The Bubbly Flow, k-ε Interface

The εinterface (

), found under the branch (

) when adding a physics interface, is used to model the flow of liquids with dispersed bubbles at high 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 calculated from a mixture-averaged continuity equation. The volume fraction of bubbles is tracked by solving a transport equation for the effective gas density. Turbulence effects are modeled using the standard two-equation k-ε model with realizability constraints and bubble-induced turbulence production. The flow near walls is modeled using wall functions.

The physics interface can also model the distribution of the number density, which 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 turbulent 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 .

Except where indicated below, the nodes settings for this physics interface are the same as for The Laminar Bubbly Flow Interface.

The default is . A different turbulence model can be selected under . The default turbulence model is ε

for the k-ε model can only be set to . More options become available by selecting another option under .

Turbulence model parameters are optimized to fit as many flow types as possible, but for some special cases, better performance can be obtained by tuning the model parameters. For a description of the turbulence model and the included model parameters see Theory for the Turbulent Flow Interfaces.

The dependent variables (field variables) are the u (SI unit: m/s), the p (SI unit: Pa), the rhogeff (SI unit: kg/m3), the ep (SI unit: m2/s3), the k (SI unit: m2/s2), and the nd (SI unit: 1/m3).

The names of variables 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. The settings for this section are the same as for The Laminar Bubbly Flow Interface with the addition of this section: stabilization for the turbulence variables in the area.

When using a turbulence model, streamline and crosswind diffusion are by default applied to the turbulence equations.

To display this section, click the button (

) and select in the dialog box. The subsection is available when the is set to .

In addition to the settings described for The Laminar Bubbly Flow Interface, enter a value for Uscale and Lfact under the subsection.

The Uscale and Lfact parameters are used to calculate absolute tolerances for the turbulence variables. The scaling parameters must only contain numerical values, units or parameters defined under . The scaling parameters cannot contain variables. The parameters are used when a new default solver for a transient study step is generated. If you change the parameters, the new values take effect the next time you generate a new default solver.