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At least 271 records · Page 15

A Dynamic Testing Approach for Particulate Erosion–Corrosion for Gas Turbine Coatings

Particle interactions in gas turbine engines can be multicomponent, complex phenomena leading to the degradation of thermal (TBCs) and environmental barrier coatings (EBCs) meant to protect engine components. Ingestion of particles into the engine can lead to recession of coatings due to particle erosion. Similarly, these same particles can become molten, adhere to coatings and result in thermochemical corrosion of coating materials. Particle erosion testing is often carried out where the particles are injected into a gas stream, accelerated within a nozzle, and impinge on sample. Conversely, most molten particle corrosion testing is often done in static laboratory furnaces, which does not capture the dynamic nature of deposition in application. Nevertheless, these damage mechanisms are often tested separately and no single standard exists to test both erosive and corrosive particle interactions with coating materials under relevant operating conditions for gas turbine engines. Understanding the synergies of particle interactions in engines is crucial in determining operating lifetimes of potential coating materials. Such considerations emphasize the need for realistic approaches in standardizing particle interaction testing in combustion environments. The current study outlines initial efforts at NASA Glenn’s Erosion Burner Rig Facility in improving dynamic erosion/corrosion testing methods by assessing the durability of state-of-the-art (SOA) TBC material 7 wt.% yttria stabilized zirconia (7YSZ) as a function of particle deposition rate, burner temperature, and particle size. Calibration data to determine particle deposition rate will be presented, and mass and optical profilometry measurements were utilized to estimate mass/volume loss versus deposition per increment of particulate used over time. Electron microscopy analyses were then carried out to assess coating damage after testing.

TBC↗

A Dynamic Testing Approach for Particulate Erosion–Corrosion for Gas Turbine Coatings

Particle interactions in gas turbine engines can be multicomponent, complex phenomena leading to the degradation of thermal (TBCs) and environmental barrier coatings (EBCs) meant to protect engine components. Ingestion of particles into the engine can lead to recession of coatings due to particle erosion. Similarly, these same particles can become molten, adhere to coatings and result in thermochemical corrosion of coating materials. Particle erosion testing is often carried out where the particles are injected into a gas stream, accelerated within a nozzle, and impinge on sample. Conversely, most molten particle corrosion testing is often done in static laboratory furnaces, which does not capture the dynamic nature of deposition in application. Nevertheless, these damage mechanisms are often tested separately and no single standard exists to test both erosive and corrosive particle interactions with coating materials under relevant operating conditions for gas turbine engines. Understanding the synergies of particle interactions in engines is crucial in determining operating lifetimes of potential coating materials. Such considerations emphasize the need for realistic approaches in standardizing particle interaction testing in combustion environments. The current study outlines initial efforts at NASA Glenn’s Erosion Burner Rig Facility in improving dynamic erosion/corrosion testing methods by assessing the durability of state-of-the-art (SOA) TBC material 7 wt.% yttria stabilized zirconia (7YSZ) as a function of particle deposition rate, burner temperature, and particle size. Calibration data to determine particle deposition rate will be presented, and mass and optical profilometry measurements were utilized to estimate mass/volume loss versus deposition per increment of particulate used over time. Electron microscopy analyses were then carried out to assess coating damage after testing.

burner rig↗

Investigation and quantification of flow unsteadiness in shock-particle cloud interaction

This work aims to study the interaction of a shock wave with a cloud of particles to quantify flow unsteadiness and velocity fluctuations using particle-resolved direct numerical simulation (PR-DNS). Three cases are studied, with each case revealing one aspect of the intricate flow phenomena involved in this interaction. The unsteady interaction of a shock wave with a transverse array of particles reveals the origin of unsteadiness under the effect of mutual wave-wave and wave-wake interactions between the particles. In the second case, the interaction of a shock with a particle cloud is studied, with a focus on the interaction of the complex wave system with the vortical structure. A budget analysis of the vorticity equation reveals the sources of strong unsteadiness in the particle cloud. A detailed analysis of the velocity fluctuation and kinetic energy in the fluctuating motion is performed to ascertain the importance of the velocity fluctuations that arise from the strong unsteadiness. Here, an analogous analysis is presented, in the third case, for a gradually-induced flow on the same particle cloud along with a comparison to the shock induced case to assess the impulsive effect of shock on intensity of the fluctuating field statistics.

