D I S C R E T I Z A T I O N

To display this section, click the Show button () and select Discretization. Select a

Discretization of fluids—P1+P1, P2+P1 (the default) or P3+P2.

P1+P1 is not permitted unless streamline diffusion is active for the

momentum transport.

Note

Fluid Properties

The Fluid Properties feature contains the material properties for the liquid and the gas. It also contains settings for the slip model.

D O M A I N S E L E C T I O N

From the Selection list, choose the domains to use the liquid and gas properties.

M A T E R I A L S

Select the materials to use for the material properties of the liquid and the gas (when they have the selection to take their value from the material). Select Domain material from the Liquid list or the Gas list (the default value) to use the material defined for the domain for the liquid or gas, respectively. Select another material from the Liquid list or the Gas list to use that material’s properties for the liquid or gas, respectively.

L I Q U I D P R O P E R T I E S

Specify the density and the viscosity of the liquid.

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Density

The default Density l (SI unit: kg/m3) uses values From material. If User defined is selected, enter another value or expression.

Viscosity

The dynamic viscosity describes the relationship between the shear stresses in a fluid and the shear rate. Intuitively, water and air have a low viscosity, and substances often described as thick, such as oil, have a higher viscosity.

For the dynamic viscosity of the liquid (SI unit: Pa·s), choose from the following options in the Viscosity list:

•The default selection is From material. The value of the viscosity is then the value defined for the material selected in the Materials section for the continuous phase.

•Select User defined to define a value or expression for the viscosity in the associated field for l.

G A S P R O P E R T I E S

Specify the density and bubble diameter of the gas.

Density

The default Density g (SI unit: kg/m3) uses values From material. If User defined is selected, enter another value or expression.

Diameter of Bubbles

Enter the bubble diameter db in the Bubble diameter field. The default value is 10 3 m (1 mm).

S L I P M O D E L

Two models for the slip velocity uslip are available in the Bubbly Flow. Or select a user defined value or expression for the slip velocity.

•Select Homogeneous flow from the Slip model list to use the simplest model, which assumes that the velocity of the two phases are equal; that is, uslip 0. This is the default slip model.

•Select Pressure-drag balance from the Slip model list to use a model based on the assumption that the pressure forces on a bubble are balanced by the viscous drag:

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Here db denotes the bubble diameter (SI unit: m), and Cd is the viscous drag coefficient (dimensionless). For the drag coefficient, either use one of the predefined models or specify an arbitrary expression from the Drag coefficient model list that appears:

-For bubbles with a diameter smaller than 2 mm, select Small spherical bubbles (Hadamard-Rybczynski) to use the Hadamard-Rybczynski drag law for spherical gas bubbles in liquids (see Crowe, Sommerfeld, and Tsuji in Ref. 3):

-For gas bubbles with a diameter larger than 2 mm, select Large bubbles to use the following predefined model for the drag coefficient (see Sokolichin, Eigenberger, and Lapin in Ref. 1):

0,622

Cd = ----------------------------

1

------- + 0,235 Eö

where Eö is the Eötvös number

g d2

Eö = --------l-----b-

Here, g is the magnitude of the gravity vector and the surface tension coefficient.

-Select User defined to enter a user defined value or expression for the drag coefficient Cd in the Drag coefficient field (default value: 1).

•Select User defined to enter user defined values or expressions for the components of the slip velocity uslip in the Slip velocity fields (SI unit: m/s).

D I S T A N C E E Q U A T I O N

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