Modeling theory

In addition to solving transport equations for the continuous phase, FLUENT allows the user to simulate a discrete second phase in a Lagrangian frame of reference. This second phase consists of spherical particles (which may be taken to represent droplets or bubbles) dispersed in the continuous phase. With different discrete phase options, a wide range of discrete phase problems (aerosol dispersion, liquid fuel combustion, etc) can be simulated. Nevertheless, some assumptions are done due to the limitations of FLUENT:

Assumptions

• The second phase is sufficiently dilute that particle-particle interactions and the effects of the particle volume fraction on the gas phase are negligible, which means that the volume fraction has not  to exceed 10-12%.
• The particle streams are injected into a continuous phase flow with a well-defined entrance and exit condition.  The Lagrangian model does not effectively model flows in which particles are in suspension, such as fluidized beds or stirred tanks.
• The dispersion of particles due to turbulence in the fluid phase can be predicted using the stochastic tracking model (statistical methods for the calculations of instantaneous turbulent velocity fluctuations on the particle trajectories) or the particle cloud model (calculations of the statistical evolution of a cloud  of particles about a mean trajectory). In both models, the particles have no direct impact on the generation or dissipation of turbulence in the continuous phase.
With these assumptions, a force balance on the particles is done to calculate the particle trajectory.

Equations of motion for Particles

The force balance equates the particle inertia with the forces acting on the particle:

1. the Drag Force represents the force applied by the continuous phase on the particle, due to the viscosity.
2. the Gravity Force represents the weight of the particle and the Archimede Force applied on the particle.
3. the additional forces depend on the choices made by the user. There are the "Virtual Mass" Force, the force required to accelerate the fluid surrounding the particle, the Thermophoretic Force, applied on particles that have a temperature gradient, the Brownian Force included for sub-micron particles and the Saffman's Lift Force which is the force due to the pressure gradient around the particle that entails a rotative motion of the particle.

Calculation procedure

FLUENT proposes two procedures: the Uncoupled Discrete Phase Calculations (UDPC) and the Coupled Discrete Phase Calculations (CDPC).
In the uncoupled approach, the particle trajectories are computed, based on a fixed continuous-phase flow field. This procedure is adequate when the discrete phase is present at a low mass and momentum loading. In this case, the continuous phase is not impacted by the presence of the discrete phase.
For the CDPC, FLUENT modifies the two-step procedure of the UDPC as follows:

1. Solve the continuous phase flow field
2. Introduce the discrete phase by calculating the particle trajectories for each injection
3. Recalculate the continuous phase flow, using the interphase exchange of momentum, heat and mass determined during the previous particle calculation
4. Recalculate the discrete phase trajectories
The last two steps are repeated until a converged solution is achieved for both phases.