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A numerical investigation of the velocity, pressure and vorticity fields very near the injection of flat and thin two-dimensional gas jets or liquid sheets between two parallel high-speed gas coflows is performed. The motivation of this research is to uncover some basic physical mechanisms underlying twin-fluid atomization. Conservation equations and boundary and initial conditions are presented for both single-phase jets and two-phase liquid sheet/gas-stream systems. Both infinitely thin and thick solid walls are considered. Apart from the gas Strouhal and Reynolds numbers appearing in the dimensionless single-phase flow equations, the liquid Reynolds number, the momentum flux ratio, the gas/liquid velocity ratio and the Weber number enter the two-phase flow dimensionless formulation. The classical numerical techniques for single-phase jets are supplemented with the volume-of-fluid (VOF) method for interface tracking and the continuum surface force (CSF) method to include surface tension in two-phase flow systems. Ad hoc convection algorithms in combination with a developed version of the fractional-step scheme allows a significant reduction of the numerical diffusion, maintaining localized and sharp interfaces. The action of the surface tension is correctly found via the CSF with a smoothed scalar-field approximation.Results for single-phase jets with thin-wall injectors indicate qualitatively correct features and trends when varying the Reynolds number and the coflow/jet ratios: thick-wall injectors significantly modify the vorticity and pressure near fields; increasing the Reynolds number leads to larger flow disturbances; larger coflow/jet velocity ratios yield more perturbed near flow fields. For single-phase jets the Strouhal number as a function of the Reynolds number follows the usual trends of flows behind a circular cylinder.For two-phase flows, increasing the gas Reynolds number leads to larger liquid-sheet deformations and to a reduction of the breakup length; a plot of the gas Strouhal number, in the presence of a liquid sheet, as a function of the gas Reynolds number displays a monotonically decreasing curve, contrary to that for a gas jet. This observation strongly suggests that the gas vortex shedding mechanism is modified by the liquid-sheet motion. The gas vortex shedding frequency as a function of the liquid-sheet oscillation frequency follows a straight line with a slope of approximately $45^{\circ}$ for momentum flux ratios greater than roughly 0.45; for values below 0.45 the gas vortex shedding frequency remains constant while the liquid sheet varies its oscillation frequency. Increasing the surface tension leads to a larger breakup length. Thin trailing edges almost double the sheet oscillation frequency and more than halve the perturbation wavelength compared to thick trailing edges.

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