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DOE OSTI2021

A mathematical framework for ejecta cloud dynamics with application to source models and piezoelectric mass measurements

We present a mathematical framework for describing the dynamical evolution of an ejecta cloud generated by a generic ejecta source model. We consider a piezoelectric sensor fielded in the path of an ejecta cloud, for experimental configurations in which the ejecta are created at a singly shocked planar surface and fly ballistically through vacuum to the stationary sensor. To do so, we introduce the concept of a time- and velocity-dependent ejecta “areal mass function.” We derive expressions for the analytic (“true”) accumulated ejecta areal mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltages. In this way, we derive an exact expression and upper bound for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation, which is commonly required for momentum diagnostic analyses. This error term is zero for truly instantaneous source models; otherwise, the standard piezoelectric analysis is guaranteed to overestimate the true mass. When combined with a piezoelectric dataset, this framework provides a unique solution for the ejecta particle velocity distribution, subject to the assumptions inherent in the data analysis. The framework also leads to strong boundary conditions that any ejecta source model must satisfy in order to be consistent with apparently global properties of piezoelectric measurements from a wide range of experiments. We demonstrate this methodology by applying it to the Richtmyer–Meshkov instability+self-similar velocity distribution ejecta source model currently under development at Los Alamos National Laboratory.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

In this study, we analyze three-dimensional particle-laden, isotropic turbulence to develop an understanding of inertial particle dynamics from a kinetic energy perspective. Data trends implying inhomogeneous sampling of the flow by particles are identified and used to support a proposed particle behavior: particles appear to accumulate in regions of low flow kinetic energy over time because they lose kinetic energy and slow down in such regions, ultimately causing them to spend more time there. To elucidate this behavior, we derive a particle kinetic energy equation from the particle momentum equation, which incorporates inertial effects through the Schiller–Naumann drag correlation. Upon extracting fundamental physics from this equation, hypotheses regarding the role of the Stokes number in the temporal change of particle kinetic energy and the previously proposed particle behavior are evaluated using simulation data considering three Stokes numbers. Finally, a Fokker–Planck equation is used to derive the steady-state probability density function of the particle kinetic energy. The model fits the simulation data well and provides a tool for further investigation into understanding preferential concentration, as well as a reduced order model for predicting particle kinetic energy in turbulent flows.

42 ENGINEERING↗

DOE OSTI2022

Magnetized laser–plasma interactions in high-energy-density systems: Parallel propagation

In this study, we investigate parametric processes in magnetized plasmas, driven by a large-amplitude pump light wave. Our focus is on laser–plasma interactions relevant to high-energy-density (HED) systems, such as the National Ignition Facility and the Sandia MagLIF concept. We present a self-contained derivation of a “parametric” dispersion relation for magnetized three-wave interactions, meaning the pump wave is included in the equilibrium, similar to the unmagnetized work of Drake et al., Phys. Fluids 17, 778 (1974). For this, we use a multi-species plasma fluid model and Maxwell's equations. The application of an external B field causes right- and left-polarized light waves to propagate with differing phase velocities. This leads to Faraday rotation of the polarization, which can be significant in HED conditions. Phase-matching and linear wave dispersion relations show that Raman and Brillouin scattering have modified spectra due to the background B field, though this effect is usually small in systems of current practical interest. We study a scattering process we call stimulated whistler scattering, where a light wave decays to an electromagnetic whistler wave (ω≲ω ce ) and a Langmuir wave. This only occurs in the presence of an external B field, which is required for the whistler wave to exist.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Kinetic simulation of a 50 mTorr capacitively coupled argon discharge over a range of frequencies and comparison to experiments

The effect of driving frequency in the range of 13.56–73 MHz on electron energy distribution and electron heating modes in a 50 mTorr capacitively coupled argon plasma discharge is studied using 1D-3V particle-in-cell simulations. Calculated electron energy probability functions exhibit three distinct “temperatures” for low-, mid-, and high-energy electrons at all the studied driving frequencies. When compared to published experimental data, the calculated probability functions show a reasonable agreement for the energy range resolved in the measurements (about 2–10 eV). Discrepancies due to limitations in experimental energy resolution outside this range lead to differences between computational and experimental values of the electron number density determined from the distribution functions, and the predicted effective electron temperature is within 25% of experimental values. The impedance of the discharge is interpreted in terms of a homogeneous equivalent circuit model, and the driving frequency dependence of the inferred combined sheath thickness is found to obey a known, theoretically derived, power law. The average power transferred from the field to the electrons (electron heating) is computed, and a region of negative heating near the sheath edge, particularly at higher driving frequencies, is identified. Analysis of the electron momentum equation shows that electron inertia, which on temporal averaging would be zero in a linear regime, is responsible for negative values of power deposition near the sheath edge at high driving frequencies due to the highly nonlinear behavior of the discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Solving the Orszag–Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks

