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DOE OSTI2025

Low fractional volume superconductivity in single crystals of Pr{sub 4}Ni{sub 3}O{sub 10} under pressure

Magnetotransport measurements of P⁢r4⁢N⁢i3⁢O10 single crystals performed under externally applied pressures up to 73 GPa in diamond anvil cells with either KBr or Nujol oil as pressure media yield signatures of superconductivity with a maximum onset temperature of approximately 31 K. True zero resistance was not observed, consistent with a nonpercolating superconducting volume fraction. Magnetization measurements provided corroborating evidence of superconductivity, with a pressure-dependent diamagnetic signal occurring below the onset temperature, and an estimate from the absolute value of the susceptibility suggests a superconducting volume fraction on the order of 10%. We observe sample to sample variations in the magnitude and pressure dependence of 𝑇𝑐 as well as a dependence on the configuration of electrical contacts on a given sample. Possible causes of this behavior may be significant inhomogeneities in the pressure and/or damage to the samples induced by the pressure media as well as inhomogeneities in the crystals themselves. The results imply that our as-grown P⁢r4⁢N⁢i3⁢O10 single crystals are not bulk superconductors but that there is a minority structure present within the crystals that is indeed superconductin

Chen, Xinglong↗

DOE OSTI2022

Flow Loop Study of ECT-Based Volume Fraction Monitoring in Oil–Water Two-Phase Flows

Measurement of phase volume fractions in water-containing multiphase flows is necessary for the optimization of a host of industrial flow processes. Many water-containing multiphase flows can be classified as either water-dispersed or water-continuous mixtures. A recently developed approach based on Hanai’s mixture formula and utilizing electrical capacitance tomography (ECT) sensors have shown good potential for obtaining water volume fraction estimates in two-phase water-containing flows with different water salinity levels. However, the proposed approach was investigated via controlled experiments restricted to static configurations while, in practice, multiphase flows can be dynamic and unpredictable. In this work, we perform a flow loop study of the proposed ECT-based method for volume fraction estimation in oil–water two-phase flows. Here, we evaluate the performance of the proposed method in both water-dispersed and water-continuous flow regimes by employing different types of capacitive sensors in cylindrical arrangements and parallel-plate rectangular arrangements.

02 PETROLEUM↗

DOE OSTI2023

The dynamics of suspensions of prolate spheroidal particles—Effects of volume fraction

Here, the effect of volume fraction on the dynamics of a gravity driven suspension of prolate spheroidal solid particles in a fully periodic domain is examined by fully resolved numerical simulations, for relatively modest Reynolds numbers (around 20, depending on the volume fraction). Three systems are examined, for volume fractions of 2.2% (20 particles), 5.5% (50 particles), and 9.9% (90 particles). The results show a transition from flow at low volume fractions dominated by the hydrodynamic interactions between the particles and the fluid, although modified by collisions, to flow dominated by collisions at higher volume fractions. The distribution of the particles with respect to each other, as measured by the probability distribution of nearest distances, is nearly random at low volume fractions but at high volume fractions, there is more clustering than for a random distribution. At lower volume fractions most of the particles fall broadside on whereas at the highest volume fraction, their orientation is essentially random.

42 ENGINEERING↗

DOE OSTI2024

Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows

In this work, the effects of the particle volume fraction gradient on fluid-particle interactions are studied. The phase interaction force is decomposed into three terms. For the first term, namely the symmetrized force density, we present theoretical reasoning and numerical evidence to assume that it is independent of the particle volume fraction gradient. The second term is the particle volume fraction gradient times a newly introduced diffusion stress. The third term is the divergence of the particle-fluid-particle (PFP) stress. If this assumption of independence of the particle volume fraction gradient for the first term can be verified, to the first order of the ratio of the mean distance between particles to the macroscopic lengthscale, all three terms can be studied and modeled in flows with uniform particle distributions. Models thus obtained are applicable to statistically inhomogeneous flows, with the second and third terms accounting for statistical inhomogeneity. To verify this assumption, numerical simulations of flows passing fixed arrays of particles are performed. Both uniform and nonuniform particle volume fractions are studied and compared for disperse multiphase flows with the particle Reynolds numbers ranging from 1 to 100, and particle volume fraction ranging from 1% to 26% in statistically steady states. It is found that the symmetrized force (first) term can be well approximated by the drag force obtained from studies of uniform flows. The diffusion stress is positive along the flow direction and negative in the directions perpendicular to the flow. In the case of moving particles, this stress could potentially cause particle aggregation in the flow direction and dispersion in the directions perpendicular to the flow. Finally, the diffusion stress is only important when there is a volume fraction gradient, while the PFP stress can be important in inhomogeneous flows with either nonuniform particle concentrations or nonuniform average relative velocities between the phases.

