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DOE OSTI2023

On relaxations of the max k -cut problem formulations

Here, a tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max k-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max k-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max k-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

Some effects of ablation on transport properties in the Jovian atmosphere

In this paper the transport properties at the inner and outer boundary for mixing between ablation products and a Jovian-like atmosphere are calculated. The dominant species at these boundaries are C, H, O, He, H+, and e. Accurate potential energy curves are obtained for the fifteen possible two-body interactions among these species by fitting good semiempirical potentials for which transport collision cross sections have been tabulated to accurate experimental and theoretical information. Results are obtained for the viscosity and translational thermal conductivity of the pure species and the binary diffusion coefficients from 1000 K to 25,000 K. In addition, the mixture translational thermal conductivity and viscosity are calculated at the inner and outer mixing boundaries. This information is required for calculating flowfield properties and surface heating. The most important conclusion is that the translational thermal conductivity is substantially lower at the inner mixing boundary than it is at the outer mixing boundary.

Biolsi, L.↗

DOE OSTI2025

Evaluation of probability density function descriptions for three-component Rayleigh–Taylor mixing

Results from simulations of a three-component Rayleigh–Taylor (RT) mixing problem are presented. These simulations are conducted in heavy–light–heavy and heavy–intermediate–light configurations, and each of these configurations are further considered in high- and low-Reynolds-number regimes. This results in RT-unstable flow with one or both interfaces initially unstable, permitting the influence of problem configuration on the statistical description of three-component RT-driven mixing to be considered. Mass fraction covariances are observed to undergo a sign change through the mixing layer in all four configurations considered. This appears to be unique to the multi-component case and represents another way in which multi-component RT mixing differs from the two-component case. Qualitative and quantitative comparisons of joint and marginal probability density function (PDF) descriptions of species concentration are made. Three-, five-, and six-parameter model PDFs are compared against simulation data to assess how accurately they describe the mixing, and it is found that three-component mixing requires at least a five-parameter model PDF to accurately describe the mixing. Notably, the marginal distributions of three-component mixing do not appear to conform to a beta distribution, representing a departure from the classical two-component RT case. In conclusion, statistical neutrality also appears to influence the optimal choice of model PDF, which is found to be a function of problem configuration.

Large-eddy simulation↗

NASA NTRS1991

Feasibility study for the Cryogenic Orbital Nitrogen Experiment (CONE)

An improved understanding of low gravity subcritical cryogenic fluid behavior is critical for the continued development of space based systems. Although early experimental programs provided some fundamental understanding of zero gravity cryogenic fluid behavior, more extensive flight data are required to design space based cryogenic liquid storage and transfer systems with confidence. As NASA's mission concepts evolve, the demand for optimized in-space cryogenic systems is increasing. Cryogenic Orbital Nitrogen Experiment (CONE) is an attached shuttle payload experiment designed to address major technological issues associated with on-orbit storage and supply of cryogenic liquids. During its 7 day mission, CONE will conduct experiments and technology demonstrations in active and passive pressure control, stratification and mixing, liquid delivery and expulsion efficiency, and pressurant bottle recharge. These experiments, conducted with liquid nitrogen as the test fluid, will substantially extend the existing low gravity fluid data base and will provide future system designers with vital performance data from an orbital environment.

Bell, R. S.↗

DOE OSTI2024

Impact of tensor couplings with scalar mixing on covariant energy density functionals

The recent pioneering campaigns conducted by the Lead Radius Experiment (PREX) and the Calcium Radius Experiment (CREX) Collaborations have uncovered major deficiencies in the theoretical description of some fundamental properties of atomic nuclei. Following a recent refinement to the isovector sector of covariant energy density functionals we present here additional improvements to the functional by including both tensor couplings and an isoscalar-isovector mixing term in the scalar sector. Motivated by the distinct surface properties of calcium and lead, we expect that the tensor terms that generate derivative couplings will help break the linear correlation between the neutron skin thickness of these two nuclei. Moreover, the addition of these new terms mitigates most of the problems identified by Reed et al. in describing the properties of both finite nuclei and neutron stars. While significant progress has been made in reconciling the PREX-CREX results without compromising other observables, the final resolution awaits the completion of a proper calibration for this new class of functionals. As a result, we expect that powerful reduced basis methods used recently to create efficient emulators will be essential to accomplish this task.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2017

Low Pressure Flame Blowoff from the Forward Stagnation Region of a Blunt-Nosed Cast PMMA Cylinder in Axial Mixed Convective Flow

