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At least 91 records · Page 5

Analytical model of plasma response to external magnetic perturbation in absence of no-slip condition

Recent simulation and experimental results suggest that the magnetic island and flow on a resonant surface often do not satisfy the “no-slip” condition in the steady state. A new theoretical model on a nonlinear plasma response to external magnetic perturbation in the absence of a no-slip condition is proposed. The model is composed of the equations for the evolution of both the width and phase of the magnetic island due to forced reconnection driven by the external magnetic perturbation, and the force-balance equation for the plasma flow. When the island width is much less than the resistive layer width, the island growth is governed by the linear Hahm–Kulsrud–Taylor solution in the presence of time-dependent plasma flow. In the other regime when the island width is much larger than the resistive layer width, the evolution of both the island width and phase can be described using the Rutherford theory. The island solution is used to construct the quasilinear electromagnetic force, which, together with the viscous one, contributes to the nonlinear variation in plasma flow. The no-slip condition assumed in the conventional error field theory is not imposed here, where the island oscillation frequency depends on but does not necessarily equal to the plasma flow frequency at the rational surface.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Analytical model for quasi-linear flow response to resonant magnetic perturbation in resistive-inertial and viscous-resistive regimes

In this work, a quasi-linear model for plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been rigorously developed in the resistive-inertial (RI) and viscousresistive (VR) regimes purely from the two-field reduced MHD model. Models for plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e. the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work we derive both the magnetic island response and the torque balance equations in a quasi-linear model for plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the physical origins of quasi-linear forces and moments in the flow response equation are also accurately calculated and clarified self-consistently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Analytical modeling of the evolution of the nonlinearity parameter of sensitized stainless steel

Austenitic stainless steels are subject to the precipitation of chromium carbides (M 23 C 6 ) during exposure to high temperatures, causing these alloys to be susceptible to intergranular corrosion due to chromium depletion along grain boundaries. The acoustic nonlinearity parameter, β, shows sensitivity to the formation of carbides in these alloys. The Thermo-Calc TC-PRISMA module was used to model the nucleation and growth of grain boundary M 23 C 6 carbides. The model was verified with scanning transmission electron microscopy analysis that allowed measurements of the grain boundary precipitates. The paper introduces a reduced-order model of the acoustic nonlinearity based on the formation of misfit dislocations at the interface of the grain boundary precipitate and matrix to explain the change in β during isothermal aging. Furthermore, a direct relationship between the radius of the M 23 C 6 grain boundary carbides and β was observed and verified with nonlinear ultrasound measurements on 304L and 316L stainless steels.

36 MATERIALS SCIENCE↗

Analytical models for the enhancement of fusion reactivity by turbulence

The reactivity of fusion plasma depends not only on its local density and temperature but also, through a recently identified kinetic effect, on the relative velocities of nearby fluid elements. Turbulence on fine spatial scales, therefore, enhances fusion reactivity. The enhancement is quantified here for general subsonic turbulent flows. Leveraging this effect in the design of inertial confinement fusion experiments could enable substantial energy savings.

Fluid dynamics↗

Analytical Models of Frequency and Voltage in Large-Scale All-Inverter Power Systems

Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the Newtonian mechanics of synchronous generators, assuming that the frequency dynamics across a system are approximately homogeneous, and assume the dynamics of nodal voltages for most operating conditions are negligible, and thus are not directly computed at all buses. As a result, the use of system frequency models results in the systematic underestimation of frequency minimum nadir and maximum RoCoF, and provides no insight into the reactive power-voltage dynamics. This paper proposes a low-order model of both frequency and voltage response in grid-forming inverter-dominated power systems. The proposed model accounts for spatial-temporal variations in frequency and voltage behavior across a system and as a result, demonstrates the heterogeneity of frequency response in future renewable power systems. Electromagnetic transient (EMT) simulations are used to validate the utility, accuracy, and computational efficiency of these models, setting the basis for them to serve as fast, scalable alternatives to EMT simulation, especially when dealing with very large-scale systems, for both planning and operational studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than \building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of MCNP, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hardware Evaluation Analytical Modeling and Node Simulation: Benefits of Tighter GPU Integration

In this report, we examine several emerging technologies of interest to the Department of Energy and its computational centers. These include: 1) quantifying the benefit of tighter CPU-GPU integration, 2) quantifying the appropriate CPU core:GPU ratio, 3) quantifying the penalty for CPU-GPU disaggregation, 4) quantifying the benefits of tighter GPU-GPU integration, 5) quantifying the benefits of unified memory, and 6) quantifying the benefits of tighter FPGA-GPU integration.