42 ENGINEERING↗

Results on the spin-dependent scattering of weakly interacting massive particles on nucleons from the Run 3 Data of the LUX Experiment

Here, we present experimental constraints on the spin-dependent WIMP (weakly interacting massive particle)-nucleon elastic cross sections from LUX data acquired in 2013. LUX is a dual-phase xenon time projection chamber operating at the Sanford Underground Research Facility (Lead, South Dakota), which is designed to observe the recoil signature of galactic WIMPs scattering from xenon nuclei. A profile likelihood ratio analysis of 1.4 × 10 4 kg day of fiducial exposure allows 90% C.L. upper limits to be set on the WIMP-neutron (WIMP-proton) cross section of σ n = 9.4 × 10 –41 cm 2 (σ p = 2.9 × 10 –39 cm 2 ) at 33 GeV/c 2 . The spin-dependent WIMP-neutron limit is the most sensitive constraint to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Interactive Terascale Particle Visualization

This paper describes the methods used to produce an interactive visualization of a 2 TB computational fluid dynamics (CFD) data set using particle tracing (streaklines). We use the method introduced by Bruckschen et al. [2001] that pre-computes a large number of particles, stores them on disk using a space-filling curve ordering that minimizes seeks, and then retrieves and displays the particles according to the user's command. We describe how the particle computation can be performed using a PC cluster, how the algorithm can be adapted to work with a multi-block curvilinear mesh, and how the out-of-core visualization can be scaled to 296 billion particles while still achieving interactive performance on PG hardware. Compared to the earlier work, our data set size and total number of particles are an order of magnitude larger. We also describe a new compression technique that allows the lossless compression of the particles by 41% and speeds the particle retrieval by about 30%.

Ellsworth, David↗

Wave-wave interactions due to scattering by electrons.

The kinetic wave equation which describes the nonlinear wave-particle interaction in a plasma is considered, and a method which uses the picture of quantized plasmons interacting with particles for the description of nonlinear wave-particle interactions is briefly described. In this method an assumption is made of the Markoffian character of the equation. It is shown that the Markoffian assumption can be justified at least for the case when the plasma is close to a stable stationary state. The diagram method developed by Nishikawa (1966) is used to derive an explicit expression for the kinetic equation. The application of the result to the case of interaction between an electron-wave and an ion-wave is discussed.

Nishikawa, K.↗

Laying the Foundation for a Predictive Theory of Electroweak Nuclear Phenomena

Reliable model-independent predictions of nuclear processes such as beta-decay and neutrinonucleus scattering are important for many fundamental science and mission-related investigations; For example, accurate descriptions of as beta-decay are required for modeling the anti-neutrino spectrum of nuclear reactor, whether for trying to detect new physics such as sterile neutrinos, or remotely identifying the purpose of that reactor. For these activities, we need accurate calculations, as well as careful and thorough analyses of theoretical error and uncertainty in the underlying models and the many-body methods and codes used in solving that model. Unfortunately, modern theoretical calculations of these processes are inadequate for this task. At the heart of this inadequacy is the interaction between nucleons and other particles known as nuclear currents. Historically, descriptions of nuclear currents took into account only the simplest of particle interactions. Recently, the development of an effective field theory known as chiral EFT has been used to derive large corrections to these particle interactions. However, the complex nature of these corrections inhibited their use in ab initio methods of predicting nuclear processes. We developed a novel method to address these complexities and applied it in a series of benchmark and demonstrative calculations using state-of-the-art quantum few-nucleon solvers. Specifically, we studied the role of two-nucleon currents in electroweak processes using light nuclei (i.e., nuclei containing fewer than five nucleons) as a workbench to compute these processes and quantify their uncertainties using Bayesian extensions of the EFT.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The plasma depletion layer beyond the heliopause: evidence, implications, and predictions for Voyager 2 and new horizons

