Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Diffusion equation”

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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Phase transformation and growth mechanism of RF sputtered ferroelectric lead scandium tantalate (PbSc 0.5 Ta 0.5 O 3 ) films

Lead scandium tantalate (PbSc 0.5 Ta 0.5 O 3 , PST), an order/disorder ferroelectric, is a potential candidate for electrocaloric cooling and pyroelectric infrared (IR) detector. In this work, we report the phase transformation kinetics from two series of samples containing pure amorphous and mixture of amorphous and pyrochlore to desired perovskite phase using postdeposition rapid thermal processing (RTP) as well as growth mechanism of RF sputtered PST thin films using excess lead target on platinized silicon (Pt/Ti/SiO 2 /Si) substrates. We find that small changes in the temperature ramp have a large effect on the degree of perovskite conversion (ferroelectric phase), orientation (crystallographic texture), and long-range order parameter (< S 111 >). Through isothermal annealing, we obtained optimal perovskite phase at ≥700°C temperature. The phase transformation is characterized by spontaneous formation of center-type in-plane radial rosette-like structures revealed by scanning electron microscopy. The PST perovskite crystallites were found to coexist with pyrochlore in RTP annealed films. The volume fractions for perovskite and pyrochlore phase were obtained from the analysis of “rosettes” and respective X-ray diffraction intensities which helped to determine various parameters associated with phase kinetics (n, k, and activation energy, Ea) and accompanying growth. The effective activation energies of perovskite transition and growth were found to be 332 ± 11 kJ/mol (345 ± 11 kJ/mol) and 114 ± 10 kJ/mol (122 ± 10 kJ/mol), respectively, for pure amorphous only (and mixed amorphous and pyrochlore) phase following nucleation-growth controlled Avrami's equation. A linear growth rate (n~1) for the perovskite phase indicates predominant interface-controlled process and diffusion-limited phenomena thus inhibiting rosette size owing to reactant depletion and soft impingement at the grain boundary. However, the growth behavior is isotropic in two-dimension parallel to the plane of the substrates for both sample series. Furthermore, lead loss was severe for in-situ growth and RTP combined with conventional furnace annealing than those of RTP only films, which were closer to stoichiometric albeit with excess lead and marginal oxygen vacancies (V o ).

36 MATERIALS SCIENCE↗
DOE OSTI2023

Microphysics of liquid water in sub-10 nm ultrafine aerosol particles

Abstract. Ultrafine aerosol particles with sizes smaller than 50 nm have been shown in recent studies to serve as a large source of cloud condensation nuclei that can promote additional cloud droplet formation under supersaturation conditions. Knowledge of the microphysics of liquid water in these droplets remains limited, particularly in the sub-10 nm particle size range, due to experimental and theoretical challenges associated with the complexity of aerosol components and the small length scales of interest (e.g., difficulty of precisely sampling the liquid–air interface, questionable validity of mean-field theoretical representations). Here, we carried out molecular dynamics (MD) simulations of aerosol particles with diameters between 1 and 10 nm and characterized atomistic-level structure and water dynamics in well-mixed and phase-separated systems with different particle sizes, NaCl salinities, and pimelic acid (PML) organic surface loadings as a function of distance from the time-averaged Gibbs dividing interface or instantaneous water–air interface. We define a sphericity factor (ϕ) that can shed light on the phase-mixing state of nanodroplets, and we reveal an unexpected dependence of mixing state on droplet size. Our results also evidence an ion concentration enhancement in ultrafine aerosols, which should modulate salt nucleation kinetics in sub-10 nm droplets, and provide detailed characterization of the influence of droplet size on surface tension and on water self-diffusivity near the interface. Analysis of water evaporation free energy and water activity demonstrates the validity of the Kelvin equation and Köhler theory at droplet sizes larger than 4 nm under moderate salinities and organic loadings and the need for further extension to account for ion concentration enhancement in sub-10 nm aerosols, droplet-size-dependent phase separation effects, and a sharp decrease in the cohesiveness of liquid water in sub-4 nm droplets. Finally, we show that an idealized fractional surface coating factor (fs) can be used to categorize and reconcile water accommodation coefficients (α*) observed in MD simulations and experimental results in the presence of organic coatings, and we resolve the droplet size dependence of α*.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

