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DOE OSTI2024

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Physics↗

DOE OSTI2024

Parallel expansion of a fuel pellet plasmoid

The problem of the assimilation of a cryogenic fuel pellet injected into a hot plasma is considered. Due to the transparency to ambient particles of the plasmoid, the localised region of high-density plasma created by ionisation of the ablated pellet material, electrons reach a ‘quasiequilibrium’ (QE) state which is characterised by a steady-state on the fastest collisional time scale. The simplified electron kinetic equation of the QE state is solved. Taking a velocity moment of the higher-order electron kinetic equation, which is valid on the expansion time scale, permits a fluid closure, yielding an evolution equation for the macroscopic parameters describing the QE distribution function. In contrast to the Braginskii equations, the closure does not require that electrons have a short mean free path compared with the size of density perturbations, and permits an anisotropic and highly non-Maxwellian distribution function. As the QE distribution function accounts for both trapped and passing electrons, the self-consistent electric potential that causes the expansion can be properly described, in contrast to earlier models of pellet plasmoid expansion with an unbounded potential. The plasmoid expansion is simulated using both a Vlasov model and a cold-fluid model for the ions. During the expansion plasmoid ions and electrons obtain nearly equal amounts of energy; as hot ambient electrons provide this energy in the form of collisional heating of plasmoid electrons, the expansion of a pellet plasmoid is expected to be a potent mechanism for the transfer of energy from electrons to ions on a time scale shorter than that of ion–electron thermalisation.

Physics↗

DOE OSTI2026

From Weibel seeds to dynamo beyond pair-plasmas

Bridging the spatiotemporal scales of magnetic seed field generation and subsequent dynamo amplification in the weakly collisional intracluster medium presents an extreme numerical challenge. We perform collisionless turbulence simulations with initially unmagnetised electrons that capture both magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification. Going beyond existing pair-plasma studies, we use an ion-to-electron mass ratio of 100 for which we find electron and ion dynamics are sufficiently decoupled. These simulations are enabled by the 10-moment collisionless fluid solver of Gkeyll, which evolves the full pressure tensor for all species. The electron heat-flux closure regulates pressure isotropisation and effectively sets the magnetic Reynolds number. We investigate how the strength of the closure influences the transition between a regime reminiscent of previous kinetic pair-plasma simulations and a regime exhibiting dynamo behaviour qualitatively similar to magnetohydrodynamics.

astrophysical plasmas↗

DOE OSTI2022

The Role of Methylaryl Radicals in the Growth of Polycyclic Aromatic Hydrocarbons: The Formation of Five-Membered Rings

The regions of the C 13 H 11 potential energy surface (PES) related to the unimolecular isomerization and decomposition of the 1-methylbiphenylyl radical and accessed by the 1-/2-methylnaphthyl + C 2 H 2 reactions have been explored by ab initio G3(MP2,CC)//B3LYP/6-311G(d,p) calculations. The kinetics of these reactions relevant to the growth of polycyclic aromatic hydrocarbons (PAH) under high-temperature conditions in circumstellar envelopes and in combustion flames has been studied employing the RRKM-Master Equation approach. The unimolecular reaction of 1-methylbiphenylyl proceeding via a five-membered ring closure followed by H elimination is predicted to be very fast, on a submicrosecond scale above 1000 K and to result in the formation of an embedded five-membered ring in the 9H-fluorene product. The 1-/2-methylnaphthyl + C 2 H 2 reaction mechanism involves acetylene addition to the radical on the methylene group followed by a six- or five-membered ring closure and aromatization via an H atom loss. Despite of the complexity of the C 13 H 11 PES, these straightforward pathways are dominant in the high-temperature regime (above ~1000 K), with the prevailing products being phenalene, with a significant contribution of 1H-cyclopenta(a)naphthalene, for 1-methylnaphthyl + C 2 H 2 , and 1H-cyclopenta(b)naphthalene and 3H-cyclopenta(a)naphthalene, for 2-methylnaphthyl + C 2 H 2 . The methylnaphthyl reactions with acetylene represent a clean source of the three-ring PAHs, but they are relatively slow owing to the high entrance barriers of ~10 kcal/mol, with the rate constants of about an order of magnitude lower as compared to those for naphthyl + allene and σ-aryl + C 2 H 2 . Here, the 1-methylnaphthyl + C 2 H 2 and 2-methylnaphthyl + C 2 H 2 reactions represent prototypes for PAH growth by an extra six- and five-membered ring on a zigzag edge or a corner of PAH and the generated modified Arrhenius expressions are recommended for kinetic modeling of PAH expansion by the mechanism of acetylene addition to methylaryl radicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Thermodynamics–Structure–Dynamics Correlations and Nonuniversal Effects in the Elastically Collective Activated Hopping Theory of Glass-Forming Liquids

