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At least 253 records · Page 14

Hybridized Discontinuous Galerkin Methods for Computational Fluid Dynamics

Hybridizable Discontinuous Galerkin (HDG) methods hold promise for any applications with significant advection character, including thermal hydraulics in light water reactors and advanced reactor concepts and fluid models of plasmas in magnetic confinement fusion. Its features include natural upwinding, local element conservation, and extensibility to arbitrarily high order accuracy. In the last fiscal year we have implemented HDG in the Multiphysics Object-Oriented Simulation Environment (MOOSE). We developed a first-of-its-kind automatic static condensation system in MOOSE’s underlying finite element library libMesh which can condense out arbitrarily many internal variables. Finally, we developed the first preconditioner for HDG discretizations of the Navier-Stokes equations which shows robust performance across a wide range of problem sizes and Reynolds numbers. This preconditioner yields solution times that are equivalent to the fastest developed for industry standard finite volume methods. Moreover, the arbitrarily high-order nature of HDG makes it a prime candidate for acceleration via graphical processing units (GPUs). We believe these developments will hold significant importance for future DOE Nuclear Energy (NE) and Fusion Energy Science (FES) programs.

97 MATHEMATICS AND COMPUTING↗

Numerical Prediction of Oscillation Behaviors of a Multiphase Core–Shell Droplet During Interfacial Tension Measurement

Interfacial tension between molten high-temperature materials is to be measured using the electrostatic levitation furnace (ELF) and the electromagnetic levitator (ISS-EML) aboard the International Space Station. A levitated compound droplet of a concentric core–shell structure is excited either by an impulsive electromagnetic field or by a superimposed electrostatic field. The oscillation behavior of the compound droplet is analyzed to measure interfacial tension at the interface of the two phases. In support of the space experiments, a computational fluid dynamic model was developed to characterize the oscillation behavior of multiphase core–shell droplet. The developed model predicted the interfacial tension between molten copper-rich and cobalt-rich phases with a difference of 3.3 pct compared to the values reported in literature. The developed model is being utilized to investigate the influence of various test parameters on measured surface tension and also being extended for molten steel–molten slag systems.

36 MATERIALS SCIENCE↗

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Stabilized bases for high-order, interpolation semi-Lagrangian, element-based tracer transport

In a computational fluid model of the atmosphere, the advective transport of trace species, or tracers, can be computationally expensive. For efficiency, models often use semi-Lagrangian advection methods. High-order interpolation semi-Lagrangian (ISL) methods, in particular, can be extremely efficient, if the problem of property preservation specific to them can be addressed. Atmosphere models often use geometrically and logically nonuniform grids for efficiency and, as a result, element-based discretizations. Such grids and discretizations make stability a particular problem for ISL methods. Generally, high-order, element-based ISL methods that use the natural polynomial interpolant associated with a nodal finite-element discretization are unstable. Here, we derive new bases having order of accuracy up to nine, with positive nodal weights, that stabilize the element-based ISL method. We use these bases to construct the linear advection operator in the property-preserving Interpolation Semi-Lagrangian Element-based Transport (Islet) method. Then we discuss key software implementation details. Finally, we show performance results for the Energy Exascale Earth System Model's atmosphere dynamical core, comparing the original and new transport methods. These simulations used up to 27,600 Graphical Processing Units (GPU) on the Oak Ridge Leadership Computing Facility's Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗

Thermal loading analysis of the ring injection dump for the Spallation Neutron Source facility

The ring injection dump (RID) is the largest beam dump in the Spallation Neutron Source facility at Oak Ridge National Laboratory and accepts a fraction of the beam from the ring that is not captured in the ring during injection. Thermo-fluid modeling of the RID components was performed during the initial design by using the software ANSYS CFX to characterize the power rating for the RID. From the calculations, the power rating was lowered from 200 kW to 150 kW, at 1.3 GeV beam energy due to concerns regarding the heating of the concrete structure. The Proton Power Upgrade project scope included reevaluating the power limit to the RID in anticipation that increasing it would provide more operational flexibility. The focus was on the shielding because it was the limiting factor, and data collected from thermocouples installed on the structure were used to benchmark the analysis. A three-stage process was adopted in the latest study. First, the already existing steady-state calculations were validated and extended with the latest Monte Carlo N-Particle source term calculations. Second, transient calculations were conducted to capture the dynamic state of the system in response to the energy dumped to the RID during the following operational period of the beam from 2005–2019 (14 years), and sensitivity analyses of crucial parameters were performed to benchmark the model with reasonable accuracy. Finally, an idealized transient cycle analysis was conducted with realistic duty factors to predict the temperature distribution at higher beam powers. Overall, the results confirmed the accuracy of the original steady state model but allowed the development of a new validated transient model with higher accuracy for future analyses.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Zonally dominated dynamics and Dimits threshold in curvature-driven ITG turbulence