A plasma depletion layer (PDL) is predicted beyond the heliopause, analogous to the PDLs observed sunwards of planetary magnetopauses: draping of interstellar medium (ISM) magnetic field lines over the heliopause should increase the magnetic field strength and, perpendicular ion temperature, cause density depletions by allowing plasma ions (and electrons) with large parallel temperatures to escape along B, and increase the temperature anisotropy until limited by wave instabilities. Published Voyager 1 magnetometer and plasma wave data provide strong evidence for the coupled magnetic amplification (≈30%) and density depletion (≈50%) expected for a weak PDL. The predicted reduction in parallel temperature is ≈50%. The locations on the sky of the PDL and the points on the heliopause of maximum magnetic draping and total pressure are predicted using the ISM magnetic field direction obtained from the Interstellar Boundary Explorer (IBEX) ribbon. The IBEX ribbon overlies the former, as expected, while the latter lies within the ridge of maximum, non-ribbon, globally distributed flux. The PDL should be strongest along the ISM field line passing through these points and the Sun–ISM velocity vector. Based on their trajectories, Voyager 2 and New Horizons should observe a much stronger PDL (stronger magnetic amplification, density depletion, and changes in temperature) than Voyager 1. Finally, the reduced cosmic ray fluxes observed near 90° pitchangle by Voyager 1 beyond the heliopause appear qualitatively consistent with wave–particle interactions transferring perpendicular particle energy to parallel energy where the PDL is strong, followed by magnetic focusing as particles propagate into weaker magnetic field regions.

79 ASTRONOMY AND ASTROPHYSICS↗

Hierarchical Assembly of Plasmonic Nanoparticle Heterodimer Arrays with Tunable Sub-5 nm Nanogaps

Nanoparticle assemblies have generated intense interest because of their novel optical, electronic, and magnetic properties that open up numerous opportunities in fundamental and applied nanophotonics, -electronics, and -magnetics. However, despite the great scientific and technological potential of these structures, it remains an outstanding challenge to reliably fabricate such assemblies with both nanometer-level structural control and precise spatial arrangements on a macroscopic scale. It is the combination of these two features that is key to realizing nanoparticle assemblies potential, particular for device applications. To address this challenge, we propose a hierarchical assembly approach consisting of both template-particle and particle-particle interactions, whereby the former ensures precise addressability of assemblies on a surface and the latter provides nanometer-level structural control. Template-particle interactions are harnessed via chemical-pattern-directed assembly, and the particle-particle interactions are controlled using DNA-directed self-assembly. To demonstrate the potential of this hierarchical assembly approach, we demonstrate the fabrication of a particularly fascinating assembly: the nanoparticle heterodimer, which possesses a surprisingly rich set of plasmonic properties and is a promising candidate to enable a variety of imaging and sensing applications. Each heterodimer is placed on the surface at predetermined locations, and the precise control of the nanogaps is confirmed by far-field scattering measurements of individual dimers. We further demonstrate that the gap size can be effectively tuned by varying the DNA length. By correlating measured spectra with finite-difference time-domain (FDTD) simulations, we determine the gap sizes to be 4.2 and 5.0 nm-with subnm deviation-for the two DNA lengths investigated. This is one of the best gap uniformities ever demonstrated for surface-bound nanoparticle assemblies. The estimated surface-enhanced Raman scattering (SERS) enhancement factor of these heterodimers is on the order of 10 5 -10 6 with high reproducibility and predictable polarization-dependence. This hierarchical fabrication technique-employing both template-particle and particle-particle interactions-constitutes a novel platform for the realization of functional nanoparticle assemblies on surfaces and thereby creates new opportunities to implement these structures in a variety of applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Implementation of Charged Particle Behavior in Discrete Element Method (DEM) Simulations

To understand the behavior of charged lunar regolith when perturbed by lunar landers, it is important to couple the grain dynamics with mechanical and electrical particle interactions. To accomplish this, improvements have been made to a discrete element method (DEM) software package to include both short- and long-range interactions between spherical particles. Short-range interactions rely on contact between the particles, such as electrical conduction and triboelectric charge transfer driven by work functions. Long-range interactions act at a distance between every pairing of particles, such as electrostatic forces and gravitational forces. Results from simulations between a few particles are compared with theory to verify these added behaviors prior to scaling up to more complex scenarios. The radii, initial charges, electrical conductivities, work functions, and separation of the particles are varied and the resultant charges as well as the time required to reach the final state are determined.

