For multiphase flows, Ansys Fluent can include the effect of lift forces on the secondary phase particles, droplets, or bubbles. These lift forces act on a particle mainly due to velocity gradients in the primary-phase flow field. The lift force will be more significant for larger particles, but the Ansys Fluent model assumes that the particle diameter is much smaller than the interparticle spacing. Thus, the inclusion of lift forces is not appropriate for closely packed particles or for very small particles.
From Drew (1993) [152]
, the lift force acting
on a secondary phase 
in a primary phase 
can be calculated as:
 | (14–298) |
|
where | |
|
| |
|
| |
|
| |
|
| |
= the secondary
phase velocity
|
The lift force 
will be added to the right-hand side of the momentum equation for both phases
(
).
In most cases, the lift force is insignificant compared to the drag force, so there is no
reason to include this extra term. If the lift force is significant (for example, if the phases
separate quickly), it may be appropriate to include this term. By default, 
is not included. The lift force and lift coefficient can be specified for each
pair of phases, if desired.
Important: It is important that if you include the lift force in your calculation, you need not include it everywhere in the computational domain since it is computationally expensive to converge. For example, in the wall boundary layer for turbulent bubbly flows in channels the lift force is significant when the slip velocity is large in the vicinity of high strain rates for the primary phase.
Fluent offers a variety of models for the lift coefficient, 
, in Equation 14–298. These models are
described in the following sections.
Alternatively, you can specify a constant, or a User-Defined Function for the Lift
Coefficient (DEFINE_EXCHANGE_PROPERTY):
Refer to Including the Lift Force in the Fluent User's Guide for details about how to include lift force in your
simulation.
The model developed by Moraga et al (1999) [458] is applicable mainly to the lift force on spherical solid particles, though it can be applied to liquid drops and bubbles. In this model the lift coefficient combines opposing actions of two phenomena:
classical aerodynamic lift resulting from the interaction between the dispersed phase particles and the primary phase shear
the vorticity-induced lift resulting from interaction between particles and vortices shed by particle wakes
As a result, the lift coefficient is defined in terms of both particle Reynolds number and vorticity Reynolds number:
 | (14–299) |
 | (14–300) |
Defining 
, the Moraga lift coefficient is formulated as:
 | (14–301) |
The Saffman-Mei model is applicable mainly to spherical solid particles, though it can be applied to liquid drops that are not significantly distorted. As in the Moraga model (Moraga Lift Force Model), the lift coefficient is correlated in terms of particle Reynolds number and vorticity Reynolds number. According to Saffman (1965, 1968) [562], [563], for low Reynolds number flow past a spherical particle, the lift coefficient can be defined as:
 | (14–302) |
where 
and 
.
Mei and Klausner (1994) [425] extended the model to a higher range of particle Reynolds numbers. The Saffman-Mei model is empirically represented as:
 | (14–303) |
|
where | |
| |
|
|
The Legendre-Magnaudet model (1998) [352] is applicable primarily to small diameter spherical fluid particles, though it can be applied to non-distorted liquid drops and bubbles. In contrast to the Saffman-Mei model for rigid solid particles, the Legendre-Magnaudet model accounts for the momentum transfer between the flow around the particle and the inner recirculation flow inside the fluid particle caused by the fluid friction/stresses at the fluid interface. Therefore, the predicted lift force coefficients are approximately 2–5 times smaller than for rigid solid particles.
The range of validity given by Legendre and Magnaudet is as follows:
where 
is defined as in the Saffman-Mei model (Saffman-Mei Lift Force Model). The lift force coefficient is then estimated as:
 | (14–304) |
where:
 | (14–305) |
The Tomiyama model is applicable to the lift force on larger-scale deformable bubbles in the ellipsoidal and spherical cap regimes. As with the Tomiyama drag and wall lubrication models, this model depends on the Eötvös number. Its main feature is prediction of the cross-over point in bubble size at which particle distortion causes a reversal in the sign of the lift force. The model implemented in Fluent is a lightly modified version of the original Tomiyama lift model (1998) [656] by Frank et al. (2004) [190] :
 | (14–306) |
where
 | (14–307) |
is a modified Eötvös number based on the
long axis of the deformable bubble, 
:
 | (14–308) |
 | (14–309) |
 | (14–310) |
where 
is the surface tension, 
is gravity, and 
is the bubble diameter.
The Hessenkemper et al. model [241] is applicable to both small diameter spherical fluid particles and large-scale deformable fluid particles in the ellipsoidal and spherical cap regimes. It provides a better prediction of the lift coefficient sign and accounts for possible hydrodynamics effects produced by the presence of small surface-active impurities in the fluid. The model significantly improves estimation of both the transition point from a positive to negative lift sign (thus improving the overall void distribution in lift-driven air-water systems) and the lift coefficient for ellipsoidal bubbles. It also considers a correction by Ziegenhein and Tomiyama for deionized and tap water [241], [734].
The lift coefficient 
is estimated by:
 | (14–311) |
Here, 
is calculated similarly to Equation 14–305
in the Legendre-Magnaudet
lift force model:
 | (14–312) |
where:
In the above equations,
= primary phase density |
and
= primary and secondary phase velocities,
respectively |
= bubble diameter |
= viscosity of the primary phase |
= shear stress |
in Equation 14–311
is a correction for
ellipsoidal bubbles expressed as:
 | (14–316) |
with
 | (14–317) |
The horizontal Eötvös number 
is estimated as Equation 14–308
and is based on the
horizontal diameter 
calculated as:
 | (14–318) |
where 
is the Eötvös number calculated by Equation 14–310.
In Equation 14–318, the coefficients 
= 0.65 and 
= 0.35 proposed by Ziegenhein and Lucas [733] are
used instead of those by Wellek et al. [699] for a better prediction of
the bubble major axis, and hence 
.