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DOE OSTI2023

Symmetry and scaling in one-dimensional compressible two-phase flow

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. We focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

CFD-DEM study of bubble properties in a cylindrical fluidized bed of Geldart Group D particles and comparison with prior MRI data

Numerical simulations of a freely bubbling cylindrical fluidized bed are carried out using a coupled computational fluid dynamics and discrete element method (CFD-DEM) model and compared to recent experimental data. The experiments were conducted using high-resolution and high-frequency magnetic resonance imaging providing high-fidelity data of the bubbling within a central 10 mm slice of the bed. Qualitatively, we nd more regular (i.e., less chaotic) structures in the simulated beds than observed experimentally. Quantitatively, however, the bubble diameter and number of bubbles as a function of height within the bed is predicted well by the base model. Unfortunately, the regularity in the simulations manifests as a considerable discrepancy in the speed of the (dense) emulsion phase. The simulated velocity probability distribution functions show an accumulation of low-speed regions and deficiency of high-speed regions. A simple parametric study of the base model is also carried out considering many of the most common CFD-DEM modeling parameters. It is found that the fluid grid size, geometry resolution, transfer kernel and drag law did not have a significant effect on bubble or particle dynamics.

42 ENGINEERING↗

DOE OSTI2024

Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence

In this article, this study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Re T = 300⁠. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.

42 ENGINEERING↗

DOE OSTI2025

Control of core–shell nanoparticles properties through plasma synthesis: a computational study

The improved properties of core–shell nanoparticles (CSNPs) over homogeneous nanoparticles (NPs) have expanded and diversified the applications of these nanomaterials. However, controlling the properties of CSNPs can be a challenging task. Low temperature plasmas have proven to be an effective method of producing NPs with uniform size and morphology, and high yield. That said, NP transport and growth dynamics are sensitive to LTP properties. We report on a computational investigation of the evolution of Ge–Si CSNP properties as a function of operating conditions through the modeling of a flowing, two-zone inductively coupled plasma (ICP) reactor. Ar/GeH 4 and Ar/SiH 4 gas mixtures were supplied to separate plasma zones at a pressure of 1 Torr to promote growth of Ge cores and Si shells. The negatively charged CSNPs are trapped electrostatically in the vicinity of the antennas where the plasma is generated and where the majority of particle growth occurs. Particles that grow to a critical size are then de-trapped by fluid drag due to neutral gas flow. A two-dimensional hybrid plasma model coupled with a three-dimensional kinetic NP transport model were utilized to resolve plasma chemistry and NP growth processes that take place on distinct timescales. The trends in CSNP properties and trapping mechanisms associated with flow rate, applied ICP power and inlet precursor fraction are discussed. While the spatial distribution of plasma produced radical species can have significant impact on the NP growth process, the NP transport dynamics are what ultimately dictates the growth environment that is unique to each particle and so determines their final dimension and composition. The key to optimizing reactor conditions involves controlling the spatial density of growth species and plasma profile as a means to tailor particle trapping dynamics suitable to produce CSNPs for a specific application.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Simulating dust grain-radiation coupling on a moving mesh

ABSTRACT We present a model for the interaction between dust and radiation fields in the radiation hydrodynamic code arepo-rt, which solves the moment-based radiative transfer equations on an unstructured moving mesh. Dust is directly treated using live simulation particles, each of which represent a population of grains that are coupled to hydrodynamic motion through a drag force. We introduce methods to calculate radiation pressure on and photon absorption by dust grains. By including a direct treatment of dust, we are able to calculate dust opacities and update radiation fields self-consistently based on the local dust distribution. This hybrid scheme coupling dust particles to an unstructured mesh for radiation is validated using several test problems with known analytic solutions, including dust driven via spherically symmetric flux from a constant luminosity source and photon absorption from radiation incident on a thin layer of dust. Our methods are compatible with the multifrequency scheme in arepo-rt, which treats UV, optical photons as single scattered and IR photons as multi scattered. At IR wavelengths, we model heating of and thermal emission from dust. Dust and gas are not assumed to be in local thermodynamic equilibrium but transfer energy through collisional exchange. We estimate dust temperatures by balancing these dust-radiation and dust-gas energy exchange rates. This framework for coupling dust and radiation can be applied in future radiation hydrodynamic simulations of galaxy formation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Numerical thermalization in 2D PIC simulations: Practical estimates for low-temperature plasma simulations

