### 5.5.5. Lift Force

The lift force acts perpendicular to the direction of relative motion of the two phases.

CFX contains a model for the shear-induced lift force acting on a dispersed phase in the presence of a rotational continuous phase. This is given by:

| (5–70)

where is a non-dimensional lift coefficient. In a rotating frame of reference with rotation vector , the lift force is given by:

| (5–71)

Currently, ANSYS CFX has the following built-in lift models:

- The Saffman Mei Lift Force Model

- The Legendre and Magnaudet Lift Force Model

- The Tomiyama Lift Force Model

#### 5.5.5.1. The Saffman Mei Lift Force Model

This model is applicable mainly to the lift force on spherical solid particles, though it could be applied to liquid drops that are not significantly distorted. It is a generalization of the older Saffman model, which was applicable to a lower range of particle Reynolds numbers than the Saffman Mei model.

The lift coefficient is correlated in terms of both particle Reynolds number and vorticity Reynolds numbers:

| (5–72)

Saffman (1965, 1968) [86][170] correlated the lift force for low Reynolds number flow past a spherical particle as follows:

| (5–73)

where , and . By inspection, Saffman’s lift coefficient is related to the one adopted in ANSYS CFX as follows:

| (5–74)

Saffman’s correlation was generalized by Mei and Klausner (1994) [87] to a higher range of particle Reynolds numbers, as follows:

| (5–75)

where , and .

#### 5.5.5.2. The Legendre and Magnaudet Lift Force Model

This model, as developed by Legendre & Magnaudet (1998) [171], is applicable mainly to the lift force of small diameter spherical fluid particles, though it could be applied to non-distorted liquid drops and bubbles. In contrast to the lift force model of Saffman-Mei for rigid solid particles, it accounts for the momentum transfer between the flow around the particle and the inner recirculation flow inside the fluid particle as caused by the fluid friction/stresses at the fluid interface. Therefore the predicted lift force coefficients are about a factor of 2-5 smaller than for rigid solid particles.

The range of validity given by Legendre & Magnaudet (1998) is as follows:

| (5–76)

The lift force coefficient is then predicted by:

| (5–77)

where

| (5–78)

#### 5.5.5.3. The Tomiyama Lift Force Model

This is a model applicable to the lift force on larger-scale deformable bubbles in the ellipsoidal and spherical cap regimes. Like the Grace and Ishii-Zuber models for drag force, it depends on Eotvos number. Hence, it requires specification of the surface tension between the dispersed and continuous phases. Its main important feature is prediction of the cross-over point in bubble size at which particle distortion causes a reversal of the sign of the lift force to take place. The lift coefficient is given by (Tomiyama 1998) [172]:

| (5–79)

where:

is a modified Eotvos number, based on the long axis, , of the deformable bubble:

The correlation has been slightly modified from Tomiyama’s original form, following Frank et al. (2004) [173], whereby the value of for has been changed to to ensure a continuous dependence on modified Eotvos number. Also, some publications omit the exponent of Eotvos number in the formula for . The formula adopted here is taken from Wellek et al.[174].

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