97 MATHEMATICS AND COMPUTING↗

Analytical Modeling of Biomass Transport and Feeding Systems

The processing of biomass solids in a biorefinery consists of pretreatment, enzyme hydrolysis / concurrent fermentation of sugars to ethanol, product recovery, and drying. Sustainable operation requires a front end that transforms wet solids into a pumpable slurry. Otherwise the biorefinery will suffer unscheduled shut-downs and inefficient operation due to solids that obstruct pumps and other equipment and resist mixing in a bioreactor. Downtime in pioneer biorefineries due to interruptions from materials handling problems has been 50% or more, leading to unsustainable manufacturing processes. This work addresses new technology, predictive computational models, and definition of operational conditions that result in formation of slurries of corn stover at up to 300 g/L using low enzyme loadings (1 to 3 FPU cellulase/g) before the biomass (corn stover) enters the pretreatment step. A team of researchers from Purdue University, Idaho National Laboratory (INL), Forest Concepts, AdvanceBio, Argonne National Laboratory, and DOE BETO have combined their knowledge in agricultural and biological engineering, bioprocess engineering, mechanical engineering, chemical engineering, agricultural economics, materials engineering and enzyme and microbial technology to address the challenge of making lignocellulose flow. This team effort has resulted in the development and validation of conditions that employ low levels of commercial enzyme in an agitated bioreactor to which corn stover pellets are added resulting in formation of slurries at high solids loadings, before pretreatment. This approach overcomes challenges caused by handling of dry, particulate biomass materials at the front end of the biorefinery. The subsequent materials handling issues cause obstruction at pumps, pipes and valves. Formation of high loadings slurries with low yield stress, as reported here, significantly decreases the potential for process interruption and enhances plant operability. Key advances in the knowledge of how slurry formation occurs is reported here and in recently published journal papers. We found that pellets are needed to achieve high solids loading, and that commercial enzymes are effective in forming slurries of corn stover particles from pellets that have not been pretreated. Our work has resulted in models that predict solids behavior for formation of compressed solids and pellets that in turn facilitate slurries made of high concentrations of corn stover particles. A computational model was developed that gives mechanistic insights into properties of particles and mixing process that gives the slurry rheology needed to facilitate pumping. Hence, the corn stover may be pumped into a pretreatment reactor in place of auguring in solids against high pressure which is a root cause of interruptions at the front end of a biorefinery. Subsequent mixing in enzyme and microbial bioreactors results in conversion of lignocellulose to sugars in a biorefinery in agitated bioreactors, with flows in and out of the vessels being less likely to be interrupted due to plugging or materials handling problems. The obtained data coupled to process models, techno-economic assessment (TEA) and Life Cycle Analysis (LCA) were used to assess whether this approach is practical. These results are based on a foundation of laboratory characterization and pilot runs. The NREL biochemical sugar model was utilized to carry out techno-economic analysis of enzyme catalyzed liquefaction followed by enzyme hydrolysis. The minimum sugar selling price was between 17.5 and 18.3 ¢/pound or about the same as calculated by the NREL model for dilute acid pretreatment followed by enzyme hydrolysis. Life cycle analysis (LCA) based on Argonne’s Greet Model showed the enzyme catalyzed route had the lowest greenhouse gas emissions of the three combinations studied (i.e., enzyme, enzyme mimetic, and enzyme + mimetic combined). GHG emissions for enzyme-based corn stover liquefaction step, alone, were about 21 g CO 2 -equivalent/kg of liquefied slurry. We believe this approach will further enhance operability of a pioneer biorefinery, and bring large-scale conversion of lignocellulosic biomass to low carbon footprint biofuels closer to implementation.

09 BIOMASS FUELS↗

Galactic Bar Resonances with Diffusion: An Analytic Model with Implications for Bar–Dark Matter Halo Dynamical Friction

Abstract The secular evolution of disk galaxies is largely driven by resonances between the orbits of “particles” (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic and photometric features observed in the Milky Way and external galaxies. In simplified cases, these resonant interactions are well understood: for instance, the dynamics of a test particle trapped near a resonance of a steadily rotating bar is easily analyzed using the angle-action tools pioneered by Binney, Monari, and others. However, such treatments do not address the stochasticity and messiness inherent to real galaxies—effects that have, with few exceptions, been previously explored only with complex N -body simulations. In this paper, we propose a simple kinetic equation describing the distribution function of particles near an orbital resonance with a rigidly rotating bar, allowing for diffusion of the particles’ slow actions. We solve this equation for various values of the dimensionless diffusion strength Δ, and then apply our theory to the calculation of bar–halo dynamical friction. For Δ = 0, we recover the classic result of Tremaine and Weinberg that friction ultimately vanishes, owing to the phase mixing of resonant orbits. However, for Δ > 0, we find that diffusion suppresses phase mixing, leading to a finite torque. Our results suggest that stochasticity—be it physical or numerical—tends to increase bar–halo friction, and that bars in cosmological simulations might experience significant artificial slowdown, even if the numerical two-body relaxation time is much longer than a Hubble time.

79 ASTRONOMY AND ASTROPHYSICS↗

A Semi-analytical Model for Stellar Evolution in AGN Disks

Disks of gas accreting onto supermassive black holes may host numerous stellar-mass objects, formed within the disk or captured from a nuclear star cluster. We present a simplified model of stellar evolution in these dense environments, which exhibits exceptional agreement with full stellar evolution calculations at a minuscule fraction of the cost. Although the model presented here is limited to stars burning hydrogen in their cores, it is sufficient to determine the evolutionary fate of disk-embedded stars: whether they proceed to later stages of nuclear burning and leave behind a compact remnant, reach a quasi-steady state where mass loss and accretion balance one another, or whether accretion proceeds faster than stellar structure can adjust, causing a runaway. We highlight how various disk parameters and phenomena such as gap opening affect stellar evolution outcomes. We also highlight how our model can accommodate time-varying conditions, such as those experienced by a star on an eccentric orbit, and can couple to N -body integrations. This model will enable more detailed studies of stellar populations and their interaction with accretion disks than have previously been possible.

79 ASTRONOMY AND ASTROPHYSICS↗