The Mixture Model, Laminar Flow Interface
The Mixture Model, Laminar Flow (mm) interface (), found under the Multiphase Flow>Mixture Model branch () when adding a physics interface, is used to model the flow at low and moderate Reynolds numbers of liquids containing a dispersed phase. The dispersed phase can be bubbles, liquid droplets, or solid particles, which are assumed to always travel with their terminal velocity.
The Mixture Model, Laminar Flow interface solves one set of Navier–Stokes equations for the momentum of the mixture. The pressure distribution is calculated from a mixture-averaged continuity equation and the velocity of the dispersed phase is described by a slip model. The volume fraction of the dispersed phase is tracked by solving a transport equation for the volume fraction.
The physics interface can also model the distribution of the number density, which in turn can be used to calculate the interfacial area, which is useful when simulating chemical reactions in the mixture.
The main physics node is the Mixture Properties feature. It adds the equations for the mixture and provides an interface for defining the fluid materials for the continuous and dispersed phases as well as which slip model and mixture viscosity model to use.
When this physics interface is added, the following default physics nodes are also added in the Model BuilderMixture Properties, Wall, 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 Mixture Model, Laminar 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 mm.
Physical Model
Specify the characteristics of the dispersed phase, the model for the slip velocity, and whether or not to solve for the interfacial area.
Dispersed Phase
To characterize the Dispersed phase, select Solid particles (the default) or Liquid droplets/bubbles.
The selection from this list is further defined for the Mixture Properties node under the Mixture Model section.
Slip Model
To compute the slip velocity jslip (SI unit: m/s), select a Slip modelHomogeneous flow (the default), Hadamard-Rybczynski, Schiller-Naumann, Haider-Levenspiel, or User defined.
The Homogeneous flow model assumes that the velocities of the two phases are equal, that is, uslip = 0.
For User defined specify an arbitrary expression for the relative velocity. For example, give a constant velocity based on experimental data. Enter the Slip velocity field uslip (SI unit: m/s) or Slip flux jslip (SI unit: m/s) in the Mixture Properties node under the Mixture Model section.
Solve For Interfacial Area
To add a transport equation for the number density of the dispersed particles, in order to determine the interfacial area, select the Solve for interfacial area check box (by default not selected).
For the Mass Transfer rate, use a two-film theory model, which includes the interfacial area per unit volume between the two phases. It is possible to compute the interfacial area per unit volume if the number density n (that is, the number of dispersed particles per volume) is known. Select the Solve for interfacial area check box to add the following equation for the number density n:
This equation states that a dispersed phase particle cannot disappear, appear, or merge with other particles, although it can expand or shrink.
The Mixture Model, Laminar Flow Interface calculates the interfacial area a (SI unit: m2/m3) from
Reference values
Reference values are global quantities used to evaluate the density of both phases 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 both phases. The default Reference pressure level pref (SI unit: Pa) is 1[atm].
Reference temperature
The reference temperature is used to define the density of both phases. The default Reference temperature Tref (SI unit: K) is 293.15[K].
Swirl Flow
For 2D axisymmetric components, select the Swirl flow check box to include the swirl velocity component — that is, the velocity component jφ in the azimuthal direction. While jφ can be nonzero, there can be no gradients in the φ direction.
Turbulence
Turbulence Model Type
The default selection is None.
Dependent Variables
Enter values for the dependent variables (field variables):
Velocity field, mixture j (SI unit: m/s)
Pressure p (SI unit: Pa)
Number density, dispersed 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.
The consistent stabilizations Streamline diffusion and Crosswind diffusion are by default applied to the Navier-Stokes and dispersed phase transport equations. In addition, when the flow is turbulent, the consistent stabilizations are also applied to the Turbulence. 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.
Penalty Diffusion can be used to suppress negative values of the dispersed volume fraction. Including this term has been observed to slow down convergence and it is therefore disabled by default.
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
Two-Phase Flow Modeling of a Dense Suspension: Application Library path CFD_Module/Verification_Examples/dense_suspension