Electrostatics↗

Fast Particle-Wave Interactions and Alfvén Eigenmodes in JET Tokamak Plasmas

This document serves as the closeout report of DOE Grant Award No. DE-FG02-99ER54563 with project period 1 April 2015 through 31 March 2020. The project comprised the international collaboration between MIT and EU scientists on the JET facility to improve our understanding of the physics of energetic particle-wave interactions by measuring the damping rates of stable Alfvén Eigenmodes (AEs) and unstable energetic particle driven modes. More specifically, this project involved the continued participation of MIT, the Culham Centre for Fusion Energy, the Swiss Plasma Center, and theorists from various European laboratories and from UC Irvine. Past contributions from the University of São Paulo are gratefully acknowledged. The Alfvén Eigenmode Active Diagnostic (AEAD) on JET discharges was successfully upgraded in this period and has extracted physically useful information, in primarily deuterium plasma discharges. It is expected that such experiments would be continued during the DT campaign in CY 2021 to assess the damping rates of similar modes in the presence of alpha particles, a product of fusing burning plasma. Only JET would carry out such experiments in the near term in the world. It is important to note that this collaboration was continued under DOE Grant Award No. DE-SC0014264 from 1 April 2020 through the present. In this grant period, the AEAD was upgraded with a set of individual amplifiers for each of a set of six antennas in two toroidally opposite locations. These new amplifiers allowed targeted selection of the antennas’ toroidal spectrum for AEs of interest with toroidal mode number | n | ≤ 20. The resonant detection and measurement of the damping rates of AEs was obtained from magnetic probes that could be compared with theory and simulations. This is a key topic of investigation for ITER and all other next-step fusion experiments, where such modes will interact with energetic particles produced by fusion reactions (alpha particles), Neutral Beam Injection (NBI) and Ion Cyclotron Resonance Heating (ICRH). The majority of the observations during this period were of Toroidal Alfvén Eigenmodes (TAEs) as these are most commonly observed on JET; a number of measurements were made during dedicated TAE experiments. However, a new set of lower frequency band filters were procured with the goal of studying Geodesic Acoustic Modes (GAMs), Beta (Acoustic) AEs (BAE/BAAEs), and Reverse Shear AEs (RSAEs), also predicted by theory. Commissioning and optimizations were successfully completed in this period, and the diagnostic has been in operation during the more recent JET campaigns. Initial results have been obtained in dedicated TAE experiments and successfully compared to drift-kinetic theory. A wide range of theoretical studies have been undertaken in support of the upcoming JET campaigns experiments. To supplement the ongoing use of ideal MHD codes, such as MISHKA during the studies of TAEs, gyrokinetic simulations of low frequency AEs were performed in collaboration with UC Irvine. The Gyrokinetic Toroidal Code (GTC) was used to determine the structure, frequencies and stability of AEs in JET plasmas. Thus, a solid scientific foundation has been laid for future DT campaigns in JET in the 2021 operation period when the damping rates of relevant modes in the presence of alpha particles could be assessed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Interactions of particles with “continuous spin” fields

Powerful general arguments allow only a few families of long-range interactions, exemplified by gauge field theories of electromagnetism and gravity. However, all of these arguments presuppose that massless fields have zero spin scale (Casimir invariant) and hence exactly boost invariant helicity. This misses the most general behavior compatible with Lorentz symmetry. We present a Lagrangian formalism describing interactions of matter particles with bosonic “continuous spin” fields with arbitrary spin scale ρ. Remarkably, physical observables are well approximated by familiar theories at frequencies larger than ρ, with calculable deviations at low frequencies and long distances. For example, we predict specific ρ-dependent modifications to the Lorentz force law and the Larmor formula, which lay the foundation for experimental tests of the photon’s spin scale. We also reproduce known soft radiation emission amplitudes for nonzero ρ. The particles’ effective matter currents are not fully localized to their worldlines when ρ ≠ 0, which motivates investigation of manifestly local completions of our theory. Our results also motivate the development of continuous spin analogues of gravity and non-Abelian gauge theories. Given the correspondence with familiar gauge theory in the small ρ limit, we conjecture that continuous spin particles may in fact mediate known long-range forces, with testable consequences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Interrelation of soft and hard X-ray emissions during solar flares. II - Simulation model

Two-dimensional electrostatic particle simulations are presented which incorporate the effect of quasi-static electric fields on particle dynamics as well as effects associated with wave-particle interactions induced by the accelerated particles. The properties of the soft and hard X-ray and microwave emissions from such systems are examined. In particular, it is shown that acceleration by quasi-static electric fields and heating via wave-particle interactions produces electron distributions with a broken-power law, similar to those inferred from hard X-ray spectra. Also, heating of the ambient plasma gives rise to a region of hot plasma propagating down to the chromosphere at about the ion sound speed.

