries ≲ 10{sup –5} of the energy flux. We infer that (1) the GRB spectrum is inconsistent with the neutron-rich wind emitted by a young magnetar or neutron torus, and points to an event horizon in the engine; (2) neutrons play a negligible role in prompt gamma-ray emission; (3) the relation between observed peak frequency and burst energy is bounded below by the observed Amati relation if the Lorentz factor ∼(opening angle){sup –1} at breakout, and the jet is surrounded by a broader sheath that interacts with a collapsing stellar core; (4) X-ray flashes are consistent with magnetized jets with ion-dominated photospheres; (5) high-frequency Alfvén waves may become charge starved in the dilute pair gas; (6) limitations on magnetic reconnection from plasma collisionality have been overestimated.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Resonance broadened quasi-linear (RBQ) model for fast ion distribution relaxation due to Alfvénic eigenmodes

The burning plasma performance is limited by the confinement of the super-alfvénic fusion products such as alpha particles and the auxiliary heating ions capable of exciting the Alfvénic eigenmodes (AEs) (Gorelenkov et al 2014 Nucl. Fusion 54 125001). Here in this work the effect of AEs on fast ions is formulated within the quasi-linear (QL) theory generalized for this problem recently (Duarte 2017 PhD Thesis University of São Paulo, Brazil). The generalization involves the resonance line broadened interaction of energetic particles (EP) with AEs supplemented by the diffusion coefficients depending on EP position in the velocity space. A new resonance broadened QL code (or RBQ1D) based on this formulation allowing for EP diffusion in radial direction is built and presented in details. In RBQ1D applications we reduce the wave particle interaction (WPI) dynamics to 1D case when the particle kinetic energy is nearly constant. The diffusion equation for EP distribution evolution is then solved simultaneously for all particles along the angular momentum direction. We make initial applications of the RBQ1D to a DIII-D plasma with elevated q-profile where the beam ions show stiff transport properties (Collins et al (The DIII-D Team) 2016 Phys. Rev. Lett. 116 095001). In conclusion, AE driven fast ion profile relaxation is studied for validations of the QL approach in realistic conditions of beam ion driven instabilities in DIII-D.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Designing a validation experiment for radio frequency condensation

Abstract Theoretical studies have suggested that nonlinear effects can lead to ‘radio frequency (RF) condensation’, where an initially broad current profile can coalesce in islands when they reach sufficient width. In suitable conditions, RF condensation can ‘self-focus’ the driven current to the center of an island, improving stabilization efficiency and reducing control complexity. In unsuitable conditions, the effect can prematurely deplete the RF energy before it reaches the island center, impairing stabilization. It is predicted that the RF condensation effect can significantly impact reactor-scale tokamaks. This paper presents a set of simulations investigating the conditions under which RF condensation might be encountered in present-day tokamaks. For concreteness, the calculations use equilibrium reconstructions for two shots from DIII-D and AUG. The Current Condensation Amid Magnetic Islands (OCCAMI) simulation code has been used for this investigation. The code takes as its input a numerically specified axisymmetric EFIT equilibrium solution, and it perturbatively constructs a 3D field with an island embedded at the appropriate rational surface. In the OCCAMI code, the GENRAY code is used for ray tracing and for calculating the power deposition along a ray trajectory, and GENRAY is coupled self-consistently to a solution of the thermal diffusion equation in the island. The simulation results described in the paper illuminate the conditions required for experimental validation of the theory of RF condensation. The simulations also provide an explanation of why the effect was not noticed in experiments prior to the publication of theoretical papers on the subject.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Coupled Charge and Radiation Transport Processes in Thermophotovoltaic and Thermoradiative Cells

Accurate modeling of charge transport and both thermal and luminescent radiation is crucial to the understanding and design of radiative thermal energy converters. Charge-carrier dynamics in semiconductors are well-described by the Poisson-drift-diffusion equations, and thermal radiation in emitter-absorber structures can be computed using multilayer fluctuational electrodynamics. These two types of energy flows interact through radiation absorption or luminescence and charge-carrier generation or recombination. However, past research has typically only assumed limited interaction, with thermal radiation absorption as an input for charge-carrier models to predict device performance. To examine this assumption, we develop a fully coupled iterative model of charge and radiation transport in semiconductor devices, and we use our model to analyze near-field and far-field GaSb thermophotovoltaic and thermoradiative systems. By comparing our results with past methods that do not consider cross-influences between charge and radiation transport, we find that a fully coupled approach is necessary to accurately model photon recycling and near-field enhancement of external luminescence. As these effects can substantially alter device performance, our modeling approach can aid in the design of efficient thermophotovoltaic and thermoradiative systems.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2021

Charge Transport and Space-Charge Formation in Cd 1 - x Zn x Te 1 - y Se y Radiation Detectors

The electron- and hole-transport properties in cadmium zinc telluride selenide (CZTS) crystals are studied using a laser-induced transient-current technique with pulsed and dc bias. The internal electric field profile and velocity of surface recombination are determined by Monte Carlo simulations of electron and hole transient currents combined with a numerical solution of the drift-diffusion equation coupled with Poisson’s equation. Electron and hole drift mobilities of μe = 830 cm 2 /Vs and μh = 40 cm 2 /Vs, respectively, are determined. We also develop a simple technique for evaluating surface recombination directly from measured current waveforms without the need for numerical simulation. The good quality of the prepared detector at pulsed bias, with electron- and hole-mobility-lifetime products of (μτ)e = 1.9 × 10 -3 cm 2 /V and (μτ)h = 1.4 × 10 -4 cm 2 /V, respectively, are observed. The formation of a positive space charge, originating from hole injection combined with a recombination level, is found. We observe a significant position dependence of the lifetime of electrons and holes in dc bias due to hole injection. The experiment is successfully fitted by a simple model dominated by a single deep recombination level with an energy of E t =E C -0.73eV; concentration of 7.3 × 10 11 cm -3 ; and electron- and hole-capture cross sections of 3.5 × 10 -14 cm 2 and 6.5 × 10 -14 cm 2 , respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Onset of anharmonicity and thermal conductivity in SnSe

