Numerical simulations of multiphase flows with both interfaces and discrete particles are challenging because they possess a wide range of length and time scales. Meanwhile, the volume of fluid (VOF) method is suitable for resolving the interface while the discrete particle model (DPM) under the Lagrangian frame better simulates unresolvable particles, a multiscale VOF-DPM combined model is urgently needed for multiscale multiphase flows. The present work implements a VOF-DPM solver that includes a two-way transition algorithm to model the transformation between discrete and continuous phases for bubbles or droplets using OpenFOAM. The interface-capturing scheme in the solver is based on the interIsoFoam solver, which supports the geometric reconstruction of the interface and adaptive mesh refinement (AMR). A connected component labeling (CCL) approach is used for particle detection and VOF-to-DPM transition for discrete bubbles or droplets produced by interface breakup. Conversely, a DPM-to-VOF transition algorithm for particles touching the interface is incorporated to achieve a two-way transition. In addition, phase change modeling between continuous phases and bubble dynamic modeling for cavitating flow cases are also implemented in the solver. Test simulations are performed for validation, including the gas-liquid two-phase dam break and cavitating flow in a convergent-divergent test section. The results demonstrate that the solver is reasonably accurate and can adequately represent the complex phase structure, including the interface and discrete particles.

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The slag droplet entrainment is a common phenomenon in steel refining processes, which may lead to inclusions and defects. In the multiphase flow system, the distinct interface and tiny blobs possess a wide range of spatial and temporal scales and make it hard to be simulated. In numerical methods, the volume of fluid (VOF) approach is appropriate for capturing the interface, but for the unresolvable tiny blobs, the Lagrangian particle tracking (LPT) is preferable. This work newly implements a bidirectional VOF−LPT transformation algorithm for developing a multiscale solver in OpenFOAM to simulate the slag droplet entrainment. The interIsoFoam solver is selected as the main solver to resolve the interface, and the resolution is improved with using the geometric reconstruction and the adaptive mesh refinement (AMR). For capturing tiny droplets, a connected component labeling (CCL) method is adopted for detecting discrete droplets in the VOF field, and then the VOF-to-LPT transition takes place for saving computational costs. Conversely, the LPT-to-VOF transformation for droplets touching the interface is also incorporated to achieve the bidirectional transition. The solver is first validated by a simple case, indicating that the two-way transition algorithm and the Eulerian−Lagrangian momentum coupling are accurate. Then the solver is applied to simulate the slag layer behavior for revealing the mechanisms of slag droplet formation and entrainment. Two main mechanisms of slag droplet formation are identified, and it is found that fewer discrete droplets are generated when the surface tension increases.