Numerical Investigation of a Gas Bubble in Complex Geometries for Industrial Process Equipment Design

This study investigates three-dimensional two-phase flows in complex geometries found in industrial process equipment design using finite-element numerical simulations. The governing equations are formulated in three-dimensional Cartesian coordinates and solved on unstructured meshes employing the Taylor–Hood “Mini” element, selected for its numerical stability and convergence properties. The convective term in the momentum equation is discretized using a first-order semi-Lagrangian scheme. The two fluid phases are separated by an interface mesh composed of triangular surface elements, which is independent of the primary volumetric fluid mesh. Surface tension effects are incorporated as a source term using the continuum surface force (CSF) model, with the curvature computed via the Laplace–Beltrami operator. At each time step, the positions of the interface mesh nodes are updated according to the local fluid velocity field. The results show that the methodology is stable and can be used to accurately model two-phase flows in complex geometries found in several engineering solutions.