We employ the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated dynamics in combination with crystal-avoiding simulations to study four inter-related questions for metastable monodisperse hard sphere fluids. The first is how significantly improved integral equation theory structural input (Modified-Verlet (MV) closure) changes the dynamical predictions of ECNLE theory. The main consequence is a modest enhancement of the importance of the collective elastic barrier relative to its local cage contribution, which increases the alpha relaxation time and fragility relative to prior results based on the Percus–Yevick closure. Second, ECNLE-MV theory predictions for the alpha time and self-diffusion constant in the metastable regime are quantitatively compared to our new simulations. The small adjustment of a numerical prefactor that enters the collective elastic barrier leads to quantitative agreement over three decades. Third, using the more accurate MV structural input, ECNLE theory is shown to predict thermodynamics–structure–dynamics “correlations” based on various long and short wavelength scalar properties all related to static two-point collective density fluctuations. The logarithm of the alpha relaxation time scales as a power law with these scalar metrics with an exponent that is significantly lower in the less dense noncooperative activated regime compared to the very dense highly cooperative regime. However, the discovered correlation of activated relaxation with a thermodynamic property (dimensionless compressibility) is not causal in ECNLE theory, but rather reflects a strong connection between the local structural quantities that quantify kinetic constraints in the theory with the amplitude of long wavelength density fluctuations. Fourth, the consequences of chemically specific nonuniversalities associated with the onset condition and relative importance of collective elasticity are studied. In conclusion, the predicted thermodynamics–structure–dynamics correlations are found to be robust, albeit with nontrivial shifts of the onset condition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials

Using a combination of experiment and simulation, we study how two-dimensional (2D) crystals of colloidal nanoparticles grow on cylindrical substrates. The cylindrical geometry allows us to examine growth in the absence of Gaussian curvature but in the presence of a closure constraint - the requirement that a crystal loops back onto itself. In some cases, this constraint results in structures that have been observed previously in theory and nonequilibrium packing experiments: chiral crystals and crystals with linear defects known as "line slips". More generally, though, the structures we see differ from those that have been observed: the line slips are kinked and contain partial vacancies. We show that these structures arise because the cylinder changes how the crystal grows. After a crystal wraps around the cylinder and touches itself, it must grow preferentially along the cylinder axis. As a result, crystals with a chiral line slip tend to trap partial vacancies. Indeed, we find that line slips that are less aligned with the cylinder axis incorporate more partial vacancies on average than the ones that are more aligned. Here, these results show that crystal growth on a cylinder is frustrated by the closure requirement, a finding that may shed some light on the assembly of biological nanosystems such as tobacco mosaic virus and might inform ways to fabricate chiral optical nanomaterials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Improving the Physical Basis for Updraft Dynamics in Deep Convection Parameterizations

