Three-dimensional temporal instabilities, leading to spray formation of a round liquid jet segment with an outer, coaxial high-density gas flow, are studied with Navier-Stokes and level-set computations. These computations predict the liquid surface shape showing the smaller structures on the conical wave crests, i.e. lobes, holes, bridges and ligaments, which are the precursors to droplet and spray formations. These structures and their time scales affect droplet size and velocity distributions as well as spray cone angles. The gas-to-liquid density ratio, liquid Reynolds number (Re) and liquid Weber number (We) range between 0.02-0.9, 320-16 000 and 2000-230 000, respectively, which cover three distinct physical domains. (1) At higher Re and We, ligaments and then drops develop following hole and liquid bridge formations. (2) At higher gas densities throughout the Re range, several holes merge forming two bridges per lobe before breaking to form ligaments; this hole merging is explained by slower development of hairpin vortices and lobe shape. (3) In cases where both gas density and Re or We are lower, the well-ordered lobes are replaced by more irregular, smaller-scale corrugations along the conical wave crest edge; ligaments form differently by stretching from the lobes before holes form. Thicker ligaments and larger droplets form in the low Re, low gas density range. The surface wave dynamics, vortex dynamics and their interactions are explained. Understandings of liquid stream break up and concurrent smaller structure formation are built upon an examination of both translation and rotation of the fluid. In all cases, hole formation is correlated with hairpin and helical vortices; fluid motion through a perforation in the thin sheet near the wave crest corresponds to these vortices. The hole formation process is dominated by inertial forces rather than capillary action, which differs from mechanisms suggested previously for other configurations. Circulation due to streamwise vorticity increases while the lobes thin and holes form. For larger surface tension, cavities in the jet core rather than perforations in a sheet occur. The more rapid radial extension of the two-phase mixture with increasing gas density is explained by greater circulation in the ring (i.e. wave crest) region. Experimental descriptions of the smaller structures are available only at lower Re and lower density, † Email address for correspondence: sirignan@uci.edu Hole, ligament and bridge formations 187 agreeing with the computations. Computed scales of bridges, ligaments, early droplets and emerging spray radii agree qualitatively with experimental evidence through the high Re and We domains.

Nonlinear, transverse-mode, liquid-propellant-rocket-motor combustion instability is examined with a twodimensional model. The three-dimensional equations are integrated over the axial direction, for a multi-orifice short nozzle. Nonlinear transverse-wave oscillations in the circular combustion chamber are examined with the primary flow in the axial direction. Turbulent mixing of methane and gaseous oxygen with coaxial injection is analyzed. The combustion has two characteristic times, one for mixing and the other for chemical kinetics, producing a time lag in the energy-release rate relative to pressure. Then, the coupled combustion process and wave dynamics are calculated for a 10-injector chamber with methane and gaseous-oxygen propellants. The linear first tangential mode is imposed initially. Nonlinear triggering occurs; above a critical initial amplitude, the amplitude grows; otherwise, it decays with time. The second tangential mode also develops, and the nonlinear resonance creates a subharmonic mode with a frequency equal to the difference between the two tangential-mode frequencies. A modification of the characteristic times leads to a triggered instability, in which the first tangential mode transfers energy to its harmonics without the appearance of the second tangential mode or the subharmonic mode. Local pulses of pressure and velocity can also trigger instabilities with a strong sensitivity to the direction of the pulse.

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