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Interference in a three-dimensional array of jets

Published online by Cambridge University Press:  28 January 2015

P. E. WESTWOOD and
F. T. SMITH
P. E. WESTWOOD
Affiliation:
Department of Mathematics, UCL, Gower Street, London WC1E 6BT, UK emails: paul.e.westwood@btinternet.com, f.smith@ucl.ac.uk
F. T. SMITH
Affiliation:
Department of Mathematics, UCL, Gower Street, London WC1E 6BT, UK emails: paul.e.westwood@btinternet.com, f.smith@ucl.ac.uk
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Abstract

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The theoretical investigation here of a three-dimensional array of jets of fluid (air guns) and their interference is motivated by applications to the food sorting industry especially. Three-dimensional motion without symmetry is addressed for arbitrary jet cross-sections and incident velocity profiles. Asymptotic analysis based on the comparatively long axial length scale of the configuration leads to a reduced longitudinal vortex system providing a slender flow model for the complete array response. Analytical and numerical studies, along with comparisons and asymptotic limits or checks, are presented for various cross-sectional shapes of nozzle and velocity inputs. The influences of swirl and of unsteady jets are examined. Substantial cross-flows are found to occur due to the interference. The flow solution is non-periodic in the cross-plane even if the nozzle array itself is periodic. The analysis shows that in general the bulk of the three-dimensional motion can be described simply in a cross-plane problem but the induced flow in the cross-plane is sensitively controlled by edge effects and incident conditions, a feature which applies to any of the array configurations examined. Interference readily alters the cross-flow direction and misdirects the jets. Design considerations centre on target positioning and jet swirling.

Keywords

air gunsfood sortingasymptotic theoryanalysisjets

Information

Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Special Anniversay Issue 5: Celebrating 75 years , October 2015, pp. 795 - 819
Copyright
Copyright © Cambridge University Press 2015 

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