Search NASA⌕ Search

SEARCH · Search NASA

Results for “Dimensionless”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Microscopic Theory of Long-Time Center-of-Mass Self-Diffusion and Anomalous Transport in Ring Polymer Liquids

We construct a microscopic theory at the level of segment-scale correlated space–time intermolecular forces for the long-time center-of-mass (CM) diffusion constant and intermediate-time non-Fickian transport in dense solutions and melts of ring polymers. The approach combines ideas of polymer, colloid, and liquid-state statistical mechanics to quantify how the multifractal intra-ring conformational structure and inter-ring packing correlations determine dynamic caging constraints and time-dependent friction. Breakdown of Rouse theory is predicted to occur due to length scale-dependent temporal correlation of forces exerted on pairs of tagged ring segments from surrounding polymers. At large enough degrees of polymerization (N), a stronger scaling of the CM diffusion constant (D ∝ N –2 ) is predicted, with a crossover N D proportional to the product of the system-specific macromolecular volume fraction and dimensionless compressibility. In analogy with caging effects in glass-forming fluids, the theory does appear to begin to fail at sufficiently high N/N D for the center-of-mass diffusivity, likely due to another crossover to an even slower activated transport regime. However, use of N/N D with the theoretically predicted N D , in conjunction with dynamic blob scaling ideas for local Rouse friction, collapses semidilute and concentrated solution simulation data onto a master curve. Based on the same physical ideas employed to predict the diffusion constant, a generalized Langevin equation description is formulated for intermediate-time CM transport. It predicts two subdiffusive regimes that emerge due to the self-similar nature of internal ring structure. Analytic and numerical predictions for the apparent non-Fickian exponent as a function of time, N/N D and dimensionless compressibility, the evolution of the maximum degree of subdiffusive motion with N/N D , and the time scale for recovering Fickian diffusion are made, all of which are in good accordance with melt simulations. Furthermore, the present work sets the stage to address activated dynamics and glass formation on the macromolecular scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Impacts of Permeability Heterogeneity and Background Flow on Supercritical CO 2 Dissolution in the Deep Subsurface

Motivated by CO 2 capture and sequestration (CCS) design considerations, we consider the coupled effects of permeability heterogeneity and background flow on the dissolution of a supercritical CO 2 lens into an underlying deep, confined aquifer. We present the results of a large-scale Monte Carlo simulation study examining the interaction of background flow rate and three parameters describing multi-Gaussian log-permeability fields: mean, variance, and correlation length. Hundreds of high-resolution simulations were performed using the PFLOTRAN finite volume software to model CO 2 dissolution in a kilometer-scale aquifer over 1,000 years. Predictive dimensionless scaling relationships relating CO 2 dissolution rate to heterogeneity statistics, Rayleigh (Ra) and Péclet (Pe) numbers were developed for both gravitationally dominated free convection to background flow-dominated forced convection regimes. An empirical criterion, Pe = Ra 3/4 , was discovered for regime transition. All simulations converged quickly to a quasi-steady, approximately linear dissolution rate. However, this rate displayed profound variability between permeability field realizations sharing the same heterogeneity statistics, even under mild permeability heterogeneity. In general, increased heterogeneity was associated with a lower mean and higher variance of dissolution rate, undesirable from a CCS design perspective. The relationship between dissolution rate and background flow was found to be complex and nonlinear. Dimensionless scaling relationships were uncovered for a number of special cases. Results call into question the validity of the Boussinesq approximation in the context of modest-to-high background flow rates and the general applicability of numerical simulations without background flow.