The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$ -pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations (Dimits et al. , Phys. Plasmas , vol. 7, 2000, 969). A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear (van Wyk et al. , J. Plasma Phys. , vol. 82, 2016, 905820609). The breakup of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system – the Reynolds stress and the advection of the diamagnetic flow by the $\boldsymbol {E}\times \boldsymbol {B}$ flow. By analysing the linear ion-temperature-gradient modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.

Physics↗

Rheology improvement for silicon nitride and resin slurries for vat photopolymerization printing and sintering

This work presents the formulation, rheological characterization, and sintering of silicon nitride (Si₃N₄) slurries for vat photopolymerization (VPP) using digital light processing (DLP). Bimodal Si₃N₄ powder was dispersed into commercial photopolymer resin using two different dispersants with opposing effects on surface charge, resulting in varied slurry stability and flow behavior. Slurries were engineered to exhibit shear-thinning behavior suitable for VPP, and their flow properties were quantified using a power-law fluid model. The formulations achieved cure depths of approximately 40 µm and enabled printing of green bodies. Post-processing included thermal debinding and liquid-phase sintering, yielding primarily β-Si₃N₄ with a minor Y-Si-Al-O-N glass phase. The sintered parts reached ~85% of theoretical density and demonstrated a flexural strength of ~330 MPa. Microstructural analysis revealed closed porosity along with some defects related to powder agglomeration and interlayer adhesion. These findings provide insights into slurry formulation strategies for additive manufacturing of high-performance non-oxide ceramics.

Aerospace engineering↗

Simulation of supersonic molecular beam injection fueling into H-mode plasmas on EAST using BOUT++

Transport dynamic 2D simulations for supersonic molecular beam injection (SMBI) fueling into H-mode deuterium plasmas on the Experimental Advanced Superconducting Tokamak (EAST) is first simulated using a seven-field two-fluid model in the BOUT++ framework. The SMB is assumed to be injected into plasma from the midplane at the low field side with a fixed width and constant molecular flux. The different densities and injection velocities of SMBI are investigated within the upper single-null geometry of EAST. The simulations indicate that the SMBI has a self-shielding effect on molecules' inward transport into the plasma, and the deposition of SMBI leads to a large increase in plasma density and decrease in plasma temperature. There is a velocity threshold for SMB penetrating the pedestal and depositing at the top of density pedestal. However, the deposition point would be back toward the plasma boundary after SMB arriving at the deepest penetration position. Comparing the different molecular injection velocities and densities, the outcomes demonstrate that the depth of deposition is closely related to the injection velocity rather than the molecular density. The simulated results show good agreement with the EAST experiments by comparing the electron density profiles obtained by simulation and experiment, respectively. These results will be helpful for guiding future experiments, as well as the design of the SMBI system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton’s equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical simulation of streamer evolution in surface dielectric barrier discharge with electrode-array

Atmospheric pressure surface dielectric barrier discharges (SDBDs) may be composed of streamers fast propagating along a dielectric surface in ambient air, producing reactive oxygen and nitrogen species, and inducing a force on the neutral gas, which can find applications, respectively, in plasma medicine and aerodynamics. In this work, a two-dimensional self-consistent fluid model was developed to study SDBDs with an electrode-array. Emphasis was placed on the interaction of counter-propagating streamers and discharge uniformity for different applied voltages and geometric configurations of the electrode-array. When two counter-propagating streamers collide, the streamers come to a stop within a certain (ultimate) distance between the streamer heads. Optimizing the applied voltages is a convenient way to improve uniformity, making the streamer heads reach a minimum distance between each other. Shortening the electrode spacing can simultaneously shorten the streamer length and the ultimate distance between streamers. Under certain discharge parameters (such as applied voltage), there exists an optimum electrode spacing maximizing uniformity.

