Numerical simulations of atomization through the nonlinear behavior of a sheared immiscible fluid interface.

Abstract

Direct numerical simulations of primary atomization using a front-tracking method are presented. The numerical method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties. Interfacial terms are accounted for by adding the appropriate sources, such as surface tension, as delta functions at the boundary separating the phases or fluids. Both two-dimensional and three-dimensional simulations of the Kelvin-Helmholtz instability of a sheared fluid interface separating immiscible fluids are performed. Unlike the Kelvin-Helmholtz instability for miscible fluids, where the sheared interface evolves into well defined concentrated vortices if the Reynolds number is large enough, the presence of surface tension leads to the generation of folds that run parallel to the jet. For two-dimensional instabilities, the evolution is determined by the density ratio of the fluids, the Reynolds number in each fluid, and the Weber number. In the limit of small density ratio the evolution is symmetric, but for a finite density difference the large amplitude stage consists of narrow fingers of the denser fluid penetrating into the lighter fluid. While the initial growth of the instability agrees with linear inviscid theory, if the Reynolds number is large enough, the nonlinear behavior is strongly affected by viscosity where longer wavelengths are the ones that grow to larger amplitudes. The three-dimensional evolution of the interface is examined by simulating a small pie shaped section of the jet. At later times the folds become unstable to azimuthal perturbations if the density ratio is high enough. This results in narrow fingers of the heavy jet fluid that can break into drops by capillary instability. The fingers are formed not as the instability grows, but only after viscous forces reduce the instability and the interface begins to stabilize. While again the initial growth rate is well predicted by linear inviscid theory, once the Reynolds numbers are sufficiently high, the large amplitude behavior is strongly affected by viscosity as well as the initial perturbation imposed. For lower density ratios equal to 2, no drop or finger formation took place.