Towards Combined Deterministic and Statistical Approaches to Modeling Dispersed Multiphase Flows

Abstract

The goal of modeling dispersed multiphase flows is to predict spatial distributions of the volume fraction, velocities and other properties of interest of the dispersed and continuous phases in geometries of practical interest. In this chapter we summarize key advances that have enabled progress towards this goal by starting with the development of interphase momentum transfer models for flow past single particles with a view to extending them to multiparticle systems. Particle-resolved direct numerical simulation of microscale (particle scale) phenomena has emerged as a powerful tool to propose statistical models for mesoscale and macroscale simulations of dispersed multiphase flow. Key advances in modeling of interphase momentum as well as particle and fluid velocity fluctuations are briefly reviewed. Building on this foundation we examine deterministic models for multiparticle effects that are based on the generalized Faxen theorem which provides a rigorous theoretical foundation for their development. In particular, the recently proposed pairwise interaction extended point-particle (PIEP) model is presented as a means of systematically including fluid-mediated particle-particle interactions in a deterministic framework. The performance of the PIEP model is assessed in different validation tests. Although the deterministic modeling approach provides physical insight and mechanistic interpretation of model terms, its limitation is it does not fully account for all the fluctuations that occur at the microscale. Therefore it is important to complement the deterministic model with a stochastic component to properly account for the statistical variability that is naturally present in all dispersed multiphase flows. We review key advances in statistical modeling of dispersed multiphase flows in terms of both the two-fluid theory as well as the Euler-Lagrange approach, with an emphasis on the latter, where we consider both Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) descriptions of the carrier phase. Finally, we propose a new paradigm for modeling dispersed multiphase flows that effectively combines the best elements of the deterministic and statistical modeling approaches as the most promising direction for development of predictive models.