The anharmonicity in SnSe is investigated through the analysis of moments of 119Sn nuclear resonant inelastic x-ray scattering and ab initio molecular dynamics calculations. Experimental evidences show that the anharmonic behavior started around 300 K, substantially lower than the usually suggested structural transition at 800 K. Both theory and experiments reveal substantial lifetime broadening and frequency renormalization of the optical phonons. Additionally, thermal conductivities calculated from the temporal energy moment using the Einstein diffusion equation are in good agreement with previous experiments. The abrupt increase of the thermal power near 800 K is driven by an electronic factor and not by the enhanced anharmonicity due to structural change.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Kinetic-energy dissipation and fluctuations in strongly damped heavy-ion collisions within the stochastic mean-field approach

Microscopic mean-field approaches have been successful in describing the most probable reaction outcomes in low-energy heavy-ion reactions. However, those approaches are known to severely underestimate dispersions of observables around the average values that has limited their applicability. Recently it has been shown that a quantal transport approach based on the stochastic mean-field (SMF) theory significantly improves the description, while its application has been limited so far to fragment mass and charge dispersions. In this work, we extend the quantal transport approach based on the SMF theory for relative kinetic energy dissipation and angular momentum transfer in low-energy heavy-ion reactions. Based on the SMF concept, analytical expressions are derived for the radial and tangential friction and associated diffusion coefficients. Those quantal transport coefficients are calculated microscopically in terms of single-particle orbitals within the time-dependent Hartree-Fock (TDHF) approach. As the first application of the proposed formalism, we consider the radial linear momentum dispersion, neglecting the coupling between radial and angular momenta. We analyze the total kinetic energy (TKE) distribution of binary reaction products in the 136 Xe + 208 Pb reaction at E c.m. =526 MeV and compare with experimental data. From time evolution of single-particle orbitals in TDHF, the radial diffusion coefficient is computed on a microscopic basis, while a phenomenological treatment is introduced for the radial friction coefficient. By solving the quantal diffusion equation for the radial linear momentum, the dispersion of the radial linear momentum is obtained, from which one can construct the TKE distribution. We find that the calculations provide a good description of the TKE distribution for strongly damped events with large energy losses, TKEL ≳ 150 MeV. However, the calculations underestimate the TKE distribution for smaller energy losses. Further studies are needed to improve the technical details of calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Dynamic scaling of order parameter fluctuations in model B

Brookhaven National Laboratory has performed a dedicated set of experiments, called the Beam Energy Scan (BES), with the goal of location a possible critical point in the phase diagram of nuclear matter, This point is analogous to the endpoint of the liquid-gas phase transition in water, where the liquid phase corresponds to a phase of hadrons, and the gas phase to a plasma of quarks and gluons. In order to describe the data generated by these experiments we have studied numerical simulations of the stochastic diffusion equation with a conserved charge. Here, we focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent z ≃ 3.972(2), which agrees with predictions of the epsilon expansion. We also study non-equilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Diffusive dynamics of critical fluctuations near the QCD critical point

A quantitatively reliable theoretical description of the dynamics of fluctuations in nonequilibrium is indispensable in the experimental search for the QCD critical point by means of ultrarelativistic heavy-ion collisions. Herein we consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point. Due to net-baryon number conservation the dynamics is described by the fluid dynamical diffusion equation, which we extend to contain a white noise stochastic current. Including nonlinear couplings from the 3d Ising model universality class in the free energy functional, we solve the fully interacting theory in a finite size system. We observe that purely Gaussian white noise generates non-Gaussian fluctuations, but finite size effects and exact net-baryon number conservation lead to significant deviations from the expected behavior in equilibrated systems. In particular the skewness shows a qualitative deviation from infinite volume expectations.With this benchmark established we study the real-time dynamics of the fluctuations. We recover the expected dynamical scaling behavior and observe retardation effects and the impact of critical slowing down near the pseudocritical temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Lattice Boltzmann method for diffusion-limited partial dissolution of fluids

A lattice Boltzmann model for two partially miscible fluids is developed. By partially miscible, we mean that although there is a definite interfacial region separating the two fluids with a surface tension force acting at all points of the transition region, each fluid can nonetheless accept molecules from the other fluid up to a set solubility limit. We allow each fluid to diffuse into the other with the solubility and diffusivity in each fluid being input parameters. The approach is to define two regions within the fluid. One interfacial region having finite width, across which most of the concentration change occurs, and in which a surface tension force and color separation step are allowed for. And one miscible fluid region where the concentration of the binary fluids follows an advection-diffusion equation and the mixture as a whole obeys the Navier-Stokes incompressible flow equations. Numerical examples are presented in which the algorithm produces results that are quantitatively compared to exact analytical results as well as qualitatively examined for their reasonableness. The model has the ability to simulate how bubbles of one fluid flow through another while dissolving their contents as well as to a range of practical invasion problems such as injecting supercritical CO 2 into a porous material saturated with water for sequestration purposes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