Radial porosity distribution in cylindrical beds packed with spheres

Goodling, J. S.; Vachon, R. I.; Stelpflug, W.S.; Ying, S.J.; Khader, M. S.

doi:10.1016/0032-5910(83)85022-0

Cited by 100 publications

(29 citation statements)

References 4 publications

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“…We have noted a number of favorable comparisons between our simulations and experiments in similar geometries [9,32,33,37], which provides further validation of the Discrete-Element Method as a realistic means of simulating granular materials. As such, it is interesting to consider various implications of our results for the theories of dense granular flow, since the simulations probe the system at a level of detail not easily attained in experiments.…”

Section: B Basic Physics Of Dense Granular Flowmentioning

confidence: 99%

“…Pebble-bed experiments [32,33] and simulations [40,41] of static sphere packings in cylinders have revealed that there are local variations in porosity near walls, at the scale of several pebble diameters, but there has been no such study of flowing packings, averaging over dynamic configurations. Similar findings would have important implications for helium flow in the core, since the local gas permeability is related to the porosity [34,35,36].…”

Section: Packing Statistics a Pebble Volume Fractionmentioning

confidence: 99%

“…Some three-dimensional particle tracking in granular materials and colloids has also been done with magnetic resonance imaging [28], confocal microscopy [29], index matching with an interstitial fluid [30], and diffusing-wave spectroscopy [31], although these systems are quite different from a pebble-bed reactor core. Experimental studies of more realistic geometries for PBR have mostly focused on the porosity distribution of static packings of spheres [32,33], which affects helium gas flow through the core [34,35,36].…”

Section: Introduction a Backgroundmentioning

confidence: 99%

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Analysis of granular flow in a pebble-bed nuclear reactor

et al. 2006

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Pebble-bed nuclear reactor technology, which is currently being revived around the world, raises fundamental questions about dense granular flow in silos. A typical reactor core is composed of graphite fuel pebbles, which drain very slowly in a continuous refueling process. Pebble flow is poorly understood and not easily accessible to experiments, and yet it has a major impact on reactor physics. To address this problem, we perform full-scale, discrete-element simulations in realistic geometries, with up to 440,000 frictional, viscoelastic 6cm-diameter spheres draining in a cylindrical vessel of diameter 3.5m and height 10m with bottom funnels angled at 30• or 60• . We also simulate a bidisperse core with a dynamic central column of smaller graphite moderator pebbles and show that little mixing occurs down to a 1:2 diameter ratio. We analyze the mean velocity, diffusion and mixing, local ordering and porosity (from Voronoi volumes), the residence-time distribution, and the effects of wall friction and discuss implications for reactor design and the basic physics of granular flow.

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Section: B Basic Physics Of Dense Granular Flowmentioning

confidence: 99%

Section: Packing Statistics a Pebble Volume Fractionmentioning

confidence: 99%

Section: Introduction a Backgroundmentioning

confidence: 99%

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Analysis of granular flow in a pebble-bed nuclear reactor

et al. 2006

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“…For characterizing their internal structure, often the voidage distribution ( x) is used, as it has been measured, e.g. in the radial direction, by several groups (Benenati and Brosilow, 1962;Goodling et al, 1983;Ridgway and Tarbuck, 1966;Roblee et al, 1958) and described analytically accordingly (Bey and Eigenberger, 1997;Cohen and Metzner, 1981;Martin, 1978;Mueller, 1992). However, it is important to recognize that the local voidage ( x) represents the probability density for the existence of fluid at position x, its volumetric average equalling exactly the fluid volume fraction 1…”

Section: Statistical Description Of the Packing Geometrymentioning

confidence: 99%

A new pseudo-continuous model for the fluid flow in packed beds

Eisfeld

Schnitzlein

2005

Chemical Engineering Science

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“…The void fraction ϵ, which ranges from 0 to 1 describes the packing of the beads inside the cylinder. For macroscopic cylindrical beds, ϵ stabilizes to 0.4 starting 5 D s from the wall (both through model and experiment [30][31][32]). Closer to the wall, the packing varies considerably, with ϵ oscillating between approximately 0.25 and 0.65.…”

Section: Capillary Emitter Designmentioning

confidence: 99%

Microfabricated electrospray emitter arrays with integrated extractor and accelerator electrodes for the propulsion of small spacecraft

Dandavino¹,

Ataman²,

Ryan³

et al. 2014

J. Micromech. Microeng.

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Microfabricated electrospray thrusters could revolutionize the spacecraft industry by providing efficient propulsion capabilities to micro and nano satellites (1–100 kg). We present the modeling, design, fabrication and characterization of a new generation of devices, for the first time integrating in the fabrication process individual accelerator electrodes capable of focusing and accelerating the emitted sprays. Integrating these electrodes is a key milestone in the development of this technology; in addition to increasing the critical performance metrics of thrust, specific impulse and propulsive efficiency, the accelerators enable a number of new system features such as power tuning and thrust vectoring and balancing. Through microfabrication, we produced high density arrays (213 emitters cm−2) of capillary emitters, assembling them at wafer-level with an extractor/accelerator electrode pair separated by micro-sandblasted glass. Through IV measurements, we could confirm that acceleration could be decoupled from the extraction of the spray—an important element towards the flexibility of this technology. We present the largest reported internally fed microfabricated arrays operation, with 127 emitters spraying in parallel, for a total beam of 10–30 µA composed by 95% of ions. Effective beam focusing was also demonstrated, with plume half-angles being reduced from approximately 30° to 15° with 2000 V acceleration. Based on these results, we predict, with 3000 V acceleration, thrust per emitter of 38.4 nN, specific impulse of 1103 s and a propulsive efficiency of 22% with <1 mW/emitter power consumption.

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Radial porosity distribution in cylindrical beds packed with spheres

Cited by 100 publications

References 4 publications

Analysis of granular flow in a pebble-bed nuclear reactor

Analysis of granular flow in a pebble-bed nuclear reactor

A new pseudo-continuous model for the fluid flow in packed beds

Microfabricated electrospray emitter arrays with integrated extractor and accelerator electrodes for the propulsion of small spacecraft

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