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TECHNICAL PAPERS

# Theoretical Parameter Study of Aerodynamic Vectoring Particle Sorting

[+] Author and Article Information
Dane N. Jackson, Barton L. Smith

Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322

J. Fluids Eng 129(7), 902-907 (Jan 10, 2007) (6 pages) doi:10.1115/1.2742732 History: Received July 21, 2006; Revised January 10, 2007

## Abstract

A new particle sorting technique called aerodynamic vectoring particle sorting (AVPS) has recently been shown to be effective at sorting particles without particles contacting surfaces. The technique relies on turning a free jet sharply without extended control surfaces. The flow turning results in a balance of particle inertia and several forces (pressure, drag, added mass, and body forces) that depend on particle size and density. The present paper describes a theoretical study of particle sorting in a turning flow. The purpose of this study is to extend AVPS to parameter spaces other than those that are currently under investigation. Spherical particles are introduced into a turning flow in which the velocity magnitude increases like $r$. The trajectory of each particle is calculated using the particle equation of motion with drag laws that are appropriate for various Knudsen number regimes. Large data sets can be collected rapidly for various particle sizes, densities, turning radii, flow speeds, and fluid properties. Ranges of particle sizes that can be sorted are determined by finding an upper bound (where particles move in a straight line) and a lower bound (where particles follow flow streamlines). It is found that the size range of particles that can be sorted is larger for smaller turning radii, and that the range moves toward smaller particles as the flow speed and the particle-to-fluid density ratio are increased. Since this flow is laminar and 2-D, and particle loading effects are ignored, the results represent a “best case” scenario.

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## Figures

Figure 1

(a) AVPS particle sorter designed to select a variable band of particle sizes from a sample. Vectoring occurs due to the combined effect of the blowing and suction slots near the jet exit. (b) Contours of the stream function of the velocity field of a vectoring result from (5) showing the circular 90deg vectoring possible with pure suction. The lower left edge of the domain is the jet exit.

Figure 2

Forces acting on a spherical particle to balance inertia

Figure 3

Acceptable data between particles following streamlines and particles with little or no change in their trajectory. Particle paths are shown with thick lines. The thin lines represent flow streamlines. Four paths of acceptable data between two paths of unacceptable data are shown.

Figure 4

Various particle diameters in the flow field. Particle diameter is (●)2μm, (◇)5μm, (▵)20μm. The other curves are flow streamlines. Inlet velocity is 30m∕s.

Figure 5

Particles of varying inlet velocity in the flow field. Particle inlet velocity of (●)1m∕s, (◆)5m∕s, (∎)20m∕s, (◇)50m∕s, (엯)90m∕s. The other curves are flow streamlines. Particle diameter is 10μm.

Figure 6

Particle paths of various particle-to-fluid density ratios and an inlet velocity of 50m∕s. Particle-to-fluid density ratio: (●)ρp∕ρ=100, (◇)ρp∕ρ=1000, (▵)ρp∕ρ=10,000. All other lines are flow streamlines. The particle diameter is 10μm and inlet velocity is 1m∕s.

Figure 7

Streamline and straight line limits for a particle-to-fluid density ratio of 100

Figure 8

Streamline and straight line limits for a particle-to-fluid density ratio of 10,000. Symbols are the same as Fig. 7.

Figure 9

Streamline and straight line limits for various particle-to-fluid density ratios. For straight line limits, (◆)ρp∕ρ=100, (∎)ρp∕ρ=1000, (●)ρp∕ρ=10,000. Streamline limits are indicated with open symbols.

Figure 10

Comparison of the data to Eq. 10 for the streamline (lower) limit

Figure 11

Comparison to model results for Knudsen number (Eq. 11)

Figure 12

Experimentally measured particle trajectory angles (엯) (glass spheres, ρp∕ρ=600) compared to the present results indicated by the shaded regions

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