The process of numerical thermalization in particle-in-cell (PIC) simulations has been studied extensively. It is analogous to Coulomb collisions in real plasmas, causing particle velocity distributions (VDFs) to evolve toward a Maxwellian as macroparticles experience polarization drag and resonantly interact with the fluctuation spectrum. This paper presents a practical tutorial on the effects of numerical thermalization in 2D PIC applications. Scenarios of interest include simulations, which must be run for many thousands of plasma periods and contain a population of cold electrons that leave the simulation space very slowly. This is particularly relevant to many low-temperature plasma discharges and materials processing applications. We present numerical drag and diffusion coefficients and their associated timescales for a variety of grid resolutions, discussing the circumstances under which the electron VDF is modified by numerical thermalization. Though the effects described here have been known for many decades, direct comparison of analytically derived, velocity-dependent numerical relaxation timescales to those of other relevant processes has not often been applied in practice due to complications that arise in calculating thermalization rates in 1D simulations. Using these comparisons, we estimate the impact of numerical thermalization in several examples of low-temperature plasma applications including capacitively coupled plasma discharges, inductively coupled plasma discharges, beam plasmas, and hollow cathode discharges. Finally, we discuss possible strategies for mitigating numerical relaxation effects in 2D PIC simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Pulsed power to control growth of silicon nanoparticles in low temperature flowing plasmas

Low-temperature plasmas have seen increasing use for synthesizing high-quality, mono-disperse nanoparticles (NPs). Recent work has highlighted that an important process in NP growth in plasmas is particle trapping—small, negatively charged nanoparticles become trapped by the positive electrostatic potential in the plasma, even if only momentarily charged. In this article, results are discussed from a computational investigation into how pulsing the power applied to an inductively coupled plasma (ICP) reactor may be used for controlling the size of NPs synthesized in the plasma. The model system is an ICP at 1 Torr to grow silicon NPs from an Ar/SiH 4 gas mixture. This system was simulated using a two-dimensional plasma hydrodynamics model coupled to a three-dimensional kinetic NP growth and trajectory tracking model. The effects of pulse frequency and pulse duty cycle are discussed. We identified separate regimes of pulsing where particles become trapped for one pulsed cycle, a few cycles, and many cycles—each having noticeable effects on particle size distributions. For the same average power, pulsing can produce a stronger trapping potential for particles when compared to continuous wave power, potentially increasing particle mono-dispersity. Pulsing may also offer a larger degree of control over particle size for the same average power. Experimental confirmation of predicted trends is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows

In this work, the effects of the particle volume fraction gradient on fluid-particle interactions are studied. The phase interaction force is decomposed into three terms. For the first term, namely the symmetrized force density, we present theoretical reasoning and numerical evidence to assume that it is independent of the particle volume fraction gradient. The second term is the particle volume fraction gradient times a newly introduced diffusion stress. The third term is the divergence of the particle-fluid-particle (PFP) stress. If this assumption of independence of the particle volume fraction gradient for the first term can be verified, to the first order of the ratio of the mean distance between particles to the macroscopic lengthscale, all three terms can be studied and modeled in flows with uniform particle distributions. Models thus obtained are applicable to statistically inhomogeneous flows, with the second and third terms accounting for statistical inhomogeneity. To verify this assumption, numerical simulations of flows passing fixed arrays of particles are performed. Both uniform and nonuniform particle volume fractions are studied and compared for disperse multiphase flows with the particle Reynolds numbers ranging from 1 to 100, and particle volume fraction ranging from 1% to 26% in statistically steady states. It is found that the symmetrized force (first) term can be well approximated by the drag force obtained from studies of uniform flows. The diffusion stress is positive along the flow direction and negative in the directions perpendicular to the flow. In the case of moving particles, this stress could potentially cause particle aggregation in the flow direction and dispersion in the directions perpendicular to the flow. Finally, the diffusion stress is only important when there is a volume fraction gradient, while the PFP stress can be important in inhomogeneous flows with either nonuniform particle concentrations or nonuniform average relative velocities between the phases.

