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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

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
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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References

[1]Ellis, A. S. & Smith, F. T. (2008) A continuum model for a chute flow of grains. SIAM J. Appl. Math. 69 (2), 305–329.CrossRefGoogle Scholar
[2]Ellis, A. S. & Smith, F. T. (2010) On the evolving flow of grains down a chute. J. Eng. Math. 68, 233–247.CrossRefGoogle Scholar
[3]Wilson, P. L. & Smith, F. T. (2005) A three-dimensional pipe flow adjusts smoothly to the sudden onset of a bend. Phys. Fluids 17 (4), 048102, 1–4.CrossRefGoogle Scholar
[4]Wilson, P. L. & Smith, F. T. (2007) The development of the turbulent flow in a bent pipe. J. Fluid Mech. 578, 467–494.CrossRefGoogle Scholar
[5]Badra, J., Masri, A. R. & Behnia, M. (2013) Enhanced transient heat transfer from arrays of jets impinging on a moving plate. Heat Transfer. Eng. 34 (4), 361–371.CrossRefGoogle Scholar
[6]Browne, E. A., Michna, G. J., Jensen, M. K. & Peles, Y. (2010) Microjet array single-phase and flow boiling heat transfer with R134a. Int. J. Heat Mass Transfer 53, 5027–5034.CrossRefGoogle Scholar
[7]Scholz, P., Casper, M., Ortmanns, J., Kähler, C. J. & Radespiel, R. (2008) Leading-edge separation control by means of pulsed vortex generator jets. AIAA J. 46 (4), 837–846.CrossRefGoogle Scholar
[8]Kuibin, P. A., Shtork, S. I. & Fernandes, E. C. (2007) Vortex structure and pressure pulsations in a swirling jet flow. In: Proc. 5th IASME/WSEAS Int. Conf. Fluid Mech Aerod, 25–27 August 2007, Athens, Greece.Google Scholar
[9]Maidi, M. & Yao, Y. (2007) On the flow interactions of multiple jets in cross-flow. In: Proc. 5th IASME/WSEAS Int. Conf. Fluid Mech Aerod, 25–27 August 2007, Athens, Greece.Google Scholar
[10]Bhat, T. R. S., Baty, R. S. & Morris, P. J. (1990) A linear shock cell model for non-circular jets using a conformal mapping with a pseudo-spectral hybrid scheme. AIAA paper no. 90-3960, 13th Aeroacoustics Conference, October 1990.CrossRefGoogle Scholar
[11]Westwood, P. E. (2005) Food-sorting jet arrays and target impact properties. Ph.D. Thesis, UCL, London.Google Scholar
[12]Smith, F. T. (2002) Interference and turning of in-parallel wakes. Quart. J. Mech. Appl. Math. 55 (1), 49–67.CrossRefGoogle Scholar
[13]Frigaard, I. A. (1995) The dynamics of spray-formed billets. SIAM J. Appl. Math. 55 (5), 1161–1203.CrossRefGoogle Scholar
[14]Lu, K. & Shaw, L. (2009) Spray deposition and coating processes. In: Materials Processing Handbook, CRC Press, pp. 11–1–11–31, Boca Raton, Florida, USA.Google Scholar
[15]Tadjfar, M. & Smith, F. T. (2004) Direct simulations and modelling of basic three-dimensional bifurcating tube flows. J. Fluid Mech. 519, 1–32.CrossRefGoogle Scholar
[16]Bowles, R. I., Ovenden, N. C. & Smith, F. T. (2008) Multi-branching three-dimensional flow with substantial changes in vessel shapes. J. Fluid Mech. 614, 329–354.CrossRefGoogle Scholar
[17]Smith, F. T., Purvis, R., Dennis, S. C. R., Jones, M. A., Ovenden, N. C. & Tadjfar, M. (2003) Fluid Flow through various branching tubes. J. Eng. Math. 47, 277–298.CrossRefGoogle Scholar
[18]Milne-Thomson, L. M. (1968) Theoretical Hydrodynamics, 5th ed., Macmillan and Co Ltd., London.CrossRefGoogle Scholar
[19]Carrier, G. F., Krook, M. & Pearson, C. E. (1966) Functions of a Complex Variable: Theory and Technique, McGraw Hill, New York.Google Scholar
[20]Kirchhoff, R. H.Inviscid incompressible flow - potential flow. In: Johnson, R.W. (editor), Handbook of Fluid Dynamics, Ch 7, CRC Press, Boca Raton, Florida, USA.Google Scholar