High-fidelity numerical simulations have been performed to study the formation and fragmentation of liquid sheets formed by two impinging jets using an improved volume-of-fluid (VOF) method augmented with several adaptive mesh refinement (AMR) techniques. An efficient topology-oriented strategy was further established to optimize the performance and accuracy of the AMR algorithm. Two benchmark cases pertaining to low-and high-velocity impinging jets are simulated as part of a grid refinement study. Calculated jet dynamics show excellent agreement with experimental observations in terms of the rim shape, droplet size distribution and impact wave structures. Detailed flow physics associated with the temporal evolution and spatial development of the jets are explored over a wide range of Reynolds and Weber numbers. A realistic rendering post-processing using a ray-tracing technique is performed to obtain direct insight to the flow evolution. Special attention is paid to the dynamics of the impact wave which dominates the atomization of the injected liquid. The work appears to be the first systematic numerical study in which all the flow patterns formed by impingement of two liquid jets are obtained. Fine structures are captured based on their characteristic length scales. Various atomization modes, from stable to highly unstable, are resolved with high fidelity.

The microfluidic inertial effect is an effective way of focusing and sorting droplets suspended in a carrier fluid in microchannels. To understand the flow dynamics of microscale droplet migration, we conduct numerical simulations on the droplet motion and deformation in a straight microchannel. The results are compared with preliminary experiments and theoretical analysis. In contrast to most existing literature, the present simulations are three-dimensional and full length in the streamwise direction and consider the confinement effects for a rectangular cross section. To thoroughly examine the effect of the velocity distribution, the release positions of single droplets are varied in a quarter of the channel cross section based on the geometrical symmetries. The migration dynamics and equilibrium positions of the droplets are obtained for different fluid velocities and droplet sizes. Droplets with diameters larger than half of the channel height migrate to the centerline in the height direction and two equilibrium positions are observed between the centerline and the wall in the width direction. In addition to the well-known Segré-Silberberg equilibrium positions, new equilibrium positions closer to the centerline are observed. This finding is validated by preliminary experiments that are designed to introduce droplets at different initial lateral positions. Small droplets also migrate to two equilibrium positions in the quarter of the channel cross section, but the coordinates in the width direction are between the centerline and the wall. The equilibrium positions move toward the centerlines with increasing Reynolds number due to increasing deformations of the droplets. The distributions of the lift forces, angular velocities, and the deformation parameters of droplets along the two confinement direction are investigated in detail. Comparisons are made with theoretical predictions to determine the fundamentals of droplet migration in microchannels. In addition, existence of the inner equilibrium position is linked to the quartic velocity distribution in the width direction through a simple model for the slip angular velocities of droplets.

In numerical simulations of multi-scale, multi-phase flows, grid refinement is required to resolve regions with small scales. A notable example is liquid-jet atomization and subsequent droplet dynamics. It is essential to characterize the detailed flow physics with variable length scales with high fidelity, in order to elucidate the underlying mechanisms. In this paper, two thickness-based mesh refinement schemes are developed based on distance-and topology-oriented criteria for thin regions with confining wall/plane of symmetry and in any situation, respectively. Both techniques are implemented in a general framework with a volume-of-fluid formulation and an adaptive-mesh-refinement capability. The distance-oriented technique compares against a critical value, the ratio of an interfacial cell size to the distance between the mass center of the cell and a reference plane. The topology-oriented technique is developed from digital topology theories to handle more general conditions. The requirement for interfacial mesh refinement can be detected swiftly, without the need of thickness information, equation solving, variable averaging or mesh repairing. The mesh refinement level increases smoothly on demand in thin regions. The schemes have been verified and validated against several benchmark cases to demonstrate their effectiveness and robustness. These include the dynamics of colliding droplets, droplet motions in a microchannel, and atomization of liquid impinging jets. Overall, the thickness-based refinement technique provides highly adaptive meshes for problems with thin regions in an efficient and fully automatic manner.