MODELLING FIBER ORIENTATION DURING ADDITIVE MANUFACTURING COMPRESSION MOLDING PROCESSES

The production of high-performance thermoplastic composites reinforced with short carbon fibers can be achieved by a novel “additive manufacturing-compression molding” technique. An advantage of such combination is two-fold: controlled fiber orientation in additive manufacturing and less void content by compression molding. In this study, a computational fluid dynamics model has been developed to predict the behavior of printed layers during fiber-reinforced thermoplastic extrusion and subsequent compression molding. The fiber orientation was modelled with a simple quadratic closure model. The interaction between the fibers is included using a rotary diffusion coefficient which becomes significant in concentrated regimes. Finally, the second order orientation tensor is coupled with the momentum equation as an anisotropic part of the stress term. The effect of processing parameters on the behavior of printed layers was investigated to determine the favorable printing scenarios. The developed numerical model enables design of high-performance composites with tunable mechanical properties.

Seta, Berin↗
DOE OSTI2026

Constraining Hamiltonians from chiral effective field theory with neutron-star data

Multi-messenger observations of neutron stars (NSs) and their mergers have placed strong constraints on the dense-matter equation of state (EOS). The EOS, in turn, depends on microscopic nuclear interactions that are described by nuclear Hamiltonians. These Hamiltonians are commonly derived within chiral effective field theory (EFT). Ideally, multi-messenger observations of NSs could be used to directly inform our understanding of EFT interactions, but such a direct inference necessitates millions of model evaluations. This is computationally prohibitive because each evaluation requires us to calculate the EOS from a Hamiltonian by solving the quantum many-body problem with methods such as auxiliary-field diffusion Monte Carlo (AFDMC), which provides very accurate and precise solutions but at a significant computational cost. Additionally, we need to solve the stellar structure equations for each EOS which further slows down each model evaluation by a few seconds. In this work, we combine emulators for AFDMC calculations of neutron matter, built using parametric matrix models, and for the stellar structure equations, built using multilayer perceptron neural networks, with the PyCBC data-analysis framework to enable a direct inference of coupling constants in an EFT Hamiltonian using multi-messenger observations of NSs. We find that astrophysical data can provide informative constraints on two-nucleon couplings despite the high densities probed in NS interiors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Path integral molecular dynamics: A high-fidelity approach to quantum dynamics of electrons

We investigate electron transport in the uniform electron gas using ring-polymer molecular dynamics (RPMD). Working in the weakly coupled, non-degenerate regime, we use RPMD to probe how the onset of quantum diffraction effects at high temperature reshapes electron–electron collisions and leads to a classical-to-quantum crossover in macroscopic transport properties. Static thermodynamics obtained with RPMD are consistent with the weak-coupling equation of state, confirming correct quantum Boltzmann sampling. Real-time transport extracted from mean square displacements exhibits the expected ballistic-to-diffusive transition and a systematic reduction of the electronic self-diffusivity as quantum effects strengthen, due to quantum diffraction modifying electron–electron collisions. Direct ring-polymer scattering simulations reveal diffractive “softening” of binary deflections, providing a micro-to-macro link between collision physics and diffusion. The present study establishes RPMD as a quantitative, trajectory-based tool for electron transport across the classical–quantum crossover and furnishes benchmarks for improving Coulomb-log interpolation models. We outline extensions to multi-component plasmas and a path to incorporate Fermi–Dirac statistics within path-integral dynamics.

Electronic transport↗
DOE OSTI2023

Equation of State and Energy Loss of Hot and Dense Quark-Gluon matter from Holographic Black Holes

By using gravity/gauge correspondence, we construct a holographic model, constrained to mimic the lattice QCD equation of state at zero density, to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the energy loss of light and heavy partons within the hot and dense plasma represented by the heavy quark drag force, Langevin diffusion coefficients and jet quenching parameter at the critical point and across the first-order transition line predicted by the model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

PINN surrogate of Li-ion battery models for parameter inference, Part II: Regularization and application of the pseudo-2D model

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of ~2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. Finally, in the low-data availability scenario, the testing error was estimated to ~2 mV for the SPM surrogate and ~10 mV for the P2D surrogate which could be mitigated with additional data.

