Skip to main content
×
Home
    • Aa
    • Aa

Stability analysis and breakup length calculations for steady planar liquid jets

  • M. R. TURNER (a1), J. J. HEALEY (a2), S. S. SAZHIN (a1) and R. PIAZZESI (a1)
Abstract

This study uses spatio-temporal stability analysis to investigate the convective and absolute instability properties of a steady unconfined planar liquid jet. The approach uses a piecewise linear velocity profile with a finite-thickness shear layer at the edge of the jet. This study investigates how properties such as the thickness of the shear layer and the value of the fluid velocity at the interface within the shear layer affect the stability properties of the jet. It is found that the presence of a finite-thickness shear layer can lead to an absolute instability for a range of density ratios, not seen when a simpler plug flow velocity profile is considered. It is also found that the inclusion of surface tension has a stabilizing effect on the convective instability but a destabilizing effect on the absolute instability. The stability results are used to obtain estimates for the breakup length of a planar liquid jet as the jet velocity varies. It is found that reducing the shear layer thickness within the jet causes the breakup length to decrease, while increasing the fluid velocity at the fluid interface within the shear layer causes the breakup length to increase. Combining these two effects into a profile, which evolves realistically with velocity, gives results in which the breakup length increases for small velocities and decreases for larger velocities. This behaviour agrees qualitatively with existing experiments on the breakup length of axisymmetric jets.

Copyright
Corresponding author
Email address for correspondence: m.r.turner@brighton.ac.uk
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G. K. Batchelor & A. E. Gill 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529551.

J. Eggers & E. Villermaux 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601–179.

R. E. Esch 1957 The instability of a shear layer between two parallel streams. J. Fluid Mech 3, 289303.

T. Funada , D. D. Joseph & S. Yamashita 2004 Stability of a liquid jet into incompressible gases and liquids. Intl J. Multiphase Flow 30, 12791310.

J. J. Healey 2006 A new convective instability of the rotating-disk boundary layer with growth normal to the disk. J. Fluid Mech. 560, 279310.

J. J. Healey 2007 Enhancing the absolute instability of a boundary layer by adding a far-away plate. J. Fluid Mech. 579, 2961.

J. J. Healey 2009 Destabilizing effects of confinement on homogeneous mixing layers. J. Fluid Mech. 623, 241271.

P. Heurre & P. A. Monkewitz 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.

E. J. Hinch 1991 Perturbation Methods. Cambridge University Press.

M. P. Juniper 2006 The effect of confinement on the stability of two-dimensional shear flows. J. Fluid Mech. 565, 171195.

M. P. Juniper 2007 The full impulse response of two-dimensional jet/wake flows and implications for confinement. J. Fluid Mech. 590, 163185.

L. Lesshafft & P. Huerre 2007 Linear impulse response in hot round jets. Phys. Fluids 19, 024102.

X. Li & R. R. Tankin 1991 On the temporal stability of a two-dimensional viscous liquid sheet. J. Fluid Mech 226, 425443.

S. P. Lin & Z. W. Lian 1989 Absolute instability of a liquid jet in a gas. Phys. Fluids 1 (3), 490493.

S. P. Lin , Z. W. Lian & B. J. Creighton 1990 Absolute and convective instability of a liquid sheet. J. Fluid Mech 220, 673689.

P. Marmottant & E. Villermaux 2004 On spray formation. J. Fluid Mech. 498, 73111.

P. A. Monkewitz & K. D. Sohn 1988 Absolute instability in hot jets. AIAA J. 26, 911916.

L. Raynal , J-L. Harion , M. Favre-Marinet & G. Binder 1996 The oscillatory instability of plane variable-density jets. Phys. Fluids 8, 9931006.

S. J. Rees & M. P. Juniper 2009 The effect of surface tension on the stability of unconfined and confined planar jets and wakes. J. Fluid Mech. 633, 7197.

S. J. Rees & M. P. Juniper 2010 The effect of confinement on the stability of viscous planar jets and wakes. J. Fluid Mech. 656, 309336.

S. S. Sazhin , C. Crua , D. A. Kennaird & M. R. Heikal 2003 The initial stage of fuel spray penetration. Fuel 82 (8), 875885.

P. J. Schmid & D. S. Henningson 2001 Stability and Transition in Shear Flows. Springer.

S. F. Shen 1961 Some considerations on the laminar stability of time-dependent basic flows. J. Aerosp. Sci. 28, 397404, 417.

L. D. Söderberg 2003 Absolute and convective instability of a relaxational plane liquid jet. J. Fluid Mech. 493, 89119.

L. D. Söderberg & P. H. Alfredsson 1998 Experimental and theoretical stability investigations of plane liquid jets. Eur. J. Mech B/Fluids 17, 689737.

K. R. Sreenivasan , S. Raghu & D. Kyle 1989 Absolute instability in variable density round jets. Exp. Fluids 7, 309317.

V. Srinivasan , M. P. Hallberg & P. J. Strykowski 2010 Viscous linear stability of axisymmetric low-density jets: parameters influencing absolute instability. Phys. Fluids 22, 024103.

R. Stone 1992 Introduction to Internal Combustion Engines. MacMillan.

M. H. Yu & P. A. Monkewitz 1990 The effect of non-uniform density on the absolute instability of planar inertial jets and wakes. Phys. Fluids A 2 (7), 11751181.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 20 *
Loading metrics...

Abstract views

Total abstract views: 110 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd September 2017. This data will be updated every 24 hours.