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Pulsatile jets

Published online by Cambridge University Press:  12 January 2011

RICHARD E. HEWITT and
PETER W. DUCK
RICHARD E. HEWITT
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
PETER W. DUCK*
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
*
†Email address for correspondence: duck@ma.man.ac.uk
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Abstract

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We consider the evolution of high-Reynolds-number, planar, pulsatile jets in an incompressible viscous fluid. The source of the jet flow comprises a mean-flow component with a superposed temporally periodic pulsation, and we address the spatiotemporal evolution of the resulting system. The analysis is presented for both a free symmetric jet and a wall jet. In both cases, pulsation of the source flow leads to a downstream short-wave linear instability, which triggers a breakdown of the boundary-layer structure in the nonlinear regime. We extend the work of Riley, Sánchez-Sans & Watson (J. Fluid Mech., vol. 638, 2009, p. 161) to show that the linear instability takes the form of a wave that propagates with the underlying jet flow, and may be viewed as a (spatially growing) weakly non-parallel analogue of the (temporally growing) short-wave modes identified by Cowley, Hocking & Tutty (Phys. Fluids, vol. 28, 1985, p. 441). The nonlinear evolution of the instability leads to wave steepening, and ultimately a singular breakdown of the jet is obtained at a critical downstream position. We speculate that the form of the breakdown is associated with the formation of a ‘pseudo-shock’ in the jet, indicating a failure of the (long-length scale) boundary-layer scaling. The numerical results that we present disagree with the recent results of Riley et al. (2009) in the case of a free jet, together with other previously published works in this area.

JFM classification

Boundary Layers: Boundary layer controlBoundary Layers: Boundary layer stabilityInstability: Instability

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011, pp. 240 - 259
Copyright
Copyright © Cambridge University Press 2011

References

REFERENCES

Ackerberg, R. C. & Phillips, J. H. 1972 The unsteady laminar boundary layer on a semi-infinite plate due to small fluctuations in the magnitude of the free-stream velocity. J. Fluid Mech. 51, 137–157.CrossRefGoogle Scholar
Akatnov, N. I. 1953 Propagation of planar laminar fluid jet along rigid wall. Proc. LPI 5, 24–31.Google Scholar
Bickley, W. G. 1937 The plane jet. Phil. Mag. 23, 727–731.CrossRefGoogle Scholar
Cowley, S. J., Hocking, L. M. & Tutty, O. R. 1985 The stability of solutions of the classical unsteady boundary-layer equation. Phys. Fluids 28, 441–443.CrossRefGoogle Scholar
Garg, V. K. 1981 Spatial stability of the non-parallel Bickley jet. J. Fluid Mech. 102, 127–140.CrossRefGoogle Scholar
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1, 625–643.CrossRefGoogle Scholar
Goldstein, M. E. 1983 The evolution of Tollmien–Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.CrossRefGoogle Scholar
Keller, H. B. 1978 Numerical methods in boundary-layer theory. Annu. Rev. Fluid Mech. 10, 417–433.CrossRefGoogle Scholar
Lam, S. H. & Rott, N. 1993 Eigenfunctions of linearized unsteady boundary layer equations. J. Fluid Engng 115, 597–602.CrossRefGoogle Scholar
Marzouk, S., Mhiri, H., El Golli, S., Le Palec, G. & Bournot, P. 2006 a Numerical study of momentum and heat transfer in a pulsed plane laminar jet. Intl J. Heat Mass Transfer 46, 4319–4334.CrossRefGoogle Scholar
Marzouk, S., Mhiri, H., El Golli, S., Le Palec, G. & Bournot, P. 2006 b Numerical study of a heated pulsed axisymmetric jet in laminar mode. Numer. Heat Transfer A Appl. 43, 409–429.CrossRefGoogle Scholar
Riley, N., Sánchez-Sans, M. & Watson, E. J. 2009 A planar pulsating jet. J. Fluid Mech. 638, 161–172.CrossRefGoogle Scholar
Ruban, A. I. & Vonatsos, K. N. 2008 Discontinuous solutions of the boundary-layer equations. J. Fluid Mech. 614, 407–424.CrossRefGoogle Scholar
Sato, H. 1960 The stability and transition of a two-dimensional jet. J. Fluid Mech 7, 53–81.CrossRefGoogle Scholar
Schlichting, H. 1933 Laminare Strahlausbreitung. Z. Angew Math. Mech. 13, 260–263.CrossRefGoogle Scholar