42 ENGINEERING↗

NASA NTRS2017

Tutorial for Collecting and Processing Images of Composite Structures to Determine the Fiber Volume Fraction

Fiber-reinforced composite structures have become more common in aerospace components due to their light weight and structural efficiency. In general, the strength and stiffness of a composite structure are directly related to the fiber volume fraction, which is defined as the fraction of fiber volume to total volume of the composite. The most common method to measure the fiber volume fraction is acid digestion, which is a useful method when the total weight of the composite, the fiber weight, and the total weight can easily be obtained. However, acid digestion is a destructive test, so the material will no longer be available for additional characterization. Acid digestion can also be difficult to machine out specific components of a composite structure with complex geometries. These disadvantages of acid digestion led the author to develop a method to calculate the fiber volume fraction. The developed method uses optical microscopy to calculate the fiber area fraction based on images of the cross section of the composite. The fiber area fraction and fiber volume fraction are understood to be the same, based on the assumption that the shape and size of the fibers are consistent in the depth of the composite. This tutorial explains the developed method for optically determining fiber area fraction performed at NASA Langley Research Center.

Conklin, Lindsey↗

NASA NTRS1992

The optimal fiber volume fraction and fiber-matrix property compatibility in fiber reinforced composites

Although the question of minimum or critical fiber volume fraction beyond which a composite can then be strengthened due to addition of fibers has been dealt with by several investigators for both continuous and short fiber composites, a study of maximum or optimal fiber volume fraction at which the composite reaches its highest strength has not been reported yet. The present analysis has investigated this issue for short fiber case based on the well-known shear lag (the elastic stress transfer) theory as the first step. Using the relationships obtained, the minimum spacing between fibers is determined upon which the maximum fiber volume fraction can be calculated, depending on the fiber packing forms within the composites. The effects on the value of this maximum fiber volume fraction due to such factors as fiber and matrix properties, fiber aspect ratio and fiber packing forms are discussed. Furthermore, combined with the previous analysis on the minimum fiber volume fraction, this maximum fiber volume fraction can be used to examine the property compatibility of fiber and matrix in forming a composite. This is deemed to be useful for composite design. Finally some examples are provided to illustrate the results.

Pan, Ning↗

NASA NTRS1993

A study of fiber volume fraction effects in notched unidirectional SCS-6/Ti-15V-3Cr-3Al-3Sn composite

Notched unidirectional SCS-6/Ti-15-3 composite of three different fiber volume fractions (vf = 0.15, 0.37, and 0.41) was investigated for various room temperature microstructural and material properties including: fatigue crack initiation, fatigue crack growth, and fracture toughness. While the matrix hardness is similar for all fiber volume fractions, the fiber/matrix interfacial shear strength and matrix residual stress increases with fiber volume fraction. The composite fatigue crack initiation stress is shown to be matrix controlled and occurs when the net maximum matrix stress approaches the endurance limit stress of the matrix. A model is presented which includes residual stresses and presents the composite initiation stress as a function of fiber volume fraction. This model predicts a maximum composite initiation stress at vf approximately 0.15 which agrees with the experimental data. The applied composite stress levels were increased as necessary for continued crack growth. The applied Delta(K) values at crack arrest increase with fiber volume fraction by an amount better approximated using an energy based formulation rather than when scaled linear with modulus. After crack arrest, the crack growth rate exponents for vf37 and vf41 were much lower and toughness much higher, when compared to the unreinforced matrix, because of the bridged region which parades with the propagating fatigue crack. However, the vf15 material exhibited a higher crack growth rate exponent and lower toughness than the unreinforced matrix because once the bridged fibers nearest the crack mouth broke, the stress redistribution broke all bridged fibers, leaving an unbridged crack. Degraded, unbridged behavior is modeled using the residual stress state in the matrix ahead of the crack tip. Plastic zone sizes were directly measured using a metallographic technique and allow prediction of an effective matrix stress intensity which agrees with the fiber pressure model if residual stresses are considered. The sophisticated macro/micro finite element models of the 0.15 and 0.37 fiber volume fractions presented show good agreement with experimental data and the fiber pressure model when an estimated effective fiber/matrix debond length is used.