42 ENGINEERING↗

DOE OSTI2023

Magnetic frame-dragging correction to the electromagnetic solution of a compact neutron star

ABSTRACT Neutron stars are usually modelled as spherical, rotating perfect conductors with a predominant intrinsic dipolar magnetic field anchored to their stellar crust. Due to their compactness, General Relativity corrections must be accounted for in Maxwell’s equations, leading to modified interior and exterior electromagnetic solutions. We present analytical solutions for slowly rotating magnetized neutron stars, taking into account the magnetic frame-dragging correction. For typical compactness values, i.e. Rs ∼ 0.5 [R*], we show that the new terms lead to a per cent order correction in the magnetic field orientation and strength compared to the case, with no magnetic frame-dragging correction. Also, we obtain a self-consistent redistribution of the surface azimuthal current. We verify the validity of the derived solution through two-dimensional particle-in-cell simulations of an isolated neutron star. Defining the azimuthal electric and magnetic field amplitudes during the transient phase as observables, we prove that the magnetic frame-dragging correction reduces the transient wave amplitude, as expected from the analytical solution. We show that simulations are more accurate and stable, when we include all first-order terms. The increased accuracy at lower spatiotemporal resolutions translates into a reduction in simulation runtimes.

Torres, R. (ORCID:0000000291820228)↗

DOE OSTI2021

Settling of two-way momentum and energy coupled particles subject to Boussinesq and non-Boussinesq heating

This work establishes a procedure to accurately compute heat transfer between an Eulerian fluid and Lagrangian point-particles. Recent work has focused on accurately computing momentum transfer between fluid and particles. The coupling term for momentum involves the undisturbed fluid velocity at the particle location which is not directly accessible in the simulation. Analogously, in the context of thermal coupling, the undisturbed fluid temperature at the particle location is not directly accessible in simulations and must be estimated. In this paper, we develop a scheme to accurately estimate the undisturbed fluid temperature of a point-particle exchanging thermal energy with a surrounding fluid. Furthermore, the temperature disturbance is correlated with the enhanced temperature curvature in the vicinity of the particle and is formally valid in the low heating, low convection limit. We conduct extensive verification of the correction procedure for a settling particle subject to radiation. This setup allows the simultaneous testing of thermal and momentum corrections. By considering equations of drag and Nusselt number extended to finite Péclet and Boussinesq numbers, we establish a large range over which the correction procedure can be applied.

42 ENGINEERING↗

DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗

DOE OSTI2022

Accurate hydrodynamic force and torque correlations for prolate spheroids from Stokes regime to high Reynolds numbers

Detailed simulations of flow around various prolate spheroids are performed using multi-relaxation time lattice Boltzmann method (LBM). The simulations are performed in the Reynolds numbers range 0.1 ≤ Re ≤ 2000 at different incident angles 0°≤ φ ≤ 90° for various prolate spheroids of aspect ratios 1 ≤ λ ≤ 8. The Re is based on the volume equivalent sphere diameter. From the simulations, accurate correlations for average drag, lift and torque coefficients (C D , C L , and C T respectively) are proposed. The mean deviations between the correlations and the simulation data for C D , C L , and C T are 2%, 6.5%, and 4.7% respectively. Furthermore, the correlations are fitted with the physics in mind such that they can be extrapolated beyond the regimes simulated. The fits are designed such that correlations reduce to analytical (C D and C L ) solutions available for prolate spheroids in the limit Re ≈ 0. At high Re, the correlations mimic the asymptotic flattening of C D as for spheres and therefore, we expect the correlations to be valid until the critical Re (≈ 10 5 ). Furthermore, extensive comparison of our correlations with other high-fidelity simulations from literature demonstrate the accuracy of our work compared to other correlations from literature. This work enables researchers to perform accurate unresolved Euler-Lagrangian simulations for a wide range of elongated particles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Urban wash-off of tire wear particles