Low-pressure blowoff experiments were conducted with a stagnation flame stabilized on the forward tip of cast PMMA rods in a vertical wind tunnel. Pressure, forced flow velocity, gravity, and ambient oxygen concentration were varied. Stagnation flame blowoff is determined from a time-stamped video recording of the test. The blowoff pressure is determined from test section pressure transducer data that is synchronized with the time stamp. The forced flow velocity is also determined from the choked flow orifice pressure. Most of the tests were performed in normal gravity, but a handful of microgravity tests were also conducted to determine the influence of buoyant flow velocity on the blowoff limits. The blowoff limits are found to have a linear dependence between the partial pressure of oxygen and the total pressure, regardless of forced flow velocity and gravity level. The flow velocity (forced and/or buoyant) affects the blowoff pressure through the critical Damkohler number residence time, which dictates the partial pressure of oxygen at blowoff. This is because the critical stretch rate increases linearly with increasing pressure at low pressure (sub-atmospheric pressures) since a second-order overall reaction rate with two-body reactions dominates in this pressure range.

flammability↗

DOE OSTI2022

Modeling ablator grain structure impacts in ICF implosions

High-density carbon is a leading ablator material for inertial confinement fusion (ICF). This and some other ablator materials have grain structure which is believed to introduce very small-scale (~nm) density inhomogeneity. In principle, such inhomogeneity can affect key ICF metrics like fuel compression and yield, by, for example, acting as a seed for instabilities and inducing mix between ablator and fuel. However, assessments of such effects are uncertain due to the difficulty of modeling this small-scale structure in ICF simulations, typically requiring reduced-resolution modeling that scales these features. We present a grain model and show both the impact of de-resolving grains and the complex mixing dynamics such structures can induce. We find that different methods for de-resolving grains can yield both different total deposition of kinetic energy perturbations and different fuel–ablator mixing. We then show a simple-to-implement approach for approximately conserving the deposition of perturbed kinetic energy and demonstrate that, for the present grain model and test cases, this approach yields a reasonably matched time history of mix width between less and more resolved grain models. The simulations here also demonstrate the complex interaction history between grain-induced mixing and instability around the fuel–ablator interface, showing, for example, that the grain-induced perturbations typically trigger instability of conduction-driven density gradients in the DT fuel, enhancing mix penetration early in the acceleration of the shell. Furthermore simulating both microscale and nanoscale grains, we find initial evidence for larger mixing in the microscale case of the present model, despite smaller deposited kinetic energy perturbation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Molecular Engineering of Biorefining Lignin Waste for Solid-State Electrolyte

Lignin is the second most abundant renewable biopolymer on Earth but also a waste in both the paper industry and lignocellulosic biorefineries. Recently, lignin valorization has been extensively sought after to return economics, enhance carbon efficiency, and improve the bioeconomy, but the commercial value and size compatibility still hinder its applications. In this study, we developed a facile strategy to apply lignin waste into a solid-state electrolyte (SSE), which represents a safe next generation energy storage. Here, lignin was grafted with polyethylene glycol (PEG), an efficient lithium-ion (Li + ) conductive polymer, to enable its ion conduction. The synthesized PEG-g-lignin was mixed with poly(vinylidene fluoride)-co-hexafluoropropylene (PVDF-HFP) and PEG-g-lignin-based bis(trifluoromethanesulfonyl)imide (LiTFSI) to prepare a solid polymer electrolyte (SPE), which has an ionic conductivity of 2.5 × 10 –5 S/cm at 25 °C. This result was further enhanced to 6.5 × 10 –5 S/cm by adding an ion-conductive ceramic of Li 6.4 La 3 Ga 0.2 Zr 2 O 12 (LLGZO), which is referred to as composite polymer electrolyte (CPE). These data represent the highest ones among reported polymer-based SSE. A mechanistic study by using 2D HSQC NMR revealed that PEG-g-lignin has increased ether type β–O–4 linkages that can promote the interchain hopping of Li+ between lignin polymer chains, and 31 P NMR revealed that the lignin phenolic end can be associated by Li + . Moreover, the abundant aromatic moieties and methoxyl in PEG-g-lignin also enhanced Li + association and improved its ionic conductivity. The superior ionic conductivity of PEG-g-lignin-based SSE can enable massive applications of this biorefining waste in all-solid-state lithium batteries (ASSLBs), which has potential to promote the energy sector by promoting the bioeconomy and enhancing the renewability and sustainability of future energy storage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1992

Sensitivity of the structure of untripped mixing layers to small changes in initial conditions

