The nonlinear growth of sinuous and dilatational disturbances on thin inviscid liquid sheets with a velocity profile across the thickness is determined. Variations of the velocity profile in the liquid sheet, with maximum velocity at the centre linearly decreasing to a minimum at the interfaces, show an optimum value of the velocity gradient, below which disintegration of the liquid sheet is accelerated. The ligaments are formed in local dilatational and global dilatational modes and are asymmetric, unlike the symmetric ligaments formed with a liquid sheet issuing at constant velocity. The presence of velocity gradients is seen to yield smaller ligaments when breakup occurs in the local dilatational mode. © 2010 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Nagabhushana Rao Vadlamani

Department of Aerospace Engineering

K. Ramamurthi

Axial velocity

Axisymmetric

Constant velocities

INVISCID LIQUID

Liquid sheets

Maximum velocity

NONLINEAR GROWTH

Optimum value

VELOCITY GRADIENTS

Velocity profiles

Ligaments

velocity

Liquids

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Role of axisymmetric axial velocity gradients in nonlinear disintegration of liquid sheets

Fluid Dynamics Research

Linear stability analysis of an inviscid liquid sheet with different velocity profiles across its thickness is reported. The velocity profiles for which there is a progressive increase or decrease in velocities between the two interfaces are demonstrated to be inherently unstable even in the absence of the destabilizing aerodynamic shear at the liquid-gas interfaces. Compared to a flat velocity profile, a linear or a parabolic profile, symmetric at the center line of the sheet reduced both the maximum growth rate and the wavelength range over which the waves grow. The convective acceleration from the velocity gradient is found to stabilize longer waves while the growth of shorter waves is hampered by the combined effect of the surface tension and a decrease in the interface velocity between gas and liquid media. The wave forms are dominantly sinuous for symmetric velocity profiles; however, with larger velocity gradients the dilatational modes are observed. The inherent instability of liquid sheets with a progressive change in velocities between the interfaces is seen to arise from the differential convective acceleration at the two interfaces in the plane of reference of the liquid sheets. © 2009 American Institute of Physics.

Fulltext

Physics of Fluids

Internal instability of thin liquid sheets

The breakup of thin planar liquid sheets due to the nonlinear growth of disturbances is determined. Conservation equations are derived using a control volume method and solved using MacCormack's predictor-corrector scheme. It is found that the size and geometry of ligaments, formed during breakup, vary with the Weber number. Antisymmetric waves, which spontaneously intensify at higher values of the Weber number, give rise to thin ligaments. At lower values of the Weber number antisymmetric waves formed initially get transformed into symmetric interfaces giving larger ligaments. The magnitude of the initial amplitude of the disturbances is shown to strongly influence the disintegration. The results are compared with experimental results obtained for thin water sheets and good agreement is demonstrated.

Journal	Data powered by TypesetFluid Dynamics Research
Publisher	Data powered by TypesetIOP Publishing
ISSN	01695983
Open Access	No