Tire wear particles (TWPs) are an important class of microplastics due to their toxicity and abundance. Because most TWPs are generated on impervious road surfaces, urban wash-off is the critical first phase of waterborne transport from their zone of production to stormwater drainage. However, little is known about the driving factors behind their mobilization. In this study, we use a rainfall simulator to investigate how surface roughness, rainfall intensity, and surface slope affect wash-off behaviors of TWPs. We also analyze how the size and shape of mobilized TWPs change over the course of simulated storm events. We found that low surface roughness, high rainfall intensity (most significant factor), and low slope result in the most rapid conveyance of TWP load. On average, large particles (>1000 µm) travelled faster than small particles (<125 µm). Particle shape explained a very small amount of variance in TWP wash-off velocity but was found to be more important under higher surface roughness conditions. In addition to wash-off velocity, we found similar conditions controlled the percent mobilization of TWPs. Low surface roughness and high rainfall intensity resulting in higher TWP wash-off rates is consistent with mineral sediment wash-off behavior. Conversely, low surface slope and large particle size leading to faster conveyance is directly opposed to mineral sediment wash-off. Our findings suggest drag-dominated flow and that sufficient runoff depth is the most important parameter governing TWP wash-off. These findings are important first steps to understanding wash-off behaviors of TWPs and informing future modeling efforts and mitigation strategies.

13 HYDRO ENERGY↗

DOE OSTI2021

Energy Exascale Earth System Model v2.0

First release of version 2 of the Energy Exascale Earth System Model. The atmosphere component remains EAM. Major changes since version 1 include: all column-physics parameterizations are computed on a separate grid that has approximately half the number of points of the dynamics grid, a new nonhydrostatic dynamical core (running in hydrostatic mode) with semi-Lagrangian tracer transport, CLUBB updated from v1 to v2, a new convective trigger (dCAPE/ULL) based on the dynamic Convective Available Potential Energy (CAPE) (dCAPE) and the Unrestricted Launch Level (ULL) concepts is used in ZM. minimum cloud droplet number changed, gravity wave drag energy conservation fixed and new tunings used, dust emission size distribution changed to emit more coarse dust particles The land component is still ELM. Major changes since version 1 include: using SNICAR-AD for radiation in snow to match the sea-ice model and fixing bugs in snow compaction and water state calculation. The ocean component remains MPAS-ocean. Major change since version 1 include: Redi isopycnal mixing has been updated, tested, and tuned in combination with the Gent-McWilliams parameterization, a sign error was fixed in the 3rd-order flux routines, the mesh used in low-resolution coupled cases was modified and the time steps adjusted, new regionally refined meshes were created, one focused on North America and another on the Southern Ocean, including ice shelf cavities. The sea-ice component remains MPAS-seaice. Major changes since version 1 include: A new heat- and freshwater-conserving coupling of frazil ice, turning off of SSH filtering, addition of SNICAR-AD and snow grain aging. The land-ice component remains MPAS-Albany-landIce (MALI) and is a static ice sheet. There is more out-of-the-box support for cryosphere configurations including the new regionally refined configuration around Antarctica with ice shelf cavities. The river model is MOSART. The half-degree river mesh was redone so it no longer treats Black and Caspian seas as ocean. The coupler remains cpl7/MCT. Major changes since version 1 include handling of ice shelf melt fluxes (heat / freshwater exchange with the ocean), and data icebergs. All components allow regional refinement of their meshes and two separate example of refinement, one in and around North America and one around Antarctica and the Southern Ocean, are provided.

