S. P. Lin

Absolute instability of a liquid jet in a gas

The effect of the ambient gas density on the onset of absolute instability in a viscous liquid jet is examined. The critical Weber number, above which the instability is convective and below which the instability is absolute, is determined as a function of Reynolds number and the density ratio of gas to liquid. It is shown that the gas density has the effect of raising the critical Weber number. It also raises the cutoff wavenumber below which disturbances are spatially amplified and above which they are damped.

Atomization of a liquid jet

Generation of ripples by wind blowing over a viscous fluid was investigated by G. I. Taylor [The Scientific Papers of G. I. Taylor (Cambridge U. P., Cambridge, 1963), Vol. 3, No. 25] with linear stability analysis. Taylor considered the case of temporally growing disturbances in a low density gas and applied his results to explain the process of atomization of a liquid jet injected into a low density gas. Taylor’s analysis is extended here to investigate the case of a spatially growing disturbance in a dense gas. Taylor showed that temporal disturbances of wavelength shorter than the capillary length are stable. The same is found for the spatial disturbances. Each type of disturbance possesses a maximum growth rate with a specific wavelength and frequency. The atomized droplet size corresponding to the maximum growth rate is shown in both theories to decrease inversely as the square of the jet velocity. While the maximum growth rate increases as the square root of the gas‐to‐liquid density ratio when A2 e...

The mechanism for surface wave instability in film flow down an inclined plane

The equation governing the average rate of change of disturbance kinetic energy is evaluated for various wavenumbers at fixed values of Reynolds number, Weber number, and angle of inclination. The dominant energy production term is associated with the work done by the perturbation shear stress at the free surface. The mechanism of instability, however, is associated with a shift of perturbation vorticity relative to the surface displacement resulting from advection.

Breakup of a liquid jet in a swirling gas

The convective instability of a viscous liquid jet emanating into a inviscid gas with a swirl is investigated. Contrary to the known case of a swirling liquid jet in a quiescent gas, the swirl in the ambient gas is shown to have a stabilizing effect. The inertia force in the gas is shown to play dual roles of both stabilization and destabilization. The gas inertia associated with the swirl has a stabilizing influence, but that associated with the interfacial pressure fluctuation has a destabilizing effect. A physical explanation of the mechanism of stabilization by the gas swirl is given.

IMAGE OF ABSOLUTE INSTABILITY IN A LIQUID JET

The existence of absolute instability in a liquid jet has been predicted for some time. The disturbance grows in time and propagates both upstream and downstream in an absolutely unstable liquid jet. The image of absolute instability is captured in the NASA 2.2 sec drop tower, and is reported here.

Absolute and convective instability of a radially expanding liquid sheet

A radially expanding liquid sheet of a finite radius can be formed by impacting a liquid jet on a circular disk [Savart, Ann. Chim. Phys. 54, 55 (1833); Ann. Chim. 54, 113 (1833)] or by impinging two jet heads on against each other [Savart, Ann. Chim. Phys. 55, 257 (1833)]. The breakup of the liquid sheet first observed by Savart at the outer rim of the sheet is explained from the point of view of absolute and convective instability. Whether the sheet is convectively or absolutely unstable depends on the local Weber number We=ρU2H/S, where ρ and S are, respectively, the liquid density and the surface tension, and H and U are, respectively, the local half-sheet thickness and the local average liquid velocity. It is shown that absolute instability occurs at We=1, and convective instability occurs in the region where We>1. In the radially expanding liquid sheet, H decreases inversely with the radial distance from the center of the sheet, but U remains constant. Thus, the local Weber number that is greater th...

Nonaxisymmetric evanescent waves in a viscous liquid jet

The linear stability of a viscous liquid jet emanating into a gas with respect to spatially growing nonaxisymmetric disturbances is analyzed. The numerical solution of the characteristic equation and some analytical arguments are used to show that the nonaxisymmetric disturbances in the liquid jet are evanescent waves. Hence, a support is given to the commonly adopted assumption that nonaxisymmetric disturbances are more stable than the axisymmetric ones in a viscous liquid jet emanating into an ambient gas.

Suppression of instability in a liquid film flow

The stability of a viscous liquid film flow down an inclined plane that oscillates in the direction parallel to the flow is analyzed by use of a Chebyshev series solution with the Floquet theory. When the inclined plane is stationary, it is known that the onset of the film instability manifests itself as long surface waves [J. Fluid Mech. 554, 505 (1957); Phys. Fluids 6, 321 (1963)] or relatively short shear waves [‘‘Critical angle of shear wave instability in a film,’’ to appear in J. Appl. Mech.; J. Eng. Math. 8, 259 (1974); Phys. Fluids 30, 983 (1987)], depending on the angle of inclination. It is demonstrated that the unstable film can be stabilized by use of appropriate amplitudes and frequencies of the plate oscillation to suppress the shear waves as well as the long waves. The ranges of amplitude and frequency in which the film can be stabilized depend on the flow parameter.

Absolute and convective instability of a viscous liquid jet surrounded by a viscous gas in a vertical pipe

The absolute and convective instability of a viscous liquid jet emanating into a viscous gas in a vertical pipe is analyzed in a parameter space spanned by the Reynolds number, the Froude number, the Weber number, the viscosity ratio, the density ratio, and the diameter ratio. The numerical results of the analysis are used to demonstrate that reduction in gravity tends to enhance the Rayleigh mode of convective instability which leads to the breakup of a liquid jet into drops of diameters comparable with the jet diameter. On the contrary, the Taylor mode of convective instability that leads to atomization is retarded at reduced gravity. The Rayleigh mode becomes absolutely unstable when the Reynolds number exceeds a critical value for a given set of the rest of the relevant parameters. The domain of absolute instability is significantly enlarged when the effect of gas viscosity is not neglected.

Transition from convective to absolute instability in a liquid jet

The critical Weber number above which a liquid jet is convectively unstable and below which it is absolutely unstable is determined experimentally for various Reynolds numbers. The experimental results compare very well with the theoretical prediction, and provide the first evidence of transition from convective to absolute instability at relatively large Reynolds numbers. Comparisons of the present results with related results are made to expand and clarify the concept of absolute instability in the context of interfacial fluid dynamics.