This article presents a new deep convective parameterization that determines cloud characteristics based on a specified cloud size distribution. The vertical profiles of cloud properties are determined by analytic equations, which formulate entrainment with an inverse relationship to cloud width. In line with recent studies of large eddy simulations (LES), cloud widths are assumed to be constant with height and vertical mass flux (M) characteristics of the clouds are therefore regulated by the vertical velocity profile. The parameterization is configured to work with existing cloud base M closure formulations, with the closure predicting the total cloud area rather than the cloud base M directly. Analytic formula are also used to connect the vertical wind shear magnitude to the cloud size distribution, wherein larger shear magnitudes result in more numerous large updrafts than weaker shear magnitudes, which is in line with recent research results. The parameterization is compared against 10 deep convective LES with varying thermodynamic and vertical wind shear profiles. Results show dramatic improvements in the prediction of normalized M, detrainment, and the properties of detrained air over the existing Zhang and McFarlane (1995) scheme. In particular, the new model is able to correctly portray the transition from a bottom-heavy M profile in weakly sheared environments, to a top-heavy M profile in strongly sheared environments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Linking Deep and Shallow Convective Mass Fluxes via an Assumed Entrainment Distribution in CAM5‐CLUBB: Parameterization and Simulated Precipitation Variability

Abstract We modify the Zhang‐McFarlane (ZM) deep convection scheme in the Community Atmosphere Model version 5 to couple it with a unified parameterization for boundary‐layer turbulence and shallow convection, that is, Cloud Layers Unified by Binormals (CLUBB). By assuming a lognormal distribution of entrainment rate across the entire moist convective regimes, we link mass fluxes between shallow and deep convection, which are partitioned by the entrainment rate of the shallowest deep convective plume. Hence, a new deep convective closure is established which is coupled to the sub‐grid vertical motion variability in CLUBB. The convection feedback (or memory) effects are also considered to decrease the entrainment spectrum width and enhance the vertical velocity variability that further affect deep convection. Results show that the revised scheme improves the precipitation simulations in terms of the mean state and variability at various timescales, such as the alleviated double‐intertropical convergence zone and more realistic simulations of the seasonal variation of monsoon precipitation over East Asia, Madden‐Julian Oscillation, and precipitation diurnal phase propagations downstream of large terrains. The improvements are still seen in many aspects such as the mean‐state precipitation when turning off the convection feedback impacts in the revised scheme, emphasizing the benefits of using the modified mass‐flux closure. However, the convection feedbacks have considerable effects on the precipitation diurnal cycle simulations over regions with late‐afternoon precipitation peaks. Overall, the revised scheme provides a unified treatment for sub‐grid vertical motions across regimes of boundary‐layer turbulence, shallow convection, and deep convection, leading to better‐simulated precipitation at various timescales.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Automated Symbolic Upscaling: 1. Model Generation for Extended Applicability Regimes

Abstract In porous media theory, upscaling techniques are fundamental to deriving rigorous Darcy‐scale models for flow and reactive transport in subsurface systems. Due to limitations in classical techniques, a number of ad hoc approaches have been proposed to address physical regimes in which reactive time scales are similar to, or faster than, diffusive time scales. In Part 1 of this two part series, we present a strategy for expanding the applicability of classical homogenization theory by generalizing the assumed closure form. We detail the implementation of this strategy on two reactive mass transport problems with moderately reactive physics. The strategy produces nontrivial homogenized models with emergent terms and effective parameters that couple reactive, diffusive, and advective transport. The differences in equation forms between the macroscopic and pore‐scale descriptions advise caution to further studies where the forms of macroscopic equations are assumed, as opposed to rigorously derived. Numerical validation is provided for each problem to show that the error estimates of homogenization theory are satisfied, and to justify the implemented strategy. In Part 2, the presented strategy is automated using symbolic computing to expedite its implementation.

Pietrzyk, Kyle↗

DOE OSTI2021

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

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

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Development of five-moment two-fluid modeling for Z-pinch physics