42 ENGINEERING↗

Sinuosity‐Driven Hyporheic Exchange: Hydrodynamics and Biogeochemical Potentials

Abstract Hydrologic exchange processes are critical for ecosystem services along river corridors. Meandering contributes to this exchange by driving channel water, solutes, and energy through the surrounding alluvium, a process called sinuosity‐driven hyporheic exchange. This exchange is embedded within and modulated by the regional groundwater flow (RGF), which compresses the hyporheic zone and potentially diminishes its overall impact. Quantifying the role of sinuosity‐driven hyporheic exchange at the reach‐to‐watershed scale requires a mechanistic understanding of the interplay between drivers (meander planform) and modulators (RGF) and its implications for biogeochemical transformations. Here, we use a 2D, vertically integrated numerical model for flow, transport, and reaction to analyze sinuosity‐driven hyporheic exchange systematically. Using this model, we propose a dimensionless framework to explore the role of meander planform and RGF in hydrodynamics and how they constrain nitrogen cycling. Our results highlight the importance of meander topology for water flow and age. We demonstrate how the meander neck induces a shielding effect that protects the hyporheic zone against RGF, imposing a physical constraint on biogeochemical transformations. Furthermore, we explore the conditions when a meander acts as a net nitrogen source or sink. This transition in the net biogeochemical potential is described by a handful of dimensionless physical and biogeochemical parameters that can be measured or constrained from literature and remote sensing. This work provides a new physically based model that quantifies sinuosity‐driven hyporheic exchange and biogeochemical reactions, a critical step toward their representation in water quality models and the design and assessment of river restoration strategies.

54 ENVIRONMENTAL SCIENCES↗

Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids

For the Rayleigh–Taylor unstable arrangement of a viscous fluid sphere embedded in a finite viscous fluid spherical shell with a rigid boundary and a radially directed acceleration, a dispersion relation is developed from a linear stability analysis using the method of normal modes. [Formula: see text] is the radially directed acceleration at the interface. ρ i denotes the density, μ i is the viscosity, and R i is the radius, where i = 1 is the inner sphere and i = 2 is the outer sphere. The dispersion relation is a function of the following dimensionless variables: viscosity ratio [Formula: see text], density ratio [Formula: see text], spherical harmonic mode n, [Formula: see text], [Formula: see text], and the dimensionless growth rate [Formula: see text], where σ is the exponential growth rate. We show that the boundedness provided by the outer spherical shell has a strong influence on the instability behavior, which is reflected not only in the modulation of the growth rate but also in the selection of the most unstable modes that are physically possible. This outer boundary effect is quantified by the relative magnitude of the radius ratio H. We find that when H is close to unity, lower order harmonics are excluded from becoming the most unstable within a vast region of the parameter space. In other words, the effect of H has precedence over the other controlling parameters d, B, and a wide range of s in establishing what the lowest most unstable mode can be. When H ~ 1, low order harmonics can become the most unstable only for s >> 1. However, in the limit when s → ∞, we show that the most unstable mode is n = 1 and derive the dispersion relation in this limit. The exclusion of most unstable low order harmonics caused by a finite outer boundary is not realized when the outer boundary extends beyond a certain threshold length-scale in which case all modes are equally possible depending on the value of B.

74 ATOMIC AND MOLECULAR PHYSICS↗

Exploring the parameter space of MagLIF implosions using similarity scaling. I. Theoretical framework

Magneto-inertial fusion concepts, such as the magnetized liner inertial fusion (MagLIF) platform, constitute an alternative path for achieving ignition and significant fusion yields in the laboratory. The space of experimental input parameters defining a MagLIF load is highly multi-dimensional, and the implosion itself is a complex event involving many physical processes. In the first paper of this series, we develop a simplified analytical model that identifies the main physical processes at play during a MagLIF implosion. Using non-dimensional analysis, we determine the most important dimensionless parameters characterizing MagLIF implosions and provide estimates of such parameters using typical fielded or experimentally observed quantities for MagLIF. Here, we then show that MagLIF loads can be “incompletely” similarity scaled, meaning that the experimental input parameters of MagLIF can be varied such that many (but not all) of the dimensionless quantities are conserved. Based on similarity-scaling arguments, we can explore the parameter space of MagLIF loads and estimate the performance of the scaled loads. Then, in the follow-up papers of this series, we test the similarity-scaling theory for MagLIF loads against simulations for two different scaling “vectors,” which include current scaling and rise-time scaling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A convergence metric for counting statistics in time-resolved small angle neutron scattering