An experimental study was conducted concerning the influence of small changes in initial conditions on the near- and far-field evolution of the three-dimensional structure of a plan mixing layer. A two-stream mixing layer with a velocity ratio of 0.6 was generated with the initial boundary layers on the splitter plate laminar and was nominally two-dimensional. The initial conditions were changed slightly by interchanging the high- and low-speed sides of the wind tunnel, while maintaining the same velocities, and hence velocity ratio. This resulted in small changes in the initial boundary layer properties, and the perturbations present in the boundary layers were interchanged between the high- and low-speed sides for the two cases. The results indicate that, even with this relatively minor change in initial conditions, the near-field regions of the two cases differ significantly. The peak Reynolds stress levels in the near-field differ by up to 100 percent, and this is attributed to a difference in the location of the initial spanwise vortex roll-up. In addition, the positions and shapes of the individual streamwise vortical structures differ for the two cases, although the overall structures differ for the two cases, although the overall qualitative description of these structures is comparable. The subsequent reorganization and decay of the streamwise vortical structures is very similar for the two cases. As a result, in the far field, both mixing layers achieve similar structure, yielding comparable growth rates, Reynolds stress, distribution, and spectral content.

Plesniak, M. W.↗

NASA NTRS1996

Influence of Geometry and Flow Variation on Jet Mixing and NO Formation in a Model Staged Combustor Mixer with Eight Orifices

A series of non-reacting parametric experiments was conducted to investigate the effect of geometric and flow variations on mixing of cold jets in an axis-symmetric, heated cross flow. The confined, cylindrical geometries tested represent the quick mix region of a Rich-Burn/Quick-Mix/Lean-Burn (RQL) combustor. The experiments show that orifice geometry and jet to mainstream momentum-flux ratio significantly impact the mixing characteristic of jets in a cylindrical cross stream. A computational code was used to extrapolate the results of the non-reacting experiments to reacting conditions in order to examine the nitric oxide (NO) formation potential of the configurations examined. The results show that the rate of NO formation is highest immediately downstream of the injection plane. For a given momentum-flux ratio, the orifice geometry that mixes effectively in both the immediate vicinity of the injection plane, and in the wall regions at downstream locations, has the potential to produce the lowest NO emissions. The results suggest that further study may not necessarily lead to a universal guideline for designing a low NO mixer. Instead, an assessment of each application may be required to determine the optimum combination of momentum-flux ratio and orifice geometry to minimize NO formation. Experiments at reacting conditions are needed to verify the present results.

Samuelsen, G. S.↗

NASA NTRS2010

Highly Conductive Multifunctional Graphene Polycarbonate Nanocomposites

Graphene nanosheet bisphenol A polycarbonate nanocomposites (0.027 2.2 vol %) prepared by both emulsion mixing and solution blending methods, followed by compression molding at 287 C, exhibited dc electrical percolation threshold of approx.0.14 and approx.0.38 vol %, respectively. The conductivities of 2.2 vol % graphene nanocomposites were 0.512 and 0.226 S/cm for emulsion and solution mixing. The 1.1 and 2.2 vol % graphene nanocomposites exhibited frequency-independent behavior. Inherent conductivity, extremely high aspect ratio, and nanostructure directed assembly of the graphene using PC nanospheres are the main factors for excellent electrical properties of the nanocomposites. Dynamic tensile moduli of nanocomposites increased with increasing graphene in the nanocomposite. The glass transition temperatures were decreased with increasing graphene for the emulsion series. High-resolution electron microscopy (HR-TEM) and small-angle neutron scattering (SANS) showed isolated graphene with no connectivity path for insulating nanocomposites and connected nanoparticles for the conductive nanocomposites. A stacked disk model was used to obtain the average particle radius, average number of graphene layers per stack, and stack spacing by simulation of the experimental SANS data. Morphology studies indicated the presence of well-dispersed graphene and small graphene stacking with infusion of polycarbonate within the stacks.

