A Numerical Characterization of Particle Beam Collimation by an Aerodynamic Lens-Nozzle System: Part I. An Individual Lens or Nozzle

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Abstract
Particle beams have traditionally been produced by supersonic expansion of a particle-laden gas through a single nozzle to vacuum. However, it has been shown that, by passing the particle-laden gas through a series of axi-symmetric subsonic contractions and expansions (an aerodynamic lens system) prior to the supersonic expansion to vacuum through a single nozzle, beam divergence can be significantly reduced. In this paper, particle motion in expansions of a gas-particle suspension through either a single lens or a single nozzle have been investigated numerically. Since the single aerodynamic lens and the isolated nozzle are the elementary components of any aerodynamic lens-nozzle inlet system, a fundamental understanding of these components is essential for designing an inlet system with the desired sampling rate, collimation, and transmission properties. If a gas undergoes subsonic contraction and expansion through an orifice, the associated particles would follow the fluid streamlines if the particles were inertialess. However, real particles may either experience a displacement toward the axis of symmetry or may impact on the front surface of the lens. The first of these effects leads to collimation of the particles near the axis, but the second effect leads to particle loss. It is found that the maximum particle displacement occurs at a particle Stokes number, St, near unity and significant impact loss also begins at St ; 1. The lens dimensionless geometry and the Reynolds number of the flow are other important parameters. When a gas containing suspended particles undergoes supersonic expansion through a nozzle to vacuum from the lens working pressure (∼300 Pa), it is found that particle beam divergence is a function of Reynolds number, nozzle geometry, and particle Stokes number. More specifically, it is found that a stepped nozzle generally helps to reduce beam divergence and that particle velocity scales with the speed of sound.

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