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Results for “Scaling laws”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Scaling laws for two-dimensional dendritic crystal growth in a narrow channel

Here, we investigate analytically and computationally the dynamics of two-dimensional needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity $\textit{V}$ decreases in time $\textit{t}$ as a power law $V ~t^{–2/3}$, which we validate by phase-field and dendritic-needle-network simulations. Simulations further reveal that, above a critical channel width $Λ ≈ 5l_D$, where $l_D$ is the diffusion length, needle crystals grow with a constant $V < V_s$, where $V_s$ is the free-growth needle crystal velocity, and approaches $V_s$ in the limit $Λ \gg l_D$.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fluctuations and power-law scaling of dry, frictionless granular rheology near the hard-particle limit

Here the flow of frictionless granular particles is studied with stress-controlled discrete element modeling simulations for systems varying in size from 300 to 100,000 particles. The volume fraction and shear-stress ratio μ are relatively insensitive to system size for a wide range of inertial numbers I. Second-order effects in strain rate, such as normal stress differences, require large system sizes to accurately extract meaningful results, notably a nonmonotonic dependence in the first normal stress difference with strain rate. The rheological response represented by the μ(I) scalar model works well at describing the lower-order aspects of the rheology, except near the quasistatic limit of these stress-controlled flows. The pressure is varied over five decades, and a pressure dependence of the coordination number is observed, which is not captured by the inertial number. Large fluctuations observed for small systems N≤1000 near the quasistatic limit can lead to the arrest of flow resulting in challenges to fitting the data to rheological relationships. The inertial number is also insufficient for capturing the pressure-dependent behavior of property fluctuations. Fluctuations in the flow and microstructural properties are measured in both the quasistatic and inertial regimes, including shear stress, pressure, strain rate, normal stress differences, volume fraction, coordination number, and contact fabric anisotropy. The fluctuations in flow properties scale self-similarly with pressure and system size. A transition in the scaling of fluctuations of stress properties and contact fabric anisotropy are measured and proposed as a quantitative identification of the transition from inertial to quasistatic flow.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Review of Experimental Decontamination Factors (DF) of Iodine in the Pilot-Scale Law Melter Off-Gas Systems

The Low Activity Waste (LAW) melters at the Hanford Tank Waste Treatment and Immobilization Plant (WTP) will convert low-activity tank wastes containing high concentrations of sodium salts into glass for onsite disposal. Much of the airborne particulates during the calcination/fusion of the feed solids will be removed by condensation and scrubbing of the melter exhaust in the Submerged Bed Scrubber (SBS) and Wet Electrostatic Precipitator (WESP)of the primary off-gas treatment system. The gases exiting the WESP enter a secondary off-gas treatment system, which includes a High-Efficiency Particulate Air (HEPA) filter, an activated carbon absorber, a Thermal Catalytic Oxidizer (TCO), a Selective Catalytic Reduction (SCR) unit, a caustic scrubber, and an exhauster. Much of the volatile organics and NOx will be removed in the TCO and SCR, respectively. Under WTP Direct Feed LAW (DFLAW) configuration, the liquid effluents from the SBS and WESP will be collected and evaporated under vacuum with the evaporator concentrate recycled back to the LAW melter, while the evaporator condensate will be merged with the caustic scrubber solution and sent to the Effluent Treatment Facility (ETF).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Theoretical power-law relationship between permeability and formation factor

Permeability k and formation factor F are important petrophysical properties that have broad applications to reservoir engineering. Although well-log analysis has advanced reservoir characterizations, direct measurement of k is still not available. Accordingly, resistivity logs and more particularly formation factor have been frequently used to estimate k. In this study, we present a theoretical framework to relate k to F. We use power-law scaling from continuum percolation theory to develop a theoretic relationship between k and F, which is similar in form to a published power-law equation with empirical coefficients. Our result gives a physical interpretation to this empirical relationship. We also compare power-law scaling laws from percolation theory with data derived from experimental measurements and numerical simulations in the literature. Finally, using the Curve Fitting toolbox of MATLAB, the parameters of the power-law equations are determined, and the significance of the non-universal power laws are discussed.

42 ENGINEERING↗
DOE OSTI2022

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Casimir-Polder potential on an excited atom near an atomic array

We develop a microscopic description of the fluctuation-mediated Casimir-Polder (CP) shifts on a 'test' two-level atom placed near a two-dimensional atomic array of two-level atoms. We derive the resonant and off-resonant CP potentials experienced by the excited test atom using fourth-order perturbation theory, under the assumption that the test atom resonance is far detuned from those of the array atoms. The total potential on the test atom can be described as the sum of the pairwise resonant and off-resonant potentials resulting from its interaction with the individual atoms of the array. We analyze the asymptotic scaling of CP shifts as a function of the test atom-array separation, and its dependence on various system parameters: array spacing and size, and dipole orientation of the array atoms. Our results bridge the description of CP potential across two distinct regimes: (i) from a single-atom limit where we recover the well-known two-atom Van der Waals potential, (ii) to a macroscopic boundary limit, where we demonstrate new asymptotic scaling laws. We demonstrate that these scaling laws can be tuned via the microscopic parameters of the atomic array, establishing atomically-controlled arrays as a versatile platform for tailoring fluctuation-induced QED phenomena.