We study the 2D Orszag–Tang vortex magnetohydrodynamics (MHD) problem through the use of physics-constrained convolutional neural networks (PCNNs) for forecasting the density, ρ, and the magnetic field, B, as well as the prediction of B given the velocity field v of the fluid. In addition to translation equivariance from the convolutional architecture, other physics constraints were embedded: absence of magnetic monopoles, non-negativity of ρ, use of only relevant variables, and the periodic boundary conditions of the problem. The use of only relevant variables and the hard constraint of non-negative ρ were found to facilitate learning greatly. The divergenceless condition ∇·B=0 was implemented as a hard constraint up to machine precision through the use of a magnetic potential to define B=∇×A. Residual networks and data augmentation were also used to improve performance. This allowed for some of the residual models to function as surrogate models and provide reasonably accurate simulations. For the prediction task, the PCNNs were evaluated against a physics-informed neural network, which had the ideal MHD induction equation as a soft constraint. Several models were able to generate highly accurate fields, which are visually almost indistinguishable and have low mean squared error. Only methods with built-in hard constraints produced physical fields with ∇·B=0. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

On Galilean invariance of mean kinetic helicity

While kinetic helicity is not Galilean invariant locally, it is known [Moffatt, J. Fluid Mech. 35, 117 (1969)] that its spatial integral quantifies the degree of knottedness of vorticity field lines. Being a topological property of the flow, mean kinetic helicity is Galilean invariant. Here, we provide a direct mathematical proof that kinetic helicity is Galilean invariant when spatially integrated over regions enclosed by vorticity surfaces, i.e., surfaces of zero vorticity flux. Here, we also discuss so-called relative kinetic helicity, which is Galilean invariant when integrated over any region in the flow.

42 ENGINEERING↗

DOE OSTI2024

Jets from shocked metal surfaces with grooves: Missing experiments

Many studies have investigated the mass outflows generated when a planar shock transits an imperfect (“defected”) metal surface, where the defects are symmetric triangular or sinusoidal grooves. Yet a fundamental question remains unanswered: how does the quantity of outflow mass and its maximum velocity vary as a function of the groove cross-sectional aspect ratio? We identify two sets of missing experiments that must be addressed to answer the question. The aspect ratio (groove depth over width) is equivalently represented by θ, the cross-sectional half angle, or by η 0 k, the amplitude multiplied by an effective wavenumber. Low θ (high η 0 k) grooves comprise the first set of missing experiments, which are necessary to determine the validity of theoretical predictions of the nonlinear regime (η 0 k ≥ 1, θ < 57.5°). The second set of missing experiments are those in which the volume of the groove (or equivalently, the axial cross-sectional area) has been held constant as θ or η 0 k are varied. Such experiments are necessary to independently measure the effects of variations in groove volume and groove aspect ratio on the resulting jets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

On transport of electrons in a magnetized plasma sheath

Electron trajectories are analyzed in the plasma sheath region in a magnetic field that intersects the surface at a shallow angle. Depending on the size of the Debye width relative to the electron gyroradius, λ D /ρ e , an electron either drifts in the sheath electric field or follows a sequence of reflections (“bouncing”) on the surface before reversing its parallel velocity. For thin sheath, λ D /ρ e ≪ 1, the conservation of the electron magnetic moment can be violated, depending on the ratio of the electron perpendicular and parallel velocities V ⊥ /V || and the magnetic field pitch angle with respect to the surface. Small-scale waviness of the surface can strongly amplify this effect, leading to violation of the magnetic moment conservation even for λ D /ρ e ≳ 1, which opens a channel of anomalous radial transport for electrons in plasma devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Compositing and Characterization of SE Quadrant Waste Exemplars

