Small Scale Modeling and Simulation of Incompressible Turbulent Multi-Phase Flow

Two-phase flows occur in many academic and applied fluid mechanics problems such as boiling crisis in a nuclear plant, chemical reactors, material coating by plasma projection, bubbles in pipes, wave breaking, oil extraction in porous media, powder and fluidized beds processes, fuel injection in engines to cite a few. Exhaustive presentation of various unsteady or turbulent multi-phase flows is given for example in [1,2]. As soon as turbulence and interface interact in a non linear way with macroscopic interfacial deformations inducing ligaments, coalescence or rupture, the experimental characterization of these flows is difficult due to the heterogenous character of the multi-phase medium. Modeling and numerical simulation thus represent an interesting way to study the physical processes that control these flows. The present book was written following a CISM course devoted to the modeling and numerical simulation of multi-phase flows with fictitious domain approaches (2005). The objective of the course was to bring an exhaustive presentation, discussion and validation of models and numerical methods for the simulation of multiphase problems for which the interfacial scale is resolved, i.e. the size of the mesh cell is smaller than the size of the interfacial structures. This book has also to be related to the special issue of Acta Mechanica published in 2019 [3]. The one-fluid model is the basis of the representation of moving and deformable interfaces, even if Ghost Fluid techniques are also undertaken. The typical scales of interfaces being assumed larger than the numerical resolution scale, i.e. the local size of the Eulerian flow mesh, in a kind of Direct Numerical Simulation of interfacial structures, while the turbulent flow characteristics can be modeled by means of DNS (in the sence) or Large Eddy Simulation (LES). Different interface tracking techniques are presented and compared as well as the management of capillary forces and incompressibility and solid constraints. In particular, penalty methods are extensively used for the numerical treatment of boundary conditions, pressure-velocity coupling or immersed obstacle representation. Various validations and applications are discussed in order to stress the capability of the model and numerical methods. In the present manuscript, much attention is paid on resolved scale fluid-fluid interfaces [4–20], with also informations on fluid-solid interactions and resolved scale particles, which can also be investigated with similar approaches [21–31]. Different aspects of modeling and simulation of multi-phase flows will be presented in a common concept for all types of multi-phase flows (free surfaces, liquid-liquid, particulate flows) that is called the fictitious domain approach. Attention will be paid to models, interface tracking, validations and applications.