E3SM Project, DOE↗

DOE OSTI2025

Alfvén eigenmode-driven zonal modes saturate and heat thermal ions by cross-scale interactions

In scenarios where a sustained energetic particle source strongly drives toroidal Alfvén eigenmodes (TAE), and phase-space transport is insufficient to saturate TAE, this novel theory of TAE-zonal mode (ZM)-turbulence—self-regulated by cross-scale interactions (including collisionless ZF damping) – merits consideration. Zonal modes are driven by Reynolds and Maxwell stresses, without the onset of modulational instability. TAE evolution in the presence of ZMs conserves energy and closes the system feedback loop. The saturated zonal shears can be sufficient to suppress ambient drift-ion temperature gradient (ITG) turbulence, achieving an enhanced core confinement regime. The saturated state is regulated by linear and turbulent zonal flow drag. This regulation leads to bursty TAE spectral oscillations, which overshoot while approaching saturation. Heating by both collisional and collisionless ZM damping deposits alpha particle energy into the thermal plasma, achieving effective alpha channeling. This theory offers a mechanism for EP-induced transport barrier formation, and predicts a novel thermal ion heating mechanism.

ITB↗

DOE OSTI2023

Revisiting the empirical particle-fluid coupling model used in DEM-CFD by high-resolution DEM-LBM-IMB simulations: A 2D perspective

The work investigates the applicability of the unresolved Computational Fluid Dynamics and Discrete Element Method (CFDDEM) technique based on empirical equations for fluid-particle coupling. We first carry out a series of representative volume element simulations using the high-resolution particle-resolved Lattice Boltzmann method and Discrete Element Method (LBMDEM) coupled by an Immersed Moving Boundary (IMB) scheme. Then, we compare the results obtained by both LBMDEM and empirical equations used in unresolved CFDDEM with analytical solutions. It is found that the existing empirical equations used in solving fluid-particle interactions in 2D CFDDEM fail to accurately calculate the hydrodynamic force applied to solid particles. The underlying reason is that the existing empirical models are obtained based on 3D experimental results and thus are not applicable to 2D problems. Based on the simulation results, a new drag coefficient model is then proposed. The estimated drag forces using the new model are compared favourably with the simulated ones, indicating the good performance of the proposed model.

42 ENGINEERING↗

DOE OSTI2025

Self-consistent hardness measurements spanning eleven decades of strain rate on a single material surface

A comprehensive understanding of material strength across strain rates typically requires the combination of results from different methods, which often vary in loading conditions and/or sampled volumes, leading to discrepancies in material behavior. This study presents a microindentation approach to measure hardness covering eleven orders of magnitude in strain rate, from quasi-static to phonon drag-dominated rates, on a single material surface under uniform testing conditions. By engineering the geometry of impactors used in laser induced particle impact testing, we extend the breadth of accessible strain rates, including multiple distinct rates exceeding 10⁵ s⁻¹. This self-consistent approach provides clearer insights into high-rate deformation mechanisms. Our results demonstrate a gradual increase in hardness with strain rate from quasi-static up to ultra-high rates, where a sharp upturn in hardness is observed.

Engineering↗

DOE OSTI2022

Novel Tube Design for Superheater Heat Exchanger Enabled Via Additive Manufacturing

Superheater tubes are critical boiler components that operate at relatively higher temperatures and pressure. Amongst the primary concerns for these tubes is the deposition of ash particles on the tube surface, leading to the reduced thickness of the tube due to material corrosion, consequently causing early creep failure of the component. In this research, a novel tube design has been proposed which resembles a teardrop or ogive shape to reduce the drag and concurrently improve the creep life of the superheater tubes. To administer the practicality of novel tubes, metal additive manufacturing (AM), for instance, laser-powder bed fusion (L-PBF), has been proposed. These unconventional designs were assessed and compared with the baseline circular tube design for mechanical design requirements (hoop stress and creep life) and the particle and flue gas flow characteristics around the differently shaped tubes. A thermomechanical finite element (FE) analysis was performed for hoop stress calculations. This study also emphasizes on effect of circumferential thermal variation on hoop stress distribution in tubes. Therefore, a detailed two-dimensional (2D) thermal simulation has been performed to report the circumferential thermal variation on the tube. A computational fluid dynamics (CFD) analysis coupled with particle tracing was performed for gas flow visualization and particle tracing around the proposed shapes and baseline circular-shaped tube design. The Schlieren optic setup was built and leveraged for qualitative validation of the proposed design. The complete design methodology established in the paper shows teardrop-shaped tubes better in terms of drag and creep life in contrast to the circular-shaped tube.

42 ENGINEERING↗