This report outlines the experimental investigation and characterization of transport properties in Hanford SE quadrant High-Level Waste (HLW). The goal of the study was to establish baseline behaviors of bulk composite rheology and settling characteristics to facilitate waste treatment process design for the Waste Treatment and Immobilization Plant (WTP) and avoid waste conditions and properties favorable to bubble cascade gas release events. The study focused on two major objectives: 1) identifying, obtaining, and preparing relevant Hanford tank waste samples for evaluation and 2) quantifying the “as-received” rheology and transport properties of the samples. Twenty-three centrifuged core segments originating from tanks AN-101, AN-106, and AW-105 were selected based on compositional relevance to SE quadrant PUREX cladding waste. These materials were composited into five waste composites enriched with target analytes: aluminum (Al), iron (Fe), phosphate (PO 4 ), uranium (U), and zirconium (Zr). Physical property and transport testing examined particle size distributions, bulk densities, settling behaviors, rheological properties, shear strengths, and just-suspended mixing speeds (NJS). Testing revealed two distinct composite classifications based on rheological characteristics: non-Newtonian composites (Fe and PO 4 ) and Newtonian composites (Al, U, and Zr). The Fe and PO 4 composites exhibited slow settling rates and reduced mobilization proclivity, attributable to strong particle-particle interactions and the formation of yield structures within non-Newtonian slurries. In contrast, the Al, U, and Zr composites displayed rapid settling and dense compaction behaviors, indicative of minimal structuring and interactions. Shear strengths for all composites were generally low relative to prior studies of SE quadrant waste, with only the U composite showing elevated strength approaching values reported in previous literature. Repeat shear strength measurements revealed contributions from dense granular material in the U composite and stronger cohesive properties in the Al composite. Settling data highlighted hindered settling behavior, with rates falling more than one order of magnitude below estimates based on Stokes’ law and rate decreasing as composite UDS content increased. NJS testing demonstrated different mobilization behaviors between cohesive and granular composites. The Fe composite required the highest mixing rate for resuspension, while the Al composite was the easiest to resuspend. Comparison of measured NJS against predictions made using the Zwietering correlation suggests non-Newtonian behavior alters resuspension mechanics, rendering non-Newtonian systems more stable against resuspension lift forces relative to their granular counterparts.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Leveraging the Polymer Glass Transition to Access Thermally Switchable Shear Jamming Suspensions

Suspensions of polymeric nano-and microparticles are fascinating stress-responsive material systems that, depending on their composition, can display a diverse range of flow properties under shear, such as drastic thinning, thickening, and even jamming (reversible solidification driven by shear). However, investigations to date have almost exclusively focused on nonresponsive particles, which do not allow in situ tuning of the flow properties. Polymeric materials possess rich phase transitions that can be directly tuned by their chemical structures, which has enabled researchers to engineer versatile adaptive materials that can respond to targeted external stimuli. Reported herein are suspensions of (readily prepared) micrometer-sized polymeric particles with accessible glass transition temperatures (T g ) designed to thermally control their non-Newtonian rheology. The underlying mechanical stiffness and interparticle friction between particles change dramatically near T g . Capitalizing on these properties, it is shown that, in contrast to conventional systems, a dramatic and nonmonotonic change in shear thickening occurs as the suspensions transition through the particles' T g . This straightforward strategy enables the in situ turning on (or off) of the system's ability to shear jam by varying the temperature relative to T g and lays the groundwork for other types of stimuli-responsive jamming systems through polymer chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Rheological Properties of Enzymatically Hydrolyzed Corn Stover Pretreated via Deacetylation and Mechanical Refining

Lignocellulosic biomass is a feedstock for fuels and chemicals that does not compete with food resources and has less contaminants than refuse-derived biomass feedstocks. To convert lignocellulosics to biofuels or value-added products, multiple processing steps are typically necessary. One method of producing biofuels from lignocellulosic biomass utilizes a deacetylation and mechanical refining pretreatment and an enzymatic hydrolysis reaction to produce fermentable sugars from cellulose and hemicellulose. The rheological properties of biomass, such as yield stress and plastic viscosity, change during enzymatic hydrolysis and alter the energy requirements for pumping and mixing, an important consideration for the design of processing equipment. The dynamic changes in rheological properties that occur in a corn stover feedstock undergoing enzymatic hydrolysis are characterized in this work, and the influence on pressure losses in piping systems is estimated. Two rheometer geometries were fabricated with stereolithography 3D printing to reduce wall slip and sample ejection. The slurries have complex rheological behaviors that include shear-thinning behavior. Shear stress ramps were performed on samples at 20 and 50 degrees C using the custom geometries, and the Herschel-Bulkley model was fit to the data. The dynamic nature of the rheological properties is correlated with changes in the average fiber length at various extents of reaction, and the influence of solids concentration on the observed rheology and piping pressure losses is discussed.

