Random particle packing by reduced dimension algorithms

Davis, I. Lee; Carter, Roger G.

doi:10.1063/1.345785

Cited by 37 publications

(21 citation statements)

References 15 publications

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“…46 The results from both the effective medium models and the multipole model were consistent in showing increases in the effective permittivity of particle aggregates with foam-type microstructures. The results between the models were not consistent, however, for particle aggregates with cluster-type microstructures.…”

Section: Resultssupporting

confidence: 53%

“…The particle packs were constructed by Monte Carlo and reduced dimension algorithms for random particle packing. [45][46][47] Aggregate microstructures with various levels of aggregation (local particle volume fractions) were generated by defining randomly distributed spherical regions in the pack and altering the particle volume fraction within the region. Five different structures were simulated for each level of aggregation to determine the average and standard deviation of the effective permittivity values.…”

Section: A Numerical Algorithmmentioning

confidence: 99%

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Effects of aggregation on the permittivity of random media containing monodisperse spheres

Doyle

Tew

Jain

et al. 2009

Journal of Applied Physics

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The NERC and CEH trade marks and logos ('the Trademarks') are registered trademarks of NERC in the UK and other countries, and may not be used without the prior written consent of the Trademark owner. AbstractNumerical simulations were used to calculate the effective permittivities of three-dimensional random particle suspensions containing up to 2440 particles and exhibiting two types of particle aggregation. The particles were modeled as 200-µm spheres that were aggregated into either large spherical clusters or into foam-type microstructures with large spherical voids. Multiple scattering of 0.01-10.0 GHz electromagnetic fields was simulated using a first-principles iterative multipole approach with matrix and particle permittivities of 1.0 and 8.5, respectively.The computational results showed both significant and highly significant trends. Aggregation 2 into spherical clusters decreased the effective permittivity by up to 3.2 ± 0.2%, whereas aggregation into foam-type microstructures increased the effective permittivity by up to 3.0 ± 1.6%. The effective permittivity trends exhibited little change with frequency. These results were compared to effective medium approximations that predicted higher permittivities than those from the simulations and showed opposite trends for cluster aggregation. Three theories are proposed to explain the simulation results. The first theory invokes a waveguide-like mechanism. The simulations indicate that the wave fields propagate more through the continuous paths of greater or lesser particle density created by aggregation, rather than through the isolated particle clusters or large voids. This quasi-continuous phase, or quasi-matrix, therefore behaves like a random waveguide structure in the material. A second theory is proposed where the quasicontinuous phase governs the behavior of the system by a percolation-like process. In this theory, the multipole interactions are modeled as the percolation of virtual charges tunneling from one particle to another. A third mechanism for the permittivity changes is also proposed involving collective polarization effects associated with the particle clusters or large voids. The simulation results challenge the general applicability of the quasistatic limit for heterogeneous media by showing how microstructural changes much smaller than the electromagnetic wavelength can alter the effective permittivity by a statistically significant degree. The results also provide a quantitative indication of the effects of aggregation and hierarchical microstructures on the electromagnetic properties of random media, and have application to the remote and in situ sensing of soils, the rational design and nondestructive evaluation of composites, and the study of biological tissues and other random materials.3

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Section: Resultssupporting

confidence: 53%

Section: A Numerical Algorithmmentioning

confidence: 99%

Effects of aggregation on the permittivity of random media containing monodisperse spheres

Doyle

Tew

Jain

et al. 2009

Journal of Applied Physics

View full text Add to dashboard Cite

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“…These models have the potential to provide the necessary boundary conditions for the diffusion flame calculations. The earliest of these is the work by Davis and Carter [10] and Webb and Davis [11] on the ParPack code that has been ongoing for some time. Sankaralingam and Chakravarthy [12] also recently developed a packing model to describe composite propellants.…”

Section: Introductionmentioning

confidence: 98%

“…Various researchers have recently developed two-and threedimensional methodologies to describe the geometric packing effects within solid propellants [10][11][12][13][14][15][16]. These models have the potential to provide the necessary boundary conditions for the diffusion flame calculations.…”

Section: Introductionmentioning

confidence: 99%

Diffusion Flame Calculations for Composite Propellants Using a Vorticity-Velocity Formulation