The Z-pinch m = 0 instability as well as its stabilization by radially sheared axial flow is studied using the nonlinear ideal five-moment twofluid (5M2F) model with an extension of that model to include Braginskii heat and momentum transport. Using the ideal 5M2F model, linear growth rate results are compared with prior work using MHD and Hall MHD. At small normalized wavenumber, 1 < k a < 4 , where a is the effective pinch radius, 5M2F results agree with Hall MHD within 20% in scenarios without radially sheared axial flow. With the sheared flow and focusing on ka = 10/3, agreement with Hall MHD is excellent. In the limit of small ion inertial length, results also match with MHD. A comparison with PIC modeling of shear-free m = 0 stability focuses on a plasma scenario based on recent experimental results. In a scan of mode wavenumber, ideal 5M2F results are qualitatively similar to PIC: the growth rate rises to a peak at a moderate wavenumber and declines at a large wavenumber in contrast to MHD results, which show the saturation of the growth rate with the increasing wavenumber rather than a decline. The peak normalized 5M2F growth rate is γ τ A = 1.5 , where sA is the Alfven transit time across the pinch. The peak occurs at normalized wavenumber ka = 10. For comparison, PIC results have a peak growth of γ τ A = 0.77 at ka = 5. Including Braginskiibased closure of the 5M2F model does not qualitatively change the ideal results in this particular case. Nonlinear saturation is studied using the 5M2F model with the dissipative Braginskii-based closure in cases with pinch-edge sheared-flow speed equal to half the Alfven speed. Nonlinear mixing due to the sheared flow yields a quasi-steady state after modest losses of pinch ion inventory and pinch thermal energy, approximately 30% and 10%, respectively. 5M2F modeling captures the essential physics of m = 0 instability and offers a computationally tractable route to high-fidelity modeling of 3D Z-pinch behavior, including m = 1 instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Compton rocket effect due to the action of radiation reaction force in degenerate plasma

A closed set of fluid equations with radiation reaction force (RRF) are constructed from the moments of the appropriate single particle kinetic equation describing a relativistic degenerate (high density) electron plasma. The closure, in analogy with the Maxwellian closure for non-degenerate plasmas, is affected via a parametrized Fermi-Dirac distribution. It is shown that the degeneracy increases RRF just as will be predicted from the so-called “Compton Rocket” effect.

Physics↗

DOE OSTI2024

A Review of Remote Welding and Nondestructive Examination Technologies for the DOE Standard Canister

The U.S. Department of Energy (DOE) manages a wide variety of spent nuclear fuel (SNF) that poses a unique management challenge. To help address this challenge, the DOE Standard Canister (DOESC), designed to remain sealed during handling, storage, transportation, and disposal, was conceptualized as a standardized containment vessel to accommodate DOE-managed SNF. Since 1999, several welding and examination processes have been independently developed for the DOESC’s closure welds. However, neither the DOESC nor these processes have been realized in an operational capacity. This review paper seeks to present and compare previously developed DOESC closure weld, nondestructive examination, and repair processes and technologies. Specific processes developed for the Idaho Spent Fuel Facility, in preparation for the Yucca Mountain geological repository, and the recent Road-Ready Demonstration Project are discussed. Further, specific focus is given to how different operating constraints and the American Society of Mechanical Engineers Boiler and Pressure Vessel Code (BPVC) have driven certain welding and nondestructive examination requirements. Historical DOESC welding and examination strategies are assessed against current regulatory and BPVC requirements. The comparison of welding processes, technologies, and DOESC designs presented in this review paper will inform further construction efforts for other commercial and DOE-managed SNF containments, including the DOESC.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Reynolds-Averaged Turbulence Modeling Using Deep Learning with Local Flow Features: An Empirical Approach

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-epsilon, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. Finally, the presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

42 ENGINEERING↗

DOE OSTI2023

Bayesian Parameter Estimation of the k-ω Shear Stress Transport Model for Accurate Simulations of Impinging-Jet Heat Transfer