09 BIOMASS FUELS↗

DOE OSTI2021

Post-Newtonian kinetic theory

A kinetic theory for relativistic gases in the presence of gravitational fields is developed in the second post-Newtonian approximation. The corresponding Boltzmann equation is determined from the evolution of the one-particle distribution function with respect to the proper time along the world line of the particle. From the knowledge of the equilibrium Maxwell–Jüttner distribution function in the second post-Newtonian approximation the components of the particle four-flow and energy–momentum tensor are obtained. The Eulerian hydrodynamic equations for the mass density, mass-energy density and momentum density in the second post-Newtonian approximation are determined from the Boltzmann equation. It is shown that the combination of the hydrodynamic equations of mass and mass-energy densities leads to the hydrodynamic equation for the internal energy density in the first post-Newtonian approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Drag reduction and the Vogel exponent of a flexible beam in transient shear flows

Interactions between a flexible beam and a fluid in a channel are of great relevance to biological hairy surfaces, aquatic vegetation, marine life (e.g., fish gills), and many industrial systems alike. While steady state response of a beam to such flows is fairly well-explored, their behavior in the transient regime is not fully understood. Here, a series of numerical simulations are performed to study the laminar Couette flow of an incompressible viscous fluid past an elastic beam in a two-dimensional channel. The flexible beam is perpendicular to the direction of flow, and its base is fixed to the stationary bottom of the channel. We measure the evolution of the Vogel exponent, drag reduction, and reconfiguration number during the transient and steady-state response of the fluid–structure system for different geometrical and physical properties. Our benchmark shows a good agreement between numerical and experimental observations. Our results show that the system's steady-state response at different bulk-fluid velocities can be reproduced by investigating the shear flow response during the transient regime. We define a new variable that characterizes the evolution of the local velocity profile in the proximity of the free end of the beam and use that to characterize the transient-regime response. The analysis yields insight into the competing effects of elasticity of the beam and non-linear flow response.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Robust Molecular Predictive Methods for Novel Polymer Discovery and Applications

Polymeric materials are ubiquitous in modern society and they play an instrumental role in almost all industries, undoubtedly including the energy and environment sectors. Increased demand of energy and awareness to sustainability both necessitates the development of novel polymers with enhanced properties. Unfortunately, their structural and behavioral complexity render such discovery challenging and impeded. To address this problem, scientists are developing various computational modeling techniques and leveraging their power to depict the relationship between structural characteristics of polymers and their properties (such as rheological behaviors), and use such prediction to guide the design and syntheses of novel polymeric materials with enhanced performances. Unfortunately, predicting the relationships between polymer structure and composition with rheological properties via atomistic modeling is still a major challenge because of the extended time and length scales involved. Studying dynamic shear viscosity and linear viscoelasticity using molecular models requires capabilities that have been elusive, including representation of large molecular weight chains with an effective internal scale capable of describing entanglement, shear-rates that are in the s-1 scale with accurate quantitative stresses, and chemically-realistic combinations of both homogeneous and heterogeneous systems. Motivated by these unmet challenges, the overall technical objective of this DOE-STTR Phase II project is to develop robust molecular predictive methods for advanced polymer discovery and applications and especially for designing and demonstrating the “smart” polymer-based waterflooding enhanced oil recovery (EOR) process. In particular, we apply state-of-the-art molecular modeling methods developed by our academic partner, Materials Stimulation Center (MSC) at California Institute of Technology (Caltech), to facilitate and accelerate the experimental discovery processes. During the Phase I of this project, we had focused on development and demonstration of the molecular modeling methods to describe rheological properties of non-Newtonian polymer fluids, and to improve our fundamental understandings of shear-thickening mechanism and kinetics. In Phase II, we further apply the theoretical models to guide our experimental programs to improve our design of smart rheology modifier (SRM) polymers and their optimization for EOR. Specifically, we have three objectives in the Phase II study: (1) to further improve out computational modeling methods, coupling with the advanced machine learning algorithms; (2) to develop cost-effective and efficient SRM-flooding process suitable for EOR applications under typical reservoir conditions; and (3) to further explore the application of our molecular predictive models for innovative material discovery in other industrial applications. The recent development of our multiscale predictive framework allows the successful prediction of rheological properties from the chemical structure for polymers of experimentally relevant molecular weights, and provides an in-silico machine learning engine for screening novel compositions and structures with optimized non-Newtonian response, required for both shear-thinning and shear-thickening applications. Our framework provides: (1) procedures and tools for systematic coarsening from atomistic models and reverse mapping of coarse-grain models to atomistic, (2) unique ab initio methods to characterize the atomistic origin of colloidal and interfacial interactions and phenomena, (3) systematic structure and composition builders based on practical descriptors that drive rheological changes in polymer melts and diluted polymer mixtures, (4) a rheological properties engine capable of predicting viscosity in the zero-shear limit and under realistic dynamic conditions (for shear-rates commensurate with experiments) for large heterogeneous systems, (5) coarse-grain force fields with improved non-bond descriptions based on accurate quantum mechanics, (6) an in-silico screening machine learning engine that feeds from the systematic model builders to cover the descriptors search space, computes the rheological properties from converged trajectories spanning sub-milliseconds and ranks them for each structure/composition using an automated viscosity-vs-shear rate fitness function that can be tuned for shear-thickening, shear-thinning and other rheological responses.