25 ENERGY STORAGE↗
DOE OSTI2021

Diffusion regime of electron–electron collisions in weakly ionized plasmas

We consider weakly ionized plasma where an elastic scattering of electrons on neutrals changes the individual acts and the rate of electron-electron collisions significantly. In this case, the kinetics of electron thermalization is very different from that in fully ionized plasma. Here, the colliding electrons do not move freely. They, instead, diffuse because of fast scattering on neutrals. We demonstrate how a proper account of this diffusion enables one to estimate the characteristic time of electron thermalization. We also present a rigorous derivation of the kinetic equation for electrons by using Bogolyubov’s method based on Liouville equations for multi-particle distribution functions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Charging of radioactive and environmental airborne particles

The charging of various airborne particles was investigated using single-particle levitation and charge-balance equations. Though radioactive decay and triboelectrification can induce charging, it is typically assumed that the aerosols in a radioactive plume will not carry significant charge at steady state since atmospheric particles can have their charge neutralized through the capture of adjacent counter-ions (i.e., diffusion charging). Here to assess this assumption, we directly measured the surface charge and charge density of various triboelectrically charged aerosols including radioactive uranium oxide (<1 μm), urban dust, Arizona desert dust, hydrophilic and hydrophobic silica nanoparticles, and graphene oxide powders using an electric field-assisted particle levitator in air. Of these particles, uranium oxide aerosols exhibited the highest surface charge density. Charge balance equations were employed to predict the average charge gained from radioactive decay as a function of time and to evaluate the effects of diffusion charging on triboelectrically charged radioactive and non-radioactive particles in the atmosphere. Simulation results show that particles, initially charged through triboelectrification, can be quickly discharged by diffusion charging in the absence of radioactive decay. Nevertheless, simulation results also indicate that particles can be strongly charged when they carry radionuclides. These experimental and simulation results suggest that radioactive decay can induce strong particle charging that may potentially affect atmospheric transport of airborne radionuclides.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Transcritical diffuse-interface hydrodynamics of propellants in high-pressure combustors of chemical propulsion systems

Rocket engines and high-power new generations of gas-turbine jet engines and diesel engines oftentimes involve the injection of one or more reactants at subcritical temperatures into combustor environments at high pressures, and more particularly at pressures higher than those corresponding to the critical points of the individual components of the mixture, which typically range from 13 to 50 bars for most propellants. This class of trajectories in the thermodynamic space has been traditionally referred to as transcritical. However, the fundamental understanding of fuel atomization, vaporization, mixing, and combustion processes at such high pressures remains elusive. In particular, whereas fuel sprays are relatively well characterized at normal pressures, analyses of dispersion of fuel in high-pressure combustors are hindered by the limited experimental diagnostics and theoretical formulations available. The description of the thermodynamics of hydrocarbon-fueled mixtures employed in chemical propulsion systems is complex and involves mixing-induced phenomena, including an elevation of the critical point whereby the coexistence region of the mixture extends up to pressures much larger than the critical pressures of the individual components. As a result, interfaces subject to surface-tension forces may persist in multicomponent systems despite the high pressures, and may give rise to unexpected spray-like atomization dynamics that are otherwise absent in monocomponent systems above their critical point. In this article, the current understanding of this phenomenon is reviewed within the context of propulsion systems fueled by heavy hydrocarbons. Emphasis is made on analytical descriptions at mesoscopic scales of interest for computational fluid dynamics. In particular, a set of modifications of the constitutive laws in the Navier–Stokes equations for multicomponent flows, supplemented with a high-pressure equation of state and appropriate redefinitions of the thermodynamic potentials, are introduced in this work based on an extended version of the diffuse-interface theory of van der Waals. The resulting formulation involves revisited forms of the stress tensor and transport fluxes of heat and species, and enables a description of the mesoscopic volumetric effects induced by transcritical interfaces consistently with the thermodynamic phase diagram of the mixture at high pressures. Additionally, applications of the theory are illustrated in canonical problems, including dodecane/nitrogen transcritical interfaces in non-isothermal systems. The results indicate that a transcritical interface is formed between the propellant streams that persists downstream of the injection orifice over distances of the same order as the characteristic thermal-entrance length of the fuel stream. The transcritical interface vanishes at an edge that gives rise to a fully supercritical mixing layer.

02 PETROLEUM↗
DOE OSTI2021

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. Here in this work we investigate this limitation through the lens of Neural Tangent Kernel (NTK) theory and elucidate how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK. Using this observation, we construct novel architectures that employ spatio-temporal and multi-scale random Fourier features, and justify how such coordinate embedding layers can lead to robust and accurate PINN models. Numerical examples are presented for several challenging cases where conventional PINN models fail, including wave propagation and reaction–diffusion dynamics, illustrating how the proposed methods can be used to effectively tackle both forward and inverse problems involving partial differential equations with multi-scale behavior.

