Many practically relevant fluid flows involve a complex interaction of phenomena occurring on widely different spatial and temporal scales. In turbulent flows, macroscopic quantities of engineering interest are influenced by small-scale, rapidly fluctuating structures that cannot normally be resolved directly. Multiphase flows introduce additional unresolved phenomena associated with bubbles, droplets, particles, interfaces, and momentum or mass transfer between phases.
This course introduces mathematical models and numerical methods for the simulation of such flows. Starting from the incompressible Navier-Stokes equations, we discuss the physical characteristics of turbulence and the need for turbulence modelling. Particular emphasis is placed on Reynolds-averaged Navier-Stokes (RANS) models, eddy-viscosity closures, wall treatment, Reynolds-stress models, and Large Eddy Simulation (LES).
The second part of the course deals with multiphase flows. We derive and discuss continuum models such as Euler-Euler/two-fluid and drift-flux formulations, including the averaging procedures and constitutive assumptions on which these models are based. Turbulence modelling and interphase coupling in dispersed flows are considered in some detail.
Throughout the course, modelling aspects are closely connected with numerical issues. The main objective is not to present a single universally applicable CFD model, but to develop an understanding of the hierarchy of modelling assumptions and numerical approximations required for reliable simulation of turbulent and multiphase flows.
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