Yoonessi, Mitra↗

NASA NTRS2011

Final Report for Intravenous Fluid Generation (IVGEN) Spaceflight Experiment

NASA designed and operated the Intravenous Fluid Generation (IVGEN) experiment onboard the International Space Station (ISS), Increment 23/24, during May 2010. This hardware was a demonstration experiment to generate intravenous (IV) fluid from ISS Water Processing Assembly (WPA) potable water using a water purification technique and pharmaceutical mixing system. The IVGEN experiment utilizes a deionizing resin bed to remove contaminants from feedstock water to a purity level that meets the standards of the United States Pharmacopeia (USP), the governing body for pharmaceuticals in the United States. The water was then introduced into an IV bag where the fluid was mixed with USP-grade crystalline salt to produce USP normal saline (NS). Inline conductivity sensors quantified the feedstock water quality, output water purity, and NS mixing uniformity. Six 1.5-L bags of purified water were produced. Two of these bags were mixed with sodium chloride to make 0.9 percent NS solution. These two bags were returned to Earth to test for compliance with USP requirements. On-orbit results indicated that all of the experimental success criteria were met with the exception of the salt concentration. Problems with a large air bubble in the first bag of purified water resulted in a slightly concentrated saline solution of 117 percent of the target value of 0.9 g/L. The second bag had an inadequate amount of salt premeasured into the mixing bag resulting in a slightly deficient salt concentration of 93.8 percent of the target value. The USP permits a range from 95 to 105 percent of the target value. The testing plans for improvements for an operational system are also presented.

McQuillen, John B.↗

DOE OSTI2022

Thermal Probes of Phonon-Coupled Kitaev Spin Liquids: From Accurate Extraction of Quantized Edge Transport to Anyon Interferometry

Recent theoretical studies inspired by experiments on the Kitaev magnet α-RuCl 3 highlight the nontrivial impact of phonons on the thermal Hall conductivity of chiral topological phases. Here, we introduce mixed mesoscopic-macroscopic devices that allow refined thermal-transport probes of non-Abelian spin liquids with Ising topological order. These devices feature a quantum-coherent region with quantized or negligible phonon conductance, flanked by macroscopic lobes that facilitate efficient thermalization between chiral Majorana edge modes and bulk phonons. We show that our devices enable (i) accurate determination of the quantized thermal Hall conductivity, (ii) identification of non-Abelian Ising anyons via the temperature dependence of the thermal conductance, and, most interestingly, (iii) single-anyon detection through heat-based anyon interferometry. Analogous results apply broadly to phonon-coupled chiral topological orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1993

Experimental study of cross flow mixing in cylindrical and rectangular ducts

An experimental investigation of non-reacting cross flow jet injection and mixing in cylindrical and rectangular ducts has been conducted with application to a low emissions combustor. Quantitative measurement of injectant concentration distributions perpendicular to the duct axis were obtained by planar digital imaging of the Mie-scattered light from an aerosol seed mixed with the injectant. The flowfield unmixedness was evaluated using (1) a mixing parameter derived from the ratio of the jet concentration fluctuations to the fully mixed concentration, and (2) probability density functions of the concentration distributions. Mixing rate was measured for 45 degree slant slot and round orifice injectors.

Liscinsky, D. S.↗

NASA NTRS2015

Electron Beam Irradiated Intercalated CNT Yarns For Aerospace Applications

Multi-walled CNT yarns have been experimentally and commercially created to yield lightweight, high conductivity fibers with good tensile properties for application as electrical wiring and multifunctional tendons. Multifunctional tendons are needed as the cable structures in tensegrity robots for use in planetary exploration. These lightweight robust tendons can provide mechanical strength for movement of the robot in addition to power distribution and data transmission. In aerospace vehicles, such as Orion, electrical wiring and harnessing mass can approach half of the avionics mass. Use of CNT yarns as electrical power and data cables could reduce mass of the wiring by thirty to seventy percent. These fibers have been intercalated with mixed halogens to increase their specific electrical conductivity to that near copper. This conductivity, combined with the superior strength and fatigue resistance makes it an attractive alternative to copper for wiring and multifunctional tendon applications. Electron beam irradiation has been shown to increase mechanical strength in pristine CNT fibers through increased cross-linking. Both pristine and intercalated CNT yarns have been irradiated using a 5-megavolt electron beam for various durations and the conductivities and tensile properties will be discussed. Structural information obtained using a field emission scanning electron microscope, energy dispersive X-ray spectroscopy (EDS), and Raman spectroscopy will correlate microstructural details with bulk properties.