42 ENGINEERING↗
DOE OSTI2021

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

German, Péter (ORCID:0000000307285283)↗
DOE OSTI2026

Sputter coating of Nb₃Sn into SRF cavity using stoichiometric target

Nb₃Sn has emerged as a leading alternative material due to its higher superconducting critical temperature (Tc) and superheating field (Hsh), promising a viable solution to the intrinsic performance limit currently faced by Nb superconducting radiofrequency (SRF) cavities. We sputter-coated Nb₃Sn inside Nb SRF cavity using a stoichiometric Nb₃Sn tube target in a DC cylindrical magnetron sputter coater. The target was fabricated by growing an estimated >20 μm thick Nb₃Sn layer on a Nb tube via Sn vapor diffusion using Jefferson Lab’s coating system. Approximately 150 nm thick Nb-Sn films were sputter-deposited onto flat Nb samples at positions representing the beam tubes and equator of a 2.6 GHz Nb cavity. Post-deposition annealing at 950 °C for 3 h resulted in the formation of Nb₃Sn. Microstructural analysis of the annealed films was carried out to investigate the morphology and structure of the Nb₃Sn films. Later, a 2.6 GHz Nb SRF cavity was coated with a ~1.2 μm thick sputtered Nb-Sn film using a stoichiometric Nb₃Sn target, followed by annealing. Cryogenic RF testing of the annealed cavity demonstrated a Tc of 17.8 K, indicating the formation of Nb₃Sn. After a light Sn recoating treatment, the cavity achieved a quality factor (Q0) of 6.7E+08 at lower field at 2.0 K.

Accelerator Physics↗
DOE OSTI2023

Fluctuating hydrodynamics and the Rayleigh–Plateau instability

The Rayleigh–Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to interfacial energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics (MD), and stochastic partial differential equation–based hydrodynamic models, such as stochastic lubrication theory. In this paper, we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh–Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in MD simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally, we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface tension–driven phenomena.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Aero-Thermal Characterization of Accelerating and Diffusing Passages Downstream of Rotating Detonation Combustors

Cycle benefits of rotating detonation engines show up to five percentage points of efficiency gain for low-pressure ratio engines. An optimal integration between the combustor and the turbine needs to be guaranteed to realize this potential gain. The rotating detonation combustor (RDC) exhausts transonic flow with shocks rotating at frequencies ranging from a few to tens of kilohertz depending on the number of present waves. Hence, the turbine design requires precise knowledge of the fluctuations and losses downstream of the combustor. This paper focuses on the quantification of fluctuations and losses for accelerating and diffusing passages. The analysis of the combustor is performed via reactive unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. The unsteady RANS equations are solved via CFD++ from Metacomp with a one-step reaction mechanism for an H2-air mixture. The resolving of the boundary layer is achieved with a structured mesh of around 36 million cells. Inlet pressure of 10 bar and two different back pressures are applied to the combustor to model the interconnection with downstream turbines. Finally, we present and assess a methodology to reduce the computational time to model these passages ten times.

Braun, James↗
DOE OSTI2020

Coupled confined phase behavior and transport of methane in slit nanopores

The proximity of the order of magnitude molecular mean free path and pore sizes in nanopores leads to remarkable interactions between molecules and walls. In such systems, the thermodynamic property and the transport behavior of fluids deviate from those at bulk conditions. Molecular dynamics (MD) simulation may be used to investigate the effects of confinement on fluid physics in nanosize pores. However, translating these subscale observations into a larger scale of interest remains a challenging task. In this work, we propose a modified extension of Peng-Robinson equation of state (PR-EOS) motivated and guided by MD simulation results. The shift of critical properties, i.e., pressure and temperature, are evaluated independently. A temperature dependent parameter is introduced to account for the existence of capillary pressure in the two-phase region. Here, this formulation is capable of capturing the shift in critical properties as well as density phase diagrams under various confinement scenarios. We incorporate the proposed EOS in the lattice Boltzmann method (LBM) to study coupled confined phase behavior and transport of methane in nano-size slit pores. Adsorptive strength is determined such that the resulting density ratio matches that from MD simulation. Results indicate that the use of the proposed EOS leads to smaller fluid velocities compared to PR-EOS. This effect is due to stronger interactions between fluid particles under confinement. Also, results show that transport characteristics are impacted by the pressure of the system: in systems with a relatively low pressure, transport seems to be dominated by Knudsen diffusion; however, at a higher pressure, the contribution from viscous flow increases as the pore widens while the influence of Knudsen and surface diffusion diminishes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