(337i) Kinetic-Based Hyperbolic Two-Fluid Models

Fox, R. O., Iowa State University
A longstanding shortcoming of two-fluid models for disperse multiphase flows is the lack of hyperbolicity when the Archimedes force of the continuous phase on the disperse phase is included. This is especially true when the material density of the disperse phase is much smaller than that of the continuous phase (e.g., bubbly flows). Mathematically, a nonhyperbolic model yields unphysical solutions and thus hyperbolicity is a necessary condition for any well-posed two-fluid model. In the literature, various ad hoc fixes have been proposed to achieve hyperbolicity and are used in commercial CFD codes, the most popular being the so-called turbulent-dispersion force. While fixing the hyperbolicity problem, the physical origin of such terms is not evident and thus they represent a mathematical fix that otherwise have only minor effects on solutions.

To improve our understanding of the origin of such terms and to provide a rational approach for physics-based hyperbolicity, we have developed a kinetic-based derivation of the two-fluid model that includes the Archimedes force starting from the Boltzmann-Enskog kinetic equation. A related approach based on the Boltzmann kinetic equation was pioneered in the 1960’s for modeling hard-sphere fluids with disparate masses (e.g. plasmas), but did not include the Archimedes force. In this presentation, the status of hyperbolic kinetic-based two-fluid models for monodisperse multiphase flows, valid for arbitrary material-density ratios, will be reviewed. The methodology of model validation using data from direct-numerical simulation of fluid-particle flows will be described. Possible extensions to include polydispersity and other physics and chemistry will be discussed.