FOS: Physical sciences↗
DOE OSTI2023

Disruption halo current rotation scaling on Alcator C-Mod and HBT-EP

Asymmetric halo currents (HCs) can exert large net forces on the vacuum vessel and other components during disruptions on tokamaks. The displacements caused by these forces can then be amplified if these asymmetric forces rotate at frequencies resonant with the vessel. This paper reports on the investigation of a recently proposed scaling law for the disruption HC rotation frequency [Saperstein et al., “Halo current rotation scaling in post-disruption plasmas,” Nucl. Fusion 62, 026044 (2022)] that combines measurements on Alcator C-Mod with those on HBT-EP. We find that a new non-circular version of the scaling law [ ⟨ f rot ⟩ m / ⟨ m ⟩ ∝ 1 B T ( S / π )] takes into consideration the dependence of frot on the poloidal structure of the MHD instability (m) driving the asymmetry and describes the disruption-averaged rotation frequency on C-Mod. Disruption rotation is also found to be insensitive to the vertical position and impurity content of the plasma at the onset of the disruption. However, a stagnation in the time evolution of frot is occasionally observed. In conclusion, observations are consistent with the dominance of poloidal rotation during the disruption, which is motivated by the poloidal drift nature of the scaling law.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

The physics of gain relevant to inertial fusion energy target designs

In inertial confinement fusion, pellets of deuterium tritium fuel are compressed and heated to the conditions where they undergo fusion and release energy. The target gain (ratio of energy released from the fusion reactions to the energy in the drive source) is a key parameter in determining the power flow and economics of an inertial fusion energy (IFE) power plant. In this study, the physics of gain is explored for laser-direct-drive targets with driver energy at the megajoule scale. This analysis is performed with the assumption of next-generation laser technologies that are expected to increase convergent drive pressures to over 200 Mbar. This is possible with the addition of bandwidth to the laser spectrum and by employing focal-spot zooming. Simple physics arguments are used to derive scaling laws that describe target gain as a function of laser energy, adiabat, ablation pressure, and implosion velocity. Scaling laws are found for the unablated mass, ablation pressure, areal density, implosion velocity, and in-flight aspect ratio. Furthermore, those scaling laws are then used to explore the design space for IFE targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Rheo-electric measurements of carbon black suspensions containing polyvinylidene difluoride in N -methyl-2-pyrrolidone

Lithium-ion battery cathode slurries have a microstructure that depends sensitively on how they are processed due to carbon black's (CB) evolving structure when subjected coating flows. While polyvinylidene difluoride (PVDF), one of the main components of the cathode slurry, plays an important role in modifying the structure and rheology of CB, a quantitative understanding is lacking. In this work, we explore the role of PVDF in determining the structural evolution of Super C65 CB in N-methyl-2-pyrrolidinone (NMP) with rheo-electric measurements. We find that PVDF enhances the viscosity of NMP resulting in a more extensive structural erosion of CB agglomerates with increasing polymer concentration and molecular weight. We also show that the relative viscosity of all suspensions can be collapsed by the fluid Mason number (Mnf), which compares the hydrodynamic forces imposed by the medium to cohesive forces holding CB agglomerates together. Using simultaneous rheo-electric measurements, we find at high Mnf, the dielectric strength (Δε) scales with Mnf, and the power-law scaling can be quantitatively predicted by considering the self-similar break up of CB agglomerates. The collapse of the relative viscosity and scaling of Δε both suggest that PVDF increases the hydrodynamic force of the suspending medium without directly changing the CB agglomerate structure. These findings are valuable for optimizing the rheology of lithium ion battery cathode slurries. We also anticipate that these findings can be extended to understand the microstructure of similar systems under flow.

Mechanics↗
DOE OSTI2020

Multi-device study of temporal characteristics of magnetohydrodynamic modes initiating disruptions

Disruptions in tokamaks are often preceded by magnetohydrodynamic (MHD) instabilities that can rotate or become locked to the wall. Measurements from magnetic diagnostics in the presence of MHD mode precursors to disruptions can yield potentially valuable input to the plasma control system, with a view to disruption avoidance, prediction and mitigation. This report presents an exploratory analysis of the growth of MHD modes and corresponding time scales on the basis of magnetic measurements in multiple tokamaks. To this end, a database was compiled using disruptive discharges from COMPASS, ASDEX Upgrade, DIII-D and JET, manually classified according to disruption root cause, and characterized by a great diversity of operational conditions and mode dynamics. The typical time during which a mode can be detected using saddle coils and the duration of the locked mode phase in the database both extend over several orders of magnitude, but generally the time scales increase with plasma size. Several additional factors are discussed that can influence these durations, including the disruption root cause. A scaling law for the locked phase duration was estimated, yielding predictions toward ITER of the order of hundreds of milliseconds or even seconds. In addition, a scaling law for the mode amplitude at the disruption onset, proposed earlier by de Vries et al. (2016), is applied to the database, and its predictive capabilities are assessed. Despite significant uncertainty on the predictions from both scaling laws, encouraging trends are observed of the fraction of disruptions that may be detected with sufficient warning time to allow mitigation or even avoidance, based solely on observations of MHD mode dynamics. When combined with similar analysis of measurements from diagnostics that are sensitive to other disruption precursors, our analysis methods and results may contribute to the reliability, robustness and generalization of disruption warning schemes for ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Water transport properties of virtual fractal porous media: Implications for the unsaturated transport properties of cement-based materials

Cement-based materials are more and more recognized as fractal materials. From a practical point of view, fractality means that the pore size distribution can be described using fractal scaling law (i.e. power functions). Here, the simplest scaling law making use of a single fractal dimension was used to generate simple and virtual fractal porous media (based on bundles of parallel cylindrical pores). The capillary curve and permeability (relative and intrinsic) of the virtual porous media were then estimated through theoretical and numerical approaches. The results show that: (1) although bereft of any physical basis, van Genuchten equation bears some fractal information; (2) although highly flexible, van Genuchten equation fails to perfectly fit the capillary curves and can thus generate error in inverse analysis (for intrinsic permeability evaluation) and (3) there seems to be a relation between the intrinsic permeability and van Genuchten pressure parameter.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

Abstract Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction . For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.

Chen, Bin↗
DOE OSTI2023

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

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

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