The relative velocity (also referred to as the slip velocity) is defined as the velocity of a secondary phase () relative to the velocity of the primary phase ():

(14–128)

The mass fraction for any phase () is defined as

(14–129)

The drift velocity and the relative velocity () are connected by the following expression:

(14–130)

where is the velocity of phase relative to phase .

Ansys Fluent’s mixture model makes use of an algebraic slip formulation. The basic assumption of the algebraic slip mixture model is that to prescribe an algebraic relation for the relative velocity, a local equilibrium between the phases should be reached over a short spatial length scale. Following Manninen et al. [411], the form of the relative velocity is given by:

(14–131)

where is the particle relaxation time

(14–132)

is the diameter of the particles (or droplets or bubbles) of secondary phase , is the secondary-phase particle’s acceleration. The default drag function is taken from Schiller and Naumann [577]:

(14–133)

and the acceleration is of the form

(14–134)

The simplest algebraic slip formulation is the so-called drift flux model, in which the acceleration of the particle is given by gravity and/or a centrifugal force and the particulate relaxation time is modified to take into account the presence of other particles.

In turbulent flows the relative velocity should contain a diffusion term due to the dispersion appearing in the momentum equation for the dispersed phase. Ansys Fluent adds this dispersion to the relative velocity:

(14–135)

where is a Prandtl/Schmidt number set to 0.75 and is the turbulent diffusivity. This diffusivity is calculated from the continuous-dispersed fluctuating velocity correlation, such that

(14–136)

(14–137)

where is the time ratio between the time scale of the energetic turbulent eddies affected by the crossing-trajectories effect and the particle relaxation time, , and .

When you are solving a mixture multiphase calculation with slip velocity, you can directly prescribe formulations for the drag function. The following choices are available:

See Interphase Exchange Coefficients for more information on these drag functions and their formulations, and Defining the Phases for the Mixture Model in the User's Guide for instructions on how to enable them.

Note that, if the slip velocity is not solved, the mixture model is reduced to a homogeneous multiphase model. In addition, the mixture model can be customized (using user-defined functions) to use a formulation other than the algebraic slip method for the slip velocity. See the Fluent Customization Manual for details.