Covey, Steven J.↗

DOE OSTI2022

An index to characterize gas‐solid and solid‐solid mixing from average volume fraction fields

Abstract A mixing index based on solid volume fraction fields is developed for gas‐solid flows. Conventional mixing indices are based on particle realizations of granular mixing and are applicable to experimental data or discrete element method simulations. However, these indices cannot be used as‐is for multifluid models, and an index for characterizing mixing in gas‐solid flows from continuous fields is needed. The performance of the new mixing index is tested in two applications. The first is a 3D simulation of the mixing of biomass and sand in a fluidized bed reactor, and the second is a 2D simulation of binary particle segregation in a fluidized bed. The simulations are performed using OpenFOAM®. The mixing index is used to quantify gas‐solid mixing using solid volume fractions and solid‐solid mixing using solid fractions. The formulation of conventional mixing indices is extended to be used with solid volume fractions fields, and methods for performance improvement are presented.

09 BIOMASS FUELS↗

NASA NTRS1976

Volume Fraction Determination in Cast Superalloys and DS Eutectic Alloys by a New Practice for Manual Point Counting

Volume fraction of a constituent or phase was estimated in six specimens of conventional and DS-eutectic superalloys, using ASTM E562-76, a new standard recommended practice for determining volume fraction by systematic manual point count. Volume fractions determined ranged from 0.086 to 0.36, and with one exception, the 95 percent relative confidence limits were approximately 10 percent of the determined volume fractions. Since the confidence-limit goal of 10 percent, which had been arbitrarily chosen previously, was achieved in all but one case, this application of the new practice was considered successful.

Andrews, C. W.↗

DOE OSTI2021

An Investigation of the Effects of Volume Fraction on Drag Coefficient of Non-Spherical Particles Using PR-DNS

Prediction of the drag coefficient is required in gas-particle multiphase flow modeling and simulation. Experimental data and correlations on the fixed-bed system of spherical particles with high volume fractions for various possible arrangements are available in the literature. However, the effect of volume fraction on the drag coefficient of non-spherical particles is not well studied. In solving the momentum equation, the volume fraction plays a vital role in determining the flow resistances. In this paper, we study the impact of volume fraction in the range of 0.069 to 0.65 on the drag coefficient using the computational fluid dynamics (CFD) simulation of air for Reynold number in the range of 10 to 10000 using particle resolved direct numerical solution (PR-DNS). Regular non-spherical particles such as a cube, tetrahedron, and spheroids are used in this study since their single particle’s drag coefficient data are available in the literature for comparison. For this work, the simulations are carried out in the Ansys Fluent using polyhedral mesh, which consumes significantly less computational time and power. The study showed the sphericity and volume fraction have significant impact on the bed pressure drop and average drag coefficient of the particles in the bed especially in high Reynolds number regime. The bed of the spheroid experiences the lowest drag being the most streamlined particle, and the particles with the edges result in a large drag coefficient due to flow separation at the discontinuity. The vector plots verify this behavior where large wake regions are observed behind the tetrahedron particle.

Mahyawansi, Pratik↗

DOE OSTI2020

Shear-induced lift force on spheres in a viscous linear shear flow at finite volume fractions

Several studies have shown a significant increase in drag on a distribution of solid spherical particles within a fluid with increasing particle volume fraction. As a result, many empirical drag laws accounting for the dependence on the Reynolds number and volume fraction can be found in the literature. This study investigates the possibility of a similar effect of the particle volume fraction on the mean hydrodynamic lift force on randomly distributed spherical particles in a linear shear flow. Particle-resolved direct numerical simulations are performed to evaluate the mean lift force, and the results are compared with the case of an isolated particle in a linear shear flow for the same Reynolds number and shear rate. The mean lift force acting on the particles appears to remain nearly the same as that on an isolated particle. However, due to the influence of neighboring particles, there is a substantial force variation in transverse directions on each individual particle, whose magnitude is comparable to the mean drag force. The distribution of drag force in a linear shear flow is shown to be nearly the same as in a uniform flow at the same volume fraction and Reynolds number. A simple stochastic model based on a Gaussian distribution is presented for the lift force variation, and its performance is compared to the prediction of the deterministic pairwise interaction extended point-particle model.