electrical wiring↗

NASA NTRS1999

Effects of Jet Swirl on Mixing of a Light Gas Jet in a Supersonic Airstream

A non reacting experiment was performed to investigate the effects of jet swirl on mixing of a light gas jet in a supersonic airstream. The experiment consisted of two parts. The first part was an investigation of the effects of jet swirl and skew on the mixing and penetration of a 25 deg. supersonic jet injected from a flat surface (flush wall injection) into a supersonic ducted airflow. Specifically, the objective was to determine whether the jet would mix more rapidly if the jet were swirling, and whether swirl, with and without skew, causes the injectant-air plume to have a net circulation (i.e., a single or dominant vortex). The second part was a preliminary study of the mixing of swirling jets injected from the base of a skewed ramp. The hypothesis was that favorable interactions between vorticity generated by the swirling jet and vortices generated by the ramp could produce mixing enhancements. Both parts of the experiment were conducted at equal injectant mass flow rate and total pressure. The results for the flush wall injection cases indicate that, except relatively close to the injection point, swirl, with or without skew, does not enhance the mixing of the jet, and can in fact reduce penetration. In addition, a plume with significant net circulation is not generated, as had previously been believed. The results for the ramp cases indicated no improvements in mixing in comparison with the baseline (swept ramp injector) case. However, it was not possible to determine the vorticity mechanisms underlying the poor performance, since no measurements of vorticity were made. Thus, since many geometric parameters were chosen arbitrarily, the results are inconclusive for this class of injector.

Doerner, Steven E.↗

DOE OSTI2020

Characterizing Baselines and Change in Gas Hydrate Systems using EM Methods

The objective of this project was to advance our understanding of gas hydrate systems in nature by characterizing their electrical properties in the field and in the laboratory. In the laboratory measurements, methane hydrate was synthesized from pure water ice and flash frozen seawater, with varying amounts of sand or silt added. Electrical conductivity was determined by impedance spectroscopy, using equivalent circuit modeling to separate the effects of electrodes and to gain insight into conduction mechanisms. Silt and sand increase the conductivity of pure hydrate, inferred to be contaminant NaCl contributing to conduction in hydrate, to a peak conductivity in agreement with peak resistivities observed in well logs through massive hydrate (3,000--10,000 Ωm). The addition of silt and sand lowers the conductivity of hydrate synthesized from seawater, by an amount consistent with Archie's Law. All samples were characterized using cryogenic scanning electron microscopy and energy dispersive spectroscopy, which shows good connectivity of salt and brine phases. Electrical conductivity measurements of pure hydrate and hydrate mixed with silt during pressure-induced dissociation supports previous conclusions that sediment increases dissociation rate. In order to characterize gas hydrate systems in the field, we collected 360 line kilometers of controlled-source electromagnetic data on Walker Ridge 313, Orca Basin (WR100), Mad Dog (GC781), and Green Canyon 955 in the Gulf of Mexico, all areas with known or seismically inferred gas hydrate deposits and which have be drilled or targeted for future drilling. We deep-towed an EM transmitter that generates an alternating electric field which propagates through the seafloor geology. Data were recorded on 6 receivers towed behind the transmitter at distances between 550 and 1550 m. In the presence of conductive geology, the electric fields will be attenuated, and conversely, in resistive geology the fields will be preserved. Our data were inverted using a 2D inversion method that first optimizes the model-data misfit, then finds the smoothest model fitting the data. This ensures that resistivity structures present in the final model are likely necessary. At each of the proposed drilling sites we found increased resistivity, interpreted as increased hydrate concentrations. However, not only were the primary drilling sites not always more resistive than the alternate sites, at WR313 the strongest resistors were not at the locations targeted for drilling.

03 NATURAL GAS↗

DOE OSTI2023

Dynamics of multilayer Rayleigh–Taylor instability at moderately high Atwood numbers

This paper investigates the multilayer Rayleigh–Taylor instability (RTI) using statistically stationary experiments conducted in a gas tunnel. Employing diagnostics such as particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF), we make simultaneous velocity–density measurements to study how dynamics and mixing are linked in this variable density flow. Experiments are conducted in a newly built, blow-down three-layer gas tunnel facility. Mixing between three gas streams is studied, where the top and bottom streams are comprised of air, and the middle stream is an air–helium mixture. Shear is minimized between these streams by matching their inlet velocities. The four experimental conditions investigated here consist of two different density ratios (Atwood numbers 0.3 and 0.6), each investigated at two instability development times (or equivalently, two streamwise locations), and all experiments are with the same middle stream thickness of 3 cm. The growth of the middle layer is measured using laser-based planar Mie scattering visualization. The mixing width is found to grow linearly with time at late times. Various quantitative measures of molecular mixing indicate a very high degree of molecular mixing at late times in the multilayer RTI flow. The vertical turbulent mass flux $a_y$ is calculated. In addition to mostly negative values of $a_y$ , typical of buoyancy-dominated flows due to negative correlation between velocity and density fluctuations, positive regions are also observed in profiles of $a_y$ due to entrainment and erosion at the lower edge of the mixing region. Global energy budgets are calculated for the multilayer RTI flow at late times and it is found that the majority of potential energy released has been dissipated due to viscous effects, and a large value of mixing efficiency ( $\sim$ 60 %) is observed.

Mechanics↗