Gross

Beckstead

2009

Journal of Propulsion and Power

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A two-dimensional model has been developed to study the flame structure above composite propellants using a vorticity-velocity formulation of the transport equations. This formulation allows for a more stable, robust, accurate, and faster solution method compared with the compressible Navier-Stokes equations in the low Mach flow regime. The model includes mass and energy coupling between the condensed and gas phases. The condensed-phase model is based on previously reported one-dimensional models and includes distributed decomposition and multistepreaction kinetics. The model uses a detailed gas-phase kinetic mechanism consisting of 37 species and 127 reactions. The kinetic mechanism and species diffusion determine the flame structure of the system; no assumptions are made beforehand, aside from appropriate boundary conditions. Numerical studies have been performed to examine the flame structure above an ammonium-perchlorate/hydroxy-terminated-polybutadiene propellant. The predicted flame structure was found to be qualitatively similar to the Beckstead-Derr-Price model with both premixed and diffusion flames present. Results present significant insight into ammonium perchlorate's ability to control a propellant's burning rate and illustrate the importance of the primary diffusion flame in composite propellant combustion.Nomenclature c p = heat capacity, erg=g=K g = gravitational acceleration vector, cm=s 2 h = specific enthalpy, erg=g i = species index M = Mach number r = radial distance, cm r = radial direction T = temperature, K t = time, s v = velocity vector, cm=ŝ v = diffusion velocity, cm=s W = molecular mass, g=mol _ w = chemical production rate, g=cm 3 =s Y = mass fraction z = axial direction = thermal conductivity, erg=s=cm=K = viscosity, poise = density, g=cm 3 = dissipation function ! = vorticity vector, 1=s

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“…One of the random microstructures was constructed using a Monte Carlo type particle dropping routine and by scaling the particle coordinates to create the desired volume fraction. 45 The other random microstructure was generated from a different but more wellknown Monte Carlo algorithm developed to compare the structures of simple liquids to random close packings. 46,47 The particles were modeled as glass spheres ͑ = 7.6͒ in air ͑ = 1.0͒.…”

Section: B Computational Approachmentioning

confidence: 99%

Modeling the permittivity of two-phase media containing monodisperse spheres: Effects of microstructure and multiple scattering

et al. 2007

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A numerical modeling approach was developed to predict the dielectric properties of heterogeneous particulate materials with arbitrary microstructures. To test the method, simulation and experimental data were acquired for the effective permittivities of various glass sphere suspensions. Both ordered lattices and random microstructures of up to 3600 spheres were modeled for volume fractions of 0.025-0.60. The electric fields in the suspensions were computed using an iterative multipole method that included multiple-scattering effects. The effective permittivities were obtained by averaging the electric field and electric displacement over a representative volume. Frequency spectra, electric field images, and single-scattering results ͑i.e., no particleparticle interactions͒ were additionally generated. The results were compared to experimental data for random close-packed microstructures, to effective-medium approximations, to exact lattice models, and to a perturbation expansion model. The comparisons showed that the iterative models agreed with the exact lattice models to within 3.31% for crystalline suspensions. Results for random suspensions agreed with the perturbation expansion model to within 1.76% for volume fractions up to 0.50. Single-scattering models additionally predicted permittivities for the microstructures as well as or better than the Maxwell Garnett approximation ͓Philos. Trans. R. Soc. London, Ser. A 203, 385 ͑1904͔͒, suggesting that microstructural effects and multipole moments higher than the dipole are required for more accurate statistical prediction of effective permittivities. The effective permittivities, convergence behavior, and dispersion behavior of the simulations were sensitive to both microstructure and the extent of multiple scattering included in the models, illustrating how the macroscopic properties depend significantly on the microscopic details of the interactions. In contrast to other approaches, the iterative multipole method can model both the frequency and spatial dependencies of the electromagnetic properties of particulate materials, as well as a wide variety of microstructures, including polydisperse and hierarchical systems.

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Random particle packing by reduced dimension algorithms

Cited by 37 publications

References 15 publications

Effects of aggregation on the permittivity of random media containing monodisperse spheres

Effects of aggregation on the permittivity of random media containing monodisperse spheres

Diffusion Flame Calculations for Composite Propellants Using a Vorticity-Velocity Formulation

Modeling the permittivity of two-phase media containing monodisperse spheres: Effects of microstructure and multiple scattering

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