Fundamentals of Particle Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 140

Fig. 6.2 Dilute and dense flows as described by Kuipers (2000). a Dilute flows where, on average,
less than one particle is present in a computational cell; b dense flows where a relatively high number
of particles are present in a computational cell; c dilute or dense flows where a large number of
computational cells are contained in a single particle
When this occurs, the volume fraction of the discrete phase can no longer be
neglected (10 − 3 < α <10 − 1 ); and, more importantly, the forces that they impart on
the fluid become significant. Then a two-way coupling approach where the fluid
influences the particle and, in return, the particle influences the fluid is used. Two-way
coupling requires that the particle force source terms be included in the momentum
equations of the fluid phase. The momentum sources are due to drag, list and other
forces. The particle originated source terms are generated for each particle as it is
tracked through the flow. These sources are applied in the control volume that the
particle is travelling in during the time step. For very high volume discrete phase
fractions, the flow is considered dense and four-way coupling can occur. That is, in
addition to the two-way couple between the continuous and the discrete phases, the
particle-particle collisional effects become quite important and need to be accounted
for. In practice, for dense flows, the Lagrangian method may not be suitable as
there are too many particles to track and the model must analyse the particle-particle
collisions, as well as the possible frictional contacts. In these cases, the Eulerian-
Eulerian approach is often used. For fluid-particle flows in the respiratory airways,
the disperse phase is typically dilute and one-way coupling is sufficient. In rare
occasions, a two-way coupling analysis may be required.
Particle-particle interactions in dense flows include collisions, leading to particle
rebound for solid particles, and breakup or coalescence for droplets Furthermore,
solid particle-wall collisions can result in particle rebounding and/or deposition.
Droplets impacting a wall lead to breakup and/or deposition. In addition to accounting
for these interactions, governing equations of particle motions are coupled to each
other by collisions, as well as coalescence, and break for the case of droplets; thus
for a large number of particles, this can be computationally prohibitive. In practice,
a separate computational method, the Discrete Element Method (DEM), is used.
This method is closely related to molecular dynamics and relies on efficient nearest
neighbour sorting. DEM is widely used for modelling granular flows. For in-depth