42 ENGINEERING↗

NASA NTRS1997

Soot Volume Fraction Maps for Normal and Reduced Gravity Laminar Acetylene Jet Diffusion Flames

The study of soot particulate distribution inside gas jet diffusion flames is important to the understanding of fundamental soot particle and thermal radiative transport processes, as well as providing findings relevant to spacecraft fire safety, soot emissions, and radiant heat loads for combustors used in air-breathing propulsion systems. Compared to those under normal gravity (1-g) conditions, the elimination of buoyancy-induced flows is expected to significantly change the flow field in microgravity (O g) flames, resulting in taller and wider flames with longer particle residence times. Work by Bahadori and Edelman demonstrate many previously unreported qualitative and semi-quantitative results, including flame shape and radiation, for sooting laminar zas jet diffusion flames. Work by Ku et al. report soot aggregate size and morphology analyses and data and model predictions of soot volume fraction maps for various gas jet diffusion flames. In this study, we present the first 1-g and 0-g comparisons of soot volume fraction maps for laminar acetylene and nitrogen-diluted acetylene jet diffusion flames. Volume fraction is one of the most useful properties in the study of sooting diffusion flames. The amount of radiation heat transfer depends directly on the volume fraction and this parameter can be measured from line-of-sight extinction measurements. Although most Soot aggregates are submicron in size, the primary particles (20 to 50 nm in diameter) are in the Rayleigh limit, so the extinction absorption) cross section of aggregates can be accurately approximated by the Rayleigh solution as a function of incident wavelength, particles' complex refractive index, and particles' volume fraction.

Greenberg, Paul S.↗

DOE OSTI2020

Toward Water Volume Fraction Calculation in Multiphase Flows Using Electrical Capacitance Tomography Sensors

Real-time monitoring of water volume fraction in multiphase flows is an important problem for a number of industrial applications. The water phase in the multiphase flows may correspond to either the dispersed phase or the continuous phase. In the past, several lowcost and nonintrusive techniques based on the electrical capacitance tomography (ECT) has been developed to image and monitor in real-time multiphase flows containing water. Furthermore, such monitoring becomes increasingly challenging for high salinity levels, and no reliable ECTbased method is presently available which could work for obtaining water volume fraction in multiphase flows for all water salinity levels. In this paper, we propose a new approach based on the Hanai’s formula for complex dielectric constant and taking advantage of the Maxwell- Wagner-Sillars effect to obtain, to a good approximation, water volume fractions in multiphase flows containing water as either dispersed or continuous phase.

02 PETROLEUM↗

DOE OSTI2020

An arbitrarily high-order three-dimensional Cartesian-grid method for reconstructing interfaces from volume fraction fields

Here Tthis work describes a newly developed, arbitrarily high-order Cartesian-grid method for reconstructing material interfaces from a volume fraction field. The method begins by identifying all of the grid cells in the volume fraction field that are intersected by the interface and need to be approximated by the reconstruction scheme. Finite-differences are used to calculate the gradient of the volume fraction field and provide an estimate of the surface normal in all of the interfacial grid cells. Groups of connected grid cells are then identified which all have the same dominant component of the normal vector. This grouping by orientation determines the proper dependent variable to use in the surface reconstruction (e.g. for a 2D curve, this step determines if the surface will be approximated by a function of x or y). A cumulative integral over the surface is constructed and fit using b-splines for two-dimensional problems or tensor-product b-splines for three-dimensional problems. This construction allows for the interface to be recovered through application of the second fundamental theorem of calculus. Fitting the cumulative integral with $\mathscr{N}$ th-order b-splines (or tensor-product b-splines) yields an ($\mathscr{N}$-1) th-order convergence rate of the interface shape. Differentiation of the b-spline interface function(s) allows for the high-order approximation of the normal vector and curvature to be obtained directly anywhere along b-spline. Together, the proposed reconstruction technique can achieve arbitrarily high mesh convergence rates. Validation tests are presented with mesh convergence rates ranging from fourth- to tenth-order.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Kernel Buffer Volume Fraction Margin of the AGR Designed Fuel Particle