42 ENGINEERING↗

Pair plasma instability in homogeneous magnetic guide fields

Pair plasmas, collections of both matter and antimatter particles of equal mass, represent a paradigm for the study of basic plasma science, and many open questions exist regarding these unique systems. They are found in many astrophysical settings, such as gamma-ray bursts, and have recently also been produced in carefully designed laboratory experiments. A central research topic in plasma physics is instability; however, unlike their more common ion–electron siblings, pair plasmas are generally thought to be stable to cross field pressure gradients in homogeneous magnetic fields. It is shown here by means of kinetic full-f simulations that, when a pressure gradient is first established, the Gradient-driven Drift Coupling mode is destabilized and becomes turbulent. Force balance is eventually achieved by a combination of flattened pressure profiles due to turbulent transport and establishment of a magnetic field gradient, saturating the growth. During the unstable phase, key physics can be captured by a δf gyrokinetic description, where it is shown analytically and numerically that parallel particle motion results in a coupling of all electromagnetic field components. A fluid model derived therefrom accurately predicts linear eigenmodes and is used to resolve global profile effects. For laser-based electron–positron plasma experiments, prompt instability is predicted with growth times much shorter than plasma lifetimes. Similarly, growth rates are calculated for the planned APEX experiment as well as gamma-ray burst scenarios, suggesting that the instability may contribute to the early evolution of these systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulations of heat fluxes in an ELMy H-mode discharge on HL-2A

In order to study the distribution and evolution of the transient heat flux on HL-2A during edge-localized-mode (ELM) bursts, the BOUT++ electromagnetic six-field two-fluid model is used to simulate the pedestal collapse under the lower single-null divertor geometry. The equilibrium profiles of HL-2A ELMy H-mode discharge No. 24 953 are adopted as the initial condition in the original case. In this instance, linear analysis shows that the resistive ballooning mode (RBM) and drift-Alfven wave are unstable to this equilibrium, and RBM is the dominant instability. The evolutions of the radial heat fluxes at the outer mid-plane and heat fluxes to the inner and outer targets during the ELM event are presented. Six more equilibria are constructed based on the original case to find out the influence of the pedestal profiles on the peak electron heat flux. The results indicate that the heat flux increases with temperature and/or density, and the theoretical analysis and simulation results consistently show that the heat flux q ∥e is proportional to n e0,SEP $T^{\frac32}_{e0,SEP}$.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Plasma physics in strong-field regimes: Theories and simulations

In strong electromagnetic fields, unique plasma phenomena and applications emerge whose description requires recently developed theories and simulations [Y. Shi, Ph.D. thesis, Princeton University (2018)]. In the classical regime, to quantify effects of strong magnetic fields on three-wave interactions, a convenient formula is derived by solving the fluid model to the second order in general geometry. As an application, magnetic resonances are exploited to mediate laser pulse compression, whereby higher intensity pulses can be produced in wider frequency ranges, as confirmed by particle-in-cell simulations. In even stronger fields, relativistic-quantum effects become important, and a plasma model based on scalar quantum electrodynamics (QED) is developed which unveils observable corrections to Faraday rotation and cyclotron absorption in strongly magnetized plasmas. Beyond the perturbative regime, lattice QED is extended as a numerical tool for plasma physics, using which the transition from wakefield acceleration to electron-positron pair production is captured when laser intensity exceeds the Schwinger threshold.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Saturation physics of threshold heat-flux reduction

The saturation physics of ion-temperature-gradient-driven turbulence is examined in relation to the temperature-gradient variation of the heat flux, which can exhibit an upshift of the critical gradient for significant flux relative to the linear instability threshold. Gyrokinetic measurements of saturation properties and spectral energy transfer, which will be defined in Sec. II, are presented, indicating that the physics of saturation is fundamentally unchanged on either side of the upshifted gradient. To analyze heat transport below and above the upshifted critical gradient, a fluid model for toroidal ion-temperature-gradient turbulence is modified to include the kinetic instability threshold. The model and the heat flux are rendered in the eigenmode decomposition to track the dominant mode-coupling channel of zonal-flow-catalyzed transfer to a conjugate stable mode. Given linear and nonlinear symmetries, the stable mode level and the cross-correlation of the unstable and stable mode amplitudes are related to the unstable mode level via linear physics. Here, the heat flux can then be written in terms of the unstable-mode level, which through a nonlinear balance depends on the eigenmode-dependent coupling coefficients and the triplet correlation time of the dominant coupled modes. Resonance in these quantities leads to suppressed heat flux above the linear threshold, with a nonlinear upshift of the critical gradient set by the resonance broadening of a finite perpendicular wavenumber and collisionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fast particles in drift wave turbulence