Here, this work introduces a model-independent, dimensionless metric for predicting optimal measurement duration in time-resolved small-angle neutron scattering using early-time data. Built on a Gaussian process regression framework, the method reconstructs scattering profiles with quantified uncertainty, even from sparse or noisy measurements. Demonstrated on the EQ-SANS instrument at the Spallation Neutron Source, the approach generalizes to general SANS instruments with a two-dimensional detector. A key result is the discovery of a dimensionless convergence metric revealing a universal power-law scaling in profile evolution across soft matter systems. When time is normalized by a system-specific characteristic time t*, the variation in inferred profiles collapses onto a single curve with an exponent between −2 and −1. This trend emerges within the first ten time steps, enabling early prediction of measurement sufficiency. The method supports real-time experimental optimization and is especially valuable for maximizing efficiency in low-flux environments such as compact accelerator-based neutron sources.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

The nontrivial effects of annealing on superconducting properties of Nb single crystals

The effect of annealing on the superconducting properties of niobium single crystals was studied using optical, magnetic, and scanning tunneling microscopy (STM) methods. Pieces of the same crystal boule were studied before and after the annealing at 800 ${^\circ}\textrm{C}$, 1400 ${^\circ}\textrm{C}$, and near the melting point of niobium (2477 ${^\circ}\textrm{C}$). The initial samples had a high hydrogen content and low-temperature imaging revealed large hydrides (hundreds of micrometers) appearing below 190 K. The formation of these large precipitates is already completely suppressed by annealing at 800 ${^\circ}\textrm{C}$. However, the overall superconducting properties of the annealed samples did not improve and, in fact, worsened. In particular, the superconducting transition temperature decreased, the upper critical field increased, and the pinning strength increased. In the STM study, the sample was annealed initially at 400 ${^\circ}\textrm{C}$, measured, annealed at 1700 ${^\circ}\textrm{C}$, and measured again. The STM revealed a ‘dirty’ superconducting gap with a significant spatial variation in tunneling conductance after annealing at 400 ${^\circ}\textrm{C}$. The clean gap was recovered after annealing at 1700 ${^\circ}\textrm{C}$. This is likely due to oxygen redistribution near the surface, which is always covered by oxide layers in as-grown crystals. Our results indicate that vacuum annealing at least up to 1400 ${^\circ}\textrm{C}$, while removing a large percentage of hydrogen, introduces additional nanosized defects, likely hydride precipitates, that act as efficient pair-breaking and pinning centers. The dimensionless scattering rate is estimated to have increased from $\Gamma = 0.2$ to about $\Gamma = 0.4$ after annealing at 1400 ${^\circ}\textrm{C}$. These results on single crystals differ drastically from those obtained in polycrystalline bulk niobium (i.e. cut from superconducting radio-frequency cavities), where annealing is known to have a significant positive effect that is attributed to the improvement of the crystalline structure masking the more subtle influence of the hydrides.

43 PARTICLE ACCELERATORS↗

Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids

Here, we employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.

36 MATERIALS SCIENCE↗

WKB Estimate of Bilayer Graphene’s Magic Twist Angles

We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.

36 MATERIALS SCIENCE↗

Computational Evaluation of Thermal Response of Open-Cell Foam With Circular Pore (Computional Evaluation of Thermal Response of Open-Cell Foam with Circular Pore)

The evaluation of effective material properties in heterogeneous materials (e.g., composites or multicomponent structures) critically relevant to a wide spectrum of applications, including nuclear power, electronic packaging, flame retardants, hypersonics, and gas turbine power. The work described in this paper is centered around the numerical assessment of the thermal behavior of porous materials obtained from finite element thermal modeling and simulation. Here, two-dimensional, steady state analyses were performed on unit cells with centered, circular pores using a second order accurate Galerkin finite element method (FEM). The effective thermal conductivities of the porous systems were examined, encompassing a range of porosities from 4.9% to 60.1%. The geometries of the models were generated based on ordered circular pores for each modeled porosity level. The system response quantity (SRQ) under investigation was the dimensionless effective thermal conductivity across the unit cell. The dimensionless effective thermal conductivity was compared across all simulated cases, producing a trend between porosity and effective thermal conductivity. In the presented investigation, the method of manufactured solutions (MMS) was used to perform code verification, and the grid convergence index (GCI) was employed to estimate discretization uncertainty as solution verification. Code verification concluded an approximately second order accurate Galerkin FEM solver. It was found that the introduction of porosity to the unit cell material structure reduces effective thermal conductivity, as anticipated. Numerical results obtained in this study are compared to an analytical solution and to a sample of empirical data.

