On spray formation

Abstract

International audienceWe depict and analyse the successive steps of atomization of a liquid jet when a fast gas stream blows parallel to its surface. Experiments performed with various liquids in a fast air flow show that the liquid destabilization proceeds from a two-stage mechanism: a shear instability first forms waves on the liquid. The transient acceleration experienced by the liquid suggests that a Rayleigh–Taylor type of instability is triggered at the wave crests, producing liquid ligaments which further stretch in the air stream and break into droplets. The primary wavelength $\lambda\,{\sim}\,\delta (\rho_{1}/\rho_{2})^{1/2}$ is set by the vorticity thickness $\delta$, in the fast air stream and the liquid/gas density ratio $\rho_{1}/\rho_{2}$. The transverse corrugations of the crests have a size $\lperp\,{\sim}\,\delta {\We_{\delta}}^{-1/3} (\rho_{1}/\rho_{2})^{1/3}$, where $\We_{\delta}\,{=}\,\rho_{2}u_{2}^{2}\delta/\sigma$ is the Weber number constructed on the gas velocity $u_{2}$ and liquid surface tension $\sigma$. The ligament dynamics gives rise, after break-up, to a well-defined droplet size distribution whose mean is given by $\lperp$. This distribution bears an exponential tail characteristic of the broad size statistics in airblast sprays

Stability analysis and breakup length calculations for steady planar liquid jets

“…This result also agrees with the experimental results of Marmottant & Villermaux (2004) who plot the velocity profiles of an air jet injected into static air and again find that the shear layer in the jet is proportional to V −1/2 . The variation of β with V is much smaller than for δ 1 ; however it still increases with increasing V , and this variation has an effect on the breakup length calculations.…”

“…In the present study we examine how the growth rate at these saddles and their positions are affected when the interface between the two fluids is placed within the shear layer. We find that this leads to important qualitative differences compared with previous studies in which the density interface was assumed to lie on only one side of the shear layer (Marmottant & Villermaux 2004;Juniper 2007). Our assumption to neglect viscosity in this study is valid because Yu & Monkewitz (1990) showed that the transition to absolute instability is caused by the interaction between the two shear layers and is not a viscous effect.…”

“…The dispersion relation can be solved for complex ω, for a given real α. For the case of planar and axisymmetric jets, the range of real wavenumbers which exhibit growth is governed by the width of the shear layer and the magnitude of the surface tension (Rayleigh 1894;Batchelor & Gill 1962;Funada, Joseph & Yamashita 2004;Marmottant & Villermaux 2004). However, a temporal stability analysis does not show certain aspects of the jet stability, such as whether or not it is absolutely or convectively unstable, which has important implications for where it breaks up.…”

Statistically steady measurements of Rayleigh-Taylor mixing in a gas channel

“…R-T generated turbulence also occurs in geophysical formations like salt domes and volcanic islands (DiPrima & Swinney 1981); in deep-sea ocean currents and in rivers and estuaries (Cui & Street 2004;Molchanov 2003). The breakup of fuel droplets in high speed flows have also been found to be R-T unstable (Marmottant & Villermaux 2004;Thomas 2003). Experiments performed to study atomization of a liquid jet when a fast gas stream blows parallel to its surface show that the liquid destabilization proceeds from a two-stage mechanism: a shear instability first forms waves on the liquid.…”

“…Experiments performed to study atomization of a liquid jet when a fast gas stream blows parallel to its surface show that the liquid destabilization proceeds from a two-stage mechanism: a shear instability first forms waves on the liquid. The transient acceleration experienced by the liquid suggests that a Rayleigh-Taylor type of instability is triggered at the wave crests, producing liquid ligaments which further stretch in the air stream and break into droplets (Marmottant & Villermaux 2004). …”