Modeling results used to assess the fuel performance of the TRISO-coated fuel particles as a function of kernel/buffer volume fraction include SiC tangential stress, formation of the buffer/IPyC gap, particle temperature profile, internal particle pressure, fission gas released from the kernel, probability of fuel particle failure, and fission product diffusion. These results were evaluated at two burnup levels and irradiation temperatures to bound expected steady-state irradiation conditions. In general, increasing the kernel/buffer volume fraction increases the SiC stress and subsequently the failure probability of a fuel particle when compared to the AGR designed particle. There was little impact on the fission product diffusion through the particle as the kernel/buffer volume fraction increased.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2013

The Effect of Fiber Strength Stochastics and Local Fiber Volume Fraction on Multiscale Progressive Failure of Composites

Continuous fiber unidirectional polymer matrix composites (PMCs) can exhibit significant local variations in fiber volume fraction as a result of processing conditions that can lead to further local differences in material properties and failure behavior. In this work, the coupled effects of both local variations in fiber volume fraction and the empirically-based statistical distribution of fiber strengths on the predicted longitudinal modulus and local tensile strength of a unidirectional AS4 carbon fiber/ Hercules 3502 epoxy composite were investigated using the special purpose NASA Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC); local effective composite properties were obtained by homogenizing the material behavior over repeating units cells (RUCs). The predicted effective longitudinal modulus was relatively insensitive to small (~8%) variations in local fiber volume fraction. The composite tensile strength, however, was highly dependent on the local distribution in fiber strengths. The RUC-averaged constitutive response can be used to characterize lower length scale material behavior within a multiscale analysis framework that couples the NASA code FEAMAC and the ABAQUS finite element solver. Such an approach can be effectively used to analyze the progressive failure of PMC structures whose failure initiates at the RUC level. Consideration of the effect of local variations in constituent properties and morphologies on progressive failure of PMCs is a central aspect of the application of Integrated Computational Materials Engineering (ICME) principles for composite materials.

multiscale analysis↗

NASA NTRS1992

The transition from columnar to equiaxed dendritic growth in proeutectic, low-volume fraction copper, Pb-Cu alloys

Lead, 17.1, 11.2, and 5 volume fraction copper (14, 9, and 4 wt pct Cu) alloys have been directionally solidified at constant growth velocities ranging from 1 to 100 microns/s. Serially increasing the growth velocity within this range results in a graded microstructural transition from fully columnar, albeit segregated, copper dendrites in a lead matrix to one consisting only of equiaxed grains. The imposed velocity necessary to effect fully equiaxed growth is found to drop rapidly as the volume fraction of copper is decreased. Factors which complicate the controlled, directional solidification of these alloys are discussed and the experimental results are interpreted in view of, and seen to be in qualitative agreement with, Hunt's theory on the transition from columnar to equiaxed growth of dendrites.

Kim, Shinwoo↗

NASA NTRS2020

A 3D Model to Predict Explicit Morphologies and Volume Fraction of Lack-of-Fusion Pores Generated in Selective Laser Melting Processes

The performance of an additively manufactured (AM) component is dependent on the distribution of process-induced defects in addition to the complex microstructure of the material, surface roughness of the component and the process-induced residual stresses. For instance, it has been well demonstrated that lack-of-fusion (LoF) pores produced in the selective laser melting (SLM) AM process can significantly limit the fatigue performance of the material. Although two-dimensional (2D) models exist to predict the 2D profiles of LoF pores, the 2D pore profiles cannot be directly inserted into a three-dimensional (3D) microstructure domain that is output from several prevailing process simulation packages. A few commercial packages that simulate the SLM process can predict LoF pores in a 3D domain, but the morphologies of LoF pores are voxelated and hence do not capture sharp corners of the pores, thereby obviating their use in fatigue crack initiation studies. In order to address the aforementioned gaps, a high-fidelity model that predicts not only the volume fraction, but also the explicit 3D morphologies and spatial distributions of LoF pores has been developed using a computer aided design-based environment. The model has been partially validated for Ti-6Al-4V alloy by comparing the predictions of the volume fraction of LoF pores predicted by the model with experimental data obtained from the literature. Absolute error in predicted volume fraction of LoF pores varied between 5.16% and 1.87% for energy density values between 13 J/mm3 and 45 J/mm3 where a significant amount (over 3% volume fraction) of LoF porosity was measured. The absolute error was within 1.87% for energy density values greater than 45 J/mm3.

Saikumar R. Yeratapally↗