Winglee, R. M.↗

Results on low-mass weakly interacting massive particles from an 11 kg d target exposure of DAMIC at SNOLAB

We present constraints on the existence of weakly interacting massive particles (WIMPs) from a 11 kg-day target exposure of the DAMIC experiment at the SNOLAB underground laboratory. The observed energy spectrum and spatial distribution of ionization events with electron-equivalent energies $>$200 eV$_{\rm ee}$ in the DAMIC CCDs are consistent with backgrounds from natural radioactivity. An excess of ionization events is observed above the analysis threshold of 50 eV$_{\rm ee}$. While the origin of this low-energy excess requires further investigation, our data exclude spin-independent WIMP-nucleon scattering cross sections $\sigma_{\chi-n}$ as low as $3\times 10^{-41}$ cm$^2$ for WIMPs with masses $m_{\chi}$ from 7 to 10 GeV$c^{-2}$ . These results are the strongest constraints from a silicon target on the existence of WIMPs with $m_{\chi}$$<$9 GeV$c^{-2}$ and are directly relevant to any dark matter interpretation of the excess of nuclear-recoil events observed by the CDMS silicon experiment in 2013.

WIMP search, Dark Matter, DAMIC, SNOLAB↗

Implementation of Charged Particle Behavior in Discrete Element Method (DEM) Simulations

Lunar landers will agitate the surface of the Moon with an exhaust plume during descent which will, due to the particulate nature of the lunar regolith, loosen and eject grains from the surface. This ejection is not only coupled with the charged plume gas, but also results in significant particle-particle interactions. Settling of these grains after plume effects have subsided takes much longer than expected in a ballistic trajectory. The prevailing hypothesis attributes this behavior to the accumulated charge on the particles. We are thus developing a discrete element method (DEM) approach to explore these charged particle interactions on the lunar surface. The Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) Improved for General Granular and Granular Heat Transfer Simulations (LIGGGHTS) software package provides a DEM modeling framework for granular interactions. It includes many complexities such as non-spherical particle shapes, cohesion and frictional forces, and heat transfer, but has no provision for inter-particle electrostatic forces and charge transfer that are important to examine in the lunar environment. In this work, a standard Coulomb potential and a Yukawa potential are integrated into the LIGGGHTS framework to provide a basis for particle-particle electrostatic interactions, as well as a gravitational potential to enable inter-grain gravitational interactions. A preliminary approach to charge transfer between grains incorporating properties such as work function and electrical conductivity to the library of available material characteristics will be presented. Several scenarios have been simulated that include charged particle interactions within a diffuse granular gas, settling of charged grains into a regolith bed, sliding of granular material along an incline, and vibration of settled grains to produce a behavior similar to fluidization. There are numerous challenges to incorporate realistic interactions between complex lunar particles. Currently, grains are modeled to behave as if the entirety of the charge acts at the center of mass, such as conductors with spherical symmetry and insulators with homogeneously distributed charge. We are developing improvements that will include the use of non-spherical particle geometries, as well as reasonable approximations of insulating/dielectric materials that have non-uniform charge distributions. The cases simulated thus far will be examined in a relevant environment within a vacuum chamber to validate the simulations. These simulations will be bounded by experiments utilizing high-speed camera observations of the motion for validation. The grains in the experiment will exchange charge during their motion and this can be quantified by collection within a charge measurement device such as a Faraday cup. Such a device may be modeled within the software by defining an integration region and computing the contained charge as a function of simulation time, allowing for side-by-side comparison of simulated and measured bulk charging results. Any differences will be reconciled by updating the mathematical mechanisms described within the simulation suite. Successfully combining results from experiments within a relevant environment into the LIGGGHTS framework will improve modeling of the charged grain dynamics experienced on the Moon to provide insights into dust behavior for future lunar exploration missions.

