Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-27T14:25:49.375Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected], [email protected]
F. T. SMITH
Affiliation:
Department of Mathematics, UCL, Gower Street, London WC1E 6BT, UK emails: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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