ABSTRACT
There are three fundamental numerical approaches for the study of the movement of particles, bubbles, and drops in fluids. The first one is the continuum model (or two-fluid model), in which both the fluid phase and the dispersed phase are treated as continuous media. The continuum model requires the knowledge of interactions at the boundaries of the phases, such as drag and heat transfer coefficients, and makes use of the apparent viscosity of the dispersed phase. The second approach is the discrete particle model. It treats the discrete phase as separate particles that interact with the flow and traces the position and velocity of all the elements of the dispersed phase by solving Lagrangian equations of motion. The fluid phase is considered a continuum phase, and the effects of the elements of the dispersed phase are included by adding the interaction terms (for mass, momentum, and energy) into the governing equations of the fluid by empirical equations. The third approach is the direct numerical simulation (DNS). This is also a Eulerian-Lagrangian method that resolves the fluid flow around particles, bubbles, and drops. The method accounts for the interactions of the fluid with the dispersed phase by solving the Navier-Stokes equations for the fluid phase and the initial value problem for the motion of the dispersed phase simultaneously. With the significant increase of computational power, the DNS method is becoming a more enabling and popular approach to study complex particulate flow problems.
