Surface Disturbance Evolution and the Splattering of Turbulent Liquid

In this study, we investigate the growth of surf ace disturbances on turbulent liquid jets in air and its relation to the amount of splattering when the jet strikes a target. A laser-based optical technique is used to measure the instantaneous local amplitude of fluctuations on jets produced by fully-turbulent tube nozzles. Measurements were made over the portion of the jet between 0.2 and 45 nozzle diameters downstream of the nozzle. Jets of water, an isopropanol-water mixture, and water with a surfactant were studied. The local rms amplitude of surface disturbances scales with the jet Weber number and the dimensionless distance from the target. The measurements show a nonexponential growth of the rms amplitude as the liquid moves downstream. Power spectra of the disturbance amplitudes show broadband turbulent disturbances to be dominant over any single wavenumber Rayleigh-type instability. The measured rms amplitude of roughness on the jet surface correlates well with the fraction of impinging liquid splattered, as hypothesized in previous models of splattering. A mathematical model of the free-surface/turbulence interaction is also given. The spectrum of surface disturbances is calculated based on the pressure spectrum of isotropic, homogeneous turbulence. Both the theoretical model and the experiments show that the high-wavenumber portion of the spectrum decays as k~ owing to the damping effect of capillary forces on the turbulent pressure spectrum that drives surface roughening.