Electrostatics↗

Gas-Granular Simulation Framework for Spacecraft Landing Plume-Surface Interaction and Debris Transport Analysis

The Gas-Granular Flow Solver (GGFS) multi-phase flow computational framework has been developed to enable simulations of particle flows complex extra-terrestrial regolith materials. Particle flows of interest include the damage of unprepared landing sites from rocket plume impingement on Moon, Mars, and asteroids. The flow solver implements an Eulerian-Eulerian two-fluid model with fluid representation of the gas phase and granular phase to avoid the need to model billions of particle interactions. The granular phase is modeled as an Eulerian fluid with constituent physics closure models derived from first-principle Discrete Element Model (DEM) particle interaction simulations that capture the complex, non-linear granular particle interaction effects. Granular phase constituent models have been developed and integrated that address the complex, non-linear granular material mechanics complexities resulting from both: the irregular, jagged particle shapes and poly-disperse mixture effects encountered in extra-terrestrial regolith, with lunar regolith as the extreme. The GGFS capabilities are being integrated into a proven NASA plume-surface interaction and debris transport simulation framework featuring the Loci/CHEM CFD program and Debris Transport Analysis (DTA) post-processing tools for applications in robotic and human Moon and Mars lander development. Integration of the three simulation tool components. Loci/CHEM, GGFS, and DTA, into a coordinated simulation framework will enable time-accurate spacecraft landing simulations that account for the alteration of the landing surface through plume-induced cratering and the resulting redirection of plume impingement flow and debris transport. Initial implementation of this simulation framework and application examples will be presented.

Liever, Peter A.↗

Results on low-mass weakly interacting massive particles from a 11 kg-day target exposure of DAMIC at SNOLAB

We present constraints on the existence of weakly interacting massive particles (WIMPs) from a 11 kg-day target exposure of the DAMIC experiment at the SNOLAB underground laboratory. The observed energy spectrum and spatial distribution of ionization events with electron-equivalent energies $>$200 eV$_{\rm ee}$ in the DAMIC CCDs are consistent with backgrounds from natural radioactivity. An excess of ionization events is observed above the analysis threshold of 50 eV$_{\rm ee}$. While the origin of this low-energy excess requires further investigation, our data exclude spin-independent WIMP-nucleon scattering cross sections $\sigma_{\chi-n}$ as low as $3\times 10^{-41}$ cm$^2$ for WIMPs with masses $m_{\chi}$ from 7 to 10 GeV$c^{-2}$ . These results are the strongest constraints from a silicon target on the existence of WIMPs with $m_{\chi}$$<$9 GeV$c^{-2}$ and are directly relevant to any dark matter interpretation of the excess of nuclear-recoil events observed by the CDMS silicon experiment in 2013.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Modified kinetic theory applied to the shear flows of granular materials

Here, granular materials are characterized by large collections of discrete particles, where the particle-particle interactions are significantly more important than the particle-fluid interactions. The current kinetic theory captures fairly accurately the granular flow behavior in the dilute case, when only binary interactions are significant, but is not accurate at all in the dense flow regime, where multi-particle interactions and contacts must be modeled. To improve the kinetic theory results for granular flows in the dense flow regime, we propose a Modified Kinetic Theory (MKT) model that utilizes the contact duration or cut-off time to account for the complex particle-particle interactions in the dense regime. The contact duration model, also called TC model, is originally proposed by Luding and McNamara to solve the inelastic collapse issue existing in the Inelastic Hard Sphere (IHS) model. This model defines a cut-off time t c such that dissipation is not counted if the time between two consecutive contacts is less than t c . As shown in their study, the use of a cut-off time t c can also reduce the dissipation during multi-particle contacts. In this paper we relate the TC model with the Discrete Element Method (DEM) by choosing the cut-off time t c to be the duration of contact calculated from the linear-spring-dashpot soft-sphere model of the DEM. We examine two types of granular flows: simple shear flow and the plane shear flow, and compare the results of the classical Kinetic Theory (KT) model, the present MKT model, and the DEM model. Here, we show that the MKT model entails a significant improvement over the KT model for simple shear flows at inertial regimes. With the MKT model the calculations are close to the DEM results at solid fractions as high as 0.57. Even for the plane shear flows, where shear rate and solid fraction are inhomogeneous, the results of the MKT model agree very well with the DEM results.

36 MATERIALS SCIENCE↗