Given the lack of fusion-relevant component test facilities, current estimates of the thermo-fluid performance of plasma-facing components are based for the most part on numerical simulations. A major source of uncertainty in these simulations is the semiempirical turbulence (closure) models for the Reynolds stresses appearing in the governing Reynolds-averaged Navier-Stokes equations, which involve a set of constants that depend upon the flow. The objective of this study is to evaluate Bayesian parameter estimation of turbulence closure constants in ANSYS Fluent to model heat transfer in impinging jets. The Bayesian statistical calibration produces a probability distribution for these constants from experimental data; the maximum a posteriori estimates are then taken to be the calibrated constants, or parameters. The turbulence model constants are calibrated using an experimental study of a submerged jet of air impinging on a flat heated surface at Reynolds numbers Re = O(10 4 ) and impingement distance in jet diameters H/d = 2. Numerical predictions using the calibrated model parameters are then compared with those generated using the default constants. Predictions obtained with model parameters calibrated on datasets of two different sizes are compared to evaluate the effect of the number of calibration samples. Lastly, the extrapolative ability of the calibrated model is examined by predictions at a Re beyond the calibration values.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

High temperature superconductivity in the candidate phases of solid hydrogen

As the simplest element in nature, unraveling the phase diagram of hydrogen is a primary task for condensed matter physics. As conjectured many decades ago, in the low-temperature and high-pressure part of the phase diagram, solid hydrogen is expected to become metallic with a high superconducting transition temperature. The metallization may occur via band gap closure in the molecular solid or via a transition to the atomic solid. Recently, a few experimental studies pushed the achievable pressures into the 400–500 GPa range. There are strong indications that at some pressure in this range metallization via either of these mechanisms occurs, although there are disagreements between experimental reports. Furthermore, there are multiple good candidate crystal phases that have emerged from recent computational and experimental studies which may be realized in upcoming experiments. Therefore, it is crucial to determine the superconducting properties of these candidate phases. In a recent study, we reported the superconducting properties of the C2/c-24 phase, which we believe to be a strong candidate for metallization via band gap closure. Here, we report the superconducting properties of the Cmca-12, Cmca-4 and I4 1 /amd-2 phases including the anharmonic effects using a Wannier function-based dense k-point and q-point sampling. Here we find that the Cmca-12 phase has a superconducting transition temperature that rises from 86 K at 400 GPa to 212 K at 500 GPa, whereas the Cmca-4 and I4 1 /amd-2 phases show a less pressure-dependent behavior with their T c in the 74–94 K and 307–343 K ranges, respectively. These properties can be used to distinguish between crystal phases in future experiments. Understanding superconductivity in pure hydrogen is also important in the study of high-T c hydrides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Large-Eddy Simulations of Idealized Atmospheric Boundary Layers Using Nalu-Wind

Accurate prediction of wind-plant performance relies, in part, on properly characterizing the turbulent atmospheric boundary layer (ABL) flow in which wind turbines operate. Large-eddy simulation (LES) is a powerful tool for simulating ABLs because it resolves the largest, most energetic scales of three-dimensional turbulent motions. Yet LES predictions are well known to depend on modeling choices such as grid resolution, numerical discretization schemes, and closures for unresolved scales of turbulence. Here, we evaluate how these choices influence predictions of ABL winds using Nalu-Wind, a wind-specific fork of the open-source, generalized, unstructured, massively parallel flow solver NaluCFD/Nalu.

17 WIND ENERGY↗

DOE OSTI2026

Emergence of vorticity and viscous stress in finite-scale quantum hydrodynamics

The Madelung equations offer a hydrodynamic description of quantum systems, from single particles to quantum fluids. In this formulation, the probability density is mapped onto the fluid density and the phase is treated as a scalar potential generating the velocity field. As examples of potential flows, quantum fluids described in this way are inherently irrotational, but quantum vortices may arise at discrete points where the phase is undefined. In this paper, starting from this irrotational description of a quantum fluid, a coarse-graining procedure is applied to arrive at a macroscopic description of the quantum fluid in terms of a hierarchy of moments in which the role of velocity is played by a Favre average of the microscopic velocity field. This hierarchy is truncated using an explicit closure derived from an expansion in a finite length scale. The resulting coarse-grained fields are shown to allow for finite vorticity at any point in the fluid. Additionally, it is shown that this vorticity obeys a similar equation to the vorticity equation in classical hydrodynamics and includes a vortex-stretching term. The particular closure employed here also gives rise to a novel stress term in the fluid equations, which in the appropriate limit appears analogous to an artificial viscous stress from computational fluid dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