36 MATERIALS SCIENCE↗

Methods—Design Guidelines for Tubular Flow-through Electrodes for Use in Electroanalytical Studies of Redox Reaction Kinetics

The tubular flow-through electrode (FTE) is a facile electroanalytical tool for investigating electrochemical reaction kinetics; however, its suitability for this purpose requires careful design and operation under conditions that guarantee uniform current distribution. In this perspective article, we provide a scaling analysis of the transport and reaction processes within a tubular FTE leading to quantitative guidelines for the FTE design and operation. Two dimensionless parameters (classical Wagner number Wa I and modified Wagner number incorporating the effect of mass transport Wa II ) are utilized to compare the magnitudes of the ohmic, activation and transport resistances of the tubular FTE, and to quantify its current distribution uniformity. With the aid of analytical modeling of the current distribution, optimal ranges for these two dimensionless parameters are defined so as to ascertain uniform current distribution. Application of these guidelines to a graphite tubular FTE is shown to enable the precise determination of the charge-transfer kinetics of the ferri/ferrocyanide redox reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling Electrochemical and Rheological Characteristics of Suspension-Based Electrodes for Redox Flow Cells

Flowable suspension-based electrodes (FSEs) have gained attention in recent years, as the integration of solid materials into electrochemical flow cells can offer improved performance and flexible operation. However, under conditions that engender favorable electrochemical properties (e.g., high particle loading, high conductivity, high surface area), FSEs can exhibit non-Newtonian characteristics that impose large pumping losses and flow-dependent transport rates. These multifaceted trade-offs motivate the use of models to broadly explore scaling relationships and better understand design rules for electrochemical devices. To this end, we present a one-dimensional model, integrating porous electrode theory with FSE rheology as well as flow-dependent electron and mass transport under pressure-driven flow. We study FSE behavior as a function of material properties and operating conditions, identifying key dimensionless groups that describe the underlying physical processes. We assess flow cell performance by quantifying electrode polarization and relative pumping losses, establishing generalized property-performance relationships for FSEs. Importantly, we expound relevant operating regimes—based on a subset of dimensionless groups—that inform practical operating envelopes, ultimately helping to guide FSE and cell engineering for electrochemical systems.

25 ENERGY STORAGE↗

Implementing an aerosol dynamic shape factor for cerium oxide powder

The shape factor (X B ) of bulk powder CeO 2 (cerium oxide) particles is estimated to be X B = 1.34 (dimensionless). This is defined in relation to the measured aerated bulk density (0.91 g cm -3 , Hosokawa Micron, Summit NJ, 2018) of the CeO 2 powder. This information is used to determine the RRF (respirable release factor), and other parameters during drop test experiments of nuclear material storage containers at Los Alamos National Laboratory. The calculation is based on an experimental shape factor (X P = 2.66 dimensionless) for CeO 2 particles of the same (chain aggregate) morphology studied by other researchers. In that work, the shape factor was defined in terms of the maximum possible (compacted) density of CeO 2 material (7.13 g cm -3 ).

61 RADIATION PROTECTION AND DOSIMETRY↗

Impact of Limited Degree of Freedom Drag Coefficients on a Floating Offshore Wind Turbine Simulation

The worldwide effort to design and commission floating offshore wind turbines (FOWT) is motivating the need for reliable numerical models that adequately represent their physical behavior under realistic sea states. However, properly representing the hydrodynamic quadratic damping for FOWT remains uncertain, because of its dependency on the choice of drag coefficients (dimensionless or not). It is hypothesized that the limited degree of freedom (DoF) drag coefficient formulation that uses only translational drag coefficients causes mischaracterization of the rotational DoF drag, leading to underestimation of FOWT global loads, such as tower base fore-aft shear. To address these hydrodynamic modeling uncertainties, different quadratic drag models implemented in the open-source mid-fidelity simulation tool, OpenFAST, were investigated and compared with the experimental data from the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project. The tower base fore-aft shear and up-wave mooring line tension were compared under an irregular wave loading condition to demonstrate the effects of the different damping models. Two types of hydrodynamic quadratic drag formulations were considered: (1) member-based dimensionless drag coefficients applied only at the translational DoF (namely limited-DoF drag model) and (2) quadratic drag matrix model (in dimensional form). Based on the results, the former consistently underestimated the 95th percentile peak loads and spectral responses when compared to the OC5 experimental data. In contrast, the drag matrix models reduced errors in estimates of the tower base shear peak load by 7–10% compared to the limited-DoF drag model. The underestimation in the tower base fore-aft shear was thus inferred be related to mischaracterization of the rotational pitch drag and the heave motion/drag by the limited-DoF model.