02 PETROLEUM↗

DOE OSTI2021

Unifying disparate rate-dependent rheological regimes in non-Brownian suspensions

A typical dense non-Brownian particulate suspension exhibits shear thinning (decreasing viscosity) at low shear rate/stress followed by a Newtonian plateau (constant viscosity) at intermediate shear rate/stress values which transitions to shear thickening (increasing viscosity) beyond a critical shear rate/stress value and finally, undergoes a second shear thinning transition at extremely high shear rate/stress values. In this study, we unify and quantitatively reproduce all the disparate rate dependent regimes and the corresponding transitions for a dense non-Brownian suspension with increasing shear rate/stress. Here, we employ discrete particle dynamics simulations based on the proposed mechanism to elucidate its accuracy. We find that a competition between inter-particle interactions of hydrodynamic and non-hydrodynamic origins and the switching in the dominant stress scale with increasing the shear rate/stress lead to each of the above transitions. Inclusion of traditional hydrodynamic interactions, attractive/repulsive DLVO (Derjaguin and Landau, Verwey and Overbeek) interactions, the inter-particle contact interactions and a constant friction (or other constraint mechanism) reproduce the initial thinning as well as the shear thickening transition. However, to quantitatively capture the intermediate Newtonian plateau and the second shear thinning, an additional non-hydrodynamic interaction of non-DLVO origin and a decreasing coefficient of friction, respectively, are essential; thus, providing the first explanation for the presence of the intermediate Newtonian plateau along with reproducing the second shear thinning in a single framework. Expressions utilized for various interactions and friction are determined from experimental measurements and hence, result in an excellent quantitative agreement between the simulations and previous experiments.

42 ENGINEERING↗

DOE OSTI2023

Activity-induced propulsion and separation of passive chiral particles in liquids

Recent literature shows that chiral particles driven by vorticity gradients of a base Newtonian liquid can separate only in nonlinear or nonstationary flows. Here, we show that a base Newtonian liquid endowed with rotational degrees of freedom, can give rise to chiral particle propulsion and separation even in the Stokes flow approximation. We consider active mechanisms generating spatially inhomogeneous vorticity in the base liquid in a channel such as a magnetic torque, a pressure gradient and a sliding wall. These mechanisms generate regions of spatially inhomogeneous vorticity maintained by the internal angular momentum, propelling the chiral particles according to their handedness. Similar conclusions can be reached when one of the channel walls is replaced by a free surface acted on by surface shear. This behavior is in contrast to the case of standard Newtonian liquids where chiral particle propulsion generated by vorticity gradients is not possible in Stokes flow. Furthermore, this effect can find applications in industry, biology and medicine.

42 ENGINEERING↗

DOE OSTI2023

Simulations of biomass compression-screw feeding using a compressible non-Newtonian constitutive model

There is global interest in the conversion of biomass into sustainable low-carbon-footprint fuels and chemicals as an alternative to non-renewable fossil feedstocks. Feeding biomass solids into pressurized reactors is one of the key steps in biomass conversion. Predicting mechanical failure and energy requirements for this step helps avoid upstream processing bottlenecks and enables efficient operation of a biorefinery. Here, in this work, we developed a predictive computational model for biomass screw feeders that capture the highly viscous, non-Newtonian and compressible behavior of biomass slurries. Biomass compressible behavior is formulated by an equation of state and the non-Newtonian rheology is represented by a density-dependent viscosity model. Experimental data from two compression screw-feeder systems are presented as a validation for our model. Our model successfully predicted the location of the compressed biomass “plug”, biomass flow rate, and the required torque at different operating conditions for the experimental conditions studied in this work.

09 BIOMASS FUELS↗