The Laminar Bubbly Flow Interface

The interface (

), found under the branch (

) when adding a physics interface, is used to model the flow of liquids with dispersed bubbles at low and moderate Reynolds numbers.

It is assumed that the bubbles only occupy a small volume fraction and that they always travel with their terminal velocity. It is thereby possible to solve only one set of Navier–Stokes equations for the liquid phase and to let the velocity of the bubbles be guided by a slip model. The pressure distribution is computed from a mixture-averaged continuity equation. The volume fraction of bubbles is tracked by solving a transport equation for the effective gas density.

The physics interface can also model the distribution of the number density, that is, the number of bubbles per unit volume which in turn can be used to calculate the interfacial area, useful when simulating chemical reactions in the mixture.

The main physics node is the Fluid Properties feature, which adds the equations for laminar bubbly flow and provides an interface for defining the fluid materials for the liquid and the gas and the slip velocity model to use.

When this physics interface is added, the following default physics nodes are also added in the — , , (the default boundary types are for the liquid and for the gas), and . Then, from the toolbar, add other nodes that implement, for example, boundary conditions and volume forces. You can also right-click to select physics features from the context menu.

The is the default physics interface name.

The is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the field. The first character must be a letter.

The default (for the first physics interface in the model) is bf.

Specify if the gas concentration is low and whether or not to solve for the interfacial area.

The check box is selected by default. This approximation is valid if the gas volume fraction is low (

less than a few percent) and its density does not have any significant effects on the continuity equation. It is then generally valid to replace the continuity equation in The Bubbly Flow Equations; see Equation 6-31 with Equation 6-34).

To add a transport equation for the bubble density in order to determine the interfacial area, select the check box.

Reference values are global quantities used to evaluate the density of the liquid and the absolute pressure pA.

There are generally two ways to include the pressure in fluid flow computations: either to use the absolute pressure pA = p + pref, or the gauge pressure p. When pref is nonzero, the physics interface solves for the gauge pressure whereas material properties are evaluated using the absolute pressure. The reference pressure level is also used to define the density of the liquid. The default pref (SI unit: Pa) is 1[atm].

The reference temperature is used to define the density of the liquid. The default Tref (SI unit: K) is 293.15[K].

For 2D axisymmetric models, select the check box to include the swirl velocity component — that is, the velocity component

in the azimuthal direction. While

can be nonzero, there can be no gradients in the

direction. Also see General Single-Phase Flow Theory in the CFD Module User’s Guide.

By default no turbulence model is used.

The dependent variables (field variables) are the u (SI unit: m/s), the p (SI unit: Pa), the rhogeff (SI unit: kg/m3), and the nd (SI unit: 1/m3). The names can be changed but the names of fields and dependent variables must be unique within a component.

To display this section, click the button (

) and select in the dialog box. This section contains the settings for stabilization of the momentum transport (the fluid flow) in the area and stabilization of the equation for the dispersed phase in the area.

Consistent streamline and crosswind diffusion is applied by default to both gas and momentum transport. Additional inconsistent stabilization terms may be added when required as isotropic diffusion.

To display this section, click the button (

) and select in the dialog box. Normally these settings do not need to be changed.

Select the check box to add pseudo time derivatives to the equation when the form is used. When selected, also choose a — (the default) or . sets the local CFL number (from the Courant–Friedrichs–Lewy condition) to the built-in variable CFLCMP which in turn triggers a PID regulator for the CFL number. For enter a CFLloc (dimensionless).