This study aims to incorporate the effects of fast particles into our present fluid model for tokamak transport. The parameter ε f = ω / ω f, where ω is the mode frequency and ω f is the typical frequency of the fast particles, which enters as a factor in front of the fast particle response. Thus, for trapped fast particles, where ω f = ω pres the precession frequency of the fast particles, this parameter is of order 10 – 2 for drift waves, and thus, the fast particle response can be neglected. However, ε f will be of order 1 for fast particle modes such as in the fishbone instability. An important turbulence property, affecting both these limits, is resonance broadening. Effects of resonance broadening have recently been considered for fast particle instabilities, often coupled directly to the linear growth rate, while we here consider the original Dupree formulation where the turbulence directly drives a nonlinear frequency shift. Resonance broadening has a general tendency to counteract dissipative wave particle resonances. This has been observed for fast particle instabilities. Here, there is a resonant external source for the fast particles, so the instability survives if this source is dominant over the resonance broadening. For drift waves, however, external sources are not resonant since ε f << 1. Furthermore, the resonance broadening is able to remove the dissipative wave particle resonance completely.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effects of NBI-induced energetic ions on internal kink stability in HL-2M

A systematic investigation is carried out, studying the effect of the neutral beam injection induced energetic particles (EPs) on the n = 1 (n is the toroidal mode number) internal kink (IK) instability in the HL-2M tokamak, utilizing the MARS-F/K code [Liu et al., Phys. Plasmas 7, 3681 (2000) and 15, 112503 (2008)]. A high-beta sawteething HL-2M scenario, simulated by the TRANSP code [Breslau et al. Computer Software (2018)], is chosen for this study. Compared to the fluid model, non-perturbative magnetohydrodynamic (MHD)-kinetic hybrid computations with MARS-K show a generally stabilization effect on the IK, due to drift kinetic resonances associated with EPs. Further, the bounce resonance of trapped EPs has minor influence on the mode stability. In the absence of the plasma equilibrium flow and with the assumed particle pitch distribution, the transit resonance of co-current (countercurrent) passing EPs destabilizes (stabilizes) the IK. With plasma flow, both co- and countercurrent passing EPs tend to stabilize the mode, but the effect is stronger with the countercurrent particles. These modeling results provide useful guidance for interpreting MHD instabilities in the future high-performance experiments in HL-2M.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonlinear dynamics of small-scale Alfvén waves

Herein we study the nonlinear evolution of very oblique small-scale Alfvén waves with k ⊥ d i ≳1. At these scales, the waves become significantly compressive, unlike in magnetohydrodynamics, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes are small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when k ⊥ d i ~1. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfvén waves, an inherently three-dimensional effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfvén wave also becomes dispersive once one or more of k ⊥ ρ s , k ⊥ d e , or k ∥ d i becomes significant: for oblique waves at low β as studied here, this can be at a much smaller scale than d i . We show that the timescale for one-dimensional steepening of two-fluid Alfvén waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfvén wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Molecular dynamics simulations of the dielectric constants of salt-free and salt-doped polar solvents

Here, we develop a Stockmayer fluid model that accounts for the dielectric responses of polar solvents (water, MeOH, EtOH, acetone, 1-propanol, DMSO, and DMF) and NaCl solutions. These solvent molecules are represented by Lennard-Jones (LJ) spheres with permanent dipole moments and the ions by charged LJ spheres. The simulated dielectric constants of these liquids are comparable to experimental values, including the substantial decrease in the dielectric constant of water upon the addition of NaCl. Moreover, the simulations predict an increase in the dielectric constant when considering the influence of ion translations in addition to the orientation of permanent dipoles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