The Laminar Bubbly Flow Interface
The Laminar Bubbly Flow (bf) interface (), found under the Multiphase Flow>Bubbly Flow 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 Model BuilderLaminar Bubbly Flow, Fluid Properties, Wall (the default boundary types are No slip for the liquid and No gas flux for the gas), and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and volume forces. You can also right-click Laminar Bubbly Flow to select physics features from the context menu.
Settings
The Label is the default physics interface name.
The Name 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 Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is bf.
Physical Model
Specify if the gas concentration is low and whether or not to solve for the interfacial area.
Low Gas Concentration
The Low gas concentration check box is selected by default. This approximation is valid if the gas volume fraction is low (ϕg 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).
Solve for Interfacial Area
To add a transport equation for the bubble density in order to determine the interfacial area, select the Solve for interfacial area check box.
Reference Values
Reference values are global quantities used to evaluate the density of the liquid and the absolute pressure pA.
Reference pressure level
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 Reference pressure level pref (SI unit: Pa) is 1 atm.
Reference temperature
The reference temperature is used to define the density of the liquid. The default Reference temperature Tref (SI unit: K) is 293.15 K.
Swirl Flow
For 2D axisymmetric models, select the Swirl flow check box to include the swirl velocity component — that is, the velocity component uφ in the azimuthal direction. While uφ can be nonzero, there can be no gradients in the φ direction. Also see General Single-Phase Flow Theory in the CFD Module User’s Guide.
Turbulence
Turbulence Model Type
By default no turbulence model is used.
Dependent Variables
The dependent variables (field variables) are the Velocity field, liquid phase u (SI unit: m/s), the Pressure p (SI unit: Pa), the Effective gas density rhogeff (SI unit: kg/m3), and the Number density, gas phase nd (SI unit: 1/m3). The names can be changed but the names of fields and dependent variables must be unique within a component.
Consistent Stabilization and Inconsistent Stabilization
To display this section, click the Show More Options button () and select Stabilization in the Show More Options dialog box. This section contains the settings for stabilization of the momentum transport (the fluid flow) in the Momentum transport area and stabilization of the equation for the dispersed phase in the Gas phase transport 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.
Advanced Settings
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box. Normally these settings do not need to be changed.
Select the Use pseudo time stepping for stationary equation form check box to add pseudo time derivatives to the equation when the Stationary equation form is used. When selected, also choose a CFL number expressionAutomatic (the default) or Manual. Automatic 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 Manual enter a Local CFL number CFLloc (dimensionless).
Pseudo Time Stepping for Laminar Flow Models in this guide and Pseudo Time Stepping in the COMSOL Multiphysics Reference Manual