17 WIND ENERGY↗

Radiant Heat Transfer to Absorbing Gases Enclosed Between Parallel Flat Plates with Flow and Conduction

An analysis is presented for obtaining two-dimensional temperature profiles and heat transfer in a radiation-absorbing gray gas of uniform absorptivity under the combined influence of thermal radiation, conduction, and gas flow. The gas is enclosed in a channel of infinite width and finite length formed by two semi-infinite parallel flat plates. These plates are black emitting surfaces, and the ends of the channel are formed by porous black surfaces through which the gas can flow into or out of the channel. These porous black end surfaces are used to simulate the radiation environment external to the channel. First, results are obtained for heat transfer between the plates in the absence of both conduction and flow. These results are found to be in good agreement with those obtained for the same conditions by previous workers. Results are then presented for heat transfer between the plates for the case of a radiating and conducting, but stagnant, gas separating the plates. The effects of the interactions between radiation and conduction are discussed. It was found that the heat transfer for combined radiation and conduction in an absorbing gas is slightly greater than the sum for each process taken separately. Finally, results are given for heat transfer from the plates to a flowing, radiating gas in the absence of conduction. The two plates are at the same temperature, and the gas enters the channel with uniform velocity and temperature. The results obtained for this case indicate that the heat transferred to the flowing gas from the constant temperature surfaces goes through a maximum as the absorptivity of the gas increases. This is in qualitative agreement with earlier results obtained by other investigators. All the results are presented in terms of dimensionless parameters, for the sake of generality, and the derivation of the dimensionless parameters, which are indicative of the effects of conduction and flow is presented.

Gray Gas↗

Finite difference solution to the three-dimensional, incompressible thermal energy boundary-layer equation

An implicit numerical method has been adopted for the solution to the three-dimensional, energy boundary-layer equation. The energy equation is written in terms of a dimensionless temperature function, the relative stagnation-enthalpy difference, and transformed by the introduction of a Blasius-type transformation of coordinates as well as dimensionless stream functions. The method is applied to the problem consisting of an infinite cylinder joined with its axis perpendicular to a thin, flat, heated plate. A Prandtl number equal to one is simply considered.

Fillo, J. A.↗

Optimization of conical hydrostatic bearing for minimum friction.

Equations for the flow rate, load capacity, and friction torque for a conical hydrostatic bearing were developed. These equations were solved by a digital computer program to determine bearing configurations for minimum friction torque. Design curves are presented that show optimal bearing dimensions for minimum friction torque as a function of dimensionless flow rate for a range of dimensionless load capacity. Results are shown for both laminar and turbulent flow conditions. The results indicate that hydrostatic pocket friction is a significant portion of the total friction torque. However, the bearing dimensions for a minimum friction design are affected very little by inclusion of pocket friction in the analysis. For laminar flow the values of the outer-land radius ratio X3 and outer bearing radius ratio X4 did not change significantly with increasing friction factor. For turbulent flow, the outer bearing radius ratio X4 did not change with increasing friction factor; therefore the value determined for X4 in the laminar flow case is valid for all turbulent flows.

Nypan, L. J.↗

Designing the brawny gas bearing.

Discussion of a graphic technique for matching specific groove parameters to operating conditions in order to optimize the load carrying capacity of a herringbone-grooved bearing. Details are given on the optimization of the film thickness ratio, the groove width ratio, the groove angle, and the groove length ratio to obtain a maximum radial load capacity. The effect of the dimensionless bearing number on optimal groove configuration parameters is shown in diagrams. Curves are also plotted to compare the capacities of a herringbone-grooved bearing and a plain bearing, showing the former has a higher load capacity than the latter when the dimensionless bearing number is large.

Hamrock, B. J.↗